Split (2)

train · 9.9k rows

name string	atp_proof string	mizar_proof string	system string
t75_bvfunc14	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t74_bvfunc14, axiom, ![X1]:(~(v1_xboole_0(X1))=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(k1_bvfunc_2(X1)))=>![X3]:(m1_eqrel_1(X3,X1)=>![X4]:(m1_eqrel_1(X4,X1)=>![X5]:(m1_eqrel_1(X5,X1)=>![X6]:(m1_eqrel_1(X6,X1)=>![X7]:(m1_eqrel_1(X7,X1)=>![X8]:(m1_eqrel_1(X8,X1)=>![X9]:(m1_eqrel_1(X9,X1)=>![X10]:(m1_eqrel_1(X10,X1)=>![X11]:(m1_eqrel_1(X11,X1)=>(X2=k7_enumset1(X3,X4,X5,X6,X7,X8,X9,X10,X11)=>(X3=X4\|(X3=X5\|(X3=X6\|(X3=X7\|(X3=X8\|(X3=X9\|(X3=X10\|(X3=X11\|(X4=X5\|(X4=X6\|(X4=X7\|(X4=X8\|(X4=X9\|(X4=X10\|(X4=X11\|(X5=X6\|(X5=X7\|(X5=X8\|(X5=X9\|(X5=X10\|(X5=X11\|(X6=X7\|(X6=X8\|(X6=X9\|(X6=X10\|(X6=X11\|(X7=X8\|(X7=X9\|(X7=X10\|(X7=X11\|(X8=X9\|(X8=X10\|(X8=X11\|(X9=X10\|(X9=X11\|(X10=X11\|k5_bvfunc_2(X1,X10,X2)=k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,X3,X4),X5),X6),X7),X8),X9),X11))))))))))))))))))))))))))))))))))))))))))))))))), file('/scratch/mptp/predsminms1/t75_bvfunc14__0', t74_bvfunc14)). fof(t83_enumset1, axiom, ![X1, X2, X3, X4, X5, X6, X7, X8, X9]:k7_enumset1(X1,X2,X3,X4,X5,X6,X7,X8,X9)=k2_xboole_0(k5_enumset1(X1,X2,X3,X4,X5,X6,X7),k2_tarski(X8,X9)), file('/scratch/mptp/predsminms1/t75_bvfunc14__0', t83_enumset1)). fof(t75_bvfunc14, conjecture, ![X1]:(~(v1_xboole_0(X1))=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(k1_bvfunc_2(X1)))=>![X3]:(m1_eqrel_1(X3,X1)=>![X4]:(m1_eqrel_1(X4,X1)=>![X5]:(m1_eqrel_1(X5,X1)=>![X6]:(m1_eqrel_1(X6,X1)=>![X7]:(m1_eqrel_1(X7,X1)=>![X8]:(m1_eqrel_1(X8,X1)=>![X9]:(m1_eqrel_1(X9,X1)=>![X10]:(m1_eqrel_1(X10,X1)=>![X11]:(m1_eqrel_1(X11,X1)=>(X2=k7_enumset1(X3,X4,X5,X6,X7,X8,X9,X10,X11)=>(X3=X4\|(X3=X5\|(X3=X6\|(X3=X7\|(X3=X8\|(X3=X9\|(X3=X10\|(X3=X11\|(X4=X5\|(X4=X6\|(X4=X7\|(X4=X8\|(X4=X9\|(X4=X10\|(X4=X11\|(X5=X6\|(X5=X7\|(X5=X8\|(X5=X9\|(X5=X10\|(X5=X11\|(X6=X7\|(X6=X8\|(X6=X9\|(X6=X10\|(X6=X11\|(X7=X8\|(X7=X9\|(X7=X10\|(X7=X11\|(X8=X9\|(X8=X10\|(X8=X11\|(X9=X10\|(X9=X11\|(X10=X11\|k5_bvfunc_2(X1,X11,X2)=k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,X3,X4),X5),X6),X7),X8),X9),X10))))))))))))))))))))))))))))))))))))))))))))))))), file('/scratch/mptp/predsminms1/t75_bvfunc14__0', t75_bvfunc14)). fof(commutativity_k2_tarski, axiom, ![X1, X2]:k2_tarski(X1,X2)=k2_tarski(X2,X1), file('/scratch/mptp/predsminms1/t75_bvfunc14__0', commutativity_k2_tarski)). fof(c_0_4, plain, ![X1, X2, X3, X4, X5, X6, X7, X8, X9, X10, X11]:(epred1_11(X11,X10,X9,X8,X7,X6,X5,X4,X3,X2,X1)<=>(X3=X4\|(X3=X5\|(X3=X6\|(X3=X7\|(X3=X8\|(X3=X9\|(X3=X10\|(X3=X11\|(X4=X5\|(X4=X6\|(X4=X7\|(X4=X8\|(X4=X9\|(X4=X10\|(X4=X11\|(X5=X6\|(X5=X7\|(X5=X8\|(X5=X9\|(X5=X10\|(X5=X11\|(X6=X7\|(X6=X8\|(X6=X9\|(X6=X10\|(X6=X11\|(X7=X8\|(X7=X9\|(X7=X10\|(X7=X11\|(X8=X9\|(X8=X10\|(X8=X11\|(X9=X10\|(X9=X11\|(X10=X11\|k5_bvfunc_2(X1,X10,X2)=k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,X3,X4),X5),X6),X7),X8),X9),X11)))))))))))))))))))))))))))))))))))))), introduced(definition)). fof(c_0_5, axiom, ![X1]:(~(v1_xboole_0(X1))=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(k1_bvfunc_2(X1)))=>![X3]:(m1_eqrel_1(X3,X1)=>![X4]:(m1_eqrel_1(X4,X1)=>![X5]:(m1_eqrel_1(X5,X1)=>![X6]:(m1_eqrel_1(X6,X1)=>![X7]:(m1_eqrel_1(X7,X1)=>![X8]:(m1_eqrel_1(X8,X1)=>![X9]:(m1_eqrel_1(X9,X1)=>![X10]:(m1_eqrel_1(X10,X1)=>![X11]:(m1_eqrel_1(X11,X1)=>(X2=k7_enumset1(X3,X4,X5,X6,X7,X8,X9,X10,X11)=>epred1_11(X11,X10,X9,X8,X7,X6,X5,X4,X3,X2,X1))))))))))))), inference(apply_def,[status(thm)],[t74_bvfunc14, c_0_4])). fof(c_0_6, plain, ![X34, X35, X36, X37, X38, X39, X40, X41, X42, X43, X44]:(v1_xboole_0(X34)\|(~m1_subset_1(X35,k1_zfmisc_1(k1_bvfunc_2(X34)))\|(~m1_eqrel_1(X36,X34)\|(~m1_eqrel_1(X37,X34)\|(~m1_eqrel_1(X38,X34)\|(~m1_eqrel_1(X39,X34)\|(~m1_eqrel_1(X40,X34)\|(~m1_eqrel_1(X41,X34)\|(~m1_eqrel_1(X42,X34)\|(~m1_eqrel_1(X43,X34)\|(~m1_eqrel_1(X44,X34)\|(X35!=k7_enumset1(X36,X37,X38,X39,X40,X41,X42,X43,X44)\|epred1_11(X44,X43,X42,X41,X40,X39,X38,X37,X36,X35,X34))))))))))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_5])])])])). fof(c_0_7, plain, ![X23, X24, X25, X26, X27, X28, X29, X30, X31]:k7_enumset1(X23,X24,X25,X26,X27,X28,X29,X30,X31)=k2_xboole_0(k5_enumset1(X23,X24,X25,X26,X27,X28,X29),k2_tarski(X30,X31)), inference(variable_rename,[status(thm)],[t83_enumset1])). fof(c_0_8, negated_conjecture, ~(![X1]:(~(v1_xboole_0(X1))=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(k1_bvfunc_2(X1)))=>![X3]:(m1_eqrel_1(X3,X1)=>![X4]:(m1_eqrel_1(X4,X1)=>![X5]:(m1_eqrel_1(X5,X1)=>![X6]:(m1_eqrel_1(X6,X1)=>![X7]:(m1_eqrel_1(X7,X1)=>![X8]:(m1_eqrel_1(X8,X1)=>![X9]:(m1_eqrel_1(X9,X1)=>![X10]:(m1_eqrel_1(X10,X1)=>![X11]:(m1_eqrel_1(X11,X1)=>(X2=k7_enumset1(X3,X4,X5,X6,X7,X8,X9,X10,X11)=>(X3=X4\|(X3=X5\|(X3=X6\|(X3=X7\|(X3=X8\|(X3=X9\|(X3=X10\|(X3=X11\|(X4=X5\|(X4=X6\|(X4=X7\|(X4=X8\|(X4=X9\|(X4=X10\|(X4=X11\|(X5=X6\|(X5=X7\|(X5=X8\|(X5=X9\|(X5=X10\|(X5=X11\|(X6=X7\|(X6=X8\|(X6=X9\|(X6=X10\|(X6=X11\|(X7=X8\|(X7=X9\|(X7=X10\|(X7=X11\|(X8=X9\|(X8=X10\|(X8=X11\|(X9=X10\|(X9=X11\|(X10=X11\|k5_bvfunc_2(X1,X11,X2)=k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,X3,X4),X5),X6),X7),X8),X9),X10)))))))))))))))))))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[t75_bvfunc14])). cnf(c_0_9, plain, (v1_xboole_0(X1)\|epred1_11(X11,X10,X9,X8,X7,X6,X5,X4,X3,X2,X1)\|~m1_subset_1(X2,k1_zfmisc_1(k1_bvfunc_2(X1)))\|~m1_eqrel_1(X3,X1)\|~m1_eqrel_1(X4,X1)\|~m1_eqrel_1(X5,X1)\|~m1_eqrel_1(X6,X1)\|~m1_eqrel_1(X7,X1)\|~m1_eqrel_1(X8,X1)\|~m1_eqrel_1(X9,X1)\|~m1_eqrel_1(X10,X1)\|~m1_eqrel_1(X11,X1)\|X2!=k7_enumset1(X3,X4,X5,X6,X7,X8,X9,X10,X11)), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_10, plain, (k7_enumset1(X1,X2,X3,X4,X5,X6,X7,X8,X9)=k2_xboole_0(k5_enumset1(X1,X2,X3,X4,X5,X6,X7),k2_tarski(X8,X9))), inference(split_conjunct,[status(thm)],[c_0_7])). fof(c_0_11, plain, ![X32, X33]:k2_tarski(X32,X33)=k2_tarski(X33,X32), inference(variable_rename,[status(thm)],[commutativity_k2_tarski])). fof(c_0_12, negated_conjecture, (~v1_xboole_0(esk1_0)&(m1_subset_1(esk2_0,k1_zfmisc_1(k1_bvfunc_2(esk1_0)))&(m1_eqrel_1(esk3_0,esk1_0)&(m1_eqrel_1(esk4_0,esk1_0)&(m1_eqrel_1(esk5_0,esk1_0)&(m1_eqrel_1(esk6_0,esk1_0)&(m1_eqrel_1(esk7_0,esk1_0)&(m1_eqrel_1(esk8_0,esk1_0)&(m1_eqrel_1(esk9_0,esk1_0)&(m1_eqrel_1(esk10_0,esk1_0)&(m1_eqrel_1(esk11_0,esk1_0)&(esk2_0=k7_enumset1(esk3_0,esk4_0,esk5_0,esk6_0,esk7_0,esk8_0,esk9_0,esk10_0,esk11_0)&(esk3_0!=esk4_0&(esk3_0!=esk5_0&(esk3_0!=esk6_0&(esk3_0!=esk7_0&(esk3_0!=esk8_0&(esk3_0!=esk9_0&(esk3_0!=esk10_0&(esk3_0!=esk11_0&(esk4_0!=esk5_0&(esk4_0!=esk6_0&(esk4_0!=esk7_0&(esk4_0!=esk8_0&(esk4_0!=esk9_0&(esk4_0!=esk10_0&(esk4_0!=esk11_0&(esk5_0!=esk6_0&(esk5_0!=esk7_0&(esk5_0!=esk8_0&(esk5_0!=esk9_0&(esk5_0!=esk10_0&(esk5_0!=esk11_0&(esk6_0!=esk7_0&(esk6_0!=esk8_0&(esk6_0!=esk9_0&(esk6_0!=esk10_0&(esk6_0!=esk11_0&(esk7_0!=esk8_0&(esk7_0!=esk9_0&(esk7_0!=esk10_0&(esk7_0!=esk11_0&(esk8_0!=esk9_0&(esk8_0!=esk10_0&(esk8_0!=esk11_0&(esk9_0!=esk10_0&(esk9_0!=esk11_0&(esk10_0!=esk11_0&k5_bvfunc_2(esk1_0,esk11_0,esk2_0)!=k2_partit1(esk1_0,k2_partit1(esk1_0,k2_partit1(esk1_0,k2_partit1(esk1_0,k2_partit1(esk1_0,k2_partit1(esk1_0,k2_partit1(esk1_0,esk3_0,esk4_0),esk5_0),esk6_0),esk7_0),esk8_0),esk9_0),esk10_0))))))))))))))))))))))))))))))))))))))))))))))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_8])])])])). cnf(c_0_13, plain, (v1_xboole_0(X1)\|epred1_11(X11,X10,X9,X8,X7,X6,X5,X4,X3,X2,X1)\|X2!=k2_xboole_0(k5_enumset1(X3,X4,X5,X6,X7,X8,X9),k2_tarski(X10,X11))\|~m1_eqrel_1(X11,X1)\|~m1_eqrel_1(X10,X1)\|~m1_eqrel_1(X9,X1)\|~m1_eqrel_1(X8,X1)\|~m1_eqrel_1(X7,X1)\|~m1_eqrel_1(X6,X1)\|~m1_eqrel_1(X5,X1)\|~m1_eqrel_1(X4,X1)\|~m1_eqrel_1(X3,X1)\|~m1_subset_1(X2,k1_zfmisc_1(k1_bvfunc_2(X1)))), inference(rw,[status(thm)],[c_0_9, c_0_10])). cnf(c_0_14, plain, (k2_tarski(X1,X2)=k2_tarski(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_15, negated_conjecture, (esk2_0=k7_enumset1(esk3_0,esk4_0,esk5_0,esk6_0,esk7_0,esk8_0,esk9_0,esk10_0,esk11_0)), inference(split_conjunct,[status(thm)],[c_0_12])). fof(c_0_16, plain, ![X1, X2, X3, X4, X5, X6, X7, X8, X9, X10, X11]:(epred1_11(X11,X10,X9,X8,X7,X6,X5,X4,X3,X2,X1)=>(X3=X4\|(X3=X5\|(X3=X6\|(X3=X7\|(X3=X8\|(X3=X9\|(X3=X10\|(X3=X11\|(X4=X5\|(X4=X6\|(X4=X7\|(X4=X8\|(X4=X9\|(X4=X10\|(X4=X11\|(X5=X6\|(X5=X7\|(X5=X8\|(X5=X9\|(X5=X10\|(X5=X11\|(X6=X7\|(X6=X8\|(X6=X9\|(X6=X10\|(X6=X11\|(X7=X8\|(X7=X9\|(X7=X10\|(X7=X11\|(X8=X9\|(X8=X10\|(X8=X11\|(X9=X10\|(X9=X11\|(X10=X11\|k5_bvfunc_2(X1,X10,X2)=k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,X3,X4),X5),X6),X7),X8),X9),X11)))))))))))))))))))))))))))))))))))))), inference(split_equiv,[status(thm)],[c_0_4])). cnf(c_0_17, plain, (v1_xboole_0(X1)\|epred1_11(X11,X10,X9,X8,X7,X6,X5,X4,X3,X2,X1)\|X2!=k2_xboole_0(k5_enumset1(X3,X4,X5,X6,X7,X8,X9),k2_tarski(X10,X11))\|~m1_eqrel_1(X11,X1)\|~m1_eqrel_1(X10,X1)\|~m1_eqrel_1(X9,X1)\|~m1_eqrel_1(X8,X1)\|~m1_eqrel_1(X7,X1)\|~m1_eqrel_1(X6,X1)\|~m1_eqrel_1(X5,X1)\|~m1_eqrel_1(X4,X1)\|~m1_eqrel_1(X3,X1)\|~m1_subset_1(X2,k1_zfmisc_1(k1_bvfunc_2(X1)))), inference(evalgc,[status(thm)],[c_0_13])). cnf(c_0_18, plain, (k2_tarski(X1,X2)=k2_tarski(X2,X1)), inference(evalgc,[status(thm)],[c_0_14])). cnf(c_0_19, negated_conjecture, (esk2_0=k2_xboole_0(k5_enumset1(esk3_0,esk4_0,esk5_0,esk6_0,esk7_0,esk8_0,esk9_0),k2_tarski(esk10_0,esk11_0))), inference(rw,[status(thm)],[c_0_15, c_0_10])). fof(c_0_20, plain, ![X45, X46, X47, X48, X49, X50, X51, X52, X53, X54, X55]:(~epred1_11(X55,X54,X53,X52,X51,X50,X49,X48,X47,X46,X45)\|(X47=X48\|(X47=X49\|(X47=X50\|(X47=X51\|(X47=X52\|(X47=X53\|(X47=X54\|(X47=X55\|(X48=X49\|(X48=X50\|(X48=X51\|(X48=X52\|(X48=X53\|(X48=X54\|(X48=X55\|(X49=X50\|(X49=X51\|(X49=X52\|(X49=X53\|(X49=X54\|(X49=X55\|(X50=X51\|(X50=X52\|(X50=X53\|(X50=X54\|(X50=X55\|(X51=X52\|(X51=X53\|(X51=X54\|(X51=X55\|(X52=X53\|(X52=X54\|(X52=X55\|(X53=X54\|(X53=X55\|(X54=X55\|k5_bvfunc_2(X45,X54,X46)=k2_partit1(X45,k2_partit1(X45,k2_partit1(X45,k2_partit1(X45,k2_partit1(X45,k2_partit1(X45,k2_partit1(X45,X47,X48),X49),X50),X51),X52),X53),X55)))))))))))))))))))))))))))))))))))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])). cnf(c_0_21, plain, (epred1_11(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11)\|v1_xboole_0(X11)\|X10!=k2_xboole_0(k5_enumset1(X9,X8,X7,X6,X5,X4,X3),k2_tarski(X1,X2))\|~m1_eqrel_1(X1,X11)\|~m1_eqrel_1(X2,X11)\|~m1_eqrel_1(X3,X11)\|~m1_eqrel_1(X4,X11)\|~m1_eqrel_1(X5,X11)\|~m1_eqrel_1(X6,X11)\|~m1_eqrel_1(X7,X11)\|~m1_eqrel_1(X8,X11)\|~m1_eqrel_1(X9,X11)\|~m1_subset_1(X10,k1_zfmisc_1(k1_bvfunc_2(X11)))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_17, c_0_18])])). cnf(c_0_22, negated_conjecture, (k2_xboole_0(k5_enumset1(esk3_0,esk4_0,esk5_0,esk6_0,esk7_0,esk8_0,esk9_0),k2_tarski(esk10_0,esk11_0))=esk2_0), inference(evalgc,[status(thm)],[c_0_19])). cnf(c_0_23, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(k1_bvfunc_2(esk1_0)))), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_24, negated_conjecture, (m1_eqrel_1(esk10_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_25, negated_conjecture, (m1_eqrel_1(esk11_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_26, negated_conjecture, (m1_eqrel_1(esk9_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_27, negated_conjecture, (m1_eqrel_1(esk8_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_28, negated_conjecture, (m1_eqrel_1(esk7_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_29, negated_conjecture, (m1_eqrel_1(esk6_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_30, negated_conjecture, (m1_eqrel_1(esk5_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_31, negated_conjecture, (m1_eqrel_1(esk4_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_32, negated_conjecture, (m1_eqrel_1(esk3_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_33, negated_conjecture, (~v1_xboole_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_34, plain, (X9=X8\|X9=X7\|X9=X6\|X9=X5\|X9=X4\|X9=X3\|X9=X2\|X9=X1\|X8=X7\|X8=X6\|X8=X5\|X8=X4\|X8=X3\|X8=X2\|X8=X1\|X7=X6\|X7=X5\|X7=X4\|X7=X3\|X7=X2\|X7=X1\|X6=X5\|X6=X4\|X6=X3\|X6=X2\|X6=X1\|X5=X4\|X5=X3\|X5=X2\|X5=X1\|X4=X3\|X4=X2\|X4=X1\|X3=X2\|X3=X1\|X2=X1\|k5_bvfunc_2(X11,X2,X10)=k2_partit1(X11,k2_partit1(X11,k2_partit1(X11,k2_partit1(X11,k2_partit1(X11,k2_partit1(X11,k2_partit1(X11,X9,X8),X7),X6),X5),X4),X3),X1)\|~epred1_11(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11)), inference(split_conjunct,[status(thm)],[c_0_20])). cnf(c_0_35, negated_conjecture, (epred1_11(esk10_0,esk11_0,esk9_0,esk8_0,esk7_0,esk6_0,esk5_0,esk4_0,esk3_0,X1,X2)\|v1_xboole_0(X2)\|X1!=esk2_0\|~m1_eqrel_1(esk10_0,X2)\|~m1_eqrel_1(esk11_0,X2)\|~m1_eqrel_1(esk9_0,X2)\|~m1_eqrel_1(esk8_0,X2)\|~m1_eqrel_1(esk7_0,X2)\|~m1_eqrel_1(esk6_0,X2)\|~m1_eqrel_1(esk5_0,X2)\|~m1_eqrel_1(esk4_0,X2)\|~m1_eqrel_1(esk3_0,X2)\|~m1_subset_1(X1,k1_zfmisc_1(k1_bvfunc_2(X2)))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_21, c_0_22])])). cnf(c_0_36, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(k1_bvfunc_2(esk1_0)))), inference(evalgc,[status(thm)],[c_0_23])). cnf(c_0_37, negated_conjecture, (m1_eqrel_1(esk10_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_24])). cnf(c_0_38, negated_conjecture, (m1_eqrel_1(esk11_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_25])). cnf(c_0_39, negated_conjecture, (m1_eqrel_1(esk9_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_26])). cnf(c_0_40, negated_conjecture, (m1_eqrel_1(esk8_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_27])). cnf(c_0_41, negated_conjecture, (m1_eqrel_1(esk7_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_28])). cnf(c_0_42, negated_conjecture, (m1_eqrel_1(esk6_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_29])). cnf(c_0_43, negated_conjecture, (m1_eqrel_1(esk5_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_30])). cnf(c_0_44, negated_conjecture, (m1_eqrel_1(esk4_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_31])). cnf(c_0_45, negated_conjecture, (m1_eqrel_1(esk3_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_32])). cnf(c_0_46, negated_conjecture, (~v1_xboole_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_33])). cnf(c_0_47, negated_conjecture, (k5_bvfunc_2(esk1_0,esk11_0,esk2_0)!=k2_partit1(esk1_0,k2_partit1(esk1_0,k2_partit1(esk1_0,k2_partit1(esk1_0,k2_partit1(esk1_0,k2_partit1(esk1_0,k2_partit1(esk1_0,esk3_0,esk4_0),esk5_0),esk6_0),esk7_0),esk8_0),esk9_0),esk10_0)), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_48, negated_conjecture, (esk10_0!=esk11_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_49, negated_conjecture, (esk9_0!=esk10_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_50, negated_conjecture, (esk8_0!=esk10_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_51, negated_conjecture, (esk7_0!=esk10_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_52, negated_conjecture, (esk6_0!=esk10_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_53, negated_conjecture, (esk5_0!=esk10_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_54, negated_conjecture, (esk4_0!=esk10_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_55, negated_conjecture, (esk3_0!=esk10_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_56, negated_conjecture, (esk9_0!=esk11_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_57, negated_conjecture, (esk8_0!=esk11_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_58, negated_conjecture, (esk7_0!=esk11_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_59, negated_conjecture, (esk6_0!=esk11_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_60, negated_conjecture, (esk5_0!=esk11_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_61, negated_conjecture, (esk4_0!=esk11_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_62, negated_conjecture, (esk3_0!=esk11_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_63, negated_conjecture, (esk8_0!=esk9_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_64, negated_conjecture, (esk7_0!=esk9_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_65, negated_conjecture, (esk6_0!=esk9_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_66, negated_conjecture, (esk5_0!=esk9_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_67, negated_conjecture, (esk4_0!=esk9_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_68, negated_conjecture, (esk3_0!=esk9_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_69, negated_conjecture, (esk7_0!=esk8_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_70, negated_conjecture, (esk6_0!=esk8_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_71, negated_conjecture, (esk5_0!=esk8_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_72, negated_conjecture, (esk4_0!=esk8_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_73, negated_conjecture, (esk3_0!=esk8_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_74, negated_conjecture, (esk6_0!=esk7_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_75, negated_conjecture, (esk5_0!=esk7_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_76, negated_conjecture, (esk4_0!=esk7_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_77, negated_conjecture, (esk3_0!=esk7_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_78, negated_conjecture, (esk5_0!=esk6_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_79, negated_conjecture, (esk4_0!=esk6_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_80, negated_conjecture, (esk3_0!=esk6_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_81, negated_conjecture, (esk4_0!=esk5_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_82, negated_conjecture, (esk3_0!=esk5_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_83, negated_conjecture, (esk3_0!=esk4_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_84, plain, (X8=X9\|X7=X9\|X7=X8\|X6=X9\|X6=X8\|X6=X7\|X5=X9\|X5=X8\|X5=X7\|X5=X6\|X4=X9\|X4=X8\|X4=X7\|X4=X6\|X4=X5\|X3=X9\|X3=X8\|X3=X7\|X3=X6\|X3=X5\|X3=X4\|X2=X9\|X2=X8\|X2=X7\|X2=X6\|X2=X5\|X2=X4\|X2=X3\|X1=X9\|X1=X8\|X1=X7\|X1=X6\|X1=X5\|X1=X4\|X1=X3\|X1=X2\|k5_bvfunc_2(X11,X2,X10)=k2_partit1(X11,k2_partit1(X11,k2_partit1(X11,k2_partit1(X11,k2_partit1(X11,k2_partit1(X11,k2_partit1(X11,X9,X8),X7),X6),X5),X4),X3),X1)\|~epred1_11(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11)), inference(evalgc,[status(thm)],[c_0_34])). cnf(c_0_85, negated_conjecture, (epred1_11(esk10_0,esk11_0,esk9_0,esk8_0,esk7_0,esk6_0,esk5_0,esk4_0,esk3_0,esk2_0,esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35, c_0_36]), c_0_37]), c_0_38]), c_0_39]), c_0_40]), c_0_41]), c_0_42]), c_0_43]), c_0_44]), c_0_45])]), c_0_46])])). cnf(c_0_86, negated_conjecture, (k2_partit1(esk1_0,k2_partit1(esk1_0,k2_partit1(esk1_0,k2_partit1(esk1_0,k2_partit1(esk1_0,k2_partit1(esk1_0,k2_partit1(esk1_0,esk3_0,esk4_0),esk5_0),esk6_0),esk7_0),esk8_0),esk9_0),esk10_0)!=k5_bvfunc_2(esk1_0,esk11_0,esk2_0)), inference(evalgc,[status(thm)],[c_0_47])). cnf(c_0_87, negated_conjecture, (esk11_0!=esk10_0), inference(evalgc,[status(thm)],[c_0_48])). cnf(c_0_88, negated_conjecture, (esk10_0!=esk9_0), inference(evalgc,[status(thm)],[c_0_49])). cnf(c_0_89, negated_conjecture, (esk10_0!=esk8_0), inference(evalgc,[status(thm)],[c_0_50])). cnf(c_0_90, negated_conjecture, (esk10_0!=esk7_0), inference(evalgc,[status(thm)],[c_0_51])). cnf(c_0_91, negated_conjecture, (esk10_0!=esk6_0), inference(evalgc,[status(thm)],[c_0_52])). cnf(c_0_92, negated_conjecture, (esk10_0!=esk5_0), inference(evalgc,[status(thm)],[c_0_53])). cnf(c_0_93, negated_conjecture, (esk10_0!=esk4_0), inference(evalgc,[status(thm)],[c_0_54])). cnf(c_0_94, negated_conjecture, (esk10_0!=esk3_0), inference(evalgc,[status(thm)],[c_0_55])). cnf(c_0_95, negated_conjecture, (esk11_0!=esk9_0), inference(evalgc,[status(thm)],[c_0_56])). cnf(c_0_96, negated_conjecture, (esk11_0!=esk8_0), inference(evalgc,[status(thm)],[c_0_57])). cnf(c_0_97, negated_conjecture, (esk11_0!=esk7_0), inference(evalgc,[status(thm)],[c_0_58])). cnf(c_0_98, negated_conjecture, (esk11_0!=esk6_0), inference(evalgc,[status(thm)],[c_0_59])). cnf(c_0_99, negated_conjecture, (esk11_0!=esk5_0), inference(evalgc,[status(thm)],[c_0_60])). cnf(c_0_100, negated_conjecture, (esk11_0!=esk4_0), inference(evalgc,[status(thm)],[c_0_61])). cnf(c_0_101, negated_conjecture, (esk11_0!=esk3_0), inference(evalgc,[status(thm)],[c_0_62])). cnf(c_0_102, negated_conjecture, (esk9_0!=esk8_0), inference(evalgc,[status(thm)],[c_0_63])). cnf(c_0_103, negated_conjecture, (esk9_0!=esk7_0), inference(evalgc,[status(thm)],[c_0_64])). cnf(c_0_104, negated_conjecture, (esk9_0!=esk6_0), inference(evalgc,[status(thm)],[c_0_65])). cnf(c_0_105, negated_conjecture, (esk9_0!=esk5_0), inference(evalgc,[status(thm)],[c_0_66])). cnf(c_0_106, negated_conjecture, (esk9_0!=esk4_0), inference(evalgc,[status(thm)],[c_0_67])). cnf(c_0_107, negated_conjecture, (esk9_0!=esk3_0), inference(evalgc,[status(thm)],[c_0_68])). cnf(c_0_108, negated_conjecture, (esk8_0!=esk7_0), inference(evalgc,[status(thm)],[c_0_69])). cnf(c_0_109, negated_conjecture, (esk8_0!=esk6_0), inference(evalgc,[status(thm)],[c_0_70])). cnf(c_0_110, negated_conjecture, (esk8_0!=esk5_0), inference(evalgc,[status(thm)],[c_0_71])). cnf(c_0_111, negated_conjecture, (esk8_0!=esk4_0), inference(evalgc,[status(thm)],[c_0_72])). cnf(c_0_112, negated_conjecture, (esk8_0!=esk3_0), inference(evalgc,[status(thm)],[c_0_73])). cnf(c_0_113, negated_conjecture, (esk7_0!=esk6_0), inference(evalgc,[status(thm)],[c_0_74])). cnf(c_0_114, negated_conjecture, (esk7_0!=esk5_0), inference(evalgc,[status(thm)],[c_0_75])). cnf(c_0_115, negated_conjecture, (esk7_0!=esk4_0), inference(evalgc,[status(thm)],[c_0_76])). cnf(c_0_116, negated_conjecture, (esk7_0!=esk3_0), inference(evalgc,[status(thm)],[c_0_77])). cnf(c_0_117, negated_conjecture, (esk6_0!=esk5_0), inference(evalgc,[status(thm)],[c_0_78])). cnf(c_0_118, negated_conjecture, (esk6_0!=esk4_0), inference(evalgc,[status(thm)],[c_0_79])). cnf(c_0_119, negated_conjecture, (esk6_0!=esk3_0), inference(evalgc,[status(thm)],[c_0_80])). cnf(c_0_120, negated_conjecture, (esk5_0!=esk4_0), inference(evalgc,[status(thm)],[c_0_81])). cnf(c_0_121, negated_conjecture, (esk5_0!=esk3_0), inference(evalgc,[status(thm)],[c_0_82])). cnf(c_0_122, negated_conjecture, (esk4_0!=esk3_0), inference(evalgc,[status(thm)],[c_0_83])). cnf(c_0_123, plain, ($false), inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_84, c_0_85]), c_0_86]), c_0_87]), c_0_88]), c_0_89]), c_0_90]), c_0_91]), c_0_92]), c_0_93]), c_0_94]), c_0_95]), c_0_96]), c_0_97]), c_0_98]), c_0_99]), c_0_100]), c_0_101]), c_0_102]), c_0_103]), c_0_104]), c_0_105]), c_0_106]), c_0_107]), c_0_108]), c_0_109]), c_0_110]), c_0_111]), c_0_112]), c_0_113]), c_0_114]), c_0_115]), c_0_116]), c_0_117]), c_0_118]), c_0_119]), c_0_120]), c_0_121]), c_0_122]), ['proof']). # SZS output end CNFRefutation	reserve Y for non empty set, G for Subset of PARTITIONS(Y), A,B,C,D,E,F for a_partition of Y; reserve Y for non empty set, G for Subset of PARTITIONS(Y), A, B, C, D, E, F, J, M for a_partition of Y, x,x1,x2,x3,x4,x5,x6,x7,x8,x9 for set; theorem for G being Subset of PARTITIONS(Y), A,B,C,D,E,F,J,M,N being a_partition of Y st G={A,B,C,D,E,F,J,M,N} & A<>B & A<>C & A<>D & A<>E & A<>F & A<>J & A<>M & A<>N & B<>C & B<>D & B<>E & B<>F & B<>J & B<>M & B<>N & C<>D & C <>E & C<>F & C<>J & C<>M & C<>N & D<>E & D<>F & D<>J & D<>M & D<>N & E<>F & E<> J & E<>M & E<>N & F<>J & F<>M & F<>N & J<>M & J<>N & M<>N holds CompF(N,G) = A '/\' B '/\' C '/\' D '/\' E '/\' F '/\' J '/\' M proof let G be Subset of PARTITIONS(Y); let A,B,C,D,E,F,J,M,N be a_partition of Y; {A,B,C,D,E,F,J,M,N} ={A,B,C,D,E,F,J} \/ {M,N} by ENUMSET1:83 .={A,B,C,D,E,F,J,N,M} by ENUMSET1:83; hence thesis by Th74; end;	Convert the following ATP output trace into a readable Mizar proof.
t62_pzfmisc1	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(d16_pboole, axiom, ![X1, X2]:((v1_relat_1(X2)&(v4_relat_1(X2,X1)&(v1_funct_1(X2)&v1_partfun1(X2,X1))))=>![X3]:((v1_relat_1(X3)&(v4_relat_1(X3,X1)&(v1_funct_1(X3)&v1_partfun1(X3,X1))))=>![X4]:((v1_relat_1(X4)&(v4_relat_1(X4,X1)&(v1_funct_1(X4)&v1_partfun1(X4,X1))))=>(X4=k6_pboole(X1,X2,X3)<=>![X5]:(r2_hidden(X5,X1)=>k1_funct_1(X4,X5)=k2_zfmisc_1(k1_funct_1(X2,X5),k1_funct_1(X3,X5))))))), file('/scratch/mptp/predsminms1/t62_pzfmisc1__0', d16_pboole)). fof(dt_k6_pboole, axiom, ![X1, X2, X3]:(((v1_relat_1(X2)&(v4_relat_1(X2,X1)&(v1_funct_1(X2)&v1_partfun1(X2,X1))))&(v1_relat_1(X3)&(v4_relat_1(X3,X1)&(v1_funct_1(X3)&v1_partfun1(X3,X1)))))=>(v1_relat_1(k6_pboole(X1,X2,X3))&(v4_relat_1(k6_pboole(X1,X2,X3),X1)&(v1_funct_1(k6_pboole(X1,X2,X3))&v1_partfun1(k6_pboole(X1,X2,X3),X1))))), file('/scratch/mptp/predsminms1/t62_pzfmisc1__0', dt_k6_pboole)). fof(t96_zfmisc_1, axiom, ![X1, X2, X3, X4]:((r1_tarski(X1,X2)&r1_tarski(X3,X4))=>r1_tarski(k2_zfmisc_1(X1,X3),k2_zfmisc_1(X2,X4))), file('/scratch/mptp/predsminms1/t62_pzfmisc1__0', t96_zfmisc_1)). fof(d2_pboole, axiom, ![X1, X2]:((v1_relat_1(X2)&(v4_relat_1(X2,X1)&(v1_funct_1(X2)&v1_partfun1(X2,X1))))=>![X3]:((v1_relat_1(X3)&(v4_relat_1(X3,X1)&(v1_funct_1(X3)&v1_partfun1(X3,X1))))=>(r2_pboole(X1,X2,X3)<=>![X4]:(r2_hidden(X4,X1)=>r1_tarski(k1_funct_1(X2,X4),k1_funct_1(X3,X4)))))), file('/scratch/mptp/predsminms1/t62_pzfmisc1__0', d2_pboole)). fof(t62_pzfmisc1, conjecture, ![X1, X2]:((v1_relat_1(X2)&(v4_relat_1(X2,X1)&(v1_funct_1(X2)&v1_partfun1(X2,X1))))=>![X3]:((v1_relat_1(X3)&(v4_relat_1(X3,X1)&(v1_funct_1(X3)&v1_partfun1(X3,X1))))=>![X4]:((v1_relat_1(X4)&(v4_relat_1(X4,X1)&(v1_funct_1(X4)&v1_partfun1(X4,X1))))=>![X5]:((v1_relat_1(X5)&(v4_relat_1(X5,X1)&(v1_funct_1(X5)&v1_partfun1(X5,X1))))=>((r2_pboole(X1,X2,X3)&r2_pboole(X1,X4,X5))=>r2_pboole(X1,k6_pboole(X1,X2,X4),k6_pboole(X1,X3,X5))))))), file('/scratch/mptp/predsminms1/t62_pzfmisc1__0', t62_pzfmisc1)). fof(c_0_5, plain, ![X11, X12, X13, X14, X15]:((X14!=k6_pboole(X11,X12,X13)\|(~r2_hidden(X15,X11)\|k1_funct_1(X14,X15)=k2_zfmisc_1(k1_funct_1(X12,X15),k1_funct_1(X13,X15)))\|(~v1_relat_1(X14)\|(~v4_relat_1(X14,X11)\|(~v1_funct_1(X14)\|~v1_partfun1(X14,X11))))\|(~v1_relat_1(X13)\|(~v4_relat_1(X13,X11)\|(~v1_funct_1(X13)\|~v1_partfun1(X13,X11))))\|(~v1_relat_1(X12)\|(~v4_relat_1(X12,X11)\|(~v1_funct_1(X12)\|~v1_partfun1(X12,X11)))))&((r2_hidden(esk6_4(X11,X12,X13,X14),X11)\|X14=k6_pboole(X11,X12,X13)\|(~v1_relat_1(X14)\|(~v4_relat_1(X14,X11)\|(~v1_funct_1(X14)\|~v1_partfun1(X14,X11))))\|(~v1_relat_1(X13)\|(~v4_relat_1(X13,X11)\|(~v1_funct_1(X13)\|~v1_partfun1(X13,X11))))\|(~v1_relat_1(X12)\|(~v4_relat_1(X12,X11)\|(~v1_funct_1(X12)\|~v1_partfun1(X12,X11)))))&(k1_funct_1(X14,esk6_4(X11,X12,X13,X14))!=k2_zfmisc_1(k1_funct_1(X12,esk6_4(X11,X12,X13,X14)),k1_funct_1(X13,esk6_4(X11,X12,X13,X14)))\|X14=k6_pboole(X11,X12,X13)\|(~v1_relat_1(X14)\|(~v4_relat_1(X14,X11)\|(~v1_funct_1(X14)\|~v1_partfun1(X14,X11))))\|(~v1_relat_1(X13)\|(~v4_relat_1(X13,X11)\|(~v1_funct_1(X13)\|~v1_partfun1(X13,X11))))\|(~v1_relat_1(X12)\|(~v4_relat_1(X12,X11)\|(~v1_funct_1(X12)\|~v1_partfun1(X12,X11))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d16_pboole])])])])])). cnf(c_0_6, plain, (k1_funct_1(X1,X5)=k2_zfmisc_1(k1_funct_1(X3,X5),k1_funct_1(X4,X5))\|X1!=k6_pboole(X2,X3,X4)\|~r2_hidden(X5,X2)\|~v1_relat_1(X1)\|~v4_relat_1(X1,X2)\|~v1_funct_1(X1)\|~v1_partfun1(X1,X2)\|~v1_relat_1(X4)\|~v4_relat_1(X4,X2)\|~v1_funct_1(X4)\|~v1_partfun1(X4,X2)\|~v1_relat_1(X3)\|~v4_relat_1(X3,X2)\|~v1_funct_1(X3)\|~v1_partfun1(X3,X2)), inference(split_conjunct,[status(thm)],[c_0_5])). fof(c_0_7, plain, ![X17, X18, X19]:((v1_relat_1(k6_pboole(X17,X18,X19))\|(~v1_relat_1(X18)\|(~v4_relat_1(X18,X17)\|(~v1_funct_1(X18)\|~v1_partfun1(X18,X17)))\|(~v1_relat_1(X19)\|(~v4_relat_1(X19,X17)\|(~v1_funct_1(X19)\|~v1_partfun1(X19,X17))))))&((v4_relat_1(k6_pboole(X17,X18,X19),X17)\|(~v1_relat_1(X18)\|(~v4_relat_1(X18,X17)\|(~v1_funct_1(X18)\|~v1_partfun1(X18,X17)))\|(~v1_relat_1(X19)\|(~v4_relat_1(X19,X17)\|(~v1_funct_1(X19)\|~v1_partfun1(X19,X17))))))&((v1_funct_1(k6_pboole(X17,X18,X19))\|(~v1_relat_1(X18)\|(~v4_relat_1(X18,X17)\|(~v1_funct_1(X18)\|~v1_partfun1(X18,X17)))\|(~v1_relat_1(X19)\|(~v4_relat_1(X19,X17)\|(~v1_funct_1(X19)\|~v1_partfun1(X19,X17))))))&(v1_partfun1(k6_pboole(X17,X18,X19),X17)\|(~v1_relat_1(X18)\|(~v4_relat_1(X18,X17)\|(~v1_funct_1(X18)\|~v1_partfun1(X18,X17)))\|(~v1_relat_1(X19)\|(~v4_relat_1(X19,X17)\|(~v1_funct_1(X19)\|~v1_partfun1(X19,X17))))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k6_pboole])])])). fof(c_0_8, plain, ![X20, X21, X22, X23]:(~r1_tarski(X20,X21)\|~r1_tarski(X22,X23)\|r1_tarski(k2_zfmisc_1(X20,X22),k2_zfmisc_1(X21,X23))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t96_zfmisc_1])])). cnf(c_0_9, plain, (k1_funct_1(X1,X5)=k2_zfmisc_1(k1_funct_1(X3,X5),k1_funct_1(X4,X5))\|X1!=k6_pboole(X2,X3,X4)\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~v1_relat_1(X1)\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v1_funct_1(X1)\|~v4_relat_1(X4,X2)\|~v4_relat_1(X3,X2)\|~v4_relat_1(X1,X2)\|~v1_partfun1(X4,X2)\|~v1_partfun1(X3,X2)\|~v1_partfun1(X1,X2)\|~r2_hidden(X5,X2)), inference(evalgc,[status(thm)],[c_0_6])). cnf(c_0_10, plain, (v1_relat_1(k6_pboole(X1,X2,X3))\|~v1_relat_1(X2)\|~v4_relat_1(X2,X1)\|~v1_funct_1(X2)\|~v1_partfun1(X2,X1)\|~v1_relat_1(X3)\|~v4_relat_1(X3,X1)\|~v1_funct_1(X3)\|~v1_partfun1(X3,X1)), inference(split_conjunct,[status(thm)],[c_0_7])). cnf(c_0_11, plain, (v4_relat_1(k6_pboole(X1,X2,X3),X1)\|~v1_relat_1(X2)\|~v4_relat_1(X2,X1)\|~v1_funct_1(X2)\|~v1_partfun1(X2,X1)\|~v1_relat_1(X3)\|~v4_relat_1(X3,X1)\|~v1_funct_1(X3)\|~v1_partfun1(X3,X1)), inference(split_conjunct,[status(thm)],[c_0_7])). cnf(c_0_12, plain, (v1_funct_1(k6_pboole(X1,X2,X3))\|~v1_relat_1(X2)\|~v4_relat_1(X2,X1)\|~v1_funct_1(X2)\|~v1_partfun1(X2,X1)\|~v1_relat_1(X3)\|~v4_relat_1(X3,X1)\|~v1_funct_1(X3)\|~v1_partfun1(X3,X1)), inference(split_conjunct,[status(thm)],[c_0_7])). cnf(c_0_13, plain, (v1_partfun1(k6_pboole(X1,X2,X3),X1)\|~v1_relat_1(X2)\|~v4_relat_1(X2,X1)\|~v1_funct_1(X2)\|~v1_partfun1(X2,X1)\|~v1_relat_1(X3)\|~v4_relat_1(X3,X1)\|~v1_funct_1(X3)\|~v1_partfun1(X3,X1)), inference(split_conjunct,[status(thm)],[c_0_7])). cnf(c_0_14, plain, (r1_tarski(k2_zfmisc_1(X1,X3),k2_zfmisc_1(X2,X4))\|~r1_tarski(X1,X2)\|~r1_tarski(X3,X4)), inference(split_conjunct,[status(thm)],[c_0_8])). cnf(c_0_15, plain, (k1_funct_1(k6_pboole(X1,X2,X3),X4)=k2_zfmisc_1(k1_funct_1(X2,X4),k1_funct_1(X3,X4))\|~r2_hidden(X4,X1)\|~v1_partfun1(X3,X1)\|~v1_partfun1(X2,X1)\|~v1_partfun1(k6_pboole(X1,X2,X3),X1)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v1_funct_1(k6_pboole(X1,X2,X3))\|~v4_relat_1(X3,X1)\|~v4_relat_1(X2,X1)\|~v4_relat_1(k6_pboole(X1,X2,X3),X1)\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_relat_1(k6_pboole(X1,X2,X3))), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_9])])). cnf(c_0_16, plain, (v1_relat_1(k6_pboole(X1,X2,X3))\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v4_relat_1(X3,X1)\|~v4_relat_1(X2,X1)\|~v1_partfun1(X3,X1)\|~v1_partfun1(X2,X1)), inference(evalgc,[status(thm)],[c_0_10])). cnf(c_0_17, plain, (v4_relat_1(k6_pboole(X1,X2,X3),X1)\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v4_relat_1(X3,X1)\|~v4_relat_1(X2,X1)\|~v1_partfun1(X3,X1)\|~v1_partfun1(X2,X1)), inference(evalgc,[status(thm)],[c_0_11])). cnf(c_0_18, plain, (v1_funct_1(k6_pboole(X1,X2,X3))\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v4_relat_1(X3,X1)\|~v4_relat_1(X2,X1)\|~v1_partfun1(X3,X1)\|~v1_partfun1(X2,X1)), inference(evalgc,[status(thm)],[c_0_12])). cnf(c_0_19, plain, (v1_partfun1(k6_pboole(X1,X2,X3),X1)\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v4_relat_1(X3,X1)\|~v4_relat_1(X2,X1)\|~v1_partfun1(X3,X1)\|~v1_partfun1(X2,X1)), inference(evalgc,[status(thm)],[c_0_13])). fof(c_0_20, plain, ![X24, X25, X26, X27]:((~r2_pboole(X24,X25,X26)\|(~r2_hidden(X27,X24)\|r1_tarski(k1_funct_1(X25,X27),k1_funct_1(X26,X27)))\|(~v1_relat_1(X26)\|(~v4_relat_1(X26,X24)\|(~v1_funct_1(X26)\|~v1_partfun1(X26,X24))))\|(~v1_relat_1(X25)\|(~v4_relat_1(X25,X24)\|(~v1_funct_1(X25)\|~v1_partfun1(X25,X24)))))&((r2_hidden(esk7_3(X24,X25,X26),X24)\|r2_pboole(X24,X25,X26)\|(~v1_relat_1(X26)\|(~v4_relat_1(X26,X24)\|(~v1_funct_1(X26)\|~v1_partfun1(X26,X24))))\|(~v1_relat_1(X25)\|(~v4_relat_1(X25,X24)\|(~v1_funct_1(X25)\|~v1_partfun1(X25,X24)))))&(~r1_tarski(k1_funct_1(X25,esk7_3(X24,X25,X26)),k1_funct_1(X26,esk7_3(X24,X25,X26)))\|r2_pboole(X24,X25,X26)\|(~v1_relat_1(X26)\|(~v4_relat_1(X26,X24)\|(~v1_funct_1(X26)\|~v1_partfun1(X26,X24))))\|(~v1_relat_1(X25)\|(~v4_relat_1(X25,X24)\|(~v1_funct_1(X25)\|~v1_partfun1(X25,X24))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d2_pboole])])])])])). cnf(c_0_21, plain, (r1_tarski(k2_zfmisc_1(X1,X3),k2_zfmisc_1(X2,X4))\|~r1_tarski(X3,X4)\|~r1_tarski(X1,X2)), inference(evalgc,[status(thm)],[c_0_14])). cnf(c_0_22, plain, (k1_funct_1(k6_pboole(X1,X2,X3),X4)=k2_zfmisc_1(k1_funct_1(X2,X4),k1_funct_1(X3,X4))\|~r2_hidden(X4,X1)\|~v1_partfun1(X3,X1)\|~v1_partfun1(X2,X1)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v4_relat_1(X3,X1)\|~v4_relat_1(X2,X1)\|~v1_relat_1(X3)\|~v1_relat_1(X2)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_15, c_0_16]), c_0_17]), c_0_18]), c_0_19])). fof(c_0_23, negated_conjecture, ~(![X1, X2]:((v1_relat_1(X2)&(v4_relat_1(X2,X1)&(v1_funct_1(X2)&v1_partfun1(X2,X1))))=>![X3]:((v1_relat_1(X3)&(v4_relat_1(X3,X1)&(v1_funct_1(X3)&v1_partfun1(X3,X1))))=>![X4]:((v1_relat_1(X4)&(v4_relat_1(X4,X1)&(v1_funct_1(X4)&v1_partfun1(X4,X1))))=>![X5]:((v1_relat_1(X5)&(v4_relat_1(X5,X1)&(v1_funct_1(X5)&v1_partfun1(X5,X1))))=>((r2_pboole(X1,X2,X3)&r2_pboole(X1,X4,X5))=>r2_pboole(X1,k6_pboole(X1,X2,X4),k6_pboole(X1,X3,X5)))))))), inference(assume_negation,[status(cth)],[t62_pzfmisc1])). cnf(c_0_24, plain, (r2_pboole(X2,X1,X3)\|~r1_tarski(k1_funct_1(X1,esk7_3(X2,X1,X3)),k1_funct_1(X3,esk7_3(X2,X1,X3)))\|~v1_relat_1(X3)\|~v4_relat_1(X3,X2)\|~v1_funct_1(X3)\|~v1_partfun1(X3,X2)\|~v1_relat_1(X1)\|~v4_relat_1(X1,X2)\|~v1_funct_1(X1)\|~v1_partfun1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_20])). cnf(c_0_25, plain, (r1_tarski(k1_funct_1(k6_pboole(X6,X1,X3),X2),k2_zfmisc_1(X4,X5))\|~r1_tarski(k1_funct_1(X3,X2),X5)\|~r1_tarski(k1_funct_1(X1,X2),X4)\|~r2_hidden(X2,X6)\|~v1_partfun1(X3,X6)\|~v1_partfun1(X1,X6)\|~v1_funct_1(X3)\|~v1_funct_1(X1)\|~v4_relat_1(X3,X6)\|~v4_relat_1(X1,X6)\|~v1_relat_1(X3)\|~v1_relat_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_21, c_0_22])])). fof(c_0_26, negated_conjecture, ((v1_relat_1(esk2_0)&(v4_relat_1(esk2_0,esk1_0)&(v1_funct_1(esk2_0)&v1_partfun1(esk2_0,esk1_0))))&((v1_relat_1(esk3_0)&(v4_relat_1(esk3_0,esk1_0)&(v1_funct_1(esk3_0)&v1_partfun1(esk3_0,esk1_0))))&((v1_relat_1(esk4_0)&(v4_relat_1(esk4_0,esk1_0)&(v1_funct_1(esk4_0)&v1_partfun1(esk4_0,esk1_0))))&((v1_relat_1(esk5_0)&(v4_relat_1(esk5_0,esk1_0)&(v1_funct_1(esk5_0)&v1_partfun1(esk5_0,esk1_0))))&((r2_pboole(esk1_0,esk2_0,esk3_0)&r2_pboole(esk1_0,esk4_0,esk5_0))&~r2_pboole(esk1_0,k6_pboole(esk1_0,esk2_0,esk4_0),k6_pboole(esk1_0,esk3_0,esk5_0))))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])])). cnf(c_0_27, plain, (r2_pboole(X2,X1,X3)\|~v1_relat_1(X3)\|~v1_relat_1(X1)\|~v1_funct_1(X3)\|~v1_funct_1(X1)\|~v4_relat_1(X3,X2)\|~v4_relat_1(X1,X2)\|~v1_partfun1(X3,X2)\|~v1_partfun1(X1,X2)\|~r1_tarski(k1_funct_1(X1,esk7_3(X2,X1,X3)),k1_funct_1(X3,esk7_3(X2,X1,X3)))), inference(evalgc,[status(thm)],[c_0_24])). cnf(c_0_28, plain, (r1_tarski(k1_funct_1(k6_pboole(X1,X2,X3),X4),k1_funct_1(k6_pboole(X8,X5,X7),X6))\|~r1_tarski(k1_funct_1(X3,X4),k1_funct_1(X7,X6))\|~r1_tarski(k1_funct_1(X2,X4),k1_funct_1(X5,X6))\|~r2_hidden(X4,X1)\|~v1_partfun1(X3,X1)\|~v1_partfun1(X2,X1)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v4_relat_1(X3,X1)\|~v4_relat_1(X2,X1)\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~r2_hidden(X6,X8)\|~v1_partfun1(X7,X8)\|~v1_partfun1(X5,X8)\|~v1_funct_1(X7)\|~v1_funct_1(X5)\|~v4_relat_1(X7,X8)\|~v4_relat_1(X5,X8)\|~v1_relat_1(X7)\|~v1_relat_1(X5)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_25, c_0_22])])). cnf(c_0_29, plain, (r1_tarski(k1_funct_1(X2,X4),k1_funct_1(X3,X4))\|~r2_pboole(X1,X2,X3)\|~r2_hidden(X4,X1)\|~v1_relat_1(X3)\|~v4_relat_1(X3,X1)\|~v1_funct_1(X3)\|~v1_partfun1(X3,X1)\|~v1_relat_1(X2)\|~v4_relat_1(X2,X1)\|~v1_funct_1(X2)\|~v1_partfun1(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_20])). cnf(c_0_30, negated_conjecture, (r2_pboole(esk1_0,esk4_0,esk5_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_31, negated_conjecture, (v1_partfun1(esk5_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_32, negated_conjecture, (v1_partfun1(esk4_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_33, negated_conjecture, (v1_funct_1(esk5_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_34, negated_conjecture, (v1_funct_1(esk4_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_35, negated_conjecture, (v4_relat_1(esk5_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_36, negated_conjecture, (v4_relat_1(esk4_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_37, negated_conjecture, (v1_relat_1(esk5_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_38, negated_conjecture, (v1_relat_1(esk4_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_39, plain, (r2_pboole(X1,k6_pboole(X2,X3,X4),k6_pboole(X5,X6,X7))\|~v1_partfun1(k6_pboole(X5,X6,X7),X1)\|~v1_partfun1(k6_pboole(X2,X3,X4),X1)\|~v1_funct_1(k6_pboole(X5,X6,X7))\|~v1_funct_1(k6_pboole(X2,X3,X4))\|~v4_relat_1(k6_pboole(X5,X6,X7),X1)\|~v4_relat_1(k6_pboole(X2,X3,X4),X1)\|~v1_relat_1(k6_pboole(X5,X6,X7))\|~v1_relat_1(k6_pboole(X2,X3,X4))\|~r1_tarski(k1_funct_1(X4,esk7_3(X1,k6_pboole(X2,X3,X4),k6_pboole(X5,X6,X7))),k1_funct_1(X7,esk7_3(X1,k6_pboole(X2,X3,X4),k6_pboole(X5,X6,X7))))\|~r1_tarski(k1_funct_1(X3,esk7_3(X1,k6_pboole(X2,X3,X4),k6_pboole(X5,X6,X7))),k1_funct_1(X6,esk7_3(X1,k6_pboole(X2,X3,X4),k6_pboole(X5,X6,X7))))\|~r2_hidden(esk7_3(X1,k6_pboole(X2,X3,X4),k6_pboole(X5,X6,X7)),X2)\|~r2_hidden(esk7_3(X1,k6_pboole(X2,X3,X4),k6_pboole(X5,X6,X7)),X5)\|~v1_partfun1(X4,X2)\|~v1_partfun1(X3,X2)\|~v1_partfun1(X7,X5)\|~v1_partfun1(X6,X5)\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v1_funct_1(X7)\|~v1_funct_1(X6)\|~v4_relat_1(X4,X2)\|~v4_relat_1(X3,X2)\|~v4_relat_1(X7,X5)\|~v4_relat_1(X6,X5)\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~v1_relat_1(X7)\|~v1_relat_1(X6)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_27, c_0_28])])). cnf(c_0_40, plain, (r1_tarski(k1_funct_1(X2,X4),k1_funct_1(X3,X4))\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v4_relat_1(X3,X1)\|~v4_relat_1(X2,X1)\|~v1_partfun1(X3,X1)\|~v1_partfun1(X2,X1)\|~r2_hidden(X4,X1)\|~r2_pboole(X1,X2,X3)), inference(evalgc,[status(thm)],[c_0_29])). cnf(c_0_41, negated_conjecture, (r2_pboole(esk1_0,esk4_0,esk5_0)), inference(evalgc,[status(thm)],[c_0_30])). cnf(c_0_42, negated_conjecture, (v1_partfun1(esk5_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_31])). cnf(c_0_43, negated_conjecture, (v1_partfun1(esk4_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_32])). cnf(c_0_44, negated_conjecture, (v1_funct_1(esk5_0)), inference(evalgc,[status(thm)],[c_0_33])). cnf(c_0_45, negated_conjecture, (v1_funct_1(esk4_0)), inference(evalgc,[status(thm)],[c_0_34])). cnf(c_0_46, negated_conjecture, (v4_relat_1(esk5_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_35])). cnf(c_0_47, negated_conjecture, (v4_relat_1(esk4_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_36])). cnf(c_0_48, negated_conjecture, (v1_relat_1(esk5_0)), inference(evalgc,[status(thm)],[c_0_37])). cnf(c_0_49, negated_conjecture, (v1_relat_1(esk4_0)), inference(evalgc,[status(thm)],[c_0_38])). cnf(c_0_50, negated_conjecture, (r2_pboole(esk1_0,esk2_0,esk3_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_51, negated_conjecture, (v1_partfun1(esk3_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_52, negated_conjecture, (v1_partfun1(esk2_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_53, negated_conjecture, (v1_funct_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_54, negated_conjecture, (v1_funct_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_55, negated_conjecture, (v4_relat_1(esk3_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_56, negated_conjecture, (v4_relat_1(esk2_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_57, negated_conjecture, (v1_relat_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_58, negated_conjecture, (v1_relat_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_59, plain, (r2_pboole(X1,k6_pboole(X2,X3,X4),k6_pboole(X5,X6,X7))\|~r1_tarski(k1_funct_1(X4,esk7_3(X1,k6_pboole(X2,X3,X4),k6_pboole(X5,X6,X7))),k1_funct_1(X7,esk7_3(X1,k6_pboole(X2,X3,X4),k6_pboole(X5,X6,X7))))\|~r1_tarski(k1_funct_1(X3,esk7_3(X1,k6_pboole(X2,X3,X4),k6_pboole(X5,X6,X7))),k1_funct_1(X6,esk7_3(X1,k6_pboole(X2,X3,X4),k6_pboole(X5,X6,X7))))\|~r2_hidden(esk7_3(X1,k6_pboole(X2,X3,X4),k6_pboole(X5,X6,X7)),X2)\|~r2_hidden(esk7_3(X1,k6_pboole(X2,X3,X4),k6_pboole(X5,X6,X7)),X5)\|~v1_partfun1(k6_pboole(X5,X6,X7),X1)\|~v1_partfun1(k6_pboole(X2,X3,X4),X1)\|~v1_partfun1(X4,X2)\|~v1_partfun1(X3,X2)\|~v1_partfun1(X7,X5)\|~v1_partfun1(X6,X5)\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v1_funct_1(X7)\|~v1_funct_1(X6)\|~v4_relat_1(k6_pboole(X5,X6,X7),X1)\|~v4_relat_1(k6_pboole(X2,X3,X4),X1)\|~v4_relat_1(X4,X2)\|~v4_relat_1(X3,X2)\|~v4_relat_1(X7,X5)\|~v4_relat_1(X6,X5)\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~v1_relat_1(X7)\|~v1_relat_1(X6)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_39, c_0_16]), c_0_16]), c_0_18]), c_0_18])). cnf(c_0_60, negated_conjecture, (r1_tarski(k1_funct_1(esk4_0,X1),k1_funct_1(esk5_0,X1))\|~r2_hidden(X1,esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40, c_0_41]), c_0_42]), c_0_43]), c_0_44]), c_0_45]), c_0_46]), c_0_47]), c_0_48]), c_0_49])])])). cnf(c_0_61, negated_conjecture, (r2_pboole(esk1_0,esk2_0,esk3_0)), inference(evalgc,[status(thm)],[c_0_50])). cnf(c_0_62, negated_conjecture, (v1_partfun1(esk3_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_51])). cnf(c_0_63, negated_conjecture, (v1_partfun1(esk2_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_52])). cnf(c_0_64, negated_conjecture, (v1_funct_1(esk3_0)), inference(evalgc,[status(thm)],[c_0_53])). cnf(c_0_65, negated_conjecture, (v1_funct_1(esk2_0)), inference(evalgc,[status(thm)],[c_0_54])). cnf(c_0_66, negated_conjecture, (v4_relat_1(esk3_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_55])). cnf(c_0_67, negated_conjecture, (v4_relat_1(esk2_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_56])). cnf(c_0_68, negated_conjecture, (v1_relat_1(esk3_0)), inference(evalgc,[status(thm)],[c_0_57])). cnf(c_0_69, negated_conjecture, (v1_relat_1(esk2_0)), inference(evalgc,[status(thm)],[c_0_58])). cnf(c_0_70, negated_conjecture, (r2_pboole(X1,k6_pboole(X2,X3,esk4_0),k6_pboole(X4,X5,esk5_0))\|~r1_tarski(k1_funct_1(X3,esk7_3(X1,k6_pboole(X2,X3,esk4_0),k6_pboole(X4,X5,esk5_0))),k1_funct_1(X5,esk7_3(X1,k6_pboole(X2,X3,esk4_0),k6_pboole(X4,X5,esk5_0))))\|~r2_hidden(esk7_3(X1,k6_pboole(X2,X3,esk4_0),k6_pboole(X4,X5,esk5_0)),X2)\|~r2_hidden(esk7_3(X1,k6_pboole(X2,X3,esk4_0),k6_pboole(X4,X5,esk5_0)),X4)\|~v1_partfun1(k6_pboole(X4,X5,esk5_0),X1)\|~v1_partfun1(k6_pboole(X2,X3,esk4_0),X1)\|~v1_partfun1(esk4_0,X2)\|~v1_partfun1(X3,X2)\|~v1_partfun1(esk5_0,X4)\|~v1_partfun1(X5,X4)\|~v1_funct_1(X3)\|~v1_funct_1(X5)\|~v4_relat_1(k6_pboole(X4,X5,esk5_0),X1)\|~v4_relat_1(k6_pboole(X2,X3,esk4_0),X1)\|~v4_relat_1(esk4_0,X2)\|~v4_relat_1(X3,X2)\|~v4_relat_1(esk5_0,X4)\|~v4_relat_1(X5,X4)\|~v1_relat_1(X3)\|~v1_relat_1(X5)\|~r2_hidden(esk7_3(X1,k6_pboole(X2,X3,esk4_0),k6_pboole(X4,X5,esk5_0)),esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59, c_0_60]), c_0_45]), c_0_44]), c_0_49]), c_0_48])])])). cnf(c_0_71, negated_conjecture, (r1_tarski(k1_funct_1(esk2_0,X1),k1_funct_1(esk3_0,X1))\|~r2_hidden(X1,esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40, c_0_61]), c_0_62]), c_0_63]), c_0_64]), c_0_65]), c_0_66]), c_0_67]), c_0_68]), c_0_69])])])). cnf(c_0_72, plain, (r2_hidden(esk7_3(X1,X2,X3),X1)\|r2_pboole(X1,X2,X3)\|~v1_relat_1(X3)\|~v4_relat_1(X3,X1)\|~v1_funct_1(X3)\|~v1_partfun1(X3,X1)\|~v1_relat_1(X2)\|~v4_relat_1(X2,X1)\|~v1_funct_1(X2)\|~v1_partfun1(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_20])). cnf(c_0_73, negated_conjecture, (r2_pboole(X1,k6_pboole(X2,esk2_0,esk4_0),k6_pboole(X3,esk3_0,esk5_0))\|~r2_hidden(esk7_3(X1,k6_pboole(X2,esk2_0,esk4_0),k6_pboole(X3,esk3_0,esk5_0)),esk1_0)\|~r2_hidden(esk7_3(X1,k6_pboole(X2,esk2_0,esk4_0),k6_pboole(X3,esk3_0,esk5_0)),X2)\|~r2_hidden(esk7_3(X1,k6_pboole(X2,esk2_0,esk4_0),k6_pboole(X3,esk3_0,esk5_0)),X3)\|~v1_partfun1(k6_pboole(X3,esk3_0,esk5_0),X1)\|~v1_partfun1(k6_pboole(X2,esk2_0,esk4_0),X1)\|~v1_partfun1(esk4_0,X2)\|~v1_partfun1(esk5_0,X3)\|~v1_partfun1(esk2_0,X2)\|~v1_partfun1(esk3_0,X3)\|~v4_relat_1(k6_pboole(X3,esk3_0,esk5_0),X1)\|~v4_relat_1(k6_pboole(X2,esk2_0,esk4_0),X1)\|~v4_relat_1(esk4_0,X2)\|~v4_relat_1(esk5_0,X3)\|~v4_relat_1(esk2_0,X2)\|~v4_relat_1(esk3_0,X3)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70, c_0_71]), c_0_65]), c_0_64]), c_0_69]), c_0_68])])])). cnf(c_0_74, plain, (r2_pboole(X1,X2,X3)\|r2_hidden(esk7_3(X1,X2,X3),X1)\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v4_relat_1(X3,X1)\|~v4_relat_1(X2,X1)\|~v1_partfun1(X3,X1)\|~v1_partfun1(X2,X1)), inference(evalgc,[status(thm)],[c_0_72])). cnf(c_0_75, negated_conjecture, (r2_pboole(esk1_0,k6_pboole(X1,esk2_0,esk4_0),k6_pboole(X2,esk3_0,esk5_0))\|~r2_hidden(esk7_3(esk1_0,k6_pboole(X1,esk2_0,esk4_0),k6_pboole(X2,esk3_0,esk5_0)),X1)\|~r2_hidden(esk7_3(esk1_0,k6_pboole(X1,esk2_0,esk4_0),k6_pboole(X2,esk3_0,esk5_0)),X2)\|~v1_partfun1(k6_pboole(X2,esk3_0,esk5_0),esk1_0)\|~v1_partfun1(k6_pboole(X1,esk2_0,esk4_0),esk1_0)\|~v1_partfun1(esk4_0,X1)\|~v1_partfun1(esk5_0,X2)\|~v1_partfun1(esk2_0,X1)\|~v1_partfun1(esk3_0,X2)\|~v4_relat_1(k6_pboole(X2,esk3_0,esk5_0),esk1_0)\|~v4_relat_1(k6_pboole(X1,esk2_0,esk4_0),esk1_0)\|~v4_relat_1(esk4_0,X1)\|~v4_relat_1(esk5_0,X2)\|~v4_relat_1(esk2_0,X1)\|~v4_relat_1(esk3_0,X2)\|~v1_funct_1(k6_pboole(X2,esk3_0,esk5_0))\|~v1_funct_1(k6_pboole(X1,esk2_0,esk4_0))\|~v1_relat_1(k6_pboole(X2,esk3_0,esk5_0))\|~v1_relat_1(k6_pboole(X1,esk2_0,esk4_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_73, c_0_74])])). cnf(c_0_76, negated_conjecture, (~r2_pboole(esk1_0,k6_pboole(esk1_0,esk2_0,esk4_0),k6_pboole(esk1_0,esk3_0,esk5_0))), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_77, negated_conjecture, (r2_pboole(esk1_0,k6_pboole(esk1_0,esk2_0,esk4_0),k6_pboole(X1,esk3_0,esk5_0))\|~r2_hidden(esk7_3(esk1_0,k6_pboole(esk1_0,esk2_0,esk4_0),k6_pboole(X1,esk3_0,esk5_0)),X1)\|~v1_partfun1(k6_pboole(X1,esk3_0,esk5_0),esk1_0)\|~v1_partfun1(k6_pboole(esk1_0,esk2_0,esk4_0),esk1_0)\|~v1_partfun1(esk5_0,X1)\|~v1_partfun1(esk3_0,X1)\|~v1_funct_1(k6_pboole(X1,esk3_0,esk5_0))\|~v1_funct_1(k6_pboole(esk1_0,esk2_0,esk4_0))\|~v4_relat_1(k6_pboole(X1,esk3_0,esk5_0),esk1_0)\|~v4_relat_1(k6_pboole(esk1_0,esk2_0,esk4_0),esk1_0)\|~v4_relat_1(esk5_0,X1)\|~v4_relat_1(esk3_0,X1)\|~v1_relat_1(k6_pboole(X1,esk3_0,esk5_0))\|~v1_relat_1(k6_pboole(esk1_0,esk2_0,esk4_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75, c_0_74]), c_0_43]), c_0_63]), c_0_47]), c_0_67])])])). cnf(c_0_78, negated_conjecture, (~r2_pboole(esk1_0,k6_pboole(esk1_0,esk2_0,esk4_0),k6_pboole(esk1_0,esk3_0,esk5_0))), inference(evalgc,[status(thm)],[c_0_76])). cnf(c_0_79, negated_conjecture, (~v1_partfun1(k6_pboole(esk1_0,esk2_0,esk4_0),esk1_0)\|~v1_partfun1(k6_pboole(esk1_0,esk3_0,esk5_0),esk1_0)\|~v1_funct_1(k6_pboole(esk1_0,esk2_0,esk4_0))\|~v1_funct_1(k6_pboole(esk1_0,esk3_0,esk5_0))\|~v4_relat_1(k6_pboole(esk1_0,esk2_0,esk4_0),esk1_0)\|~v4_relat_1(k6_pboole(esk1_0,esk3_0,esk5_0),esk1_0)\|~v1_relat_1(k6_pboole(esk1_0,esk2_0,esk4_0))\|~v1_relat_1(k6_pboole(esk1_0,esk3_0,esk5_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77, c_0_74]), c_0_42]), c_0_62]), c_0_46]), c_0_66])]), c_0_78])])). cnf(c_0_80, negated_conjecture, (~v1_partfun1(k6_pboole(esk1_0,esk3_0,esk5_0),esk1_0)\|~v1_funct_1(k6_pboole(esk1_0,esk2_0,esk4_0))\|~v1_funct_1(k6_pboole(esk1_0,esk3_0,esk5_0))\|~v4_relat_1(k6_pboole(esk1_0,esk2_0,esk4_0),esk1_0)\|~v4_relat_1(k6_pboole(esk1_0,esk3_0,esk5_0),esk1_0)\|~v1_relat_1(k6_pboole(esk1_0,esk2_0,esk4_0))\|~v1_relat_1(k6_pboole(esk1_0,esk3_0,esk5_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79, c_0_19]), c_0_43]), c_0_63]), c_0_45]), c_0_65]), c_0_47]), c_0_67]), c_0_49]), c_0_69])])])). cnf(c_0_81, negated_conjecture, (~v1_funct_1(k6_pboole(esk1_0,esk2_0,esk4_0))\|~v1_funct_1(k6_pboole(esk1_0,esk3_0,esk5_0))\|~v4_relat_1(k6_pboole(esk1_0,esk2_0,esk4_0),esk1_0)\|~v4_relat_1(k6_pboole(esk1_0,esk3_0,esk5_0),esk1_0)\|~v1_relat_1(k6_pboole(esk1_0,esk2_0,esk4_0))\|~v1_relat_1(k6_pboole(esk1_0,esk3_0,esk5_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80, c_0_19]), c_0_42]), c_0_62]), c_0_44]), c_0_64]), c_0_46]), c_0_66]), c_0_48]), c_0_68])])])). cnf(c_0_82, negated_conjecture, (~v1_funct_1(k6_pboole(esk1_0,esk2_0,esk4_0))\|~v1_funct_1(k6_pboole(esk1_0,esk3_0,esk5_0))\|~v4_relat_1(k6_pboole(esk1_0,esk3_0,esk5_0),esk1_0)\|~v1_relat_1(k6_pboole(esk1_0,esk2_0,esk4_0))\|~v1_relat_1(k6_pboole(esk1_0,esk3_0,esk5_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81, c_0_17]), c_0_43]), c_0_63]), c_0_45]), c_0_65]), c_0_47]), c_0_67]), c_0_49]), c_0_69])])])). cnf(c_0_83, negated_conjecture, (~v1_funct_1(k6_pboole(esk1_0,esk2_0,esk4_0))\|~v1_funct_1(k6_pboole(esk1_0,esk3_0,esk5_0))\|~v1_relat_1(k6_pboole(esk1_0,esk2_0,esk4_0))\|~v1_relat_1(k6_pboole(esk1_0,esk3_0,esk5_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82, c_0_17]), c_0_42]), c_0_62]), c_0_44]), c_0_64]), c_0_46]), c_0_66]), c_0_48]), c_0_68])])])). cnf(c_0_84, negated_conjecture, (~v1_funct_1(k6_pboole(esk1_0,esk3_0,esk5_0))\|~v1_relat_1(k6_pboole(esk1_0,esk2_0,esk4_0))\|~v1_relat_1(k6_pboole(esk1_0,esk3_0,esk5_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83, c_0_18]), c_0_43]), c_0_63]), c_0_45]), c_0_65]), c_0_47]), c_0_67]), c_0_49]), c_0_69])])])). cnf(c_0_85, negated_conjecture, (~v1_relat_1(k6_pboole(esk1_0,esk2_0,esk4_0))\|~v1_relat_1(k6_pboole(esk1_0,esk3_0,esk5_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84, c_0_18]), c_0_42]), c_0_62]), c_0_44]), c_0_64]), c_0_46]), c_0_66]), c_0_48]), c_0_68])])])). cnf(c_0_86, negated_conjecture, (~v1_relat_1(k6_pboole(esk1_0,esk3_0,esk5_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85, c_0_16]), c_0_43]), c_0_63]), c_0_45]), c_0_65]), c_0_47]), c_0_67]), c_0_49]), c_0_69])])])). cnf(c_0_87, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86, c_0_16]), c_0_42]), c_0_62]), c_0_44]), c_0_64]), c_0_46]), c_0_66]), c_0_48]), c_0_68])]), ['proof']). # SZS output end CNFRefutation	reserve i, I for set, f for Function, x, x1, x2, y, A, B, X, Y, Z for ManySortedSet of I; theorem :: ZFMISC_1:119 x1 c= A & x2 c= B implies [\|x1,x2\|] c= [\|A,B\|] proof assume that A1: x1 c= A and A2: x2 c= B; let i; assume A3: i in I; then A4: x1.i c= A.i by A1,PBOOLE:def 2; x2.i c= B.i by A2,A3,PBOOLE:def 2; then [:x1.i,x2.i:] c= [:A.i,B.i:] by A4,ZFMISC_1:96; then [\|x1,x2\|].i c= [:A.i,B.i:] by A3,PBOOLE:def 16; hence thesis by A3,PBOOLE:def 16; end;	Convert the following ATP output trace into a readable Mizar proof.
t2_funct_4	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t2_funct_4, conjecture, ![X1]:((v1_relat_1(X1)&v1_funct_1(X1))=>![X2]:((v1_relat_1(X2)&v1_funct_1(X2))=>k3_relat_1(X2,X1)=k3_relat_1(X2,k5_relat_1(X1,k10_xtuple_0(X2))))), file('/scratch/mptp/predsminms1/t2_funct_4__0', t2_funct_4)). fof(t53_relat_1, axiom, ![X1, X2]:(v1_relat_1(X2)=>(r1_tarski(k10_xtuple_0(X2),X1)=>k3_relat_1(X2,k4_relat_1(X1))=X2)), file('/scratch/mptp/predsminms1/t2_funct_4__0', t53_relat_1)). fof(reflexivity_r1_tarski, axiom, ![X1, X2]:r1_tarski(X1,X1), file('/scratch/mptp/predsminms1/t2_funct_4__0', reflexivity_r1_tarski)). fof(t65_relat_1, axiom, ![X1, X2]:(v1_relat_1(X2)=>k5_relat_1(X2,X1)=k3_relat_1(k4_relat_1(X1),X2)), file('/scratch/mptp/predsminms1/t2_funct_4__0', t65_relat_1)). fof(t36_relat_1, axiom, ![X1]:(v1_relat_1(X1)=>![X2]:(v1_relat_1(X2)=>![X3]:(v1_relat_1(X3)=>k3_relat_1(k3_relat_1(X1,X2),X3)=k3_relat_1(X1,k3_relat_1(X2,X3))))), file('/scratch/mptp/predsminms1/t2_funct_4__0', t36_relat_1)). fof(dt_k4_relat_1, axiom, ![X1]:v1_relat_1(k4_relat_1(X1)), file('/scratch/mptp/predsminms1/t2_funct_4__0', dt_k4_relat_1)). fof(c_0_6, negated_conjecture, ~(![X1]:((v1_relat_1(X1)&v1_funct_1(X1))=>![X2]:((v1_relat_1(X2)&v1_funct_1(X2))=>k3_relat_1(X2,X1)=k3_relat_1(X2,k5_relat_1(X1,k10_xtuple_0(X2)))))), inference(assume_negation,[status(cth)],[t2_funct_4])). fof(c_0_7, plain, ![X6, X7]:(~v1_relat_1(X7)\|(~r1_tarski(k10_xtuple_0(X7),X6)\|k3_relat_1(X7,k4_relat_1(X6))=X7)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t53_relat_1])])). fof(c_0_8, plain, ![X8]:r1_tarski(X8,X8), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])])). fof(c_0_9, negated_conjecture, ((v1_relat_1(esk1_0)&v1_funct_1(esk1_0))&((v1_relat_1(esk2_0)&v1_funct_1(esk2_0))&k3_relat_1(esk2_0,esk1_0)!=k3_relat_1(esk2_0,k5_relat_1(esk1_0,k10_xtuple_0(esk2_0))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])). fof(c_0_10, plain, ![X9, X10]:(~v1_relat_1(X10)\|k5_relat_1(X10,X9)=k3_relat_1(k4_relat_1(X9),X10)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t65_relat_1])])). fof(c_0_11, plain, ![X11, X12, X13]:(~v1_relat_1(X11)\|(~v1_relat_1(X12)\|(~v1_relat_1(X13)\|k3_relat_1(k3_relat_1(X11,X12),X13)=k3_relat_1(X11,k3_relat_1(X12,X13))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t36_relat_1])])])). cnf(c_0_12, plain, (k3_relat_1(X1,k4_relat_1(X2))=X1\|~v1_relat_1(X1)\|~r1_tarski(k10_xtuple_0(X1),X2)), inference(split_conjunct,[status(thm)],[c_0_7])). cnf(c_0_13, plain, (r1_tarski(X1,X1)), inference(split_conjunct,[status(thm)],[c_0_8])). fof(c_0_14, plain, ![X14]:v1_relat_1(k4_relat_1(X14)), inference(variable_rename,[status(thm)],[dt_k4_relat_1])). cnf(c_0_15, negated_conjecture, (k3_relat_1(esk2_0,esk1_0)!=k3_relat_1(esk2_0,k5_relat_1(esk1_0,k10_xtuple_0(esk2_0)))), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_16, plain, (k5_relat_1(X1,X2)=k3_relat_1(k4_relat_1(X2),X1)\|~v1_relat_1(X1)), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_17, negated_conjecture, (v1_relat_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_18, plain, (k3_relat_1(k3_relat_1(X1,X2),X3)=k3_relat_1(X1,k3_relat_1(X2,X3))\|~v1_relat_1(X1)\|~v1_relat_1(X2)\|~v1_relat_1(X3)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_19, plain, (k3_relat_1(X1,k4_relat_1(X2))=X1\|~v1_relat_1(X1)\|~r1_tarski(k10_xtuple_0(X1),X2)), inference(evalgc,[status(thm)],[c_0_12])). cnf(c_0_20, plain, (r1_tarski(X1,X1)), inference(evalgc,[status(thm)],[c_0_13])). cnf(c_0_21, plain, (v1_relat_1(k4_relat_1(X1))), inference(split_conjunct,[status(thm)],[c_0_14])). cnf(c_0_22, negated_conjecture, (k3_relat_1(esk2_0,k5_relat_1(esk1_0,k10_xtuple_0(esk2_0)))!=k3_relat_1(esk2_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_15])). cnf(c_0_23, plain, (k5_relat_1(X1,X2)=k3_relat_1(k4_relat_1(X2),X1)\|~v1_relat_1(X1)), inference(evalgc,[status(thm)],[c_0_16])). cnf(c_0_24, negated_conjecture, (v1_relat_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_17])). cnf(c_0_25, plain, (k3_relat_1(k3_relat_1(X1,X2),X3)=k3_relat_1(X1,k3_relat_1(X2,X3))\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_relat_1(X1)), inference(evalgc,[status(thm)],[c_0_18])). cnf(c_0_26, plain, (k3_relat_1(X1,k4_relat_1(k10_xtuple_0(X1)))=X1\|~v1_relat_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_19, c_0_20])])). cnf(c_0_27, plain, (v1_relat_1(k4_relat_1(X1))), inference(evalgc,[status(thm)],[c_0_21])). cnf(c_0_28, negated_conjecture, (v1_relat_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_29, negated_conjecture, (k3_relat_1(esk2_0,k3_relat_1(k4_relat_1(k10_xtuple_0(esk2_0)),esk1_0))!=k3_relat_1(esk2_0,esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22, c_0_23]), c_0_24])])])). cnf(c_0_30, plain, (k3_relat_1(X1,k3_relat_1(k4_relat_1(k10_xtuple_0(X1)),X2))=k3_relat_1(X1,X2)\|~v1_relat_1(X2)\|~v1_relat_1(X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25, c_0_26]), c_0_27])])])). cnf(c_0_31, negated_conjecture, (v1_relat_1(esk2_0)), inference(evalgc,[status(thm)],[c_0_28])). cnf(c_0_32, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29, c_0_30]), c_0_24]), c_0_31])]), ['proof']). # SZS output end CNFRefutation	reserve a,b,p,x,x9,x1,x19,x2,y,y9,y1,y19,y2,z,z9,z1,z2,X,X9,Y,Y9,Z,Z9 for set; reserve A,D,D9 for non empty set; reserve f,g,h for Function; theorem gf = (g\|rng f)f proof x in dom(gf) iff x in dom((g\|rng f)f) proof A1: dom(g\|rng f) = dom g /\ rng f by RELAT_1:61; thus x in dom(gf) implies x in dom((g\|rng f)f) proof assume A2: x in dom(gf); then A3: x in dom f by FUNCT_1:11; x in dom f by A2,FUNCT_1:11; then A4: f.x in rng f by FUNCT_1:def 3; f.x in dom g by A2,FUNCT_1:11; then f.x in dom(g\|rng f) by A1,A4,XBOOLE_0:def 4; hence thesis by A3,FUNCT_1:11; end; assume A5: x in dom((g\|rng f)f); then f.x in dom(g\|rng f) by FUNCT_1:11; then A6: f.x in dom g by A1,XBOOLE_0:def 4; x in dom f by A5,FUNCT_1:11; hence thesis by A6,FUNCT_1:11; end; then A7: dom(gf) = dom((g\|rng f)f) by TARSKI:1; x in dom(gf) implies (gf).x = ((g\|rng f)f).x proof assume A8: x in dom(gf); then A9: x in dom f by FUNCT_1:11; then A10: f.x in rng f by FUNCT_1:def 3; thus (gf).x = g.(f.x) by A8,FUNCT_1:12 .= (g\|rng f).(f.x) by A10,FUNCT_1:49 .= ((g\|rng f)f).x by A9,FUNCT_1:13; end; hence thesis by A7,FUNCT_1:2; end;	Convert the following ATP output trace into a readable Mizar proof.
t18_borsuk_5	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t18_borsuk_5, conjecture, ![X1]:(v1_rat_1(X1)=>![X2]:((v1_xreal_0(X2)&~(v1_rat_1(X2)))=>~(v1_rat_1(k2_xcmplx_0(X1,X2))))), file('/scratch/mptp/predsminms1/t18_borsuk_5__0', t18_borsuk_5)). fof(fc4_borsuk_5, axiom, ![X1, X2]:((v1_rat_1(X1)&(v1_xreal_0(X2)&~(v1_rat_1(X2))))=>~(v1_rat_1(k2_xcmplx_0(X1,X2)))), file('/scratch/mptp/predsminms1/t18_borsuk_5__0', fc4_borsuk_5)). fof(c_0_2, negated_conjecture, ~(![X1]:(v1_rat_1(X1)=>![X2]:((v1_xreal_0(X2)&~(v1_rat_1(X2)))=>~(v1_rat_1(k2_xcmplx_0(X1,X2)))))), inference(assume_negation,[status(cth)],[t18_borsuk_5])). fof(c_0_3, plain, ![X5, X6]:(~v1_rat_1(X5)\|(~v1_xreal_0(X6)\|v1_rat_1(X6))\|~v1_rat_1(k2_xcmplx_0(X5,X6))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fc4_borsuk_5])])])). fof(c_0_4, negated_conjecture, (v1_rat_1(esk1_0)&((v1_xreal_0(esk2_0)&~v1_rat_1(esk2_0))&v1_rat_1(k2_xcmplx_0(esk1_0,esk2_0)))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_2])])])])). cnf(c_0_5, plain, (v1_rat_1(X2)\|~v1_rat_1(X1)\|~v1_xreal_0(X2)\|~v1_rat_1(k2_xcmplx_0(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_3])). cnf(c_0_6, negated_conjecture, (v1_rat_1(k2_xcmplx_0(esk1_0,esk2_0))), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_7, negated_conjecture, (v1_xreal_0(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_8, negated_conjecture, (v1_rat_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_9, negated_conjecture, (~v1_rat_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_10, plain, (v1_rat_1(X2)\|~v1_rat_1(X1)\|~v1_xreal_0(X2)\|~v1_rat_1(k2_xcmplx_0(X1,X2))), inference(evalgc,[status(thm)],[c_0_5])). cnf(c_0_11, negated_conjecture, (v1_rat_1(k2_xcmplx_0(esk1_0,esk2_0))), inference(evalgc,[status(thm)],[c_0_6])). cnf(c_0_12, negated_conjecture, (v1_xreal_0(esk2_0)), inference(evalgc,[status(thm)],[c_0_7])). cnf(c_0_13, negated_conjecture, (v1_rat_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_8])). cnf(c_0_14, negated_conjecture, (~v1_rat_1(esk2_0)), inference(evalgc,[status(thm)],[c_0_9])). cnf(c_0_15, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10, c_0_11]), c_0_12]), c_0_13])]), c_0_14]), ['proof']). # SZS output end CNFRefutation	reserve x1, x2, x3, x4, x5, x6, x7 for set; theorem for a being rational number, b being irrational real number holds a + b is irrational;	Convert the following ATP output trace into a readable Mizar proof.
t4_groupp_1	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t4_groupp_1, conjecture, ![X1]:((~(v2_struct_0(X1))&(v2_group_1(X1)&(v3_group_1(X1)&l3_algstr_0(X1))))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(v7_ordinal1(X3)=>(k5_group_1(X1,X3,k2_group_1(X1,X2))=k1_group_1(X1)=>k5_group_1(X1,X3,X2)=k1_group_1(X1))))), file('/scratch/mptp/predsminms1/t4_groupp_1__0', t4_groupp_1)). fof(involutiveness_k2_group_1, axiom, ![X1, X2]:(((~(v2_struct_0(X1))&(v2_group_1(X1)&(v3_group_1(X1)&l3_algstr_0(X1))))&m1_subset_1(X2,u1_struct_0(X1)))=>k2_group_1(X1,k2_group_1(X1,X2))=X2), file('/scratch/mptp/predsminms1/t4_groupp_1__0', involutiveness_k2_group_1)). fof(dt_k5_group_1, axiom, ![X1, X2, X3]:(((~(v2_struct_0(X1))&(v2_group_1(X1)&(v3_group_1(X1)&l3_algstr_0(X1))))&(v1_int_1(X2)&m1_subset_1(X3,u1_struct_0(X1))))=>m1_subset_1(k5_group_1(X1,X2,X3),u1_struct_0(X1))), file('/scratch/mptp/predsminms1/t4_groupp_1__0', dt_k5_group_1)). fof(l46_group_1, axiom, ![X1]:(v7_ordinal1(X1)=>![X2]:((~(v2_struct_0(X2))&(v2_group_1(X2)&(v3_group_1(X2)&l3_algstr_0(X2))))=>![X3]:(m1_subset_1(X3,u1_struct_0(X2))=>k5_group_1(X2,X1,k2_group_1(X2,X3))=k2_group_1(X2,k5_group_1(X2,X1,X3))))), file('/scratch/mptp/predsminms1/t4_groupp_1__0', l46_group_1)). fof(t8_group_1, axiom, ![X1]:((~(v2_struct_0(X1))&(v2_group_1(X1)&(v3_group_1(X1)&l3_algstr_0(X1))))=>k2_group_1(X1,k1_group_1(X1))=k1_group_1(X1)), file('/scratch/mptp/predsminms1/t4_groupp_1__0', t8_group_1)). fof(cc2_int_1, axiom, ![X1]:(v7_ordinal1(X1)=>v1_int_1(X1)), file('/scratch/mptp/predsminms1/t4_groupp_1__0', cc2_int_1)). fof(c_0_6, negated_conjecture, ~(![X1]:((~(v2_struct_0(X1))&(v2_group_1(X1)&(v3_group_1(X1)&l3_algstr_0(X1))))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(v7_ordinal1(X3)=>(k5_group_1(X1,X3,k2_group_1(X1,X2))=k1_group_1(X1)=>k5_group_1(X1,X3,X2)=k1_group_1(X1)))))), inference(assume_negation,[status(cth)],[t4_groupp_1])). fof(c_0_7, plain, ![X10, X11]:(v2_struct_0(X10)\|(~v2_group_1(X10)\|(~v3_group_1(X10)\|~l3_algstr_0(X10)))\|~m1_subset_1(X11,u1_struct_0(X10))\|k2_group_1(X10,k2_group_1(X10,X11))=X11), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[involutiveness_k2_group_1])])])). fof(c_0_8, plain, ![X12, X13, X14]:(v2_struct_0(X12)\|(~v2_group_1(X12)\|(~v3_group_1(X12)\|~l3_algstr_0(X12)))\|(~v1_int_1(X13)\|~m1_subset_1(X14,u1_struct_0(X12)))\|m1_subset_1(k5_group_1(X12,X13,X14),u1_struct_0(X12))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k5_group_1])])])). fof(c_0_9, negated_conjecture, ((~v2_struct_0(esk1_0)&(v2_group_1(esk1_0)&(v3_group_1(esk1_0)&l3_algstr_0(esk1_0))))&(m1_subset_1(esk2_0,u1_struct_0(esk1_0))&(v7_ordinal1(esk3_0)&(k5_group_1(esk1_0,esk3_0,k2_group_1(esk1_0,esk2_0))=k1_group_1(esk1_0)&k5_group_1(esk1_0,esk3_0,esk2_0)!=k1_group_1(esk1_0))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_6])])])])). fof(c_0_10, plain, ![X7, X8, X9]:(~v7_ordinal1(X7)\|(v2_struct_0(X8)\|(~v2_group_1(X8)\|(~v3_group_1(X8)\|~l3_algstr_0(X8)))\|(~m1_subset_1(X9,u1_struct_0(X8))\|k5_group_1(X8,X7,k2_group_1(X8,X9))=k2_group_1(X8,k5_group_1(X8,X7,X9))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[l46_group_1])])])])). cnf(c_0_11, plain, (v2_struct_0(X1)\|k2_group_1(X1,k2_group_1(X1,X2))=X2\|~v2_group_1(X1)\|~v3_group_1(X1)\|~l3_algstr_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_7])). cnf(c_0_12, plain, (v2_struct_0(X1)\|m1_subset_1(k5_group_1(X1,X2,X3),u1_struct_0(X1))\|~v2_group_1(X1)\|~v3_group_1(X1)\|~l3_algstr_0(X1)\|~v1_int_1(X2)\|~m1_subset_1(X3,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_8])). cnf(c_0_13, negated_conjecture, (k5_group_1(esk1_0,esk3_0,k2_group_1(esk1_0,esk2_0))=k1_group_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_14, plain, (v2_struct_0(X2)\|k5_group_1(X2,X1,k2_group_1(X2,X3))=k2_group_1(X2,k5_group_1(X2,X1,X3))\|~v7_ordinal1(X1)\|~v2_group_1(X2)\|~v3_group_1(X2)\|~l3_algstr_0(X2)\|~m1_subset_1(X3,u1_struct_0(X2))), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_15, negated_conjecture, (v7_ordinal1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_16, negated_conjecture, (m1_subset_1(esk2_0,u1_struct_0(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_17, negated_conjecture, (l3_algstr_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_18, negated_conjecture, (v3_group_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_19, negated_conjecture, (v2_group_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_20, negated_conjecture, (~v2_struct_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_9])). fof(c_0_21, plain, ![X16]:(v2_struct_0(X16)\|(~v2_group_1(X16)\|(~v3_group_1(X16)\|~l3_algstr_0(X16)))\|k2_group_1(X16,k1_group_1(X16))=k1_group_1(X16)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t8_group_1])])])). cnf(c_0_22, plain, (k2_group_1(X1,k2_group_1(X1,X2))=X2\|v2_struct_0(X1)\|~v2_group_1(X1)\|~v3_group_1(X1)\|~l3_algstr_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_11])). cnf(c_0_23, plain, (v2_struct_0(X1)\|m1_subset_1(k5_group_1(X1,X2,X3),u1_struct_0(X1))\|~v2_group_1(X1)\|~v3_group_1(X1)\|~l3_algstr_0(X1)\|~v1_int_1(X2)\|~m1_subset_1(X3,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_12])). cnf(c_0_24, negated_conjecture, (k5_group_1(esk1_0,esk3_0,k2_group_1(esk1_0,esk2_0))=k1_group_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_13])). cnf(c_0_25, plain, (k5_group_1(X2,X1,k2_group_1(X2,X3))=k2_group_1(X2,k5_group_1(X2,X1,X3))\|v2_struct_0(X2)\|~v2_group_1(X2)\|~v3_group_1(X2)\|~l3_algstr_0(X2)\|~v7_ordinal1(X1)\|~m1_subset_1(X3,u1_struct_0(X2))), inference(evalgc,[status(thm)],[c_0_14])). cnf(c_0_26, negated_conjecture, (v7_ordinal1(esk3_0)), inference(evalgc,[status(thm)],[c_0_15])). cnf(c_0_27, negated_conjecture, (m1_subset_1(esk2_0,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[c_0_16])). cnf(c_0_28, negated_conjecture, (l3_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_17])). cnf(c_0_29, negated_conjecture, (v3_group_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_18])). cnf(c_0_30, negated_conjecture, (v2_group_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_19])). cnf(c_0_31, negated_conjecture, (~v2_struct_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_20])). cnf(c_0_32, plain, (v2_struct_0(X1)\|k2_group_1(X1,k1_group_1(X1))=k1_group_1(X1)\|~v2_group_1(X1)\|~v3_group_1(X1)\|~l3_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_21])). cnf(c_0_33, plain, (k2_group_1(X1,k2_group_1(X1,k5_group_1(X1,X2,X3)))=k5_group_1(X1,X2,X3)\|v2_struct_0(X1)\|~l3_algstr_0(X1)\|~v3_group_1(X1)\|~v2_group_1(X1)\|~v1_int_1(X2)\|~m1_subset_1(X3,u1_struct_0(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_22, c_0_23])])). cnf(c_0_34, negated_conjecture, (k2_group_1(esk1_0,k5_group_1(esk1_0,esk3_0,esk2_0))=k1_group_1(esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24, c_0_25]), c_0_26]), c_0_27]), c_0_28]), c_0_29]), c_0_30])]), c_0_31])])). cnf(c_0_35, negated_conjecture, (k5_group_1(esk1_0,esk3_0,esk2_0)!=k1_group_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_9])). fof(c_0_36, plain, ![X15]:(~v7_ordinal1(X15)\|v1_int_1(X15)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_int_1])])). cnf(c_0_37, plain, (k2_group_1(X1,k1_group_1(X1))=k1_group_1(X1)\|v2_struct_0(X1)\|~v2_group_1(X1)\|~v3_group_1(X1)\|~l3_algstr_0(X1)), inference(evalgc,[status(thm)],[c_0_32])). cnf(c_0_38, negated_conjecture, (k2_group_1(esk1_0,k1_group_1(esk1_0))=k5_group_1(esk1_0,esk3_0,esk2_0)\|~v1_int_1(esk3_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33, c_0_34]), c_0_27]), c_0_28]), c_0_29]), c_0_30])]), c_0_31])])). cnf(c_0_39, negated_conjecture, (k5_group_1(esk1_0,esk3_0,esk2_0)!=k1_group_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_35])). cnf(c_0_40, plain, (v1_int_1(X1)\|~v7_ordinal1(X1)), inference(split_conjunct,[status(thm)],[c_0_36])). cnf(c_0_41, negated_conjecture, (~v1_int_1(esk3_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37, c_0_38]), c_0_28]), c_0_29]), c_0_30])]), c_0_39]), c_0_31])])). cnf(c_0_42, plain, (v1_int_1(X1)\|~v7_ordinal1(X1)), inference(evalgc,[status(thm)],[c_0_40])). cnf(c_0_43, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41, c_0_42]), c_0_26])]), ['proof']). # SZS output end CNFRefutation	reserve G for Group, a,b for Element of G, m, n for Nat, p for prime Nat; theorem Th4: a" \|^ n = 1_G implies a \|^ n = 1_G proof a"" = a; hence thesis by Th3; end;	Convert the following ATP output trace into a readable Mizar proof.
t34_cqc_the3	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(d5_cqc_the3, axiom, ![X1]:(m1_qc_lang1(X1)=>![X2]:(m2_subset_1(X2,k9_qc_lang1(X1),k3_cqc_lang(X1))=>![X3]:(m2_subset_1(X3,k9_qc_lang1(X1),k3_cqc_lang(X1))=>(r5_cqc_the3(X1,X2,X3)<=>(r1_cqc_the3(X1,X2,X3)&r1_cqc_the3(X1,X3,X2)))))), file('/scratch/mptp/predsminms1/t34_cqc_the3__0', d5_cqc_the3)). fof(dt_k7_cqc_lang, axiom, ![X1, X2, X3]:((m1_qc_lang1(X1)&(m1_subset_1(X2,k3_cqc_lang(X1))&m1_subset_1(X3,k3_cqc_lang(X1))))=>m2_subset_1(k7_cqc_lang(X1,X2,X3),k9_qc_lang1(X1),k3_cqc_lang(X1))), file('/scratch/mptp/predsminms1/t34_cqc_the3__0', dt_k7_cqc_lang)). fof(redefinition_m2_subset_1, axiom, ![X1, X2]:((~(v1_xboole_0(X1))&(~(v1_xboole_0(X2))&m1_subset_1(X2,k1_zfmisc_1(X1))))=>![X3]:(m2_subset_1(X3,X1,X2)<=>m1_subset_1(X3,X2))), file('/scratch/mptp/predsminms1/t34_cqc_the3__0', redefinition_m2_subset_1)). fof(dt_k3_cqc_lang, axiom, ![X1]:(m1_qc_lang1(X1)=>m1_subset_1(k3_cqc_lang(X1),k1_zfmisc_1(k9_qc_lang1(X1)))), file('/scratch/mptp/predsminms1/t34_cqc_the3__0', dt_k3_cqc_lang)). fof(l42_cqc_the3, axiom, ![X1]:(m1_qc_lang1(X1)=>![X2]:(m2_subset_1(X2,k9_qc_lang1(X1),k3_cqc_lang(X1))=>![X3]:(m2_subset_1(X3,k9_qc_lang1(X1),k3_cqc_lang(X1))=>![X4]:(m2_subset_1(X4,k9_qc_lang1(X1),k3_cqc_lang(X1))=>![X5]:(m2_subset_1(X5,k9_qc_lang1(X1),k3_cqc_lang(X1))=>((r5_cqc_the3(X1,X2,X3)&r5_cqc_the3(X1,X4,X5))=>r1_cqc_the3(X1,k7_cqc_lang(X1,X2,X4),k7_cqc_lang(X1,X3,X5)))))))), file('/scratch/mptp/predsminms1/t34_cqc_the3__0', l42_cqc_the3)). fof(dt_k9_qc_lang1, axiom, ![X1]:(m1_qc_lang1(X1)=>~(v1_xboole_0(k9_qc_lang1(X1)))), file('/scratch/mptp/predsminms1/t34_cqc_the3__0', dt_k9_qc_lang1)). fof(fc2_cqc_lang, axiom, ![X1]:(m1_qc_lang1(X1)=>~(v1_xboole_0(k3_cqc_lang(X1)))), file('/scratch/mptp/predsminms1/t34_cqc_the3__0', fc2_cqc_lang)). fof(t34_cqc_the3, conjecture, ![X1]:(m1_qc_lang1(X1)=>![X2]:(m2_subset_1(X2,k9_qc_lang1(X1),k3_cqc_lang(X1))=>![X3]:(m2_subset_1(X3,k9_qc_lang1(X1),k3_cqc_lang(X1))=>![X4]:(m2_subset_1(X4,k9_qc_lang1(X1),k3_cqc_lang(X1))=>![X5]:(m2_subset_1(X5,k9_qc_lang1(X1),k3_cqc_lang(X1))=>((r5_cqc_the3(X1,X2,X3)&r5_cqc_the3(X1,X4,X5))=>r5_cqc_the3(X1,k7_cqc_lang(X1,X2,X4),k7_cqc_lang(X1,X3,X5)))))))), file('/scratch/mptp/predsminms1/t34_cqc_the3__0', t34_cqc_the3)). fof(c_0_8, plain, ![X12, X13, X14]:(((r1_cqc_the3(X12,X13,X14)\|~r5_cqc_the3(X12,X13,X14)\|~m2_subset_1(X14,k9_qc_lang1(X12),k3_cqc_lang(X12))\|~m2_subset_1(X13,k9_qc_lang1(X12),k3_cqc_lang(X12))\|~m1_qc_lang1(X12))&(r1_cqc_the3(X12,X14,X13)\|~r5_cqc_the3(X12,X13,X14)\|~m2_subset_1(X14,k9_qc_lang1(X12),k3_cqc_lang(X12))\|~m2_subset_1(X13,k9_qc_lang1(X12),k3_cqc_lang(X12))\|~m1_qc_lang1(X12)))&(~r1_cqc_the3(X12,X13,X14)\|~r1_cqc_the3(X12,X14,X13)\|r5_cqc_the3(X12,X13,X14)\|~m2_subset_1(X14,k9_qc_lang1(X12),k3_cqc_lang(X12))\|~m2_subset_1(X13,k9_qc_lang1(X12),k3_cqc_lang(X12))\|~m1_qc_lang1(X12))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_cqc_the3])])])])). fof(c_0_9, plain, ![X23, X24, X25]:(~m1_qc_lang1(X23)\|(~m1_subset_1(X24,k3_cqc_lang(X23))\|~m1_subset_1(X25,k3_cqc_lang(X23)))\|m2_subset_1(k7_cqc_lang(X23,X24,X25),k9_qc_lang1(X23),k3_cqc_lang(X23))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k7_cqc_lang])])). fof(c_0_10, plain, ![X15, X16, X17]:((~m2_subset_1(X17,X15,X16)\|m1_subset_1(X17,X16)\|(v1_xboole_0(X15)\|(v1_xboole_0(X16)\|~m1_subset_1(X16,k1_zfmisc_1(X15)))))&(~m1_subset_1(X17,X16)\|m2_subset_1(X17,X15,X16)\|(v1_xboole_0(X15)\|(v1_xboole_0(X16)\|~m1_subset_1(X16,k1_zfmisc_1(X15)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[redefinition_m2_subset_1])])])])])). fof(c_0_11, plain, ![X11]:(~m1_qc_lang1(X11)\|m1_subset_1(k3_cqc_lang(X11),k1_zfmisc_1(k9_qc_lang1(X11)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k3_cqc_lang])])). cnf(c_0_12, plain, (r5_cqc_the3(X1,X2,X3)\|~r1_cqc_the3(X1,X2,X3)\|~r1_cqc_the3(X1,X3,X2)\|~m2_subset_1(X3,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m2_subset_1(X2,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m1_qc_lang1(X1)), inference(split_conjunct,[status(thm)],[c_0_8])). cnf(c_0_13, plain, (m2_subset_1(k7_cqc_lang(X1,X2,X3),k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m1_qc_lang1(X1)\|~m1_subset_1(X2,k3_cqc_lang(X1))\|~m1_subset_1(X3,k3_cqc_lang(X1))), inference(split_conjunct,[status(thm)],[c_0_9])). fof(c_0_14, plain, ![X18, X19, X20, X21, X22]:(~m1_qc_lang1(X18)\|(~m2_subset_1(X19,k9_qc_lang1(X18),k3_cqc_lang(X18))\|(~m2_subset_1(X20,k9_qc_lang1(X18),k3_cqc_lang(X18))\|(~m2_subset_1(X21,k9_qc_lang1(X18),k3_cqc_lang(X18))\|(~m2_subset_1(X22,k9_qc_lang1(X18),k3_cqc_lang(X18))\|(~r5_cqc_the3(X18,X19,X20)\|~r5_cqc_the3(X18,X21,X22)\|r1_cqc_the3(X18,k7_cqc_lang(X18,X19,X21),k7_cqc_lang(X18,X20,X22)))))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l42_cqc_the3])])])). cnf(c_0_15, plain, (m2_subset_1(X1,X3,X2)\|v1_xboole_0(X3)\|v1_xboole_0(X2)\|~m1_subset_1(X1,X2)\|~m1_subset_1(X2,k1_zfmisc_1(X3))), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_16, plain, (m1_subset_1(k3_cqc_lang(X1),k1_zfmisc_1(k9_qc_lang1(X1)))\|~m1_qc_lang1(X1)), inference(split_conjunct,[status(thm)],[c_0_11])). fof(c_0_17, plain, ![X26]:(~m1_qc_lang1(X26)\|~v1_xboole_0(k9_qc_lang1(X26))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k9_qc_lang1])])])). fof(c_0_18, plain, ![X27]:(~m1_qc_lang1(X27)\|~v1_xboole_0(k3_cqc_lang(X27))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fc2_cqc_lang])])])). fof(c_0_19, negated_conjecture, ~(![X1]:(m1_qc_lang1(X1)=>![X2]:(m2_subset_1(X2,k9_qc_lang1(X1),k3_cqc_lang(X1))=>![X3]:(m2_subset_1(X3,k9_qc_lang1(X1),k3_cqc_lang(X1))=>![X4]:(m2_subset_1(X4,k9_qc_lang1(X1),k3_cqc_lang(X1))=>![X5]:(m2_subset_1(X5,k9_qc_lang1(X1),k3_cqc_lang(X1))=>((r5_cqc_the3(X1,X2,X3)&r5_cqc_the3(X1,X4,X5))=>r5_cqc_the3(X1,k7_cqc_lang(X1,X2,X4),k7_cqc_lang(X1,X3,X5))))))))), inference(assume_negation,[status(cth)],[t34_cqc_the3])). cnf(c_0_20, plain, (r5_cqc_the3(X1,X2,X3)\|~m1_qc_lang1(X1)\|~r1_cqc_the3(X1,X3,X2)\|~r1_cqc_the3(X1,X2,X3)\|~m2_subset_1(X3,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m2_subset_1(X2,k9_qc_lang1(X1),k3_cqc_lang(X1))), inference(evalgc,[status(thm)],[c_0_12])). cnf(c_0_21, plain, (m2_subset_1(k7_cqc_lang(X1,X2,X3),k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m1_qc_lang1(X1)\|~m1_subset_1(X3,k3_cqc_lang(X1))\|~m1_subset_1(X2,k3_cqc_lang(X1))), inference(evalgc,[status(thm)],[c_0_13])). cnf(c_0_22, plain, (r1_cqc_the3(X1,k7_cqc_lang(X1,X2,X4),k7_cqc_lang(X1,X3,X5))\|~m1_qc_lang1(X1)\|~m2_subset_1(X2,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m2_subset_1(X3,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m2_subset_1(X4,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m2_subset_1(X5,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~r5_cqc_the3(X1,X2,X3)\|~r5_cqc_the3(X1,X4,X5)), inference(split_conjunct,[status(thm)],[c_0_14])). cnf(c_0_23, plain, (v1_xboole_0(X3)\|v1_xboole_0(X2)\|m2_subset_1(X1,X3,X2)\|~m1_subset_1(X1,X2)\|~m1_subset_1(X2,k1_zfmisc_1(X3))), inference(evalgc,[status(thm)],[c_0_15])). cnf(c_0_24, plain, (m1_subset_1(k3_cqc_lang(X1),k1_zfmisc_1(k9_qc_lang1(X1)))\|~m1_qc_lang1(X1)), inference(evalgc,[status(thm)],[c_0_16])). cnf(c_0_25, plain, (~m1_qc_lang1(X1)\|~v1_xboole_0(k9_qc_lang1(X1))), inference(split_conjunct,[status(thm)],[c_0_17])). cnf(c_0_26, plain, (~m1_qc_lang1(X1)\|~v1_xboole_0(k3_cqc_lang(X1))), inference(split_conjunct,[status(thm)],[c_0_18])). fof(c_0_27, negated_conjecture, (m1_qc_lang1(esk1_0)&(m2_subset_1(esk2_0,k9_qc_lang1(esk1_0),k3_cqc_lang(esk1_0))&(m2_subset_1(esk3_0,k9_qc_lang1(esk1_0),k3_cqc_lang(esk1_0))&(m2_subset_1(esk4_0,k9_qc_lang1(esk1_0),k3_cqc_lang(esk1_0))&(m2_subset_1(esk5_0,k9_qc_lang1(esk1_0),k3_cqc_lang(esk1_0))&((r5_cqc_the3(esk1_0,esk2_0,esk3_0)&r5_cqc_the3(esk1_0,esk4_0,esk5_0))&~r5_cqc_the3(esk1_0,k7_cqc_lang(esk1_0,esk2_0,esk4_0),k7_cqc_lang(esk1_0,esk3_0,esk5_0)))))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])). cnf(c_0_28, plain, (r5_cqc_the3(X1,X2,k7_cqc_lang(X1,X3,X4))\|~r1_cqc_the3(X1,k7_cqc_lang(X1,X3,X4),X2)\|~r1_cqc_the3(X1,X2,k7_cqc_lang(X1,X3,X4))\|~m2_subset_1(X2,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m1_qc_lang1(X1)\|~m1_subset_1(X4,k3_cqc_lang(X1))\|~m1_subset_1(X3,k3_cqc_lang(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_20, c_0_21])])). cnf(c_0_29, plain, (r1_cqc_the3(X1,k7_cqc_lang(X1,X2,X4),k7_cqc_lang(X1,X3,X5))\|~m1_qc_lang1(X1)\|~r5_cqc_the3(X1,X4,X5)\|~r5_cqc_the3(X1,X2,X3)\|~m2_subset_1(X5,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m2_subset_1(X4,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m2_subset_1(X3,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m2_subset_1(X2,k9_qc_lang1(X1),k3_cqc_lang(X1))), inference(evalgc,[status(thm)],[c_0_22])). cnf(c_0_30, plain, (v1_xboole_0(k3_cqc_lang(X1))\|v1_xboole_0(k9_qc_lang1(X1))\|m2_subset_1(X2,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m1_subset_1(X2,k3_cqc_lang(X1))\|~m1_qc_lang1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_23, c_0_24])])). cnf(c_0_31, plain, (~m1_qc_lang1(X1)\|~v1_xboole_0(k9_qc_lang1(X1))), inference(evalgc,[status(thm)],[c_0_25])). cnf(c_0_32, plain, (~m1_qc_lang1(X1)\|~v1_xboole_0(k3_cqc_lang(X1))), inference(evalgc,[status(thm)],[c_0_26])). cnf(c_0_33, plain, (m1_subset_1(X1,X3)\|v1_xboole_0(X2)\|v1_xboole_0(X3)\|~m2_subset_1(X1,X2,X3)\|~m1_subset_1(X3,k1_zfmisc_1(X2))), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_34, negated_conjecture, (m2_subset_1(esk4_0,k9_qc_lang1(esk1_0),k3_cqc_lang(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_27])). cnf(c_0_35, negated_conjecture, (m1_qc_lang1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_27])). cnf(c_0_36, plain, (r1_cqc_the3(X1,X2,X3)\|~r5_cqc_the3(X1,X2,X3)\|~m2_subset_1(X3,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m2_subset_1(X2,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m1_qc_lang1(X1)), inference(split_conjunct,[status(thm)],[c_0_8])). cnf(c_0_37, negated_conjecture, (m2_subset_1(esk5_0,k9_qc_lang1(esk1_0),k3_cqc_lang(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_27])). cnf(c_0_38, negated_conjecture, (m2_subset_1(esk2_0,k9_qc_lang1(esk1_0),k3_cqc_lang(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_27])). cnf(c_0_39, negated_conjecture, (m2_subset_1(esk3_0,k9_qc_lang1(esk1_0),k3_cqc_lang(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_27])). cnf(c_0_40, plain, (r5_cqc_the3(X1,k7_cqc_lang(X1,X2,X3),k7_cqc_lang(X1,X4,X5))\|~r1_cqc_the3(X1,k7_cqc_lang(X1,X2,X3),k7_cqc_lang(X1,X4,X5))\|~m1_subset_1(X5,k3_cqc_lang(X1))\|~m1_subset_1(X4,k3_cqc_lang(X1))\|~m2_subset_1(k7_cqc_lang(X1,X2,X3),k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m1_qc_lang1(X1)\|~r5_cqc_the3(X1,X5,X3)\|~r5_cqc_the3(X1,X4,X2)\|~m2_subset_1(X3,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m2_subset_1(X5,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m2_subset_1(X2,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m2_subset_1(X4,k9_qc_lang1(X1),k3_cqc_lang(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_28, c_0_29])])). cnf(c_0_41, plain, (m2_subset_1(X1,k9_qc_lang1(X2),k3_cqc_lang(X2))\|~m1_subset_1(X1,k3_cqc_lang(X2))\|~m1_qc_lang1(X2)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_30, c_0_31]), c_0_32])). cnf(c_0_42, plain, (v1_xboole_0(X3)\|v1_xboole_0(X2)\|m1_subset_1(X1,X3)\|~m2_subset_1(X1,X2,X3)\|~m1_subset_1(X3,k1_zfmisc_1(X2))), inference(evalgc,[status(thm)],[c_0_33])). cnf(c_0_43, negated_conjecture, (m2_subset_1(esk4_0,k9_qc_lang1(esk1_0),k3_cqc_lang(esk1_0))), inference(evalgc,[status(thm)],[c_0_34])). cnf(c_0_44, negated_conjecture, (m1_qc_lang1(esk1_0)), inference(evalgc,[status(thm)],[c_0_35])). cnf(c_0_45, plain, (r1_cqc_the3(X1,X2,X3)\|~m1_qc_lang1(X1)\|~r5_cqc_the3(X1,X2,X3)\|~m2_subset_1(X3,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m2_subset_1(X2,k9_qc_lang1(X1),k3_cqc_lang(X1))), inference(evalgc,[status(thm)],[c_0_36])). cnf(c_0_46, negated_conjecture, (m2_subset_1(esk5_0,k9_qc_lang1(esk1_0),k3_cqc_lang(esk1_0))), inference(evalgc,[status(thm)],[c_0_37])). cnf(c_0_47, negated_conjecture, (r5_cqc_the3(esk1_0,esk4_0,esk5_0)), inference(split_conjunct,[status(thm)],[c_0_27])). cnf(c_0_48, plain, (r1_cqc_the3(X1,X2,X3)\|~r5_cqc_the3(X1,X3,X2)\|~m2_subset_1(X2,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m2_subset_1(X3,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m1_qc_lang1(X1)), inference(split_conjunct,[status(thm)],[c_0_8])). cnf(c_0_49, negated_conjecture, (m2_subset_1(esk2_0,k9_qc_lang1(esk1_0),k3_cqc_lang(esk1_0))), inference(evalgc,[status(thm)],[c_0_38])). cnf(c_0_50, negated_conjecture, (m2_subset_1(esk3_0,k9_qc_lang1(esk1_0),k3_cqc_lang(esk1_0))), inference(evalgc,[status(thm)],[c_0_39])). cnf(c_0_51, negated_conjecture, (r5_cqc_the3(esk1_0,esk2_0,esk3_0)), inference(split_conjunct,[status(thm)],[c_0_27])). cnf(c_0_52, plain, (r5_cqc_the3(X1,k7_cqc_lang(X1,X2,X3),k7_cqc_lang(X1,X4,X5))\|~r1_cqc_the3(X1,k7_cqc_lang(X1,X2,X3),k7_cqc_lang(X1,X4,X5))\|~m1_subset_1(X5,k3_cqc_lang(X1))\|~m1_subset_1(X4,k3_cqc_lang(X1))\|~r5_cqc_the3(X1,X5,X3)\|~r5_cqc_the3(X1,X4,X2)\|~m2_subset_1(k7_cqc_lang(X1,X2,X3),k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m2_subset_1(X3,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m2_subset_1(X2,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m1_qc_lang1(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_40, c_0_41]), c_0_41])). cnf(c_0_53, plain, (v1_xboole_0(k9_qc_lang1(X1))\|v1_xboole_0(k3_cqc_lang(X1))\|m1_subset_1(X2,k3_cqc_lang(X1))\|~m2_subset_1(X2,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m1_qc_lang1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_42, c_0_24])])). cnf(c_0_54, negated_conjecture, (r5_cqc_the3(esk1_0,X1,esk4_0)\|~r1_cqc_the3(esk1_0,esk4_0,X1)\|~r1_cqc_the3(esk1_0,X1,esk4_0)\|~m2_subset_1(X1,k9_qc_lang1(esk1_0),k3_cqc_lang(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20, c_0_43]), c_0_44])])])). cnf(c_0_55, negated_conjecture, (r1_cqc_the3(esk1_0,X1,esk5_0)\|~r5_cqc_the3(esk1_0,X1,esk5_0)\|~m2_subset_1(X1,k9_qc_lang1(esk1_0),k3_cqc_lang(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45, c_0_46]), c_0_44])])])). cnf(c_0_56, negated_conjecture, (r5_cqc_the3(esk1_0,esk4_0,esk5_0)), inference(evalgc,[status(thm)],[c_0_47])). cnf(c_0_57, plain, (r1_cqc_the3(X1,X2,X3)\|~m1_qc_lang1(X1)\|~r5_cqc_the3(X1,X3,X2)\|~m2_subset_1(X3,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m2_subset_1(X2,k9_qc_lang1(X1),k3_cqc_lang(X1))), inference(evalgc,[status(thm)],[c_0_48])). cnf(c_0_58, negated_conjecture, (r5_cqc_the3(esk1_0,X1,esk2_0)\|~r1_cqc_the3(esk1_0,esk2_0,X1)\|~r1_cqc_the3(esk1_0,X1,esk2_0)\|~m2_subset_1(X1,k9_qc_lang1(esk1_0),k3_cqc_lang(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20, c_0_49]), c_0_44])])])). cnf(c_0_59, negated_conjecture, (r1_cqc_the3(esk1_0,X1,esk3_0)\|~r5_cqc_the3(esk1_0,X1,esk3_0)\|~m2_subset_1(X1,k9_qc_lang1(esk1_0),k3_cqc_lang(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45, c_0_50]), c_0_44])])])). cnf(c_0_60, negated_conjecture, (r5_cqc_the3(esk1_0,esk2_0,esk3_0)), inference(evalgc,[status(thm)],[c_0_51])). cnf(c_0_61, negated_conjecture, (~r5_cqc_the3(esk1_0,k7_cqc_lang(esk1_0,esk2_0,esk4_0),k7_cqc_lang(esk1_0,esk3_0,esk5_0))), inference(split_conjunct,[status(thm)],[c_0_27])). cnf(c_0_62, plain, (r5_cqc_the3(X1,k7_cqc_lang(X1,X2,X3),k7_cqc_lang(X1,X4,X5))\|~m1_subset_1(X5,k3_cqc_lang(X1))\|~m1_subset_1(X4,k3_cqc_lang(X1))\|~r5_cqc_the3(X1,X5,X3)\|~r5_cqc_the3(X1,X4,X2)\|~m2_subset_1(k7_cqc_lang(X1,X2,X3),k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m2_subset_1(X3,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m2_subset_1(X2,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m1_qc_lang1(X1)\|~r5_cqc_the3(X1,X3,X5)\|~r5_cqc_the3(X1,X2,X4)\|~m2_subset_1(X5,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m2_subset_1(X4,k9_qc_lang1(X1),k3_cqc_lang(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_52, c_0_29])])). cnf(c_0_63, plain, (m1_subset_1(X1,k3_cqc_lang(X2))\|~m2_subset_1(X1,k9_qc_lang1(X2),k3_cqc_lang(X2))\|~m1_qc_lang1(X2)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_53, c_0_32]), c_0_31])). cnf(c_0_64, negated_conjecture, (r5_cqc_the3(esk1_0,esk5_0,esk4_0)\|~r1_cqc_the3(esk1_0,esk5_0,esk4_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54, c_0_55]), c_0_46]), c_0_56]), c_0_43])])])). cnf(c_0_65, negated_conjecture, (r1_cqc_the3(esk1_0,X1,esk4_0)\|~r5_cqc_the3(esk1_0,esk4_0,X1)\|~m2_subset_1(X1,k9_qc_lang1(esk1_0),k3_cqc_lang(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57, c_0_43]), c_0_44])])])). cnf(c_0_66, negated_conjecture, (r5_cqc_the3(esk1_0,esk3_0,esk2_0)\|~r1_cqc_the3(esk1_0,esk3_0,esk2_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58, c_0_59]), c_0_50]), c_0_60]), c_0_49])])])). cnf(c_0_67, negated_conjecture, (r1_cqc_the3(esk1_0,X1,esk2_0)\|~r5_cqc_the3(esk1_0,esk2_0,X1)\|~m2_subset_1(X1,k9_qc_lang1(esk1_0),k3_cqc_lang(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57, c_0_49]), c_0_44])])])). cnf(c_0_68, negated_conjecture, (~r5_cqc_the3(esk1_0,k7_cqc_lang(esk1_0,esk2_0,esk4_0),k7_cqc_lang(esk1_0,esk3_0,esk5_0))), inference(evalgc,[status(thm)],[c_0_61])). cnf(c_0_69, plain, (r5_cqc_the3(X1,k7_cqc_lang(X1,X2,X3),k7_cqc_lang(X1,X4,X5))\|~m1_subset_1(X5,k3_cqc_lang(X1))\|~m1_subset_1(X4,k3_cqc_lang(X1))\|~r5_cqc_the3(X1,X5,X3)\|~r5_cqc_the3(X1,X4,X2)\|~r5_cqc_the3(X1,X3,X5)\|~r5_cqc_the3(X1,X2,X4)\|~m2_subset_1(k7_cqc_lang(X1,X2,X3),k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m2_subset_1(X3,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m2_subset_1(X2,k9_qc_lang1(X1),k3_cqc_lang(X1))\|~m1_qc_lang1(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_62, c_0_41]), c_0_41])). cnf(c_0_70, negated_conjecture, (m1_subset_1(esk5_0,k3_cqc_lang(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63, c_0_46]), c_0_44])])])). cnf(c_0_71, negated_conjecture, (m1_subset_1(esk3_0,k3_cqc_lang(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63, c_0_50]), c_0_44])])])). cnf(c_0_72, negated_conjecture, (r5_cqc_the3(esk1_0,esk5_0,esk4_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64, c_0_65]), c_0_56]), c_0_46])])])). cnf(c_0_73, negated_conjecture, (r5_cqc_the3(esk1_0,esk3_0,esk2_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66, c_0_67]), c_0_60]), c_0_50])])])). cnf(c_0_74, negated_conjecture, (~m2_subset_1(k7_cqc_lang(esk1_0,esk2_0,esk4_0),k9_qc_lang1(esk1_0),k3_cqc_lang(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68, c_0_69]), c_0_70]), c_0_71]), c_0_72]), c_0_73]), c_0_56]), c_0_60]), c_0_43]), c_0_49]), c_0_44])])])). cnf(c_0_75, negated_conjecture, (m1_subset_1(esk4_0,k3_cqc_lang(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63, c_0_43]), c_0_44])])])). cnf(c_0_76, negated_conjecture, (m1_subset_1(esk2_0,k3_cqc_lang(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63, c_0_49]), c_0_44])])])). cnf(c_0_77, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74, c_0_21]), c_0_75]), c_0_76]), c_0_44])]), ['proof']). # SZS output end CNFRefutation	reserve A for QC-alphabet; reserve p, q, r, s, p1, q1 for Element of CQC-WFF(A), X, Y, Z, X1, X2 for Subset of CQC-WFF(A), h for QC-formula of A, x, y for bound_QC-variable of A, n for Element of NAT; theorem p \|-\| q & r \|-\| s implies p '&' r \|-\| q '&' s proof assume that A1: p \|-\| q and A2: r \|-\| s; A3: q '&' s \|- p '&' r by A1,A2,Lm4; p '&' r \|- q '&' s by A1,A2,Lm4; hence thesis by A3,Def5; end;	Convert the following ATP output trace into a readable Mizar proof.
t10_lfuzzy_1	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(redefinition_r2_relset_1, axiom, ![X1, X2, X3, X4]:((m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))&m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2))))=>(r2_relset_1(X1,X2,X3,X4)<=>X3=X4)), file('/scratch/mptp/predsminms1/t10_lfuzzy_1__0', redefinition_r2_relset_1)). fof(d4_lfuzzy_1, axiom, ![X1]:(~(v1_xboole_0(X1))=>![X2]:((v5_relat_1(X2,k1_rcomp_1(k6_numbers,np__1))&(v1_funct_1(X2)&(v1_funct_2(X2,k2_zfmisc_1(X1,X1),k1_numbers)&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X1),k1_numbers))))))=>(v2_lfuzzy_1(X2,X1)<=>r2_relset_1(k2_zfmisc_1(X1,X1),k1_numbers,k2_fuzzy_4(X1,X1,X2),X2)))), file('/scratch/mptp/predsminms1/t10_lfuzzy_1__0', d4_lfuzzy_1)). fof(dt_k2_fuzzy_4, axiom, ![X1, X2, X3]:((~(v1_xboole_0(X1))&(~(v1_xboole_0(X2))&(v5_relat_1(X3,k1_rcomp_1(k6_numbers,np__1))&(v1_funct_1(X3)&(v1_funct_2(X3,k2_zfmisc_1(X2,X1),k1_numbers)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X2,X1),k1_numbers))))))))=>(v5_relat_1(k2_fuzzy_4(X1,X2,X3),k1_rcomp_1(k6_numbers,np__1))&(v1_funct_1(k2_fuzzy_4(X1,X2,X3))&(v1_funct_2(k2_fuzzy_4(X1,X2,X3),k2_zfmisc_1(X1,X2),k1_numbers)&m1_subset_1(k2_fuzzy_4(X1,X2,X3),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X2),k1_numbers))))))), file('/scratch/mptp/predsminms1/t10_lfuzzy_1__0', dt_k2_fuzzy_4)). fof(t10_lfuzzy_1, conjecture, ![X1]:(~(v1_xboole_0(X1))=>![X2]:((v5_relat_1(X2,k1_rcomp_1(k6_numbers,np__1))&(v1_funct_1(X2)&(v1_funct_2(X2,k2_zfmisc_1(X1,X1),k1_numbers)&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X1),k1_numbers))))))=>![X3]:((v5_relat_1(X3,k1_rcomp_1(k6_numbers,np__1))&(v1_funct_1(X3)&(v1_funct_2(X3,k2_zfmisc_1(X1,X1),k1_numbers)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X1),k1_numbers))))))=>((v2_lfuzzy_1(X2,X1)&v2_lfuzzy_1(X3,X1))=>r2_relset_1(k2_zfmisc_1(X1,X1),k1_numbers,k2_fuzzy_4(X1,X1,k2_lfuzzy_1(k2_zfmisc_1(X1,X1),X2,X3)),k2_lfuzzy_1(k2_zfmisc_1(X1,X1),X2,X3)))))), file('/scratch/mptp/predsminms1/t10_lfuzzy_1__0', t10_lfuzzy_1)). fof(t7_fuzzy_4, axiom, ![X1]:(~(v1_xboole_0(X1))=>![X2]:(~(v1_xboole_0(X2))=>![X3]:((v5_relat_1(X3,k1_rcomp_1(k6_numbers,np__1))&(v1_funct_1(X3)&(v1_funct_2(X3,k2_zfmisc_1(X1,X2),k1_numbers)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X2),k1_numbers))))))=>![X4]:((v5_relat_1(X4,k1_rcomp_1(k6_numbers,np__1))&(v1_funct_1(X4)&(v1_funct_2(X4,k2_zfmisc_1(X1,X2),k1_numbers)&m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X2),k1_numbers))))))=>r2_relset_1(k2_zfmisc_1(X2,X1),k1_numbers,k2_fuzzy_4(X2,X1,k2_fuzzy_1(k2_zfmisc_1(X1,X2),X3,X4)),k2_fuzzy_1(k2_zfmisc_1(X2,X1),k2_fuzzy_4(X2,X1,X3),k2_fuzzy_4(X2,X1,X4))))))), file('/scratch/mptp/predsminms1/t10_lfuzzy_1__0', t7_fuzzy_4)). fof(redefinition_k2_lfuzzy_1, axiom, ![X1, X2, X3]:((~(v1_xboole_0(X1))&((v5_relat_1(X2,k1_rcomp_1(k6_numbers,np__1))&(v1_funct_1(X2)&(v1_funct_2(X2,X1,k1_numbers)&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers))))))&(v5_relat_1(X3,k1_rcomp_1(k6_numbers,np__1))&(v1_funct_1(X3)&(v1_funct_2(X3,X1,k1_numbers)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers))))))))=>k2_lfuzzy_1(X1,X2,X3)=k2_fuzzy_1(X1,X2,X3)), file('/scratch/mptp/predsminms1/t10_lfuzzy_1__0', redefinition_k2_lfuzzy_1)). fof(fc10_subset_1, axiom, ![X1, X2]:((~(v1_xboole_0(X1))&~(v1_xboole_0(X2)))=>~(v1_xboole_0(k2_zfmisc_1(X1,X2)))), file('/scratch/mptp/predsminms1/t10_lfuzzy_1__0', fc10_subset_1)). fof(c_0_7, plain, ![X8, X9, X10, X11]:((~r2_relset_1(X8,X9,X10,X11)\|X10=X11\|(~m1_subset_1(X10,k1_zfmisc_1(k2_zfmisc_1(X8,X9)))\|~m1_subset_1(X11,k1_zfmisc_1(k2_zfmisc_1(X8,X9)))))&(X10!=X11\|r2_relset_1(X8,X9,X10,X11)\|(~m1_subset_1(X10,k1_zfmisc_1(k2_zfmisc_1(X8,X9)))\|~m1_subset_1(X11,k1_zfmisc_1(k2_zfmisc_1(X8,X9)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_r2_relset_1])])])). fof(c_0_8, plain, ![X12, X13]:((~v2_lfuzzy_1(X13,X12)\|r2_relset_1(k2_zfmisc_1(X12,X12),k1_numbers,k2_fuzzy_4(X12,X12,X13),X13)\|(~v5_relat_1(X13,k1_rcomp_1(k6_numbers,np__1))\|(~v1_funct_1(X13)\|(~v1_funct_2(X13,k2_zfmisc_1(X12,X12),k1_numbers)\|~m1_subset_1(X13,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X12,X12),k1_numbers))))))\|v1_xboole_0(X12))&(~r2_relset_1(k2_zfmisc_1(X12,X12),k1_numbers,k2_fuzzy_4(X12,X12,X13),X13)\|v2_lfuzzy_1(X13,X12)\|(~v5_relat_1(X13,k1_rcomp_1(k6_numbers,np__1))\|(~v1_funct_1(X13)\|(~v1_funct_2(X13,k2_zfmisc_1(X12,X12),k1_numbers)\|~m1_subset_1(X13,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X12,X12),k1_numbers))))))\|v1_xboole_0(X12))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d4_lfuzzy_1])])])])])). cnf(c_0_9, plain, (X3=X4\|~r2_relset_1(X1,X2,X3,X4)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_7])). cnf(c_0_10, plain, (r2_relset_1(k2_zfmisc_1(X2,X2),k1_numbers,k2_fuzzy_4(X2,X2,X1),X1)\|v1_xboole_0(X2)\|~v2_lfuzzy_1(X1,X2)\|~v5_relat_1(X1,k1_rcomp_1(k6_numbers,np__1))\|~v1_funct_1(X1)\|~v1_funct_2(X1,k2_zfmisc_1(X2,X2),k1_numbers)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X2,X2),k1_numbers)))), inference(split_conjunct,[status(thm)],[c_0_8])). fof(c_0_11, plain, ![X14, X15, X16]:((v5_relat_1(k2_fuzzy_4(X14,X15,X16),k1_rcomp_1(k6_numbers,np__1))\|(v1_xboole_0(X14)\|(v1_xboole_0(X15)\|(~v5_relat_1(X16,k1_rcomp_1(k6_numbers,np__1))\|(~v1_funct_1(X16)\|(~v1_funct_2(X16,k2_zfmisc_1(X15,X14),k1_numbers)\|~m1_subset_1(X16,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X15,X14),k1_numbers)))))))))&((v1_funct_1(k2_fuzzy_4(X14,X15,X16))\|(v1_xboole_0(X14)\|(v1_xboole_0(X15)\|(~v5_relat_1(X16,k1_rcomp_1(k6_numbers,np__1))\|(~v1_funct_1(X16)\|(~v1_funct_2(X16,k2_zfmisc_1(X15,X14),k1_numbers)\|~m1_subset_1(X16,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X15,X14),k1_numbers)))))))))&((v1_funct_2(k2_fuzzy_4(X14,X15,X16),k2_zfmisc_1(X14,X15),k1_numbers)\|(v1_xboole_0(X14)\|(v1_xboole_0(X15)\|(~v5_relat_1(X16,k1_rcomp_1(k6_numbers,np__1))\|(~v1_funct_1(X16)\|(~v1_funct_2(X16,k2_zfmisc_1(X15,X14),k1_numbers)\|~m1_subset_1(X16,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X15,X14),k1_numbers)))))))))&(m1_subset_1(k2_fuzzy_4(X14,X15,X16),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X14,X15),k1_numbers)))\|(v1_xboole_0(X14)\|(v1_xboole_0(X15)\|(~v5_relat_1(X16,k1_rcomp_1(k6_numbers,np__1))\|(~v1_funct_1(X16)\|(~v1_funct_2(X16,k2_zfmisc_1(X15,X14),k1_numbers)\|~m1_subset_1(X16,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X15,X14),k1_numbers)))))))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k2_fuzzy_4])])])])). fof(c_0_12, negated_conjecture, ~(![X1]:(~(v1_xboole_0(X1))=>![X2]:((v5_relat_1(X2,k1_rcomp_1(k6_numbers,np__1))&(v1_funct_1(X2)&(v1_funct_2(X2,k2_zfmisc_1(X1,X1),k1_numbers)&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X1),k1_numbers))))))=>![X3]:((v5_relat_1(X3,k1_rcomp_1(k6_numbers,np__1))&(v1_funct_1(X3)&(v1_funct_2(X3,k2_zfmisc_1(X1,X1),k1_numbers)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X1),k1_numbers))))))=>((v2_lfuzzy_1(X2,X1)&v2_lfuzzy_1(X3,X1))=>r2_relset_1(k2_zfmisc_1(X1,X1),k1_numbers,k2_fuzzy_4(X1,X1,k2_lfuzzy_1(k2_zfmisc_1(X1,X1),X2,X3)),k2_lfuzzy_1(k2_zfmisc_1(X1,X1),X2,X3))))))), inference(assume_negation,[status(cth)],[t10_lfuzzy_1])). cnf(c_0_13, plain, (X3=X4\|~r2_relset_1(X1,X2,X3,X4)\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(evalgc,[status(thm)],[c_0_9])). cnf(c_0_14, plain, (v1_xboole_0(X2)\|r2_relset_1(k2_zfmisc_1(X2,X2),k1_numbers,k2_fuzzy_4(X2,X2,X1),X1)\|~v1_funct_1(X1)\|~v2_lfuzzy_1(X1,X2)\|~v5_relat_1(X1,k1_rcomp_1(k6_numbers,np__1))\|~v1_funct_2(X1,k2_zfmisc_1(X2,X2),k1_numbers)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X2,X2),k1_numbers)))), inference(evalgc,[status(thm)],[c_0_10])). cnf(c_0_15, plain, (m1_subset_1(k2_fuzzy_4(X1,X2,X3),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X2),k1_numbers)))\|v1_xboole_0(X1)\|v1_xboole_0(X2)\|~v5_relat_1(X3,k1_rcomp_1(k6_numbers,np__1))\|~v1_funct_1(X3)\|~v1_funct_2(X3,k2_zfmisc_1(X2,X1),k1_numbers)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X2,X1),k1_numbers)))), inference(split_conjunct,[status(thm)],[c_0_11])). fof(c_0_16, negated_conjecture, (~v1_xboole_0(esk1_0)&((v5_relat_1(esk2_0,k1_rcomp_1(k6_numbers,np__1))&(v1_funct_1(esk2_0)&(v1_funct_2(esk2_0,k2_zfmisc_1(esk1_0,esk1_0),k1_numbers)&m1_subset_1(esk2_0,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(esk1_0,esk1_0),k1_numbers))))))&((v5_relat_1(esk3_0,k1_rcomp_1(k6_numbers,np__1))&(v1_funct_1(esk3_0)&(v1_funct_2(esk3_0,k2_zfmisc_1(esk1_0,esk1_0),k1_numbers)&m1_subset_1(esk3_0,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(esk1_0,esk1_0),k1_numbers))))))&((v2_lfuzzy_1(esk2_0,esk1_0)&v2_lfuzzy_1(esk3_0,esk1_0))&~r2_relset_1(k2_zfmisc_1(esk1_0,esk1_0),k1_numbers,k2_fuzzy_4(esk1_0,esk1_0,k2_lfuzzy_1(k2_zfmisc_1(esk1_0,esk1_0),esk2_0,esk3_0)),k2_lfuzzy_1(k2_zfmisc_1(esk1_0,esk1_0),esk2_0,esk3_0)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_12])])])])). fof(c_0_17, plain, ![X17, X18, X19, X20]:(v1_xboole_0(X17)\|(v1_xboole_0(X18)\|(~v5_relat_1(X19,k1_rcomp_1(k6_numbers,np__1))\|(~v1_funct_1(X19)\|(~v1_funct_2(X19,k2_zfmisc_1(X17,X18),k1_numbers)\|~m1_subset_1(X19,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X17,X18),k1_numbers)))))\|(~v5_relat_1(X20,k1_rcomp_1(k6_numbers,np__1))\|(~v1_funct_1(X20)\|(~v1_funct_2(X20,k2_zfmisc_1(X17,X18),k1_numbers)\|~m1_subset_1(X20,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X17,X18),k1_numbers)))))\|r2_relset_1(k2_zfmisc_1(X18,X17),k1_numbers,k2_fuzzy_4(X18,X17,k2_fuzzy_1(k2_zfmisc_1(X17,X18),X19,X20)),k2_fuzzy_1(k2_zfmisc_1(X18,X17),k2_fuzzy_4(X18,X17,X19),k2_fuzzy_4(X18,X17,X20))))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t7_fuzzy_4])])])])). cnf(c_0_18, plain, (k2_fuzzy_4(X1,X1,X2)=X2\|v1_xboole_0(X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X1),k1_numbers)))\|~m1_subset_1(k2_fuzzy_4(X1,X1,X2),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X1),k1_numbers)))\|~v2_lfuzzy_1(X2,X1)\|~v1_funct_2(X2,k2_zfmisc_1(X1,X1),k1_numbers)\|~v1_funct_1(X2)\|~v5_relat_1(X2,k1_rcomp_1(k6_numbers,np__1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_13, c_0_14])])). cnf(c_0_19, plain, (v1_xboole_0(X2)\|v1_xboole_0(X1)\|m1_subset_1(k2_fuzzy_4(X1,X2,X3),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X2),k1_numbers)))\|~v1_funct_1(X3)\|~v5_relat_1(X3,k1_rcomp_1(k6_numbers,np__1))\|~v1_funct_2(X3,k2_zfmisc_1(X2,X1),k1_numbers)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X2,X1),k1_numbers)))), inference(evalgc,[status(thm)],[c_0_15])). cnf(c_0_20, negated_conjecture, (m1_subset_1(esk3_0,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(esk1_0,esk1_0),k1_numbers)))), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_21, negated_conjecture, (v2_lfuzzy_1(esk3_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_22, negated_conjecture, (v1_funct_2(esk3_0,k2_zfmisc_1(esk1_0,esk1_0),k1_numbers)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_23, negated_conjecture, (v1_funct_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_24, negated_conjecture, (v5_relat_1(esk3_0,k1_rcomp_1(k6_numbers,np__1))), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_25, negated_conjecture, (~v1_xboole_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_16])). fof(c_0_26, plain, ![X21, X22, X23]:(v1_xboole_0(X21)\|(~v5_relat_1(X22,k1_rcomp_1(k6_numbers,np__1))\|(~v1_funct_1(X22)\|(~v1_funct_2(X22,X21,k1_numbers)\|~m1_subset_1(X22,k1_zfmisc_1(k2_zfmisc_1(X21,k1_numbers)))))\|(~v5_relat_1(X23,k1_rcomp_1(k6_numbers,np__1))\|(~v1_funct_1(X23)\|(~v1_funct_2(X23,X21,k1_numbers)\|~m1_subset_1(X23,k1_zfmisc_1(k2_zfmisc_1(X21,k1_numbers)))))))\|k2_lfuzzy_1(X21,X22,X23)=k2_fuzzy_1(X21,X22,X23)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[redefinition_k2_lfuzzy_1])])])). cnf(c_0_27, plain, (v1_xboole_0(X1)\|v1_xboole_0(X2)\|r2_relset_1(k2_zfmisc_1(X2,X1),k1_numbers,k2_fuzzy_4(X2,X1,k2_fuzzy_1(k2_zfmisc_1(X1,X2),X3,X4)),k2_fuzzy_1(k2_zfmisc_1(X2,X1),k2_fuzzy_4(X2,X1,X3),k2_fuzzy_4(X2,X1,X4)))\|~v5_relat_1(X3,k1_rcomp_1(k6_numbers,np__1))\|~v1_funct_1(X3)\|~v1_funct_2(X3,k2_zfmisc_1(X1,X2),k1_numbers)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X2),k1_numbers)))\|~v5_relat_1(X4,k1_rcomp_1(k6_numbers,np__1))\|~v1_funct_1(X4)\|~v1_funct_2(X4,k2_zfmisc_1(X1,X2),k1_numbers)\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X2),k1_numbers)))), inference(split_conjunct,[status(thm)],[c_0_17])). cnf(c_0_28, plain, (k2_fuzzy_4(X1,X1,X2)=X2\|v1_xboole_0(X1)\|~v2_lfuzzy_1(X2,X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X1),k1_numbers)))\|~v1_funct_2(X2,k2_zfmisc_1(X1,X1),k1_numbers)\|~v1_funct_1(X2)\|~v5_relat_1(X2,k1_rcomp_1(k6_numbers,np__1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_18, c_0_19])])). cnf(c_0_29, negated_conjecture, (m1_subset_1(esk3_0,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(esk1_0,esk1_0),k1_numbers)))), inference(evalgc,[status(thm)],[c_0_20])). cnf(c_0_30, negated_conjecture, (v2_lfuzzy_1(esk3_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_21])). cnf(c_0_31, negated_conjecture, (v1_funct_2(esk3_0,k2_zfmisc_1(esk1_0,esk1_0),k1_numbers)), inference(evalgc,[status(thm)],[c_0_22])). cnf(c_0_32, negated_conjecture, (v1_funct_1(esk3_0)), inference(evalgc,[status(thm)],[c_0_23])). cnf(c_0_33, negated_conjecture, (v5_relat_1(esk3_0,k1_rcomp_1(k6_numbers,np__1))), inference(evalgc,[status(thm)],[c_0_24])). cnf(c_0_34, negated_conjecture, (~v1_xboole_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_25])). cnf(c_0_35, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(esk1_0,esk1_0),k1_numbers)))), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_36, negated_conjecture, (v2_lfuzzy_1(esk2_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_37, negated_conjecture, (v1_funct_2(esk2_0,k2_zfmisc_1(esk1_0,esk1_0),k1_numbers)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_38, negated_conjecture, (v1_funct_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_39, negated_conjecture, (v5_relat_1(esk2_0,k1_rcomp_1(k6_numbers,np__1))), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_40, negated_conjecture, (~r2_relset_1(k2_zfmisc_1(esk1_0,esk1_0),k1_numbers,k2_fuzzy_4(esk1_0,esk1_0,k2_lfuzzy_1(k2_zfmisc_1(esk1_0,esk1_0),esk2_0,esk3_0)),k2_lfuzzy_1(k2_zfmisc_1(esk1_0,esk1_0),esk2_0,esk3_0))), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_41, plain, (v1_xboole_0(X1)\|k2_lfuzzy_1(X1,X2,X3)=k2_fuzzy_1(X1,X2,X3)\|~v5_relat_1(X2,k1_rcomp_1(k6_numbers,np__1))\|~v1_funct_1(X2)\|~v1_funct_2(X2,X1,k1_numbers)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~v5_relat_1(X3,k1_rcomp_1(k6_numbers,np__1))\|~v1_funct_1(X3)\|~v1_funct_2(X3,X1,k1_numbers)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_42, plain, (v1_xboole_0(X2)\|v1_xboole_0(X1)\|r2_relset_1(k2_zfmisc_1(X2,X1),k1_numbers,k2_fuzzy_4(X2,X1,k2_fuzzy_1(k2_zfmisc_1(X1,X2),X3,X4)),k2_fuzzy_1(k2_zfmisc_1(X2,X1),k2_fuzzy_4(X2,X1,X3),k2_fuzzy_4(X2,X1,X4)))\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v5_relat_1(X4,k1_rcomp_1(k6_numbers,np__1))\|~v5_relat_1(X3,k1_rcomp_1(k6_numbers,np__1))\|~v1_funct_2(X4,k2_zfmisc_1(X1,X2),k1_numbers)\|~v1_funct_2(X3,k2_zfmisc_1(X1,X2),k1_numbers)\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X2),k1_numbers)))\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X2),k1_numbers)))), inference(evalgc,[status(thm)],[c_0_27])). cnf(c_0_43, negated_conjecture, (k2_fuzzy_4(esk1_0,esk1_0,esk3_0)=esk3_0), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28, c_0_29]), c_0_30]), c_0_31]), c_0_32]), c_0_33])]), c_0_34])])). cnf(c_0_44, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(esk1_0,esk1_0),k1_numbers)))), inference(evalgc,[status(thm)],[c_0_35])). cnf(c_0_45, negated_conjecture, (v2_lfuzzy_1(esk2_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_36])). cnf(c_0_46, negated_conjecture, (v1_funct_2(esk2_0,k2_zfmisc_1(esk1_0,esk1_0),k1_numbers)), inference(evalgc,[status(thm)],[c_0_37])). cnf(c_0_47, negated_conjecture, (v1_funct_1(esk2_0)), inference(evalgc,[status(thm)],[c_0_38])). cnf(c_0_48, negated_conjecture, (v5_relat_1(esk2_0,k1_rcomp_1(k6_numbers,np__1))), inference(evalgc,[status(thm)],[c_0_39])). fof(c_0_49, plain, ![X24, X25]:(v1_xboole_0(X24)\|v1_xboole_0(X25)\|~v1_xboole_0(k2_zfmisc_1(X24,X25))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fc10_subset_1])])])). cnf(c_0_50, negated_conjecture, (~r2_relset_1(k2_zfmisc_1(esk1_0,esk1_0),k1_numbers,k2_fuzzy_4(esk1_0,esk1_0,k2_lfuzzy_1(k2_zfmisc_1(esk1_0,esk1_0),esk2_0,esk3_0)),k2_lfuzzy_1(k2_zfmisc_1(esk1_0,esk1_0),esk2_0,esk3_0))), inference(evalgc,[status(thm)],[c_0_40])). cnf(c_0_51, plain, (k2_lfuzzy_1(X1,X2,X3)=k2_fuzzy_1(X1,X2,X3)\|v1_xboole_0(X1)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v1_funct_2(X3,X1,k1_numbers)\|~v1_funct_2(X2,X1,k1_numbers)\|~v5_relat_1(X3,k1_rcomp_1(k6_numbers,np__1))\|~v5_relat_1(X2,k1_rcomp_1(k6_numbers,np__1))\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))), inference(evalgc,[status(thm)],[c_0_41])). cnf(c_0_52, negated_conjecture, (r2_relset_1(k2_zfmisc_1(esk1_0,esk1_0),k1_numbers,k2_fuzzy_4(esk1_0,esk1_0,k2_fuzzy_1(k2_zfmisc_1(esk1_0,esk1_0),X1,esk3_0)),k2_fuzzy_1(k2_zfmisc_1(esk1_0,esk1_0),k2_fuzzy_4(esk1_0,esk1_0,X1),esk3_0))\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(esk1_0,esk1_0),k1_numbers)))\|~v1_funct_2(X1,k2_zfmisc_1(esk1_0,esk1_0),k1_numbers)\|~v1_funct_1(X1)\|~v5_relat_1(X1,k1_rcomp_1(k6_numbers,np__1))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42, c_0_43]), c_0_29]), c_0_31]), c_0_32]), c_0_33])]), c_0_34])])). cnf(c_0_53, negated_conjecture, (k2_fuzzy_4(esk1_0,esk1_0,esk2_0)=esk2_0), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28, c_0_44]), c_0_45]), c_0_46]), c_0_47]), c_0_48])]), c_0_34])])). cnf(c_0_54, plain, (v1_xboole_0(X1)\|v1_xboole_0(X2)\|~v1_xboole_0(k2_zfmisc_1(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_49])). cnf(c_0_55, negated_conjecture, (v1_xboole_0(k2_zfmisc_1(esk1_0,esk1_0))\|~r2_relset_1(k2_zfmisc_1(esk1_0,esk1_0),k1_numbers,k2_fuzzy_4(esk1_0,esk1_0,k2_fuzzy_1(k2_zfmisc_1(esk1_0,esk1_0),esk2_0,esk3_0)),k2_fuzzy_1(k2_zfmisc_1(esk1_0,esk1_0),esk2_0,esk3_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50, c_0_51]), c_0_29]), c_0_44]), c_0_31]), c_0_46]), c_0_32]), c_0_47]), c_0_33]), c_0_48])])])). cnf(c_0_56, negated_conjecture, (r2_relset_1(k2_zfmisc_1(esk1_0,esk1_0),k1_numbers,k2_fuzzy_4(esk1_0,esk1_0,k2_fuzzy_1(k2_zfmisc_1(esk1_0,esk1_0),esk2_0,esk3_0)),k2_fuzzy_1(k2_zfmisc_1(esk1_0,esk1_0),esk2_0,esk3_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52, c_0_53]), c_0_44]), c_0_46]), c_0_47]), c_0_48])])])). cnf(c_0_57, plain, (v1_xboole_0(X2)\|v1_xboole_0(X1)\|~v1_xboole_0(k2_zfmisc_1(X1,X2))), inference(evalgc,[status(thm)],[c_0_54])). cnf(c_0_58, negated_conjecture, (v1_xboole_0(k2_zfmisc_1(esk1_0,esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_55, c_0_56])])])). cnf(c_0_59, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_57, c_0_58]), c_0_34]), ['proof']). # SZS output end CNFRefutation	reserve X, Y for non empty set; theorem Th10: for R,S being RMembership_Func of X,X holds R is symmetric & S is symmetric implies converse max(R,S) = max(R,S) proof let R,S be RMembership_Func of X,X; assume R is symmetric & S is symmetric; then converse R = R & converse S =S by Def4; hence thesis by FUZZY_4:7; end;	Convert the following ATP output trace into a readable Mizar proof.
t36_yellow_3	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t36_yellow_3, conjecture, ![X1]:((~(v2_struct_0(X1))&(v5_orders_2(X1)&l1_orders_2(X1)))=>![X2]:((~(v2_struct_0(X2))&(v5_orders_2(X2)&l1_orders_2(X2)))=>![X3]:(m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))=>![X4]:(m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))=>![X5]:(m1_subset_1(X5,u1_struct_0(X1))=>![X6]:(m1_subset_1(X6,u1_struct_0(X2))=>((r2_yellow_0(X1,X3)&(r2_yellow_0(X2,X4)&![X7]:(m1_subset_1(X7,u1_struct_0(k3_yellow_3(X1,X2)))=>(r1_lattice3(k3_yellow_3(X1,X2),k6_yellow_3(X1,X2,X3,X4),X7)=>r1_orders_2(k3_yellow_3(X1,X2),X7,k7_yellow_3(X1,X2,X5,X6))))))=>(![X7]:(m1_subset_1(X7,u1_struct_0(X1))=>(r1_lattice3(X1,X3,X7)=>r1_orders_2(X1,X7,X5)))&![X7]:(m1_subset_1(X7,u1_struct_0(X2))=>(r1_lattice3(X2,X4,X7)=>r1_orders_2(X2,X7,X6))))))))))), file('/scratch/mptp/predsminms1/t36_yellow_3__0', t36_yellow_3)). fof(t33_yellow_3, axiom, ![X1]:((~(v2_struct_0(X1))&l1_orders_2(X1))=>![X2]:((~(v2_struct_0(X2))&l1_orders_2(X2))=>![X3]:(m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))=>![X4]:(m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))=>![X5]:(m1_subset_1(X5,u1_struct_0(X1))=>![X6]:(m1_subset_1(X6,u1_struct_0(X2))=>((r1_lattice3(X1,X3,X5)&r1_lattice3(X2,X4,X6))=>r1_lattice3(k3_yellow_3(X1,X2),k6_yellow_3(X1,X2,X3,X4),k7_yellow_3(X1,X2,X5,X6))))))))), file('/scratch/mptp/predsminms1/t36_yellow_3__0', t33_yellow_3)). fof(t11_yellow_3, axiom, ![X1]:((~(v2_struct_0(X1))&l1_orders_2(X1))=>![X2]:((~(v2_struct_0(X2))&l1_orders_2(X2))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>![X4]:(m1_subset_1(X4,u1_struct_0(X1))=>![X5]:(m1_subset_1(X5,u1_struct_0(X2))=>![X6]:(m1_subset_1(X6,u1_struct_0(X2))=>((r1_orders_2(X1,X3,X4)&r1_orders_2(X2,X5,X6))<=>r1_orders_2(k3_yellow_3(X1,X2),k7_yellow_3(X1,X2,X3,X5),k7_yellow_3(X1,X2,X4,X6))))))))), file('/scratch/mptp/predsminms1/t36_yellow_3__0', t11_yellow_3)). fof(dt_k7_yellow_3, axiom, ![X1, X2, X3, X4]:(((~(v2_struct_0(X1))&l1_orders_2(X1))&((~(v2_struct_0(X2))&l1_orders_2(X2))&(m1_subset_1(X3,u1_struct_0(X1))&m1_subset_1(X4,u1_struct_0(X2)))))=>m1_subset_1(k7_yellow_3(X1,X2,X3,X4),u1_struct_0(k3_yellow_3(X1,X2)))), file('/scratch/mptp/predsminms1/t36_yellow_3__0', dt_k7_yellow_3)). fof(d8_yellow_0, axiom, ![X1]:(l1_orders_2(X1)=>![X2]:(r2_yellow_0(X1,X2)<=>?[X3]:(m1_subset_1(X3,u1_struct_0(X1))&(r1_lattice3(X1,X2,X3)&(![X4]:(m1_subset_1(X4,u1_struct_0(X1))=>(r1_lattice3(X1,X2,X4)=>r1_orders_2(X1,X4,X3)))&![X4]:(m1_subset_1(X4,u1_struct_0(X1))=>((r1_lattice3(X1,X2,X4)&![X5]:(m1_subset_1(X5,u1_struct_0(X1))=>(r1_lattice3(X1,X2,X5)=>r1_orders_2(X1,X5,X4))))=>X4=X3))))))), file('/scratch/mptp/predsminms1/t36_yellow_3__0', d8_yellow_0)). fof(c_0_5, negated_conjecture, ~(![X1]:((~(v2_struct_0(X1))&(v5_orders_2(X1)&l1_orders_2(X1)))=>![X2]:((~(v2_struct_0(X2))&(v5_orders_2(X2)&l1_orders_2(X2)))=>![X3]:(m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))=>![X4]:(m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))=>![X5]:(m1_subset_1(X5,u1_struct_0(X1))=>![X6]:(m1_subset_1(X6,u1_struct_0(X2))=>((r2_yellow_0(X1,X3)&(r2_yellow_0(X2,X4)&![X7]:(m1_subset_1(X7,u1_struct_0(k3_yellow_3(X1,X2)))=>(r1_lattice3(k3_yellow_3(X1,X2),k6_yellow_3(X1,X2,X3,X4),X7)=>r1_orders_2(k3_yellow_3(X1,X2),X7,k7_yellow_3(X1,X2,X5,X6))))))=>(![X7]:(m1_subset_1(X7,u1_struct_0(X1))=>(r1_lattice3(X1,X3,X7)=>r1_orders_2(X1,X7,X5)))&![X7]:(m1_subset_1(X7,u1_struct_0(X2))=>(r1_lattice3(X2,X4,X7)=>r1_orders_2(X2,X7,X6)))))))))))), inference(assume_negation,[status(cth)],[t36_yellow_3])). fof(c_0_6, negated_conjecture, ![X14]:((~v2_struct_0(esk1_0)&(v5_orders_2(esk1_0)&l1_orders_2(esk1_0)))&((~v2_struct_0(esk2_0)&(v5_orders_2(esk2_0)&l1_orders_2(esk2_0)))&(m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(esk1_0)))&(m1_subset_1(esk4_0,k1_zfmisc_1(u1_struct_0(esk2_0)))&(m1_subset_1(esk5_0,u1_struct_0(esk1_0))&(m1_subset_1(esk6_0,u1_struct_0(esk2_0))&((r2_yellow_0(esk1_0,esk3_0)&(r2_yellow_0(esk2_0,esk4_0)&(~m1_subset_1(X14,u1_struct_0(k3_yellow_3(esk1_0,esk2_0)))\|(~r1_lattice3(k3_yellow_3(esk1_0,esk2_0),k6_yellow_3(esk1_0,esk2_0,esk3_0,esk4_0),X14)\|r1_orders_2(k3_yellow_3(esk1_0,esk2_0),X14,k7_yellow_3(esk1_0,esk2_0,esk5_0,esk6_0))))))&(((m1_subset_1(esk8_0,u1_struct_0(esk2_0))\|m1_subset_1(esk7_0,u1_struct_0(esk1_0)))&((r1_lattice3(esk2_0,esk4_0,esk8_0)\|m1_subset_1(esk7_0,u1_struct_0(esk1_0)))&(~r1_orders_2(esk2_0,esk8_0,esk6_0)\|m1_subset_1(esk7_0,u1_struct_0(esk1_0)))))&(((m1_subset_1(esk8_0,u1_struct_0(esk2_0))\|r1_lattice3(esk1_0,esk3_0,esk7_0))&((r1_lattice3(esk2_0,esk4_0,esk8_0)\|r1_lattice3(esk1_0,esk3_0,esk7_0))&(~r1_orders_2(esk2_0,esk8_0,esk6_0)\|r1_lattice3(esk1_0,esk3_0,esk7_0))))&((m1_subset_1(esk8_0,u1_struct_0(esk2_0))\|~r1_orders_2(esk1_0,esk7_0,esk5_0))&((r1_lattice3(esk2_0,esk4_0,esk8_0)\|~r1_orders_2(esk1_0,esk7_0,esk5_0))&(~r1_orders_2(esk2_0,esk8_0,esk6_0)\|~r1_orders_2(esk1_0,esk7_0,esk5_0))))))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_5])])])])])])). fof(c_0_7, plain, ![X17, X18, X19, X20, X21, X22]:(v2_struct_0(X17)\|~l1_orders_2(X17)\|(v2_struct_0(X18)\|~l1_orders_2(X18)\|(~m1_subset_1(X19,k1_zfmisc_1(u1_struct_0(X17)))\|(~m1_subset_1(X20,k1_zfmisc_1(u1_struct_0(X18)))\|(~m1_subset_1(X21,u1_struct_0(X17))\|(~m1_subset_1(X22,u1_struct_0(X18))\|(~r1_lattice3(X17,X19,X21)\|~r1_lattice3(X18,X20,X22)\|r1_lattice3(k3_yellow_3(X17,X18),k6_yellow_3(X17,X18,X19,X20),k7_yellow_3(X17,X18,X21,X22))))))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t33_yellow_3])])])])). fof(c_0_8, plain, ![X23, X24, X25, X26, X27, X28]:((~r1_orders_2(X23,X25,X26)\|~r1_orders_2(X24,X27,X28)\|r1_orders_2(k3_yellow_3(X23,X24),k7_yellow_3(X23,X24,X25,X27),k7_yellow_3(X23,X24,X26,X28))\|~m1_subset_1(X28,u1_struct_0(X24))\|~m1_subset_1(X27,u1_struct_0(X24))\|~m1_subset_1(X26,u1_struct_0(X23))\|~m1_subset_1(X25,u1_struct_0(X23))\|(v2_struct_0(X24)\|~l1_orders_2(X24))\|(v2_struct_0(X23)\|~l1_orders_2(X23)))&((r1_orders_2(X23,X25,X26)\|~r1_orders_2(k3_yellow_3(X23,X24),k7_yellow_3(X23,X24,X25,X27),k7_yellow_3(X23,X24,X26,X28))\|~m1_subset_1(X28,u1_struct_0(X24))\|~m1_subset_1(X27,u1_struct_0(X24))\|~m1_subset_1(X26,u1_struct_0(X23))\|~m1_subset_1(X25,u1_struct_0(X23))\|(v2_struct_0(X24)\|~l1_orders_2(X24))\|(v2_struct_0(X23)\|~l1_orders_2(X23)))&(r1_orders_2(X24,X27,X28)\|~r1_orders_2(k3_yellow_3(X23,X24),k7_yellow_3(X23,X24,X25,X27),k7_yellow_3(X23,X24,X26,X28))\|~m1_subset_1(X28,u1_struct_0(X24))\|~m1_subset_1(X27,u1_struct_0(X24))\|~m1_subset_1(X26,u1_struct_0(X23))\|~m1_subset_1(X25,u1_struct_0(X23))\|(v2_struct_0(X24)\|~l1_orders_2(X24))\|(v2_struct_0(X23)\|~l1_orders_2(X23))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t11_yellow_3])])])])])). cnf(c_0_9, negated_conjecture, (r1_orders_2(k3_yellow_3(esk1_0,esk2_0),X1,k7_yellow_3(esk1_0,esk2_0,esk5_0,esk6_0))\|~m1_subset_1(X1,u1_struct_0(k3_yellow_3(esk1_0,esk2_0)))\|~r1_lattice3(k3_yellow_3(esk1_0,esk2_0),k6_yellow_3(esk1_0,esk2_0,esk3_0,esk4_0),X1)), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_10, plain, (v2_struct_0(X1)\|v2_struct_0(X2)\|r1_lattice3(k3_yellow_3(X1,X2),k6_yellow_3(X1,X2,X3,X4),k7_yellow_3(X1,X2,X5,X6))\|~l1_orders_2(X1)\|~l1_orders_2(X2)\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X5,u1_struct_0(X1))\|~m1_subset_1(X6,u1_struct_0(X2))\|~r1_lattice3(X1,X3,X5)\|~r1_lattice3(X2,X4,X6)), inference(split_conjunct,[status(thm)],[c_0_7])). cnf(c_0_11, negated_conjecture, (m1_subset_1(esk4_0,k1_zfmisc_1(u1_struct_0(esk2_0)))), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_12, negated_conjecture, (m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(esk1_0)))), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_13, negated_conjecture, (l1_orders_2(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_14, negated_conjecture, (l1_orders_2(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_15, negated_conjecture, (~v2_struct_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_16, negated_conjecture, (~v2_struct_0(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_17, plain, (r1_orders_2(X1,X2,X3)\|v2_struct_0(X1)\|v2_struct_0(X4)\|~r1_orders_2(k3_yellow_3(X4,X1),k7_yellow_3(X4,X1,X5,X2),k7_yellow_3(X4,X1,X6,X3))\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X6,u1_struct_0(X4))\|~m1_subset_1(X5,u1_struct_0(X4))\|~l1_orders_2(X1)\|~l1_orders_2(X4)), inference(split_conjunct,[status(thm)],[c_0_8])). cnf(c_0_18, negated_conjecture, (r1_orders_2(k3_yellow_3(esk1_0,esk2_0),X1,k7_yellow_3(esk1_0,esk2_0,esk5_0,esk6_0))\|~m1_subset_1(X1,u1_struct_0(k3_yellow_3(esk1_0,esk2_0)))\|~r1_lattice3(k3_yellow_3(esk1_0,esk2_0),k6_yellow_3(esk1_0,esk2_0,esk3_0,esk4_0),X1)), inference(evalgc,[status(thm)],[c_0_9])). cnf(c_0_19, plain, (v2_struct_0(X2)\|v2_struct_0(X1)\|r1_lattice3(k3_yellow_3(X1,X2),k6_yellow_3(X1,X2,X3,X4),k7_yellow_3(X1,X2,X5,X6))\|~l1_orders_2(X2)\|~l1_orders_2(X1)\|~r1_lattice3(X2,X4,X6)\|~r1_lattice3(X1,X3,X5)\|~m1_subset_1(X6,u1_struct_0(X2))\|~m1_subset_1(X5,u1_struct_0(X1))\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))), inference(evalgc,[status(thm)],[c_0_10])). cnf(c_0_20, negated_conjecture, (m1_subset_1(esk4_0,k1_zfmisc_1(u1_struct_0(esk2_0)))), inference(evalgc,[status(thm)],[c_0_11])). cnf(c_0_21, negated_conjecture, (m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(esk1_0)))), inference(evalgc,[status(thm)],[c_0_12])). cnf(c_0_22, negated_conjecture, (l1_orders_2(esk2_0)), inference(evalgc,[status(thm)],[c_0_13])). cnf(c_0_23, negated_conjecture, (l1_orders_2(esk1_0)), inference(evalgc,[status(thm)],[c_0_14])). cnf(c_0_24, negated_conjecture, (~v2_struct_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_15])). cnf(c_0_25, negated_conjecture, (~v2_struct_0(esk2_0)), inference(evalgc,[status(thm)],[c_0_16])). cnf(c_0_26, negated_conjecture, (m1_subset_1(esk5_0,u1_struct_0(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_27, negated_conjecture, (m1_subset_1(esk6_0,u1_struct_0(esk2_0))), inference(split_conjunct,[status(thm)],[c_0_6])). fof(c_0_28, plain, ![X29, X30, X31, X32]:(v2_struct_0(X29)\|~l1_orders_2(X29)\|(v2_struct_0(X30)\|~l1_orders_2(X30)\|(~m1_subset_1(X31,u1_struct_0(X29))\|~m1_subset_1(X32,u1_struct_0(X30))))\|m1_subset_1(k7_yellow_3(X29,X30,X31,X32),u1_struct_0(k3_yellow_3(X29,X30)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k7_yellow_3])])])). cnf(c_0_29, plain, (r1_orders_2(X1,X2,X3)\|v2_struct_0(X4)\|v2_struct_0(X1)\|~r1_orders_2(k3_yellow_3(X1,X4),k7_yellow_3(X1,X4,X2,X5),k7_yellow_3(X1,X4,X3,X6))\|~m1_subset_1(X6,u1_struct_0(X4))\|~m1_subset_1(X5,u1_struct_0(X4))\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l1_orders_2(X4)\|~l1_orders_2(X1)), inference(split_conjunct,[status(thm)],[c_0_8])). cnf(c_0_30, plain, (v2_struct_0(X4)\|v2_struct_0(X1)\|r1_orders_2(X1,X2,X3)\|~l1_orders_2(X4)\|~l1_orders_2(X1)\|~m1_subset_1(X6,u1_struct_0(X4))\|~m1_subset_1(X5,u1_struct_0(X4))\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~r1_orders_2(k3_yellow_3(X4,X1),k7_yellow_3(X4,X1,X5,X2),k7_yellow_3(X4,X1,X6,X3))), inference(evalgc,[status(thm)],[c_0_17])). cnf(c_0_31, negated_conjecture, (r1_orders_2(k3_yellow_3(esk1_0,esk2_0),k7_yellow_3(esk1_0,esk2_0,X1,X2),k7_yellow_3(esk1_0,esk2_0,esk5_0,esk6_0))\|~m1_subset_1(k7_yellow_3(esk1_0,esk2_0,X1,X2),u1_struct_0(k3_yellow_3(esk1_0,esk2_0)))\|~r1_lattice3(esk2_0,esk4_0,X2)\|~r1_lattice3(esk1_0,esk3_0,X1)\|~m1_subset_1(X2,u1_struct_0(esk2_0))\|~m1_subset_1(X1,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18, c_0_19]), c_0_20]), c_0_21]), c_0_22]), c_0_23])]), c_0_24]), c_0_25])])). cnf(c_0_32, negated_conjecture, (m1_subset_1(esk5_0,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[c_0_26])). cnf(c_0_33, negated_conjecture, (m1_subset_1(esk6_0,u1_struct_0(esk2_0))), inference(evalgc,[status(thm)],[c_0_27])). cnf(c_0_34, plain, (v2_struct_0(X1)\|v2_struct_0(X2)\|m1_subset_1(k7_yellow_3(X1,X2,X3,X4),u1_struct_0(k3_yellow_3(X1,X2)))\|~l1_orders_2(X1)\|~l1_orders_2(X2)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X4,u1_struct_0(X2))), inference(split_conjunct,[status(thm)],[c_0_28])). fof(c_0_35, plain, ![X33, X34, X36, X37, X39, X40, X43]:(((m1_subset_1(esk9_2(X33,X34),u1_struct_0(X33))\|~r2_yellow_0(X33,X34)\|~l1_orders_2(X33))&((r1_lattice3(X33,X34,esk9_2(X33,X34))\|~r2_yellow_0(X33,X34)\|~l1_orders_2(X33))&((~m1_subset_1(X36,u1_struct_0(X33))\|(~r1_lattice3(X33,X34,X36)\|r1_orders_2(X33,X36,esk9_2(X33,X34)))\|~r2_yellow_0(X33,X34)\|~l1_orders_2(X33))&((m1_subset_1(esk10_3(X33,X34,X37),u1_struct_0(X33))\|~r1_lattice3(X33,X34,X37)\|X37=esk9_2(X33,X34)\|~m1_subset_1(X37,u1_struct_0(X33))\|~r2_yellow_0(X33,X34)\|~l1_orders_2(X33))&((r1_lattice3(X33,X34,esk10_3(X33,X34,X37))\|~r1_lattice3(X33,X34,X37)\|X37=esk9_2(X33,X34)\|~m1_subset_1(X37,u1_struct_0(X33))\|~r2_yellow_0(X33,X34)\|~l1_orders_2(X33))&(~r1_orders_2(X33,esk10_3(X33,X34,X37),X37)\|~r1_lattice3(X33,X34,X37)\|X37=esk9_2(X33,X34)\|~m1_subset_1(X37,u1_struct_0(X33))\|~r2_yellow_0(X33,X34)\|~l1_orders_2(X33)))))))&(((m1_subset_1(esk12_3(X33,X39,X40),u1_struct_0(X33))\|m1_subset_1(esk11_3(X33,X39,X40),u1_struct_0(X33))\|~r1_lattice3(X33,X39,X40)\|~m1_subset_1(X40,u1_struct_0(X33))\|r2_yellow_0(X33,X39)\|~l1_orders_2(X33))&(((r1_lattice3(X33,X39,esk12_3(X33,X39,X40))\|m1_subset_1(esk11_3(X33,X39,X40),u1_struct_0(X33))\|~r1_lattice3(X33,X39,X40)\|~m1_subset_1(X40,u1_struct_0(X33))\|r2_yellow_0(X33,X39)\|~l1_orders_2(X33))&(~m1_subset_1(X43,u1_struct_0(X33))\|(~r1_lattice3(X33,X39,X43)\|r1_orders_2(X33,X43,esk12_3(X33,X39,X40)))\|m1_subset_1(esk11_3(X33,X39,X40),u1_struct_0(X33))\|~r1_lattice3(X33,X39,X40)\|~m1_subset_1(X40,u1_struct_0(X33))\|r2_yellow_0(X33,X39)\|~l1_orders_2(X33)))&(esk12_3(X33,X39,X40)!=X40\|m1_subset_1(esk11_3(X33,X39,X40),u1_struct_0(X33))\|~r1_lattice3(X33,X39,X40)\|~m1_subset_1(X40,u1_struct_0(X33))\|r2_yellow_0(X33,X39)\|~l1_orders_2(X33))))&(((m1_subset_1(esk12_3(X33,X39,X40),u1_struct_0(X33))\|r1_lattice3(X33,X39,esk11_3(X33,X39,X40))\|~r1_lattice3(X33,X39,X40)\|~m1_subset_1(X40,u1_struct_0(X33))\|r2_yellow_0(X33,X39)\|~l1_orders_2(X33))&(((r1_lattice3(X33,X39,esk12_3(X33,X39,X40))\|r1_lattice3(X33,X39,esk11_3(X33,X39,X40))\|~r1_lattice3(X33,X39,X40)\|~m1_subset_1(X40,u1_struct_0(X33))\|r2_yellow_0(X33,X39)\|~l1_orders_2(X33))&(~m1_subset_1(X43,u1_struct_0(X33))\|(~r1_lattice3(X33,X39,X43)\|r1_orders_2(X33,X43,esk12_3(X33,X39,X40)))\|r1_lattice3(X33,X39,esk11_3(X33,X39,X40))\|~r1_lattice3(X33,X39,X40)\|~m1_subset_1(X40,u1_struct_0(X33))\|r2_yellow_0(X33,X39)\|~l1_orders_2(X33)))&(esk12_3(X33,X39,X40)!=X40\|r1_lattice3(X33,X39,esk11_3(X33,X39,X40))\|~r1_lattice3(X33,X39,X40)\|~m1_subset_1(X40,u1_struct_0(X33))\|r2_yellow_0(X33,X39)\|~l1_orders_2(X33))))&((m1_subset_1(esk12_3(X33,X39,X40),u1_struct_0(X33))\|~r1_orders_2(X33,esk11_3(X33,X39,X40),X40)\|~r1_lattice3(X33,X39,X40)\|~m1_subset_1(X40,u1_struct_0(X33))\|r2_yellow_0(X33,X39)\|~l1_orders_2(X33))&(((r1_lattice3(X33,X39,esk12_3(X33,X39,X40))\|~r1_orders_2(X33,esk11_3(X33,X39,X40),X40)\|~r1_lattice3(X33,X39,X40)\|~m1_subset_1(X40,u1_struct_0(X33))\|r2_yellow_0(X33,X39)\|~l1_orders_2(X33))&(~m1_subset_1(X43,u1_struct_0(X33))\|(~r1_lattice3(X33,X39,X43)\|r1_orders_2(X33,X43,esk12_3(X33,X39,X40)))\|~r1_orders_2(X33,esk11_3(X33,X39,X40),X40)\|~r1_lattice3(X33,X39,X40)\|~m1_subset_1(X40,u1_struct_0(X33))\|r2_yellow_0(X33,X39)\|~l1_orders_2(X33)))&(esk12_3(X33,X39,X40)!=X40\|~r1_orders_2(X33,esk11_3(X33,X39,X40),X40)\|~r1_lattice3(X33,X39,X40)\|~m1_subset_1(X40,u1_struct_0(X33))\|r2_yellow_0(X33,X39)\|~l1_orders_2(X33))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_yellow_0])])])])])])). cnf(c_0_36, plain, (v2_struct_0(X4)\|v2_struct_0(X1)\|r1_orders_2(X1,X2,X3)\|~l1_orders_2(X4)\|~l1_orders_2(X1)\|~m1_subset_1(X6,u1_struct_0(X4))\|~m1_subset_1(X5,u1_struct_0(X4))\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~r1_orders_2(k3_yellow_3(X1,X4),k7_yellow_3(X1,X4,X2,X5),k7_yellow_3(X1,X4,X3,X6))), inference(evalgc,[status(thm)],[c_0_29])). cnf(c_0_37, negated_conjecture, (r1_orders_2(esk2_0,X1,esk6_0)\|~m1_subset_1(X2,u1_struct_0(esk1_0))\|~m1_subset_1(X1,u1_struct_0(esk2_0))\|~r1_lattice3(esk2_0,esk4_0,X1)\|~r1_lattice3(esk1_0,esk3_0,X2)\|~m1_subset_1(k7_yellow_3(esk1_0,esk2_0,X2,X1),u1_struct_0(k3_yellow_3(esk1_0,esk2_0)))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30, c_0_31]), c_0_32]), c_0_33]), c_0_23]), c_0_22])]), c_0_25]), c_0_24])])). cnf(c_0_38, plain, (v2_struct_0(X2)\|v2_struct_0(X1)\|m1_subset_1(k7_yellow_3(X1,X2,X3,X4),u1_struct_0(k3_yellow_3(X1,X2)))\|~l1_orders_2(X2)\|~l1_orders_2(X1)\|~m1_subset_1(X4,u1_struct_0(X2))\|~m1_subset_1(X3,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_34])). cnf(c_0_39, plain, (r1_lattice3(X1,X2,esk9_2(X1,X2))\|~r2_yellow_0(X1,X2)\|~l1_orders_2(X1)), inference(split_conjunct,[status(thm)],[c_0_35])). cnf(c_0_40, negated_conjecture, (r2_yellow_0(esk1_0,esk3_0)), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_41, negated_conjecture, (r1_orders_2(esk1_0,X1,esk5_0)\|~m1_subset_1(X2,u1_struct_0(esk2_0))\|~m1_subset_1(X1,u1_struct_0(esk1_0))\|~r1_lattice3(esk2_0,esk4_0,X2)\|~r1_lattice3(esk1_0,esk3_0,X1)\|~m1_subset_1(k7_yellow_3(esk1_0,esk2_0,X1,X2),u1_struct_0(k3_yellow_3(esk1_0,esk2_0)))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36, c_0_31]), c_0_33]), c_0_32]), c_0_22]), c_0_23])]), c_0_24]), c_0_25])])). cnf(c_0_42, negated_conjecture, (r2_yellow_0(esk2_0,esk4_0)), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_43, negated_conjecture, (r1_orders_2(esk2_0,X1,esk6_0)\|~r1_lattice3(esk2_0,esk4_0,X1)\|~r1_lattice3(esk1_0,esk3_0,X2)\|~m1_subset_1(X2,u1_struct_0(esk1_0))\|~m1_subset_1(X1,u1_struct_0(esk2_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37, c_0_38]), c_0_22]), c_0_23])]), c_0_24]), c_0_25])])). cnf(c_0_44, plain, (r1_lattice3(X1,X2,esk9_2(X1,X2))\|~l1_orders_2(X1)\|~r2_yellow_0(X1,X2)), inference(evalgc,[status(thm)],[c_0_39])). cnf(c_0_45, negated_conjecture, (r2_yellow_0(esk1_0,esk3_0)), inference(evalgc,[status(thm)],[c_0_40])). cnf(c_0_46, plain, (m1_subset_1(esk9_2(X1,X2),u1_struct_0(X1))\|~r2_yellow_0(X1,X2)\|~l1_orders_2(X1)), inference(split_conjunct,[status(thm)],[c_0_35])). cnf(c_0_47, negated_conjecture, (r1_orders_2(esk1_0,X1,esk5_0)\|~r1_lattice3(esk2_0,esk4_0,X2)\|~r1_lattice3(esk1_0,esk3_0,X1)\|~m1_subset_1(X2,u1_struct_0(esk2_0))\|~m1_subset_1(X1,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41, c_0_38]), c_0_22]), c_0_23])]), c_0_24]), c_0_25])])). cnf(c_0_48, negated_conjecture, (r2_yellow_0(esk2_0,esk4_0)), inference(evalgc,[status(thm)],[c_0_42])). cnf(c_0_49, negated_conjecture, (r1_lattice3(esk1_0,esk3_0,esk7_0)\|~r1_orders_2(esk2_0,esk8_0,esk6_0)), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_50, negated_conjecture, (r1_orders_2(esk2_0,X1,esk6_0)\|~r1_lattice3(esk2_0,esk4_0,X1)\|~m1_subset_1(esk9_2(esk1_0,esk3_0),u1_struct_0(esk1_0))\|~m1_subset_1(X1,u1_struct_0(esk2_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43, c_0_44]), c_0_45]), c_0_23])])])). cnf(c_0_51, plain, (m1_subset_1(esk9_2(X1,X2),u1_struct_0(X1))\|~l1_orders_2(X1)\|~r2_yellow_0(X1,X2)), inference(evalgc,[status(thm)],[c_0_46])). cnf(c_0_52, negated_conjecture, (r1_lattice3(esk2_0,esk4_0,esk8_0)\|~r1_orders_2(esk1_0,esk7_0,esk5_0)), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_53, negated_conjecture, (r1_orders_2(esk1_0,X1,esk5_0)\|~r1_lattice3(esk1_0,esk3_0,X1)\|~m1_subset_1(esk9_2(esk2_0,esk4_0),u1_struct_0(esk2_0))\|~m1_subset_1(X1,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47, c_0_44]), c_0_48]), c_0_22])])])). cnf(c_0_54, negated_conjecture, (r1_lattice3(esk1_0,esk3_0,esk7_0)\|~r1_orders_2(esk2_0,esk8_0,esk6_0)), inference(evalgc,[status(thm)],[c_0_49])). cnf(c_0_55, negated_conjecture, (r1_orders_2(esk2_0,X1,esk6_0)\|~r1_lattice3(esk2_0,esk4_0,X1)\|~m1_subset_1(X1,u1_struct_0(esk2_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50, c_0_51]), c_0_45]), c_0_23])])])). cnf(c_0_56, negated_conjecture, (m1_subset_1(esk8_0,u1_struct_0(esk2_0))\|r1_lattice3(esk1_0,esk3_0,esk7_0)), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_57, negated_conjecture, (r1_lattice3(esk2_0,esk4_0,esk8_0)\|r1_lattice3(esk1_0,esk3_0,esk7_0)), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_58, negated_conjecture, (~r1_orders_2(esk2_0,esk8_0,esk6_0)\|~r1_orders_2(esk1_0,esk7_0,esk5_0)), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_59, negated_conjecture, (m1_subset_1(esk7_0,u1_struct_0(esk1_0))\|~r1_orders_2(esk2_0,esk8_0,esk6_0)), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_60, negated_conjecture, (r1_lattice3(esk2_0,esk4_0,esk8_0)\|~r1_orders_2(esk1_0,esk7_0,esk5_0)), inference(evalgc,[status(thm)],[c_0_52])). cnf(c_0_61, negated_conjecture, (r1_orders_2(esk1_0,X1,esk5_0)\|~r1_lattice3(esk1_0,esk3_0,X1)\|~m1_subset_1(X1,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53, c_0_51]), c_0_48]), c_0_22])])])). cnf(c_0_62, negated_conjecture, (r1_lattice3(esk1_0,esk3_0,esk7_0)\|~r1_lattice3(esk2_0,esk4_0,esk8_0)\|~m1_subset_1(esk8_0,u1_struct_0(esk2_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_54, c_0_55])])). cnf(c_0_63, negated_conjecture, (m1_subset_1(esk8_0,u1_struct_0(esk2_0))\|r1_lattice3(esk1_0,esk3_0,esk7_0)), inference(evalgc,[status(thm)],[c_0_56])). cnf(c_0_64, negated_conjecture, (r1_lattice3(esk1_0,esk3_0,esk7_0)\|r1_lattice3(esk2_0,esk4_0,esk8_0)), inference(evalgc,[status(thm)],[c_0_57])). cnf(c_0_65, negated_conjecture, (r1_lattice3(esk2_0,esk4_0,esk8_0)\|m1_subset_1(esk7_0,u1_struct_0(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_66, negated_conjecture, (~r1_orders_2(esk1_0,esk7_0,esk5_0)\|~r1_orders_2(esk2_0,esk8_0,esk6_0)), inference(evalgc,[status(thm)],[c_0_58])). cnf(c_0_67, negated_conjecture, (m1_subset_1(esk8_0,u1_struct_0(esk2_0))\|~r1_orders_2(esk1_0,esk7_0,esk5_0)), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_68, negated_conjecture, (m1_subset_1(esk7_0,u1_struct_0(esk1_0))\|~r1_orders_2(esk2_0,esk8_0,esk6_0)), inference(evalgc,[status(thm)],[c_0_59])). cnf(c_0_69, negated_conjecture, (r1_lattice3(esk2_0,esk4_0,esk8_0)\|~r1_lattice3(esk1_0,esk3_0,esk7_0)\|~m1_subset_1(esk7_0,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_60, c_0_61])])). cnf(c_0_70, negated_conjecture, (r1_lattice3(esk1_0,esk3_0,esk7_0)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_62, c_0_63]), c_0_64])). cnf(c_0_71, negated_conjecture, (m1_subset_1(esk7_0,u1_struct_0(esk1_0))\|r1_lattice3(esk2_0,esk4_0,esk8_0)), inference(evalgc,[status(thm)],[c_0_65])). cnf(c_0_72, negated_conjecture, (m1_subset_1(esk8_0,u1_struct_0(esk2_0))\|m1_subset_1(esk7_0,u1_struct_0(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_73, negated_conjecture, (~r1_orders_2(esk2_0,esk8_0,esk6_0)\|~r1_lattice3(esk1_0,esk3_0,esk7_0)\|~m1_subset_1(esk7_0,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_66, c_0_61])])). cnf(c_0_74, negated_conjecture, (m1_subset_1(esk8_0,u1_struct_0(esk2_0))\|~r1_orders_2(esk1_0,esk7_0,esk5_0)), inference(evalgc,[status(thm)],[c_0_67])). cnf(c_0_75, negated_conjecture, (m1_subset_1(esk7_0,u1_struct_0(esk1_0))\|~r1_lattice3(esk2_0,esk4_0,esk8_0)\|~m1_subset_1(esk8_0,u1_struct_0(esk2_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_68, c_0_55])])). cnf(c_0_76, negated_conjecture, (r1_lattice3(esk2_0,esk4_0,esk8_0)), inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_69, c_0_70])]), c_0_71])). cnf(c_0_77, negated_conjecture, (m1_subset_1(esk7_0,u1_struct_0(esk1_0))\|m1_subset_1(esk8_0,u1_struct_0(esk2_0))), inference(evalgc,[status(thm)],[c_0_72])). cnf(c_0_78, negated_conjecture, (~r1_orders_2(esk2_0,esk8_0,esk6_0)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_73, c_0_68]), c_0_54])). cnf(c_0_79, negated_conjecture, (m1_subset_1(esk8_0,u1_struct_0(esk2_0))\|~r1_lattice3(esk1_0,esk3_0,esk7_0)\|~m1_subset_1(esk7_0,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_74, c_0_61])])). cnf(c_0_80, negated_conjecture, (m1_subset_1(esk7_0,u1_struct_0(esk1_0))), inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_75, c_0_76])]), c_0_77])). cnf(c_0_81, negated_conjecture, (~r1_lattice3(esk2_0,esk4_0,esk8_0)\|~m1_subset_1(esk8_0,u1_struct_0(esk2_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_78, c_0_55])])). cnf(c_0_82, negated_conjecture, (m1_subset_1(esk8_0,u1_struct_0(esk2_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_79, c_0_70]), c_0_80])])). cnf(c_0_83, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_81, c_0_76]), c_0_82])]), ['proof']). # SZS output end CNFRefutation	theorem Th36: for S1, S2 being antisymmetric non empty RelStr for D1 being Subset of S1, D2 being Subset of S2 for x being Element of S1, y being Element of S2 st ex_inf_of D1,S1 & ex_inf_of D2,S2 & for b being Element of [:S1,S2:] st b is_<=_than [:D1,D2:] holds [x,y] >= b holds (for c being Element of S1 st c is_<=_than D1 holds x >= c) & for d being Element of S2 st d is_<=_than D2 holds y >= d proof let S1, S2 be antisymmetric non empty RelStr, D1 be Subset of S1, D2 be Subset of S2, x be Element of S1, y be Element of S2 such that A1: ex_inf_of D1,S1 and A2: ex_inf_of D2,S2 and A3: for b being Element of [:S1,S2:] st b is_<=_than [:D1,D2:] holds [x, y] >= b; thus for c being Element of S1 st c is_<=_than D1 holds x >= c proof A4: inf D2 is_<=_than D2 by A2,YELLOW_0:31; let b be Element of S1; assume b is_<=_than D1; then [x,y] >= [b,inf D2] by A3,A4,Th33; hence thesis by Th11; end; A5: inf D1 is_<=_than D1 by A1,YELLOW_0:31; let b be Element of S2; assume b is_<=_than D2; then [x,y] >= [inf D1,b] by A3,A5,Th33; hence thesis by Th11; end;	Convert the following ATP output trace into a readable Mizar proof.
t23_graph_5	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t23_graph_5, conjecture, ![X1, X2, X3]:((~(v2_struct_0(X3))&l1_graph_1(X3))=>![X4]:(m2_finseq_1(X4,u4_struct_0(X3))=>![X5]:(m2_finseq_1(X5,u4_struct_0(X3))=>(r1_tarski(k7_subset_1(u1_struct_0(X3),k2_graph_5(X3,k8_finseq_1(u4_struct_0(X3),X4,X5)),X1),X2)=>(r1_tarski(k7_subset_1(u1_struct_0(X3),k2_graph_5(X3,X4),X1),X2)&r1_tarski(k7_subset_1(u1_struct_0(X3),k2_graph_5(X3,X5),X1),X2)))))), file('/scratch/mptp/predsminms1/t23_graph_5__0', t23_graph_5)). fof(redefinition_k8_finseq_1, axiom, ![X1, X2, X3]:((m1_finseq_1(X2,X1)&m1_finseq_1(X3,X1))=>k8_finseq_1(X1,X2,X3)=k7_finseq_1(X2,X3)), file('/scratch/mptp/predsminms1/t23_graph_5__0', redefinition_k8_finseq_1)). fof(redefinition_m2_finseq_1, axiom, ![X1, X2]:(m2_finseq_1(X2,X1)<=>m1_finseq_1(X2,X1)), file('/scratch/mptp/predsminms1/t23_graph_5__0', redefinition_m2_finseq_1)). fof(t22_graph_5, axiom, ![X1, X2, X3]:((~(v2_struct_0(X3))&l1_graph_1(X3))=>![X4]:(m2_finseq_1(X4,u4_struct_0(X3))=>![X5]:(m2_finseq_1(X5,u4_struct_0(X3))=>((r1_tarski(k10_xtuple_0(X4),k10_xtuple_0(X5))&r1_tarski(k7_subset_1(u1_struct_0(X3),k2_graph_5(X3,X5),X1),X2))=>r1_tarski(k7_subset_1(u1_struct_0(X3),k2_graph_5(X3,X4),X1),X2))))), file('/scratch/mptp/predsminms1/t23_graph_5__0', t22_graph_5)). fof(dt_m1_finseq_1, axiom, ![X1, X2]:(m1_finseq_1(X2,X1)=>(v1_relat_1(X2)&(v1_funct_1(X2)&v1_finseq_1(X2)))), file('/scratch/mptp/predsminms1/t23_graph_5__0', dt_m1_finseq_1)). fof(t30_finseq_1, axiom, ![X1]:((v1_relat_1(X1)&(v1_funct_1(X1)&v1_finseq_1(X1)))=>![X2]:((v1_relat_1(X2)&(v1_funct_1(X2)&v1_finseq_1(X2)))=>r1_tarski(k10_xtuple_0(X1),k10_xtuple_0(k7_finseq_1(X2,X1))))), file('/scratch/mptp/predsminms1/t23_graph_5__0', t30_finseq_1)). fof(t29_finseq_1, axiom, ![X1]:((v1_relat_1(X1)&(v1_funct_1(X1)&v1_finseq_1(X1)))=>![X2]:((v1_relat_1(X2)&(v1_funct_1(X2)&v1_finseq_1(X2)))=>r1_tarski(k10_xtuple_0(X1),k10_xtuple_0(k7_finseq_1(X1,X2))))), file('/scratch/mptp/predsminms1/t23_graph_5__0', t29_finseq_1)). fof(dt_k8_finseq_1, axiom, ![X1, X2, X3]:((m1_finseq_1(X2,X1)&m1_finseq_1(X3,X1))=>m2_finseq_1(k8_finseq_1(X1,X2,X3),X1)), file('/scratch/mptp/predsminms1/t23_graph_5__0', dt_k8_finseq_1)). fof(c_0_8, negated_conjecture, ~(![X1, X2, X3]:((~(v2_struct_0(X3))&l1_graph_1(X3))=>![X4]:(m2_finseq_1(X4,u4_struct_0(X3))=>![X5]:(m2_finseq_1(X5,u4_struct_0(X3))=>(r1_tarski(k7_subset_1(u1_struct_0(X3),k2_graph_5(X3,k8_finseq_1(u4_struct_0(X3),X4,X5)),X1),X2)=>(r1_tarski(k7_subset_1(u1_struct_0(X3),k2_graph_5(X3,X4),X1),X2)&r1_tarski(k7_subset_1(u1_struct_0(X3),k2_graph_5(X3,X5),X1),X2))))))), inference(assume_negation,[status(cth)],[t23_graph_5])). fof(c_0_9, negated_conjecture, ((~v2_struct_0(esk3_0)&l1_graph_1(esk3_0))&(m2_finseq_1(esk4_0,u4_struct_0(esk3_0))&(m2_finseq_1(esk5_0,u4_struct_0(esk3_0))&(r1_tarski(k7_subset_1(u1_struct_0(esk3_0),k2_graph_5(esk3_0,k8_finseq_1(u4_struct_0(esk3_0),esk4_0,esk5_0)),esk1_0),esk2_0)&(~r1_tarski(k7_subset_1(u1_struct_0(esk3_0),k2_graph_5(esk3_0,esk4_0),esk1_0),esk2_0)\|~r1_tarski(k7_subset_1(u1_struct_0(esk3_0),k2_graph_5(esk3_0,esk5_0),esk1_0),esk2_0)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_8])])])])). fof(c_0_10, plain, ![X17, X18, X19]:(~m1_finseq_1(X18,X17)\|~m1_finseq_1(X19,X17)\|k8_finseq_1(X17,X18,X19)=k7_finseq_1(X18,X19)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k8_finseq_1])])). fof(c_0_11, plain, ![X13, X14]:((~m2_finseq_1(X14,X13)\|m1_finseq_1(X14,X13))&(~m1_finseq_1(X14,X13)\|m2_finseq_1(X14,X13))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_finseq_1])])). cnf(c_0_12, negated_conjecture, (r1_tarski(k7_subset_1(u1_struct_0(esk3_0),k2_graph_5(esk3_0,k8_finseq_1(u4_struct_0(esk3_0),esk4_0,esk5_0)),esk1_0),esk2_0)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_13, plain, (k8_finseq_1(X2,X1,X3)=k7_finseq_1(X1,X3)\|~m1_finseq_1(X1,X2)\|~m1_finseq_1(X3,X2)), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_14, plain, (m1_finseq_1(X1,X2)\|~m2_finseq_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_15, negated_conjecture, (m2_finseq_1(esk5_0,u4_struct_0(esk3_0))), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_16, negated_conjecture, (m2_finseq_1(esk4_0,u4_struct_0(esk3_0))), inference(split_conjunct,[status(thm)],[c_0_9])). fof(c_0_17, plain, ![X25, X26, X27, X28, X29]:(v2_struct_0(X27)\|~l1_graph_1(X27)\|(~m2_finseq_1(X28,u4_struct_0(X27))\|(~m2_finseq_1(X29,u4_struct_0(X27))\|(~r1_tarski(k10_xtuple_0(X28),k10_xtuple_0(X29))\|~r1_tarski(k7_subset_1(u1_struct_0(X27),k2_graph_5(X27,X29),X25),X26)\|r1_tarski(k7_subset_1(u1_struct_0(X27),k2_graph_5(X27,X28),X25),X26))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t22_graph_5])])])])). cnf(c_0_18, negated_conjecture, (r1_tarski(k7_subset_1(u1_struct_0(esk3_0),k2_graph_5(esk3_0,k8_finseq_1(u4_struct_0(esk3_0),esk4_0,esk5_0)),esk1_0),esk2_0)), inference(evalgc,[status(thm)],[c_0_12])). cnf(c_0_19, plain, (k8_finseq_1(X2,X1,X3)=k7_finseq_1(X1,X3)\|~m1_finseq_1(X3,X2)\|~m1_finseq_1(X1,X2)), inference(evalgc,[status(thm)],[c_0_13])). cnf(c_0_20, plain, (m1_finseq_1(X1,X2)\|~m2_finseq_1(X1,X2)), inference(evalgc,[status(thm)],[c_0_14])). cnf(c_0_21, negated_conjecture, (m2_finseq_1(esk5_0,u4_struct_0(esk3_0))), inference(evalgc,[status(thm)],[c_0_15])). cnf(c_0_22, negated_conjecture, (m2_finseq_1(esk4_0,u4_struct_0(esk3_0))), inference(evalgc,[status(thm)],[c_0_16])). cnf(c_0_23, plain, (v2_struct_0(X1)\|r1_tarski(k7_subset_1(u1_struct_0(X1),k2_graph_5(X1,X2),X4),X5)\|~l1_graph_1(X1)\|~m2_finseq_1(X2,u4_struct_0(X1))\|~m2_finseq_1(X3,u4_struct_0(X1))\|~r1_tarski(k10_xtuple_0(X2),k10_xtuple_0(X3))\|~r1_tarski(k7_subset_1(u1_struct_0(X1),k2_graph_5(X1,X3),X4),X5)), inference(split_conjunct,[status(thm)],[c_0_17])). cnf(c_0_24, negated_conjecture, (r1_tarski(k7_subset_1(u1_struct_0(esk3_0),k2_graph_5(esk3_0,k7_finseq_1(esk4_0,esk5_0)),esk1_0),esk2_0)\|~m1_finseq_1(esk5_0,u4_struct_0(esk3_0))\|~m1_finseq_1(esk4_0,u4_struct_0(esk3_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_18, c_0_19])])). cnf(c_0_25, negated_conjecture, (m1_finseq_1(esk5_0,u4_struct_0(esk3_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_20, c_0_21])])). cnf(c_0_26, negated_conjecture, (m1_finseq_1(esk4_0,u4_struct_0(esk3_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_20, c_0_22])])). cnf(c_0_27, negated_conjecture, (l1_graph_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_28, negated_conjecture, (~v2_struct_0(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_29, negated_conjecture, (~r1_tarski(k7_subset_1(u1_struct_0(esk3_0),k2_graph_5(esk3_0,esk4_0),esk1_0),esk2_0)\|~r1_tarski(k7_subset_1(u1_struct_0(esk3_0),k2_graph_5(esk3_0,esk5_0),esk1_0),esk2_0)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_30, plain, (v2_struct_0(X1)\|r1_tarski(k7_subset_1(u1_struct_0(X1),k2_graph_5(X1,X2),X4),X5)\|~l1_graph_1(X1)\|~m2_finseq_1(X3,u4_struct_0(X1))\|~m2_finseq_1(X2,u4_struct_0(X1))\|~r1_tarski(k10_xtuple_0(X2),k10_xtuple_0(X3))\|~r1_tarski(k7_subset_1(u1_struct_0(X1),k2_graph_5(X1,X3),X4),X5)), inference(evalgc,[status(thm)],[c_0_23])). cnf(c_0_31, negated_conjecture, (r1_tarski(k7_subset_1(u1_struct_0(esk3_0),k2_graph_5(esk3_0,k7_finseq_1(esk4_0,esk5_0)),esk1_0),esk2_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24, c_0_25]), c_0_26])])). cnf(c_0_32, negated_conjecture, (l1_graph_1(esk3_0)), inference(evalgc,[status(thm)],[c_0_27])). cnf(c_0_33, negated_conjecture, (~v2_struct_0(esk3_0)), inference(evalgc,[status(thm)],[c_0_28])). fof(c_0_34, plain, ![X11, X12]:((v1_relat_1(X12)\|~m1_finseq_1(X12,X11))&((v1_funct_1(X12)\|~m1_finseq_1(X12,X11))&(v1_finseq_1(X12)\|~m1_finseq_1(X12,X11)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m1_finseq_1])])])). cnf(c_0_35, negated_conjecture, (~r1_tarski(k7_subset_1(u1_struct_0(esk3_0),k2_graph_5(esk3_0,esk4_0),esk1_0),esk2_0)\|~r1_tarski(k7_subset_1(u1_struct_0(esk3_0),k2_graph_5(esk3_0,esk5_0),esk1_0),esk2_0)), inference(evalgc,[status(thm)],[c_0_29])). cnf(c_0_36, negated_conjecture, (r1_tarski(k7_subset_1(u1_struct_0(esk3_0),k2_graph_5(esk3_0,X1),esk1_0),esk2_0)\|~r1_tarski(k10_xtuple_0(X1),k10_xtuple_0(k7_finseq_1(esk4_0,esk5_0)))\|~m2_finseq_1(k7_finseq_1(esk4_0,esk5_0),u4_struct_0(esk3_0))\|~m2_finseq_1(X1,u4_struct_0(esk3_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30, c_0_31]), c_0_32])]), c_0_33])])). fof(c_0_37, plain, ![X15, X16]:(~v1_relat_1(X15)\|(~v1_funct_1(X15)\|~v1_finseq_1(X15))\|(~v1_relat_1(X16)\|(~v1_funct_1(X16)\|~v1_finseq_1(X16))\|r1_tarski(k10_xtuple_0(X15),k10_xtuple_0(k7_finseq_1(X16,X15))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t30_finseq_1])])])). cnf(c_0_38, plain, (v1_finseq_1(X1)\|~m1_finseq_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_34])). cnf(c_0_39, plain, (v1_funct_1(X1)\|~m1_finseq_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_34])). cnf(c_0_40, plain, (v1_relat_1(X1)\|~m1_finseq_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_34])). cnf(c_0_41, negated_conjecture, (~r1_tarski(k7_subset_1(u1_struct_0(esk3_0),k2_graph_5(esk3_0,esk4_0),esk1_0),esk2_0)\|~r1_tarski(k10_xtuple_0(esk5_0),k10_xtuple_0(k7_finseq_1(esk4_0,esk5_0)))\|~m2_finseq_1(k7_finseq_1(esk4_0,esk5_0),u4_struct_0(esk3_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35, c_0_36]), c_0_21])])])). cnf(c_0_42, plain, (r1_tarski(k10_xtuple_0(X1),k10_xtuple_0(k7_finseq_1(X2,X1)))\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v1_finseq_1(X1)\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v1_finseq_1(X2)), inference(split_conjunct,[status(thm)],[c_0_37])). cnf(c_0_43, plain, (v1_finseq_1(X1)\|~m1_finseq_1(X1,X2)), inference(evalgc,[status(thm)],[c_0_38])). cnf(c_0_44, plain, (v1_funct_1(X1)\|~m1_finseq_1(X1,X2)), inference(evalgc,[status(thm)],[c_0_39])). cnf(c_0_45, plain, (v1_relat_1(X1)\|~m1_finseq_1(X1,X2)), inference(evalgc,[status(thm)],[c_0_40])). fof(c_0_46, plain, ![X20, X21]:(~v1_relat_1(X20)\|(~v1_funct_1(X20)\|~v1_finseq_1(X20))\|(~v1_relat_1(X21)\|(~v1_funct_1(X21)\|~v1_finseq_1(X21))\|r1_tarski(k10_xtuple_0(X20),k10_xtuple_0(k7_finseq_1(X20,X21))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t29_finseq_1])])])). fof(c_0_47, plain, ![X22, X23, X24]:(~m1_finseq_1(X23,X22)\|~m1_finseq_1(X24,X22)\|m2_finseq_1(k8_finseq_1(X22,X23,X24),X22)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k8_finseq_1])])). cnf(c_0_48, negated_conjecture, (~r1_tarski(k10_xtuple_0(esk5_0),k10_xtuple_0(k7_finseq_1(esk4_0,esk5_0)))\|~m2_finseq_1(k7_finseq_1(esk4_0,esk5_0),u4_struct_0(esk3_0))\|~r1_tarski(k10_xtuple_0(esk4_0),k10_xtuple_0(k7_finseq_1(esk4_0,esk5_0)))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41, c_0_36]), c_0_22])])])). cnf(c_0_49, plain, (r1_tarski(k10_xtuple_0(X1),k10_xtuple_0(k7_finseq_1(X2,X1)))\|~v1_relat_1(X2)\|~v1_relat_1(X1)\|~v1_funct_1(X2)\|~v1_funct_1(X1)\|~v1_finseq_1(X2)\|~v1_finseq_1(X1)), inference(evalgc,[status(thm)],[c_0_42])). cnf(c_0_50, negated_conjecture, (v1_finseq_1(esk4_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_43, c_0_26])])). cnf(c_0_51, negated_conjecture, (v1_finseq_1(esk5_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_43, c_0_25])])). cnf(c_0_52, negated_conjecture, (v1_funct_1(esk4_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_44, c_0_26])])). cnf(c_0_53, negated_conjecture, (v1_funct_1(esk5_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_44, c_0_25])])). cnf(c_0_54, negated_conjecture, (v1_relat_1(esk4_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_45, c_0_26])])). cnf(c_0_55, negated_conjecture, (v1_relat_1(esk5_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_45, c_0_25])])). cnf(c_0_56, plain, (r1_tarski(k10_xtuple_0(X1),k10_xtuple_0(k7_finseq_1(X1,X2)))\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v1_finseq_1(X1)\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v1_finseq_1(X2)), inference(split_conjunct,[status(thm)],[c_0_46])). cnf(c_0_57, plain, (m2_finseq_1(k8_finseq_1(X2,X1,X3),X2)\|~m1_finseq_1(X1,X2)\|~m1_finseq_1(X3,X2)), inference(split_conjunct,[status(thm)],[c_0_47])). cnf(c_0_58, negated_conjecture, (~r1_tarski(k10_xtuple_0(esk4_0),k10_xtuple_0(k7_finseq_1(esk4_0,esk5_0)))\|~m2_finseq_1(k7_finseq_1(esk4_0,esk5_0),u4_struct_0(esk3_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48, c_0_49]), c_0_50]), c_0_51]), c_0_52]), c_0_53]), c_0_54]), c_0_55])])])). cnf(c_0_59, plain, (r1_tarski(k10_xtuple_0(X1),k10_xtuple_0(k7_finseq_1(X1,X2)))\|~v1_relat_1(X2)\|~v1_relat_1(X1)\|~v1_funct_1(X2)\|~v1_funct_1(X1)\|~v1_finseq_1(X2)\|~v1_finseq_1(X1)), inference(evalgc,[status(thm)],[c_0_56])). cnf(c_0_60, plain, (m2_finseq_1(k8_finseq_1(X2,X1,X3),X2)\|~m1_finseq_1(X3,X2)\|~m1_finseq_1(X1,X2)), inference(evalgc,[status(thm)],[c_0_57])). cnf(c_0_61, negated_conjecture, (~m2_finseq_1(k7_finseq_1(esk4_0,esk5_0),u4_struct_0(esk3_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58, c_0_59]), c_0_51]), c_0_50]), c_0_53]), c_0_52]), c_0_55]), c_0_54])])])). cnf(c_0_62, plain, (m2_finseq_1(k7_finseq_1(X2,X3),X1)\|~m1_finseq_1(X3,X1)\|~m1_finseq_1(X2,X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_60, c_0_19])])). cnf(c_0_63, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61, c_0_62]), c_0_25]), c_0_26])]), ['proof']). # SZS output end CNFRefutation	reserve n,m,i,j,k for Element of NAT, x,y,e,X,V,U for set, W,f,g for Function; reserve p,q for FinSequence; reserve G for Graph, pe,qe for FinSequence of the carrier' of G; theorem Th23: vertices(pe^qe) \ X c= V implies vertices(pe) \ X c= V & vertices(qe) \ X c= V proof A1: rng pe c= rng(pe^qe) & rng qe c= rng(pe^qe) by FINSEQ_1:29,30; assume vertices(pe^qe) \ X c= V; hence thesis by A1,Th22; end;	Convert the following ATP output trace into a readable Mizar proof.
t75_exchsort	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t12_funct_5, axiom, ![X1, X2]:(k9_xtuple_0(k1_tarski(k4_tarski(X1,X2)))=k1_tarski(X1)&k10_xtuple_0(k1_tarski(k4_tarski(X1,X2)))=k1_tarski(X2)), file('/scratch/mptp/predsminms1/t75_exchsort__0', t12_funct_5)). fof(d5_tarski, axiom, ![X1, X2]:k4_tarski(X1,X2)=k2_tarski(k2_tarski(X1,X2),k1_tarski(X1)), file('/scratch/mptp/predsminms1/t75_exchsort__0', d5_tarski)). fof(commutativity_k2_tarski, axiom, ![X1, X2]:k2_tarski(X1,X2)=k2_tarski(X2,X1), file('/scratch/mptp/predsminms1/t75_exchsort__0', commutativity_k2_tarski)). fof(fc1_funct_1, axiom, ![X1, X2]:v1_funct_1(k1_tarski(k4_tarski(X1,X2))), file('/scratch/mptp/predsminms1/t75_exchsort__0', fc1_funct_1)). fof(fc5_relat_1, axiom, ![X1, X2]:v1_relat_1(k1_tarski(k4_tarski(X1,X2))), file('/scratch/mptp/predsminms1/t75_exchsort__0', fc5_relat_1)). fof(d4_exchsort, axiom, ![X1]:((v1_relat_1(X1)&v1_funct_1(X1))=>![X2]:(v3_ordinal1(X2)=>((?[X3]:(v3_ordinal1(X3)&r2_hidden(X3,k9_xtuple_0(X1)))=>(X2=k1_exchsort(X1)<=>v2_exchsort(X1,X2)))&(![X3]:(v3_ordinal1(X3)=>~(r2_hidden(X3,k9_xtuple_0(X1))))=>(X2=k1_exchsort(X1)<=>X2=k1_xboole_0))))), file('/scratch/mptp/predsminms1/t75_exchsort__0', d4_exchsort)). fof(fc6_exchsort, axiom, ![X1, X2]:(v3_ordinal1(X1)=>(v1_relat_1(k1_tarski(k4_tarski(X1,X2)))&(v1_funct_1(k1_tarski(k4_tarski(X1,X2)))&(v1_exchsort(k1_tarski(k4_tarski(X1,X2)))&(v2_exchsort(k1_tarski(k4_tarski(X1,X2)),X1)&v3_exchsort(k1_tarski(k4_tarski(X1,X2)),k1_ordinal1(X1))))))), file('/scratch/mptp/predsminms1/t75_exchsort__0', fc6_exchsort)). fof(t6_grfunc_1, axiom, ![X1, X2, X3]:((v1_relat_1(X3)&v1_funct_1(X3))=>(X3=k1_tarski(k4_tarski(X1,X2))=>k1_funct_1(X3,X1)=X2)), file('/scratch/mptp/predsminms1/t75_exchsort__0', t6_grfunc_1)). fof(d1_tarski, axiom, ![X1, X2]:(X2=k1_tarski(X1)<=>![X3]:(r2_hidden(X3,X2)<=>X3=X1)), file('/scratch/mptp/predsminms1/t75_exchsort__0', d1_tarski)). fof(t75_exchsort, conjecture, ![X1]:(v3_ordinal1(X1)=>![X2]:((~(v2_struct_0(X2))&(v3_orders_2(X2)&(v4_orders_2(X2)&(v5_orders_2(X2)&(v16_waybel_0(X2)&l1_orders_2(X2))))))=>![X3]:((v1_relat_1(X3)&(v5_relat_1(X3,u1_struct_0(X2))&(v1_funct_1(X3)&v1_exchsort(X3))))=>m2_exchsort(k1_tarski(k4_tarski(X1,X3)),X2,X3)))), file('/scratch/mptp/predsminms1/t75_exchsort__0', t75_exchsort)). fof(fc2_xboole_0, axiom, ![X1]:~(v1_xboole_0(k1_tarski(X1))), file('/scratch/mptp/predsminms1/t75_exchsort__0', fc2_xboole_0)). fof(d1_ordinal1, axiom, ![X1]:k1_ordinal1(X1)=k2_xboole_0(X1,k1_tarski(X1)), file('/scratch/mptp/predsminms1/t75_exchsort__0', d1_ordinal1)). fof(d14_exchsort, axiom, ![X1]:((~(v2_struct_0(X1))&(v3_orders_2(X1)&(v4_orders_2(X1)&(v5_orders_2(X1)&(v16_waybel_0(X1)&l1_orders_2(X1))))))=>![X2]:((v1_relat_1(X2)&(v5_relat_1(X2,u1_struct_0(X1))&(v1_funct_1(X2)&v1_exchsort(X2))))=>![X3]:((~(v1_xboole_0(X3))&(v1_relat_1(X3)&(v1_funct_1(X3)&v1_exchsort(X3))))=>(m2_exchsort(X3,X1,X2)<=>(k1_funct_1(X3,k1_exchsort(X3))=X2&(![X4]:(v3_ordinal1(X4)=>(r2_hidden(X4,k9_xtuple_0(X3))=>(v1_relat_1(k1_funct_1(X3,X4))&(v5_relat_1(k1_funct_1(X3,X4),u1_struct_0(X1))&(v1_funct_1(k1_funct_1(X3,X4))&v1_exchsort(k1_funct_1(X3,X4)))))))&![X4]:(v3_ordinal1(X4)=>~((r2_hidden(X4,k9_xtuple_0(X3))&(r2_hidden(k1_ordinal1(X4),k9_xtuple_0(X3))&![X5]:((v1_relat_1(X5)&(v5_relat_1(X5,u1_struct_0(X1))&(v1_funct_1(X5)&v1_exchsort(X5))))=>![X6, X7]:~((r2_hidden(k4_tarski(X6,X7),k6_exchsort(X1,X5))&(k1_funct_1(X3,X4)=X5&k1_funct_1(X3,k1_ordinal1(X4))=k10_funct_7(X5,X6,X7))))))))))))))), file('/scratch/mptp/predsminms1/t75_exchsort__0', d14_exchsort)). fof(t6_ordinal1, axiom, ![X1]:r2_hidden(X1,k1_ordinal1(X1)), file('/scratch/mptp/predsminms1/t75_exchsort__0', t6_ordinal1)). fof(antisymmetry_r2_hidden, axiom, ![X1, X2]:(r2_hidden(X1,X2)=>~(r2_hidden(X2,X1))), file('/scratch/mptp/predsminms1/t75_exchsort__0', antisymmetry_r2_hidden)). fof(c_0_15, plain, ![X29, X30]:(k9_xtuple_0(k1_tarski(k4_tarski(X29,X30)))=k1_tarski(X29)&k10_xtuple_0(k1_tarski(k4_tarski(X29,X30)))=k1_tarski(X30)), inference(variable_rename,[status(thm)],[t12_funct_5])). fof(c_0_16, plain, ![X20, X21]:k4_tarski(X20,X21)=k2_tarski(k2_tarski(X20,X21),k1_tarski(X20)), inference(variable_rename,[status(thm)],[d5_tarski])). cnf(c_0_17, plain, (k9_xtuple_0(k1_tarski(k4_tarski(X1,X2)))=k1_tarski(X1)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_18, plain, (k4_tarski(X1,X2)=k2_tarski(k2_tarski(X1,X2),k1_tarski(X1))), inference(split_conjunct,[status(thm)],[c_0_16])). fof(c_0_19, plain, ![X18, X19]:k2_tarski(X18,X19)=k2_tarski(X19,X18), inference(variable_rename,[status(thm)],[commutativity_k2_tarski])). fof(c_0_20, plain, ![X22, X23]:v1_funct_1(k1_tarski(k4_tarski(X22,X23))), inference(variable_rename,[status(thm)],[fc1_funct_1])). fof(c_0_21, plain, ![X25, X26]:v1_relat_1(k1_tarski(k4_tarski(X25,X26))), inference(variable_rename,[status(thm)],[fc5_relat_1])). fof(c_0_22, plain, ![X36, X37, X38]:(((X37!=k1_exchsort(X36)\|v2_exchsort(X36,X37)\|(~v3_ordinal1(X38)\|~r2_hidden(X38,k9_xtuple_0(X36)))\|~v3_ordinal1(X37)\|(~v1_relat_1(X36)\|~v1_funct_1(X36)))&(~v2_exchsort(X36,X37)\|X37=k1_exchsort(X36)\|(~v3_ordinal1(X38)\|~r2_hidden(X38,k9_xtuple_0(X36)))\|~v3_ordinal1(X37)\|(~v1_relat_1(X36)\|~v1_funct_1(X36))))&(((X37!=k1_exchsort(X36)\|X37=k1_xboole_0\|v3_ordinal1(esk5_2(X36,X37))\|~v3_ordinal1(X37)\|(~v1_relat_1(X36)\|~v1_funct_1(X36)))&(X37!=k1_xboole_0\|X37=k1_exchsort(X36)\|v3_ordinal1(esk5_2(X36,X37))\|~v3_ordinal1(X37)\|(~v1_relat_1(X36)\|~v1_funct_1(X36))))&((X37!=k1_exchsort(X36)\|X37=k1_xboole_0\|r2_hidden(esk5_2(X36,X37),k9_xtuple_0(X36))\|~v3_ordinal1(X37)\|(~v1_relat_1(X36)\|~v1_funct_1(X36)))&(X37!=k1_xboole_0\|X37=k1_exchsort(X36)\|r2_hidden(esk5_2(X36,X37),k9_xtuple_0(X36))\|~v3_ordinal1(X37)\|(~v1_relat_1(X36)\|~v1_funct_1(X36)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d4_exchsort])])])])])])). cnf(c_0_23, plain, (k9_xtuple_0(k1_tarski(k2_tarski(k2_tarski(X1,X2),k1_tarski(X1))))=k1_tarski(X1)), inference(rw,[status(thm)],[c_0_17, c_0_18])). cnf(c_0_24, plain, (k2_tarski(X1,X2)=k2_tarski(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_19])). cnf(c_0_25, plain, (v1_funct_1(k1_tarski(k4_tarski(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_20])). cnf(c_0_26, plain, (v1_relat_1(k1_tarski(k4_tarski(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_21])). fof(c_0_27, plain, ![X34, X35]:((v1_relat_1(k1_tarski(k4_tarski(X34,X35)))\|~v3_ordinal1(X34))&((v1_funct_1(k1_tarski(k4_tarski(X34,X35)))\|~v3_ordinal1(X34))&((v1_exchsort(k1_tarski(k4_tarski(X34,X35)))\|~v3_ordinal1(X34))&((v2_exchsort(k1_tarski(k4_tarski(X34,X35)),X34)\|~v3_ordinal1(X34))&(v3_exchsort(k1_tarski(k4_tarski(X34,X35)),k1_ordinal1(X34))\|~v3_ordinal1(X34)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc6_exchsort])])])). fof(c_0_28, plain, ![X2, X1]:(epred1_2(X1,X2)<=>![X3]:((~(v1_xboole_0(X3))&(v1_relat_1(X3)&(v1_funct_1(X3)&v1_exchsort(X3))))=>(m2_exchsort(X3,X1,X2)<=>(k1_funct_1(X3,k1_exchsort(X3))=X2&(![X4]:(v3_ordinal1(X4)=>(r2_hidden(X4,k9_xtuple_0(X3))=>(v1_relat_1(k1_funct_1(X3,X4))&(v5_relat_1(k1_funct_1(X3,X4),u1_struct_0(X1))&(v1_funct_1(k1_funct_1(X3,X4))&v1_exchsort(k1_funct_1(X3,X4)))))))&![X4]:(v3_ordinal1(X4)=>~((r2_hidden(X4,k9_xtuple_0(X3))&(r2_hidden(k1_ordinal1(X4),k9_xtuple_0(X3))&![X5]:((v1_relat_1(X5)&(v5_relat_1(X5,u1_struct_0(X1))&(v1_funct_1(X5)&v1_exchsort(X5))))=>![X6, X7]:~((r2_hidden(k4_tarski(X6,X7),k6_exchsort(X1,X5))&(k1_funct_1(X3,X4)=X5&k1_funct_1(X3,k1_ordinal1(X4))=k10_funct_7(X5,X6,X7)))))))))))))), introduced(definition)). cnf(c_0_29, plain, (X2=k1_exchsort(X1)\|~v2_exchsort(X1,X2)\|~v3_ordinal1(X3)\|~r2_hidden(X3,k9_xtuple_0(X1))\|~v3_ordinal1(X2)\|~v1_relat_1(X1)\|~v1_funct_1(X1)), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_30, plain, (k9_xtuple_0(k1_tarski(k2_tarski(k2_tarski(X1,X2),k1_tarski(X1))))=k1_tarski(X1)), inference(evalgc,[status(thm)],[c_0_23])). cnf(c_0_31, plain, (k2_tarski(X1,X2)=k2_tarski(X2,X1)), inference(evalgc,[status(thm)],[c_0_24])). cnf(c_0_32, plain, (v1_funct_1(k1_tarski(k2_tarski(k2_tarski(X1,X2),k1_tarski(X1))))), inference(rw,[status(thm)],[c_0_25, c_0_18])). cnf(c_0_33, plain, (v1_relat_1(k1_tarski(k2_tarski(k2_tarski(X1,X2),k1_tarski(X1))))), inference(rw,[status(thm)],[c_0_26, c_0_18])). cnf(c_0_34, plain, (v2_exchsort(k1_tarski(k4_tarski(X1,X2)),X1)\|~v3_ordinal1(X1)), inference(split_conjunct,[status(thm)],[c_0_27])). fof(c_0_35, plain, ![X31, X32, X33]:(~v1_relat_1(X33)\|~v1_funct_1(X33)\|(X33!=k1_tarski(k4_tarski(X31,X32))\|k1_funct_1(X33,X31)=X32)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_grfunc_1])])). fof(c_0_36, plain, ![X2, X1]:(epred1_2(X1,X2)=>![X3]:((~(v1_xboole_0(X3))&(v1_relat_1(X3)&(v1_funct_1(X3)&v1_exchsort(X3))))=>(m2_exchsort(X3,X1,X2)<=>(k1_funct_1(X3,k1_exchsort(X3))=X2&(![X4]:(v3_ordinal1(X4)=>(r2_hidden(X4,k9_xtuple_0(X3))=>(v1_relat_1(k1_funct_1(X3,X4))&(v5_relat_1(k1_funct_1(X3,X4),u1_struct_0(X1))&(v1_funct_1(k1_funct_1(X3,X4))&v1_exchsort(k1_funct_1(X3,X4)))))))&![X4]:(v3_ordinal1(X4)=>~((r2_hidden(X4,k9_xtuple_0(X3))&(r2_hidden(k1_ordinal1(X4),k9_xtuple_0(X3))&![X5]:((v1_relat_1(X5)&(v5_relat_1(X5,u1_struct_0(X1))&(v1_funct_1(X5)&v1_exchsort(X5))))=>![X6, X7]:~((r2_hidden(k4_tarski(X6,X7),k6_exchsort(X1,X5))&(k1_funct_1(X3,X4)=X5&k1_funct_1(X3,k1_ordinal1(X4))=k10_funct_7(X5,X6,X7)))))))))))))), inference(split_equiv,[status(thm)],[c_0_28])). cnf(c_0_37, plain, (X2=k1_exchsort(X1)\|~v3_ordinal1(X3)\|~v3_ordinal1(X2)\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v2_exchsort(X1,X2)\|~r2_hidden(X3,k9_xtuple_0(X1))), inference(evalgc,[status(thm)],[c_0_29])). cnf(c_0_38, plain, (k9_xtuple_0(k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X1,X2))))=k1_tarski(X1)), inference(rw,[status(thm)],[c_0_30, c_0_31])). cnf(c_0_39, plain, (v1_funct_1(k1_tarski(k2_tarski(k2_tarski(X1,X2),k1_tarski(X1))))), inference(evalgc,[status(thm)],[c_0_32])). cnf(c_0_40, plain, (v1_relat_1(k1_tarski(k2_tarski(k2_tarski(X1,X2),k1_tarski(X1))))), inference(evalgc,[status(thm)],[c_0_33])). cnf(c_0_41, plain, (v2_exchsort(k1_tarski(k2_tarski(k2_tarski(X1,X2),k1_tarski(X1))),X1)\|~v3_ordinal1(X1)), inference(rw,[status(thm)],[c_0_34, c_0_18])). fof(c_0_42, plain, ![X11, X12, X13, X14, X15, X16]:(((~r2_hidden(X13,X12)\|X13=X11\|X12!=k1_tarski(X11))&(X14!=X11\|r2_hidden(X14,X12)\|X12!=k1_tarski(X11)))&((~r2_hidden(esk4_2(X15,X16),X16)\|esk4_2(X15,X16)!=X15\|X16=k1_tarski(X15))&(r2_hidden(esk4_2(X15,X16),X16)\|esk4_2(X15,X16)=X15\|X16=k1_tarski(X15)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_tarski])])])])])])). cnf(c_0_43, plain, (k1_funct_1(X1,X2)=X3\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|X1!=k1_tarski(k4_tarski(X2,X3))), inference(split_conjunct,[status(thm)],[c_0_35])). fof(c_0_44, plain, ![X44, X45, X46, X47, X48, X54, X55, X56]:(((k1_funct_1(X46,k1_exchsort(X46))=X44\|~m2_exchsort(X46,X45,X44)\|(v1_xboole_0(X46)\|(~v1_relat_1(X46)\|(~v1_funct_1(X46)\|~v1_exchsort(X46))))\|~epred1_2(X45,X44))&(((v1_relat_1(k1_funct_1(X46,X47))\|~r2_hidden(X47,k9_xtuple_0(X46))\|~v3_ordinal1(X47)\|~m2_exchsort(X46,X45,X44)\|(v1_xboole_0(X46)\|(~v1_relat_1(X46)\|(~v1_funct_1(X46)\|~v1_exchsort(X46))))\|~epred1_2(X45,X44))&((v5_relat_1(k1_funct_1(X46,X47),u1_struct_0(X45))\|~r2_hidden(X47,k9_xtuple_0(X46))\|~v3_ordinal1(X47)\|~m2_exchsort(X46,X45,X44)\|(v1_xboole_0(X46)\|(~v1_relat_1(X46)\|(~v1_funct_1(X46)\|~v1_exchsort(X46))))\|~epred1_2(X45,X44))&((v1_funct_1(k1_funct_1(X46,X47))\|~r2_hidden(X47,k9_xtuple_0(X46))\|~v3_ordinal1(X47)\|~m2_exchsort(X46,X45,X44)\|(v1_xboole_0(X46)\|(~v1_relat_1(X46)\|(~v1_funct_1(X46)\|~v1_exchsort(X46))))\|~epred1_2(X45,X44))&(v1_exchsort(k1_funct_1(X46,X47))\|~r2_hidden(X47,k9_xtuple_0(X46))\|~v3_ordinal1(X47)\|~m2_exchsort(X46,X45,X44)\|(v1_xboole_0(X46)\|(~v1_relat_1(X46)\|(~v1_funct_1(X46)\|~v1_exchsort(X46))))\|~epred1_2(X45,X44)))))&(((v1_relat_1(esk6_4(X44,X45,X46,X48))\|~r2_hidden(k1_ordinal1(X48),k9_xtuple_0(X46))\|~r2_hidden(X48,k9_xtuple_0(X46))\|~v3_ordinal1(X48)\|~m2_exchsort(X46,X45,X44)\|(v1_xboole_0(X46)\|(~v1_relat_1(X46)\|(~v1_funct_1(X46)\|~v1_exchsort(X46))))\|~epred1_2(X45,X44))&((v5_relat_1(esk6_4(X44,X45,X46,X48),u1_struct_0(X45))\|~r2_hidden(k1_ordinal1(X48),k9_xtuple_0(X46))\|~r2_hidden(X48,k9_xtuple_0(X46))\|~v3_ordinal1(X48)\|~m2_exchsort(X46,X45,X44)\|(v1_xboole_0(X46)\|(~v1_relat_1(X46)\|(~v1_funct_1(X46)\|~v1_exchsort(X46))))\|~epred1_2(X45,X44))&((v1_funct_1(esk6_4(X44,X45,X46,X48))\|~r2_hidden(k1_ordinal1(X48),k9_xtuple_0(X46))\|~r2_hidden(X48,k9_xtuple_0(X46))\|~v3_ordinal1(X48)\|~m2_exchsort(X46,X45,X44)\|(v1_xboole_0(X46)\|(~v1_relat_1(X46)\|(~v1_funct_1(X46)\|~v1_exchsort(X46))))\|~epred1_2(X45,X44))&(v1_exchsort(esk6_4(X44,X45,X46,X48))\|~r2_hidden(k1_ordinal1(X48),k9_xtuple_0(X46))\|~r2_hidden(X48,k9_xtuple_0(X46))\|~v3_ordinal1(X48)\|~m2_exchsort(X46,X45,X44)\|(v1_xboole_0(X46)\|(~v1_relat_1(X46)\|(~v1_funct_1(X46)\|~v1_exchsort(X46))))\|~epred1_2(X45,X44)))))&((r2_hidden(k4_tarski(esk7_4(X44,X45,X46,X48),esk8_4(X44,X45,X46,X48)),k6_exchsort(X45,esk6_4(X44,X45,X46,X48)))\|~r2_hidden(k1_ordinal1(X48),k9_xtuple_0(X46))\|~r2_hidden(X48,k9_xtuple_0(X46))\|~v3_ordinal1(X48)\|~m2_exchsort(X46,X45,X44)\|(v1_xboole_0(X46)\|(~v1_relat_1(X46)\|(~v1_funct_1(X46)\|~v1_exchsort(X46))))\|~epred1_2(X45,X44))&((k1_funct_1(X46,X48)=esk6_4(X44,X45,X46,X48)\|~r2_hidden(k1_ordinal1(X48),k9_xtuple_0(X46))\|~r2_hidden(X48,k9_xtuple_0(X46))\|~v3_ordinal1(X48)\|~m2_exchsort(X46,X45,X44)\|(v1_xboole_0(X46)\|(~v1_relat_1(X46)\|(~v1_funct_1(X46)\|~v1_exchsort(X46))))\|~epred1_2(X45,X44))&(k1_funct_1(X46,k1_ordinal1(X48))=k10_funct_7(esk6_4(X44,X45,X46,X48),esk7_4(X44,X45,X46,X48),esk8_4(X44,X45,X46,X48))\|~r2_hidden(k1_ordinal1(X48),k9_xtuple_0(X46))\|~r2_hidden(X48,k9_xtuple_0(X46))\|~v3_ordinal1(X48)\|~m2_exchsort(X46,X45,X44)\|(v1_xboole_0(X46)\|(~v1_relat_1(X46)\|(~v1_funct_1(X46)\|~v1_exchsort(X46))))\|~epred1_2(X45,X44)))))))&(((v3_ordinal1(esk10_3(X44,X45,X46))\|v3_ordinal1(esk9_3(X44,X45,X46))\|k1_funct_1(X46,k1_exchsort(X46))!=X44\|m2_exchsort(X46,X45,X44)\|(v1_xboole_0(X46)\|(~v1_relat_1(X46)\|(~v1_funct_1(X46)\|~v1_exchsort(X46))))\|~epred1_2(X45,X44))&((r2_hidden(esk10_3(X44,X45,X46),k9_xtuple_0(X46))\|v3_ordinal1(esk9_3(X44,X45,X46))\|k1_funct_1(X46,k1_exchsort(X46))!=X44\|m2_exchsort(X46,X45,X44)\|(v1_xboole_0(X46)\|(~v1_relat_1(X46)\|(~v1_funct_1(X46)\|~v1_exchsort(X46))))\|~epred1_2(X45,X44))&((r2_hidden(k1_ordinal1(esk10_3(X44,X45,X46)),k9_xtuple_0(X46))\|v3_ordinal1(esk9_3(X44,X45,X46))\|k1_funct_1(X46,k1_exchsort(X46))!=X44\|m2_exchsort(X46,X45,X44)\|(v1_xboole_0(X46)\|(~v1_relat_1(X46)\|(~v1_funct_1(X46)\|~v1_exchsort(X46))))\|~epred1_2(X45,X44))&(~v1_relat_1(X54)\|(~v5_relat_1(X54,u1_struct_0(X45))\|(~v1_funct_1(X54)\|~v1_exchsort(X54)))\|(~r2_hidden(k4_tarski(X55,X56),k6_exchsort(X45,X54))\|(k1_funct_1(X46,esk10_3(X44,X45,X46))!=X54\|k1_funct_1(X46,k1_ordinal1(esk10_3(X44,X45,X46)))!=k10_funct_7(X54,X55,X56)))\|v3_ordinal1(esk9_3(X44,X45,X46))\|k1_funct_1(X46,k1_exchsort(X46))!=X44\|m2_exchsort(X46,X45,X44)\|(v1_xboole_0(X46)\|(~v1_relat_1(X46)\|(~v1_funct_1(X46)\|~v1_exchsort(X46))))\|~epred1_2(X45,X44)))))&(((v3_ordinal1(esk10_3(X44,X45,X46))\|r2_hidden(esk9_3(X44,X45,X46),k9_xtuple_0(X46))\|k1_funct_1(X46,k1_exchsort(X46))!=X44\|m2_exchsort(X46,X45,X44)\|(v1_xboole_0(X46)\|(~v1_relat_1(X46)\|(~v1_funct_1(X46)\|~v1_exchsort(X46))))\|~epred1_2(X45,X44))&((r2_hidden(esk10_3(X44,X45,X46),k9_xtuple_0(X46))\|r2_hidden(esk9_3(X44,X45,X46),k9_xtuple_0(X46))\|k1_funct_1(X46,k1_exchsort(X46))!=X44\|m2_exchsort(X46,X45,X44)\|(v1_xboole_0(X46)\|(~v1_relat_1(X46)\|(~v1_funct_1(X46)\|~v1_exchsort(X46))))\|~epred1_2(X45,X44))&((r2_hidden(k1_ordinal1(esk10_3(X44,X45,X46)),k9_xtuple_0(X46))\|r2_hidden(esk9_3(X44,X45,X46),k9_xtuple_0(X46))\|k1_funct_1(X46,k1_exchsort(X46))!=X44\|m2_exchsort(X46,X45,X44)\|(v1_xboole_0(X46)\|(~v1_relat_1(X46)\|(~v1_funct_1(X46)\|~v1_exchsort(X46))))\|~epred1_2(X45,X44))&(~v1_relat_1(X54)\|(~v5_relat_1(X54,u1_struct_0(X45))\|(~v1_funct_1(X54)\|~v1_exchsort(X54)))\|(~r2_hidden(k4_tarski(X55,X56),k6_exchsort(X45,X54))\|(k1_funct_1(X46,esk10_3(X44,X45,X46))!=X54\|k1_funct_1(X46,k1_ordinal1(esk10_3(X44,X45,X46)))!=k10_funct_7(X54,X55,X56)))\|r2_hidden(esk9_3(X44,X45,X46),k9_xtuple_0(X46))\|k1_funct_1(X46,k1_exchsort(X46))!=X44\|m2_exchsort(X46,X45,X44)\|(v1_xboole_0(X46)\|(~v1_relat_1(X46)\|(~v1_funct_1(X46)\|~v1_exchsort(X46))))\|~epred1_2(X45,X44)))))&((v3_ordinal1(esk10_3(X44,X45,X46))\|(~v1_relat_1(k1_funct_1(X46,esk9_3(X44,X45,X46)))\|(~v5_relat_1(k1_funct_1(X46,esk9_3(X44,X45,X46)),u1_struct_0(X45))\|(~v1_funct_1(k1_funct_1(X46,esk9_3(X44,X45,X46)))\|~v1_exchsort(k1_funct_1(X46,esk9_3(X44,X45,X46))))))\|k1_funct_1(X46,k1_exchsort(X46))!=X44\|m2_exchsort(X46,X45,X44)\|(v1_xboole_0(X46)\|(~v1_relat_1(X46)\|(~v1_funct_1(X46)\|~v1_exchsort(X46))))\|~epred1_2(X45,X44))&((r2_hidden(esk10_3(X44,X45,X46),k9_xtuple_0(X46))\|(~v1_relat_1(k1_funct_1(X46,esk9_3(X44,X45,X46)))\|(~v5_relat_1(k1_funct_1(X46,esk9_3(X44,X45,X46)),u1_struct_0(X45))\|(~v1_funct_1(k1_funct_1(X46,esk9_3(X44,X45,X46)))\|~v1_exchsort(k1_funct_1(X46,esk9_3(X44,X45,X46))))))\|k1_funct_1(X46,k1_exchsort(X46))!=X44\|m2_exchsort(X46,X45,X44)\|(v1_xboole_0(X46)\|(~v1_relat_1(X46)\|(~v1_funct_1(X46)\|~v1_exchsort(X46))))\|~epred1_2(X45,X44))&((r2_hidden(k1_ordinal1(esk10_3(X44,X45,X46)),k9_xtuple_0(X46))\|(~v1_relat_1(k1_funct_1(X46,esk9_3(X44,X45,X46)))\|(~v5_relat_1(k1_funct_1(X46,esk9_3(X44,X45,X46)),u1_struct_0(X45))\|(~v1_funct_1(k1_funct_1(X46,esk9_3(X44,X45,X46)))\|~v1_exchsort(k1_funct_1(X46,esk9_3(X44,X45,X46))))))\|k1_funct_1(X46,k1_exchsort(X46))!=X44\|m2_exchsort(X46,X45,X44)\|(v1_xboole_0(X46)\|(~v1_relat_1(X46)\|(~v1_funct_1(X46)\|~v1_exchsort(X46))))\|~epred1_2(X45,X44))&(~v1_relat_1(X54)\|(~v5_relat_1(X54,u1_struct_0(X45))\|(~v1_funct_1(X54)\|~v1_exchsort(X54)))\|(~r2_hidden(k4_tarski(X55,X56),k6_exchsort(X45,X54))\|(k1_funct_1(X46,esk10_3(X44,X45,X46))!=X54\|k1_funct_1(X46,k1_ordinal1(esk10_3(X44,X45,X46)))!=k10_funct_7(X54,X55,X56)))\|(~v1_relat_1(k1_funct_1(X46,esk9_3(X44,X45,X46)))\|(~v5_relat_1(k1_funct_1(X46,esk9_3(X44,X45,X46)),u1_struct_0(X45))\|(~v1_funct_1(k1_funct_1(X46,esk9_3(X44,X45,X46)))\|~v1_exchsort(k1_funct_1(X46,esk9_3(X44,X45,X46))))))\|k1_funct_1(X46,k1_exchsort(X46))!=X44\|m2_exchsort(X46,X45,X44)\|(v1_xboole_0(X46)\|(~v1_relat_1(X46)\|(~v1_funct_1(X46)\|~v1_exchsort(X46))))\|~epred1_2(X45,X44)))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_36])])])])])])). cnf(c_0_45, plain, (X1=k1_exchsort(k1_tarski(k2_tarski(k1_tarski(X2),k2_tarski(X2,X3))))\|~v2_exchsort(k1_tarski(k2_tarski(k1_tarski(X2),k2_tarski(X2,X3))),X1)\|~r2_hidden(X4,k1_tarski(X2))\|~v1_funct_1(k1_tarski(k2_tarski(k1_tarski(X2),k2_tarski(X2,X3))))\|~v1_relat_1(k1_tarski(k2_tarski(k1_tarski(X2),k2_tarski(X2,X3))))\|~v3_ordinal1(X4)\|~v3_ordinal1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_37, c_0_38])])). cnf(c_0_46, plain, (v1_funct_1(k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X1,X2))))), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[c_0_39, c_0_31])])). cnf(c_0_47, plain, (v1_relat_1(k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X1,X2))))), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[c_0_40, c_0_31])])). cnf(c_0_48, plain, (v2_exchsort(k1_tarski(k2_tarski(k2_tarski(X1,X2),k1_tarski(X1))),X1)\|~v3_ordinal1(X1)), inference(evalgc,[status(thm)],[c_0_41])). cnf(c_0_49, plain, (r2_hidden(X1,X3)\|X1!=X2\|X3!=k1_tarski(X2)), inference(split_conjunct,[status(thm)],[c_0_42])). fof(c_0_50, negated_conjecture, ~(![X1]:(v3_ordinal1(X1)=>![X2]:((~(v2_struct_0(X2))&(v3_orders_2(X2)&(v4_orders_2(X2)&(v5_orders_2(X2)&(v16_waybel_0(X2)&l1_orders_2(X2))))))=>![X3]:((v1_relat_1(X3)&(v5_relat_1(X3,u1_struct_0(X2))&(v1_funct_1(X3)&v1_exchsort(X3))))=>m2_exchsort(k1_tarski(k4_tarski(X1,X3)),X2,X3))))), inference(assume_negation,[status(cth)],[t75_exchsort])). cnf(c_0_51, plain, (k1_funct_1(X1,X2)=X3\|X1!=k1_tarski(k2_tarski(k2_tarski(X2,X3),k1_tarski(X2)))\|~v1_relat_1(X1)\|~v1_funct_1(X1)), inference(rw,[status(thm)],[c_0_43, c_0_18])). cnf(c_0_52, plain, (X1=X3\|~r2_hidden(X1,X2)\|X2!=k1_tarski(X3)), inference(split_conjunct,[status(thm)],[c_0_42])). cnf(c_0_53, plain, (r2_hidden(esk10_3(X1,X2,X3),k9_xtuple_0(X3))\|r2_hidden(esk9_3(X1,X2,X3),k9_xtuple_0(X3))\|m2_exchsort(X3,X2,X1)\|v1_xboole_0(X3)\|k1_funct_1(X3,k1_exchsort(X3))!=X1\|~v1_relat_1(X3)\|~v1_funct_1(X3)\|~v1_exchsort(X3)\|~epred1_2(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_44])). fof(c_0_54, plain, ![X24]:~v1_xboole_0(k1_tarski(X24)), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fc2_xboole_0])])). cnf(c_0_55, plain, (X1=k1_exchsort(k1_tarski(k2_tarski(k1_tarski(X2),k2_tarski(X2,X3))))\|~v2_exchsort(k1_tarski(k2_tarski(k1_tarski(X2),k2_tarski(X2,X3))),X1)\|~r2_hidden(X4,k1_tarski(X2))\|~v3_ordinal1(X4)\|~v3_ordinal1(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45, c_0_46]), c_0_47])])). cnf(c_0_56, plain, (v2_exchsort(k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X1,X2))),X1)\|~v3_ordinal1(X1)), inference(rw,[status(thm)],[c_0_48, c_0_31])). cnf(c_0_57, plain, (r2_hidden(X1,X3)\|X1!=X2\|X3!=k1_tarski(X2)), inference(evalgc,[status(thm)],[c_0_49])). fof(c_0_58, negated_conjecture, (v3_ordinal1(esk1_0)&((~v2_struct_0(esk2_0)&(v3_orders_2(esk2_0)&(v4_orders_2(esk2_0)&(v5_orders_2(esk2_0)&(v16_waybel_0(esk2_0)&l1_orders_2(esk2_0))))))&((v1_relat_1(esk3_0)&(v5_relat_1(esk3_0,u1_struct_0(esk2_0))&(v1_funct_1(esk3_0)&v1_exchsort(esk3_0))))&~m2_exchsort(k1_tarski(k4_tarski(esk1_0,esk3_0)),esk2_0,esk3_0)))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_50])])])])). cnf(c_0_59, plain, (k1_funct_1(X1,X2)=X3\|X1!=k1_tarski(k2_tarski(k2_tarski(X2,X3),k1_tarski(X2)))\|~v1_relat_1(X1)\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[c_0_51])). cnf(c_0_60, plain, (X1=X3\|X2!=k1_tarski(X3)\|~r2_hidden(X1,X2)), inference(evalgc,[status(thm)],[c_0_52])). cnf(c_0_61, plain, (v1_xboole_0(X3)\|m2_exchsort(X3,X2,X1)\|r2_hidden(esk9_3(X1,X2,X3),k9_xtuple_0(X3))\|r2_hidden(esk10_3(X1,X2,X3),k9_xtuple_0(X3))\|k1_funct_1(X3,k1_exchsort(X3))!=X1\|~v1_relat_1(X3)\|~v1_funct_1(X3)\|~v1_exchsort(X3)\|~epred1_2(X2,X1)), inference(evalgc,[status(thm)],[c_0_53])). cnf(c_0_62, plain, (~v1_xboole_0(k1_tarski(X1))), inference(split_conjunct,[status(thm)],[c_0_54])). cnf(c_0_63, plain, (k1_exchsort(k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X1,X2))))=X1\|~r2_hidden(X3,k1_tarski(X1))\|~v3_ordinal1(X3)\|~v3_ordinal1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_55, c_0_56])])). cnf(c_0_64, plain, (r2_hidden(X1,X2)\|X2!=k1_tarski(X1)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_57])])). cnf(c_0_65, negated_conjecture, (v3_ordinal1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_58])). cnf(c_0_66, plain, (k1_funct_1(X1,X2)=X3\|X1!=k1_tarski(k2_tarski(k1_tarski(X2),k2_tarski(X2,X3)))\|~v1_funct_1(X1)\|~v1_relat_1(X1)), inference(rw,[status(thm)],[c_0_59, c_0_31])). cnf(c_0_67, plain, (v1_exchsort(k1_tarski(k4_tarski(X1,X2)))\|~v3_ordinal1(X1)), inference(split_conjunct,[status(thm)],[c_0_27])). cnf(c_0_68, plain, (esk10_3(X1,X2,X3)=X4\|v1_xboole_0(X3)\|r2_hidden(esk9_3(X1,X2,X3),k9_xtuple_0(X3))\|m2_exchsort(X3,X2,X1)\|k9_xtuple_0(X3)!=k1_tarski(X4)\|k1_funct_1(X3,k1_exchsort(X3))!=X1\|~epred1_2(X2,X1)\|~v1_exchsort(X3)\|~v1_funct_1(X3)\|~v1_relat_1(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_60, c_0_61])])). cnf(c_0_69, plain, (~v1_xboole_0(k1_tarski(X1))), inference(evalgc,[status(thm)],[c_0_62])). cnf(c_0_70, plain, (k1_exchsort(k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X1,X2))))=X1\|~v3_ordinal1(X3)\|~v3_ordinal1(X1)\|k1_tarski(X1)!=k1_tarski(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_63, c_0_64])])). cnf(c_0_71, negated_conjecture, (v3_ordinal1(esk1_0)), inference(evalgc,[status(thm)],[c_0_65])). cnf(c_0_72, plain, (k1_funct_1(k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X1,X2))),X1)=X2\|~v1_funct_1(k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X1,X2))))\|~v1_relat_1(k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X1,X2))))), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_66])])). cnf(c_0_73, plain, (v1_exchsort(k1_tarski(k2_tarski(k2_tarski(X1,X2),k1_tarski(X1))))\|~v3_ordinal1(X1)), inference(rw,[status(thm)],[c_0_67, c_0_18])). cnf(c_0_74, plain, (esk10_3(X1,X2,k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X3,X4))))=X5\|r2_hidden(esk9_3(X1,X2,k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X3,X4)))),k1_tarski(X3))\|m2_exchsort(k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X3,X4))),X2,X1)\|k1_funct_1(k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X3,X4))),k1_exchsort(k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X3,X4)))))!=X1\|k1_tarski(X3)!=k1_tarski(X5)\|~epred1_2(X2,X1)\|~v1_exchsort(k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X3,X4))))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68, c_0_38]), c_0_46]), c_0_47])]), c_0_69])])). cnf(c_0_75, negated_conjecture, (k1_exchsort(k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X1,X2))))=X1\|k1_tarski(X1)!=k1_tarski(esk1_0)\|~v3_ordinal1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_70, c_0_71])])). cnf(c_0_76, plain, (k1_funct_1(k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X1,X2))),X1)=X2), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_72, c_0_46]), c_0_47])])). cnf(c_0_77, plain, (v1_exchsort(k1_tarski(k2_tarski(k2_tarski(X1,X2),k1_tarski(X1))))\|~v3_ordinal1(X1)), inference(evalgc,[status(thm)],[c_0_73])). cnf(c_0_78, plain, (esk10_3(X1,X2,k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X3,X1))))=X4\|r2_hidden(esk9_3(X1,X2,k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X3,X1)))),k1_tarski(X3))\|m2_exchsort(k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X3,X1))),X2,X1)\|k1_tarski(X3)!=k1_tarski(X4)\|~epred1_2(X2,X1)\|~v1_exchsort(k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X3,X1))))\|k1_tarski(X3)!=k1_tarski(esk1_0)\|~v3_ordinal1(X3)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74, c_0_75]), c_0_76])])])). cnf(c_0_79, plain, (v1_exchsort(k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X1,X2))))\|~v3_ordinal1(X1)), inference(rw,[status(thm)],[c_0_77, c_0_31])). fof(c_0_80, plain, ![X42]:k1_ordinal1(X42)=k2_xboole_0(X42,k1_tarski(X42)), inference(variable_rename,[status(thm)],[d1_ordinal1])). cnf(c_0_81, plain, (esk10_3(X1,X2,k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X3,X1))))=X4\|r2_hidden(esk9_3(X1,X2,k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X3,X1)))),k1_tarski(X3))\|m2_exchsort(k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X3,X1))),X2,X1)\|k1_tarski(X3)!=k1_tarski(esk1_0)\|k1_tarski(X3)!=k1_tarski(X4)\|~epred1_2(X2,X1)\|~v3_ordinal1(X3)), inference(csr,[status(thm)],[c_0_78, c_0_79])). cnf(c_0_82, plain, (r2_hidden(k1_ordinal1(esk10_3(X1,X2,X3)),k9_xtuple_0(X3))\|r2_hidden(esk9_3(X1,X2,X3),k9_xtuple_0(X3))\|m2_exchsort(X3,X2,X1)\|v1_xboole_0(X3)\|k1_funct_1(X3,k1_exchsort(X3))!=X1\|~v1_relat_1(X3)\|~v1_funct_1(X3)\|~v1_exchsort(X3)\|~epred1_2(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_44])). cnf(c_0_83, plain, (k1_ordinal1(X1)=k2_xboole_0(X1,k1_tarski(X1))), inference(split_conjunct,[status(thm)],[c_0_80])). cnf(c_0_84, plain, (esk10_3(X1,X2,k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X3,X1))))=X3\|r2_hidden(esk9_3(X1,X2,k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X3,X1)))),k1_tarski(X3))\|m2_exchsort(k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X3,X1))),X2,X1)\|k1_tarski(X3)!=k1_tarski(esk1_0)\|~epred1_2(X2,X1)\|~v3_ordinal1(X3)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_81])])). cnf(c_0_85, plain, (v1_xboole_0(X3)\|m2_exchsort(X3,X2,X1)\|r2_hidden(esk9_3(X1,X2,X3),k9_xtuple_0(X3))\|r2_hidden(k2_xboole_0(esk10_3(X1,X2,X3),k1_tarski(esk10_3(X1,X2,X3))),k9_xtuple_0(X3))\|k1_funct_1(X3,k1_exchsort(X3))!=X1\|~v1_relat_1(X3)\|~v1_funct_1(X3)\|~v1_exchsort(X3)\|~epred1_2(X2,X1)), inference(rw,[status(thm)],[c_0_82, c_0_83])). cnf(c_0_86, plain, (esk9_3(X1,X2,k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X3,X1))))=X4\|esk10_3(X1,X2,k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X3,X1))))=X3\|m2_exchsort(k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X3,X1))),X2,X1)\|k1_tarski(X3)!=k1_tarski(X4)\|k1_tarski(X3)!=k1_tarski(esk1_0)\|~epred1_2(X2,X1)\|~v3_ordinal1(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_60, c_0_84])])). cnf(c_0_87, plain, (v1_xboole_0(X3)\|m2_exchsort(X3,X2,X1)\|r2_hidden(esk9_3(X1,X2,X3),k9_xtuple_0(X3))\|r2_hidden(k2_xboole_0(esk10_3(X1,X2,X3),k1_tarski(esk10_3(X1,X2,X3))),k9_xtuple_0(X3))\|k1_funct_1(X3,k1_exchsort(X3))!=X1\|~v1_relat_1(X3)\|~v1_funct_1(X3)\|~v1_exchsort(X3)\|~epred1_2(X2,X1)), inference(evalgc,[status(thm)],[c_0_85])). cnf(c_0_88, plain, (esk10_3(X1,X2,k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X3,X1))))=X3\|esk9_3(X1,X2,k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X3,X1))))=X3\|m2_exchsort(k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X3,X1))),X2,X1)\|k1_tarski(X3)!=k1_tarski(esk1_0)\|~epred1_2(X2,X1)\|~v3_ordinal1(X3)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_86])])). cnf(c_0_89, plain, (r2_hidden(k2_xboole_0(X1,k1_tarski(X1)),k1_tarski(X1))\|r2_hidden(esk9_3(X2,X3,k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X1,X2)))),k1_tarski(X1))\|m2_exchsort(k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X1,X2))),X3,X2)\|esk9_3(X2,X3,k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X1,X2))))=X1\|k1_funct_1(k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X1,X2))),k1_exchsort(k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X1,X2)))))!=X2\|~epred1_2(X3,X2)\|~v1_exchsort(k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X1,X2))))\|k1_tarski(X1)!=k1_tarski(esk1_0)\|~v3_ordinal1(X1)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87, c_0_88]), c_0_38]), c_0_38]), c_0_46]), c_0_47])]), c_0_69])])). fof(c_0_90, axiom, ![X1]:((~(v2_struct_0(X1))&(v3_orders_2(X1)&(v4_orders_2(X1)&(v5_orders_2(X1)&(v16_waybel_0(X1)&l1_orders_2(X1))))))=>![X2]:((v1_relat_1(X2)&(v5_relat_1(X2,u1_struct_0(X1))&(v1_funct_1(X2)&v1_exchsort(X2))))=>epred1_2(X1,X2))), inference(apply_def,[status(thm)],[d14_exchsort, c_0_28])). cnf(c_0_91, plain, (k9_xtuple_0(k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X2,X1))))=k1_tarski(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_38, c_0_31])])). cnf(c_0_92, plain, (X1=k1_exchsort(X2)\|~v2_exchsort(X2,X1)\|~v1_funct_1(X2)\|~v1_relat_1(X2)\|~v3_ordinal1(X3)\|~v3_ordinal1(X1)\|k9_xtuple_0(X2)!=k1_tarski(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_37, c_0_64])])). cnf(c_0_93, plain, (v2_exchsort(k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X2,X1))),X1)\|~v3_ordinal1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_56, c_0_31])])). cnf(c_0_94, plain, (v1_funct_1(k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X2,X1))))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_46, c_0_31])])). cnf(c_0_95, plain, (v1_relat_1(k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X2,X1))))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_47, c_0_31])])). cnf(c_0_96, plain, (esk9_3(X1,X2,k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X3,X1))))=X3\|r2_hidden(esk9_3(X1,X2,k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X3,X1)))),k1_tarski(X3))\|r2_hidden(k2_xboole_0(X3,k1_tarski(X3)),k1_tarski(X3))\|m2_exchsort(k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X3,X1))),X2,X1)\|k1_funct_1(k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X3,X1))),k1_exchsort(k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X3,X1)))))!=X1\|k1_tarski(X3)!=k1_tarski(esk1_0)\|~epred1_2(X2,X1)\|~v3_ordinal1(X3)), inference(csr,[status(thm)],[c_0_89, c_0_79])). fof(c_0_97, plain, ![X27, X28]:(v2_struct_0(X27)\|(~v3_orders_2(X27)\|(~v4_orders_2(X27)\|(~v5_orders_2(X27)\|(~v16_waybel_0(X27)\|~l1_orders_2(X27)))))\|(~v1_relat_1(X28)\|(~v5_relat_1(X28,u1_struct_0(X27))\|(~v1_funct_1(X28)\|~v1_exchsort(X28)))\|epred1_2(X27,X28))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_90])])])])). cnf(c_0_98, plain, (r2_hidden(esk10_3(X3,X4,k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X1,X2)))),k1_tarski(X1))\|r2_hidden(esk9_3(X3,X4,k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X1,X2)))),k1_tarski(X1))\|m2_exchsort(k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X1,X2))),X4,X3)\|k1_funct_1(k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X1,X2))),k1_exchsort(k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X1,X2)))))!=X3\|~epred1_2(X4,X3)\|~v1_exchsort(k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X1,X2))))\|~v1_funct_1(k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X1,X2))))\|~v1_relat_1(k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X1,X2))))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_61, c_0_38]), c_0_69])])). cnf(c_0_99, plain, (esk10_3(X1,X2,k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X4,X3))))=X5\|r2_hidden(esk9_3(X1,X2,k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X4,X3)))),k1_tarski(X3))\|m2_exchsort(k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X4,X3))),X2,X1)\|k1_funct_1(k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X4,X3))),k1_exchsort(k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X4,X3)))))!=X1\|k1_tarski(X3)!=k1_tarski(X5)\|~epred1_2(X2,X1)\|~v1_exchsort(k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X4,X3))))\|~v1_funct_1(k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X4,X3))))\|~v1_relat_1(k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X4,X3))))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_68, c_0_91]), c_0_69])])). cnf(c_0_100, plain, (k1_exchsort(k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X2,X1))))=X1\|k1_tarski(X1)!=k1_tarski(X3)\|~v3_ordinal1(X3)\|~v3_ordinal1(X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92, c_0_93]), c_0_91]), c_0_94]), c_0_95])])])). cnf(c_0_101, negated_conjecture, (esk9_3(X1,X2,k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X3,X1))))=X3\|r2_hidden(esk9_3(X1,X2,k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X3,X1)))),k1_tarski(X3))\|r2_hidden(k2_xboole_0(X3,k1_tarski(X3)),k1_tarski(X3))\|m2_exchsort(k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X3,X1))),X2,X1)\|k1_tarski(X3)!=k1_tarski(esk1_0)\|~epred1_2(X2,X1)\|~v3_ordinal1(X3)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96, c_0_75]), c_0_76])])])). cnf(c_0_102, plain, (v2_struct_0(X1)\|epred1_2(X1,X2)\|~v3_orders_2(X1)\|~v4_orders_2(X1)\|~v5_orders_2(X1)\|~v16_waybel_0(X1)\|~l1_orders_2(X1)\|~v1_relat_1(X2)\|~v5_relat_1(X2,u1_struct_0(X1))\|~v1_funct_1(X2)\|~v1_exchsort(X2)), inference(split_conjunct,[status(thm)],[c_0_97])). cnf(c_0_103, negated_conjecture, (v5_relat_1(esk3_0,u1_struct_0(esk2_0))), inference(split_conjunct,[status(thm)],[c_0_58])). cnf(c_0_104, negated_conjecture, (v1_exchsort(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_58])). cnf(c_0_105, negated_conjecture, (v1_funct_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_58])). cnf(c_0_106, negated_conjecture, (v1_relat_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_58])). cnf(c_0_107, negated_conjecture, (l1_orders_2(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_58])). cnf(c_0_108, negated_conjecture, (v16_waybel_0(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_58])). cnf(c_0_109, negated_conjecture, (v5_orders_2(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_58])). cnf(c_0_110, negated_conjecture, (v4_orders_2(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_58])). cnf(c_0_111, negated_conjecture, (v3_orders_2(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_58])). cnf(c_0_112, negated_conjecture, (~v2_struct_0(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_58])). cnf(c_0_113, negated_conjecture, (~m2_exchsort(k1_tarski(k4_tarski(esk1_0,esk3_0)),esk2_0,esk3_0)), inference(split_conjunct,[status(thm)],[c_0_58])). cnf(c_0_114, plain, (r2_hidden(esk4_2(X1,X2),X2)\|esk4_2(X1,X2)=X1\|X2=k1_tarski(X1)), inference(split_conjunct,[status(thm)],[c_0_42])). cnf(c_0_115, plain, (r2_hidden(esk9_3(X1,X2,k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X3,X4)))),k1_tarski(X3))\|r2_hidden(esk10_3(X1,X2,k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X3,X4)))),k1_tarski(X3))\|m2_exchsort(k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X3,X4))),X2,X1)\|k1_funct_1(k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X3,X4))),k1_exchsort(k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X3,X4)))))!=X1\|~epred1_2(X2,X1)\|~v1_exchsort(k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X3,X4))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_98, c_0_46]), c_0_47])])). cnf(c_0_116, plain, (esk10_3(X1,X2,k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X4,X3))))=X5\|r2_hidden(esk9_3(X1,X2,k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X4,X3)))),k1_tarski(X3))\|m2_exchsort(k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X4,X3))),X2,X1)\|k1_funct_1(k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X4,X3))),k1_exchsort(k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X4,X3)))))!=X1\|k1_tarski(X3)!=k1_tarski(X5)\|~epred1_2(X2,X1)\|~v1_exchsort(k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X4,X3))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_99, c_0_94]), c_0_95])])). cnf(c_0_117, negated_conjecture, (k1_exchsort(k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X2,X1))))=X1\|k1_tarski(X1)!=k1_tarski(esk1_0)\|~v3_ordinal1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_100, c_0_71])])). cnf(c_0_118, plain, (k1_funct_1(k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X2,X1))),X1)=X2), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_76, c_0_31])])). cnf(c_0_119, negated_conjecture, (esk9_3(X1,X2,k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X3,X1))))=X4\|esk9_3(X1,X2,k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X3,X1))))=X3\|r2_hidden(k2_xboole_0(X3,k1_tarski(X3)),k1_tarski(X3))\|m2_exchsort(k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X3,X1))),X2,X1)\|k1_tarski(X3)!=k1_tarski(X4)\|k1_tarski(X3)!=k1_tarski(esk1_0)\|~epred1_2(X2,X1)\|~v3_ordinal1(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_60, c_0_101])])). cnf(c_0_120, plain, (v2_struct_0(X1)\|epred1_2(X1,X2)\|~v3_orders_2(X1)\|~v4_orders_2(X1)\|~v5_orders_2(X1)\|~v16_waybel_0(X1)\|~l1_orders_2(X1)\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v1_exchsort(X2)\|~v5_relat_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_102])). cnf(c_0_121, negated_conjecture, (v5_relat_1(esk3_0,u1_struct_0(esk2_0))), inference(evalgc,[status(thm)],[c_0_103])). cnf(c_0_122, negated_conjecture, (v1_exchsort(esk3_0)), inference(evalgc,[status(thm)],[c_0_104])). cnf(c_0_123, negated_conjecture, (v1_funct_1(esk3_0)), inference(evalgc,[status(thm)],[c_0_105])). cnf(c_0_124, negated_conjecture, (v1_relat_1(esk3_0)), inference(evalgc,[status(thm)],[c_0_106])). cnf(c_0_125, negated_conjecture, (l1_orders_2(esk2_0)), inference(evalgc,[status(thm)],[c_0_107])). cnf(c_0_126, negated_conjecture, (v16_waybel_0(esk2_0)), inference(evalgc,[status(thm)],[c_0_108])). cnf(c_0_127, negated_conjecture, (v5_orders_2(esk2_0)), inference(evalgc,[status(thm)],[c_0_109])). cnf(c_0_128, negated_conjecture, (v4_orders_2(esk2_0)), inference(evalgc,[status(thm)],[c_0_110])). cnf(c_0_129, negated_conjecture, (v3_orders_2(esk2_0)), inference(evalgc,[status(thm)],[c_0_111])). cnf(c_0_130, negated_conjecture, (~v2_struct_0(esk2_0)), inference(evalgc,[status(thm)],[c_0_112])). cnf(c_0_131, negated_conjecture, (~m2_exchsort(k1_tarski(k2_tarski(k2_tarski(esk1_0,esk3_0),k1_tarski(esk1_0))),esk2_0,esk3_0)), inference(rw,[status(thm)],[c_0_113, c_0_18])). cnf(c_0_132, plain, (X2=k1_tarski(X1)\|esk4_2(X1,X2)=X1\|r2_hidden(esk4_2(X1,X2),X2)), inference(evalgc,[status(thm)],[c_0_114])). cnf(c_0_133, plain, (r2_hidden(esk9_3(k1_funct_1(k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X1,X2))),k1_exchsort(k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X1,X2))))),X3,k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X1,X2)))),k1_tarski(X1))\|r2_hidden(esk10_3(k1_funct_1(k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X1,X2))),k1_exchsort(k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X1,X2))))),X3,k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X1,X2)))),k1_tarski(X1))\|m2_exchsort(k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X1,X2))),X3,k1_funct_1(k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X1,X2))),k1_exchsort(k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X1,X2))))))\|~epred1_2(X3,k1_funct_1(k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X1,X2))),k1_exchsort(k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X1,X2))))))\|~v1_exchsort(k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X1,X2))))), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_115])])). cnf(c_0_134, plain, (esk10_3(X1,X2,k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X1,X3))))=X4\|r2_hidden(esk9_3(X1,X2,k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X1,X3)))),k1_tarski(X3))\|m2_exchsort(k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X1,X3))),X2,X1)\|k1_tarski(X3)!=k1_tarski(X4)\|~epred1_2(X2,X1)\|~v1_exchsort(k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X1,X3))))\|k1_tarski(X3)!=k1_tarski(esk1_0)\|~v3_ordinal1(X3)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116, c_0_117]), c_0_118])])])). cnf(c_0_135, plain, (v1_exchsort(k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X2,X1))))\|~v3_ordinal1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_79, c_0_31])])). cnf(c_0_136, negated_conjecture, (esk9_3(X1,X2,k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X3,X1))))=X3\|r2_hidden(k2_xboole_0(X3,k1_tarski(X3)),k1_tarski(X3))\|m2_exchsort(k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X3,X1))),X2,X1)\|k1_tarski(X3)!=k1_tarski(esk1_0)\|~epred1_2(X2,X1)\|~v3_ordinal1(X3)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_119])])). cnf(c_0_137, negated_conjecture, (epred1_2(esk2_0,esk3_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120, c_0_121]), c_0_122]), c_0_123]), c_0_124]), c_0_125]), c_0_126]), c_0_127]), c_0_128]), c_0_129])]), c_0_130])])). cnf(c_0_138, negated_conjecture, (~m2_exchsort(k1_tarski(k2_tarski(k2_tarski(esk1_0,esk3_0),k1_tarski(esk1_0))),esk2_0,esk3_0)), inference(evalgc,[status(thm)],[c_0_131])). cnf(c_0_139, plain, (X2=k1_tarski(X1)\|~r2_hidden(esk4_2(X1,X2),X2)\|esk4_2(X1,X2)!=X1), inference(split_conjunct,[status(thm)],[c_0_42])). cnf(c_0_140, plain, (esk4_2(X1,X2)=X3\|esk4_2(X1,X2)=X1\|X2=k1_tarski(X1)\|X2!=k1_tarski(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_60, c_0_132])])). cnf(c_0_141, plain, (r2_hidden(esk10_3(X2,X3,k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X1,X2)))),k1_tarski(X1))\|r2_hidden(esk9_3(X2,X3,k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X1,X2)))),k1_tarski(X1))\|m2_exchsort(k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X1,X2))),X3,X2)\|~epred1_2(X3,X2)\|~v1_exchsort(k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X1,X2))))\|k1_tarski(X1)!=k1_tarski(esk1_0)\|~v3_ordinal1(X1)), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133, c_0_75]), c_0_76]), c_0_76]), c_0_76]), c_0_76])])). cnf(c_0_142, plain, (esk10_3(X1,X2,k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X1,X3))))=X4\|r2_hidden(esk9_3(X1,X2,k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X1,X3)))),k1_tarski(X3))\|m2_exchsort(k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X1,X3))),X2,X1)\|k1_tarski(X3)!=k1_tarski(esk1_0)\|k1_tarski(X3)!=k1_tarski(X4)\|~epred1_2(X2,X1)\|~v3_ordinal1(X3)), inference(csr,[status(thm)],[c_0_134, c_0_135])). cnf(c_0_143, negated_conjecture, (esk9_3(esk3_0,esk2_0,k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X1,esk3_0))))=X1\|r2_hidden(k2_xboole_0(X1,k1_tarski(X1)),k1_tarski(X1))\|m2_exchsort(k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X1,esk3_0))),esk2_0,esk3_0)\|k1_tarski(X1)!=k1_tarski(esk1_0)\|~v3_ordinal1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_136, c_0_137])])). cnf(c_0_144, negated_conjecture, (~m2_exchsort(k1_tarski(k2_tarski(k1_tarski(esk1_0),k2_tarski(esk3_0,esk1_0))),esk2_0,esk3_0)), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_138, c_0_31]), c_0_31])])). cnf(c_0_145, plain, (r2_hidden(esk10_3(X1,X2,X3),k9_xtuple_0(X3))\|m2_exchsort(X3,X2,X1)\|v1_xboole_0(X3)\|~v1_relat_1(k1_funct_1(X3,esk9_3(X1,X2,X3)))\|~v5_relat_1(k1_funct_1(X3,esk9_3(X1,X2,X3)),u1_struct_0(X2))\|~v1_funct_1(k1_funct_1(X3,esk9_3(X1,X2,X3)))\|~v1_exchsort(k1_funct_1(X3,esk9_3(X1,X2,X3)))\|k1_funct_1(X3,k1_exchsort(X3))!=X1\|~v1_relat_1(X3)\|~v1_funct_1(X3)\|~v1_exchsort(X3)\|~epred1_2(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_44])). cnf(c_0_146, plain, (X2=k1_tarski(X1)\|esk4_2(X1,X2)!=X1\|~r2_hidden(esk4_2(X1,X2),X2)), inference(evalgc,[status(thm)],[c_0_139])). cnf(c_0_147, plain, (esk4_2(X1,k1_tarski(X2))=X1\|esk4_2(X1,k1_tarski(X2))=X2\|k1_tarski(X2)=k1_tarski(X1)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_140])])). cnf(c_0_148, plain, (r2_hidden(esk9_3(X1,X2,k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X3,X1)))),k1_tarski(X3))\|r2_hidden(esk10_3(X1,X2,k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X3,X1)))),k1_tarski(X3))\|m2_exchsort(k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X3,X1))),X2,X1)\|k1_tarski(X3)!=k1_tarski(esk1_0)\|~epred1_2(X2,X1)\|~v3_ordinal1(X3)), inference(csr,[status(thm)],[c_0_141, c_0_79])). cnf(c_0_149, plain, (esk10_3(X1,X2,k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X1,X3))))=X3\|r2_hidden(esk9_3(X1,X2,k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X1,X3)))),k1_tarski(X3))\|m2_exchsort(k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X1,X3))),X2,X1)\|k1_tarski(X3)!=k1_tarski(esk1_0)\|~epred1_2(X2,X1)\|~v3_ordinal1(X3)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_142])])). cnf(c_0_150, negated_conjecture, (esk9_3(esk3_0,esk2_0,k1_tarski(k2_tarski(k1_tarski(esk1_0),k2_tarski(esk3_0,esk1_0))))=esk1_0\|r2_hidden(k2_xboole_0(esk1_0,k1_tarski(esk1_0)),k1_tarski(esk1_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_143]), c_0_31]), c_0_31]), c_0_71])]), c_0_144])])). cnf(c_0_151, plain, (v1_xboole_0(X3)\|m2_exchsort(X3,X2,X1)\|r2_hidden(esk10_3(X1,X2,X3),k9_xtuple_0(X3))\|k1_funct_1(X3,k1_exchsort(X3))!=X1\|~v1_relat_1(X3)\|~v1_funct_1(X3)\|~v1_exchsort(X3)\|~epred1_2(X2,X1)\|~v1_relat_1(k1_funct_1(X3,esk9_3(X1,X2,X3)))\|~v1_funct_1(k1_funct_1(X3,esk9_3(X1,X2,X3)))\|~v1_exchsort(k1_funct_1(X3,esk9_3(X1,X2,X3)))\|~v5_relat_1(k1_funct_1(X3,esk9_3(X1,X2,X3)),u1_struct_0(X2))), inference(evalgc,[status(thm)],[c_0_145])). cnf(c_0_152, plain, (k1_tarski(X1)=k1_tarski(X2)\|esk4_2(X2,k1_tarski(X1))=X1\|~r2_hidden(X2,k1_tarski(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_146, c_0_147])])). cnf(c_0_153, plain, (X1=X2\|X3!=k1_tarski(X2)\|X3!=k1_tarski(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_60, c_0_64])])). cnf(c_0_154, plain, (r2_hidden(esk9_3(X1,X2,k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X1,X3)))),k1_tarski(X3))\|r2_hidden(esk10_3(X1,X2,k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X1,X3)))),k1_tarski(X3))\|m2_exchsort(k1_tarski(k2_tarski(k1_tarski(X3),k2_tarski(X1,X3))),X2,X1)\|k1_tarski(X3)!=k1_tarski(esk1_0)\|~epred1_2(X2,X1)\|~v3_ordinal1(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_148, c_0_31])])). cnf(c_0_155, plain, (esk10_3(esk3_0,esk2_0,k1_tarski(k2_tarski(k1_tarski(esk1_0),k2_tarski(esk3_0,esk1_0))))=esk1_0\|r2_hidden(esk1_0,k1_tarski(esk1_0))\|r2_hidden(k2_xboole_0(esk1_0,k1_tarski(esk1_0)),k1_tarski(esk1_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149, c_0_150]), c_0_137]), c_0_71])]), c_0_144])])). cnf(c_0_156, plain, (r2_hidden(esk10_3(esk3_0,esk2_0,k1_tarski(k2_tarski(k1_tarski(esk1_0),k2_tarski(esk3_0,esk1_0)))),k1_tarski(esk1_0))\|r2_hidden(k2_xboole_0(esk1_0,k1_tarski(esk1_0)),k1_tarski(esk1_0))\|k1_funct_1(k1_tarski(k2_tarski(k1_tarski(esk1_0),k2_tarski(esk3_0,esk1_0))),k1_exchsort(k1_tarski(k2_tarski(k1_tarski(esk1_0),k2_tarski(esk3_0,esk1_0)))))!=esk3_0\|~v1_exchsort(k1_tarski(k2_tarski(k1_tarski(esk1_0),k2_tarski(esk3_0,esk1_0))))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151, c_0_150]), c_0_91]), c_0_137]), c_0_118]), c_0_122]), c_0_118]), c_0_123]), c_0_94]), c_0_118]), c_0_121]), c_0_118]), c_0_124]), c_0_95])]), c_0_69]), c_0_144])])). cnf(c_0_157, plain, (X2=X1\|k1_tarski(X2)=k1_tarski(X1)\|r2_hidden(X2,k1_tarski(X2))\|~r2_hidden(X1,k1_tarski(X2))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_132, c_0_152])])). cnf(c_0_158, plain, (X1=X2\|k1_tarski(X2)!=k1_tarski(X1)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_153])])). cnf(c_0_159, plain, (r2_hidden(esk1_0,k1_tarski(esk1_0))\|r2_hidden(esk9_3(esk3_0,esk2_0,k1_tarski(k2_tarski(k1_tarski(esk1_0),k2_tarski(esk3_0,esk1_0)))),k1_tarski(esk1_0))\|r2_hidden(k2_xboole_0(esk1_0,k1_tarski(esk1_0)),k1_tarski(esk1_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154, c_0_155]), c_0_137]), c_0_71])]), c_0_144])])). cnf(c_0_160, plain, (r2_hidden(k1_ordinal1(esk10_3(X1,X2,X3)),k9_xtuple_0(X3))\|m2_exchsort(X3,X2,X1)\|v1_xboole_0(X3)\|~v1_relat_1(k1_funct_1(X3,esk9_3(X1,X2,X3)))\|~v5_relat_1(k1_funct_1(X3,esk9_3(X1,X2,X3)),u1_struct_0(X2))\|~v1_funct_1(k1_funct_1(X3,esk9_3(X1,X2,X3)))\|~v1_exchsort(k1_funct_1(X3,esk9_3(X1,X2,X3)))\|k1_funct_1(X3,k1_exchsort(X3))!=X1\|~v1_relat_1(X3)\|~v1_funct_1(X3)\|~v1_exchsort(X3)\|~epred1_2(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_44])). cnf(c_0_161, negated_conjecture, (r2_hidden(esk10_3(esk3_0,esk2_0,k1_tarski(k2_tarski(k1_tarski(esk1_0),k2_tarski(esk3_0,esk1_0)))),k1_tarski(esk1_0))\|r2_hidden(k2_xboole_0(esk1_0,k1_tarski(esk1_0)),k1_tarski(esk1_0))\|~v1_exchsort(k1_tarski(k2_tarski(k1_tarski(esk1_0),k2_tarski(esk3_0,esk1_0))))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156, c_0_117]), c_0_118]), c_0_71])])])). cnf(c_0_162, plain, (X1=X2\|r2_hidden(X1,k1_tarski(X1))\|~r2_hidden(X2,k1_tarski(X1))), inference(csr,[status(thm)],[c_0_157, c_0_158])). cnf(c_0_163, negated_conjecture, (r2_hidden(esk1_0,k1_tarski(esk1_0))\|r2_hidden(k2_xboole_0(esk1_0,k1_tarski(esk1_0)),k1_tarski(esk1_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_159, c_0_150])])). cnf(c_0_164, plain, (v1_xboole_0(X3)\|m2_exchsort(X3,X2,X1)\|r2_hidden(k2_xboole_0(esk10_3(X1,X2,X3),k1_tarski(esk10_3(X1,X2,X3))),k9_xtuple_0(X3))\|k1_funct_1(X3,k1_exchsort(X3))!=X1\|~v1_relat_1(X3)\|~v1_funct_1(X3)\|~v1_exchsort(X3)\|~epred1_2(X2,X1)\|~v1_relat_1(k1_funct_1(X3,esk9_3(X1,X2,X3)))\|~v1_funct_1(k1_funct_1(X3,esk9_3(X1,X2,X3)))\|~v1_exchsort(k1_funct_1(X3,esk9_3(X1,X2,X3)))\|~v5_relat_1(k1_funct_1(X3,esk9_3(X1,X2,X3)),u1_struct_0(X2))), inference(rw,[status(thm)],[c_0_160, c_0_83])). cnf(c_0_165, negated_conjecture, (esk10_3(esk3_0,esk2_0,k1_tarski(k2_tarski(k1_tarski(esk1_0),k2_tarski(esk3_0,esk1_0))))=X1\|r2_hidden(k2_xboole_0(esk1_0,k1_tarski(esk1_0)),k1_tarski(esk1_0))\|k1_tarski(esk1_0)!=k1_tarski(X1)\|~v1_exchsort(k1_tarski(k2_tarski(k1_tarski(esk1_0),k2_tarski(esk3_0,esk1_0))))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_60, c_0_161])])). cnf(c_0_166, plain, (X1=k1_exchsort(k1_tarski(k2_tarski(k1_tarski(X2),k2_tarski(X3,X2))))\|~v2_exchsort(k1_tarski(k2_tarski(k1_tarski(X2),k2_tarski(X3,X2))),X1)\|~r2_hidden(X4,k1_tarski(X2))\|~v3_ordinal1(X4)\|~v3_ordinal1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_55, c_0_31])])). cnf(c_0_167, negated_conjecture, (k2_xboole_0(esk1_0,k1_tarski(esk1_0))=esk1_0\|r2_hidden(esk1_0,k1_tarski(esk1_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_162, c_0_163])])). cnf(c_0_168, plain, (v1_xboole_0(X3)\|m2_exchsort(X3,X2,X1)\|r2_hidden(k2_xboole_0(esk10_3(X1,X2,X3),k1_tarski(esk10_3(X1,X2,X3))),k9_xtuple_0(X3))\|k1_funct_1(X3,k1_exchsort(X3))!=X1\|~v1_relat_1(X3)\|~v1_funct_1(X3)\|~v1_exchsort(X3)\|~epred1_2(X2,X1)\|~v1_relat_1(k1_funct_1(X3,esk9_3(X1,X2,X3)))\|~v1_funct_1(k1_funct_1(X3,esk9_3(X1,X2,X3)))\|~v1_exchsort(k1_funct_1(X3,esk9_3(X1,X2,X3)))\|~v5_relat_1(k1_funct_1(X3,esk9_3(X1,X2,X3)),u1_struct_0(X2))), inference(evalgc,[status(thm)],[c_0_164])). cnf(c_0_169, negated_conjecture, (esk10_3(esk3_0,esk2_0,k1_tarski(k2_tarski(k1_tarski(esk1_0),k2_tarski(esk3_0,esk1_0))))=esk1_0\|r2_hidden(k2_xboole_0(esk1_0,k1_tarski(esk1_0)),k1_tarski(esk1_0))\|~v1_exchsort(k1_tarski(k2_tarski(k1_tarski(esk1_0),k2_tarski(esk3_0,esk1_0))))), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_165])])). cnf(c_0_170, plain, (k1_exchsort(k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X2,X1))))=X1\|~r2_hidden(X3,k1_tarski(X1))\|~v3_ordinal1(X3)\|~v3_ordinal1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_166, c_0_93])])). cnf(c_0_171, negated_conjecture, (r2_hidden(esk1_0,k1_tarski(esk1_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_163, c_0_167])])). cnf(c_0_172, plain, (r2_hidden(k2_xboole_0(esk1_0,k1_tarski(esk1_0)),k1_tarski(esk1_0))\|k1_funct_1(k1_tarski(k2_tarski(k1_tarski(esk1_0),k2_tarski(esk3_0,esk1_0))),k1_exchsort(k1_tarski(k2_tarski(k1_tarski(esk1_0),k2_tarski(esk3_0,esk1_0)))))!=esk3_0\|~v1_exchsort(k1_funct_1(k1_tarski(k2_tarski(k1_tarski(esk1_0),k2_tarski(esk3_0,esk1_0))),esk9_3(esk3_0,esk2_0,k1_tarski(k2_tarski(k1_tarski(esk1_0),k2_tarski(esk3_0,esk1_0))))))\|~v1_exchsort(k1_tarski(k2_tarski(k1_tarski(esk1_0),k2_tarski(esk3_0,esk1_0))))\|~v1_funct_1(k1_funct_1(k1_tarski(k2_tarski(k1_tarski(esk1_0),k2_tarski(esk3_0,esk1_0))),esk9_3(esk3_0,esk2_0,k1_tarski(k2_tarski(k1_tarski(esk1_0),k2_tarski(esk3_0,esk1_0))))))\|~v5_relat_1(k1_funct_1(k1_tarski(k2_tarski(k1_tarski(esk1_0),k2_tarski(esk3_0,esk1_0))),esk9_3(esk3_0,esk2_0,k1_tarski(k2_tarski(k1_tarski(esk1_0),k2_tarski(esk3_0,esk1_0))))),u1_struct_0(esk2_0))\|~v1_relat_1(k1_funct_1(k1_tarski(k2_tarski(k1_tarski(esk1_0),k2_tarski(esk3_0,esk1_0))),esk9_3(esk3_0,esk2_0,k1_tarski(k2_tarski(k1_tarski(esk1_0),k2_tarski(esk3_0,esk1_0))))))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_168, c_0_169]), c_0_91]), c_0_137]), c_0_94]), c_0_95])]), c_0_69]), c_0_144])])). cnf(c_0_173, negated_conjecture, (k1_exchsort(k1_tarski(k2_tarski(k1_tarski(esk1_0),k2_tarski(X1,esk1_0))))=esk1_0), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170, c_0_171]), c_0_71])])])). cnf(c_0_174, plain, (r2_hidden(k2_xboole_0(esk1_0,k1_tarski(esk1_0)),k1_tarski(esk1_0))\|~v1_exchsort(k1_funct_1(k1_tarski(k2_tarski(k1_tarski(esk1_0),k2_tarski(esk3_0,esk1_0))),esk9_3(esk3_0,esk2_0,k1_tarski(k2_tarski(k1_tarski(esk1_0),k2_tarski(esk3_0,esk1_0))))))\|~v1_exchsort(k1_tarski(k2_tarski(k1_tarski(esk1_0),k2_tarski(esk3_0,esk1_0))))\|~v1_funct_1(k1_funct_1(k1_tarski(k2_tarski(k1_tarski(esk1_0),k2_tarski(esk3_0,esk1_0))),esk9_3(esk3_0,esk2_0,k1_tarski(k2_tarski(k1_tarski(esk1_0),k2_tarski(esk3_0,esk1_0))))))\|~v5_relat_1(k1_funct_1(k1_tarski(k2_tarski(k1_tarski(esk1_0),k2_tarski(esk3_0,esk1_0))),esk9_3(esk3_0,esk2_0,k1_tarski(k2_tarski(k1_tarski(esk1_0),k2_tarski(esk3_0,esk1_0))))),u1_struct_0(esk2_0))\|~v1_relat_1(k1_funct_1(k1_tarski(k2_tarski(k1_tarski(esk1_0),k2_tarski(esk3_0,esk1_0))),esk9_3(esk3_0,esk2_0,k1_tarski(k2_tarski(k1_tarski(esk1_0),k2_tarski(esk3_0,esk1_0))))))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_172, c_0_173]), c_0_118])])])). fof(c_0_175, plain, ![X43]:r2_hidden(X43,k1_ordinal1(X43)), inference(variable_rename,[status(thm)],[t6_ordinal1])). cnf(c_0_176, negated_conjecture, (r2_hidden(k2_xboole_0(esk1_0,k1_tarski(esk1_0)),k1_tarski(esk1_0))\|~v1_exchsort(k1_tarski(k2_tarski(k1_tarski(esk1_0),k2_tarski(esk3_0,esk1_0))))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174, c_0_150]), c_0_118]), c_0_122]), c_0_118]), c_0_123]), c_0_118]), c_0_121]), c_0_118]), c_0_124])])])). cnf(c_0_177, plain, (r2_hidden(X1,k1_ordinal1(X1))), inference(split_conjunct,[status(thm)],[c_0_175])). cnf(c_0_178, negated_conjecture, (r2_hidden(k2_xboole_0(esk1_0,k1_tarski(esk1_0)),k1_tarski(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176, c_0_135]), c_0_71])])])). fof(c_0_179, plain, ![X40, X41]:(~r2_hidden(X40,X41)\|~r2_hidden(X41,X40)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden])])])). cnf(c_0_180, plain, (r2_hidden(X1,k2_xboole_0(X1,k1_tarski(X1)))), inference(rw,[status(thm)],[c_0_177, c_0_83])). cnf(c_0_181, negated_conjecture, (k2_xboole_0(esk1_0,k1_tarski(esk1_0))=X1\|k1_tarski(esk1_0)!=k1_tarski(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_60, c_0_178])])). cnf(c_0_182, plain, (~r2_hidden(X1,X2)\|~r2_hidden(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_179])). cnf(c_0_183, plain, (r2_hidden(X1,k2_xboole_0(X1,k1_tarski(X1)))), inference(evalgc,[status(thm)],[c_0_180])). cnf(c_0_184, negated_conjecture, (k2_xboole_0(esk1_0,k1_tarski(esk1_0))=esk1_0), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_181])])). cnf(c_0_185, plain, (~r2_hidden(X2,X1)\|~r2_hidden(X1,X2)), inference(evalgc,[status(thm)],[c_0_182])). cnf(c_0_186, negated_conjecture, (r2_hidden(esk1_0,esk1_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_183, c_0_184])])). cnf(c_0_187, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185, c_0_186]), c_0_186])]), ['proof']). # SZS output end CNFRefutation	reserve a,a1,a2,b,c,d for ordinal number, n,m,k for Nat, x,y,z,t,X,Y,Z for set; reserve f,g for Function; reserve A,B,C for array; reserve O for connected non empty Poset; reserve R,Q for array of O; reserve T for non empty array of O; reserve p,q,r,s for Element of dom T; theorem Th75: {[a,R]} is arr_computation of R proof reconsider C = {[a,R]} as a-based non empty array; C is arr_computation of R proof A1: dom C = {a} & a in {a} by FUNCT_5:12,TARSKI:def 1; then base-C = a by Def4; hence C.(base-C) = R by GRFUNC_1:6; hereby let b; assume b in dom C; then a = b by A1,TARSKI:def 1; hence C.b is array of O by GRFUNC_1:6; end; let b; assume b in dom C & succ b in dom C; then a = b & a = succ b by A1,TARSKI:def 1; then a in a by ORDINAL1:6; hence thesis; end; hence thesis; end;	Convert the following ATP output trace into a readable Mizar proof.
t84_sincos10	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t6_boole, axiom, ![X1]:(v1_xboole_0(X1)=>X1=k1_xboole_0), file('/scratch/mptp/predsminms1/t84_sincos10__0', t6_boole)). fof(cc2_relset_1, axiom, ![X1, X2, X3]:(m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))=>(v4_relat_1(X3,X1)&v5_relat_1(X3,X2))), file('/scratch/mptp/predsminms1/t84_sincos10__0', cc2_relset_1)). fof(dt_k2_partfun1, axiom, ![X1, X2, X3, X4]:((v1_funct_1(X3)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2))))=>(v1_funct_1(k2_partfun1(X1,X2,X3,X4))&m1_subset_1(k2_partfun1(X1,X2,X3,X4),k1_zfmisc_1(k2_zfmisc_1(X1,X2))))), file('/scratch/mptp/predsminms1/t84_sincos10__0', dt_k2_partfun1)). fof(t29_rfunct_2, axiom, ![X1, X2, X3]:((v1_funct_1(X3)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))))=>((r1_tarski(X1,X2)&v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,X3,X2)))=>v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,X3,X1)))), file('/scratch/mptp/predsminms1/t84_sincos10__0', t29_rfunct_2)). fof(redefinition_k6_numbers, axiom, k6_numbers=k1_xboole_0, file('/scratch/mptp/predsminms1/t84_sincos10__0', redefinition_k6_numbers)). fof(rc4_xreal_0, axiom, ?[X1]:(v1_xboole_0(X1)&(v1_xcmplx_0(X1)&(v1_xxreal_0(X1)&v1_xreal_0(X1)))), file('/scratch/mptp/predsminms1/t84_sincos10__0', rc4_xreal_0)). fof(redefinition_k2_relset_1, axiom, ![X1, X2]:((v1_relat_1(X2)&v5_relat_1(X2,X1))=>k2_relset_1(X1,X2)=k10_xtuple_0(X2)), file('/scratch/mptp/predsminms1/t84_sincos10__0', redefinition_k2_relset_1)). fof(cc1_relset_1, axiom, ![X1, X2, X3]:(m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))=>v1_relat_1(X3)), file('/scratch/mptp/predsminms1/t84_sincos10__0', cc1_relset_1)). fof(redefinition_k2_partfun1, axiom, ![X1, X2, X3, X4]:((v1_funct_1(X3)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2))))=>k2_partfun1(X1,X2,X3,X4)=k5_relat_1(X3,X4)), file('/scratch/mptp/predsminms1/t84_sincos10__0', redefinition_k2_partfun1)). fof(t80_sincos10, axiom, v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,k4_sincos10,k7_relset_1(k1_numbers,k1_numbers,k2_fdiff_9,k4_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__2))))), file('/scratch/mptp/predsminms1/t84_sincos10__0', t80_sincos10)). fof(dt_k4_sincos10, axiom, (v1_funct_1(k4_sincos10)&m1_subset_1(k4_sincos10,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))), file('/scratch/mptp/predsminms1/t84_sincos10__0', dt_k4_sincos10)). fof(t115_relat_1, axiom, ![X1, X2]:(v1_relat_1(X2)=>k10_xtuple_0(k5_relat_1(X2,X1))=k7_relat_1(X2,X1)), file('/scratch/mptp/predsminms1/t84_sincos10__0', t115_relat_1)). fof(dt_k2_fdiff_9, axiom, (v1_funct_1(k2_fdiff_9)&m1_subset_1(k2_fdiff_9,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))), file('/scratch/mptp/predsminms1/t84_sincos10__0', dt_k2_fdiff_9)). fof(redefinition_k7_relset_1, axiom, ![X1, X2, X3, X4]:(m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))=>k7_relset_1(X1,X2,X3,X4)=k7_relat_1(X3,X4)), file('/scratch/mptp/predsminms1/t84_sincos10__0', redefinition_k7_relset_1)). fof(t123_relat_1, axiom, ![X1, X2, X3]:(v1_relat_1(X3)=>(r1_tarski(X1,X2)=>r1_tarski(k7_relat_1(X3,X1),k7_relat_1(X3,X2)))), file('/scratch/mptp/predsminms1/t84_sincos10__0', t123_relat_1)). fof(t44_sincos10, axiom, k2_relset_1(k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k2_fdiff_9,k1_rcomp_1(k10_real_1(k32_sin_cos,np__4),k10_real_1(k32_sin_cos,np__2))))=k1_rcomp_1(np__1,k7_square_1(np__2)), file('/scratch/mptp/predsminms1/t84_sincos10__0', t44_sincos10)). fof(t84_sincos10, conjecture, v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,k4_sincos10,k1_rcomp_1(np__1,k7_square_1(np__2)))), file('/scratch/mptp/predsminms1/t84_sincos10__0', t84_sincos10)). fof(d12_xxreal_2, axiom, ![X1]:(v2_membered(X1)=>(v6_xxreal_2(X1)<=>![X2]:(v1_xxreal_0(X2)=>![X3]:(v1_xxreal_0(X3)=>((r2_hidden(X2,X1)&r2_hidden(X3,X1))=>r1_tarski(k1_xxreal_1(X2,X3),X1)))))), file('/scratch/mptp/predsminms1/t84_sincos10__0', d12_xxreal_2)). fof(redefinition_k1_rcomp_1, axiom, ![X1, X2]:((v1_xreal_0(X1)&v1_xreal_0(X2))=>k1_rcomp_1(X1,X2)=k1_xxreal_1(X1,X2)), file('/scratch/mptp/predsminms1/t84_sincos10__0', redefinition_k1_rcomp_1)). fof(cc4_xreal_0, axiom, ![X1]:(v1_xreal_0(X1)=>v1_xxreal_0(X1)), file('/scratch/mptp/predsminms1/t84_sincos10__0', cc4_xreal_0)). fof(fc14_xxreal_2, axiom, ![X1, X2]:((v1_xxreal_0(X1)&v1_xxreal_0(X2))=>v6_xxreal_2(k3_xxreal_1(X1,X2))), file('/scratch/mptp/predsminms1/t84_sincos10__0', fc14_xxreal_2)). fof(redefinition_k4_rcomp_1, axiom, ![X1, X2]:((v1_xxreal_0(X1)&v1_xreal_0(X2))=>k4_rcomp_1(X1,X2)=k3_xxreal_1(X1,X2)), file('/scratch/mptp/predsminms1/t84_sincos10__0', redefinition_k4_rcomp_1)). fof(l20_sincos10, axiom, (r2_hidden(k10_real_1(k32_sin_cos,np__4),k4_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__2)))&r2_hidden(k10_real_1(k32_sin_cos,np__2),k4_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__2)))), file('/scratch/mptp/predsminms1/t84_sincos10__0', l20_sincos10)). fof(cc20_membered, axiom, ![X1]:(v2_membered(X1)=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(X1))=>v2_membered(X2))), file('/scratch/mptp/predsminms1/t84_sincos10__0', cc20_membered)). fof(dt_k4_rcomp_1, axiom, ![X1, X2]:((v1_xxreal_0(X1)&v1_xreal_0(X2))=>m1_subset_1(k4_rcomp_1(X1,X2),k1_zfmisc_1(k1_numbers))), file('/scratch/mptp/predsminms1/t84_sincos10__0', dt_k4_rcomp_1)). fof(cc4_membered, axiom, ![X1]:(v3_membered(X1)=>v2_membered(X1)), file('/scratch/mptp/predsminms1/t84_sincos10__0', cc4_membered)). fof(fc3_membered, axiom, v3_membered(k1_numbers), file('/scratch/mptp/predsminms1/t84_sincos10__0', fc3_membered)). fof(t4_subset, axiom, ![X1, X2, X3]:((r2_hidden(X1,X2)&m1_subset_1(X2,k1_zfmisc_1(X3)))=>m1_subset_1(X1,X3)), file('/scratch/mptp/predsminms1/t84_sincos10__0', t4_subset)). fof(cc1_xreal_0, axiom, ![X1]:(m1_subset_1(X1,k1_numbers)=>v1_xreal_0(X1)), file('/scratch/mptp/predsminms1/t84_sincos10__0', cc1_xreal_0)). fof(dt_k10_real_1, axiom, ![X1, X2]:((m1_subset_1(X1,k1_numbers)&v1_xreal_0(X2))=>m1_subset_1(k10_real_1(X1,X2),k1_numbers)), file('/scratch/mptp/predsminms1/t84_sincos10__0', dt_k10_real_1)). fof(dt_k32_sin_cos, axiom, m1_subset_1(k32_sin_cos,k1_numbers), file('/scratch/mptp/predsminms1/t84_sincos10__0', dt_k32_sin_cos)). fof(spc2_numerals, axiom, ((v2_xxreal_0(np__2)&m2_subset_1(np__2,k1_numbers,k5_numbers))&(m1_subset_1(np__2,k5_numbers)&m1_subset_1(np__2,k1_numbers))), file('/scratch/mptp/predsminms1/t84_sincos10__0', spc2_numerals)). fof(c_0_32, plain, ![X24]:(~v1_xboole_0(X24)\|X24=k1_xboole_0), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])])). fof(c_0_33, plain, ![X20, X21, X22]:((v4_relat_1(X22,X20)\|~m1_subset_1(X22,k1_zfmisc_1(k2_zfmisc_1(X20,X21))))&(v5_relat_1(X22,X21)\|~m1_subset_1(X22,k1_zfmisc_1(k2_zfmisc_1(X20,X21))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_relset_1])])])). fof(c_0_34, plain, ![X14, X15, X16, X17]:((v1_funct_1(k2_partfun1(X14,X15,X16,X17))\|(~v1_funct_1(X16)\|~m1_subset_1(X16,k1_zfmisc_1(k2_zfmisc_1(X14,X15)))))&(m1_subset_1(k2_partfun1(X14,X15,X16,X17),k1_zfmisc_1(k2_zfmisc_1(X14,X15)))\|(~v1_funct_1(X16)\|~m1_subset_1(X16,k1_zfmisc_1(k2_zfmisc_1(X14,X15)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_partfun1])])])). fof(c_0_35, plain, ![X37, X38, X39]:(~v1_funct_1(X39)\|~m1_subset_1(X39,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))\|(~r1_tarski(X37,X38)\|~v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,X39,X38))\|v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,X39,X37)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t29_rfunct_2])])). cnf(c_0_36, plain, (X1=k1_xboole_0\|~v1_xboole_0(X1)), inference(split_conjunct,[status(thm)],[c_0_32])). cnf(c_0_37, plain, (k6_numbers=k1_xboole_0), inference(split_conjunct,[status(thm)],[redefinition_k6_numbers])). fof(c_0_38, plain, (v1_xboole_0(esk1_0)&(v1_xcmplx_0(esk1_0)&(v1_xxreal_0(esk1_0)&v1_xreal_0(esk1_0)))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc4_xreal_0])])). fof(c_0_39, plain, ![X18, X19]:(~v1_relat_1(X19)\|~v5_relat_1(X19,X18)\|k2_relset_1(X18,X19)=k10_xtuple_0(X19)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k2_relset_1])])). cnf(c_0_40, plain, (v5_relat_1(X1,X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X3,X2)))), inference(split_conjunct,[status(thm)],[c_0_33])). cnf(c_0_41, plain, (m1_subset_1(k2_partfun1(X1,X2,X3,X4),k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_34])). fof(c_0_42, plain, ![X9, X10, X11]:(~m1_subset_1(X11,k1_zfmisc_1(k2_zfmisc_1(X9,X10)))\|v1_relat_1(X11)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relset_1])])). fof(c_0_43, plain, ![X5, X6, X7, X8]:(~v1_funct_1(X7)\|~m1_subset_1(X7,k1_zfmisc_1(k2_zfmisc_1(X5,X6)))\|k2_partfun1(X5,X6,X7,X8)=k5_relat_1(X7,X8)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k2_partfun1])])). cnf(c_0_44, plain, (v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,X1,X2))\|~v1_funct_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))\|~r1_tarski(X2,X3)\|~v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,X1,X3))), inference(split_conjunct,[status(thm)],[c_0_35])). cnf(c_0_45, plain, (v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,k4_sincos10,k7_relset_1(k1_numbers,k1_numbers,k2_fdiff_9,k4_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__2)))))), inference(split_conjunct,[status(thm)],[t80_sincos10])). cnf(c_0_46, plain, (m1_subset_1(k4_sincos10,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))), inference(split_conjunct,[status(thm)],[dt_k4_sincos10])). cnf(c_0_47, plain, (v1_funct_1(k4_sincos10)), inference(split_conjunct,[status(thm)],[dt_k4_sincos10])). cnf(c_0_48, plain, (X1=k1_xboole_0\|~v1_xboole_0(X1)), inference(evalgc,[status(thm)],[c_0_36])). cnf(c_0_49, plain, (k1_xboole_0=k6_numbers), inference(evalgc,[status(thm)],[c_0_37])). cnf(c_0_50, plain, (v1_xboole_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_38])). cnf(c_0_51, plain, (k2_relset_1(X2,X1)=k10_xtuple_0(X1)\|~v1_relat_1(X1)\|~v5_relat_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_39])). cnf(c_0_52, plain, (v5_relat_1(X1,X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X3,X2)))), inference(evalgc,[status(thm)],[c_0_40])). cnf(c_0_53, plain, (m1_subset_1(k2_partfun1(X1,X2,X3,X4),k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(evalgc,[status(thm)],[c_0_41])). cnf(c_0_54, plain, (v1_relat_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_42])). fof(c_0_55, plain, ![X12, X13]:(~v1_relat_1(X13)\|k10_xtuple_0(k5_relat_1(X13,X12))=k7_relat_1(X13,X12)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t115_relat_1])])). cnf(c_0_56, plain, (k2_partfun1(X2,X3,X1,X4)=k5_relat_1(X1,X4)\|~v1_funct_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_43])). cnf(c_0_57, plain, (m1_subset_1(k2_fdiff_9,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))), inference(split_conjunct,[status(thm)],[dt_k2_fdiff_9])). cnf(c_0_58, plain, (v1_funct_1(k2_fdiff_9)), inference(split_conjunct,[status(thm)],[dt_k2_fdiff_9])). cnf(c_0_59, plain, (v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,X1,X2))\|~v1_funct_1(X1)\|~r1_tarski(X2,X3)\|~v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,X1,X3))\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))), inference(evalgc,[status(thm)],[c_0_44])). cnf(c_0_60, plain, (v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,k4_sincos10,k7_relset_1(k1_numbers,k1_numbers,k2_fdiff_9,k4_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__2)))))), inference(evalgc,[status(thm)],[c_0_45])). cnf(c_0_61, plain, (m1_subset_1(k4_sincos10,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))), inference(evalgc,[status(thm)],[c_0_46])). cnf(c_0_62, plain, (v1_funct_1(k4_sincos10)), inference(evalgc,[status(thm)],[c_0_47])). cnf(c_0_63, plain, (X1=k6_numbers\|~v1_xboole_0(X1)), inference(rw,[status(thm)],[c_0_48, c_0_49])). cnf(c_0_64, plain, (v1_xboole_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_50])). fof(c_0_65, plain, ![X33, X34, X35, X36]:(~m1_subset_1(X35,k1_zfmisc_1(k2_zfmisc_1(X33,X34)))\|k7_relset_1(X33,X34,X35,X36)=k7_relat_1(X35,X36)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k7_relset_1])])). cnf(c_0_66, plain, (k2_relset_1(X2,X1)=k10_xtuple_0(X1)\|~v1_relat_1(X1)\|~v5_relat_1(X1,X2)), inference(evalgc,[status(thm)],[c_0_51])). cnf(c_0_67, plain, (v5_relat_1(k2_partfun1(X1,X2,X3,X4),X2)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_52, c_0_53])])). cnf(c_0_68, plain, (v1_relat_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(evalgc,[status(thm)],[c_0_54])). cnf(c_0_69, plain, (k10_xtuple_0(k5_relat_1(X1,X2))=k7_relat_1(X1,X2)\|~v1_relat_1(X1)), inference(split_conjunct,[status(thm)],[c_0_55])). cnf(c_0_70, plain, (k2_partfun1(X2,X3,X1,X4)=k5_relat_1(X1,X4)\|~v1_funct_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(evalgc,[status(thm)],[c_0_56])). cnf(c_0_71, plain, (m1_subset_1(k2_fdiff_9,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))), inference(evalgc,[status(thm)],[c_0_57])). cnf(c_0_72, plain, (v1_funct_1(k2_fdiff_9)), inference(evalgc,[status(thm)],[c_0_58])). cnf(c_0_73, plain, (v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,k4_sincos10,X1))\|~r1_tarski(X1,k7_relset_1(k1_numbers,k1_numbers,k2_fdiff_9,k4_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__2))))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59, c_0_60]), c_0_61]), c_0_62])])])). cnf(c_0_74, plain, (k6_numbers=esk1_0), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_63, c_0_64])])). cnf(c_0_75, plain, (k7_relset_1(X2,X3,X1,X4)=k7_relat_1(X1,X4)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_65])). fof(c_0_76, plain, ![X30, X31, X32]:(~v1_relat_1(X32)\|(~r1_tarski(X30,X31)\|r1_tarski(k7_relat_1(X32,X30),k7_relat_1(X32,X31)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t123_relat_1])])). cnf(c_0_77, plain, (k2_relset_1(k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k2_fdiff_9,k1_rcomp_1(k10_real_1(k32_sin_cos,np__4),k10_real_1(k32_sin_cos,np__2))))=k1_rcomp_1(np__1,k7_square_1(np__2))), inference(split_conjunct,[status(thm)],[t44_sincos10])). cnf(c_0_78, plain, (k2_relset_1(X1,k2_partfun1(X2,X1,X3,X4))=k10_xtuple_0(k2_partfun1(X2,X1,X3,X4))\|~v1_relat_1(k2_partfun1(X2,X1,X3,X4))\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X2,X1)))\|~v1_funct_1(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_66, c_0_67])])). cnf(c_0_79, plain, (v1_relat_1(k2_partfun1(X1,X2,X3,X4))\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_68, c_0_53])])). cnf(c_0_80, plain, (k10_xtuple_0(k5_relat_1(X1,X2))=k7_relat_1(X1,X2)\|~v1_relat_1(X1)), inference(evalgc,[status(thm)],[c_0_69])). cnf(c_0_81, plain, (k5_relat_1(k2_fdiff_9,X1)=k2_partfun1(k1_numbers,k1_numbers,k2_fdiff_9,X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70, c_0_71]), c_0_72])])])). fof(c_0_82, negated_conjecture, ~(v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,k4_sincos10,k1_rcomp_1(np__1,k7_square_1(np__2))))), inference(assume_negation,[status(cth)],[t84_sincos10])). fof(c_0_83, plain, ![X43, X44, X45]:((~v6_xxreal_2(X43)\|(~v1_xxreal_0(X44)\|(~v1_xxreal_0(X45)\|(~r2_hidden(X44,X43)\|~r2_hidden(X45,X43)\|r1_tarski(k1_xxreal_1(X44,X45),X43))))\|~v2_membered(X43))&((v1_xxreal_0(esk2_1(X43))\|v6_xxreal_2(X43)\|~v2_membered(X43))&((v1_xxreal_0(esk3_1(X43))\|v6_xxreal_2(X43)\|~v2_membered(X43))&(((r2_hidden(esk2_1(X43),X43)\|v6_xxreal_2(X43)\|~v2_membered(X43))&(r2_hidden(esk3_1(X43),X43)\|v6_xxreal_2(X43)\|~v2_membered(X43)))&(~r1_tarski(k1_xxreal_1(esk2_1(X43),esk3_1(X43)),X43)\|v6_xxreal_2(X43)\|~v2_membered(X43)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d12_xxreal_2])])])])])). fof(c_0_84, plain, ![X41, X42]:(~v1_xreal_0(X41)\|~v1_xreal_0(X42)\|k1_rcomp_1(X41,X42)=k1_xxreal_1(X41,X42)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k1_rcomp_1])])). cnf(c_0_85, plain, (v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,k4_sincos10,X1))\|~r1_tarski(X1,k7_relset_1(k1_numbers,k1_numbers,k2_fdiff_9,k4_rcomp_1(esk1_0,k10_real_1(k32_sin_cos,np__2))))), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[c_0_73, c_0_74])])). cnf(c_0_86, plain, (k7_relset_1(X2,X3,X1,X4)=k7_relat_1(X1,X4)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(evalgc,[status(thm)],[c_0_75])). cnf(c_0_87, plain, (r1_tarski(k7_relat_1(X1,X2),k7_relat_1(X1,X3))\|~v1_relat_1(X1)\|~r1_tarski(X2,X3)), inference(split_conjunct,[status(thm)],[c_0_76])). cnf(c_0_88, plain, (k2_relset_1(k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k2_fdiff_9,k1_rcomp_1(k10_real_1(k32_sin_cos,np__4),k10_real_1(k32_sin_cos,np__2))))=k1_rcomp_1(np__1,k7_square_1(np__2))), inference(evalgc,[status(thm)],[c_0_77])). cnf(c_0_89, plain, (k2_relset_1(X1,k2_partfun1(X2,X1,X3,X4))=k10_xtuple_0(k2_partfun1(X2,X1,X3,X4))\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X2,X1)))\|~v1_funct_1(X3)), inference(csr,[status(thm)],[c_0_78, c_0_79])). cnf(c_0_90, plain, (k10_xtuple_0(k2_partfun1(k1_numbers,k1_numbers,k2_fdiff_9,X1))=k7_relat_1(k2_fdiff_9,X1)\|~v1_relat_1(k2_fdiff_9)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_80, c_0_81])])). cnf(c_0_91, plain, (v1_relat_1(k2_fdiff_9)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_68, c_0_71])])). fof(c_0_92, negated_conjecture, ~v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,k4_sincos10,k1_rcomp_1(np__1,k7_square_1(np__2)))), inference(fof_simplification,[status(thm)],[c_0_82])). cnf(c_0_93, plain, (r1_tarski(k1_xxreal_1(X2,X3),X1)\|~v6_xxreal_2(X1)\|~v1_xxreal_0(X2)\|~v1_xxreal_0(X3)\|~r2_hidden(X2,X1)\|~r2_hidden(X3,X1)\|~v2_membered(X1)), inference(split_conjunct,[status(thm)],[c_0_83])). cnf(c_0_94, plain, (k1_rcomp_1(X1,X2)=k1_xxreal_1(X1,X2)\|~v1_xreal_0(X1)\|~v1_xreal_0(X2)), inference(split_conjunct,[status(thm)],[c_0_84])). fof(c_0_95, plain, ![X25]:(~v1_xreal_0(X25)\|v1_xxreal_0(X25)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc4_xreal_0])])). fof(c_0_96, plain, ![X28, X29]:(~v1_xxreal_0(X28)\|~v1_xxreal_0(X29)\|v6_xxreal_2(k3_xxreal_1(X28,X29))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc14_xxreal_2])])). fof(c_0_97, plain, ![X26, X27]:(~v1_xxreal_0(X26)\|~v1_xreal_0(X27)\|k4_rcomp_1(X26,X27)=k3_xxreal_1(X26,X27)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k4_rcomp_1])])). cnf(c_0_98, plain, (v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,k4_sincos10,X1))\|~r1_tarski(X1,k7_relat_1(k2_fdiff_9,k4_rcomp_1(esk1_0,k10_real_1(k32_sin_cos,np__2))))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85, c_0_86]), c_0_71])])])). cnf(c_0_99, plain, (r1_tarski(k7_relat_1(X1,X2),k7_relat_1(X1,X3))\|~v1_relat_1(X1)\|~r1_tarski(X2,X3)), inference(evalgc,[status(thm)],[c_0_87])). cnf(c_0_100, plain, (k10_xtuple_0(k2_partfun1(k1_numbers,k1_numbers,k2_fdiff_9,k1_rcomp_1(k10_real_1(k32_sin_cos,np__4),k10_real_1(k32_sin_cos,np__2))))=k1_rcomp_1(np__1,k7_square_1(np__2))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88, c_0_89]), c_0_71]), c_0_72])])])). cnf(c_0_101, plain, (k10_xtuple_0(k2_partfun1(k1_numbers,k1_numbers,k2_fdiff_9,X1))=k7_relat_1(k2_fdiff_9,X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_90, c_0_91])])). cnf(c_0_102, negated_conjecture, (~v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,k4_sincos10,k1_rcomp_1(np__1,k7_square_1(np__2))))), inference(split_conjunct,[status(thm)],[c_0_92])). cnf(c_0_103, plain, (r1_tarski(k1_xxreal_1(X2,X3),X1)\|~v1_xxreal_0(X3)\|~v1_xxreal_0(X2)\|~v6_xxreal_2(X1)\|~v2_membered(X1)\|~r2_hidden(X3,X1)\|~r2_hidden(X2,X1)), inference(evalgc,[status(thm)],[c_0_93])). cnf(c_0_104, plain, (k1_xxreal_1(X1,X2)=k1_rcomp_1(X1,X2)\|~v1_xreal_0(X2)\|~v1_xreal_0(X1)), inference(evalgc,[status(thm)],[c_0_94])). cnf(c_0_105, plain, (v1_xxreal_0(X1)\|~v1_xreal_0(X1)), inference(split_conjunct,[status(thm)],[c_0_95])). cnf(c_0_106, plain, (r2_hidden(k10_real_1(k32_sin_cos,np__2),k4_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__2)))), inference(split_conjunct,[status(thm)],[l20_sincos10])). cnf(c_0_107, plain, (r2_hidden(k10_real_1(k32_sin_cos,np__4),k4_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__2)))), inference(split_conjunct,[status(thm)],[l20_sincos10])). cnf(c_0_108, plain, (v6_xxreal_2(k3_xxreal_1(X1,X2))\|~v1_xxreal_0(X1)\|~v1_xxreal_0(X2)), inference(split_conjunct,[status(thm)],[c_0_96])). cnf(c_0_109, plain, (k4_rcomp_1(X1,X2)=k3_xxreal_1(X1,X2)\|~v1_xxreal_0(X1)\|~v1_xreal_0(X2)), inference(split_conjunct,[status(thm)],[c_0_97])). fof(c_0_110, plain, ![X49, X50]:(~v2_membered(X49)\|(~m1_subset_1(X50,k1_zfmisc_1(X49))\|v2_membered(X50))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc20_membered])])])). fof(c_0_111, plain, ![X51, X52]:(~v1_xxreal_0(X51)\|~v1_xreal_0(X52)\|m1_subset_1(k4_rcomp_1(X51,X52),k1_zfmisc_1(k1_numbers))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k4_rcomp_1])])). fof(c_0_112, plain, ![X48]:(~v3_membered(X48)\|v2_membered(X48)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc4_membered])])). cnf(c_0_113, plain, (v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,k4_sincos10,k7_relat_1(k2_fdiff_9,X1)))\|~r1_tarski(X1,k4_rcomp_1(esk1_0,k10_real_1(k32_sin_cos,np__2)))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98, c_0_99]), c_0_91])])])). cnf(c_0_114, plain, (k7_relat_1(k2_fdiff_9,k1_rcomp_1(k10_real_1(k32_sin_cos,np__4),k10_real_1(k32_sin_cos,np__2)))=k1_rcomp_1(np__1,k7_square_1(np__2))), inference(rw,[status(thm)],[c_0_100, c_0_101])). cnf(c_0_115, negated_conjecture, (~v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,k4_sincos10,k1_rcomp_1(np__1,k7_square_1(np__2))))), inference(evalgc,[status(thm)],[c_0_102])). cnf(c_0_116, plain, (r1_tarski(k1_rcomp_1(X1,X2),X3)\|~v2_membered(X3)\|~r2_hidden(X2,X3)\|~r2_hidden(X1,X3)\|~v6_xxreal_2(X3)\|~v1_xxreal_0(X2)\|~v1_xxreal_0(X1)\|~v1_xreal_0(X2)\|~v1_xreal_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_103, c_0_104])])). cnf(c_0_117, plain, (v1_xxreal_0(X1)\|~v1_xreal_0(X1)), inference(evalgc,[status(thm)],[c_0_105])). cnf(c_0_118, plain, (r2_hidden(k10_real_1(k32_sin_cos,np__2),k4_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__2)))), inference(evalgc,[status(thm)],[c_0_106])). cnf(c_0_119, plain, (r2_hidden(k10_real_1(k32_sin_cos,np__4),k4_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__2)))), inference(evalgc,[status(thm)],[c_0_107])). cnf(c_0_120, plain, (v6_xxreal_2(k3_xxreal_1(X1,X2))\|~v1_xxreal_0(X2)\|~v1_xxreal_0(X1)), inference(evalgc,[status(thm)],[c_0_108])). cnf(c_0_121, plain, (k3_xxreal_1(X1,X2)=k4_rcomp_1(X1,X2)\|~v1_xxreal_0(X1)\|~v1_xreal_0(X2)), inference(evalgc,[status(thm)],[c_0_109])). cnf(c_0_122, plain, (v2_membered(X2)\|~v2_membered(X1)\|~m1_subset_1(X2,k1_zfmisc_1(X1))), inference(split_conjunct,[status(thm)],[c_0_110])). cnf(c_0_123, plain, (m1_subset_1(k4_rcomp_1(X1,X2),k1_zfmisc_1(k1_numbers))\|~v1_xxreal_0(X1)\|~v1_xreal_0(X2)), inference(split_conjunct,[status(thm)],[c_0_111])). cnf(c_0_124, plain, (v2_membered(X1)\|~v3_membered(X1)), inference(split_conjunct,[status(thm)],[c_0_112])). cnf(c_0_125, plain, (v3_membered(k1_numbers)), inference(split_conjunct,[status(thm)],[fc3_membered])). cnf(c_0_126, plain, (~r1_tarski(k1_rcomp_1(k10_real_1(k32_sin_cos,np__4),k10_real_1(k32_sin_cos,np__2)),k4_rcomp_1(esk1_0,k10_real_1(k32_sin_cos,np__2)))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_113, c_0_114]), c_0_115])])). cnf(c_0_127, plain, (r1_tarski(k1_rcomp_1(X1,X2),X3)\|~v2_membered(X3)\|~r2_hidden(X2,X3)\|~r2_hidden(X1,X3)\|~v6_xxreal_2(X3)\|~v1_xreal_0(X2)\|~v1_xreal_0(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_116, c_0_117]), c_0_117])). cnf(c_0_128, plain, (r2_hidden(k10_real_1(k32_sin_cos,np__2),k4_rcomp_1(esk1_0,k10_real_1(k32_sin_cos,np__2)))), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[c_0_118, c_0_74])])). cnf(c_0_129, plain, (r2_hidden(k10_real_1(k32_sin_cos,np__4),k4_rcomp_1(esk1_0,k10_real_1(k32_sin_cos,np__2)))), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[c_0_119, c_0_74])])). cnf(c_0_130, plain, (v6_xxreal_2(k4_rcomp_1(X1,X2))\|~v1_xxreal_0(X2)\|~v1_xxreal_0(X1)\|~v1_xreal_0(X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_120, c_0_121])])). cnf(c_0_131, plain, (v1_xxreal_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_38])). cnf(c_0_132, plain, (v2_membered(X2)\|~v2_membered(X1)\|~m1_subset_1(X2,k1_zfmisc_1(X1))), inference(evalgc,[status(thm)],[c_0_122])). cnf(c_0_133, plain, (m1_subset_1(k4_rcomp_1(X1,X2),k1_zfmisc_1(k1_numbers))\|~v1_xxreal_0(X1)\|~v1_xreal_0(X2)), inference(evalgc,[status(thm)],[c_0_123])). cnf(c_0_134, plain, (v2_membered(X1)\|~v3_membered(X1)), inference(evalgc,[status(thm)],[c_0_124])). cnf(c_0_135, plain, (v3_membered(k1_numbers)), inference(evalgc,[status(thm)],[c_0_125])). fof(c_0_136, plain, ![X55, X56, X57]:(~r2_hidden(X55,X56)\|~m1_subset_1(X56,k1_zfmisc_1(X57))\|m1_subset_1(X55,X57)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])])). cnf(c_0_137, plain, (~v2_membered(k4_rcomp_1(esk1_0,k10_real_1(k32_sin_cos,np__2)))\|~v6_xxreal_2(k4_rcomp_1(esk1_0,k10_real_1(k32_sin_cos,np__2)))\|~v1_xreal_0(k10_real_1(k32_sin_cos,np__2))\|~v1_xreal_0(k10_real_1(k32_sin_cos,np__4))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126, c_0_127]), c_0_128]), c_0_129])])])). cnf(c_0_138, plain, (v6_xxreal_2(k4_rcomp_1(X1,X2))\|~v1_xreal_0(X2)\|~v1_xxreal_0(X1)), inference(csr,[status(thm)],[c_0_130, c_0_117])). cnf(c_0_139, plain, (v1_xxreal_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_131])). cnf(c_0_140, plain, (v2_membered(k4_rcomp_1(X1,X2))\|~v2_membered(k1_numbers)\|~v1_xreal_0(X2)\|~v1_xxreal_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_132, c_0_133])])). cnf(c_0_141, plain, (v2_membered(k1_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_134, c_0_135])])). fof(c_0_142, plain, ![X40]:(~m1_subset_1(X40,k1_numbers)\|v1_xreal_0(X40)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_xreal_0])])). cnf(c_0_143, plain, (m1_subset_1(X1,X3)\|~r2_hidden(X1,X2)\|~m1_subset_1(X2,k1_zfmisc_1(X3))), inference(split_conjunct,[status(thm)],[c_0_136])). cnf(c_0_144, plain, (~v2_membered(k4_rcomp_1(esk1_0,k10_real_1(k32_sin_cos,np__2)))\|~v1_xreal_0(k10_real_1(k32_sin_cos,np__2))\|~v1_xreal_0(k10_real_1(k32_sin_cos,np__4))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137, c_0_138]), c_0_139])])])). cnf(c_0_145, plain, (v2_membered(k4_rcomp_1(X1,X2))\|~v1_xreal_0(X2)\|~v1_xxreal_0(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_140, c_0_141])])). cnf(c_0_146, plain, (v1_xreal_0(X1)\|~m1_subset_1(X1,k1_numbers)), inference(split_conjunct,[status(thm)],[c_0_142])). cnf(c_0_147, plain, (m1_subset_1(X1,X3)\|~r2_hidden(X1,X2)\|~m1_subset_1(X2,k1_zfmisc_1(X3))), inference(evalgc,[status(thm)],[c_0_143])). cnf(c_0_148, plain, (~v1_xreal_0(k10_real_1(k32_sin_cos,np__2))\|~v1_xreal_0(k10_real_1(k32_sin_cos,np__4))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144, c_0_145]), c_0_139])])])). cnf(c_0_149, plain, (v1_xreal_0(X1)\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[c_0_146])). cnf(c_0_150, plain, (m1_subset_1(X1,k1_numbers)\|~r2_hidden(X1,k4_rcomp_1(X2,X3))\|~v1_xreal_0(X3)\|~v1_xxreal_0(X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_147, c_0_133])])). cnf(c_0_151, plain, (~v1_xreal_0(k10_real_1(k32_sin_cos,np__2))\|~m1_subset_1(k10_real_1(k32_sin_cos,np__4),k1_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_148, c_0_149])])). cnf(c_0_152, plain, (m1_subset_1(k10_real_1(k32_sin_cos,np__4),k1_numbers)\|~v1_xreal_0(k10_real_1(k32_sin_cos,np__2))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150, c_0_129]), c_0_139])])])). fof(c_0_153, plain, ![X53, X54]:(~m1_subset_1(X53,k1_numbers)\|~v1_xreal_0(X54)\|m1_subset_1(k10_real_1(X53,X54),k1_numbers)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k10_real_1])])). cnf(c_0_154, plain, (~v1_xreal_0(k10_real_1(k32_sin_cos,np__2))), inference(csr,[status(thm)],[c_0_151, c_0_152])). cnf(c_0_155, plain, (m1_subset_1(k10_real_1(X1,X2),k1_numbers)\|~m1_subset_1(X1,k1_numbers)\|~v1_xreal_0(X2)), inference(split_conjunct,[status(thm)],[c_0_153])). cnf(c_0_156, plain, (m1_subset_1(k32_sin_cos,k1_numbers)), inference(split_conjunct,[status(thm)],[dt_k32_sin_cos])). cnf(c_0_157, plain, (~m1_subset_1(k10_real_1(k32_sin_cos,np__2),k1_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_154, c_0_149])])). cnf(c_0_158, plain, (m1_subset_1(k10_real_1(X1,X2),k1_numbers)\|~v1_xreal_0(X2)\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[c_0_155])). cnf(c_0_159, plain, (m1_subset_1(k32_sin_cos,k1_numbers)), inference(evalgc,[status(thm)],[c_0_156])). cnf(c_0_160, plain, (m1_subset_1(np__2,k1_numbers)), inference(split_conjunct,[status(thm)],[spc2_numerals])). cnf(c_0_161, plain, (~v1_xreal_0(np__2)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157, c_0_158]), c_0_159])])])). cnf(c_0_162, plain, (m1_subset_1(np__2,k1_numbers)), inference(evalgc,[status(thm)],[c_0_160])). cnf(c_0_163, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161, c_0_149]), c_0_162])]), ['proof']). # SZS output end CNFRefutation	reserve x, r for Real, th for real number, rr for set, rseq for Real_Sequence; theorem Th84: arccosec2\|[.1,sqrt 2.] is decreasing proof [.1,sqrt 2.] = cosec.:[.PI/4,PI/2.] & [.PI/4,PI/2.] c= ].0,PI/2.] by Lm8,Th44 ,RELAT_1:115,XXREAL_2:def 12; hence thesis by Th80,RELAT_1:123,RFUNCT_2:29; end;	Convert the following ATP output trace into a readable Mizar proof.
t5_asympt_1	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t5_asympt_1, conjecture, (r1_tarski(k6_asympt_0(k2_asympt_1),k6_asympt_0(k3_asympt_1(k10_real_1(np__1,np__2))))&~(k6_asympt_0(k2_asympt_1)=k6_asympt_0(k3_asympt_1(k10_real_1(np__1,np__2))))), file('/scratch/mptp/predsminms1/t5_asympt_1__0', t5_asympt_1)). fof(t4_asympt_1, axiom, ![X1]:((v1_funct_1(X1)&(v1_funct_2(X1,k5_numbers,k1_numbers)&(v2_asympt_0(X1)&m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers))))))=>![X2]:((v1_funct_1(X2)&(v1_funct_2(X2,k5_numbers,k1_numbers)&(v2_asympt_0(X2)&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers))))))=>((r1_tarski(k6_asympt_0(X1),k6_asympt_0(X2))=>(k6_asympt_0(X1)=k6_asympt_0(X2)\|(r2_hidden(X1,k6_asympt_0(X2))&~(r2_hidden(X1,k7_asympt_0(X2))))))&(r2_hidden(X1,k6_asympt_0(X2))=>(r2_hidden(X1,k7_asympt_0(X2))\|(r1_tarski(k6_asympt_0(X1),k6_asympt_0(X2))&~(k6_asympt_0(X1)=k6_asympt_0(X2)))))))), file('/scratch/mptp/predsminms1/t5_asympt_1__0', t4_asympt_1)). fof(cc2_asympt_0, axiom, ![X1]:(m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers)))=>((v1_funct_1(X1)&(v1_funct_2(X1,k5_numbers,k1_numbers)&v4_asympt_0(X1)))=>(v1_funct_1(X1)&(v1_funct_2(X1,k5_numbers,k1_numbers)&(v2_asympt_0(X1)&v5_asympt_0(X1)))))), file('/scratch/mptp/predsminms1/t5_asympt_1__0', cc2_asympt_0)). fof(dt_k2_asympt_1, axiom, (v1_funct_1(k2_asympt_1)&(v1_funct_2(k2_asympt_1,k5_numbers,k1_numbers)&m1_subset_1(k2_asympt_1,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers))))), file('/scratch/mptp/predsminms1/t5_asympt_1__0', dt_k2_asympt_1)). fof(fc2_asympt_1, axiom, (v1_funct_1(k2_asympt_1)&(v1_funct_2(k2_asympt_1,k5_numbers,k1_numbers)&v4_asympt_0(k2_asympt_1))), file('/scratch/mptp/predsminms1/t5_asympt_1__0', fc2_asympt_1)). fof(t19_asympt_0, axiom, ![X1]:((v1_funct_1(X1)&(v1_funct_2(X1,k5_numbers,k1_numbers)&(v2_asympt_0(X1)&m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers))))))=>![X2]:((v1_funct_1(X2)&(v1_funct_2(X2,k5_numbers,k1_numbers)&(v2_asympt_0(X2)&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers))))))=>(r2_hidden(X1,k7_asympt_0(X2))<=>r2_hidden(X2,k6_asympt_0(X1))))), file('/scratch/mptp/predsminms1/t5_asympt_1__0', t19_asympt_0)). fof(dt_k3_asympt_1, axiom, ![X1]:(m1_subset_1(X1,k1_numbers)=>(v1_funct_1(k3_asympt_1(X1))&(v1_funct_2(k3_asympt_1(X1),k5_numbers,k1_numbers)&m1_subset_1(k3_asympt_1(X1),k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers)))))), file('/scratch/mptp/predsminms1/t5_asympt_1__0', dt_k3_asympt_1)). fof(fc3_asympt_1, axiom, ![X1]:(m1_subset_1(X1,k1_numbers)=>(v1_funct_1(k3_asympt_1(X1))&(v1_funct_2(k3_asympt_1(X1),k5_numbers,k1_numbers)&v4_asympt_0(k3_asympt_1(X1))))), file('/scratch/mptp/predsminms1/t5_asympt_1__0', fc3_asympt_1)). fof(t16_asympt_0, axiom, ![X1]:((v1_funct_1(X1)&(v1_funct_2(X1,k5_numbers,k1_numbers)&(v4_asympt_0(X1)&m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers))))))=>![X2]:((v1_funct_1(X2)&(v1_funct_2(X2,k5_numbers,k1_numbers)&(v4_asympt_0(X2)&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers))))))=>((v2_comseq_2(k52_valued_1(k5_numbers,k1_numbers,k1_numbers,X1,X2))&k2_seq_2(k52_valued_1(k5_numbers,k1_numbers,k1_numbers,X1,X2))=k6_numbers)=>(r2_hidden(X1,k6_asympt_0(X2))&~(r2_hidden(X2,k6_asympt_0(X1))))))), file('/scratch/mptp/predsminms1/t5_asympt_1__0', t16_asympt_0)). fof(l18_asympt_1, axiom, ![X1]:(m1_subset_1(X1,k1_numbers)=>(~(r1_xxreal_0(X1,k6_numbers))=>(v2_comseq_2(k52_valued_1(k5_numbers,k1_numbers,k1_numbers,k2_asympt_1,k3_asympt_1(X1)))&k2_seq_2(k52_valued_1(k5_numbers,k1_numbers,k1_numbers,k2_asympt_1,k3_asympt_1(X1)))=k6_numbers))), file('/scratch/mptp/predsminms1/t5_asympt_1__0', l18_asympt_1)). fof(dt_k8_real_1, axiom, ![X1, X2]:((m1_subset_1(X1,k1_numbers)&v1_xreal_0(X2))=>m1_subset_1(k8_real_1(X1,X2),k1_numbers)), file('/scratch/mptp/predsminms1/t5_asympt_1__0', dt_k8_real_1)). fof(redefinition_k8_real_1, axiom, ![X1, X2]:((m1_subset_1(X1,k1_numbers)&v1_xreal_0(X2))=>k8_real_1(X1,X2)=k3_xcmplx_0(X1,X2)), file('/scratch/mptp/predsminms1/t5_asympt_1__0', redefinition_k8_real_1)). fof(spc3_arithm, axiom, ![X1]:(v1_xcmplx_0(X1)=>k7_xcmplx_0(np__1,X1)=k5_xcmplx_0(X1)), file('/scratch/mptp/predsminms1/t5_asympt_1__0', spc3_arithm)). fof(cc3_xreal_0, axiom, ![X1]:(v1_xreal_0(X1)=>v1_xcmplx_0(X1)), file('/scratch/mptp/predsminms1/t5_asympt_1__0', cc3_xreal_0)). fof(t6_boole, axiom, ![X1]:(v1_xboole_0(X1)=>X1=k1_xboole_0), file('/scratch/mptp/predsminms1/t5_asympt_1__0', t6_boole)). fof(fc4_xreal_0, axiom, ![X1]:(v1_xreal_0(X1)=>(v1_xcmplx_0(k5_xcmplx_0(X1))&v1_xreal_0(k5_xcmplx_0(X1)))), file('/scratch/mptp/predsminms1/t5_asympt_1__0', fc4_xreal_0)). fof(cc14_membered, axiom, ![X1]:(v3_membered(X1)=>![X2]:(m1_subset_1(X2,X1)=>v1_xreal_0(X2))), file('/scratch/mptp/predsminms1/t5_asympt_1__0', cc14_membered)). fof(redefinition_k6_numbers, axiom, k6_numbers=k1_xboole_0, file('/scratch/mptp/predsminms1/t5_asympt_1__0', redefinition_k6_numbers)). fof(rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2, axiom, k3_xcmplx_0(np__1,k7_xcmplx_0(np__1,np__2))=k7_xcmplx_0(np__1,np__2), file('/scratch/mptp/predsminms1/t5_asympt_1__0', rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2)). fof(spc1_numerals, axiom, ((v2_xxreal_0(np__1)&m2_subset_1(np__1,k1_numbers,k5_numbers))&(m1_subset_1(np__1,k5_numbers)&m1_subset_1(np__1,k1_numbers))), file('/scratch/mptp/predsminms1/t5_asympt_1__0', spc1_numerals)). fof(spc2_numerals, axiom, ((v2_xxreal_0(np__2)&m2_subset_1(np__2,k1_numbers,k5_numbers))&(m1_subset_1(np__2,k5_numbers)&m1_subset_1(np__2,k1_numbers))), file('/scratch/mptp/predsminms1/t5_asympt_1__0', spc2_numerals)). fof(fc3_membered, axiom, v3_membered(k1_numbers), file('/scratch/mptp/predsminms1/t5_asympt_1__0', fc3_membered)). fof(rqLessOrEqual__r1_xxreal_0__rn1d2_r0, axiom, ~(r1_xxreal_0(k7_xcmplx_0(np__1,np__2),np__0)), file('/scratch/mptp/predsminms1/t5_asympt_1__0', rqLessOrEqual__r1_xxreal_0__rn1d2_r0)). fof(spc0_boole, axiom, v1_xboole_0(np__0), file('/scratch/mptp/predsminms1/t5_asympt_1__0', spc0_boole)). fof(redefinition_k10_real_1, axiom, ![X1, X2]:((m1_subset_1(X1,k1_numbers)&v1_xreal_0(X2))=>k10_real_1(X1,X2)=k7_xcmplx_0(X1,X2)), file('/scratch/mptp/predsminms1/t5_asympt_1__0', redefinition_k10_real_1)). fof(c_0_25, negated_conjecture, ~((r1_tarski(k6_asympt_0(k2_asympt_1),k6_asympt_0(k3_asympt_1(k10_real_1(np__1,np__2))))&~(k6_asympt_0(k2_asympt_1)=k6_asympt_0(k3_asympt_1(k10_real_1(np__1,np__2)))))), inference(assume_negation,[status(cth)],[t5_asympt_1])). fof(c_0_26, negated_conjecture, (~r1_tarski(k6_asympt_0(k2_asympt_1),k6_asympt_0(k3_asympt_1(k10_real_1(np__1,np__2))))\|k6_asympt_0(k2_asympt_1)=k6_asympt_0(k3_asympt_1(k10_real_1(np__1,np__2)))), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_25])])). fof(c_0_27, plain, ![X3, X4]:(((r2_hidden(X3,k6_asympt_0(X4))\|k6_asympt_0(X3)=k6_asympt_0(X4)\|~r1_tarski(k6_asympt_0(X3),k6_asympt_0(X4))\|(~v1_funct_1(X4)\|(~v1_funct_2(X4,k5_numbers,k1_numbers)\|(~v2_asympt_0(X4)\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers))))))\|(~v1_funct_1(X3)\|(~v1_funct_2(X3,k5_numbers,k1_numbers)\|(~v2_asympt_0(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers)))))))&(~r2_hidden(X3,k7_asympt_0(X4))\|k6_asympt_0(X3)=k6_asympt_0(X4)\|~r1_tarski(k6_asympt_0(X3),k6_asympt_0(X4))\|(~v1_funct_1(X4)\|(~v1_funct_2(X4,k5_numbers,k1_numbers)\|(~v2_asympt_0(X4)\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers))))))\|(~v1_funct_1(X3)\|(~v1_funct_2(X3,k5_numbers,k1_numbers)\|(~v2_asympt_0(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers))))))))&((r1_tarski(k6_asympt_0(X3),k6_asympt_0(X4))\|r2_hidden(X3,k7_asympt_0(X4))\|~r2_hidden(X3,k6_asympt_0(X4))\|(~v1_funct_1(X4)\|(~v1_funct_2(X4,k5_numbers,k1_numbers)\|(~v2_asympt_0(X4)\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers))))))\|(~v1_funct_1(X3)\|(~v1_funct_2(X3,k5_numbers,k1_numbers)\|(~v2_asympt_0(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers)))))))&(k6_asympt_0(X3)!=k6_asympt_0(X4)\|r2_hidden(X3,k7_asympt_0(X4))\|~r2_hidden(X3,k6_asympt_0(X4))\|(~v1_funct_1(X4)\|(~v1_funct_2(X4,k5_numbers,k1_numbers)\|(~v2_asympt_0(X4)\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers))))))\|(~v1_funct_1(X3)\|(~v1_funct_2(X3,k5_numbers,k1_numbers)\|(~v2_asympt_0(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t4_asympt_1])])])])])). fof(c_0_28, plain, ![X5]:((v1_funct_1(X5)\|(~v1_funct_1(X5)\|(~v1_funct_2(X5,k5_numbers,k1_numbers)\|~v4_asympt_0(X5)))\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers))))&((v1_funct_2(X5,k5_numbers,k1_numbers)\|(~v1_funct_1(X5)\|(~v1_funct_2(X5,k5_numbers,k1_numbers)\|~v4_asympt_0(X5)))\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers))))&((v2_asympt_0(X5)\|(~v1_funct_1(X5)\|(~v1_funct_2(X5,k5_numbers,k1_numbers)\|~v4_asympt_0(X5)))\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers))))&(v5_asympt_0(X5)\|(~v1_funct_1(X5)\|(~v1_funct_2(X5,k5_numbers,k1_numbers)\|~v4_asympt_0(X5)))\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_asympt_0])])])). cnf(c_0_29, negated_conjecture, (k6_asympt_0(k2_asympt_1)=k6_asympt_0(k3_asympt_1(k10_real_1(np__1,np__2)))\|~r1_tarski(k6_asympt_0(k2_asympt_1),k6_asympt_0(k3_asympt_1(k10_real_1(np__1,np__2))))), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_30, plain, (r1_tarski(k6_asympt_0(X1),k6_asympt_0(X2))\|r2_hidden(X1,k7_asympt_0(X2))\|~r2_hidden(X1,k6_asympt_0(X2))\|~v1_funct_1(X2)\|~v1_funct_2(X2,k5_numbers,k1_numbers)\|~v2_asympt_0(X2)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers)))\|~v1_funct_1(X1)\|~v1_funct_2(X1,k5_numbers,k1_numbers)\|~v2_asympt_0(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers)))), inference(split_conjunct,[status(thm)],[c_0_27])). cnf(c_0_31, plain, (m1_subset_1(k2_asympt_1,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers)))), inference(split_conjunct,[status(thm)],[dt_k2_asympt_1])). cnf(c_0_32, plain, (v1_funct_2(k2_asympt_1,k5_numbers,k1_numbers)), inference(split_conjunct,[status(thm)],[dt_k2_asympt_1])). cnf(c_0_33, plain, (v1_funct_1(k2_asympt_1)), inference(split_conjunct,[status(thm)],[dt_k2_asympt_1])). cnf(c_0_34, plain, (v2_asympt_0(X1)\|~v1_funct_1(X1)\|~v1_funct_2(X1,k5_numbers,k1_numbers)\|~v4_asympt_0(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers)))), inference(split_conjunct,[status(thm)],[c_0_28])). cnf(c_0_35, plain, (v4_asympt_0(k2_asympt_1)), inference(split_conjunct,[status(thm)],[fc2_asympt_1])). fof(c_0_36, plain, ![X9, X10]:((~r2_hidden(X9,k7_asympt_0(X10))\|r2_hidden(X10,k6_asympt_0(X9))\|(~v1_funct_1(X10)\|(~v1_funct_2(X10,k5_numbers,k1_numbers)\|(~v2_asympt_0(X10)\|~m1_subset_1(X10,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers))))))\|(~v1_funct_1(X9)\|(~v1_funct_2(X9,k5_numbers,k1_numbers)\|(~v2_asympt_0(X9)\|~m1_subset_1(X9,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers)))))))&(~r2_hidden(X10,k6_asympt_0(X9))\|r2_hidden(X9,k7_asympt_0(X10))\|(~v1_funct_1(X10)\|(~v1_funct_2(X10,k5_numbers,k1_numbers)\|(~v2_asympt_0(X10)\|~m1_subset_1(X10,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers))))))\|(~v1_funct_1(X9)\|(~v1_funct_2(X9,k5_numbers,k1_numbers)\|(~v2_asympt_0(X9)\|~m1_subset_1(X9,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers)))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t19_asympt_0])])])])). fof(c_0_37, plain, ![X11]:((v1_funct_1(k3_asympt_1(X11))\|~m1_subset_1(X11,k1_numbers))&((v1_funct_2(k3_asympt_1(X11),k5_numbers,k1_numbers)\|~m1_subset_1(X11,k1_numbers))&(m1_subset_1(k3_asympt_1(X11),k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers)))\|~m1_subset_1(X11,k1_numbers)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k3_asympt_1])])])). cnf(c_0_38, negated_conjecture, (k6_asympt_0(k3_asympt_1(k10_real_1(np__1,np__2)))=k6_asympt_0(k2_asympt_1)\|~r1_tarski(k6_asympt_0(k2_asympt_1),k6_asympt_0(k3_asympt_1(k10_real_1(np__1,np__2))))), inference(evalgc,[status(thm)],[c_0_29])). cnf(c_0_39, plain, (r2_hidden(X1,k7_asympt_0(X2))\|r1_tarski(k6_asympt_0(X1),k6_asympt_0(X2))\|~v1_funct_1(X2)\|~v1_funct_1(X1)\|~v2_asympt_0(X2)\|~v2_asympt_0(X1)\|~r2_hidden(X1,k6_asympt_0(X2))\|~v1_funct_2(X2,k5_numbers,k1_numbers)\|~v1_funct_2(X1,k5_numbers,k1_numbers)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers)))\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers)))), inference(evalgc,[status(thm)],[c_0_30])). cnf(c_0_40, plain, (m1_subset_1(k2_asympt_1,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers)))), inference(evalgc,[status(thm)],[c_0_31])). cnf(c_0_41, plain, (v1_funct_2(k2_asympt_1,k5_numbers,k1_numbers)), inference(evalgc,[status(thm)],[c_0_32])). cnf(c_0_42, plain, (v1_funct_1(k2_asympt_1)), inference(evalgc,[status(thm)],[c_0_33])). cnf(c_0_43, plain, (v2_asympt_0(X1)\|~v1_funct_1(X1)\|~v4_asympt_0(X1)\|~v1_funct_2(X1,k5_numbers,k1_numbers)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers)))), inference(evalgc,[status(thm)],[c_0_34])). cnf(c_0_44, plain, (v4_asympt_0(k2_asympt_1)), inference(evalgc,[status(thm)],[c_0_35])). cnf(c_0_45, plain, (r2_hidden(X2,k6_asympt_0(X1))\|~r2_hidden(X1,k7_asympt_0(X2))\|~v1_funct_1(X2)\|~v1_funct_2(X2,k5_numbers,k1_numbers)\|~v2_asympt_0(X2)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers)))\|~v1_funct_1(X1)\|~v1_funct_2(X1,k5_numbers,k1_numbers)\|~v2_asympt_0(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers)))), inference(split_conjunct,[status(thm)],[c_0_36])). cnf(c_0_46, plain, (r2_hidden(X1,k7_asympt_0(X2))\|k6_asympt_0(X1)!=k6_asympt_0(X2)\|~r2_hidden(X1,k6_asympt_0(X2))\|~v1_funct_1(X2)\|~v1_funct_2(X2,k5_numbers,k1_numbers)\|~v2_asympt_0(X2)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers)))\|~v1_funct_1(X1)\|~v1_funct_2(X1,k5_numbers,k1_numbers)\|~v2_asympt_0(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers)))), inference(split_conjunct,[status(thm)],[c_0_27])). cnf(c_0_47, plain, (m1_subset_1(k3_asympt_1(X1),k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers)))\|~m1_subset_1(X1,k1_numbers)), inference(split_conjunct,[status(thm)],[c_0_37])). fof(c_0_48, plain, ![X12]:((v1_funct_1(k3_asympt_1(X12))\|~m1_subset_1(X12,k1_numbers))&((v1_funct_2(k3_asympt_1(X12),k5_numbers,k1_numbers)\|~m1_subset_1(X12,k1_numbers))&(v4_asympt_0(k3_asympt_1(X12))\|~m1_subset_1(X12,k1_numbers)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc3_asympt_1])])])). fof(c_0_49, plain, ![X6, X7]:((r2_hidden(X6,k6_asympt_0(X7))\|(~v2_comseq_2(k52_valued_1(k5_numbers,k1_numbers,k1_numbers,X6,X7))\|k2_seq_2(k52_valued_1(k5_numbers,k1_numbers,k1_numbers,X6,X7))!=k6_numbers)\|(~v1_funct_1(X7)\|(~v1_funct_2(X7,k5_numbers,k1_numbers)\|(~v4_asympt_0(X7)\|~m1_subset_1(X7,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers))))))\|(~v1_funct_1(X6)\|(~v1_funct_2(X6,k5_numbers,k1_numbers)\|(~v4_asympt_0(X6)\|~m1_subset_1(X6,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers)))))))&(~r2_hidden(X7,k6_asympt_0(X6))\|(~v2_comseq_2(k52_valued_1(k5_numbers,k1_numbers,k1_numbers,X6,X7))\|k2_seq_2(k52_valued_1(k5_numbers,k1_numbers,k1_numbers,X6,X7))!=k6_numbers)\|(~v1_funct_1(X7)\|(~v1_funct_2(X7,k5_numbers,k1_numbers)\|(~v4_asympt_0(X7)\|~m1_subset_1(X7,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers))))))\|(~v1_funct_1(X6)\|(~v1_funct_2(X6,k5_numbers,k1_numbers)\|(~v4_asympt_0(X6)\|~m1_subset_1(X6,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers)))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t16_asympt_0])])])])])). fof(c_0_50, plain, ![X8]:((v2_comseq_2(k52_valued_1(k5_numbers,k1_numbers,k1_numbers,k2_asympt_1,k3_asympt_1(X8)))\|r1_xxreal_0(X8,k6_numbers)\|~m1_subset_1(X8,k1_numbers))&(k2_seq_2(k52_valued_1(k5_numbers,k1_numbers,k1_numbers,k2_asympt_1,k3_asympt_1(X8)))=k6_numbers\|r1_xxreal_0(X8,k6_numbers)\|~m1_subset_1(X8,k1_numbers))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[l18_asympt_1])])])])). cnf(c_0_51, negated_conjecture, (k6_asympt_0(k3_asympt_1(k10_real_1(np__1,np__2)))=k6_asympt_0(k2_asympt_1)\|r2_hidden(k2_asympt_1,k7_asympt_0(k3_asympt_1(k10_real_1(np__1,np__2))))\|~r2_hidden(k2_asympt_1,k6_asympt_0(k3_asympt_1(k10_real_1(np__1,np__2))))\|~m1_subset_1(k3_asympt_1(k10_real_1(np__1,np__2)),k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers)))\|~v2_asympt_0(k3_asympt_1(k10_real_1(np__1,np__2)))\|~v2_asympt_0(k2_asympt_1)\|~v1_funct_2(k3_asympt_1(k10_real_1(np__1,np__2)),k5_numbers,k1_numbers)\|~v1_funct_1(k3_asympt_1(k10_real_1(np__1,np__2)))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38, c_0_39]), c_0_40]), c_0_41]), c_0_42])])])). cnf(c_0_52, plain, (v2_asympt_0(k2_asympt_1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43, c_0_40]), c_0_44]), c_0_41]), c_0_42])])])). cnf(c_0_53, plain, (r2_hidden(X2,k6_asympt_0(X1))\|~v1_funct_1(X2)\|~v1_funct_1(X1)\|~v2_asympt_0(X2)\|~v2_asympt_0(X1)\|~r2_hidden(X1,k7_asympt_0(X2))\|~v1_funct_2(X2,k5_numbers,k1_numbers)\|~v1_funct_2(X1,k5_numbers,k1_numbers)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers)))\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers)))), inference(evalgc,[status(thm)],[c_0_45])). cnf(c_0_54, plain, (r2_hidden(X1,k7_asympt_0(X2))\|k6_asympt_0(X1)!=k6_asympt_0(X2)\|~v1_funct_1(X2)\|~v1_funct_1(X1)\|~v2_asympt_0(X2)\|~v2_asympt_0(X1)\|~r2_hidden(X1,k6_asympt_0(X2))\|~v1_funct_2(X2,k5_numbers,k1_numbers)\|~v1_funct_2(X1,k5_numbers,k1_numbers)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers)))\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers)))), inference(evalgc,[status(thm)],[c_0_46])). cnf(c_0_55, plain, (m1_subset_1(k3_asympt_1(X1),k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers)))\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[c_0_47])). cnf(c_0_56, plain, (v1_funct_1(k3_asympt_1(X1))\|~m1_subset_1(X1,k1_numbers)), inference(split_conjunct,[status(thm)],[c_0_37])). cnf(c_0_57, plain, (v1_funct_2(k3_asympt_1(X1),k5_numbers,k1_numbers)\|~m1_subset_1(X1,k1_numbers)), inference(split_conjunct,[status(thm)],[c_0_37])). cnf(c_0_58, plain, (v4_asympt_0(k3_asympt_1(X1))\|~m1_subset_1(X1,k1_numbers)), inference(split_conjunct,[status(thm)],[c_0_48])). cnf(c_0_59, plain, (r2_hidden(X1,k6_asympt_0(X2))\|~v2_comseq_2(k52_valued_1(k5_numbers,k1_numbers,k1_numbers,X1,X2))\|k2_seq_2(k52_valued_1(k5_numbers,k1_numbers,k1_numbers,X1,X2))!=k6_numbers\|~v1_funct_1(X2)\|~v1_funct_2(X2,k5_numbers,k1_numbers)\|~v4_asympt_0(X2)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers)))\|~v1_funct_1(X1)\|~v1_funct_2(X1,k5_numbers,k1_numbers)\|~v4_asympt_0(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers)))), inference(split_conjunct,[status(thm)],[c_0_49])). cnf(c_0_60, plain, (v2_comseq_2(k52_valued_1(k5_numbers,k1_numbers,k1_numbers,k2_asympt_1,k3_asympt_1(X1)))\|r1_xxreal_0(X1,k6_numbers)\|~m1_subset_1(X1,k1_numbers)), inference(split_conjunct,[status(thm)],[c_0_50])). cnf(c_0_61, plain, (~r2_hidden(X1,k6_asympt_0(X2))\|~v2_comseq_2(k52_valued_1(k5_numbers,k1_numbers,k1_numbers,X2,X1))\|k2_seq_2(k52_valued_1(k5_numbers,k1_numbers,k1_numbers,X2,X1))!=k6_numbers\|~v1_funct_1(X1)\|~v1_funct_2(X1,k5_numbers,k1_numbers)\|~v4_asympt_0(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers)))\|~v1_funct_1(X2)\|~v1_funct_2(X2,k5_numbers,k1_numbers)\|~v4_asympt_0(X2)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers)))), inference(split_conjunct,[status(thm)],[c_0_49])). cnf(c_0_62, negated_conjecture, (k6_asympt_0(k3_asympt_1(k10_real_1(np__1,np__2)))=k6_asympt_0(k2_asympt_1)\|r2_hidden(k2_asympt_1,k7_asympt_0(k3_asympt_1(k10_real_1(np__1,np__2))))\|~r2_hidden(k2_asympt_1,k6_asympt_0(k3_asympt_1(k10_real_1(np__1,np__2))))\|~m1_subset_1(k3_asympt_1(k10_real_1(np__1,np__2)),k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers)))\|~v2_asympt_0(k3_asympt_1(k10_real_1(np__1,np__2)))\|~v1_funct_2(k3_asympt_1(k10_real_1(np__1,np__2)),k5_numbers,k1_numbers)\|~v1_funct_1(k3_asympt_1(k10_real_1(np__1,np__2)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51, c_0_52])])). cnf(c_0_63, plain, (r2_hidden(X1,k6_asympt_0(X2))\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers)))\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers)))\|~v2_asympt_0(X1)\|~v2_asympt_0(X2)\|~v1_funct_2(X1,k5_numbers,k1_numbers)\|~v1_funct_2(X2,k5_numbers,k1_numbers)\|~v1_funct_1(X1)\|~v1_funct_1(X2)\|k6_asympt_0(X2)!=k6_asympt_0(X1)\|~r2_hidden(X2,k6_asympt_0(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_53, c_0_54])])). cnf(c_0_64, plain, (v2_asympt_0(k3_asympt_1(X1))\|~v4_asympt_0(k3_asympt_1(X1))\|~v1_funct_2(k3_asympt_1(X1),k5_numbers,k1_numbers)\|~v1_funct_1(k3_asympt_1(X1))\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_43, c_0_55])])). cnf(c_0_65, plain, (v1_funct_1(k3_asympt_1(X1))\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[c_0_56])). cnf(c_0_66, plain, (v1_funct_2(k3_asympt_1(X1),k5_numbers,k1_numbers)\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[c_0_57])). cnf(c_0_67, plain, (v4_asympt_0(k3_asympt_1(X1))\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[c_0_58])). cnf(c_0_68, plain, (r2_hidden(X1,k6_asympt_0(X2))\|k2_seq_2(k52_valued_1(k5_numbers,k1_numbers,k1_numbers,X1,X2))!=k6_numbers\|~v1_funct_1(X2)\|~v1_funct_1(X1)\|~v4_asympt_0(X2)\|~v4_asympt_0(X1)\|~v1_funct_2(X2,k5_numbers,k1_numbers)\|~v1_funct_2(X1,k5_numbers,k1_numbers)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers)))\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers)))\|~v2_comseq_2(k52_valued_1(k5_numbers,k1_numbers,k1_numbers,X1,X2))), inference(evalgc,[status(thm)],[c_0_59])). cnf(c_0_69, plain, (r1_xxreal_0(X1,k6_numbers)\|v2_comseq_2(k52_valued_1(k5_numbers,k1_numbers,k1_numbers,k2_asympt_1,k3_asympt_1(X1)))\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[c_0_60])). cnf(c_0_70, plain, (k2_seq_2(k52_valued_1(k5_numbers,k1_numbers,k1_numbers,k2_asympt_1,k3_asympt_1(X1)))=k6_numbers\|r1_xxreal_0(X1,k6_numbers)\|~m1_subset_1(X1,k1_numbers)), inference(split_conjunct,[status(thm)],[c_0_50])). fof(c_0_71, plain, ![X20, X21]:(~m1_subset_1(X20,k1_numbers)\|~v1_xreal_0(X21)\|m1_subset_1(k8_real_1(X20,X21),k1_numbers)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k8_real_1])])). fof(c_0_72, plain, ![X22, X23]:(~m1_subset_1(X22,k1_numbers)\|~v1_xreal_0(X23)\|k8_real_1(X22,X23)=k3_xcmplx_0(X22,X23)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k8_real_1])])). fof(c_0_73, plain, ![X14]:(~v1_xcmplx_0(X14)\|k7_xcmplx_0(np__1,X14)=k5_xcmplx_0(X14)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[spc3_arithm])])). fof(c_0_74, plain, ![X17]:(~v1_xreal_0(X17)\|v1_xcmplx_0(X17)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc3_xreal_0])])). fof(c_0_75, plain, ![X16]:(~v1_xboole_0(X16)\|X16=k1_xboole_0), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])])). cnf(c_0_76, plain, (k2_seq_2(k52_valued_1(k5_numbers,k1_numbers,k1_numbers,X2,X1))!=k6_numbers\|~v1_funct_1(X2)\|~v1_funct_1(X1)\|~v4_asympt_0(X2)\|~v4_asympt_0(X1)\|~r2_hidden(X1,k6_asympt_0(X2))\|~v1_funct_2(X2,k5_numbers,k1_numbers)\|~v1_funct_2(X1,k5_numbers,k1_numbers)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers)))\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers)))\|~v2_comseq_2(k52_valued_1(k5_numbers,k1_numbers,k1_numbers,X2,X1))), inference(evalgc,[status(thm)],[c_0_61])). cnf(c_0_77, negated_conjecture, (r2_hidden(k3_asympt_1(k10_real_1(np__1,np__2)),k6_asympt_0(k2_asympt_1))\|k6_asympt_0(k3_asympt_1(k10_real_1(np__1,np__2)))=k6_asympt_0(k2_asympt_1)\|~m1_subset_1(k3_asympt_1(k10_real_1(np__1,np__2)),k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers)))\|~v2_asympt_0(k3_asympt_1(k10_real_1(np__1,np__2)))\|~v1_funct_2(k3_asympt_1(k10_real_1(np__1,np__2)),k5_numbers,k1_numbers)\|~v1_funct_1(k3_asympt_1(k10_real_1(np__1,np__2)))\|~r2_hidden(k2_asympt_1,k6_asympt_0(k3_asympt_1(k10_real_1(np__1,np__2))))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53, c_0_62]), c_0_40]), c_0_52]), c_0_41]), c_0_42])])])). cnf(c_0_78, plain, (r2_hidden(k3_asympt_1(X1),k6_asympt_0(X2))\|k6_asympt_0(X2)!=k6_asympt_0(k3_asympt_1(X1))\|~r2_hidden(X2,k6_asympt_0(k3_asympt_1(X1)))\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers)))\|~v2_asympt_0(k3_asympt_1(X1))\|~v2_asympt_0(X2)\|~v1_funct_2(k3_asympt_1(X1),k5_numbers,k1_numbers)\|~v1_funct_2(X2,k5_numbers,k1_numbers)\|~v1_funct_1(k3_asympt_1(X1))\|~v1_funct_1(X2)\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_63, c_0_55])])). cnf(c_0_79, plain, (v2_asympt_0(k3_asympt_1(X1))\|~m1_subset_1(X1,k1_numbers)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_64, c_0_65]), c_0_66]), c_0_67])). cnf(c_0_80, plain, (r2_hidden(k2_asympt_1,k6_asympt_0(k3_asympt_1(X1)))\|r1_xxreal_0(X1,k6_numbers)\|k2_seq_2(k52_valued_1(k5_numbers,k1_numbers,k1_numbers,k2_asympt_1,k3_asympt_1(X1)))!=k6_numbers\|~v4_asympt_0(k3_asympt_1(X1))\|~m1_subset_1(k3_asympt_1(X1),k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers)))\|~v1_funct_2(k3_asympt_1(X1),k5_numbers,k1_numbers)\|~v1_funct_1(k3_asympt_1(X1))\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68, c_0_69]), c_0_44]), c_0_40]), c_0_41]), c_0_42])])])). cnf(c_0_81, plain, (k2_seq_2(k52_valued_1(k5_numbers,k1_numbers,k1_numbers,k2_asympt_1,k3_asympt_1(X1)))=k6_numbers\|r1_xxreal_0(X1,k6_numbers)\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[c_0_70])). cnf(c_0_82, plain, (m1_subset_1(k8_real_1(X1,X2),k1_numbers)\|~m1_subset_1(X1,k1_numbers)\|~v1_xreal_0(X2)), inference(split_conjunct,[status(thm)],[c_0_71])). cnf(c_0_83, plain, (k8_real_1(X1,X2)=k3_xcmplx_0(X1,X2)\|~m1_subset_1(X1,k1_numbers)\|~v1_xreal_0(X2)), inference(split_conjunct,[status(thm)],[c_0_72])). fof(c_0_84, plain, ![X15]:((v1_xcmplx_0(k5_xcmplx_0(X15))\|~v1_xreal_0(X15))&(v1_xreal_0(k5_xcmplx_0(X15))\|~v1_xreal_0(X15))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc4_xreal_0])])])). cnf(c_0_85, plain, (k7_xcmplx_0(np__1,X1)=k5_xcmplx_0(X1)\|~v1_xcmplx_0(X1)), inference(split_conjunct,[status(thm)],[c_0_73])). cnf(c_0_86, plain, (v1_xcmplx_0(X1)\|~v1_xreal_0(X1)), inference(split_conjunct,[status(thm)],[c_0_74])). fof(c_0_87, plain, ![X18, X19]:(~v3_membered(X18)\|(~m1_subset_1(X19,X18)\|v1_xreal_0(X19))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc14_membered])])])). cnf(c_0_88, plain, (X1=k1_xboole_0\|~v1_xboole_0(X1)), inference(split_conjunct,[status(thm)],[c_0_75])). cnf(c_0_89, plain, (k6_numbers=k1_xboole_0), inference(split_conjunct,[status(thm)],[redefinition_k6_numbers])). cnf(c_0_90, plain, (r1_xxreal_0(X1,k6_numbers)\|k2_seq_2(k52_valued_1(k5_numbers,k1_numbers,k1_numbers,k2_asympt_1,k3_asympt_1(X1)))!=k6_numbers\|~v4_asympt_0(k3_asympt_1(X1))\|~r2_hidden(k3_asympt_1(X1),k6_asympt_0(k2_asympt_1))\|~m1_subset_1(k3_asympt_1(X1),k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers)))\|~v1_funct_2(k3_asympt_1(X1),k5_numbers,k1_numbers)\|~v1_funct_1(k3_asympt_1(X1))\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76, c_0_69]), c_0_44]), c_0_40]), c_0_41]), c_0_42])])])). cnf(c_0_91, negated_conjecture, (k6_asympt_0(k3_asympt_1(k10_real_1(np__1,np__2)))=k6_asympt_0(k2_asympt_1)\|r2_hidden(k3_asympt_1(k10_real_1(np__1,np__2)),k6_asympt_0(k2_asympt_1))\|~r2_hidden(k2_asympt_1,k6_asympt_0(k3_asympt_1(k10_real_1(np__1,np__2))))\|~v2_asympt_0(k3_asympt_1(k10_real_1(np__1,np__2)))\|~v1_funct_2(k3_asympt_1(k10_real_1(np__1,np__2)),k5_numbers,k1_numbers)\|~v1_funct_1(k3_asympt_1(k10_real_1(np__1,np__2)))\|~m1_subset_1(k10_real_1(np__1,np__2),k1_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_77, c_0_55])])). cnf(c_0_92, plain, (r2_hidden(k3_asympt_1(X1),k6_asympt_0(X2))\|k6_asympt_0(X2)!=k6_asympt_0(k3_asympt_1(X1))\|~r2_hidden(X2,k6_asympt_0(k3_asympt_1(X1)))\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,k1_numbers)))\|~m1_subset_1(X1,k1_numbers)\|~v2_asympt_0(X2)\|~v1_funct_2(X2,k5_numbers,k1_numbers)\|~v1_funct_1(X2)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_78, c_0_65]), c_0_66]), c_0_79])). cnf(c_0_93, plain, (r1_xxreal_0(X1,k6_numbers)\|r2_hidden(k2_asympt_1,k6_asympt_0(k3_asympt_1(X1)))\|~m1_subset_1(X1,k1_numbers)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_80, c_0_65]), c_0_66]), c_0_55]), c_0_67]), c_0_81])). cnf(c_0_94, plain, (m1_subset_1(k8_real_1(X1,X2),k1_numbers)\|~v1_xreal_0(X2)\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[c_0_82])). cnf(c_0_95, plain, (k8_real_1(X1,X2)=k3_xcmplx_0(X1,X2)\|~v1_xreal_0(X2)\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[c_0_83])). cnf(c_0_96, plain, (k3_xcmplx_0(np__1,k7_xcmplx_0(np__1,np__2))=k7_xcmplx_0(np__1,np__2)), inference(split_conjunct,[status(thm)],[rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2])). cnf(c_0_97, plain, (m1_subset_1(np__1,k1_numbers)), inference(split_conjunct,[status(thm)],[spc1_numerals])). cnf(c_0_98, plain, (v1_xreal_0(k5_xcmplx_0(X1))\|~v1_xreal_0(X1)), inference(split_conjunct,[status(thm)],[c_0_84])). cnf(c_0_99, plain, (k5_xcmplx_0(X1)=k7_xcmplx_0(np__1,X1)\|~v1_xcmplx_0(X1)), inference(evalgc,[status(thm)],[c_0_85])). cnf(c_0_100, plain, (v1_xcmplx_0(X1)\|~v1_xreal_0(X1)), inference(evalgc,[status(thm)],[c_0_86])). cnf(c_0_101, plain, (v1_xreal_0(X2)\|~v3_membered(X1)\|~m1_subset_1(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_87])). cnf(c_0_102, plain, (m1_subset_1(np__2,k1_numbers)), inference(split_conjunct,[status(thm)],[spc2_numerals])). cnf(c_0_103, plain, (v3_membered(k1_numbers)), inference(split_conjunct,[status(thm)],[fc3_membered])). fof(c_0_104, plain, ~r1_xxreal_0(k7_xcmplx_0(np__1,np__2),np__0), inference(fof_simplification,[status(thm)],[rqLessOrEqual__r1_xxreal_0__rn1d2_r0])). cnf(c_0_105, plain, (X1=k1_xboole_0\|~v1_xboole_0(X1)), inference(evalgc,[status(thm)],[c_0_88])). cnf(c_0_106, plain, (k1_xboole_0=k6_numbers), inference(evalgc,[status(thm)],[c_0_89])). cnf(c_0_107, plain, (v1_xboole_0(np__0)), inference(split_conjunct,[status(thm)],[spc0_boole])). cnf(c_0_108, plain, (r1_xxreal_0(X1,k6_numbers)\|~r2_hidden(k3_asympt_1(X1),k6_asympt_0(k2_asympt_1))\|~m1_subset_1(X1,k1_numbers)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_90, c_0_65]), c_0_66]), c_0_55]), c_0_67]), c_0_81])). cnf(c_0_109, negated_conjecture, (k6_asympt_0(k3_asympt_1(k10_real_1(np__1,np__2)))=k6_asympt_0(k2_asympt_1)\|r2_hidden(k3_asympt_1(k10_real_1(np__1,np__2)),k6_asympt_0(k2_asympt_1))\|~r2_hidden(k2_asympt_1,k6_asympt_0(k3_asympt_1(k10_real_1(np__1,np__2))))\|~m1_subset_1(k10_real_1(np__1,np__2),k1_numbers)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_91, c_0_65]), c_0_66]), c_0_79])). cnf(c_0_110, plain, (r2_hidden(k3_asympt_1(X1),k6_asympt_0(k2_asympt_1))\|r1_xxreal_0(X1,k6_numbers)\|k6_asympt_0(k3_asympt_1(X1))!=k6_asympt_0(k2_asympt_1)\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92, c_0_93]), c_0_40]), c_0_52]), c_0_41]), c_0_42])])])). fof(c_0_111, plain, ![X24, X25]:(~m1_subset_1(X24,k1_numbers)\|~v1_xreal_0(X25)\|k10_real_1(X24,X25)=k7_xcmplx_0(X24,X25)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k10_real_1])])). cnf(c_0_112, plain, (m1_subset_1(k3_xcmplx_0(X1,X2),k1_numbers)\|~v1_xreal_0(X2)\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_94, c_0_95])])). cnf(c_0_113, plain, (k3_xcmplx_0(np__1,k7_xcmplx_0(np__1,np__2))=k7_xcmplx_0(np__1,np__2)), inference(evalgc,[status(thm)],[c_0_96])). cnf(c_0_114, plain, (m1_subset_1(np__1,k1_numbers)), inference(evalgc,[status(thm)],[c_0_97])). cnf(c_0_115, plain, (v1_xreal_0(k5_xcmplx_0(X1))\|~v1_xreal_0(X1)), inference(evalgc,[status(thm)],[c_0_98])). cnf(c_0_116, plain, (k5_xcmplx_0(X1)=k7_xcmplx_0(np__1,X1)\|~v1_xreal_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_99, c_0_100])])). cnf(c_0_117, plain, (v1_xreal_0(X2)\|~v3_membered(X1)\|~m1_subset_1(X2,X1)), inference(evalgc,[status(thm)],[c_0_101])). cnf(c_0_118, plain, (m1_subset_1(np__2,k1_numbers)), inference(evalgc,[status(thm)],[c_0_102])). cnf(c_0_119, plain, (v3_membered(k1_numbers)), inference(evalgc,[status(thm)],[c_0_103])). cnf(c_0_120, plain, (~r1_xxreal_0(k7_xcmplx_0(np__1,np__2),np__0)), inference(split_conjunct,[status(thm)],[c_0_104])). cnf(c_0_121, plain, (X1=k6_numbers\|~v1_xboole_0(X1)), inference(rw,[status(thm)],[c_0_105, c_0_106])). cnf(c_0_122, plain, (v1_xboole_0(np__0)), inference(evalgc,[status(thm)],[c_0_107])). cnf(c_0_123, negated_conjecture, (r1_xxreal_0(k10_real_1(np__1,np__2),k6_numbers)\|k6_asympt_0(k3_asympt_1(k10_real_1(np__1,np__2)))=k6_asympt_0(k2_asympt_1)\|~m1_subset_1(k10_real_1(np__1,np__2),k1_numbers)\|~r2_hidden(k2_asympt_1,k6_asympt_0(k3_asympt_1(k10_real_1(np__1,np__2))))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_108, c_0_109])])). cnf(c_0_124, plain, (r1_xxreal_0(X1,k6_numbers)\|k6_asympt_0(k3_asympt_1(X1))!=k6_asympt_0(k2_asympt_1)\|~m1_subset_1(X1,k1_numbers)), inference(csr,[status(thm)],[c_0_110, c_0_108])). cnf(c_0_125, plain, (k10_real_1(X1,X2)=k7_xcmplx_0(X1,X2)\|~m1_subset_1(X1,k1_numbers)\|~v1_xreal_0(X2)), inference(split_conjunct,[status(thm)],[c_0_111])). cnf(c_0_126, plain, (m1_subset_1(k7_xcmplx_0(np__1,np__2),k1_numbers)\|~v1_xreal_0(k7_xcmplx_0(np__1,np__2))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112, c_0_113]), c_0_114])])])). cnf(c_0_127, plain, (v1_xreal_0(k7_xcmplx_0(np__1,X1))\|~v1_xreal_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_115, c_0_116])])). cnf(c_0_128, plain, (v1_xreal_0(np__2)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117, c_0_118]), c_0_119])])])). cnf(c_0_129, plain, (~r1_xxreal_0(k7_xcmplx_0(np__1,np__2),np__0)), inference(evalgc,[status(thm)],[c_0_120])). cnf(c_0_130, plain, (np__0=k6_numbers), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_121, c_0_122])])). cnf(c_0_131, negated_conjecture, (r1_xxreal_0(k10_real_1(np__1,np__2),k6_numbers)\|~m1_subset_1(k10_real_1(np__1,np__2),k1_numbers)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_123, c_0_93]), c_0_124])). cnf(c_0_132, plain, (k10_real_1(X1,X2)=k7_xcmplx_0(X1,X2)\|~v1_xreal_0(X2)\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[c_0_125])). cnf(c_0_133, plain, (m1_subset_1(k7_xcmplx_0(np__1,np__2),k1_numbers)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126, c_0_127]), c_0_128])])])). cnf(c_0_134, plain, (~r1_xxreal_0(k7_xcmplx_0(np__1,np__2),k6_numbers)), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[c_0_129, c_0_130])])). cnf(c_0_135, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131, c_0_132]), c_0_133]), c_0_128]), c_0_114])]), c_0_134]), ['proof']). # SZS output end CNFRefutation	reserve c, c1, c2, d, d1, d2, e for Real, k, n, m, N, n1, N0, N1, N2, N3, M for Element of NAT, x for set; theorem Th5: Big_Oh(seq_logn) c= Big_Oh(seq_n^(1/2)) & not Big_Oh(seq_logn) = Big_Oh(seq_n^(1/2)) proof set g = seq_n^(1/2); set f = seq_logn; A1: lim (f/"g) = 0 by Lm11; A2: f/"g is convergent by Lm11; then not g in Big_Oh(f) by A1,ASYMPT_0:16; then A3: not f in Big_Omega(g) by ASYMPT_0:19; f in Big_Oh(g) by A2,A1,ASYMPT_0:16; hence thesis by A3,Th4; end;	Convert the following ATP output trace into a readable Mizar proof.
t16_pdiff_1	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t16_pdiff_1, conjecture, ![X1]:(m2_subset_1(X1,k1_numbers,k5_numbers)=>![X2]:((~(v1_xboole_0(X2))&m2_subset_1(X2,k1_numbers,k5_numbers))=>![X3]:((~(v1_xboole_0(X3))&m2_subset_1(X3,k1_numbers,k5_numbers))=>![X4]:((v1_funct_1(X4)&m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k4_real_ns1(X2)),u1_struct_0(k4_real_ns1(X3))))))=>![X5]:((v1_funct_1(X5)&m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(X2),k1_euclid(X3)))))=>![X6]:(m1_subset_1(X6,u1_struct_0(k4_real_ns1(X2)))=>![X7]:(m2_finseq_2(X7,k1_numbers,k1_euclid(X2))=>((X4=X5&X6=X7)=>(r2_pdiff_1(X3,X2,X1,X4,X6)<=>r4_pdiff_1(X2,X3,X1,X5,X7)))))))))), file('/scratch/mptp/predsminms1/t16_pdiff_1__0', t16_pdiff_1)). fof(d13_pdiff_1, axiom, ![X1]:((~(v1_xboole_0(X1))&m2_subset_1(X1,k1_numbers,k5_numbers))=>![X2]:((~(v1_xboole_0(X2))&m2_subset_1(X2,k1_numbers,k5_numbers))=>![X3]:(m2_subset_1(X3,k1_numbers,k5_numbers)=>![X4]:((v1_funct_1(X4)&m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(X1),k1_euclid(X2)))))=>![X5]:(m2_finseq_2(X5,k1_numbers,k1_euclid(X1))=>(r4_pdiff_1(X1,X2,X3,X4,X5)<=>?[X6]:((v1_funct_1(X6)&m1_subset_1(X6,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k4_real_ns1(X1)),u1_struct_0(k4_real_ns1(X2))))))&?[X7]:(m1_subset_1(X7,u1_struct_0(k4_real_ns1(X1)))&(X4=X6&(X5=X7&r2_pdiff_1(X2,X1,X3,X6,X7))))))))))), file('/scratch/mptp/predsminms1/t16_pdiff_1__0', d13_pdiff_1)). fof(c_0_2, negated_conjecture, ~(![X1]:(m2_subset_1(X1,k1_numbers,k5_numbers)=>![X2]:((~(v1_xboole_0(X2))&m2_subset_1(X2,k1_numbers,k5_numbers))=>![X3]:((~(v1_xboole_0(X3))&m2_subset_1(X3,k1_numbers,k5_numbers))=>![X4]:((v1_funct_1(X4)&m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k4_real_ns1(X2)),u1_struct_0(k4_real_ns1(X3))))))=>![X5]:((v1_funct_1(X5)&m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(X2),k1_euclid(X3)))))=>![X6]:(m1_subset_1(X6,u1_struct_0(k4_real_ns1(X2)))=>![X7]:(m2_finseq_2(X7,k1_numbers,k1_euclid(X2))=>((X4=X5&X6=X7)=>(r2_pdiff_1(X3,X2,X1,X4,X6)<=>r4_pdiff_1(X2,X3,X1,X5,X7))))))))))), inference(assume_negation,[status(cth)],[t16_pdiff_1])). fof(c_0_3, plain, ![X15, X16, X17, X18, X19, X22, X23]:((((v1_funct_1(esk8_5(X15,X16,X17,X18,X19))\|~r4_pdiff_1(X15,X16,X17,X18,X19)\|~m2_finseq_2(X19,k1_numbers,k1_euclid(X15))\|(~v1_funct_1(X18)\|~m1_subset_1(X18,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(X15),k1_euclid(X16)))))\|~m2_subset_1(X17,k1_numbers,k5_numbers)\|(v1_xboole_0(X16)\|~m2_subset_1(X16,k1_numbers,k5_numbers))\|(v1_xboole_0(X15)\|~m2_subset_1(X15,k1_numbers,k5_numbers)))&(m1_subset_1(esk8_5(X15,X16,X17,X18,X19),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k4_real_ns1(X15)),u1_struct_0(k4_real_ns1(X16)))))\|~r4_pdiff_1(X15,X16,X17,X18,X19)\|~m2_finseq_2(X19,k1_numbers,k1_euclid(X15))\|(~v1_funct_1(X18)\|~m1_subset_1(X18,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(X15),k1_euclid(X16)))))\|~m2_subset_1(X17,k1_numbers,k5_numbers)\|(v1_xboole_0(X16)\|~m2_subset_1(X16,k1_numbers,k5_numbers))\|(v1_xboole_0(X15)\|~m2_subset_1(X15,k1_numbers,k5_numbers))))&((m1_subset_1(esk9_5(X15,X16,X17,X18,X19),u1_struct_0(k4_real_ns1(X15)))\|~r4_pdiff_1(X15,X16,X17,X18,X19)\|~m2_finseq_2(X19,k1_numbers,k1_euclid(X15))\|(~v1_funct_1(X18)\|~m1_subset_1(X18,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(X15),k1_euclid(X16)))))\|~m2_subset_1(X17,k1_numbers,k5_numbers)\|(v1_xboole_0(X16)\|~m2_subset_1(X16,k1_numbers,k5_numbers))\|(v1_xboole_0(X15)\|~m2_subset_1(X15,k1_numbers,k5_numbers)))&((X18=esk8_5(X15,X16,X17,X18,X19)\|~r4_pdiff_1(X15,X16,X17,X18,X19)\|~m2_finseq_2(X19,k1_numbers,k1_euclid(X15))\|(~v1_funct_1(X18)\|~m1_subset_1(X18,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(X15),k1_euclid(X16)))))\|~m2_subset_1(X17,k1_numbers,k5_numbers)\|(v1_xboole_0(X16)\|~m2_subset_1(X16,k1_numbers,k5_numbers))\|(v1_xboole_0(X15)\|~m2_subset_1(X15,k1_numbers,k5_numbers)))&((X19=esk9_5(X15,X16,X17,X18,X19)\|~r4_pdiff_1(X15,X16,X17,X18,X19)\|~m2_finseq_2(X19,k1_numbers,k1_euclid(X15))\|(~v1_funct_1(X18)\|~m1_subset_1(X18,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(X15),k1_euclid(X16)))))\|~m2_subset_1(X17,k1_numbers,k5_numbers)\|(v1_xboole_0(X16)\|~m2_subset_1(X16,k1_numbers,k5_numbers))\|(v1_xboole_0(X15)\|~m2_subset_1(X15,k1_numbers,k5_numbers)))&(r2_pdiff_1(X16,X15,X17,esk8_5(X15,X16,X17,X18,X19),esk9_5(X15,X16,X17,X18,X19))\|~r4_pdiff_1(X15,X16,X17,X18,X19)\|~m2_finseq_2(X19,k1_numbers,k1_euclid(X15))\|(~v1_funct_1(X18)\|~m1_subset_1(X18,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(X15),k1_euclid(X16)))))\|~m2_subset_1(X17,k1_numbers,k5_numbers)\|(v1_xboole_0(X16)\|~m2_subset_1(X16,k1_numbers,k5_numbers))\|(v1_xboole_0(X15)\|~m2_subset_1(X15,k1_numbers,k5_numbers)))))))&(~v1_funct_1(X22)\|~m1_subset_1(X22,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k4_real_ns1(X15)),u1_struct_0(k4_real_ns1(X16)))))\|(~m1_subset_1(X23,u1_struct_0(k4_real_ns1(X15)))\|(X18!=X22\|(X19!=X23\|~r2_pdiff_1(X16,X15,X17,X22,X23))))\|r4_pdiff_1(X15,X16,X17,X18,X19)\|~m2_finseq_2(X19,k1_numbers,k1_euclid(X15))\|(~v1_funct_1(X18)\|~m1_subset_1(X18,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(X15),k1_euclid(X16)))))\|~m2_subset_1(X17,k1_numbers,k5_numbers)\|(v1_xboole_0(X16)\|~m2_subset_1(X16,k1_numbers,k5_numbers))\|(v1_xboole_0(X15)\|~m2_subset_1(X15,k1_numbers,k5_numbers)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d13_pdiff_1])])])])])])). fof(c_0_4, negated_conjecture, (m2_subset_1(esk1_0,k1_numbers,k5_numbers)&((~v1_xboole_0(esk2_0)&m2_subset_1(esk2_0,k1_numbers,k5_numbers))&((~v1_xboole_0(esk3_0)&m2_subset_1(esk3_0,k1_numbers,k5_numbers))&((v1_funct_1(esk4_0)&m1_subset_1(esk4_0,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k4_real_ns1(esk2_0)),u1_struct_0(k4_real_ns1(esk3_0))))))&((v1_funct_1(esk5_0)&m1_subset_1(esk5_0,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(esk2_0),k1_euclid(esk3_0)))))&(m1_subset_1(esk6_0,u1_struct_0(k4_real_ns1(esk2_0)))&(m2_finseq_2(esk7_0,k1_numbers,k1_euclid(esk2_0))&((esk4_0=esk5_0&esk6_0=esk7_0)&((~r2_pdiff_1(esk3_0,esk2_0,esk1_0,esk4_0,esk6_0)\|~r4_pdiff_1(esk2_0,esk3_0,esk1_0,esk5_0,esk7_0))&(r2_pdiff_1(esk3_0,esk2_0,esk1_0,esk4_0,esk6_0)\|r4_pdiff_1(esk2_0,esk3_0,esk1_0,esk5_0,esk7_0))))))))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_2])])])])). cnf(c_0_5, plain, (r4_pdiff_1(X2,X3,X7,X5,X6)\|v1_xboole_0(X3)\|v1_xboole_0(X2)\|~v1_funct_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k4_real_ns1(X2)),u1_struct_0(k4_real_ns1(X3)))))\|~m1_subset_1(X4,u1_struct_0(k4_real_ns1(X2)))\|X5!=X1\|X6!=X4\|~r2_pdiff_1(X3,X2,X7,X1,X4)\|~m2_finseq_2(X6,k1_numbers,k1_euclid(X2))\|~v1_funct_1(X5)\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(X2),k1_euclid(X3))))\|~m2_subset_1(X7,k1_numbers,k5_numbers)\|~m2_subset_1(X3,k1_numbers,k5_numbers)\|~m2_subset_1(X2,k1_numbers,k5_numbers)), inference(split_conjunct,[status(thm)],[c_0_3])). cnf(c_0_6, negated_conjecture, (m1_subset_1(esk5_0,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(esk2_0),k1_euclid(esk3_0))))), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_7, negated_conjecture, (esk4_0=esk5_0), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_8, plain, (v1_xboole_0(X3)\|v1_xboole_0(X2)\|r4_pdiff_1(X2,X3,X7,X5,X6)\|X4!=X6\|X1!=X5\|~v1_funct_1(X5)\|~v1_funct_1(X1)\|~m2_subset_1(X7,k1_numbers,k5_numbers)\|~m2_subset_1(X3,k1_numbers,k5_numbers)\|~m2_subset_1(X2,k1_numbers,k5_numbers)\|~r2_pdiff_1(X3,X2,X7,X1,X4)\|~m1_subset_1(X4,u1_struct_0(k4_real_ns1(X2)))\|~m2_finseq_2(X6,k1_numbers,k1_euclid(X2))\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(X2),k1_euclid(X3))))\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k4_real_ns1(X2)),u1_struct_0(k4_real_ns1(X3)))))), inference(evalgc,[status(thm)],[c_0_5])). cnf(c_0_9, negated_conjecture, (m1_subset_1(esk4_0,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k4_real_ns1(esk2_0)),u1_struct_0(k4_real_ns1(esk3_0)))))), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_10, negated_conjecture, (m1_subset_1(esk5_0,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(esk2_0),k1_euclid(esk3_0))))), inference(evalgc,[status(thm)],[c_0_6])). cnf(c_0_11, negated_conjecture, (esk5_0=esk4_0), inference(evalgc,[status(thm)],[c_0_7])). cnf(c_0_12, negated_conjecture, (v1_funct_1(esk4_0)), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_13, negated_conjecture, (m2_subset_1(esk3_0,k1_numbers,k5_numbers)), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_14, negated_conjecture, (m2_subset_1(esk2_0,k1_numbers,k5_numbers)), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_15, negated_conjecture, (~v1_xboole_0(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_16, negated_conjecture, (~v1_xboole_0(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_17, negated_conjecture, (r2_pdiff_1(esk3_0,esk2_0,esk1_0,esk4_0,esk6_0)\|r4_pdiff_1(esk2_0,esk3_0,esk1_0,esk5_0,esk7_0)), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_18, negated_conjecture, (esk6_0=esk7_0), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_19, negated_conjecture, (m1_subset_1(esk6_0,u1_struct_0(k4_real_ns1(esk2_0)))), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_20, plain, (X1=esk9_5(X2,X3,X4,X5,X1)\|v1_xboole_0(X3)\|v1_xboole_0(X2)\|~r4_pdiff_1(X2,X3,X4,X5,X1)\|~m2_finseq_2(X1,k1_numbers,k1_euclid(X2))\|~v1_funct_1(X5)\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(X2),k1_euclid(X3))))\|~m2_subset_1(X4,k1_numbers,k5_numbers)\|~m2_subset_1(X3,k1_numbers,k5_numbers)\|~m2_subset_1(X2,k1_numbers,k5_numbers)), inference(split_conjunct,[status(thm)],[c_0_3])). cnf(c_0_21, negated_conjecture, (~r2_pdiff_1(esk3_0,esk2_0,esk1_0,esk4_0,esk6_0)\|~r4_pdiff_1(esk2_0,esk3_0,esk1_0,esk5_0,esk7_0)), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_22, plain, (r4_pdiff_1(X1,X2,X3,X4,X5)\|v1_xboole_0(X1)\|v1_xboole_0(X2)\|~r2_pdiff_1(X2,X1,X3,X4,X5)\|~m2_finseq_2(X5,k1_numbers,k1_euclid(X1))\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k4_real_ns1(X1)),u1_struct_0(k4_real_ns1(X2)))))\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(X1),k1_euclid(X2))))\|~m1_subset_1(X5,u1_struct_0(k4_real_ns1(X1)))\|~v1_funct_1(X4)\|~m2_subset_1(X3,k1_numbers,k5_numbers)\|~m2_subset_1(X2,k1_numbers,k5_numbers)\|~m2_subset_1(X1,k1_numbers,k5_numbers)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_8])])])). cnf(c_0_23, negated_conjecture, (m1_subset_1(esk4_0,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k4_real_ns1(esk2_0)),u1_struct_0(k4_real_ns1(esk3_0)))))), inference(evalgc,[status(thm)],[c_0_9])). cnf(c_0_24, negated_conjecture, (m1_subset_1(esk4_0,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(esk2_0),k1_euclid(esk3_0))))), inference(rw,[status(thm)],[c_0_10, c_0_11])). cnf(c_0_25, negated_conjecture, (v1_funct_1(esk4_0)), inference(evalgc,[status(thm)],[c_0_12])). cnf(c_0_26, negated_conjecture, (m2_subset_1(esk3_0,k1_numbers,k5_numbers)), inference(evalgc,[status(thm)],[c_0_13])). cnf(c_0_27, negated_conjecture, (m2_subset_1(esk2_0,k1_numbers,k5_numbers)), inference(evalgc,[status(thm)],[c_0_14])). cnf(c_0_28, negated_conjecture, (~v1_xboole_0(esk3_0)), inference(evalgc,[status(thm)],[c_0_15])). cnf(c_0_29, negated_conjecture, (~v1_xboole_0(esk2_0)), inference(evalgc,[status(thm)],[c_0_16])). cnf(c_0_30, negated_conjecture, (r2_pdiff_1(esk3_0,esk2_0,esk1_0,esk4_0,esk6_0)\|r4_pdiff_1(esk2_0,esk3_0,esk1_0,esk5_0,esk7_0)), inference(evalgc,[status(thm)],[c_0_17])). cnf(c_0_31, negated_conjecture, (esk6_0=esk7_0), inference(evalgc,[status(thm)],[c_0_18])). cnf(c_0_32, negated_conjecture, (m2_finseq_2(esk7_0,k1_numbers,k1_euclid(esk2_0))), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_33, negated_conjecture, (m1_subset_1(esk6_0,u1_struct_0(k4_real_ns1(esk2_0)))), inference(evalgc,[status(thm)],[c_0_19])). cnf(c_0_34, negated_conjecture, (m2_subset_1(esk1_0,k1_numbers,k5_numbers)), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_35, plain, (r2_pdiff_1(X1,X2,X3,esk8_5(X2,X1,X3,X4,X5),esk9_5(X2,X1,X3,X4,X5))\|v1_xboole_0(X1)\|v1_xboole_0(X2)\|~r4_pdiff_1(X2,X1,X3,X4,X5)\|~m2_finseq_2(X5,k1_numbers,k1_euclid(X2))\|~v1_funct_1(X4)\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(X2),k1_euclid(X1))))\|~m2_subset_1(X3,k1_numbers,k5_numbers)\|~m2_subset_1(X1,k1_numbers,k5_numbers)\|~m2_subset_1(X2,k1_numbers,k5_numbers)), inference(split_conjunct,[status(thm)],[c_0_3])). cnf(c_0_36, plain, (esk9_5(X2,X3,X4,X5,X1)=X1\|v1_xboole_0(X3)\|v1_xboole_0(X2)\|~v1_funct_1(X5)\|~m2_subset_1(X4,k1_numbers,k5_numbers)\|~m2_subset_1(X3,k1_numbers,k5_numbers)\|~m2_subset_1(X2,k1_numbers,k5_numbers)\|~r4_pdiff_1(X2,X3,X4,X5,X1)\|~m2_finseq_2(X1,k1_numbers,k1_euclid(X2))\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(X2),k1_euclid(X3))))), inference(evalgc,[status(thm)],[c_0_20])). cnf(c_0_37, plain, (X1=esk8_5(X2,X3,X4,X1,X5)\|v1_xboole_0(X3)\|v1_xboole_0(X2)\|~r4_pdiff_1(X2,X3,X4,X1,X5)\|~m2_finseq_2(X5,k1_numbers,k1_euclid(X2))\|~v1_funct_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(X2),k1_euclid(X3))))\|~m2_subset_1(X4,k1_numbers,k5_numbers)\|~m2_subset_1(X3,k1_numbers,k5_numbers)\|~m2_subset_1(X2,k1_numbers,k5_numbers)), inference(split_conjunct,[status(thm)],[c_0_3])). cnf(c_0_38, negated_conjecture, (~r2_pdiff_1(esk3_0,esk2_0,esk1_0,esk4_0,esk6_0)\|~r4_pdiff_1(esk2_0,esk3_0,esk1_0,esk5_0,esk7_0)), inference(evalgc,[status(thm)],[c_0_21])). cnf(c_0_39, negated_conjecture, (r4_pdiff_1(esk2_0,esk3_0,X1,esk4_0,X2)\|~r2_pdiff_1(esk3_0,esk2_0,X1,esk4_0,X2)\|~m2_finseq_2(X2,k1_numbers,k1_euclid(esk2_0))\|~m1_subset_1(X2,u1_struct_0(k4_real_ns1(esk2_0)))\|~m2_subset_1(X1,k1_numbers,k5_numbers)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22, c_0_23]), c_0_24]), c_0_25]), c_0_26]), c_0_27])]), c_0_28]), c_0_29])])). cnf(c_0_40, negated_conjecture, (r4_pdiff_1(esk2_0,esk3_0,esk1_0,esk4_0,esk7_0)\|r2_pdiff_1(esk3_0,esk2_0,esk1_0,esk4_0,esk7_0)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30, c_0_31]), c_0_11])). cnf(c_0_41, negated_conjecture, (m2_finseq_2(esk7_0,k1_numbers,k1_euclid(esk2_0))), inference(evalgc,[status(thm)],[c_0_32])). cnf(c_0_42, negated_conjecture, (m1_subset_1(esk7_0,u1_struct_0(k4_real_ns1(esk2_0)))), inference(rw,[status(thm)],[c_0_33, c_0_31])). cnf(c_0_43, negated_conjecture, (m2_subset_1(esk1_0,k1_numbers,k5_numbers)), inference(evalgc,[status(thm)],[c_0_34])). cnf(c_0_44, plain, (v1_xboole_0(X2)\|v1_xboole_0(X1)\|r2_pdiff_1(X1,X2,X3,esk8_5(X2,X1,X3,X4,X5),esk9_5(X2,X1,X3,X4,X5))\|~v1_funct_1(X4)\|~m2_subset_1(X3,k1_numbers,k5_numbers)\|~m2_subset_1(X2,k1_numbers,k5_numbers)\|~m2_subset_1(X1,k1_numbers,k5_numbers)\|~r4_pdiff_1(X2,X1,X3,X4,X5)\|~m2_finseq_2(X5,k1_numbers,k1_euclid(X2))\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(X2),k1_euclid(X1))))), inference(evalgc,[status(thm)],[c_0_35])). cnf(c_0_45, negated_conjecture, (esk9_5(esk2_0,esk3_0,X1,esk4_0,X2)=X2\|~r4_pdiff_1(esk2_0,esk3_0,X1,esk4_0,X2)\|~m2_finseq_2(X2,k1_numbers,k1_euclid(esk2_0))\|~m2_subset_1(X1,k1_numbers,k5_numbers)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36, c_0_24]), c_0_25]), c_0_26]), c_0_27])]), c_0_29]), c_0_28])])). cnf(c_0_46, plain, (esk8_5(X2,X3,X4,X1,X5)=X1\|v1_xboole_0(X3)\|v1_xboole_0(X2)\|~v1_funct_1(X1)\|~m2_subset_1(X4,k1_numbers,k5_numbers)\|~m2_subset_1(X3,k1_numbers,k5_numbers)\|~m2_subset_1(X2,k1_numbers,k5_numbers)\|~r4_pdiff_1(X2,X3,X4,X1,X5)\|~m2_finseq_2(X5,k1_numbers,k1_euclid(X2))\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(X2),k1_euclid(X3))))), inference(evalgc,[status(thm)],[c_0_37])). cnf(c_0_47, negated_conjecture, (~r4_pdiff_1(esk2_0,esk3_0,esk1_0,esk4_0,esk7_0)\|~r2_pdiff_1(esk3_0,esk2_0,esk1_0,esk4_0,esk7_0)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38, c_0_31]), c_0_11])). cnf(c_0_48, negated_conjecture, (r4_pdiff_1(esk2_0,esk3_0,esk1_0,esk4_0,esk7_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39, c_0_40]), c_0_41]), c_0_42]), c_0_43])])])). cnf(c_0_49, negated_conjecture, (r2_pdiff_1(esk3_0,esk2_0,X1,esk8_5(esk2_0,esk3_0,X1,esk4_0,X2),X2)\|~r4_pdiff_1(esk2_0,esk3_0,X1,esk4_0,X2)\|~m2_finseq_2(X2,k1_numbers,k1_euclid(esk2_0))\|~m2_subset_1(X1,k1_numbers,k5_numbers)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44, c_0_45]), c_0_24]), c_0_25]), c_0_27]), c_0_26])]), c_0_28]), c_0_29])])). cnf(c_0_50, negated_conjecture, (esk8_5(esk2_0,esk3_0,X1,esk4_0,X2)=esk4_0\|~r4_pdiff_1(esk2_0,esk3_0,X1,esk4_0,X2)\|~m2_finseq_2(X2,k1_numbers,k1_euclid(esk2_0))\|~m2_subset_1(X1,k1_numbers,k5_numbers)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46, c_0_24]), c_0_25]), c_0_26]), c_0_27])]), c_0_29]), c_0_28])])). cnf(c_0_51, negated_conjecture, (~r2_pdiff_1(esk3_0,esk2_0,esk1_0,esk4_0,esk7_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47, c_0_48])])])). cnf(c_0_52, negated_conjecture, (r2_pdiff_1(esk3_0,esk2_0,X1,esk4_0,X2)\|~r4_pdiff_1(esk2_0,esk3_0,X1,esk4_0,X2)\|~m2_finseq_2(X2,k1_numbers,k1_euclid(esk2_0))\|~m2_subset_1(X1,k1_numbers,k5_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_49, c_0_50])])). cnf(c_0_53, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51, c_0_52]), c_0_48]), c_0_41]), c_0_43])]), ['proof']). # SZS output end CNFRefutation	reserve f for PartFunc of REAL-NS 1,REAL-NS 1; reserve g for PartFunc of REAL,REAL; reserve x for Point of REAL-NS 1; reserve y for Element of REAL; reserve m,n for non empty Element of NAT; reserve i,j for Element of NAT; reserve f for PartFunc of REAL-NS n,REAL-NS 1; reserve g for PartFunc of REAL n,REAL; reserve x for Point of REAL-NS n; reserve y for Element of REAL n; theorem Th16: for m,n be non empty Element of NAT, F be PartFunc of REAL-NS m, REAL-NS n, G be PartFunc of REAL m,REAL n, x be Point of REAL-NS m, y be Element of REAL m st F = G & x = y holds F is_partial_differentiable_in x,i iff G is_partial_differentiable_in y,i proof let m,n be non empty Element of NAT, F be PartFunc of REAL-NS m,REAL-NS n, G be PartFunc of REAL m,REAL n, x be Point of REAL-NS m, y be Element of REAL m; assume that A1: F=G and A2: x=y; now assume G is_partial_differentiable_in y,i; then ex f1 be PartFunc of REAL-NS m,REAL-NS n, y1 be Point of REAL-NS m st G=f1 & y=y1 & f1 is_partial_differentiable_in y1,i by Def13; hence F is_partial_differentiable_in x,i by A1,A2; end; hence thesis by A1,A2,Def13; end;	Convert the following ATP output trace into a readable Mizar proof.
t44_yellow_0	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t44_yellow_0, conjecture, ![X1]:((~(v2_struct_0(X1))&(v5_orders_2(X1)&(v1_yellow_0(X1)&l1_orders_2(X1))))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>r1_orders_2(X1,k3_yellow_0(X1),X2))), file('/scratch/mptp/predsminms1/t44_yellow_0__0', t44_yellow_0)). fof(d11_yellow_0, axiom, ![X1]:(l1_orders_2(X1)=>k3_yellow_0(X1)=k1_yellow_0(X1,k1_xboole_0)), file('/scratch/mptp/predsminms1/t44_yellow_0__0', d11_yellow_0)). fof(d9_yellow_0, axiom, ![X1]:(l1_orders_2(X1)=>![X2, X3]:(m1_subset_1(X3,u1_struct_0(X1))=>(r1_yellow_0(X1,X2)=>(X3=k1_yellow_0(X1,X2)<=>(r2_lattice3(X1,X2,X3)&![X4]:(m1_subset_1(X4,u1_struct_0(X1))=>(r2_lattice3(X1,X2,X4)=>r1_orders_2(X1,X3,X4)))))))), file('/scratch/mptp/predsminms1/t44_yellow_0__0', d9_yellow_0)). fof(t6_yellow_0, axiom, ![X1]:(l1_orders_2(X1)=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>(r2_lattice3(X1,k1_xboole_0,X2)&r1_lattice3(X1,k1_xboole_0,X2)))), file('/scratch/mptp/predsminms1/t44_yellow_0__0', t6_yellow_0)). fof(t42_yellow_0, axiom, ![X1]:((~(v2_struct_0(X1))&(v5_orders_2(X1)&(v1_yellow_0(X1)&l1_orders_2(X1))))=>(r1_yellow_0(X1,k1_xboole_0)&r2_yellow_0(X1,u1_struct_0(X1)))), file('/scratch/mptp/predsminms1/t44_yellow_0__0', t42_yellow_0)). fof(dt_k3_yellow_0, axiom, ![X1]:(l1_orders_2(X1)=>m1_subset_1(k3_yellow_0(X1),u1_struct_0(X1))), file('/scratch/mptp/predsminms1/t44_yellow_0__0', dt_k3_yellow_0)). fof(c_0_6, negated_conjecture, ~(![X1]:((~(v2_struct_0(X1))&(v5_orders_2(X1)&(v1_yellow_0(X1)&l1_orders_2(X1))))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>r1_orders_2(X1,k3_yellow_0(X1),X2)))), inference(assume_negation,[status(cth)],[t44_yellow_0])). fof(c_0_7, negated_conjecture, ((~v2_struct_0(esk1_0)&(v5_orders_2(esk1_0)&(v1_yellow_0(esk1_0)&l1_orders_2(esk1_0))))&(m1_subset_1(esk2_0,u1_struct_0(esk1_0))&~r1_orders_2(esk1_0,k3_yellow_0(esk1_0),esk2_0))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_6])])])])). fof(c_0_8, plain, ![X7]:(~l1_orders_2(X7)\|k3_yellow_0(X7)=k1_yellow_0(X7,k1_xboole_0)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d11_yellow_0])])). fof(c_0_9, plain, ![X8, X9, X10, X11]:(((r2_lattice3(X8,X9,X10)\|X10!=k1_yellow_0(X8,X9)\|~r1_yellow_0(X8,X9)\|~m1_subset_1(X10,u1_struct_0(X8))\|~l1_orders_2(X8))&(~m1_subset_1(X11,u1_struct_0(X8))\|(~r2_lattice3(X8,X9,X11)\|r1_orders_2(X8,X10,X11))\|X10!=k1_yellow_0(X8,X9)\|~r1_yellow_0(X8,X9)\|~m1_subset_1(X10,u1_struct_0(X8))\|~l1_orders_2(X8)))&((m1_subset_1(esk3_3(X8,X9,X10),u1_struct_0(X8))\|~r2_lattice3(X8,X9,X10)\|X10=k1_yellow_0(X8,X9)\|~r1_yellow_0(X8,X9)\|~m1_subset_1(X10,u1_struct_0(X8))\|~l1_orders_2(X8))&((r2_lattice3(X8,X9,esk3_3(X8,X9,X10))\|~r2_lattice3(X8,X9,X10)\|X10=k1_yellow_0(X8,X9)\|~r1_yellow_0(X8,X9)\|~m1_subset_1(X10,u1_struct_0(X8))\|~l1_orders_2(X8))&(~r1_orders_2(X8,X10,esk3_3(X8,X9,X10))\|~r2_lattice3(X8,X9,X10)\|X10=k1_yellow_0(X8,X9)\|~r1_yellow_0(X8,X9)\|~m1_subset_1(X10,u1_struct_0(X8))\|~l1_orders_2(X8))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d9_yellow_0])])])])])). fof(c_0_10, plain, ![X13, X14]:((r2_lattice3(X13,k1_xboole_0,X14)\|~m1_subset_1(X14,u1_struct_0(X13))\|~l1_orders_2(X13))&(r1_lattice3(X13,k1_xboole_0,X14)\|~m1_subset_1(X14,u1_struct_0(X13))\|~l1_orders_2(X13))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_yellow_0])])])])). fof(c_0_11, plain, ![X15]:((r1_yellow_0(X15,k1_xboole_0)\|(v2_struct_0(X15)\|(~v5_orders_2(X15)\|(~v1_yellow_0(X15)\|~l1_orders_2(X15)))))&(r2_yellow_0(X15,u1_struct_0(X15))\|(v2_struct_0(X15)\|(~v5_orders_2(X15)\|(~v1_yellow_0(X15)\|~l1_orders_2(X15)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t42_yellow_0])])])])). cnf(c_0_12, negated_conjecture, (~r1_orders_2(esk1_0,k3_yellow_0(esk1_0),esk2_0)), inference(split_conjunct,[status(thm)],[c_0_7])). cnf(c_0_13, plain, (k3_yellow_0(X1)=k1_yellow_0(X1,k1_xboole_0)\|~l1_orders_2(X1)), inference(split_conjunct,[status(thm)],[c_0_8])). cnf(c_0_14, negated_conjecture, (l1_orders_2(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_7])). cnf(c_0_15, plain, (r1_orders_2(X2,X4,X1)\|~m1_subset_1(X1,u1_struct_0(X2))\|~r2_lattice3(X2,X3,X1)\|X4!=k1_yellow_0(X2,X3)\|~r1_yellow_0(X2,X3)\|~m1_subset_1(X4,u1_struct_0(X2))\|~l1_orders_2(X2)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_16, plain, (r2_lattice3(X1,k1_xboole_0,X2)\|~m1_subset_1(X2,u1_struct_0(X1))\|~l1_orders_2(X1)), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_17, negated_conjecture, (~v2_struct_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_7])). cnf(c_0_18, plain, (r1_yellow_0(X1,k1_xboole_0)\|v2_struct_0(X1)\|~v5_orders_2(X1)\|~v1_yellow_0(X1)\|~l1_orders_2(X1)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_19, negated_conjecture, (v1_yellow_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_7])). cnf(c_0_20, negated_conjecture, (v5_orders_2(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_7])). fof(c_0_21, plain, ![X16]:(~l1_orders_2(X16)\|m1_subset_1(k3_yellow_0(X16),u1_struct_0(X16))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k3_yellow_0])])). cnf(c_0_22, negated_conjecture, (~r1_orders_2(esk1_0,k3_yellow_0(esk1_0),esk2_0)), inference(evalgc,[status(thm)],[c_0_12])). cnf(c_0_23, plain, (k3_yellow_0(X1)=k1_yellow_0(X1,k1_xboole_0)\|~l1_orders_2(X1)), inference(evalgc,[status(thm)],[c_0_13])). cnf(c_0_24, negated_conjecture, (l1_orders_2(esk1_0)), inference(evalgc,[status(thm)],[c_0_14])). cnf(c_0_25, plain, (r1_orders_2(X2,X4,X1)\|X4!=k1_yellow_0(X2,X3)\|~l1_orders_2(X2)\|~r1_yellow_0(X2,X3)\|~r2_lattice3(X2,X3,X1)\|~m1_subset_1(X4,u1_struct_0(X2))\|~m1_subset_1(X1,u1_struct_0(X2))), inference(evalgc,[status(thm)],[c_0_15])). cnf(c_0_26, plain, (r2_lattice3(X1,k1_xboole_0,X2)\|~l1_orders_2(X1)\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_16])). cnf(c_0_27, negated_conjecture, (~v2_struct_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_17])). cnf(c_0_28, plain, (v2_struct_0(X1)\|r1_yellow_0(X1,k1_xboole_0)\|~v5_orders_2(X1)\|~v1_yellow_0(X1)\|~l1_orders_2(X1)), inference(evalgc,[status(thm)],[c_0_18])). cnf(c_0_29, negated_conjecture, (v1_yellow_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_19])). cnf(c_0_30, negated_conjecture, (v5_orders_2(esk1_0)), inference(evalgc,[status(thm)],[c_0_20])). cnf(c_0_31, negated_conjecture, (m1_subset_1(esk2_0,u1_struct_0(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_7])). cnf(c_0_32, plain, (m1_subset_1(k3_yellow_0(X1),u1_struct_0(X1))\|~l1_orders_2(X1)), inference(split_conjunct,[status(thm)],[c_0_21])). cnf(c_0_33, negated_conjecture, (~r1_orders_2(esk1_0,k1_yellow_0(esk1_0,k1_xboole_0),esk2_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22, c_0_23]), c_0_24])])])). cnf(c_0_34, plain, (r1_orders_2(X1,X2,X3)\|X2!=k1_yellow_0(X1,k1_xboole_0)\|~r1_yellow_0(X1,k1_xboole_0)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~l1_orders_2(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_25, c_0_26])])). cnf(c_0_35, negated_conjecture, (r1_yellow_0(esk1_0,k1_xboole_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27, c_0_28]), c_0_24]), c_0_29]), c_0_30])])])). cnf(c_0_36, negated_conjecture, (m1_subset_1(esk2_0,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[c_0_31])). cnf(c_0_37, plain, (m1_subset_1(k3_yellow_0(X1),u1_struct_0(X1))\|~l1_orders_2(X1)), inference(evalgc,[status(thm)],[c_0_32])). cnf(c_0_38, negated_conjecture, (~m1_subset_1(k1_yellow_0(esk1_0,k1_xboole_0),u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33, c_0_34]), c_0_35]), c_0_36]), c_0_24])])])). cnf(c_0_39, plain, (m1_subset_1(k1_yellow_0(X1,k1_xboole_0),u1_struct_0(X1))\|~l1_orders_2(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_37, c_0_23])])). cnf(c_0_40, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38, c_0_39]), c_0_24])]), ['proof']). # SZS output end CNFRefutation	theorem for L being lower-bounded antisymmetric non empty RelStr for x being Element of L holds Bottom L <= x proof let L be lower-bounded antisymmetric non empty RelStr; let x be Element of L; {} is_<=_than x & ex_sup_of {},L by Th6,Th42; hence thesis by Th30; end;	Convert the following ATP output trace into a readable Mizar proof.
t3_sin_cos9	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t3_sin_cos9, conjecture, (r2_fdiff_1(k29_sin_cos,k2_rcomp_1(k1_real_1(k10_real_1(k32_sin_cos,np__2)),k10_real_1(k32_sin_cos,np__2)))&![X1]:(m1_subset_1(X1,k1_numbers)=>(r2_hidden(X1,k2_rcomp_1(k1_real_1(k10_real_1(k32_sin_cos,np__2)),k10_real_1(k32_sin_cos,np__2)))=>k1_fdiff_1(k29_sin_cos,X1)=k10_real_1(np__1,k5_square_1(k1_seq_1(k19_sin_cos,X1)))))), file('/scratch/mptp/predsminms1/t3_sin_cos9__0', t3_sin_cos9)). fof(l5_sin_cos9, axiom, ![X1]:(m1_subset_1(X1,k1_numbers)=>(r2_hidden(X1,k2_rcomp_1(k1_real_1(k10_real_1(k32_sin_cos,np__2)),k10_real_1(k32_sin_cos,np__2)))=>k1_fdiff_1(k29_sin_cos,X1)=k10_real_1(np__1,k5_square_1(k1_seq_1(k19_sin_cos,X1))))), file('/scratch/mptp/predsminms1/t3_sin_cos9__0', l5_sin_cos9)). fof(l3_sin_cos9, axiom, r2_fdiff_1(k29_sin_cos,k2_rcomp_1(k1_real_1(k10_real_1(k32_sin_cos,np__2)),k10_real_1(k32_sin_cos,np__2))), file('/scratch/mptp/predsminms1/t3_sin_cos9__0', l3_sin_cos9)). fof(c_0_3, negated_conjecture, ~((r2_fdiff_1(k29_sin_cos,k2_rcomp_1(k1_real_1(k10_real_1(k32_sin_cos,np__2)),k10_real_1(k32_sin_cos,np__2)))&![X1]:(m1_subset_1(X1,k1_numbers)=>(r2_hidden(X1,k2_rcomp_1(k1_real_1(k10_real_1(k32_sin_cos,np__2)),k10_real_1(k32_sin_cos,np__2)))=>k1_fdiff_1(k29_sin_cos,X1)=k10_real_1(np__1,k5_square_1(k1_seq_1(k19_sin_cos,X1))))))), inference(assume_negation,[status(cth)],[t3_sin_cos9])). fof(c_0_4, negated_conjecture, ((m1_subset_1(esk1_0,k1_numbers)\|~r2_fdiff_1(k29_sin_cos,k2_rcomp_1(k1_real_1(k10_real_1(k32_sin_cos,np__2)),k10_real_1(k32_sin_cos,np__2))))&((r2_hidden(esk1_0,k2_rcomp_1(k1_real_1(k10_real_1(k32_sin_cos,np__2)),k10_real_1(k32_sin_cos,np__2)))\|~r2_fdiff_1(k29_sin_cos,k2_rcomp_1(k1_real_1(k10_real_1(k32_sin_cos,np__2)),k10_real_1(k32_sin_cos,np__2))))&(k1_fdiff_1(k29_sin_cos,esk1_0)!=k10_real_1(np__1,k5_square_1(k1_seq_1(k19_sin_cos,esk1_0)))\|~r2_fdiff_1(k29_sin_cos,k2_rcomp_1(k1_real_1(k10_real_1(k32_sin_cos,np__2)),k10_real_1(k32_sin_cos,np__2)))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])])). fof(c_0_5, plain, ![X3]:(~m1_subset_1(X3,k1_numbers)\|(~r2_hidden(X3,k2_rcomp_1(k1_real_1(k10_real_1(k32_sin_cos,np__2)),k10_real_1(k32_sin_cos,np__2)))\|k1_fdiff_1(k29_sin_cos,X3)=k10_real_1(np__1,k5_square_1(k1_seq_1(k19_sin_cos,X3))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l5_sin_cos9])])). cnf(c_0_6, negated_conjecture, (r2_hidden(esk1_0,k2_rcomp_1(k1_real_1(k10_real_1(k32_sin_cos,np__2)),k10_real_1(k32_sin_cos,np__2)))\|~r2_fdiff_1(k29_sin_cos,k2_rcomp_1(k1_real_1(k10_real_1(k32_sin_cos,np__2)),k10_real_1(k32_sin_cos,np__2)))), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_7, plain, (r2_fdiff_1(k29_sin_cos,k2_rcomp_1(k1_real_1(k10_real_1(k32_sin_cos,np__2)),k10_real_1(k32_sin_cos,np__2)))), inference(split_conjunct,[status(thm)],[l3_sin_cos9])). cnf(c_0_8, negated_conjecture, (m1_subset_1(esk1_0,k1_numbers)\|~r2_fdiff_1(k29_sin_cos,k2_rcomp_1(k1_real_1(k10_real_1(k32_sin_cos,np__2)),k10_real_1(k32_sin_cos,np__2)))), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_9, negated_conjecture, (k1_fdiff_1(k29_sin_cos,esk1_0)!=k10_real_1(np__1,k5_square_1(k1_seq_1(k19_sin_cos,esk1_0)))\|~r2_fdiff_1(k29_sin_cos,k2_rcomp_1(k1_real_1(k10_real_1(k32_sin_cos,np__2)),k10_real_1(k32_sin_cos,np__2)))), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_10, plain, (k1_fdiff_1(k29_sin_cos,X1)=k10_real_1(np__1,k5_square_1(k1_seq_1(k19_sin_cos,X1)))\|~m1_subset_1(X1,k1_numbers)\|~r2_hidden(X1,k2_rcomp_1(k1_real_1(k10_real_1(k32_sin_cos,np__2)),k10_real_1(k32_sin_cos,np__2)))), inference(split_conjunct,[status(thm)],[c_0_5])). cnf(c_0_11, negated_conjecture, (r2_hidden(esk1_0,k2_rcomp_1(k1_real_1(k10_real_1(k32_sin_cos,np__2)),k10_real_1(k32_sin_cos,np__2)))\|~r2_fdiff_1(k29_sin_cos,k2_rcomp_1(k1_real_1(k10_real_1(k32_sin_cos,np__2)),k10_real_1(k32_sin_cos,np__2)))), inference(evalgc,[status(thm)],[c_0_6])). cnf(c_0_12, plain, (r2_fdiff_1(k29_sin_cos,k2_rcomp_1(k1_real_1(k10_real_1(k32_sin_cos,np__2)),k10_real_1(k32_sin_cos,np__2)))), inference(evalgc,[status(thm)],[c_0_7])). cnf(c_0_13, negated_conjecture, (m1_subset_1(esk1_0,k1_numbers)\|~r2_fdiff_1(k29_sin_cos,k2_rcomp_1(k1_real_1(k10_real_1(k32_sin_cos,np__2)),k10_real_1(k32_sin_cos,np__2)))), inference(evalgc,[status(thm)],[c_0_8])). cnf(c_0_14, negated_conjecture, (k10_real_1(np__1,k5_square_1(k1_seq_1(k19_sin_cos,esk1_0)))!=k1_fdiff_1(k29_sin_cos,esk1_0)\|~r2_fdiff_1(k29_sin_cos,k2_rcomp_1(k1_real_1(k10_real_1(k32_sin_cos,np__2)),k10_real_1(k32_sin_cos,np__2)))), inference(evalgc,[status(thm)],[c_0_9])). cnf(c_0_15, plain, (k10_real_1(np__1,k5_square_1(k1_seq_1(k19_sin_cos,X1)))=k1_fdiff_1(k29_sin_cos,X1)\|~m1_subset_1(X1,k1_numbers)\|~r2_hidden(X1,k2_rcomp_1(k1_real_1(k10_real_1(k32_sin_cos,np__2)),k10_real_1(k32_sin_cos,np__2)))), inference(evalgc,[status(thm)],[c_0_10])). cnf(c_0_16, negated_conjecture, (r2_hidden(esk1_0,k2_rcomp_1(k1_real_1(k10_real_1(k32_sin_cos,np__2)),k10_real_1(k32_sin_cos,np__2)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_11, c_0_12])])). cnf(c_0_17, negated_conjecture, (m1_subset_1(esk1_0,k1_numbers)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_13, c_0_12])])). cnf(c_0_18, negated_conjecture, (k10_real_1(np__1,k5_square_1(k1_seq_1(k19_sin_cos,esk1_0)))!=k1_fdiff_1(k29_sin_cos,esk1_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14, c_0_12])])). cnf(c_0_19, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15, c_0_16]), c_0_17])]), c_0_18]), ['proof']). # SZS output end CNFRefutation	reserve x, r, s, h for Real, n for Element of NAT, rr, y for set, Z for open Subset of REAL, f, f1, f2 for PartFunc of REAL,REAL; theorem tan is_differentiable_on ].-PI/2,PI/2.[ & for x st x in ].-PI/2,PI/2.[ holds diff(tan,x) = 1/(cos.x)^2 by Lm1,Lm3;	Convert the following ATP output trace into a readable Mizar proof.
t53_topgrp_1	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(fraenkel_a_3_0_group_2, axiom, ![X1, X2, X3, X4]:(((~(v2_struct_0(X2))&l3_algstr_0(X2))&(m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))&m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))))=>(r2_hidden(X1,a_3_0_group_2(X2,X3,X4))<=>?[X5, X6]:((m1_subset_1(X5,u1_struct_0(X2))&m1_subset_1(X6,u1_struct_0(X2)))&(X1=k6_algstr_0(X2,X5,X6)&(r2_hidden(X5,X3)&r2_hidden(X6,X4)))))), file('/scratch/mptp/predsminms1/t53_topgrp_1__0', fraenkel_a_3_0_group_2)). fof(t4_subset, axiom, ![X1, X2, X3]:((r2_hidden(X1,X2)&m1_subset_1(X2,k1_zfmisc_1(X3)))=>m1_subset_1(X1,X3)), file('/scratch/mptp/predsminms1/t53_topgrp_1__0', t4_subset)). fof(t27_group_2, axiom, ![X1, X2]:((~(v2_struct_0(X2))&l3_algstr_0(X2))=>![X3]:(m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))=>![X4]:(m1_subset_1(X4,u1_struct_0(X2))=>(r2_hidden(X1,k4_group_2(X2,X4,X3))<=>?[X5]:(m1_subset_1(X5,u1_struct_0(X2))&(X1=k6_algstr_0(X2,X4,X5)&r2_hidden(X5,X3))))))), file('/scratch/mptp/predsminms1/t53_topgrp_1__0', t27_group_2)). fof(d3_tarski, axiom, ![X1, X2]:(r1_tarski(X1,X2)<=>![X3]:(r2_hidden(X3,X1)=>r2_hidden(X3,X2))), file('/scratch/mptp/predsminms1/t53_topgrp_1__0', d3_tarski)). fof(t22_tops_1, axiom, ![X1]:((v2_pre_topc(X1)&l1_pre_topc(X1))=>![X2, X3]:(m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))=>(r2_hidden(X2,k1_tops_1(X1,X3))<=>?[X4]:(m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X1)))&(v3_pre_topc(X4,X1)&(r1_tarski(X4,X3)&r2_hidden(X2,X4))))))), file('/scratch/mptp/predsminms1/t53_topgrp_1__0', t22_tops_1)). fof(fc18_topgrp_1, axiom, ![X1, X2, X3]:(((~(v2_struct_0(X1))&(v2_pre_topc(X1)&(v2_group_1(X1)&(v3_group_1(X1)&(v4_topgrp_1(X1)&l1_topgrp_1(X1))))))&((v3_pre_topc(X2,X1)&m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))))&m1_subset_1(X3,u1_struct_0(X1))))=>v3_pre_topc(k4_group_2(X1,X3,X2),X1)), file('/scratch/mptp/predsminms1/t53_topgrp_1__0', fc18_topgrp_1)). fof(dt_k2_group_2, axiom, ![X1, X2, X3]:(((~(v2_struct_0(X1))&l3_algstr_0(X1))&(m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))&m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))))=>m1_subset_1(k2_group_2(X1,X2,X3),k1_zfmisc_1(u1_struct_0(X1)))), file('/scratch/mptp/predsminms1/t53_topgrp_1__0', dt_k2_group_2)). fof(d2_group_2, axiom, ![X1]:((~(v2_struct_0(X1))&l3_algstr_0(X1))=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))=>![X3]:(m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))=>k2_group_2(X1,X2,X3)=a_3_0_group_2(X1,X2,X3)))), file('/scratch/mptp/predsminms1/t53_topgrp_1__0', d2_group_2)). fof(dt_l1_topgrp_1, axiom, ![X1]:(l1_topgrp_1(X1)=>(l3_algstr_0(X1)&l1_pre_topc(X1))), file('/scratch/mptp/predsminms1/t53_topgrp_1__0', dt_l1_topgrp_1)). fof(dt_k4_group_2, axiom, ![X1, X2, X3]:(((~(v2_struct_0(X1))&l3_algstr_0(X1))&(m1_subset_1(X2,u1_struct_0(X1))&m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))))=>m1_subset_1(k4_group_2(X1,X2,X3),k1_zfmisc_1(u1_struct_0(X1)))), file('/scratch/mptp/predsminms1/t53_topgrp_1__0', dt_k4_group_2)). fof(d10_xboole_0, axiom, ![X1, X2]:(X1=X2<=>(r1_tarski(X1,X2)&r1_tarski(X2,X1))), file('/scratch/mptp/predsminms1/t53_topgrp_1__0', d10_xboole_0)). fof(t16_tops_1, axiom, ![X1]:(l1_pre_topc(X1)=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))=>r1_tarski(k1_tops_1(X1,X2),X2))), file('/scratch/mptp/predsminms1/t53_topgrp_1__0', t16_tops_1)). fof(t53_topgrp_1, conjecture, ![X1]:((~(v2_struct_0(X1))&(v2_pre_topc(X1)&(v2_group_1(X1)&(v3_group_1(X1)&(v4_topgrp_1(X1)&l1_topgrp_1(X1))))))=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))=>![X3]:(m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))=>(v3_pre_topc(X3,X1)=>v3_pre_topc(k2_group_2(X1,X2,X3),X1))))), file('/scratch/mptp/predsminms1/t53_topgrp_1__0', t53_topgrp_1)). fof(fc9_tops_1, axiom, ![X1, X2]:(((v2_pre_topc(X1)&l1_pre_topc(X1))&m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))))=>v3_pre_topc(k1_tops_1(X1,X2),X1)), file('/scratch/mptp/predsminms1/t53_topgrp_1__0', fc9_tops_1)). fof(c_0_14, plain, ![X10, X11, X12, X13, X16, X17]:((((m1_subset_1(esk4_4(X10,X11,X12,X13),u1_struct_0(X11))\|~r2_hidden(X10,a_3_0_group_2(X11,X12,X13))\|(v2_struct_0(X11)\|~l3_algstr_0(X11)\|(~m1_subset_1(X12,k1_zfmisc_1(u1_struct_0(X11)))\|~m1_subset_1(X13,k1_zfmisc_1(u1_struct_0(X11))))))&(m1_subset_1(esk5_4(X10,X11,X12,X13),u1_struct_0(X11))\|~r2_hidden(X10,a_3_0_group_2(X11,X12,X13))\|(v2_struct_0(X11)\|~l3_algstr_0(X11)\|(~m1_subset_1(X12,k1_zfmisc_1(u1_struct_0(X11)))\|~m1_subset_1(X13,k1_zfmisc_1(u1_struct_0(X11)))))))&((X10=k6_algstr_0(X11,esk4_4(X10,X11,X12,X13),esk5_4(X10,X11,X12,X13))\|~r2_hidden(X10,a_3_0_group_2(X11,X12,X13))\|(v2_struct_0(X11)\|~l3_algstr_0(X11)\|(~m1_subset_1(X12,k1_zfmisc_1(u1_struct_0(X11)))\|~m1_subset_1(X13,k1_zfmisc_1(u1_struct_0(X11))))))&((r2_hidden(esk4_4(X10,X11,X12,X13),X12)\|~r2_hidden(X10,a_3_0_group_2(X11,X12,X13))\|(v2_struct_0(X11)\|~l3_algstr_0(X11)\|(~m1_subset_1(X12,k1_zfmisc_1(u1_struct_0(X11)))\|~m1_subset_1(X13,k1_zfmisc_1(u1_struct_0(X11))))))&(r2_hidden(esk5_4(X10,X11,X12,X13),X13)\|~r2_hidden(X10,a_3_0_group_2(X11,X12,X13))\|(v2_struct_0(X11)\|~l3_algstr_0(X11)\|(~m1_subset_1(X12,k1_zfmisc_1(u1_struct_0(X11)))\|~m1_subset_1(X13,k1_zfmisc_1(u1_struct_0(X11)))))))))&(~m1_subset_1(X16,u1_struct_0(X11))\|~m1_subset_1(X17,u1_struct_0(X11))\|(X10!=k6_algstr_0(X11,X16,X17)\|(~r2_hidden(X16,X12)\|~r2_hidden(X17,X13)))\|r2_hidden(X10,a_3_0_group_2(X11,X12,X13))\|(v2_struct_0(X11)\|~l3_algstr_0(X11)\|(~m1_subset_1(X12,k1_zfmisc_1(u1_struct_0(X11)))\|~m1_subset_1(X13,k1_zfmisc_1(u1_struct_0(X11))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fraenkel_a_3_0_group_2])])])])])])). fof(c_0_15, plain, ![X18, X19, X20]:(~r2_hidden(X18,X19)\|~m1_subset_1(X19,k1_zfmisc_1(X20))\|m1_subset_1(X18,X20)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])])). cnf(c_0_16, plain, (r2_hidden(X4,a_3_0_group_2(X2,X5,X6))\|v2_struct_0(X2)\|~m1_subset_1(X1,u1_struct_0(X2))\|~m1_subset_1(X3,u1_struct_0(X2))\|X4!=k6_algstr_0(X2,X1,X3)\|~r2_hidden(X1,X5)\|~r2_hidden(X3,X6)\|~l3_algstr_0(X2)\|~m1_subset_1(X5,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X6,k1_zfmisc_1(u1_struct_0(X2)))), inference(split_conjunct,[status(thm)],[c_0_14])). cnf(c_0_17, plain, (m1_subset_1(X1,X3)\|~r2_hidden(X1,X2)\|~m1_subset_1(X2,k1_zfmisc_1(X3))), inference(split_conjunct,[status(thm)],[c_0_15])). fof(c_0_18, plain, ![X21, X22, X23, X24, X26]:(((m1_subset_1(esk6_4(X21,X22,X23,X24),u1_struct_0(X22))\|~r2_hidden(X21,k4_group_2(X22,X24,X23))\|~m1_subset_1(X24,u1_struct_0(X22))\|~m1_subset_1(X23,k1_zfmisc_1(u1_struct_0(X22)))\|(v2_struct_0(X22)\|~l3_algstr_0(X22)))&((X21=k6_algstr_0(X22,X24,esk6_4(X21,X22,X23,X24))\|~r2_hidden(X21,k4_group_2(X22,X24,X23))\|~m1_subset_1(X24,u1_struct_0(X22))\|~m1_subset_1(X23,k1_zfmisc_1(u1_struct_0(X22)))\|(v2_struct_0(X22)\|~l3_algstr_0(X22)))&(r2_hidden(esk6_4(X21,X22,X23,X24),X23)\|~r2_hidden(X21,k4_group_2(X22,X24,X23))\|~m1_subset_1(X24,u1_struct_0(X22))\|~m1_subset_1(X23,k1_zfmisc_1(u1_struct_0(X22)))\|(v2_struct_0(X22)\|~l3_algstr_0(X22)))))&(~m1_subset_1(X26,u1_struct_0(X22))\|(X21!=k6_algstr_0(X22,X24,X26)\|~r2_hidden(X26,X23))\|r2_hidden(X21,k4_group_2(X22,X24,X23))\|~m1_subset_1(X24,u1_struct_0(X22))\|~m1_subset_1(X23,k1_zfmisc_1(u1_struct_0(X22)))\|(v2_struct_0(X22)\|~l3_algstr_0(X22)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t27_group_2])])])])])])). cnf(c_0_19, plain, (v2_struct_0(X2)\|r2_hidden(X4,a_3_0_group_2(X2,X5,X6))\|X4!=k6_algstr_0(X2,X1,X3)\|~l3_algstr_0(X2)\|~r2_hidden(X3,X6)\|~r2_hidden(X1,X5)\|~m1_subset_1(X3,u1_struct_0(X2))\|~m1_subset_1(X1,u1_struct_0(X2))\|~m1_subset_1(X6,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X5,k1_zfmisc_1(u1_struct_0(X2)))), inference(evalgc,[status(thm)],[c_0_16])). cnf(c_0_20, plain, (m1_subset_1(X1,X3)\|~r2_hidden(X1,X2)\|~m1_subset_1(X2,k1_zfmisc_1(X3))), inference(evalgc,[status(thm)],[c_0_17])). cnf(c_0_21, plain, (X1=k6_algstr_0(X2,X3,esk6_4(X1,X2,X4,X3))\|v2_struct_0(X2)\|~r2_hidden(X1,k4_group_2(X2,X3,X4))\|~m1_subset_1(X3,u1_struct_0(X2))\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))\|~l3_algstr_0(X2)), inference(split_conjunct,[status(thm)],[c_0_18])). cnf(c_0_22, plain, (r2_hidden(X1,a_3_0_group_2(X2,X3,X4))\|v2_struct_0(X2)\|X1!=k6_algstr_0(X2,X5,X6)\|~r2_hidden(X6,X4)\|~r2_hidden(X5,X3)\|~l3_algstr_0(X2)\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_19, c_0_20]), c_0_20])). cnf(c_0_23, plain, (k6_algstr_0(X2,X3,esk6_4(X1,X2,X4,X3))=X1\|v2_struct_0(X2)\|~l3_algstr_0(X2)\|~m1_subset_1(X3,u1_struct_0(X2))\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))\|~r2_hidden(X1,k4_group_2(X2,X3,X4))), inference(evalgc,[status(thm)],[c_0_21])). cnf(c_0_24, plain, (r2_hidden(X1,a_3_0_group_2(X2,X3,X4))\|v2_struct_0(X2)\|~r2_hidden(esk6_4(X1,X2,X5,X6),X4)\|~r2_hidden(X6,X3)\|~l3_algstr_0(X2)\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~r2_hidden(X1,k4_group_2(X2,X6,X5))\|~m1_subset_1(X5,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X6,u1_struct_0(X2))), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_22, c_0_23])])])). cnf(c_0_25, plain, (r2_hidden(esk6_4(X1,X2,X3,X4),X3)\|v2_struct_0(X2)\|~r2_hidden(X1,k4_group_2(X2,X4,X3))\|~m1_subset_1(X4,u1_struct_0(X2))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~l3_algstr_0(X2)), inference(split_conjunct,[status(thm)],[c_0_18])). cnf(c_0_26, plain, (r2_hidden(X1,a_3_0_group_2(X2,X3,X4))\|v2_struct_0(X2)\|~r2_hidden(esk6_4(X1,X2,X5,X6),X4)\|~r2_hidden(X1,k4_group_2(X2,X6,X5))\|~r2_hidden(X6,X3)\|~l3_algstr_0(X2)\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X5,k1_zfmisc_1(u1_struct_0(X2)))), inference(csr,[status(thm)],[c_0_24, c_0_20])). cnf(c_0_27, plain, (v2_struct_0(X2)\|r2_hidden(esk6_4(X1,X2,X3,X4),X3)\|~l3_algstr_0(X2)\|~m1_subset_1(X4,u1_struct_0(X2))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~r2_hidden(X1,k4_group_2(X2,X4,X3))), inference(evalgc,[status(thm)],[c_0_25])). fof(c_0_28, plain, ![X27, X28, X29, X30, X31]:((~r1_tarski(X27,X28)\|(~r2_hidden(X29,X27)\|r2_hidden(X29,X28)))&((r2_hidden(esk7_2(X30,X31),X30)\|r1_tarski(X30,X31))&(~r2_hidden(esk7_2(X30,X31),X31)\|r1_tarski(X30,X31)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_tarski])])])])])])). cnf(c_0_29, plain, (r2_hidden(X1,a_3_0_group_2(X2,X3,X4))\|v2_struct_0(X2)\|~r2_hidden(X1,k4_group_2(X2,X5,X4))\|~r2_hidden(X5,X3)\|~l3_algstr_0(X2)\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X5,u1_struct_0(X2))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_26, c_0_27])])). cnf(c_0_30, plain, (r2_hidden(esk7_2(X1,X2),X1)\|r1_tarski(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_28])). fof(c_0_31, plain, ![X33, X34, X35, X37]:(((m1_subset_1(esk8_3(X33,X34,X35),k1_zfmisc_1(u1_struct_0(X33)))\|~r2_hidden(X34,k1_tops_1(X33,X35))\|~m1_subset_1(X35,k1_zfmisc_1(u1_struct_0(X33)))\|(~v2_pre_topc(X33)\|~l1_pre_topc(X33)))&((v3_pre_topc(esk8_3(X33,X34,X35),X33)\|~r2_hidden(X34,k1_tops_1(X33,X35))\|~m1_subset_1(X35,k1_zfmisc_1(u1_struct_0(X33)))\|(~v2_pre_topc(X33)\|~l1_pre_topc(X33)))&((r1_tarski(esk8_3(X33,X34,X35),X35)\|~r2_hidden(X34,k1_tops_1(X33,X35))\|~m1_subset_1(X35,k1_zfmisc_1(u1_struct_0(X33)))\|(~v2_pre_topc(X33)\|~l1_pre_topc(X33)))&(r2_hidden(X34,esk8_3(X33,X34,X35))\|~r2_hidden(X34,k1_tops_1(X33,X35))\|~m1_subset_1(X35,k1_zfmisc_1(u1_struct_0(X33)))\|(~v2_pre_topc(X33)\|~l1_pre_topc(X33))))))&(~m1_subset_1(X37,k1_zfmisc_1(u1_struct_0(X33)))\|(~v3_pre_topc(X37,X33)\|(~r1_tarski(X37,X35)\|~r2_hidden(X34,X37)))\|r2_hidden(X34,k1_tops_1(X33,X35))\|~m1_subset_1(X35,k1_zfmisc_1(u1_struct_0(X33)))\|(~v2_pre_topc(X33)\|~l1_pre_topc(X33)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t22_tops_1])])])])])). cnf(c_0_32, plain, (r1_tarski(X1,X2)\|~r2_hidden(esk7_2(X1,X2),X2)), inference(split_conjunct,[status(thm)],[c_0_28])). cnf(c_0_33, plain, (r2_hidden(X1,a_3_0_group_2(X2,X3,X4))\|v2_struct_0(X2)\|~r2_hidden(X1,k4_group_2(X2,X5,X4))\|~r2_hidden(X5,X3)\|~l3_algstr_0(X2)\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))), inference(csr,[status(thm)],[c_0_29, c_0_20])). cnf(c_0_34, plain, (r1_tarski(X1,X2)\|r2_hidden(esk7_2(X1,X2),X1)), inference(evalgc,[status(thm)],[c_0_30])). cnf(c_0_35, plain, (r2_hidden(X4,k1_tops_1(X2,X3))\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X2)))\|~v3_pre_topc(X1,X2)\|~r1_tarski(X1,X3)\|~r2_hidden(X4,X1)\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~v2_pre_topc(X2)\|~l1_pre_topc(X2)), inference(split_conjunct,[status(thm)],[c_0_31])). cnf(c_0_36, plain, (r1_tarski(X1,X2)\|~r2_hidden(esk7_2(X1,X2),X2)), inference(evalgc,[status(thm)],[c_0_32])). cnf(c_0_37, plain, (r2_hidden(esk7_2(k4_group_2(X1,X2,X3),X4),a_3_0_group_2(X1,X5,X3))\|v2_struct_0(X1)\|r1_tarski(k4_group_2(X1,X2,X3),X4)\|~r2_hidden(X2,X5)\|~l3_algstr_0(X1)\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X5,k1_zfmisc_1(u1_struct_0(X1)))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_33, c_0_34])])). fof(c_0_38, plain, ![X38, X39, X40]:(v2_struct_0(X38)\|(~v2_pre_topc(X38)\|(~v2_group_1(X38)\|(~v3_group_1(X38)\|(~v4_topgrp_1(X38)\|~l1_topgrp_1(X38)))))\|(~v3_pre_topc(X39,X38)\|~m1_subset_1(X39,k1_zfmisc_1(u1_struct_0(X38)))\|~m1_subset_1(X40,u1_struct_0(X38)))\|v3_pre_topc(k4_group_2(X38,X40,X39),X38)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fc18_topgrp_1])])])). fof(c_0_39, plain, ![X41, X42, X43]:(v2_struct_0(X41)\|~l3_algstr_0(X41)\|(~m1_subset_1(X42,k1_zfmisc_1(u1_struct_0(X41)))\|~m1_subset_1(X43,k1_zfmisc_1(u1_struct_0(X41))))\|m1_subset_1(k2_group_2(X41,X42,X43),k1_zfmisc_1(u1_struct_0(X41)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k2_group_2])])])). fof(c_0_40, plain, ![X44, X45, X46]:(v2_struct_0(X44)\|~l3_algstr_0(X44)\|(~m1_subset_1(X45,k1_zfmisc_1(u1_struct_0(X44)))\|(~m1_subset_1(X46,k1_zfmisc_1(u1_struct_0(X44)))\|k2_group_2(X44,X45,X46)=a_3_0_group_2(X44,X45,X46)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d2_group_2])])])])). cnf(c_0_41, plain, (r2_hidden(X4,k1_tops_1(X2,X3))\|~v2_pre_topc(X2)\|~l1_pre_topc(X2)\|~v3_pre_topc(X1,X2)\|~r2_hidden(X4,X1)\|~r1_tarski(X1,X3)\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X2)))), inference(evalgc,[status(thm)],[c_0_35])). cnf(c_0_42, plain, (r1_tarski(k4_group_2(X1,X2,X3),a_3_0_group_2(X1,X4,X3))\|v2_struct_0(X1)\|~r2_hidden(X2,X4)\|~l3_algstr_0(X1)\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X1)))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_36, c_0_37])])). cnf(c_0_43, plain, (v2_struct_0(X1)\|v3_pre_topc(k4_group_2(X1,X3,X2),X1)\|~v2_pre_topc(X1)\|~v2_group_1(X1)\|~v3_group_1(X1)\|~v4_topgrp_1(X1)\|~l1_topgrp_1(X1)\|~v3_pre_topc(X2,X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X3,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_38])). cnf(c_0_44, plain, (v2_struct_0(X1)\|m1_subset_1(k2_group_2(X1,X2,X3),k1_zfmisc_1(u1_struct_0(X1)))\|~l3_algstr_0(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))), inference(split_conjunct,[status(thm)],[c_0_39])). cnf(c_0_45, plain, (v2_struct_0(X1)\|k2_group_2(X1,X2,X3)=a_3_0_group_2(X1,X2,X3)\|~l3_algstr_0(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))), inference(split_conjunct,[status(thm)],[c_0_40])). fof(c_0_46, plain, ![X47]:((l3_algstr_0(X47)\|~l1_topgrp_1(X47))&(l1_pre_topc(X47)\|~l1_topgrp_1(X47))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_topgrp_1])])])). cnf(c_0_47, plain, (r2_hidden(X1,k1_tops_1(X2,a_3_0_group_2(X3,X4,X5)))\|v2_struct_0(X3)\|~l1_pre_topc(X2)\|~r2_hidden(X1,k4_group_2(X3,X6,X5))\|~v3_pre_topc(k4_group_2(X3,X6,X5),X2)\|~m1_subset_1(a_3_0_group_2(X3,X4,X5),k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(k4_group_2(X3,X6,X5),k1_zfmisc_1(u1_struct_0(X2)))\|~v2_pre_topc(X2)\|~r2_hidden(X6,X4)\|~l3_algstr_0(X3)\|~m1_subset_1(X5,k1_zfmisc_1(u1_struct_0(X3)))\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X3)))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_41, c_0_42])])). cnf(c_0_48, plain, (v2_struct_0(X1)\|v3_pre_topc(k4_group_2(X1,X3,X2),X1)\|~v2_pre_topc(X1)\|~v2_group_1(X1)\|~v3_group_1(X1)\|~v4_topgrp_1(X1)\|~l1_topgrp_1(X1)\|~v3_pre_topc(X2,X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(evalgc,[status(thm)],[c_0_43])). cnf(c_0_49, plain, (v2_struct_0(X1)\|m1_subset_1(k2_group_2(X1,X2,X3),k1_zfmisc_1(u1_struct_0(X1)))\|~l3_algstr_0(X1)\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(evalgc,[status(thm)],[c_0_44])). cnf(c_0_50, plain, (k2_group_2(X1,X2,X3)=a_3_0_group_2(X1,X2,X3)\|v2_struct_0(X1)\|~l3_algstr_0(X1)\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(evalgc,[status(thm)],[c_0_45])). cnf(c_0_51, plain, (l3_algstr_0(X1)\|~l1_topgrp_1(X1)), inference(split_conjunct,[status(thm)],[c_0_46])). cnf(c_0_52, plain, (l1_pre_topc(X1)\|~l1_topgrp_1(X1)), inference(split_conjunct,[status(thm)],[c_0_46])). fof(c_0_53, plain, ![X48, X49, X50]:(v2_struct_0(X48)\|~l3_algstr_0(X48)\|(~m1_subset_1(X49,u1_struct_0(X48))\|~m1_subset_1(X50,k1_zfmisc_1(u1_struct_0(X48))))\|m1_subset_1(k4_group_2(X48,X49,X50),k1_zfmisc_1(u1_struct_0(X48)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k4_group_2])])])). cnf(c_0_54, plain, (r2_hidden(X3,k4_group_2(X2,X4,X5))\|v2_struct_0(X2)\|~m1_subset_1(X1,u1_struct_0(X2))\|X3!=k6_algstr_0(X2,X4,X1)\|~r2_hidden(X1,X5)\|~m1_subset_1(X4,u1_struct_0(X2))\|~m1_subset_1(X5,k1_zfmisc_1(u1_struct_0(X2)))\|~l3_algstr_0(X2)), inference(split_conjunct,[status(thm)],[c_0_18])). cnf(c_0_55, plain, (r2_hidden(X1,k1_tops_1(X2,a_3_0_group_2(X2,X3,X4)))\|v2_struct_0(X2)\|~l1_pre_topc(X2)\|~r2_hidden(X1,k4_group_2(X2,X5,X4))\|~r2_hidden(X5,X3)\|~l3_algstr_0(X2)\|~m1_subset_1(a_3_0_group_2(X2,X3,X4),k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(k4_group_2(X2,X5,X4),k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~v2_pre_topc(X2)\|~v3_pre_topc(X4,X2)\|~m1_subset_1(X5,u1_struct_0(X2))\|~l1_topgrp_1(X2)\|~v4_topgrp_1(X2)\|~v3_group_1(X2)\|~v2_group_1(X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_47, c_0_48])])). cnf(c_0_56, plain, (m1_subset_1(a_3_0_group_2(X1,X2,X3),k1_zfmisc_1(u1_struct_0(X1)))\|v2_struct_0(X1)\|~l3_algstr_0(X1)\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_49, c_0_50])])). cnf(c_0_57, plain, (l3_algstr_0(X1)\|~l1_topgrp_1(X1)), inference(evalgc,[status(thm)],[c_0_51])). cnf(c_0_58, plain, (l1_pre_topc(X1)\|~l1_topgrp_1(X1)), inference(evalgc,[status(thm)],[c_0_52])). cnf(c_0_59, plain, (v2_struct_0(X1)\|m1_subset_1(k4_group_2(X1,X2,X3),k1_zfmisc_1(u1_struct_0(X1)))\|~l3_algstr_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))), inference(split_conjunct,[status(thm)],[c_0_53])). cnf(c_0_60, plain, (v2_struct_0(X2)\|r2_hidden(X3,k4_group_2(X2,X4,X5))\|X3!=k6_algstr_0(X2,X4,X1)\|~l3_algstr_0(X2)\|~r2_hidden(X1,X5)\|~m1_subset_1(X4,u1_struct_0(X2))\|~m1_subset_1(X1,u1_struct_0(X2))\|~m1_subset_1(X5,k1_zfmisc_1(u1_struct_0(X2)))), inference(evalgc,[status(thm)],[c_0_54])). cnf(c_0_61, plain, (X1=k6_algstr_0(X2,esk4_4(X1,X2,X3,X4),esk5_4(X1,X2,X3,X4))\|v2_struct_0(X2)\|~r2_hidden(X1,a_3_0_group_2(X2,X3,X4))\|~l3_algstr_0(X2)\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))), inference(split_conjunct,[status(thm)],[c_0_14])). cnf(c_0_62, plain, (r2_hidden(X1,k1_tops_1(X2,a_3_0_group_2(X2,X3,X4)))\|v2_struct_0(X2)\|~r2_hidden(X1,k4_group_2(X2,X5,X4))\|~r2_hidden(X5,X3)\|~v3_pre_topc(X4,X2)\|~m1_subset_1(k4_group_2(X2,X5,X4),k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~l1_topgrp_1(X2)\|~v4_topgrp_1(X2)\|~v3_group_1(X2)\|~v2_group_1(X2)\|~v2_pre_topc(X2)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_55, c_0_20]), c_0_56]), c_0_57]), c_0_58])). cnf(c_0_63, plain, (v2_struct_0(X1)\|m1_subset_1(k4_group_2(X1,X2,X3),k1_zfmisc_1(u1_struct_0(X1)))\|~l3_algstr_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))), inference(evalgc,[status(thm)],[c_0_59])). cnf(c_0_64, plain, (r2_hidden(X1,k4_group_2(X2,X3,X4))\|v2_struct_0(X2)\|X1!=k6_algstr_0(X2,X3,X5)\|~r2_hidden(X5,X4)\|~l3_algstr_0(X2)\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X3,u1_struct_0(X2))), inference(csr,[status(thm)],[c_0_60, c_0_20])). cnf(c_0_65, plain, (k6_algstr_0(X2,esk4_4(X1,X2,X3,X4),esk5_4(X1,X2,X3,X4))=X1\|v2_struct_0(X2)\|~l3_algstr_0(X2)\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~r2_hidden(X1,a_3_0_group_2(X2,X3,X4))), inference(evalgc,[status(thm)],[c_0_61])). cnf(c_0_66, plain, (m1_subset_1(esk4_4(X1,X2,X3,X4),u1_struct_0(X2))\|v2_struct_0(X2)\|~r2_hidden(X1,a_3_0_group_2(X2,X3,X4))\|~l3_algstr_0(X2)\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))), inference(split_conjunct,[status(thm)],[c_0_14])). cnf(c_0_67, plain, (r2_hidden(X1,k1_tops_1(X2,a_3_0_group_2(X2,X3,X4)))\|v2_struct_0(X2)\|~r2_hidden(X1,k4_group_2(X2,X5,X4))\|~r2_hidden(X5,X3)\|~v3_pre_topc(X4,X2)\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~l1_topgrp_1(X2)\|~v4_topgrp_1(X2)\|~v3_group_1(X2)\|~v2_group_1(X2)\|~v2_pre_topc(X2)\|~l3_algstr_0(X2)\|~m1_subset_1(X5,u1_struct_0(X2))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_62, c_0_63])])). cnf(c_0_68, plain, (r2_hidden(X1,k4_group_2(X2,esk4_4(X1,X2,X3,X4),X5))\|v2_struct_0(X2)\|~r2_hidden(esk5_4(X1,X2,X3,X4),X5)\|~l3_algstr_0(X2)\|~m1_subset_1(X5,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(esk4_4(X1,X2,X3,X4),u1_struct_0(X2))\|~r2_hidden(X1,a_3_0_group_2(X2,X3,X4))\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_64, c_0_65])])])). cnf(c_0_69, plain, (v2_struct_0(X2)\|m1_subset_1(esk4_4(X1,X2,X3,X4),u1_struct_0(X2))\|~l3_algstr_0(X2)\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~r2_hidden(X1,a_3_0_group_2(X2,X3,X4))), inference(evalgc,[status(thm)],[c_0_66])). cnf(c_0_70, plain, (r2_hidden(X1,k1_tops_1(X2,a_3_0_group_2(X2,X3,X4)))\|v2_struct_0(X2)\|~r2_hidden(X1,k4_group_2(X2,X5,X4))\|~r2_hidden(X5,X3)\|~v3_pre_topc(X4,X2)\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~l1_topgrp_1(X2)\|~v4_topgrp_1(X2)\|~v3_group_1(X2)\|~v2_group_1(X2)\|~v2_pre_topc(X2)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_67, c_0_20]), c_0_57])). cnf(c_0_71, plain, (r2_hidden(X1,k4_group_2(X2,esk4_4(X1,X2,X3,X4),X5))\|v2_struct_0(X2)\|~r2_hidden(esk5_4(X1,X2,X3,X4),X5)\|~r2_hidden(X1,a_3_0_group_2(X2,X3,X4))\|~l3_algstr_0(X2)\|~m1_subset_1(X5,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))), inference(csr,[status(thm)],[c_0_68, c_0_69])). cnf(c_0_72, plain, (r2_hidden(X1,k1_tops_1(X2,a_3_0_group_2(X2,X3,X4)))\|v2_struct_0(X2)\|~r2_hidden(esk4_4(X1,X2,X5,X6),X3)\|~v3_pre_topc(X4,X2)\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~l1_topgrp_1(X2)\|~v4_topgrp_1(X2)\|~v3_group_1(X2)\|~v2_group_1(X2)\|~v2_pre_topc(X2)\|~r2_hidden(esk5_4(X1,X2,X5,X6),X4)\|~r2_hidden(X1,a_3_0_group_2(X2,X5,X6))\|~l3_algstr_0(X2)\|~m1_subset_1(X6,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X5,k1_zfmisc_1(u1_struct_0(X2)))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_70, c_0_71])])). cnf(c_0_73, plain, (r2_hidden(esk4_4(X1,X2,X3,X4),X3)\|v2_struct_0(X2)\|~r2_hidden(X1,a_3_0_group_2(X2,X3,X4))\|~l3_algstr_0(X2)\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))), inference(split_conjunct,[status(thm)],[c_0_14])). cnf(c_0_74, plain, (r2_hidden(X1,k1_tops_1(X2,a_3_0_group_2(X2,X3,X4)))\|v2_struct_0(X2)\|~r2_hidden(esk4_4(X1,X2,X5,X6),X3)\|~r2_hidden(esk5_4(X1,X2,X5,X6),X4)\|~r2_hidden(X1,a_3_0_group_2(X2,X5,X6))\|~v3_pre_topc(X4,X2)\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X6,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X5,k1_zfmisc_1(u1_struct_0(X2)))\|~l1_topgrp_1(X2)\|~v4_topgrp_1(X2)\|~v3_group_1(X2)\|~v2_group_1(X2)\|~v2_pre_topc(X2)), inference(csr,[status(thm)],[c_0_72, c_0_57])). cnf(c_0_75, plain, (v2_struct_0(X2)\|r2_hidden(esk4_4(X1,X2,X3,X4),X3)\|~l3_algstr_0(X2)\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~r2_hidden(X1,a_3_0_group_2(X2,X3,X4))), inference(evalgc,[status(thm)],[c_0_73])). cnf(c_0_76, plain, (r2_hidden(X1,k1_tops_1(X2,a_3_0_group_2(X2,X3,X4)))\|v2_struct_0(X2)\|~r2_hidden(esk5_4(X1,X2,X3,X5),X4)\|~r2_hidden(X1,a_3_0_group_2(X2,X3,X5))\|~v3_pre_topc(X4,X2)\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X5,k1_zfmisc_1(u1_struct_0(X2)))\|~l1_topgrp_1(X2)\|~v4_topgrp_1(X2)\|~v3_group_1(X2)\|~v2_group_1(X2)\|~v2_pre_topc(X2)\|~l3_algstr_0(X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_74, c_0_75])])). cnf(c_0_77, plain, (r2_hidden(esk5_4(X1,X2,X3,X4),X4)\|v2_struct_0(X2)\|~r2_hidden(X1,a_3_0_group_2(X2,X3,X4))\|~l3_algstr_0(X2)\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))), inference(split_conjunct,[status(thm)],[c_0_14])). cnf(c_0_78, plain, (r2_hidden(X1,k1_tops_1(X2,a_3_0_group_2(X2,X3,X4)))\|v2_struct_0(X2)\|~r2_hidden(esk5_4(X1,X2,X3,X5),X4)\|~r2_hidden(X1,a_3_0_group_2(X2,X3,X5))\|~v3_pre_topc(X4,X2)\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X5,k1_zfmisc_1(u1_struct_0(X2)))\|~l1_topgrp_1(X2)\|~v4_topgrp_1(X2)\|~v3_group_1(X2)\|~v2_group_1(X2)\|~v2_pre_topc(X2)), inference(csr,[status(thm)],[c_0_76, c_0_57])). cnf(c_0_79, plain, (v2_struct_0(X2)\|r2_hidden(esk5_4(X1,X2,X3,X4),X4)\|~l3_algstr_0(X2)\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~r2_hidden(X1,a_3_0_group_2(X2,X3,X4))), inference(evalgc,[status(thm)],[c_0_77])). fof(c_0_80, plain, ![X51, X52]:(((r1_tarski(X51,X52)\|X51!=X52)&(r1_tarski(X52,X51)\|X51!=X52))&(~r1_tarski(X51,X52)\|~r1_tarski(X52,X51)\|X51=X52)), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])])). fof(c_0_81, plain, ![X53, X54]:(~l1_pre_topc(X53)\|(~m1_subset_1(X54,k1_zfmisc_1(u1_struct_0(X53)))\|r1_tarski(k1_tops_1(X53,X54),X54))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t16_tops_1])])])). cnf(c_0_82, plain, (r2_hidden(X1,k1_tops_1(X2,a_3_0_group_2(X2,X3,X4)))\|v2_struct_0(X2)\|~r2_hidden(X1,a_3_0_group_2(X2,X3,X4))\|~v3_pre_topc(X4,X2)\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~l1_topgrp_1(X2)\|~v4_topgrp_1(X2)\|~v3_group_1(X2)\|~v2_group_1(X2)\|~v2_pre_topc(X2)\|~l3_algstr_0(X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_78, c_0_79])])). cnf(c_0_83, plain, (X1=X2\|~r1_tarski(X1,X2)\|~r1_tarski(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_80])). cnf(c_0_84, plain, (r1_tarski(k1_tops_1(X1,X2),X2)\|~l1_pre_topc(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(split_conjunct,[status(thm)],[c_0_81])). cnf(c_0_85, plain, (r2_hidden(X1,k1_tops_1(X2,a_3_0_group_2(X2,X3,X4)))\|v2_struct_0(X2)\|~r2_hidden(X1,a_3_0_group_2(X2,X3,X4))\|~v3_pre_topc(X4,X2)\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~l1_topgrp_1(X2)\|~v4_topgrp_1(X2)\|~v3_group_1(X2)\|~v2_group_1(X2)\|~v2_pre_topc(X2)), inference(csr,[status(thm)],[c_0_82, c_0_57])). fof(c_0_86, negated_conjecture, ~(![X1]:((~(v2_struct_0(X1))&(v2_pre_topc(X1)&(v2_group_1(X1)&(v3_group_1(X1)&(v4_topgrp_1(X1)&l1_topgrp_1(X1))))))=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))=>![X3]:(m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))=>(v3_pre_topc(X3,X1)=>v3_pre_topc(k2_group_2(X1,X2,X3),X1)))))), inference(assume_negation,[status(cth)],[t53_topgrp_1])). cnf(c_0_87, plain, (X1=X2\|~r1_tarski(X2,X1)\|~r1_tarski(X1,X2)), inference(evalgc,[status(thm)],[c_0_83])). cnf(c_0_88, plain, (r1_tarski(k1_tops_1(X1,X2),X2)\|~l1_pre_topc(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(evalgc,[status(thm)],[c_0_84])). cnf(c_0_89, plain, (r1_tarski(X1,k1_tops_1(X2,a_3_0_group_2(X2,X3,X4)))\|v2_struct_0(X2)\|~r2_hidden(esk7_2(X1,k1_tops_1(X2,a_3_0_group_2(X2,X3,X4))),a_3_0_group_2(X2,X3,X4))\|~v3_pre_topc(X4,X2)\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~l1_topgrp_1(X2)\|~v4_topgrp_1(X2)\|~v3_group_1(X2)\|~v2_group_1(X2)\|~v2_pre_topc(X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_36, c_0_85])])). fof(c_0_90, negated_conjecture, ((~v2_struct_0(esk1_0)&(v2_pre_topc(esk1_0)&(v2_group_1(esk1_0)&(v3_group_1(esk1_0)&(v4_topgrp_1(esk1_0)&l1_topgrp_1(esk1_0))))))&(m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(esk1_0)))&(m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(esk1_0)))&(v3_pre_topc(esk3_0,esk1_0)&~v3_pre_topc(k2_group_2(esk1_0,esk2_0,esk3_0),esk1_0))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_86])])])])). fof(c_0_91, plain, ![X55, X56]:(~v2_pre_topc(X55)\|~l1_pre_topc(X55)\|~m1_subset_1(X56,k1_zfmisc_1(u1_struct_0(X55)))\|v3_pre_topc(k1_tops_1(X55,X56),X55)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc9_tops_1])])). cnf(c_0_92, plain, (k1_tops_1(X2,X1)=X1\|~r1_tarski(X1,k1_tops_1(X2,X1))\|~l1_pre_topc(X2)\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X2)))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_87, c_0_88])])). cnf(c_0_93, plain, (r1_tarski(a_3_0_group_2(X1,X2,X3),k1_tops_1(X1,a_3_0_group_2(X1,X2,X3)))\|v2_struct_0(X1)\|~v3_pre_topc(X3,X1)\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~l1_topgrp_1(X1)\|~v4_topgrp_1(X1)\|~v3_group_1(X1)\|~v2_group_1(X1)\|~v2_pre_topc(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_89, c_0_34])])). cnf(c_0_94, negated_conjecture, (~v3_pre_topc(k2_group_2(esk1_0,esk2_0,esk3_0),esk1_0)), inference(split_conjunct,[status(thm)],[c_0_90])). cnf(c_0_95, negated_conjecture, (m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(esk1_0)))), inference(split_conjunct,[status(thm)],[c_0_90])). cnf(c_0_96, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(esk1_0)))), inference(split_conjunct,[status(thm)],[c_0_90])). cnf(c_0_97, negated_conjecture, (~v2_struct_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_90])). cnf(c_0_98, negated_conjecture, (l1_topgrp_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_90])). cnf(c_0_99, plain, (v3_pre_topc(k1_tops_1(X1,X2),X1)\|~v2_pre_topc(X1)\|~l1_pre_topc(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(split_conjunct,[status(thm)],[c_0_91])). cnf(c_0_100, plain, (k1_tops_1(X1,a_3_0_group_2(X1,X2,X3))=a_3_0_group_2(X1,X2,X3)\|v2_struct_0(X1)\|~l1_pre_topc(X1)\|~m1_subset_1(a_3_0_group_2(X1,X2,X3),k1_zfmisc_1(u1_struct_0(X1)))\|~v3_pre_topc(X3,X1)\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~l1_topgrp_1(X1)\|~v4_topgrp_1(X1)\|~v3_group_1(X1)\|~v2_group_1(X1)\|~v2_pre_topc(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_92, c_0_93])])). cnf(c_0_101, negated_conjecture, (~v3_pre_topc(k2_group_2(esk1_0,esk2_0,esk3_0),esk1_0)), inference(evalgc,[status(thm)],[c_0_94])). cnf(c_0_102, negated_conjecture, (m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(esk1_0)))), inference(evalgc,[status(thm)],[c_0_95])). cnf(c_0_103, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(esk1_0)))), inference(evalgc,[status(thm)],[c_0_96])). cnf(c_0_104, negated_conjecture, (~v2_struct_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_97])). cnf(c_0_105, negated_conjecture, (l1_topgrp_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_98])). cnf(c_0_106, plain, (v3_pre_topc(k1_tops_1(X1,X2),X1)\|~v2_pre_topc(X1)\|~l1_pre_topc(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(evalgc,[status(thm)],[c_0_99])). cnf(c_0_107, plain, (k1_tops_1(X1,a_3_0_group_2(X1,X2,X3))=a_3_0_group_2(X1,X2,X3)\|v2_struct_0(X1)\|~v3_pre_topc(X3,X1)\|~m1_subset_1(a_3_0_group_2(X1,X2,X3),k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~l1_topgrp_1(X1)\|~v4_topgrp_1(X1)\|~v3_group_1(X1)\|~v2_group_1(X1)\|~v2_pre_topc(X1)), inference(csr,[status(thm)],[c_0_100, c_0_58])). cnf(c_0_108, negated_conjecture, (~v3_pre_topc(a_3_0_group_2(esk1_0,esk2_0,esk3_0),esk1_0)\|~l3_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101, c_0_50]), c_0_102]), c_0_103])]), c_0_104])])). cnf(c_0_109, negated_conjecture, (l3_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_57, c_0_105])])). cnf(c_0_110, plain, (v3_pre_topc(a_3_0_group_2(X1,X2,X3),X1)\|v2_struct_0(X1)\|~l1_pre_topc(X1)\|~m1_subset_1(a_3_0_group_2(X1,X2,X3),k1_zfmisc_1(u1_struct_0(X1)))\|~v2_pre_topc(X1)\|~v3_pre_topc(X3,X1)\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~l1_topgrp_1(X1)\|~v4_topgrp_1(X1)\|~v3_group_1(X1)\|~v2_group_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_106, c_0_107])])). cnf(c_0_111, negated_conjecture, (v3_pre_topc(esk3_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_90])). cnf(c_0_112, negated_conjecture, (v4_topgrp_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_90])). cnf(c_0_113, negated_conjecture, (v3_group_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_90])). cnf(c_0_114, negated_conjecture, (v2_group_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_90])). cnf(c_0_115, negated_conjecture, (v2_pre_topc(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_90])). cnf(c_0_116, negated_conjecture, (~v3_pre_topc(a_3_0_group_2(esk1_0,esk2_0,esk3_0),esk1_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_108, c_0_109])])). cnf(c_0_117, plain, (v3_pre_topc(a_3_0_group_2(X1,X2,X3),X1)\|v2_struct_0(X1)\|~v3_pre_topc(X3,X1)\|~m1_subset_1(a_3_0_group_2(X1,X2,X3),k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~l1_topgrp_1(X1)\|~v4_topgrp_1(X1)\|~v3_group_1(X1)\|~v2_group_1(X1)\|~v2_pre_topc(X1)), inference(csr,[status(thm)],[c_0_110, c_0_58])). cnf(c_0_118, negated_conjecture, (v3_pre_topc(esk3_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_111])). cnf(c_0_119, negated_conjecture, (v4_topgrp_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_112])). cnf(c_0_120, negated_conjecture, (v3_group_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_113])). cnf(c_0_121, negated_conjecture, (v2_group_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_114])). cnf(c_0_122, negated_conjecture, (v2_pre_topc(esk1_0)), inference(evalgc,[status(thm)],[c_0_115])). cnf(c_0_123, negated_conjecture, (~m1_subset_1(a_3_0_group_2(esk1_0,esk2_0,esk3_0),k1_zfmisc_1(u1_struct_0(esk1_0)))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116, c_0_117]), c_0_118]), c_0_102]), c_0_103]), c_0_105]), c_0_119]), c_0_120]), c_0_121]), c_0_122])]), c_0_104])])). cnf(c_0_124, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123, c_0_56]), c_0_109]), c_0_102]), c_0_103])]), c_0_104]), ['proof']). # SZS output end CNFRefutation	reserve S, R for 1-sorted, X for Subset of R, T for TopStruct, x for set; reserve H for non empty multMagma, P, Q, P1, Q1 for Subset of H, h for Element of H; reserve G for Group, A, B for Subset of G, a for Element of G; theorem Th53: for G being BinContinuous TopGroup, A, O being Subset of G st O is open holds A * O is open proof let G be BinContinuous TopGroup, A, O be Subset of G such that A1: O is open; Int (A * O) = A * O proof thus Int (A * O) c= A * O by TOPS_1:16; let x be set; assume x in A * O; then consider a, o being Element of G such that A2: x = a * o and A3: a in A and A4: o in O; set Q = a * O; A5: Q c= A * O proof let q be set; assume q in Q; then ex h being Element of G st q = a * h & h in O by GROUP_2:27; hence thesis by A3; end; x in Q by A2,A4,GROUP_2:27; hence thesis by A1,A5,TOPS_1:22; end; hence thesis; end;	Convert the following ATP output trace into a readable Mizar proof.
t28_funct_2	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t28_funct_2, conjecture, ![X1, X2, X3]:((v1_funct_1(X3)&(v1_funct_2(X3,X1,X2)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))))=>![X4]:((v1_funct_1(X4)&(v1_funct_2(X4,X2,X1)&m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X2,X1)))))=>((k2_relset_1(X2,X3)=X2&(v2_funct_1(X3)&![X5, X6]:(((r2_hidden(X5,X2)&k1_funct_1(X4,X5)=X6)=>(r2_hidden(X6,X1)&k1_funct_1(X3,X6)=X5))&((r2_hidden(X6,X1)&k1_funct_1(X3,X6)=X5)=>(r2_hidden(X5,X2)&k1_funct_1(X4,X5)=X6)))))=>(X1=k1_xboole_0\|(X2=k1_xboole_0\|X4=k2_funct_1(X3)))))), file('/scratch/mptp/predsminms1/t28_funct_2__0', t28_funct_2)). fof(cc2_relset_1, axiom, ![X1, X2, X3]:(m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))=>(v4_relat_1(X3,X1)&v5_relat_1(X3,X2))), file('/scratch/mptp/predsminms1/t28_funct_2__0', cc2_relset_1)). fof(cc2_relat_1, axiom, ![X1]:(v1_relat_1(X1)=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(X1))=>v1_relat_1(X2))), file('/scratch/mptp/predsminms1/t28_funct_2__0', cc2_relat_1)). fof(fc6_relat_1, axiom, ![X1, X2]:v1_relat_1(k2_zfmisc_1(X1,X2)), file('/scratch/mptp/predsminms1/t28_funct_2__0', fc6_relat_1)). fof(redefinition_k1_relset_1, axiom, ![X1, X2]:((v1_relat_1(X2)&v4_relat_1(X2,X1))=>k1_relset_1(X1,X2)=k9_xtuple_0(X2)), file('/scratch/mptp/predsminms1/t28_funct_2__0', redefinition_k1_relset_1)). fof(d1_funct_2, axiom, ![X1, X2, X3]:(m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))=>((~(X2=k1_xboole_0)=>(v1_funct_2(X3,X1,X2)<=>X1=k1_relset_1(X1,X3)))&(X2=k1_xboole_0=>(v1_funct_2(X3,X1,X2)<=>X3=k1_xboole_0)))), file('/scratch/mptp/predsminms1/t28_funct_2__0', d1_funct_2)). fof(t32_funct_1, axiom, ![X1]:((v1_relat_1(X1)&v1_funct_1(X1))=>(v2_funct_1(X1)=>![X2]:((v1_relat_1(X2)&v1_funct_1(X2))=>(X2=k2_funct_1(X1)<=>(k9_xtuple_0(X2)=k10_xtuple_0(X1)&![X3, X4]:(((r2_hidden(X3,k10_xtuple_0(X1))&X4=k1_funct_1(X2,X3))=>(r2_hidden(X4,k9_xtuple_0(X1))&X3=k1_funct_1(X1,X4)))&((r2_hidden(X4,k9_xtuple_0(X1))&X3=k1_funct_1(X1,X4))=>(r2_hidden(X3,k10_xtuple_0(X1))&X4=k1_funct_1(X2,X3))))))))), file('/scratch/mptp/predsminms1/t28_funct_2__0', t32_funct_1)). fof(redefinition_k2_relset_1, axiom, ![X1, X2]:((v1_relat_1(X2)&v5_relat_1(X2,X1))=>k2_relset_1(X1,X2)=k10_xtuple_0(X2)), file('/scratch/mptp/predsminms1/t28_funct_2__0', redefinition_k2_relset_1)). fof(c_0_8, negated_conjecture, ~(![X1, X2, X3]:((v1_funct_1(X3)&(v1_funct_2(X3,X1,X2)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))))=>![X4]:((v1_funct_1(X4)&(v1_funct_2(X4,X2,X1)&m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X2,X1)))))=>((k2_relset_1(X2,X3)=X2&(v2_funct_1(X3)&![X5, X6]:(((r2_hidden(X5,X2)&k1_funct_1(X4,X5)=X6)=>(r2_hidden(X6,X1)&k1_funct_1(X3,X6)=X5))&((r2_hidden(X6,X1)&k1_funct_1(X3,X6)=X5)=>(r2_hidden(X5,X2)&k1_funct_1(X4,X5)=X6)))))=>(X1=k1_xboole_0\|(X2=k1_xboole_0\|X4=k2_funct_1(X3))))))), inference(assume_negation,[status(cth)],[t28_funct_2])). fof(c_0_9, plain, ![X22, X23, X24]:((v4_relat_1(X24,X22)\|~m1_subset_1(X24,k1_zfmisc_1(k2_zfmisc_1(X22,X23))))&(v5_relat_1(X24,X23)\|~m1_subset_1(X24,k1_zfmisc_1(k2_zfmisc_1(X22,X23))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_relset_1])])])). fof(c_0_10, negated_conjecture, ![X11, X12]:((v1_funct_1(esk3_0)&(v1_funct_2(esk3_0,esk1_0,esk2_0)&m1_subset_1(esk3_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,esk2_0)))))&((v1_funct_1(esk4_0)&(v1_funct_2(esk4_0,esk2_0,esk1_0)&m1_subset_1(esk4_0,k1_zfmisc_1(k2_zfmisc_1(esk2_0,esk1_0)))))&((k2_relset_1(esk2_0,esk3_0)=esk2_0&(v2_funct_1(esk3_0)&(((r2_hidden(X12,esk1_0)\|(~r2_hidden(X11,esk2_0)\|k1_funct_1(esk4_0,X11)!=X12))&(k1_funct_1(esk3_0,X12)=X11\|(~r2_hidden(X11,esk2_0)\|k1_funct_1(esk4_0,X11)!=X12)))&((r2_hidden(X11,esk2_0)\|(~r2_hidden(X12,esk1_0)\|k1_funct_1(esk3_0,X12)!=X11))&(k1_funct_1(esk4_0,X11)=X12\|(~r2_hidden(X12,esk1_0)\|k1_funct_1(esk3_0,X12)!=X11))))))&(esk1_0!=k1_xboole_0&(esk2_0!=k1_xboole_0&esk4_0!=k2_funct_1(esk3_0)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])])])). fof(c_0_11, plain, ![X15, X16]:(~v1_relat_1(X15)\|(~m1_subset_1(X16,k1_zfmisc_1(X15))\|v1_relat_1(X16))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_relat_1])])])). fof(c_0_12, plain, ![X17, X18]:v1_relat_1(k2_zfmisc_1(X17,X18)), inference(variable_rename,[status(thm)],[fc6_relat_1])). fof(c_0_13, plain, ![X35, X36]:(~v1_relat_1(X36)\|~v4_relat_1(X36,X35)\|k1_relset_1(X35,X36)=k9_xtuple_0(X36)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k1_relset_1])])). cnf(c_0_14, plain, (v4_relat_1(X1,X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_15, negated_conjecture, (m1_subset_1(esk4_0,k1_zfmisc_1(k2_zfmisc_1(esk2_0,esk1_0)))), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_16, plain, (v1_relat_1(X2)\|~v1_relat_1(X1)\|~m1_subset_1(X2,k1_zfmisc_1(X1))), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_17, plain, (v1_relat_1(k2_zfmisc_1(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_12])). fof(c_0_18, plain, ![X19, X20, X21]:(((~v1_funct_2(X21,X19,X20)\|X19=k1_relset_1(X19,X21)\|X20=k1_xboole_0\|~m1_subset_1(X21,k1_zfmisc_1(k2_zfmisc_1(X19,X20))))&(X19!=k1_relset_1(X19,X21)\|v1_funct_2(X21,X19,X20)\|X20=k1_xboole_0\|~m1_subset_1(X21,k1_zfmisc_1(k2_zfmisc_1(X19,X20)))))&((~v1_funct_2(X21,X19,X20)\|X21=k1_xboole_0\|X20!=k1_xboole_0\|~m1_subset_1(X21,k1_zfmisc_1(k2_zfmisc_1(X19,X20))))&(X21!=k1_xboole_0\|v1_funct_2(X21,X19,X20)\|X20!=k1_xboole_0\|~m1_subset_1(X21,k1_zfmisc_1(k2_zfmisc_1(X19,X20)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d1_funct_2])])])])). fof(c_0_19, plain, ![X25, X26, X27, X28, X29, X30]:(((k9_xtuple_0(X26)=k10_xtuple_0(X25)\|X26!=k2_funct_1(X25)\|(~v1_relat_1(X26)\|~v1_funct_1(X26))\|~v2_funct_1(X25)\|(~v1_relat_1(X25)\|~v1_funct_1(X25)))&(((r2_hidden(X28,k9_xtuple_0(X25))\|(~r2_hidden(X27,k10_xtuple_0(X25))\|X28!=k1_funct_1(X26,X27))\|X26!=k2_funct_1(X25)\|(~v1_relat_1(X26)\|~v1_funct_1(X26))\|~v2_funct_1(X25)\|(~v1_relat_1(X25)\|~v1_funct_1(X25)))&(X27=k1_funct_1(X25,X28)\|(~r2_hidden(X27,k10_xtuple_0(X25))\|X28!=k1_funct_1(X26,X27))\|X26!=k2_funct_1(X25)\|(~v1_relat_1(X26)\|~v1_funct_1(X26))\|~v2_funct_1(X25)\|(~v1_relat_1(X25)\|~v1_funct_1(X25))))&((r2_hidden(X29,k10_xtuple_0(X25))\|(~r2_hidden(X30,k9_xtuple_0(X25))\|X29!=k1_funct_1(X25,X30))\|X26!=k2_funct_1(X25)\|(~v1_relat_1(X26)\|~v1_funct_1(X26))\|~v2_funct_1(X25)\|(~v1_relat_1(X25)\|~v1_funct_1(X25)))&(X30=k1_funct_1(X26,X29)\|(~r2_hidden(X30,k9_xtuple_0(X25))\|X29!=k1_funct_1(X25,X30))\|X26!=k2_funct_1(X25)\|(~v1_relat_1(X26)\|~v1_funct_1(X26))\|~v2_funct_1(X25)\|(~v1_relat_1(X25)\|~v1_funct_1(X25))))))&(((((r2_hidden(esk8_2(X25,X26),k9_xtuple_0(X25))\|r2_hidden(esk5_2(X25,X26),k10_xtuple_0(X25))\|k9_xtuple_0(X26)!=k10_xtuple_0(X25)\|X26=k2_funct_1(X25)\|(~v1_relat_1(X26)\|~v1_funct_1(X26))\|~v2_funct_1(X25)\|(~v1_relat_1(X25)\|~v1_funct_1(X25)))&(esk7_2(X25,X26)=k1_funct_1(X25,esk8_2(X25,X26))\|r2_hidden(esk5_2(X25,X26),k10_xtuple_0(X25))\|k9_xtuple_0(X26)!=k10_xtuple_0(X25)\|X26=k2_funct_1(X25)\|(~v1_relat_1(X26)\|~v1_funct_1(X26))\|~v2_funct_1(X25)\|(~v1_relat_1(X25)\|~v1_funct_1(X25))))&(~r2_hidden(esk7_2(X25,X26),k10_xtuple_0(X25))\|esk8_2(X25,X26)!=k1_funct_1(X26,esk7_2(X25,X26))\|r2_hidden(esk5_2(X25,X26),k10_xtuple_0(X25))\|k9_xtuple_0(X26)!=k10_xtuple_0(X25)\|X26=k2_funct_1(X25)\|(~v1_relat_1(X26)\|~v1_funct_1(X26))\|~v2_funct_1(X25)\|(~v1_relat_1(X25)\|~v1_funct_1(X25))))&(((r2_hidden(esk8_2(X25,X26),k9_xtuple_0(X25))\|esk6_2(X25,X26)=k1_funct_1(X26,esk5_2(X25,X26))\|k9_xtuple_0(X26)!=k10_xtuple_0(X25)\|X26=k2_funct_1(X25)\|(~v1_relat_1(X26)\|~v1_funct_1(X26))\|~v2_funct_1(X25)\|(~v1_relat_1(X25)\|~v1_funct_1(X25)))&(esk7_2(X25,X26)=k1_funct_1(X25,esk8_2(X25,X26))\|esk6_2(X25,X26)=k1_funct_1(X26,esk5_2(X25,X26))\|k9_xtuple_0(X26)!=k10_xtuple_0(X25)\|X26=k2_funct_1(X25)\|(~v1_relat_1(X26)\|~v1_funct_1(X26))\|~v2_funct_1(X25)\|(~v1_relat_1(X25)\|~v1_funct_1(X25))))&(~r2_hidden(esk7_2(X25,X26),k10_xtuple_0(X25))\|esk8_2(X25,X26)!=k1_funct_1(X26,esk7_2(X25,X26))\|esk6_2(X25,X26)=k1_funct_1(X26,esk5_2(X25,X26))\|k9_xtuple_0(X26)!=k10_xtuple_0(X25)\|X26=k2_funct_1(X25)\|(~v1_relat_1(X26)\|~v1_funct_1(X26))\|~v2_funct_1(X25)\|(~v1_relat_1(X25)\|~v1_funct_1(X25)))))&(((r2_hidden(esk8_2(X25,X26),k9_xtuple_0(X25))\|(~r2_hidden(esk6_2(X25,X26),k9_xtuple_0(X25))\|esk5_2(X25,X26)!=k1_funct_1(X25,esk6_2(X25,X26)))\|k9_xtuple_0(X26)!=k10_xtuple_0(X25)\|X26=k2_funct_1(X25)\|(~v1_relat_1(X26)\|~v1_funct_1(X26))\|~v2_funct_1(X25)\|(~v1_relat_1(X25)\|~v1_funct_1(X25)))&(esk7_2(X25,X26)=k1_funct_1(X25,esk8_2(X25,X26))\|(~r2_hidden(esk6_2(X25,X26),k9_xtuple_0(X25))\|esk5_2(X25,X26)!=k1_funct_1(X25,esk6_2(X25,X26)))\|k9_xtuple_0(X26)!=k10_xtuple_0(X25)\|X26=k2_funct_1(X25)\|(~v1_relat_1(X26)\|~v1_funct_1(X26))\|~v2_funct_1(X25)\|(~v1_relat_1(X25)\|~v1_funct_1(X25))))&(~r2_hidden(esk7_2(X25,X26),k10_xtuple_0(X25))\|esk8_2(X25,X26)!=k1_funct_1(X26,esk7_2(X25,X26))\|(~r2_hidden(esk6_2(X25,X26),k9_xtuple_0(X25))\|esk5_2(X25,X26)!=k1_funct_1(X25,esk6_2(X25,X26)))\|k9_xtuple_0(X26)!=k10_xtuple_0(X25)\|X26=k2_funct_1(X25)\|(~v1_relat_1(X26)\|~v1_funct_1(X26))\|~v2_funct_1(X25)\|(~v1_relat_1(X25)\|~v1_funct_1(X25)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[t32_funct_1])])])])])])). cnf(c_0_20, plain, (k1_relset_1(X2,X1)=k9_xtuple_0(X1)\|~v1_relat_1(X1)\|~v4_relat_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_13])). cnf(c_0_21, plain, (v4_relat_1(X1,X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(evalgc,[status(thm)],[c_0_14])). cnf(c_0_22, negated_conjecture, (m1_subset_1(esk4_0,k1_zfmisc_1(k2_zfmisc_1(esk2_0,esk1_0)))), inference(evalgc,[status(thm)],[c_0_15])). cnf(c_0_23, plain, (v1_relat_1(X2)\|~v1_relat_1(X1)\|~m1_subset_1(X2,k1_zfmisc_1(X1))), inference(evalgc,[status(thm)],[c_0_16])). cnf(c_0_24, plain, (v1_relat_1(k2_zfmisc_1(X1,X2))), inference(evalgc,[status(thm)],[c_0_17])). cnf(c_0_25, plain, (X2=k1_relset_1(X2,X1)\|X3=k1_xboole_0\|~v1_funct_2(X1,X2,X3)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_18])). cnf(c_0_26, negated_conjecture, (v1_funct_2(esk4_0,esk2_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_27, negated_conjecture, (esk1_0!=k1_xboole_0), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_28, plain, (esk7_2(X1,X2)=k1_funct_1(X1,esk8_2(X1,X2))\|esk6_2(X1,X2)=k1_funct_1(X2,esk5_2(X1,X2))\|X2=k2_funct_1(X1)\|k9_xtuple_0(X2)!=k10_xtuple_0(X1)\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v2_funct_1(X1)\|~v1_relat_1(X1)\|~v1_funct_1(X1)), inference(split_conjunct,[status(thm)],[c_0_19])). cnf(c_0_29, negated_conjecture, (v1_funct_1(esk4_0)), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_30, plain, (k1_relset_1(X2,X1)=k9_xtuple_0(X1)\|~v1_relat_1(X1)\|~v4_relat_1(X1,X2)), inference(evalgc,[status(thm)],[c_0_20])). cnf(c_0_31, negated_conjecture, (v4_relat_1(esk4_0,esk2_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_21, c_0_22])])). cnf(c_0_32, negated_conjecture, (v1_relat_1(esk4_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23, c_0_22]), c_0_24])])])). cnf(c_0_33, plain, (X3=k1_xboole_0\|k1_relset_1(X2,X1)=X2\|~v1_funct_2(X1,X2,X3)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(evalgc,[status(thm)],[c_0_25])). cnf(c_0_34, negated_conjecture, (v1_funct_2(esk4_0,esk2_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_26])). cnf(c_0_35, negated_conjecture, (k1_xboole_0!=esk1_0), inference(evalgc,[status(thm)],[c_0_27])). fof(c_0_36, plain, ![X13, X14]:(~v1_relat_1(X14)\|~v5_relat_1(X14,X13)\|k2_relset_1(X13,X14)=k10_xtuple_0(X14)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k2_relset_1])])). cnf(c_0_37, plain, (v5_relat_1(X1,X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X3,X2)))), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_38, negated_conjecture, (m1_subset_1(esk3_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,esk2_0)))), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_39, plain, (X2=k2_funct_1(X1)\|k1_funct_1(X2,esk5_2(X1,X2))=esk6_2(X1,X2)\|k1_funct_1(X1,esk8_2(X1,X2))=esk7_2(X1,X2)\|k9_xtuple_0(X2)!=k10_xtuple_0(X1)\|~v1_funct_1(X2)\|~v1_funct_1(X1)\|~v2_funct_1(X1)\|~v1_relat_1(X2)\|~v1_relat_1(X1)), inference(evalgc,[status(thm)],[c_0_28])). cnf(c_0_40, negated_conjecture, (v1_funct_1(esk4_0)), inference(evalgc,[status(thm)],[c_0_29])). cnf(c_0_41, negated_conjecture, (k1_relset_1(esk2_0,esk4_0)=k9_xtuple_0(esk4_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30, c_0_31]), c_0_32])])])). cnf(c_0_42, negated_conjecture, (k1_relset_1(esk2_0,esk4_0)=esk2_0), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33, c_0_22]), c_0_34])]), c_0_35])])). cnf(c_0_43, plain, (k2_relset_1(X2,X1)=k10_xtuple_0(X1)\|~v1_relat_1(X1)\|~v5_relat_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_36])). cnf(c_0_44, plain, (v5_relat_1(X1,X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X3,X2)))), inference(evalgc,[status(thm)],[c_0_37])). cnf(c_0_45, negated_conjecture, (m1_subset_1(esk3_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,esk2_0)))), inference(evalgc,[status(thm)],[c_0_38])). cnf(c_0_46, negated_conjecture, (k2_relset_1(esk2_0,esk3_0)=esk2_0), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_47, negated_conjecture, (v1_funct_2(esk3_0,esk1_0,esk2_0)), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_48, negated_conjecture, (esk2_0!=k1_xboole_0), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_49, negated_conjecture, (r2_hidden(X1,esk1_0)\|~r2_hidden(X2,esk2_0)\|k1_funct_1(esk4_0,X2)!=X1), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_50, negated_conjecture, (k1_funct_1(X1,esk8_2(X1,esk4_0))=esk7_2(X1,esk4_0)\|k1_funct_1(esk4_0,esk5_2(X1,esk4_0))=esk6_2(X1,esk4_0)\|k2_funct_1(X1)=esk4_0\|k9_xtuple_0(esk4_0)!=k10_xtuple_0(X1)\|~v1_relat_1(X1)\|~v2_funct_1(X1)\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39, c_0_32]), c_0_40])])])). cnf(c_0_51, negated_conjecture, (k9_xtuple_0(esk4_0)=esk2_0), inference(rw,[status(thm)],[c_0_41, c_0_42])). cnf(c_0_52, plain, (k2_relset_1(X2,X1)=k10_xtuple_0(X1)\|~v1_relat_1(X1)\|~v5_relat_1(X1,X2)), inference(evalgc,[status(thm)],[c_0_43])). cnf(c_0_53, negated_conjecture, (v5_relat_1(esk3_0,esk2_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_44, c_0_45])])). cnf(c_0_54, negated_conjecture, (k2_relset_1(esk2_0,esk3_0)=esk2_0), inference(evalgc,[status(thm)],[c_0_46])). cnf(c_0_55, negated_conjecture, (v1_relat_1(esk3_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23, c_0_45]), c_0_24])])])). cnf(c_0_56, negated_conjecture, (v2_funct_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_57, negated_conjecture, (v1_funct_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_58, negated_conjecture, (esk4_0!=k2_funct_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_59, negated_conjecture, (v1_funct_2(esk3_0,esk1_0,esk2_0)), inference(evalgc,[status(thm)],[c_0_47])). cnf(c_0_60, negated_conjecture, (k1_xboole_0!=esk2_0), inference(evalgc,[status(thm)],[c_0_48])). cnf(c_0_61, negated_conjecture, (r2_hidden(X1,esk1_0)\|k1_funct_1(esk4_0,X2)!=X1\|~r2_hidden(X2,esk2_0)), inference(evalgc,[status(thm)],[c_0_49])). cnf(c_0_62, negated_conjecture, (k1_funct_1(esk4_0,esk5_2(X1,esk4_0))=esk6_2(X1,esk4_0)\|k1_funct_1(X1,esk8_2(X1,esk4_0))=esk7_2(X1,esk4_0)\|k2_funct_1(X1)=esk4_0\|k10_xtuple_0(X1)!=esk2_0\|~v1_relat_1(X1)\|~v2_funct_1(X1)\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[c_0_50, c_0_51])])). cnf(c_0_63, negated_conjecture, (k10_xtuple_0(esk3_0)=esk2_0), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52, c_0_53]), c_0_54]), c_0_55])])])). cnf(c_0_64, negated_conjecture, (v2_funct_1(esk3_0)), inference(evalgc,[status(thm)],[c_0_56])). cnf(c_0_65, negated_conjecture, (v1_funct_1(esk3_0)), inference(evalgc,[status(thm)],[c_0_57])). cnf(c_0_66, negated_conjecture, (k2_funct_1(esk3_0)!=esk4_0), inference(evalgc,[status(thm)],[c_0_58])). cnf(c_0_67, plain, (esk7_2(X1,X2)=k1_funct_1(X1,esk8_2(X1,X2))\|r2_hidden(esk5_2(X1,X2),k10_xtuple_0(X1))\|X2=k2_funct_1(X1)\|k9_xtuple_0(X2)!=k10_xtuple_0(X1)\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v2_funct_1(X1)\|~v1_relat_1(X1)\|~v1_funct_1(X1)), inference(split_conjunct,[status(thm)],[c_0_19])). cnf(c_0_68, negated_conjecture, (k1_funct_1(esk3_0,X1)=X2\|~r2_hidden(X2,esk2_0)\|k1_funct_1(esk4_0,X2)!=X1), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_69, plain, (esk7_2(X1,X2)=k1_funct_1(X1,esk8_2(X1,X2))\|X2=k2_funct_1(X1)\|~r2_hidden(esk6_2(X1,X2),k9_xtuple_0(X1))\|esk5_2(X1,X2)!=k1_funct_1(X1,esk6_2(X1,X2))\|k9_xtuple_0(X2)!=k10_xtuple_0(X1)\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v2_funct_1(X1)\|~v1_relat_1(X1)\|~v1_funct_1(X1)), inference(split_conjunct,[status(thm)],[c_0_19])). cnf(c_0_70, negated_conjecture, (v4_relat_1(esk3_0,esk1_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_21, c_0_45])])). cnf(c_0_71, negated_conjecture, (k1_relset_1(esk1_0,esk3_0)=esk1_0), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33, c_0_45]), c_0_59])]), c_0_60])])). cnf(c_0_72, negated_conjecture, (r2_hidden(k1_funct_1(esk4_0,X1),esk1_0)\|~r2_hidden(X1,esk2_0)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_61])])). cnf(c_0_73, negated_conjecture, (k1_funct_1(esk4_0,esk5_2(esk3_0,esk4_0))=esk6_2(esk3_0,esk4_0)\|k1_funct_1(esk3_0,esk8_2(esk3_0,esk4_0))=esk7_2(esk3_0,esk4_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62, c_0_55]), c_0_63]), c_0_64]), c_0_65])]), c_0_66])])). cnf(c_0_74, plain, (X2=k2_funct_1(X1)\|k1_funct_1(X1,esk8_2(X1,X2))=esk7_2(X1,X2)\|r2_hidden(esk5_2(X1,X2),k10_xtuple_0(X1))\|k9_xtuple_0(X2)!=k10_xtuple_0(X1)\|~v1_funct_1(X2)\|~v1_funct_1(X1)\|~v2_funct_1(X1)\|~v1_relat_1(X2)\|~v1_relat_1(X1)), inference(evalgc,[status(thm)],[c_0_67])). cnf(c_0_75, negated_conjecture, (k1_funct_1(esk3_0,X1)=X2\|k1_funct_1(esk4_0,X2)!=X1\|~r2_hidden(X2,esk2_0)), inference(evalgc,[status(thm)],[c_0_68])). cnf(c_0_76, plain, (X2=k2_funct_1(X1)\|k1_funct_1(X1,esk8_2(X1,X2))=esk7_2(X1,X2)\|k9_xtuple_0(X2)!=k10_xtuple_0(X1)\|k1_funct_1(X1,esk6_2(X1,X2))!=esk5_2(X1,X2)\|~v1_funct_1(X2)\|~v1_funct_1(X1)\|~v2_funct_1(X1)\|~v1_relat_1(X2)\|~v1_relat_1(X1)\|~r2_hidden(esk6_2(X1,X2),k9_xtuple_0(X1))), inference(evalgc,[status(thm)],[c_0_69])). cnf(c_0_77, negated_conjecture, (k9_xtuple_0(esk3_0)=esk1_0), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30, c_0_70]), c_0_71]), c_0_55])])])). cnf(c_0_78, negated_conjecture, (r2_hidden(esk6_2(esk3_0,esk4_0),esk1_0)\|k1_funct_1(esk3_0,esk8_2(esk3_0,esk4_0))=esk7_2(esk3_0,esk4_0)\|~r2_hidden(esk5_2(esk3_0,esk4_0),esk2_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_72, c_0_73])])). cnf(c_0_79, negated_conjecture, (k1_funct_1(esk3_0,esk8_2(esk3_0,X1))=esk7_2(esk3_0,X1)\|X1=k2_funct_1(esk3_0)\|r2_hidden(esk5_2(esk3_0,X1),esk2_0)\|k9_xtuple_0(X1)!=esk2_0\|~v1_relat_1(X1)\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74, c_0_63]), c_0_55]), c_0_64]), c_0_65])])])). cnf(c_0_80, negated_conjecture, (k1_funct_1(esk3_0,k1_funct_1(esk4_0,X1))=X1\|~r2_hidden(X1,esk2_0)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_75])])). cnf(c_0_81, plain, (r2_hidden(esk8_2(X1,X2),k9_xtuple_0(X1))\|esk6_2(X1,X2)=k1_funct_1(X2,esk5_2(X1,X2))\|X2=k2_funct_1(X1)\|k9_xtuple_0(X2)!=k10_xtuple_0(X1)\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v2_funct_1(X1)\|~v1_relat_1(X1)\|~v1_funct_1(X1)), inference(split_conjunct,[status(thm)],[c_0_19])). cnf(c_0_82, negated_conjecture, (r2_hidden(X1,esk2_0)\|~r2_hidden(X2,esk1_0)\|k1_funct_1(esk3_0,X2)!=X1), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_83, negated_conjecture, (k1_funct_1(esk3_0,esk8_2(esk3_0,X1))=esk7_2(esk3_0,X1)\|X1=k2_funct_1(esk3_0)\|k1_funct_1(esk3_0,esk6_2(esk3_0,X1))!=esk5_2(esk3_0,X1)\|k9_xtuple_0(X1)!=esk2_0\|~v1_relat_1(X1)\|~r2_hidden(esk6_2(esk3_0,X1),esk1_0)\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76, c_0_77]), c_0_63]), c_0_55]), c_0_64]), c_0_65])])])). cnf(c_0_84, negated_conjecture, (k1_funct_1(esk3_0,esk8_2(esk3_0,esk4_0))=esk7_2(esk3_0,esk4_0)\|r2_hidden(esk6_2(esk3_0,esk4_0),esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78, c_0_79]), c_0_51]), c_0_32]), c_0_40])]), c_0_66])])). cnf(c_0_85, negated_conjecture, (k1_funct_1(esk3_0,esk6_2(esk3_0,esk4_0))=esk5_2(esk3_0,esk4_0)\|k1_funct_1(esk3_0,esk8_2(esk3_0,esk4_0))=esk7_2(esk3_0,esk4_0)\|~r2_hidden(esk5_2(esk3_0,esk4_0),esk2_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_80, c_0_73])])). cnf(c_0_86, plain, (X2=k2_funct_1(X1)\|k1_funct_1(X2,esk5_2(X1,X2))=esk6_2(X1,X2)\|r2_hidden(esk8_2(X1,X2),k9_xtuple_0(X1))\|k9_xtuple_0(X2)!=k10_xtuple_0(X1)\|~v1_funct_1(X2)\|~v1_funct_1(X1)\|~v2_funct_1(X1)\|~v1_relat_1(X2)\|~v1_relat_1(X1)), inference(evalgc,[status(thm)],[c_0_81])). cnf(c_0_87, negated_conjecture, (r2_hidden(X1,esk2_0)\|k1_funct_1(esk3_0,X2)!=X1\|~r2_hidden(X2,esk1_0)), inference(evalgc,[status(thm)],[c_0_82])). cnf(c_0_88, negated_conjecture, (k1_funct_1(esk3_0,esk8_2(esk3_0,esk4_0))=esk7_2(esk3_0,esk4_0)\|k1_funct_1(esk3_0,esk6_2(esk3_0,esk4_0))!=esk5_2(esk3_0,esk4_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83, c_0_84]), c_0_51]), c_0_32]), c_0_40])]), c_0_66])])). cnf(c_0_89, negated_conjecture, (k1_funct_1(esk3_0,esk8_2(esk3_0,esk4_0))=esk7_2(esk3_0,esk4_0)\|k1_funct_1(esk3_0,esk6_2(esk3_0,esk4_0))=esk5_2(esk3_0,esk4_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85, c_0_79]), c_0_51]), c_0_32]), c_0_40])]), c_0_66])])). cnf(c_0_90, negated_conjecture, (k1_funct_1(esk4_0,esk5_2(X1,esk4_0))=esk6_2(X1,esk4_0)\|k2_funct_1(X1)=esk4_0\|r2_hidden(esk8_2(X1,esk4_0),k9_xtuple_0(X1))\|k9_xtuple_0(esk4_0)!=k10_xtuple_0(X1)\|~v1_relat_1(X1)\|~v2_funct_1(X1)\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86, c_0_32]), c_0_40])])])). cnf(c_0_91, negated_conjecture, (k1_funct_1(esk4_0,X1)=X2\|~r2_hidden(X2,esk1_0)\|k1_funct_1(esk3_0,X2)!=X1), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_92, plain, (esk6_2(X1,X2)=k1_funct_1(X2,esk5_2(X1,X2))\|X2=k2_funct_1(X1)\|~r2_hidden(esk7_2(X1,X2),k10_xtuple_0(X1))\|esk8_2(X1,X2)!=k1_funct_1(X2,esk7_2(X1,X2))\|k9_xtuple_0(X2)!=k10_xtuple_0(X1)\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v2_funct_1(X1)\|~v1_relat_1(X1)\|~v1_funct_1(X1)), inference(split_conjunct,[status(thm)],[c_0_19])). cnf(c_0_93, negated_conjecture, (r2_hidden(k1_funct_1(esk3_0,X1),esk2_0)\|~r2_hidden(X1,esk1_0)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_87])])). cnf(c_0_94, negated_conjecture, (k1_funct_1(esk3_0,esk8_2(esk3_0,esk4_0))=esk7_2(esk3_0,esk4_0)), inference(csr,[status(thm)],[c_0_88, c_0_89])). cnf(c_0_95, negated_conjecture, (k1_funct_1(esk4_0,esk5_2(X1,esk4_0))=esk6_2(X1,esk4_0)\|k2_funct_1(X1)=esk4_0\|r2_hidden(esk8_2(X1,esk4_0),k9_xtuple_0(X1))\|k10_xtuple_0(X1)!=esk2_0\|~v1_relat_1(X1)\|~v2_funct_1(X1)\|~v1_funct_1(X1)), inference(rw,[status(thm)],[c_0_90, c_0_51])). cnf(c_0_96, negated_conjecture, (k1_funct_1(esk4_0,X1)=X2\|k1_funct_1(esk3_0,X2)!=X1\|~r2_hidden(X2,esk1_0)), inference(evalgc,[status(thm)],[c_0_91])). cnf(c_0_97, plain, (r2_hidden(esk8_2(X1,X2),k9_xtuple_0(X1))\|r2_hidden(esk5_2(X1,X2),k10_xtuple_0(X1))\|X2=k2_funct_1(X1)\|k9_xtuple_0(X2)!=k10_xtuple_0(X1)\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v2_funct_1(X1)\|~v1_relat_1(X1)\|~v1_funct_1(X1)), inference(split_conjunct,[status(thm)],[c_0_19])). cnf(c_0_98, plain, (X2=k2_funct_1(X1)\|~r2_hidden(esk7_2(X1,X2),k10_xtuple_0(X1))\|esk8_2(X1,X2)!=k1_funct_1(X2,esk7_2(X1,X2))\|~r2_hidden(esk6_2(X1,X2),k9_xtuple_0(X1))\|esk5_2(X1,X2)!=k1_funct_1(X1,esk6_2(X1,X2))\|k9_xtuple_0(X2)!=k10_xtuple_0(X1)\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v2_funct_1(X1)\|~v1_relat_1(X1)\|~v1_funct_1(X1)), inference(split_conjunct,[status(thm)],[c_0_19])). cnf(c_0_99, plain, (r2_hidden(esk8_2(X1,X2),k9_xtuple_0(X1))\|X2=k2_funct_1(X1)\|~r2_hidden(esk6_2(X1,X2),k9_xtuple_0(X1))\|esk5_2(X1,X2)!=k1_funct_1(X1,esk6_2(X1,X2))\|k9_xtuple_0(X2)!=k10_xtuple_0(X1)\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v2_funct_1(X1)\|~v1_relat_1(X1)\|~v1_funct_1(X1)), inference(split_conjunct,[status(thm)],[c_0_19])). cnf(c_0_100, plain, (X2=k2_funct_1(X1)\|k1_funct_1(X2,esk5_2(X1,X2))=esk6_2(X1,X2)\|k9_xtuple_0(X2)!=k10_xtuple_0(X1)\|k1_funct_1(X2,esk7_2(X1,X2))!=esk8_2(X1,X2)\|~v1_funct_1(X2)\|~v1_funct_1(X1)\|~v2_funct_1(X1)\|~v1_relat_1(X2)\|~v1_relat_1(X1)\|~r2_hidden(esk7_2(X1,X2),k10_xtuple_0(X1))), inference(evalgc,[status(thm)],[c_0_92])). cnf(c_0_101, negated_conjecture, (r2_hidden(esk7_2(esk3_0,esk4_0),esk2_0)\|~r2_hidden(esk8_2(esk3_0,esk4_0),esk1_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_93, c_0_94])])). cnf(c_0_102, negated_conjecture, (k1_funct_1(esk4_0,esk5_2(esk3_0,esk4_0))=esk6_2(esk3_0,esk4_0)\|r2_hidden(esk8_2(esk3_0,esk4_0),esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95, c_0_77]), c_0_63]), c_0_55]), c_0_64]), c_0_65])]), c_0_66])])). cnf(c_0_103, negated_conjecture, (k1_funct_1(esk4_0,k1_funct_1(esk3_0,X1))=X1\|~r2_hidden(X1,esk1_0)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_96])])). cnf(c_0_104, plain, (r2_hidden(esk5_2(X1,X2),k10_xtuple_0(X1))\|X2=k2_funct_1(X1)\|~r2_hidden(esk7_2(X1,X2),k10_xtuple_0(X1))\|esk8_2(X1,X2)!=k1_funct_1(X2,esk7_2(X1,X2))\|k9_xtuple_0(X2)!=k10_xtuple_0(X1)\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v2_funct_1(X1)\|~v1_relat_1(X1)\|~v1_funct_1(X1)), inference(split_conjunct,[status(thm)],[c_0_19])). cnf(c_0_105, plain, (X2=k2_funct_1(X1)\|r2_hidden(esk5_2(X1,X2),k10_xtuple_0(X1))\|r2_hidden(esk8_2(X1,X2),k9_xtuple_0(X1))\|k9_xtuple_0(X2)!=k10_xtuple_0(X1)\|~v1_funct_1(X2)\|~v1_funct_1(X1)\|~v2_funct_1(X1)\|~v1_relat_1(X2)\|~v1_relat_1(X1)), inference(evalgc,[status(thm)],[c_0_97])). cnf(c_0_106, plain, (X2=k2_funct_1(X1)\|k9_xtuple_0(X2)!=k10_xtuple_0(X1)\|k1_funct_1(X1,esk6_2(X1,X2))!=esk5_2(X1,X2)\|k1_funct_1(X2,esk7_2(X1,X2))!=esk8_2(X1,X2)\|~v1_funct_1(X2)\|~v1_funct_1(X1)\|~v2_funct_1(X1)\|~v1_relat_1(X2)\|~v1_relat_1(X1)\|~r2_hidden(esk6_2(X1,X2),k9_xtuple_0(X1))\|~r2_hidden(esk7_2(X1,X2),k10_xtuple_0(X1))), inference(evalgc,[status(thm)],[c_0_98])). cnf(c_0_107, plain, (X2=k2_funct_1(X1)\|r2_hidden(esk8_2(X1,X2),k9_xtuple_0(X1))\|k9_xtuple_0(X2)!=k10_xtuple_0(X1)\|k1_funct_1(X1,esk6_2(X1,X2))!=esk5_2(X1,X2)\|~v1_funct_1(X2)\|~v1_funct_1(X1)\|~v2_funct_1(X1)\|~v1_relat_1(X2)\|~v1_relat_1(X1)\|~r2_hidden(esk6_2(X1,X2),k9_xtuple_0(X1))), inference(evalgc,[status(thm)],[c_0_99])). cnf(c_0_108, negated_conjecture, (k1_funct_1(X1,esk5_2(esk3_0,X1))=esk6_2(esk3_0,X1)\|X1=k2_funct_1(esk3_0)\|k1_funct_1(X1,esk7_2(esk3_0,X1))!=esk8_2(esk3_0,X1)\|k9_xtuple_0(X1)!=esk2_0\|~v1_relat_1(X1)\|~r2_hidden(esk7_2(esk3_0,X1),esk2_0)\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100, c_0_63]), c_0_55]), c_0_64]), c_0_65])])])). cnf(c_0_109, negated_conjecture, (r2_hidden(esk7_2(esk3_0,esk4_0),esk2_0)\|k1_funct_1(esk4_0,esk5_2(esk3_0,esk4_0))=esk6_2(esk3_0,esk4_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_101, c_0_102])])). cnf(c_0_110, negated_conjecture, (k1_funct_1(esk4_0,esk7_2(esk3_0,esk4_0))=esk8_2(esk3_0,esk4_0)\|~r2_hidden(esk8_2(esk3_0,esk4_0),esk1_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_103, c_0_94])])). cnf(c_0_111, plain, (X2=k2_funct_1(X1)\|r2_hidden(esk5_2(X1,X2),k10_xtuple_0(X1))\|k9_xtuple_0(X2)!=k10_xtuple_0(X1)\|k1_funct_1(X2,esk7_2(X1,X2))!=esk8_2(X1,X2)\|~v1_funct_1(X2)\|~v1_funct_1(X1)\|~v2_funct_1(X1)\|~v1_relat_1(X2)\|~v1_relat_1(X1)\|~r2_hidden(esk7_2(X1,X2),k10_xtuple_0(X1))), inference(evalgc,[status(thm)],[c_0_104])). cnf(c_0_112, negated_conjecture, (X1=k2_funct_1(esk3_0)\|r2_hidden(esk8_2(esk3_0,X1),esk1_0)\|r2_hidden(esk5_2(esk3_0,X1),esk2_0)\|k9_xtuple_0(X1)!=esk2_0\|~v1_relat_1(X1)\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105, c_0_77]), c_0_63]), c_0_63]), c_0_55]), c_0_64]), c_0_65])])])). cnf(c_0_113, negated_conjecture, (X1=k2_funct_1(esk3_0)\|k1_funct_1(esk3_0,esk6_2(esk3_0,X1))!=esk5_2(esk3_0,X1)\|k1_funct_1(X1,esk7_2(esk3_0,X1))!=esk8_2(esk3_0,X1)\|k9_xtuple_0(X1)!=esk2_0\|~v1_relat_1(X1)\|~r2_hidden(esk6_2(esk3_0,X1),k9_xtuple_0(esk3_0))\|~r2_hidden(esk7_2(esk3_0,X1),esk2_0)\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106, c_0_63]), c_0_55]), c_0_64]), c_0_65])])])). cnf(c_0_114, negated_conjecture, (X1=k2_funct_1(esk3_0)\|r2_hidden(esk8_2(esk3_0,X1),esk1_0)\|k1_funct_1(esk3_0,esk6_2(esk3_0,X1))!=esk5_2(esk3_0,X1)\|k9_xtuple_0(X1)!=esk2_0\|~v1_relat_1(X1)\|~r2_hidden(esk6_2(esk3_0,X1),esk1_0)\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107, c_0_77]), c_0_63]), c_0_55]), c_0_64]), c_0_65])])])). cnf(c_0_115, negated_conjecture, (k1_funct_1(esk4_0,esk5_2(esk3_0,esk4_0))=esk6_2(esk3_0,esk4_0)\|k1_funct_1(esk4_0,esk7_2(esk3_0,esk4_0))!=esk8_2(esk3_0,esk4_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108, c_0_109]), c_0_51]), c_0_32]), c_0_40])]), c_0_66])])). cnf(c_0_116, negated_conjecture, (k1_funct_1(esk4_0,esk7_2(esk3_0,esk4_0))=esk8_2(esk3_0,esk4_0)\|k1_funct_1(esk4_0,esk5_2(esk3_0,esk4_0))=esk6_2(esk3_0,esk4_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_110, c_0_102])])). cnf(c_0_117, negated_conjecture, (X1=k2_funct_1(esk3_0)\|r2_hidden(esk5_2(esk3_0,X1),esk2_0)\|k1_funct_1(X1,esk7_2(esk3_0,X1))!=esk8_2(esk3_0,X1)\|k9_xtuple_0(X1)!=esk2_0\|~v1_relat_1(X1)\|~r2_hidden(esk7_2(esk3_0,X1),esk2_0)\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111, c_0_63]), c_0_55]), c_0_64]), c_0_65])])])). cnf(c_0_118, negated_conjecture, (r2_hidden(esk7_2(esk3_0,esk4_0),esk2_0)\|r2_hidden(esk5_2(esk3_0,esk4_0),esk2_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101, c_0_112]), c_0_51]), c_0_32]), c_0_40])]), c_0_66])])). cnf(c_0_119, negated_conjecture, (X1=k2_funct_1(esk3_0)\|k1_funct_1(esk3_0,esk6_2(esk3_0,X1))!=esk5_2(esk3_0,X1)\|k1_funct_1(X1,esk7_2(esk3_0,X1))!=esk8_2(esk3_0,X1)\|k9_xtuple_0(X1)!=esk2_0\|~v1_relat_1(X1)\|~r2_hidden(esk6_2(esk3_0,X1),esk1_0)\|~r2_hidden(esk7_2(esk3_0,X1),esk2_0)\|~v1_funct_1(X1)), inference(rw,[status(thm)],[c_0_113, c_0_77])). cnf(c_0_120, negated_conjecture, (r2_hidden(esk7_2(esk3_0,esk4_0),esk2_0)\|k1_funct_1(esk3_0,esk6_2(esk3_0,esk4_0))!=esk5_2(esk3_0,esk4_0)\|~r2_hidden(esk6_2(esk3_0,esk4_0),esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101, c_0_114]), c_0_51]), c_0_32]), c_0_40])]), c_0_66])])). cnf(c_0_121, negated_conjecture, (k1_funct_1(esk4_0,esk5_2(esk3_0,esk4_0))=esk6_2(esk3_0,esk4_0)), inference(csr,[status(thm)],[c_0_115, c_0_116])). cnf(c_0_122, negated_conjecture, (r2_hidden(esk5_2(esk3_0,esk4_0),esk2_0)\|k1_funct_1(esk4_0,esk7_2(esk3_0,esk4_0))!=esk8_2(esk3_0,esk4_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117, c_0_118]), c_0_51]), c_0_32]), c_0_40])]), c_0_66])])). cnf(c_0_123, negated_conjecture, (k1_funct_1(esk4_0,esk7_2(esk3_0,esk4_0))=esk8_2(esk3_0,esk4_0)\|r2_hidden(esk5_2(esk3_0,esk4_0),esk2_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110, c_0_112]), c_0_51]), c_0_32]), c_0_40])]), c_0_66])])). cnf(c_0_124, negated_conjecture, (k1_funct_1(esk3_0,esk6_2(esk3_0,esk4_0))!=esk5_2(esk3_0,esk4_0)\|k1_funct_1(esk4_0,esk7_2(esk3_0,esk4_0))!=esk8_2(esk3_0,esk4_0)\|~r2_hidden(esk6_2(esk3_0,esk4_0),esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119, c_0_120]), c_0_51]), c_0_32]), c_0_40])]), c_0_66])])). cnf(c_0_125, negated_conjecture, (k1_funct_1(esk4_0,esk7_2(esk3_0,esk4_0))=esk8_2(esk3_0,esk4_0)\|k1_funct_1(esk3_0,esk6_2(esk3_0,esk4_0))!=esk5_2(esk3_0,esk4_0)\|~r2_hidden(esk6_2(esk3_0,esk4_0),esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110, c_0_114]), c_0_51]), c_0_32]), c_0_40])]), c_0_66])])). cnf(c_0_126, negated_conjecture, (r2_hidden(esk6_2(esk3_0,esk4_0),esk1_0)\|~r2_hidden(esk5_2(esk3_0,esk4_0),esk2_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_72, c_0_121])])). cnf(c_0_127, negated_conjecture, (r2_hidden(esk5_2(esk3_0,esk4_0),esk2_0)), inference(csr,[status(thm)],[c_0_122, c_0_123])). cnf(c_0_128, negated_conjecture, (k1_funct_1(esk3_0,esk6_2(esk3_0,esk4_0))!=esk5_2(esk3_0,esk4_0)\|~r2_hidden(esk6_2(esk3_0,esk4_0),esk1_0)), inference(csr,[status(thm)],[c_0_124, c_0_125])). cnf(c_0_129, negated_conjecture, (r2_hidden(esk6_2(esk3_0,esk4_0),esk1_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_126, c_0_127])])). cnf(c_0_130, negated_conjecture, (k1_funct_1(esk3_0,esk6_2(esk3_0,esk4_0))=esk5_2(esk3_0,esk4_0)\|~r2_hidden(esk5_2(esk3_0,esk4_0),esk2_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_80, c_0_121])])). cnf(c_0_131, negated_conjecture, (k1_funct_1(esk3_0,esk6_2(esk3_0,esk4_0))!=esk5_2(esk3_0,esk4_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_128, c_0_129])])])). cnf(c_0_132, negated_conjecture, (k1_funct_1(esk3_0,esk6_2(esk3_0,esk4_0))=esk5_2(esk3_0,esk4_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_130, c_0_127])])). cnf(c_0_133, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_131, c_0_132])]), ['proof']). # SZS output end CNFRefutation	reserve P,Q,X,Y,Z,p,x,x9,x1,x2,y,z for set; theorem for f being Function of X,Y for g being Function of Y,X st X <> {} & Y <> {} & rng f = Y & f is one-to-one & for y,x holds y in Y & g.y = x iff x in X & f.x = y holds g = f" proof let f be Function of X,Y; let g be Function of Y,X; assume X <> {} & Y <> {}; then dom f = X & dom g = Y by Def1; hence thesis by FUNCT_1:32; end;	Convert the following ATP output trace into a readable Mizar proof.
t48_ideal_1	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t44_ideal_1, axiom, ![X1]:((~(v2_struct_0(X1))&l6_algstr_0(X1))=>![X2]:((~(v1_xboole_0(X2))&(v1_ideal_1(X2,X1)&(v2_ideal_1(X2,X1)&(v3_ideal_1(X2,X1)&m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))))))=>k7_ideal_1(X1,X2)=X2)), file('/scratch/mptp/predsminms1/t48_ideal_1__0', t44_ideal_1)). fof(fc2_ideal_1, axiom, ![X1]:((~(v2_struct_0(X1))&(v6_algstr_0(X1)&(v1_vectsp_1(X1)&(v1_algstr_1(X1)&l6_algstr_0(X1)))))=>v2_ideal_1(k1_tarski(k4_struct_0(X1)),X1)), file('/scratch/mptp/predsminms1/t48_ideal_1__0', fc2_ideal_1)). fof(fc2_xboole_0, axiom, ![X1]:~(v1_xboole_0(k1_tarski(X1))), file('/scratch/mptp/predsminms1/t48_ideal_1__0', fc2_xboole_0)). fof(fc3_ideal_1, axiom, ![X1]:((~(v2_struct_0(X1))&(v5_algstr_0(X1)&(v4_rlvect_1(X1)&(v2_vectsp_1(X1)&l6_algstr_0(X1)))))=>v3_ideal_1(k1_tarski(k4_struct_0(X1)),X1)), file('/scratch/mptp/predsminms1/t48_ideal_1__0', fc3_ideal_1)). fof(fc1_ideal_1, axiom, ![X1]:((~(v2_struct_0(X1))&(v4_rlvect_1(X1)&l2_algstr_0(X1)))=>v1_ideal_1(k1_tarski(k4_struct_0(X1)),X1)), file('/scratch/mptp/predsminms1/t48_ideal_1__0', fc1_ideal_1)). fof(t48_ideal_1, conjecture, ![X1]:((~(v2_struct_0(X1))&(v7_algstr_0(X1)&(v4_rlvect_1(X1)&(v5_vectsp_1(X1)&(v1_algstr_1(X1)&l6_algstr_0(X1))))))=>k7_ideal_1(X1,k6_domain_1(u1_struct_0(X1),k4_struct_0(X1)))=k6_domain_1(u1_struct_0(X1),k4_struct_0(X1))), file('/scratch/mptp/predsminms1/t48_ideal_1__0', t48_ideal_1)). fof(dt_l6_algstr_0, axiom, ![X1]:(l6_algstr_0(X1)=>(l2_algstr_0(X1)&l5_algstr_0(X1))), file('/scratch/mptp/predsminms1/t48_ideal_1__0', dt_l6_algstr_0)). fof(dt_k6_domain_1, axiom, ![X1, X2]:((~(v1_xboole_0(X1))&m1_subset_1(X2,X1))=>m1_subset_1(k6_domain_1(X1,X2),k1_zfmisc_1(X1))), file('/scratch/mptp/predsminms1/t48_ideal_1__0', dt_k6_domain_1)). fof(redefinition_k6_domain_1, axiom, ![X1, X2]:((~(v1_xboole_0(X1))&m1_subset_1(X2,X1))=>k6_domain_1(X1,X2)=k1_tarski(X2)), file('/scratch/mptp/predsminms1/t48_ideal_1__0', redefinition_k6_domain_1)). fof(dt_k4_struct_0, axiom, ![X1]:(l2_struct_0(X1)=>m1_subset_1(k4_struct_0(X1),u1_struct_0(X1))), file('/scratch/mptp/predsminms1/t48_ideal_1__0', dt_k4_struct_0)). fof(cc1_vectsp_1, axiom, ![X1]:(l6_algstr_0(X1)=>((~(v2_struct_0(X1))&v5_vectsp_1(X1))=>(~(v2_struct_0(X1))&(v1_vectsp_1(X1)&v2_vectsp_1(X1))))), file('/scratch/mptp/predsminms1/t48_ideal_1__0', cc1_vectsp_1)). fof(cc4_algstr_0, axiom, ![X1]:(l1_algstr_0(X1)=>(v7_algstr_0(X1)=>(v5_algstr_0(X1)&v6_algstr_0(X1)))), file('/scratch/mptp/predsminms1/t48_ideal_1__0', cc4_algstr_0)). fof(t8_boole, axiom, ![X1, X2]:~((v1_xboole_0(X1)&(~(X1=X2)&v1_xboole_0(X2)))), file('/scratch/mptp/predsminms1/t48_ideal_1__0', t8_boole)). fof(rc1_xboole_0, axiom, ?[X1]:v1_xboole_0(X1), file('/scratch/mptp/predsminms1/t48_ideal_1__0', rc1_xboole_0)). fof(cc1_subset_1, axiom, ![X1]:(v1_xboole_0(X1)=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(X1))=>v1_xboole_0(X2))), file('/scratch/mptp/predsminms1/t48_ideal_1__0', cc1_subset_1)). fof(dt_k7_ideal_1, axiom, ![X1, X2]:(((~(v2_struct_0(X1))&l6_algstr_0(X1))&m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))))=>(~(v1_xboole_0(k7_ideal_1(X1,X2)))&(v1_ideal_1(k7_ideal_1(X1,X2),X1)&(v2_ideal_1(k7_ideal_1(X1,X2),X1)&(v3_ideal_1(k7_ideal_1(X1,X2),X1)&m1_subset_1(k7_ideal_1(X1,X2),k1_zfmisc_1(u1_struct_0(X1)))))))), file('/scratch/mptp/predsminms1/t48_ideal_1__0', dt_k7_ideal_1)). fof(rc2_subset_1, axiom, ![X1]:?[X2]:(m1_subset_1(X2,k1_zfmisc_1(X1))&v1_xboole_0(X2)), file('/scratch/mptp/predsminms1/t48_ideal_1__0', rc2_subset_1)). fof(dt_l2_algstr_0, axiom, ![X1]:(l2_algstr_0(X1)=>(l2_struct_0(X1)&l1_algstr_0(X1))), file('/scratch/mptp/predsminms1/t48_ideal_1__0', dt_l2_algstr_0)). fof(c_0_18, plain, ![X26, X27]:(v2_struct_0(X26)\|~l6_algstr_0(X26)\|(v1_xboole_0(X27)\|(~v1_ideal_1(X27,X26)\|(~v2_ideal_1(X27,X26)\|(~v3_ideal_1(X27,X26)\|~m1_subset_1(X27,k1_zfmisc_1(u1_struct_0(X26))))))\|k7_ideal_1(X26,X27)=X27)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t44_ideal_1])])])])). fof(c_0_19, plain, ![X12]:(v2_struct_0(X12)\|(~v6_algstr_0(X12)\|(~v1_vectsp_1(X12)\|(~v1_algstr_1(X12)\|~l6_algstr_0(X12))))\|v2_ideal_1(k1_tarski(k4_struct_0(X12)),X12)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fc2_ideal_1])])])). fof(c_0_20, plain, ![X14]:~v1_xboole_0(k1_tarski(X14)), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fc2_xboole_0])])). cnf(c_0_21, plain, (v2_struct_0(X1)\|v1_xboole_0(X2)\|k7_ideal_1(X1,X2)=X2\|~l6_algstr_0(X1)\|~v1_ideal_1(X2,X1)\|~v2_ideal_1(X2,X1)\|~v3_ideal_1(X2,X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(split_conjunct,[status(thm)],[c_0_18])). cnf(c_0_22, plain, (v2_struct_0(X1)\|v2_ideal_1(k1_tarski(k4_struct_0(X1)),X1)\|~v6_algstr_0(X1)\|~v1_vectsp_1(X1)\|~v1_algstr_1(X1)\|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_19])). cnf(c_0_23, plain, (~v1_xboole_0(k1_tarski(X1))), inference(split_conjunct,[status(thm)],[c_0_20])). fof(c_0_24, plain, ![X11]:(v2_struct_0(X11)\|(~v5_algstr_0(X11)\|(~v4_rlvect_1(X11)\|(~v2_vectsp_1(X11)\|~l6_algstr_0(X11))))\|v3_ideal_1(k1_tarski(k4_struct_0(X11)),X11)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fc3_ideal_1])])])). cnf(c_0_25, plain, (k7_ideal_1(X1,X2)=X2\|v2_struct_0(X1)\|v1_xboole_0(X2)\|~l6_algstr_0(X1)\|~v3_ideal_1(X2,X1)\|~v2_ideal_1(X2,X1)\|~v1_ideal_1(X2,X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(evalgc,[status(thm)],[c_0_21])). cnf(c_0_26, plain, (v2_struct_0(X1)\|v2_ideal_1(k1_tarski(k4_struct_0(X1)),X1)\|~v1_algstr_1(X1)\|~l6_algstr_0(X1)\|~v6_algstr_0(X1)\|~v1_vectsp_1(X1)), inference(evalgc,[status(thm)],[c_0_22])). cnf(c_0_27, plain, (~v1_xboole_0(k1_tarski(X1))), inference(evalgc,[status(thm)],[c_0_23])). cnf(c_0_28, plain, (v2_struct_0(X1)\|v3_ideal_1(k1_tarski(k4_struct_0(X1)),X1)\|~v5_algstr_0(X1)\|~v4_rlvect_1(X1)\|~v2_vectsp_1(X1)\|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_24])). fof(c_0_29, plain, ![X13]:(v2_struct_0(X13)\|(~v4_rlvect_1(X13)\|~l2_algstr_0(X13))\|v1_ideal_1(k1_tarski(k4_struct_0(X13)),X13)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fc1_ideal_1])])])). fof(c_0_30, negated_conjecture, ~(![X1]:((~(v2_struct_0(X1))&(v7_algstr_0(X1)&(v4_rlvect_1(X1)&(v5_vectsp_1(X1)&(v1_algstr_1(X1)&l6_algstr_0(X1))))))=>k7_ideal_1(X1,k6_domain_1(u1_struct_0(X1),k4_struct_0(X1)))=k6_domain_1(u1_struct_0(X1),k4_struct_0(X1)))), inference(assume_negation,[status(cth)],[t48_ideal_1])). cnf(c_0_31, plain, (k7_ideal_1(X1,k1_tarski(k4_struct_0(X1)))=k1_tarski(k4_struct_0(X1))\|v2_struct_0(X1)\|~v1_ideal_1(k1_tarski(k4_struct_0(X1)),X1)\|~v3_ideal_1(k1_tarski(k4_struct_0(X1)),X1)\|~m1_subset_1(k1_tarski(k4_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))\|~l6_algstr_0(X1)\|~v1_vectsp_1(X1)\|~v6_algstr_0(X1)\|~v1_algstr_1(X1)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25, c_0_26]), c_0_27])])). cnf(c_0_32, plain, (v2_struct_0(X1)\|v3_ideal_1(k1_tarski(k4_struct_0(X1)),X1)\|~v4_rlvect_1(X1)\|~l6_algstr_0(X1)\|~v5_algstr_0(X1)\|~v2_vectsp_1(X1)), inference(evalgc,[status(thm)],[c_0_28])). cnf(c_0_33, plain, (v2_struct_0(X1)\|v1_ideal_1(k1_tarski(k4_struct_0(X1)),X1)\|~v4_rlvect_1(X1)\|~l2_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_29])). fof(c_0_34, plain, ![X4]:((l2_algstr_0(X4)\|~l6_algstr_0(X4))&(l5_algstr_0(X4)\|~l6_algstr_0(X4))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l6_algstr_0])])])). fof(c_0_35, plain, ![X24, X25]:(v1_xboole_0(X24)\|~m1_subset_1(X25,X24)\|m1_subset_1(k6_domain_1(X24,X25),k1_zfmisc_1(X24))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k6_domain_1])])])). fof(c_0_36, plain, ![X7, X8]:(v1_xboole_0(X7)\|~m1_subset_1(X8,X7)\|k6_domain_1(X7,X8)=k1_tarski(X8)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[redefinition_k6_domain_1])])])). fof(c_0_37, negated_conjecture, ((~v2_struct_0(esk1_0)&(v7_algstr_0(esk1_0)&(v4_rlvect_1(esk1_0)&(v5_vectsp_1(esk1_0)&(v1_algstr_1(esk1_0)&l6_algstr_0(esk1_0))))))&k7_ideal_1(esk1_0,k6_domain_1(u1_struct_0(esk1_0),k4_struct_0(esk1_0)))!=k6_domain_1(u1_struct_0(esk1_0),k4_struct_0(esk1_0))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_30])])])])). cnf(c_0_38, plain, (k7_ideal_1(X1,k1_tarski(k4_struct_0(X1)))=k1_tarski(k4_struct_0(X1))\|v2_struct_0(X1)\|~v1_ideal_1(k1_tarski(k4_struct_0(X1)),X1)\|~v1_vectsp_1(X1)\|~v6_algstr_0(X1)\|~m1_subset_1(k1_tarski(k4_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))\|~l6_algstr_0(X1)\|~v1_algstr_1(X1)\|~v2_vectsp_1(X1)\|~v5_algstr_0(X1)\|~v4_rlvect_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_31, c_0_32])])). cnf(c_0_39, plain, (v2_struct_0(X1)\|v1_ideal_1(k1_tarski(k4_struct_0(X1)),X1)\|~v4_rlvect_1(X1)\|~l2_algstr_0(X1)), inference(evalgc,[status(thm)],[c_0_33])). cnf(c_0_40, plain, (l2_algstr_0(X1)\|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_34])). cnf(c_0_41, plain, (v1_xboole_0(X1)\|m1_subset_1(k6_domain_1(X1,X2),k1_zfmisc_1(X1))\|~m1_subset_1(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_35])). cnf(c_0_42, plain, (v1_xboole_0(X1)\|k6_domain_1(X1,X2)=k1_tarski(X2)\|~m1_subset_1(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_36])). cnf(c_0_43, negated_conjecture, (k7_ideal_1(esk1_0,k6_domain_1(u1_struct_0(esk1_0),k4_struct_0(esk1_0)))!=k6_domain_1(u1_struct_0(esk1_0),k4_struct_0(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_37])). cnf(c_0_44, plain, (k7_ideal_1(X1,k1_tarski(k4_struct_0(X1)))=k1_tarski(k4_struct_0(X1))\|v2_struct_0(X1)\|~v2_vectsp_1(X1)\|~v1_vectsp_1(X1)\|~v6_algstr_0(X1)\|~v5_algstr_0(X1)\|~m1_subset_1(k1_tarski(k4_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))\|~l6_algstr_0(X1)\|~v1_algstr_1(X1)\|~v4_rlvect_1(X1)\|~l2_algstr_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_38, c_0_39])])). cnf(c_0_45, plain, (l2_algstr_0(X1)\|~l6_algstr_0(X1)), inference(evalgc,[status(thm)],[c_0_40])). cnf(c_0_46, plain, (v1_xboole_0(X1)\|m1_subset_1(k6_domain_1(X1,X2),k1_zfmisc_1(X1))\|~m1_subset_1(X2,X1)), inference(evalgc,[status(thm)],[c_0_41])). cnf(c_0_47, plain, (k6_domain_1(X1,X2)=k1_tarski(X2)\|v1_xboole_0(X1)\|~m1_subset_1(X2,X1)), inference(evalgc,[status(thm)],[c_0_42])). cnf(c_0_48, negated_conjecture, (k7_ideal_1(esk1_0,k6_domain_1(u1_struct_0(esk1_0),k4_struct_0(esk1_0)))!=k6_domain_1(u1_struct_0(esk1_0),k4_struct_0(esk1_0))), inference(evalgc,[status(thm)],[c_0_43])). cnf(c_0_49, plain, (k7_ideal_1(X1,k1_tarski(k4_struct_0(X1)))=k1_tarski(k4_struct_0(X1))\|v2_struct_0(X1)\|~v2_vectsp_1(X1)\|~v1_vectsp_1(X1)\|~v6_algstr_0(X1)\|~v5_algstr_0(X1)\|~m1_subset_1(k1_tarski(k4_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))\|~l6_algstr_0(X1)\|~v1_algstr_1(X1)\|~v4_rlvect_1(X1)), inference(csr,[status(thm)],[c_0_44, c_0_45])). cnf(c_0_50, plain, (v1_xboole_0(X1)\|m1_subset_1(k1_tarski(X2),k1_zfmisc_1(X1))\|~m1_subset_1(X2,X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_46, c_0_47])])). cnf(c_0_51, negated_conjecture, (l6_algstr_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_37])). cnf(c_0_52, negated_conjecture, (v1_algstr_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_37])). cnf(c_0_53, negated_conjecture, (v4_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_37])). cnf(c_0_54, negated_conjecture, (~v2_struct_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_37])). fof(c_0_55, plain, ![X6]:(~l2_struct_0(X6)\|m1_subset_1(k4_struct_0(X6),u1_struct_0(X6))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k4_struct_0])])). cnf(c_0_56, negated_conjecture, (v1_xboole_0(u1_struct_0(esk1_0))\|k7_ideal_1(esk1_0,k1_tarski(k4_struct_0(esk1_0)))!=k1_tarski(k4_struct_0(esk1_0))\|~m1_subset_1(k4_struct_0(esk1_0),u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_48, c_0_47])])). cnf(c_0_57, plain, (k7_ideal_1(X1,k1_tarski(k4_struct_0(X1)))=k1_tarski(k4_struct_0(X1))\|v2_struct_0(X1)\|v1_xboole_0(u1_struct_0(X1))\|~v2_vectsp_1(X1)\|~v1_vectsp_1(X1)\|~v6_algstr_0(X1)\|~v5_algstr_0(X1)\|~l6_algstr_0(X1)\|~v1_algstr_1(X1)\|~v4_rlvect_1(X1)\|~m1_subset_1(k4_struct_0(X1),u1_struct_0(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_49, c_0_50])])). cnf(c_0_58, negated_conjecture, (l6_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_51])). cnf(c_0_59, negated_conjecture, (v1_algstr_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_52])). cnf(c_0_60, negated_conjecture, (v4_rlvect_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_53])). cnf(c_0_61, negated_conjecture, (~v2_struct_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_54])). cnf(c_0_62, plain, (m1_subset_1(k4_struct_0(X1),u1_struct_0(X1))\|~l2_struct_0(X1)), inference(split_conjunct,[status(thm)],[c_0_55])). fof(c_0_63, plain, ![X10]:((~v2_struct_0(X10)\|(v2_struct_0(X10)\|~v5_vectsp_1(X10))\|~l6_algstr_0(X10))&((v1_vectsp_1(X10)\|(v2_struct_0(X10)\|~v5_vectsp_1(X10))\|~l6_algstr_0(X10))&(v2_vectsp_1(X10)\|(v2_struct_0(X10)\|~v5_vectsp_1(X10))\|~l6_algstr_0(X10)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[cc1_vectsp_1])])])])). cnf(c_0_64, negated_conjecture, (v1_xboole_0(u1_struct_0(esk1_0))\|~m1_subset_1(k4_struct_0(esk1_0),u1_struct_0(esk1_0))\|~v2_vectsp_1(esk1_0)\|~v1_vectsp_1(esk1_0)\|~v6_algstr_0(esk1_0)\|~v5_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56, c_0_57]), c_0_58]), c_0_59]), c_0_60])]), c_0_61])])). cnf(c_0_65, plain, (m1_subset_1(k4_struct_0(X1),u1_struct_0(X1))\|~l2_struct_0(X1)), inference(evalgc,[status(thm)],[c_0_62])). cnf(c_0_66, plain, (v2_vectsp_1(X1)\|v2_struct_0(X1)\|~v5_vectsp_1(X1)\|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_63])). cnf(c_0_67, negated_conjecture, (v5_vectsp_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_37])). cnf(c_0_68, negated_conjecture, (v1_xboole_0(u1_struct_0(esk1_0))\|~v2_vectsp_1(esk1_0)\|~v1_vectsp_1(esk1_0)\|~v6_algstr_0(esk1_0)\|~v5_algstr_0(esk1_0)\|~l2_struct_0(esk1_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_64, c_0_65])])). cnf(c_0_69, plain, (v2_struct_0(X1)\|v2_vectsp_1(X1)\|~v5_vectsp_1(X1)\|~l6_algstr_0(X1)), inference(evalgc,[status(thm)],[c_0_66])). cnf(c_0_70, negated_conjecture, (v5_vectsp_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_67])). cnf(c_0_71, plain, (v1_vectsp_1(X1)\|v2_struct_0(X1)\|~v5_vectsp_1(X1)\|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_63])). fof(c_0_72, plain, ![X9]:((v5_algstr_0(X9)\|~v7_algstr_0(X9)\|~l1_algstr_0(X9))&(v6_algstr_0(X9)\|~v7_algstr_0(X9)\|~l1_algstr_0(X9))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc4_algstr_0])])])). fof(c_0_73, plain, ![X18, X19]:(~v1_xboole_0(X18)\|(X18=X19\|~v1_xboole_0(X19))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t8_boole])])])). fof(c_0_74, plain, v1_xboole_0(esk3_0), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])])). cnf(c_0_75, negated_conjecture, (v1_xboole_0(u1_struct_0(esk1_0))\|~v1_vectsp_1(esk1_0)\|~v6_algstr_0(esk1_0)\|~v5_algstr_0(esk1_0)\|~l2_struct_0(esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68, c_0_69]), c_0_58]), c_0_70])]), c_0_61])])). cnf(c_0_76, plain, (v2_struct_0(X1)\|v1_vectsp_1(X1)\|~v5_vectsp_1(X1)\|~l6_algstr_0(X1)), inference(evalgc,[status(thm)],[c_0_71])). cnf(c_0_77, plain, (v6_algstr_0(X1)\|~v7_algstr_0(X1)\|~l1_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_72])). cnf(c_0_78, negated_conjecture, (v7_algstr_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_37])). fof(c_0_79, plain, ![X22, X23]:(~v1_xboole_0(X22)\|(~m1_subset_1(X23,k1_zfmisc_1(X22))\|v1_xboole_0(X23))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_subset_1])])])). fof(c_0_80, plain, ![X20, X21]:((~v1_xboole_0(k7_ideal_1(X20,X21))\|(v2_struct_0(X20)\|~l6_algstr_0(X20)\|~m1_subset_1(X21,k1_zfmisc_1(u1_struct_0(X20)))))&((v1_ideal_1(k7_ideal_1(X20,X21),X20)\|(v2_struct_0(X20)\|~l6_algstr_0(X20)\|~m1_subset_1(X21,k1_zfmisc_1(u1_struct_0(X20)))))&((v2_ideal_1(k7_ideal_1(X20,X21),X20)\|(v2_struct_0(X20)\|~l6_algstr_0(X20)\|~m1_subset_1(X21,k1_zfmisc_1(u1_struct_0(X20)))))&((v3_ideal_1(k7_ideal_1(X20,X21),X20)\|(v2_struct_0(X20)\|~l6_algstr_0(X20)\|~m1_subset_1(X21,k1_zfmisc_1(u1_struct_0(X20)))))&(m1_subset_1(k7_ideal_1(X20,X21),k1_zfmisc_1(u1_struct_0(X20)))\|(v2_struct_0(X20)\|~l6_algstr_0(X20)\|~m1_subset_1(X21,k1_zfmisc_1(u1_struct_0(X20))))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k7_ideal_1])])])])). cnf(c_0_81, plain, (X1=X2\|~v1_xboole_0(X1)\|~v1_xboole_0(X2)), inference(split_conjunct,[status(thm)],[c_0_73])). cnf(c_0_82, plain, (v1_xboole_0(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_74])). fof(c_0_83, plain, ![X15]:(m1_subset_1(esk2_1(X15),k1_zfmisc_1(X15))&v1_xboole_0(esk2_1(X15))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_subset_1])])). cnf(c_0_84, negated_conjecture, (v1_xboole_0(u1_struct_0(esk1_0))\|~v6_algstr_0(esk1_0)\|~v5_algstr_0(esk1_0)\|~l2_struct_0(esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75, c_0_76]), c_0_58]), c_0_70])]), c_0_61])])). cnf(c_0_85, plain, (v6_algstr_0(X1)\|~v7_algstr_0(X1)\|~l1_algstr_0(X1)), inference(evalgc,[status(thm)],[c_0_77])). cnf(c_0_86, negated_conjecture, (v7_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_78])). cnf(c_0_87, plain, (v5_algstr_0(X1)\|~v7_algstr_0(X1)\|~l1_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_72])). fof(c_0_88, plain, ![X5]:((l2_struct_0(X5)\|~l2_algstr_0(X5))&(l1_algstr_0(X5)\|~l2_algstr_0(X5))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l2_algstr_0])])])). cnf(c_0_89, plain, (v1_xboole_0(X2)\|~v1_xboole_0(X1)\|~m1_subset_1(X2,k1_zfmisc_1(X1))), inference(split_conjunct,[status(thm)],[c_0_79])). cnf(c_0_90, plain, (m1_subset_1(k7_ideal_1(X1,X2),k1_zfmisc_1(u1_struct_0(X1)))\|v2_struct_0(X1)\|~l6_algstr_0(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(split_conjunct,[status(thm)],[c_0_80])). cnf(c_0_91, plain, (X1=X2\|~v1_xboole_0(X2)\|~v1_xboole_0(X1)), inference(evalgc,[status(thm)],[c_0_81])). cnf(c_0_92, plain, (v1_xboole_0(esk3_0)), inference(evalgc,[status(thm)],[c_0_82])). cnf(c_0_93, plain, (v1_xboole_0(esk2_1(X1))), inference(split_conjunct,[status(thm)],[c_0_83])). cnf(c_0_94, negated_conjecture, (v1_xboole_0(u1_struct_0(esk1_0))\|~v5_algstr_0(esk1_0)\|~l2_struct_0(esk1_0)\|~l1_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84, c_0_85]), c_0_86])])])). cnf(c_0_95, plain, (v5_algstr_0(X1)\|~v7_algstr_0(X1)\|~l1_algstr_0(X1)), inference(evalgc,[status(thm)],[c_0_87])). cnf(c_0_96, plain, (l2_struct_0(X1)\|~l2_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_88])). cnf(c_0_97, plain, (v1_xboole_0(X2)\|~v1_xboole_0(X1)\|~m1_subset_1(X2,k1_zfmisc_1(X1))), inference(evalgc,[status(thm)],[c_0_89])). cnf(c_0_98, plain, (v2_struct_0(X1)\|m1_subset_1(k7_ideal_1(X1,X2),k1_zfmisc_1(u1_struct_0(X1)))\|~l6_algstr_0(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(evalgc,[status(thm)],[c_0_90])). cnf(c_0_99, plain, (v2_struct_0(X1)\|~v1_xboole_0(k7_ideal_1(X1,X2))\|~l6_algstr_0(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(split_conjunct,[status(thm)],[c_0_80])). cnf(c_0_100, plain, (m1_subset_1(esk2_1(X1),k1_zfmisc_1(X1))), inference(split_conjunct,[status(thm)],[c_0_83])). cnf(c_0_101, plain, (X1=esk3_0\|~v1_xboole_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_91, c_0_92])])). cnf(c_0_102, plain, (v1_xboole_0(esk2_1(X1))), inference(evalgc,[status(thm)],[c_0_93])). cnf(c_0_103, negated_conjecture, (v1_xboole_0(u1_struct_0(esk1_0))\|~l1_algstr_0(esk1_0)\|~l2_struct_0(esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94, c_0_95]), c_0_86])])])). cnf(c_0_104, plain, (l2_struct_0(X1)\|~l2_algstr_0(X1)), inference(evalgc,[status(thm)],[c_0_96])). cnf(c_0_105, plain, (l1_algstr_0(X1)\|~l2_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_88])). cnf(c_0_106, plain, (v1_xboole_0(k7_ideal_1(X1,X2))\|v2_struct_0(X1)\|~v1_xboole_0(u1_struct_0(X1))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~l6_algstr_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_97, c_0_98])])). cnf(c_0_107, plain, (v2_struct_0(X1)\|~l6_algstr_0(X1)\|~v1_xboole_0(k7_ideal_1(X1,X2))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(evalgc,[status(thm)],[c_0_99])). cnf(c_0_108, plain, (m1_subset_1(esk2_1(X1),k1_zfmisc_1(X1))), inference(evalgc,[status(thm)],[c_0_100])). cnf(c_0_109, plain, (esk2_1(X1)=esk3_0), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_101, c_0_102])])). cnf(c_0_110, negated_conjecture, (v1_xboole_0(u1_struct_0(esk1_0))\|~l1_algstr_0(esk1_0)\|~l2_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_103, c_0_104])])). cnf(c_0_111, plain, (l1_algstr_0(X1)\|~l2_algstr_0(X1)), inference(evalgc,[status(thm)],[c_0_105])). cnf(c_0_112, plain, (v2_struct_0(X1)\|~v1_xboole_0(u1_struct_0(X1))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~l6_algstr_0(X1)), inference(csr,[status(thm)],[c_0_106, c_0_107])). cnf(c_0_113, plain, (m1_subset_1(esk3_0,k1_zfmisc_1(X1))), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[c_0_108, c_0_109])])). cnf(c_0_114, negated_conjecture, (v1_xboole_0(u1_struct_0(esk1_0))\|~l2_algstr_0(esk1_0)), inference(csr,[status(thm)],[c_0_110, c_0_111])). cnf(c_0_115, plain, (v2_struct_0(X1)\|~v1_xboole_0(u1_struct_0(X1))\|~l6_algstr_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_112, c_0_113])])). cnf(c_0_116, negated_conjecture, (v1_xboole_0(u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114, c_0_45]), c_0_58])])])). cnf(c_0_117, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115, c_0_116]), c_0_58])]), c_0_61]), ['proof']). # SZS output end CNFRefutation	theorem for L being left_zeroed right_zeroed add-cancelable distributive non empty doubleLoopStr holds {0.L}-Ideal = {0.L} by Th44;	Convert the following ATP output trace into a readable Mizar proof.
t79_rfunct_1	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t6_boole, axiom, ![X1]:(v1_xboole_0(X1)=>X1=k1_xboole_0), file('/scratch/mptp/predsminms1/t79_rfunct_1__0', t6_boole)). fof(t79_rfunct_1, conjecture, ![X1, X2]:(v1_xreal_0(X2)=>![X3]:((v1_relat_1(X3)&(v1_funct_1(X3)&v3_valued_0(X3)))=>(((v2_seq_2(k5_relat_1(X3,X1))&r1_xxreal_0(k6_numbers,X2))=>v2_seq_2(k5_relat_1(k24_valued_1(X3,X2),X1)))&((v2_seq_2(k5_relat_1(X3,X1))&r1_xxreal_0(X2,k6_numbers))=>v1_seq_2(k5_relat_1(k24_valued_1(X3,X2),X1)))))), file('/scratch/mptp/predsminms1/t79_rfunct_1__0', t79_rfunct_1)). fof(redefinition_k6_numbers, axiom, k6_numbers=k1_xboole_0, file('/scratch/mptp/predsminms1/t79_rfunct_1__0', redefinition_k6_numbers)). fof(rc4_xreal_0, axiom, ?[X1]:(v1_xboole_0(X1)&(v1_xcmplx_0(X1)&(v1_xxreal_0(X1)&v1_xreal_0(X1)))), file('/scratch/mptp/predsminms1/t79_rfunct_1__0', rc4_xreal_0)). fof(fc9_rfunct_1, axiom, ![X1, X2]:(((v1_relat_1(X1)&(v1_funct_1(X1)&(v3_valued_0(X1)&v2_seq_2(X1))))&(~(v3_xxreal_0(X2))&v1_xreal_0(X2)))=>(v1_relat_1(k24_valued_1(X1,X2))&(v1_funct_1(k24_valued_1(X1,X2))&(v3_valued_0(k24_valued_1(X1,X2))&v2_seq_2(k24_valued_1(X1,X2)))))), file('/scratch/mptp/predsminms1/t79_rfunct_1__0', fc9_rfunct_1)). fof(fc45_valued_0, axiom, ![X1, X2]:((v1_relat_1(X1)&v3_valued_0(X1))=>(v1_relat_1(k5_relat_1(X1,X2))&v3_valued_0(k5_relat_1(X1,X2)))), file('/scratch/mptp/predsminms1/t79_rfunct_1__0', fc45_valued_0)). fof(t49_rfunct_1, axiom, ![X1, X2]:((v1_relat_1(X2)&(v1_funct_1(X2)&v1_valued_0(X2)))=>![X3]:(v1_xcmplx_0(X3)=>k5_relat_1(k24_valued_1(X2,X3),X1)=k24_valued_1(k5_relat_1(X2,X1),X3))), file('/scratch/mptp/predsminms1/t79_rfunct_1__0', t49_rfunct_1)). fof(cc6_valued_0, axiom, ![X1]:((v1_relat_1(X1)&v3_valued_0(X1))=>(v1_relat_1(X1)&v1_valued_0(X1))), file('/scratch/mptp/predsminms1/t79_rfunct_1__0', cc6_valued_0)). fof(t3_real, axiom, ![X1]:(v1_xreal_0(X1)=>![X2]:(v1_xreal_0(X2)=>~((r1_xxreal_0(X1,X2)&(~(v3_xxreal_0(X1))&v3_xxreal_0(X2)))))), file('/scratch/mptp/predsminms1/t79_rfunct_1__0', t3_real)). fof(cc5_xxreal_0, axiom, ![X1]:((v1_xxreal_0(X1)&v3_xxreal_0(X1))=>(~(v1_xboole_0(X1))&(v1_xxreal_0(X1)&~(v2_xxreal_0(X1))))), file('/scratch/mptp/predsminms1/t79_rfunct_1__0', cc5_xxreal_0)). fof(cc3_xxreal_0, axiom, ![X1]:((v1_xxreal_0(X1)&v2_xxreal_0(X1))=>(~(v1_xboole_0(X1))&(v1_xxreal_0(X1)&~(v3_xxreal_0(X1))))), file('/scratch/mptp/predsminms1/t79_rfunct_1__0', cc3_xxreal_0)). fof(dt_k5_relat_1, axiom, ![X1, X2]:(v1_relat_1(X1)=>v1_relat_1(k5_relat_1(X1,X2))), file('/scratch/mptp/predsminms1/t79_rfunct_1__0', dt_k5_relat_1)). fof(cc3_xreal_0, axiom, ![X1]:(v1_xreal_0(X1)=>v1_xcmplx_0(X1)), file('/scratch/mptp/predsminms1/t79_rfunct_1__0', cc3_xreal_0)). fof(t4_real, axiom, ![X1]:(v1_xreal_0(X1)=>![X2]:(v1_xreal_0(X2)=>~((r1_xxreal_0(X1,X2)&(~(v2_xxreal_0(X2))&v2_xxreal_0(X1)))))), file('/scratch/mptp/predsminms1/t79_rfunct_1__0', t4_real)). fof(fc11_rfunct_1, axiom, ![X1, X2]:(((v1_relat_1(X1)&(v1_funct_1(X1)&(v3_valued_0(X1)&v2_seq_2(X1))))&(~(v2_xxreal_0(X2))&v1_xreal_0(X2)))=>(v1_relat_1(k24_valued_1(X1,X2))&(v1_funct_1(k24_valued_1(X1,X2))&(v3_valued_0(k24_valued_1(X1,X2))&v1_seq_2(k24_valued_1(X1,X2)))))), file('/scratch/mptp/predsminms1/t79_rfunct_1__0', fc11_rfunct_1)). fof(fc8_funct_1, axiom, ![X1, X2]:((v1_relat_1(X1)&v1_funct_1(X1))=>(v1_relat_1(k5_relat_1(X1,X2))&v1_funct_1(k5_relat_1(X1,X2)))), file('/scratch/mptp/predsminms1/t79_rfunct_1__0', fc8_funct_1)). fof(c_0_16, plain, ![X8]:(~v1_xboole_0(X8)\|X8=k1_xboole_0), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])])). fof(c_0_17, negated_conjecture, ~(![X1, X2]:(v1_xreal_0(X2)=>![X3]:((v1_relat_1(X3)&(v1_funct_1(X3)&v3_valued_0(X3)))=>(((v2_seq_2(k5_relat_1(X3,X1))&r1_xxreal_0(k6_numbers,X2))=>v2_seq_2(k5_relat_1(k24_valued_1(X3,X2),X1)))&((v2_seq_2(k5_relat_1(X3,X1))&r1_xxreal_0(X2,k6_numbers))=>v1_seq_2(k5_relat_1(k24_valued_1(X3,X2),X1))))))), inference(assume_negation,[status(cth)],[t79_rfunct_1])). cnf(c_0_18, plain, (X1=k1_xboole_0\|~v1_xboole_0(X1)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_19, plain, (k6_numbers=k1_xboole_0), inference(split_conjunct,[status(thm)],[redefinition_k6_numbers])). fof(c_0_20, plain, (v1_xboole_0(esk4_0)&(v1_xcmplx_0(esk4_0)&(v1_xxreal_0(esk4_0)&v1_xreal_0(esk4_0)))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc4_xreal_0])])). fof(c_0_21, plain, ![X10, X11]:((v1_relat_1(k24_valued_1(X10,X11))\|(~v1_relat_1(X10)\|(~v1_funct_1(X10)\|(~v3_valued_0(X10)\|~v2_seq_2(X10)))\|(v3_xxreal_0(X11)\|~v1_xreal_0(X11))))&((v1_funct_1(k24_valued_1(X10,X11))\|(~v1_relat_1(X10)\|(~v1_funct_1(X10)\|(~v3_valued_0(X10)\|~v2_seq_2(X10)))\|(v3_xxreal_0(X11)\|~v1_xreal_0(X11))))&((v3_valued_0(k24_valued_1(X10,X11))\|(~v1_relat_1(X10)\|(~v1_funct_1(X10)\|(~v3_valued_0(X10)\|~v2_seq_2(X10)))\|(v3_xxreal_0(X11)\|~v1_xreal_0(X11))))&(v2_seq_2(k24_valued_1(X10,X11))\|(~v1_relat_1(X10)\|(~v1_funct_1(X10)\|(~v3_valued_0(X10)\|~v2_seq_2(X10)))\|(v3_xxreal_0(X11)\|~v1_xreal_0(X11))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fc9_rfunct_1])])])])). fof(c_0_22, plain, ![X22, X23]:((v1_relat_1(k5_relat_1(X22,X23))\|(~v1_relat_1(X22)\|~v3_valued_0(X22)))&(v3_valued_0(k5_relat_1(X22,X23))\|(~v1_relat_1(X22)\|~v3_valued_0(X22)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc45_valued_0])])])). fof(c_0_23, plain, ![X14, X15, X16]:(~v1_relat_1(X15)\|(~v1_funct_1(X15)\|~v1_valued_0(X15))\|(~v1_xcmplx_0(X16)\|k5_relat_1(k24_valued_1(X15,X16),X14)=k24_valued_1(k5_relat_1(X15,X14),X16))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t49_rfunct_1])])])). fof(c_0_24, plain, ![X12]:((v1_relat_1(X12)\|(~v1_relat_1(X12)\|~v3_valued_0(X12)))&(v1_valued_0(X12)\|(~v1_relat_1(X12)\|~v3_valued_0(X12)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc6_valued_0])])])). fof(c_0_25, plain, ![X17, X18]:(~v1_xreal_0(X17)\|(~v1_xreal_0(X18)\|(~r1_xxreal_0(X17,X18)\|(v3_xxreal_0(X17)\|~v3_xxreal_0(X18))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t3_real])])])])). fof(c_0_26, negated_conjecture, (v1_xreal_0(esk2_0)&((v1_relat_1(esk3_0)&(v1_funct_1(esk3_0)&v3_valued_0(esk3_0)))&(((((v2_seq_2(k5_relat_1(esk3_0,esk1_0))\|v2_seq_2(k5_relat_1(esk3_0,esk1_0)))&(r1_xxreal_0(esk2_0,k6_numbers)\|v2_seq_2(k5_relat_1(esk3_0,esk1_0))))&(~v1_seq_2(k5_relat_1(k24_valued_1(esk3_0,esk2_0),esk1_0))\|v2_seq_2(k5_relat_1(esk3_0,esk1_0))))&(((v2_seq_2(k5_relat_1(esk3_0,esk1_0))\|r1_xxreal_0(k6_numbers,esk2_0))&(r1_xxreal_0(esk2_0,k6_numbers)\|r1_xxreal_0(k6_numbers,esk2_0)))&(~v1_seq_2(k5_relat_1(k24_valued_1(esk3_0,esk2_0),esk1_0))\|r1_xxreal_0(k6_numbers,esk2_0))))&(((v2_seq_2(k5_relat_1(esk3_0,esk1_0))\|~v2_seq_2(k5_relat_1(k24_valued_1(esk3_0,esk2_0),esk1_0)))&(r1_xxreal_0(esk2_0,k6_numbers)\|~v2_seq_2(k5_relat_1(k24_valued_1(esk3_0,esk2_0),esk1_0))))&(~v1_seq_2(k5_relat_1(k24_valued_1(esk3_0,esk2_0),esk1_0))\|~v2_seq_2(k5_relat_1(k24_valued_1(esk3_0,esk2_0),esk1_0))))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])])). cnf(c_0_27, plain, (X1=k1_xboole_0\|~v1_xboole_0(X1)), inference(evalgc,[status(thm)],[c_0_18])). cnf(c_0_28, plain, (k1_xboole_0=k6_numbers), inference(evalgc,[status(thm)],[c_0_19])). cnf(c_0_29, plain, (v1_xboole_0(esk4_0)), inference(split_conjunct,[status(thm)],[c_0_20])). fof(c_0_30, plain, ![X9]:((~v1_xboole_0(X9)\|(~v1_xxreal_0(X9)\|~v3_xxreal_0(X9)))&((v1_xxreal_0(X9)\|(~v1_xxreal_0(X9)\|~v3_xxreal_0(X9)))&(~v2_xxreal_0(X9)\|(~v1_xxreal_0(X9)\|~v3_xxreal_0(X9))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[cc5_xxreal_0])])])])). fof(c_0_31, plain, ![X19]:((~v1_xboole_0(X19)\|(~v1_xxreal_0(X19)\|~v2_xxreal_0(X19)))&((v1_xxreal_0(X19)\|(~v1_xxreal_0(X19)\|~v2_xxreal_0(X19)))&(~v3_xxreal_0(X19)\|(~v1_xxreal_0(X19)\|~v2_xxreal_0(X19))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[cc3_xxreal_0])])])])). cnf(c_0_32, plain, (v2_seq_2(k24_valued_1(X1,X2))\|v3_xxreal_0(X2)\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v3_valued_0(X1)\|~v2_seq_2(X1)\|~v1_xreal_0(X2)), inference(split_conjunct,[status(thm)],[c_0_21])). cnf(c_0_33, plain, (v3_valued_0(k5_relat_1(X1,X2))\|~v1_relat_1(X1)\|~v3_valued_0(X1)), inference(split_conjunct,[status(thm)],[c_0_22])). fof(c_0_34, plain, ![X26, X27]:(~v1_relat_1(X26)\|v1_relat_1(k5_relat_1(X26,X27))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k5_relat_1])])). cnf(c_0_35, plain, (k5_relat_1(k24_valued_1(X1,X2),X3)=k24_valued_1(k5_relat_1(X1,X3),X2)\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v1_valued_0(X1)\|~v1_xcmplx_0(X2)), inference(split_conjunct,[status(thm)],[c_0_23])). cnf(c_0_36, plain, (v1_valued_0(X1)\|~v1_relat_1(X1)\|~v3_valued_0(X1)), inference(split_conjunct,[status(thm)],[c_0_24])). fof(c_0_37, plain, ![X13]:(~v1_xreal_0(X13)\|v1_xcmplx_0(X13)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc3_xreal_0])])). cnf(c_0_38, plain, (v3_xxreal_0(X1)\|~v1_xreal_0(X1)\|~v1_xreal_0(X2)\|~r1_xxreal_0(X1,X2)\|~v3_xxreal_0(X2)), inference(split_conjunct,[status(thm)],[c_0_25])). cnf(c_0_39, negated_conjecture, (r1_xxreal_0(esk2_0,k6_numbers)\|r1_xxreal_0(k6_numbers,esk2_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_40, negated_conjecture, (v1_xreal_0(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_41, plain, (v1_xreal_0(esk4_0)), inference(split_conjunct,[status(thm)],[c_0_20])). cnf(c_0_42, plain, (X1=k6_numbers\|~v1_xboole_0(X1)), inference(rw,[status(thm)],[c_0_27, c_0_28])). cnf(c_0_43, plain, (v1_xboole_0(esk4_0)), inference(evalgc,[status(thm)],[c_0_29])). cnf(c_0_44, plain, (~v1_xboole_0(X1)\|~v1_xxreal_0(X1)\|~v3_xxreal_0(X1)), inference(split_conjunct,[status(thm)],[c_0_30])). cnf(c_0_45, plain, (v1_xxreal_0(esk4_0)), inference(split_conjunct,[status(thm)],[c_0_20])). fof(c_0_46, plain, ![X28, X29]:(~v1_xreal_0(X28)\|(~v1_xreal_0(X29)\|(~r1_xxreal_0(X28,X29)\|(v2_xxreal_0(X29)\|~v2_xxreal_0(X28))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t4_real])])])])). cnf(c_0_47, plain, (~v1_xboole_0(X1)\|~v1_xxreal_0(X1)\|~v2_xxreal_0(X1)), inference(split_conjunct,[status(thm)],[c_0_31])). cnf(c_0_48, plain, (v3_xxreal_0(X2)\|v2_seq_2(k24_valued_1(X1,X2))\|~v1_xreal_0(X2)\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v3_valued_0(X1)\|~v2_seq_2(X1)), inference(evalgc,[status(thm)],[c_0_32])). cnf(c_0_49, plain, (v3_valued_0(k5_relat_1(X1,X2))\|~v1_relat_1(X1)\|~v3_valued_0(X1)), inference(evalgc,[status(thm)],[c_0_33])). cnf(c_0_50, plain, (v1_relat_1(k5_relat_1(X1,X2))\|~v1_relat_1(X1)), inference(split_conjunct,[status(thm)],[c_0_34])). cnf(c_0_51, plain, (k24_valued_1(k5_relat_1(X1,X3),X2)=k5_relat_1(k24_valued_1(X1,X2),X3)\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v1_xcmplx_0(X2)\|~v1_valued_0(X1)), inference(evalgc,[status(thm)],[c_0_35])). cnf(c_0_52, plain, (v1_valued_0(X1)\|~v1_relat_1(X1)\|~v3_valued_0(X1)), inference(evalgc,[status(thm)],[c_0_36])). cnf(c_0_53, plain, (v1_xcmplx_0(X1)\|~v1_xreal_0(X1)), inference(split_conjunct,[status(thm)],[c_0_37])). fof(c_0_54, plain, ![X20, X21]:((v1_relat_1(k24_valued_1(X20,X21))\|(~v1_relat_1(X20)\|(~v1_funct_1(X20)\|(~v3_valued_0(X20)\|~v2_seq_2(X20)))\|(v2_xxreal_0(X21)\|~v1_xreal_0(X21))))&((v1_funct_1(k24_valued_1(X20,X21))\|(~v1_relat_1(X20)\|(~v1_funct_1(X20)\|(~v3_valued_0(X20)\|~v2_seq_2(X20)))\|(v2_xxreal_0(X21)\|~v1_xreal_0(X21))))&((v3_valued_0(k24_valued_1(X20,X21))\|(~v1_relat_1(X20)\|(~v1_funct_1(X20)\|(~v3_valued_0(X20)\|~v2_seq_2(X20)))\|(v2_xxreal_0(X21)\|~v1_xreal_0(X21))))&(v1_seq_2(k24_valued_1(X20,X21))\|(~v1_relat_1(X20)\|(~v1_funct_1(X20)\|(~v3_valued_0(X20)\|~v2_seq_2(X20)))\|(v2_xxreal_0(X21)\|~v1_xreal_0(X21))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fc11_rfunct_1])])])])). cnf(c_0_55, plain, (v3_xxreal_0(X1)\|~v1_xreal_0(X2)\|~v1_xreal_0(X1)\|~v3_xxreal_0(X2)\|~r1_xxreal_0(X1,X2)), inference(evalgc,[status(thm)],[c_0_38])). cnf(c_0_56, negated_conjecture, (r1_xxreal_0(k6_numbers,esk2_0)\|r1_xxreal_0(esk2_0,k6_numbers)), inference(evalgc,[status(thm)],[c_0_39])). cnf(c_0_57, negated_conjecture, (v1_xreal_0(esk2_0)), inference(evalgc,[status(thm)],[c_0_40])). cnf(c_0_58, plain, (v1_xreal_0(esk4_0)), inference(evalgc,[status(thm)],[c_0_41])). cnf(c_0_59, plain, (esk4_0=k6_numbers), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_42, c_0_43])])). cnf(c_0_60, plain, (~v1_xboole_0(X1)\|~v1_xxreal_0(X1)\|~v3_xxreal_0(X1)), inference(evalgc,[status(thm)],[c_0_44])). cnf(c_0_61, plain, (v1_xxreal_0(esk4_0)), inference(evalgc,[status(thm)],[c_0_45])). cnf(c_0_62, plain, (v2_xxreal_0(X2)\|~v1_xreal_0(X1)\|~v1_xreal_0(X2)\|~r1_xxreal_0(X1,X2)\|~v2_xxreal_0(X1)), inference(split_conjunct,[status(thm)],[c_0_46])). cnf(c_0_63, negated_conjecture, (r1_xxreal_0(esk2_0,k6_numbers)\|~v2_seq_2(k5_relat_1(k24_valued_1(esk3_0,esk2_0),esk1_0))), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_64, plain, (~v1_xboole_0(X1)\|~v1_xxreal_0(X1)\|~v2_xxreal_0(X1)), inference(evalgc,[status(thm)],[c_0_47])). cnf(c_0_65, plain, (v3_xxreal_0(X1)\|v2_seq_2(k24_valued_1(k5_relat_1(X2,X3),X1))\|~v2_seq_2(k5_relat_1(X2,X3))\|~v1_funct_1(k5_relat_1(X2,X3))\|~v1_relat_1(k5_relat_1(X2,X3))\|~v1_xreal_0(X1)\|~v3_valued_0(X2)\|~v1_relat_1(X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_48, c_0_49])])). cnf(c_0_66, plain, (v1_relat_1(k5_relat_1(X1,X2))\|~v1_relat_1(X1)), inference(evalgc,[status(thm)],[c_0_50])). cnf(c_0_67, plain, (k24_valued_1(k5_relat_1(X1,X2),X3)=k5_relat_1(k24_valued_1(X1,X3),X2)\|~v1_xcmplx_0(X3)\|~v1_funct_1(X1)\|~v1_relat_1(X1)\|~v3_valued_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_51, c_0_52])])). cnf(c_0_68, plain, (v1_xcmplx_0(X1)\|~v1_xreal_0(X1)), inference(evalgc,[status(thm)],[c_0_53])). fof(c_0_69, plain, ![X24, X25]:((v1_relat_1(k5_relat_1(X24,X25))\|(~v1_relat_1(X24)\|~v1_funct_1(X24)))&(v1_funct_1(k5_relat_1(X24,X25))\|(~v1_relat_1(X24)\|~v1_funct_1(X24)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc8_funct_1])])])). cnf(c_0_70, plain, (v1_seq_2(k24_valued_1(X1,X2))\|v2_xxreal_0(X2)\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v3_valued_0(X1)\|~v2_seq_2(X1)\|~v1_xreal_0(X2)), inference(split_conjunct,[status(thm)],[c_0_54])). cnf(c_0_71, negated_conjecture, (v3_xxreal_0(k6_numbers)\|r1_xxreal_0(esk2_0,k6_numbers)\|~v3_xxreal_0(esk2_0)\|~v1_xreal_0(k6_numbers)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55, c_0_56]), c_0_57])])])). cnf(c_0_72, plain, (v1_xreal_0(k6_numbers)), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[c_0_58, c_0_59])])). cnf(c_0_73, plain, (~v3_xxreal_0(esk4_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60, c_0_61]), c_0_43])])])). cnf(c_0_74, plain, (v2_xxreal_0(X2)\|~v1_xreal_0(X2)\|~v1_xreal_0(X1)\|~v2_xxreal_0(X1)\|~r1_xxreal_0(X1,X2)), inference(evalgc,[status(thm)],[c_0_62])). cnf(c_0_75, negated_conjecture, (r1_xxreal_0(esk2_0,k6_numbers)\|~v2_seq_2(k5_relat_1(k24_valued_1(esk3_0,esk2_0),esk1_0))), inference(evalgc,[status(thm)],[c_0_63])). cnf(c_0_76, plain, (~v2_xxreal_0(esk4_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64, c_0_61]), c_0_43])])])). cnf(c_0_77, plain, (v3_xxreal_0(X1)\|v2_seq_2(k24_valued_1(k5_relat_1(X2,X3),X1))\|~v2_seq_2(k5_relat_1(X2,X3))\|~v3_valued_0(X2)\|~v1_funct_1(k5_relat_1(X2,X3))\|~v1_relat_1(X2)\|~v1_xreal_0(X1)), inference(csr,[status(thm)],[c_0_65, c_0_66])). cnf(c_0_78, plain, (k24_valued_1(k5_relat_1(X1,X2),X3)=k5_relat_1(k24_valued_1(X1,X3),X2)\|~v3_valued_0(X1)\|~v1_funct_1(X1)\|~v1_relat_1(X1)\|~v1_xreal_0(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_67, c_0_68])])). cnf(c_0_79, plain, (v1_funct_1(k5_relat_1(X1,X2))\|~v1_relat_1(X1)\|~v1_funct_1(X1)), inference(split_conjunct,[status(thm)],[c_0_69])). cnf(c_0_80, negated_conjecture, (v2_seq_2(k5_relat_1(esk3_0,esk1_0))\|v2_seq_2(k5_relat_1(esk3_0,esk1_0))), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_81, plain, (v2_xxreal_0(X2)\|v1_seq_2(k24_valued_1(X1,X2))\|~v1_xreal_0(X2)\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v3_valued_0(X1)\|~v2_seq_2(X1)), inference(evalgc,[status(thm)],[c_0_70])). cnf(c_0_82, negated_conjecture, (v3_xxreal_0(k6_numbers)\|r1_xxreal_0(esk2_0,k6_numbers)\|~v3_xxreal_0(esk2_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_71, c_0_72])])])). cnf(c_0_83, plain, (~v3_xxreal_0(k6_numbers)), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[c_0_73, c_0_59])])). cnf(c_0_84, negated_conjecture, (v2_xxreal_0(k6_numbers)\|~v2_xxreal_0(esk2_0)\|~v1_xreal_0(k6_numbers)\|~v2_seq_2(k5_relat_1(k24_valued_1(esk3_0,esk2_0),esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74, c_0_75]), c_0_57])])])). cnf(c_0_85, plain, (~v2_xxreal_0(k6_numbers)), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[c_0_76, c_0_59])])). cnf(c_0_86, plain, (v3_xxreal_0(X1)\|v2_seq_2(k5_relat_1(k24_valued_1(X2,X1),X3))\|~v2_seq_2(k5_relat_1(X2,X3))\|~v3_valued_0(X2)\|~v1_funct_1(k5_relat_1(X2,X3))\|~v1_relat_1(X2)\|~v1_xreal_0(X1)\|~v1_funct_1(X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_77, c_0_78])])). cnf(c_0_87, plain, (v1_funct_1(k5_relat_1(X1,X2))\|~v1_relat_1(X1)\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[c_0_79])). cnf(c_0_88, negated_conjecture, (v2_seq_2(k5_relat_1(esk3_0,esk1_0))), inference(cn,[status(thm)],[c_0_80])). cnf(c_0_89, negated_conjecture, (v3_valued_0(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_90, negated_conjecture, (v1_funct_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_91, negated_conjecture, (v1_relat_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_92, negated_conjecture, (~v1_seq_2(k5_relat_1(k24_valued_1(esk3_0,esk2_0),esk1_0))\|~v2_seq_2(k5_relat_1(k24_valued_1(esk3_0,esk2_0),esk1_0))), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_93, plain, (v2_xxreal_0(X1)\|v1_seq_2(k5_relat_1(k24_valued_1(X2,X1),X3))\|~v2_seq_2(k5_relat_1(X2,X3))\|~v3_valued_0(k5_relat_1(X2,X3))\|~v1_funct_1(k5_relat_1(X2,X3))\|~v1_relat_1(k5_relat_1(X2,X3))\|~v1_xreal_0(X1)\|~v3_valued_0(X2)\|~v1_funct_1(X2)\|~v1_relat_1(X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_81, c_0_78])])). cnf(c_0_94, negated_conjecture, (r1_xxreal_0(k6_numbers,esk2_0)\|~v1_seq_2(k5_relat_1(k24_valued_1(esk3_0,esk2_0),esk1_0))), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_95, negated_conjecture, (r1_xxreal_0(esk2_0,k6_numbers)\|~v3_xxreal_0(esk2_0)), inference(sr,[status(thm)],[c_0_82, c_0_83])). cnf(c_0_96, negated_conjecture, (~v2_xxreal_0(esk2_0)\|~v2_seq_2(k5_relat_1(k24_valued_1(esk3_0,esk2_0),esk1_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_84, c_0_72])]), c_0_85])])). cnf(c_0_97, plain, (v3_xxreal_0(X1)\|v2_seq_2(k5_relat_1(k24_valued_1(X2,X1),X3))\|~v2_seq_2(k5_relat_1(X2,X3))\|~v3_valued_0(X2)\|~v1_funct_1(X2)\|~v1_relat_1(X2)\|~v1_xreal_0(X1)), inference(csr,[status(thm)],[c_0_86, c_0_87])). cnf(c_0_98, negated_conjecture, (v2_seq_2(k5_relat_1(esk3_0,esk1_0))), inference(evalgc,[status(thm)],[c_0_88])). cnf(c_0_99, negated_conjecture, (v3_valued_0(esk3_0)), inference(evalgc,[status(thm)],[c_0_89])). cnf(c_0_100, negated_conjecture, (v1_funct_1(esk3_0)), inference(evalgc,[status(thm)],[c_0_90])). cnf(c_0_101, negated_conjecture, (v1_relat_1(esk3_0)), inference(evalgc,[status(thm)],[c_0_91])). cnf(c_0_102, negated_conjecture, (~v2_seq_2(k5_relat_1(k24_valued_1(esk3_0,esk2_0),esk1_0))\|~v1_seq_2(k5_relat_1(k24_valued_1(esk3_0,esk2_0),esk1_0))), inference(evalgc,[status(thm)],[c_0_92])). cnf(c_0_103, plain, (v2_xxreal_0(X1)\|v1_seq_2(k5_relat_1(k24_valued_1(X2,X1),X3))\|~v2_seq_2(k5_relat_1(X2,X3))\|~v3_valued_0(X2)\|~v1_funct_1(X2)\|~v1_relat_1(X2)\|~v1_xreal_0(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_93, c_0_66]), c_0_87]), c_0_49])). cnf(c_0_104, negated_conjecture, (r1_xxreal_0(k6_numbers,esk2_0)\|~v1_seq_2(k5_relat_1(k24_valued_1(esk3_0,esk2_0),esk1_0))), inference(evalgc,[status(thm)],[c_0_94])). cnf(c_0_105, negated_conjecture, (~v2_xxreal_0(esk2_0)\|~v3_xxreal_0(esk2_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74, c_0_95]), c_0_72]), c_0_57])]), c_0_85])])). cnf(c_0_106, negated_conjecture, (v3_xxreal_0(esk2_0)\|~v2_xxreal_0(esk2_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96, c_0_97]), c_0_98]), c_0_99]), c_0_100]), c_0_101]), c_0_57])])])). cnf(c_0_107, negated_conjecture, (v2_xxreal_0(esk2_0)\|~v2_seq_2(k5_relat_1(k24_valued_1(esk3_0,esk2_0),esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102, c_0_103]), c_0_98]), c_0_99]), c_0_100]), c_0_101]), c_0_57])])])). cnf(c_0_108, negated_conjecture, (r1_xxreal_0(k6_numbers,esk2_0)\|v2_xxreal_0(esk2_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104, c_0_103]), c_0_98]), c_0_99]), c_0_100]), c_0_101]), c_0_57])])])). cnf(c_0_109, negated_conjecture, (~v2_xxreal_0(esk2_0)), inference(csr,[status(thm)],[c_0_105, c_0_106])). cnf(c_0_110, negated_conjecture, (~v2_seq_2(k5_relat_1(k24_valued_1(esk3_0,esk2_0),esk1_0))), inference(csr,[status(thm)],[c_0_107, c_0_96])). cnf(c_0_111, negated_conjecture, (r1_xxreal_0(k6_numbers,esk2_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[c_0_108, c_0_109])])). cnf(c_0_112, negated_conjecture, (v3_xxreal_0(esk2_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110, c_0_97]), c_0_98]), c_0_99]), c_0_100]), c_0_101]), c_0_57])])])). cnf(c_0_113, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55, c_0_111]), c_0_112]), c_0_57]), c_0_72])]), c_0_83]), ['proof']). # SZS output end CNFRefutation	reserve x,X,Y for set; reserve C for non empty set; reserve c for Element of C; reserve f,f1,f2,f3,g,g1 for complex-valued Function; reserve r,p for complex number; reserve r,r1,r2,p for real number; reserve f,f1,f2 for PartFunc of C,REAL; reserve f for real-valued Function; theorem Th79: (f\|Y is bounded_below & 0<=r implies (r(#)f)\|Y is bounded_below) & (f\|Y is bounded_below & r<=0 implies (r(#)f)\|Y is bounded_above) proof (r(#)f)\|Y = r(#)(f\|Y) by Th49; hence thesis; end;	Convert the following ATP output trace into a readable Mizar proof.
t9_scmring3	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t9_scmring3, conjecture, ![X1]:((~(v2_struct_0(X1))&(v13_algstr_0(X1)&(v2_rlvect_1(X1)&(v3_rlvect_1(X1)&(v4_rlvect_1(X1)&(v3_group_1(X1)&(v4_vectsp_1(X1)&(v5_vectsp_1(X1)&l6_algstr_0(X1)))))))))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:((v1_ami_2(X3)&m1_subset_1(X3,u1_struct_0(k1_scmring2(X1))))=>k2_compos_0(u1_compos_1(k1_scmring2(X1)),k7_scmring2(X1,X3,X2))=np__5))), file('/scratch/mptp/predsminms1/t9_scmring3__0', t9_scmring3)). fof(redefinition_k2_compos_0, axiom, ![X1, X2]:(((~(v1_xboole_0(X1))&v1_compos_0(X1))&m1_subset_1(X2,X1))=>k2_compos_0(X1,X2)=k4_xtuple_0(X2)), file('/scratch/mptp/predsminms1/t9_scmring3__0', redefinition_k2_compos_0)). fof(d6_xtuple_0, axiom, ![X1]:k4_xtuple_0(X1)=k1_xtuple_0(k1_xtuple_0(X1)), file('/scratch/mptp/predsminms1/t9_scmring3__0', d6_xtuple_0)). fof(d1_recdef_2, axiom, ![X1]:(v2_xtuple_0(X1)=>![X2]:(X2=k4_xtuple_0(X1)<=>![X3, X4, X5]:(X1=k3_xtuple_0(X3,X4,X5)=>X2=X3))), file('/scratch/mptp/predsminms1/t9_scmring3__0', d1_recdef_2)). fof(d4_xtuple_0, axiom, ![X1, X2, X3]:k3_xtuple_0(X1,X2,X3)=k4_tarski(k4_tarski(X1,X2),X3), file('/scratch/mptp/predsminms1/t9_scmring3__0', d4_xtuple_0)). fof(d5_tarski, axiom, ![X1, X2]:k4_tarski(X1,X2)=k2_tarski(k2_tarski(X1,X2),k1_tarski(X1)), file('/scratch/mptp/predsminms1/t9_scmring3__0', d5_tarski)). fof(fc2_xtuple_0, axiom, ![X1, X2, X3]:v2_xtuple_0(k3_xtuple_0(X1,X2,X3)), file('/scratch/mptp/predsminms1/t9_scmring3__0', fc2_xtuple_0)). fof(d7_scmring2, axiom, ![X1]:((~(v2_struct_0(X1))&(v13_algstr_0(X1)&(v2_rlvect_1(X1)&(v3_rlvect_1(X1)&(v4_rlvect_1(X1)&(v3_group_1(X1)&(v4_vectsp_1(X1)&(v5_vectsp_1(X1)&l6_algstr_0(X1)))))))))=>![X2]:((v1_ami_2(X2)&m1_subset_1(X2,u1_struct_0(k1_scmring2(X1))))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>k7_scmring2(X1,X2,X3)=k3_xtuple_0(np__5,k1_xboole_0,k10_finseq_1(X2,X3))))), file('/scratch/mptp/predsminms1/t9_scmring3__0', d7_scmring2)). fof(dt_k7_scmring2, axiom, ![X1, X2, X3]:(((~(v2_struct_0(X1))&(v13_algstr_0(X1)&(v2_rlvect_1(X1)&(v3_rlvect_1(X1)&(v4_rlvect_1(X1)&(v3_group_1(X1)&(v4_vectsp_1(X1)&(v5_vectsp_1(X1)&l6_algstr_0(X1)))))))))&((v1_ami_2(X2)&m1_subset_1(X2,u1_struct_0(k1_scmring2(X1))))&m1_subset_1(X3,u1_struct_0(X1))))=>m1_subset_1(k7_scmring2(X1,X2,X3),u1_compos_1(k1_scmring2(X1)))), file('/scratch/mptp/predsminms1/t9_scmring3__0', dt_k7_scmring2)). fof(commutativity_k2_tarski, axiom, ![X1, X2]:k2_tarski(X1,X2)=k2_tarski(X2,X1), file('/scratch/mptp/predsminms1/t9_scmring3__0', commutativity_k2_tarski)). fof(cc2_compos_0, axiom, ![X1]:(v5_compos_0(X1)=>~(v1_xboole_0(X1))), file('/scratch/mptp/predsminms1/t9_scmring3__0', cc2_compos_0)). fof(dt_u1_compos_1, axiom, ![X1]:(l1_compos_1(X1)=>(v1_compos_0(u1_compos_1(X1))&(v2_compos_0(u1_compos_1(X1))&(v3_compos_0(u1_compos_1(X1))&v5_compos_0(u1_compos_1(X1)))))), file('/scratch/mptp/predsminms1/t9_scmring3__0', dt_u1_compos_1)). fof(dt_l1_extpro_1, axiom, ![X1, X2]:(l1_extpro_1(X2,X1)=>(l1_memstr_0(X2,X1)&l1_compos_1(X2))), file('/scratch/mptp/predsminms1/t9_scmring3__0', dt_l1_extpro_1)). fof(dt_k1_scmring2, axiom, ![X1]:((~(v2_struct_0(X1))&(v13_algstr_0(X1)&(v2_rlvect_1(X1)&(v3_rlvect_1(X1)&(v4_rlvect_1(X1)&(v3_group_1(X1)&(v4_vectsp_1(X1)&(v5_vectsp_1(X1)&l6_algstr_0(X1)))))))))=>(v1_extpro_1(k1_scmring2(X1),np__2)&l1_extpro_1(k1_scmring2(X1),np__2))), file('/scratch/mptp/predsminms1/t9_scmring3__0', dt_k1_scmring2)). fof(c_0_14, negated_conjecture, ~(![X1]:((~(v2_struct_0(X1))&(v13_algstr_0(X1)&(v2_rlvect_1(X1)&(v3_rlvect_1(X1)&(v4_rlvect_1(X1)&(v3_group_1(X1)&(v4_vectsp_1(X1)&(v5_vectsp_1(X1)&l6_algstr_0(X1)))))))))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:((v1_ami_2(X3)&m1_subset_1(X3,u1_struct_0(k1_scmring2(X1))))=>k2_compos_0(u1_compos_1(k1_scmring2(X1)),k7_scmring2(X1,X3,X2))=np__5)))), inference(assume_negation,[status(cth)],[t9_scmring3])). fof(c_0_15, plain, ![X32, X33]:(v1_xboole_0(X32)\|~v1_compos_0(X32)\|~m1_subset_1(X33,X32)\|k2_compos_0(X32,X33)=k4_xtuple_0(X33)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[redefinition_k2_compos_0])])])). fof(c_0_16, plain, ![X18]:k4_xtuple_0(X18)=k1_xtuple_0(k1_xtuple_0(X18)), inference(variable_rename,[status(thm)],[d6_xtuple_0])). fof(c_0_17, negated_conjecture, ((~v2_struct_0(esk1_0)&(v13_algstr_0(esk1_0)&(v2_rlvect_1(esk1_0)&(v3_rlvect_1(esk1_0)&(v4_rlvect_1(esk1_0)&(v3_group_1(esk1_0)&(v4_vectsp_1(esk1_0)&(v5_vectsp_1(esk1_0)&l6_algstr_0(esk1_0)))))))))&(m1_subset_1(esk2_0,u1_struct_0(esk1_0))&((v1_ami_2(esk3_0)&m1_subset_1(esk3_0,u1_struct_0(k1_scmring2(esk1_0))))&k2_compos_0(u1_compos_1(k1_scmring2(esk1_0)),k7_scmring2(esk1_0,esk3_0,esk2_0))!=np__5))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_14])])])])). cnf(c_0_18, plain, (v1_xboole_0(X1)\|k2_compos_0(X1,X2)=k4_xtuple_0(X2)\|~v1_compos_0(X1)\|~m1_subset_1(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_19, plain, (k4_xtuple_0(X1)=k1_xtuple_0(k1_xtuple_0(X1))), inference(split_conjunct,[status(thm)],[c_0_16])). fof(c_0_20, plain, ![X9, X10, X11, X12, X13, X14]:((X10!=k4_xtuple_0(X9)\|(X9!=k3_xtuple_0(X11,X12,X13)\|X10=X11)\|~v2_xtuple_0(X9))&((X9=k3_xtuple_0(esk4_2(X9,X14),esk5_2(X9,X14),esk6_2(X9,X14))\|X14=k4_xtuple_0(X9)\|~v2_xtuple_0(X9))&(X14!=esk4_2(X9,X14)\|X14=k4_xtuple_0(X9)\|~v2_xtuple_0(X9)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_recdef_2])])])])])])). fof(c_0_21, plain, ![X19, X20, X21]:k3_xtuple_0(X19,X20,X21)=k4_tarski(k4_tarski(X19,X20),X21), inference(variable_rename,[status(thm)],[d4_xtuple_0])). fof(c_0_22, plain, ![X22, X23]:k4_tarski(X22,X23)=k2_tarski(k2_tarski(X22,X23),k1_tarski(X22)), inference(variable_rename,[status(thm)],[d5_tarski])). fof(c_0_23, plain, ![X29, X30, X31]:v2_xtuple_0(k3_xtuple_0(X29,X30,X31)), inference(variable_rename,[status(thm)],[fc2_xtuple_0])). fof(c_0_24, plain, ![X24, X25, X26]:(v2_struct_0(X24)\|(~v13_algstr_0(X24)\|(~v2_rlvect_1(X24)\|(~v3_rlvect_1(X24)\|(~v4_rlvect_1(X24)\|(~v3_group_1(X24)\|(~v4_vectsp_1(X24)\|(~v5_vectsp_1(X24)\|~l6_algstr_0(X24))))))))\|(~v1_ami_2(X25)\|~m1_subset_1(X25,u1_struct_0(k1_scmring2(X24)))\|(~m1_subset_1(X26,u1_struct_0(X24))\|k7_scmring2(X24,X25,X26)=k3_xtuple_0(np__5,k1_xboole_0,k10_finseq_1(X25,X26))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d7_scmring2])])])])). cnf(c_0_25, negated_conjecture, (k2_compos_0(u1_compos_1(k1_scmring2(esk1_0)),k7_scmring2(esk1_0,esk3_0,esk2_0))!=np__5), inference(split_conjunct,[status(thm)],[c_0_17])). cnf(c_0_26, plain, (k2_compos_0(X1,X2)=k1_xtuple_0(k1_xtuple_0(X2))\|v1_xboole_0(X1)\|~v1_compos_0(X1)\|~m1_subset_1(X2,X1)), inference(rw,[status(thm)],[c_0_18, c_0_19])). fof(c_0_27, plain, ![X34, X35, X36]:(v2_struct_0(X34)\|(~v13_algstr_0(X34)\|(~v2_rlvect_1(X34)\|(~v3_rlvect_1(X34)\|(~v4_rlvect_1(X34)\|(~v3_group_1(X34)\|(~v4_vectsp_1(X34)\|(~v5_vectsp_1(X34)\|~l6_algstr_0(X34))))))))\|(~v1_ami_2(X35)\|~m1_subset_1(X35,u1_struct_0(k1_scmring2(X34)))\|~m1_subset_1(X36,u1_struct_0(X34)))\|m1_subset_1(k7_scmring2(X34,X35,X36),u1_compos_1(k1_scmring2(X34)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k7_scmring2])])])). cnf(c_0_28, plain, (X1=X3\|X1!=k4_xtuple_0(X2)\|X2!=k3_xtuple_0(X3,X4,X5)\|~v2_xtuple_0(X2)), inference(split_conjunct,[status(thm)],[c_0_20])). cnf(c_0_29, plain, (k3_xtuple_0(X1,X2,X3)=k4_tarski(k4_tarski(X1,X2),X3)), inference(split_conjunct,[status(thm)],[c_0_21])). cnf(c_0_30, plain, (k4_tarski(X1,X2)=k2_tarski(k2_tarski(X1,X2),k1_tarski(X1))), inference(split_conjunct,[status(thm)],[c_0_22])). fof(c_0_31, plain, ![X27, X28]:k2_tarski(X27,X28)=k2_tarski(X28,X27), inference(variable_rename,[status(thm)],[commutativity_k2_tarski])). cnf(c_0_32, plain, (v2_xtuple_0(k3_xtuple_0(X1,X2,X3))), inference(split_conjunct,[status(thm)],[c_0_23])). cnf(c_0_33, plain, (v2_struct_0(X1)\|k7_scmring2(X1,X2,X3)=k3_xtuple_0(np__5,k1_xboole_0,k10_finseq_1(X2,X3))\|~v13_algstr_0(X1)\|~v2_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_group_1(X1)\|~v4_vectsp_1(X1)\|~v5_vectsp_1(X1)\|~l6_algstr_0(X1)\|~v1_ami_2(X2)\|~m1_subset_1(X2,u1_struct_0(k1_scmring2(X1)))\|~m1_subset_1(X3,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_24])). fof(c_0_34, plain, ![X38]:(~v5_compos_0(X38)\|~v1_xboole_0(X38)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[cc2_compos_0])])])). cnf(c_0_35, negated_conjecture, (k2_compos_0(u1_compos_1(k1_scmring2(esk1_0)),k7_scmring2(esk1_0,esk3_0,esk2_0))!=np__5), inference(evalgc,[status(thm)],[c_0_25])). cnf(c_0_36, plain, (k2_compos_0(X1,X2)=k1_xtuple_0(k1_xtuple_0(X2))\|v1_xboole_0(X1)\|~v1_compos_0(X1)\|~m1_subset_1(X2,X1)), inference(evalgc,[status(thm)],[c_0_26])). cnf(c_0_37, plain, (v2_struct_0(X1)\|m1_subset_1(k7_scmring2(X1,X2,X3),u1_compos_1(k1_scmring2(X1)))\|~v13_algstr_0(X1)\|~v2_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_group_1(X1)\|~v4_vectsp_1(X1)\|~v5_vectsp_1(X1)\|~l6_algstr_0(X1)\|~v1_ami_2(X2)\|~m1_subset_1(X2,u1_struct_0(k1_scmring2(X1)))\|~m1_subset_1(X3,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_27])). cnf(c_0_38, negated_conjecture, (v1_ami_2(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_17])). cnf(c_0_39, negated_conjecture, (m1_subset_1(esk3_0,u1_struct_0(k1_scmring2(esk1_0)))), inference(split_conjunct,[status(thm)],[c_0_17])). cnf(c_0_40, negated_conjecture, (m1_subset_1(esk2_0,u1_struct_0(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_17])). cnf(c_0_41, negated_conjecture, (l6_algstr_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_17])). cnf(c_0_42, negated_conjecture, (v5_vectsp_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_17])). cnf(c_0_43, negated_conjecture, (v4_vectsp_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_17])). cnf(c_0_44, negated_conjecture, (v3_group_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_17])). cnf(c_0_45, negated_conjecture, (v4_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_17])). cnf(c_0_46, negated_conjecture, (v3_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_17])). cnf(c_0_47, negated_conjecture, (v2_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_17])). cnf(c_0_48, negated_conjecture, (v13_algstr_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_17])). cnf(c_0_49, negated_conjecture, (~v2_struct_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_17])). cnf(c_0_50, plain, (X1=X3\|X1!=k1_xtuple_0(k1_xtuple_0(X2))\|X2!=k2_tarski(k2_tarski(k2_tarski(k2_tarski(X3,X4),k1_tarski(X3)),X5),k1_tarski(k2_tarski(k2_tarski(X3,X4),k1_tarski(X3))))\|~v2_xtuple_0(X2)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28, c_0_19]), c_0_29]), c_0_30]), c_0_30])). cnf(c_0_51, plain, (k2_tarski(X1,X2)=k2_tarski(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_31])). cnf(c_0_52, plain, (v2_xtuple_0(k2_tarski(k2_tarski(k2_tarski(k2_tarski(X1,X2),k1_tarski(X1)),X3),k1_tarski(k2_tarski(k2_tarski(X1,X2),k1_tarski(X1)))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32, c_0_29]), c_0_30]), c_0_30])). cnf(c_0_53, plain, (k7_scmring2(X1,X2,X3)=k2_tarski(k2_tarski(k2_tarski(k2_tarski(np__5,k1_xboole_0),k1_tarski(np__5)),k10_finseq_1(X2,X3)),k1_tarski(k2_tarski(k2_tarski(np__5,k1_xboole_0),k1_tarski(np__5))))\|v2_struct_0(X1)\|~v13_algstr_0(X1)\|~v2_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_group_1(X1)\|~v4_vectsp_1(X1)\|~v5_vectsp_1(X1)\|~l6_algstr_0(X1)\|~v1_ami_2(X2)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(k1_scmring2(X1)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33, c_0_29]), c_0_30]), c_0_30])). cnf(c_0_54, plain, (~v5_compos_0(X1)\|~v1_xboole_0(X1)), inference(split_conjunct,[status(thm)],[c_0_34])). cnf(c_0_55, negated_conjecture, (v1_xboole_0(u1_compos_1(k1_scmring2(esk1_0)))\|k1_xtuple_0(k1_xtuple_0(k7_scmring2(esk1_0,esk3_0,esk2_0)))!=np__5\|~v1_compos_0(u1_compos_1(k1_scmring2(esk1_0)))\|~m1_subset_1(k7_scmring2(esk1_0,esk3_0,esk2_0),u1_compos_1(k1_scmring2(esk1_0)))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_35, c_0_36])])). cnf(c_0_56, plain, (v2_struct_0(X1)\|m1_subset_1(k7_scmring2(X1,X2,X3),u1_compos_1(k1_scmring2(X1)))\|~v13_algstr_0(X1)\|~v2_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_group_1(X1)\|~v4_vectsp_1(X1)\|~v5_vectsp_1(X1)\|~l6_algstr_0(X1)\|~v1_ami_2(X2)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(k1_scmring2(X1)))), inference(evalgc,[status(thm)],[c_0_37])). cnf(c_0_57, negated_conjecture, (v1_ami_2(esk3_0)), inference(evalgc,[status(thm)],[c_0_38])). cnf(c_0_58, negated_conjecture, (m1_subset_1(esk3_0,u1_struct_0(k1_scmring2(esk1_0)))), inference(evalgc,[status(thm)],[c_0_39])). cnf(c_0_59, negated_conjecture, (m1_subset_1(esk2_0,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[c_0_40])). cnf(c_0_60, negated_conjecture, (l6_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_41])). cnf(c_0_61, negated_conjecture, (v5_vectsp_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_42])). cnf(c_0_62, negated_conjecture, (v4_vectsp_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_43])). cnf(c_0_63, negated_conjecture, (v3_group_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_44])). cnf(c_0_64, negated_conjecture, (v4_rlvect_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_45])). cnf(c_0_65, negated_conjecture, (v3_rlvect_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_46])). cnf(c_0_66, negated_conjecture, (v2_rlvect_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_47])). cnf(c_0_67, negated_conjecture, (v13_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_48])). cnf(c_0_68, negated_conjecture, (~v2_struct_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_49])). fof(c_0_69, plain, ![X37]:((v1_compos_0(u1_compos_1(X37))\|~l1_compos_1(X37))&((v2_compos_0(u1_compos_1(X37))\|~l1_compos_1(X37))&((v3_compos_0(u1_compos_1(X37))\|~l1_compos_1(X37))&(v5_compos_0(u1_compos_1(X37))\|~l1_compos_1(X37))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u1_compos_1])])])). cnf(c_0_70, plain, (X1=X3\|X1!=k1_xtuple_0(k1_xtuple_0(X2))\|X2!=k2_tarski(k2_tarski(k2_tarski(k2_tarski(X3,X4),k1_tarski(X3)),X5),k1_tarski(k2_tarski(k2_tarski(X3,X4),k1_tarski(X3))))\|~v2_xtuple_0(X2)), inference(evalgc,[status(thm)],[c_0_50])). cnf(c_0_71, plain, (k2_tarski(X1,X2)=k2_tarski(X2,X1)), inference(evalgc,[status(thm)],[c_0_51])). cnf(c_0_72, plain, (v2_xtuple_0(k2_tarski(k2_tarski(k2_tarski(k2_tarski(X1,X2),k1_tarski(X1)),X3),k1_tarski(k2_tarski(k2_tarski(X1,X2),k1_tarski(X1)))))), inference(evalgc,[status(thm)],[c_0_52])). cnf(c_0_73, plain, (k7_scmring2(X1,X2,X3)=k2_tarski(k2_tarski(k2_tarski(k2_tarski(np__5,k1_xboole_0),k1_tarski(np__5)),k10_finseq_1(X2,X3)),k1_tarski(k2_tarski(k2_tarski(np__5,k1_xboole_0),k1_tarski(np__5))))\|v2_struct_0(X1)\|~v13_algstr_0(X1)\|~v2_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_group_1(X1)\|~v4_vectsp_1(X1)\|~v5_vectsp_1(X1)\|~l6_algstr_0(X1)\|~v1_ami_2(X2)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(k1_scmring2(X1)))), inference(evalgc,[status(thm)],[c_0_53])). cnf(c_0_74, plain, (~v1_xboole_0(X1)\|~v5_compos_0(X1)), inference(evalgc,[status(thm)],[c_0_54])). cnf(c_0_75, negated_conjecture, (v1_xboole_0(u1_compos_1(k1_scmring2(esk1_0)))\|k1_xtuple_0(k1_xtuple_0(k7_scmring2(esk1_0,esk3_0,esk2_0)))!=np__5\|~v1_compos_0(u1_compos_1(k1_scmring2(esk1_0)))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55, c_0_56]), c_0_57]), c_0_58]), c_0_59]), c_0_60]), c_0_61]), c_0_62]), c_0_63]), c_0_64]), c_0_65]), c_0_66]), c_0_67])]), c_0_68])])). cnf(c_0_76, plain, (v5_compos_0(u1_compos_1(X1))\|~l1_compos_1(X1)), inference(split_conjunct,[status(thm)],[c_0_69])). cnf(c_0_77, plain, (X1=X2\|X3!=k2_tarski(k1_tarski(k2_tarski(k2_tarski(X2,X4),k1_tarski(X2))),k2_tarski(k2_tarski(k2_tarski(X2,X4),k1_tarski(X2)),X5))\|X1!=k1_xtuple_0(k1_xtuple_0(X3))\|~v2_xtuple_0(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_70, c_0_71])])). cnf(c_0_78, plain, (v2_xtuple_0(k2_tarski(k1_tarski(k2_tarski(k2_tarski(X1,X2),k1_tarski(X1))),k2_tarski(k2_tarski(k2_tarski(X1,X2),k1_tarski(X1)),X3)))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_72, c_0_71])])). cnf(c_0_79, plain, (k7_scmring2(X1,X2,X3)=k2_tarski(k1_tarski(k2_tarski(k2_tarski(np__5,k1_xboole_0),k1_tarski(np__5))),k2_tarski(k2_tarski(k2_tarski(np__5,k1_xboole_0),k1_tarski(np__5)),k10_finseq_1(X2,X3)))\|v2_struct_0(X1)\|~v1_ami_2(X2)\|~m1_subset_1(X2,u1_struct_0(k1_scmring2(X1)))\|~m1_subset_1(X3,u1_struct_0(X1))\|~l6_algstr_0(X1)\|~v5_vectsp_1(X1)\|~v4_vectsp_1(X1)\|~v3_group_1(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v13_algstr_0(X1)), inference(rw,[status(thm)],[c_0_73, c_0_71])). cnf(c_0_80, negated_conjecture, (~v5_compos_0(u1_compos_1(k1_scmring2(esk1_0)))\|k1_xtuple_0(k1_xtuple_0(k7_scmring2(esk1_0,esk3_0,esk2_0)))!=np__5\|~v1_compos_0(u1_compos_1(k1_scmring2(esk1_0)))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_74, c_0_75])])). cnf(c_0_81, plain, (v5_compos_0(u1_compos_1(X1))\|~l1_compos_1(X1)), inference(evalgc,[status(thm)],[c_0_76])). cnf(c_0_82, plain, (v1_compos_0(u1_compos_1(X1))\|~l1_compos_1(X1)), inference(split_conjunct,[status(thm)],[c_0_69])). cnf(c_0_83, plain, (X1=X2\|X1!=k1_xtuple_0(k1_xtuple_0(k2_tarski(k1_tarski(k2_tarski(k2_tarski(X2,X3),k1_tarski(X2))),k2_tarski(k2_tarski(k2_tarski(X2,X3),k1_tarski(X2)),X4))))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_77]), c_0_78])])])). cnf(c_0_84, negated_conjecture, (k2_tarski(k1_tarski(k2_tarski(k2_tarski(np__5,k1_xboole_0),k1_tarski(np__5))),k2_tarski(k2_tarski(k2_tarski(np__5,k1_xboole_0),k1_tarski(np__5)),k10_finseq_1(esk3_0,X1)))=k7_scmring2(esk1_0,esk3_0,X1)\|~m1_subset_1(X1,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79, c_0_58]), c_0_57]), c_0_60]), c_0_61]), c_0_62]), c_0_63]), c_0_64]), c_0_65]), c_0_66]), c_0_67])]), c_0_68])])). fof(c_0_85, plain, ![X39, X40]:((l1_memstr_0(X40,X39)\|~l1_extpro_1(X40,X39))&(l1_compos_1(X40)\|~l1_extpro_1(X40,X39))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_extpro_1])])])). fof(c_0_86, plain, ![X41]:((v1_extpro_1(k1_scmring2(X41),np__2)\|(v2_struct_0(X41)\|(~v13_algstr_0(X41)\|(~v2_rlvect_1(X41)\|(~v3_rlvect_1(X41)\|(~v4_rlvect_1(X41)\|(~v3_group_1(X41)\|(~v4_vectsp_1(X41)\|(~v5_vectsp_1(X41)\|~l6_algstr_0(X41))))))))))&(l1_extpro_1(k1_scmring2(X41),np__2)\|(v2_struct_0(X41)\|(~v13_algstr_0(X41)\|(~v2_rlvect_1(X41)\|(~v3_rlvect_1(X41)\|(~v4_rlvect_1(X41)\|(~v3_group_1(X41)\|(~v4_vectsp_1(X41)\|(~v5_vectsp_1(X41)\|~l6_algstr_0(X41))))))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k1_scmring2])])])])). cnf(c_0_87, negated_conjecture, (k1_xtuple_0(k1_xtuple_0(k7_scmring2(esk1_0,esk3_0,esk2_0)))!=np__5\|~v1_compos_0(u1_compos_1(k1_scmring2(esk1_0)))\|~l1_compos_1(k1_scmring2(esk1_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_80, c_0_81])])). cnf(c_0_88, plain, (v1_compos_0(u1_compos_1(X1))\|~l1_compos_1(X1)), inference(evalgc,[status(thm)],[c_0_82])). cnf(c_0_89, negated_conjecture, (X1=np__5\|X1!=k1_xtuple_0(k1_xtuple_0(k7_scmring2(esk1_0,esk3_0,X2)))\|~m1_subset_1(X2,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_83, c_0_84])])). cnf(c_0_90, plain, (l1_compos_1(X1)\|~l1_extpro_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_85])). cnf(c_0_91, plain, (l1_extpro_1(k1_scmring2(X1),np__2)\|v2_struct_0(X1)\|~v13_algstr_0(X1)\|~v2_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_group_1(X1)\|~v4_vectsp_1(X1)\|~v5_vectsp_1(X1)\|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_86])). cnf(c_0_92, negated_conjecture, (k1_xtuple_0(k1_xtuple_0(k7_scmring2(esk1_0,esk3_0,esk2_0)))!=np__5\|~l1_compos_1(k1_scmring2(esk1_0))), inference(csr,[status(thm)],[c_0_87, c_0_88])). cnf(c_0_93, negated_conjecture, (k1_xtuple_0(k1_xtuple_0(k7_scmring2(esk1_0,esk3_0,X1)))=np__5\|~m1_subset_1(X1,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_89])])). cnf(c_0_94, plain, (l1_compos_1(X1)\|~l1_extpro_1(X1,X2)), inference(evalgc,[status(thm)],[c_0_90])). cnf(c_0_95, plain, (v2_struct_0(X1)\|l1_extpro_1(k1_scmring2(X1),np__2)\|~v13_algstr_0(X1)\|~v2_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_group_1(X1)\|~v4_vectsp_1(X1)\|~v5_vectsp_1(X1)\|~l6_algstr_0(X1)), inference(evalgc,[status(thm)],[c_0_91])). cnf(c_0_96, negated_conjecture, (~l1_compos_1(k1_scmring2(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92, c_0_93]), c_0_59])])])). cnf(c_0_97, plain, (l1_compos_1(k1_scmring2(X1))\|v2_struct_0(X1)\|~l6_algstr_0(X1)\|~v5_vectsp_1(X1)\|~v4_vectsp_1(X1)\|~v3_group_1(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v13_algstr_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_94, c_0_95])])). cnf(c_0_98, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96, c_0_97]), c_0_60]), c_0_61]), c_0_62]), c_0_63]), c_0_64]), c_0_65]), c_0_66]), c_0_67])]), c_0_68]), ['proof']). # SZS output end CNFRefutation	reserve R for Ring, r for Element of R, a, b, d1, d2 for Data-Location of R, il, i1, i2 for Element of NAT, I for Instruction of SCM R, s,s1, s2 for State of SCM R, T for InsType of the InstructionsF of SCM R, k for Nat; theorem InsCode (a:=r) = 5 by RECDEF_2:def 1;	Convert the following ATP output trace into a readable Mizar proof.
t117_group_2	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t37_group_2, axiom, ![X1]:((~(v2_struct_0(X1))&(v2_group_1(X1)&l3_algstr_0(X1)))=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))=>(k4_group_2(X1,k1_group_1(X1),X2)=X2&k5_group_2(X1,k1_group_1(X1),X2)=X2))), file('/scratch/mptp/predsminms1/t117_group_2__0', t37_group_2)). fof(d13_group_2, axiom, ![X1]:((~(v2_struct_0(X1))&(v2_group_1(X1)&(v3_group_1(X1)&l3_algstr_0(X1))))=>![X2]:(m1_group_2(X2,X1)=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>k13_group_2(X1,X2,X3)=k4_group_2(X1,X3,k8_group_2(X1,X2))))), file('/scratch/mptp/predsminms1/t117_group_2__0', d13_group_2)). fof(t116_group_2, axiom, ![X1]:((~(v2_struct_0(X1))&(v2_group_1(X1)&(v3_group_1(X1)&l3_algstr_0(X1))))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>![X4]:(m1_group_2(X4,X1)=>r1_tarski(k13_group_2(X1,X4,k6_algstr_0(X1,X2,X3)),k2_group_2(X1,k13_group_2(X1,X4,X2),k13_group_2(X1,X4,X3))))))), file('/scratch/mptp/predsminms1/t117_group_2__0', t116_group_2)). fof(d5_group_1, axiom, ![X1]:((~(v2_struct_0(X1))&(v2_group_1(X1)&(v3_group_1(X1)&l3_algstr_0(X1))))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>(X3=k2_group_1(X1,X2)<=>(k6_algstr_0(X1,X2,X3)=k1_group_1(X1)&k6_algstr_0(X1,X3,X2)=k1_group_1(X1)))))), file('/scratch/mptp/predsminms1/t117_group_2__0', d5_group_1)). fof(dt_k8_group_2, axiom, ![X1, X2]:(((~(v2_struct_0(X1))&(v2_group_1(X1)&(v3_group_1(X1)&l3_algstr_0(X1))))&m1_group_2(X2,X1))=>m1_subset_1(k8_group_2(X1,X2),k1_zfmisc_1(u1_struct_0(X1)))), file('/scratch/mptp/predsminms1/t117_group_2__0', dt_k8_group_2)). fof(dt_k6_algstr_0, axiom, ![X1, X2, X3]:((l3_algstr_0(X1)&(m1_subset_1(X2,u1_struct_0(X1))&m1_subset_1(X3,u1_struct_0(X1))))=>m1_subset_1(k6_algstr_0(X1,X2,X3),u1_struct_0(X1))), file('/scratch/mptp/predsminms1/t117_group_2__0', dt_k6_algstr_0)). fof(t117_group_2, conjecture, ![X1]:((~(v2_struct_0(X1))&(v2_group_1(X1)&(v3_group_1(X1)&l3_algstr_0(X1))))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_group_2(X3,X1)=>(r1_tarski(k8_group_2(X1,X3),k2_group_2(X1,k13_group_2(X1,X3,X2),k13_group_2(X1,X3,k2_group_1(X1,X2))))&r1_tarski(k8_group_2(X1,X3),k2_group_2(X1,k13_group_2(X1,X3,k2_group_1(X1,X2)),k13_group_2(X1,X3,X2))))))), file('/scratch/mptp/predsminms1/t117_group_2__0', t117_group_2)). fof(dt_k2_group_1, axiom, ![X1, X2]:(((~(v2_struct_0(X1))&(v2_group_1(X1)&(v3_group_1(X1)&l3_algstr_0(X1))))&m1_subset_1(X2,u1_struct_0(X1)))=>m1_subset_1(k2_group_1(X1,X2),u1_struct_0(X1))), file('/scratch/mptp/predsminms1/t117_group_2__0', dt_k2_group_1)). fof(c_0_8, plain, ![X8, X9]:((k4_group_2(X8,k1_group_1(X8),X9)=X9\|~m1_subset_1(X9,k1_zfmisc_1(u1_struct_0(X8)))\|(v2_struct_0(X8)\|(~v2_group_1(X8)\|~l3_algstr_0(X8))))&(k5_group_2(X8,k1_group_1(X8),X9)=X9\|~m1_subset_1(X9,k1_zfmisc_1(u1_struct_0(X8)))\|(v2_struct_0(X8)\|(~v2_group_1(X8)\|~l3_algstr_0(X8))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t37_group_2])])])])])). fof(c_0_9, plain, ![X12, X13, X14]:(v2_struct_0(X12)\|(~v2_group_1(X12)\|(~v3_group_1(X12)\|~l3_algstr_0(X12)))\|(~m1_group_2(X13,X12)\|(~m1_subset_1(X14,u1_struct_0(X12))\|k13_group_2(X12,X13,X14)=k4_group_2(X12,X14,k8_group_2(X12,X13))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d13_group_2])])])])). fof(c_0_10, plain, ![X20, X21, X22, X23]:(v2_struct_0(X20)\|(~v2_group_1(X20)\|(~v3_group_1(X20)\|~l3_algstr_0(X20)))\|(~m1_subset_1(X21,u1_struct_0(X20))\|(~m1_subset_1(X22,u1_struct_0(X20))\|(~m1_group_2(X23,X20)\|r1_tarski(k13_group_2(X20,X23,k6_algstr_0(X20,X21,X22)),k2_group_2(X20,k13_group_2(X20,X23,X21),k13_group_2(X20,X23,X22))))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t116_group_2])])])])). fof(c_0_11, plain, ![X17, X18, X19]:(((k6_algstr_0(X17,X18,X19)=k1_group_1(X17)\|X19!=k2_group_1(X17,X18)\|~m1_subset_1(X19,u1_struct_0(X17))\|~m1_subset_1(X18,u1_struct_0(X17))\|(v2_struct_0(X17)\|(~v2_group_1(X17)\|(~v3_group_1(X17)\|~l3_algstr_0(X17)))))&(k6_algstr_0(X17,X19,X18)=k1_group_1(X17)\|X19!=k2_group_1(X17,X18)\|~m1_subset_1(X19,u1_struct_0(X17))\|~m1_subset_1(X18,u1_struct_0(X17))\|(v2_struct_0(X17)\|(~v2_group_1(X17)\|(~v3_group_1(X17)\|~l3_algstr_0(X17))))))&(k6_algstr_0(X17,X18,X19)!=k1_group_1(X17)\|k6_algstr_0(X17,X19,X18)!=k1_group_1(X17)\|X19=k2_group_1(X17,X18)\|~m1_subset_1(X19,u1_struct_0(X17))\|~m1_subset_1(X18,u1_struct_0(X17))\|(v2_struct_0(X17)\|(~v2_group_1(X17)\|(~v3_group_1(X17)\|~l3_algstr_0(X17)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d5_group_1])])])])])). cnf(c_0_12, plain, (k4_group_2(X1,k1_group_1(X1),X2)=X2\|v2_struct_0(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~v2_group_1(X1)\|~l3_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_8])). cnf(c_0_13, plain, (v2_struct_0(X1)\|k13_group_2(X1,X2,X3)=k4_group_2(X1,X3,k8_group_2(X1,X2))\|~v2_group_1(X1)\|~v3_group_1(X1)\|~l3_algstr_0(X1)\|~m1_group_2(X2,X1)\|~m1_subset_1(X3,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_9])). fof(c_0_14, plain, ![X10, X11]:(v2_struct_0(X10)\|(~v2_group_1(X10)\|(~v3_group_1(X10)\|~l3_algstr_0(X10)))\|~m1_group_2(X11,X10)\|m1_subset_1(k8_group_2(X10,X11),k1_zfmisc_1(u1_struct_0(X10)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k8_group_2])])])). cnf(c_0_15, plain, (v2_struct_0(X1)\|r1_tarski(k13_group_2(X1,X4,k6_algstr_0(X1,X2,X3)),k2_group_2(X1,k13_group_2(X1,X4,X2),k13_group_2(X1,X4,X3)))\|~v2_group_1(X1)\|~v3_group_1(X1)\|~l3_algstr_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_group_2(X4,X1)), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_16, plain, (k6_algstr_0(X1,X2,X3)=k1_group_1(X1)\|v2_struct_0(X1)\|X2!=k2_group_1(X1,X3)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~v2_group_1(X1)\|~v3_group_1(X1)\|~l3_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_17, plain, (k4_group_2(X1,k1_group_1(X1),X2)=X2\|v2_struct_0(X1)\|~v2_group_1(X1)\|~l3_algstr_0(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(evalgc,[status(thm)],[c_0_12])). cnf(c_0_18, plain, (k4_group_2(X1,X3,k8_group_2(X1,X2))=k13_group_2(X1,X2,X3)\|v2_struct_0(X1)\|~v2_group_1(X1)\|~v3_group_1(X1)\|~l3_algstr_0(X1)\|~m1_group_2(X2,X1)\|~m1_subset_1(X3,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_13])). cnf(c_0_19, plain, (v2_struct_0(X1)\|m1_subset_1(k8_group_2(X1,X2),k1_zfmisc_1(u1_struct_0(X1)))\|~v2_group_1(X1)\|~v3_group_1(X1)\|~l3_algstr_0(X1)\|~m1_group_2(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_14])). fof(c_0_20, plain, ![X24, X25, X26]:(~l3_algstr_0(X24)\|(~m1_subset_1(X25,u1_struct_0(X24))\|~m1_subset_1(X26,u1_struct_0(X24)))\|m1_subset_1(k6_algstr_0(X24,X25,X26),u1_struct_0(X24))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k6_algstr_0])])). fof(c_0_21, negated_conjecture, ~(![X1]:((~(v2_struct_0(X1))&(v2_group_1(X1)&(v3_group_1(X1)&l3_algstr_0(X1))))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_group_2(X3,X1)=>(r1_tarski(k8_group_2(X1,X3),k2_group_2(X1,k13_group_2(X1,X3,X2),k13_group_2(X1,X3,k2_group_1(X1,X2))))&r1_tarski(k8_group_2(X1,X3),k2_group_2(X1,k13_group_2(X1,X3,k2_group_1(X1,X2)),k13_group_2(X1,X3,X2)))))))), inference(assume_negation,[status(cth)],[t117_group_2])). cnf(c_0_22, plain, (v2_struct_0(X1)\|r1_tarski(k13_group_2(X1,X4,k6_algstr_0(X1,X2,X3)),k2_group_2(X1,k13_group_2(X1,X4,X2),k13_group_2(X1,X4,X3)))\|~v2_group_1(X1)\|~v3_group_1(X1)\|~l3_algstr_0(X1)\|~m1_group_2(X4,X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_15])). cnf(c_0_23, plain, (k6_algstr_0(X1,X2,X3)=k1_group_1(X1)\|v2_struct_0(X1)\|X2!=k2_group_1(X1,X3)\|~v2_group_1(X1)\|~v3_group_1(X1)\|~l3_algstr_0(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_16])). cnf(c_0_24, plain, (k13_group_2(X1,X2,k1_group_1(X1))=k8_group_2(X1,X2)\|v2_struct_0(X1)\|~m1_subset_1(k8_group_2(X1,X2),k1_zfmisc_1(u1_struct_0(X1)))\|~l3_algstr_0(X1)\|~v2_group_1(X1)\|~m1_group_2(X2,X1)\|~m1_subset_1(k1_group_1(X1),u1_struct_0(X1))\|~v3_group_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_17, c_0_18])])). cnf(c_0_25, plain, (v2_struct_0(X1)\|m1_subset_1(k8_group_2(X1,X2),k1_zfmisc_1(u1_struct_0(X1)))\|~v2_group_1(X1)\|~v3_group_1(X1)\|~l3_algstr_0(X1)\|~m1_group_2(X2,X1)), inference(evalgc,[status(thm)],[c_0_19])). cnf(c_0_26, plain, (m1_subset_1(k6_algstr_0(X1,X2,X3),u1_struct_0(X1))\|~l3_algstr_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_20])). cnf(c_0_27, plain, (k6_algstr_0(X1,X2,X3)=k1_group_1(X1)\|v2_struct_0(X1)\|X3!=k2_group_1(X1,X2)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~v2_group_1(X1)\|~v3_group_1(X1)\|~l3_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_11])). fof(c_0_28, negated_conjecture, ((~v2_struct_0(esk1_0)&(v2_group_1(esk1_0)&(v3_group_1(esk1_0)&l3_algstr_0(esk1_0))))&(m1_subset_1(esk2_0,u1_struct_0(esk1_0))&(m1_group_2(esk3_0,esk1_0)&(~r1_tarski(k8_group_2(esk1_0,esk3_0),k2_group_2(esk1_0,k13_group_2(esk1_0,esk3_0,esk2_0),k13_group_2(esk1_0,esk3_0,k2_group_1(esk1_0,esk2_0))))\|~r1_tarski(k8_group_2(esk1_0,esk3_0),k2_group_2(esk1_0,k13_group_2(esk1_0,esk3_0,k2_group_1(esk1_0,esk2_0)),k13_group_2(esk1_0,esk3_0,esk2_0))))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_21])])])])). cnf(c_0_29, plain, (r1_tarski(k13_group_2(X1,X2,k1_group_1(X1)),k2_group_2(X1,k13_group_2(X1,X2,X3),k13_group_2(X1,X2,X4)))\|v2_struct_0(X1)\|~m1_group_2(X2,X1)\|~m1_subset_1(X4,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~l3_algstr_0(X1)\|~v3_group_1(X1)\|~v2_group_1(X1)\|X3!=k2_group_1(X1,X4)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_22, c_0_23])])). cnf(c_0_30, plain, (k13_group_2(X1,X2,k1_group_1(X1))=k8_group_2(X1,X2)\|v2_struct_0(X1)\|~m1_group_2(X2,X1)\|~m1_subset_1(k1_group_1(X1),u1_struct_0(X1))\|~l3_algstr_0(X1)\|~v3_group_1(X1)\|~v2_group_1(X1)), inference(csr,[status(thm)],[c_0_24, c_0_25])). cnf(c_0_31, plain, (m1_subset_1(k6_algstr_0(X1,X2,X3),u1_struct_0(X1))\|~l3_algstr_0(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_26])). cnf(c_0_32, plain, (k6_algstr_0(X1,X2,X3)=k1_group_1(X1)\|v2_struct_0(X1)\|X3!=k2_group_1(X1,X2)\|~v2_group_1(X1)\|~v3_group_1(X1)\|~l3_algstr_0(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_27])). cnf(c_0_33, negated_conjecture, (~r1_tarski(k8_group_2(esk1_0,esk3_0),k2_group_2(esk1_0,k13_group_2(esk1_0,esk3_0,esk2_0),k13_group_2(esk1_0,esk3_0,k2_group_1(esk1_0,esk2_0))))\|~r1_tarski(k8_group_2(esk1_0,esk3_0),k2_group_2(esk1_0,k13_group_2(esk1_0,esk3_0,k2_group_1(esk1_0,esk2_0)),k13_group_2(esk1_0,esk3_0,esk2_0)))), inference(split_conjunct,[status(thm)],[c_0_28])). cnf(c_0_34, plain, (r1_tarski(k8_group_2(X1,X2),k2_group_2(X1,k13_group_2(X1,X2,X3),k13_group_2(X1,X2,X4)))\|v2_struct_0(X1)\|X3!=k2_group_1(X1,X4)\|~m1_group_2(X2,X1)\|~m1_subset_1(X4,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~l3_algstr_0(X1)\|~v3_group_1(X1)\|~v2_group_1(X1)\|~m1_subset_1(k1_group_1(X1),u1_struct_0(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_29, c_0_30])])). cnf(c_0_35, plain, (m1_subset_1(k1_group_1(X1),u1_struct_0(X1))\|v2_struct_0(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l3_algstr_0(X1)\|X3!=k2_group_1(X1,X2)\|~v3_group_1(X1)\|~v2_group_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_31, c_0_32])])). cnf(c_0_36, negated_conjecture, (m1_group_2(esk3_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_28])). cnf(c_0_37, negated_conjecture, (m1_subset_1(esk2_0,u1_struct_0(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_28])). cnf(c_0_38, negated_conjecture, (l3_algstr_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_28])). cnf(c_0_39, negated_conjecture, (v3_group_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_28])). cnf(c_0_40, negated_conjecture, (v2_group_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_28])). cnf(c_0_41, negated_conjecture, (~v2_struct_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_28])). cnf(c_0_42, plain, (r1_tarski(k13_group_2(X1,X2,k1_group_1(X1)),k2_group_2(X1,k13_group_2(X1,X2,X3),k13_group_2(X1,X2,X4)))\|v2_struct_0(X1)\|~m1_group_2(X2,X1)\|~m1_subset_1(X4,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~l3_algstr_0(X1)\|~v3_group_1(X1)\|~v2_group_1(X1)\|X4!=k2_group_1(X1,X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_22, c_0_32])])). cnf(c_0_43, negated_conjecture, (~r1_tarski(k8_group_2(esk1_0,esk3_0),k2_group_2(esk1_0,k13_group_2(esk1_0,esk3_0,esk2_0),k13_group_2(esk1_0,esk3_0,k2_group_1(esk1_0,esk2_0))))\|~r1_tarski(k8_group_2(esk1_0,esk3_0),k2_group_2(esk1_0,k13_group_2(esk1_0,esk3_0,k2_group_1(esk1_0,esk2_0)),k13_group_2(esk1_0,esk3_0,esk2_0)))), inference(evalgc,[status(thm)],[c_0_33])). cnf(c_0_44, plain, (r1_tarski(k8_group_2(X1,X2),k2_group_2(X1,k13_group_2(X1,X2,X3),k13_group_2(X1,X2,X4)))\|v2_struct_0(X1)\|X3!=k2_group_1(X1,X4)\|~m1_group_2(X2,X1)\|~m1_subset_1(X4,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~l3_algstr_0(X1)\|~v3_group_1(X1)\|~v2_group_1(X1)), inference(csr,[status(thm)],[c_0_34, c_0_35])). cnf(c_0_45, negated_conjecture, (m1_group_2(esk3_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_36])). cnf(c_0_46, negated_conjecture, (m1_subset_1(esk2_0,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[c_0_37])). cnf(c_0_47, negated_conjecture, (l3_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_38])). cnf(c_0_48, negated_conjecture, (v3_group_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_39])). cnf(c_0_49, negated_conjecture, (v2_group_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_40])). cnf(c_0_50, negated_conjecture, (~v2_struct_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_41])). cnf(c_0_51, plain, (r1_tarski(k8_group_2(X1,X2),k2_group_2(X1,k13_group_2(X1,X2,X3),k13_group_2(X1,X2,X4)))\|v2_struct_0(X1)\|X4!=k2_group_1(X1,X3)\|~m1_group_2(X2,X1)\|~m1_subset_1(X4,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~l3_algstr_0(X1)\|~v3_group_1(X1)\|~v2_group_1(X1)\|~m1_subset_1(k1_group_1(X1),u1_struct_0(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_42, c_0_30])])). fof(c_0_52, plain, ![X15, X16]:(v2_struct_0(X15)\|(~v2_group_1(X15)\|(~v3_group_1(X15)\|~l3_algstr_0(X15)))\|~m1_subset_1(X16,u1_struct_0(X15))\|m1_subset_1(k2_group_1(X15,X16),u1_struct_0(X15))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k2_group_1])])])). cnf(c_0_53, negated_conjecture, (~r1_tarski(k8_group_2(esk1_0,esk3_0),k2_group_2(esk1_0,k13_group_2(esk1_0,esk3_0,esk2_0),k13_group_2(esk1_0,esk3_0,k2_group_1(esk1_0,esk2_0))))\|~m1_subset_1(k2_group_1(esk1_0,esk2_0),u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43, c_0_44]), c_0_45]), c_0_46]), c_0_47]), c_0_48]), c_0_49])]), c_0_50])])). cnf(c_0_54, plain, (r1_tarski(k8_group_2(X1,X2),k2_group_2(X1,k13_group_2(X1,X2,X3),k13_group_2(X1,X2,X4)))\|v2_struct_0(X1)\|X4!=k2_group_1(X1,X3)\|~m1_group_2(X2,X1)\|~m1_subset_1(X4,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~l3_algstr_0(X1)\|~v3_group_1(X1)\|~v2_group_1(X1)), inference(csr,[status(thm)],[c_0_51, c_0_35])). cnf(c_0_55, plain, (v2_struct_0(X1)\|m1_subset_1(k2_group_1(X1,X2),u1_struct_0(X1))\|~v2_group_1(X1)\|~v3_group_1(X1)\|~l3_algstr_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_52])). cnf(c_0_56, negated_conjecture, (~m1_subset_1(k2_group_1(esk1_0,esk2_0),u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53, c_0_54]), c_0_45]), c_0_46]), c_0_47]), c_0_48]), c_0_49])]), c_0_50])])). cnf(c_0_57, plain, (v2_struct_0(X1)\|m1_subset_1(k2_group_1(X1,X2),u1_struct_0(X1))\|~v2_group_1(X1)\|~v3_group_1(X1)\|~l3_algstr_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_55])). cnf(c_0_58, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56, c_0_57]), c_0_46]), c_0_47]), c_0_48]), c_0_49])]), c_0_50]), ['proof']). # SZS output end CNFRefutation	reserve x for set; reserve G for non empty 1-sorted; reserve A for Subset of G; reserve y,y1,y2,Y,Z for set; reserve k for Nat; reserve G for Group; reserve a,g,h for Element of G; reserve A for Subset of G; reserve G for non empty multMagma, A,B,C for Subset of G; reserve a,b,g,g1,g2,h,h1,h2 for Element of G; reserve G for Group-like non empty multMagma; reserve h,g,g1,g2 for Element of G; reserve A for Subset of G; reserve H for Subgroup of G; reserve h,h1,h2 for Element of H; reserve G,G1,G2,G3 for Group; reserve a,a1,a2,b,b1,b2,g,g1,g2 for Element of G; reserve A,B for Subset of G; reserve H,H1,H2,H3 for Subgroup of G; reserve h,h1,h2 for Element of H; theorem carr(H) c= (a * H) * (a" * H) & carr(H) c= (a" * H) * (a * H) proof A1: a" * a * H = 1_G * H by GROUP_1:def 5 .= carr(H) by Th37; a * a" * H = 1_G * H by GROUP_1:def 5 .= carr(H) by Th37; hence thesis by A1,Th116; end;	Convert the following ATP output trace into a readable Mizar proof.
t23_unialg_2	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(d9_unialg_2, axiom, ![X1]:((~(v2_struct_0(X1))&(v2_unialg_1(X1)&(v3_unialg_1(X1)&(v4_unialg_1(X1)&l1_unialg_1(X1)))))=>![X2]:(m1_unialg_2(X2,X1)=>![X3]:(m1_unialg_2(X3,X1)=>(~(r2_subset_1(u1_struct_0(X2),u1_struct_0(X3)))=>![X4]:((v1_unialg_1(X4)&m1_unialg_2(X4,X1))=>(X4=k5_unialg_2(X1,X2,X3)<=>(u1_struct_0(X4)=k3_xboole_0(u1_struct_0(X2),u1_struct_0(X3))&![X5]:((~(v1_xboole_0(X5))&m1_subset_1(X5,k1_zfmisc_1(u1_struct_0(X1))))=>(X5=u1_struct_0(X4)=>(u1_unialg_1(X4)=k3_unialg_2(X1,X5)&v1_unialg_2(X5,X1))))))))))), file('/scratch/mptp/predsminms1/t23_unialg_2__0', d9_unialg_2)). fof(dt_k5_unialg_2, axiom, ![X1, X2, X3]:(((~(v2_struct_0(X1))&(v2_unialg_1(X1)&(v3_unialg_1(X1)&(v4_unialg_1(X1)&l1_unialg_1(X1)))))&(m1_unialg_2(X2,X1)&m1_unialg_2(X3,X1)))=>(v1_unialg_1(k5_unialg_2(X1,X2,X3))&m1_unialg_2(k5_unialg_2(X1,X2,X3),X1))), file('/scratch/mptp/predsminms1/t23_unialg_2__0', dt_k5_unialg_2)). fof(t23_unialg_2, conjecture, ![X1]:((~(v2_struct_0(X1))&(v2_unialg_1(X1)&(v3_unialg_1(X1)&(v4_unialg_1(X1)&(v2_unialg_2(X1)&l1_unialg_1(X1))))))=>![X2]:((v1_unialg_1(X2)&m1_unialg_2(X2,X1))=>![X3]:((v1_unialg_1(X3)&m1_unialg_2(X3,X1))=>k8_unialg_2(X1,k5_unialg_2(X1,X2,X3),X3)=X3))), file('/scratch/mptp/predsminms1/t23_unialg_2__0', t23_unialg_2)). fof(t19_unialg_2, axiom, ![X1]:((~(v2_struct_0(X1))&(v2_unialg_1(X1)&(v3_unialg_1(X1)&(v4_unialg_1(X1)&l1_unialg_1(X1)))))=>![X2]:((v1_unialg_1(X2)&m1_unialg_2(X2,X1))=>![X3]:((~(v1_xboole_0(X3))&m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1))))=>(X3=u1_struct_0(X2)=>k7_unialg_2(X1,X3)=X2)))), file('/scratch/mptp/predsminms1/t23_unialg_2__0', t19_unialg_2)). fof(t17_unialg_2, axiom, ![X1]:((~(v2_struct_0(X1))&(v2_unialg_1(X1)&(v3_unialg_1(X1)&(v4_unialg_1(X1)&(v2_unialg_2(X1)&l1_unialg_1(X1))))))=>![X2]:(m1_unialg_2(X2,X1)=>![X3]:(m1_unialg_2(X3,X1)=>~(r2_subset_1(u1_struct_0(X2),u1_struct_0(X3)))))), file('/scratch/mptp/predsminms1/t23_unialg_2__0', t17_unialg_2)). fof(d13_unialg_2, axiom, ![X1]:((~(v2_struct_0(X1))&(v2_unialg_1(X1)&(v3_unialg_1(X1)&(v4_unialg_1(X1)&l1_unialg_1(X1)))))=>![X2]:(m1_unialg_2(X2,X1)=>![X3]:(m1_unialg_2(X3,X1)=>![X4]:((v1_unialg_1(X4)&m1_unialg_2(X4,X1))=>(X4=k8_unialg_2(X1,X2,X3)<=>![X5]:((~(v1_xboole_0(X5))&m1_subset_1(X5,k1_zfmisc_1(u1_struct_0(X1))))=>(X5=k2_xboole_0(u1_struct_0(X2),u1_struct_0(X3))=>X4=k7_unialg_2(X1,X5)))))))), file('/scratch/mptp/predsminms1/t23_unialg_2__0', d13_unialg_2)). fof(commutativity_k3_xboole_0, axiom, ![X1, X2]:k3_xboole_0(X1,X2)=k3_xboole_0(X2,X1), file('/scratch/mptp/predsminms1/t23_unialg_2__0', commutativity_k3_xboole_0)). fof(t12_xboole_1, axiom, ![X1, X2]:(r1_tarski(X1,X2)=>k2_xboole_0(X1,X2)=X2), file('/scratch/mptp/predsminms1/t23_unialg_2__0', t12_xboole_1)). fof(t17_xboole_1, axiom, ![X1, X2]:r1_tarski(k3_xboole_0(X1,X2),X1), file('/scratch/mptp/predsminms1/t23_unialg_2__0', t17_xboole_1)). fof(c_0_9, plain, ![X15, X16, X17, X18, X19]:(((u1_struct_0(X18)=k3_xboole_0(u1_struct_0(X16),u1_struct_0(X17))\|X18!=k5_unialg_2(X15,X16,X17)\|(~v1_unialg_1(X18)\|~m1_unialg_2(X18,X15))\|r2_subset_1(u1_struct_0(X16),u1_struct_0(X17))\|~m1_unialg_2(X17,X15)\|~m1_unialg_2(X16,X15)\|(v2_struct_0(X15)\|(~v2_unialg_1(X15)\|(~v3_unialg_1(X15)\|(~v4_unialg_1(X15)\|~l1_unialg_1(X15))))))&((u1_unialg_1(X18)=k3_unialg_2(X15,X19)\|X19!=u1_struct_0(X18)\|(v1_xboole_0(X19)\|~m1_subset_1(X19,k1_zfmisc_1(u1_struct_0(X15))))\|X18!=k5_unialg_2(X15,X16,X17)\|(~v1_unialg_1(X18)\|~m1_unialg_2(X18,X15))\|r2_subset_1(u1_struct_0(X16),u1_struct_0(X17))\|~m1_unialg_2(X17,X15)\|~m1_unialg_2(X16,X15)\|(v2_struct_0(X15)\|(~v2_unialg_1(X15)\|(~v3_unialg_1(X15)\|(~v4_unialg_1(X15)\|~l1_unialg_1(X15))))))&(v1_unialg_2(X19,X15)\|X19!=u1_struct_0(X18)\|(v1_xboole_0(X19)\|~m1_subset_1(X19,k1_zfmisc_1(u1_struct_0(X15))))\|X18!=k5_unialg_2(X15,X16,X17)\|(~v1_unialg_1(X18)\|~m1_unialg_2(X18,X15))\|r2_subset_1(u1_struct_0(X16),u1_struct_0(X17))\|~m1_unialg_2(X17,X15)\|~m1_unialg_2(X16,X15)\|(v2_struct_0(X15)\|(~v2_unialg_1(X15)\|(~v3_unialg_1(X15)\|(~v4_unialg_1(X15)\|~l1_unialg_1(X15))))))))&(((~v1_xboole_0(esk4_4(X15,X16,X17,X18))\|u1_struct_0(X18)!=k3_xboole_0(u1_struct_0(X16),u1_struct_0(X17))\|X18=k5_unialg_2(X15,X16,X17)\|(~v1_unialg_1(X18)\|~m1_unialg_2(X18,X15))\|r2_subset_1(u1_struct_0(X16),u1_struct_0(X17))\|~m1_unialg_2(X17,X15)\|~m1_unialg_2(X16,X15)\|(v2_struct_0(X15)\|(~v2_unialg_1(X15)\|(~v3_unialg_1(X15)\|(~v4_unialg_1(X15)\|~l1_unialg_1(X15))))))&(m1_subset_1(esk4_4(X15,X16,X17,X18),k1_zfmisc_1(u1_struct_0(X15)))\|u1_struct_0(X18)!=k3_xboole_0(u1_struct_0(X16),u1_struct_0(X17))\|X18=k5_unialg_2(X15,X16,X17)\|(~v1_unialg_1(X18)\|~m1_unialg_2(X18,X15))\|r2_subset_1(u1_struct_0(X16),u1_struct_0(X17))\|~m1_unialg_2(X17,X15)\|~m1_unialg_2(X16,X15)\|(v2_struct_0(X15)\|(~v2_unialg_1(X15)\|(~v3_unialg_1(X15)\|(~v4_unialg_1(X15)\|~l1_unialg_1(X15)))))))&((esk4_4(X15,X16,X17,X18)=u1_struct_0(X18)\|u1_struct_0(X18)!=k3_xboole_0(u1_struct_0(X16),u1_struct_0(X17))\|X18=k5_unialg_2(X15,X16,X17)\|(~v1_unialg_1(X18)\|~m1_unialg_2(X18,X15))\|r2_subset_1(u1_struct_0(X16),u1_struct_0(X17))\|~m1_unialg_2(X17,X15)\|~m1_unialg_2(X16,X15)\|(v2_struct_0(X15)\|(~v2_unialg_1(X15)\|(~v3_unialg_1(X15)\|(~v4_unialg_1(X15)\|~l1_unialg_1(X15))))))&(u1_unialg_1(X18)!=k3_unialg_2(X15,esk4_4(X15,X16,X17,X18))\|~v1_unialg_2(esk4_4(X15,X16,X17,X18),X15)\|u1_struct_0(X18)!=k3_xboole_0(u1_struct_0(X16),u1_struct_0(X17))\|X18=k5_unialg_2(X15,X16,X17)\|(~v1_unialg_1(X18)\|~m1_unialg_2(X18,X15))\|r2_subset_1(u1_struct_0(X16),u1_struct_0(X17))\|~m1_unialg_2(X17,X15)\|~m1_unialg_2(X16,X15)\|(v2_struct_0(X15)\|(~v2_unialg_1(X15)\|(~v3_unialg_1(X15)\|(~v4_unialg_1(X15)\|~l1_unialg_1(X15))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d9_unialg_2])])])])])])). cnf(c_0_10, plain, (u1_struct_0(X1)=k3_xboole_0(u1_struct_0(X2),u1_struct_0(X3))\|r2_subset_1(u1_struct_0(X2),u1_struct_0(X3))\|v2_struct_0(X4)\|X1!=k5_unialg_2(X4,X2,X3)\|~v1_unialg_1(X1)\|~m1_unialg_2(X1,X4)\|~m1_unialg_2(X3,X4)\|~m1_unialg_2(X2,X4)\|~v2_unialg_1(X4)\|~v3_unialg_1(X4)\|~v4_unialg_1(X4)\|~l1_unialg_1(X4)), inference(split_conjunct,[status(thm)],[c_0_9])). fof(c_0_11, plain, ![X12, X13, X14]:((v1_unialg_1(k5_unialg_2(X12,X13,X14))\|(v2_struct_0(X12)\|(~v2_unialg_1(X12)\|(~v3_unialg_1(X12)\|(~v4_unialg_1(X12)\|~l1_unialg_1(X12))))\|(~m1_unialg_2(X13,X12)\|~m1_unialg_2(X14,X12))))&(m1_unialg_2(k5_unialg_2(X12,X13,X14),X12)\|(v2_struct_0(X12)\|(~v2_unialg_1(X12)\|(~v3_unialg_1(X12)\|(~v4_unialg_1(X12)\|~l1_unialg_1(X12))))\|(~m1_unialg_2(X13,X12)\|~m1_unialg_2(X14,X12))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k5_unialg_2])])])])). fof(c_0_12, negated_conjecture, ~(![X1]:((~(v2_struct_0(X1))&(v2_unialg_1(X1)&(v3_unialg_1(X1)&(v4_unialg_1(X1)&(v2_unialg_2(X1)&l1_unialg_1(X1))))))=>![X2]:((v1_unialg_1(X2)&m1_unialg_2(X2,X1))=>![X3]:((v1_unialg_1(X3)&m1_unialg_2(X3,X1))=>k8_unialg_2(X1,k5_unialg_2(X1,X2,X3),X3)=X3)))), inference(assume_negation,[status(cth)],[t23_unialg_2])). cnf(c_0_13, plain, (u1_struct_0(X1)=k3_xboole_0(u1_struct_0(X2),u1_struct_0(X3))\|v2_struct_0(X4)\|r2_subset_1(u1_struct_0(X2),u1_struct_0(X3))\|X1!=k5_unialg_2(X4,X2,X3)\|~v2_unialg_1(X4)\|~v3_unialg_1(X4)\|~v4_unialg_1(X4)\|~l1_unialg_1(X4)\|~v1_unialg_1(X1)\|~m1_unialg_2(X3,X4)\|~m1_unialg_2(X2,X4)\|~m1_unialg_2(X1,X4)), inference(evalgc,[status(thm)],[c_0_10])). cnf(c_0_14, plain, (v1_unialg_1(k5_unialg_2(X1,X2,X3))\|v2_struct_0(X1)\|~v2_unialg_1(X1)\|~v3_unialg_1(X1)\|~v4_unialg_1(X1)\|~l1_unialg_1(X1)\|~m1_unialg_2(X2,X1)\|~m1_unialg_2(X3,X1)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_15, plain, (m1_unialg_2(k5_unialg_2(X1,X2,X3),X1)\|v2_struct_0(X1)\|~v2_unialg_1(X1)\|~v3_unialg_1(X1)\|~v4_unialg_1(X1)\|~l1_unialg_1(X1)\|~m1_unialg_2(X2,X1)\|~m1_unialg_2(X3,X1)), inference(split_conjunct,[status(thm)],[c_0_11])). fof(c_0_16, negated_conjecture, ((~v2_struct_0(esk1_0)&(v2_unialg_1(esk1_0)&(v3_unialg_1(esk1_0)&(v4_unialg_1(esk1_0)&(v2_unialg_2(esk1_0)&l1_unialg_1(esk1_0))))))&((v1_unialg_1(esk2_0)&m1_unialg_2(esk2_0,esk1_0))&((v1_unialg_1(esk3_0)&m1_unialg_2(esk3_0,esk1_0))&k8_unialg_2(esk1_0,k5_unialg_2(esk1_0,esk2_0,esk3_0),esk3_0)!=esk3_0))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_12])])])])). fof(c_0_17, plain, ![X39, X40, X41]:(v2_struct_0(X39)\|(~v2_unialg_1(X39)\|(~v3_unialg_1(X39)\|(~v4_unialg_1(X39)\|~l1_unialg_1(X39))))\|(~v1_unialg_1(X40)\|~m1_unialg_2(X40,X39)\|(v1_xboole_0(X41)\|~m1_subset_1(X41,k1_zfmisc_1(u1_struct_0(X39)))\|(X41!=u1_struct_0(X40)\|k7_unialg_2(X39,X41)=X40)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t19_unialg_2])])])])). fof(c_0_18, plain, ![X9, X10, X11]:(v2_struct_0(X9)\|(~v2_unialg_1(X9)\|(~v3_unialg_1(X9)\|(~v4_unialg_1(X9)\|(~v2_unialg_2(X9)\|~l1_unialg_1(X9)))))\|(~m1_unialg_2(X10,X9)\|(~m1_unialg_2(X11,X9)\|~r2_subset_1(u1_struct_0(X10),u1_struct_0(X11))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t17_unialg_2])])])])). cnf(c_0_19, plain, (u1_struct_0(k5_unialg_2(X1,X2,X3))=k3_xboole_0(u1_struct_0(X2),u1_struct_0(X3))\|r2_subset_1(u1_struct_0(X2),u1_struct_0(X3))\|v2_struct_0(X1)\|~m1_unialg_2(X3,X1)\|~m1_unialg_2(X2,X1)\|~m1_unialg_2(k5_unialg_2(X1,X2,X3),X1)\|~v1_unialg_1(k5_unialg_2(X1,X2,X3))\|~l1_unialg_1(X1)\|~v4_unialg_1(X1)\|~v3_unialg_1(X1)\|~v2_unialg_1(X1)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_13])])). cnf(c_0_20, plain, (v2_struct_0(X1)\|v1_unialg_1(k5_unialg_2(X1,X2,X3))\|~v2_unialg_1(X1)\|~v3_unialg_1(X1)\|~v4_unialg_1(X1)\|~l1_unialg_1(X1)\|~m1_unialg_2(X3,X1)\|~m1_unialg_2(X2,X1)), inference(evalgc,[status(thm)],[c_0_14])). cnf(c_0_21, plain, (v2_struct_0(X1)\|m1_unialg_2(k5_unialg_2(X1,X2,X3),X1)\|~v2_unialg_1(X1)\|~v3_unialg_1(X1)\|~v4_unialg_1(X1)\|~l1_unialg_1(X1)\|~m1_unialg_2(X3,X1)\|~m1_unialg_2(X2,X1)), inference(evalgc,[status(thm)],[c_0_15])). cnf(c_0_22, negated_conjecture, (m1_unialg_2(esk3_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_23, negated_conjecture, (l1_unialg_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_24, negated_conjecture, (v4_unialg_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_25, negated_conjecture, (v3_unialg_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_26, negated_conjecture, (v2_unialg_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_27, negated_conjecture, (~v2_struct_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_16])). fof(c_0_28, plain, ![X27, X28, X29, X30, X31]:((X30!=k8_unialg_2(X27,X28,X29)\|(v1_xboole_0(X31)\|~m1_subset_1(X31,k1_zfmisc_1(u1_struct_0(X27)))\|(X31!=k2_xboole_0(u1_struct_0(X28),u1_struct_0(X29))\|X30=k7_unialg_2(X27,X31)))\|(~v1_unialg_1(X30)\|~m1_unialg_2(X30,X27))\|~m1_unialg_2(X29,X27)\|~m1_unialg_2(X28,X27)\|(v2_struct_0(X27)\|(~v2_unialg_1(X27)\|(~v3_unialg_1(X27)\|(~v4_unialg_1(X27)\|~l1_unialg_1(X27))))))&(((~v1_xboole_0(esk5_4(X27,X28,X29,X30))\|X30=k8_unialg_2(X27,X28,X29)\|(~v1_unialg_1(X30)\|~m1_unialg_2(X30,X27))\|~m1_unialg_2(X29,X27)\|~m1_unialg_2(X28,X27)\|(v2_struct_0(X27)\|(~v2_unialg_1(X27)\|(~v3_unialg_1(X27)\|(~v4_unialg_1(X27)\|~l1_unialg_1(X27))))))&(m1_subset_1(esk5_4(X27,X28,X29,X30),k1_zfmisc_1(u1_struct_0(X27)))\|X30=k8_unialg_2(X27,X28,X29)\|(~v1_unialg_1(X30)\|~m1_unialg_2(X30,X27))\|~m1_unialg_2(X29,X27)\|~m1_unialg_2(X28,X27)\|(v2_struct_0(X27)\|(~v2_unialg_1(X27)\|(~v3_unialg_1(X27)\|(~v4_unialg_1(X27)\|~l1_unialg_1(X27)))))))&((esk5_4(X27,X28,X29,X30)=k2_xboole_0(u1_struct_0(X28),u1_struct_0(X29))\|X30=k8_unialg_2(X27,X28,X29)\|(~v1_unialg_1(X30)\|~m1_unialg_2(X30,X27))\|~m1_unialg_2(X29,X27)\|~m1_unialg_2(X28,X27)\|(v2_struct_0(X27)\|(~v2_unialg_1(X27)\|(~v3_unialg_1(X27)\|(~v4_unialg_1(X27)\|~l1_unialg_1(X27))))))&(X30!=k7_unialg_2(X27,esk5_4(X27,X28,X29,X30))\|X30=k8_unialg_2(X27,X28,X29)\|(~v1_unialg_1(X30)\|~m1_unialg_2(X30,X27))\|~m1_unialg_2(X29,X27)\|~m1_unialg_2(X28,X27)\|(v2_struct_0(X27)\|(~v2_unialg_1(X27)\|(~v3_unialg_1(X27)\|(~v4_unialg_1(X27)\|~l1_unialg_1(X27))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d13_unialg_2])])])])])])). cnf(c_0_29, plain, (v2_struct_0(X1)\|v1_xboole_0(X3)\|k7_unialg_2(X1,X3)=X2\|~v2_unialg_1(X1)\|~v3_unialg_1(X1)\|~v4_unialg_1(X1)\|~l1_unialg_1(X1)\|~v1_unialg_1(X2)\|~m1_unialg_2(X2,X1)\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))\|X3!=u1_struct_0(X2)), inference(split_conjunct,[status(thm)],[c_0_17])). cnf(c_0_30, negated_conjecture, (v1_unialg_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_31, negated_conjecture, (m1_unialg_2(esk2_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_32, plain, (v2_struct_0(X1)\|~v2_unialg_1(X1)\|~v3_unialg_1(X1)\|~v4_unialg_1(X1)\|~v2_unialg_2(X1)\|~l1_unialg_1(X1)\|~m1_unialg_2(X2,X1)\|~m1_unialg_2(X3,X1)\|~r2_subset_1(u1_struct_0(X2),u1_struct_0(X3))), inference(split_conjunct,[status(thm)],[c_0_18])). cnf(c_0_33, plain, (u1_struct_0(k5_unialg_2(X1,X2,X3))=k3_xboole_0(u1_struct_0(X2),u1_struct_0(X3))\|r2_subset_1(u1_struct_0(X2),u1_struct_0(X3))\|v2_struct_0(X1)\|~m1_unialg_2(X3,X1)\|~m1_unialg_2(X2,X1)\|~l1_unialg_1(X1)\|~v4_unialg_1(X1)\|~v3_unialg_1(X1)\|~v2_unialg_1(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_19, c_0_20]), c_0_21])). cnf(c_0_34, negated_conjecture, (m1_unialg_2(esk3_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_22])). cnf(c_0_35, negated_conjecture, (l1_unialg_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_23])). cnf(c_0_36, negated_conjecture, (v4_unialg_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_24])). cnf(c_0_37, negated_conjecture, (v3_unialg_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_25])). cnf(c_0_38, negated_conjecture, (v2_unialg_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_26])). cnf(c_0_39, negated_conjecture, (~v2_struct_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_27])). cnf(c_0_40, plain, (X1=k8_unialg_2(X2,X3,X4)\|v2_struct_0(X2)\|X1!=k7_unialg_2(X2,esk5_4(X2,X3,X4,X1))\|~v1_unialg_1(X1)\|~m1_unialg_2(X1,X2)\|~m1_unialg_2(X4,X2)\|~m1_unialg_2(X3,X2)\|~v2_unialg_1(X2)\|~v3_unialg_1(X2)\|~v4_unialg_1(X2)\|~l1_unialg_1(X2)), inference(split_conjunct,[status(thm)],[c_0_28])). cnf(c_0_41, plain, (k7_unialg_2(X1,X3)=X2\|v2_struct_0(X1)\|v1_xboole_0(X3)\|X3!=u1_struct_0(X2)\|~v2_unialg_1(X1)\|~v3_unialg_1(X1)\|~v4_unialg_1(X1)\|~l1_unialg_1(X1)\|~v1_unialg_1(X2)\|~m1_unialg_2(X2,X1)\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))), inference(evalgc,[status(thm)],[c_0_29])). cnf(c_0_42, negated_conjecture, (v1_unialg_1(esk3_0)), inference(evalgc,[status(thm)],[c_0_30])). cnf(c_0_43, negated_conjecture, (m1_unialg_2(esk2_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_31])). cnf(c_0_44, plain, (v2_struct_0(X1)\|~v2_unialg_1(X1)\|~v3_unialg_1(X1)\|~v4_unialg_1(X1)\|~v2_unialg_2(X1)\|~l1_unialg_1(X1)\|~m1_unialg_2(X3,X1)\|~m1_unialg_2(X2,X1)\|~r2_subset_1(u1_struct_0(X2),u1_struct_0(X3))), inference(evalgc,[status(thm)],[c_0_32])). cnf(c_0_45, negated_conjecture, (k3_xboole_0(u1_struct_0(X1),u1_struct_0(esk3_0))=u1_struct_0(k5_unialg_2(esk1_0,X1,esk3_0))\|r2_subset_1(u1_struct_0(X1),u1_struct_0(esk3_0))\|~m1_unialg_2(X1,esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33, c_0_34]), c_0_35]), c_0_36]), c_0_37]), c_0_38])]), c_0_39])])). cnf(c_0_46, negated_conjecture, (v2_unialg_2(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_16])). fof(c_0_47, plain, ![X23, X24]:k3_xboole_0(X23,X24)=k3_xboole_0(X24,X23), inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0])). cnf(c_0_48, plain, (X1=k8_unialg_2(X2,X3,X4)\|v2_struct_0(X2)\|k7_unialg_2(X2,esk5_4(X2,X3,X4,X1))!=X1\|~v2_unialg_1(X2)\|~v3_unialg_1(X2)\|~v4_unialg_1(X2)\|~l1_unialg_1(X2)\|~v1_unialg_1(X1)\|~m1_unialg_2(X4,X2)\|~m1_unialg_2(X3,X2)\|~m1_unialg_2(X1,X2)), inference(evalgc,[status(thm)],[c_0_40])). cnf(c_0_49, negated_conjecture, (k7_unialg_2(esk1_0,X1)=esk3_0\|v1_xboole_0(X1)\|X1!=u1_struct_0(esk3_0)\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(esk1_0)))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41, c_0_34]), c_0_42]), c_0_35]), c_0_36]), c_0_37]), c_0_38])]), c_0_39])])). cnf(c_0_50, plain, (m1_subset_1(esk5_4(X1,X2,X3,X4),k1_zfmisc_1(u1_struct_0(X1)))\|X4=k8_unialg_2(X1,X2,X3)\|v2_struct_0(X1)\|~v1_unialg_1(X4)\|~m1_unialg_2(X4,X1)\|~m1_unialg_2(X3,X1)\|~m1_unialg_2(X2,X1)\|~v2_unialg_1(X1)\|~v3_unialg_1(X1)\|~v4_unialg_1(X1)\|~l1_unialg_1(X1)), inference(split_conjunct,[status(thm)],[c_0_28])). cnf(c_0_51, negated_conjecture, (k3_xboole_0(u1_struct_0(X1),u1_struct_0(esk2_0))=u1_struct_0(k5_unialg_2(esk1_0,X1,esk2_0))\|r2_subset_1(u1_struct_0(X1),u1_struct_0(esk2_0))\|~m1_unialg_2(X1,esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33, c_0_43]), c_0_35]), c_0_36]), c_0_37]), c_0_38])]), c_0_39])])). cnf(c_0_52, negated_conjecture, (v2_struct_0(X1)\|k3_xboole_0(u1_struct_0(X2),u1_struct_0(esk3_0))=u1_struct_0(k5_unialg_2(esk1_0,X2,esk3_0))\|~m1_unialg_2(esk3_0,X1)\|~m1_unialg_2(X2,X1)\|~l1_unialg_1(X1)\|~v2_unialg_2(X1)\|~v4_unialg_1(X1)\|~v3_unialg_1(X1)\|~v2_unialg_1(X1)\|~m1_unialg_2(X2,esk1_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_44, c_0_45])])). cnf(c_0_53, negated_conjecture, (v2_unialg_2(esk1_0)), inference(evalgc,[status(thm)],[c_0_46])). cnf(c_0_54, plain, (k3_xboole_0(X1,X2)=k3_xboole_0(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_47])). cnf(c_0_55, plain, (X4=k8_unialg_2(X1,X2,X3)\|v2_struct_0(X1)\|~v1_xboole_0(esk5_4(X1,X2,X3,X4))\|~v1_unialg_1(X4)\|~m1_unialg_2(X4,X1)\|~m1_unialg_2(X3,X1)\|~m1_unialg_2(X2,X1)\|~v2_unialg_1(X1)\|~v3_unialg_1(X1)\|~v4_unialg_1(X1)\|~l1_unialg_1(X1)), inference(split_conjunct,[status(thm)],[c_0_28])). cnf(c_0_56, negated_conjecture, (X1=k8_unialg_2(esk1_0,X2,X3)\|v1_xboole_0(esk5_4(esk1_0,X2,X3,X1))\|esk3_0!=X1\|~m1_unialg_2(X3,esk1_0)\|~m1_unialg_2(X2,esk1_0)\|~m1_unialg_2(X1,esk1_0)\|~v1_unialg_1(X1)\|esk5_4(esk1_0,X2,X3,X1)!=u1_struct_0(esk3_0)\|~m1_subset_1(esk5_4(esk1_0,X2,X3,X1),k1_zfmisc_1(u1_struct_0(esk1_0)))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48, c_0_49]), c_0_35]), c_0_36]), c_0_37]), c_0_38])]), c_0_39])])). cnf(c_0_57, plain, (X4=k8_unialg_2(X1,X2,X3)\|v2_struct_0(X1)\|m1_subset_1(esk5_4(X1,X2,X3,X4),k1_zfmisc_1(u1_struct_0(X1)))\|~v2_unialg_1(X1)\|~v3_unialg_1(X1)\|~v4_unialg_1(X1)\|~l1_unialg_1(X1)\|~v1_unialg_1(X4)\|~m1_unialg_2(X4,X1)\|~m1_unialg_2(X3,X1)\|~m1_unialg_2(X2,X1)), inference(evalgc,[status(thm)],[c_0_50])). fof(c_0_58, plain, ![X21, X22]:(~r1_tarski(X21,X22)\|k2_xboole_0(X21,X22)=X22), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_xboole_1])])). fof(c_0_59, plain, ![X25, X26]:r1_tarski(k3_xboole_0(X25,X26),X25), inference(variable_rename,[status(thm)],[t17_xboole_1])). cnf(c_0_60, negated_conjecture, (v2_struct_0(X1)\|k3_xboole_0(u1_struct_0(X2),u1_struct_0(esk2_0))=u1_struct_0(k5_unialg_2(esk1_0,X2,esk2_0))\|~m1_unialg_2(esk2_0,X1)\|~m1_unialg_2(X2,X1)\|~l1_unialg_1(X1)\|~v2_unialg_2(X1)\|~v4_unialg_1(X1)\|~v3_unialg_1(X1)\|~v2_unialg_1(X1)\|~m1_unialg_2(X2,esk1_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_44, c_0_51])])). cnf(c_0_61, negated_conjecture, (k3_xboole_0(u1_struct_0(esk2_0),u1_struct_0(esk3_0))=u1_struct_0(k5_unialg_2(esk1_0,esk2_0,esk3_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52, c_0_43]), c_0_34]), c_0_43]), c_0_35]), c_0_53]), c_0_36]), c_0_37]), c_0_38])]), c_0_39])])). cnf(c_0_62, plain, (k3_xboole_0(X1,X2)=k3_xboole_0(X2,X1)), inference(evalgc,[status(thm)],[c_0_54])). cnf(c_0_63, plain, (X4=k8_unialg_2(X1,X2,X3)\|v2_struct_0(X1)\|~v2_unialg_1(X1)\|~v3_unialg_1(X1)\|~v4_unialg_1(X1)\|~l1_unialg_1(X1)\|~v1_unialg_1(X4)\|~m1_unialg_2(X4,X1)\|~m1_unialg_2(X3,X1)\|~m1_unialg_2(X2,X1)\|~v1_xboole_0(esk5_4(X1,X2,X3,X4))), inference(evalgc,[status(thm)],[c_0_55])). cnf(c_0_64, negated_conjecture, (X1=k8_unialg_2(esk1_0,X2,X3)\|v1_xboole_0(esk5_4(esk1_0,X2,X3,X1))\|esk5_4(esk1_0,X2,X3,X1)!=u1_struct_0(esk3_0)\|esk3_0!=X1\|~m1_unialg_2(X3,esk1_0)\|~m1_unialg_2(X2,esk1_0)\|~m1_unialg_2(X1,esk1_0)\|~v1_unialg_1(X1)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56, c_0_57]), c_0_35]), c_0_36]), c_0_37]), c_0_38])]), c_0_39])])). cnf(c_0_65, plain, (esk5_4(X1,X2,X3,X4)=k2_xboole_0(u1_struct_0(X2),u1_struct_0(X3))\|X4=k8_unialg_2(X1,X2,X3)\|v2_struct_0(X1)\|~v1_unialg_1(X4)\|~m1_unialg_2(X4,X1)\|~m1_unialg_2(X3,X1)\|~m1_unialg_2(X2,X1)\|~v2_unialg_1(X1)\|~v3_unialg_1(X1)\|~v4_unialg_1(X1)\|~l1_unialg_1(X1)), inference(split_conjunct,[status(thm)],[c_0_28])). cnf(c_0_66, plain, (k2_xboole_0(X1,X2)=X2\|~r1_tarski(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_58])). cnf(c_0_67, plain, (r1_tarski(k3_xboole_0(X1,X2),X1)), inference(split_conjunct,[status(thm)],[c_0_59])). cnf(c_0_68, negated_conjecture, (k3_xboole_0(u1_struct_0(esk3_0),u1_struct_0(esk2_0))=u1_struct_0(k5_unialg_2(esk1_0,esk3_0,esk2_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60, c_0_34]), c_0_43]), c_0_34]), c_0_35]), c_0_53]), c_0_36]), c_0_37]), c_0_38])]), c_0_39])])). cnf(c_0_69, negated_conjecture, (k3_xboole_0(u1_struct_0(esk3_0),u1_struct_0(esk2_0))=u1_struct_0(k5_unialg_2(esk1_0,esk2_0,esk3_0))), inference(rw,[status(thm)],[c_0_61, c_0_62])). cnf(c_0_70, negated_conjecture, (X1=k8_unialg_2(esk1_0,X2,X3)\|~m1_unialg_2(X1,esk1_0)\|~m1_unialg_2(X3,esk1_0)\|~m1_unialg_2(X2,esk1_0)\|~v1_unialg_1(X1)\|esk5_4(esk1_0,X2,X3,X1)!=u1_struct_0(esk3_0)\|esk3_0!=X1), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63, c_0_64]), c_0_35]), c_0_36]), c_0_37]), c_0_38])]), c_0_39])])). cnf(c_0_71, plain, (X4=k8_unialg_2(X1,X2,X3)\|esk5_4(X1,X2,X3,X4)=k2_xboole_0(u1_struct_0(X2),u1_struct_0(X3))\|v2_struct_0(X1)\|~v2_unialg_1(X1)\|~v3_unialg_1(X1)\|~v4_unialg_1(X1)\|~l1_unialg_1(X1)\|~v1_unialg_1(X4)\|~m1_unialg_2(X4,X1)\|~m1_unialg_2(X3,X1)\|~m1_unialg_2(X2,X1)), inference(evalgc,[status(thm)],[c_0_65])). cnf(c_0_72, plain, (k2_xboole_0(X1,X2)=X2\|~r1_tarski(X1,X2)), inference(evalgc,[status(thm)],[c_0_66])). cnf(c_0_73, plain, (r1_tarski(k3_xboole_0(X1,X2),X1)), inference(evalgc,[status(thm)],[c_0_67])). cnf(c_0_74, negated_conjecture, (u1_struct_0(k5_unialg_2(esk1_0,esk2_0,esk3_0))=u1_struct_0(k5_unialg_2(esk1_0,esk3_0,esk2_0))), inference(rw,[status(thm)],[c_0_68, c_0_69])). cnf(c_0_75, negated_conjecture, (X1=k8_unialg_2(esk1_0,X2,X3)\|k2_xboole_0(u1_struct_0(X2),u1_struct_0(X3))!=u1_struct_0(esk3_0)\|esk3_0!=X1\|~m1_unialg_2(X1,esk1_0)\|~m1_unialg_2(X3,esk1_0)\|~m1_unialg_2(X2,esk1_0)\|~v1_unialg_1(X1)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70, c_0_71]), c_0_35]), c_0_36]), c_0_37]), c_0_38])]), c_0_39])])). cnf(c_0_76, plain, (k2_xboole_0(k3_xboole_0(X1,X2),X1)=X1), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_72, c_0_73])])). cnf(c_0_77, negated_conjecture, (k3_xboole_0(u1_struct_0(esk3_0),u1_struct_0(esk2_0))=u1_struct_0(k5_unialg_2(esk1_0,esk3_0,esk2_0))), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[c_0_69, c_0_74])])). cnf(c_0_78, negated_conjecture, (X1=k8_unialg_2(esk1_0,k5_unialg_2(esk1_0,esk2_0,esk3_0),X2)\|k2_xboole_0(u1_struct_0(k5_unialg_2(esk1_0,esk3_0,esk2_0)),u1_struct_0(X2))!=u1_struct_0(esk3_0)\|esk3_0!=X1\|~m1_unialg_2(X1,esk1_0)\|~m1_unialg_2(X2,esk1_0)\|~m1_unialg_2(k5_unialg_2(esk1_0,esk2_0,esk3_0),esk1_0)\|~v1_unialg_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_75, c_0_74])])). cnf(c_0_79, negated_conjecture, (k2_xboole_0(u1_struct_0(k5_unialg_2(esk1_0,esk3_0,esk2_0)),u1_struct_0(esk3_0))=u1_struct_0(esk3_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_76, c_0_77])])). cnf(c_0_80, negated_conjecture, (k8_unialg_2(esk1_0,k5_unialg_2(esk1_0,esk2_0,esk3_0),esk3_0)!=esk3_0), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_81, negated_conjecture, (X1=k8_unialg_2(esk1_0,k5_unialg_2(esk1_0,esk2_0,esk3_0),esk3_0)\|esk3_0!=X1\|~m1_unialg_2(k5_unialg_2(esk1_0,esk2_0,esk3_0),esk1_0)\|~m1_unialg_2(X1,esk1_0)\|~v1_unialg_1(X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78, c_0_79]), c_0_34])])])). cnf(c_0_82, negated_conjecture, (k8_unialg_2(esk1_0,k5_unialg_2(esk1_0,esk2_0,esk3_0),esk3_0)!=esk3_0), inference(evalgc,[status(thm)],[c_0_80])). cnf(c_0_83, negated_conjecture, (~m1_unialg_2(k5_unialg_2(esk1_0,esk2_0,esk3_0),esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81, c_0_42]), c_0_34])]), c_0_82])])). cnf(c_0_84, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83, c_0_21]), c_0_34]), c_0_43]), c_0_35]), c_0_36]), c_0_37]), c_0_38])]), c_0_39]), ['proof']). # SZS output end CNFRefutation	reserve U0,U1,U2,U3 for Universal_Algebra, n for Nat, x,y for set; reserve A for non empty Subset of U0, o for operation of U0, x1,y1 for FinSequence of A; theorem Th23: for U0 be with_const_op Universal_Algebra,U1,U2 be strict SubAlgebra of U0 holds (U1 /\ U2)"\/"U2 = U2 proof let U0 be with_const_op Universal_Algebra, U1,U2 be strict SubAlgebra of U0; reconsider u12= the carrier of (U1 /\ U2), u2 = the carrier of U2 as non empty Subset of U0 by Def7; reconsider A=u12 \/ u2 as non empty Subset of U0; (the carrier of U1) meets (the carrier of U2) by Th17; then u12 = (the carrier of U1) /\ (the carrier of U2) by Def9; then A1: u12 c= u2 by XBOOLE_1:17; (U1 /\ U2)"\/"U2=GenUnivAlg(A) by Def13; hence thesis by A1,Th19,XBOOLE_1:12; end;	Convert the following ATP output trace into a readable Mizar proof.
t13_autalg_1	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(d4_msualg_3, axiom, ![X1, X2]:((v1_relat_1(X2)&(v4_relat_1(X2,X1)&(v1_funct_1(X2)&v1_partfun1(X2,X1))))=>![X3]:((v1_relat_1(X3)&(v4_relat_1(X3,X1)&(v1_funct_1(X3)&v1_partfun1(X3,X1))))=>![X4]:(m2_pboole(X4,X1,X2,X3)=>((v1_msualg_3(X4)&v2_msualg_3(X4,X1,X2,X3))=>![X5]:(m2_pboole(X5,X1,X3,X2)=>(X5=k4_msualg_3(X1,X2,X3,X4)<=>![X6]:(r2_hidden(X6,X1)=>k1_funct_1(X5,X6)=k2_funct_1(k1_funct_1(X4,X6))))))))), file('/scratch/mptp/predsminms1/t13_autalg_1__0', d4_msualg_3)). fof(dt_k4_msualg_3, axiom, ![X1, X2, X3, X4]:(((v1_relat_1(X2)&(v4_relat_1(X2,X1)&(v1_funct_1(X2)&v1_partfun1(X2,X1))))&((v1_relat_1(X3)&(v4_relat_1(X3,X1)&(v1_funct_1(X3)&v1_partfun1(X3,X1))))&m2_pboole(X4,X1,X2,X3)))=>m2_pboole(k4_msualg_3(X1,X2,X3,X4),X1,X3,X2)), file('/scratch/mptp/predsminms1/t13_autalg_1__0', dt_k4_msualg_3)). fof(t43_funct_1, axiom, ![X1]:((v1_relat_1(X1)&v1_funct_1(X1))=>(v2_funct_1(X1)=>k2_funct_1(k2_funct_1(X1))=X1)), file('/scratch/mptp/predsminms1/t13_autalg_1__0', t43_funct_1)). fof(t1_msualg_3, axiom, ![X1, X2]:((v1_relat_1(X2)&(v4_relat_1(X2,X1)&(v1_funct_1(X2)&(v1_partfun1(X2,X1)&v1_funcop_1(X2)))))=>(v1_msualg_3(X2)<=>![X3]:(r2_hidden(X3,X1)=>v2_funct_1(k1_funct_1(X2,X3))))), file('/scratch/mptp/predsminms1/t13_autalg_1__0', t1_msualg_3)). fof(dt_m2_pboole, axiom, ![X1, X2, X3]:(((v1_relat_1(X2)&(v4_relat_1(X2,X1)&(v1_funct_1(X2)&v1_partfun1(X2,X1))))&(v1_relat_1(X3)&(v4_relat_1(X3,X1)&(v1_funct_1(X3)&v1_partfun1(X3,X1)))))=>![X4]:(m2_pboole(X4,X1,X2,X3)=>(v1_relat_1(X4)&(v4_relat_1(X4,X1)&(v1_funct_1(X4)&v1_partfun1(X4,X1)))))), file('/scratch/mptp/predsminms1/t13_autalg_1__0', dt_m2_pboole)). fof(cc3_pboole, axiom, ![X1, X2, X3]:(((v1_relat_1(X2)&(v4_relat_1(X2,X1)&(v1_funct_1(X2)&v1_partfun1(X2,X1))))&(v1_relat_1(X3)&(v4_relat_1(X3,X1)&(v1_funct_1(X3)&v1_partfun1(X3,X1)))))=>![X4]:(m2_pboole(X4,X1,X2,X3)=>v1_funcop_1(X4))), file('/scratch/mptp/predsminms1/t13_autalg_1__0', cc3_pboole)). fof(fc8_funcop_1, axiom, ![X1, X2]:((v1_relat_1(X1)&(v1_funct_1(X1)&v1_funcop_1(X1)))=>(v1_relat_1(k1_funct_1(X1,X2))&v1_funct_1(k1_funct_1(X1,X2)))), file('/scratch/mptp/predsminms1/t13_autalg_1__0', fc8_funcop_1)). fof(t12_autalg_1, axiom, ![X1, X2]:((v1_relat_1(X2)&(v2_relat_1(X2)&(v4_relat_1(X2,X1)&(v1_funct_1(X2)&v1_partfun1(X2,X1)))))=>![X3]:((v1_relat_1(X3)&(v2_relat_1(X3)&(v4_relat_1(X3,X1)&(v1_funct_1(X3)&v1_partfun1(X3,X1)))))=>![X4]:(m2_pboole(X4,X1,X2,X3)=>((v1_msualg_3(X4)&v2_msualg_3(X4,X1,X2,X3))=>(v1_msualg_3(k4_msualg_3(X1,X2,X3,X4))&v2_msualg_3(k4_msualg_3(X1,X2,X3,X4),X1,X3,X2)))))), file('/scratch/mptp/predsminms1/t13_autalg_1__0', t12_autalg_1)). fof(t13_autalg_1, conjecture, ![X1, X2]:((v1_relat_1(X2)&(v2_relat_1(X2)&(v4_relat_1(X2,X1)&(v1_funct_1(X2)&v1_partfun1(X2,X1)))))=>![X3]:((v1_relat_1(X3)&(v2_relat_1(X3)&(v4_relat_1(X3,X1)&(v1_funct_1(X3)&v1_partfun1(X3,X1)))))=>![X4]:(m2_pboole(X4,X1,X2,X3)=>((v1_msualg_3(X4)&v2_msualg_3(X4,X1,X2,X3))=>r6_pboole(X1,k4_msualg_3(X1,X3,X2,k4_msualg_3(X1,X2,X3,X4)),X4))))), file('/scratch/mptp/predsminms1/t13_autalg_1__0', t13_autalg_1)). fof(reflexivity_r6_pboole, axiom, ![X1, X2, X3]:(((v1_relat_1(X2)&(v4_relat_1(X2,X1)&(v1_funct_1(X2)&v1_partfun1(X2,X1))))&(v1_relat_1(X3)&(v4_relat_1(X3,X1)&(v1_funct_1(X3)&v1_partfun1(X3,X1)))))=>r6_pboole(X1,X2,X2)), file('/scratch/mptp/predsminms1/t13_autalg_1__0', reflexivity_r6_pboole)). fof(rc4_pboole, axiom, ![X1]:?[X2]:(v1_relat_1(X2)&(v4_relat_1(X2,X1)&(v1_funct_1(X2)&(v1_partfun1(X2,X1)&v1_funcop_1(X2))))), file('/scratch/mptp/predsminms1/t13_autalg_1__0', rc4_pboole)). fof(c_0_11, plain, ![X11, X12, X13, X14, X15, X16]:((X15!=k4_msualg_3(X11,X12,X13,X14)\|(~r2_hidden(X16,X11)\|k1_funct_1(X15,X16)=k2_funct_1(k1_funct_1(X14,X16)))\|~m2_pboole(X15,X11,X13,X12)\|(~v1_msualg_3(X14)\|~v2_msualg_3(X14,X11,X12,X13))\|~m2_pboole(X14,X11,X12,X13)\|(~v1_relat_1(X13)\|(~v4_relat_1(X13,X11)\|(~v1_funct_1(X13)\|~v1_partfun1(X13,X11))))\|(~v1_relat_1(X12)\|(~v4_relat_1(X12,X11)\|(~v1_funct_1(X12)\|~v1_partfun1(X12,X11)))))&((r2_hidden(esk5_5(X11,X12,X13,X14,X15),X11)\|X15=k4_msualg_3(X11,X12,X13,X14)\|~m2_pboole(X15,X11,X13,X12)\|(~v1_msualg_3(X14)\|~v2_msualg_3(X14,X11,X12,X13))\|~m2_pboole(X14,X11,X12,X13)\|(~v1_relat_1(X13)\|(~v4_relat_1(X13,X11)\|(~v1_funct_1(X13)\|~v1_partfun1(X13,X11))))\|(~v1_relat_1(X12)\|(~v4_relat_1(X12,X11)\|(~v1_funct_1(X12)\|~v1_partfun1(X12,X11)))))&(k1_funct_1(X15,esk5_5(X11,X12,X13,X14,X15))!=k2_funct_1(k1_funct_1(X14,esk5_5(X11,X12,X13,X14,X15)))\|X15=k4_msualg_3(X11,X12,X13,X14)\|~m2_pboole(X15,X11,X13,X12)\|(~v1_msualg_3(X14)\|~v2_msualg_3(X14,X11,X12,X13))\|~m2_pboole(X14,X11,X12,X13)\|(~v1_relat_1(X13)\|(~v4_relat_1(X13,X11)\|(~v1_funct_1(X13)\|~v1_partfun1(X13,X11))))\|(~v1_relat_1(X12)\|(~v4_relat_1(X12,X11)\|(~v1_funct_1(X12)\|~v1_partfun1(X12,X11))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d4_msualg_3])])])])])). cnf(c_0_12, plain, (k1_funct_1(X1,X6)=k2_funct_1(k1_funct_1(X5,X6))\|X1!=k4_msualg_3(X2,X3,X4,X5)\|~r2_hidden(X6,X2)\|~m2_pboole(X1,X2,X4,X3)\|~v1_msualg_3(X5)\|~v2_msualg_3(X5,X2,X3,X4)\|~m2_pboole(X5,X2,X3,X4)\|~v1_relat_1(X4)\|~v4_relat_1(X4,X2)\|~v1_funct_1(X4)\|~v1_partfun1(X4,X2)\|~v1_relat_1(X3)\|~v4_relat_1(X3,X2)\|~v1_funct_1(X3)\|~v1_partfun1(X3,X2)), inference(split_conjunct,[status(thm)],[c_0_11])). fof(c_0_13, plain, ![X18, X19, X20, X21]:(~v1_relat_1(X19)\|(~v4_relat_1(X19,X18)\|(~v1_funct_1(X19)\|~v1_partfun1(X19,X18)))\|(~v1_relat_1(X20)\|(~v4_relat_1(X20,X18)\|(~v1_funct_1(X20)\|~v1_partfun1(X20,X18)))\|~m2_pboole(X21,X18,X19,X20))\|m2_pboole(k4_msualg_3(X18,X19,X20,X21),X18,X20,X19)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k4_msualg_3])])). fof(c_0_14, plain, ![X22]:(~v1_relat_1(X22)\|~v1_funct_1(X22)\|(~v2_funct_1(X22)\|k2_funct_1(k2_funct_1(X22))=X22)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t43_funct_1])])). cnf(c_0_15, plain, (k1_funct_1(X1,X6)=k2_funct_1(k1_funct_1(X5,X6))\|X1!=k4_msualg_3(X2,X3,X4,X5)\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v1_msualg_3(X5)\|~v4_relat_1(X4,X2)\|~v4_relat_1(X3,X2)\|~v1_partfun1(X4,X2)\|~v1_partfun1(X3,X2)\|~r2_hidden(X6,X2)\|~m2_pboole(X5,X2,X3,X4)\|~m2_pboole(X1,X2,X4,X3)\|~v2_msualg_3(X5,X2,X3,X4)), inference(evalgc,[status(thm)],[c_0_12])). cnf(c_0_16, plain, (m2_pboole(k4_msualg_3(X2,X1,X3,X4),X2,X3,X1)\|~v1_relat_1(X1)\|~v4_relat_1(X1,X2)\|~v1_funct_1(X1)\|~v1_partfun1(X1,X2)\|~v1_relat_1(X3)\|~v4_relat_1(X3,X2)\|~v1_funct_1(X3)\|~v1_partfun1(X3,X2)\|~m2_pboole(X4,X2,X1,X3)), inference(split_conjunct,[status(thm)],[c_0_13])). cnf(c_0_17, plain, (k2_funct_1(k2_funct_1(X1))=X1\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v2_funct_1(X1)), inference(split_conjunct,[status(thm)],[c_0_14])). cnf(c_0_18, plain, (k1_funct_1(k4_msualg_3(X1,X2,X3,X4),X5)=k2_funct_1(k1_funct_1(X4,X5))\|~r2_hidden(X5,X1)\|~v2_msualg_3(X4,X1,X2,X3)\|~v1_msualg_3(X4)\|~m2_pboole(X4,X1,X2,X3)\|~m2_pboole(k4_msualg_3(X1,X2,X3,X4),X1,X3,X2)\|~v1_partfun1(X3,X1)\|~v1_partfun1(X2,X1)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v4_relat_1(X3,X1)\|~v4_relat_1(X2,X1)\|~v1_relat_1(X3)\|~v1_relat_1(X2)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_15])])). cnf(c_0_19, plain, (m2_pboole(k4_msualg_3(X2,X1,X3,X4),X2,X3,X1)\|~v1_relat_1(X3)\|~v1_relat_1(X1)\|~v1_funct_1(X3)\|~v1_funct_1(X1)\|~v4_relat_1(X3,X2)\|~v4_relat_1(X1,X2)\|~v1_partfun1(X3,X2)\|~v1_partfun1(X1,X2)\|~m2_pboole(X4,X2,X1,X3)), inference(evalgc,[status(thm)],[c_0_16])). fof(c_0_20, plain, ![X23, X24, X25]:((~v1_msualg_3(X24)\|(~r2_hidden(X25,X23)\|v2_funct_1(k1_funct_1(X24,X25)))\|(~v1_relat_1(X24)\|(~v4_relat_1(X24,X23)\|(~v1_funct_1(X24)\|(~v1_partfun1(X24,X23)\|~v1_funcop_1(X24))))))&((r2_hidden(esk6_2(X23,X24),X23)\|v1_msualg_3(X24)\|(~v1_relat_1(X24)\|(~v4_relat_1(X24,X23)\|(~v1_funct_1(X24)\|(~v1_partfun1(X24,X23)\|~v1_funcop_1(X24))))))&(~v2_funct_1(k1_funct_1(X24,esk6_2(X23,X24)))\|v1_msualg_3(X24)\|(~v1_relat_1(X24)\|(~v4_relat_1(X24,X23)\|(~v1_funct_1(X24)\|(~v1_partfun1(X24,X23)\|~v1_funcop_1(X24)))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_msualg_3])])])])])). cnf(c_0_21, plain, (X1=k4_msualg_3(X2,X3,X4,X5)\|k1_funct_1(X1,esk5_5(X2,X3,X4,X5,X1))!=k2_funct_1(k1_funct_1(X5,esk5_5(X2,X3,X4,X5,X1)))\|~m2_pboole(X1,X2,X4,X3)\|~v1_msualg_3(X5)\|~v2_msualg_3(X5,X2,X3,X4)\|~m2_pboole(X5,X2,X3,X4)\|~v1_relat_1(X4)\|~v4_relat_1(X4,X2)\|~v1_funct_1(X4)\|~v1_partfun1(X4,X2)\|~v1_relat_1(X3)\|~v4_relat_1(X3,X2)\|~v1_funct_1(X3)\|~v1_partfun1(X3,X2)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_22, plain, (k2_funct_1(k2_funct_1(X1))=X1\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v2_funct_1(X1)), inference(evalgc,[status(thm)],[c_0_17])). cnf(c_0_23, plain, (k1_funct_1(k4_msualg_3(X1,X2,X3,X4),X5)=k2_funct_1(k1_funct_1(X4,X5))\|~r2_hidden(X5,X1)\|~v2_msualg_3(X4,X1,X2,X3)\|~v1_msualg_3(X4)\|~m2_pboole(X4,X1,X2,X3)\|~v1_partfun1(X3,X1)\|~v1_partfun1(X2,X1)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v4_relat_1(X3,X1)\|~v4_relat_1(X2,X1)\|~v1_relat_1(X3)\|~v1_relat_1(X2)), inference(csr,[status(thm)],[c_0_18, c_0_19])). cnf(c_0_24, plain, (v2_funct_1(k1_funct_1(X1,X2))\|~v1_msualg_3(X1)\|~r2_hidden(X2,X3)\|~v1_relat_1(X1)\|~v4_relat_1(X1,X3)\|~v1_funct_1(X1)\|~v1_partfun1(X1,X3)\|~v1_funcop_1(X1)), inference(split_conjunct,[status(thm)],[c_0_20])). cnf(c_0_25, plain, (r2_hidden(esk5_5(X1,X2,X3,X4,X5),X1)\|X5=k4_msualg_3(X1,X2,X3,X4)\|~m2_pboole(X5,X1,X3,X2)\|~v1_msualg_3(X4)\|~v2_msualg_3(X4,X1,X2,X3)\|~m2_pboole(X4,X1,X2,X3)\|~v1_relat_1(X3)\|~v4_relat_1(X3,X1)\|~v1_funct_1(X3)\|~v1_partfun1(X3,X1)\|~v1_relat_1(X2)\|~v4_relat_1(X2,X1)\|~v1_funct_1(X2)\|~v1_partfun1(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_26, plain, (X1=k4_msualg_3(X2,X3,X4,X5)\|k1_funct_1(X1,esk5_5(X2,X3,X4,X5,X1))!=k2_funct_1(k1_funct_1(X5,esk5_5(X2,X3,X4,X5,X1)))\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v1_msualg_3(X5)\|~v4_relat_1(X4,X2)\|~v4_relat_1(X3,X2)\|~v1_partfun1(X4,X2)\|~v1_partfun1(X3,X2)\|~m2_pboole(X5,X2,X3,X4)\|~m2_pboole(X1,X2,X4,X3)\|~v2_msualg_3(X5,X2,X3,X4)), inference(evalgc,[status(thm)],[c_0_21])). cnf(c_0_27, plain, (k2_funct_1(k1_funct_1(k4_msualg_3(X3,X4,X5,X1),X2))=k1_funct_1(X1,X2)\|~v2_funct_1(k1_funct_1(X1,X2))\|~v1_funct_1(k1_funct_1(X1,X2))\|~v1_relat_1(k1_funct_1(X1,X2))\|~r2_hidden(X2,X3)\|~v2_msualg_3(X1,X3,X4,X5)\|~v1_msualg_3(X1)\|~m2_pboole(X1,X3,X4,X5)\|~v1_partfun1(X5,X3)\|~v1_partfun1(X4,X3)\|~v1_funct_1(X5)\|~v1_funct_1(X4)\|~v4_relat_1(X5,X3)\|~v4_relat_1(X4,X3)\|~v1_relat_1(X5)\|~v1_relat_1(X4)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_22, c_0_23])])). cnf(c_0_28, plain, (v2_funct_1(k1_funct_1(X1,X2))\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v1_msualg_3(X1)\|~v1_funcop_1(X1)\|~v4_relat_1(X1,X3)\|~v1_partfun1(X1,X3)\|~r2_hidden(X2,X3)), inference(evalgc,[status(thm)],[c_0_24])). cnf(c_0_29, plain, (X5=k4_msualg_3(X1,X2,X3,X4)\|r2_hidden(esk5_5(X1,X2,X3,X4,X5),X1)\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v1_msualg_3(X4)\|~v4_relat_1(X3,X1)\|~v4_relat_1(X2,X1)\|~v1_partfun1(X3,X1)\|~v1_partfun1(X2,X1)\|~m2_pboole(X5,X1,X3,X2)\|~m2_pboole(X4,X1,X2,X3)\|~v2_msualg_3(X4,X1,X2,X3)), inference(evalgc,[status(thm)],[c_0_25])). fof(c_0_30, plain, ![X31, X32, X33, X34]:((v1_relat_1(X34)\|~m2_pboole(X34,X31,X32,X33)\|(~v1_relat_1(X32)\|(~v4_relat_1(X32,X31)\|(~v1_funct_1(X32)\|~v1_partfun1(X32,X31)))\|(~v1_relat_1(X33)\|(~v4_relat_1(X33,X31)\|(~v1_funct_1(X33)\|~v1_partfun1(X33,X31))))))&((v4_relat_1(X34,X31)\|~m2_pboole(X34,X31,X32,X33)\|(~v1_relat_1(X32)\|(~v4_relat_1(X32,X31)\|(~v1_funct_1(X32)\|~v1_partfun1(X32,X31)))\|(~v1_relat_1(X33)\|(~v4_relat_1(X33,X31)\|(~v1_funct_1(X33)\|~v1_partfun1(X33,X31))))))&((v1_funct_1(X34)\|~m2_pboole(X34,X31,X32,X33)\|(~v1_relat_1(X32)\|(~v4_relat_1(X32,X31)\|(~v1_funct_1(X32)\|~v1_partfun1(X32,X31)))\|(~v1_relat_1(X33)\|(~v4_relat_1(X33,X31)\|(~v1_funct_1(X33)\|~v1_partfun1(X33,X31))))))&(v1_partfun1(X34,X31)\|~m2_pboole(X34,X31,X32,X33)\|(~v1_relat_1(X32)\|(~v4_relat_1(X32,X31)\|(~v1_funct_1(X32)\|~v1_partfun1(X32,X31)))\|(~v1_relat_1(X33)\|(~v4_relat_1(X33,X31)\|(~v1_funct_1(X33)\|~v1_partfun1(X33,X31))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m2_pboole])])])])). fof(c_0_31, plain, ![X27, X28, X29, X30]:(~v1_relat_1(X28)\|(~v4_relat_1(X28,X27)\|(~v1_funct_1(X28)\|~v1_partfun1(X28,X27)))\|(~v1_relat_1(X29)\|(~v4_relat_1(X29,X27)\|(~v1_funct_1(X29)\|~v1_partfun1(X29,X27))))\|(~m2_pboole(X30,X27,X28,X29)\|v1_funcop_1(X30))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc3_pboole])])])). cnf(c_0_32, plain, (X1=k4_msualg_3(X2,X3,X4,k4_msualg_3(X5,X6,X7,X8))\|k1_funct_1(X1,esk5_5(X2,X3,X4,k4_msualg_3(X5,X6,X7,X8),X1))!=k1_funct_1(X8,esk5_5(X2,X3,X4,k4_msualg_3(X5,X6,X7,X8),X1))\|~v2_msualg_3(k4_msualg_3(X5,X6,X7,X8),X2,X3,X4)\|~v1_msualg_3(k4_msualg_3(X5,X6,X7,X8))\|~m2_pboole(k4_msualg_3(X5,X6,X7,X8),X2,X3,X4)\|~m2_pboole(X1,X2,X4,X3)\|~v1_partfun1(X4,X2)\|~v1_partfun1(X3,X2)\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v4_relat_1(X4,X2)\|~v4_relat_1(X3,X2)\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~v2_funct_1(k1_funct_1(X8,esk5_5(X2,X3,X4,k4_msualg_3(X5,X6,X7,X8),X1)))\|~r2_hidden(esk5_5(X2,X3,X4,k4_msualg_3(X5,X6,X7,X8),X1),X5)\|~v2_msualg_3(X8,X5,X6,X7)\|~v1_msualg_3(X8)\|~m2_pboole(X8,X5,X6,X7)\|~v1_partfun1(X7,X5)\|~v1_partfun1(X6,X5)\|~v1_funct_1(k1_funct_1(X8,esk5_5(X2,X3,X4,k4_msualg_3(X5,X6,X7,X8),X1)))\|~v1_funct_1(X7)\|~v1_funct_1(X6)\|~v4_relat_1(X7,X5)\|~v4_relat_1(X6,X5)\|~v1_relat_1(k1_funct_1(X8,esk5_5(X2,X3,X4,k4_msualg_3(X5,X6,X7,X8),X1)))\|~v1_relat_1(X7)\|~v1_relat_1(X6)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_26, c_0_27])])). cnf(c_0_33, plain, (v2_funct_1(k1_funct_1(X1,esk5_5(X2,X3,X4,X5,X6)))\|X6=k4_msualg_3(X2,X3,X4,X5)\|~v1_funcop_1(X1)\|~v1_msualg_3(X1)\|~v1_partfun1(X1,X2)\|~v1_funct_1(X1)\|~v4_relat_1(X1,X2)\|~v1_relat_1(X1)\|~v2_msualg_3(X5,X2,X3,X4)\|~v1_msualg_3(X5)\|~m2_pboole(X6,X2,X4,X3)\|~m2_pboole(X5,X2,X3,X4)\|~v1_partfun1(X4,X2)\|~v1_partfun1(X3,X2)\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v4_relat_1(X4,X2)\|~v4_relat_1(X3,X2)\|~v1_relat_1(X4)\|~v1_relat_1(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_28, c_0_29])])). cnf(c_0_34, plain, (v1_relat_1(X1)\|~m2_pboole(X1,X2,X3,X4)\|~v1_relat_1(X3)\|~v4_relat_1(X3,X2)\|~v1_funct_1(X3)\|~v1_partfun1(X3,X2)\|~v1_relat_1(X4)\|~v4_relat_1(X4,X2)\|~v1_funct_1(X4)\|~v1_partfun1(X4,X2)), inference(split_conjunct,[status(thm)],[c_0_30])). cnf(c_0_35, plain, (v1_funct_1(X1)\|~m2_pboole(X1,X2,X3,X4)\|~v1_relat_1(X3)\|~v4_relat_1(X3,X2)\|~v1_funct_1(X3)\|~v1_partfun1(X3,X2)\|~v1_relat_1(X4)\|~v4_relat_1(X4,X2)\|~v1_funct_1(X4)\|~v1_partfun1(X4,X2)), inference(split_conjunct,[status(thm)],[c_0_30])). cnf(c_0_36, plain, (v1_funcop_1(X4)\|~v1_relat_1(X1)\|~v4_relat_1(X1,X2)\|~v1_funct_1(X1)\|~v1_partfun1(X1,X2)\|~v1_relat_1(X3)\|~v4_relat_1(X3,X2)\|~v1_funct_1(X3)\|~v1_partfun1(X3,X2)\|~m2_pboole(X4,X2,X1,X3)), inference(split_conjunct,[status(thm)],[c_0_31])). fof(c_0_37, plain, ![X35, X36]:((v1_relat_1(k1_funct_1(X35,X36))\|(~v1_relat_1(X35)\|(~v1_funct_1(X35)\|~v1_funcop_1(X35))))&(v1_funct_1(k1_funct_1(X35,X36))\|(~v1_relat_1(X35)\|(~v1_funct_1(X35)\|~v1_funcop_1(X35))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc8_funcop_1])])])). cnf(c_0_38, plain, (X1=k4_msualg_3(X2,X3,X4,k4_msualg_3(X5,X6,X7,X8))\|k1_funct_1(X1,esk5_5(X2,X3,X4,k4_msualg_3(X5,X6,X7,X8),X1))!=k1_funct_1(X8,esk5_5(X2,X3,X4,k4_msualg_3(X5,X6,X7,X8),X1))\|~r2_hidden(esk5_5(X2,X3,X4,k4_msualg_3(X5,X6,X7,X8),X1),X5)\|~v2_msualg_3(k4_msualg_3(X5,X6,X7,X8),X2,X3,X4)\|~v2_msualg_3(X8,X5,X6,X7)\|~v1_msualg_3(k4_msualg_3(X5,X6,X7,X8))\|~v1_msualg_3(X8)\|~m2_pboole(k4_msualg_3(X5,X6,X7,X8),X2,X3,X4)\|~m2_pboole(X1,X2,X4,X3)\|~m2_pboole(X8,X5,X6,X7)\|~v1_partfun1(X4,X2)\|~v1_partfun1(X3,X2)\|~v1_partfun1(X7,X5)\|~v1_partfun1(X6,X5)\|~v1_funct_1(k1_funct_1(X8,esk5_5(X2,X3,X4,k4_msualg_3(X5,X6,X7,X8),X1)))\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v1_funct_1(X7)\|~v1_funct_1(X6)\|~v4_relat_1(X4,X2)\|~v4_relat_1(X3,X2)\|~v4_relat_1(X7,X5)\|~v4_relat_1(X6,X5)\|~v1_relat_1(k1_funct_1(X8,esk5_5(X2,X3,X4,k4_msualg_3(X5,X6,X7,X8),X1)))\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~v1_relat_1(X7)\|~v1_relat_1(X6)\|~v1_funcop_1(X8)\|~v1_partfun1(X8,X2)\|~v1_funct_1(X8)\|~v4_relat_1(X8,X2)\|~v1_relat_1(X8)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_32, c_0_33])])). cnf(c_0_39, plain, (v1_relat_1(X1)\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v4_relat_1(X4,X2)\|~v4_relat_1(X3,X2)\|~v1_partfun1(X4,X2)\|~v1_partfun1(X3,X2)\|~m2_pboole(X1,X2,X3,X4)), inference(evalgc,[status(thm)],[c_0_34])). cnf(c_0_40, plain, (v1_funct_1(X1)\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v4_relat_1(X4,X2)\|~v4_relat_1(X3,X2)\|~v1_partfun1(X4,X2)\|~v1_partfun1(X3,X2)\|~m2_pboole(X1,X2,X3,X4)), inference(evalgc,[status(thm)],[c_0_35])). cnf(c_0_41, plain, (v1_funcop_1(X4)\|~v1_relat_1(X3)\|~v1_relat_1(X1)\|~v1_funct_1(X3)\|~v1_funct_1(X1)\|~v4_relat_1(X3,X2)\|~v4_relat_1(X1,X2)\|~v1_partfun1(X3,X2)\|~v1_partfun1(X1,X2)\|~m2_pboole(X4,X2,X1,X3)), inference(evalgc,[status(thm)],[c_0_36])). cnf(c_0_42, plain, (v1_funct_1(k1_funct_1(X1,X2))\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v1_funcop_1(X1)), inference(split_conjunct,[status(thm)],[c_0_37])). cnf(c_0_43, plain, (X1=k4_msualg_3(X2,X3,X4,k4_msualg_3(X5,X6,X7,X8))\|k1_funct_1(X1,esk5_5(X2,X3,X4,k4_msualg_3(X5,X6,X7,X8),X1))!=k1_funct_1(X8,esk5_5(X2,X3,X4,k4_msualg_3(X5,X6,X7,X8),X1))\|~r2_hidden(esk5_5(X2,X3,X4,k4_msualg_3(X5,X6,X7,X8),X1),X5)\|~v2_msualg_3(k4_msualg_3(X5,X6,X7,X8),X2,X3,X4)\|~v2_msualg_3(X8,X5,X6,X7)\|~v1_msualg_3(k4_msualg_3(X5,X6,X7,X8))\|~v1_msualg_3(X8)\|~m2_pboole(k4_msualg_3(X5,X6,X7,X8),X2,X3,X4)\|~m2_pboole(X1,X2,X4,X3)\|~m2_pboole(X8,X5,X6,X7)\|~v1_partfun1(X4,X2)\|~v1_partfun1(X3,X2)\|~v1_partfun1(X7,X5)\|~v1_partfun1(X6,X5)\|~v1_partfun1(X8,X2)\|~v1_funct_1(k1_funct_1(X8,esk5_5(X2,X3,X4,k4_msualg_3(X5,X6,X7,X8),X1)))\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v1_funct_1(X7)\|~v1_funct_1(X6)\|~v4_relat_1(X4,X2)\|~v4_relat_1(X3,X2)\|~v4_relat_1(X7,X5)\|~v4_relat_1(X6,X5)\|~v4_relat_1(X8,X2)\|~v1_relat_1(k1_funct_1(X8,esk5_5(X2,X3,X4,k4_msualg_3(X5,X6,X7,X8),X1)))\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~v1_relat_1(X7)\|~v1_relat_1(X6)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_38, c_0_39]), c_0_40]), c_0_41])). cnf(c_0_44, plain, (v1_funct_1(k1_funct_1(X1,X2))\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v1_funcop_1(X1)), inference(evalgc,[status(thm)],[c_0_42])). cnf(c_0_45, plain, (X1=k4_msualg_3(X2,X3,X4,k4_msualg_3(X5,X6,X7,X8))\|k1_funct_1(X1,esk5_5(X2,X3,X4,k4_msualg_3(X5,X6,X7,X8),X1))!=k1_funct_1(X8,esk5_5(X2,X3,X4,k4_msualg_3(X5,X6,X7,X8),X1))\|~r2_hidden(esk5_5(X2,X3,X4,k4_msualg_3(X5,X6,X7,X8),X1),X5)\|~v2_msualg_3(k4_msualg_3(X5,X6,X7,X8),X2,X3,X4)\|~v2_msualg_3(X8,X5,X6,X7)\|~v1_msualg_3(k4_msualg_3(X5,X6,X7,X8))\|~v1_msualg_3(X8)\|~m2_pboole(k4_msualg_3(X5,X6,X7,X8),X2,X3,X4)\|~m2_pboole(X1,X2,X4,X3)\|~m2_pboole(X8,X5,X6,X7)\|~v1_partfun1(X4,X2)\|~v1_partfun1(X3,X2)\|~v1_partfun1(X7,X5)\|~v1_partfun1(X6,X5)\|~v1_partfun1(X8,X2)\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v1_funct_1(X7)\|~v1_funct_1(X6)\|~v4_relat_1(X4,X2)\|~v4_relat_1(X3,X2)\|~v4_relat_1(X7,X5)\|~v4_relat_1(X6,X5)\|~v4_relat_1(X8,X2)\|~v1_relat_1(k1_funct_1(X8,esk5_5(X2,X3,X4,k4_msualg_3(X5,X6,X7,X8),X1)))\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~v1_relat_1(X7)\|~v1_relat_1(X6)\|~v1_funcop_1(X8)\|~v1_funct_1(X8)\|~v1_relat_1(X8)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_43, c_0_44])])). cnf(c_0_46, plain, (v1_relat_1(k1_funct_1(X1,X2))\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v1_funcop_1(X1)), inference(split_conjunct,[status(thm)],[c_0_37])). cnf(c_0_47, plain, (X1=k4_msualg_3(X2,X3,X4,k4_msualg_3(X5,X6,X7,X8))\|k1_funct_1(X1,esk5_5(X2,X3,X4,k4_msualg_3(X5,X6,X7,X8),X1))!=k1_funct_1(X8,esk5_5(X2,X3,X4,k4_msualg_3(X5,X6,X7,X8),X1))\|~r2_hidden(esk5_5(X2,X3,X4,k4_msualg_3(X5,X6,X7,X8),X1),X5)\|~v2_msualg_3(k4_msualg_3(X5,X6,X7,X8),X2,X3,X4)\|~v2_msualg_3(X8,X5,X6,X7)\|~v1_msualg_3(k4_msualg_3(X5,X6,X7,X8))\|~v1_msualg_3(X8)\|~m2_pboole(k4_msualg_3(X5,X6,X7,X8),X2,X3,X4)\|~m2_pboole(X1,X2,X4,X3)\|~m2_pboole(X8,X5,X6,X7)\|~v1_partfun1(X4,X2)\|~v1_partfun1(X3,X2)\|~v1_partfun1(X7,X5)\|~v1_partfun1(X6,X5)\|~v1_partfun1(X8,X2)\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v1_funct_1(X7)\|~v1_funct_1(X6)\|~v4_relat_1(X4,X2)\|~v4_relat_1(X3,X2)\|~v4_relat_1(X7,X5)\|~v4_relat_1(X6,X5)\|~v4_relat_1(X8,X2)\|~v1_relat_1(k1_funct_1(X8,esk5_5(X2,X3,X4,k4_msualg_3(X5,X6,X7,X8),X1)))\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~v1_relat_1(X7)\|~v1_relat_1(X6)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_45, c_0_39]), c_0_40]), c_0_41])). cnf(c_0_48, plain, (v1_relat_1(k1_funct_1(X1,X2))\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v1_funcop_1(X1)), inference(evalgc,[status(thm)],[c_0_46])). cnf(c_0_49, plain, (X1=k4_msualg_3(X2,X3,X4,k4_msualg_3(X5,X6,X7,X8))\|k1_funct_1(X1,esk5_5(X2,X3,X4,k4_msualg_3(X5,X6,X7,X8),X1))!=k1_funct_1(X8,esk5_5(X2,X3,X4,k4_msualg_3(X5,X6,X7,X8),X1))\|~r2_hidden(esk5_5(X2,X3,X4,k4_msualg_3(X5,X6,X7,X8),X1),X5)\|~v2_msualg_3(k4_msualg_3(X5,X6,X7,X8),X2,X3,X4)\|~v2_msualg_3(X8,X5,X6,X7)\|~v1_msualg_3(k4_msualg_3(X5,X6,X7,X8))\|~v1_msualg_3(X8)\|~m2_pboole(k4_msualg_3(X5,X6,X7,X8),X2,X3,X4)\|~m2_pboole(X1,X2,X4,X3)\|~m2_pboole(X8,X5,X6,X7)\|~v1_partfun1(X4,X2)\|~v1_partfun1(X3,X2)\|~v1_partfun1(X7,X5)\|~v1_partfun1(X6,X5)\|~v1_partfun1(X8,X2)\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v1_funct_1(X7)\|~v1_funct_1(X6)\|~v4_relat_1(X4,X2)\|~v4_relat_1(X3,X2)\|~v4_relat_1(X7,X5)\|~v4_relat_1(X6,X5)\|~v4_relat_1(X8,X2)\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~v1_relat_1(X7)\|~v1_relat_1(X6)\|~v1_funcop_1(X8)\|~v1_funct_1(X8)\|~v1_relat_1(X8)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_47, c_0_48])])). cnf(c_0_50, plain, (X1=k4_msualg_3(X2,X3,X4,k4_msualg_3(X5,X6,X7,X8))\|k1_funct_1(X1,esk5_5(X2,X3,X4,k4_msualg_3(X5,X6,X7,X8),X1))!=k1_funct_1(X8,esk5_5(X2,X3,X4,k4_msualg_3(X5,X6,X7,X8),X1))\|~r2_hidden(esk5_5(X2,X3,X4,k4_msualg_3(X5,X6,X7,X8),X1),X5)\|~v2_msualg_3(k4_msualg_3(X5,X6,X7,X8),X2,X3,X4)\|~v2_msualg_3(X8,X5,X6,X7)\|~v1_msualg_3(k4_msualg_3(X5,X6,X7,X8))\|~v1_msualg_3(X8)\|~m2_pboole(k4_msualg_3(X5,X6,X7,X8),X2,X3,X4)\|~m2_pboole(X1,X2,X4,X3)\|~m2_pboole(X8,X5,X6,X7)\|~v1_partfun1(X4,X2)\|~v1_partfun1(X3,X2)\|~v1_partfun1(X7,X5)\|~v1_partfun1(X6,X5)\|~v1_partfun1(X8,X2)\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v1_funct_1(X7)\|~v1_funct_1(X6)\|~v4_relat_1(X4,X2)\|~v4_relat_1(X3,X2)\|~v4_relat_1(X7,X5)\|~v4_relat_1(X6,X5)\|~v4_relat_1(X8,X2)\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~v1_relat_1(X7)\|~v1_relat_1(X6)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_49, c_0_39]), c_0_40]), c_0_41])). cnf(c_0_51, plain, (v4_relat_1(X1,X2)\|~m2_pboole(X1,X2,X3,X4)\|~v1_relat_1(X3)\|~v4_relat_1(X3,X2)\|~v1_funct_1(X3)\|~v1_partfun1(X3,X2)\|~v1_relat_1(X4)\|~v4_relat_1(X4,X2)\|~v1_funct_1(X4)\|~v1_partfun1(X4,X2)), inference(split_conjunct,[status(thm)],[c_0_30])). cnf(c_0_52, plain, (v1_partfun1(X1,X2)\|~m2_pboole(X1,X2,X3,X4)\|~v1_relat_1(X3)\|~v4_relat_1(X3,X2)\|~v1_funct_1(X3)\|~v1_partfun1(X3,X2)\|~v1_relat_1(X4)\|~v4_relat_1(X4,X2)\|~v1_funct_1(X4)\|~v1_partfun1(X4,X2)), inference(split_conjunct,[status(thm)],[c_0_30])). cnf(c_0_53, plain, (X1=k4_msualg_3(X2,X3,X4,k4_msualg_3(X2,X5,X6,X7))\|k1_funct_1(X1,esk5_5(X2,X3,X4,k4_msualg_3(X2,X5,X6,X7),X1))!=k1_funct_1(X7,esk5_5(X2,X3,X4,k4_msualg_3(X2,X5,X6,X7),X1))\|~v2_msualg_3(k4_msualg_3(X2,X5,X6,X7),X2,X3,X4)\|~v2_msualg_3(X7,X2,X5,X6)\|~v1_msualg_3(k4_msualg_3(X2,X5,X6,X7))\|~v1_msualg_3(X7)\|~m2_pboole(k4_msualg_3(X2,X5,X6,X7),X2,X3,X4)\|~m2_pboole(X1,X2,X4,X3)\|~m2_pboole(X7,X2,X5,X6)\|~v1_partfun1(X4,X2)\|~v1_partfun1(X3,X2)\|~v1_partfun1(X6,X2)\|~v1_partfun1(X5,X2)\|~v1_partfun1(X7,X2)\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v1_funct_1(X6)\|~v1_funct_1(X5)\|~v4_relat_1(X4,X2)\|~v4_relat_1(X3,X2)\|~v4_relat_1(X6,X2)\|~v4_relat_1(X5,X2)\|~v4_relat_1(X7,X2)\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~v1_relat_1(X6)\|~v1_relat_1(X5)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_50, c_0_29])])). cnf(c_0_54, plain, (v4_relat_1(X1,X2)\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v4_relat_1(X4,X2)\|~v4_relat_1(X3,X2)\|~v1_partfun1(X4,X2)\|~v1_partfun1(X3,X2)\|~m2_pboole(X1,X2,X3,X4)), inference(evalgc,[status(thm)],[c_0_51])). cnf(c_0_55, plain, (v1_partfun1(X1,X2)\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v4_relat_1(X4,X2)\|~v4_relat_1(X3,X2)\|~v1_partfun1(X4,X2)\|~v1_partfun1(X3,X2)\|~m2_pboole(X1,X2,X3,X4)), inference(evalgc,[status(thm)],[c_0_52])). fof(c_0_56, plain, ![X37, X38, X39, X40]:((v1_msualg_3(k4_msualg_3(X37,X38,X39,X40))\|(~v1_msualg_3(X40)\|~v2_msualg_3(X40,X37,X38,X39))\|~m2_pboole(X40,X37,X38,X39)\|(~v1_relat_1(X39)\|(~v2_relat_1(X39)\|(~v4_relat_1(X39,X37)\|(~v1_funct_1(X39)\|~v1_partfun1(X39,X37)))))\|(~v1_relat_1(X38)\|(~v2_relat_1(X38)\|(~v4_relat_1(X38,X37)\|(~v1_funct_1(X38)\|~v1_partfun1(X38,X37))))))&(v2_msualg_3(k4_msualg_3(X37,X38,X39,X40),X37,X39,X38)\|(~v1_msualg_3(X40)\|~v2_msualg_3(X40,X37,X38,X39))\|~m2_pboole(X40,X37,X38,X39)\|(~v1_relat_1(X39)\|(~v2_relat_1(X39)\|(~v4_relat_1(X39,X37)\|(~v1_funct_1(X39)\|~v1_partfun1(X39,X37)))))\|(~v1_relat_1(X38)\|(~v2_relat_1(X38)\|(~v4_relat_1(X38,X37)\|(~v1_funct_1(X38)\|~v1_partfun1(X38,X37))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_autalg_1])])])])). fof(c_0_57, negated_conjecture, ~(![X1, X2]:((v1_relat_1(X2)&(v2_relat_1(X2)&(v4_relat_1(X2,X1)&(v1_funct_1(X2)&v1_partfun1(X2,X1)))))=>![X3]:((v1_relat_1(X3)&(v2_relat_1(X3)&(v4_relat_1(X3,X1)&(v1_funct_1(X3)&v1_partfun1(X3,X1)))))=>![X4]:(m2_pboole(X4,X1,X2,X3)=>((v1_msualg_3(X4)&v2_msualg_3(X4,X1,X2,X3))=>r6_pboole(X1,k4_msualg_3(X1,X3,X2,k4_msualg_3(X1,X2,X3,X4)),X4)))))), inference(assume_negation,[status(cth)],[t13_autalg_1])). cnf(c_0_58, plain, (X1=k4_msualg_3(X2,X3,X4,k4_msualg_3(X2,X5,X6,X7))\|k1_funct_1(X1,esk5_5(X2,X3,X4,k4_msualg_3(X2,X5,X6,X7),X1))!=k1_funct_1(X7,esk5_5(X2,X3,X4,k4_msualg_3(X2,X5,X6,X7),X1))\|~v2_msualg_3(k4_msualg_3(X2,X5,X6,X7),X2,X3,X4)\|~v2_msualg_3(X7,X2,X5,X6)\|~v1_msualg_3(k4_msualg_3(X2,X5,X6,X7))\|~v1_msualg_3(X7)\|~m2_pboole(k4_msualg_3(X2,X5,X6,X7),X2,X3,X4)\|~m2_pboole(X1,X2,X4,X3)\|~m2_pboole(X7,X2,X5,X6)\|~v1_partfun1(X4,X2)\|~v1_partfun1(X3,X2)\|~v1_partfun1(X6,X2)\|~v1_partfun1(X5,X2)\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v1_funct_1(X6)\|~v1_funct_1(X5)\|~v4_relat_1(X4,X2)\|~v4_relat_1(X3,X2)\|~v4_relat_1(X6,X2)\|~v4_relat_1(X5,X2)\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~v1_relat_1(X6)\|~v1_relat_1(X5)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_53, c_0_54]), c_0_55])). cnf(c_0_59, plain, (v2_msualg_3(k4_msualg_3(X1,X2,X3,X4),X1,X3,X2)\|~v1_msualg_3(X4)\|~v2_msualg_3(X4,X1,X2,X3)\|~m2_pboole(X4,X1,X2,X3)\|~v1_relat_1(X3)\|~v2_relat_1(X3)\|~v4_relat_1(X3,X1)\|~v1_funct_1(X3)\|~v1_partfun1(X3,X1)\|~v1_relat_1(X2)\|~v2_relat_1(X2)\|~v4_relat_1(X2,X1)\|~v1_funct_1(X2)\|~v1_partfun1(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_56])). fof(c_0_60, negated_conjecture, ((v1_relat_1(esk2_0)&(v2_relat_1(esk2_0)&(v4_relat_1(esk2_0,esk1_0)&(v1_funct_1(esk2_0)&v1_partfun1(esk2_0,esk1_0)))))&((v1_relat_1(esk3_0)&(v2_relat_1(esk3_0)&(v4_relat_1(esk3_0,esk1_0)&(v1_funct_1(esk3_0)&v1_partfun1(esk3_0,esk1_0)))))&(m2_pboole(esk4_0,esk1_0,esk2_0,esk3_0)&((v1_msualg_3(esk4_0)&v2_msualg_3(esk4_0,esk1_0,esk2_0,esk3_0))&~r6_pboole(esk1_0,k4_msualg_3(esk1_0,esk3_0,esk2_0,k4_msualg_3(esk1_0,esk2_0,esk3_0,esk4_0)),esk4_0))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_57])])])). cnf(c_0_61, plain, (k4_msualg_3(X2,X3,X4,k4_msualg_3(X2,X5,X6,X1))=X1\|~v2_msualg_3(k4_msualg_3(X2,X5,X6,X1),X2,X3,X4)\|~v2_msualg_3(X1,X2,X5,X6)\|~v1_msualg_3(k4_msualg_3(X2,X5,X6,X1))\|~v1_msualg_3(X1)\|~m2_pboole(k4_msualg_3(X2,X5,X6,X1),X2,X3,X4)\|~m2_pboole(X1,X2,X4,X3)\|~m2_pboole(X1,X2,X5,X6)\|~v1_partfun1(X4,X2)\|~v1_partfun1(X3,X2)\|~v1_partfun1(X6,X2)\|~v1_partfun1(X5,X2)\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v1_funct_1(X6)\|~v1_funct_1(X5)\|~v4_relat_1(X4,X2)\|~v4_relat_1(X3,X2)\|~v4_relat_1(X6,X2)\|~v4_relat_1(X5,X2)\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~v1_relat_1(X6)\|~v1_relat_1(X5)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_58])])). cnf(c_0_62, plain, (v2_msualg_3(k4_msualg_3(X1,X2,X3,X4),X1,X3,X2)\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v2_relat_1(X3)\|~v2_relat_1(X2)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v1_msualg_3(X4)\|~v4_relat_1(X3,X1)\|~v4_relat_1(X2,X1)\|~v1_partfun1(X3,X1)\|~v1_partfun1(X2,X1)\|~m2_pboole(X4,X1,X2,X3)\|~v2_msualg_3(X4,X1,X2,X3)), inference(evalgc,[status(thm)],[c_0_59])). cnf(c_0_63, plain, (v1_msualg_3(k4_msualg_3(X1,X2,X3,X4))\|~v1_msualg_3(X4)\|~v2_msualg_3(X4,X1,X2,X3)\|~m2_pboole(X4,X1,X2,X3)\|~v1_relat_1(X3)\|~v2_relat_1(X3)\|~v4_relat_1(X3,X1)\|~v1_funct_1(X3)\|~v1_partfun1(X3,X1)\|~v1_relat_1(X2)\|~v2_relat_1(X2)\|~v4_relat_1(X2,X1)\|~v1_funct_1(X2)\|~v1_partfun1(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_56])). fof(c_0_64, plain, ![X41, X42, X43]:(~v1_relat_1(X42)\|(~v4_relat_1(X42,X41)\|(~v1_funct_1(X42)\|~v1_partfun1(X42,X41)))\|(~v1_relat_1(X43)\|(~v4_relat_1(X43,X41)\|(~v1_funct_1(X43)\|~v1_partfun1(X43,X41))))\|r6_pboole(X41,X42,X42)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[reflexivity_r6_pboole])])). fof(c_0_65, plain, ![X44]:(v1_relat_1(esk7_1(X44))&(v4_relat_1(esk7_1(X44),X44)&(v1_funct_1(esk7_1(X44))&(v1_partfun1(esk7_1(X44),X44)&v1_funcop_1(esk7_1(X44)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc4_pboole])])). cnf(c_0_66, negated_conjecture, (~r6_pboole(esk1_0,k4_msualg_3(esk1_0,esk3_0,esk2_0,k4_msualg_3(esk1_0,esk2_0,esk3_0,esk4_0)),esk4_0)), inference(split_conjunct,[status(thm)],[c_0_60])). cnf(c_0_67, plain, (k4_msualg_3(X1,X2,X3,k4_msualg_3(X1,X3,X2,X4))=X4\|~v2_msualg_3(X4,X1,X3,X2)\|~v1_msualg_3(k4_msualg_3(X1,X3,X2,X4))\|~v1_msualg_3(X4)\|~m2_pboole(k4_msualg_3(X1,X3,X2,X4),X1,X2,X3)\|~m2_pboole(X4,X1,X3,X2)\|~v1_partfun1(X3,X1)\|~v1_partfun1(X2,X1)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v4_relat_1(X3,X1)\|~v4_relat_1(X2,X1)\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v2_relat_1(X2)\|~v2_relat_1(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_61, c_0_62])])). cnf(c_0_68, plain, (v1_msualg_3(k4_msualg_3(X1,X2,X3,X4))\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v2_relat_1(X3)\|~v2_relat_1(X2)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v1_msualg_3(X4)\|~v4_relat_1(X3,X1)\|~v4_relat_1(X2,X1)\|~v1_partfun1(X3,X1)\|~v1_partfun1(X2,X1)\|~m2_pboole(X4,X1,X2,X3)\|~v2_msualg_3(X4,X1,X2,X3)), inference(evalgc,[status(thm)],[c_0_63])). cnf(c_0_69, negated_conjecture, (v2_msualg_3(esk4_0,esk1_0,esk2_0,esk3_0)), inference(split_conjunct,[status(thm)],[c_0_60])). cnf(c_0_70, negated_conjecture, (v1_msualg_3(esk4_0)), inference(split_conjunct,[status(thm)],[c_0_60])). cnf(c_0_71, negated_conjecture, (m2_pboole(esk4_0,esk1_0,esk2_0,esk3_0)), inference(split_conjunct,[status(thm)],[c_0_60])). cnf(c_0_72, negated_conjecture, (v1_partfun1(esk2_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_60])). cnf(c_0_73, negated_conjecture, (v1_partfun1(esk3_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_60])). cnf(c_0_74, negated_conjecture, (v1_funct_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_60])). cnf(c_0_75, negated_conjecture, (v1_funct_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_60])). cnf(c_0_76, negated_conjecture, (v4_relat_1(esk2_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_60])). cnf(c_0_77, negated_conjecture, (v4_relat_1(esk3_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_60])). cnf(c_0_78, negated_conjecture, (v2_relat_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_60])). cnf(c_0_79, negated_conjecture, (v2_relat_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_60])). cnf(c_0_80, negated_conjecture, (v1_relat_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_60])). cnf(c_0_81, negated_conjecture, (v1_relat_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_60])). cnf(c_0_82, plain, (r6_pboole(X2,X1,X1)\|~v1_relat_1(X1)\|~v4_relat_1(X1,X2)\|~v1_funct_1(X1)\|~v1_partfun1(X1,X2)\|~v1_relat_1(X3)\|~v4_relat_1(X3,X2)\|~v1_funct_1(X3)\|~v1_partfun1(X3,X2)), inference(split_conjunct,[status(thm)],[c_0_64])). cnf(c_0_83, plain, (v1_partfun1(esk7_1(X1),X1)), inference(split_conjunct,[status(thm)],[c_0_65])). cnf(c_0_84, plain, (v1_funct_1(esk7_1(X1))), inference(split_conjunct,[status(thm)],[c_0_65])). cnf(c_0_85, plain, (v4_relat_1(esk7_1(X1),X1)), inference(split_conjunct,[status(thm)],[c_0_65])). cnf(c_0_86, plain, (v1_relat_1(esk7_1(X1))), inference(split_conjunct,[status(thm)],[c_0_65])). cnf(c_0_87, negated_conjecture, (~r6_pboole(esk1_0,k4_msualg_3(esk1_0,esk3_0,esk2_0,k4_msualg_3(esk1_0,esk2_0,esk3_0,esk4_0)),esk4_0)), inference(evalgc,[status(thm)],[c_0_66])). cnf(c_0_88, plain, (k4_msualg_3(X1,X2,X3,k4_msualg_3(X1,X3,X2,X4))=X4\|~v2_msualg_3(X4,X1,X3,X2)\|~v1_msualg_3(X4)\|~m2_pboole(X4,X1,X3,X2)\|~v1_partfun1(X3,X1)\|~v1_partfun1(X2,X1)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v4_relat_1(X3,X1)\|~v4_relat_1(X2,X1)\|~v2_relat_1(X2)\|~v2_relat_1(X3)\|~v1_relat_1(X3)\|~v1_relat_1(X2)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_67, c_0_19]), c_0_68])). cnf(c_0_89, negated_conjecture, (v2_msualg_3(esk4_0,esk1_0,esk2_0,esk3_0)), inference(evalgc,[status(thm)],[c_0_69])). cnf(c_0_90, negated_conjecture, (v1_msualg_3(esk4_0)), inference(evalgc,[status(thm)],[c_0_70])). cnf(c_0_91, negated_conjecture, (m2_pboole(esk4_0,esk1_0,esk2_0,esk3_0)), inference(evalgc,[status(thm)],[c_0_71])). cnf(c_0_92, negated_conjecture, (v1_partfun1(esk2_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_72])). cnf(c_0_93, negated_conjecture, (v1_partfun1(esk3_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_73])). cnf(c_0_94, negated_conjecture, (v1_funct_1(esk2_0)), inference(evalgc,[status(thm)],[c_0_74])). cnf(c_0_95, negated_conjecture, (v1_funct_1(esk3_0)), inference(evalgc,[status(thm)],[c_0_75])). cnf(c_0_96, negated_conjecture, (v4_relat_1(esk2_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_76])). cnf(c_0_97, negated_conjecture, (v4_relat_1(esk3_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_77])). cnf(c_0_98, negated_conjecture, (v2_relat_1(esk3_0)), inference(evalgc,[status(thm)],[c_0_78])). cnf(c_0_99, negated_conjecture, (v2_relat_1(esk2_0)), inference(evalgc,[status(thm)],[c_0_79])). cnf(c_0_100, negated_conjecture, (v1_relat_1(esk2_0)), inference(evalgc,[status(thm)],[c_0_80])). cnf(c_0_101, negated_conjecture, (v1_relat_1(esk3_0)), inference(evalgc,[status(thm)],[c_0_81])). cnf(c_0_102, plain, (r6_pboole(X2,X1,X1)\|~v1_relat_1(X3)\|~v1_relat_1(X1)\|~v1_funct_1(X3)\|~v1_funct_1(X1)\|~v4_relat_1(X3,X2)\|~v4_relat_1(X1,X2)\|~v1_partfun1(X3,X2)\|~v1_partfun1(X1,X2)), inference(evalgc,[status(thm)],[c_0_82])). cnf(c_0_103, plain, (v1_partfun1(esk7_1(X1),X1)), inference(evalgc,[status(thm)],[c_0_83])). cnf(c_0_104, plain, (v1_funct_1(esk7_1(X1))), inference(evalgc,[status(thm)],[c_0_84])). cnf(c_0_105, plain, (v4_relat_1(esk7_1(X1),X1)), inference(evalgc,[status(thm)],[c_0_85])). cnf(c_0_106, plain, (v1_relat_1(esk7_1(X1))), inference(evalgc,[status(thm)],[c_0_86])). cnf(c_0_107, negated_conjecture, (~r6_pboole(esk1_0,esk4_0,esk4_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87, c_0_88]), c_0_89]), c_0_90]), c_0_91]), c_0_92]), c_0_93]), c_0_94]), c_0_95]), c_0_96]), c_0_97]), c_0_98]), c_0_99]), c_0_100]), c_0_101])])])). cnf(c_0_108, plain, (r6_pboole(X1,X2,X2)\|~v1_partfun1(X2,X1)\|~v1_funct_1(X2)\|~v4_relat_1(X2,X1)\|~v1_relat_1(X2)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102, c_0_103]), c_0_104]), c_0_105]), c_0_106])])])). cnf(c_0_109, negated_conjecture, (v1_partfun1(esk4_0,esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55, c_0_91]), c_0_93]), c_0_92]), c_0_95]), c_0_94]), c_0_97]), c_0_96]), c_0_101]), c_0_100])])])). cnf(c_0_110, negated_conjecture, (v1_funct_1(esk4_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40, c_0_91]), c_0_93]), c_0_92]), c_0_95]), c_0_94]), c_0_97]), c_0_96]), c_0_101]), c_0_100])])])). cnf(c_0_111, negated_conjecture, (v4_relat_1(esk4_0,esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54, c_0_91]), c_0_93]), c_0_92]), c_0_95]), c_0_94]), c_0_97]), c_0_96]), c_0_101]), c_0_100])])])). cnf(c_0_112, negated_conjecture, (v1_relat_1(esk4_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39, c_0_91]), c_0_93]), c_0_92]), c_0_95]), c_0_94]), c_0_97]), c_0_96]), c_0_101]), c_0_100])])])). cnf(c_0_113, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107, c_0_108]), c_0_109]), c_0_110]), c_0_111]), c_0_112])]), ['proof']). # SZS output end CNFRefutation	reserve UA for Universal_Algebra, f, g for Function of UA, UA; reserve I for set, A, B, C for ManySortedSet of I; theorem for A, B be non-empty ManySortedSet of I for F be ManySortedFunction of A, B st F is "1-1" "onto" holds (F"")"" = F proof let A, B be non-empty ManySortedSet of I; let F be ManySortedFunction of A, B; assume A1: F is "1-1" "onto"; now let i be set; assume A2: i in I; then reconsider f = F.i as Function of A.i, B.i by PBOOLE:def 15; reconsider f9 = (F"").i as Function of B.i, A.i by A2,PBOOLE:def 15; f is one-to-one by A1,A2,MSUALG_3:1; then A3: (f")" = f by FUNCT_1:43; F"" is "1-1" "onto" by A1,Th12; then (F"")"".i = f9" by A2,MSUALG_3:def 4; hence (F"")"".i = F.i by A1,A2,A3,MSUALG_3:def 4; end; hence thesis by PBOOLE:3; end;	Convert the following ATP output trace into a readable Mizar proof.
t20_subset_1	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t49_xboole_1, axiom, ![X1, X2, X3]:k3_xboole_0(X1,k4_xboole_0(X2,X3))=k4_xboole_0(k3_xboole_0(X1,X2),X3), file('/scratch/mptp/predsminms1/t20_subset_1__0', t49_xboole_1)). fof(t28_xboole_1, axiom, ![X1, X2]:(r1_tarski(X1,X2)=>k3_xboole_0(X1,X2)=X1), file('/scratch/mptp/predsminms1/t20_subset_1__0', t28_xboole_1)). fof(commutativity_k3_xboole_0, axiom, ![X1, X2]:k3_xboole_0(X1,X2)=k3_xboole_0(X2,X1), file('/scratch/mptp/predsminms1/t20_subset_1__0', commutativity_k3_xboole_0)). fof(l32_xboole_1, axiom, ![X1, X2]:(k4_xboole_0(X1,X2)=k1_xboole_0<=>r1_tarski(X1,X2)), file('/scratch/mptp/predsminms1/t20_subset_1__0', l32_xboole_1)). fof(t2_xboole_1, axiom, ![X1]:r1_tarski(k1_xboole_0,X1), file('/scratch/mptp/predsminms1/t20_subset_1__0', t2_xboole_1)). fof(t20_subset_1, conjecture, ![X1, X2, X3]:(m1_subset_1(X3,k1_zfmisc_1(X1))=>((r1_tarski(X2,X3)&r1_tarski(X2,k3_subset_1(X1,X3)))=>X2=k1_xboole_0)), file('/scratch/mptp/predsminms1/t20_subset_1__0', t20_subset_1)). fof(d4_subset_1, axiom, ![X1, X2]:(m1_subset_1(X2,k1_zfmisc_1(X1))=>k3_subset_1(X1,X2)=k4_xboole_0(X1,X2)), file('/scratch/mptp/predsminms1/t20_subset_1__0', d4_subset_1)). fof(c_0_7, plain, ![X14, X15, X16]:k3_xboole_0(X14,k4_xboole_0(X15,X16))=k4_xboole_0(k3_xboole_0(X14,X15),X16), inference(variable_rename,[status(thm)],[t49_xboole_1])). fof(c_0_8, plain, ![X10, X11]:(~r1_tarski(X10,X11)\|k3_xboole_0(X10,X11)=X10), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t28_xboole_1])])). fof(c_0_9, plain, ![X7, X8]:k3_xboole_0(X7,X8)=k3_xboole_0(X8,X7), inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0])). cnf(c_0_10, plain, (k3_xboole_0(X1,k4_xboole_0(X2,X3))=k4_xboole_0(k3_xboole_0(X1,X2),X3)), inference(split_conjunct,[status(thm)],[c_0_7])). cnf(c_0_11, plain, (k3_xboole_0(X1,X2)=X1\|~r1_tarski(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_8])). cnf(c_0_12, plain, (k3_xboole_0(X1,X2)=k3_xboole_0(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_13, plain, (k4_xboole_0(k3_xboole_0(X1,X2),X3)=k3_xboole_0(X1,k4_xboole_0(X2,X3))), inference(evalgc,[status(thm)],[c_0_10])). cnf(c_0_14, plain, (k3_xboole_0(X1,X2)=X1\|~r1_tarski(X1,X2)), inference(evalgc,[status(thm)],[c_0_11])). cnf(c_0_15, plain, (k3_xboole_0(X1,X2)=k3_xboole_0(X2,X1)), inference(evalgc,[status(thm)],[c_0_12])). fof(c_0_16, plain, ![X12, X13]:((k4_xboole_0(X12,X13)!=k1_xboole_0\|r1_tarski(X12,X13))&(~r1_tarski(X12,X13)\|k4_xboole_0(X12,X13)=k1_xboole_0)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l32_xboole_1])])). cnf(c_0_17, plain, (k3_xboole_0(X1,k4_xboole_0(X2,X3))=k4_xboole_0(X1,X3)\|~r1_tarski(X1,X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_13, c_0_14])])). cnf(c_0_18, plain, (k3_xboole_0(X2,k4_xboole_0(X1,X3))=k3_xboole_0(X1,k4_xboole_0(X2,X3))), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13, c_0_15]), c_0_13])])). cnf(c_0_19, plain, (r1_tarski(X1,X2)\|k4_xboole_0(X1,X2)!=k1_xboole_0), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_20, plain, (k3_xboole_0(k4_xboole_0(X1,X2),X3)=k4_xboole_0(X3,X2)\|~r1_tarski(X3,X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_15, c_0_17])])). cnf(c_0_21, plain, (k3_xboole_0(k4_xboole_0(X2,X3),X1)=k3_xboole_0(X2,k4_xboole_0(X1,X3))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_15, c_0_18])])). cnf(c_0_22, plain, (k4_xboole_0(X1,X2)=k1_xboole_0\|~r1_tarski(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_16])). fof(c_0_23, plain, ![X9]:r1_tarski(k1_xboole_0,X9), inference(variable_rename,[status(thm)],[t2_xboole_1])). fof(c_0_24, negated_conjecture, ~(![X1, X2, X3]:(m1_subset_1(X3,k1_zfmisc_1(X1))=>((r1_tarski(X2,X3)&r1_tarski(X2,k3_subset_1(X1,X3)))=>X2=k1_xboole_0))), inference(assume_negation,[status(cth)],[t20_subset_1])). cnf(c_0_25, plain, (r1_tarski(X1,X2)\|k4_xboole_0(X1,X2)!=k1_xboole_0), inference(evalgc,[status(thm)],[c_0_19])). cnf(c_0_26, plain, (k3_xboole_0(X1,k4_xboole_0(X2,X3))=k4_xboole_0(X2,X3)\|~r1_tarski(X2,X1)), inference(rw,[status(thm)],[c_0_20, c_0_21])). cnf(c_0_27, plain, (k4_xboole_0(X1,X2)=k1_xboole_0\|~r1_tarski(X1,X2)), inference(evalgc,[status(thm)],[c_0_22])). cnf(c_0_28, plain, (r1_tarski(k1_xboole_0,X1)), inference(split_conjunct,[status(thm)],[c_0_23])). fof(c_0_29, plain, ![X17, X18]:(~m1_subset_1(X18,k1_zfmisc_1(X17))\|k3_subset_1(X17,X18)=k4_xboole_0(X17,X18)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d4_subset_1])])). fof(c_0_30, negated_conjecture, (m1_subset_1(esk3_0,k1_zfmisc_1(esk1_0))&((r1_tarski(esk2_0,esk3_0)&r1_tarski(esk2_0,k3_subset_1(esk1_0,esk3_0)))&esk2_0!=k1_xboole_0)), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])])). cnf(c_0_31, plain, (r1_tarski(k3_xboole_0(X1,X2),X3)\|k3_xboole_0(X1,k4_xboole_0(X2,X3))!=k1_xboole_0), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_25, c_0_13])])). cnf(c_0_32, plain, (k3_xboole_0(X1,k1_xboole_0)=k1_xboole_0\|~r1_tarski(X2,X1)\|~r1_tarski(X2,X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_26, c_0_27])])). cnf(c_0_33, plain, (r1_tarski(k1_xboole_0,X1)), inference(evalgc,[status(thm)],[c_0_28])). cnf(c_0_34, plain, (k3_subset_1(X2,X1)=k4_xboole_0(X2,X1)\|~m1_subset_1(X1,k1_zfmisc_1(X2))), inference(split_conjunct,[status(thm)],[c_0_29])). cnf(c_0_35, negated_conjecture, (m1_subset_1(esk3_0,k1_zfmisc_1(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_30])). cnf(c_0_36, plain, (k3_xboole_0(X1,k4_xboole_0(X2,X3))=k1_xboole_0\|~r1_tarski(k3_xboole_0(X1,X2),X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_27, c_0_13])])). cnf(c_0_37, plain, (k3_xboole_0(X2,k4_xboole_0(X1,X3))=X1\|~r1_tarski(X1,k4_xboole_0(X2,X3))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_14, c_0_18])])). cnf(c_0_38, plain, (r1_tarski(k3_xboole_0(X1,X2),X3)\|k3_xboole_0(X1,k1_xboole_0)!=k1_xboole_0\|~r1_tarski(X2,X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_31, c_0_27])])). cnf(c_0_39, plain, (k3_xboole_0(X1,k1_xboole_0)=k1_xboole_0), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32, c_0_33]), c_0_33])])])). cnf(c_0_40, negated_conjecture, (r1_tarski(esk2_0,k3_subset_1(esk1_0,esk3_0))), inference(split_conjunct,[status(thm)],[c_0_30])). cnf(c_0_41, plain, (k3_subset_1(X2,X1)=k4_xboole_0(X2,X1)\|~m1_subset_1(X1,k1_zfmisc_1(X2))), inference(evalgc,[status(thm)],[c_0_34])). cnf(c_0_42, negated_conjecture, (m1_subset_1(esk3_0,k1_zfmisc_1(esk1_0))), inference(evalgc,[status(thm)],[c_0_35])). cnf(c_0_43, plain, (X2=k1_xboole_0\|~r1_tarski(k3_xboole_0(X1,X2),X3)\|~r1_tarski(X2,k4_xboole_0(X1,X3))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_36, c_0_37])])). cnf(c_0_44, plain, (r1_tarski(k3_xboole_0(X1,X2),X3)\|~r1_tarski(X2,X3)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38, c_0_39])])])). cnf(c_0_45, negated_conjecture, (r1_tarski(esk2_0,k3_subset_1(esk1_0,esk3_0))), inference(evalgc,[status(thm)],[c_0_40])). cnf(c_0_46, negated_conjecture, (k3_subset_1(esk1_0,esk3_0)=k4_xboole_0(esk1_0,esk3_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_41, c_0_42])])). cnf(c_0_47, negated_conjecture, (r1_tarski(esk2_0,esk3_0)), inference(split_conjunct,[status(thm)],[c_0_30])). cnf(c_0_48, negated_conjecture, (esk2_0!=k1_xboole_0), inference(split_conjunct,[status(thm)],[c_0_30])). cnf(c_0_49, plain, (X1=k1_xboole_0\|~r1_tarski(X1,k4_xboole_0(X2,X3))\|~r1_tarski(X1,X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_43, c_0_44])])). cnf(c_0_50, negated_conjecture, (r1_tarski(esk2_0,k4_xboole_0(esk1_0,esk3_0))), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[c_0_45, c_0_46])])). cnf(c_0_51, negated_conjecture, (r1_tarski(esk2_0,esk3_0)), inference(evalgc,[status(thm)],[c_0_47])). cnf(c_0_52, negated_conjecture, (esk2_0!=k1_xboole_0), inference(evalgc,[status(thm)],[c_0_48])). cnf(c_0_53, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49, c_0_50]), c_0_51])]), c_0_52]), ['proof']). # SZS output end CNFRefutation	reserve E,X,x,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10 for set; reserve A,B,C for Subset of E; theorem X c= A & X c= A` implies X = {} by XBOOLE_1:67,79;	Convert the following ATP output trace into a readable Mizar proof.
t104_seq_4	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(redefinition_k13_seq_4, axiom, ![X1]:(m1_finseq_1(X1,k2_numbers)=>k13_seq_4(X1)=k54_valued_1(X1)), file('/scratch/mptp/predsminms1/t104_seq_4__0', redefinition_k13_seq_4)). fof(redefinition_k21_seq_4, axiom, ![X1, X2]:((m1_subset_1(X1,k5_numbers)&m1_subset_1(X2,k14_seq_4(X1)))=>k21_seq_4(X1,X2)=k54_valued_1(X2)), file('/scratch/mptp/predsminms1/t104_seq_4__0', redefinition_k21_seq_4)). fof(t91_seq_4, axiom, ![X1]:(m2_subset_1(X1,k1_numbers,k5_numbers)=>![X2]:(m2_finseq_2(X2,k2_numbers,k14_seq_4(X1))=>k21_seq_4(X1,k18_seq_4(X1,X2))=k21_seq_4(X1,X2))), file('/scratch/mptp/predsminms1/t104_seq_4__0', t91_seq_4)). fof(t71_seq_4, axiom, ![X1]:(m2_subset_1(X1,k1_numbers,k5_numbers)=>![X2]:(m2_finseq_2(X2,k2_numbers,k14_seq_4(X1))=>![X3]:(m2_finseq_2(X3,k2_numbers,k14_seq_4(X1))=>k18_seq_4(X1,k19_seq_4(X1,X2,X3))=k19_seq_4(X1,X3,X2)))), file('/scratch/mptp/predsminms1/t104_seq_4__0', t71_seq_4)). fof(redefinition_m2_subset_1, axiom, ![X1, X2]:((~(v1_xboole_0(X1))&(~(v1_xboole_0(X2))&m1_subset_1(X2,k1_zfmisc_1(X1))))=>![X3]:(m2_subset_1(X3,X1,X2)<=>m1_subset_1(X3,X2))), file('/scratch/mptp/predsminms1/t104_seq_4__0', redefinition_m2_subset_1)). fof(cc1_subset_1, axiom, ![X1]:(v1_xboole_0(X1)=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(X1))=>v1_xboole_0(X2))), file('/scratch/mptp/predsminms1/t104_seq_4__0', cc1_subset_1)). fof(fc6_ordinal1, axiom, (~(v1_xboole_0(k4_ordinal1))&v3_ordinal1(k4_ordinal1)), file('/scratch/mptp/predsminms1/t104_seq_4__0', fc6_ordinal1)). fof(d13_seq_4, axiom, ![X1]:(m2_finseq_1(X1,k2_numbers)=>k22_seq_4(X1)=k7_square_1(k18_rvsum_1(k12_rvsum_1(k13_seq_4(X1))))), file('/scratch/mptp/predsminms1/t104_seq_4__0', d13_seq_4)). fof(redefinition_k5_numbers, axiom, k5_numbers=k4_ordinal1, file('/scratch/mptp/predsminms1/t104_seq_4__0', redefinition_k5_numbers)). fof(redefinition_m2_finseq_2, axiom, ![X1, X2]:(m1_finseq_2(X2,X1)=>![X3]:(m2_finseq_2(X3,X1,X2)<=>m1_subset_1(X3,X2))), file('/scratch/mptp/predsminms1/t104_seq_4__0', redefinition_m2_finseq_2)). fof(dt_k14_seq_4, axiom, ![X1]:(m1_subset_1(X1,k5_numbers)=>m1_finseq_2(k14_seq_4(X1),k2_numbers)), file('/scratch/mptp/predsminms1/t104_seq_4__0', dt_k14_seq_4)). fof(redefinition_m2_finseq_1, axiom, ![X1, X2]:(m2_finseq_1(X2,X1)<=>m1_finseq_1(X2,X1)), file('/scratch/mptp/predsminms1/t104_seq_4__0', redefinition_m2_finseq_1)). fof(dt_k5_numbers, axiom, m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)), file('/scratch/mptp/predsminms1/t104_seq_4__0', dt_k5_numbers)). fof(dt_k19_seq_4, axiom, ![X1, X2, X3]:((m1_subset_1(X1,k5_numbers)&(m1_subset_1(X2,k14_seq_4(X1))&m1_subset_1(X3,k14_seq_4(X1))))=>m2_finseq_2(k19_seq_4(X1,X2,X3),k2_numbers,k14_seq_4(X1))), file('/scratch/mptp/predsminms1/t104_seq_4__0', dt_k19_seq_4)). fof(dt_m2_finseq_2, axiom, ![X1, X2]:(m1_finseq_2(X2,X1)=>![X3]:(m2_finseq_2(X3,X1,X2)=>m2_finseq_1(X3,X1))), file('/scratch/mptp/predsminms1/t104_seq_4__0', dt_m2_finseq_2)). fof(t104_seq_4, conjecture, ![X1]:(m2_subset_1(X1,k1_numbers,k5_numbers)=>![X2]:(m2_finseq_2(X2,k2_numbers,k14_seq_4(X1))=>![X3]:(m2_finseq_2(X3,k2_numbers,k14_seq_4(X1))=>k22_seq_4(k19_seq_4(X1,X2,X3))=k22_seq_4(k19_seq_4(X1,X3,X2))))), file('/scratch/mptp/predsminms1/t104_seq_4__0', t104_seq_4)). fof(c_0_16, plain, ![X22]:(~m1_finseq_1(X22,k2_numbers)\|k13_seq_4(X22)=k54_valued_1(X22)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k13_seq_4])])). fof(c_0_17, plain, ![X19, X20]:(~m1_subset_1(X19,k5_numbers)\|~m1_subset_1(X20,k14_seq_4(X19))\|k21_seq_4(X19,X20)=k54_valued_1(X20)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k21_seq_4])])). fof(c_0_18, plain, ![X7, X8]:(~m2_subset_1(X7,k1_numbers,k5_numbers)\|(~m2_finseq_2(X8,k2_numbers,k14_seq_4(X7))\|k21_seq_4(X7,k18_seq_4(X7,X8))=k21_seq_4(X7,X8))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t91_seq_4])])])). fof(c_0_19, plain, ![X9, X10, X11]:(~m2_subset_1(X9,k1_numbers,k5_numbers)\|(~m2_finseq_2(X10,k2_numbers,k14_seq_4(X9))\|(~m2_finseq_2(X11,k2_numbers,k14_seq_4(X9))\|k18_seq_4(X9,k19_seq_4(X9,X10,X11))=k19_seq_4(X9,X11,X10)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t71_seq_4])])])). fof(c_0_20, plain, ![X28, X29, X30]:((~m2_subset_1(X30,X28,X29)\|m1_subset_1(X30,X29)\|(v1_xboole_0(X28)\|(v1_xboole_0(X29)\|~m1_subset_1(X29,k1_zfmisc_1(X28)))))&(~m1_subset_1(X30,X29)\|m2_subset_1(X30,X28,X29)\|(v1_xboole_0(X28)\|(v1_xboole_0(X29)\|~m1_subset_1(X29,k1_zfmisc_1(X28)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[redefinition_m2_subset_1])])])])])). fof(c_0_21, plain, ![X31, X32]:(~v1_xboole_0(X31)\|(~m1_subset_1(X32,k1_zfmisc_1(X31))\|v1_xboole_0(X32))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_subset_1])])])). fof(c_0_22, plain, (~v1_xboole_0(k4_ordinal1)&v3_ordinal1(k4_ordinal1)), inference(fof_simplification,[status(thm)],[fc6_ordinal1])). fof(c_0_23, plain, ![X21]:(~m2_finseq_1(X21,k2_numbers)\|k22_seq_4(X21)=k7_square_1(k18_rvsum_1(k12_rvsum_1(k13_seq_4(X21))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d13_seq_4])])). cnf(c_0_24, plain, (k13_seq_4(X1)=k54_valued_1(X1)\|~m1_finseq_1(X1,k2_numbers)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_25, plain, (k21_seq_4(X1,X2)=k54_valued_1(X2)\|~m1_subset_1(X1,k5_numbers)\|~m1_subset_1(X2,k14_seq_4(X1))), inference(split_conjunct,[status(thm)],[c_0_17])). cnf(c_0_26, plain, (k21_seq_4(X1,k18_seq_4(X1,X2))=k21_seq_4(X1,X2)\|~m2_subset_1(X1,k1_numbers,k5_numbers)\|~m2_finseq_2(X2,k2_numbers,k14_seq_4(X1))), inference(split_conjunct,[status(thm)],[c_0_18])). cnf(c_0_27, plain, (k18_seq_4(X1,k19_seq_4(X1,X2,X3))=k19_seq_4(X1,X3,X2)\|~m2_subset_1(X1,k1_numbers,k5_numbers)\|~m2_finseq_2(X2,k2_numbers,k14_seq_4(X1))\|~m2_finseq_2(X3,k2_numbers,k14_seq_4(X1))), inference(split_conjunct,[status(thm)],[c_0_19])). cnf(c_0_28, plain, (m2_subset_1(X1,X3,X2)\|v1_xboole_0(X3)\|v1_xboole_0(X2)\|~m1_subset_1(X1,X2)\|~m1_subset_1(X2,k1_zfmisc_1(X3))), inference(split_conjunct,[status(thm)],[c_0_20])). cnf(c_0_29, plain, (v1_xboole_0(X2)\|~v1_xboole_0(X1)\|~m1_subset_1(X2,k1_zfmisc_1(X1))), inference(split_conjunct,[status(thm)],[c_0_21])). cnf(c_0_30, plain, (~v1_xboole_0(k4_ordinal1)), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_31, plain, (k5_numbers=k4_ordinal1), inference(split_conjunct,[status(thm)],[redefinition_k5_numbers])). fof(c_0_32, plain, ![X15, X16, X17]:((~m2_finseq_2(X17,X15,X16)\|m1_subset_1(X17,X16)\|~m1_finseq_2(X16,X15))&(~m1_subset_1(X17,X16)\|m2_finseq_2(X17,X15,X16)\|~m1_finseq_2(X16,X15))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_finseq_2])])])])). fof(c_0_33, plain, ![X18]:(~m1_subset_1(X18,k5_numbers)\|m1_finseq_2(k14_seq_4(X18),k2_numbers)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k14_seq_4])])). cnf(c_0_34, plain, (k22_seq_4(X1)=k7_square_1(k18_rvsum_1(k12_rvsum_1(k13_seq_4(X1))))\|~m2_finseq_1(X1,k2_numbers)), inference(split_conjunct,[status(thm)],[c_0_23])). cnf(c_0_35, plain, (k54_valued_1(X1)=k13_seq_4(X1)\|~m1_finseq_1(X1,k2_numbers)), inference(evalgc,[status(thm)],[c_0_24])). cnf(c_0_36, plain, (k21_seq_4(X1,X2)=k54_valued_1(X2)\|~m1_subset_1(X1,k5_numbers)\|~m1_subset_1(X2,k14_seq_4(X1))), inference(evalgc,[status(thm)],[c_0_25])). fof(c_0_37, plain, ![X23, X24]:((~m2_finseq_1(X24,X23)\|m1_finseq_1(X24,X23))&(~m1_finseq_1(X24,X23)\|m2_finseq_1(X24,X23))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_finseq_1])])). cnf(c_0_38, plain, (k21_seq_4(X1,k18_seq_4(X1,X2))=k21_seq_4(X1,X2)\|~m2_subset_1(X1,k1_numbers,k5_numbers)\|~m2_finseq_2(X2,k2_numbers,k14_seq_4(X1))), inference(evalgc,[status(thm)],[c_0_26])). cnf(c_0_39, plain, (k18_seq_4(X1,k19_seq_4(X1,X2,X3))=k19_seq_4(X1,X3,X2)\|~m2_subset_1(X1,k1_numbers,k5_numbers)\|~m2_finseq_2(X3,k2_numbers,k14_seq_4(X1))\|~m2_finseq_2(X2,k2_numbers,k14_seq_4(X1))), inference(evalgc,[status(thm)],[c_0_27])). cnf(c_0_40, plain, (v1_xboole_0(X3)\|v1_xboole_0(X2)\|m2_subset_1(X1,X3,X2)\|~m1_subset_1(X1,X2)\|~m1_subset_1(X2,k1_zfmisc_1(X3))), inference(evalgc,[status(thm)],[c_0_28])). cnf(c_0_41, plain, (v1_xboole_0(X2)\|~v1_xboole_0(X1)\|~m1_subset_1(X2,k1_zfmisc_1(X1))), inference(evalgc,[status(thm)],[c_0_29])). cnf(c_0_42, plain, (m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers))), inference(split_conjunct,[status(thm)],[dt_k5_numbers])). cnf(c_0_43, plain, (~v1_xboole_0(k4_ordinal1)), inference(evalgc,[status(thm)],[c_0_30])). cnf(c_0_44, plain, (k4_ordinal1=k5_numbers), inference(evalgc,[status(thm)],[c_0_31])). cnf(c_0_45, plain, (m2_finseq_2(X1,X3,X2)\|~m1_subset_1(X1,X2)\|~m1_finseq_2(X2,X3)), inference(split_conjunct,[status(thm)],[c_0_32])). cnf(c_0_46, plain, (m1_finseq_2(k14_seq_4(X1),k2_numbers)\|~m1_subset_1(X1,k5_numbers)), inference(split_conjunct,[status(thm)],[c_0_33])). fof(c_0_47, plain, ![X12, X13, X14]:(~m1_subset_1(X12,k5_numbers)\|(~m1_subset_1(X13,k14_seq_4(X12))\|~m1_subset_1(X14,k14_seq_4(X12)))\|m2_finseq_2(k19_seq_4(X12,X13,X14),k2_numbers,k14_seq_4(X12))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k19_seq_4])])). cnf(c_0_48, plain, (k7_square_1(k18_rvsum_1(k12_rvsum_1(k13_seq_4(X1))))=k22_seq_4(X1)\|~m2_finseq_1(X1,k2_numbers)), inference(evalgc,[status(thm)],[c_0_34])). cnf(c_0_49, plain, (k21_seq_4(X2,X1)=k13_seq_4(X1)\|~m1_finseq_1(X1,k2_numbers)\|~m1_subset_1(X1,k14_seq_4(X2))\|~m1_subset_1(X2,k5_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_35, c_0_36])])). cnf(c_0_50, plain, (m2_finseq_1(X1,X2)\|~m1_finseq_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_37])). cnf(c_0_51, plain, (k21_seq_4(X1,k19_seq_4(X1,X3,X2))=k21_seq_4(X1,k19_seq_4(X1,X2,X3))\|~m2_finseq_2(k19_seq_4(X1,X2,X3),k2_numbers,k14_seq_4(X1))\|~m2_subset_1(X1,k1_numbers,k5_numbers)\|~m2_finseq_2(X3,k2_numbers,k14_seq_4(X1))\|~m2_finseq_2(X2,k2_numbers,k14_seq_4(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_38, c_0_39])])). cnf(c_0_52, plain, (v1_xboole_0(X1)\|m2_subset_1(X2,X3,X1)\|~m1_subset_1(X1,k1_zfmisc_1(X3))\|~m1_subset_1(X2,X1)), inference(csr,[status(thm)],[c_0_40, c_0_41])). cnf(c_0_53, plain, (m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers))), inference(evalgc,[status(thm)],[c_0_42])). cnf(c_0_54, plain, (~v1_xboole_0(k5_numbers)), inference(rw,[status(thm)],[c_0_43, c_0_44])). cnf(c_0_55, plain, (m2_finseq_2(X1,X3,X2)\|~m1_subset_1(X1,X2)\|~m1_finseq_2(X2,X3)), inference(evalgc,[status(thm)],[c_0_45])). cnf(c_0_56, plain, (m1_finseq_2(k14_seq_4(X1),k2_numbers)\|~m1_subset_1(X1,k5_numbers)), inference(evalgc,[status(thm)],[c_0_46])). cnf(c_0_57, plain, (m1_subset_1(X1,X3)\|~m2_finseq_2(X1,X2,X3)\|~m1_finseq_2(X3,X2)), inference(split_conjunct,[status(thm)],[c_0_32])). cnf(c_0_58, plain, (m2_finseq_2(k19_seq_4(X1,X2,X3),k2_numbers,k14_seq_4(X1))\|~m1_subset_1(X1,k5_numbers)\|~m1_subset_1(X2,k14_seq_4(X1))\|~m1_subset_1(X3,k14_seq_4(X1))), inference(split_conjunct,[status(thm)],[c_0_47])). cnf(c_0_59, plain, (k7_square_1(k18_rvsum_1(k12_rvsum_1(k21_seq_4(X2,X1))))=k22_seq_4(X1)\|~m2_finseq_1(X1,k2_numbers)\|~m1_finseq_1(X1,k2_numbers)\|~m1_subset_1(X1,k14_seq_4(X2))\|~m1_subset_1(X2,k5_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_48, c_0_49])])). cnf(c_0_60, plain, (m2_finseq_1(X1,X2)\|~m1_finseq_1(X1,X2)), inference(evalgc,[status(thm)],[c_0_50])). cnf(c_0_61, plain, (k21_seq_4(X1,k19_seq_4(X1,X2,X3))=k13_seq_4(k19_seq_4(X1,X3,X2))\|~m2_finseq_2(k19_seq_4(X1,X3,X2),k2_numbers,k14_seq_4(X1))\|~m2_finseq_2(X2,k2_numbers,k14_seq_4(X1))\|~m2_finseq_2(X3,k2_numbers,k14_seq_4(X1))\|~m2_subset_1(X1,k1_numbers,k5_numbers)\|~m1_finseq_1(k19_seq_4(X1,X3,X2),k2_numbers)\|~m1_subset_1(k19_seq_4(X1,X3,X2),k14_seq_4(X1))\|~m1_subset_1(X1,k5_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_51, c_0_49])])). cnf(c_0_62, plain, (m2_subset_1(X1,k1_numbers,k5_numbers)\|~m1_subset_1(X1,k5_numbers)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_52, c_0_53]), c_0_54])])). cnf(c_0_63, plain, (m2_finseq_2(X1,k2_numbers,k14_seq_4(X2))\|~m1_subset_1(X1,k14_seq_4(X2))\|~m1_subset_1(X2,k5_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_55, c_0_56])])). cnf(c_0_64, plain, (m1_subset_1(X1,X3)\|~m1_finseq_2(X3,X2)\|~m2_finseq_2(X1,X2,X3)), inference(evalgc,[status(thm)],[c_0_57])). cnf(c_0_65, plain, (m2_finseq_2(k19_seq_4(X1,X2,X3),k2_numbers,k14_seq_4(X1))\|~m1_subset_1(X1,k5_numbers)\|~m1_subset_1(X3,k14_seq_4(X1))\|~m1_subset_1(X2,k14_seq_4(X1))), inference(evalgc,[status(thm)],[c_0_58])). cnf(c_0_66, plain, (k7_square_1(k18_rvsum_1(k12_rvsum_1(k21_seq_4(X1,X2))))=k22_seq_4(X2)\|~m1_finseq_1(X2,k2_numbers)\|~m1_subset_1(X2,k14_seq_4(X1))\|~m1_subset_1(X1,k5_numbers)), inference(csr,[status(thm)],[c_0_59, c_0_60])). cnf(c_0_67, plain, (k21_seq_4(X1,k19_seq_4(X1,X2,X3))=k13_seq_4(k19_seq_4(X1,X3,X2))\|~m1_finseq_1(k19_seq_4(X1,X3,X2),k2_numbers)\|~m1_subset_1(k19_seq_4(X1,X3,X2),k14_seq_4(X1))\|~m1_subset_1(X1,k5_numbers)\|~m2_finseq_2(X2,k2_numbers,k14_seq_4(X1))\|~m2_finseq_2(X3,k2_numbers,k14_seq_4(X1))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_61, c_0_62]), c_0_63])). cnf(c_0_68, plain, (m1_subset_1(k19_seq_4(X1,X2,X3),k14_seq_4(X1))\|~m1_finseq_2(k14_seq_4(X1),k2_numbers)\|~m1_subset_1(X3,k14_seq_4(X1))\|~m1_subset_1(X2,k14_seq_4(X1))\|~m1_subset_1(X1,k5_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_64, c_0_65])])). cnf(c_0_69, plain, (k7_square_1(k18_rvsum_1(k12_rvsum_1(k13_seq_4(k19_seq_4(X1,X3,X2)))))=k22_seq_4(k19_seq_4(X1,X2,X3))\|~m1_finseq_1(k19_seq_4(X1,X2,X3),k2_numbers)\|~m1_subset_1(k19_seq_4(X1,X2,X3),k14_seq_4(X1))\|~m1_subset_1(X1,k5_numbers)\|~m1_finseq_1(k19_seq_4(X1,X3,X2),k2_numbers)\|~m1_subset_1(k19_seq_4(X1,X3,X2),k14_seq_4(X1))\|~m2_finseq_2(X2,k2_numbers,k14_seq_4(X1))\|~m2_finseq_2(X3,k2_numbers,k14_seq_4(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_66, c_0_67])])). cnf(c_0_70, plain, (m1_subset_1(k19_seq_4(X1,X2,X3),k14_seq_4(X1))\|~m1_subset_1(X3,k14_seq_4(X1))\|~m1_subset_1(X2,k14_seq_4(X1))\|~m1_subset_1(X1,k5_numbers)), inference(csr,[status(thm)],[c_0_68, c_0_56])). cnf(c_0_71, plain, (k7_square_1(k18_rvsum_1(k12_rvsum_1(k13_seq_4(k19_seq_4(X1,X2,X3)))))=k22_seq_4(k19_seq_4(X1,X3,X2))\|~m1_finseq_1(k19_seq_4(X1,X3,X2),k2_numbers)\|~m1_finseq_1(k19_seq_4(X1,X2,X3),k2_numbers)\|~m1_subset_1(k19_seq_4(X1,X2,X3),k14_seq_4(X1))\|~m1_subset_1(X1,k5_numbers)\|~m2_finseq_2(X3,k2_numbers,k14_seq_4(X1))\|~m2_finseq_2(X2,k2_numbers,k14_seq_4(X1))\|~m1_subset_1(X2,k14_seq_4(X1))\|~m1_subset_1(X3,k14_seq_4(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_69, c_0_70])])). fof(c_0_72, plain, ![X25, X26, X27]:(~m1_finseq_2(X26,X25)\|(~m2_finseq_2(X27,X25,X26)\|m2_finseq_1(X27,X25))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m2_finseq_2])])])). cnf(c_0_73, plain, (k7_square_1(k18_rvsum_1(k12_rvsum_1(k13_seq_4(k19_seq_4(X1,X2,X3)))))=k22_seq_4(k19_seq_4(X1,X3,X2))\|~m1_finseq_1(k19_seq_4(X1,X3,X2),k2_numbers)\|~m1_finseq_1(k19_seq_4(X1,X2,X3),k2_numbers)\|~m1_subset_1(X2,k14_seq_4(X1))\|~m1_subset_1(X3,k14_seq_4(X1))\|~m1_subset_1(X1,k5_numbers)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_71, c_0_63]), c_0_63]), c_0_70])). cnf(c_0_74, plain, (m2_finseq_1(X3,X2)\|~m1_finseq_2(X1,X2)\|~m2_finseq_2(X3,X2,X1)), inference(split_conjunct,[status(thm)],[c_0_72])). fof(c_0_75, negated_conjecture, ~(![X1]:(m2_subset_1(X1,k1_numbers,k5_numbers)=>![X2]:(m2_finseq_2(X2,k2_numbers,k14_seq_4(X1))=>![X3]:(m2_finseq_2(X3,k2_numbers,k14_seq_4(X1))=>k22_seq_4(k19_seq_4(X1,X2,X3))=k22_seq_4(k19_seq_4(X1,X3,X2)))))), inference(assume_negation,[status(cth)],[t104_seq_4])). cnf(c_0_76, plain, (k22_seq_4(k19_seq_4(X1,X3,X2))=k22_seq_4(k19_seq_4(X1,X2,X3))\|~m2_finseq_1(k19_seq_4(X1,X2,X3),k2_numbers)\|~m1_finseq_1(k19_seq_4(X1,X3,X2),k2_numbers)\|~m1_finseq_1(k19_seq_4(X1,X2,X3),k2_numbers)\|~m1_subset_1(X2,k14_seq_4(X1))\|~m1_subset_1(X3,k14_seq_4(X1))\|~m1_subset_1(X1,k5_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_48, c_0_73])])). cnf(c_0_77, plain, (m1_finseq_1(X1,X2)\|~m2_finseq_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_37])). cnf(c_0_78, plain, (m2_finseq_1(X3,X2)\|~m1_finseq_2(X1,X2)\|~m2_finseq_2(X3,X2,X1)), inference(evalgc,[status(thm)],[c_0_74])). fof(c_0_79, negated_conjecture, (m2_subset_1(esk1_0,k1_numbers,k5_numbers)&(m2_finseq_2(esk2_0,k2_numbers,k14_seq_4(esk1_0))&(m2_finseq_2(esk3_0,k2_numbers,k14_seq_4(esk1_0))&k22_seq_4(k19_seq_4(esk1_0,esk2_0,esk3_0))!=k22_seq_4(k19_seq_4(esk1_0,esk3_0,esk2_0))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_75])])])). cnf(c_0_80, plain, (m1_subset_1(X1,X3)\|v1_xboole_0(X2)\|v1_xboole_0(X3)\|~m2_subset_1(X1,X2,X3)\|~m1_subset_1(X3,k1_zfmisc_1(X2))), inference(split_conjunct,[status(thm)],[c_0_20])). cnf(c_0_81, plain, (k22_seq_4(k19_seq_4(X1,X2,X3))=k22_seq_4(k19_seq_4(X1,X3,X2))\|~m1_finseq_1(k19_seq_4(X1,X2,X3),k2_numbers)\|~m1_finseq_1(k19_seq_4(X1,X3,X2),k2_numbers)\|~m1_subset_1(X3,k14_seq_4(X1))\|~m1_subset_1(X2,k14_seq_4(X1))\|~m1_subset_1(X1,k5_numbers)), inference(csr,[status(thm)],[c_0_76, c_0_60])). cnf(c_0_82, plain, (m1_finseq_1(X1,X2)\|~m2_finseq_1(X1,X2)), inference(evalgc,[status(thm)],[c_0_77])). cnf(c_0_83, plain, (m2_finseq_1(k19_seq_4(X1,X2,X3),k2_numbers)\|~m1_finseq_2(k14_seq_4(X1),k2_numbers)\|~m1_subset_1(X3,k14_seq_4(X1))\|~m1_subset_1(X2,k14_seq_4(X1))\|~m1_subset_1(X1,k5_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_78, c_0_65])])). cnf(c_0_84, negated_conjecture, (m2_finseq_2(esk3_0,k2_numbers,k14_seq_4(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_79])). cnf(c_0_85, plain, (v1_xboole_0(X3)\|v1_xboole_0(X2)\|m1_subset_1(X1,X3)\|~m2_subset_1(X1,X2,X3)\|~m1_subset_1(X3,k1_zfmisc_1(X2))), inference(evalgc,[status(thm)],[c_0_80])). cnf(c_0_86, negated_conjecture, (m2_finseq_2(esk2_0,k2_numbers,k14_seq_4(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_79])). cnf(c_0_87, plain, (k22_seq_4(k19_seq_4(X1,X2,X3))=k22_seq_4(k19_seq_4(X1,X3,X2))\|~m1_finseq_1(k19_seq_4(X1,X3,X2),k2_numbers)\|~m1_subset_1(X3,k14_seq_4(X1))\|~m1_subset_1(X2,k14_seq_4(X1))\|~m1_subset_1(X1,k5_numbers)\|~m2_finseq_1(k19_seq_4(X1,X2,X3),k2_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_81, c_0_82])])). cnf(c_0_88, plain, (m2_finseq_1(k19_seq_4(X1,X2,X3),k2_numbers)\|~m1_subset_1(X3,k14_seq_4(X1))\|~m1_subset_1(X2,k14_seq_4(X1))\|~m1_subset_1(X1,k5_numbers)), inference(csr,[status(thm)],[c_0_83, c_0_56])). cnf(c_0_89, negated_conjecture, (m2_finseq_2(esk3_0,k2_numbers,k14_seq_4(esk1_0))), inference(evalgc,[status(thm)],[c_0_84])). cnf(c_0_90, plain, (v1_xboole_0(X1)\|m1_subset_1(X2,X1)\|~m1_subset_1(X1,k1_zfmisc_1(X3))\|~m2_subset_1(X2,X3,X1)), inference(csr,[status(thm)],[c_0_85, c_0_41])). cnf(c_0_91, negated_conjecture, (m2_subset_1(esk1_0,k1_numbers,k5_numbers)), inference(split_conjunct,[status(thm)],[c_0_79])). cnf(c_0_92, negated_conjecture, (m2_finseq_2(esk2_0,k2_numbers,k14_seq_4(esk1_0))), inference(evalgc,[status(thm)],[c_0_86])). cnf(c_0_93, plain, (k22_seq_4(k19_seq_4(X1,X2,X3))=k22_seq_4(k19_seq_4(X1,X3,X2))\|~m1_finseq_1(k19_seq_4(X1,X3,X2),k2_numbers)\|~m1_subset_1(X3,k14_seq_4(X1))\|~m1_subset_1(X2,k14_seq_4(X1))\|~m1_subset_1(X1,k5_numbers)), inference(csr,[status(thm)],[c_0_87, c_0_88])). cnf(c_0_94, negated_conjecture, (m1_subset_1(esk3_0,k14_seq_4(esk1_0))\|~m1_finseq_2(k14_seq_4(esk1_0),k2_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_64, c_0_89])])). cnf(c_0_95, plain, (m1_subset_1(X1,k5_numbers)\|~m2_subset_1(X1,k1_numbers,k5_numbers)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_90, c_0_53]), c_0_54])])). cnf(c_0_96, negated_conjecture, (m2_subset_1(esk1_0,k1_numbers,k5_numbers)), inference(evalgc,[status(thm)],[c_0_91])). cnf(c_0_97, negated_conjecture, (m1_subset_1(esk2_0,k14_seq_4(esk1_0))\|~m1_finseq_2(k14_seq_4(esk1_0),k2_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_64, c_0_92])])). cnf(c_0_98, negated_conjecture, (k22_seq_4(k19_seq_4(esk1_0,esk2_0,esk3_0))!=k22_seq_4(k19_seq_4(esk1_0,esk3_0,esk2_0))), inference(split_conjunct,[status(thm)],[c_0_79])). cnf(c_0_99, plain, (k22_seq_4(k19_seq_4(X1,X2,X3))=k22_seq_4(k19_seq_4(X1,X3,X2))\|~m1_subset_1(X3,k14_seq_4(X1))\|~m1_subset_1(X2,k14_seq_4(X1))\|~m1_subset_1(X1,k5_numbers)\|~m2_finseq_1(k19_seq_4(X1,X3,X2),k2_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_93, c_0_82])])). cnf(c_0_100, negated_conjecture, (m1_subset_1(esk3_0,k14_seq_4(esk1_0))\|~m1_subset_1(esk1_0,k5_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_94, c_0_56])])). cnf(c_0_101, negated_conjecture, (m1_subset_1(esk1_0,k5_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_95, c_0_96])])). cnf(c_0_102, negated_conjecture, (m1_subset_1(esk2_0,k14_seq_4(esk1_0))\|~m1_subset_1(esk1_0,k5_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_97, c_0_56])])). cnf(c_0_103, negated_conjecture, (k22_seq_4(k19_seq_4(esk1_0,esk3_0,esk2_0))!=k22_seq_4(k19_seq_4(esk1_0,esk2_0,esk3_0))), inference(evalgc,[status(thm)],[c_0_98])). cnf(c_0_104, plain, (k22_seq_4(k19_seq_4(X1,X2,X3))=k22_seq_4(k19_seq_4(X1,X3,X2))\|~m1_subset_1(X3,k14_seq_4(X1))\|~m1_subset_1(X2,k14_seq_4(X1))\|~m1_subset_1(X1,k5_numbers)), inference(csr,[status(thm)],[c_0_99, c_0_88])). cnf(c_0_105, negated_conjecture, (m1_subset_1(esk3_0,k14_seq_4(esk1_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_100, c_0_101])])). cnf(c_0_106, negated_conjecture, (m1_subset_1(esk2_0,k14_seq_4(esk1_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_102, c_0_101])])). cnf(c_0_107, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103, c_0_104]), c_0_105]), c_0_106]), c_0_101])]), ['proof']). # SZS output end CNFRefutation	reserve n,k,k1,m,m1,n1,n2,l for Element of NAT; reserve r,r1,r2,p,p1,g,g1,g2,s,s1,s2,t for real number; reserve seq,seq1,seq2 for Real_Sequence; reserve Nseq for increasing sequence of NAT; reserve x for set; reserve X,Y for Subset of REAL; reserve k,n for Element of NAT, r,r9,r1,r2 for Real, c,c9,c1,c2,c3 for Element of COMPLEX; reserve z,z1,z2 for FinSequence of COMPLEX; reserve x,z,z1,z2,z3 for Element of COMPLEX n, A,B for Subset of COMPLEX n; theorem Th104: \|.z1 - z2.\| = \|.z2 - z1.\| proof thus \|.z1 - z2.\| = \|.-(z2 - z1).\| by Th71 .= \|.z2 - z1.\| by Th91; end;	Convert the following ATP output trace into a readable Mizar proof.
t94_rfunct_1	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t94_rfunct_1, conjecture, ![X1, X2, X3]:(~(v1_xboole_0(X3))=>![X4]:((v1_funct_1(X4)&m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X3,k1_numbers))))=>![X5]:((v1_funct_1(X5)&m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X3,k1_numbers))))=>(((v1_seq_2(k2_partfun1(X3,k1_numbers,X4,X1))&v3_funct_1(k2_partfun1(X3,k1_numbers,X5,X2)))=>v1_seq_2(k2_partfun1(X3,k1_numbers,k47_valued_1(X3,k1_numbers,k1_numbers,X4,X5),k3_xboole_0(X1,X2))))&(((v2_seq_2(k2_partfun1(X3,k1_numbers,X4,X1))&v3_funct_1(k2_partfun1(X3,k1_numbers,X5,X2)))=>v2_seq_2(k2_partfun1(X3,k1_numbers,k47_valued_1(X3,k1_numbers,k1_numbers,X4,X5),k3_xboole_0(X1,X2))))&((v1_comseq_2(k2_partfun1(X3,k1_numbers,X4,X1))&v3_funct_1(k2_partfun1(X3,k1_numbers,X5,X2)))=>(v1_comseq_2(k2_partfun1(X3,k1_numbers,k47_valued_1(X3,k1_numbers,k1_numbers,X4,X5),k3_xboole_0(X1,X2)))&(v1_comseq_2(k2_partfun1(X3,k1_numbers,k47_valued_1(X3,k1_numbers,k1_numbers,X5,X4),k3_xboole_0(X1,X2)))&v1_comseq_2(k2_partfun1(X3,k1_numbers,k20_valued_1(X3,k1_numbers,k1_numbers,X4,X5),k3_xboole_0(X1,X2))))))))))), file('/scratch/mptp/predsminms1/t94_rfunct_1__0', t94_rfunct_1)). fof(redefinition_k2_partfun1, axiom, ![X1, X2, X3, X4]:((v1_funct_1(X3)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2))))=>k2_partfun1(X1,X2,X3,X4)=k5_relat_1(X3,X4)), file('/scratch/mptp/predsminms1/t94_rfunct_1__0', redefinition_k2_partfun1)). fof(dt_k20_valued_1, axiom, ![X1, X2, X3, X4, X5]:((v3_membered(X2)&(v3_membered(X3)&((v1_funct_1(X4)&m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2))))&(v1_funct_1(X5)&m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))))))=>(v1_funct_1(k20_valued_1(X1,X2,X3,X4,X5))&m1_subset_1(k20_valued_1(X1,X2,X3,X4,X5),k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers))))), file('/scratch/mptp/predsminms1/t94_rfunct_1__0', dt_k20_valued_1)). fof(cc1_rfunct_1, axiom, ![X1]:((v1_relat_1(X1)&(v1_funct_1(X1)&(v3_funct_1(X1)&v3_valued_0(X1))))=>(v1_relat_1(X1)&(v1_funct_1(X1)&(v3_valued_0(X1)&v1_comseq_2(X1))))), file('/scratch/mptp/predsminms1/t94_rfunct_1__0', cc1_rfunct_1)). fof(fc45_valued_0, axiom, ![X1, X2]:((v1_relat_1(X1)&v3_valued_0(X1))=>(v1_relat_1(k5_relat_1(X1,X2))&v3_valued_0(k5_relat_1(X1,X2)))), file('/scratch/mptp/predsminms1/t94_rfunct_1__0', fc45_valued_0)). fof(dt_k47_valued_1, axiom, ![X1, X2, X3, X4, X5]:((v3_membered(X2)&(v3_membered(X3)&((v1_funct_1(X4)&m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2))))&(v1_funct_1(X5)&m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))))))=>(v1_funct_1(k47_valued_1(X1,X2,X3,X4,X5))&m1_subset_1(k47_valued_1(X1,X2,X3,X4,X5),k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers))))), file('/scratch/mptp/predsminms1/t94_rfunct_1__0', dt_k47_valued_1)). fof(redefinition_k20_valued_1, axiom, ![X1, X2, X3, X4, X5]:((v3_membered(X2)&(v3_membered(X3)&((v1_funct_1(X4)&m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2))))&(v1_funct_1(X5)&m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))))))=>k20_valued_1(X1,X2,X3,X4,X5)=k18_valued_1(X4,X5)), file('/scratch/mptp/predsminms1/t94_rfunct_1__0', redefinition_k20_valued_1)). fof(dt_k5_relat_1, axiom, ![X1, X2]:(v1_relat_1(X1)=>v1_relat_1(k5_relat_1(X1,X2))), file('/scratch/mptp/predsminms1/t94_rfunct_1__0', dt_k5_relat_1)). fof(cc18_valued_0, axiom, ![X1, X2]:(v3_membered(X2)=>![X3]:(m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))=>v3_valued_0(X3))), file('/scratch/mptp/predsminms1/t94_rfunct_1__0', cc18_valued_0)). fof(cc2_relat_1, axiom, ![X1]:(v1_relat_1(X1)=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(X1))=>v1_relat_1(X2))), file('/scratch/mptp/predsminms1/t94_rfunct_1__0', cc2_relat_1)). fof(fc6_relat_1, axiom, ![X1, X2]:v1_relat_1(k2_zfmisc_1(X1,X2)), file('/scratch/mptp/predsminms1/t94_rfunct_1__0', fc6_relat_1)). fof(fc3_membered, axiom, v3_membered(k1_numbers), file('/scratch/mptp/predsminms1/t94_rfunct_1__0', fc3_membered)). fof(dt_k2_partfun1, axiom, ![X1, X2, X3, X4]:((v1_funct_1(X3)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2))))=>(v1_funct_1(k2_partfun1(X1,X2,X3,X4))&m1_subset_1(k2_partfun1(X1,X2,X3,X4),k1_zfmisc_1(k2_zfmisc_1(X1,X2))))), file('/scratch/mptp/predsminms1/t94_rfunct_1__0', dt_k2_partfun1)). fof(cc1_seq_2, axiom, ![X1]:((v1_relat_1(X1)&(v1_funct_1(X1)&(v3_valued_0(X1)&v1_comseq_2(X1))))=>(v1_relat_1(X1)&(v1_funct_1(X1)&(v3_valued_0(X1)&(v1_seq_2(X1)&v2_seq_2(X1)))))), file('/scratch/mptp/predsminms1/t94_rfunct_1__0', cc1_seq_2)). fof(t84_rfunct_1, axiom, ![X1, X2, X3]:((v1_relat_1(X3)&(v1_funct_1(X3)&v3_valued_0(X3)))=>![X4]:((v1_relat_1(X4)&(v1_funct_1(X4)&v3_valued_0(X4)))=>((v1_comseq_2(k5_relat_1(X3,X1))&v1_comseq_2(k5_relat_1(X4,X2)))=>(v1_comseq_2(k5_relat_1(k18_valued_1(X3,X4),k3_xboole_0(X1,X2)))&v1_comseq_2(k5_relat_1(k45_valued_1(X3,X4),k3_xboole_0(X1,X2))))))), file('/scratch/mptp/predsminms1/t94_rfunct_1__0', t84_rfunct_1)). fof(redefinition_k47_valued_1, axiom, ![X1, X2, X3, X4, X5]:((v3_membered(X2)&(v3_membered(X3)&((v1_funct_1(X4)&m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2))))&(v1_funct_1(X5)&m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))))))=>k47_valued_1(X1,X2,X3,X4,X5)=k45_valued_1(X4,X5)), file('/scratch/mptp/predsminms1/t94_rfunct_1__0', redefinition_k47_valued_1)). fof(commutativity_k3_xboole_0, axiom, ![X1, X2]:k3_xboole_0(X1,X2)=k3_xboole_0(X2,X1), file('/scratch/mptp/predsminms1/t94_rfunct_1__0', commutativity_k3_xboole_0)). fof(cc16_valued_0, axiom, ![X1, X2]:(v1_membered(X2)=>![X3]:(m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))=>v1_valued_0(X3))), file('/scratch/mptp/predsminms1/t94_rfunct_1__0', cc16_valued_0)). fof(dt_k32_valued_1, axiom, ![X1, X2, X3]:((v3_membered(X2)&(v1_funct_1(X3)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))))=>(v1_funct_1(k32_valued_1(X1,X2,X3))&m1_subset_1(k32_valued_1(X1,X2,X3),k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers))))), file('/scratch/mptp/predsminms1/t94_rfunct_1__0', dt_k32_valued_1)). fof(d9_valued_1, axiom, ![X1]:((v1_relat_1(X1)&(v1_funct_1(X1)&v1_valued_0(X1)))=>![X2]:((v1_relat_1(X2)&(v1_funct_1(X2)&v1_valued_0(X2)))=>k45_valued_1(X1,X2)=k1_valued_1(X1,k30_valued_1(X2)))), file('/scratch/mptp/predsminms1/t94_rfunct_1__0', d9_valued_1)). fof(redefinition_k32_valued_1, axiom, ![X1, X2, X3]:((v3_membered(X2)&(v1_funct_1(X3)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))))=>k32_valued_1(X1,X2,X3)=k30_valued_1(X3)), file('/scratch/mptp/predsminms1/t94_rfunct_1__0', redefinition_k32_valued_1)). fof(cc5_membered, axiom, ![X1]:(v3_membered(X1)=>v1_membered(X1)), file('/scratch/mptp/predsminms1/t94_rfunct_1__0', cc5_membered)). fof(t83_rfunct_1, axiom, ![X1, X2, X3]:((v1_relat_1(X3)&(v1_funct_1(X3)&v3_valued_0(X3)))=>![X4]:((v1_relat_1(X4)&(v1_funct_1(X4)&v3_valued_0(X4)))=>(((v1_seq_2(k5_relat_1(X3,X1))&v1_seq_2(k5_relat_1(X4,X2)))=>v1_seq_2(k5_relat_1(k1_valued_1(X3,X4),k3_xboole_0(X1,X2))))&(((v2_seq_2(k5_relat_1(X3,X1))&v2_seq_2(k5_relat_1(X4,X2)))=>v2_seq_2(k5_relat_1(k1_valued_1(X3,X4),k3_xboole_0(X1,X2))))&((v1_comseq_2(k5_relat_1(X3,X1))&v1_comseq_2(k5_relat_1(X4,X2)))=>v1_comseq_2(k5_relat_1(k1_valued_1(X3,X4),k3_xboole_0(X1,X2)))))))), file('/scratch/mptp/predsminms1/t94_rfunct_1__0', t83_rfunct_1)). fof(t90_rfunct_1, axiom, ![X1, X2]:(~(v1_xboole_0(X2))=>![X3]:((v1_funct_1(X3)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X2,k1_numbers))))=>(v3_funct_1(k2_partfun1(X2,k1_numbers,X3,X1))=>v3_funct_1(k2_partfun1(X2,k1_numbers,k32_valued_1(X2,k1_numbers,X3),X1))))), file('/scratch/mptp/predsminms1/t94_rfunct_1__0', t90_rfunct_1)). fof(c_0_24, negated_conjecture, ~(![X1, X2, X3]:(~(v1_xboole_0(X3))=>![X4]:((v1_funct_1(X4)&m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X3,k1_numbers))))=>![X5]:((v1_funct_1(X5)&m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X3,k1_numbers))))=>(((v1_seq_2(k2_partfun1(X3,k1_numbers,X4,X1))&v3_funct_1(k2_partfun1(X3,k1_numbers,X5,X2)))=>v1_seq_2(k2_partfun1(X3,k1_numbers,k47_valued_1(X3,k1_numbers,k1_numbers,X4,X5),k3_xboole_0(X1,X2))))&(((v2_seq_2(k2_partfun1(X3,k1_numbers,X4,X1))&v3_funct_1(k2_partfun1(X3,k1_numbers,X5,X2)))=>v2_seq_2(k2_partfun1(X3,k1_numbers,k47_valued_1(X3,k1_numbers,k1_numbers,X4,X5),k3_xboole_0(X1,X2))))&((v1_comseq_2(k2_partfun1(X3,k1_numbers,X4,X1))&v3_funct_1(k2_partfun1(X3,k1_numbers,X5,X2)))=>(v1_comseq_2(k2_partfun1(X3,k1_numbers,k47_valued_1(X3,k1_numbers,k1_numbers,X4,X5),k3_xboole_0(X1,X2)))&(v1_comseq_2(k2_partfun1(X3,k1_numbers,k47_valued_1(X3,k1_numbers,k1_numbers,X5,X4),k3_xboole_0(X1,X2)))&v1_comseq_2(k2_partfun1(X3,k1_numbers,k20_valued_1(X3,k1_numbers,k1_numbers,X4,X5),k3_xboole_0(X1,X2)))))))))))), inference(assume_negation,[status(cth)],[t94_rfunct_1])). fof(c_0_25, plain, ![X18, X19, X20, X21]:(~v1_funct_1(X20)\|~m1_subset_1(X20,k1_zfmisc_1(k2_zfmisc_1(X18,X19)))\|k2_partfun1(X18,X19,X20,X21)=k5_relat_1(X20,X21)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k2_partfun1])])). fof(c_0_26, plain, ![X40, X41, X42, X43, X44]:((v1_funct_1(k20_valued_1(X40,X41,X42,X43,X44))\|(~v3_membered(X41)\|(~v3_membered(X42)\|(~v1_funct_1(X43)\|~m1_subset_1(X43,k1_zfmisc_1(k2_zfmisc_1(X40,X41)))\|(~v1_funct_1(X44)\|~m1_subset_1(X44,k1_zfmisc_1(k2_zfmisc_1(X40,X42))))))))&(m1_subset_1(k20_valued_1(X40,X41,X42,X43,X44),k1_zfmisc_1(k2_zfmisc_1(X40,k1_numbers)))\|(~v3_membered(X41)\|(~v3_membered(X42)\|(~v1_funct_1(X43)\|~m1_subset_1(X43,k1_zfmisc_1(k2_zfmisc_1(X40,X41)))\|(~v1_funct_1(X44)\|~m1_subset_1(X44,k1_zfmisc_1(k2_zfmisc_1(X40,X42))))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k20_valued_1])])])). fof(c_0_27, plain, ![X30]:((v1_relat_1(X30)\|(~v1_relat_1(X30)\|(~v1_funct_1(X30)\|(~v3_funct_1(X30)\|~v3_valued_0(X30)))))&((v1_funct_1(X30)\|(~v1_relat_1(X30)\|(~v1_funct_1(X30)\|(~v3_funct_1(X30)\|~v3_valued_0(X30)))))&((v3_valued_0(X30)\|(~v1_relat_1(X30)\|(~v1_funct_1(X30)\|(~v3_funct_1(X30)\|~v3_valued_0(X30)))))&(v1_comseq_2(X30)\|(~v1_relat_1(X30)\|(~v1_funct_1(X30)\|(~v3_funct_1(X30)\|~v3_valued_0(X30)))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_rfunct_1])])])). fof(c_0_28, plain, ![X28, X29]:((v1_relat_1(k5_relat_1(X28,X29))\|(~v1_relat_1(X28)\|~v3_valued_0(X28)))&(v3_valued_0(k5_relat_1(X28,X29))\|(~v1_relat_1(X28)\|~v3_valued_0(X28)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc45_valued_0])])])). fof(c_0_29, plain, ![X52, X53, X54, X55, X56]:((v1_funct_1(k47_valued_1(X52,X53,X54,X55,X56))\|(~v3_membered(X53)\|(~v3_membered(X54)\|(~v1_funct_1(X55)\|~m1_subset_1(X55,k1_zfmisc_1(k2_zfmisc_1(X52,X53)))\|(~v1_funct_1(X56)\|~m1_subset_1(X56,k1_zfmisc_1(k2_zfmisc_1(X52,X54))))))))&(m1_subset_1(k47_valued_1(X52,X53,X54,X55,X56),k1_zfmisc_1(k2_zfmisc_1(X52,k1_numbers)))\|(~v3_membered(X53)\|(~v3_membered(X54)\|(~v1_funct_1(X55)\|~m1_subset_1(X55,k1_zfmisc_1(k2_zfmisc_1(X52,X53)))\|(~v1_funct_1(X56)\|~m1_subset_1(X56,k1_zfmisc_1(k2_zfmisc_1(X52,X54))))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k47_valued_1])])])). fof(c_0_30, plain, ![X35, X36, X37, X38, X39]:(~v3_membered(X36)\|(~v3_membered(X37)\|(~v1_funct_1(X38)\|~m1_subset_1(X38,k1_zfmisc_1(k2_zfmisc_1(X35,X36)))\|(~v1_funct_1(X39)\|~m1_subset_1(X39,k1_zfmisc_1(k2_zfmisc_1(X35,X37))))))\|k20_valued_1(X35,X36,X37,X38,X39)=k18_valued_1(X38,X39)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k20_valued_1])])). fof(c_0_31, negated_conjecture, (~v1_xboole_0(esk3_0)&((v1_funct_1(esk4_0)&m1_subset_1(esk4_0,k1_zfmisc_1(k2_zfmisc_1(esk3_0,k1_numbers))))&((v1_funct_1(esk5_0)&m1_subset_1(esk5_0,k1_zfmisc_1(k2_zfmisc_1(esk3_0,k1_numbers))))&(((((((v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))\|v2_seq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))\|v1_seq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0)))&(v3_funct_1(k2_partfun1(esk3_0,k1_numbers,esk5_0,esk2_0))\|v2_seq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))\|v1_seq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))))&(~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))\|(~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk5_0,esk4_0),k3_xboole_0(esk1_0,esk2_0)))\|~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k20_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0))))\|v2_seq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))\|v1_seq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))))&(((v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))\|v3_funct_1(k2_partfun1(esk3_0,k1_numbers,esk5_0,esk2_0))\|v1_seq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0)))&(v3_funct_1(k2_partfun1(esk3_0,k1_numbers,esk5_0,esk2_0))\|v3_funct_1(k2_partfun1(esk3_0,k1_numbers,esk5_0,esk2_0))\|v1_seq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))))&(~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))\|(~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk5_0,esk4_0),k3_xboole_0(esk1_0,esk2_0)))\|~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k20_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0))))\|v3_funct_1(k2_partfun1(esk3_0,k1_numbers,esk5_0,esk2_0))\|v1_seq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0)))))&(((v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))\|~v2_seq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))\|v1_seq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0)))&(v3_funct_1(k2_partfun1(esk3_0,k1_numbers,esk5_0,esk2_0))\|~v2_seq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))\|v1_seq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))))&(~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))\|(~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk5_0,esk4_0),k3_xboole_0(esk1_0,esk2_0)))\|~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k20_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0))))\|~v2_seq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))\|v1_seq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0)))))&(((((v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))\|v2_seq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))\|v3_funct_1(k2_partfun1(esk3_0,k1_numbers,esk5_0,esk2_0)))&(v3_funct_1(k2_partfun1(esk3_0,k1_numbers,esk5_0,esk2_0))\|v2_seq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))\|v3_funct_1(k2_partfun1(esk3_0,k1_numbers,esk5_0,esk2_0))))&(~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))\|(~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk5_0,esk4_0),k3_xboole_0(esk1_0,esk2_0)))\|~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k20_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0))))\|v2_seq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))\|v3_funct_1(k2_partfun1(esk3_0,k1_numbers,esk5_0,esk2_0))))&(((v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))\|v3_funct_1(k2_partfun1(esk3_0,k1_numbers,esk5_0,esk2_0))\|v3_funct_1(k2_partfun1(esk3_0,k1_numbers,esk5_0,esk2_0)))&(v3_funct_1(k2_partfun1(esk3_0,k1_numbers,esk5_0,esk2_0))\|v3_funct_1(k2_partfun1(esk3_0,k1_numbers,esk5_0,esk2_0))\|v3_funct_1(k2_partfun1(esk3_0,k1_numbers,esk5_0,esk2_0))))&(~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))\|(~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk5_0,esk4_0),k3_xboole_0(esk1_0,esk2_0)))\|~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k20_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0))))\|v3_funct_1(k2_partfun1(esk3_0,k1_numbers,esk5_0,esk2_0))\|v3_funct_1(k2_partfun1(esk3_0,k1_numbers,esk5_0,esk2_0)))))&(((v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))\|~v2_seq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))\|v3_funct_1(k2_partfun1(esk3_0,k1_numbers,esk5_0,esk2_0)))&(v3_funct_1(k2_partfun1(esk3_0,k1_numbers,esk5_0,esk2_0))\|~v2_seq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))\|v3_funct_1(k2_partfun1(esk3_0,k1_numbers,esk5_0,esk2_0))))&(~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))\|(~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk5_0,esk4_0),k3_xboole_0(esk1_0,esk2_0)))\|~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k20_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0))))\|~v2_seq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))\|v3_funct_1(k2_partfun1(esk3_0,k1_numbers,esk5_0,esk2_0))))))&(((((v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))\|v2_seq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))\|~v1_seq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0))))&(v3_funct_1(k2_partfun1(esk3_0,k1_numbers,esk5_0,esk2_0))\|v2_seq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))\|~v1_seq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))))&(~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))\|(~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk5_0,esk4_0),k3_xboole_0(esk1_0,esk2_0)))\|~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k20_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0))))\|v2_seq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))\|~v1_seq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))))&(((v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))\|v3_funct_1(k2_partfun1(esk3_0,k1_numbers,esk5_0,esk2_0))\|~v1_seq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0))))&(v3_funct_1(k2_partfun1(esk3_0,k1_numbers,esk5_0,esk2_0))\|v3_funct_1(k2_partfun1(esk3_0,k1_numbers,esk5_0,esk2_0))\|~v1_seq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))))&(~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))\|(~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk5_0,esk4_0),k3_xboole_0(esk1_0,esk2_0)))\|~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k20_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0))))\|v3_funct_1(k2_partfun1(esk3_0,k1_numbers,esk5_0,esk2_0))\|~v1_seq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0))))))&(((v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))\|~v2_seq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))\|~v1_seq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0))))&(v3_funct_1(k2_partfun1(esk3_0,k1_numbers,esk5_0,esk2_0))\|~v2_seq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))\|~v1_seq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))))&(~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))\|(~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk5_0,esk4_0),k3_xboole_0(esk1_0,esk2_0)))\|~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k20_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0))))\|~v2_seq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))\|~v1_seq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))))))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_24])])])])])). cnf(c_0_32, plain, (k2_partfun1(X2,X3,X1,X4)=k5_relat_1(X1,X4)\|~v1_funct_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_25])). cnf(c_0_33, plain, (m1_subset_1(k20_valued_1(X1,X2,X3,X4,X5),k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~v3_membered(X2)\|~v3_membered(X3)\|~v1_funct_1(X4)\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X5)\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_34, plain, (v1_comseq_2(X1)\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v3_funct_1(X1)\|~v3_valued_0(X1)), inference(split_conjunct,[status(thm)],[c_0_27])). cnf(c_0_35, plain, (v3_valued_0(k5_relat_1(X1,X2))\|~v1_relat_1(X1)\|~v3_valued_0(X1)), inference(split_conjunct,[status(thm)],[c_0_28])). fof(c_0_36, plain, ![X26, X27]:(~v1_relat_1(X26)\|v1_relat_1(k5_relat_1(X26,X27))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k5_relat_1])])). fof(c_0_37, plain, ![X15, X16, X17]:(~v3_membered(X16)\|(~m1_subset_1(X17,k1_zfmisc_1(k2_zfmisc_1(X15,X16)))\|v3_valued_0(X17))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc18_valued_0])])])). fof(c_0_38, plain, ![X13, X14]:(~v1_relat_1(X13)\|(~m1_subset_1(X14,k1_zfmisc_1(X13))\|v1_relat_1(X14))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_relat_1])])])). fof(c_0_39, plain, ![X11, X12]:v1_relat_1(k2_zfmisc_1(X11,X12)), inference(variable_rename,[status(thm)],[fc6_relat_1])). cnf(c_0_40, plain, (m1_subset_1(k47_valued_1(X1,X2,X3,X4,X5),k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~v3_membered(X2)\|~v3_membered(X3)\|~v1_funct_1(X4)\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X5)\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_29])). cnf(c_0_41, plain, (k20_valued_1(X4,X1,X2,X3,X5)=k18_valued_1(X3,X5)\|~v3_membered(X1)\|~v3_membered(X2)\|~v1_funct_1(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X4,X1)))\|~v1_funct_1(X5)\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X4,X2)))), inference(split_conjunct,[status(thm)],[c_0_30])). cnf(c_0_42, negated_conjecture, (m1_subset_1(esk5_0,k1_zfmisc_1(k2_zfmisc_1(esk3_0,k1_numbers)))), inference(split_conjunct,[status(thm)],[c_0_31])). cnf(c_0_43, plain, (v3_membered(k1_numbers)), inference(split_conjunct,[status(thm)],[fc3_membered])). cnf(c_0_44, negated_conjecture, (v1_funct_1(esk5_0)), inference(split_conjunct,[status(thm)],[c_0_31])). cnf(c_0_45, plain, (k2_partfun1(X2,X3,X1,X4)=k5_relat_1(X1,X4)\|~v1_funct_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(evalgc,[status(thm)],[c_0_32])). cnf(c_0_46, plain, (m1_subset_1(k20_valued_1(X1,X2,X3,X4,X5),k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~v1_funct_1(X5)\|~v1_funct_1(X4)\|~v3_membered(X3)\|~v3_membered(X2)\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(evalgc,[status(thm)],[c_0_33])). cnf(c_0_47, plain, (v1_funct_1(k20_valued_1(X1,X2,X3,X4,X5))\|~v3_membered(X2)\|~v3_membered(X3)\|~v1_funct_1(X4)\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X5)\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_48, plain, (v1_comseq_2(X1)\|~v1_funct_1(X1)\|~v3_funct_1(X1)\|~v1_relat_1(X1)\|~v3_valued_0(X1)), inference(evalgc,[status(thm)],[c_0_34])). cnf(c_0_49, plain, (v3_valued_0(k5_relat_1(X1,X2))\|~v1_relat_1(X1)\|~v3_valued_0(X1)), inference(evalgc,[status(thm)],[c_0_35])). cnf(c_0_50, plain, (v1_relat_1(k5_relat_1(X1,X2))\|~v1_relat_1(X1)), inference(split_conjunct,[status(thm)],[c_0_36])). cnf(c_0_51, plain, (v3_valued_0(X2)\|~v3_membered(X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_37])). cnf(c_0_52, plain, (v1_relat_1(X2)\|~v1_relat_1(X1)\|~m1_subset_1(X2,k1_zfmisc_1(X1))), inference(split_conjunct,[status(thm)],[c_0_38])). cnf(c_0_53, plain, (v1_relat_1(k2_zfmisc_1(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_39])). fof(c_0_54, plain, ![X22, X23, X24, X25]:((v1_funct_1(k2_partfun1(X22,X23,X24,X25))\|(~v1_funct_1(X24)\|~m1_subset_1(X24,k1_zfmisc_1(k2_zfmisc_1(X22,X23)))))&(m1_subset_1(k2_partfun1(X22,X23,X24,X25),k1_zfmisc_1(k2_zfmisc_1(X22,X23)))\|(~v1_funct_1(X24)\|~m1_subset_1(X24,k1_zfmisc_1(k2_zfmisc_1(X22,X23)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_partfun1])])])). fof(c_0_55, plain, ![X63]:((v1_relat_1(X63)\|(~v1_relat_1(X63)\|(~v1_funct_1(X63)\|(~v3_valued_0(X63)\|~v1_comseq_2(X63)))))&((v1_funct_1(X63)\|(~v1_relat_1(X63)\|(~v1_funct_1(X63)\|(~v3_valued_0(X63)\|~v1_comseq_2(X63)))))&((v3_valued_0(X63)\|(~v1_relat_1(X63)\|(~v1_funct_1(X63)\|(~v3_valued_0(X63)\|~v1_comseq_2(X63)))))&((v1_seq_2(X63)\|(~v1_relat_1(X63)\|(~v1_funct_1(X63)\|(~v3_valued_0(X63)\|~v1_comseq_2(X63)))))&(v2_seq_2(X63)\|(~v1_relat_1(X63)\|(~v1_funct_1(X63)\|(~v3_valued_0(X63)\|~v1_comseq_2(X63))))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_seq_2])])])). cnf(c_0_56, plain, (m1_subset_1(k47_valued_1(X1,X2,X3,X4,X5),k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~v1_funct_1(X5)\|~v1_funct_1(X4)\|~v3_membered(X3)\|~v3_membered(X2)\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(evalgc,[status(thm)],[c_0_40])). cnf(c_0_57, plain, (v1_funct_1(k47_valued_1(X1,X2,X3,X4,X5))\|~v3_membered(X2)\|~v3_membered(X3)\|~v1_funct_1(X4)\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X5)\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_29])). fof(c_0_58, plain, ![X31, X32, X33, X34]:((v1_comseq_2(k5_relat_1(k18_valued_1(X33,X34),k3_xboole_0(X31,X32)))\|(~v1_comseq_2(k5_relat_1(X33,X31))\|~v1_comseq_2(k5_relat_1(X34,X32)))\|(~v1_relat_1(X34)\|(~v1_funct_1(X34)\|~v3_valued_0(X34)))\|(~v1_relat_1(X33)\|(~v1_funct_1(X33)\|~v3_valued_0(X33))))&(v1_comseq_2(k5_relat_1(k45_valued_1(X33,X34),k3_xboole_0(X31,X32)))\|(~v1_comseq_2(k5_relat_1(X33,X31))\|~v1_comseq_2(k5_relat_1(X34,X32)))\|(~v1_relat_1(X34)\|(~v1_funct_1(X34)\|~v3_valued_0(X34)))\|(~v1_relat_1(X33)\|(~v1_funct_1(X33)\|~v3_valued_0(X33))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t84_rfunct_1])])])])). cnf(c_0_59, plain, (k20_valued_1(X4,X1,X2,X3,X5)=k18_valued_1(X3,X5)\|~v1_funct_1(X5)\|~v1_funct_1(X3)\|~v3_membered(X2)\|~v3_membered(X1)\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X4,X2)))\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X4,X1)))), inference(evalgc,[status(thm)],[c_0_41])). cnf(c_0_60, negated_conjecture, (m1_subset_1(esk5_0,k1_zfmisc_1(k2_zfmisc_1(esk3_0,k1_numbers)))), inference(evalgc,[status(thm)],[c_0_42])). cnf(c_0_61, plain, (v3_membered(k1_numbers)), inference(evalgc,[status(thm)],[c_0_43])). cnf(c_0_62, negated_conjecture, (v1_funct_1(esk5_0)), inference(evalgc,[status(thm)],[c_0_44])). cnf(c_0_63, negated_conjecture, (m1_subset_1(esk4_0,k1_zfmisc_1(k2_zfmisc_1(esk3_0,k1_numbers)))), inference(split_conjunct,[status(thm)],[c_0_31])). cnf(c_0_64, negated_conjecture, (v1_funct_1(esk4_0)), inference(split_conjunct,[status(thm)],[c_0_31])). cnf(c_0_65, plain, (k2_partfun1(X1,k1_numbers,k20_valued_1(X1,X2,X3,X4,X5),X6)=k5_relat_1(k20_valued_1(X1,X2,X3,X4,X5),X6)\|~v1_funct_1(k20_valued_1(X1,X2,X3,X4,X5))\|~v3_membered(X3)\|~v3_membered(X2)\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X5)\|~v1_funct_1(X4)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_45, c_0_46])])). cnf(c_0_66, plain, (v1_funct_1(k20_valued_1(X1,X2,X3,X4,X5))\|~v1_funct_1(X5)\|~v1_funct_1(X4)\|~v3_membered(X3)\|~v3_membered(X2)\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(evalgc,[status(thm)],[c_0_47])). cnf(c_0_67, plain, (v1_comseq_2(k5_relat_1(X1,X2))\|~v1_relat_1(k5_relat_1(X1,X2))\|~v3_funct_1(k5_relat_1(X1,X2))\|~v1_funct_1(k5_relat_1(X1,X2))\|~v3_valued_0(X1)\|~v1_relat_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_48, c_0_49])])). cnf(c_0_68, plain, (v1_relat_1(k5_relat_1(X1,X2))\|~v1_relat_1(X1)), inference(evalgc,[status(thm)],[c_0_50])). cnf(c_0_69, plain, (v3_valued_0(X2)\|~v3_membered(X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X3,X1)))), inference(evalgc,[status(thm)],[c_0_51])). cnf(c_0_70, plain, (v1_relat_1(X2)\|~v1_relat_1(X1)\|~m1_subset_1(X2,k1_zfmisc_1(X1))), inference(evalgc,[status(thm)],[c_0_52])). cnf(c_0_71, plain, (v1_relat_1(k2_zfmisc_1(X1,X2))), inference(evalgc,[status(thm)],[c_0_53])). cnf(c_0_72, plain, (v1_funct_1(k2_partfun1(X1,X2,X3,X4))\|~v1_funct_1(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_54])). cnf(c_0_73, plain, (v2_seq_2(X1)\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v3_valued_0(X1)\|~v1_comseq_2(X1)), inference(split_conjunct,[status(thm)],[c_0_55])). cnf(c_0_74, plain, (k2_partfun1(X1,k1_numbers,k47_valued_1(X1,X2,X3,X4,X5),X6)=k5_relat_1(k47_valued_1(X1,X2,X3,X4,X5),X6)\|~v1_funct_1(k47_valued_1(X1,X2,X3,X4,X5))\|~v3_membered(X3)\|~v3_membered(X2)\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X5)\|~v1_funct_1(X4)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_45, c_0_56])])). cnf(c_0_75, plain, (v1_funct_1(k47_valued_1(X1,X2,X3,X4,X5))\|~v1_funct_1(X5)\|~v1_funct_1(X4)\|~v3_membered(X3)\|~v3_membered(X2)\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(evalgc,[status(thm)],[c_0_57])). cnf(c_0_76, plain, (v1_comseq_2(k5_relat_1(k18_valued_1(X1,X2),k3_xboole_0(X3,X4)))\|~v1_comseq_2(k5_relat_1(X1,X3))\|~v1_comseq_2(k5_relat_1(X2,X4))\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v3_valued_0(X2)\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v3_valued_0(X1)), inference(split_conjunct,[status(thm)],[c_0_58])). cnf(c_0_77, negated_conjecture, (k20_valued_1(esk3_0,X1,k1_numbers,X2,esk5_0)=k18_valued_1(X2,esk5_0)\|~v3_membered(X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(esk3_0,X1)))\|~v1_funct_1(X2)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59, c_0_60]), c_0_61]), c_0_62])])])). cnf(c_0_78, negated_conjecture, (m1_subset_1(esk4_0,k1_zfmisc_1(k2_zfmisc_1(esk3_0,k1_numbers)))), inference(evalgc,[status(thm)],[c_0_63])). cnf(c_0_79, negated_conjecture, (v1_funct_1(esk4_0)), inference(evalgc,[status(thm)],[c_0_64])). cnf(c_0_80, plain, (k2_partfun1(X1,k1_numbers,k20_valued_1(X1,X2,X3,X4,X5),X6)=k5_relat_1(k20_valued_1(X1,X2,X3,X4,X5),X6)\|~v3_membered(X3)\|~v3_membered(X2)\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X5)\|~v1_funct_1(X4)), inference(csr,[status(thm)],[c_0_65, c_0_66])). cnf(c_0_81, plain, (v1_comseq_2(k5_relat_1(X1,X2))\|~v3_valued_0(X1)\|~v1_relat_1(X1)\|~v3_funct_1(k5_relat_1(X1,X2))\|~v1_funct_1(k5_relat_1(X1,X2))), inference(csr,[status(thm)],[c_0_67, c_0_68])). cnf(c_0_82, negated_conjecture, (k5_relat_1(esk5_0,X1)=k2_partfun1(esk3_0,k1_numbers,esk5_0,X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45, c_0_60]), c_0_62])])])). cnf(c_0_83, negated_conjecture, (v3_valued_0(esk5_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69, c_0_60]), c_0_61])])])). cnf(c_0_84, negated_conjecture, (v1_relat_1(esk5_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70, c_0_60]), c_0_71])])])). cnf(c_0_85, plain, (v1_funct_1(k2_partfun1(X1,X2,X3,X4))\|~v1_funct_1(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(evalgc,[status(thm)],[c_0_72])). cnf(c_0_86, negated_conjecture, (v3_funct_1(k2_partfun1(esk3_0,k1_numbers,esk5_0,esk2_0))\|v3_funct_1(k2_partfun1(esk3_0,k1_numbers,esk5_0,esk2_0))\|v3_funct_1(k2_partfun1(esk3_0,k1_numbers,esk5_0,esk2_0))), inference(split_conjunct,[status(thm)],[c_0_31])). cnf(c_0_87, plain, (v2_seq_2(X1)\|~v1_funct_1(X1)\|~v1_comseq_2(X1)\|~v1_relat_1(X1)\|~v3_valued_0(X1)), inference(evalgc,[status(thm)],[c_0_73])). cnf(c_0_88, plain, (k2_partfun1(X1,k1_numbers,k47_valued_1(X1,X2,X3,X4,X5),X6)=k5_relat_1(k47_valued_1(X1,X2,X3,X4,X5),X6)\|~v3_membered(X3)\|~v3_membered(X2)\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X5)\|~v1_funct_1(X4)), inference(csr,[status(thm)],[c_0_74, c_0_75])). cnf(c_0_89, plain, (v1_seq_2(X1)\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v3_valued_0(X1)\|~v1_comseq_2(X1)), inference(split_conjunct,[status(thm)],[c_0_55])). cnf(c_0_90, plain, (v1_comseq_2(k5_relat_1(k18_valued_1(X1,X2),k3_xboole_0(X3,X4)))\|~v1_funct_1(X2)\|~v1_funct_1(X1)\|~v1_relat_1(X2)\|~v1_relat_1(X1)\|~v3_valued_0(X2)\|~v3_valued_0(X1)\|~v1_comseq_2(k5_relat_1(X2,X4))\|~v1_comseq_2(k5_relat_1(X1,X3))), inference(evalgc,[status(thm)],[c_0_76])). cnf(c_0_91, negated_conjecture, (k18_valued_1(esk4_0,esk5_0)=k20_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77, c_0_78]), c_0_61]), c_0_79])])])). cnf(c_0_92, negated_conjecture, (v3_valued_0(esk4_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69, c_0_78]), c_0_61])])])). cnf(c_0_93, negated_conjecture, (v1_relat_1(esk4_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70, c_0_78]), c_0_71])])])). cnf(c_0_94, negated_conjecture, (k5_relat_1(esk4_0,X1)=k2_partfun1(esk3_0,k1_numbers,esk4_0,X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45, c_0_78]), c_0_79])])])). cnf(c_0_95, negated_conjecture, (k5_relat_1(k20_valued_1(esk3_0,X1,k1_numbers,X2,esk5_0),X3)=k2_partfun1(esk3_0,k1_numbers,k20_valued_1(esk3_0,X1,k1_numbers,X2,esk5_0),X3)\|~v3_membered(X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(esk3_0,X1)))\|~v1_funct_1(X2)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80, c_0_60]), c_0_61]), c_0_62])])])). cnf(c_0_96, negated_conjecture, (v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,esk5_0,X1))\|~v3_funct_1(k2_partfun1(esk3_0,k1_numbers,esk5_0,X1))\|~v1_funct_1(k2_partfun1(esk3_0,k1_numbers,esk5_0,X1))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81, c_0_82]), c_0_83]), c_0_84])])])). cnf(c_0_97, negated_conjecture, (v1_funct_1(k2_partfun1(esk3_0,k1_numbers,esk5_0,X1))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85, c_0_60]), c_0_62])])])). cnf(c_0_98, negated_conjecture, (v3_funct_1(k2_partfun1(esk3_0,k1_numbers,esk5_0,esk2_0))), inference(cn,[status(thm)],[c_0_86])). cnf(c_0_99, plain, (v2_seq_2(k5_relat_1(X1,X2))\|~v1_relat_1(k5_relat_1(X1,X2))\|~v1_comseq_2(k5_relat_1(X1,X2))\|~v1_funct_1(k5_relat_1(X1,X2))\|~v3_valued_0(X1)\|~v1_relat_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_87, c_0_49])])). cnf(c_0_100, negated_conjecture, (k5_relat_1(k47_valued_1(esk3_0,X1,k1_numbers,X2,esk5_0),X3)=k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,X1,k1_numbers,X2,esk5_0),X3)\|~v3_membered(X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(esk3_0,X1)))\|~v1_funct_1(X2)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88, c_0_60]), c_0_61]), c_0_62])])])). cnf(c_0_101, plain, (v1_relat_1(k47_valued_1(X1,X2,X3,X4,X5))\|~v3_membered(X3)\|~v3_membered(X2)\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X5)\|~v1_funct_1(X4)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70, c_0_56]), c_0_71])])])). cnf(c_0_102, plain, (v1_seq_2(X1)\|~v1_funct_1(X1)\|~v1_comseq_2(X1)\|~v1_relat_1(X1)\|~v3_valued_0(X1)), inference(evalgc,[status(thm)],[c_0_89])). cnf(c_0_103, negated_conjecture, (~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))\|~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk5_0,esk4_0),k3_xboole_0(esk1_0,esk2_0)))\|~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k20_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))\|~v2_seq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))\|~v1_seq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))), inference(split_conjunct,[status(thm)],[c_0_31])). cnf(c_0_104, negated_conjecture, (v1_comseq_2(k5_relat_1(k20_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(X1,X2)))\|~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,esk5_0,X2))\|~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,X1))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90, c_0_91]), c_0_83]), c_0_92]), c_0_84]), c_0_93]), c_0_82]), c_0_94]), c_0_62]), c_0_79])])])). cnf(c_0_105, negated_conjecture, (k5_relat_1(k20_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),X1)=k2_partfun1(esk3_0,k1_numbers,k20_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95, c_0_78]), c_0_61]), c_0_79])])])). cnf(c_0_106, negated_conjecture, (v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,esk5_0,X1))\|~v3_funct_1(k2_partfun1(esk3_0,k1_numbers,esk5_0,X1))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_96, c_0_97])])). cnf(c_0_107, negated_conjecture, (v3_funct_1(k2_partfun1(esk3_0,k1_numbers,esk5_0,esk2_0))), inference(evalgc,[status(thm)],[c_0_98])). cnf(c_0_108, plain, (v2_seq_2(k5_relat_1(X1,X2))\|~v3_valued_0(X1)\|~v1_relat_1(X1)\|~v1_comseq_2(k5_relat_1(X1,X2))\|~v1_funct_1(k5_relat_1(X1,X2))), inference(csr,[status(thm)],[c_0_99, c_0_68])). cnf(c_0_109, negated_conjecture, (k5_relat_1(k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),X1)=k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100, c_0_78]), c_0_61]), c_0_79])])])). cnf(c_0_110, negated_conjecture, (v1_relat_1(k47_valued_1(esk3_0,X1,k1_numbers,X2,esk5_0))\|~v3_membered(X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(esk3_0,X1)))\|~v1_funct_1(X2)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101, c_0_60]), c_0_61]), c_0_62])])])). cnf(c_0_111, plain, (v3_valued_0(k47_valued_1(X1,X2,X3,X4,X5))\|~v3_membered(X3)\|~v3_membered(X2)\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X5)\|~v1_funct_1(X4)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69, c_0_56]), c_0_61])])])). cnf(c_0_112, plain, (v1_seq_2(k5_relat_1(X1,X2))\|~v1_relat_1(k5_relat_1(X1,X2))\|~v1_comseq_2(k5_relat_1(X1,X2))\|~v1_funct_1(k5_relat_1(X1,X2))\|~v3_valued_0(X1)\|~v1_relat_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_102, c_0_49])])). fof(c_0_113, plain, ![X47, X48, X49, X50, X51]:(~v3_membered(X48)\|(~v3_membered(X49)\|(~v1_funct_1(X50)\|~m1_subset_1(X50,k1_zfmisc_1(k2_zfmisc_1(X47,X48)))\|(~v1_funct_1(X51)\|~m1_subset_1(X51,k1_zfmisc_1(k2_zfmisc_1(X47,X49))))))\|k47_valued_1(X47,X48,X49,X50,X51)=k45_valued_1(X50,X51)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k47_valued_1])])). cnf(c_0_114, negated_conjecture, (~v1_seq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))\|~v2_seq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))\|~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))\|~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk5_0,esk4_0),k3_xboole_0(esk1_0,esk2_0)))\|~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k20_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))), inference(evalgc,[status(thm)],[c_0_103])). cnf(c_0_115, negated_conjecture, (v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k20_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(X1,X2)))\|~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,esk5_0,X2))\|~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,X1))), inference(rw,[status(thm)],[c_0_104, c_0_105])). cnf(c_0_116, negated_conjecture, (v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,esk5_0,esk2_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_106, c_0_107])])). cnf(c_0_117, negated_conjecture, (v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))\|~v2_seq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))\|~v1_seq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))), inference(split_conjunct,[status(thm)],[c_0_31])). cnf(c_0_118, negated_conjecture, (v2_seq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),X1))\|~v3_valued_0(k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0))\|~v1_relat_1(k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0))\|~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),X1))\|~v1_funct_1(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_108, c_0_109])])). cnf(c_0_119, negated_conjecture, (v1_relat_1(k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110, c_0_78]), c_0_61]), c_0_79])])])). cnf(c_0_120, negated_conjecture, (v3_valued_0(k47_valued_1(esk3_0,X1,k1_numbers,X2,esk5_0))\|~v3_membered(X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(esk3_0,X1)))\|~v1_funct_1(X2)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111, c_0_60]), c_0_61]), c_0_62])])])). cnf(c_0_121, plain, (v1_seq_2(k5_relat_1(X1,X2))\|~v3_valued_0(X1)\|~v1_relat_1(X1)\|~v1_comseq_2(k5_relat_1(X1,X2))\|~v1_funct_1(k5_relat_1(X1,X2))), inference(csr,[status(thm)],[c_0_112, c_0_68])). fof(c_0_122, plain, ![X45, X46]:k3_xboole_0(X45,X46)=k3_xboole_0(X46,X45), inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0])). cnf(c_0_123, plain, (k47_valued_1(X4,X1,X2,X3,X5)=k45_valued_1(X3,X5)\|~v3_membered(X1)\|~v3_membered(X2)\|~v1_funct_1(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X4,X1)))\|~v1_funct_1(X5)\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X4,X2)))), inference(split_conjunct,[status(thm)],[c_0_113])). fof(c_0_124, plain, ![X1, X4, X3, X2]:(epred1_4(X2,X3,X4,X1)<=>(((v1_seq_2(k5_relat_1(X3,X1))&v1_seq_2(k5_relat_1(X4,X2)))=>v1_seq_2(k5_relat_1(k1_valued_1(X3,X4),k3_xboole_0(X1,X2))))&(((v2_seq_2(k5_relat_1(X3,X1))&v2_seq_2(k5_relat_1(X4,X2)))=>v2_seq_2(k5_relat_1(k1_valued_1(X3,X4),k3_xboole_0(X1,X2))))&((v1_comseq_2(k5_relat_1(X3,X1))&v1_comseq_2(k5_relat_1(X4,X2)))=>v1_comseq_2(k5_relat_1(k1_valued_1(X3,X4),k3_xboole_0(X1,X2))))))), introduced(definition)). cnf(c_0_125, negated_conjecture, (~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))\|~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk5_0,esk4_0),k3_xboole_0(esk1_0,esk2_0)))\|~v2_seq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))\|~v1_seq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))\|~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114, c_0_115]), c_0_116])])])). cnf(c_0_126, negated_conjecture, (v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))\|~v1_seq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))\|~v2_seq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))), inference(evalgc,[status(thm)],[c_0_117])). cnf(c_0_127, negated_conjecture, (v2_seq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),X1))\|~v3_valued_0(k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0))\|~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),X1))\|~v1_funct_1(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),X1))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_118, c_0_119])])])). cnf(c_0_128, negated_conjecture, (v3_valued_0(k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120, c_0_78]), c_0_61]), c_0_79])])])). cnf(c_0_129, negated_conjecture, (v1_seq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),X1))\|~v3_valued_0(k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0))\|~v1_relat_1(k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0))\|~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),X1))\|~v1_funct_1(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_121, c_0_109])])). cnf(c_0_130, plain, (v1_funct_1(k2_partfun1(X1,k1_numbers,k47_valued_1(X1,X2,X3,X4,X5),X6))\|~v1_funct_1(k47_valued_1(X1,X2,X3,X4,X5))\|~v3_membered(X3)\|~v3_membered(X2)\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X5)\|~v1_funct_1(X4)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_85, c_0_56])])). cnf(c_0_131, plain, (v1_comseq_2(k5_relat_1(k45_valued_1(X1,X2),k3_xboole_0(X3,X4)))\|~v1_comseq_2(k5_relat_1(X1,X3))\|~v1_comseq_2(k5_relat_1(X2,X4))\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v3_valued_0(X2)\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v3_valued_0(X1)), inference(split_conjunct,[status(thm)],[c_0_58])). cnf(c_0_132, plain, (k3_xboole_0(X1,X2)=k3_xboole_0(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_122])). cnf(c_0_133, plain, (k47_valued_1(X4,X1,X2,X3,X5)=k45_valued_1(X3,X5)\|~v1_funct_1(X5)\|~v1_funct_1(X3)\|~v3_membered(X2)\|~v3_membered(X1)\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X4,X2)))\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X4,X1)))), inference(evalgc,[status(thm)],[c_0_123])). fof(c_0_134, plain, ![X1, X4, X3, X2]:(epred1_4(X2,X3,X4,X1)=>(((v1_seq_2(k5_relat_1(X3,X1))&v1_seq_2(k5_relat_1(X4,X2)))=>v1_seq_2(k5_relat_1(k1_valued_1(X3,X4),k3_xboole_0(X1,X2))))&(((v2_seq_2(k5_relat_1(X3,X1))&v2_seq_2(k5_relat_1(X4,X2)))=>v2_seq_2(k5_relat_1(k1_valued_1(X3,X4),k3_xboole_0(X1,X2))))&((v1_comseq_2(k5_relat_1(X3,X1))&v1_comseq_2(k5_relat_1(X4,X2)))=>v1_comseq_2(k5_relat_1(k1_valued_1(X3,X4),k3_xboole_0(X1,X2))))))), inference(split_equiv,[status(thm)],[c_0_124])). fof(c_0_135, plain, ![X68, X69, X70]:(~v1_membered(X69)\|(~m1_subset_1(X70,k1_zfmisc_1(k2_zfmisc_1(X68,X69)))\|v1_valued_0(X70))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc16_valued_0])])])). fof(c_0_136, plain, ![X60, X61, X62]:((v1_funct_1(k32_valued_1(X60,X61,X62))\|(~v3_membered(X61)\|(~v1_funct_1(X62)\|~m1_subset_1(X62,k1_zfmisc_1(k2_zfmisc_1(X60,X61))))))&(m1_subset_1(k32_valued_1(X60,X61,X62),k1_zfmisc_1(k2_zfmisc_1(X60,k1_numbers)))\|(~v3_membered(X61)\|(~v1_funct_1(X62)\|~m1_subset_1(X62,k1_zfmisc_1(k2_zfmisc_1(X60,X61))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k32_valued_1])])])). cnf(c_0_137, negated_conjecture, (~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))\|~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk5_0,esk4_0),k3_xboole_0(esk1_0,esk2_0)))\|~v2_seq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))\|~v1_seq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))), inference(csr,[status(thm)],[c_0_125, c_0_126])). cnf(c_0_138, negated_conjecture, (v2_seq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),X1))\|~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),X1))\|~v1_funct_1(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),X1))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_127, c_0_128])])). cnf(c_0_139, negated_conjecture, (v1_seq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),X1))\|~v3_valued_0(k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0))\|~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),X1))\|~v1_funct_1(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),X1))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_129, c_0_119])])])). cnf(c_0_140, plain, (v1_funct_1(k2_partfun1(X1,k1_numbers,k47_valued_1(X1,X2,X3,X4,X5),X6))\|~v3_membered(X3)\|~v3_membered(X2)\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X5)\|~v1_funct_1(X4)), inference(csr,[status(thm)],[c_0_130, c_0_75])). cnf(c_0_141, plain, (v1_comseq_2(k5_relat_1(k45_valued_1(X1,X2),k3_xboole_0(X3,X4)))\|~v1_funct_1(X2)\|~v1_funct_1(X1)\|~v1_relat_1(X2)\|~v1_relat_1(X1)\|~v3_valued_0(X2)\|~v3_valued_0(X1)\|~v1_comseq_2(k5_relat_1(X2,X4))\|~v1_comseq_2(k5_relat_1(X1,X3))), inference(evalgc,[status(thm)],[c_0_131])). cnf(c_0_142, plain, (k3_xboole_0(X1,X2)=k3_xboole_0(X2,X1)), inference(evalgc,[status(thm)],[c_0_132])). cnf(c_0_143, negated_conjecture, (k47_valued_1(esk3_0,X1,k1_numbers,X2,esk4_0)=k45_valued_1(X2,esk4_0)\|~v3_membered(X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(esk3_0,X1)))\|~v1_funct_1(X2)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133, c_0_78]), c_0_61]), c_0_79])])])). fof(c_0_144, plain, ![X77, X78, X79, X80]:((~v1_seq_2(k5_relat_1(X79,X77))\|~v1_seq_2(k5_relat_1(X78,X80))\|v1_seq_2(k5_relat_1(k1_valued_1(X79,X78),k3_xboole_0(X77,X80)))\|~epred1_4(X80,X79,X78,X77))&((~v2_seq_2(k5_relat_1(X79,X77))\|~v2_seq_2(k5_relat_1(X78,X80))\|v2_seq_2(k5_relat_1(k1_valued_1(X79,X78),k3_xboole_0(X77,X80)))\|~epred1_4(X80,X79,X78,X77))&(~v1_comseq_2(k5_relat_1(X79,X77))\|~v1_comseq_2(k5_relat_1(X78,X80))\|v1_comseq_2(k5_relat_1(k1_valued_1(X79,X78),k3_xboole_0(X77,X80)))\|~epred1_4(X80,X79,X78,X77)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_134])])])). fof(c_0_145, plain, ![X71, X72]:(~v1_relat_1(X71)\|(~v1_funct_1(X71)\|~v1_valued_0(X71))\|(~v1_relat_1(X72)\|(~v1_funct_1(X72)\|~v1_valued_0(X72))\|k45_valued_1(X71,X72)=k1_valued_1(X71,k30_valued_1(X72)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d9_valued_1])])])). fof(c_0_146, plain, ![X57, X58, X59]:(~v3_membered(X58)\|(~v1_funct_1(X59)\|~m1_subset_1(X59,k1_zfmisc_1(k2_zfmisc_1(X57,X58))))\|k32_valued_1(X57,X58,X59)=k30_valued_1(X59)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k32_valued_1])])). cnf(c_0_147, plain, (v1_valued_0(X2)\|~v1_membered(X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_135])). fof(c_0_148, plain, ![X67]:(~v3_membered(X67)\|v1_membered(X67)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc5_membered])])). cnf(c_0_149, plain, (m1_subset_1(k32_valued_1(X1,X2,X3),k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~v3_membered(X2)\|~v1_funct_1(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_136])). cnf(c_0_150, negated_conjecture, (~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))\|~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk5_0,esk4_0),k3_xboole_0(esk1_0,esk2_0)))\|~v1_seq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))\|~v1_funct_1(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_137, c_0_138])])). cnf(c_0_151, negated_conjecture, (v1_seq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),X1))\|~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),X1))\|~v1_funct_1(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),X1))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_139, c_0_128])])). cnf(c_0_152, negated_conjecture, (v1_funct_1(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,X1,k1_numbers,X2,esk5_0),X3))\|~v3_membered(X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(esk3_0,X1)))\|~v1_funct_1(X2)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140, c_0_60]), c_0_61]), c_0_62])])])). cnf(c_0_153, plain, (v1_comseq_2(k5_relat_1(k45_valued_1(X1,X2),k3_xboole_0(X4,X3)))\|~v3_valued_0(X2)\|~v3_valued_0(X1)\|~v1_relat_1(X2)\|~v1_relat_1(X1)\|~v1_comseq_2(k5_relat_1(X2,X4))\|~v1_comseq_2(k5_relat_1(X1,X3))\|~v1_funct_1(X2)\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_141, c_0_142])])). cnf(c_0_154, negated_conjecture, (k45_valued_1(esk5_0,esk4_0)=k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk5_0,esk4_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143, c_0_60]), c_0_61]), c_0_62])])])). cnf(c_0_155, negated_conjecture, (k5_relat_1(k47_valued_1(esk3_0,X1,k1_numbers,X2,esk4_0),X3)=k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,X1,k1_numbers,X2,esk4_0),X3)\|~v3_membered(X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(esk3_0,X1)))\|~v1_funct_1(X2)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88, c_0_78]), c_0_61]), c_0_79])])])). cnf(c_0_156, plain, (v2_seq_2(k5_relat_1(k1_valued_1(X1,X3),k3_xboole_0(X2,X4)))\|~v2_seq_2(k5_relat_1(X1,X2))\|~v2_seq_2(k5_relat_1(X3,X4))\|~epred1_4(X4,X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_144])). cnf(c_0_157, plain, (v1_seq_2(k5_relat_1(k1_valued_1(X1,X3),k3_xboole_0(X2,X4)))\|~v1_seq_2(k5_relat_1(X1,X2))\|~v1_seq_2(k5_relat_1(X3,X4))\|~epred1_4(X4,X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_144])). cnf(c_0_158, plain, (k45_valued_1(X1,X2)=k1_valued_1(X1,k30_valued_1(X2))\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v1_valued_0(X1)\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v1_valued_0(X2)), inference(split_conjunct,[status(thm)],[c_0_145])). cnf(c_0_159, plain, (k32_valued_1(X3,X1,X2)=k30_valued_1(X2)\|~v3_membered(X1)\|~v1_funct_1(X2)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_146])). cnf(c_0_160, plain, (v1_valued_0(X2)\|~v1_membered(X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X3,X1)))), inference(evalgc,[status(thm)],[c_0_147])). cnf(c_0_161, plain, (v1_membered(X1)\|~v3_membered(X1)), inference(split_conjunct,[status(thm)],[c_0_148])). cnf(c_0_162, plain, (m1_subset_1(k32_valued_1(X1,X2,X3),k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~v1_funct_1(X3)\|~v3_membered(X2)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(evalgc,[status(thm)],[c_0_149])). cnf(c_0_163, plain, (v1_funct_1(k32_valued_1(X1,X2,X3))\|~v3_membered(X2)\|~v1_funct_1(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_136])). cnf(c_0_164, negated_conjecture, (~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))\|~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk5_0,esk4_0),k3_xboole_0(esk1_0,esk2_0)))\|~v1_funct_1(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))), inference(csr,[status(thm)],[c_0_150, c_0_151])). cnf(c_0_165, negated_conjecture, (v1_funct_1(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),X1))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152, c_0_78]), c_0_61]), c_0_79])])])). cnf(c_0_166, negated_conjecture, (v1_comseq_2(k5_relat_1(k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk5_0,esk4_0),k3_xboole_0(X1,X2)))\|~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,X1))\|~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,esk5_0,X2))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153, c_0_154]), c_0_92]), c_0_83]), c_0_93]), c_0_84]), c_0_94]), c_0_82]), c_0_79]), c_0_62])])])). cnf(c_0_167, negated_conjecture, (k5_relat_1(k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk5_0,esk4_0),X1)=k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk5_0,esk4_0),X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155, c_0_60]), c_0_61]), c_0_62])])])). cnf(c_0_168, negated_conjecture, (v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))\|~v1_seq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))\|~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))\|~v1_funct_1(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_126, c_0_138])])). cnf(c_0_169, negated_conjecture, (k47_valued_1(esk3_0,X1,k1_numbers,X2,esk5_0)=k45_valued_1(X2,esk5_0)\|~v3_membered(X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(esk3_0,X1)))\|~v1_funct_1(X2)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133, c_0_60]), c_0_61]), c_0_62])])])). cnf(c_0_170, plain, (m1_subset_1(k2_partfun1(X1,X2,X3,X4),k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_54])). cnf(c_0_171, plain, (v2_seq_2(k5_relat_1(k1_valued_1(X1,X3),k3_xboole_0(X2,X4)))\|~v2_seq_2(k5_relat_1(X3,X4))\|~v2_seq_2(k5_relat_1(X1,X2))\|~epred1_4(X4,X1,X3,X2)), inference(evalgc,[status(thm)],[c_0_156])). cnf(c_0_172, plain, (v1_seq_2(k5_relat_1(k1_valued_1(X1,X3),k3_xboole_0(X2,X4)))\|~v1_seq_2(k5_relat_1(X3,X4))\|~v1_seq_2(k5_relat_1(X1,X2))\|~epred1_4(X4,X1,X3,X2)), inference(evalgc,[status(thm)],[c_0_157])). cnf(c_0_173, plain, (k1_valued_1(X1,k30_valued_1(X2))=k45_valued_1(X1,X2)\|~v1_funct_1(X2)\|~v1_funct_1(X1)\|~v1_relat_1(X2)\|~v1_relat_1(X1)\|~v1_valued_0(X2)\|~v1_valued_0(X1)), inference(evalgc,[status(thm)],[c_0_158])). cnf(c_0_174, plain, (k32_valued_1(X3,X1,X2)=k30_valued_1(X2)\|~v1_funct_1(X2)\|~v3_membered(X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X3,X1)))), inference(evalgc,[status(thm)],[c_0_159])). cnf(c_0_175, negated_conjecture, (v1_valued_0(esk5_0)\|~v1_membered(k1_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_160, c_0_60])])). cnf(c_0_176, plain, (v1_membered(X1)\|~v3_membered(X1)), inference(evalgc,[status(thm)],[c_0_161])). cnf(c_0_177, negated_conjecture, (v1_valued_0(esk4_0)\|~v1_membered(k1_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_160, c_0_78])])). cnf(c_0_178, plain, (k2_partfun1(X1,k1_numbers,k32_valued_1(X1,X2,X3),X4)=k5_relat_1(k32_valued_1(X1,X2,X3),X4)\|~v1_funct_1(k32_valued_1(X1,X2,X3))\|~v3_membered(X2)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_45, c_0_162])])). cnf(c_0_179, plain, (v1_funct_1(k32_valued_1(X1,X2,X3))\|~v1_funct_1(X3)\|~v3_membered(X2)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(evalgc,[status(thm)],[c_0_163])). cnf(c_0_180, negated_conjecture, (~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))\|~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk5_0,esk4_0),k3_xboole_0(esk1_0,esk2_0)))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_164, c_0_165])])])). cnf(c_0_181, negated_conjecture, (v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk5_0,esk4_0),k3_xboole_0(X1,X2)))\|~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,X1))\|~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,esk5_0,X2))), inference(rw,[status(thm)],[c_0_166, c_0_167])). cnf(c_0_182, negated_conjecture, (v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))\|~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))\|~v1_funct_1(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))), inference(csr,[status(thm)],[c_0_168, c_0_151])). cnf(c_0_183, negated_conjecture, (k45_valued_1(esk4_0,esk5_0)=k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169, c_0_78]), c_0_61]), c_0_79])])])). cnf(c_0_184, plain, (m1_subset_1(k2_partfun1(X1,X2,X3,X4),k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(evalgc,[status(thm)],[c_0_170])). cnf(c_0_185, plain, (v2_seq_2(k5_relat_1(k1_valued_1(X1,X2),k3_xboole_0(X4,X3)))\|~epred1_4(X4,X1,X2,X3)\|~v2_seq_2(k5_relat_1(X2,X4))\|~v2_seq_2(k5_relat_1(X1,X3))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_171, c_0_142])])). cnf(c_0_186, plain, (v1_seq_2(k5_relat_1(k45_valued_1(X1,X2),k3_xboole_0(X3,X4)))\|~epred1_4(X4,X1,k30_valued_1(X2),X3)\|~v1_seq_2(k5_relat_1(k30_valued_1(X2),X4))\|~v1_seq_2(k5_relat_1(X1,X3))\|~v1_valued_0(X2)\|~v1_valued_0(X1)\|~v1_relat_1(X2)\|~v1_relat_1(X1)\|~v1_funct_1(X2)\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_172, c_0_173])])). cnf(c_0_187, negated_conjecture, (k30_valued_1(esk5_0)=k32_valued_1(esk3_0,k1_numbers,esk5_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174, c_0_60]), c_0_61]), c_0_62])])])). cnf(c_0_188, negated_conjecture, (v1_valued_0(esk5_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_175, c_0_176]), c_0_61])])])). cnf(c_0_189, negated_conjecture, (v1_valued_0(esk4_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177, c_0_176]), c_0_61])])])). cnf(c_0_190, plain, (k2_partfun1(X1,k1_numbers,k32_valued_1(X1,X2,X3),X4)=k5_relat_1(k32_valued_1(X1,X2,X3),X4)\|~v3_membered(X2)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X3)), inference(csr,[status(thm)],[c_0_178, c_0_179])). cnf(c_0_191, negated_conjecture, (~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))\|~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_180, c_0_181]), c_0_116])])])). cnf(c_0_192, negated_conjecture, (v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))\|~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_182, c_0_165])])])). cnf(c_0_193, negated_conjecture, (v1_comseq_2(k5_relat_1(k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(X1,X2)))\|~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,esk5_0,X2))\|~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,X1))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141, c_0_183]), c_0_83]), c_0_92]), c_0_84]), c_0_93]), c_0_82]), c_0_94]), c_0_62]), c_0_79])])])). cnf(c_0_194, plain, (v3_valued_0(k2_partfun1(X1,X2,X3,X4))\|~v3_membered(X2)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_69, c_0_184])])). cnf(c_0_195, plain, (v2_seq_2(k5_relat_1(k45_valued_1(X1,X2),k3_xboole_0(X3,X4)))\|~epred1_4(X3,X1,k30_valued_1(X2),X4)\|~v2_seq_2(k5_relat_1(k30_valued_1(X2),X3))\|~v2_seq_2(k5_relat_1(X1,X4))\|~v1_valued_0(X2)\|~v1_valued_0(X1)\|~v1_relat_1(X2)\|~v1_relat_1(X1)\|~v1_funct_1(X2)\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_185, c_0_173])])). cnf(c_0_196, negated_conjecture, (v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))\|v2_seq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))\|~v1_seq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))), inference(split_conjunct,[status(thm)],[c_0_31])). cnf(c_0_197, negated_conjecture, (v1_seq_2(k5_relat_1(k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(X1,X2)))\|~epred1_4(X2,esk4_0,k32_valued_1(esk3_0,k1_numbers,esk5_0),X1)\|~v1_seq_2(k5_relat_1(k32_valued_1(esk3_0,k1_numbers,esk5_0),X2))\|~v1_seq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,X1))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_186, c_0_183]), c_0_187]), c_0_188]), c_0_189]), c_0_84]), c_0_93]), c_0_187]), c_0_94]), c_0_62]), c_0_79])])])). cnf(c_0_198, negated_conjecture, (k5_relat_1(k32_valued_1(esk3_0,k1_numbers,esk5_0),X1)=k2_partfun1(esk3_0,k1_numbers,k32_valued_1(esk3_0,k1_numbers,esk5_0),X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_190, c_0_60]), c_0_61]), c_0_62])])])). cnf(c_0_199, negated_conjecture, (~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))), inference(csr,[status(thm)],[c_0_191, c_0_192])). cnf(c_0_200, negated_conjecture, (v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(X1,X2)))\|~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,esk5_0,X2))\|~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,X1))), inference(rw,[status(thm)],[c_0_193, c_0_109])). cnf(c_0_201, negated_conjecture, (v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))\|v2_seq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))\|v1_seq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))), inference(split_conjunct,[status(thm)],[c_0_31])). fof(c_0_202, axiom, ![X1, X2, X3]:((v1_relat_1(X3)&(v1_funct_1(X3)&v3_valued_0(X3)))=>![X4]:((v1_relat_1(X4)&(v1_funct_1(X4)&v3_valued_0(X4)))=>epred1_4(X2,X3,X4,X1))), inference(apply_def,[status(thm)],[t83_rfunct_1, c_0_124])). cnf(c_0_203, plain, (v3_valued_0(k2_partfun1(X1,k1_numbers,k32_valued_1(X1,X2,X3),X4))\|~v1_funct_1(k32_valued_1(X1,X2,X3))\|~v3_membered(X2)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X3)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_194, c_0_162]), c_0_61])])])). cnf(c_0_204, plain, (v1_relat_1(k2_partfun1(X1,X2,X3,X4))\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X3)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70, c_0_184]), c_0_71])])])). cnf(c_0_205, negated_conjecture, (v2_seq_2(k5_relat_1(k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(X1,X2)))\|~epred1_4(X1,esk4_0,k32_valued_1(esk3_0,k1_numbers,esk5_0),X2)\|~v2_seq_2(k5_relat_1(k32_valued_1(esk3_0,k1_numbers,esk5_0),X1))\|~v2_seq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,X2))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_195, c_0_183]), c_0_187]), c_0_188]), c_0_189]), c_0_84]), c_0_93]), c_0_187]), c_0_94]), c_0_62]), c_0_79])])])). cnf(c_0_206, negated_conjecture, (v2_seq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))\|v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))\|~v1_seq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))), inference(evalgc,[status(thm)],[c_0_196])). cnf(c_0_207, negated_conjecture, (v1_seq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(X1,X2)))\|~epred1_4(X2,esk4_0,k32_valued_1(esk3_0,k1_numbers,esk5_0),X1)\|~v1_seq_2(k2_partfun1(esk3_0,k1_numbers,k32_valued_1(esk3_0,k1_numbers,esk5_0),X2))\|~v1_seq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_197, c_0_109]), c_0_198])). cnf(c_0_208, negated_conjecture, (~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_199, c_0_200]), c_0_116])])])). cnf(c_0_209, negated_conjecture, (v1_seq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))\|v2_seq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))\|v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))), inference(evalgc,[status(thm)],[c_0_201])). fof(c_0_210, plain, ![X73, X74, X75, X76]:(~v1_relat_1(X75)\|(~v1_funct_1(X75)\|~v3_valued_0(X75))\|(~v1_relat_1(X76)\|(~v1_funct_1(X76)\|~v3_valued_0(X76))\|epred1_4(X74,X75,X76,X73))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_202])])])). cnf(c_0_211, plain, (v3_valued_0(k2_partfun1(X1,k1_numbers,k32_valued_1(X1,X2,X3),X4))\|~v3_membered(X2)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X3)), inference(csr,[status(thm)],[c_0_203, c_0_179])). cnf(c_0_212, plain, (v1_funct_1(k2_partfun1(X1,k1_numbers,k32_valued_1(X1,X2,X3),X4))\|~v1_funct_1(k32_valued_1(X1,X2,X3))\|~v3_membered(X2)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_85, c_0_162])])). cnf(c_0_213, plain, (v1_relat_1(k2_partfun1(X1,k1_numbers,k32_valued_1(X1,X2,X3),X4))\|~v1_funct_1(k32_valued_1(X1,X2,X3))\|~v3_membered(X2)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_204, c_0_162])])). fof(c_0_214, plain, ![X64, X65, X66]:(v1_xboole_0(X65)\|(~v1_funct_1(X66)\|~m1_subset_1(X66,k1_zfmisc_1(k2_zfmisc_1(X65,k1_numbers)))\|(~v3_funct_1(k2_partfun1(X65,k1_numbers,X66,X64))\|v3_funct_1(k2_partfun1(X65,k1_numbers,k32_valued_1(X65,k1_numbers,X66),X64))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t90_rfunct_1])])])])). cnf(c_0_215, negated_conjecture, (v2_seq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(X1,X2)))\|~epred1_4(X1,esk4_0,k32_valued_1(esk3_0,k1_numbers,esk5_0),X2)\|~v2_seq_2(k5_relat_1(k32_valued_1(esk3_0,k1_numbers,esk5_0),X1))\|~v2_seq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,X2))), inference(rw,[status(thm)],[c_0_205, c_0_109])). cnf(c_0_216, negated_conjecture, (v2_seq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))\|~epred1_4(esk2_0,esk4_0,k32_valued_1(esk3_0,k1_numbers,esk5_0),esk1_0)\|~v1_seq_2(k2_partfun1(esk3_0,k1_numbers,k32_valued_1(esk3_0,k1_numbers,esk5_0),esk2_0))\|~v1_seq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_206, c_0_207]), c_0_208])])). cnf(c_0_217, negated_conjecture, (v2_seq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))\|v1_seq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[c_0_209, c_0_208])])). cnf(c_0_218, plain, (epred1_4(X3,X1,X2,X4)\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v3_valued_0(X1)\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v3_valued_0(X2)), inference(split_conjunct,[status(thm)],[c_0_210])). cnf(c_0_219, plain, (v3_valued_0(k32_valued_1(X1,X2,X3))\|~v3_membered(X2)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X3)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69, c_0_162]), c_0_61])])])). cnf(c_0_220, plain, (v1_relat_1(k32_valued_1(X1,X2,X3))\|~v3_membered(X2)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X3)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70, c_0_162]), c_0_71])])])). cnf(c_0_221, plain, (v1_comseq_2(k2_partfun1(X1,k1_numbers,k32_valued_1(X1,X2,X3),X4))\|~v1_relat_1(k2_partfun1(X1,k1_numbers,k32_valued_1(X1,X2,X3),X4))\|~v3_funct_1(k2_partfun1(X1,k1_numbers,k32_valued_1(X1,X2,X3),X4))\|~v1_funct_1(k2_partfun1(X1,k1_numbers,k32_valued_1(X1,X2,X3),X4))\|~v3_membered(X2)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_48, c_0_211])])). cnf(c_0_222, plain, (v1_funct_1(k2_partfun1(X1,k1_numbers,k32_valued_1(X1,X2,X3),X4))\|~v3_membered(X2)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X3)), inference(csr,[status(thm)],[c_0_212, c_0_179])). cnf(c_0_223, plain, (v1_relat_1(k2_partfun1(X1,k1_numbers,k32_valued_1(X1,X2,X3),X4))\|~v3_membered(X2)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X3)), inference(csr,[status(thm)],[c_0_213, c_0_179])). cnf(c_0_224, plain, (v1_xboole_0(X1)\|v3_funct_1(k2_partfun1(X1,k1_numbers,k32_valued_1(X1,k1_numbers,X2),X3))\|~v1_funct_1(X2)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~v3_funct_1(k2_partfun1(X1,k1_numbers,X2,X3))), inference(split_conjunct,[status(thm)],[c_0_214])). cnf(c_0_225, negated_conjecture, (v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))\|v1_seq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))\|~v2_seq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))), inference(split_conjunct,[status(thm)],[c_0_31])). cnf(c_0_226, negated_conjecture, (v2_seq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(X1,X2)))\|~epred1_4(X1,esk4_0,k32_valued_1(esk3_0,k1_numbers,esk5_0),X2)\|~v2_seq_2(k2_partfun1(esk3_0,k1_numbers,k32_valued_1(esk3_0,k1_numbers,esk5_0),X1))\|~v2_seq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,X2))), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[c_0_215, c_0_198])])). cnf(c_0_227, negated_conjecture, (v2_seq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))\|~epred1_4(esk2_0,esk4_0,k32_valued_1(esk3_0,k1_numbers,esk5_0),esk1_0)\|~v1_seq_2(k2_partfun1(esk3_0,k1_numbers,k32_valued_1(esk3_0,k1_numbers,esk5_0),esk2_0))), inference(csr,[status(thm)],[c_0_216, c_0_217])). cnf(c_0_228, plain, (epred1_4(X3,X1,X2,X4)\|~v1_funct_1(X2)\|~v1_funct_1(X1)\|~v1_relat_1(X2)\|~v1_relat_1(X1)\|~v3_valued_0(X2)\|~v3_valued_0(X1)), inference(evalgc,[status(thm)],[c_0_218])). cnf(c_0_229, negated_conjecture, (v3_valued_0(k32_valued_1(esk3_0,k1_numbers,esk5_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_219, c_0_60]), c_0_61]), c_0_62])])])). cnf(c_0_230, negated_conjecture, (v1_relat_1(k32_valued_1(esk3_0,k1_numbers,esk5_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_220, c_0_60]), c_0_61]), c_0_62])])])). cnf(c_0_231, negated_conjecture, (v1_funct_1(k32_valued_1(esk3_0,k1_numbers,esk5_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_179, c_0_60]), c_0_61]), c_0_62])])])). cnf(c_0_232, plain, (v1_seq_2(k2_partfun1(X1,k1_numbers,k32_valued_1(X1,X2,X3),X4))\|~v1_relat_1(k2_partfun1(X1,k1_numbers,k32_valued_1(X1,X2,X3),X4))\|~v1_comseq_2(k2_partfun1(X1,k1_numbers,k32_valued_1(X1,X2,X3),X4))\|~v1_funct_1(k2_partfun1(X1,k1_numbers,k32_valued_1(X1,X2,X3),X4))\|~v3_membered(X2)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_102, c_0_211])])). cnf(c_0_233, plain, (v1_comseq_2(k2_partfun1(X1,k1_numbers,k32_valued_1(X1,X2,X3),X4))\|~v3_membered(X2)\|~v3_funct_1(k2_partfun1(X1,k1_numbers,k32_valued_1(X1,X2,X3),X4))\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X3)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_221, c_0_222]), c_0_223])). cnf(c_0_234, plain, (v1_xboole_0(X1)\|v3_funct_1(k2_partfun1(X1,k1_numbers,k32_valued_1(X1,k1_numbers,X2),X3))\|~v1_funct_1(X2)\|~v3_funct_1(k2_partfun1(X1,k1_numbers,X2,X3))\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))), inference(evalgc,[status(thm)],[c_0_224])). cnf(c_0_235, negated_conjecture, (~v1_xboole_0(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_31])). cnf(c_0_236, negated_conjecture, (v1_seq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))\|v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))\|~v2_seq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))), inference(evalgc,[status(thm)],[c_0_225])). cnf(c_0_237, negated_conjecture, (v2_seq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(X2,X1)))\|~epred1_4(X1,esk4_0,k32_valued_1(esk3_0,k1_numbers,esk5_0),X2)\|~v2_seq_2(k2_partfun1(esk3_0,k1_numbers,k32_valued_1(esk3_0,k1_numbers,esk5_0),X1))\|~v2_seq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,X2))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_226, c_0_142])])). cnf(c_0_238, negated_conjecture, (v2_seq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))\|~v1_seq_2(k2_partfun1(esk3_0,k1_numbers,k32_valued_1(esk3_0,k1_numbers,esk5_0),esk2_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_227, c_0_228]), c_0_229]), c_0_92]), c_0_230]), c_0_93]), c_0_231]), c_0_79])])])). cnf(c_0_239, plain, (v1_seq_2(k2_partfun1(X1,k1_numbers,k32_valued_1(X1,X2,X3),X4))\|~v3_membered(X2)\|~v1_comseq_2(k2_partfun1(X1,k1_numbers,k32_valued_1(X1,X2,X3),X4))\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X3)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_232, c_0_222]), c_0_223])). cnf(c_0_240, plain, (v1_comseq_2(k2_partfun1(X1,k1_numbers,k32_valued_1(X1,k1_numbers,X2),X3))\|v1_xboole_0(X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~v1_funct_1(X2)\|~v3_funct_1(k2_partfun1(X1,k1_numbers,X2,X3))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_233, c_0_234]), c_0_61])])])). cnf(c_0_241, negated_conjecture, (~v1_xboole_0(esk3_0)), inference(evalgc,[status(thm)],[c_0_235])). cnf(c_0_242, negated_conjecture, (v1_seq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))\|~epred1_4(esk2_0,esk4_0,k32_valued_1(esk3_0,k1_numbers,esk5_0),esk1_0)\|~v2_seq_2(k2_partfun1(esk3_0,k1_numbers,k32_valued_1(esk3_0,k1_numbers,esk5_0),esk2_0))\|~v2_seq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_236, c_0_237]), c_0_208])])). cnf(c_0_243, negated_conjecture, (v2_seq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))\|~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k32_valued_1(esk3_0,k1_numbers,esk5_0),esk2_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_238, c_0_239]), c_0_61]), c_0_60]), c_0_62])])])). cnf(c_0_244, negated_conjecture, (v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k32_valued_1(esk3_0,k1_numbers,esk5_0),X1))\|~v3_funct_1(k2_partfun1(esk3_0,k1_numbers,esk5_0,X1))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_240, c_0_60]), c_0_62])]), c_0_241])])). cnf(c_0_245, negated_conjecture, (v1_seq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))\|~epred1_4(esk2_0,esk4_0,k32_valued_1(esk3_0,k1_numbers,esk5_0),esk1_0)\|~v2_seq_2(k2_partfun1(esk3_0,k1_numbers,k32_valued_1(esk3_0,k1_numbers,esk5_0),esk2_0))), inference(csr,[status(thm)],[c_0_242, c_0_217])). cnf(c_0_246, plain, (v2_seq_2(k2_partfun1(X1,k1_numbers,k32_valued_1(X1,X2,X3),X4))\|~v1_relat_1(k2_partfun1(X1,k1_numbers,k32_valued_1(X1,X2,X3),X4))\|~v1_comseq_2(k2_partfun1(X1,k1_numbers,k32_valued_1(X1,X2,X3),X4))\|~v1_funct_1(k2_partfun1(X1,k1_numbers,k32_valued_1(X1,X2,X3),X4))\|~v3_membered(X2)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_87, c_0_211])])). cnf(c_0_247, negated_conjecture, (~v1_seq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))\|~epred1_4(esk2_0,esk4_0,k32_valued_1(esk3_0,k1_numbers,esk5_0),esk1_0)\|~v2_seq_2(k2_partfun1(esk3_0,k1_numbers,k32_valued_1(esk3_0,k1_numbers,esk5_0),esk2_0))\|~v2_seq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_126, c_0_237]), c_0_208])])). cnf(c_0_248, negated_conjecture, (v2_seq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_243, c_0_244]), c_0_107])])])). cnf(c_0_249, negated_conjecture, (v1_seq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))\|~v2_seq_2(k2_partfun1(esk3_0,k1_numbers,k32_valued_1(esk3_0,k1_numbers,esk5_0),esk2_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_245, c_0_228]), c_0_229]), c_0_92]), c_0_230]), c_0_93]), c_0_231]), c_0_79])])])). cnf(c_0_250, plain, (v2_seq_2(k2_partfun1(X1,k1_numbers,k32_valued_1(X1,X2,X3),X4))\|~v3_membered(X2)\|~v1_comseq_2(k2_partfun1(X1,k1_numbers,k32_valued_1(X1,X2,X3),X4))\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X3)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_246, c_0_222]), c_0_223])). cnf(c_0_251, negated_conjecture, (~epred1_4(esk2_0,esk4_0,k32_valued_1(esk3_0,k1_numbers,esk5_0),esk1_0)\|~v2_seq_2(k2_partfun1(esk3_0,k1_numbers,k32_valued_1(esk3_0,k1_numbers,esk5_0),esk2_0))\|~v1_seq_2(k2_partfun1(esk3_0,k1_numbers,k47_valued_1(esk3_0,k1_numbers,k1_numbers,esk4_0,esk5_0),k3_xboole_0(esk1_0,esk2_0)))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_247, c_0_248])])])). cnf(c_0_252, negated_conjecture, (v1_seq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))\|~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k32_valued_1(esk3_0,k1_numbers,esk5_0),esk2_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_249, c_0_250]), c_0_61]), c_0_60]), c_0_62])])])). cnf(c_0_253, negated_conjecture, (~epred1_4(esk2_0,esk4_0,k32_valued_1(esk3_0,k1_numbers,esk5_0),esk1_0)\|~v2_seq_2(k2_partfun1(esk3_0,k1_numbers,k32_valued_1(esk3_0,k1_numbers,esk5_0),esk2_0))\|~v1_seq_2(k2_partfun1(esk3_0,k1_numbers,k32_valued_1(esk3_0,k1_numbers,esk5_0),esk2_0))\|~v1_seq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_251, c_0_207])])). cnf(c_0_254, negated_conjecture, (v1_seq_2(k2_partfun1(esk3_0,k1_numbers,esk4_0,esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_252, c_0_244]), c_0_107])])])). cnf(c_0_255, negated_conjecture, (~epred1_4(esk2_0,esk4_0,k32_valued_1(esk3_0,k1_numbers,esk5_0),esk1_0)\|~v2_seq_2(k2_partfun1(esk3_0,k1_numbers,k32_valued_1(esk3_0,k1_numbers,esk5_0),esk2_0))\|~v1_seq_2(k2_partfun1(esk3_0,k1_numbers,k32_valued_1(esk3_0,k1_numbers,esk5_0),esk2_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_253, c_0_254])])). cnf(c_0_256, negated_conjecture, (~v2_seq_2(k2_partfun1(esk3_0,k1_numbers,k32_valued_1(esk3_0,k1_numbers,esk5_0),esk2_0))\|~v1_seq_2(k2_partfun1(esk3_0,k1_numbers,k32_valued_1(esk3_0,k1_numbers,esk5_0),esk2_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_255, c_0_228]), c_0_229]), c_0_92]), c_0_230]), c_0_93]), c_0_231]), c_0_79])])])). cnf(c_0_257, negated_conjecture, (v1_funct_1(k2_partfun1(esk3_0,k1_numbers,k32_valued_1(esk3_0,k1_numbers,esk5_0),X1))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_222, c_0_60]), c_0_61]), c_0_62])])])). cnf(c_0_258, negated_conjecture, (~v1_seq_2(k2_partfun1(esk3_0,k1_numbers,k32_valued_1(esk3_0,k1_numbers,esk5_0),esk2_0))\|~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k32_valued_1(esk3_0,k1_numbers,esk5_0),esk2_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_256, c_0_250]), c_0_61]), c_0_60]), c_0_62])])])). cnf(c_0_259, negated_conjecture, (v1_seq_2(k2_partfun1(esk3_0,k1_numbers,k32_valued_1(esk3_0,k1_numbers,esk5_0),X1))\|~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k32_valued_1(esk3_0,k1_numbers,esk5_0),X1))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121, c_0_198]), c_0_229]), c_0_230]), c_0_257])])])). cnf(c_0_260, negated_conjecture, (~v1_comseq_2(k2_partfun1(esk3_0,k1_numbers,k32_valued_1(esk3_0,k1_numbers,esk5_0),esk2_0))), inference(csr,[status(thm)],[c_0_258, c_0_259])). cnf(c_0_261, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_260, c_0_244]), c_0_107])]), ['proof']). # SZS output end CNFRefutation	reserve x,X,Y for set; reserve C for non empty set; reserve c for Element of C; reserve f,f1,f2,f3,g,g1 for complex-valued Function; reserve r,p for complex number; reserve r,r1,r2,p for real number; reserve f,f1,f2 for PartFunc of C,REAL; reserve f for real-valued Function; reserve f1,f2 for real-valued Function; reserve f,f1,f2 for PartFunc of C,REAL; theorem (f1\|X is bounded_above & f2\|Y is constant implies (f1-f2)\|(X /\ Y) is bounded_above) & (f1\|X is bounded_below & f2\|Y is constant implies (f1-f2)\|(X /\ Y) is bounded_below) & (f1\|X is bounded & f2\|Y is constant implies (f1-f2)\|( X /\ Y) is bounded & (f2-f1)\|(X /\ Y) is bounded& (f1(#)f2)\|(X /\ Y) is bounded ) proof thus f1\|X is bounded_above & f2\|Y is constant implies (f1-f2)\|(X /\ Y) is bounded_above proof assume that A1: f1\|X is bounded_above and A2: f2\|Y is constant; (-f2)\|Y is constant by A2,Th90; hence thesis by A1,Th83; end; thus f1\|X is bounded_below & f2\|Y is constant implies (f1-f2)\|(X /\ Y) is bounded_below proof assume that A3: f1\|X is bounded_below and A4: f2\|Y is constant; (-f2)\|Y is constant by A4,Th90; hence thesis by A3,Th83; end; assume that A5: f1\|X is bounded and A6: f2\|Y is constant; (-f2)\|Y is constant by A6,Th90; hence (f1-f2)\|(X /\ Y) is bounded by A5,Th83; thus (f2-f1)\|(X /\ Y) is bounded by A5,A6,Th84; thus thesis by A5,A6,Th84; end;	Convert the following ATP output trace into a readable Mizar proof.
t4_cat_3	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(d1_cat_3, axiom, ![X1]:((~(v2_struct_0(X1))&(~(v11_struct_0(X1))&(v2_cat_1(X1)&(v3_cat_1(X1)&(v4_cat_1(X1)&(v5_cat_1(X1)&(v6_cat_1(X1)&l1_cat_1(X1))))))))=>![X2, X3]:((v1_funct_1(X3)&(v1_funct_2(X3,X2,u4_struct_0(X1))&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X2,u4_struct_0(X1))))))=>![X4]:((v1_funct_1(X4)&(v1_funct_2(X4,X2,u1_struct_0(X1))&m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X2,u1_struct_0(X1))))))=>(X4=k2_cat_3(X1,X2,X3)<=>![X5]:(r2_hidden(X5,X2)=>k7_partfun1(u1_struct_0(X1),X4,X5)=k3_graph_1(X1,k7_partfun1(u4_struct_0(X1),X3,X5))))))), file('/scratch/mptp/predsminms1/t4_cat_3__0', d1_cat_3)). fof(dt_k2_cat_3, axiom, ![X1, X2, X3]:(((~(v2_struct_0(X1))&(~(v11_struct_0(X1))&(v2_cat_1(X1)&(v3_cat_1(X1)&(v4_cat_1(X1)&(v5_cat_1(X1)&(v6_cat_1(X1)&l1_cat_1(X1))))))))&(v1_funct_1(X3)&(v1_funct_2(X3,X2,u4_struct_0(X1))&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X2,u4_struct_0(X1)))))))=>(v1_funct_1(k2_cat_3(X1,X2,X3))&(v1_funct_2(k2_cat_3(X1,X2,X3),X2,u1_struct_0(X1))&m1_subset_1(k2_cat_3(X1,X2,X3),k1_zfmisc_1(k2_zfmisc_1(X2,u1_struct_0(X1))))))), file('/scratch/mptp/predsminms1/t4_cat_3__0', dt_k2_cat_3)). fof(t2_cat_3, axiom, ![X1, X2, X3]:(~(v1_xboole_0(X3))=>![X4]:(m1_subset_1(X4,X3)=>(r2_hidden(X2,X1)=>k7_partfun1(X3,k8_funcop_1(X3,X1,X4),X2)=X4))), file('/scratch/mptp/predsminms1/t4_cat_3__0', t2_cat_3)). fof(dt_k8_funcop_1, axiom, ![X1, X2, X3]:((~(v1_xboole_0(X1))&m1_subset_1(X3,X1))=>(v1_funct_1(k8_funcop_1(X1,X2,X3))&(v1_funct_2(k8_funcop_1(X1,X2,X3),X2,X1)&m1_subset_1(k8_funcop_1(X1,X2,X3),k1_zfmisc_1(k2_zfmisc_1(X2,X1)))))), file('/scratch/mptp/predsminms1/t4_cat_3__0', dt_k8_funcop_1)). fof(dt_l1_graph_1, axiom, ![X1]:(l1_graph_1(X1)=>l5_struct_0(X1)), file('/scratch/mptp/predsminms1/t4_cat_3__0', dt_l1_graph_1)). fof(dt_l1_cat_1, axiom, ![X1]:(l1_cat_1(X1)=>l1_graph_1(X1)), file('/scratch/mptp/predsminms1/t4_cat_3__0', dt_l1_cat_1)). fof(fc14_struct_0, axiom, ![X1]:((~(v11_struct_0(X1))&l5_struct_0(X1))=>~(v1_xboole_0(u4_struct_0(X1)))), file('/scratch/mptp/predsminms1/t4_cat_3__0', fc14_struct_0)). fof(redefinition_k8_funcop_1, axiom, ![X1, X2, X3]:((~(v1_xboole_0(X1))&m1_subset_1(X3,X1))=>k8_funcop_1(X1,X2,X3)=k2_funcop_1(X2,X3)), file('/scratch/mptp/predsminms1/t4_cat_3__0', redefinition_k8_funcop_1)). fof(d2_funcop_1, axiom, ![X1, X2]:k2_funcop_1(X1,X2)=k2_zfmisc_1(X1,k1_tarski(X2)), file('/scratch/mptp/predsminms1/t4_cat_3__0', d2_funcop_1)). fof(cc2_relset_1, axiom, ![X1, X2, X3]:(m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))=>(v4_relat_1(X3,X1)&v5_relat_1(X3,X2))), file('/scratch/mptp/predsminms1/t4_cat_3__0', cc2_relset_1)). fof(dt_k7_partfun1, axiom, ![X1, X2, X3]:((v1_relat_1(X2)&(v5_relat_1(X2,X1)&v1_funct_1(X2)))=>m1_subset_1(k7_partfun1(X1,X2,X3),X1)), file('/scratch/mptp/predsminms1/t4_cat_3__0', dt_k7_partfun1)). fof(cc1_relset_1, axiom, ![X1, X2, X3]:(m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))=>v1_relat_1(X3)), file('/scratch/mptp/predsminms1/t4_cat_3__0', cc1_relset_1)). fof(t4_cat_3, conjecture, ![X1, X2]:((~(v2_struct_0(X2))&(~(v11_struct_0(X2))&(v2_cat_1(X2)&(v3_cat_1(X2)&(v4_cat_1(X2)&(v5_cat_1(X2)&(v6_cat_1(X2)&l1_cat_1(X2))))))))=>![X3]:(m1_subset_1(X3,u4_struct_0(X2))=>r2_funct_2(X1,u1_struct_0(X2),k2_cat_3(X2,X1,k8_funcop_1(u4_struct_0(X2),X1,X3)),k8_funcop_1(u1_struct_0(X2),X1,k3_graph_1(X2,X3))))), file('/scratch/mptp/predsminms1/t4_cat_3__0', t4_cat_3)). fof(redefinition_r2_funct_2, axiom, ![X1, X2, X3, X4]:(((v1_funct_1(X3)&(v1_funct_2(X3,X1,X2)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))))&(v1_funct_1(X4)&(v1_funct_2(X4,X1,X2)&m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2))))))=>(r2_funct_2(X1,X2,X3,X4)<=>X3=X4)), file('/scratch/mptp/predsminms1/t4_cat_3__0', redefinition_r2_funct_2)). fof(t2_subset, axiom, ![X1, X2]:(m1_subset_1(X1,X2)=>(v1_xboole_0(X2)\|r2_hidden(X1,X2))), file('/scratch/mptp/predsminms1/t4_cat_3__0', t2_subset)). fof(fc2_struct_0, axiom, ![X1]:((~(v2_struct_0(X1))&l1_struct_0(X1))=>~(v1_xboole_0(u1_struct_0(X1)))), file('/scratch/mptp/predsminms1/t4_cat_3__0', fc2_struct_0)). fof(dt_l5_struct_0, axiom, ![X1]:(l5_struct_0(X1)=>l1_struct_0(X1)), file('/scratch/mptp/predsminms1/t4_cat_3__0', dt_l5_struct_0)). fof(c_0_17, plain, ![X30, X31, X32, X33, X34]:((X33!=k2_cat_3(X30,X31,X32)\|(~r2_hidden(X34,X31)\|k7_partfun1(u1_struct_0(X30),X33,X34)=k3_graph_1(X30,k7_partfun1(u4_struct_0(X30),X32,X34)))\|(~v1_funct_1(X33)\|(~v1_funct_2(X33,X31,u1_struct_0(X30))\|~m1_subset_1(X33,k1_zfmisc_1(k2_zfmisc_1(X31,u1_struct_0(X30))))))\|(~v1_funct_1(X32)\|(~v1_funct_2(X32,X31,u4_struct_0(X30))\|~m1_subset_1(X32,k1_zfmisc_1(k2_zfmisc_1(X31,u4_struct_0(X30))))))\|(v2_struct_0(X30)\|(v11_struct_0(X30)\|(~v2_cat_1(X30)\|(~v3_cat_1(X30)\|(~v4_cat_1(X30)\|(~v5_cat_1(X30)\|(~v6_cat_1(X30)\|~l1_cat_1(X30)))))))))&((r2_hidden(esk4_4(X30,X31,X32,X33),X31)\|X33=k2_cat_3(X30,X31,X32)\|(~v1_funct_1(X33)\|(~v1_funct_2(X33,X31,u1_struct_0(X30))\|~m1_subset_1(X33,k1_zfmisc_1(k2_zfmisc_1(X31,u1_struct_0(X30))))))\|(~v1_funct_1(X32)\|(~v1_funct_2(X32,X31,u4_struct_0(X30))\|~m1_subset_1(X32,k1_zfmisc_1(k2_zfmisc_1(X31,u4_struct_0(X30))))))\|(v2_struct_0(X30)\|(v11_struct_0(X30)\|(~v2_cat_1(X30)\|(~v3_cat_1(X30)\|(~v4_cat_1(X30)\|(~v5_cat_1(X30)\|(~v6_cat_1(X30)\|~l1_cat_1(X30)))))))))&(k7_partfun1(u1_struct_0(X30),X33,esk4_4(X30,X31,X32,X33))!=k3_graph_1(X30,k7_partfun1(u4_struct_0(X30),X32,esk4_4(X30,X31,X32,X33)))\|X33=k2_cat_3(X30,X31,X32)\|(~v1_funct_1(X33)\|(~v1_funct_2(X33,X31,u1_struct_0(X30))\|~m1_subset_1(X33,k1_zfmisc_1(k2_zfmisc_1(X31,u1_struct_0(X30))))))\|(~v1_funct_1(X32)\|(~v1_funct_2(X32,X31,u4_struct_0(X30))\|~m1_subset_1(X32,k1_zfmisc_1(k2_zfmisc_1(X31,u4_struct_0(X30))))))\|(v2_struct_0(X30)\|(v11_struct_0(X30)\|(~v2_cat_1(X30)\|(~v3_cat_1(X30)\|(~v4_cat_1(X30)\|(~v5_cat_1(X30)\|(~v6_cat_1(X30)\|~l1_cat_1(X30))))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d1_cat_3])])])])])])). fof(c_0_18, plain, ![X20, X21, X22]:((v1_funct_1(k2_cat_3(X20,X21,X22))\|(v2_struct_0(X20)\|(v11_struct_0(X20)\|(~v2_cat_1(X20)\|(~v3_cat_1(X20)\|(~v4_cat_1(X20)\|(~v5_cat_1(X20)\|(~v6_cat_1(X20)\|~l1_cat_1(X20)))))))\|(~v1_funct_1(X22)\|(~v1_funct_2(X22,X21,u4_struct_0(X20))\|~m1_subset_1(X22,k1_zfmisc_1(k2_zfmisc_1(X21,u4_struct_0(X20))))))))&((v1_funct_2(k2_cat_3(X20,X21,X22),X21,u1_struct_0(X20))\|(v2_struct_0(X20)\|(v11_struct_0(X20)\|(~v2_cat_1(X20)\|(~v3_cat_1(X20)\|(~v4_cat_1(X20)\|(~v5_cat_1(X20)\|(~v6_cat_1(X20)\|~l1_cat_1(X20)))))))\|(~v1_funct_1(X22)\|(~v1_funct_2(X22,X21,u4_struct_0(X20))\|~m1_subset_1(X22,k1_zfmisc_1(k2_zfmisc_1(X21,u4_struct_0(X20))))))))&(m1_subset_1(k2_cat_3(X20,X21,X22),k1_zfmisc_1(k2_zfmisc_1(X21,u1_struct_0(X20))))\|(v2_struct_0(X20)\|(v11_struct_0(X20)\|(~v2_cat_1(X20)\|(~v3_cat_1(X20)\|(~v4_cat_1(X20)\|(~v5_cat_1(X20)\|(~v6_cat_1(X20)\|~l1_cat_1(X20)))))))\|(~v1_funct_1(X22)\|(~v1_funct_2(X22,X21,u4_struct_0(X20))\|~m1_subset_1(X22,k1_zfmisc_1(k2_zfmisc_1(X21,u4_struct_0(X20)))))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k2_cat_3])])])])). fof(c_0_19, plain, ![X26, X27, X28, X29]:(v1_xboole_0(X28)\|(~m1_subset_1(X29,X28)\|(~r2_hidden(X27,X26)\|k7_partfun1(X28,k8_funcop_1(X28,X26,X29),X27)=X29))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t2_cat_3])])])])). cnf(c_0_20, plain, (k7_partfun1(u1_struct_0(X2),X1,X5)=k3_graph_1(X2,k7_partfun1(u4_struct_0(X2),X4,X5))\|v2_struct_0(X2)\|v11_struct_0(X2)\|X1!=k2_cat_3(X2,X3,X4)\|~r2_hidden(X5,X3)\|~v1_funct_1(X1)\|~v1_funct_2(X1,X3,u1_struct_0(X2))\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X3,u1_struct_0(X2))))\|~v1_funct_1(X4)\|~v1_funct_2(X4,X3,u4_struct_0(X2))\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X3,u4_struct_0(X2))))\|~v2_cat_1(X2)\|~v3_cat_1(X2)\|~v4_cat_1(X2)\|~v5_cat_1(X2)\|~v6_cat_1(X2)\|~l1_cat_1(X2)), inference(split_conjunct,[status(thm)],[c_0_17])). cnf(c_0_21, plain, (v1_funct_2(k2_cat_3(X1,X2,X3),X2,u1_struct_0(X1))\|v2_struct_0(X1)\|v11_struct_0(X1)\|~v2_cat_1(X1)\|~v3_cat_1(X1)\|~v4_cat_1(X1)\|~v5_cat_1(X1)\|~v6_cat_1(X1)\|~l1_cat_1(X1)\|~v1_funct_1(X3)\|~v1_funct_2(X3,X2,u4_struct_0(X1))\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X2,u4_struct_0(X1))))), inference(split_conjunct,[status(thm)],[c_0_18])). cnf(c_0_22, plain, (X2=k2_cat_3(X1,X3,X4)\|v2_struct_0(X1)\|v11_struct_0(X1)\|k7_partfun1(u1_struct_0(X1),X2,esk4_4(X1,X3,X4,X2))!=k3_graph_1(X1,k7_partfun1(u4_struct_0(X1),X4,esk4_4(X1,X3,X4,X2)))\|~v1_funct_1(X2)\|~v1_funct_2(X2,X3,u1_struct_0(X1))\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X3,u1_struct_0(X1))))\|~v1_funct_1(X4)\|~v1_funct_2(X4,X3,u4_struct_0(X1))\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X3,u4_struct_0(X1))))\|~v2_cat_1(X1)\|~v3_cat_1(X1)\|~v4_cat_1(X1)\|~v5_cat_1(X1)\|~v6_cat_1(X1)\|~l1_cat_1(X1)), inference(split_conjunct,[status(thm)],[c_0_17])). cnf(c_0_23, plain, (v1_xboole_0(X1)\|k7_partfun1(X1,k8_funcop_1(X1,X4,X2),X3)=X2\|~m1_subset_1(X2,X1)\|~r2_hidden(X3,X4)), inference(split_conjunct,[status(thm)],[c_0_19])). fof(c_0_24, plain, ![X14, X15, X16]:((v1_funct_1(k8_funcop_1(X14,X15,X16))\|(v1_xboole_0(X14)\|~m1_subset_1(X16,X14)))&((v1_funct_2(k8_funcop_1(X14,X15,X16),X15,X14)\|(v1_xboole_0(X14)\|~m1_subset_1(X16,X14)))&(m1_subset_1(k8_funcop_1(X14,X15,X16),k1_zfmisc_1(k2_zfmisc_1(X15,X14)))\|(v1_xboole_0(X14)\|~m1_subset_1(X16,X14))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k8_funcop_1])])])])). cnf(c_0_25, plain, (k7_partfun1(u1_struct_0(X2),X1,X5)=k3_graph_1(X2,k7_partfun1(u4_struct_0(X2),X4,X5))\|v2_struct_0(X2)\|v11_struct_0(X2)\|X1!=k2_cat_3(X2,X3,X4)\|~v2_cat_1(X2)\|~v3_cat_1(X2)\|~v4_cat_1(X2)\|~v5_cat_1(X2)\|~v6_cat_1(X2)\|~l1_cat_1(X2)\|~v1_funct_1(X4)\|~v1_funct_1(X1)\|~r2_hidden(X5,X3)\|~v1_funct_2(X4,X3,u4_struct_0(X2))\|~v1_funct_2(X1,X3,u1_struct_0(X2))\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X3,u4_struct_0(X2))))\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X3,u1_struct_0(X2))))), inference(evalgc,[status(thm)],[c_0_20])). cnf(c_0_26, plain, (v2_struct_0(X1)\|v11_struct_0(X1)\|v1_funct_2(k2_cat_3(X1,X2,X3),X2,u1_struct_0(X1))\|~v2_cat_1(X1)\|~v3_cat_1(X1)\|~v4_cat_1(X1)\|~v5_cat_1(X1)\|~v6_cat_1(X1)\|~l1_cat_1(X1)\|~v1_funct_1(X3)\|~v1_funct_2(X3,X2,u4_struct_0(X1))\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X2,u4_struct_0(X1))))), inference(evalgc,[status(thm)],[c_0_21])). cnf(c_0_27, plain, (m1_subset_1(k2_cat_3(X1,X2,X3),k1_zfmisc_1(k2_zfmisc_1(X2,u1_struct_0(X1))))\|v2_struct_0(X1)\|v11_struct_0(X1)\|~v2_cat_1(X1)\|~v3_cat_1(X1)\|~v4_cat_1(X1)\|~v5_cat_1(X1)\|~v6_cat_1(X1)\|~l1_cat_1(X1)\|~v1_funct_1(X3)\|~v1_funct_2(X3,X2,u4_struct_0(X1))\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X2,u4_struct_0(X1))))), inference(split_conjunct,[status(thm)],[c_0_18])). cnf(c_0_28, plain, (v1_funct_1(k2_cat_3(X1,X2,X3))\|v2_struct_0(X1)\|v11_struct_0(X1)\|~v2_cat_1(X1)\|~v3_cat_1(X1)\|~v4_cat_1(X1)\|~v5_cat_1(X1)\|~v6_cat_1(X1)\|~l1_cat_1(X1)\|~v1_funct_1(X3)\|~v1_funct_2(X3,X2,u4_struct_0(X1))\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X2,u4_struct_0(X1))))), inference(split_conjunct,[status(thm)],[c_0_18])). fof(c_0_29, plain, ![X43]:(~l1_graph_1(X43)\|l5_struct_0(X43)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_graph_1])])). fof(c_0_30, plain, ![X44]:(~l1_cat_1(X44)\|l1_graph_1(X44)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_cat_1])])). cnf(c_0_31, plain, (X2=k2_cat_3(X1,X3,X4)\|v2_struct_0(X1)\|v11_struct_0(X1)\|k7_partfun1(u1_struct_0(X1),X2,esk4_4(X1,X3,X4,X2))!=k3_graph_1(X1,k7_partfun1(u4_struct_0(X1),X4,esk4_4(X1,X3,X4,X2)))\|~v2_cat_1(X1)\|~v3_cat_1(X1)\|~v4_cat_1(X1)\|~v5_cat_1(X1)\|~v6_cat_1(X1)\|~l1_cat_1(X1)\|~v1_funct_1(X4)\|~v1_funct_1(X2)\|~v1_funct_2(X4,X3,u4_struct_0(X1))\|~v1_funct_2(X2,X3,u1_struct_0(X1))\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X3,u4_struct_0(X1))))\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X3,u1_struct_0(X1))))), inference(evalgc,[status(thm)],[c_0_22])). cnf(c_0_32, plain, (k7_partfun1(X1,k8_funcop_1(X1,X4,X2),X3)=X2\|v1_xboole_0(X1)\|~m1_subset_1(X2,X1)\|~r2_hidden(X3,X4)), inference(evalgc,[status(thm)],[c_0_23])). cnf(c_0_33, plain, (v1_funct_1(k8_funcop_1(X1,X2,X3))\|v1_xboole_0(X1)\|~m1_subset_1(X3,X1)), inference(split_conjunct,[status(thm)],[c_0_24])). cnf(c_0_34, plain, (k7_partfun1(u1_struct_0(X1),k2_cat_3(X1,X2,X3),X4)=k3_graph_1(X1,k7_partfun1(u4_struct_0(X1),X5,X4))\|v11_struct_0(X1)\|v2_struct_0(X1)\|k2_cat_3(X1,X2,X3)!=k2_cat_3(X1,X2,X5)\|~r2_hidden(X4,X2)\|~v1_funct_2(X5,X2,u4_struct_0(X1))\|~v1_funct_1(X5)\|~v1_funct_1(k2_cat_3(X1,X2,X3))\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X2,u4_struct_0(X1))))\|~m1_subset_1(k2_cat_3(X1,X2,X3),k1_zfmisc_1(k2_zfmisc_1(X2,u1_struct_0(X1))))\|~l1_cat_1(X1)\|~v6_cat_1(X1)\|~v5_cat_1(X1)\|~v4_cat_1(X1)\|~v3_cat_1(X1)\|~v2_cat_1(X1)\|~v1_funct_2(X3,X2,u4_struct_0(X1))\|~v1_funct_1(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X2,u4_struct_0(X1))))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_25, c_0_26])])). cnf(c_0_35, plain, (v2_struct_0(X1)\|v11_struct_0(X1)\|m1_subset_1(k2_cat_3(X1,X2,X3),k1_zfmisc_1(k2_zfmisc_1(X2,u1_struct_0(X1))))\|~v2_cat_1(X1)\|~v3_cat_1(X1)\|~v4_cat_1(X1)\|~v5_cat_1(X1)\|~v6_cat_1(X1)\|~l1_cat_1(X1)\|~v1_funct_1(X3)\|~v1_funct_2(X3,X2,u4_struct_0(X1))\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X2,u4_struct_0(X1))))), inference(evalgc,[status(thm)],[c_0_27])). cnf(c_0_36, plain, (v2_struct_0(X1)\|v11_struct_0(X1)\|v1_funct_1(k2_cat_3(X1,X2,X3))\|~v2_cat_1(X1)\|~v3_cat_1(X1)\|~v4_cat_1(X1)\|~v5_cat_1(X1)\|~v6_cat_1(X1)\|~l1_cat_1(X1)\|~v1_funct_1(X3)\|~v1_funct_2(X3,X2,u4_struct_0(X1))\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X2,u4_struct_0(X1))))), inference(evalgc,[status(thm)],[c_0_28])). fof(c_0_37, plain, ![X47]:(v11_struct_0(X47)\|~l5_struct_0(X47)\|~v1_xboole_0(u4_struct_0(X47))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fc14_struct_0])])])). cnf(c_0_38, plain, (l5_struct_0(X1)\|~l1_graph_1(X1)), inference(split_conjunct,[status(thm)],[c_0_29])). cnf(c_0_39, plain, (l1_graph_1(X1)\|~l1_cat_1(X1)), inference(split_conjunct,[status(thm)],[c_0_30])). cnf(c_0_40, plain, (X1=k2_cat_3(X2,X3,k8_funcop_1(u4_struct_0(X2),X4,X5))\|v11_struct_0(X2)\|v2_struct_0(X2)\|v1_xboole_0(u4_struct_0(X2))\|k7_partfun1(u1_struct_0(X2),X1,esk4_4(X2,X3,k8_funcop_1(u4_struct_0(X2),X4,X5),X1))!=k3_graph_1(X2,X5)\|~v1_funct_2(k8_funcop_1(u4_struct_0(X2),X4,X5),X3,u4_struct_0(X2))\|~v1_funct_2(X1,X3,u1_struct_0(X2))\|~v1_funct_1(k8_funcop_1(u4_struct_0(X2),X4,X5))\|~v1_funct_1(X1)\|~m1_subset_1(k8_funcop_1(u4_struct_0(X2),X4,X5),k1_zfmisc_1(k2_zfmisc_1(X3,u4_struct_0(X2))))\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X3,u1_struct_0(X2))))\|~l1_cat_1(X2)\|~v6_cat_1(X2)\|~v5_cat_1(X2)\|~v4_cat_1(X2)\|~v3_cat_1(X2)\|~v2_cat_1(X2)\|~r2_hidden(esk4_4(X2,X3,k8_funcop_1(u4_struct_0(X2),X4,X5),X1),X4)\|~m1_subset_1(X5,u4_struct_0(X2))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_31, c_0_32])])). cnf(c_0_41, plain, (v1_xboole_0(X1)\|v1_funct_1(k8_funcop_1(X1,X2,X3))\|~m1_subset_1(X3,X1)), inference(evalgc,[status(thm)],[c_0_33])). cnf(c_0_42, plain, (k7_partfun1(u1_struct_0(X1),k2_cat_3(X1,X2,X3),X4)=k3_graph_1(X1,k7_partfun1(u4_struct_0(X1),X5,X4))\|v11_struct_0(X1)\|v2_struct_0(X1)\|k2_cat_3(X1,X2,X3)!=k2_cat_3(X1,X2,X5)\|~r2_hidden(X4,X2)\|~v1_funct_2(X5,X2,u4_struct_0(X1))\|~v1_funct_2(X3,X2,u4_struct_0(X1))\|~v1_funct_1(X5)\|~v1_funct_1(X3)\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X2,u4_struct_0(X1))))\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X2,u4_struct_0(X1))))\|~l1_cat_1(X1)\|~v6_cat_1(X1)\|~v5_cat_1(X1)\|~v4_cat_1(X1)\|~v3_cat_1(X1)\|~v2_cat_1(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_34, c_0_35]), c_0_36])). cnf(c_0_43, plain, (v11_struct_0(X1)\|~l5_struct_0(X1)\|~v1_xboole_0(u4_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_37])). cnf(c_0_44, plain, (l5_struct_0(X1)\|~l1_graph_1(X1)), inference(evalgc,[status(thm)],[c_0_38])). cnf(c_0_45, plain, (l1_graph_1(X1)\|~l1_cat_1(X1)), inference(evalgc,[status(thm)],[c_0_39])). cnf(c_0_46, plain, (X1=k2_cat_3(X2,X3,k8_funcop_1(u4_struct_0(X2),X4,X5))\|v1_xboole_0(u4_struct_0(X2))\|v11_struct_0(X2)\|v2_struct_0(X2)\|k7_partfun1(u1_struct_0(X2),X1,esk4_4(X2,X3,k8_funcop_1(u4_struct_0(X2),X4,X5),X1))!=k3_graph_1(X2,X5)\|~r2_hidden(esk4_4(X2,X3,k8_funcop_1(u4_struct_0(X2),X4,X5),X1),X4)\|~v1_funct_2(k8_funcop_1(u4_struct_0(X2),X4,X5),X3,u4_struct_0(X2))\|~v1_funct_2(X1,X3,u1_struct_0(X2))\|~v1_funct_1(X1)\|~m1_subset_1(k8_funcop_1(u4_struct_0(X2),X4,X5),k1_zfmisc_1(k2_zfmisc_1(X3,u4_struct_0(X2))))\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X3,u1_struct_0(X2))))\|~m1_subset_1(X5,u4_struct_0(X2))\|~l1_cat_1(X2)\|~v6_cat_1(X2)\|~v5_cat_1(X2)\|~v4_cat_1(X2)\|~v3_cat_1(X2)\|~v2_cat_1(X2)), inference(csr,[status(thm)],[c_0_40, c_0_41])). cnf(c_0_47, plain, (k7_partfun1(u1_struct_0(X1),k2_cat_3(X1,X2,X3),X4)=k3_graph_1(X1,k7_partfun1(u4_struct_0(X1),X3,X4))\|v11_struct_0(X1)\|v2_struct_0(X1)\|~r2_hidden(X4,X2)\|~v1_funct_2(X3,X2,u4_struct_0(X1))\|~v1_funct_1(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X2,u4_struct_0(X1))))\|~l1_cat_1(X1)\|~v6_cat_1(X1)\|~v5_cat_1(X1)\|~v4_cat_1(X1)\|~v3_cat_1(X1)\|~v2_cat_1(X1)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_42])])). cnf(c_0_48, plain, (v11_struct_0(X1)\|~l5_struct_0(X1)\|~v1_xboole_0(u4_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_43])). cnf(c_0_49, plain, (l5_struct_0(X1)\|~l1_cat_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_44, c_0_45])])). cnf(c_0_50, plain, (k2_cat_3(X1,X2,X3)=k2_cat_3(X1,X4,k8_funcop_1(u4_struct_0(X1),X5,X6))\|v1_xboole_0(u4_struct_0(X1))\|v11_struct_0(X1)\|v2_struct_0(X1)\|k3_graph_1(X1,k7_partfun1(u4_struct_0(X1),X3,esk4_4(X1,X4,k8_funcop_1(u4_struct_0(X1),X5,X6),k2_cat_3(X1,X2,X3))))!=k3_graph_1(X1,X6)\|~r2_hidden(esk4_4(X1,X4,k8_funcop_1(u4_struct_0(X1),X5,X6),k2_cat_3(X1,X2,X3)),X5)\|~v1_funct_2(k8_funcop_1(u4_struct_0(X1),X5,X6),X4,u4_struct_0(X1))\|~v1_funct_2(k2_cat_3(X1,X2,X3),X4,u1_struct_0(X1))\|~v1_funct_1(k2_cat_3(X1,X2,X3))\|~m1_subset_1(k8_funcop_1(u4_struct_0(X1),X5,X6),k1_zfmisc_1(k2_zfmisc_1(X4,u4_struct_0(X1))))\|~m1_subset_1(k2_cat_3(X1,X2,X3),k1_zfmisc_1(k2_zfmisc_1(X4,u1_struct_0(X1))))\|~m1_subset_1(X6,u4_struct_0(X1))\|~l1_cat_1(X1)\|~v6_cat_1(X1)\|~v5_cat_1(X1)\|~v4_cat_1(X1)\|~v3_cat_1(X1)\|~v2_cat_1(X1)\|~r2_hidden(esk4_4(X1,X4,k8_funcop_1(u4_struct_0(X1),X5,X6),k2_cat_3(X1,X2,X3)),X2)\|~v1_funct_2(X3,X2,u4_struct_0(X1))\|~v1_funct_1(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X2,u4_struct_0(X1))))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_46, c_0_47])])). cnf(c_0_51, plain, (v11_struct_0(X1)\|~v1_xboole_0(u4_struct_0(X1))\|~l1_cat_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_48, c_0_49])])). cnf(c_0_52, plain, (k2_cat_3(X1,X2,X3)=k2_cat_3(X1,X4,k8_funcop_1(u4_struct_0(X1),X5,X6))\|v11_struct_0(X1)\|v2_struct_0(X1)\|k3_graph_1(X1,k7_partfun1(u4_struct_0(X1),X3,esk4_4(X1,X4,k8_funcop_1(u4_struct_0(X1),X5,X6),k2_cat_3(X1,X2,X3))))!=k3_graph_1(X1,X6)\|~r2_hidden(esk4_4(X1,X4,k8_funcop_1(u4_struct_0(X1),X5,X6),k2_cat_3(X1,X2,X3)),X5)\|~r2_hidden(esk4_4(X1,X4,k8_funcop_1(u4_struct_0(X1),X5,X6),k2_cat_3(X1,X2,X3)),X2)\|~v1_funct_2(k8_funcop_1(u4_struct_0(X1),X5,X6),X4,u4_struct_0(X1))\|~v1_funct_2(k2_cat_3(X1,X2,X3),X4,u1_struct_0(X1))\|~v1_funct_2(X3,X2,u4_struct_0(X1))\|~v1_funct_1(X3)\|~m1_subset_1(k8_funcop_1(u4_struct_0(X1),X5,X6),k1_zfmisc_1(k2_zfmisc_1(X4,u4_struct_0(X1))))\|~m1_subset_1(k2_cat_3(X1,X2,X3),k1_zfmisc_1(k2_zfmisc_1(X4,u1_struct_0(X1))))\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X2,u4_struct_0(X1))))\|~m1_subset_1(X6,u4_struct_0(X1))\|~l1_cat_1(X1)\|~v6_cat_1(X1)\|~v5_cat_1(X1)\|~v4_cat_1(X1)\|~v3_cat_1(X1)\|~v2_cat_1(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_50, c_0_36]), c_0_51])). cnf(c_0_53, plain, (k2_cat_3(X1,X2,k8_funcop_1(u4_struct_0(X1),X3,X4))=k2_cat_3(X1,X5,k8_funcop_1(u4_struct_0(X1),X6,X7))\|v11_struct_0(X1)\|v2_struct_0(X1)\|v1_xboole_0(u4_struct_0(X1))\|k3_graph_1(X1,X4)!=k3_graph_1(X1,X7)\|~r2_hidden(esk4_4(X1,X5,k8_funcop_1(u4_struct_0(X1),X6,X7),k2_cat_3(X1,X2,k8_funcop_1(u4_struct_0(X1),X3,X4))),X6)\|~r2_hidden(esk4_4(X1,X5,k8_funcop_1(u4_struct_0(X1),X6,X7),k2_cat_3(X1,X2,k8_funcop_1(u4_struct_0(X1),X3,X4))),X2)\|~v1_funct_2(k8_funcop_1(u4_struct_0(X1),X6,X7),X5,u4_struct_0(X1))\|~v1_funct_2(k2_cat_3(X1,X2,k8_funcop_1(u4_struct_0(X1),X3,X4)),X5,u1_struct_0(X1))\|~v1_funct_2(k8_funcop_1(u4_struct_0(X1),X3,X4),X2,u4_struct_0(X1))\|~v1_funct_1(k8_funcop_1(u4_struct_0(X1),X3,X4))\|~m1_subset_1(k8_funcop_1(u4_struct_0(X1),X6,X7),k1_zfmisc_1(k2_zfmisc_1(X5,u4_struct_0(X1))))\|~m1_subset_1(k2_cat_3(X1,X2,k8_funcop_1(u4_struct_0(X1),X3,X4)),k1_zfmisc_1(k2_zfmisc_1(X5,u1_struct_0(X1))))\|~m1_subset_1(k8_funcop_1(u4_struct_0(X1),X3,X4),k1_zfmisc_1(k2_zfmisc_1(X2,u4_struct_0(X1))))\|~m1_subset_1(X7,u4_struct_0(X1))\|~l1_cat_1(X1)\|~v6_cat_1(X1)\|~v5_cat_1(X1)\|~v4_cat_1(X1)\|~v3_cat_1(X1)\|~v2_cat_1(X1)\|~r2_hidden(esk4_4(X1,X5,k8_funcop_1(u4_struct_0(X1),X6,X7),k2_cat_3(X1,X2,k8_funcop_1(u4_struct_0(X1),X3,X4))),X3)\|~m1_subset_1(X4,u4_struct_0(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_52, c_0_32])])). cnf(c_0_54, plain, (r2_hidden(esk4_4(X1,X2,X3,X4),X2)\|X4=k2_cat_3(X1,X2,X3)\|v2_struct_0(X1)\|v11_struct_0(X1)\|~v1_funct_1(X4)\|~v1_funct_2(X4,X2,u1_struct_0(X1))\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X2,u1_struct_0(X1))))\|~v1_funct_1(X3)\|~v1_funct_2(X3,X2,u4_struct_0(X1))\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X2,u4_struct_0(X1))))\|~v2_cat_1(X1)\|~v3_cat_1(X1)\|~v4_cat_1(X1)\|~v5_cat_1(X1)\|~v6_cat_1(X1)\|~l1_cat_1(X1)), inference(split_conjunct,[status(thm)],[c_0_17])). fof(c_0_55, plain, ![X11, X12, X13]:(v1_xboole_0(X11)\|~m1_subset_1(X13,X11)\|k8_funcop_1(X11,X12,X13)=k2_funcop_1(X12,X13)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[redefinition_k8_funcop_1])])])). fof(c_0_56, plain, ![X9, X10]:k2_funcop_1(X9,X10)=k2_zfmisc_1(X9,k1_tarski(X10)), inference(variable_rename,[status(thm)],[d2_funcop_1])). cnf(c_0_57, plain, (k8_funcop_1(u1_struct_0(X1),X2,X3)=k2_cat_3(X1,X4,k8_funcop_1(u4_struct_0(X1),X5,X6))\|v1_xboole_0(u4_struct_0(X1))\|v11_struct_0(X1)\|v2_struct_0(X1)\|v1_xboole_0(u1_struct_0(X1))\|X3!=k3_graph_1(X1,X6)\|~r2_hidden(esk4_4(X1,X4,k8_funcop_1(u4_struct_0(X1),X5,X6),k8_funcop_1(u1_struct_0(X1),X2,X3)),X5)\|~v1_funct_2(k8_funcop_1(u4_struct_0(X1),X5,X6),X4,u4_struct_0(X1))\|~v1_funct_2(k8_funcop_1(u1_struct_0(X1),X2,X3),X4,u1_struct_0(X1))\|~v1_funct_1(k8_funcop_1(u1_struct_0(X1),X2,X3))\|~m1_subset_1(k8_funcop_1(u4_struct_0(X1),X5,X6),k1_zfmisc_1(k2_zfmisc_1(X4,u4_struct_0(X1))))\|~m1_subset_1(k8_funcop_1(u1_struct_0(X1),X2,X3),k1_zfmisc_1(k2_zfmisc_1(X4,u1_struct_0(X1))))\|~m1_subset_1(X6,u4_struct_0(X1))\|~l1_cat_1(X1)\|~v6_cat_1(X1)\|~v5_cat_1(X1)\|~v4_cat_1(X1)\|~v3_cat_1(X1)\|~v2_cat_1(X1)\|~r2_hidden(esk4_4(X1,X4,k8_funcop_1(u4_struct_0(X1),X5,X6),k8_funcop_1(u1_struct_0(X1),X2,X3)),X2)\|~m1_subset_1(X3,u1_struct_0(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_46, c_0_32])])). cnf(c_0_58, plain, (k2_cat_3(X1,X2,k8_funcop_1(u4_struct_0(X1),X3,X4))=k2_cat_3(X1,X5,k8_funcop_1(u4_struct_0(X1),X6,X7))\|v11_struct_0(X1)\|v2_struct_0(X1)\|k3_graph_1(X1,X4)!=k3_graph_1(X1,X7)\|~r2_hidden(esk4_4(X1,X5,k8_funcop_1(u4_struct_0(X1),X6,X7),k2_cat_3(X1,X2,k8_funcop_1(u4_struct_0(X1),X3,X4))),X6)\|~r2_hidden(esk4_4(X1,X5,k8_funcop_1(u4_struct_0(X1),X6,X7),k2_cat_3(X1,X2,k8_funcop_1(u4_struct_0(X1),X3,X4))),X2)\|~r2_hidden(esk4_4(X1,X5,k8_funcop_1(u4_struct_0(X1),X6,X7),k2_cat_3(X1,X2,k8_funcop_1(u4_struct_0(X1),X3,X4))),X3)\|~v1_funct_2(k2_cat_3(X1,X2,k8_funcop_1(u4_struct_0(X1),X3,X4)),X5,u1_struct_0(X1))\|~v1_funct_2(k8_funcop_1(u4_struct_0(X1),X6,X7),X5,u4_struct_0(X1))\|~v1_funct_2(k8_funcop_1(u4_struct_0(X1),X3,X4),X2,u4_struct_0(X1))\|~m1_subset_1(k2_cat_3(X1,X2,k8_funcop_1(u4_struct_0(X1),X3,X4)),k1_zfmisc_1(k2_zfmisc_1(X5,u1_struct_0(X1))))\|~m1_subset_1(k8_funcop_1(u4_struct_0(X1),X6,X7),k1_zfmisc_1(k2_zfmisc_1(X5,u4_struct_0(X1))))\|~m1_subset_1(k8_funcop_1(u4_struct_0(X1),X3,X4),k1_zfmisc_1(k2_zfmisc_1(X2,u4_struct_0(X1))))\|~m1_subset_1(X7,u4_struct_0(X1))\|~m1_subset_1(X4,u4_struct_0(X1))\|~l1_cat_1(X1)\|~v6_cat_1(X1)\|~v5_cat_1(X1)\|~v4_cat_1(X1)\|~v3_cat_1(X1)\|~v2_cat_1(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_53, c_0_41]), c_0_51])). cnf(c_0_59, plain, (X4=k2_cat_3(X1,X2,X3)\|v2_struct_0(X1)\|v11_struct_0(X1)\|r2_hidden(esk4_4(X1,X2,X3,X4),X2)\|~v2_cat_1(X1)\|~v3_cat_1(X1)\|~v4_cat_1(X1)\|~v5_cat_1(X1)\|~v6_cat_1(X1)\|~l1_cat_1(X1)\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v1_funct_2(X4,X2,u1_struct_0(X1))\|~v1_funct_2(X3,X2,u4_struct_0(X1))\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X2,u1_struct_0(X1))))\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X2,u4_struct_0(X1))))), inference(evalgc,[status(thm)],[c_0_54])). cnf(c_0_60, plain, (v1_xboole_0(X1)\|k8_funcop_1(X1,X3,X2)=k2_funcop_1(X3,X2)\|~m1_subset_1(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_55])). cnf(c_0_61, plain, (k2_funcop_1(X1,X2)=k2_zfmisc_1(X1,k1_tarski(X2))), inference(split_conjunct,[status(thm)],[c_0_56])). cnf(c_0_62, plain, (k8_funcop_1(u1_struct_0(X1),X2,X3)=k2_cat_3(X1,X4,k8_funcop_1(u4_struct_0(X1),X5,X6))\|v1_xboole_0(u1_struct_0(X1))\|v11_struct_0(X1)\|v2_struct_0(X1)\|X3!=k3_graph_1(X1,X6)\|~r2_hidden(esk4_4(X1,X4,k8_funcop_1(u4_struct_0(X1),X5,X6),k8_funcop_1(u1_struct_0(X1),X2,X3)),X5)\|~r2_hidden(esk4_4(X1,X4,k8_funcop_1(u4_struct_0(X1),X5,X6),k8_funcop_1(u1_struct_0(X1),X2,X3)),X2)\|~v1_funct_2(k8_funcop_1(u4_struct_0(X1),X5,X6),X4,u4_struct_0(X1))\|~v1_funct_2(k8_funcop_1(u1_struct_0(X1),X2,X3),X4,u1_struct_0(X1))\|~m1_subset_1(k8_funcop_1(u4_struct_0(X1),X5,X6),k1_zfmisc_1(k2_zfmisc_1(X4,u4_struct_0(X1))))\|~m1_subset_1(k8_funcop_1(u1_struct_0(X1),X2,X3),k1_zfmisc_1(k2_zfmisc_1(X4,u1_struct_0(X1))))\|~m1_subset_1(X6,u4_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~l1_cat_1(X1)\|~v6_cat_1(X1)\|~v5_cat_1(X1)\|~v4_cat_1(X1)\|~v3_cat_1(X1)\|~v2_cat_1(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_57, c_0_41]), c_0_51])). cnf(c_0_63, plain, (k2_cat_3(X1,X2,k8_funcop_1(u4_struct_0(X1),X3,X4))=k2_cat_3(X1,X5,k8_funcop_1(u4_struct_0(X1),X5,X6))\|v11_struct_0(X1)\|v2_struct_0(X1)\|k3_graph_1(X1,X4)!=k3_graph_1(X1,X6)\|~r2_hidden(esk4_4(X1,X5,k8_funcop_1(u4_struct_0(X1),X5,X6),k2_cat_3(X1,X2,k8_funcop_1(u4_struct_0(X1),X3,X4))),X2)\|~r2_hidden(esk4_4(X1,X5,k8_funcop_1(u4_struct_0(X1),X5,X6),k2_cat_3(X1,X2,k8_funcop_1(u4_struct_0(X1),X3,X4))),X3)\|~v1_funct_2(k2_cat_3(X1,X2,k8_funcop_1(u4_struct_0(X1),X3,X4)),X5,u1_struct_0(X1))\|~v1_funct_2(k8_funcop_1(u4_struct_0(X1),X5,X6),X5,u4_struct_0(X1))\|~v1_funct_2(k8_funcop_1(u4_struct_0(X1),X3,X4),X2,u4_struct_0(X1))\|~m1_subset_1(k2_cat_3(X1,X2,k8_funcop_1(u4_struct_0(X1),X3,X4)),k1_zfmisc_1(k2_zfmisc_1(X5,u1_struct_0(X1))))\|~m1_subset_1(k8_funcop_1(u4_struct_0(X1),X5,X6),k1_zfmisc_1(k2_zfmisc_1(X5,u4_struct_0(X1))))\|~m1_subset_1(k8_funcop_1(u4_struct_0(X1),X3,X4),k1_zfmisc_1(k2_zfmisc_1(X2,u4_struct_0(X1))))\|~m1_subset_1(X6,u4_struct_0(X1))\|~m1_subset_1(X4,u4_struct_0(X1))\|~l1_cat_1(X1)\|~v6_cat_1(X1)\|~v5_cat_1(X1)\|~v4_cat_1(X1)\|~v3_cat_1(X1)\|~v2_cat_1(X1)\|~v1_funct_1(k2_cat_3(X1,X2,k8_funcop_1(u4_struct_0(X1),X3,X4)))\|~v1_funct_1(k8_funcop_1(u4_struct_0(X1),X5,X6))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_58, c_0_59])])). cnf(c_0_64, plain, (k8_funcop_1(X1,X3,X2)=k2_zfmisc_1(X3,k1_tarski(X2))\|v1_xboole_0(X1)\|~m1_subset_1(X2,X1)), inference(rw,[status(thm)],[c_0_60, c_0_61])). cnf(c_0_65, plain, (k8_funcop_1(u1_struct_0(X1),X2,X3)=k2_cat_3(X1,X4,k8_funcop_1(u4_struct_0(X1),X4,X5))\|v1_xboole_0(u1_struct_0(X1))\|v11_struct_0(X1)\|v2_struct_0(X1)\|X3!=k3_graph_1(X1,X5)\|~r2_hidden(esk4_4(X1,X4,k8_funcop_1(u4_struct_0(X1),X4,X5),k8_funcop_1(u1_struct_0(X1),X2,X3)),X2)\|~v1_funct_2(k8_funcop_1(u4_struct_0(X1),X4,X5),X4,u4_struct_0(X1))\|~v1_funct_2(k8_funcop_1(u1_struct_0(X1),X2,X3),X4,u1_struct_0(X1))\|~m1_subset_1(k8_funcop_1(u4_struct_0(X1),X4,X5),k1_zfmisc_1(k2_zfmisc_1(X4,u4_struct_0(X1))))\|~m1_subset_1(k8_funcop_1(u1_struct_0(X1),X2,X3),k1_zfmisc_1(k2_zfmisc_1(X4,u1_struct_0(X1))))\|~m1_subset_1(X5,u4_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~l1_cat_1(X1)\|~v6_cat_1(X1)\|~v5_cat_1(X1)\|~v4_cat_1(X1)\|~v3_cat_1(X1)\|~v2_cat_1(X1)\|~v1_funct_1(k8_funcop_1(u1_struct_0(X1),X2,X3))\|~v1_funct_1(k8_funcop_1(u4_struct_0(X1),X4,X5))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_62, c_0_59])])). fof(c_0_66, plain, ![X23, X24, X25]:((v4_relat_1(X25,X23)\|~m1_subset_1(X25,k1_zfmisc_1(k2_zfmisc_1(X23,X24))))&(v5_relat_1(X25,X24)\|~m1_subset_1(X25,k1_zfmisc_1(k2_zfmisc_1(X23,X24))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_relset_1])])])). cnf(c_0_67, plain, (k2_cat_3(X1,X2,k8_funcop_1(u4_struct_0(X1),X3,X4))=k2_cat_3(X1,X2,k8_funcop_1(u4_struct_0(X1),X2,X5))\|v11_struct_0(X1)\|v2_struct_0(X1)\|k3_graph_1(X1,X4)!=k3_graph_1(X1,X5)\|~r2_hidden(esk4_4(X1,X2,k8_funcop_1(u4_struct_0(X1),X2,X5),k2_cat_3(X1,X2,k8_funcop_1(u4_struct_0(X1),X3,X4))),X3)\|~v1_funct_2(k2_cat_3(X1,X2,k8_funcop_1(u4_struct_0(X1),X3,X4)),X2,u1_struct_0(X1))\|~v1_funct_2(k8_funcop_1(u4_struct_0(X1),X2,X5),X2,u4_struct_0(X1))\|~v1_funct_2(k8_funcop_1(u4_struct_0(X1),X3,X4),X2,u4_struct_0(X1))\|~v1_funct_1(k2_cat_3(X1,X2,k8_funcop_1(u4_struct_0(X1),X3,X4)))\|~v1_funct_1(k8_funcop_1(u4_struct_0(X1),X2,X5))\|~m1_subset_1(k2_cat_3(X1,X2,k8_funcop_1(u4_struct_0(X1),X3,X4)),k1_zfmisc_1(k2_zfmisc_1(X2,u1_struct_0(X1))))\|~m1_subset_1(k8_funcop_1(u4_struct_0(X1),X2,X5),k1_zfmisc_1(k2_zfmisc_1(X2,u4_struct_0(X1))))\|~m1_subset_1(k8_funcop_1(u4_struct_0(X1),X3,X4),k1_zfmisc_1(k2_zfmisc_1(X2,u4_struct_0(X1))))\|~m1_subset_1(X5,u4_struct_0(X1))\|~m1_subset_1(X4,u4_struct_0(X1))\|~l1_cat_1(X1)\|~v6_cat_1(X1)\|~v5_cat_1(X1)\|~v4_cat_1(X1)\|~v3_cat_1(X1)\|~v2_cat_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_63, c_0_59])])). cnf(c_0_68, plain, (k8_funcop_1(X1,X3,X2)=k2_zfmisc_1(X3,k1_tarski(X2))\|v1_xboole_0(X1)\|~m1_subset_1(X2,X1)), inference(evalgc,[status(thm)],[c_0_64])). cnf(c_0_69, plain, (m1_subset_1(k8_funcop_1(X1,X2,X3),k1_zfmisc_1(k2_zfmisc_1(X2,X1)))\|v1_xboole_0(X1)\|~m1_subset_1(X3,X1)), inference(split_conjunct,[status(thm)],[c_0_24])). cnf(c_0_70, plain, (v1_funct_2(k8_funcop_1(X1,X2,X3),X2,X1)\|v1_xboole_0(X1)\|~m1_subset_1(X3,X1)), inference(split_conjunct,[status(thm)],[c_0_24])). cnf(c_0_71, plain, (k8_funcop_1(u1_struct_0(X1),X2,X3)=k2_cat_3(X1,X4,k8_funcop_1(u4_struct_0(X1),X4,X5))\|v1_xboole_0(u1_struct_0(X1))\|v11_struct_0(X1)\|v2_struct_0(X1)\|X3!=k3_graph_1(X1,X5)\|~r2_hidden(esk4_4(X1,X4,k8_funcop_1(u4_struct_0(X1),X4,X5),k8_funcop_1(u1_struct_0(X1),X2,X3)),X2)\|~v1_funct_2(k8_funcop_1(u4_struct_0(X1),X4,X5),X4,u4_struct_0(X1))\|~v1_funct_2(k8_funcop_1(u1_struct_0(X1),X2,X3),X4,u1_struct_0(X1))\|~v1_funct_1(k8_funcop_1(u4_struct_0(X1),X4,X5))\|~m1_subset_1(k8_funcop_1(u4_struct_0(X1),X4,X5),k1_zfmisc_1(k2_zfmisc_1(X4,u4_struct_0(X1))))\|~m1_subset_1(k8_funcop_1(u1_struct_0(X1),X2,X3),k1_zfmisc_1(k2_zfmisc_1(X4,u1_struct_0(X1))))\|~m1_subset_1(X5,u4_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~l1_cat_1(X1)\|~v6_cat_1(X1)\|~v5_cat_1(X1)\|~v4_cat_1(X1)\|~v3_cat_1(X1)\|~v2_cat_1(X1)), inference(csr,[status(thm)],[c_0_65, c_0_41])). fof(c_0_72, plain, ![X36, X37, X38]:(~v1_relat_1(X37)\|(~v5_relat_1(X37,X36)\|~v1_funct_1(X37))\|m1_subset_1(k7_partfun1(X36,X37,X38),X36)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k7_partfun1])])). cnf(c_0_73, plain, (v5_relat_1(X1,X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X3,X2)))), inference(split_conjunct,[status(thm)],[c_0_66])). fof(c_0_74, plain, ![X17, X18, X19]:(~m1_subset_1(X19,k1_zfmisc_1(k2_zfmisc_1(X17,X18)))\|v1_relat_1(X19)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relset_1])])). fof(c_0_75, negated_conjecture, ~(![X1, X2]:((~(v2_struct_0(X2))&(~(v11_struct_0(X2))&(v2_cat_1(X2)&(v3_cat_1(X2)&(v4_cat_1(X2)&(v5_cat_1(X2)&(v6_cat_1(X2)&l1_cat_1(X2))))))))=>![X3]:(m1_subset_1(X3,u4_struct_0(X2))=>r2_funct_2(X1,u1_struct_0(X2),k2_cat_3(X2,X1,k8_funcop_1(u4_struct_0(X2),X1,X3)),k8_funcop_1(u1_struct_0(X2),X1,k3_graph_1(X2,X3)))))), inference(assume_negation,[status(cth)],[t4_cat_3])). cnf(c_0_76, plain, (k2_cat_3(X1,X2,k8_funcop_1(u4_struct_0(X1),X2,X3))=k2_cat_3(X1,X2,k8_funcop_1(u4_struct_0(X1),X2,X4))\|v11_struct_0(X1)\|v2_struct_0(X1)\|k3_graph_1(X1,X3)!=k3_graph_1(X1,X4)\|~v1_funct_2(k2_cat_3(X1,X2,k8_funcop_1(u4_struct_0(X1),X2,X3)),X2,u1_struct_0(X1))\|~v1_funct_2(k8_funcop_1(u4_struct_0(X1),X2,X4),X2,u4_struct_0(X1))\|~v1_funct_2(k8_funcop_1(u4_struct_0(X1),X2,X3),X2,u4_struct_0(X1))\|~v1_funct_1(k2_cat_3(X1,X2,k8_funcop_1(u4_struct_0(X1),X2,X3)))\|~v1_funct_1(k8_funcop_1(u4_struct_0(X1),X2,X4))\|~m1_subset_1(k2_cat_3(X1,X2,k8_funcop_1(u4_struct_0(X1),X2,X3)),k1_zfmisc_1(k2_zfmisc_1(X2,u1_struct_0(X1))))\|~m1_subset_1(k8_funcop_1(u4_struct_0(X1),X2,X4),k1_zfmisc_1(k2_zfmisc_1(X2,u4_struct_0(X1))))\|~m1_subset_1(k8_funcop_1(u4_struct_0(X1),X2,X3),k1_zfmisc_1(k2_zfmisc_1(X2,u4_struct_0(X1))))\|~m1_subset_1(X4,u4_struct_0(X1))\|~m1_subset_1(X3,u4_struct_0(X1))\|~l1_cat_1(X1)\|~v6_cat_1(X1)\|~v5_cat_1(X1)\|~v4_cat_1(X1)\|~v3_cat_1(X1)\|~v2_cat_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_67, c_0_59])])). cnf(c_0_77, plain, (k8_funcop_1(X1,X2,X3)=k8_funcop_1(X4,X2,X3)\|v1_xboole_0(X1)\|v1_xboole_0(X4)\|~m1_subset_1(X3,X1)\|~m1_subset_1(X3,X4)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_68, c_0_68])])). cnf(c_0_78, plain, (v1_xboole_0(X1)\|m1_subset_1(k8_funcop_1(X1,X2,X3),k1_zfmisc_1(k2_zfmisc_1(X2,X1)))\|~m1_subset_1(X3,X1)), inference(evalgc,[status(thm)],[c_0_69])). cnf(c_0_79, plain, (v1_xboole_0(X1)\|v1_funct_2(k8_funcop_1(X1,X2,X3),X2,X1)\|~m1_subset_1(X3,X1)), inference(evalgc,[status(thm)],[c_0_70])). cnf(c_0_80, plain, (k8_funcop_1(u1_struct_0(X1),X2,X3)=k2_cat_3(X1,X2,k8_funcop_1(u4_struct_0(X1),X2,X4))\|v1_xboole_0(u1_struct_0(X1))\|v11_struct_0(X1)\|v2_struct_0(X1)\|X3!=k3_graph_1(X1,X4)\|~v1_funct_2(k8_funcop_1(u4_struct_0(X1),X2,X4),X2,u4_struct_0(X1))\|~v1_funct_2(k8_funcop_1(u1_struct_0(X1),X2,X3),X2,u1_struct_0(X1))\|~v1_funct_1(k8_funcop_1(u4_struct_0(X1),X2,X4))\|~m1_subset_1(k8_funcop_1(u4_struct_0(X1),X2,X4),k1_zfmisc_1(k2_zfmisc_1(X2,u4_struct_0(X1))))\|~m1_subset_1(k8_funcop_1(u1_struct_0(X1),X2,X3),k1_zfmisc_1(k2_zfmisc_1(X2,u1_struct_0(X1))))\|~m1_subset_1(X4,u4_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~l1_cat_1(X1)\|~v6_cat_1(X1)\|~v5_cat_1(X1)\|~v4_cat_1(X1)\|~v3_cat_1(X1)\|~v2_cat_1(X1)\|~v1_funct_1(k8_funcop_1(u1_struct_0(X1),X2,X3))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_71, c_0_59])])). cnf(c_0_81, plain, (m1_subset_1(k7_partfun1(X2,X1,X3),X2)\|~v1_relat_1(X1)\|~v5_relat_1(X1,X2)\|~v1_funct_1(X1)), inference(split_conjunct,[status(thm)],[c_0_72])). cnf(c_0_82, plain, (v5_relat_1(X1,X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X3,X2)))), inference(evalgc,[status(thm)],[c_0_73])). cnf(c_0_83, plain, (v1_relat_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_74])). fof(c_0_84, negated_conjecture, ((~v2_struct_0(esk2_0)&(~v11_struct_0(esk2_0)&(v2_cat_1(esk2_0)&(v3_cat_1(esk2_0)&(v4_cat_1(esk2_0)&(v5_cat_1(esk2_0)&(v6_cat_1(esk2_0)&l1_cat_1(esk2_0))))))))&(m1_subset_1(esk3_0,u4_struct_0(esk2_0))&~r2_funct_2(esk1_0,u1_struct_0(esk2_0),k2_cat_3(esk2_0,esk1_0,k8_funcop_1(u4_struct_0(esk2_0),esk1_0,esk3_0)),k8_funcop_1(u1_struct_0(esk2_0),esk1_0,k3_graph_1(esk2_0,esk3_0))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_75])])])])). cnf(c_0_85, plain, (k2_cat_3(X1,X2,k8_funcop_1(X5,X2,X3))=k2_cat_3(X1,X2,k8_funcop_1(u4_struct_0(X1),X2,X4))\|v11_struct_0(X1)\|v2_struct_0(X1)\|v1_xboole_0(X5)\|v1_xboole_0(u4_struct_0(X1))\|k3_graph_1(X1,X3)!=k3_graph_1(X1,X4)\|~v1_funct_2(k2_cat_3(X1,X2,k8_funcop_1(X5,X2,X3)),X2,u1_struct_0(X1))\|~v1_funct_2(k8_funcop_1(u4_struct_0(X1),X2,X4),X2,u4_struct_0(X1))\|~v1_funct_2(k8_funcop_1(X5,X2,X3),X2,u4_struct_0(X1))\|~v1_funct_1(k2_cat_3(X1,X2,k8_funcop_1(X5,X2,X3)))\|~v1_funct_1(k8_funcop_1(u4_struct_0(X1),X2,X4))\|~m1_subset_1(k2_cat_3(X1,X2,k8_funcop_1(X5,X2,X3)),k1_zfmisc_1(k2_zfmisc_1(X2,u1_struct_0(X1))))\|~m1_subset_1(k8_funcop_1(u4_struct_0(X1),X2,X4),k1_zfmisc_1(k2_zfmisc_1(X2,u4_struct_0(X1))))\|~m1_subset_1(k8_funcop_1(X5,X2,X3),k1_zfmisc_1(k2_zfmisc_1(X2,u4_struct_0(X1))))\|~m1_subset_1(X4,u4_struct_0(X1))\|~m1_subset_1(X3,u4_struct_0(X1))\|~l1_cat_1(X1)\|~v6_cat_1(X1)\|~v5_cat_1(X1)\|~v4_cat_1(X1)\|~v3_cat_1(X1)\|~v2_cat_1(X1)\|~m1_subset_1(X3,X5)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_76, c_0_77])])). cnf(c_0_86, plain, (v1_xboole_0(X1)\|m1_subset_1(k8_funcop_1(X4,X2,X3),k1_zfmisc_1(k2_zfmisc_1(X2,X1)))\|v1_xboole_0(X4)\|~m1_subset_1(X3,X1)\|~m1_subset_1(X3,X4)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_78, c_0_77])])). cnf(c_0_87, plain, (v1_funct_2(k8_funcop_1(X4,X2,X3),X2,X1)\|v1_xboole_0(X1)\|v1_xboole_0(X4)\|~m1_subset_1(X3,X1)\|~m1_subset_1(X3,X4)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_79, c_0_77])])). cnf(c_0_88, plain, (k8_funcop_1(u1_struct_0(X1),X2,X3)=k2_cat_3(X1,X2,k8_funcop_1(u4_struct_0(X1),X2,X4))\|v1_xboole_0(u1_struct_0(X1))\|v11_struct_0(X1)\|v2_struct_0(X1)\|X3!=k3_graph_1(X1,X4)\|~v1_funct_2(k8_funcop_1(u4_struct_0(X1),X2,X4),X2,u4_struct_0(X1))\|~v1_funct_1(k8_funcop_1(u4_struct_0(X1),X2,X4))\|~m1_subset_1(k8_funcop_1(u4_struct_0(X1),X2,X4),k1_zfmisc_1(k2_zfmisc_1(X2,u4_struct_0(X1))))\|~m1_subset_1(X4,u4_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~l1_cat_1(X1)\|~v6_cat_1(X1)\|~v5_cat_1(X1)\|~v4_cat_1(X1)\|~v3_cat_1(X1)\|~v2_cat_1(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_80, c_0_78]), c_0_41]), c_0_79])). cnf(c_0_89, plain, (m1_subset_1(k7_partfun1(X2,X1,X3),X2)\|~v1_funct_1(X1)\|~v1_relat_1(X1)\|~v5_relat_1(X1,X2)), inference(evalgc,[status(thm)],[c_0_81])). cnf(c_0_90, plain, (v5_relat_1(k2_cat_3(X1,X2,X3),u1_struct_0(X1))\|v11_struct_0(X1)\|v2_struct_0(X1)\|~v1_funct_2(X3,X2,u4_struct_0(X1))\|~v1_funct_1(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X2,u4_struct_0(X1))))\|~l1_cat_1(X1)\|~v6_cat_1(X1)\|~v5_cat_1(X1)\|~v4_cat_1(X1)\|~v3_cat_1(X1)\|~v2_cat_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_82, c_0_35])])). cnf(c_0_91, plain, (v1_relat_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(evalgc,[status(thm)],[c_0_83])). cnf(c_0_92, negated_conjecture, (~r2_funct_2(esk1_0,u1_struct_0(esk2_0),k2_cat_3(esk2_0,esk1_0,k8_funcop_1(u4_struct_0(esk2_0),esk1_0,esk3_0)),k8_funcop_1(u1_struct_0(esk2_0),esk1_0,k3_graph_1(esk2_0,esk3_0)))), inference(split_conjunct,[status(thm)],[c_0_84])). cnf(c_0_93, plain, (k2_cat_3(X1,X2,k8_funcop_1(X3,X2,X4))=k2_cat_3(X1,X2,k8_funcop_1(u4_struct_0(X1),X2,X5))\|v1_xboole_0(X3)\|v11_struct_0(X1)\|v2_struct_0(X1)\|k3_graph_1(X1,X4)!=k3_graph_1(X1,X5)\|~v1_funct_2(k2_cat_3(X1,X2,k8_funcop_1(X3,X2,X4)),X2,u1_struct_0(X1))\|~v1_funct_1(k2_cat_3(X1,X2,k8_funcop_1(X3,X2,X4)))\|~m1_subset_1(k2_cat_3(X1,X2,k8_funcop_1(X3,X2,X4)),k1_zfmisc_1(k2_zfmisc_1(X2,u1_struct_0(X1))))\|~m1_subset_1(X5,u4_struct_0(X1))\|~m1_subset_1(X4,u4_struct_0(X1))\|~m1_subset_1(X4,X3)\|~l1_cat_1(X1)\|~v6_cat_1(X1)\|~v5_cat_1(X1)\|~v4_cat_1(X1)\|~v3_cat_1(X1)\|~v2_cat_1(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_85, c_0_86]), c_0_78]), c_0_41]), c_0_87]), c_0_79]), c_0_51])). cnf(c_0_94, plain, (k8_funcop_1(u1_struct_0(X1),X2,k3_graph_1(X1,X3))=k2_cat_3(X1,X2,k8_funcop_1(u4_struct_0(X1),X2,X3))\|v1_xboole_0(u1_struct_0(X1))\|v11_struct_0(X1)\|v2_struct_0(X1)\|~v1_funct_2(k8_funcop_1(u4_struct_0(X1),X2,X3),X2,u4_struct_0(X1))\|~v1_funct_1(k8_funcop_1(u4_struct_0(X1),X2,X3))\|~m1_subset_1(k8_funcop_1(u4_struct_0(X1),X2,X3),k1_zfmisc_1(k2_zfmisc_1(X2,u4_struct_0(X1))))\|~m1_subset_1(X3,u4_struct_0(X1))\|~m1_subset_1(k3_graph_1(X1,X3),u1_struct_0(X1))\|~l1_cat_1(X1)\|~v6_cat_1(X1)\|~v5_cat_1(X1)\|~v4_cat_1(X1)\|~v3_cat_1(X1)\|~v2_cat_1(X1)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_88])])). cnf(c_0_95, plain, (m1_subset_1(k7_partfun1(u1_struct_0(X1),k2_cat_3(X1,X2,X3),X4),u1_struct_0(X1))\|v11_struct_0(X1)\|v2_struct_0(X1)\|~v1_relat_1(k2_cat_3(X1,X2,X3))\|~v1_funct_1(k2_cat_3(X1,X2,X3))\|~v1_funct_2(X3,X2,u4_struct_0(X1))\|~v1_funct_1(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X2,u4_struct_0(X1))))\|~l1_cat_1(X1)\|~v6_cat_1(X1)\|~v5_cat_1(X1)\|~v4_cat_1(X1)\|~v3_cat_1(X1)\|~v2_cat_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_89, c_0_90])])). cnf(c_0_96, plain, (v1_relat_1(k2_cat_3(X1,X2,X3))\|v11_struct_0(X1)\|v2_struct_0(X1)\|~v1_funct_2(X3,X2,u4_struct_0(X1))\|~v1_funct_1(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X2,u4_struct_0(X1))))\|~l1_cat_1(X1)\|~v6_cat_1(X1)\|~v5_cat_1(X1)\|~v4_cat_1(X1)\|~v3_cat_1(X1)\|~v2_cat_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_91, c_0_35])])). cnf(c_0_97, negated_conjecture, (~r2_funct_2(esk1_0,u1_struct_0(esk2_0),k2_cat_3(esk2_0,esk1_0,k8_funcop_1(u4_struct_0(esk2_0),esk1_0,esk3_0)),k8_funcop_1(u1_struct_0(esk2_0),esk1_0,k3_graph_1(esk2_0,esk3_0)))), inference(evalgc,[status(thm)],[c_0_92])). cnf(c_0_98, plain, (k8_funcop_1(u1_struct_0(X1),X2,k3_graph_1(X1,X3))=k2_cat_3(X1,X2,k8_funcop_1(u4_struct_0(X1),X2,X4))\|v1_xboole_0(u4_struct_0(X1))\|v11_struct_0(X1)\|v2_struct_0(X1)\|v1_xboole_0(u1_struct_0(X1))\|k3_graph_1(X1,X3)!=k3_graph_1(X1,X4)\|~v1_funct_2(k8_funcop_1(u1_struct_0(X1),X2,k3_graph_1(X1,X3)),X2,u1_struct_0(X1))\|~v1_funct_1(k8_funcop_1(u1_struct_0(X1),X2,k3_graph_1(X1,X3)))\|~m1_subset_1(k8_funcop_1(u1_struct_0(X1),X2,k3_graph_1(X1,X3)),k1_zfmisc_1(k2_zfmisc_1(X2,u1_struct_0(X1))))\|~m1_subset_1(X4,u4_struct_0(X1))\|~m1_subset_1(X3,u4_struct_0(X1))\|~l1_cat_1(X1)\|~v6_cat_1(X1)\|~v5_cat_1(X1)\|~v4_cat_1(X1)\|~v3_cat_1(X1)\|~v2_cat_1(X1)\|~v1_funct_2(k8_funcop_1(u4_struct_0(X1),X2,X3),X2,u4_struct_0(X1))\|~v1_funct_1(k8_funcop_1(u4_struct_0(X1),X2,X3))\|~m1_subset_1(k8_funcop_1(u4_struct_0(X1),X2,X3),k1_zfmisc_1(k2_zfmisc_1(X2,u4_struct_0(X1))))\|~m1_subset_1(k3_graph_1(X1,X3),u1_struct_0(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_93, c_0_94])])). fof(c_0_99, plain, ![X39, X40, X41, X42]:((~r2_funct_2(X39,X40,X41,X42)\|X41=X42\|(~v1_funct_1(X41)\|(~v1_funct_2(X41,X39,X40)\|~m1_subset_1(X41,k1_zfmisc_1(k2_zfmisc_1(X39,X40))))\|(~v1_funct_1(X42)\|(~v1_funct_2(X42,X39,X40)\|~m1_subset_1(X42,k1_zfmisc_1(k2_zfmisc_1(X39,X40)))))))&(X41!=X42\|r2_funct_2(X39,X40,X41,X42)\|(~v1_funct_1(X41)\|(~v1_funct_2(X41,X39,X40)\|~m1_subset_1(X41,k1_zfmisc_1(k2_zfmisc_1(X39,X40))))\|(~v1_funct_1(X42)\|(~v1_funct_2(X42,X39,X40)\|~m1_subset_1(X42,k1_zfmisc_1(k2_zfmisc_1(X39,X40)))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_r2_funct_2])])])). cnf(c_0_100, plain, (m1_subset_1(k7_partfun1(u1_struct_0(X1),k2_cat_3(X1,X2,X3),X4),u1_struct_0(X1))\|v11_struct_0(X1)\|v2_struct_0(X1)\|~v1_funct_2(X3,X2,u4_struct_0(X1))\|~v1_funct_1(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X2,u4_struct_0(X1))))\|~l1_cat_1(X1)\|~v6_cat_1(X1)\|~v5_cat_1(X1)\|~v4_cat_1(X1)\|~v3_cat_1(X1)\|~v2_cat_1(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_95, c_0_36]), c_0_96])). cnf(c_0_101, negated_conjecture, (v1_xboole_0(u1_struct_0(esk2_0))\|~r2_funct_2(esk1_0,u1_struct_0(esk2_0),k2_cat_3(esk2_0,esk1_0,k8_funcop_1(u4_struct_0(esk2_0),esk1_0,esk3_0)),k2_zfmisc_1(esk1_0,k1_tarski(k3_graph_1(esk2_0,esk3_0))))\|~m1_subset_1(k3_graph_1(esk2_0,esk3_0),u1_struct_0(esk2_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_97, c_0_68])])). cnf(c_0_102, plain, (k8_funcop_1(u1_struct_0(X1),X2,k3_graph_1(X1,X3))=k2_cat_3(X1,X2,k8_funcop_1(u4_struct_0(X1),X2,X4))\|v1_xboole_0(u1_struct_0(X1))\|v11_struct_0(X1)\|v2_struct_0(X1)\|k3_graph_1(X1,X3)!=k3_graph_1(X1,X4)\|~m1_subset_1(k3_graph_1(X1,X3),u1_struct_0(X1))\|~m1_subset_1(X4,u4_struct_0(X1))\|~m1_subset_1(X3,u4_struct_0(X1))\|~l1_cat_1(X1)\|~v6_cat_1(X1)\|~v5_cat_1(X1)\|~v4_cat_1(X1)\|~v3_cat_1(X1)\|~v2_cat_1(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_98, c_0_78]), c_0_78]), c_0_41]), c_0_41]), c_0_79]), c_0_79]), c_0_51])). cnf(c_0_103, negated_conjecture, (m1_subset_1(esk3_0,u4_struct_0(esk2_0))), inference(split_conjunct,[status(thm)],[c_0_84])). cnf(c_0_104, negated_conjecture, (l1_cat_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_84])). cnf(c_0_105, negated_conjecture, (v6_cat_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_84])). cnf(c_0_106, negated_conjecture, (v5_cat_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_84])). cnf(c_0_107, negated_conjecture, (v4_cat_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_84])). cnf(c_0_108, negated_conjecture, (v3_cat_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_84])). cnf(c_0_109, negated_conjecture, (v2_cat_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_84])). cnf(c_0_110, negated_conjecture, (~v11_struct_0(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_84])). cnf(c_0_111, negated_conjecture, (~v2_struct_0(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_84])). cnf(c_0_112, plain, (r2_funct_2(X3,X4,X1,X2)\|X1!=X2\|~v1_funct_1(X1)\|~v1_funct_2(X1,X3,X4)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X3,X4)))\|~v1_funct_1(X2)\|~v1_funct_2(X2,X3,X4)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X3,X4)))), inference(split_conjunct,[status(thm)],[c_0_99])). cnf(c_0_113, plain, (m1_subset_1(k3_graph_1(X1,k7_partfun1(u4_struct_0(X1),X3,X4)),u1_struct_0(X1))\|v11_struct_0(X1)\|v2_struct_0(X1)\|~v1_funct_2(X3,X2,u4_struct_0(X1))\|~v1_funct_1(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X2,u4_struct_0(X1))))\|~l1_cat_1(X1)\|~v6_cat_1(X1)\|~v5_cat_1(X1)\|~v4_cat_1(X1)\|~v3_cat_1(X1)\|~v2_cat_1(X1)\|~r2_hidden(X4,X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_100, c_0_47])])). cnf(c_0_114, plain, (v1_funct_2(k2_zfmisc_1(X2,k1_tarski(X3)),X2,X1)\|v1_xboole_0(X1)\|~m1_subset_1(X3,X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_79, c_0_68])])). cnf(c_0_115, negated_conjecture, (v1_xboole_0(u1_struct_0(esk2_0))\|v1_xboole_0(X1)\|~r2_funct_2(esk1_0,u1_struct_0(esk2_0),k2_cat_3(esk2_0,esk1_0,k8_funcop_1(u4_struct_0(esk2_0),esk1_0,esk3_0)),k8_funcop_1(X1,esk1_0,k3_graph_1(esk2_0,esk3_0)))\|~m1_subset_1(k3_graph_1(esk2_0,esk3_0),u1_struct_0(esk2_0))\|~m1_subset_1(k3_graph_1(esk2_0,esk3_0),X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_101, c_0_68])])). cnf(c_0_116, plain, (k8_funcop_1(u1_struct_0(X1),X2,k3_graph_1(X1,X3))=k2_cat_3(X1,X2,k8_funcop_1(u4_struct_0(X1),X2,X3))\|v1_xboole_0(u1_struct_0(X1))\|v11_struct_0(X1)\|v2_struct_0(X1)\|~m1_subset_1(k3_graph_1(X1,X3),u1_struct_0(X1))\|~m1_subset_1(X3,u4_struct_0(X1))\|~l1_cat_1(X1)\|~v6_cat_1(X1)\|~v5_cat_1(X1)\|~v4_cat_1(X1)\|~v3_cat_1(X1)\|~v2_cat_1(X1)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_102])])). cnf(c_0_117, negated_conjecture, (m1_subset_1(esk3_0,u4_struct_0(esk2_0))), inference(evalgc,[status(thm)],[c_0_103])). cnf(c_0_118, negated_conjecture, (l1_cat_1(esk2_0)), inference(evalgc,[status(thm)],[c_0_104])). cnf(c_0_119, negated_conjecture, (v6_cat_1(esk2_0)), inference(evalgc,[status(thm)],[c_0_105])). cnf(c_0_120, negated_conjecture, (v5_cat_1(esk2_0)), inference(evalgc,[status(thm)],[c_0_106])). cnf(c_0_121, negated_conjecture, (v4_cat_1(esk2_0)), inference(evalgc,[status(thm)],[c_0_107])). cnf(c_0_122, negated_conjecture, (v3_cat_1(esk2_0)), inference(evalgc,[status(thm)],[c_0_108])). cnf(c_0_123, negated_conjecture, (v2_cat_1(esk2_0)), inference(evalgc,[status(thm)],[c_0_109])). cnf(c_0_124, negated_conjecture, (~v11_struct_0(esk2_0)), inference(evalgc,[status(thm)],[c_0_110])). cnf(c_0_125, negated_conjecture, (~v2_struct_0(esk2_0)), inference(evalgc,[status(thm)],[c_0_111])). cnf(c_0_126, plain, (r2_funct_2(X3,X4,X1,X2)\|X1!=X2\|~v1_funct_1(X2)\|~v1_funct_1(X1)\|~v1_funct_2(X2,X3,X4)\|~v1_funct_2(X1,X3,X4)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X3,X4)))\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X3,X4)))), inference(evalgc,[status(thm)],[c_0_112])). cnf(c_0_127, plain, (m1_subset_1(k3_graph_1(X1,k7_partfun1(u4_struct_0(X1),k2_zfmisc_1(X2,k1_tarski(X3)),X4)),u1_struct_0(X1))\|v11_struct_0(X1)\|v2_struct_0(X1)\|v1_xboole_0(u4_struct_0(X1))\|~r2_hidden(X4,X2)\|~v1_funct_1(k2_zfmisc_1(X2,k1_tarski(X3)))\|~m1_subset_1(k2_zfmisc_1(X2,k1_tarski(X3)),k1_zfmisc_1(k2_zfmisc_1(X2,u4_struct_0(X1))))\|~l1_cat_1(X1)\|~v6_cat_1(X1)\|~v5_cat_1(X1)\|~v4_cat_1(X1)\|~v3_cat_1(X1)\|~v2_cat_1(X1)\|~m1_subset_1(X3,u4_struct_0(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_113, c_0_114])])). cnf(c_0_128, plain, (v1_xboole_0(X1)\|m1_subset_1(k2_zfmisc_1(X2,k1_tarski(X3)),k1_zfmisc_1(k2_zfmisc_1(X2,X1)))\|~m1_subset_1(X3,X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_78, c_0_68])])). cnf(c_0_129, plain, (v1_funct_1(k2_zfmisc_1(X2,k1_tarski(X3)))\|v1_xboole_0(X1)\|~m1_subset_1(X3,X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_41, c_0_68])])). cnf(c_0_130, negated_conjecture, (v1_xboole_0(u1_struct_0(esk2_0))\|~r2_funct_2(esk1_0,u1_struct_0(esk2_0),k2_cat_3(esk2_0,esk1_0,k8_funcop_1(u4_struct_0(esk2_0),esk1_0,esk3_0)),k2_cat_3(esk2_0,esk1_0,k8_funcop_1(u4_struct_0(esk2_0),esk1_0,esk3_0)))\|~m1_subset_1(k3_graph_1(esk2_0,esk3_0),u1_struct_0(esk2_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115, c_0_116]), c_0_117]), c_0_118]), c_0_119]), c_0_120]), c_0_121]), c_0_122]), c_0_123])]), c_0_124]), c_0_125])])). cnf(c_0_131, plain, (r2_funct_2(X1,X2,X3,X3)\|~v1_funct_2(X3,X1,X2)\|~v1_funct_1(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_126])])). cnf(c_0_132, plain, (m1_subset_1(k3_graph_1(X1,k7_partfun1(u4_struct_0(X1),k2_zfmisc_1(X2,k1_tarski(X3)),X4)),u1_struct_0(X1))\|v11_struct_0(X1)\|v2_struct_0(X1)\|~r2_hidden(X4,X2)\|~m1_subset_1(X3,u4_struct_0(X1))\|~l1_cat_1(X1)\|~v6_cat_1(X1)\|~v5_cat_1(X1)\|~v4_cat_1(X1)\|~v3_cat_1(X1)\|~v2_cat_1(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_127, c_0_128]), c_0_129]), c_0_51])). cnf(c_0_133, plain, (k7_partfun1(X1,k2_zfmisc_1(X2,k1_tarski(X3)),X4)=X3\|v1_xboole_0(X1)\|~r2_hidden(X4,X2)\|~m1_subset_1(X3,X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_32, c_0_68])])). fof(c_0_134, plain, ![X48, X49]:(~m1_subset_1(X48,X49)\|(v1_xboole_0(X49)\|r2_hidden(X48,X49))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])])). cnf(c_0_135, negated_conjecture, (v1_xboole_0(u1_struct_0(esk2_0))\|~m1_subset_1(k3_graph_1(esk2_0,esk3_0),u1_struct_0(esk2_0))\|~v1_funct_2(k2_cat_3(esk2_0,esk1_0,k8_funcop_1(u4_struct_0(esk2_0),esk1_0,esk3_0)),esk1_0,u1_struct_0(esk2_0))\|~v1_funct_1(k2_cat_3(esk2_0,esk1_0,k8_funcop_1(u4_struct_0(esk2_0),esk1_0,esk3_0)))\|~m1_subset_1(k2_cat_3(esk2_0,esk1_0,k8_funcop_1(u4_struct_0(esk2_0),esk1_0,esk3_0)),k1_zfmisc_1(k2_zfmisc_1(esk1_0,u1_struct_0(esk2_0))))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_130, c_0_131])])). cnf(c_0_136, plain, (v1_funct_2(k2_cat_3(X1,X2,k8_funcop_1(u4_struct_0(X1),X2,X3)),X2,u1_struct_0(X1))\|v1_xboole_0(u1_struct_0(X1))\|v11_struct_0(X1)\|v2_struct_0(X1)\|~m1_subset_1(k3_graph_1(X1,X3),u1_struct_0(X1))\|~m1_subset_1(X3,u4_struct_0(X1))\|~l1_cat_1(X1)\|~v6_cat_1(X1)\|~v5_cat_1(X1)\|~v4_cat_1(X1)\|~v3_cat_1(X1)\|~v2_cat_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_79, c_0_116])])). cnf(c_0_137, plain, (m1_subset_1(k3_graph_1(X1,X3),u1_struct_0(X1))\|v11_struct_0(X1)\|v2_struct_0(X1)\|v1_xboole_0(u4_struct_0(X1))\|~r2_hidden(X4,X2)\|~m1_subset_1(X3,u4_struct_0(X1))\|~l1_cat_1(X1)\|~v6_cat_1(X1)\|~v5_cat_1(X1)\|~v4_cat_1(X1)\|~v3_cat_1(X1)\|~v2_cat_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_132, c_0_133])])). cnf(c_0_138, plain, (v1_xboole_0(X2)\|r2_hidden(X1,X2)\|~m1_subset_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_134])). cnf(c_0_139, negated_conjecture, (v1_xboole_0(u1_struct_0(esk2_0))\|~v1_funct_1(k2_cat_3(esk2_0,esk1_0,k8_funcop_1(u4_struct_0(esk2_0),esk1_0,esk3_0)))\|~m1_subset_1(k2_cat_3(esk2_0,esk1_0,k8_funcop_1(u4_struct_0(esk2_0),esk1_0,esk3_0)),k1_zfmisc_1(k2_zfmisc_1(esk1_0,u1_struct_0(esk2_0))))\|~m1_subset_1(k3_graph_1(esk2_0,esk3_0),u1_struct_0(esk2_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135, c_0_136]), c_0_117]), c_0_118]), c_0_119]), c_0_120]), c_0_121]), c_0_122]), c_0_123])]), c_0_124]), c_0_125])])). cnf(c_0_140, plain, (v1_xboole_0(u1_struct_0(X1))\|m1_subset_1(k2_cat_3(X1,X2,k8_funcop_1(u4_struct_0(X1),X2,X3)),k1_zfmisc_1(k2_zfmisc_1(X2,u1_struct_0(X1))))\|v11_struct_0(X1)\|v2_struct_0(X1)\|~m1_subset_1(k3_graph_1(X1,X3),u1_struct_0(X1))\|~m1_subset_1(X3,u4_struct_0(X1))\|~l1_cat_1(X1)\|~v6_cat_1(X1)\|~v5_cat_1(X1)\|~v4_cat_1(X1)\|~v3_cat_1(X1)\|~v2_cat_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_78, c_0_116])])). cnf(c_0_141, plain, (m1_subset_1(k3_graph_1(X1,X2),u1_struct_0(X1))\|v11_struct_0(X1)\|v2_struct_0(X1)\|~r2_hidden(X3,X4)\|~m1_subset_1(X2,u4_struct_0(X1))\|~l1_cat_1(X1)\|~v6_cat_1(X1)\|~v5_cat_1(X1)\|~v4_cat_1(X1)\|~v3_cat_1(X1)\|~v2_cat_1(X1)), inference(csr,[status(thm)],[c_0_137, c_0_51])). cnf(c_0_142, plain, (v1_xboole_0(X2)\|r2_hidden(X1,X2)\|~m1_subset_1(X1,X2)), inference(evalgc,[status(thm)],[c_0_138])). fof(c_0_143, plain, ![X46]:(v2_struct_0(X46)\|~l1_struct_0(X46)\|~v1_xboole_0(u1_struct_0(X46))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fc2_struct_0])])])). cnf(c_0_144, negated_conjecture, (v1_xboole_0(u1_struct_0(esk2_0))\|~v1_funct_1(k2_cat_3(esk2_0,esk1_0,k8_funcop_1(u4_struct_0(esk2_0),esk1_0,esk3_0)))\|~m1_subset_1(k3_graph_1(esk2_0,esk3_0),u1_struct_0(esk2_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139, c_0_140]), c_0_117]), c_0_118]), c_0_119]), c_0_120]), c_0_121]), c_0_122]), c_0_123])]), c_0_124]), c_0_125])])). cnf(c_0_145, plain, (v1_funct_1(k2_cat_3(X1,X2,k8_funcop_1(u4_struct_0(X1),X2,X3)))\|v1_xboole_0(u1_struct_0(X1))\|v11_struct_0(X1)\|v2_struct_0(X1)\|~m1_subset_1(k3_graph_1(X1,X3),u1_struct_0(X1))\|~m1_subset_1(X3,u4_struct_0(X1))\|~l1_cat_1(X1)\|~v6_cat_1(X1)\|~v5_cat_1(X1)\|~v4_cat_1(X1)\|~v3_cat_1(X1)\|~v2_cat_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_41, c_0_116])])). cnf(c_0_146, plain, (m1_subset_1(k3_graph_1(X1,X2),u1_struct_0(X1))\|v11_struct_0(X1)\|v2_struct_0(X1)\|v1_xboole_0(X4)\|~m1_subset_1(X2,u4_struct_0(X1))\|~l1_cat_1(X1)\|~v6_cat_1(X1)\|~v5_cat_1(X1)\|~v4_cat_1(X1)\|~v3_cat_1(X1)\|~v2_cat_1(X1)\|~m1_subset_1(X3,X4)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_141, c_0_142])])). cnf(c_0_147, plain, (v2_struct_0(X1)\|~l1_struct_0(X1)\|~v1_xboole_0(u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_143])). cnf(c_0_148, negated_conjecture, (v1_xboole_0(u1_struct_0(esk2_0))\|~m1_subset_1(k3_graph_1(esk2_0,esk3_0),u1_struct_0(esk2_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144, c_0_145]), c_0_117]), c_0_118]), c_0_119]), c_0_120]), c_0_121]), c_0_122]), c_0_123])]), c_0_124]), c_0_125])])). cnf(c_0_149, negated_conjecture, (v1_xboole_0(u4_struct_0(esk2_0))\|m1_subset_1(k3_graph_1(X1,X2),u1_struct_0(X1))\|v11_struct_0(X1)\|v2_struct_0(X1)\|~m1_subset_1(X2,u4_struct_0(X1))\|~l1_cat_1(X1)\|~v6_cat_1(X1)\|~v5_cat_1(X1)\|~v4_cat_1(X1)\|~v3_cat_1(X1)\|~v2_cat_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_146, c_0_117])])). fof(c_0_150, plain, ![X45]:(~l5_struct_0(X45)\|l1_struct_0(X45)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l5_struct_0])])). cnf(c_0_151, plain, (v2_struct_0(X1)\|~l1_struct_0(X1)\|~v1_xboole_0(u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_147])). cnf(c_0_152, negated_conjecture, (v1_xboole_0(u1_struct_0(esk2_0))\|v1_xboole_0(u4_struct_0(esk2_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148, c_0_149]), c_0_117]), c_0_118]), c_0_119]), c_0_120]), c_0_121]), c_0_122]), c_0_123])]), c_0_124]), c_0_125])])). cnf(c_0_153, plain, (l1_struct_0(X1)\|~l5_struct_0(X1)), inference(split_conjunct,[status(thm)],[c_0_150])). cnf(c_0_154, negated_conjecture, (v1_xboole_0(u4_struct_0(esk2_0))\|~l1_struct_0(esk2_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_151, c_0_152]), c_0_125])])). cnf(c_0_155, plain, (l1_struct_0(X1)\|~l5_struct_0(X1)), inference(evalgc,[status(thm)],[c_0_153])). cnf(c_0_156, negated_conjecture, (v1_xboole_0(u4_struct_0(esk2_0))\|~l5_struct_0(esk2_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_154, c_0_155])])). cnf(c_0_157, negated_conjecture, (v1_xboole_0(u4_struct_0(esk2_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156, c_0_49]), c_0_118])])])). cnf(c_0_158, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51, c_0_157]), c_0_118])]), c_0_124]), ['proof']). # SZS output end CNFRefutation	reserve I for set, x,x1,x2,y,z for set, A for non empty set; reserve C,D for Category; reserve a,b,c,d for Object of C; reserve f,g,h,i,j,k,p1,p2,q1,q2,i1,i2,j1,j2 for Morphism of C; theorem Th4: doms(I-->f) = I-->(dom f) proof set F = I-->f, F9 = I-->(dom f); now let x; assume A1: x in I; then F/.x = f & F9/.x = dom f by Th2; hence (doms F)/.x = F9/.x by A1,Def1; end; hence thesis by Th1; end;	Convert the following ATP output trace into a readable Mizar proof.
t8_graphsp	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t8_graphsp, conjecture, ![X1]:((~(v2_struct_0(X1))&l1_graph_1(X1))=>![X2]:((v7_graph_1(X2,X1)&m2_graph_1(X2,X1))=>![X3]:((v1_relat_1(X3)&v1_funct_1(X3))=>![X4, X5]:(m1_subset_1(X5,u1_struct_0(X1))=>![X6]:(m1_subset_1(X6,u1_struct_0(X1))=>(r8_graph_5(X1,X5,X6,X2,X4,X3)<=>r8_graph_5(X1,X5,X6,X2,k2_xboole_0(X4,k1_tarski(X6)),X3))))))), file('/scratch/mptp/predsminms1/t8_graphsp__0', t8_graphsp)). fof(d18_graph_5, axiom, ![X1]:((~(v2_struct_0(X1))&l1_graph_1(X1))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>![X4]:((v7_graph_1(X4,X1)&m2_graph_1(X4,X1))=>![X5, X6]:((v1_relat_1(X6)&v1_funct_1(X6))=>(r8_graph_5(X1,X2,X3,X4,X5,X6)<=>(r2_graph_5(X1,X2,X3,X4,X5)&![X7]:((v7_graph_1(X7,X1)&m2_graph_1(X7,X1))=>(r2_graph_5(X1,X2,X3,X7,X5)=>r1_xxreal_0(k10_graph_5(X1,X4,X6),k10_graph_5(X1,X7,X6))))))))))), file('/scratch/mptp/predsminms1/t8_graphsp__0', d18_graph_5)). fof(t7_graphsp, axiom, ![X1]:((~(v2_struct_0(X1))&l1_graph_1(X1))=>![X2]:((v7_graph_1(X2,X1)&m2_graph_1(X2,X1))=>![X3, X4]:(m1_subset_1(X4,u1_struct_0(X1))=>![X5]:(m1_subset_1(X5,u1_struct_0(X1))=>(r2_graph_5(X1,X4,X5,X2,X3)<=>r2_graph_5(X1,X4,X5,X2,k2_xboole_0(X3,k1_tarski(X5)))))))), file('/scratch/mptp/predsminms1/t8_graphsp__0', t7_graphsp)). fof(c_0_3, negated_conjecture, ~(![X1]:((~(v2_struct_0(X1))&l1_graph_1(X1))=>![X2]:((v7_graph_1(X2,X1)&m2_graph_1(X2,X1))=>![X3]:((v1_relat_1(X3)&v1_funct_1(X3))=>![X4, X5]:(m1_subset_1(X5,u1_struct_0(X1))=>![X6]:(m1_subset_1(X6,u1_struct_0(X1))=>(r8_graph_5(X1,X5,X6,X2,X4,X3)<=>r8_graph_5(X1,X5,X6,X2,k2_xboole_0(X4,k1_tarski(X6)),X3)))))))), inference(assume_negation,[status(cth)],[t8_graphsp])). fof(c_0_4, plain, ![X14, X15, X16, X17, X18, X19, X20]:(((r2_graph_5(X14,X15,X16,X17,X18)\|~r8_graph_5(X14,X15,X16,X17,X18,X19)\|(~v1_relat_1(X19)\|~v1_funct_1(X19))\|(~v7_graph_1(X17,X14)\|~m2_graph_1(X17,X14))\|~m1_subset_1(X16,u1_struct_0(X14))\|~m1_subset_1(X15,u1_struct_0(X14))\|(v2_struct_0(X14)\|~l1_graph_1(X14)))&(~v7_graph_1(X20,X14)\|~m2_graph_1(X20,X14)\|(~r2_graph_5(X14,X15,X16,X20,X18)\|r1_xxreal_0(k10_graph_5(X14,X17,X19),k10_graph_5(X14,X20,X19)))\|~r8_graph_5(X14,X15,X16,X17,X18,X19)\|(~v1_relat_1(X19)\|~v1_funct_1(X19))\|(~v7_graph_1(X17,X14)\|~m2_graph_1(X17,X14))\|~m1_subset_1(X16,u1_struct_0(X14))\|~m1_subset_1(X15,u1_struct_0(X14))\|(v2_struct_0(X14)\|~l1_graph_1(X14))))&(((v7_graph_1(esk7_6(X14,X15,X16,X17,X18,X19),X14)\|~r2_graph_5(X14,X15,X16,X17,X18)\|r8_graph_5(X14,X15,X16,X17,X18,X19)\|(~v1_relat_1(X19)\|~v1_funct_1(X19))\|(~v7_graph_1(X17,X14)\|~m2_graph_1(X17,X14))\|~m1_subset_1(X16,u1_struct_0(X14))\|~m1_subset_1(X15,u1_struct_0(X14))\|(v2_struct_0(X14)\|~l1_graph_1(X14)))&(m2_graph_1(esk7_6(X14,X15,X16,X17,X18,X19),X14)\|~r2_graph_5(X14,X15,X16,X17,X18)\|r8_graph_5(X14,X15,X16,X17,X18,X19)\|(~v1_relat_1(X19)\|~v1_funct_1(X19))\|(~v7_graph_1(X17,X14)\|~m2_graph_1(X17,X14))\|~m1_subset_1(X16,u1_struct_0(X14))\|~m1_subset_1(X15,u1_struct_0(X14))\|(v2_struct_0(X14)\|~l1_graph_1(X14))))&((r2_graph_5(X14,X15,X16,esk7_6(X14,X15,X16,X17,X18,X19),X18)\|~r2_graph_5(X14,X15,X16,X17,X18)\|r8_graph_5(X14,X15,X16,X17,X18,X19)\|(~v1_relat_1(X19)\|~v1_funct_1(X19))\|(~v7_graph_1(X17,X14)\|~m2_graph_1(X17,X14))\|~m1_subset_1(X16,u1_struct_0(X14))\|~m1_subset_1(X15,u1_struct_0(X14))\|(v2_struct_0(X14)\|~l1_graph_1(X14)))&(~r1_xxreal_0(k10_graph_5(X14,X17,X19),k10_graph_5(X14,esk7_6(X14,X15,X16,X17,X18,X19),X19))\|~r2_graph_5(X14,X15,X16,X17,X18)\|r8_graph_5(X14,X15,X16,X17,X18,X19)\|(~v1_relat_1(X19)\|~v1_funct_1(X19))\|(~v7_graph_1(X17,X14)\|~m2_graph_1(X17,X14))\|~m1_subset_1(X16,u1_struct_0(X14))\|~m1_subset_1(X15,u1_struct_0(X14))\|(v2_struct_0(X14)\|~l1_graph_1(X14)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d18_graph_5])])])])])])). fof(c_0_5, negated_conjecture, ((~v2_struct_0(esk1_0)&l1_graph_1(esk1_0))&((v7_graph_1(esk2_0,esk1_0)&m2_graph_1(esk2_0,esk1_0))&((v1_relat_1(esk3_0)&v1_funct_1(esk3_0))&(m1_subset_1(esk5_0,u1_struct_0(esk1_0))&(m1_subset_1(esk6_0,u1_struct_0(esk1_0))&((~r8_graph_5(esk1_0,esk5_0,esk6_0,esk2_0,esk4_0,esk3_0)\|~r8_graph_5(esk1_0,esk5_0,esk6_0,esk2_0,k2_xboole_0(esk4_0,k1_tarski(esk6_0)),esk3_0))&(r8_graph_5(esk1_0,esk5_0,esk6_0,esk2_0,esk4_0,esk3_0)\|r8_graph_5(esk1_0,esk5_0,esk6_0,esk2_0,k2_xboole_0(esk4_0,k1_tarski(esk6_0)),esk3_0)))))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_3])])])])). cnf(c_0_6, plain, (r1_xxreal_0(k10_graph_5(X2,X6,X7),k10_graph_5(X2,X1,X7))\|v2_struct_0(X2)\|~v7_graph_1(X1,X2)\|~m2_graph_1(X1,X2)\|~r2_graph_5(X2,X3,X4,X1,X5)\|~r8_graph_5(X2,X3,X4,X6,X5,X7)\|~v1_relat_1(X7)\|~v1_funct_1(X7)\|~v7_graph_1(X6,X2)\|~m2_graph_1(X6,X2)\|~m1_subset_1(X4,u1_struct_0(X2))\|~m1_subset_1(X3,u1_struct_0(X2))\|~l1_graph_1(X2)), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_7, negated_conjecture, (r8_graph_5(esk1_0,esk5_0,esk6_0,esk2_0,esk4_0,esk3_0)\|r8_graph_5(esk1_0,esk5_0,esk6_0,esk2_0,k2_xboole_0(esk4_0,k1_tarski(esk6_0)),esk3_0)), inference(split_conjunct,[status(thm)],[c_0_5])). cnf(c_0_8, negated_conjecture, (m1_subset_1(esk6_0,u1_struct_0(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_5])). cnf(c_0_9, negated_conjecture, (m1_subset_1(esk5_0,u1_struct_0(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_5])). cnf(c_0_10, negated_conjecture, (v1_funct_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_5])). cnf(c_0_11, negated_conjecture, (v1_relat_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_5])). cnf(c_0_12, negated_conjecture, (m2_graph_1(esk2_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_5])). cnf(c_0_13, negated_conjecture, (v7_graph_1(esk2_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_5])). cnf(c_0_14, negated_conjecture, (l1_graph_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_5])). cnf(c_0_15, negated_conjecture, (~v2_struct_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_5])). fof(c_0_16, plain, ![X22, X23, X24, X25, X26]:((~r2_graph_5(X22,X25,X26,X23,X24)\|r2_graph_5(X22,X25,X26,X23,k2_xboole_0(X24,k1_tarski(X26)))\|~m1_subset_1(X26,u1_struct_0(X22))\|~m1_subset_1(X25,u1_struct_0(X22))\|(~v7_graph_1(X23,X22)\|~m2_graph_1(X23,X22))\|(v2_struct_0(X22)\|~l1_graph_1(X22)))&(~r2_graph_5(X22,X25,X26,X23,k2_xboole_0(X24,k1_tarski(X26)))\|r2_graph_5(X22,X25,X26,X23,X24)\|~m1_subset_1(X26,u1_struct_0(X22))\|~m1_subset_1(X25,u1_struct_0(X22))\|(~v7_graph_1(X23,X22)\|~m2_graph_1(X23,X22))\|(v2_struct_0(X22)\|~l1_graph_1(X22)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t7_graphsp])])])])])). cnf(c_0_17, plain, (r2_graph_5(X1,X2,X3,X4,X5)\|v2_struct_0(X1)\|~r8_graph_5(X1,X2,X3,X4,X5,X6)\|~v1_relat_1(X6)\|~v1_funct_1(X6)\|~v7_graph_1(X4,X1)\|~m2_graph_1(X4,X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l1_graph_1(X1)), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_18, plain, (r8_graph_5(X1,X4,X5,X2,X6,X3)\|v2_struct_0(X1)\|~r1_xxreal_0(k10_graph_5(X1,X2,X3),k10_graph_5(X1,esk7_6(X1,X4,X5,X2,X6,X3),X3))\|~r2_graph_5(X1,X4,X5,X2,X6)\|~v1_relat_1(X3)\|~v1_funct_1(X3)\|~v7_graph_1(X2,X1)\|~m2_graph_1(X2,X1)\|~m1_subset_1(X5,u1_struct_0(X1))\|~m1_subset_1(X4,u1_struct_0(X1))\|~l1_graph_1(X1)), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_19, plain, (v2_struct_0(X2)\|r1_xxreal_0(k10_graph_5(X2,X6,X7),k10_graph_5(X2,X1,X7))\|~l1_graph_1(X2)\|~v1_relat_1(X7)\|~v1_funct_1(X7)\|~v7_graph_1(X6,X2)\|~v7_graph_1(X1,X2)\|~m2_graph_1(X6,X2)\|~m2_graph_1(X1,X2)\|~m1_subset_1(X4,u1_struct_0(X2))\|~m1_subset_1(X3,u1_struct_0(X2))\|~r2_graph_5(X2,X3,X4,X1,X5)\|~r8_graph_5(X2,X3,X4,X6,X5,X7)), inference(evalgc,[status(thm)],[c_0_6])). cnf(c_0_20, negated_conjecture, (r8_graph_5(esk1_0,esk5_0,esk6_0,esk2_0,esk4_0,esk3_0)\|r8_graph_5(esk1_0,esk5_0,esk6_0,esk2_0,k2_xboole_0(esk4_0,k1_tarski(esk6_0)),esk3_0)), inference(evalgc,[status(thm)],[c_0_7])). cnf(c_0_21, negated_conjecture, (m1_subset_1(esk6_0,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[c_0_8])). cnf(c_0_22, negated_conjecture, (m1_subset_1(esk5_0,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[c_0_9])). cnf(c_0_23, negated_conjecture, (v1_funct_1(esk3_0)), inference(evalgc,[status(thm)],[c_0_10])). cnf(c_0_24, negated_conjecture, (v1_relat_1(esk3_0)), inference(evalgc,[status(thm)],[c_0_11])). cnf(c_0_25, negated_conjecture, (m2_graph_1(esk2_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_12])). cnf(c_0_26, negated_conjecture, (v7_graph_1(esk2_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_13])). cnf(c_0_27, negated_conjecture, (l1_graph_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_14])). cnf(c_0_28, negated_conjecture, (~v2_struct_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_15])). cnf(c_0_29, plain, (r2_graph_5(X1,X2,X3,X4,X5)\|v2_struct_0(X1)\|~r2_graph_5(X1,X2,X3,X4,k2_xboole_0(X5,k1_tarski(X3)))\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~v7_graph_1(X4,X1)\|~m2_graph_1(X4,X1)\|~l1_graph_1(X1)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_30, plain, (v2_struct_0(X1)\|r2_graph_5(X1,X2,X3,X4,X5)\|~l1_graph_1(X1)\|~v1_relat_1(X6)\|~v1_funct_1(X6)\|~v7_graph_1(X4,X1)\|~m2_graph_1(X4,X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~r8_graph_5(X1,X2,X3,X4,X5,X6)), inference(evalgc,[status(thm)],[c_0_17])). cnf(c_0_31, plain, (v2_struct_0(X1)\|r8_graph_5(X1,X4,X5,X2,X6,X3)\|~l1_graph_1(X1)\|~v1_relat_1(X3)\|~v1_funct_1(X3)\|~v7_graph_1(X2,X1)\|~m2_graph_1(X2,X1)\|~m1_subset_1(X5,u1_struct_0(X1))\|~m1_subset_1(X4,u1_struct_0(X1))\|~r2_graph_5(X1,X4,X5,X2,X6)\|~r1_xxreal_0(k10_graph_5(X1,X2,X3),k10_graph_5(X1,esk7_6(X1,X4,X5,X2,X6,X3),X3))), inference(evalgc,[status(thm)],[c_0_18])). cnf(c_0_32, negated_conjecture, (r1_xxreal_0(k10_graph_5(esk1_0,esk2_0,esk3_0),k10_graph_5(esk1_0,X1,esk3_0))\|r8_graph_5(esk1_0,esk5_0,esk6_0,esk2_0,esk4_0,esk3_0)\|~r2_graph_5(esk1_0,esk5_0,esk6_0,X1,k2_xboole_0(esk4_0,k1_tarski(esk6_0)))\|~m2_graph_1(X1,esk1_0)\|~v7_graph_1(X1,esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19, c_0_20]), c_0_21]), c_0_22]), c_0_23]), c_0_24]), c_0_25]), c_0_26]), c_0_27])]), c_0_28])])). cnf(c_0_33, plain, (r2_graph_5(X1,X2,X3,X4,k2_xboole_0(X5,k1_tarski(X3)))\|v2_struct_0(X1)\|~r2_graph_5(X1,X2,X3,X4,X5)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~v7_graph_1(X4,X1)\|~m2_graph_1(X4,X1)\|~l1_graph_1(X1)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_34, plain, (v2_struct_0(X1)\|r2_graph_5(X1,X2,X3,X4,X5)\|~l1_graph_1(X1)\|~v7_graph_1(X4,X1)\|~m2_graph_1(X4,X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~r2_graph_5(X1,X2,X3,X4,k2_xboole_0(X5,k1_tarski(X3)))), inference(evalgc,[status(thm)],[c_0_29])). cnf(c_0_35, negated_conjecture, (r2_graph_5(esk1_0,esk5_0,esk6_0,esk2_0,k2_xboole_0(esk4_0,k1_tarski(esk6_0)))\|r8_graph_5(esk1_0,esk5_0,esk6_0,esk2_0,esk4_0,esk3_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30, c_0_20]), c_0_21]), c_0_22]), c_0_23]), c_0_24]), c_0_25]), c_0_26]), c_0_27])]), c_0_28])])). cnf(c_0_36, negated_conjecture, (r8_graph_5(esk1_0,X1,X2,esk2_0,X3,esk3_0)\|r8_graph_5(esk1_0,esk5_0,esk6_0,esk2_0,esk4_0,esk3_0)\|~r2_graph_5(esk1_0,X1,X2,esk2_0,X3)\|~m1_subset_1(X2,u1_struct_0(esk1_0))\|~m1_subset_1(X1,u1_struct_0(esk1_0))\|~r2_graph_5(esk1_0,esk5_0,esk6_0,esk7_6(esk1_0,X1,X2,esk2_0,X3,esk3_0),k2_xboole_0(esk4_0,k1_tarski(esk6_0)))\|~m2_graph_1(esk7_6(esk1_0,X1,X2,esk2_0,X3,esk3_0),esk1_0)\|~v7_graph_1(esk7_6(esk1_0,X1,X2,esk2_0,X3,esk3_0),esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31, c_0_32]), c_0_23]), c_0_24]), c_0_25]), c_0_26]), c_0_27])]), c_0_28])])). cnf(c_0_37, plain, (v2_struct_0(X1)\|r2_graph_5(X1,X2,X3,X4,k2_xboole_0(X5,k1_tarski(X3)))\|~l1_graph_1(X1)\|~v7_graph_1(X4,X1)\|~m2_graph_1(X4,X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~r2_graph_5(X1,X2,X3,X4,X5)), inference(evalgc,[status(thm)],[c_0_33])). cnf(c_0_38, plain, (r2_graph_5(X1,X2,X3,esk7_6(X1,X2,X3,X4,X5,X6),X5)\|r8_graph_5(X1,X2,X3,X4,X5,X6)\|v2_struct_0(X1)\|~r2_graph_5(X1,X2,X3,X4,X5)\|~v1_relat_1(X6)\|~v1_funct_1(X6)\|~v7_graph_1(X4,X1)\|~m2_graph_1(X4,X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l1_graph_1(X1)), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_39, negated_conjecture, (r2_graph_5(esk1_0,esk5_0,esk6_0,esk2_0,esk4_0)\|r8_graph_5(esk1_0,esk5_0,esk6_0,esk2_0,esk4_0,esk3_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34, c_0_35]), c_0_21]), c_0_22]), c_0_25]), c_0_26]), c_0_27])]), c_0_28])])). cnf(c_0_40, negated_conjecture, (r8_graph_5(esk1_0,esk5_0,esk6_0,esk2_0,esk4_0,esk3_0)\|r8_graph_5(esk1_0,X1,X2,esk2_0,X3,esk3_0)\|~r2_graph_5(esk1_0,X1,X2,esk2_0,X3)\|~m1_subset_1(X2,u1_struct_0(esk1_0))\|~m1_subset_1(X1,u1_struct_0(esk1_0))\|~m2_graph_1(esk7_6(esk1_0,X1,X2,esk2_0,X3,esk3_0),esk1_0)\|~v7_graph_1(esk7_6(esk1_0,X1,X2,esk2_0,X3,esk3_0),esk1_0)\|~r2_graph_5(esk1_0,esk5_0,esk6_0,esk7_6(esk1_0,X1,X2,esk2_0,X3,esk3_0),esk4_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36, c_0_37]), c_0_21]), c_0_22]), c_0_27])]), c_0_28])])). cnf(c_0_41, plain, (v2_struct_0(X1)\|r8_graph_5(X1,X2,X3,X4,X5,X6)\|r2_graph_5(X1,X2,X3,esk7_6(X1,X2,X3,X4,X5,X6),X5)\|~l1_graph_1(X1)\|~v1_relat_1(X6)\|~v1_funct_1(X6)\|~v7_graph_1(X4,X1)\|~m2_graph_1(X4,X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~r2_graph_5(X1,X2,X3,X4,X5)), inference(evalgc,[status(thm)],[c_0_38])). cnf(c_0_42, negated_conjecture, (r2_graph_5(esk1_0,esk5_0,esk6_0,esk2_0,esk4_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30, c_0_39]), c_0_21]), c_0_22]), c_0_23]), c_0_24]), c_0_25]), c_0_26]), c_0_27])]), c_0_28])])). cnf(c_0_43, plain, (m2_graph_1(esk7_6(X1,X2,X3,X4,X5,X6),X1)\|r8_graph_5(X1,X2,X3,X4,X5,X6)\|v2_struct_0(X1)\|~r2_graph_5(X1,X2,X3,X4,X5)\|~v1_relat_1(X6)\|~v1_funct_1(X6)\|~v7_graph_1(X4,X1)\|~m2_graph_1(X4,X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l1_graph_1(X1)), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_44, negated_conjecture, (r8_graph_5(esk1_0,esk5_0,esk6_0,esk2_0,esk4_0,esk3_0)\|~m2_graph_1(esk7_6(esk1_0,esk5_0,esk6_0,esk2_0,esk4_0,esk3_0),esk1_0)\|~v7_graph_1(esk7_6(esk1_0,esk5_0,esk6_0,esk2_0,esk4_0,esk3_0),esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40, c_0_41]), c_0_42]), c_0_21]), c_0_22]), c_0_23]), c_0_24]), c_0_25]), c_0_26]), c_0_27])]), c_0_28])])). cnf(c_0_45, plain, (v2_struct_0(X1)\|r8_graph_5(X1,X2,X3,X4,X5,X6)\|m2_graph_1(esk7_6(X1,X2,X3,X4,X5,X6),X1)\|~l1_graph_1(X1)\|~v1_relat_1(X6)\|~v1_funct_1(X6)\|~v7_graph_1(X4,X1)\|~m2_graph_1(X4,X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~r2_graph_5(X1,X2,X3,X4,X5)), inference(evalgc,[status(thm)],[c_0_43])). cnf(c_0_46, plain, (v7_graph_1(esk7_6(X1,X2,X3,X4,X5,X6),X1)\|r8_graph_5(X1,X2,X3,X4,X5,X6)\|v2_struct_0(X1)\|~r2_graph_5(X1,X2,X3,X4,X5)\|~v1_relat_1(X6)\|~v1_funct_1(X6)\|~v7_graph_1(X4,X1)\|~m2_graph_1(X4,X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l1_graph_1(X1)), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_47, negated_conjecture, (r8_graph_5(esk1_0,esk5_0,esk6_0,esk2_0,esk4_0,esk3_0)\|~v7_graph_1(esk7_6(esk1_0,esk5_0,esk6_0,esk2_0,esk4_0,esk3_0),esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44, c_0_45]), c_0_42]), c_0_21]), c_0_22]), c_0_23]), c_0_24]), c_0_25]), c_0_26]), c_0_27])]), c_0_28])])). cnf(c_0_48, plain, (v2_struct_0(X1)\|r8_graph_5(X1,X2,X3,X4,X5,X6)\|v7_graph_1(esk7_6(X1,X2,X3,X4,X5,X6),X1)\|~l1_graph_1(X1)\|~v1_relat_1(X6)\|~v1_funct_1(X6)\|~v7_graph_1(X4,X1)\|~m2_graph_1(X4,X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~r2_graph_5(X1,X2,X3,X4,X5)), inference(evalgc,[status(thm)],[c_0_46])). cnf(c_0_49, negated_conjecture, (r8_graph_5(esk1_0,esk5_0,esk6_0,esk2_0,esk4_0,esk3_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47, c_0_48]), c_0_42]), c_0_21]), c_0_22]), c_0_23]), c_0_24]), c_0_25]), c_0_26]), c_0_27])]), c_0_28])])). cnf(c_0_50, negated_conjecture, (~r8_graph_5(esk1_0,esk5_0,esk6_0,esk2_0,esk4_0,esk3_0)\|~r8_graph_5(esk1_0,esk5_0,esk6_0,esk2_0,k2_xboole_0(esk4_0,k1_tarski(esk6_0)),esk3_0)), inference(split_conjunct,[status(thm)],[c_0_5])). cnf(c_0_51, negated_conjecture, (r1_xxreal_0(k10_graph_5(esk1_0,esk2_0,esk3_0),k10_graph_5(esk1_0,X1,esk3_0))\|~r2_graph_5(esk1_0,esk5_0,esk6_0,X1,esk4_0)\|~m2_graph_1(X1,esk1_0)\|~v7_graph_1(X1,esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19, c_0_49]), c_0_21]), c_0_22]), c_0_23]), c_0_24]), c_0_25]), c_0_26]), c_0_27])]), c_0_28])])). cnf(c_0_52, plain, (r2_graph_5(X1,X2,X3,esk7_6(X1,X2,X3,X4,k2_xboole_0(X5,k1_tarski(X3)),X6),X5)\|v2_struct_0(X1)\|r8_graph_5(X1,X2,X3,X4,k2_xboole_0(X5,k1_tarski(X3)),X6)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~m2_graph_1(esk7_6(X1,X2,X3,X4,k2_xboole_0(X5,k1_tarski(X3)),X6),X1)\|~v7_graph_1(esk7_6(X1,X2,X3,X4,k2_xboole_0(X5,k1_tarski(X3)),X6),X1)\|~l1_graph_1(X1)\|~r2_graph_5(X1,X2,X3,X4,k2_xboole_0(X5,k1_tarski(X3)))\|~v1_funct_1(X6)\|~v1_relat_1(X6)\|~m2_graph_1(X4,X1)\|~v7_graph_1(X4,X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_34, c_0_41])])). cnf(c_0_53, negated_conjecture, (~r8_graph_5(esk1_0,esk5_0,esk6_0,esk2_0,esk4_0,esk3_0)\|~r8_graph_5(esk1_0,esk5_0,esk6_0,esk2_0,k2_xboole_0(esk4_0,k1_tarski(esk6_0)),esk3_0)), inference(evalgc,[status(thm)],[c_0_50])). cnf(c_0_54, negated_conjecture, (r8_graph_5(esk1_0,X1,X2,esk2_0,X3,esk3_0)\|~r2_graph_5(esk1_0,X1,X2,esk2_0,X3)\|~m1_subset_1(X2,u1_struct_0(esk1_0))\|~m1_subset_1(X1,u1_struct_0(esk1_0))\|~r2_graph_5(esk1_0,esk5_0,esk6_0,esk7_6(esk1_0,X1,X2,esk2_0,X3,esk3_0),esk4_0)\|~m2_graph_1(esk7_6(esk1_0,X1,X2,esk2_0,X3,esk3_0),esk1_0)\|~v7_graph_1(esk7_6(esk1_0,X1,X2,esk2_0,X3,esk3_0),esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31, c_0_51]), c_0_23]), c_0_24]), c_0_25]), c_0_26]), c_0_27])]), c_0_28])])). cnf(c_0_55, plain, (r2_graph_5(X1,X2,X3,esk7_6(X1,X2,X3,X4,k2_xboole_0(X5,k1_tarski(X3)),X6),X5)\|r8_graph_5(X1,X2,X3,X4,k2_xboole_0(X5,k1_tarski(X3)),X6)\|v2_struct_0(X1)\|~r2_graph_5(X1,X2,X3,X4,k2_xboole_0(X5,k1_tarski(X3)))\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~v1_funct_1(X6)\|~v1_relat_1(X6)\|~m2_graph_1(X4,X1)\|~v7_graph_1(X4,X1)\|~l1_graph_1(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_52, c_0_48]), c_0_45])). cnf(c_0_56, negated_conjecture, (~r8_graph_5(esk1_0,esk5_0,esk6_0,esk2_0,k2_xboole_0(esk4_0,k1_tarski(esk6_0)),esk3_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_53, c_0_49])])])). cnf(c_0_57, negated_conjecture, (~r2_graph_5(esk1_0,esk5_0,esk6_0,esk2_0,k2_xboole_0(esk4_0,k1_tarski(esk6_0)))\|~m2_graph_1(esk7_6(esk1_0,esk5_0,esk6_0,esk2_0,k2_xboole_0(esk4_0,k1_tarski(esk6_0)),esk3_0),esk1_0)\|~v7_graph_1(esk7_6(esk1_0,esk5_0,esk6_0,esk2_0,k2_xboole_0(esk4_0,k1_tarski(esk6_0)),esk3_0),esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54, c_0_55]), c_0_21]), c_0_22]), c_0_23]), c_0_24]), c_0_25]), c_0_26]), c_0_27])]), c_0_56]), c_0_28])])). cnf(c_0_58, negated_conjecture, (~r2_graph_5(esk1_0,esk5_0,esk6_0,esk2_0,k2_xboole_0(esk4_0,k1_tarski(esk6_0)))\|~v7_graph_1(esk7_6(esk1_0,esk5_0,esk6_0,esk2_0,k2_xboole_0(esk4_0,k1_tarski(esk6_0)),esk3_0),esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57, c_0_45]), c_0_21]), c_0_22]), c_0_23]), c_0_24]), c_0_25]), c_0_26]), c_0_27])]), c_0_56]), c_0_28])])). cnf(c_0_59, negated_conjecture, (~r2_graph_5(esk1_0,esk5_0,esk6_0,esk2_0,k2_xboole_0(esk4_0,k1_tarski(esk6_0)))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58, c_0_48]), c_0_21]), c_0_22]), c_0_23]), c_0_24]), c_0_25]), c_0_26]), c_0_27])]), c_0_56]), c_0_28])])). cnf(c_0_60, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59, c_0_37]), c_0_42]), c_0_21]), c_0_22]), c_0_25]), c_0_26]), c_0_27])]), c_0_28]), ['proof']). # SZS output end CNFRefutation	reserve x,y,X for set, i,j,k,m,n for Element of NAT, p for FinSequence of X, ii for Integer; reserve G for Graph, pe,qe for FinSequence of the carrier' of G, p,q for oriented Chain of G, W for Function, U,V,e,ee for set, v1,v2,v3,v4 for Vertex of G; theorem Th8: p is_shortestpath_of v1,v2,V,W iff p is_shortestpath_of v1,v2,V \/{v2},W proof set V9=V \/ {v2}; hereby assume A1: p is_shortestpath_of v1,v2,V,W; A2: now let q; assume q is_orientedpath_of v1,v2,V9; then q is_orientedpath_of v1,v2,V by Th7; hence cost(p,W) <= cost(q,W) by A1,GRAPH_5:def 18; end; p is_orientedpath_of v1,v2,V by A1,GRAPH_5:def 18; then p is_orientedpath_of v1,v2,V9 by Th7; hence p is_shortestpath_of v1,v2,V9,W by A2,GRAPH_5:def 18; end; assume A3: p is_shortestpath_of v1,v2,V9,W; A4: now let q; assume q is_orientedpath_of v1,v2,V; then q is_orientedpath_of v1,v2,V9 by Th7; hence cost(p,W) <= cost(q,W) by A3,GRAPH_5:def 18; end; p is_orientedpath_of v1,v2,V9 by A3,GRAPH_5:def 18; then p is_orientedpath_of v1,v2,V by Th7; hence thesis by A4,GRAPH_5:def 18; end;	Convert the following ATP output trace into a readable Mizar proof.
t2_filter_1	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t2_filter_1, conjecture, ![X1]:((~(v2_struct_0(X1))&(v10_lattices(X1)&l3_lattices(X1)))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>(k2_filter_0(X1,X2)=k2_filter_0(X1,X3)=>X2=X3)))), file('/scratch/mptp/predsminms1/t2_filter_1__0', t2_filter_1)). fof(t8_lattices, axiom, ![X1]:((~(v2_struct_0(X1))&(v4_lattices(X1)&l2_lattices(X1)))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>((r1_lattices(X1,X2,X3)&r1_lattices(X1,X3,X2))=>X2=X3)))), file('/scratch/mptp/predsminms1/t2_filter_1__0', t8_lattices)). fof(redefinition_r3_lattices, axiom, ![X1, X2, X3]:(((~(v2_struct_0(X1))&(v6_lattices(X1)&(v8_lattices(X1)&(v9_lattices(X1)&l3_lattices(X1)))))&(m1_subset_1(X2,u1_struct_0(X1))&m1_subset_1(X3,u1_struct_0(X1))))=>(r3_lattices(X1,X2,X3)<=>r1_lattices(X1,X2,X3))), file('/scratch/mptp/predsminms1/t2_filter_1__0', redefinition_r3_lattices)). fof(d2_filter_0, axiom, ![X1]:((~(v2_struct_0(X1))&(v10_lattices(X1)&l3_lattices(X1)))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>k2_filter_0(X1,X2)=a_2_0_filter_0(X1,X2))), file('/scratch/mptp/predsminms1/t2_filter_1__0', d2_filter_0)). fof(dt_l3_lattices, axiom, ![X1]:(l3_lattices(X1)=>(l1_lattices(X1)&l2_lattices(X1))), file('/scratch/mptp/predsminms1/t2_filter_1__0', dt_l3_lattices)). fof(fraenkel_a_2_0_filter_0, axiom, ![X1, X2, X3]:(((~(v2_struct_0(X2))&(v10_lattices(X2)&l3_lattices(X2)))&m1_subset_1(X3,u1_struct_0(X2)))=>(r2_hidden(X1,a_2_0_filter_0(X2,X3))<=>?[X4]:(m1_subset_1(X4,u1_struct_0(X2))&(X1=X4&r3_lattices(X2,X3,X4))))), file('/scratch/mptp/predsminms1/t2_filter_1__0', fraenkel_a_2_0_filter_0)). fof(cc1_lattices, axiom, ![X1]:(l3_lattices(X1)=>((~(v2_struct_0(X1))&v10_lattices(X1))=>(~(v2_struct_0(X1))&(v4_lattices(X1)&(v5_lattices(X1)&(v6_lattices(X1)&(v7_lattices(X1)&(v8_lattices(X1)&v9_lattices(X1))))))))), file('/scratch/mptp/predsminms1/t2_filter_1__0', cc1_lattices)). fof(reflexivity_r3_lattices, axiom, ![X1, X2, X3]:(((~(v2_struct_0(X1))&(v6_lattices(X1)&(v8_lattices(X1)&(v9_lattices(X1)&l3_lattices(X1)))))&(m1_subset_1(X2,u1_struct_0(X1))&m1_subset_1(X3,u1_struct_0(X1))))=>r3_lattices(X1,X2,X2)), file('/scratch/mptp/predsminms1/t2_filter_1__0', reflexivity_r3_lattices)). fof(c_0_8, negated_conjecture, ~(![X1]:((~(v2_struct_0(X1))&(v10_lattices(X1)&l3_lattices(X1)))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>(k2_filter_0(X1,X2)=k2_filter_0(X1,X3)=>X2=X3))))), inference(assume_negation,[status(cth)],[t2_filter_1])). fof(c_0_9, plain, ![X20, X21, X22]:(v2_struct_0(X20)\|(~v4_lattices(X20)\|~l2_lattices(X20))\|(~m1_subset_1(X21,u1_struct_0(X20))\|(~m1_subset_1(X22,u1_struct_0(X20))\|(~r1_lattices(X20,X21,X22)\|~r1_lattices(X20,X22,X21)\|X21=X22)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t8_lattices])])])])). fof(c_0_10, plain, ![X23, X24, X25]:((~r3_lattices(X23,X24,X25)\|r1_lattices(X23,X24,X25)\|(v2_struct_0(X23)\|(~v6_lattices(X23)\|(~v8_lattices(X23)\|(~v9_lattices(X23)\|~l3_lattices(X23))))\|(~m1_subset_1(X24,u1_struct_0(X23))\|~m1_subset_1(X25,u1_struct_0(X23)))))&(~r1_lattices(X23,X24,X25)\|r3_lattices(X23,X24,X25)\|(v2_struct_0(X23)\|(~v6_lattices(X23)\|(~v8_lattices(X23)\|(~v9_lattices(X23)\|~l3_lattices(X23))))\|(~m1_subset_1(X24,u1_struct_0(X23))\|~m1_subset_1(X25,u1_struct_0(X23)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[redefinition_r3_lattices])])])])). fof(c_0_11, negated_conjecture, ((~v2_struct_0(esk1_0)&(v10_lattices(esk1_0)&l3_lattices(esk1_0)))&(m1_subset_1(esk2_0,u1_struct_0(esk1_0))&(m1_subset_1(esk3_0,u1_struct_0(esk1_0))&(k2_filter_0(esk1_0,esk2_0)=k2_filter_0(esk1_0,esk3_0)&esk2_0!=esk3_0)))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_8])])])])). fof(c_0_12, plain, ![X12, X13]:(v2_struct_0(X12)\|(~v10_lattices(X12)\|~l3_lattices(X12))\|(~m1_subset_1(X13,u1_struct_0(X12))\|k2_filter_0(X12,X13)=a_2_0_filter_0(X12,X13))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d2_filter_0])])])])). cnf(c_0_13, plain, (v2_struct_0(X1)\|X2=X3\|~v4_lattices(X1)\|~l2_lattices(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~r1_lattices(X1,X2,X3)\|~r1_lattices(X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_14, plain, (r1_lattices(X1,X2,X3)\|v2_struct_0(X1)\|~r3_lattices(X1,X2,X3)\|~v6_lattices(X1)\|~v8_lattices(X1)\|~v9_lattices(X1)\|~l3_lattices(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_10])). fof(c_0_15, plain, ![X19]:((l1_lattices(X19)\|~l3_lattices(X19))&(l2_lattices(X19)\|~l3_lattices(X19))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_lattices])])])). fof(c_0_16, plain, ![X14, X15, X16, X18]:(((m1_subset_1(esk4_3(X14,X15,X16),u1_struct_0(X15))\|~r2_hidden(X14,a_2_0_filter_0(X15,X16))\|(v2_struct_0(X15)\|(~v10_lattices(X15)\|~l3_lattices(X15))\|~m1_subset_1(X16,u1_struct_0(X15))))&((X14=esk4_3(X14,X15,X16)\|~r2_hidden(X14,a_2_0_filter_0(X15,X16))\|(v2_struct_0(X15)\|(~v10_lattices(X15)\|~l3_lattices(X15))\|~m1_subset_1(X16,u1_struct_0(X15))))&(r3_lattices(X15,X16,esk4_3(X14,X15,X16))\|~r2_hidden(X14,a_2_0_filter_0(X15,X16))\|(v2_struct_0(X15)\|(~v10_lattices(X15)\|~l3_lattices(X15))\|~m1_subset_1(X16,u1_struct_0(X15))))))&(~m1_subset_1(X18,u1_struct_0(X15))\|(X14!=X18\|~r3_lattices(X15,X16,X18))\|r2_hidden(X14,a_2_0_filter_0(X15,X16))\|(v2_struct_0(X15)\|(~v10_lattices(X15)\|~l3_lattices(X15))\|~m1_subset_1(X16,u1_struct_0(X15))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fraenkel_a_2_0_filter_0])])])])])])). cnf(c_0_17, negated_conjecture, (k2_filter_0(esk1_0,esk2_0)=k2_filter_0(esk1_0,esk3_0)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_18, plain, (v2_struct_0(X1)\|k2_filter_0(X1,X2)=a_2_0_filter_0(X1,X2)\|~v10_lattices(X1)\|~l3_lattices(X1)\|~m1_subset_1(X2,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_19, negated_conjecture, (m1_subset_1(esk3_0,u1_struct_0(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_20, negated_conjecture, (l3_lattices(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_21, negated_conjecture, (v10_lattices(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_22, negated_conjecture, (~v2_struct_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_23, plain, (X2=X3\|v2_struct_0(X1)\|~v4_lattices(X1)\|~l2_lattices(X1)\|~r1_lattices(X1,X3,X2)\|~r1_lattices(X1,X2,X3)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_13])). cnf(c_0_24, plain, (v2_struct_0(X1)\|r1_lattices(X1,X2,X3)\|~l3_lattices(X1)\|~v6_lattices(X1)\|~v8_lattices(X1)\|~v9_lattices(X1)\|~r3_lattices(X1,X2,X3)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_14])). cnf(c_0_25, plain, (l2_lattices(X1)\|~l3_lattices(X1)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_26, plain, (r2_hidden(X3,a_2_0_filter_0(X2,X4))\|v2_struct_0(X2)\|~m1_subset_1(X1,u1_struct_0(X2))\|X3!=X1\|~r3_lattices(X2,X4,X1)\|~v10_lattices(X2)\|~l3_lattices(X2)\|~m1_subset_1(X4,u1_struct_0(X2))), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_27, negated_conjecture, (k2_filter_0(esk1_0,esk3_0)=k2_filter_0(esk1_0,esk2_0)), inference(evalgc,[status(thm)],[c_0_17])). cnf(c_0_28, plain, (k2_filter_0(X1,X2)=a_2_0_filter_0(X1,X2)\|v2_struct_0(X1)\|~v10_lattices(X1)\|~l3_lattices(X1)\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_18])). cnf(c_0_29, negated_conjecture, (m1_subset_1(esk3_0,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[c_0_19])). cnf(c_0_30, negated_conjecture, (l3_lattices(esk1_0)), inference(evalgc,[status(thm)],[c_0_20])). cnf(c_0_31, negated_conjecture, (v10_lattices(esk1_0)), inference(evalgc,[status(thm)],[c_0_21])). cnf(c_0_32, negated_conjecture, (~v2_struct_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_22])). cnf(c_0_33, negated_conjecture, (m1_subset_1(esk2_0,u1_struct_0(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_34, plain, (X1=X2\|v2_struct_0(X3)\|~r1_lattices(X3,X1,X2)\|~l2_lattices(X3)\|~v4_lattices(X3)\|~m1_subset_1(X2,u1_struct_0(X3))\|~m1_subset_1(X1,u1_struct_0(X3))\|~r3_lattices(X3,X2,X1)\|~v9_lattices(X3)\|~v8_lattices(X3)\|~v6_lattices(X3)\|~l3_lattices(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_23, c_0_24])])). cnf(c_0_35, plain, (l2_lattices(X1)\|~l3_lattices(X1)), inference(evalgc,[status(thm)],[c_0_25])). cnf(c_0_36, plain, (v2_struct_0(X2)\|r2_hidden(X3,a_2_0_filter_0(X2,X4))\|X1!=X3\|~v10_lattices(X2)\|~l3_lattices(X2)\|~r3_lattices(X2,X4,X1)\|~m1_subset_1(X4,u1_struct_0(X2))\|~m1_subset_1(X1,u1_struct_0(X2))), inference(evalgc,[status(thm)],[c_0_26])). cnf(c_0_37, negated_conjecture, (k2_filter_0(esk1_0,esk2_0)=a_2_0_filter_0(esk1_0,esk3_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27, c_0_28]), c_0_29]), c_0_30]), c_0_31])]), c_0_32])])). cnf(c_0_38, negated_conjecture, (m1_subset_1(esk2_0,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[c_0_33])). cnf(c_0_39, plain, (X1=X2\|v2_struct_0(X3)\|~r1_lattices(X3,X1,X2)\|~r3_lattices(X3,X2,X1)\|~v9_lattices(X3)\|~v8_lattices(X3)\|~v6_lattices(X3)\|~v4_lattices(X3)\|~m1_subset_1(X2,u1_struct_0(X3))\|~m1_subset_1(X1,u1_struct_0(X3))\|~l3_lattices(X3)), inference(csr,[status(thm)],[c_0_34, c_0_35])). cnf(c_0_40, plain, (r3_lattices(X1,X2,esk4_3(X3,X1,X2))\|v2_struct_0(X1)\|~r2_hidden(X3,a_2_0_filter_0(X1,X2))\|~v10_lattices(X1)\|~l3_lattices(X1)\|~m1_subset_1(X2,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_16])). fof(c_0_41, plain, ![X8]:((~v2_struct_0(X8)\|(v2_struct_0(X8)\|~v10_lattices(X8))\|~l3_lattices(X8))&((v4_lattices(X8)\|(v2_struct_0(X8)\|~v10_lattices(X8))\|~l3_lattices(X8))&((v5_lattices(X8)\|(v2_struct_0(X8)\|~v10_lattices(X8))\|~l3_lattices(X8))&((v6_lattices(X8)\|(v2_struct_0(X8)\|~v10_lattices(X8))\|~l3_lattices(X8))&((v7_lattices(X8)\|(v2_struct_0(X8)\|~v10_lattices(X8))\|~l3_lattices(X8))&((v8_lattices(X8)\|(v2_struct_0(X8)\|~v10_lattices(X8))\|~l3_lattices(X8))&(v9_lattices(X8)\|(v2_struct_0(X8)\|~v10_lattices(X8))\|~l3_lattices(X8)))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[cc1_lattices])])])])). cnf(c_0_42, plain, (X1=esk4_3(X1,X2,X3)\|v2_struct_0(X2)\|~r2_hidden(X1,a_2_0_filter_0(X2,X3))\|~v10_lattices(X2)\|~l3_lattices(X2)\|~m1_subset_1(X3,u1_struct_0(X2))), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_43, plain, (r2_hidden(X1,a_2_0_filter_0(X2,X3))\|v2_struct_0(X2)\|~r3_lattices(X2,X3,X1)\|~m1_subset_1(X3,u1_struct_0(X2))\|~m1_subset_1(X1,u1_struct_0(X2))\|~l3_lattices(X2)\|~v10_lattices(X2)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_36])])). cnf(c_0_44, negated_conjecture, (a_2_0_filter_0(esk1_0,esk3_0)=a_2_0_filter_0(esk1_0,esk2_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28, c_0_37]), c_0_38]), c_0_30]), c_0_31])]), c_0_32])])). cnf(c_0_45, plain, (X1=X2\|v2_struct_0(X3)\|~r3_lattices(X3,X2,X1)\|~v9_lattices(X3)\|~v8_lattices(X3)\|~v6_lattices(X3)\|~v4_lattices(X3)\|~m1_subset_1(X2,u1_struct_0(X3))\|~m1_subset_1(X1,u1_struct_0(X3))\|~l3_lattices(X3)\|~r3_lattices(X3,X1,X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_39, c_0_24])])). cnf(c_0_46, plain, (v2_struct_0(X1)\|r3_lattices(X1,X2,esk4_3(X3,X1,X2))\|~v10_lattices(X1)\|~l3_lattices(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~r2_hidden(X3,a_2_0_filter_0(X1,X2))), inference(evalgc,[status(thm)],[c_0_40])). cnf(c_0_47, plain, (m1_subset_1(esk4_3(X1,X2,X3),u1_struct_0(X2))\|v2_struct_0(X2)\|~r2_hidden(X1,a_2_0_filter_0(X2,X3))\|~v10_lattices(X2)\|~l3_lattices(X2)\|~m1_subset_1(X3,u1_struct_0(X2))), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_48, plain, (v4_lattices(X1)\|v2_struct_0(X1)\|~v10_lattices(X1)\|~l3_lattices(X1)), inference(split_conjunct,[status(thm)],[c_0_41])). cnf(c_0_49, plain, (v6_lattices(X1)\|v2_struct_0(X1)\|~v10_lattices(X1)\|~l3_lattices(X1)), inference(split_conjunct,[status(thm)],[c_0_41])). cnf(c_0_50, plain, (v8_lattices(X1)\|v2_struct_0(X1)\|~v10_lattices(X1)\|~l3_lattices(X1)), inference(split_conjunct,[status(thm)],[c_0_41])). cnf(c_0_51, plain, (v9_lattices(X1)\|v2_struct_0(X1)\|~v10_lattices(X1)\|~l3_lattices(X1)), inference(split_conjunct,[status(thm)],[c_0_41])). cnf(c_0_52, plain, (esk4_3(X1,X2,X3)=X1\|v2_struct_0(X2)\|~v10_lattices(X2)\|~l3_lattices(X2)\|~m1_subset_1(X3,u1_struct_0(X2))\|~r2_hidden(X1,a_2_0_filter_0(X2,X3))), inference(evalgc,[status(thm)],[c_0_42])). cnf(c_0_53, negated_conjecture, (r2_hidden(X1,a_2_0_filter_0(esk1_0,esk2_0))\|~r3_lattices(esk1_0,esk3_0,X1)\|~m1_subset_1(X1,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43, c_0_44]), c_0_29]), c_0_30]), c_0_31])]), c_0_32])])). fof(c_0_54, plain, ![X9, X10, X11]:(v2_struct_0(X9)\|(~v6_lattices(X9)\|(~v8_lattices(X9)\|(~v9_lattices(X9)\|~l3_lattices(X9))))\|(~m1_subset_1(X10,u1_struct_0(X9))\|~m1_subset_1(X11,u1_struct_0(X9)))\|r3_lattices(X9,X10,X10)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r3_lattices])])])). cnf(c_0_55, plain, (esk4_3(X1,X2,X3)=X3\|v2_struct_0(X2)\|~r3_lattices(X2,esk4_3(X1,X2,X3),X3)\|~v9_lattices(X2)\|~v8_lattices(X2)\|~v6_lattices(X2)\|~v4_lattices(X2)\|~m1_subset_1(X3,u1_struct_0(X2))\|~m1_subset_1(esk4_3(X1,X2,X3),u1_struct_0(X2))\|~l3_lattices(X2)\|~r2_hidden(X1,a_2_0_filter_0(X2,X3))\|~v10_lattices(X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_45, c_0_46])])). cnf(c_0_56, plain, (v2_struct_0(X2)\|m1_subset_1(esk4_3(X1,X2,X3),u1_struct_0(X2))\|~v10_lattices(X2)\|~l3_lattices(X2)\|~m1_subset_1(X3,u1_struct_0(X2))\|~r2_hidden(X1,a_2_0_filter_0(X2,X3))), inference(evalgc,[status(thm)],[c_0_47])). cnf(c_0_57, plain, (v2_struct_0(X1)\|v4_lattices(X1)\|~v10_lattices(X1)\|~l3_lattices(X1)), inference(evalgc,[status(thm)],[c_0_48])). cnf(c_0_58, plain, (v2_struct_0(X1)\|v6_lattices(X1)\|~v10_lattices(X1)\|~l3_lattices(X1)), inference(evalgc,[status(thm)],[c_0_49])). cnf(c_0_59, plain, (v2_struct_0(X1)\|v8_lattices(X1)\|~v10_lattices(X1)\|~l3_lattices(X1)), inference(evalgc,[status(thm)],[c_0_50])). cnf(c_0_60, plain, (v2_struct_0(X1)\|v9_lattices(X1)\|~v10_lattices(X1)\|~l3_lattices(X1)), inference(evalgc,[status(thm)],[c_0_51])). cnf(c_0_61, negated_conjecture, (esk4_3(X1,esk1_0,esk3_0)=X1\|~r2_hidden(X1,a_2_0_filter_0(esk1_0,esk2_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52, c_0_44]), c_0_29]), c_0_30]), c_0_31])]), c_0_32])])). cnf(c_0_62, negated_conjecture, (esk4_3(X1,esk1_0,esk2_0)=X1\|~r3_lattices(esk1_0,esk3_0,X1)\|~m1_subset_1(X1,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52, c_0_53]), c_0_38]), c_0_30]), c_0_31])]), c_0_32])])). cnf(c_0_63, plain, (v2_struct_0(X1)\|r3_lattices(X1,X2,X2)\|~v6_lattices(X1)\|~v8_lattices(X1)\|~v9_lattices(X1)\|~l3_lattices(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_54])). cnf(c_0_64, plain, (esk4_3(X1,X2,X3)=X3\|v2_struct_0(X2)\|~r2_hidden(X1,a_2_0_filter_0(X2,X3))\|~r3_lattices(X2,esk4_3(X1,X2,X3),X3)\|~m1_subset_1(X3,u1_struct_0(X2))\|~l3_lattices(X2)\|~v10_lattices(X2)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_55, c_0_56]), c_0_57]), c_0_58]), c_0_59]), c_0_60])). cnf(c_0_65, negated_conjecture, (esk4_3(X1,esk1_0,esk3_0)=X1\|~r3_lattices(esk1_0,esk2_0,X1)\|~m1_subset_1(X1,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61, c_0_43]), c_0_38]), c_0_30]), c_0_31])]), c_0_32])])). cnf(c_0_66, negated_conjecture, (r3_lattices(esk1_0,esk2_0,X1)\|~r2_hidden(X1,a_2_0_filter_0(esk1_0,esk2_0))\|~r3_lattices(esk1_0,esk3_0,X1)\|~m1_subset_1(X1,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46, c_0_62]), c_0_38]), c_0_30]), c_0_31])]), c_0_32])])). cnf(c_0_67, plain, (v2_struct_0(X1)\|r3_lattices(X1,X2,X2)\|~l3_lattices(X1)\|~v6_lattices(X1)\|~v8_lattices(X1)\|~v9_lattices(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_63])). cnf(c_0_68, negated_conjecture, (X1=esk3_0\|~r2_hidden(X1,a_2_0_filter_0(esk1_0,esk2_0))\|~r3_lattices(esk1_0,X1,esk3_0)\|~r3_lattices(esk1_0,esk2_0,X1)\|~m1_subset_1(X1,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64, c_0_65]), c_0_44]), c_0_29]), c_0_30]), c_0_31])]), c_0_32])])). cnf(c_0_69, negated_conjecture, (r3_lattices(esk1_0,esk2_0,X1)\|~r3_lattices(esk1_0,esk3_0,X1)\|~m1_subset_1(X1,u1_struct_0(esk1_0))), inference(csr,[status(thm)],[c_0_66, c_0_53])). cnf(c_0_70, negated_conjecture, (r3_lattices(esk1_0,X1,X1)\|~v9_lattices(esk1_0)\|~v8_lattices(esk1_0)\|~v6_lattices(esk1_0)\|~m1_subset_1(X1,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67, c_0_29]), c_0_30])]), c_0_32])])). cnf(c_0_71, negated_conjecture, (esk2_0!=esk3_0), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_72, negated_conjecture, (X1=esk3_0\|~r3_lattices(esk1_0,X1,esk3_0)\|~r3_lattices(esk1_0,esk2_0,X1)\|~m1_subset_1(X1,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68, c_0_43]), c_0_38]), c_0_30]), c_0_31])]), c_0_32])])). cnf(c_0_73, negated_conjecture, (r3_lattices(esk1_0,esk2_0,esk3_0)\|~v9_lattices(esk1_0)\|~v8_lattices(esk1_0)\|~v6_lattices(esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69, c_0_70]), c_0_29])])])). cnf(c_0_74, negated_conjecture, (esk3_0!=esk2_0), inference(evalgc,[status(thm)],[c_0_71])). cnf(c_0_75, negated_conjecture, (~r3_lattices(esk1_0,esk2_0,esk2_0)\|~v9_lattices(esk1_0)\|~v8_lattices(esk1_0)\|~v6_lattices(esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72, c_0_73]), c_0_38])]), c_0_74])])). cnf(c_0_76, negated_conjecture, (~v9_lattices(esk1_0)\|~v8_lattices(esk1_0)\|~v6_lattices(esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75, c_0_70]), c_0_38])])])). cnf(c_0_77, negated_conjecture, (~v8_lattices(esk1_0)\|~v6_lattices(esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76, c_0_60]), c_0_30]), c_0_31])]), c_0_32])])). cnf(c_0_78, negated_conjecture, (~v6_lattices(esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77, c_0_59]), c_0_30]), c_0_31])]), c_0_32])])). cnf(c_0_79, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78, c_0_58]), c_0_30]), c_0_31])]), c_0_32]), ['proof']). # SZS output end CNFRefutation	reserve L,L1,L2 for Lattice, F1,F2 for Filter of L, p,q,r,s for Element of L, p1,q1,r1,s1 for Element of L1, p2,q2,r2,s2 for Element of L2, X,x,x1,x2,y,y1,y2 for set, D,D1,D2 for non empty set, R for Relation, RD for Equivalence_Relation of D, a,b,d for Element of D, a1,b1,c1 for Element of D1, a2,b2,c2 for Element of D2, B for B_Lattice, FB for Filter of B, I for I_Lattice, FI for Filter of I , i,i1,i2,j,j1,j2,k for Element of I, f1,g1 for BinOp of D1, f2,g2 for BinOp of D2; theorem <.p.) = <.q.) implies p = q proof assume A1: <.p.) = <.q.); then q in <.p.); then A2: p [= q by FILTER_0:15; p in <.q.) by A1; then q [= p by FILTER_0:15; hence thesis by A2,LATTICES:8; end;	Convert the following ATP output trace into a readable Mizar proof.
t54_afinsq_2	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t38_afinsq_2, axiom, ![X1]:(~(v1_xboole_0(X1))=>![X2]:((v1_funct_1(X2)&(v1_funct_2(X2,k2_zfmisc_1(X1,X1),X1)&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X1),X1)))))=>![X3]:(m1_subset_1(X3,X1)=>![X4]:(m1_subset_1(X4,X1)=>k6_afinsq_2(X1,k6_afinsq_1(X3,X4),X2)=k5_binop_1(X1,X2,X3,X4))))), file('/scratch/mptp/predsminms1/t54_afinsq_2__0', t38_afinsq_2)). fof(fc2_numbers, axiom, ~(v1_xboole_0(k2_numbers)), file('/scratch/mptp/predsminms1/t54_afinsq_2__0', fc2_numbers)). fof(t1_subset, axiom, ![X1, X2]:(r2_hidden(X1,X2)=>m1_subset_1(X1,X2)), file('/scratch/mptp/predsminms1/t54_afinsq_2__0', t1_subset)). fof(d2_xcmplx_0, axiom, ![X1]:(v1_xcmplx_0(X1)<=>r2_hidden(X1,k2_numbers)), file('/scratch/mptp/predsminms1/t54_afinsq_2__0', d2_xcmplx_0)). fof(t54_afinsq_2, conjecture, ![X1]:(v1_xcmplx_0(X1)=>![X2]:(v1_xcmplx_0(X2)=>k7_afinsq_2(k6_afinsq_1(X1,X2))=k3_binop_2(X1,X2))), file('/scratch/mptp/predsminms1/t54_afinsq_2__0', t54_afinsq_2)). fof(d9_afinsq_2, axiom, ![X1]:((v1_relat_1(X1)&(v1_funct_1(X1)&(v5_ordinal1(X1)&v1_finset_1(X1))))=>k7_afinsq_2(X1)=k6_afinsq_2(k2_numbers,X1,k27_binop_2)), file('/scratch/mptp/predsminms1/t54_afinsq_2__0', d9_afinsq_2)). fof(dt_k27_binop_2, axiom, (v1_funct_1(k27_binop_2)&(v1_funct_2(k27_binop_2,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers)&m1_subset_1(k27_binop_2,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers))))), file('/scratch/mptp/predsminms1/t54_afinsq_2__0', dt_k27_binop_2)). fof(fc11_afinsq_1, axiom, ![X1, X2]:(v5_ordinal1(k6_afinsq_1(X1,X2))&v1_finset_1(k6_afinsq_1(X1,X2))), file('/scratch/mptp/predsminms1/t54_afinsq_2__0', fc11_afinsq_1)). fof(fc9_afinsq_1, axiom, ![X1, X2]:(v1_relat_1(k6_afinsq_1(X1,X2))&v1_funct_1(k6_afinsq_1(X1,X2))), file('/scratch/mptp/predsminms1/t54_afinsq_2__0', fc9_afinsq_1)). fof(redefinition_k5_binop_1, axiom, ![X1, X2, X3, X4]:(((v1_funct_1(X2)&(v1_funct_2(X2,k2_zfmisc_1(X1,X1),X1)&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X1),X1)))))&(m1_subset_1(X3,X1)&m1_subset_1(X4,X1)))=>k5_binop_1(X1,X2,X3,X4)=k1_binop_1(X2,X3,X4)), file('/scratch/mptp/predsminms1/t54_afinsq_2__0', redefinition_k5_binop_1)). fof(d3_binop_2, axiom, ![X1]:((v1_funct_1(X1)&(v1_funct_2(X1,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers)&m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers)))))=>(X1=k27_binop_2<=>![X2]:(v1_xcmplx_0(X2)=>![X3]:(v1_xcmplx_0(X3)=>k1_binop_1(X1,X2,X3)=k3_binop_2(X2,X3))))), file('/scratch/mptp/predsminms1/t54_afinsq_2__0', d3_binop_2)). fof(c_0_11, plain, ![X7, X8, X9, X10]:(v1_xboole_0(X7)\|(~v1_funct_1(X8)\|(~v1_funct_2(X8,k2_zfmisc_1(X7,X7),X7)\|~m1_subset_1(X8,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X7,X7),X7))))\|(~m1_subset_1(X9,X7)\|(~m1_subset_1(X10,X7)\|k6_afinsq_2(X7,k6_afinsq_1(X9,X10),X8)=k5_binop_1(X7,X8,X9,X10))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t38_afinsq_2])])])])). fof(c_0_12, plain, ~v1_xboole_0(k2_numbers), inference(fof_simplification,[status(thm)],[fc2_numbers])). fof(c_0_13, plain, ![X11, X12]:(~r2_hidden(X11,X12)\|m1_subset_1(X11,X12)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])])). fof(c_0_14, plain, ![X13]:((~v1_xcmplx_0(X13)\|r2_hidden(X13,k2_numbers))&(~r2_hidden(X13,k2_numbers)\|v1_xcmplx_0(X13))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d2_xcmplx_0])])). fof(c_0_15, negated_conjecture, ~(![X1]:(v1_xcmplx_0(X1)=>![X2]:(v1_xcmplx_0(X2)=>k7_afinsq_2(k6_afinsq_1(X1,X2))=k3_binop_2(X1,X2)))), inference(assume_negation,[status(cth)],[t54_afinsq_2])). fof(c_0_16, plain, ![X14]:(~v1_relat_1(X14)\|(~v1_funct_1(X14)\|(~v5_ordinal1(X14)\|~v1_finset_1(X14)))\|k7_afinsq_2(X14)=k6_afinsq_2(k2_numbers,X14,k27_binop_2)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d9_afinsq_2])])). cnf(c_0_17, plain, (v1_xboole_0(X1)\|k6_afinsq_2(X1,k6_afinsq_1(X3,X4),X2)=k5_binop_1(X1,X2,X3,X4)\|~v1_funct_1(X2)\|~v1_funct_2(X2,k2_zfmisc_1(X1,X1),X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X1),X1)))\|~m1_subset_1(X3,X1)\|~m1_subset_1(X4,X1)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_18, plain, (m1_subset_1(k27_binop_2,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers)))), inference(split_conjunct,[status(thm)],[dt_k27_binop_2])). cnf(c_0_19, plain, (v1_funct_2(k27_binop_2,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers)), inference(split_conjunct,[status(thm)],[dt_k27_binop_2])). cnf(c_0_20, plain, (v1_funct_1(k27_binop_2)), inference(split_conjunct,[status(thm)],[dt_k27_binop_2])). cnf(c_0_21, plain, (~v1_xboole_0(k2_numbers)), inference(split_conjunct,[status(thm)],[c_0_12])). fof(c_0_22, plain, ![X15, X16]:(v5_ordinal1(k6_afinsq_1(X15,X16))&v1_finset_1(k6_afinsq_1(X15,X16))), inference(variable_rename,[status(thm)],[fc11_afinsq_1])). fof(c_0_23, plain, ![X17, X18]:(v1_relat_1(k6_afinsq_1(X17,X18))&v1_funct_1(k6_afinsq_1(X17,X18))), inference(variable_rename,[status(thm)],[fc9_afinsq_1])). cnf(c_0_24, plain, (m1_subset_1(X1,X2)\|~r2_hidden(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_13])). cnf(c_0_25, plain, (r2_hidden(X1,k2_numbers)\|~v1_xcmplx_0(X1)), inference(split_conjunct,[status(thm)],[c_0_14])). fof(c_0_26, negated_conjecture, (v1_xcmplx_0(esk1_0)&(v1_xcmplx_0(esk2_0)&k7_afinsq_2(k6_afinsq_1(esk1_0,esk2_0))!=k3_binop_2(esk1_0,esk2_0))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])). cnf(c_0_27, plain, (k7_afinsq_2(X1)=k6_afinsq_2(k2_numbers,X1,k27_binop_2)\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v5_ordinal1(X1)\|~v1_finset_1(X1)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_28, plain, (k6_afinsq_2(X1,k6_afinsq_1(X3,X4),X2)=k5_binop_1(X1,X2,X3,X4)\|v1_xboole_0(X1)\|~v1_funct_1(X2)\|~m1_subset_1(X4,X1)\|~m1_subset_1(X3,X1)\|~v1_funct_2(X2,k2_zfmisc_1(X1,X1),X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X1),X1)))), inference(evalgc,[status(thm)],[c_0_17])). cnf(c_0_29, plain, (m1_subset_1(k27_binop_2,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers)))), inference(evalgc,[status(thm)],[c_0_18])). cnf(c_0_30, plain, (v1_funct_2(k27_binop_2,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers)), inference(evalgc,[status(thm)],[c_0_19])). cnf(c_0_31, plain, (v1_funct_1(k27_binop_2)), inference(evalgc,[status(thm)],[c_0_20])). cnf(c_0_32, plain, (~v1_xboole_0(k2_numbers)), inference(evalgc,[status(thm)],[c_0_21])). cnf(c_0_33, plain, (v1_finset_1(k6_afinsq_1(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_34, plain, (v5_ordinal1(k6_afinsq_1(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_35, plain, (v1_relat_1(k6_afinsq_1(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_23])). cnf(c_0_36, plain, (v1_funct_1(k6_afinsq_1(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_23])). cnf(c_0_37, plain, (m1_subset_1(X1,X2)\|~r2_hidden(X1,X2)), inference(evalgc,[status(thm)],[c_0_24])). cnf(c_0_38, plain, (r2_hidden(X1,k2_numbers)\|~v1_xcmplx_0(X1)), inference(evalgc,[status(thm)],[c_0_25])). cnf(c_0_39, negated_conjecture, (v1_xcmplx_0(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_40, negated_conjecture, (k7_afinsq_2(k6_afinsq_1(esk1_0,esk2_0))!=k3_binop_2(esk1_0,esk2_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_41, plain, (k6_afinsq_2(k2_numbers,X1,k27_binop_2)=k7_afinsq_2(X1)\|~v1_funct_1(X1)\|~v1_relat_1(X1)\|~v5_ordinal1(X1)\|~v1_finset_1(X1)), inference(evalgc,[status(thm)],[c_0_27])). cnf(c_0_42, plain, (k6_afinsq_2(k2_numbers,k6_afinsq_1(X1,X2),k27_binop_2)=k5_binop_1(k2_numbers,k27_binop_2,X1,X2)\|~m1_subset_1(X2,k2_numbers)\|~m1_subset_1(X1,k2_numbers)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28, c_0_29]), c_0_30]), c_0_31])]), c_0_32])])). cnf(c_0_43, plain, (v1_finset_1(k6_afinsq_1(X1,X2))), inference(evalgc,[status(thm)],[c_0_33])). cnf(c_0_44, plain, (v5_ordinal1(k6_afinsq_1(X1,X2))), inference(evalgc,[status(thm)],[c_0_34])). cnf(c_0_45, plain, (v1_relat_1(k6_afinsq_1(X1,X2))), inference(evalgc,[status(thm)],[c_0_35])). cnf(c_0_46, plain, (v1_funct_1(k6_afinsq_1(X1,X2))), inference(evalgc,[status(thm)],[c_0_36])). cnf(c_0_47, plain, (m1_subset_1(X1,k2_numbers)\|~v1_xcmplx_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_37, c_0_38])])). cnf(c_0_48, negated_conjecture, (v1_xcmplx_0(esk2_0)), inference(evalgc,[status(thm)],[c_0_39])). cnf(c_0_49, negated_conjecture, (v1_xcmplx_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_26])). fof(c_0_50, plain, ![X19, X20, X21, X22]:(~v1_funct_1(X20)\|(~v1_funct_2(X20,k2_zfmisc_1(X19,X19),X19)\|~m1_subset_1(X20,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X19,X19),X19))))\|(~m1_subset_1(X21,X19)\|~m1_subset_1(X22,X19))\|k5_binop_1(X19,X20,X21,X22)=k1_binop_1(X20,X21,X22)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k5_binop_1])])). cnf(c_0_51, negated_conjecture, (k7_afinsq_2(k6_afinsq_1(esk1_0,esk2_0))!=k3_binop_2(esk1_0,esk2_0)), inference(evalgc,[status(thm)],[c_0_40])). cnf(c_0_52, plain, (k7_afinsq_2(k6_afinsq_1(X1,X2))=k5_binop_1(k2_numbers,k27_binop_2,X1,X2)\|~m1_subset_1(X2,k2_numbers)\|~m1_subset_1(X1,k2_numbers)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41, c_0_42]), c_0_43]), c_0_44]), c_0_45]), c_0_46])])])). cnf(c_0_53, negated_conjecture, (m1_subset_1(esk2_0,k2_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_47, c_0_48])])). cnf(c_0_54, negated_conjecture, (v1_xcmplx_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_49])). cnf(c_0_55, plain, (k5_binop_1(X2,X1,X3,X4)=k1_binop_1(X1,X3,X4)\|~v1_funct_1(X1)\|~v1_funct_2(X1,k2_zfmisc_1(X2,X2),X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X2,X2),X2)))\|~m1_subset_1(X3,X2)\|~m1_subset_1(X4,X2)), inference(split_conjunct,[status(thm)],[c_0_50])). fof(c_0_56, plain, ![X23, X24, X25]:((X23!=k27_binop_2\|(~v1_xcmplx_0(X24)\|(~v1_xcmplx_0(X25)\|k1_binop_1(X23,X24,X25)=k3_binop_2(X24,X25)))\|(~v1_funct_1(X23)\|(~v1_funct_2(X23,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers)\|~m1_subset_1(X23,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers))))))&((v1_xcmplx_0(esk3_1(X23))\|X23=k27_binop_2\|(~v1_funct_1(X23)\|(~v1_funct_2(X23,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers)\|~m1_subset_1(X23,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers))))))&((v1_xcmplx_0(esk4_1(X23))\|X23=k27_binop_2\|(~v1_funct_1(X23)\|(~v1_funct_2(X23,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers)\|~m1_subset_1(X23,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers))))))&(k1_binop_1(X23,esk3_1(X23),esk4_1(X23))!=k3_binop_2(esk3_1(X23),esk4_1(X23))\|X23=k27_binop_2\|(~v1_funct_1(X23)\|(~v1_funct_2(X23,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers)\|~m1_subset_1(X23,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_binop_2])])])])])). cnf(c_0_57, negated_conjecture, (k5_binop_1(k2_numbers,k27_binop_2,esk1_0,esk2_0)!=k3_binop_2(esk1_0,esk2_0)\|~m1_subset_1(esk1_0,k2_numbers)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51, c_0_52]), c_0_53])])])). cnf(c_0_58, negated_conjecture, (m1_subset_1(esk1_0,k2_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_47, c_0_54])])). cnf(c_0_59, plain, (k5_binop_1(X2,X1,X3,X4)=k1_binop_1(X1,X3,X4)\|~v1_funct_1(X1)\|~m1_subset_1(X4,X2)\|~m1_subset_1(X3,X2)\|~v1_funct_2(X1,k2_zfmisc_1(X2,X2),X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X2,X2),X2)))), inference(evalgc,[status(thm)],[c_0_55])). cnf(c_0_60, plain, (k1_binop_1(X1,X2,X3)=k3_binop_2(X2,X3)\|X1!=k27_binop_2\|~v1_xcmplx_0(X2)\|~v1_xcmplx_0(X3)\|~v1_funct_1(X1)\|~v1_funct_2(X1,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers)))), inference(split_conjunct,[status(thm)],[c_0_56])). cnf(c_0_61, negated_conjecture, (k5_binop_1(k2_numbers,k27_binop_2,esk1_0,esk2_0)!=k3_binop_2(esk1_0,esk2_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57, c_0_58])])). cnf(c_0_62, plain, (k5_binop_1(k2_numbers,k27_binop_2,X1,X2)=k1_binop_1(k27_binop_2,X1,X2)\|~m1_subset_1(X2,k2_numbers)\|~m1_subset_1(X1,k2_numbers)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59, c_0_29]), c_0_30]), c_0_31])])])). cnf(c_0_63, plain, (k1_binop_1(X1,X2,X3)=k3_binop_2(X2,X3)\|X1!=k27_binop_2\|~v1_xcmplx_0(X3)\|~v1_xcmplx_0(X2)\|~v1_funct_1(X1)\|~v1_funct_2(X1,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers)))), inference(evalgc,[status(thm)],[c_0_60])). cnf(c_0_64, negated_conjecture, (k1_binop_1(k27_binop_2,esk1_0,esk2_0)!=k3_binop_2(esk1_0,esk2_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61, c_0_62]), c_0_53]), c_0_58])])])). cnf(c_0_65, plain, (k1_binop_1(k27_binop_2,X1,X2)=k3_binop_2(X1,X2)\|~v1_xcmplx_0(X2)\|~v1_xcmplx_0(X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63, c_0_29]), c_0_30]), c_0_31])])])). cnf(c_0_66, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64, c_0_65]), c_0_48]), c_0_54])]), ['proof']). # SZS output end CNFRefutation	reserve i,j,k,n,m for Nat, x,y,z,y1,y2,X,Y,D for set, p,q for XFinSequence; reserve k1,k2 for Nat; reserve D for non empty set, F,G for XFinSequence of D, b for BinOp of D, d,d1,d2 for Element of D; reserve F for XFinSequence, rF,rF1,rF2 for real-valued XFinSequence, r for real number, cF,cF1,cF2 for complex-valued XFinSequence, c,c1,c2 for complex number; theorem Sum <%c1,c2%> = c1 + c2 proof c1 in COMPLEX & c2 in COMPLEX by XCMPLX_0:def 2; then addcomplex "**" <%c1,c2%> = addcomplex.(c1,c2) by Th38 .= c1+c2 by BINOP_2:def 3; hence thesis; end;	Convert the following ATP output trace into a readable Mizar proof.
t1_sheffer1	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t1_sheffer1, conjecture, ![X1]:((~(v2_struct_0(X1))&(v4_lattices(X1)&(v5_lattices(X1)&(v6_robbins1(X1)&l2_robbins1(X1)))))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>k3_robbins1(X1,k5_robbins1(X1,X2,X3))=k6_robbins1(X1,k3_robbins1(X1,X2),k3_robbins1(X1,X3))))), file('/scratch/mptp/predsminms1/t1_sheffer1__0', t1_sheffer1)). fof(t3_robbins1, axiom, ![X1]:((~(v2_struct_0(X1))&(v4_lattices(X1)&(v5_lattices(X1)&(v6_robbins1(X1)&l2_robbins1(X1)))))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>k3_robbins1(X1,k3_robbins1(X1,X2))=X2)), file('/scratch/mptp/predsminms1/t1_sheffer1__0', t3_robbins1)). fof(d4_robbins1, axiom, ![X1]:((~(v2_struct_0(X1))&l2_robbins1(X1))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>k4_robbins1(X1,X2,X3)=k3_robbins1(X1,k1_lattices(X1,k3_robbins1(X1,X2),k3_robbins1(X1,X3)))))), file('/scratch/mptp/predsminms1/t1_sheffer1__0', d4_robbins1)). fof(redefinition_k6_robbins1, axiom, ![X1, X2, X3]:(((~(v2_struct_0(X1))&(v4_lattices(X1)&(v5_lattices(X1)&l2_robbins1(X1))))&(m1_subset_1(X2,u1_struct_0(X1))&m1_subset_1(X3,u1_struct_0(X1))))=>k6_robbins1(X1,X2,X3)=k4_robbins1(X1,X2,X3)), file('/scratch/mptp/predsminms1/t1_sheffer1__0', redefinition_k6_robbins1)). fof(redefinition_k5_robbins1, axiom, ![X1, X2, X3]:(((~(v2_struct_0(X1))&(v4_lattices(X1)&l2_robbins1(X1)))&(m1_subset_1(X2,u1_struct_0(X1))&m1_subset_1(X3,u1_struct_0(X1))))=>k5_robbins1(X1,X2,X3)=k1_lattices(X1,X2,X3)), file('/scratch/mptp/predsminms1/t1_sheffer1__0', redefinition_k5_robbins1)). fof(dt_k3_robbins1, axiom, ![X1, X2]:(((~(v2_struct_0(X1))&l1_robbins1(X1))&m1_subset_1(X2,u1_struct_0(X1)))=>m1_subset_1(k3_robbins1(X1,X2),u1_struct_0(X1))), file('/scratch/mptp/predsminms1/t1_sheffer1__0', dt_k3_robbins1)). fof(dt_l2_robbins1, axiom, ![X1]:(l2_robbins1(X1)=>(l2_lattices(X1)&l1_robbins1(X1))), file('/scratch/mptp/predsminms1/t1_sheffer1__0', dt_l2_robbins1)). fof(c_0_7, negated_conjecture, ~(![X1]:((~(v2_struct_0(X1))&(v4_lattices(X1)&(v5_lattices(X1)&(v6_robbins1(X1)&l2_robbins1(X1)))))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>k3_robbins1(X1,k5_robbins1(X1,X2,X3))=k6_robbins1(X1,k3_robbins1(X1,X2),k3_robbins1(X1,X3)))))), inference(assume_negation,[status(cth)],[t1_sheffer1])). fof(c_0_8, plain, ![X10, X11]:(v2_struct_0(X10)\|(~v4_lattices(X10)\|(~v5_lattices(X10)\|(~v6_robbins1(X10)\|~l2_robbins1(X10))))\|(~m1_subset_1(X11,u1_struct_0(X10))\|k3_robbins1(X10,k3_robbins1(X10,X11))=X11)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t3_robbins1])])])])). fof(c_0_9, negated_conjecture, ((~v2_struct_0(esk1_0)&(v4_lattices(esk1_0)&(v5_lattices(esk1_0)&(v6_robbins1(esk1_0)&l2_robbins1(esk1_0)))))&(m1_subset_1(esk2_0,u1_struct_0(esk1_0))&(m1_subset_1(esk3_0,u1_struct_0(esk1_0))&k3_robbins1(esk1_0,k5_robbins1(esk1_0,esk2_0,esk3_0))!=k6_robbins1(esk1_0,k3_robbins1(esk1_0,esk2_0),k3_robbins1(esk1_0,esk3_0))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_7])])])])). fof(c_0_10, plain, ![X7, X8, X9]:(v2_struct_0(X7)\|~l2_robbins1(X7)\|(~m1_subset_1(X8,u1_struct_0(X7))\|(~m1_subset_1(X9,u1_struct_0(X7))\|k4_robbins1(X7,X8,X9)=k3_robbins1(X7,k1_lattices(X7,k3_robbins1(X7,X8),k3_robbins1(X7,X9)))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d4_robbins1])])])])). cnf(c_0_11, plain, (v2_struct_0(X1)\|k3_robbins1(X1,k3_robbins1(X1,X2))=X2\|~v4_lattices(X1)\|~v5_lattices(X1)\|~v6_robbins1(X1)\|~l2_robbins1(X1)\|~m1_subset_1(X2,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_8])). cnf(c_0_12, negated_conjecture, (v6_robbins1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_13, negated_conjecture, (l2_robbins1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_14, negated_conjecture, (v5_lattices(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_15, negated_conjecture, (v4_lattices(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_16, negated_conjecture, (~v2_struct_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_9])). fof(c_0_17, plain, ![X12, X13, X14]:(v2_struct_0(X12)\|(~v4_lattices(X12)\|(~v5_lattices(X12)\|~l2_robbins1(X12)))\|(~m1_subset_1(X13,u1_struct_0(X12))\|~m1_subset_1(X14,u1_struct_0(X12)))\|k6_robbins1(X12,X13,X14)=k4_robbins1(X12,X13,X14)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[redefinition_k6_robbins1])])])). cnf(c_0_18, plain, (v2_struct_0(X1)\|k4_robbins1(X1,X2,X3)=k3_robbins1(X1,k1_lattices(X1,k3_robbins1(X1,X2),k3_robbins1(X1,X3)))\|~l2_robbins1(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_19, plain, (k3_robbins1(X1,k3_robbins1(X1,X2))=X2\|v2_struct_0(X1)\|~v4_lattices(X1)\|~v5_lattices(X1)\|~v6_robbins1(X1)\|~l2_robbins1(X1)\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_11])). cnf(c_0_20, negated_conjecture, (v6_robbins1(esk1_0)), inference(evalgc,[status(thm)],[c_0_12])). cnf(c_0_21, negated_conjecture, (l2_robbins1(esk1_0)), inference(evalgc,[status(thm)],[c_0_13])). cnf(c_0_22, negated_conjecture, (v5_lattices(esk1_0)), inference(evalgc,[status(thm)],[c_0_14])). cnf(c_0_23, negated_conjecture, (v4_lattices(esk1_0)), inference(evalgc,[status(thm)],[c_0_15])). cnf(c_0_24, negated_conjecture, (~v2_struct_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_16])). cnf(c_0_25, negated_conjecture, (k3_robbins1(esk1_0,k5_robbins1(esk1_0,esk2_0,esk3_0))!=k6_robbins1(esk1_0,k3_robbins1(esk1_0,esk2_0),k3_robbins1(esk1_0,esk3_0))), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_26, plain, (v2_struct_0(X1)\|k6_robbins1(X1,X2,X3)=k4_robbins1(X1,X2,X3)\|~v4_lattices(X1)\|~v5_lattices(X1)\|~l2_robbins1(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_17])). cnf(c_0_27, plain, (k3_robbins1(X1,k1_lattices(X1,k3_robbins1(X1,X2),k3_robbins1(X1,X3)))=k4_robbins1(X1,X2,X3)\|v2_struct_0(X1)\|~l2_robbins1(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_18])). cnf(c_0_28, negated_conjecture, (k3_robbins1(esk1_0,k3_robbins1(esk1_0,X1))=X1\|~m1_subset_1(X1,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19, c_0_20]), c_0_21]), c_0_22]), c_0_23])]), c_0_24])])). cnf(c_0_29, negated_conjecture, (k6_robbins1(esk1_0,k3_robbins1(esk1_0,esk2_0),k3_robbins1(esk1_0,esk3_0))!=k3_robbins1(esk1_0,k5_robbins1(esk1_0,esk2_0,esk3_0))), inference(evalgc,[status(thm)],[c_0_25])). cnf(c_0_30, plain, (k6_robbins1(X1,X2,X3)=k4_robbins1(X1,X2,X3)\|v2_struct_0(X1)\|~v4_lattices(X1)\|~v5_lattices(X1)\|~l2_robbins1(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_26])). cnf(c_0_31, negated_conjecture, (k3_robbins1(esk1_0,k1_lattices(esk1_0,X1,k3_robbins1(esk1_0,X2)))=k4_robbins1(esk1_0,k3_robbins1(esk1_0,X1),X2)\|~m1_subset_1(X2,u1_struct_0(esk1_0))\|~m1_subset_1(k3_robbins1(esk1_0,X1),u1_struct_0(esk1_0))\|~m1_subset_1(X1,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27, c_0_28]), c_0_21])]), c_0_24])])). cnf(c_0_32, negated_conjecture, (m1_subset_1(esk2_0,u1_struct_0(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_33, negated_conjecture, (m1_subset_1(esk3_0,u1_struct_0(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_9])). fof(c_0_34, plain, ![X15, X16, X17]:(v2_struct_0(X15)\|(~v4_lattices(X15)\|~l2_robbins1(X15))\|(~m1_subset_1(X16,u1_struct_0(X15))\|~m1_subset_1(X17,u1_struct_0(X15)))\|k5_robbins1(X15,X16,X17)=k1_lattices(X15,X16,X17)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[redefinition_k5_robbins1])])])). cnf(c_0_35, negated_conjecture, (k4_robbins1(esk1_0,k3_robbins1(esk1_0,esk2_0),k3_robbins1(esk1_0,esk3_0))!=k3_robbins1(esk1_0,k5_robbins1(esk1_0,esk2_0,esk3_0))\|~m1_subset_1(k3_robbins1(esk1_0,esk3_0),u1_struct_0(esk1_0))\|~m1_subset_1(k3_robbins1(esk1_0,esk2_0),u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29, c_0_30]), c_0_21]), c_0_22]), c_0_23])]), c_0_24])])). cnf(c_0_36, negated_conjecture, (k4_robbins1(esk1_0,k3_robbins1(esk1_0,X1),k3_robbins1(esk1_0,X2))=k3_robbins1(esk1_0,k1_lattices(esk1_0,X1,X2))\|~m1_subset_1(k3_robbins1(esk1_0,X1),u1_struct_0(esk1_0))\|~m1_subset_1(k3_robbins1(esk1_0,X2),u1_struct_0(esk1_0))\|~m1_subset_1(X1,u1_struct_0(esk1_0))\|~m1_subset_1(X2,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_31, c_0_28])])). cnf(c_0_37, negated_conjecture, (m1_subset_1(esk2_0,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[c_0_32])). cnf(c_0_38, negated_conjecture, (m1_subset_1(esk3_0,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[c_0_33])). cnf(c_0_39, plain, (v2_struct_0(X1)\|k5_robbins1(X1,X2,X3)=k1_lattices(X1,X2,X3)\|~v4_lattices(X1)\|~l2_robbins1(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_34])). fof(c_0_40, plain, ![X18, X19]:(v2_struct_0(X18)\|~l1_robbins1(X18)\|~m1_subset_1(X19,u1_struct_0(X18))\|m1_subset_1(k3_robbins1(X18,X19),u1_struct_0(X18))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k3_robbins1])])])). cnf(c_0_41, negated_conjecture, (k3_robbins1(esk1_0,k5_robbins1(esk1_0,esk2_0,esk3_0))!=k3_robbins1(esk1_0,k1_lattices(esk1_0,esk2_0,esk3_0))\|~m1_subset_1(k3_robbins1(esk1_0,esk3_0),u1_struct_0(esk1_0))\|~m1_subset_1(k3_robbins1(esk1_0,esk2_0),u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35, c_0_36]), c_0_37]), c_0_38])])])). cnf(c_0_42, plain, (k5_robbins1(X1,X2,X3)=k1_lattices(X1,X2,X3)\|v2_struct_0(X1)\|~v4_lattices(X1)\|~l2_robbins1(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_39])). cnf(c_0_43, plain, (v2_struct_0(X1)\|m1_subset_1(k3_robbins1(X1,X2),u1_struct_0(X1))\|~l1_robbins1(X1)\|~m1_subset_1(X2,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_40])). cnf(c_0_44, negated_conjecture, (~m1_subset_1(k3_robbins1(esk1_0,esk3_0),u1_struct_0(esk1_0))\|~m1_subset_1(k3_robbins1(esk1_0,esk2_0),u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41, c_0_42]), c_0_38]), c_0_37]), c_0_21]), c_0_23])]), c_0_24])])). cnf(c_0_45, plain, (v2_struct_0(X1)\|m1_subset_1(k3_robbins1(X1,X2),u1_struct_0(X1))\|~l1_robbins1(X1)\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_43])). fof(c_0_46, plain, ![X20]:((l2_lattices(X20)\|~l2_robbins1(X20))&(l1_robbins1(X20)\|~l2_robbins1(X20))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l2_robbins1])])])). cnf(c_0_47, negated_conjecture, (~m1_subset_1(k3_robbins1(esk1_0,esk2_0),u1_struct_0(esk1_0))\|~l1_robbins1(esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44, c_0_45]), c_0_38])]), c_0_24])])). cnf(c_0_48, plain, (l1_robbins1(X1)\|~l2_robbins1(X1)), inference(split_conjunct,[status(thm)],[c_0_46])). cnf(c_0_49, negated_conjecture, (~l1_robbins1(esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47, c_0_45]), c_0_37])]), c_0_24])])). cnf(c_0_50, plain, (l1_robbins1(X1)\|~l2_robbins1(X1)), inference(evalgc,[status(thm)],[c_0_48])). cnf(c_0_51, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49, c_0_50]), c_0_21])]), ['proof']). # SZS output end CNFRefutation	theorem Th1: for L being join-commutative join-associative Huntington non empty ComplLLattStr, a, b being Element of L holds (a + b)` = a` ' b` proof let L be join-commutative join-associative Huntington non empty ComplLLattStr; let a, b be Element of L; a + b = (a` ' b`)` by ROBBINS1:17; hence thesis by ROBBINS1:3; end;	Convert the following ATP output trace into a readable Mizar proof.
t46_pzfmisc1	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t46_pzfmisc1, conjecture, ![X1, X2]:((v1_relat_1(X2)&(v4_relat_1(X2,X1)&(v1_funct_1(X2)&v1_partfun1(X2,X1))))=>![X3]:((v1_relat_1(X3)&(v4_relat_1(X3,X1)&(v1_funct_1(X3)&v1_partfun1(X3,X1))))=>~((~(v1_xboole_0(X1))&(r6_pboole(X1,k3_pboole(X1,k1_pzfmisc1(X1,X2),X3),k1_pboole(X1))&r1_pboole(X1,X2,X3)))))), file('/scratch/mptp/predsminms1/t46_pzfmisc1__0', t46_pzfmisc1)). fof(d3_pboole, axiom, ![X1]:k1_pboole(X1)=k7_funcop_1(X1,k1_xboole_0), file('/scratch/mptp/predsminms1/t46_pzfmisc1__0', d3_pboole)). fof(dt_k1_pboole, axiom, ![X1]:(v1_relat_1(k1_pboole(X1))&(v4_relat_1(k1_pboole(X1),X1)&(v1_funct_1(k1_pboole(X1))&v1_partfun1(k1_pboole(X1),X1)))), file('/scratch/mptp/predsminms1/t46_pzfmisc1__0', dt_k1_pboole)). fof(redefinition_r6_pboole, axiom, ![X1, X2, X3]:(((v1_relat_1(X2)&(v4_relat_1(X2,X1)&(v1_funct_1(X2)&v1_partfun1(X2,X1))))&(v1_relat_1(X3)&(v4_relat_1(X3,X1)&(v1_funct_1(X3)&v1_partfun1(X3,X1)))))=>(r6_pboole(X1,X2,X3)<=>X2=X3)), file('/scratch/mptp/predsminms1/t46_pzfmisc1__0', redefinition_r6_pboole)). fof(d1_pzfmisc1, axiom, ![X1, X2]:((v1_relat_1(X2)&(v4_relat_1(X2,X1)&(v1_funct_1(X2)&v1_partfun1(X2,X1))))=>![X3]:((v1_relat_1(X3)&(v4_relat_1(X3,X1)&(v1_funct_1(X3)&v1_partfun1(X3,X1))))=>(X3=k1_pzfmisc1(X1,X2)<=>![X4]:(r2_hidden(X4,X1)=>k1_funct_1(X3,X4)=k1_tarski(k1_funct_1(X2,X4)))))), file('/scratch/mptp/predsminms1/t46_pzfmisc1__0', d1_pzfmisc1)). fof(t48_zfmisc_1, axiom, ![X1, X2]:~((r1_xboole_0(k1_tarski(X1),X2)&r2_hidden(X1,X2))), file('/scratch/mptp/predsminms1/t46_pzfmisc1__0', t48_zfmisc_1)). fof(d7_xboole_0, axiom, ![X1, X2]:(r1_xboole_0(X1,X2)<=>k3_xboole_0(X1,X2)=k1_xboole_0), file('/scratch/mptp/predsminms1/t46_pzfmisc1__0', d7_xboole_0)). fof(dt_k1_pzfmisc1, axiom, ![X1, X2]:((v1_relat_1(X2)&(v4_relat_1(X2,X1)&(v1_funct_1(X2)&v1_partfun1(X2,X1))))=>(v1_relat_1(k1_pzfmisc1(X1,X2))&(v4_relat_1(k1_pzfmisc1(X1,X2),X1)&(v1_funct_1(k1_pzfmisc1(X1,X2))&v1_partfun1(k1_pzfmisc1(X1,X2),X1))))), file('/scratch/mptp/predsminms1/t46_pzfmisc1__0', dt_k1_pzfmisc1)). fof(d5_pboole, axiom, ![X1, X2]:((v1_relat_1(X2)&(v4_relat_1(X2,X1)&(v1_funct_1(X2)&v1_partfun1(X2,X1))))=>![X3]:((v1_relat_1(X3)&(v4_relat_1(X3,X1)&(v1_funct_1(X3)&v1_partfun1(X3,X1))))=>![X4]:((v1_relat_1(X4)&(v4_relat_1(X4,X1)&(v1_funct_1(X4)&v1_partfun1(X4,X1))))=>(X4=k3_pboole(X1,X2,X3)<=>![X5]:(r2_hidden(X5,X1)=>k1_funct_1(X4,X5)=k3_xboole_0(k1_funct_1(X2,X5),k1_funct_1(X3,X5))))))), file('/scratch/mptp/predsminms1/t46_pzfmisc1__0', d5_pboole)). fof(dt_k3_pboole, axiom, ![X1, X2, X3]:(((v1_relat_1(X2)&(v4_relat_1(X2,X1)&(v1_funct_1(X2)&v1_partfun1(X2,X1))))&(v1_relat_1(X3)&(v4_relat_1(X3,X1)&(v1_funct_1(X3)&v1_partfun1(X3,X1)))))=>(v1_relat_1(k3_pboole(X1,X2,X3))&(v4_relat_1(k3_pboole(X1,X2,X3),X1)&(v1_funct_1(k3_pboole(X1,X2,X3))&v1_partfun1(k3_pboole(X1,X2,X3),X1))))), file('/scratch/mptp/predsminms1/t46_pzfmisc1__0', dt_k3_pboole)). fof(t5_pboole, axiom, ![X1, X2]:k1_funct_1(k1_pboole(X2),X1)=k1_xboole_0, file('/scratch/mptp/predsminms1/t46_pzfmisc1__0', t5_pboole)). fof(d1_pboole, axiom, ![X1, X2]:((v1_relat_1(X2)&(v4_relat_1(X2,X1)&(v1_funct_1(X2)&v1_partfun1(X2,X1))))=>![X3]:((v1_relat_1(X3)&(v4_relat_1(X3,X1)&(v1_funct_1(X3)&v1_partfun1(X3,X1))))=>(r1_pboole(X1,X2,X3)<=>![X4]:(r2_hidden(X4,X1)=>r2_hidden(k1_funct_1(X2,X4),k1_funct_1(X3,X4)))))), file('/scratch/mptp/predsminms1/t46_pzfmisc1__0', d1_pboole)). fof(d1_xboole_0, axiom, ![X1]:(v1_xboole_0(X1)<=>![X2]:~(r2_hidden(X2,X1))), file('/scratch/mptp/predsminms1/t46_pzfmisc1__0', d1_xboole_0)). fof(c_0_13, negated_conjecture, ~(![X1, X2]:((v1_relat_1(X2)&(v4_relat_1(X2,X1)&(v1_funct_1(X2)&v1_partfun1(X2,X1))))=>![X3]:((v1_relat_1(X3)&(v4_relat_1(X3,X1)&(v1_funct_1(X3)&v1_partfun1(X3,X1))))=>~((~(v1_xboole_0(X1))&(r6_pboole(X1,k3_pboole(X1,k1_pzfmisc1(X1,X2),X3),k1_pboole(X1))&r1_pboole(X1,X2,X3))))))), inference(assume_negation,[status(cth)],[t46_pzfmisc1])). fof(c_0_14, negated_conjecture, ((v1_relat_1(esk2_0)&(v4_relat_1(esk2_0,esk1_0)&(v1_funct_1(esk2_0)&v1_partfun1(esk2_0,esk1_0))))&((v1_relat_1(esk3_0)&(v4_relat_1(esk3_0,esk1_0)&(v1_funct_1(esk3_0)&v1_partfun1(esk3_0,esk1_0))))&(~v1_xboole_0(esk1_0)&(r6_pboole(esk1_0,k3_pboole(esk1_0,k1_pzfmisc1(esk1_0,esk2_0),esk3_0),k1_pboole(esk1_0))&r1_pboole(esk1_0,esk2_0,esk3_0))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_13])])])])). fof(c_0_15, plain, ![X27]:k1_pboole(X27)=k7_funcop_1(X27,k1_xboole_0), inference(variable_rename,[status(thm)],[d3_pboole])). fof(c_0_16, plain, ![X30]:(v1_relat_1(k1_pboole(X30))&(v4_relat_1(k1_pboole(X30),X30)&(v1_funct_1(k1_pboole(X30))&v1_partfun1(k1_pboole(X30),X30)))), inference(variable_rename,[status(thm)],[dt_k1_pboole])). fof(c_0_17, plain, ![X42, X43, X44]:((~r6_pboole(X42,X43,X44)\|X43=X44\|(~v1_relat_1(X43)\|(~v4_relat_1(X43,X42)\|(~v1_funct_1(X43)\|~v1_partfun1(X43,X42)))\|(~v1_relat_1(X44)\|(~v4_relat_1(X44,X42)\|(~v1_funct_1(X44)\|~v1_partfun1(X44,X42))))))&(X43!=X44\|r6_pboole(X42,X43,X44)\|(~v1_relat_1(X43)\|(~v4_relat_1(X43,X42)\|(~v1_funct_1(X43)\|~v1_partfun1(X43,X42)))\|(~v1_relat_1(X44)\|(~v4_relat_1(X44,X42)\|(~v1_funct_1(X44)\|~v1_partfun1(X44,X42))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_r6_pboole])])])). cnf(c_0_18, negated_conjecture, (r6_pboole(esk1_0,k3_pboole(esk1_0,k1_pzfmisc1(esk1_0,esk2_0),esk3_0),k1_pboole(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_14])). cnf(c_0_19, plain, (k1_pboole(X1)=k7_funcop_1(X1,k1_xboole_0)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_20, plain, (v1_funct_1(k1_pboole(X1))), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_21, plain, (v4_relat_1(k1_pboole(X1),X1)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_22, plain, (v1_relat_1(k1_pboole(X1))), inference(split_conjunct,[status(thm)],[c_0_16])). fof(c_0_23, plain, ![X22, X23, X24, X25]:((X24!=k1_pzfmisc1(X22,X23)\|(~r2_hidden(X25,X22)\|k1_funct_1(X24,X25)=k1_tarski(k1_funct_1(X23,X25)))\|(~v1_relat_1(X24)\|(~v4_relat_1(X24,X22)\|(~v1_funct_1(X24)\|~v1_partfun1(X24,X22))))\|(~v1_relat_1(X23)\|(~v4_relat_1(X23,X22)\|(~v1_funct_1(X23)\|~v1_partfun1(X23,X22)))))&((r2_hidden(esk6_3(X22,X23,X24),X22)\|X24=k1_pzfmisc1(X22,X23)\|(~v1_relat_1(X24)\|(~v4_relat_1(X24,X22)\|(~v1_funct_1(X24)\|~v1_partfun1(X24,X22))))\|(~v1_relat_1(X23)\|(~v4_relat_1(X23,X22)\|(~v1_funct_1(X23)\|~v1_partfun1(X23,X22)))))&(k1_funct_1(X24,esk6_3(X22,X23,X24))!=k1_tarski(k1_funct_1(X23,esk6_3(X22,X23,X24)))\|X24=k1_pzfmisc1(X22,X23)\|(~v1_relat_1(X24)\|(~v4_relat_1(X24,X22)\|(~v1_funct_1(X24)\|~v1_partfun1(X24,X22))))\|(~v1_relat_1(X23)\|(~v4_relat_1(X23,X22)\|(~v1_funct_1(X23)\|~v1_partfun1(X23,X22))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_pzfmisc1])])])])])). cnf(c_0_24, plain, (X2=X3\|~r6_pboole(X1,X2,X3)\|~v1_relat_1(X2)\|~v4_relat_1(X2,X1)\|~v1_funct_1(X2)\|~v1_partfun1(X2,X1)\|~v1_relat_1(X3)\|~v4_relat_1(X3,X1)\|~v1_funct_1(X3)\|~v1_partfun1(X3,X1)), inference(split_conjunct,[status(thm)],[c_0_17])). cnf(c_0_25, negated_conjecture, (r6_pboole(esk1_0,k3_pboole(esk1_0,k1_pzfmisc1(esk1_0,esk2_0),esk3_0),k7_funcop_1(esk1_0,k1_xboole_0))), inference(rw,[status(thm)],[c_0_18, c_0_19])). cnf(c_0_26, plain, (v1_funct_1(k7_funcop_1(X1,k1_xboole_0))), inference(rw,[status(thm)],[c_0_20, c_0_19])). cnf(c_0_27, plain, (v4_relat_1(k7_funcop_1(X1,k1_xboole_0),X1)), inference(rw,[status(thm)],[c_0_21, c_0_19])). cnf(c_0_28, plain, (v1_relat_1(k7_funcop_1(X1,k1_xboole_0))), inference(rw,[status(thm)],[c_0_22, c_0_19])). cnf(c_0_29, plain, (v1_partfun1(k1_pboole(X1),X1)), inference(split_conjunct,[status(thm)],[c_0_16])). fof(c_0_30, plain, ![X18, X19]:(~r1_xboole_0(k1_tarski(X18),X19)\|~r2_hidden(X18,X19)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t48_zfmisc_1])])). fof(c_0_31, plain, ![X37, X38]:((~r1_xboole_0(X37,X38)\|k3_xboole_0(X37,X38)=k1_xboole_0)&(k3_xboole_0(X37,X38)!=k1_xboole_0\|r1_xboole_0(X37,X38))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_xboole_0])])). cnf(c_0_32, plain, (k1_funct_1(X1,X4)=k1_tarski(k1_funct_1(X3,X4))\|X1!=k1_pzfmisc1(X2,X3)\|~r2_hidden(X4,X2)\|~v1_relat_1(X1)\|~v4_relat_1(X1,X2)\|~v1_funct_1(X1)\|~v1_partfun1(X1,X2)\|~v1_relat_1(X3)\|~v4_relat_1(X3,X2)\|~v1_funct_1(X3)\|~v1_partfun1(X3,X2)), inference(split_conjunct,[status(thm)],[c_0_23])). fof(c_0_33, plain, ![X20, X21]:((v1_relat_1(k1_pzfmisc1(X20,X21))\|(~v1_relat_1(X21)\|(~v4_relat_1(X21,X20)\|(~v1_funct_1(X21)\|~v1_partfun1(X21,X20)))))&((v4_relat_1(k1_pzfmisc1(X20,X21),X20)\|(~v1_relat_1(X21)\|(~v4_relat_1(X21,X20)\|(~v1_funct_1(X21)\|~v1_partfun1(X21,X20)))))&((v1_funct_1(k1_pzfmisc1(X20,X21))\|(~v1_relat_1(X21)\|(~v4_relat_1(X21,X20)\|(~v1_funct_1(X21)\|~v1_partfun1(X21,X20)))))&(v1_partfun1(k1_pzfmisc1(X20,X21),X20)\|(~v1_relat_1(X21)\|(~v4_relat_1(X21,X20)\|(~v1_funct_1(X21)\|~v1_partfun1(X21,X20)))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_pzfmisc1])])])). fof(c_0_34, plain, ![X31, X32, X33, X34, X35]:((X34!=k3_pboole(X31,X32,X33)\|(~r2_hidden(X35,X31)\|k1_funct_1(X34,X35)=k3_xboole_0(k1_funct_1(X32,X35),k1_funct_1(X33,X35)))\|(~v1_relat_1(X34)\|(~v4_relat_1(X34,X31)\|(~v1_funct_1(X34)\|~v1_partfun1(X34,X31))))\|(~v1_relat_1(X33)\|(~v4_relat_1(X33,X31)\|(~v1_funct_1(X33)\|~v1_partfun1(X33,X31))))\|(~v1_relat_1(X32)\|(~v4_relat_1(X32,X31)\|(~v1_funct_1(X32)\|~v1_partfun1(X32,X31)))))&((r2_hidden(esk7_4(X31,X32,X33,X34),X31)\|X34=k3_pboole(X31,X32,X33)\|(~v1_relat_1(X34)\|(~v4_relat_1(X34,X31)\|(~v1_funct_1(X34)\|~v1_partfun1(X34,X31))))\|(~v1_relat_1(X33)\|(~v4_relat_1(X33,X31)\|(~v1_funct_1(X33)\|~v1_partfun1(X33,X31))))\|(~v1_relat_1(X32)\|(~v4_relat_1(X32,X31)\|(~v1_funct_1(X32)\|~v1_partfun1(X32,X31)))))&(k1_funct_1(X34,esk7_4(X31,X32,X33,X34))!=k3_xboole_0(k1_funct_1(X32,esk7_4(X31,X32,X33,X34)),k1_funct_1(X33,esk7_4(X31,X32,X33,X34)))\|X34=k3_pboole(X31,X32,X33)\|(~v1_relat_1(X34)\|(~v4_relat_1(X34,X31)\|(~v1_funct_1(X34)\|~v1_partfun1(X34,X31))))\|(~v1_relat_1(X33)\|(~v4_relat_1(X33,X31)\|(~v1_funct_1(X33)\|~v1_partfun1(X33,X31))))\|(~v1_relat_1(X32)\|(~v4_relat_1(X32,X31)\|(~v1_funct_1(X32)\|~v1_partfun1(X32,X31))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_pboole])])])])])). cnf(c_0_35, plain, (X2=X3\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v4_relat_1(X3,X1)\|~v4_relat_1(X2,X1)\|~v1_partfun1(X3,X1)\|~v1_partfun1(X2,X1)\|~r6_pboole(X1,X2,X3)), inference(evalgc,[status(thm)],[c_0_24])). cnf(c_0_36, negated_conjecture, (r6_pboole(esk1_0,k3_pboole(esk1_0,k1_pzfmisc1(esk1_0,esk2_0),esk3_0),k7_funcop_1(esk1_0,k1_xboole_0))), inference(evalgc,[status(thm)],[c_0_25])). cnf(c_0_37, plain, (v1_funct_1(k7_funcop_1(X1,k1_xboole_0))), inference(evalgc,[status(thm)],[c_0_26])). cnf(c_0_38, plain, (v4_relat_1(k7_funcop_1(X1,k1_xboole_0),X1)), inference(evalgc,[status(thm)],[c_0_27])). cnf(c_0_39, plain, (v1_relat_1(k7_funcop_1(X1,k1_xboole_0))), inference(evalgc,[status(thm)],[c_0_28])). cnf(c_0_40, plain, (v1_partfun1(k7_funcop_1(X1,k1_xboole_0),X1)), inference(rw,[status(thm)],[c_0_29, c_0_19])). fof(c_0_41, plain, ![X39, X40, X41]:((v1_relat_1(k3_pboole(X39,X40,X41))\|(~v1_relat_1(X40)\|(~v4_relat_1(X40,X39)\|(~v1_funct_1(X40)\|~v1_partfun1(X40,X39)))\|(~v1_relat_1(X41)\|(~v4_relat_1(X41,X39)\|(~v1_funct_1(X41)\|~v1_partfun1(X41,X39))))))&((v4_relat_1(k3_pboole(X39,X40,X41),X39)\|(~v1_relat_1(X40)\|(~v4_relat_1(X40,X39)\|(~v1_funct_1(X40)\|~v1_partfun1(X40,X39)))\|(~v1_relat_1(X41)\|(~v4_relat_1(X41,X39)\|(~v1_funct_1(X41)\|~v1_partfun1(X41,X39))))))&((v1_funct_1(k3_pboole(X39,X40,X41))\|(~v1_relat_1(X40)\|(~v4_relat_1(X40,X39)\|(~v1_funct_1(X40)\|~v1_partfun1(X40,X39)))\|(~v1_relat_1(X41)\|(~v4_relat_1(X41,X39)\|(~v1_funct_1(X41)\|~v1_partfun1(X41,X39))))))&(v1_partfun1(k3_pboole(X39,X40,X41),X39)\|(~v1_relat_1(X40)\|(~v4_relat_1(X40,X39)\|(~v1_funct_1(X40)\|~v1_partfun1(X40,X39)))\|(~v1_relat_1(X41)\|(~v4_relat_1(X41,X39)\|(~v1_funct_1(X41)\|~v1_partfun1(X41,X39))))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k3_pboole])])])). cnf(c_0_42, plain, (~r1_xboole_0(k1_tarski(X1),X2)\|~r2_hidden(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_30])). cnf(c_0_43, plain, (r1_xboole_0(X1,X2)\|k3_xboole_0(X1,X2)!=k1_xboole_0), inference(split_conjunct,[status(thm)],[c_0_31])). cnf(c_0_44, plain, (k1_funct_1(X1,X4)=k1_tarski(k1_funct_1(X3,X4))\|X1!=k1_pzfmisc1(X2,X3)\|~v1_relat_1(X3)\|~v1_relat_1(X1)\|~v1_funct_1(X3)\|~v1_funct_1(X1)\|~v4_relat_1(X3,X2)\|~v4_relat_1(X1,X2)\|~v1_partfun1(X3,X2)\|~v1_partfun1(X1,X2)\|~r2_hidden(X4,X2)), inference(evalgc,[status(thm)],[c_0_32])). cnf(c_0_45, plain, (v1_relat_1(k1_pzfmisc1(X1,X2))\|~v1_relat_1(X2)\|~v4_relat_1(X2,X1)\|~v1_funct_1(X2)\|~v1_partfun1(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_33])). cnf(c_0_46, plain, (v4_relat_1(k1_pzfmisc1(X1,X2),X1)\|~v1_relat_1(X2)\|~v4_relat_1(X2,X1)\|~v1_funct_1(X2)\|~v1_partfun1(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_33])). cnf(c_0_47, plain, (v1_funct_1(k1_pzfmisc1(X1,X2))\|~v1_relat_1(X2)\|~v4_relat_1(X2,X1)\|~v1_funct_1(X2)\|~v1_partfun1(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_33])). cnf(c_0_48, plain, (v1_partfun1(k1_pzfmisc1(X1,X2),X1)\|~v1_relat_1(X2)\|~v4_relat_1(X2,X1)\|~v1_funct_1(X2)\|~v1_partfun1(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_33])). cnf(c_0_49, plain, (k1_funct_1(X1,X5)=k3_xboole_0(k1_funct_1(X3,X5),k1_funct_1(X4,X5))\|X1!=k3_pboole(X2,X3,X4)\|~r2_hidden(X5,X2)\|~v1_relat_1(X1)\|~v4_relat_1(X1,X2)\|~v1_funct_1(X1)\|~v1_partfun1(X1,X2)\|~v1_relat_1(X4)\|~v4_relat_1(X4,X2)\|~v1_funct_1(X4)\|~v1_partfun1(X4,X2)\|~v1_relat_1(X3)\|~v4_relat_1(X3,X2)\|~v1_funct_1(X3)\|~v1_partfun1(X3,X2)), inference(split_conjunct,[status(thm)],[c_0_34])). cnf(c_0_50, negated_conjecture, (k3_pboole(esk1_0,k1_pzfmisc1(esk1_0,esk2_0),esk3_0)=k7_funcop_1(esk1_0,k1_xboole_0)\|~v1_partfun1(k7_funcop_1(esk1_0,k1_xboole_0),esk1_0)\|~v1_partfun1(k3_pboole(esk1_0,k1_pzfmisc1(esk1_0,esk2_0),esk3_0),esk1_0)\|~v1_funct_1(k3_pboole(esk1_0,k1_pzfmisc1(esk1_0,esk2_0),esk3_0))\|~v4_relat_1(k3_pboole(esk1_0,k1_pzfmisc1(esk1_0,esk2_0),esk3_0),esk1_0)\|~v1_relat_1(k3_pboole(esk1_0,k1_pzfmisc1(esk1_0,esk2_0),esk3_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35, c_0_36]), c_0_37]), c_0_38]), c_0_39])])])). cnf(c_0_51, plain, (v1_partfun1(k7_funcop_1(X1,k1_xboole_0),X1)), inference(evalgc,[status(thm)],[c_0_40])). cnf(c_0_52, plain, (v1_partfun1(k3_pboole(X1,X2,X3),X1)\|~v1_relat_1(X2)\|~v4_relat_1(X2,X1)\|~v1_funct_1(X2)\|~v1_partfun1(X2,X1)\|~v1_relat_1(X3)\|~v4_relat_1(X3,X1)\|~v1_funct_1(X3)\|~v1_partfun1(X3,X1)), inference(split_conjunct,[status(thm)],[c_0_41])). cnf(c_0_53, negated_conjecture, (v1_partfun1(esk3_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_14])). cnf(c_0_54, negated_conjecture, (v1_funct_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_14])). cnf(c_0_55, negated_conjecture, (v4_relat_1(esk3_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_14])). cnf(c_0_56, negated_conjecture, (v1_relat_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_14])). cnf(c_0_57, plain, (~r2_hidden(X1,X2)\|~r1_xboole_0(k1_tarski(X1),X2)), inference(evalgc,[status(thm)],[c_0_42])). cnf(c_0_58, plain, (r1_xboole_0(X1,X2)\|k3_xboole_0(X1,X2)!=k1_xboole_0), inference(evalgc,[status(thm)],[c_0_43])). cnf(c_0_59, plain, (k1_funct_1(k1_pzfmisc1(X1,X2),X3)=k1_tarski(k1_funct_1(X2,X3))\|~r2_hidden(X3,X1)\|~v1_partfun1(X2,X1)\|~v1_partfun1(k1_pzfmisc1(X1,X2),X1)\|~v1_funct_1(X2)\|~v1_funct_1(k1_pzfmisc1(X1,X2))\|~v4_relat_1(X2,X1)\|~v4_relat_1(k1_pzfmisc1(X1,X2),X1)\|~v1_relat_1(X2)\|~v1_relat_1(k1_pzfmisc1(X1,X2))), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_44])])). cnf(c_0_60, plain, (v1_relat_1(k1_pzfmisc1(X1,X2))\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v4_relat_1(X2,X1)\|~v1_partfun1(X2,X1)), inference(evalgc,[status(thm)],[c_0_45])). cnf(c_0_61, plain, (v4_relat_1(k1_pzfmisc1(X1,X2),X1)\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v4_relat_1(X2,X1)\|~v1_partfun1(X2,X1)), inference(evalgc,[status(thm)],[c_0_46])). cnf(c_0_62, plain, (v1_funct_1(k1_pzfmisc1(X1,X2))\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v4_relat_1(X2,X1)\|~v1_partfun1(X2,X1)), inference(evalgc,[status(thm)],[c_0_47])). cnf(c_0_63, plain, (v1_partfun1(k1_pzfmisc1(X1,X2),X1)\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v4_relat_1(X2,X1)\|~v1_partfun1(X2,X1)), inference(evalgc,[status(thm)],[c_0_48])). cnf(c_0_64, plain, (k1_funct_1(X1,X5)=k3_xboole_0(k1_funct_1(X3,X5),k1_funct_1(X4,X5))\|X1!=k3_pboole(X2,X3,X4)\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~v1_relat_1(X1)\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v1_funct_1(X1)\|~v4_relat_1(X4,X2)\|~v4_relat_1(X3,X2)\|~v4_relat_1(X1,X2)\|~v1_partfun1(X4,X2)\|~v1_partfun1(X3,X2)\|~v1_partfun1(X1,X2)\|~r2_hidden(X5,X2)), inference(evalgc,[status(thm)],[c_0_49])). cnf(c_0_65, plain, (v1_relat_1(k3_pboole(X1,X2,X3))\|~v1_relat_1(X2)\|~v4_relat_1(X2,X1)\|~v1_funct_1(X2)\|~v1_partfun1(X2,X1)\|~v1_relat_1(X3)\|~v4_relat_1(X3,X1)\|~v1_funct_1(X3)\|~v1_partfun1(X3,X1)), inference(split_conjunct,[status(thm)],[c_0_41])). cnf(c_0_66, plain, (v4_relat_1(k3_pboole(X1,X2,X3),X1)\|~v1_relat_1(X2)\|~v4_relat_1(X2,X1)\|~v1_funct_1(X2)\|~v1_partfun1(X2,X1)\|~v1_relat_1(X3)\|~v4_relat_1(X3,X1)\|~v1_funct_1(X3)\|~v1_partfun1(X3,X1)), inference(split_conjunct,[status(thm)],[c_0_41])). cnf(c_0_67, plain, (v1_funct_1(k3_pboole(X1,X2,X3))\|~v1_relat_1(X2)\|~v4_relat_1(X2,X1)\|~v1_funct_1(X2)\|~v1_partfun1(X2,X1)\|~v1_relat_1(X3)\|~v4_relat_1(X3,X1)\|~v1_funct_1(X3)\|~v1_partfun1(X3,X1)), inference(split_conjunct,[status(thm)],[c_0_41])). cnf(c_0_68, negated_conjecture, (k3_pboole(esk1_0,k1_pzfmisc1(esk1_0,esk2_0),esk3_0)=k7_funcop_1(esk1_0,k1_xboole_0)\|~v1_partfun1(k3_pboole(esk1_0,k1_pzfmisc1(esk1_0,esk2_0),esk3_0),esk1_0)\|~v1_funct_1(k3_pboole(esk1_0,k1_pzfmisc1(esk1_0,esk2_0),esk3_0))\|~v4_relat_1(k3_pboole(esk1_0,k1_pzfmisc1(esk1_0,esk2_0),esk3_0),esk1_0)\|~v1_relat_1(k3_pboole(esk1_0,k1_pzfmisc1(esk1_0,esk2_0),esk3_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_50, c_0_51])])). cnf(c_0_69, plain, (v1_partfun1(k3_pboole(X1,X2,X3),X1)\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v4_relat_1(X3,X1)\|~v4_relat_1(X2,X1)\|~v1_partfun1(X3,X1)\|~v1_partfun1(X2,X1)), inference(evalgc,[status(thm)],[c_0_52])). cnf(c_0_70, negated_conjecture, (v1_partfun1(esk3_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_53])). cnf(c_0_71, negated_conjecture, (v1_funct_1(esk3_0)), inference(evalgc,[status(thm)],[c_0_54])). cnf(c_0_72, negated_conjecture, (v4_relat_1(esk3_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_55])). cnf(c_0_73, negated_conjecture, (v1_relat_1(esk3_0)), inference(evalgc,[status(thm)],[c_0_56])). cnf(c_0_74, plain, (~r2_hidden(X1,X2)\|k3_xboole_0(k1_tarski(X1),X2)!=k1_xboole_0), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_57, c_0_58])])). cnf(c_0_75, plain, (k1_funct_1(k1_pzfmisc1(X1,X2),X3)=k1_tarski(k1_funct_1(X2,X3))\|~r2_hidden(X3,X1)\|~v1_partfun1(X2,X1)\|~v1_funct_1(X2)\|~v4_relat_1(X2,X1)\|~v1_relat_1(X2)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_59, c_0_60]), c_0_61]), c_0_62]), c_0_63])). cnf(c_0_76, plain, (k1_funct_1(k3_pboole(X1,X2,X3),X4)=k3_xboole_0(k1_funct_1(X2,X4),k1_funct_1(X3,X4))\|~r2_hidden(X4,X1)\|~v1_partfun1(X3,X1)\|~v1_partfun1(X2,X1)\|~v1_partfun1(k3_pboole(X1,X2,X3),X1)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v1_funct_1(k3_pboole(X1,X2,X3))\|~v4_relat_1(X3,X1)\|~v4_relat_1(X2,X1)\|~v4_relat_1(k3_pboole(X1,X2,X3),X1)\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_relat_1(k3_pboole(X1,X2,X3))), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_64])])). cnf(c_0_77, plain, (v1_relat_1(k3_pboole(X1,X2,X3))\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v4_relat_1(X3,X1)\|~v4_relat_1(X2,X1)\|~v1_partfun1(X3,X1)\|~v1_partfun1(X2,X1)), inference(evalgc,[status(thm)],[c_0_65])). cnf(c_0_78, plain, (v4_relat_1(k3_pboole(X1,X2,X3),X1)\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v4_relat_1(X3,X1)\|~v4_relat_1(X2,X1)\|~v1_partfun1(X3,X1)\|~v1_partfun1(X2,X1)), inference(evalgc,[status(thm)],[c_0_66])). cnf(c_0_79, plain, (v1_funct_1(k3_pboole(X1,X2,X3))\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v4_relat_1(X3,X1)\|~v4_relat_1(X2,X1)\|~v1_partfun1(X3,X1)\|~v1_partfun1(X2,X1)), inference(evalgc,[status(thm)],[c_0_67])). cnf(c_0_80, negated_conjecture, (k3_pboole(esk1_0,k1_pzfmisc1(esk1_0,esk2_0),esk3_0)=k7_funcop_1(esk1_0,k1_xboole_0)\|~v1_funct_1(k3_pboole(esk1_0,k1_pzfmisc1(esk1_0,esk2_0),esk3_0))\|~v4_relat_1(k3_pboole(esk1_0,k1_pzfmisc1(esk1_0,esk2_0),esk3_0),esk1_0)\|~v1_relat_1(k3_pboole(esk1_0,k1_pzfmisc1(esk1_0,esk2_0),esk3_0))\|~v1_partfun1(k1_pzfmisc1(esk1_0,esk2_0),esk1_0)\|~v1_funct_1(k1_pzfmisc1(esk1_0,esk2_0))\|~v4_relat_1(k1_pzfmisc1(esk1_0,esk2_0),esk1_0)\|~v1_relat_1(k1_pzfmisc1(esk1_0,esk2_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68, c_0_69]), c_0_70]), c_0_71]), c_0_72]), c_0_73])])])). fof(c_0_81, plain, ![X28, X29]:k1_funct_1(k1_pboole(X29),X28)=k1_xboole_0, inference(variable_rename,[status(thm)],[t5_pboole])). cnf(c_0_82, plain, (k3_xboole_0(k1_funct_1(k1_pzfmisc1(X4,X1),X2),X3)!=k1_xboole_0\|~r2_hidden(k1_funct_1(X1,X2),X3)\|~r2_hidden(X2,X4)\|~v1_partfun1(X1,X4)\|~v1_funct_1(X1)\|~v4_relat_1(X1,X4)\|~v1_relat_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_74, c_0_75])])). cnf(c_0_83, plain, (k1_funct_1(k3_pboole(X1,X2,X3),X4)=k3_xboole_0(k1_funct_1(X2,X4),k1_funct_1(X3,X4))\|~r2_hidden(X4,X1)\|~v1_partfun1(X3,X1)\|~v1_partfun1(X2,X1)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v4_relat_1(X3,X1)\|~v4_relat_1(X2,X1)\|~v1_relat_1(X3)\|~v1_relat_1(X2)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_76, c_0_77]), c_0_78]), c_0_79]), c_0_69])). cnf(c_0_84, negated_conjecture, (k3_pboole(esk1_0,k1_pzfmisc1(esk1_0,esk2_0),esk3_0)=k7_funcop_1(esk1_0,k1_xboole_0)\|~v1_partfun1(k1_pzfmisc1(esk1_0,esk2_0),esk1_0)\|~v1_funct_1(k3_pboole(esk1_0,k1_pzfmisc1(esk1_0,esk2_0),esk3_0))\|~v1_funct_1(k1_pzfmisc1(esk1_0,esk2_0))\|~v4_relat_1(k1_pzfmisc1(esk1_0,esk2_0),esk1_0)\|~v1_relat_1(k3_pboole(esk1_0,k1_pzfmisc1(esk1_0,esk2_0),esk3_0))\|~v1_relat_1(k1_pzfmisc1(esk1_0,esk2_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80, c_0_78]), c_0_70]), c_0_71]), c_0_72]), c_0_73])])])). cnf(c_0_85, plain, (k1_funct_1(k1_pboole(X1),X2)=k1_xboole_0), inference(split_conjunct,[status(thm)],[c_0_81])). fof(c_0_86, plain, ![X13, X14, X15, X16]:((~r1_pboole(X13,X14,X15)\|(~r2_hidden(X16,X13)\|r2_hidden(k1_funct_1(X14,X16),k1_funct_1(X15,X16)))\|(~v1_relat_1(X15)\|(~v4_relat_1(X15,X13)\|(~v1_funct_1(X15)\|~v1_partfun1(X15,X13))))\|(~v1_relat_1(X14)\|(~v4_relat_1(X14,X13)\|(~v1_funct_1(X14)\|~v1_partfun1(X14,X13)))))&((r2_hidden(esk5_3(X13,X14,X15),X13)\|r1_pboole(X13,X14,X15)\|(~v1_relat_1(X15)\|(~v4_relat_1(X15,X13)\|(~v1_funct_1(X15)\|~v1_partfun1(X15,X13))))\|(~v1_relat_1(X14)\|(~v4_relat_1(X14,X13)\|(~v1_funct_1(X14)\|~v1_partfun1(X14,X13)))))&(~r2_hidden(k1_funct_1(X14,esk5_3(X13,X14,X15)),k1_funct_1(X15,esk5_3(X13,X14,X15)))\|r1_pboole(X13,X14,X15)\|(~v1_relat_1(X15)\|(~v4_relat_1(X15,X13)\|(~v1_funct_1(X15)\|~v1_partfun1(X15,X13))))\|(~v1_relat_1(X14)\|(~v4_relat_1(X14,X13)\|(~v1_funct_1(X14)\|~v1_partfun1(X14,X13))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_pboole])])])])])). cnf(c_0_87, plain, (k1_funct_1(k3_pboole(X5,k1_pzfmisc1(X1,X2),X4),X3)!=k1_xboole_0\|~r2_hidden(k1_funct_1(X2,X3),k1_funct_1(X4,X3))\|~r2_hidden(X3,X1)\|~v1_partfun1(X2,X1)\|~v1_funct_1(X2)\|~v4_relat_1(X2,X1)\|~v1_relat_1(X2)\|~r2_hidden(X3,X5)\|~v1_partfun1(X4,X5)\|~v1_partfun1(k1_pzfmisc1(X1,X2),X5)\|~v1_funct_1(X4)\|~v1_funct_1(k1_pzfmisc1(X1,X2))\|~v4_relat_1(X4,X5)\|~v4_relat_1(k1_pzfmisc1(X1,X2),X5)\|~v1_relat_1(X4)\|~v1_relat_1(k1_pzfmisc1(X1,X2))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_82, c_0_83])])). cnf(c_0_88, negated_conjecture, (k3_pboole(esk1_0,k1_pzfmisc1(esk1_0,esk2_0),esk3_0)=k7_funcop_1(esk1_0,k1_xboole_0)\|~v1_partfun1(k1_pzfmisc1(esk1_0,esk2_0),esk1_0)\|~v1_funct_1(k1_pzfmisc1(esk1_0,esk2_0))\|~v4_relat_1(k1_pzfmisc1(esk1_0,esk2_0),esk1_0)\|~v1_relat_1(k3_pboole(esk1_0,k1_pzfmisc1(esk1_0,esk2_0),esk3_0))\|~v1_relat_1(k1_pzfmisc1(esk1_0,esk2_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84, c_0_79]), c_0_70]), c_0_71]), c_0_72]), c_0_73])])])). cnf(c_0_89, plain, (k1_funct_1(k7_funcop_1(X1,k1_xboole_0),X2)=k1_xboole_0), inference(rw,[status(thm)],[c_0_85, c_0_19])). cnf(c_0_90, negated_conjecture, (v1_partfun1(esk2_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_14])). cnf(c_0_91, negated_conjecture, (v1_funct_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_14])). cnf(c_0_92, negated_conjecture, (v4_relat_1(esk2_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_14])). cnf(c_0_93, negated_conjecture, (v1_relat_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_14])). cnf(c_0_94, plain, (r2_hidden(k1_funct_1(X2,X4),k1_funct_1(X3,X4))\|~r1_pboole(X1,X2,X3)\|~r2_hidden(X4,X1)\|~v1_relat_1(X3)\|~v4_relat_1(X3,X1)\|~v1_funct_1(X3)\|~v1_partfun1(X3,X1)\|~v1_relat_1(X2)\|~v4_relat_1(X2,X1)\|~v1_funct_1(X2)\|~v1_partfun1(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_86])). cnf(c_0_95, negated_conjecture, (r1_pboole(esk1_0,esk2_0,esk3_0)), inference(split_conjunct,[status(thm)],[c_0_14])). cnf(c_0_96, plain, (k1_funct_1(k3_pboole(X1,k1_pzfmisc1(X2,X3),X4),X5)!=k1_xboole_0\|~r2_hidden(k1_funct_1(X3,X5),k1_funct_1(X4,X5))\|~r2_hidden(X5,X2)\|~r2_hidden(X5,X1)\|~v1_partfun1(k1_pzfmisc1(X2,X3),X1)\|~v1_partfun1(X3,X2)\|~v1_partfun1(X4,X1)\|~v1_funct_1(X3)\|~v1_funct_1(X4)\|~v4_relat_1(k1_pzfmisc1(X2,X3),X1)\|~v4_relat_1(X3,X2)\|~v4_relat_1(X4,X1)\|~v1_relat_1(X3)\|~v1_relat_1(X4)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_87, c_0_60]), c_0_62])). cnf(c_0_97, negated_conjecture, (k3_pboole(esk1_0,k1_pzfmisc1(esk1_0,esk2_0),esk3_0)=k7_funcop_1(esk1_0,k1_xboole_0)\|~v1_partfun1(k1_pzfmisc1(esk1_0,esk2_0),esk1_0)\|~v1_funct_1(k1_pzfmisc1(esk1_0,esk2_0))\|~v4_relat_1(k1_pzfmisc1(esk1_0,esk2_0),esk1_0)\|~v1_relat_1(k1_pzfmisc1(esk1_0,esk2_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88, c_0_77]), c_0_70]), c_0_71]), c_0_72]), c_0_73])])])). cnf(c_0_98, plain, (k1_funct_1(k7_funcop_1(X1,k1_xboole_0),X2)=k1_xboole_0), inference(evalgc,[status(thm)],[c_0_89])). cnf(c_0_99, negated_conjecture, (v1_partfun1(esk2_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_90])). cnf(c_0_100, negated_conjecture, (v1_funct_1(esk2_0)), inference(evalgc,[status(thm)],[c_0_91])). cnf(c_0_101, negated_conjecture, (v4_relat_1(esk2_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_92])). cnf(c_0_102, negated_conjecture, (v1_relat_1(esk2_0)), inference(evalgc,[status(thm)],[c_0_93])). cnf(c_0_103, plain, (r2_hidden(k1_funct_1(X2,X4),k1_funct_1(X3,X4))\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v4_relat_1(X3,X1)\|~v4_relat_1(X2,X1)\|~v1_partfun1(X3,X1)\|~v1_partfun1(X2,X1)\|~r2_hidden(X4,X1)\|~r1_pboole(X1,X2,X3)), inference(evalgc,[status(thm)],[c_0_94])). cnf(c_0_104, negated_conjecture, (r1_pboole(esk1_0,esk2_0,esk3_0)), inference(evalgc,[status(thm)],[c_0_95])). cnf(c_0_105, negated_conjecture, (~r2_hidden(k1_funct_1(esk2_0,X1),k1_funct_1(esk3_0,X1))\|~r2_hidden(X1,esk1_0)\|~v1_partfun1(k1_pzfmisc1(esk1_0,esk2_0),esk1_0)\|~v4_relat_1(k1_pzfmisc1(esk1_0,esk2_0),esk1_0)\|~v1_funct_1(k1_pzfmisc1(esk1_0,esk2_0))\|~v1_relat_1(k1_pzfmisc1(esk1_0,esk2_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96, c_0_97]), c_0_98]), c_0_99]), c_0_70]), c_0_100]), c_0_71]), c_0_101]), c_0_72]), c_0_102]), c_0_73])])])). cnf(c_0_106, negated_conjecture, (r2_hidden(k1_funct_1(esk2_0,X1),k1_funct_1(esk3_0,X1))\|~r2_hidden(X1,esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103, c_0_104]), c_0_70]), c_0_99]), c_0_71]), c_0_100]), c_0_72]), c_0_101]), c_0_73]), c_0_102])])])). cnf(c_0_107, negated_conjecture, (~r2_hidden(X1,esk1_0)\|~v1_partfun1(k1_pzfmisc1(esk1_0,esk2_0),esk1_0)\|~v1_funct_1(k1_pzfmisc1(esk1_0,esk2_0))\|~v4_relat_1(k1_pzfmisc1(esk1_0,esk2_0),esk1_0)\|~v1_relat_1(k1_pzfmisc1(esk1_0,esk2_0))), inference(csr,[status(thm)],[c_0_105, c_0_106])). cnf(c_0_108, negated_conjecture, (~r2_hidden(X1,esk1_0)\|~v1_funct_1(k1_pzfmisc1(esk1_0,esk2_0))\|~v4_relat_1(k1_pzfmisc1(esk1_0,esk2_0),esk1_0)\|~v1_relat_1(k1_pzfmisc1(esk1_0,esk2_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107, c_0_63]), c_0_99]), c_0_100]), c_0_101]), c_0_102])])])). cnf(c_0_109, negated_conjecture, (~r2_hidden(X1,esk1_0)\|~v1_funct_1(k1_pzfmisc1(esk1_0,esk2_0))\|~v1_relat_1(k1_pzfmisc1(esk1_0,esk2_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108, c_0_61]), c_0_99]), c_0_100]), c_0_101]), c_0_102])])])). fof(c_0_110, plain, ![X9, X10, X11]:((~v1_xboole_0(X9)\|~r2_hidden(X10,X9))&(r2_hidden(esk4_1(X11),X11)\|v1_xboole_0(X11))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d1_xboole_0])])])])])])). cnf(c_0_111, negated_conjecture, (~r2_hidden(X1,esk1_0)\|~v1_relat_1(k1_pzfmisc1(esk1_0,esk2_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109, c_0_62]), c_0_99]), c_0_100]), c_0_101]), c_0_102])])])). cnf(c_0_112, plain, (r2_hidden(esk4_1(X1),X1)\|v1_xboole_0(X1)), inference(split_conjunct,[status(thm)],[c_0_110])). cnf(c_0_113, negated_conjecture, (~v1_xboole_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_14])). cnf(c_0_114, negated_conjecture, (~r2_hidden(X1,esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111, c_0_60]), c_0_99]), c_0_100]), c_0_101]), c_0_102])])])). cnf(c_0_115, plain, (v1_xboole_0(X1)\|r2_hidden(esk4_1(X1),X1)), inference(evalgc,[status(thm)],[c_0_112])). cnf(c_0_116, negated_conjecture, (~v1_xboole_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_113])). cnf(c_0_117, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_114, c_0_115]), c_0_116]), ['proof']). # SZS output end CNFRefutation	reserve i, I for set, f for Function, x, x1, x2, y, A, B, X, Y, Z for ManySortedSet of I; theorem :: ZFMISC_1:54 I is non empty & {x} /\ X = [[0]]I implies not x in X proof assume that A1: I is non empty and A2: {x} /\ X = [[0]]I and A3: x in X; consider i such that A4: i in I by A1,XBOOLE_0:def 1; {x.i} /\ X.i = {x}.i /\ X.i by A4,Def1 .= ({x} /\ X).i by A4,PBOOLE:def 5 .= {} by A2,PBOOLE:5; then {x.i} misses X.i by XBOOLE_0:def 7; then not x.i in X.i by ZFMISC_1:48; hence contradiction by A3,A4,PBOOLE:def 1; end;	Convert the following ATP output trace into a readable Mizar proof.
t43_bhsp_1	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t30_bhsp_1, axiom, ![X1]:((~(v2_struct_0(X1))&(v13_algstr_0(X1)&(v2_rlvect_1(X1)&(v3_rlvect_1(X1)&(v4_rlvect_1(X1)&(v5_rlvect_1(X1)&(v6_rlvect_1(X1)&(v7_rlvect_1(X1)&(v8_rlvect_1(X1)&(v2_bhsp_1(X1)&l1_bhsp_1(X1)))))))))))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>r1_xxreal_0(k3_bhsp_1(X1,k3_rlvect_1(X1,X2,X3)),k7_real_1(k3_bhsp_1(X1,X2),k3_bhsp_1(X1,X3)))))), file('/scratch/mptp/predsminms1/t43_bhsp_1__0', t30_bhsp_1)). fof(redefinition_k3_rlvect_1, axiom, ![X1, X2, X3]:(((v2_rlvect_1(X1)&l1_algstr_0(X1))&(m1_subset_1(X2,u1_struct_0(X1))&m1_subset_1(X3,u1_struct_0(X1))))=>k3_rlvect_1(X1,X2,X3)=k1_algstr_0(X1,X2,X3)), file('/scratch/mptp/predsminms1/t43_bhsp_1__0', redefinition_k3_rlvect_1)). fof(d14_algstr_0, axiom, ![X1]:(l2_algstr_0(X1)=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>k5_algstr_0(X1,X2,X3)=k1_algstr_0(X1,X2,k4_algstr_0(X1,X3))))), file('/scratch/mptp/predsminms1/t43_bhsp_1__0', d14_algstr_0)). fof(dt_l1_rlvect_1, axiom, ![X1]:(l1_rlvect_1(X1)=>l2_algstr_0(X1)), file('/scratch/mptp/predsminms1/t43_bhsp_1__0', dt_l1_rlvect_1)). fof(dt_l1_bhsp_1, axiom, ![X1]:(l1_bhsp_1(X1)=>l1_rlvect_1(X1)), file('/scratch/mptp/predsminms1/t43_bhsp_1__0', dt_l1_bhsp_1)). fof(dt_k4_algstr_0, axiom, ![X1, X2]:((l2_algstr_0(X1)&m1_subset_1(X2,u1_struct_0(X1)))=>m1_subset_1(k4_algstr_0(X1,X2),u1_struct_0(X1))), file('/scratch/mptp/predsminms1/t43_bhsp_1__0', dt_k4_algstr_0)). fof(d5_bhsp_1, axiom, ![X1]:((~(v2_struct_0(X1))&(v13_algstr_0(X1)&(v2_rlvect_1(X1)&(v3_rlvect_1(X1)&(v4_rlvect_1(X1)&(v5_rlvect_1(X1)&(v6_rlvect_1(X1)&(v7_rlvect_1(X1)&(v8_rlvect_1(X1)&(v2_bhsp_1(X1)&l1_bhsp_1(X1)))))))))))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>k4_bhsp_1(X1,X2,X3)=k3_bhsp_1(X1,k5_algstr_0(X1,X2,X3))))), file('/scratch/mptp/predsminms1/t43_bhsp_1__0', d5_bhsp_1)). fof(t33_rlvect_1, axiom, ![X1]:((~(v2_struct_0(X1))&(v13_algstr_0(X1)&(v3_rlvect_1(X1)&(v4_rlvect_1(X1)&l2_algstr_0(X1)))))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>k4_algstr_0(X1,k5_algstr_0(X1,X2,X3))=k1_algstr_0(X1,X3,k4_algstr_0(X1,X2))))), file('/scratch/mptp/predsminms1/t43_bhsp_1__0', t33_rlvect_1)). fof(dt_k5_algstr_0, axiom, ![X1, X2, X3]:((l2_algstr_0(X1)&(m1_subset_1(X2,u1_struct_0(X1))&m1_subset_1(X3,u1_struct_0(X1))))=>m1_subset_1(k5_algstr_0(X1,X2,X3),u1_struct_0(X1))), file('/scratch/mptp/predsminms1/t43_bhsp_1__0', dt_k5_algstr_0)). fof(t43_bhsp_1, conjecture, ![X1]:((~(v2_struct_0(X1))&(v13_algstr_0(X1)&(v2_rlvect_1(X1)&(v3_rlvect_1(X1)&(v4_rlvect_1(X1)&(v5_rlvect_1(X1)&(v6_rlvect_1(X1)&(v7_rlvect_1(X1)&(v8_rlvect_1(X1)&(v2_bhsp_1(X1)&l1_bhsp_1(X1)))))))))))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>![X4]:(m1_subset_1(X4,u1_struct_0(X1))=>r1_xxreal_0(k4_bhsp_1(X1,k5_algstr_0(X1,X2,X3),k5_algstr_0(X1,X4,X3)),k7_real_1(k4_bhsp_1(X1,X3,X2),k4_bhsp_1(X1,X3,X4))))))), file('/scratch/mptp/predsminms1/t43_bhsp_1__0', t43_bhsp_1)). fof(commutativity_k4_bhsp_1, axiom, ![X1, X2, X3]:(((~(v2_struct_0(X1))&(v13_algstr_0(X1)&(v2_rlvect_1(X1)&(v3_rlvect_1(X1)&(v4_rlvect_1(X1)&(v5_rlvect_1(X1)&(v6_rlvect_1(X1)&(v7_rlvect_1(X1)&(v8_rlvect_1(X1)&(v2_bhsp_1(X1)&l1_bhsp_1(X1)))))))))))&(m1_subset_1(X2,u1_struct_0(X1))&m1_subset_1(X3,u1_struct_0(X1))))=>k4_bhsp_1(X1,X2,X3)=k4_bhsp_1(X1,X3,X2)), file('/scratch/mptp/predsminms1/t43_bhsp_1__0', commutativity_k4_bhsp_1)). fof(dt_l2_algstr_0, axiom, ![X1]:(l2_algstr_0(X1)=>(l2_struct_0(X1)&l1_algstr_0(X1))), file('/scratch/mptp/predsminms1/t43_bhsp_1__0', dt_l2_algstr_0)). fof(c_0_12, plain, ![X32, X33, X34]:(v2_struct_0(X32)\|(~v13_algstr_0(X32)\|(~v2_rlvect_1(X32)\|(~v3_rlvect_1(X32)\|(~v4_rlvect_1(X32)\|(~v5_rlvect_1(X32)\|(~v6_rlvect_1(X32)\|(~v7_rlvect_1(X32)\|(~v8_rlvect_1(X32)\|(~v2_bhsp_1(X32)\|~l1_bhsp_1(X32))))))))))\|(~m1_subset_1(X33,u1_struct_0(X32))\|(~m1_subset_1(X34,u1_struct_0(X32))\|r1_xxreal_0(k3_bhsp_1(X32,k3_rlvect_1(X32,X33,X34)),k7_real_1(k3_bhsp_1(X32,X33),k3_bhsp_1(X32,X34)))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t30_bhsp_1])])])])). fof(c_0_13, plain, ![X23, X24, X25]:(~v2_rlvect_1(X23)\|~l1_algstr_0(X23)\|(~m1_subset_1(X24,u1_struct_0(X23))\|~m1_subset_1(X25,u1_struct_0(X23)))\|k3_rlvect_1(X23,X24,X25)=k1_algstr_0(X23,X24,X25)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k3_rlvect_1])])). cnf(c_0_14, plain, (v2_struct_0(X1)\|r1_xxreal_0(k3_bhsp_1(X1,k3_rlvect_1(X1,X2,X3)),k7_real_1(k3_bhsp_1(X1,X2),k3_bhsp_1(X1,X3)))\|~v13_algstr_0(X1)\|~v2_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v8_rlvect_1(X1)\|~v2_bhsp_1(X1)\|~l1_bhsp_1(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_15, plain, (k3_rlvect_1(X1,X2,X3)=k1_algstr_0(X1,X2,X3)\|~v2_rlvect_1(X1)\|~l1_algstr_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_13])). fof(c_0_16, plain, ![X14, X15, X16]:(~l2_algstr_0(X14)\|(~m1_subset_1(X15,u1_struct_0(X14))\|(~m1_subset_1(X16,u1_struct_0(X14))\|k5_algstr_0(X14,X15,X16)=k1_algstr_0(X14,X15,k4_algstr_0(X14,X16))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d14_algstr_0])])])). fof(c_0_17, plain, ![X12]:(~l1_rlvect_1(X12)\|l2_algstr_0(X12)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_rlvect_1])])). fof(c_0_18, plain, ![X13]:(~l1_bhsp_1(X13)\|l1_rlvect_1(X13)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_bhsp_1])])). cnf(c_0_19, plain, (v2_struct_0(X1)\|r1_xxreal_0(k3_bhsp_1(X1,k3_rlvect_1(X1,X2,X3)),k7_real_1(k3_bhsp_1(X1,X2),k3_bhsp_1(X1,X3)))\|~v13_algstr_0(X1)\|~v2_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v8_rlvect_1(X1)\|~v2_bhsp_1(X1)\|~l1_bhsp_1(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_14])). cnf(c_0_20, plain, (k3_rlvect_1(X1,X2,X3)=k1_algstr_0(X1,X2,X3)\|~v2_rlvect_1(X1)\|~l1_algstr_0(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_15])). cnf(c_0_21, plain, (k5_algstr_0(X1,X2,X3)=k1_algstr_0(X1,X2,k4_algstr_0(X1,X3))\|~l2_algstr_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_16])). fof(c_0_22, plain, ![X21, X22]:(~l2_algstr_0(X21)\|~m1_subset_1(X22,u1_struct_0(X21))\|m1_subset_1(k4_algstr_0(X21,X22),u1_struct_0(X21))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k4_algstr_0])])). cnf(c_0_23, plain, (l2_algstr_0(X1)\|~l1_rlvect_1(X1)), inference(split_conjunct,[status(thm)],[c_0_17])). cnf(c_0_24, plain, (l1_rlvect_1(X1)\|~l1_bhsp_1(X1)), inference(split_conjunct,[status(thm)],[c_0_18])). cnf(c_0_25, plain, (r1_xxreal_0(k3_bhsp_1(X1,k1_algstr_0(X1,X2,X3)),k7_real_1(k3_bhsp_1(X1,X2),k3_bhsp_1(X1,X3)))\|v2_struct_0(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l1_bhsp_1(X1)\|~v2_bhsp_1(X1)\|~v8_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v13_algstr_0(X1)\|~l1_algstr_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_19, c_0_20])])). cnf(c_0_26, plain, (k1_algstr_0(X1,X2,k4_algstr_0(X1,X3))=k5_algstr_0(X1,X2,X3)\|~l2_algstr_0(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_21])). cnf(c_0_27, plain, (m1_subset_1(k4_algstr_0(X1,X2),u1_struct_0(X1))\|~l2_algstr_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_28, plain, (l2_algstr_0(X1)\|~l1_rlvect_1(X1)), inference(evalgc,[status(thm)],[c_0_23])). cnf(c_0_29, plain, (l1_rlvect_1(X1)\|~l1_bhsp_1(X1)), inference(evalgc,[status(thm)],[c_0_24])). fof(c_0_30, plain, ![X26, X27, X28]:(v2_struct_0(X26)\|(~v13_algstr_0(X26)\|(~v2_rlvect_1(X26)\|(~v3_rlvect_1(X26)\|(~v4_rlvect_1(X26)\|(~v5_rlvect_1(X26)\|(~v6_rlvect_1(X26)\|(~v7_rlvect_1(X26)\|(~v8_rlvect_1(X26)\|(~v2_bhsp_1(X26)\|~l1_bhsp_1(X26))))))))))\|(~m1_subset_1(X27,u1_struct_0(X26))\|(~m1_subset_1(X28,u1_struct_0(X26))\|k4_bhsp_1(X26,X27,X28)=k3_bhsp_1(X26,k5_algstr_0(X26,X27,X28))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d5_bhsp_1])])])])). fof(c_0_31, plain, ![X17, X18, X19]:(v2_struct_0(X17)\|(~v13_algstr_0(X17)\|(~v3_rlvect_1(X17)\|(~v4_rlvect_1(X17)\|~l2_algstr_0(X17))))\|(~m1_subset_1(X18,u1_struct_0(X17))\|(~m1_subset_1(X19,u1_struct_0(X17))\|k4_algstr_0(X17,k5_algstr_0(X17,X18,X19))=k1_algstr_0(X17,X19,k4_algstr_0(X17,X18))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t33_rlvect_1])])])])). cnf(c_0_32, plain, (r1_xxreal_0(k3_bhsp_1(X1,k5_algstr_0(X1,X2,X3)),k7_real_1(k3_bhsp_1(X1,X2),k3_bhsp_1(X1,k4_algstr_0(X1,X3))))\|v2_struct_0(X1)\|~l1_algstr_0(X1)\|~m1_subset_1(k4_algstr_0(X1,X3),u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l1_bhsp_1(X1)\|~v2_bhsp_1(X1)\|~v8_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v13_algstr_0(X1)\|~l2_algstr_0(X1)\|~m1_subset_1(X3,u1_struct_0(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_25, c_0_26])])). cnf(c_0_33, plain, (m1_subset_1(k4_algstr_0(X1,X2),u1_struct_0(X1))\|~l2_algstr_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_27])). cnf(c_0_34, plain, (l2_algstr_0(X1)\|~l1_bhsp_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_28, c_0_29])])). cnf(c_0_35, plain, (v2_struct_0(X1)\|k4_bhsp_1(X1,X2,X3)=k3_bhsp_1(X1,k5_algstr_0(X1,X2,X3))\|~v13_algstr_0(X1)\|~v2_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v8_rlvect_1(X1)\|~v2_bhsp_1(X1)\|~l1_bhsp_1(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_30])). cnf(c_0_36, plain, (v2_struct_0(X1)\|k4_algstr_0(X1,k5_algstr_0(X1,X2,X3))=k1_algstr_0(X1,X3,k4_algstr_0(X1,X2))\|~v13_algstr_0(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~l2_algstr_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_31])). cnf(c_0_37, plain, (r1_xxreal_0(k3_bhsp_1(X1,k5_algstr_0(X1,X2,X3)),k7_real_1(k3_bhsp_1(X1,X2),k3_bhsp_1(X1,k4_algstr_0(X1,X3))))\|v2_struct_0(X1)\|~l1_algstr_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~l1_bhsp_1(X1)\|~v2_bhsp_1(X1)\|~v8_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v13_algstr_0(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_32, c_0_33]), c_0_34])). cnf(c_0_38, plain, (k3_bhsp_1(X1,k5_algstr_0(X1,X2,X3))=k4_bhsp_1(X1,X2,X3)\|v2_struct_0(X1)\|~v13_algstr_0(X1)\|~v2_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v8_rlvect_1(X1)\|~v2_bhsp_1(X1)\|~l1_bhsp_1(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_35])). cnf(c_0_39, plain, (k1_algstr_0(X1,X3,k4_algstr_0(X1,X2))=k4_algstr_0(X1,k5_algstr_0(X1,X2,X3))\|v2_struct_0(X1)\|~v13_algstr_0(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~l2_algstr_0(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_36])). fof(c_0_40, plain, ![X29, X30, X31]:(~l2_algstr_0(X29)\|(~m1_subset_1(X30,u1_struct_0(X29))\|~m1_subset_1(X31,u1_struct_0(X29)))\|m1_subset_1(k5_algstr_0(X29,X30,X31),u1_struct_0(X29))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k5_algstr_0])])). cnf(c_0_41, plain, (r1_xxreal_0(k4_bhsp_1(X1,X2,X3),k7_real_1(k3_bhsp_1(X1,X2),k3_bhsp_1(X1,k4_algstr_0(X1,X3))))\|v2_struct_0(X1)\|~l1_algstr_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~l1_bhsp_1(X1)\|~v2_bhsp_1(X1)\|~v8_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v13_algstr_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_37, c_0_38])])). cnf(c_0_42, plain, (k4_algstr_0(X1,k5_algstr_0(X1,X3,X2))=k5_algstr_0(X1,X2,X3)\|v2_struct_0(X1)\|~l2_algstr_0(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v13_algstr_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_26, c_0_39])])). cnf(c_0_43, plain, (m1_subset_1(k5_algstr_0(X1,X2,X3),u1_struct_0(X1))\|~l2_algstr_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_40])). fof(c_0_44, negated_conjecture, ~(![X1]:((~(v2_struct_0(X1))&(v13_algstr_0(X1)&(v2_rlvect_1(X1)&(v3_rlvect_1(X1)&(v4_rlvect_1(X1)&(v5_rlvect_1(X1)&(v6_rlvect_1(X1)&(v7_rlvect_1(X1)&(v8_rlvect_1(X1)&(v2_bhsp_1(X1)&l1_bhsp_1(X1)))))))))))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>![X4]:(m1_subset_1(X4,u1_struct_0(X1))=>r1_xxreal_0(k4_bhsp_1(X1,k5_algstr_0(X1,X2,X3),k5_algstr_0(X1,X4,X3)),k7_real_1(k4_bhsp_1(X1,X3,X2),k4_bhsp_1(X1,X3,X4)))))))), inference(assume_negation,[status(cth)],[t43_bhsp_1])). cnf(c_0_45, plain, (r1_xxreal_0(k4_bhsp_1(X1,X2,k5_algstr_0(X1,X3,X4)),k7_real_1(k3_bhsp_1(X1,X2),k3_bhsp_1(X1,k5_algstr_0(X1,X4,X3))))\|v2_struct_0(X1)\|~l1_algstr_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(k5_algstr_0(X1,X3,X4),u1_struct_0(X1))\|~l1_bhsp_1(X1)\|~v2_bhsp_1(X1)\|~v8_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v13_algstr_0(X1)\|~l2_algstr_0(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X4,u1_struct_0(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_41, c_0_42])])). cnf(c_0_46, plain, (m1_subset_1(k5_algstr_0(X1,X2,X3),u1_struct_0(X1))\|~l2_algstr_0(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_43])). fof(c_0_47, plain, ![X9, X10, X11]:(v2_struct_0(X9)\|(~v13_algstr_0(X9)\|(~v2_rlvect_1(X9)\|(~v3_rlvect_1(X9)\|(~v4_rlvect_1(X9)\|(~v5_rlvect_1(X9)\|(~v6_rlvect_1(X9)\|(~v7_rlvect_1(X9)\|(~v8_rlvect_1(X9)\|(~v2_bhsp_1(X9)\|~l1_bhsp_1(X9))))))))))\|(~m1_subset_1(X10,u1_struct_0(X9))\|~m1_subset_1(X11,u1_struct_0(X9)))\|k4_bhsp_1(X9,X10,X11)=k4_bhsp_1(X9,X11,X10)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[commutativity_k4_bhsp_1])])])). fof(c_0_48, negated_conjecture, ((~v2_struct_0(esk1_0)&(v13_algstr_0(esk1_0)&(v2_rlvect_1(esk1_0)&(v3_rlvect_1(esk1_0)&(v4_rlvect_1(esk1_0)&(v5_rlvect_1(esk1_0)&(v6_rlvect_1(esk1_0)&(v7_rlvect_1(esk1_0)&(v8_rlvect_1(esk1_0)&(v2_bhsp_1(esk1_0)&l1_bhsp_1(esk1_0)))))))))))&(m1_subset_1(esk2_0,u1_struct_0(esk1_0))&(m1_subset_1(esk3_0,u1_struct_0(esk1_0))&(m1_subset_1(esk4_0,u1_struct_0(esk1_0))&~r1_xxreal_0(k4_bhsp_1(esk1_0,k5_algstr_0(esk1_0,esk2_0,esk3_0),k5_algstr_0(esk1_0,esk4_0,esk3_0)),k7_real_1(k4_bhsp_1(esk1_0,esk3_0,esk2_0),k4_bhsp_1(esk1_0,esk3_0,esk4_0))))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_44])])])])). cnf(c_0_49, plain, (r1_xxreal_0(k4_bhsp_1(X1,X2,k5_algstr_0(X1,X3,X4)),k7_real_1(k3_bhsp_1(X1,X2),k3_bhsp_1(X1,k5_algstr_0(X1,X4,X3))))\|v2_struct_0(X1)\|~l1_algstr_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X4,u1_struct_0(X1))\|~l1_bhsp_1(X1)\|~v2_bhsp_1(X1)\|~v8_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v13_algstr_0(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_45, c_0_46]), c_0_34])). cnf(c_0_50, plain, (v2_struct_0(X1)\|k4_bhsp_1(X1,X2,X3)=k4_bhsp_1(X1,X3,X2)\|~v13_algstr_0(X1)\|~v2_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v8_rlvect_1(X1)\|~v2_bhsp_1(X1)\|~l1_bhsp_1(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_47])). cnf(c_0_51, negated_conjecture, (v2_bhsp_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_48])). cnf(c_0_52, negated_conjecture, (l1_bhsp_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_48])). cnf(c_0_53, negated_conjecture, (v8_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_48])). cnf(c_0_54, negated_conjecture, (v7_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_48])). cnf(c_0_55, negated_conjecture, (v6_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_48])). cnf(c_0_56, negated_conjecture, (v5_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_48])). cnf(c_0_57, negated_conjecture, (v4_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_48])). cnf(c_0_58, negated_conjecture, (v3_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_48])). cnf(c_0_59, negated_conjecture, (v2_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_48])). cnf(c_0_60, negated_conjecture, (v13_algstr_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_48])). cnf(c_0_61, negated_conjecture, (~v2_struct_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_48])). cnf(c_0_62, plain, (r1_xxreal_0(k4_bhsp_1(X1,X2,k5_algstr_0(X1,X3,X4)),k7_real_1(k3_bhsp_1(X1,X2),k4_bhsp_1(X1,X4,X3)))\|v2_struct_0(X1)\|~l1_algstr_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X4,u1_struct_0(X1))\|~l1_bhsp_1(X1)\|~v2_bhsp_1(X1)\|~v8_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v13_algstr_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_49, c_0_38])])). cnf(c_0_63, plain, (k4_bhsp_1(X1,X2,X3)=k4_bhsp_1(X1,X3,X2)\|v2_struct_0(X1)\|~v13_algstr_0(X1)\|~v2_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v8_rlvect_1(X1)\|~v2_bhsp_1(X1)\|~l1_bhsp_1(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_50])). cnf(c_0_64, negated_conjecture, (v2_bhsp_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_51])). cnf(c_0_65, negated_conjecture, (l1_bhsp_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_52])). cnf(c_0_66, negated_conjecture, (v8_rlvect_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_53])). cnf(c_0_67, negated_conjecture, (v7_rlvect_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_54])). cnf(c_0_68, negated_conjecture, (v6_rlvect_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_55])). cnf(c_0_69, negated_conjecture, (v5_rlvect_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_56])). cnf(c_0_70, negated_conjecture, (v4_rlvect_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_57])). cnf(c_0_71, negated_conjecture, (v3_rlvect_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_58])). cnf(c_0_72, negated_conjecture, (v2_rlvect_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_59])). cnf(c_0_73, negated_conjecture, (v13_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_60])). cnf(c_0_74, negated_conjecture, (~v2_struct_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_61])). cnf(c_0_75, negated_conjecture, (~r1_xxreal_0(k4_bhsp_1(esk1_0,k5_algstr_0(esk1_0,esk2_0,esk3_0),k5_algstr_0(esk1_0,esk4_0,esk3_0)),k7_real_1(k4_bhsp_1(esk1_0,esk3_0,esk2_0),k4_bhsp_1(esk1_0,esk3_0,esk4_0)))), inference(split_conjunct,[status(thm)],[c_0_48])). cnf(c_0_76, plain, (r1_xxreal_0(k4_bhsp_1(X1,k5_algstr_0(X1,X2,X3),k5_algstr_0(X1,X4,X5)),k7_real_1(k4_bhsp_1(X1,X2,X3),k4_bhsp_1(X1,X5,X4)))\|v2_struct_0(X1)\|~l1_algstr_0(X1)\|~m1_subset_1(k5_algstr_0(X1,X2,X3),u1_struct_0(X1))\|~m1_subset_1(X4,u1_struct_0(X1))\|~m1_subset_1(X5,u1_struct_0(X1))\|~l1_bhsp_1(X1)\|~v2_bhsp_1(X1)\|~v8_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v13_algstr_0(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_62, c_0_38])])). cnf(c_0_77, negated_conjecture, (k4_bhsp_1(esk1_0,X1,X2)=k4_bhsp_1(esk1_0,X2,X1)\|~m1_subset_1(X2,u1_struct_0(esk1_0))\|~m1_subset_1(X1,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63, c_0_64]), c_0_65]), c_0_66]), c_0_67]), c_0_68]), c_0_69]), c_0_70]), c_0_71]), c_0_72]), c_0_73])]), c_0_74])])). cnf(c_0_78, negated_conjecture, (m1_subset_1(esk4_0,u1_struct_0(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_48])). cnf(c_0_79, negated_conjecture, (m1_subset_1(esk3_0,u1_struct_0(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_48])). cnf(c_0_80, negated_conjecture, (m1_subset_1(esk2_0,u1_struct_0(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_48])). cnf(c_0_81, negated_conjecture, (~r1_xxreal_0(k4_bhsp_1(esk1_0,k5_algstr_0(esk1_0,esk2_0,esk3_0),k5_algstr_0(esk1_0,esk4_0,esk3_0)),k7_real_1(k4_bhsp_1(esk1_0,esk3_0,esk2_0),k4_bhsp_1(esk1_0,esk3_0,esk4_0)))), inference(evalgc,[status(thm)],[c_0_75])). cnf(c_0_82, negated_conjecture, (r1_xxreal_0(k4_bhsp_1(esk1_0,k5_algstr_0(esk1_0,X1,X2),k5_algstr_0(esk1_0,X3,X4)),k7_real_1(k4_bhsp_1(esk1_0,X2,X1),k4_bhsp_1(esk1_0,X4,X3)))\|~l1_algstr_0(esk1_0)\|~m1_subset_1(k5_algstr_0(esk1_0,X1,X2),u1_struct_0(esk1_0))\|~m1_subset_1(X3,u1_struct_0(esk1_0))\|~m1_subset_1(X4,u1_struct_0(esk1_0))\|~m1_subset_1(X2,u1_struct_0(esk1_0))\|~m1_subset_1(X1,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76, c_0_77]), c_0_65]), c_0_64]), c_0_66]), c_0_67]), c_0_68]), c_0_69]), c_0_70]), c_0_71]), c_0_72]), c_0_73])]), c_0_74])])). cnf(c_0_83, negated_conjecture, (m1_subset_1(esk4_0,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[c_0_78])). cnf(c_0_84, negated_conjecture, (m1_subset_1(esk3_0,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[c_0_79])). cnf(c_0_85, negated_conjecture, (m1_subset_1(esk2_0,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[c_0_80])). fof(c_0_86, plain, ![X20]:((l2_struct_0(X20)\|~l2_algstr_0(X20))&(l1_algstr_0(X20)\|~l2_algstr_0(X20))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l2_algstr_0])])])). cnf(c_0_87, negated_conjecture, (~l1_algstr_0(esk1_0)\|~m1_subset_1(k5_algstr_0(esk1_0,esk2_0,esk3_0),u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81, c_0_82]), c_0_83]), c_0_84]), c_0_85])])])). cnf(c_0_88, negated_conjecture, (l2_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_34, c_0_65])])). cnf(c_0_89, plain, (l1_algstr_0(X1)\|~l2_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_86])). cnf(c_0_90, negated_conjecture, (~l1_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87, c_0_46]), c_0_88]), c_0_84]), c_0_85])])])). cnf(c_0_91, plain, (l1_algstr_0(X1)\|~l2_algstr_0(X1)), inference(evalgc,[status(thm)],[c_0_89])). cnf(c_0_92, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90, c_0_91]), c_0_88])]), ['proof']). # SZS output end CNFRefutation	reserve X for non empty UNITSTR; reserve a, b for Real; reserve x, y for Point of X; reserve X for RealUnitarySpace; reserve x, y, z, u, v for Point of X; theorem dist(x - z,y - z) <= dist(z,x) + dist(z,y) proof dist(x - z,y - z) = \|\|.(x - z) + (z - y).\|\| by RLVECT_1:33 .= \|\|.-(z - x) + (z - y).\|\| by RLVECT_1:33; then dist(x - z,y - z) <= \|\|.-(z - x).\|\| + \|\|.z - y.\|\| by Th30; hence thesis by Th31; end;	Convert the following ATP output trace into a readable Mizar proof.
t26_rusub_5	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(fraenkel_a_2_2_rusub_5, axiom, ![X1, X2, X3]:(((~(v2_struct_0(X2))&(v13_algstr_0(X2)&(v2_rlvect_1(X2)&(v3_rlvect_1(X2)&(v4_rlvect_1(X2)&(v5_rlvect_1(X2)&(v6_rlvect_1(X2)&(v7_rlvect_1(X2)&(v8_rlvect_1(X2)&(v2_bhsp_1(X2)&l1_bhsp_1(X2)))))))))))&(~(v1_xboole_0(X3))&m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))))=>(r2_hidden(X1,a_2_2_rusub_5(X2,X3))<=>?[X4]:(m1_subset_1(X4,u1_struct_0(X2))&(X1=X4&![X5]:(m1_subset_1(X5,u1_struct_0(X2))=>(r2_hidden(X5,X3)=>r1_bhsp_1(X2,X5,X4))))))), file('/scratch/mptp/predsminms1/t26_rusub_5__0', fraenkel_a_2_2_rusub_5)). fof(d3_tarski, axiom, ![X1, X2]:(r1_tarski(X1,X2)<=>![X3]:(r2_hidden(X3,X1)=>r2_hidden(X3,X2))), file('/scratch/mptp/predsminms1/t26_rusub_5__0', d3_tarski)). fof(t26_rusub_5, conjecture, ![X1]:((~(v2_struct_0(X1))&(v13_algstr_0(X1)&(v2_rlvect_1(X1)&(v3_rlvect_1(X1)&(v4_rlvect_1(X1)&(v5_rlvect_1(X1)&(v6_rlvect_1(X1)&(v7_rlvect_1(X1)&(v8_rlvect_1(X1)&(v2_bhsp_1(X1)&l1_bhsp_1(X1)))))))))))=>![X2]:((~(v1_xboole_0(X2))&m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))))=>![X3]:((~(v1_xboole_0(X3))&m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1))))=>(r1_tarski(X2,X3)=>r1_tarski(u1_struct_0(k3_rusub_5(X1,X3)),u1_struct_0(k3_rusub_5(X1,X2))))))), file('/scratch/mptp/predsminms1/t26_rusub_5__0', t26_rusub_5)). fof(d4_rusub_5, axiom, ![X1]:((~(v2_struct_0(X1))&(v13_algstr_0(X1)&(v2_rlvect_1(X1)&(v3_rlvect_1(X1)&(v4_rlvect_1(X1)&(v5_rlvect_1(X1)&(v6_rlvect_1(X1)&(v7_rlvect_1(X1)&(v8_rlvect_1(X1)&(v2_bhsp_1(X1)&l1_bhsp_1(X1)))))))))))=>![X2]:((~(v1_xboole_0(X2))&m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))))=>![X3]:((v1_bhsp_1(X3)&m1_rusub_1(X3,X1))=>(X3=k3_rusub_5(X1,X2)<=>u1_struct_0(X3)=a_2_2_rusub_5(X1,X2))))), file('/scratch/mptp/predsminms1/t26_rusub_5__0', d4_rusub_5)). fof(dt_k3_rusub_5, axiom, ![X1, X2]:(((~(v2_struct_0(X1))&(v13_algstr_0(X1)&(v2_rlvect_1(X1)&(v3_rlvect_1(X1)&(v4_rlvect_1(X1)&(v5_rlvect_1(X1)&(v6_rlvect_1(X1)&(v7_rlvect_1(X1)&(v8_rlvect_1(X1)&(v2_bhsp_1(X1)&l1_bhsp_1(X1)))))))))))&(~(v1_xboole_0(X2))&m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))))=>(v1_bhsp_1(k3_rusub_5(X1,X2))&m1_rusub_1(k3_rusub_5(X1,X2),X1))), file('/scratch/mptp/predsminms1/t26_rusub_5__0', dt_k3_rusub_5)). fof(c_0_5, plain, ![X9, X10, X11, X13, X14]:(((m1_subset_1(esk4_3(X9,X10,X11),u1_struct_0(X10))\|~r2_hidden(X9,a_2_2_rusub_5(X10,X11))\|(v2_struct_0(X10)\|(~v13_algstr_0(X10)\|(~v2_rlvect_1(X10)\|(~v3_rlvect_1(X10)\|(~v4_rlvect_1(X10)\|(~v5_rlvect_1(X10)\|(~v6_rlvect_1(X10)\|(~v7_rlvect_1(X10)\|(~v8_rlvect_1(X10)\|(~v2_bhsp_1(X10)\|~l1_bhsp_1(X10))))))))))\|(v1_xboole_0(X11)\|~m1_subset_1(X11,k1_zfmisc_1(u1_struct_0(X10))))))&((X9=esk4_3(X9,X10,X11)\|~r2_hidden(X9,a_2_2_rusub_5(X10,X11))\|(v2_struct_0(X10)\|(~v13_algstr_0(X10)\|(~v2_rlvect_1(X10)\|(~v3_rlvect_1(X10)\|(~v4_rlvect_1(X10)\|(~v5_rlvect_1(X10)\|(~v6_rlvect_1(X10)\|(~v7_rlvect_1(X10)\|(~v8_rlvect_1(X10)\|(~v2_bhsp_1(X10)\|~l1_bhsp_1(X10))))))))))\|(v1_xboole_0(X11)\|~m1_subset_1(X11,k1_zfmisc_1(u1_struct_0(X10))))))&(~m1_subset_1(X13,u1_struct_0(X10))\|(~r2_hidden(X13,X11)\|r1_bhsp_1(X10,X13,esk4_3(X9,X10,X11)))\|~r2_hidden(X9,a_2_2_rusub_5(X10,X11))\|(v2_struct_0(X10)\|(~v13_algstr_0(X10)\|(~v2_rlvect_1(X10)\|(~v3_rlvect_1(X10)\|(~v4_rlvect_1(X10)\|(~v5_rlvect_1(X10)\|(~v6_rlvect_1(X10)\|(~v7_rlvect_1(X10)\|(~v8_rlvect_1(X10)\|(~v2_bhsp_1(X10)\|~l1_bhsp_1(X10))))))))))\|(v1_xboole_0(X11)\|~m1_subset_1(X11,k1_zfmisc_1(u1_struct_0(X10))))))))&((m1_subset_1(esk5_4(X9,X10,X11,X14),u1_struct_0(X10))\|X9!=X14\|~m1_subset_1(X14,u1_struct_0(X10))\|r2_hidden(X9,a_2_2_rusub_5(X10,X11))\|(v2_struct_0(X10)\|(~v13_algstr_0(X10)\|(~v2_rlvect_1(X10)\|(~v3_rlvect_1(X10)\|(~v4_rlvect_1(X10)\|(~v5_rlvect_1(X10)\|(~v6_rlvect_1(X10)\|(~v7_rlvect_1(X10)\|(~v8_rlvect_1(X10)\|(~v2_bhsp_1(X10)\|~l1_bhsp_1(X10))))))))))\|(v1_xboole_0(X11)\|~m1_subset_1(X11,k1_zfmisc_1(u1_struct_0(X10))))))&((r2_hidden(esk5_4(X9,X10,X11,X14),X11)\|X9!=X14\|~m1_subset_1(X14,u1_struct_0(X10))\|r2_hidden(X9,a_2_2_rusub_5(X10,X11))\|(v2_struct_0(X10)\|(~v13_algstr_0(X10)\|(~v2_rlvect_1(X10)\|(~v3_rlvect_1(X10)\|(~v4_rlvect_1(X10)\|(~v5_rlvect_1(X10)\|(~v6_rlvect_1(X10)\|(~v7_rlvect_1(X10)\|(~v8_rlvect_1(X10)\|(~v2_bhsp_1(X10)\|~l1_bhsp_1(X10))))))))))\|(v1_xboole_0(X11)\|~m1_subset_1(X11,k1_zfmisc_1(u1_struct_0(X10))))))&(~r1_bhsp_1(X10,esk5_4(X9,X10,X11,X14),X14)\|X9!=X14\|~m1_subset_1(X14,u1_struct_0(X10))\|r2_hidden(X9,a_2_2_rusub_5(X10,X11))\|(v2_struct_0(X10)\|(~v13_algstr_0(X10)\|(~v2_rlvect_1(X10)\|(~v3_rlvect_1(X10)\|(~v4_rlvect_1(X10)\|(~v5_rlvect_1(X10)\|(~v6_rlvect_1(X10)\|(~v7_rlvect_1(X10)\|(~v8_rlvect_1(X10)\|(~v2_bhsp_1(X10)\|~l1_bhsp_1(X10))))))))))\|(v1_xboole_0(X11)\|~m1_subset_1(X11,k1_zfmisc_1(u1_struct_0(X10))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fraenkel_a_2_2_rusub_5])])])])])])). cnf(c_0_6, plain, (r1_bhsp_1(X2,X1,esk4_3(X4,X2,X3))\|v2_struct_0(X2)\|v1_xboole_0(X3)\|~m1_subset_1(X1,u1_struct_0(X2))\|~r2_hidden(X1,X3)\|~r2_hidden(X4,a_2_2_rusub_5(X2,X3))\|~v13_algstr_0(X2)\|~v2_rlvect_1(X2)\|~v3_rlvect_1(X2)\|~v4_rlvect_1(X2)\|~v5_rlvect_1(X2)\|~v6_rlvect_1(X2)\|~v7_rlvect_1(X2)\|~v8_rlvect_1(X2)\|~v2_bhsp_1(X2)\|~l1_bhsp_1(X2)\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))), inference(split_conjunct,[status(thm)],[c_0_5])). cnf(c_0_7, plain, (X1=esk4_3(X1,X2,X3)\|v2_struct_0(X2)\|v1_xboole_0(X3)\|~r2_hidden(X1,a_2_2_rusub_5(X2,X3))\|~v13_algstr_0(X2)\|~v2_rlvect_1(X2)\|~v3_rlvect_1(X2)\|~v4_rlvect_1(X2)\|~v5_rlvect_1(X2)\|~v6_rlvect_1(X2)\|~v7_rlvect_1(X2)\|~v8_rlvect_1(X2)\|~v2_bhsp_1(X2)\|~l1_bhsp_1(X2)\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))), inference(split_conjunct,[status(thm)],[c_0_5])). fof(c_0_8, plain, ![X16, X17, X18, X19, X20]:((~r1_tarski(X16,X17)\|(~r2_hidden(X18,X16)\|r2_hidden(X18,X17)))&((r2_hidden(esk6_2(X19,X20),X19)\|r1_tarski(X19,X20))&(~r2_hidden(esk6_2(X19,X20),X20)\|r1_tarski(X19,X20)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_tarski])])])])])])). cnf(c_0_9, plain, (r2_hidden(X2,a_2_2_rusub_5(X1,X3))\|v2_struct_0(X1)\|v1_xboole_0(X3)\|~r1_bhsp_1(X1,esk5_4(X2,X1,X3,X4),X4)\|X2!=X4\|~m1_subset_1(X4,u1_struct_0(X1))\|~v13_algstr_0(X1)\|~v2_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v8_rlvect_1(X1)\|~v2_bhsp_1(X1)\|~l1_bhsp_1(X1)\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))), inference(split_conjunct,[status(thm)],[c_0_5])). cnf(c_0_10, plain, (v2_struct_0(X2)\|v1_xboole_0(X3)\|r1_bhsp_1(X2,X1,esk4_3(X4,X2,X3))\|~v13_algstr_0(X2)\|~v2_rlvect_1(X2)\|~v3_rlvect_1(X2)\|~v4_rlvect_1(X2)\|~v5_rlvect_1(X2)\|~v6_rlvect_1(X2)\|~v7_rlvect_1(X2)\|~v8_rlvect_1(X2)\|~v2_bhsp_1(X2)\|~l1_bhsp_1(X2)\|~r2_hidden(X1,X3)\|~m1_subset_1(X1,u1_struct_0(X2))\|~r2_hidden(X4,a_2_2_rusub_5(X2,X3))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))), inference(evalgc,[status(thm)],[c_0_6])). cnf(c_0_11, plain, (esk4_3(X1,X2,X3)=X1\|v2_struct_0(X2)\|v1_xboole_0(X3)\|~v13_algstr_0(X2)\|~v2_rlvect_1(X2)\|~v3_rlvect_1(X2)\|~v4_rlvect_1(X2)\|~v5_rlvect_1(X2)\|~v6_rlvect_1(X2)\|~v7_rlvect_1(X2)\|~v8_rlvect_1(X2)\|~v2_bhsp_1(X2)\|~l1_bhsp_1(X2)\|~r2_hidden(X1,a_2_2_rusub_5(X2,X3))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))), inference(evalgc,[status(thm)],[c_0_7])). cnf(c_0_12, plain, (r2_hidden(esk6_2(X1,X2),X1)\|r1_tarski(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_8])). cnf(c_0_13, plain, (m1_subset_1(esk4_3(X1,X2,X3),u1_struct_0(X2))\|v2_struct_0(X2)\|v1_xboole_0(X3)\|~r2_hidden(X1,a_2_2_rusub_5(X2,X3))\|~v13_algstr_0(X2)\|~v2_rlvect_1(X2)\|~v3_rlvect_1(X2)\|~v4_rlvect_1(X2)\|~v5_rlvect_1(X2)\|~v6_rlvect_1(X2)\|~v7_rlvect_1(X2)\|~v8_rlvect_1(X2)\|~v2_bhsp_1(X2)\|~l1_bhsp_1(X2)\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))), inference(split_conjunct,[status(thm)],[c_0_5])). cnf(c_0_14, plain, (v2_struct_0(X1)\|v1_xboole_0(X3)\|r2_hidden(X2,a_2_2_rusub_5(X1,X3))\|X2!=X4\|~v13_algstr_0(X1)\|~v2_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v8_rlvect_1(X1)\|~v2_bhsp_1(X1)\|~l1_bhsp_1(X1)\|~m1_subset_1(X4,u1_struct_0(X1))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))\|~r1_bhsp_1(X1,esk5_4(X2,X1,X3,X4),X4)), inference(evalgc,[status(thm)],[c_0_9])). cnf(c_0_15, plain, (r1_bhsp_1(X1,X2,X3)\|v1_xboole_0(X4)\|v2_struct_0(X1)\|~r2_hidden(X3,a_2_2_rusub_5(X1,X4))\|~r2_hidden(X2,X4)\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l1_bhsp_1(X1)\|~v2_bhsp_1(X1)\|~v8_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v13_algstr_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_10, c_0_11])])). cnf(c_0_16, plain, (r1_tarski(X1,X2)\|r2_hidden(esk6_2(X1,X2),X1)), inference(evalgc,[status(thm)],[c_0_12])). cnf(c_0_17, plain, (v2_struct_0(X2)\|v1_xboole_0(X3)\|m1_subset_1(esk4_3(X1,X2,X3),u1_struct_0(X2))\|~v13_algstr_0(X2)\|~v2_rlvect_1(X2)\|~v3_rlvect_1(X2)\|~v4_rlvect_1(X2)\|~v5_rlvect_1(X2)\|~v6_rlvect_1(X2)\|~v7_rlvect_1(X2)\|~v8_rlvect_1(X2)\|~v2_bhsp_1(X2)\|~l1_bhsp_1(X2)\|~r2_hidden(X1,a_2_2_rusub_5(X2,X3))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))), inference(evalgc,[status(thm)],[c_0_13])). cnf(c_0_18, plain, (r2_hidden(X1,a_2_2_rusub_5(X2,X3))\|v1_xboole_0(X3)\|v2_struct_0(X2)\|~r1_bhsp_1(X2,esk5_4(X1,X2,X3,X1),X1)\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X1,u1_struct_0(X2))\|~l1_bhsp_1(X2)\|~v2_bhsp_1(X2)\|~v8_rlvect_1(X2)\|~v7_rlvect_1(X2)\|~v6_rlvect_1(X2)\|~v5_rlvect_1(X2)\|~v4_rlvect_1(X2)\|~v3_rlvect_1(X2)\|~v2_rlvect_1(X2)\|~v13_algstr_0(X2)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_14])])). cnf(c_0_19, plain, (r1_bhsp_1(X1,X2,esk6_2(a_2_2_rusub_5(X1,X3),X4))\|v1_xboole_0(X3)\|v2_struct_0(X1)\|r1_tarski(a_2_2_rusub_5(X1,X3),X4)\|~r2_hidden(X2,X3)\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l1_bhsp_1(X1)\|~v2_bhsp_1(X1)\|~v8_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v13_algstr_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_15, c_0_16])])). cnf(c_0_20, plain, (m1_subset_1(X1,u1_struct_0(X2))\|v1_xboole_0(X3)\|v2_struct_0(X2)\|~r2_hidden(X1,a_2_2_rusub_5(X2,X3))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~l1_bhsp_1(X2)\|~v2_bhsp_1(X2)\|~v8_rlvect_1(X2)\|~v7_rlvect_1(X2)\|~v6_rlvect_1(X2)\|~v5_rlvect_1(X2)\|~v4_rlvect_1(X2)\|~v3_rlvect_1(X2)\|~v2_rlvect_1(X2)\|~v13_algstr_0(X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_17, c_0_11])])). cnf(c_0_21, plain, (m1_subset_1(esk5_4(X1,X2,X3,X4),u1_struct_0(X2))\|r2_hidden(X1,a_2_2_rusub_5(X2,X3))\|v2_struct_0(X2)\|v1_xboole_0(X3)\|X1!=X4\|~m1_subset_1(X4,u1_struct_0(X2))\|~v13_algstr_0(X2)\|~v2_rlvect_1(X2)\|~v3_rlvect_1(X2)\|~v4_rlvect_1(X2)\|~v5_rlvect_1(X2)\|~v6_rlvect_1(X2)\|~v7_rlvect_1(X2)\|~v8_rlvect_1(X2)\|~v2_bhsp_1(X2)\|~l1_bhsp_1(X2)\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))), inference(split_conjunct,[status(thm)],[c_0_5])). fof(c_0_22, negated_conjecture, ~(![X1]:((~(v2_struct_0(X1))&(v13_algstr_0(X1)&(v2_rlvect_1(X1)&(v3_rlvect_1(X1)&(v4_rlvect_1(X1)&(v5_rlvect_1(X1)&(v6_rlvect_1(X1)&(v7_rlvect_1(X1)&(v8_rlvect_1(X1)&(v2_bhsp_1(X1)&l1_bhsp_1(X1)))))))))))=>![X2]:((~(v1_xboole_0(X2))&m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))))=>![X3]:((~(v1_xboole_0(X3))&m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1))))=>(r1_tarski(X2,X3)=>r1_tarski(u1_struct_0(k3_rusub_5(X1,X3)),u1_struct_0(k3_rusub_5(X1,X2)))))))), inference(assume_negation,[status(cth)],[t26_rusub_5])). cnf(c_0_23, plain, (r2_hidden(esk6_2(a_2_2_rusub_5(X1,X2),X3),a_2_2_rusub_5(X1,X4))\|v1_xboole_0(X4)\|v2_struct_0(X1)\|r1_tarski(a_2_2_rusub_5(X1,X2),X3)\|v1_xboole_0(X2)\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(esk6_2(a_2_2_rusub_5(X1,X2),X3),u1_struct_0(X1))\|~l1_bhsp_1(X1)\|~v2_bhsp_1(X1)\|~v8_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v13_algstr_0(X1)\|~r2_hidden(esk5_4(esk6_2(a_2_2_rusub_5(X1,X2),X3),X1,X4,esk6_2(a_2_2_rusub_5(X1,X2),X3)),X2)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(esk5_4(esk6_2(a_2_2_rusub_5(X1,X2),X3),X1,X4,esk6_2(a_2_2_rusub_5(X1,X2),X3)),u1_struct_0(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_18, c_0_19])])). cnf(c_0_24, plain, (m1_subset_1(esk6_2(a_2_2_rusub_5(X1,X2),X3),u1_struct_0(X1))\|v1_xboole_0(X2)\|v2_struct_0(X1)\|r1_tarski(a_2_2_rusub_5(X1,X2),X3)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~l1_bhsp_1(X1)\|~v2_bhsp_1(X1)\|~v8_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v13_algstr_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_20, c_0_16])])). cnf(c_0_25, plain, (v2_struct_0(X2)\|v1_xboole_0(X3)\|r2_hidden(X1,a_2_2_rusub_5(X2,X3))\|m1_subset_1(esk5_4(X1,X2,X3,X4),u1_struct_0(X2))\|X1!=X4\|~v13_algstr_0(X2)\|~v2_rlvect_1(X2)\|~v3_rlvect_1(X2)\|~v4_rlvect_1(X2)\|~v5_rlvect_1(X2)\|~v6_rlvect_1(X2)\|~v7_rlvect_1(X2)\|~v8_rlvect_1(X2)\|~v2_bhsp_1(X2)\|~l1_bhsp_1(X2)\|~m1_subset_1(X4,u1_struct_0(X2))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))), inference(evalgc,[status(thm)],[c_0_21])). fof(c_0_26, negated_conjecture, ((~v2_struct_0(esk1_0)&(v13_algstr_0(esk1_0)&(v2_rlvect_1(esk1_0)&(v3_rlvect_1(esk1_0)&(v4_rlvect_1(esk1_0)&(v5_rlvect_1(esk1_0)&(v6_rlvect_1(esk1_0)&(v7_rlvect_1(esk1_0)&(v8_rlvect_1(esk1_0)&(v2_bhsp_1(esk1_0)&l1_bhsp_1(esk1_0)))))))))))&((~v1_xboole_0(esk2_0)&m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(esk1_0))))&((~v1_xboole_0(esk3_0)&m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(esk1_0))))&(r1_tarski(esk2_0,esk3_0)&~r1_tarski(u1_struct_0(k3_rusub_5(esk1_0,esk3_0)),u1_struct_0(k3_rusub_5(esk1_0,esk2_0))))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_22])])])])). fof(c_0_27, plain, ![X22, X23, X24]:((X24!=k3_rusub_5(X22,X23)\|u1_struct_0(X24)=a_2_2_rusub_5(X22,X23)\|(~v1_bhsp_1(X24)\|~m1_rusub_1(X24,X22))\|(v1_xboole_0(X23)\|~m1_subset_1(X23,k1_zfmisc_1(u1_struct_0(X22))))\|(v2_struct_0(X22)\|(~v13_algstr_0(X22)\|(~v2_rlvect_1(X22)\|(~v3_rlvect_1(X22)\|(~v4_rlvect_1(X22)\|(~v5_rlvect_1(X22)\|(~v6_rlvect_1(X22)\|(~v7_rlvect_1(X22)\|(~v8_rlvect_1(X22)\|(~v2_bhsp_1(X22)\|~l1_bhsp_1(X22))))))))))))&(u1_struct_0(X24)!=a_2_2_rusub_5(X22,X23)\|X24=k3_rusub_5(X22,X23)\|(~v1_bhsp_1(X24)\|~m1_rusub_1(X24,X22))\|(v1_xboole_0(X23)\|~m1_subset_1(X23,k1_zfmisc_1(u1_struct_0(X22))))\|(v2_struct_0(X22)\|(~v13_algstr_0(X22)\|(~v2_rlvect_1(X22)\|(~v3_rlvect_1(X22)\|(~v4_rlvect_1(X22)\|(~v5_rlvect_1(X22)\|(~v6_rlvect_1(X22)\|(~v7_rlvect_1(X22)\|(~v8_rlvect_1(X22)\|(~v2_bhsp_1(X22)\|~l1_bhsp_1(X22))))))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d4_rusub_5])])])])])). cnf(c_0_28, plain, (r2_hidden(esk6_2(a_2_2_rusub_5(X1,X2),X3),a_2_2_rusub_5(X1,X4))\|r1_tarski(a_2_2_rusub_5(X1,X2),X3)\|v1_xboole_0(X2)\|v1_xboole_0(X4)\|v2_struct_0(X1)\|~r2_hidden(esk5_4(esk6_2(a_2_2_rusub_5(X1,X2),X3),X1,X4,esk6_2(a_2_2_rusub_5(X1,X2),X3)),X2)\|~m1_subset_1(esk5_4(esk6_2(a_2_2_rusub_5(X1,X2),X3),X1,X4,esk6_2(a_2_2_rusub_5(X1,X2),X3)),u1_struct_0(X1))\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~l1_bhsp_1(X1)\|~v2_bhsp_1(X1)\|~v8_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v13_algstr_0(X1)), inference(csr,[status(thm)],[c_0_23, c_0_24])). cnf(c_0_29, plain, (r2_hidden(X1,a_2_2_rusub_5(X2,X3))\|m1_subset_1(esk5_4(X1,X2,X3,X1),u1_struct_0(X2))\|v1_xboole_0(X3)\|v2_struct_0(X2)\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X1,u1_struct_0(X2))\|~l1_bhsp_1(X2)\|~v2_bhsp_1(X2)\|~v8_rlvect_1(X2)\|~v7_rlvect_1(X2)\|~v6_rlvect_1(X2)\|~v5_rlvect_1(X2)\|~v4_rlvect_1(X2)\|~v3_rlvect_1(X2)\|~v2_rlvect_1(X2)\|~v13_algstr_0(X2)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_25])])). cnf(c_0_30, plain, (r2_hidden(X3,X2)\|~r1_tarski(X1,X2)\|~r2_hidden(X3,X1)), inference(split_conjunct,[status(thm)],[c_0_8])). cnf(c_0_31, negated_conjecture, (r1_tarski(esk2_0,esk3_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_32, plain, (u1_struct_0(X1)=a_2_2_rusub_5(X2,X3)\|v1_xboole_0(X3)\|v2_struct_0(X2)\|X1!=k3_rusub_5(X2,X3)\|~v1_bhsp_1(X1)\|~m1_rusub_1(X1,X2)\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~v13_algstr_0(X2)\|~v2_rlvect_1(X2)\|~v3_rlvect_1(X2)\|~v4_rlvect_1(X2)\|~v5_rlvect_1(X2)\|~v6_rlvect_1(X2)\|~v7_rlvect_1(X2)\|~v8_rlvect_1(X2)\|~v2_bhsp_1(X2)\|~l1_bhsp_1(X2)), inference(split_conjunct,[status(thm)],[c_0_27])). fof(c_0_33, plain, ![X25, X26]:((v1_bhsp_1(k3_rusub_5(X25,X26))\|(v2_struct_0(X25)\|(~v13_algstr_0(X25)\|(~v2_rlvect_1(X25)\|(~v3_rlvect_1(X25)\|(~v4_rlvect_1(X25)\|(~v5_rlvect_1(X25)\|(~v6_rlvect_1(X25)\|(~v7_rlvect_1(X25)\|(~v8_rlvect_1(X25)\|(~v2_bhsp_1(X25)\|~l1_bhsp_1(X25))))))))))\|(v1_xboole_0(X26)\|~m1_subset_1(X26,k1_zfmisc_1(u1_struct_0(X25))))))&(m1_rusub_1(k3_rusub_5(X25,X26),X25)\|(v2_struct_0(X25)\|(~v13_algstr_0(X25)\|(~v2_rlvect_1(X25)\|(~v3_rlvect_1(X25)\|(~v4_rlvect_1(X25)\|(~v5_rlvect_1(X25)\|(~v6_rlvect_1(X25)\|(~v7_rlvect_1(X25)\|(~v8_rlvect_1(X25)\|(~v2_bhsp_1(X25)\|~l1_bhsp_1(X25))))))))))\|(v1_xboole_0(X26)\|~m1_subset_1(X26,k1_zfmisc_1(u1_struct_0(X25))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k3_rusub_5])])])])). cnf(c_0_34, plain, (r2_hidden(esk6_2(a_2_2_rusub_5(X1,X2),X3),a_2_2_rusub_5(X1,X4))\|r1_tarski(a_2_2_rusub_5(X1,X2),X3)\|v1_xboole_0(X2)\|v1_xboole_0(X4)\|v2_struct_0(X1)\|~r2_hidden(esk5_4(esk6_2(a_2_2_rusub_5(X1,X2),X3),X1,X4,esk6_2(a_2_2_rusub_5(X1,X2),X3)),X2)\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~l1_bhsp_1(X1)\|~v2_bhsp_1(X1)\|~v8_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v13_algstr_0(X1)\|~m1_subset_1(esk6_2(a_2_2_rusub_5(X1,X2),X3),u1_struct_0(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_28, c_0_29])])). cnf(c_0_35, plain, (r2_hidden(X3,X2)\|~r1_tarski(X1,X2)\|~r2_hidden(X3,X1)), inference(evalgc,[status(thm)],[c_0_30])). cnf(c_0_36, negated_conjecture, (r1_tarski(esk2_0,esk3_0)), inference(evalgc,[status(thm)],[c_0_31])). cnf(c_0_37, negated_conjecture, (~v1_xboole_0(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_38, plain, (r2_hidden(esk5_4(X1,X2,X3,X4),X3)\|r2_hidden(X1,a_2_2_rusub_5(X2,X3))\|v2_struct_0(X2)\|v1_xboole_0(X3)\|X1!=X4\|~m1_subset_1(X4,u1_struct_0(X2))\|~v13_algstr_0(X2)\|~v2_rlvect_1(X2)\|~v3_rlvect_1(X2)\|~v4_rlvect_1(X2)\|~v5_rlvect_1(X2)\|~v6_rlvect_1(X2)\|~v7_rlvect_1(X2)\|~v8_rlvect_1(X2)\|~v2_bhsp_1(X2)\|~l1_bhsp_1(X2)\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))), inference(split_conjunct,[status(thm)],[c_0_5])). cnf(c_0_39, plain, (u1_struct_0(X1)=a_2_2_rusub_5(X2,X3)\|v2_struct_0(X2)\|v1_xboole_0(X3)\|X1!=k3_rusub_5(X2,X3)\|~v13_algstr_0(X2)\|~v2_rlvect_1(X2)\|~v3_rlvect_1(X2)\|~v4_rlvect_1(X2)\|~v5_rlvect_1(X2)\|~v6_rlvect_1(X2)\|~v7_rlvect_1(X2)\|~v8_rlvect_1(X2)\|~v2_bhsp_1(X2)\|~l1_bhsp_1(X2)\|~v1_bhsp_1(X1)\|~m1_rusub_1(X1,X2)\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))), inference(evalgc,[status(thm)],[c_0_32])). cnf(c_0_40, plain, (v1_bhsp_1(k3_rusub_5(X1,X2))\|v2_struct_0(X1)\|v1_xboole_0(X2)\|~v13_algstr_0(X1)\|~v2_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v8_rlvect_1(X1)\|~v2_bhsp_1(X1)\|~l1_bhsp_1(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(split_conjunct,[status(thm)],[c_0_33])). cnf(c_0_41, plain, (m1_rusub_1(k3_rusub_5(X1,X2),X1)\|v2_struct_0(X1)\|v1_xboole_0(X2)\|~v13_algstr_0(X1)\|~v2_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v8_rlvect_1(X1)\|~v2_bhsp_1(X1)\|~l1_bhsp_1(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(split_conjunct,[status(thm)],[c_0_33])). cnf(c_0_42, plain, (r2_hidden(esk6_2(a_2_2_rusub_5(X1,X2),X3),a_2_2_rusub_5(X1,X4))\|r1_tarski(a_2_2_rusub_5(X1,X2),X3)\|v1_xboole_0(X4)\|v1_xboole_0(X2)\|v2_struct_0(X1)\|~r2_hidden(esk5_4(esk6_2(a_2_2_rusub_5(X1,X2),X3),X1,X4,esk6_2(a_2_2_rusub_5(X1,X2),X3)),X2)\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~l1_bhsp_1(X1)\|~v2_bhsp_1(X1)\|~v8_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v13_algstr_0(X1)), inference(csr,[status(thm)],[c_0_34, c_0_24])). cnf(c_0_43, negated_conjecture, (r2_hidden(X1,esk3_0)\|~r2_hidden(X1,esk2_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_35, c_0_36])])). cnf(c_0_44, negated_conjecture, (~v1_xboole_0(esk3_0)), inference(evalgc,[status(thm)],[c_0_37])). cnf(c_0_45, plain, (v2_struct_0(X2)\|v1_xboole_0(X3)\|r2_hidden(X1,a_2_2_rusub_5(X2,X3))\|r2_hidden(esk5_4(X1,X2,X3,X4),X3)\|X1!=X4\|~v13_algstr_0(X2)\|~v2_rlvect_1(X2)\|~v3_rlvect_1(X2)\|~v4_rlvect_1(X2)\|~v5_rlvect_1(X2)\|~v6_rlvect_1(X2)\|~v7_rlvect_1(X2)\|~v8_rlvect_1(X2)\|~v2_bhsp_1(X2)\|~l1_bhsp_1(X2)\|~m1_subset_1(X4,u1_struct_0(X2))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))), inference(evalgc,[status(thm)],[c_0_38])). cnf(c_0_46, negated_conjecture, (~v1_xboole_0(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_47, negated_conjecture, (~r1_tarski(u1_struct_0(k3_rusub_5(esk1_0,esk3_0)),u1_struct_0(k3_rusub_5(esk1_0,esk2_0)))), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_48, plain, (u1_struct_0(k3_rusub_5(X1,X2))=a_2_2_rusub_5(X1,X2)\|v1_xboole_0(X2)\|v2_struct_0(X1)\|~m1_rusub_1(k3_rusub_5(X1,X2),X1)\|~v1_bhsp_1(k3_rusub_5(X1,X2))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~l1_bhsp_1(X1)\|~v2_bhsp_1(X1)\|~v8_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v13_algstr_0(X1)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_39])])). cnf(c_0_49, plain, (v2_struct_0(X1)\|v1_xboole_0(X2)\|v1_bhsp_1(k3_rusub_5(X1,X2))\|~v13_algstr_0(X1)\|~v2_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v8_rlvect_1(X1)\|~v2_bhsp_1(X1)\|~l1_bhsp_1(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(evalgc,[status(thm)],[c_0_40])). cnf(c_0_50, plain, (v2_struct_0(X1)\|v1_xboole_0(X2)\|m1_rusub_1(k3_rusub_5(X1,X2),X1)\|~v13_algstr_0(X1)\|~v2_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v8_rlvect_1(X1)\|~v2_bhsp_1(X1)\|~l1_bhsp_1(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(evalgc,[status(thm)],[c_0_41])). cnf(c_0_51, negated_conjecture, (m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(esk1_0)))), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_52, negated_conjecture, (l1_bhsp_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_53, negated_conjecture, (v2_bhsp_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_54, negated_conjecture, (v8_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_55, negated_conjecture, (v7_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_56, negated_conjecture, (v6_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_57, negated_conjecture, (v5_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_58, negated_conjecture, (v4_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_59, negated_conjecture, (v3_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_60, negated_conjecture, (v2_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_61, negated_conjecture, (v13_algstr_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_62, negated_conjecture, (~v2_struct_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_63, plain, (r1_tarski(X1,X2)\|~r2_hidden(esk6_2(X1,X2),X2)), inference(split_conjunct,[status(thm)],[c_0_8])). cnf(c_0_64, negated_conjecture, (r2_hidden(esk6_2(a_2_2_rusub_5(X1,esk3_0),X2),a_2_2_rusub_5(X1,X3))\|r1_tarski(a_2_2_rusub_5(X1,esk3_0),X2)\|v1_xboole_0(X3)\|v2_struct_0(X1)\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(X1)))\|~l1_bhsp_1(X1)\|~v2_bhsp_1(X1)\|~v8_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v13_algstr_0(X1)\|~r2_hidden(esk5_4(esk6_2(a_2_2_rusub_5(X1,esk3_0),X2),X1,X3,esk6_2(a_2_2_rusub_5(X1,esk3_0),X2)),esk2_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42, c_0_43]), c_0_44])])). cnf(c_0_65, plain, (r2_hidden(esk5_4(X1,X2,X3,X1),X3)\|r2_hidden(X1,a_2_2_rusub_5(X2,X3))\|v1_xboole_0(X3)\|v2_struct_0(X2)\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X1,u1_struct_0(X2))\|~l1_bhsp_1(X2)\|~v2_bhsp_1(X2)\|~v8_rlvect_1(X2)\|~v7_rlvect_1(X2)\|~v6_rlvect_1(X2)\|~v5_rlvect_1(X2)\|~v4_rlvect_1(X2)\|~v3_rlvect_1(X2)\|~v2_rlvect_1(X2)\|~v13_algstr_0(X2)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_45])])). cnf(c_0_66, negated_conjecture, (~v1_xboole_0(esk2_0)), inference(evalgc,[status(thm)],[c_0_46])). cnf(c_0_67, negated_conjecture, (~r1_tarski(u1_struct_0(k3_rusub_5(esk1_0,esk3_0)),u1_struct_0(k3_rusub_5(esk1_0,esk2_0)))), inference(evalgc,[status(thm)],[c_0_47])). cnf(c_0_68, plain, (u1_struct_0(k3_rusub_5(X1,X2))=a_2_2_rusub_5(X1,X2)\|v1_xboole_0(X2)\|v2_struct_0(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~l1_bhsp_1(X1)\|~v2_bhsp_1(X1)\|~v8_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v13_algstr_0(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_48, c_0_49]), c_0_50])). cnf(c_0_69, negated_conjecture, (m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(esk1_0)))), inference(evalgc,[status(thm)],[c_0_51])). cnf(c_0_70, negated_conjecture, (l1_bhsp_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_52])). cnf(c_0_71, negated_conjecture, (v2_bhsp_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_53])). cnf(c_0_72, negated_conjecture, (v8_rlvect_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_54])). cnf(c_0_73, negated_conjecture, (v7_rlvect_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_55])). cnf(c_0_74, negated_conjecture, (v6_rlvect_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_56])). cnf(c_0_75, negated_conjecture, (v5_rlvect_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_57])). cnf(c_0_76, negated_conjecture, (v4_rlvect_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_58])). cnf(c_0_77, negated_conjecture, (v3_rlvect_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_59])). cnf(c_0_78, negated_conjecture, (v2_rlvect_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_60])). cnf(c_0_79, negated_conjecture, (v13_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_61])). cnf(c_0_80, negated_conjecture, (~v2_struct_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_62])). cnf(c_0_81, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(esk1_0)))), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_82, plain, (r1_tarski(X1,X2)\|~r2_hidden(esk6_2(X1,X2),X2)), inference(evalgc,[status(thm)],[c_0_63])). cnf(c_0_83, negated_conjecture, (r2_hidden(esk6_2(a_2_2_rusub_5(X1,esk3_0),X2),a_2_2_rusub_5(X1,esk2_0))\|r1_tarski(a_2_2_rusub_5(X1,esk3_0),X2)\|v2_struct_0(X1)\|~m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(X1)))\|~l1_bhsp_1(X1)\|~v2_bhsp_1(X1)\|~v8_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v13_algstr_0(X1)\|~m1_subset_1(esk6_2(a_2_2_rusub_5(X1,esk3_0),X2),u1_struct_0(X1))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_64, c_0_65]), c_0_66])])). cnf(c_0_84, negated_conjecture, (~r1_tarski(a_2_2_rusub_5(esk1_0,esk3_0),u1_struct_0(k3_rusub_5(esk1_0,esk2_0)))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67, c_0_68]), c_0_69]), c_0_70]), c_0_71]), c_0_72]), c_0_73]), c_0_74]), c_0_75]), c_0_76]), c_0_77]), c_0_78]), c_0_79])]), c_0_44]), c_0_80])])). cnf(c_0_85, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(esk1_0)))), inference(evalgc,[status(thm)],[c_0_81])). cnf(c_0_86, negated_conjecture, (r1_tarski(a_2_2_rusub_5(X1,esk3_0),a_2_2_rusub_5(X1,esk2_0))\|v2_struct_0(X1)\|~m1_subset_1(esk6_2(a_2_2_rusub_5(X1,esk3_0),a_2_2_rusub_5(X1,esk2_0)),u1_struct_0(X1))\|~m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(X1)))\|~l1_bhsp_1(X1)\|~v2_bhsp_1(X1)\|~v8_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v13_algstr_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_82, c_0_83])])). cnf(c_0_87, negated_conjecture, (~r1_tarski(a_2_2_rusub_5(esk1_0,esk3_0),a_2_2_rusub_5(esk1_0,esk2_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84, c_0_68]), c_0_85]), c_0_70]), c_0_71]), c_0_72]), c_0_73]), c_0_74]), c_0_75]), c_0_76]), c_0_77]), c_0_78]), c_0_79])]), c_0_66]), c_0_80])])). cnf(c_0_88, negated_conjecture, (r1_tarski(a_2_2_rusub_5(X1,esk3_0),a_2_2_rusub_5(X1,esk2_0))\|v2_struct_0(X1)\|~m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(X1)))\|~l1_bhsp_1(X1)\|~v2_bhsp_1(X1)\|~v8_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v13_algstr_0(X1)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_86, c_0_24]), c_0_44])])). cnf(c_0_89, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87, c_0_88]), c_0_69]), c_0_85]), c_0_70]), c_0_71]), c_0_72]), c_0_73]), c_0_74]), c_0_75]), c_0_76]), c_0_77]), c_0_78]), c_0_79])]), c_0_80]), ['proof']). # SZS output end CNFRefutation	theorem Th26: for V being RealUnitarySpace, M,N being non empty Subset of V st M c= N holds the carrier of Ort_Comp N c= the carrier of Ort_Comp M proof let V be RealUnitarySpace; let M,N be non empty Subset of V; assume A1: M c= N; for x being set st x in the carrier of Ort_Comp N holds x in the carrier of Ort_Comp M proof let x be set; assume x in the carrier of Ort_Comp N; then x in {v where v is VECTOR of V : for w being VECTOR of V st w in N holds w, v are_orthogonal} by Def4; then A2: ex v1 being VECTOR of V st x = v1 & for w being VECTOR of V st w in N holds w,v1 are_orthogonal; then reconsider x as VECTOR of V; for y being VECTOR of V st y in M holds y,x are_orthogonal by A1,A2; then x in {v where v is VECTOR of V : for w being VECTOR of V st w in M holds w,v are_orthogonal}; hence thesis by Def4; end; hence thesis by TARSKI:def 3; end;	Convert the following ATP output trace into a readable Mizar proof.
t10_valued_1	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(d7_valued_1, axiom, ![X1]:((v1_relat_1(X1)&(v1_funct_1(X1)&v1_valued_0(X1)))=>![X2]:((v1_relat_1(X2)&(v1_funct_1(X2)&v1_valued_0(X2)))=>(X2=k35_valued_1(X1)<=>(k9_xtuple_0(X2)=k9_xtuple_0(X1)&![X3]:(r2_hidden(X3,k9_xtuple_0(X2))=>k1_funct_1(X2,X3)=k5_xcmplx_0(k1_funct_1(X1,X3))))))), file('/scratch/mptp/predsminms1/t10_valued_1__0', d7_valued_1)). fof(d2_funct_1, axiom, ![X1]:((v1_relat_1(X1)&v1_funct_1(X1))=>![X2, X3]:((r2_hidden(X2,k9_xtuple_0(X1))=>(X3=k1_funct_1(X1,X2)<=>r2_hidden(k4_tarski(X2,X3),X1)))&(~(r2_hidden(X2,k9_xtuple_0(X1)))=>(X3=k1_funct_1(X1,X2)<=>X3=k1_xboole_0)))), file('/scratch/mptp/predsminms1/t10_valued_1__0', d2_funct_1)). fof(dt_k35_valued_1, axiom, ![X1]:((v1_relat_1(X1)&(v1_funct_1(X1)&v1_valued_0(X1)))=>(v1_relat_1(k35_valued_1(X1))&(v1_funct_1(k35_valued_1(X1))&v1_valued_0(k35_valued_1(X1))))), file('/scratch/mptp/predsminms1/t10_valued_1__0', dt_k35_valued_1)). fof(cc4_xxreal_0, axiom, ![X1]:((~(v1_xboole_0(X1))&(v1_xxreal_0(X1)&~(v3_xxreal_0(X1))))=>(v1_xxreal_0(X1)&v2_xxreal_0(X1))), file('/scratch/mptp/predsminms1/t10_valued_1__0', cc4_xxreal_0)). fof(cc4_xreal_0, axiom, ![X1]:(v1_xreal_0(X1)=>v1_xxreal_0(X1)), file('/scratch/mptp/predsminms1/t10_valued_1__0', cc4_xreal_0)). fof(t10_valued_1, conjecture, ![X1]:((v1_relat_1(X1)&(v1_funct_1(X1)&v1_valued_0(X1)))=>![X2]:k1_funct_1(k35_valued_1(X1),X2)=k5_xcmplx_0(k1_funct_1(X1,X2))), file('/scratch/mptp/predsminms1/t10_valued_1__0', t10_valued_1)). fof(t6_boole, axiom, ![X1]:(v1_xboole_0(X1)=>X1=k1_xboole_0), file('/scratch/mptp/predsminms1/t10_valued_1__0', t6_boole)). fof(fc30_xreal_0, axiom, ![X1]:((~(v3_xxreal_0(X1))&v1_xreal_0(X1))=>(v1_xcmplx_0(k5_xcmplx_0(X1))&~(v3_xxreal_0(k5_xcmplx_0(X1))))), file('/scratch/mptp/predsminms1/t10_valued_1__0', fc30_xreal_0)). fof(cc3_xxreal_0, axiom, ![X1]:((v1_xxreal_0(X1)&v2_xxreal_0(X1))=>(~(v1_xboole_0(X1))&(v1_xxreal_0(X1)&~(v3_xxreal_0(X1))))), file('/scratch/mptp/predsminms1/t10_valued_1__0', cc3_xxreal_0)). fof(rc4_xreal_0, axiom, ?[X1]:(v1_xboole_0(X1)&(v1_xcmplx_0(X1)&(v1_xxreal_0(X1)&v1_xreal_0(X1)))), file('/scratch/mptp/predsminms1/t10_valued_1__0', rc4_xreal_0)). fof(fc4_xreal_0, axiom, ![X1]:(v1_xreal_0(X1)=>(v1_xcmplx_0(k5_xcmplx_0(X1))&v1_xreal_0(k5_xcmplx_0(X1)))), file('/scratch/mptp/predsminms1/t10_valued_1__0', fc4_xreal_0)). fof(cc2_nat_1, axiom, ![X1]:(m1_subset_1(X1,k5_numbers)=>~(v3_xxreal_0(X1))), file('/scratch/mptp/predsminms1/t10_valued_1__0', cc2_nat_1)). fof(t1_numerals, axiom, m1_subset_1(k1_xboole_0,k4_ordinal1), file('/scratch/mptp/predsminms1/t10_valued_1__0', t1_numerals)). fof(redefinition_k5_numbers, axiom, k5_numbers=k4_ordinal1, file('/scratch/mptp/predsminms1/t10_valued_1__0', redefinition_k5_numbers)). fof(fc28_xreal_0, axiom, ![X1]:((~(v2_xxreal_0(X1))&v1_xreal_0(X1))=>(v1_xcmplx_0(k5_xcmplx_0(X1))&~(v2_xxreal_0(k5_xcmplx_0(X1))))), file('/scratch/mptp/predsminms1/t10_valued_1__0', fc28_xreal_0)). fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0), file('/scratch/mptp/predsminms1/t10_valued_1__0', fc1_xboole_0)). fof(c_0_16, plain, ![X10, X11, X12]:(((k9_xtuple_0(X11)=k9_xtuple_0(X10)\|X11!=k35_valued_1(X10)\|(~v1_relat_1(X11)\|(~v1_funct_1(X11)\|~v1_valued_0(X11)))\|(~v1_relat_1(X10)\|(~v1_funct_1(X10)\|~v1_valued_0(X10))))&(~r2_hidden(X12,k9_xtuple_0(X11))\|k1_funct_1(X11,X12)=k5_xcmplx_0(k1_funct_1(X10,X12))\|X11!=k35_valued_1(X10)\|(~v1_relat_1(X11)\|(~v1_funct_1(X11)\|~v1_valued_0(X11)))\|(~v1_relat_1(X10)\|(~v1_funct_1(X10)\|~v1_valued_0(X10)))))&((r2_hidden(esk3_2(X10,X11),k9_xtuple_0(X11))\|k9_xtuple_0(X11)!=k9_xtuple_0(X10)\|X11=k35_valued_1(X10)\|(~v1_relat_1(X11)\|(~v1_funct_1(X11)\|~v1_valued_0(X11)))\|(~v1_relat_1(X10)\|(~v1_funct_1(X10)\|~v1_valued_0(X10))))&(k1_funct_1(X11,esk3_2(X10,X11))!=k5_xcmplx_0(k1_funct_1(X10,esk3_2(X10,X11)))\|k9_xtuple_0(X11)!=k9_xtuple_0(X10)\|X11=k35_valued_1(X10)\|(~v1_relat_1(X11)\|(~v1_funct_1(X11)\|~v1_valued_0(X11)))\|(~v1_relat_1(X10)\|(~v1_funct_1(X10)\|~v1_valued_0(X10)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_valued_1])])])])])). fof(c_0_17, plain, ![X7, X8, X9]:(((X9!=k1_funct_1(X7,X8)\|r2_hidden(k4_tarski(X8,X9),X7)\|~r2_hidden(X8,k9_xtuple_0(X7))\|(~v1_relat_1(X7)\|~v1_funct_1(X7)))&(~r2_hidden(k4_tarski(X8,X9),X7)\|X9=k1_funct_1(X7,X8)\|~r2_hidden(X8,k9_xtuple_0(X7))\|(~v1_relat_1(X7)\|~v1_funct_1(X7))))&((X9!=k1_funct_1(X7,X8)\|X9=k1_xboole_0\|r2_hidden(X8,k9_xtuple_0(X7))\|(~v1_relat_1(X7)\|~v1_funct_1(X7)))&(X9!=k1_xboole_0\|X9=k1_funct_1(X7,X8)\|r2_hidden(X8,k9_xtuple_0(X7))\|(~v1_relat_1(X7)\|~v1_funct_1(X7))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d2_funct_1])])])])])). cnf(c_0_18, plain, (k9_xtuple_0(X1)=k9_xtuple_0(X2)\|X1!=k35_valued_1(X2)\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v1_valued_0(X1)\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v1_valued_0(X2)), inference(split_conjunct,[status(thm)],[c_0_16])). fof(c_0_19, plain, ![X6]:((v1_relat_1(k35_valued_1(X6))\|(~v1_relat_1(X6)\|(~v1_funct_1(X6)\|~v1_valued_0(X6))))&((v1_funct_1(k35_valued_1(X6))\|(~v1_relat_1(X6)\|(~v1_funct_1(X6)\|~v1_valued_0(X6))))&(v1_valued_0(k35_valued_1(X6))\|(~v1_relat_1(X6)\|(~v1_funct_1(X6)\|~v1_valued_0(X6)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k35_valued_1])])])). cnf(c_0_20, plain, (X1=k1_funct_1(X2,X3)\|r2_hidden(X3,k9_xtuple_0(X2))\|X1!=k1_xboole_0\|~v1_relat_1(X2)\|~v1_funct_1(X2)), inference(split_conjunct,[status(thm)],[c_0_17])). cnf(c_0_21, plain, (k9_xtuple_0(X1)=k9_xtuple_0(X2)\|X1!=k35_valued_1(X2)\|~v1_relat_1(X2)\|~v1_relat_1(X1)\|~v1_funct_1(X2)\|~v1_funct_1(X1)\|~v1_valued_0(X2)\|~v1_valued_0(X1)), inference(evalgc,[status(thm)],[c_0_18])). cnf(c_0_22, plain, (v1_relat_1(k35_valued_1(X1))\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v1_valued_0(X1)), inference(split_conjunct,[status(thm)],[c_0_19])). cnf(c_0_23, plain, (v1_funct_1(k35_valued_1(X1))\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v1_valued_0(X1)), inference(split_conjunct,[status(thm)],[c_0_19])). cnf(c_0_24, plain, (v1_valued_0(k35_valued_1(X1))\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v1_valued_0(X1)), inference(split_conjunct,[status(thm)],[c_0_19])). cnf(c_0_25, plain, (k1_funct_1(X2,X1)=k5_xcmplx_0(k1_funct_1(X3,X1))\|~r2_hidden(X1,k9_xtuple_0(X2))\|X2!=k35_valued_1(X3)\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v1_valued_0(X2)\|~v1_relat_1(X3)\|~v1_funct_1(X3)\|~v1_valued_0(X3)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_26, plain, (X1=k1_funct_1(X2,X3)\|r2_hidden(X3,k9_xtuple_0(X2))\|X1!=k1_xboole_0\|~v1_relat_1(X2)\|~v1_funct_1(X2)), inference(evalgc,[status(thm)],[c_0_20])). fof(c_0_27, plain, ![X22]:((v1_xxreal_0(X22)\|(v1_xboole_0(X22)\|(~v1_xxreal_0(X22)\|v3_xxreal_0(X22))))&(v2_xxreal_0(X22)\|(v1_xboole_0(X22)\|(~v1_xxreal_0(X22)\|v3_xxreal_0(X22))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[cc4_xxreal_0])])])])). fof(c_0_28, plain, ![X20]:(~v1_xreal_0(X20)\|v1_xxreal_0(X20)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc4_xreal_0])])). cnf(c_0_29, plain, (k9_xtuple_0(k35_valued_1(X1))=k9_xtuple_0(X1)\|~v1_valued_0(X1)\|~v1_valued_0(k35_valued_1(X1))\|~v1_funct_1(X1)\|~v1_funct_1(k35_valued_1(X1))\|~v1_relat_1(X1)\|~v1_relat_1(k35_valued_1(X1))), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_21])])). cnf(c_0_30, plain, (v1_relat_1(k35_valued_1(X1))\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v1_valued_0(X1)), inference(evalgc,[status(thm)],[c_0_22])). cnf(c_0_31, plain, (v1_funct_1(k35_valued_1(X1))\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v1_valued_0(X1)), inference(evalgc,[status(thm)],[c_0_23])). cnf(c_0_32, plain, (v1_valued_0(k35_valued_1(X1))\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v1_valued_0(X1)), inference(evalgc,[status(thm)],[c_0_24])). fof(c_0_33, negated_conjecture, ~(![X1]:((v1_relat_1(X1)&(v1_funct_1(X1)&v1_valued_0(X1)))=>![X2]:k1_funct_1(k35_valued_1(X1),X2)=k5_xcmplx_0(k1_funct_1(X1,X2)))), inference(assume_negation,[status(cth)],[t10_valued_1])). cnf(c_0_34, plain, (k1_funct_1(X2,X1)=k5_xcmplx_0(k1_funct_1(X3,X1))\|X2!=k35_valued_1(X3)\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v1_valued_0(X3)\|~v1_valued_0(X2)\|~r2_hidden(X1,k9_xtuple_0(X2))), inference(evalgc,[status(thm)],[c_0_25])). cnf(c_0_35, plain, (k1_funct_1(X1,X2)=k1_xboole_0\|r2_hidden(X2,k9_xtuple_0(X1))\|~v1_funct_1(X1)\|~v1_relat_1(X1)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_26])])). fof(c_0_36, plain, ![X15]:(~v1_xboole_0(X15)\|X15=k1_xboole_0), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])])). cnf(c_0_37, plain, (v2_xxreal_0(X1)\|v1_xboole_0(X1)\|v3_xxreal_0(X1)\|~v1_xxreal_0(X1)), inference(split_conjunct,[status(thm)],[c_0_27])). cnf(c_0_38, plain, (v1_xxreal_0(X1)\|~v1_xreal_0(X1)), inference(split_conjunct,[status(thm)],[c_0_28])). cnf(c_0_39, plain, (k9_xtuple_0(k35_valued_1(X1))=k9_xtuple_0(X1)\|~v1_valued_0(X1)\|~v1_funct_1(X1)\|~v1_relat_1(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_29, c_0_30]), c_0_31]), c_0_32])). fof(c_0_40, negated_conjecture, ((v1_relat_1(esk1_0)&(v1_funct_1(esk1_0)&v1_valued_0(esk1_0)))&k1_funct_1(k35_valued_1(esk1_0),esk2_0)!=k5_xcmplx_0(k1_funct_1(esk1_0,esk2_0))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])])])). cnf(c_0_41, plain, (k1_funct_1(X1,X2)=k5_xcmplx_0(k1_funct_1(X3,X2))\|k1_funct_1(X1,X2)=k1_xboole_0\|X1!=k35_valued_1(X3)\|~v1_valued_0(X3)\|~v1_valued_0(X1)\|~v1_funct_1(X3)\|~v1_funct_1(X1)\|~v1_relat_1(X3)\|~v1_relat_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_34, c_0_35])])). fof(c_0_42, plain, ![X19]:((v1_xcmplx_0(k5_xcmplx_0(X19))\|(v3_xxreal_0(X19)\|~v1_xreal_0(X19)))&(~v3_xxreal_0(k5_xcmplx_0(X19))\|(v3_xxreal_0(X19)\|~v1_xreal_0(X19)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fc30_xreal_0])])])])). cnf(c_0_43, plain, (X1=k1_xboole_0\|~v1_xboole_0(X1)), inference(split_conjunct,[status(thm)],[c_0_36])). cnf(c_0_44, plain, (v1_xboole_0(X1)\|v2_xxreal_0(X1)\|v3_xxreal_0(X1)\|~v1_xxreal_0(X1)), inference(evalgc,[status(thm)],[c_0_37])). cnf(c_0_45, plain, (v1_xxreal_0(X1)\|~v1_xreal_0(X1)), inference(evalgc,[status(thm)],[c_0_38])). fof(c_0_46, plain, ![X16]:((~v1_xboole_0(X16)\|(~v1_xxreal_0(X16)\|~v2_xxreal_0(X16)))&((v1_xxreal_0(X16)\|(~v1_xxreal_0(X16)\|~v2_xxreal_0(X16)))&(~v3_xxreal_0(X16)\|(~v1_xxreal_0(X16)\|~v2_xxreal_0(X16))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[cc3_xxreal_0])])])])). fof(c_0_47, plain, (v1_xboole_0(esk4_0)&(v1_xcmplx_0(esk4_0)&(v1_xxreal_0(esk4_0)&v1_xreal_0(esk4_0)))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc4_xreal_0])])). cnf(c_0_48, plain, (k1_funct_1(k35_valued_1(X1),X2)=k5_xcmplx_0(k1_funct_1(X3,X2))\|k35_valued_1(X1)!=k35_valued_1(X3)\|~r2_hidden(X2,k9_xtuple_0(X1))\|~v1_valued_0(X3)\|~v1_valued_0(k35_valued_1(X1))\|~v1_funct_1(X3)\|~v1_funct_1(k35_valued_1(X1))\|~v1_relat_1(X3)\|~v1_relat_1(k35_valued_1(X1))\|~v1_valued_0(X1)\|~v1_funct_1(X1)\|~v1_relat_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_34, c_0_39])])). cnf(c_0_49, negated_conjecture, (k1_funct_1(k35_valued_1(esk1_0),esk2_0)!=k5_xcmplx_0(k1_funct_1(esk1_0,esk2_0))), inference(split_conjunct,[status(thm)],[c_0_40])). cnf(c_0_50, plain, (k1_funct_1(k35_valued_1(X1),X2)=k5_xcmplx_0(k1_funct_1(X1,X2))\|k1_funct_1(k35_valued_1(X1),X2)=k1_xboole_0\|~v1_valued_0(X1)\|~v1_valued_0(k35_valued_1(X1))\|~v1_funct_1(X1)\|~v1_funct_1(k35_valued_1(X1))\|~v1_relat_1(X1)\|~v1_relat_1(k35_valued_1(X1))), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_41])])). cnf(c_0_51, negated_conjecture, (v1_valued_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_40])). cnf(c_0_52, negated_conjecture, (v1_funct_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_40])). cnf(c_0_53, negated_conjecture, (v1_relat_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_40])). cnf(c_0_54, plain, (v3_xxreal_0(X1)\|~v3_xxreal_0(k5_xcmplx_0(X1))\|~v1_xreal_0(X1)), inference(split_conjunct,[status(thm)],[c_0_42])). cnf(c_0_55, plain, (X1=k1_xboole_0\|~v1_xboole_0(X1)), inference(evalgc,[status(thm)],[c_0_43])). cnf(c_0_56, plain, (v3_xxreal_0(X1)\|v2_xxreal_0(X1)\|v1_xboole_0(X1)\|~v1_xreal_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_44, c_0_45])])). fof(c_0_57, plain, ![X21]:((v1_xcmplx_0(k5_xcmplx_0(X21))\|~v1_xreal_0(X21))&(v1_xreal_0(k5_xcmplx_0(X21))\|~v1_xreal_0(X21))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc4_xreal_0])])])). cnf(c_0_58, plain, (~v1_xboole_0(X1)\|~v1_xxreal_0(X1)\|~v2_xxreal_0(X1)), inference(split_conjunct,[status(thm)],[c_0_46])). cnf(c_0_59, plain, (v1_xboole_0(esk4_0)), inference(split_conjunct,[status(thm)],[c_0_47])). cnf(c_0_60, plain, (k1_funct_1(k35_valued_1(X1),X2)=k5_xcmplx_0(k1_funct_1(X3,X2))\|k35_valued_1(X1)!=k35_valued_1(X3)\|~r2_hidden(X2,k9_xtuple_0(X1))\|~v1_valued_0(X3)\|~v1_valued_0(X1)\|~v1_funct_1(X3)\|~v1_funct_1(X1)\|~v1_relat_1(X3)\|~v1_relat_1(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_48, c_0_30]), c_0_31]), c_0_32])). cnf(c_0_61, negated_conjecture, (k1_funct_1(k35_valued_1(esk1_0),esk2_0)!=k5_xcmplx_0(k1_funct_1(esk1_0,esk2_0))), inference(evalgc,[status(thm)],[c_0_49])). cnf(c_0_62, plain, (k1_funct_1(k35_valued_1(X1),X2)=k5_xcmplx_0(k1_funct_1(X1,X2))\|k1_funct_1(k35_valued_1(X1),X2)=k1_xboole_0\|~v1_valued_0(X1)\|~v1_funct_1(X1)\|~v1_relat_1(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_50, c_0_30]), c_0_31]), c_0_32])). cnf(c_0_63, negated_conjecture, (v1_valued_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_51])). cnf(c_0_64, negated_conjecture, (v1_funct_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_52])). cnf(c_0_65, negated_conjecture, (v1_relat_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_53])). fof(c_0_66, plain, ![X17]:(~m1_subset_1(X17,k5_numbers)\|~v3_xxreal_0(X17)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[cc2_nat_1])])])). cnf(c_0_67, plain, (m1_subset_1(k1_xboole_0,k4_ordinal1)), inference(split_conjunct,[status(thm)],[t1_numerals])). cnf(c_0_68, plain, (k5_numbers=k4_ordinal1), inference(split_conjunct,[status(thm)],[redefinition_k5_numbers])). fof(c_0_69, plain, ![X18]:((v1_xcmplx_0(k5_xcmplx_0(X18))\|(v2_xxreal_0(X18)\|~v1_xreal_0(X18)))&(~v2_xxreal_0(k5_xcmplx_0(X18))\|(v2_xxreal_0(X18)\|~v1_xreal_0(X18)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fc28_xreal_0])])])])). cnf(c_0_70, plain, (v3_xxreal_0(X1)\|~v1_xreal_0(X1)\|~v3_xxreal_0(k5_xcmplx_0(X1))), inference(evalgc,[status(thm)],[c_0_54])). cnf(c_0_71, plain, (X1=k1_xboole_0\|v3_xxreal_0(X1)\|v2_xxreal_0(X1)\|~v1_xreal_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_55, c_0_56])])). cnf(c_0_72, plain, (v1_xreal_0(k5_xcmplx_0(X1))\|~v1_xreal_0(X1)), inference(split_conjunct,[status(thm)],[c_0_57])). cnf(c_0_73, plain, (~v1_xboole_0(X1)\|~v1_xxreal_0(X1)\|~v2_xxreal_0(X1)), inference(evalgc,[status(thm)],[c_0_58])). cnf(c_0_74, plain, (v1_xboole_0(k1_xboole_0)), inference(split_conjunct,[status(thm)],[fc1_xboole_0])). cnf(c_0_75, plain, (v1_xreal_0(esk4_0)), inference(split_conjunct,[status(thm)],[c_0_47])). cnf(c_0_76, plain, (v1_xboole_0(esk4_0)), inference(evalgc,[status(thm)],[c_0_59])). cnf(c_0_77, plain, (k1_funct_1(k35_valued_1(X1),X2)=k5_xcmplx_0(k1_funct_1(X1,X2))\|~r2_hidden(X2,k9_xtuple_0(X1))\|~v1_valued_0(X1)\|~v1_funct_1(X1)\|~v1_relat_1(X1)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_60])])). cnf(c_0_78, negated_conjecture, (k1_funct_1(k35_valued_1(esk1_0),esk2_0)=k1_xboole_0), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61, c_0_62]), c_0_63]), c_0_64]), c_0_65])])])). cnf(c_0_79, plain, (~m1_subset_1(X1,k5_numbers)\|~v3_xxreal_0(X1)), inference(split_conjunct,[status(thm)],[c_0_66])). cnf(c_0_80, plain, (m1_subset_1(k1_xboole_0,k4_ordinal1)), inference(evalgc,[status(thm)],[c_0_67])). cnf(c_0_81, plain, (k4_ordinal1=k5_numbers), inference(evalgc,[status(thm)],[c_0_68])). cnf(c_0_82, plain, (v2_xxreal_0(X1)\|~v2_xxreal_0(k5_xcmplx_0(X1))\|~v1_xreal_0(X1)), inference(split_conjunct,[status(thm)],[c_0_69])). cnf(c_0_83, plain, (v3_xxreal_0(X1)\|k5_xcmplx_0(X1)=k1_xboole_0\|v2_xxreal_0(k5_xcmplx_0(X1))\|~v1_xreal_0(X1)\|~v1_xreal_0(k5_xcmplx_0(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_70, c_0_71])])). cnf(c_0_84, plain, (v1_xreal_0(k5_xcmplx_0(X1))\|~v1_xreal_0(X1)), inference(evalgc,[status(thm)],[c_0_72])). cnf(c_0_85, plain, (~v2_xxreal_0(X1)\|~v1_xboole_0(X1)\|~v1_xreal_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_73, c_0_45])])). cnf(c_0_86, plain, (v1_xboole_0(k1_xboole_0)), inference(evalgc,[status(thm)],[c_0_74])). cnf(c_0_87, plain, (v1_xreal_0(esk4_0)), inference(evalgc,[status(thm)],[c_0_75])). cnf(c_0_88, plain, (esk4_0=k1_xboole_0), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_55, c_0_76])])). cnf(c_0_89, negated_conjecture, (k5_xcmplx_0(k1_funct_1(esk1_0,esk2_0))=k1_xboole_0\|~r2_hidden(esk2_0,k9_xtuple_0(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77, c_0_78]), c_0_63]), c_0_64]), c_0_65])])])). cnf(c_0_90, negated_conjecture, (k5_xcmplx_0(k1_funct_1(esk1_0,esk2_0))!=k1_xboole_0), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[c_0_61, c_0_78])])). cnf(c_0_91, plain, (~v3_xxreal_0(X1)\|~m1_subset_1(X1,k5_numbers)), inference(evalgc,[status(thm)],[c_0_79])). cnf(c_0_92, plain, (m1_subset_1(k1_xboole_0,k5_numbers)), inference(rw,[status(thm)],[c_0_80, c_0_81])). cnf(c_0_93, plain, (v2_xxreal_0(X1)\|~v1_xreal_0(X1)\|~v2_xxreal_0(k5_xcmplx_0(X1))), inference(evalgc,[status(thm)],[c_0_82])). cnf(c_0_94, plain, (k5_xcmplx_0(X1)=k1_xboole_0\|v3_xxreal_0(X1)\|v2_xxreal_0(k5_xcmplx_0(X1))\|~v1_xreal_0(X1)), inference(csr,[status(thm)],[c_0_83, c_0_84])). cnf(c_0_95, plain, (~v2_xxreal_0(k1_xboole_0)\|~v1_xreal_0(k1_xboole_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_85, c_0_86])])). cnf(c_0_96, plain, (v1_xreal_0(k1_xboole_0)), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[c_0_87, c_0_88])])). cnf(c_0_97, negated_conjecture, (~r2_hidden(esk2_0,k9_xtuple_0(esk1_0))), inference(sr,[status(thm)],[c_0_89, c_0_90])). cnf(c_0_98, plain, (~v3_xxreal_0(k1_xboole_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_91, c_0_92])])). cnf(c_0_99, plain, (v2_xxreal_0(X1)\|k5_xcmplx_0(X1)=k1_xboole_0\|v3_xxreal_0(X1)\|~v1_xreal_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_93, c_0_94])])). cnf(c_0_100, plain, (~v2_xxreal_0(k1_xboole_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_95, c_0_96])])). cnf(c_0_101, negated_conjecture, (k1_funct_1(esk1_0,esk2_0)=k1_xboole_0), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97, c_0_35]), c_0_64]), c_0_65])])])). cnf(c_0_102, plain, (k5_xcmplx_0(k1_xboole_0)=k1_xboole_0), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98, c_0_99]), c_0_96])]), c_0_100])])). cnf(c_0_103, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_90, c_0_101]), c_0_102])]), ['proof']). # SZS output end CNFRefutation	theorem Th10: for f being complex-valued Function holds for c being set holds f".c = (f.c)" proof let f be complex-valued Function; let c be set; A1: dom (f") = dom f by Def7; per cases; suppose c in dom f; hence thesis by A1,Def7; end; suppose A2: not c in dom f; hence f".c = 0 qua complex number" by A1,FUNCT_1:def 2 .= (f.c)" by A2,FUNCT_1:def 2; end; end;	Convert the following ATP output trace into a readable Mizar proof.
t101_relat_1	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(d12_relat_1, axiom, ![X1, X2]:(v1_relat_1(X2)=>![X3]:(v1_relat_1(X3)=>(X3=k6_relat_1(X1,X2)<=>![X4, X5]:(r2_hidden(k4_tarski(X4,X5),X3)<=>(r2_hidden(X5,X1)&r2_hidden(k4_tarski(X4,X5),X2)))))), file('/scratch/mptp/predsminms1/t101_relat_1__0', d12_relat_1)). fof(d3_relat_1, axiom, ![X1]:(v1_relat_1(X1)=>![X2]:(r1_tarski(X1,X2)<=>![X3, X4]:(r2_hidden(k4_tarski(X3,X4),X1)=>r2_hidden(k4_tarski(X3,X4),X2)))), file('/scratch/mptp/predsminms1/t101_relat_1__0', d3_relat_1)). fof(dt_k6_relat_1, axiom, ![X1, X2]:(v1_relat_1(X2)=>v1_relat_1(k6_relat_1(X1,X2))), file('/scratch/mptp/predsminms1/t101_relat_1__0', dt_k6_relat_1)). fof(t101_relat_1, conjecture, ![X1, X2]:(v1_relat_1(X2)=>![X3]:(v1_relat_1(X3)=>(r1_tarski(X2,X3)=>r1_tarski(k6_relat_1(X1,X2),k6_relat_1(X1,X3))))), file('/scratch/mptp/predsminms1/t101_relat_1__0', t101_relat_1)). fof(c_0_4, plain, ![X9, X10, X11, X12, X13, X14, X15]:((((r2_hidden(X13,X9)\|~r2_hidden(k4_tarski(X12,X13),X11)\|X11!=k6_relat_1(X9,X10)\|~v1_relat_1(X11)\|~v1_relat_1(X10))&(r2_hidden(k4_tarski(X12,X13),X10)\|~r2_hidden(k4_tarski(X12,X13),X11)\|X11!=k6_relat_1(X9,X10)\|~v1_relat_1(X11)\|~v1_relat_1(X10)))&(~r2_hidden(X15,X9)\|~r2_hidden(k4_tarski(X14,X15),X10)\|r2_hidden(k4_tarski(X14,X15),X11)\|X11!=k6_relat_1(X9,X10)\|~v1_relat_1(X11)\|~v1_relat_1(X10)))&((~r2_hidden(k4_tarski(esk4_3(X9,X10,X11),esk5_3(X9,X10,X11)),X11)\|(~r2_hidden(esk5_3(X9,X10,X11),X9)\|~r2_hidden(k4_tarski(esk4_3(X9,X10,X11),esk5_3(X9,X10,X11)),X10))\|X11=k6_relat_1(X9,X10)\|~v1_relat_1(X11)\|~v1_relat_1(X10))&((r2_hidden(esk5_3(X9,X10,X11),X9)\|r2_hidden(k4_tarski(esk4_3(X9,X10,X11),esk5_3(X9,X10,X11)),X11)\|X11=k6_relat_1(X9,X10)\|~v1_relat_1(X11)\|~v1_relat_1(X10))&(r2_hidden(k4_tarski(esk4_3(X9,X10,X11),esk5_3(X9,X10,X11)),X10)\|r2_hidden(k4_tarski(esk4_3(X9,X10,X11),esk5_3(X9,X10,X11)),X11)\|X11=k6_relat_1(X9,X10)\|~v1_relat_1(X11)\|~v1_relat_1(X10))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d12_relat_1])])])])])])). fof(c_0_5, plain, ![X18, X19, X20, X21, X22]:((~r1_tarski(X18,X19)\|(~r2_hidden(k4_tarski(X20,X21),X18)\|r2_hidden(k4_tarski(X20,X21),X19))\|~v1_relat_1(X18))&((r2_hidden(k4_tarski(esk6_2(X18,X22),esk7_2(X18,X22)),X18)\|r1_tarski(X18,X22)\|~v1_relat_1(X18))&(~r2_hidden(k4_tarski(esk6_2(X18,X22),esk7_2(X18,X22)),X22)\|r1_tarski(X18,X22)\|~v1_relat_1(X18)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_relat_1])])])])])])). cnf(c_0_6, plain, (r2_hidden(k4_tarski(X1,X2),X3)\|~r2_hidden(k4_tarski(X1,X2),X4)\|X4!=k6_relat_1(X5,X3)\|~v1_relat_1(X4)\|~v1_relat_1(X3)), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_7, plain, (r2_hidden(k4_tarski(esk6_2(X1,X2),esk7_2(X1,X2)),X1)\|r1_tarski(X1,X2)\|~v1_relat_1(X1)), inference(split_conjunct,[status(thm)],[c_0_5])). cnf(c_0_8, plain, (r2_hidden(k4_tarski(X1,X2),X3)\|X4!=k6_relat_1(X5,X3)\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~r2_hidden(k4_tarski(X1,X2),X4)), inference(evalgc,[status(thm)],[c_0_6])). cnf(c_0_9, plain, (r1_tarski(X1,X2)\|r2_hidden(k4_tarski(esk6_2(X1,X2),esk7_2(X1,X2)),X1)\|~v1_relat_1(X1)), inference(evalgc,[status(thm)],[c_0_7])). fof(c_0_10, plain, ![X25, X26]:(~v1_relat_1(X26)\|v1_relat_1(k6_relat_1(X25,X26))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k6_relat_1])])). cnf(c_0_11, plain, (r2_hidden(k4_tarski(esk6_2(X1,X2),esk7_2(X1,X2)),X3)\|r1_tarski(X1,X2)\|X1!=k6_relat_1(X4,X3)\|~v1_relat_1(X1)\|~v1_relat_1(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_8, c_0_9])])). cnf(c_0_12, plain, (v1_relat_1(k6_relat_1(X2,X1))\|~v1_relat_1(X1)), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_13, plain, (r2_hidden(X1,X2)\|~r2_hidden(k4_tarski(X3,X1),X4)\|X4!=k6_relat_1(X2,X5)\|~v1_relat_1(X4)\|~v1_relat_1(X5)), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_14, plain, (r2_hidden(k4_tarski(X3,X4),X2)\|~r1_tarski(X1,X2)\|~r2_hidden(k4_tarski(X3,X4),X1)\|~v1_relat_1(X1)), inference(split_conjunct,[status(thm)],[c_0_5])). cnf(c_0_15, plain, (r2_hidden(k4_tarski(esk6_2(k6_relat_1(X1,X2),X3),esk7_2(k6_relat_1(X1,X2),X3)),X2)\|r1_tarski(k6_relat_1(X1,X2),X3)\|~v1_relat_1(k6_relat_1(X1,X2))\|~v1_relat_1(X2)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_11])])). cnf(c_0_16, plain, (v1_relat_1(k6_relat_1(X2,X1))\|~v1_relat_1(X1)), inference(evalgc,[status(thm)],[c_0_12])). cnf(c_0_17, plain, (r2_hidden(X1,X2)\|X4!=k6_relat_1(X2,X5)\|~v1_relat_1(X5)\|~v1_relat_1(X4)\|~r2_hidden(k4_tarski(X3,X1),X4)), inference(evalgc,[status(thm)],[c_0_13])). cnf(c_0_18, plain, (r2_hidden(k4_tarski(X3,X1),X5)\|~r2_hidden(X1,X2)\|~r2_hidden(k4_tarski(X3,X1),X4)\|X5!=k6_relat_1(X2,X4)\|~v1_relat_1(X5)\|~v1_relat_1(X4)), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_19, plain, (r2_hidden(k4_tarski(X3,X4),X2)\|~v1_relat_1(X1)\|~r1_tarski(X1,X2)\|~r2_hidden(k4_tarski(X3,X4),X1)), inference(evalgc,[status(thm)],[c_0_14])). cnf(c_0_20, plain, (r2_hidden(k4_tarski(esk6_2(k6_relat_1(X1,X2),X3),esk7_2(k6_relat_1(X1,X2),X3)),X2)\|r1_tarski(k6_relat_1(X1,X2),X3)\|~v1_relat_1(X2)), inference(csr,[status(thm)],[c_0_15, c_0_16])). cnf(c_0_21, plain, (r2_hidden(esk7_2(X1,X2),X3)\|r1_tarski(X1,X2)\|X1!=k6_relat_1(X3,X4)\|~v1_relat_1(X4)\|~v1_relat_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_17, c_0_9])])). cnf(c_0_22, plain, (r2_hidden(k4_tarski(X3,X1),X5)\|X5!=k6_relat_1(X2,X4)\|~v1_relat_1(X5)\|~v1_relat_1(X4)\|~r2_hidden(X1,X2)\|~r2_hidden(k4_tarski(X3,X1),X4)), inference(evalgc,[status(thm)],[c_0_18])). cnf(c_0_23, plain, (r2_hidden(k4_tarski(esk6_2(k6_relat_1(X1,X2),X3),esk7_2(k6_relat_1(X1,X2),X3)),X4)\|r1_tarski(k6_relat_1(X1,X2),X3)\|~r1_tarski(X2,X4)\|~v1_relat_1(X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_19, c_0_20])])). cnf(c_0_24, plain, (r2_hidden(esk7_2(k6_relat_1(X1,X2),X3),X1)\|r1_tarski(k6_relat_1(X1,X2),X3)\|~v1_relat_1(X2)\|~v1_relat_1(k6_relat_1(X1,X2))), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_21])])). cnf(c_0_25, plain, (r2_hidden(k4_tarski(esk6_2(k6_relat_1(X1,X2),X3),esk7_2(k6_relat_1(X1,X2),X3)),X4)\|r1_tarski(k6_relat_1(X1,X2),X3)\|X4!=k6_relat_1(X5,X6)\|~r2_hidden(esk7_2(k6_relat_1(X1,X2),X3),X5)\|~v1_relat_1(X4)\|~v1_relat_1(X6)\|~r1_tarski(X2,X6)\|~v1_relat_1(X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_22, c_0_23])])). cnf(c_0_26, plain, (r2_hidden(esk7_2(k6_relat_1(X1,X2),X3),X1)\|r1_tarski(k6_relat_1(X1,X2),X3)\|~v1_relat_1(X2)), inference(csr,[status(thm)],[c_0_24, c_0_16])). cnf(c_0_27, plain, (r2_hidden(k4_tarski(esk6_2(k6_relat_1(X1,X2),X3),esk7_2(k6_relat_1(X1,X2),X3)),X4)\|r1_tarski(k6_relat_1(X1,X2),X3)\|X4!=k6_relat_1(X1,X5)\|~r1_tarski(X2,X5)\|~v1_relat_1(X4)\|~v1_relat_1(X5)\|~v1_relat_1(X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_25, c_0_26])])). fof(c_0_28, negated_conjecture, ~(![X1, X2]:(v1_relat_1(X2)=>![X3]:(v1_relat_1(X3)=>(r1_tarski(X2,X3)=>r1_tarski(k6_relat_1(X1,X2),k6_relat_1(X1,X3)))))), inference(assume_negation,[status(cth)],[t101_relat_1])). cnf(c_0_29, plain, (r1_tarski(X1,X2)\|~r2_hidden(k4_tarski(esk6_2(X1,X2),esk7_2(X1,X2)),X2)\|~v1_relat_1(X1)), inference(split_conjunct,[status(thm)],[c_0_5])). cnf(c_0_30, plain, (r2_hidden(k4_tarski(esk6_2(k6_relat_1(X1,X2),X3),esk7_2(k6_relat_1(X1,X2),X3)),k6_relat_1(X1,X4))\|r1_tarski(k6_relat_1(X1,X2),X3)\|~r1_tarski(X2,X4)\|~v1_relat_1(k6_relat_1(X1,X4))\|~v1_relat_1(X4)\|~v1_relat_1(X2)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_27])])). fof(c_0_31, negated_conjecture, (v1_relat_1(esk2_0)&(v1_relat_1(esk3_0)&(r1_tarski(esk2_0,esk3_0)&~r1_tarski(k6_relat_1(esk1_0,esk2_0),k6_relat_1(esk1_0,esk3_0))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])])). cnf(c_0_32, plain, (r1_tarski(X1,X2)\|~v1_relat_1(X1)\|~r2_hidden(k4_tarski(esk6_2(X1,X2),esk7_2(X1,X2)),X2)), inference(evalgc,[status(thm)],[c_0_29])). cnf(c_0_33, plain, (r2_hidden(k4_tarski(esk6_2(k6_relat_1(X1,X2),X3),esk7_2(k6_relat_1(X1,X2),X3)),k6_relat_1(X1,X4))\|r1_tarski(k6_relat_1(X1,X2),X3)\|~r1_tarski(X2,X4)\|~v1_relat_1(X4)\|~v1_relat_1(X2)), inference(csr,[status(thm)],[c_0_30, c_0_16])). cnf(c_0_34, negated_conjecture, (~r1_tarski(k6_relat_1(esk1_0,esk2_0),k6_relat_1(esk1_0,esk3_0))), inference(split_conjunct,[status(thm)],[c_0_31])). cnf(c_0_35, plain, (r1_tarski(k6_relat_1(X1,X2),k6_relat_1(X1,X3))\|~v1_relat_1(k6_relat_1(X1,X2))\|~r1_tarski(X2,X3)\|~v1_relat_1(X3)\|~v1_relat_1(X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_32, c_0_33])])). cnf(c_0_36, negated_conjecture, (r1_tarski(esk2_0,esk3_0)), inference(split_conjunct,[status(thm)],[c_0_31])). cnf(c_0_37, negated_conjecture, (v1_relat_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_31])). cnf(c_0_38, negated_conjecture, (v1_relat_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_31])). cnf(c_0_39, negated_conjecture, (~r1_tarski(k6_relat_1(esk1_0,esk2_0),k6_relat_1(esk1_0,esk3_0))), inference(evalgc,[status(thm)],[c_0_34])). cnf(c_0_40, plain, (r1_tarski(k6_relat_1(X1,X2),k6_relat_1(X1,X3))\|~r1_tarski(X2,X3)\|~v1_relat_1(X3)\|~v1_relat_1(X2)), inference(csr,[status(thm)],[c_0_35, c_0_16])). cnf(c_0_41, negated_conjecture, (r1_tarski(esk2_0,esk3_0)), inference(evalgc,[status(thm)],[c_0_36])). cnf(c_0_42, negated_conjecture, (v1_relat_1(esk3_0)), inference(evalgc,[status(thm)],[c_0_37])). cnf(c_0_43, negated_conjecture, (v1_relat_1(esk2_0)), inference(evalgc,[status(thm)],[c_0_38])). cnf(c_0_44, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39, c_0_40]), c_0_41]), c_0_42]), c_0_43])]), ['proof']). # SZS output end CNFRefutation	reserve A,X,X1,X2,Y,Y1,Y2,a,b,c,d,x,y,z for set; reserve P,P1,P2,Q,R,S for Relation; theorem Th101: P1 c= P2 implies Y\|`P1 c= Y\|`P2 proof assume A1: P1 c= P2; let x,y; assume [x,y] in Y\|`P1; then [x,y] in P1 & y in Y by Def12; hence thesis by A1,Def12; end;	Convert the following ATP output trace into a readable Mizar proof.
t9_pre_topc	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t9_pre_topc, conjecture, ![X1]:(l1_pre_topc(X1)=>![X2]:((~(v2_struct_0(X2))&l1_pre_topc(X2))=>![X3]:((v1_funct_1(X3)&(v1_funct_2(X3,u1_struct_0(X1),u1_struct_0(X2))&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X2))))))=>![X4]:(m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X1)))=>(v1_funct_1(k5_relset_1(u1_struct_0(X1),u1_struct_0(X2),X3,X4))&(v1_funct_2(k5_relset_1(u1_struct_0(X1),u1_struct_0(X2),X3,X4),u1_struct_0(k1_pre_topc(X1,X4)),u1_struct_0(X2))&m1_subset_1(k5_relset_1(u1_struct_0(X1),u1_struct_0(X2),X3,X4),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k1_pre_topc(X1,X4)),u1_struct_0(X2)))))))))), file('/scratch/mptp/predsminms1/t9_pre_topc__0', t9_pre_topc)). fof(t8_pre_topc, axiom, ![X1]:(l1_pre_topc(X1)=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))=>u1_struct_0(k1_pre_topc(X1,X2))=X2)), file('/scratch/mptp/predsminms1/t9_pre_topc__0', t8_pre_topc)). fof(dt_k2_partfun1, axiom, ![X1, X2, X3, X4]:((v1_funct_1(X3)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2))))=>(v1_funct_1(k2_partfun1(X1,X2,X3,X4))&m1_subset_1(k2_partfun1(X1,X2,X3,X4),k1_zfmisc_1(k2_zfmisc_1(X1,X2))))), file('/scratch/mptp/predsminms1/t9_pre_topc__0', dt_k2_partfun1)). fof(redefinition_k2_partfun1, axiom, ![X1, X2, X3, X4]:((v1_funct_1(X3)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2))))=>k2_partfun1(X1,X2,X3,X4)=k5_relat_1(X3,X4)), file('/scratch/mptp/predsminms1/t9_pre_topc__0', redefinition_k2_partfun1)). fof(redefinition_k5_relset_1, axiom, ![X1, X2, X3, X4]:(m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))=>k5_relset_1(X1,X2,X3,X4)=k5_relat_1(X3,X4)), file('/scratch/mptp/predsminms1/t9_pre_topc__0', redefinition_k5_relset_1)). fof(t32_funct_2, axiom, ![X1, X2, X3, X4]:((v1_funct_1(X4)&(v1_funct_2(X4,X1,X2)&m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))))=>(r1_tarski(X3,X1)=>((X2=k1_xboole_0&~(X1=k1_xboole_0))\|(v1_funct_1(k2_partfun1(X1,X2,X4,X3))&(v1_funct_2(k2_partfun1(X1,X2,X4,X3),X3,X2)&m1_subset_1(k2_partfun1(X1,X2,X4,X3),k1_zfmisc_1(k2_zfmisc_1(X3,X2)))))))), file('/scratch/mptp/predsminms1/t9_pre_topc__0', t32_funct_2)). fof(t6_boole, axiom, ![X1]:(v1_xboole_0(X1)=>X1=k1_xboole_0), file('/scratch/mptp/predsminms1/t9_pre_topc__0', t6_boole)). fof(rc1_xboole_0, axiom, ?[X1]:v1_xboole_0(X1), file('/scratch/mptp/predsminms1/t9_pre_topc__0', rc1_xboole_0)). fof(t3_subset, axiom, ![X1, X2]:(m1_subset_1(X1,k1_zfmisc_1(X2))<=>r1_tarski(X1,X2)), file('/scratch/mptp/predsminms1/t9_pre_topc__0', t3_subset)). fof(fc2_struct_0, axiom, ![X1]:((~(v2_struct_0(X1))&l1_struct_0(X1))=>~(v1_xboole_0(u1_struct_0(X1)))), file('/scratch/mptp/predsminms1/t9_pre_topc__0', fc2_struct_0)). fof(dt_l1_pre_topc, axiom, ![X1]:(l1_pre_topc(X1)=>l1_struct_0(X1)), file('/scratch/mptp/predsminms1/t9_pre_topc__0', dt_l1_pre_topc)). fof(c_0_11, negated_conjecture, ~(![X1]:(l1_pre_topc(X1)=>![X2]:((~(v2_struct_0(X2))&l1_pre_topc(X2))=>![X3]:((v1_funct_1(X3)&(v1_funct_2(X3,u1_struct_0(X1),u1_struct_0(X2))&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X2))))))=>![X4]:(m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X1)))=>(v1_funct_1(k5_relset_1(u1_struct_0(X1),u1_struct_0(X2),X3,X4))&(v1_funct_2(k5_relset_1(u1_struct_0(X1),u1_struct_0(X2),X3,X4),u1_struct_0(k1_pre_topc(X1,X4)),u1_struct_0(X2))&m1_subset_1(k5_relset_1(u1_struct_0(X1),u1_struct_0(X2),X3,X4),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k1_pre_topc(X1,X4)),u1_struct_0(X2))))))))))), inference(assume_negation,[status(cth)],[t9_pre_topc])). fof(c_0_12, negated_conjecture, (l1_pre_topc(esk1_0)&((~v2_struct_0(esk2_0)&l1_pre_topc(esk2_0))&((v1_funct_1(esk3_0)&(v1_funct_2(esk3_0,u1_struct_0(esk1_0),u1_struct_0(esk2_0))&m1_subset_1(esk3_0,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(esk1_0),u1_struct_0(esk2_0))))))&(m1_subset_1(esk4_0,k1_zfmisc_1(u1_struct_0(esk1_0)))&(~v1_funct_1(k5_relset_1(u1_struct_0(esk1_0),u1_struct_0(esk2_0),esk3_0,esk4_0))\|(~v1_funct_2(k5_relset_1(u1_struct_0(esk1_0),u1_struct_0(esk2_0),esk3_0,esk4_0),u1_struct_0(k1_pre_topc(esk1_0,esk4_0)),u1_struct_0(esk2_0))\|~m1_subset_1(k5_relset_1(u1_struct_0(esk1_0),u1_struct_0(esk2_0),esk3_0,esk4_0),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k1_pre_topc(esk1_0,esk4_0)),u1_struct_0(esk2_0)))))))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_11])])])])). fof(c_0_13, plain, ![X11, X12]:(~l1_pre_topc(X11)\|(~m1_subset_1(X12,k1_zfmisc_1(u1_struct_0(X11)))\|u1_struct_0(k1_pre_topc(X11,X12))=X12)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_pre_topc])])])). fof(c_0_14, plain, ![X21, X22, X23, X24]:((v1_funct_1(k2_partfun1(X21,X22,X23,X24))\|(~v1_funct_1(X23)\|~m1_subset_1(X23,k1_zfmisc_1(k2_zfmisc_1(X21,X22)))))&(m1_subset_1(k2_partfun1(X21,X22,X23,X24),k1_zfmisc_1(k2_zfmisc_1(X21,X22)))\|(~v1_funct_1(X23)\|~m1_subset_1(X23,k1_zfmisc_1(k2_zfmisc_1(X21,X22)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_partfun1])])])). fof(c_0_15, plain, ![X25, X26, X27, X28]:(~v1_funct_1(X27)\|~m1_subset_1(X27,k1_zfmisc_1(k2_zfmisc_1(X25,X26)))\|k2_partfun1(X25,X26,X27,X28)=k5_relat_1(X27,X28)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k2_partfun1])])). cnf(c_0_16, negated_conjecture, (~v1_funct_1(k5_relset_1(u1_struct_0(esk1_0),u1_struct_0(esk2_0),esk3_0,esk4_0))\|~v1_funct_2(k5_relset_1(u1_struct_0(esk1_0),u1_struct_0(esk2_0),esk3_0,esk4_0),u1_struct_0(k1_pre_topc(esk1_0,esk4_0)),u1_struct_0(esk2_0))\|~m1_subset_1(k5_relset_1(u1_struct_0(esk1_0),u1_struct_0(esk2_0),esk3_0,esk4_0),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k1_pre_topc(esk1_0,esk4_0)),u1_struct_0(esk2_0))))), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_17, plain, (u1_struct_0(k1_pre_topc(X1,X2))=X2\|~l1_pre_topc(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(split_conjunct,[status(thm)],[c_0_13])). cnf(c_0_18, negated_conjecture, (m1_subset_1(esk4_0,k1_zfmisc_1(u1_struct_0(esk1_0)))), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_19, negated_conjecture, (l1_pre_topc(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_12])). fof(c_0_20, plain, ![X17, X18, X19, X20]:(~m1_subset_1(X19,k1_zfmisc_1(k2_zfmisc_1(X17,X18)))\|k5_relset_1(X17,X18,X19,X20)=k5_relat_1(X19,X20)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k5_relset_1])])). cnf(c_0_21, plain, (v1_funct_1(k2_partfun1(X1,X2,X3,X4))\|~v1_funct_1(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_14])). cnf(c_0_22, plain, (k2_partfun1(X2,X3,X1,X4)=k5_relat_1(X1,X4)\|~v1_funct_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_15])). fof(c_0_23, plain, ![X13, X14, X15, X16]:(((v1_funct_1(k2_partfun1(X13,X14,X16,X15))\|X14=k1_xboole_0\|~r1_tarski(X15,X13)\|(~v1_funct_1(X16)\|(~v1_funct_2(X16,X13,X14)\|~m1_subset_1(X16,k1_zfmisc_1(k2_zfmisc_1(X13,X14))))))&((v1_funct_2(k2_partfun1(X13,X14,X16,X15),X15,X14)\|X14=k1_xboole_0\|~r1_tarski(X15,X13)\|(~v1_funct_1(X16)\|(~v1_funct_2(X16,X13,X14)\|~m1_subset_1(X16,k1_zfmisc_1(k2_zfmisc_1(X13,X14))))))&(m1_subset_1(k2_partfun1(X13,X14,X16,X15),k1_zfmisc_1(k2_zfmisc_1(X15,X14)))\|X14=k1_xboole_0\|~r1_tarski(X15,X13)\|(~v1_funct_1(X16)\|(~v1_funct_2(X16,X13,X14)\|~m1_subset_1(X16,k1_zfmisc_1(k2_zfmisc_1(X13,X14))))))))&((v1_funct_1(k2_partfun1(X13,X14,X16,X15))\|X13!=k1_xboole_0\|~r1_tarski(X15,X13)\|(~v1_funct_1(X16)\|(~v1_funct_2(X16,X13,X14)\|~m1_subset_1(X16,k1_zfmisc_1(k2_zfmisc_1(X13,X14))))))&((v1_funct_2(k2_partfun1(X13,X14,X16,X15),X15,X14)\|X13!=k1_xboole_0\|~r1_tarski(X15,X13)\|(~v1_funct_1(X16)\|(~v1_funct_2(X16,X13,X14)\|~m1_subset_1(X16,k1_zfmisc_1(k2_zfmisc_1(X13,X14))))))&(m1_subset_1(k2_partfun1(X13,X14,X16,X15),k1_zfmisc_1(k2_zfmisc_1(X15,X14)))\|X13!=k1_xboole_0\|~r1_tarski(X15,X13)\|(~v1_funct_1(X16)\|(~v1_funct_2(X16,X13,X14)\|~m1_subset_1(X16,k1_zfmisc_1(k2_zfmisc_1(X13,X14))))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t32_funct_2])])])])). cnf(c_0_24, negated_conjecture, (~v1_funct_1(k5_relset_1(u1_struct_0(esk1_0),u1_struct_0(esk2_0),esk3_0,esk4_0))\|~v1_funct_2(k5_relset_1(u1_struct_0(esk1_0),u1_struct_0(esk2_0),esk3_0,esk4_0),u1_struct_0(k1_pre_topc(esk1_0,esk4_0)),u1_struct_0(esk2_0))\|~m1_subset_1(k5_relset_1(u1_struct_0(esk1_0),u1_struct_0(esk2_0),esk3_0,esk4_0),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k1_pre_topc(esk1_0,esk4_0)),u1_struct_0(esk2_0))))), inference(evalgc,[status(thm)],[c_0_16])). cnf(c_0_25, plain, (u1_struct_0(k1_pre_topc(X1,X2))=X2\|~l1_pre_topc(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(evalgc,[status(thm)],[c_0_17])). cnf(c_0_26, negated_conjecture, (m1_subset_1(esk4_0,k1_zfmisc_1(u1_struct_0(esk1_0)))), inference(evalgc,[status(thm)],[c_0_18])). cnf(c_0_27, negated_conjecture, (l1_pre_topc(esk1_0)), inference(evalgc,[status(thm)],[c_0_19])). cnf(c_0_28, plain, (k5_relset_1(X2,X3,X1,X4)=k5_relat_1(X1,X4)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_20])). cnf(c_0_29, negated_conjecture, (m1_subset_1(esk3_0,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(esk1_0),u1_struct_0(esk2_0))))), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_30, plain, (v1_funct_1(k2_partfun1(X1,X2,X3,X4))\|~v1_funct_1(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(evalgc,[status(thm)],[c_0_21])). cnf(c_0_31, plain, (k2_partfun1(X2,X3,X1,X4)=k5_relat_1(X1,X4)\|~v1_funct_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(evalgc,[status(thm)],[c_0_22])). cnf(c_0_32, negated_conjecture, (v1_funct_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_33, plain, (v1_funct_2(k2_partfun1(X1,X2,X3,X4),X4,X2)\|X2=k1_xboole_0\|~r1_tarski(X4,X1)\|~v1_funct_1(X3)\|~v1_funct_2(X3,X1,X2)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_23])). cnf(c_0_34, negated_conjecture, (~m1_subset_1(k5_relset_1(u1_struct_0(esk1_0),u1_struct_0(esk2_0),esk3_0,esk4_0),k1_zfmisc_1(k2_zfmisc_1(esk4_0,u1_struct_0(esk2_0))))\|~v1_funct_2(k5_relset_1(u1_struct_0(esk1_0),u1_struct_0(esk2_0),esk3_0,esk4_0),esk4_0,u1_struct_0(esk2_0))\|~v1_funct_1(k5_relset_1(u1_struct_0(esk1_0),u1_struct_0(esk2_0),esk3_0,esk4_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24, c_0_25]), c_0_26]), c_0_27])])])). cnf(c_0_35, plain, (k5_relset_1(X2,X3,X1,X4)=k5_relat_1(X1,X4)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(evalgc,[status(thm)],[c_0_28])). cnf(c_0_36, negated_conjecture, (m1_subset_1(esk3_0,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(esk1_0),u1_struct_0(esk2_0))))), inference(evalgc,[status(thm)],[c_0_29])). cnf(c_0_37, plain, (v1_funct_1(k5_relat_1(X3,X4))\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_30, c_0_31])])). cnf(c_0_38, negated_conjecture, (v1_funct_1(esk3_0)), inference(evalgc,[status(thm)],[c_0_32])). cnf(c_0_39, plain, (X2=k1_xboole_0\|v1_funct_2(k2_partfun1(X1,X2,X3,X4),X4,X2)\|~v1_funct_1(X3)\|~r1_tarski(X4,X1)\|~v1_funct_2(X3,X1,X2)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(evalgc,[status(thm)],[c_0_33])). cnf(c_0_40, negated_conjecture, (v1_funct_2(esk3_0,u1_struct_0(esk1_0),u1_struct_0(esk2_0))), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_41, plain, (m1_subset_1(k2_partfun1(X1,X2,X3,X4),k1_zfmisc_1(k2_zfmisc_1(X4,X2)))\|X2=k1_xboole_0\|~r1_tarski(X4,X1)\|~v1_funct_1(X3)\|~v1_funct_2(X3,X1,X2)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_23])). cnf(c_0_42, negated_conjecture, (~m1_subset_1(k5_relat_1(esk3_0,esk4_0),k1_zfmisc_1(k2_zfmisc_1(esk4_0,u1_struct_0(esk2_0))))\|~v1_funct_2(k5_relat_1(esk3_0,esk4_0),esk4_0,u1_struct_0(esk2_0))\|~v1_funct_1(k5_relat_1(esk3_0,esk4_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34, c_0_35]), c_0_36])])])). cnf(c_0_43, negated_conjecture, (v1_funct_1(k5_relat_1(esk3_0,X1))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37, c_0_36]), c_0_38])])])). cnf(c_0_44, plain, (X1=k1_xboole_0\|v1_funct_2(k5_relat_1(X3,X4),X4,X1)\|~r1_tarski(X4,X2)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X2,X1)))\|~v1_funct_2(X3,X2,X1)\|~v1_funct_1(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_39, c_0_31])])). cnf(c_0_45, negated_conjecture, (v1_funct_2(esk3_0,u1_struct_0(esk1_0),u1_struct_0(esk2_0))), inference(evalgc,[status(thm)],[c_0_40])). cnf(c_0_46, plain, (X2=k1_xboole_0\|m1_subset_1(k2_partfun1(X1,X2,X3,X4),k1_zfmisc_1(k2_zfmisc_1(X4,X2)))\|~v1_funct_1(X3)\|~r1_tarski(X4,X1)\|~v1_funct_2(X3,X1,X2)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(evalgc,[status(thm)],[c_0_41])). fof(c_0_47, plain, ![X9]:(~v1_xboole_0(X9)\|X9=k1_xboole_0), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])])). fof(c_0_48, plain, v1_xboole_0(esk5_0), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])])). cnf(c_0_49, negated_conjecture, (~m1_subset_1(k5_relat_1(esk3_0,esk4_0),k1_zfmisc_1(k2_zfmisc_1(esk4_0,u1_struct_0(esk2_0))))\|~v1_funct_2(k5_relat_1(esk3_0,esk4_0),esk4_0,u1_struct_0(esk2_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42, c_0_43])])])). cnf(c_0_50, negated_conjecture, (u1_struct_0(esk2_0)=k1_xboole_0\|v1_funct_2(k5_relat_1(esk3_0,X1),X1,u1_struct_0(esk2_0))\|~r1_tarski(X1,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44, c_0_45]), c_0_36]), c_0_38])])])). cnf(c_0_51, plain, (X1=k1_xboole_0\|m1_subset_1(k5_relat_1(X3,X4),k1_zfmisc_1(k2_zfmisc_1(X4,X1)))\|~r1_tarski(X4,X2)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X2,X1)))\|~v1_funct_2(X3,X2,X1)\|~v1_funct_1(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_46, c_0_31])])). fof(c_0_52, plain, ![X29, X30]:((~m1_subset_1(X29,k1_zfmisc_1(X30))\|r1_tarski(X29,X30))&(~r1_tarski(X29,X30)\|m1_subset_1(X29,k1_zfmisc_1(X30)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])])). cnf(c_0_53, plain, (X1=k1_xboole_0\|~v1_xboole_0(X1)), inference(split_conjunct,[status(thm)],[c_0_47])). cnf(c_0_54, plain, (v1_xboole_0(esk5_0)), inference(split_conjunct,[status(thm)],[c_0_48])). fof(c_0_55, plain, ![X32]:(v2_struct_0(X32)\|~l1_struct_0(X32)\|~v1_xboole_0(u1_struct_0(X32))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fc2_struct_0])])])). cnf(c_0_56, negated_conjecture, (u1_struct_0(esk2_0)=k1_xboole_0\|~m1_subset_1(k5_relat_1(esk3_0,esk4_0),k1_zfmisc_1(k2_zfmisc_1(esk4_0,u1_struct_0(esk2_0))))\|~r1_tarski(esk4_0,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_49, c_0_50])])). cnf(c_0_57, negated_conjecture, (u1_struct_0(esk2_0)=k1_xboole_0\|m1_subset_1(k5_relat_1(esk3_0,X1),k1_zfmisc_1(k2_zfmisc_1(X1,u1_struct_0(esk2_0))))\|~r1_tarski(X1,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51, c_0_45]), c_0_36]), c_0_38])])])). cnf(c_0_58, plain, (r1_tarski(X1,X2)\|~m1_subset_1(X1,k1_zfmisc_1(X2))), inference(split_conjunct,[status(thm)],[c_0_52])). cnf(c_0_59, plain, (X1=k1_xboole_0\|~v1_xboole_0(X1)), inference(evalgc,[status(thm)],[c_0_53])). cnf(c_0_60, plain, (v1_xboole_0(esk5_0)), inference(evalgc,[status(thm)],[c_0_54])). cnf(c_0_61, plain, (v2_struct_0(X1)\|~l1_struct_0(X1)\|~v1_xboole_0(u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_55])). cnf(c_0_62, negated_conjecture, (u1_struct_0(esk2_0)=k1_xboole_0\|~r1_tarski(esk4_0,u1_struct_0(esk1_0))), inference(csr,[status(thm)],[c_0_56, c_0_57])). cnf(c_0_63, plain, (r1_tarski(X1,X2)\|~m1_subset_1(X1,k1_zfmisc_1(X2))), inference(evalgc,[status(thm)],[c_0_58])). cnf(c_0_64, plain, (esk5_0=k1_xboole_0), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_59, c_0_60])])). cnf(c_0_65, negated_conjecture, (~v2_struct_0(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_12])). fof(c_0_66, plain, ![X31]:(~l1_pre_topc(X31)\|l1_struct_0(X31)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_pre_topc])])). cnf(c_0_67, plain, (v2_struct_0(X1)\|~l1_struct_0(X1)\|~v1_xboole_0(u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_61])). cnf(c_0_68, negated_conjecture, (u1_struct_0(esk2_0)=k1_xboole_0), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62, c_0_63]), c_0_26])])])). cnf(c_0_69, plain, (v1_xboole_0(k1_xboole_0)), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[c_0_60, c_0_64])])). cnf(c_0_70, negated_conjecture, (~v2_struct_0(esk2_0)), inference(evalgc,[status(thm)],[c_0_65])). cnf(c_0_71, plain, (l1_struct_0(X1)\|~l1_pre_topc(X1)), inference(split_conjunct,[status(thm)],[c_0_66])). cnf(c_0_72, negated_conjecture, (l1_pre_topc(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_73, negated_conjecture, (~l1_struct_0(esk2_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67, c_0_68]), c_0_69])]), c_0_70])])). cnf(c_0_74, plain, (l1_struct_0(X1)\|~l1_pre_topc(X1)), inference(evalgc,[status(thm)],[c_0_71])). cnf(c_0_75, negated_conjecture, (l1_pre_topc(esk2_0)), inference(evalgc,[status(thm)],[c_0_72])). cnf(c_0_76, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73, c_0_74]), c_0_75])]), ['proof']). # SZS output end CNFRefutation	reserve T for TopStruct; reserve GX for TopSpace; theorem :: JGRAPH_3:12, AK, 20.02.2006 for X being TopStruct,Y being non empty TopStruct, f being Function of X,Y, P being Subset of X holds f\|P is Function of X\|P,Y proof let X be TopStruct,Y be non empty TopStruct,f be Function of X,Y, P be Subset of X; P = the carrier of (X\|P) by Th8; hence thesis by FUNCT_2:32; end;	Convert the following ATP output trace into a readable Mizar proof.
t66_borsuk_6	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t66_borsuk_6, conjecture, (r2_hidden(k4_tarski(k10_real_1(np__1,np__2),k6_numbers),k8_borsuk_6)&r2_hidden(k4_tarski(np__1,np__1),k8_borsuk_6)), file('/scratch/mptp/predsminms1/t66_borsuk_6__0', t66_borsuk_6)). fof(fc7_xreal_0, axiom, ![X1, X2]:((v1_xreal_0(X1)&v1_xreal_0(X2))=>v1_xreal_0(k6_xcmplx_0(X1,X2))), file('/scratch/mptp/predsminms1/t66_borsuk_6__0', fc7_xreal_0)). fof(cc14_membered, axiom, ![X1]:(v3_membered(X1)=>![X2]:(m1_subset_1(X2,X1)=>v1_xreal_0(X2))), file('/scratch/mptp/predsminms1/t66_borsuk_6__0', cc14_membered)). fof(t6_boole, axiom, ![X1]:(v1_xboole_0(X1)=>X1=k1_xboole_0), file('/scratch/mptp/predsminms1/t66_borsuk_6__0', t6_boole)). fof(d5_tarski, axiom, ![X1, X2]:k4_tarski(X1,X2)=k2_tarski(k2_tarski(X1,X2),k1_tarski(X1)), file('/scratch/mptp/predsminms1/t66_borsuk_6__0', d5_tarski)). fof(d10_borsuk_6, axiom, ![X1]:(m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr))))=>(X1=k8_borsuk_6<=>![X2]:(r2_hidden(X2,X1)<=>?[X3]:(m1_subset_1(X3,u1_struct_0(k5_topmetr))&?[X4]:(m1_subset_1(X4,u1_struct_0(k5_topmetr))&(X2=k4_borsuk_1(k5_topmetr,k5_topmetr,X3,X4)&r1_xxreal_0(X4,k9_real_1(k8_real_1(np__2,X3),np__1)))))))), file('/scratch/mptp/predsminms1/t66_borsuk_6__0', d10_borsuk_6)). fof(reflexivity_r1_xxreal_0, axiom, ![X1, X2]:((v1_xxreal_0(X1)&v1_xxreal_0(X2))=>r1_xxreal_0(X1,X1)), file('/scratch/mptp/predsminms1/t66_borsuk_6__0', reflexivity_r1_xxreal_0)). fof(rc3_xxreal_0, axiom, ?[X1]:(v1_xxreal_0(X1)&v3_xxreal_0(X1)), file('/scratch/mptp/predsminms1/t66_borsuk_6__0', rc3_xxreal_0)). fof(fc3_xreal_0, axiom, ![X1]:(v1_xreal_0(X1)=>(v1_xcmplx_0(k4_xcmplx_0(X1))&v1_xreal_0(k4_xcmplx_0(X1)))), file('/scratch/mptp/predsminms1/t66_borsuk_6__0', fc3_xreal_0)). fof(rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2, axiom, k4_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(np__1),np__2))=k7_xcmplx_0(np__1,np__2), file('/scratch/mptp/predsminms1/t66_borsuk_6__0', rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2)). fof(rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2, axiom, k7_xcmplx_0(np__1,k4_xcmplx_0(np__2))=k7_xcmplx_0(k4_xcmplx_0(np__1),np__2), file('/scratch/mptp/predsminms1/t66_borsuk_6__0', rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2)). fof(rqRealDiff__k6_xcmplx_0__r0_r2_rm2, axiom, k6_xcmplx_0(np__0,np__2)=k4_xcmplx_0(np__2), file('/scratch/mptp/predsminms1/t66_borsuk_6__0', rqRealDiff__k6_xcmplx_0__r0_r2_rm2)). fof(spc2_numerals, axiom, ((v2_xxreal_0(np__2)&m2_subset_1(np__2,k1_numbers,k5_numbers))&(m1_subset_1(np__2,k5_numbers)&m1_subset_1(np__2,k1_numbers))), file('/scratch/mptp/predsminms1/t66_borsuk_6__0', spc2_numerals)). fof(fc3_membered, axiom, v3_membered(k1_numbers), file('/scratch/mptp/predsminms1/t66_borsuk_6__0', fc3_membered)). fof(spc0_numerals, axiom, (m2_subset_1(np__0,k1_numbers,k5_numbers)&(m1_subset_1(np__0,k5_numbers)&m1_subset_1(np__0,k1_numbers))), file('/scratch/mptp/predsminms1/t66_borsuk_6__0', spc0_numerals)). fof(t43_borsuk_1, axiom, ![X1]:(v1_xreal_0(X1)=>((r1_xxreal_0(k6_numbers,X1)&r1_xxreal_0(X1,np__1))<=>r2_hidden(X1,u1_struct_0(k17_borsuk_1)))), file('/scratch/mptp/predsminms1/t66_borsuk_6__0', t43_borsuk_1)). fof(redefinition_k6_numbers, axiom, k6_numbers=k1_xboole_0, file('/scratch/mptp/predsminms1/t66_borsuk_6__0', redefinition_k6_numbers)). fof(t3_arithm, axiom, ![X1]:(v1_xcmplx_0(X1)=>k3_xcmplx_0(np__1,X1)=X1), file('/scratch/mptp/predsminms1/t66_borsuk_6__0', t3_arithm)). fof(redefinition_k8_real_1, axiom, ![X1, X2]:((m1_subset_1(X1,k1_numbers)&v1_xreal_0(X2))=>k8_real_1(X1,X2)=k3_xcmplx_0(X1,X2)), file('/scratch/mptp/predsminms1/t66_borsuk_6__0', redefinition_k8_real_1)). fof(commutativity_k2_tarski, axiom, ![X1, X2]:k2_tarski(X1,X2)=k2_tarski(X2,X1), file('/scratch/mptp/predsminms1/t66_borsuk_6__0', commutativity_k2_tarski)). fof(redefinition_k4_borsuk_1, axiom, ![X1, X2, X3, X4]:(((~(v2_struct_0(X1))&(v2_pre_topc(X1)&l1_pre_topc(X1)))&((~(v2_struct_0(X2))&(v2_pre_topc(X2)&l1_pre_topc(X2)))&(m1_subset_1(X3,u1_struct_0(X1))&m1_subset_1(X4,u1_struct_0(X2)))))=>k4_borsuk_1(X1,X2,X3,X4)=k4_tarski(X3,X4)), file('/scratch/mptp/predsminms1/t66_borsuk_6__0', redefinition_k4_borsuk_1)). fof(dt_k8_borsuk_6, axiom, m1_subset_1(k8_borsuk_6,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr)))), file('/scratch/mptp/predsminms1/t66_borsuk_6__0', dt_k8_borsuk_6)). fof(redefinition_k9_real_1, axiom, ![X1, X2]:((m1_subset_1(X1,k1_numbers)&v1_xreal_0(X2))=>k9_real_1(X1,X2)=k6_xcmplx_0(X1,X2)), file('/scratch/mptp/predsminms1/t66_borsuk_6__0', redefinition_k9_real_1)). fof(spc1_numerals, axiom, ((v2_xxreal_0(np__1)&m2_subset_1(np__1,k1_numbers,k5_numbers))&(m1_subset_1(np__1,k5_numbers)&m1_subset_1(np__1,k1_numbers))), file('/scratch/mptp/predsminms1/t66_borsuk_6__0', spc1_numerals)). fof(cc4_xreal_0, axiom, ![X1]:(v1_xreal_0(X1)=>v1_xxreal_0(X1)), file('/scratch/mptp/predsminms1/t66_borsuk_6__0', cc4_xreal_0)). fof(fc8_xreal_0, axiom, ![X1, X2]:((v1_xreal_0(X1)&v1_xreal_0(X2))=>v1_xreal_0(k7_xcmplx_0(X1,X2))), file('/scratch/mptp/predsminms1/t66_borsuk_6__0', fc8_xreal_0)). fof(redefinition_k5_topmetr, axiom, k5_topmetr=k17_borsuk_1, file('/scratch/mptp/predsminms1/t66_borsuk_6__0', redefinition_k5_topmetr)). fof(spc0_boole, axiom, v1_xboole_0(np__0), file('/scratch/mptp/predsminms1/t66_borsuk_6__0', spc0_boole)). fof(cc3_xreal_0, axiom, ![X1]:(v1_xreal_0(X1)=>v1_xcmplx_0(X1)), file('/scratch/mptp/predsminms1/t66_borsuk_6__0', cc3_xreal_0)). fof(rqRealMult__k3_xcmplx_0__r2_rn1d2_r1, axiom, k3_xcmplx_0(np__2,k7_xcmplx_0(np__1,np__2))=np__1, file('/scratch/mptp/predsminms1/t66_borsuk_6__0', rqRealMult__k3_xcmplx_0__r2_rn1d2_r1)). fof(t1_subset, axiom, ![X1, X2]:(r2_hidden(X1,X2)=>m1_subset_1(X1,X2)), file('/scratch/mptp/predsminms1/t66_borsuk_6__0', t1_subset)). fof(commutativity_k8_real_1, axiom, ![X1, X2]:((m1_subset_1(X1,k1_numbers)&v1_xreal_0(X2))=>k8_real_1(X1,X2)=k8_real_1(X2,X1)), file('/scratch/mptp/predsminms1/t66_borsuk_6__0', commutativity_k8_real_1)). fof(rqRealDiff__k6_xcmplx_0__r1_r1_r0, axiom, k6_xcmplx_0(np__1,np__1)=np__0, file('/scratch/mptp/predsminms1/t66_borsuk_6__0', rqRealDiff__k6_xcmplx_0__r1_r1_r0)). fof(rqLessOrEqual__r1_xxreal_0__r0_r1, axiom, r1_xxreal_0(np__0,np__1), file('/scratch/mptp/predsminms1/t66_borsuk_6__0', rqLessOrEqual__r1_xxreal_0__r0_r1)). fof(rqLessOrEqual__r1_xxreal_0__r0_r0, axiom, r1_xxreal_0(np__0,np__0), file('/scratch/mptp/predsminms1/t66_borsuk_6__0', rqLessOrEqual__r1_xxreal_0__r0_r0)). fof(rqLessOrEqual__r1_xxreal_0__rn1d2_r1, axiom, r1_xxreal_0(k7_xcmplx_0(np__1,np__2),np__1), file('/scratch/mptp/predsminms1/t66_borsuk_6__0', rqLessOrEqual__r1_xxreal_0__rn1d2_r1)). fof(rqLessOrEqual__r1_xxreal_0__r0_rn1d2, axiom, r1_xxreal_0(np__0,k7_xcmplx_0(np__1,np__2)), file('/scratch/mptp/predsminms1/t66_borsuk_6__0', rqLessOrEqual__r1_xxreal_0__r0_rn1d2)). fof(rqRealDiff__k6_xcmplx_0__r2_r1_r1, axiom, k6_xcmplx_0(np__2,np__1)=np__1, file('/scratch/mptp/predsminms1/t66_borsuk_6__0', rqRealDiff__k6_xcmplx_0__r2_r1_r1)). fof(rqLessOrEqual__r1_xxreal_0__r1_r1, axiom, r1_xxreal_0(np__1,np__1), file('/scratch/mptp/predsminms1/t66_borsuk_6__0', rqLessOrEqual__r1_xxreal_0__r1_r1)). fof(redefinition_k10_real_1, axiom, ![X1, X2]:((m1_subset_1(X1,k1_numbers)&v1_xreal_0(X2))=>k10_real_1(X1,X2)=k7_xcmplx_0(X1,X2)), file('/scratch/mptp/predsminms1/t66_borsuk_6__0', redefinition_k10_real_1)). fof(fc9_borsuk_1, axiom, (~(v2_struct_0(k17_borsuk_1))&(v1_pre_topc(k17_borsuk_1)&v2_pre_topc(k17_borsuk_1))), file('/scratch/mptp/predsminms1/t66_borsuk_6__0', fc9_borsuk_1)). fof(dt_k17_borsuk_1, axiom, l1_pre_topc(k17_borsuk_1), file('/scratch/mptp/predsminms1/t66_borsuk_6__0', dt_k17_borsuk_1)). fof(c_0_42, negated_conjecture, ~((r2_hidden(k4_tarski(k10_real_1(np__1,np__2),k6_numbers),k8_borsuk_6)&r2_hidden(k4_tarski(np__1,np__1),k8_borsuk_6))), inference(assume_negation,[status(cth)],[t66_borsuk_6])). fof(c_0_43, plain, ![X5, X6]:(~v1_xreal_0(X5)\|~v1_xreal_0(X6)\|v1_xreal_0(k6_xcmplx_0(X5,X6))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc7_xreal_0])])). fof(c_0_44, plain, ![X7, X8]:(~v3_membered(X7)\|(~m1_subset_1(X8,X7)\|v1_xreal_0(X8))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc14_membered])])])). fof(c_0_45, plain, ![X9]:(~v1_xboole_0(X9)\|X9=k1_xboole_0), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])])). fof(c_0_46, negated_conjecture, (~r2_hidden(k4_tarski(k10_real_1(np__1,np__2),k6_numbers),k8_borsuk_6)\|~r2_hidden(k4_tarski(np__1,np__1),k8_borsuk_6)), inference(fof_nnf,[status(thm)],[c_0_42])). fof(c_0_47, plain, ![X13, X14]:k4_tarski(X13,X14)=k2_tarski(k2_tarski(X13,X14),k1_tarski(X13)), inference(variable_rename,[status(thm)],[d5_tarski])). fof(c_0_48, plain, ![X15, X16, X19, X20, X21, X23, X24]:((((m1_subset_1(esk1_2(X15,X16),u1_struct_0(k5_topmetr))\|~r2_hidden(X16,X15)\|X15!=k8_borsuk_6\|~m1_subset_1(X15,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr)))))&((m1_subset_1(esk2_2(X15,X16),u1_struct_0(k5_topmetr))\|~r2_hidden(X16,X15)\|X15!=k8_borsuk_6\|~m1_subset_1(X15,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr)))))&((X16=k4_borsuk_1(k5_topmetr,k5_topmetr,esk1_2(X15,X16),esk2_2(X15,X16))\|~r2_hidden(X16,X15)\|X15!=k8_borsuk_6\|~m1_subset_1(X15,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr)))))&(r1_xxreal_0(esk2_2(X15,X16),k9_real_1(k8_real_1(np__2,esk1_2(X15,X16)),np__1))\|~r2_hidden(X16,X15)\|X15!=k8_borsuk_6\|~m1_subset_1(X15,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr))))))))&(~m1_subset_1(X20,u1_struct_0(k5_topmetr))\|(~m1_subset_1(X21,u1_struct_0(k5_topmetr))\|(X19!=k4_borsuk_1(k5_topmetr,k5_topmetr,X20,X21)\|~r1_xxreal_0(X21,k9_real_1(k8_real_1(np__2,X20),np__1))))\|r2_hidden(X19,X15)\|X15!=k8_borsuk_6\|~m1_subset_1(X15,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr))))))&((~r2_hidden(esk3_1(X15),X15)\|(~m1_subset_1(X23,u1_struct_0(k5_topmetr))\|(~m1_subset_1(X24,u1_struct_0(k5_topmetr))\|(esk3_1(X15)!=k4_borsuk_1(k5_topmetr,k5_topmetr,X23,X24)\|~r1_xxreal_0(X24,k9_real_1(k8_real_1(np__2,X23),np__1)))))\|X15=k8_borsuk_6\|~m1_subset_1(X15,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr)))))&((m1_subset_1(esk4_1(X15),u1_struct_0(k5_topmetr))\|r2_hidden(esk3_1(X15),X15)\|X15=k8_borsuk_6\|~m1_subset_1(X15,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr)))))&((m1_subset_1(esk5_1(X15),u1_struct_0(k5_topmetr))\|r2_hidden(esk3_1(X15),X15)\|X15=k8_borsuk_6\|~m1_subset_1(X15,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr)))))&((esk3_1(X15)=k4_borsuk_1(k5_topmetr,k5_topmetr,esk4_1(X15),esk5_1(X15))\|r2_hidden(esk3_1(X15),X15)\|X15=k8_borsuk_6\|~m1_subset_1(X15,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr)))))&(r1_xxreal_0(esk5_1(X15),k9_real_1(k8_real_1(np__2,esk4_1(X15)),np__1))\|r2_hidden(esk3_1(X15),X15)\|X15=k8_borsuk_6\|~m1_subset_1(X15,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr)))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_borsuk_6])])])])])])). fof(c_0_49, plain, ![X27, X28]:(~v1_xxreal_0(X27)\|~v1_xxreal_0(X28)\|r1_xxreal_0(X27,X27)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[reflexivity_r1_xxreal_0])])). fof(c_0_50, plain, (v1_xxreal_0(esk6_0)&v3_xxreal_0(esk6_0)), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc3_xxreal_0])])). fof(c_0_51, plain, ![X30]:((v1_xcmplx_0(k4_xcmplx_0(X30))\|~v1_xreal_0(X30))&(v1_xreal_0(k4_xcmplx_0(X30))\|~v1_xreal_0(X30))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc3_xreal_0])])])). cnf(c_0_52, plain, (k4_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(np__1),np__2))=k7_xcmplx_0(np__1,np__2)), inference(split_conjunct,[status(thm)],[rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2])). cnf(c_0_53, plain, (k7_xcmplx_0(np__1,k4_xcmplx_0(np__2))=k7_xcmplx_0(k4_xcmplx_0(np__1),np__2)), inference(split_conjunct,[status(thm)],[rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2])). cnf(c_0_54, plain, (v1_xreal_0(k6_xcmplx_0(X1,X2))\|~v1_xreal_0(X1)\|~v1_xreal_0(X2)), inference(split_conjunct,[status(thm)],[c_0_43])). cnf(c_0_55, plain, (k6_xcmplx_0(np__0,np__2)=k4_xcmplx_0(np__2)), inference(split_conjunct,[status(thm)],[rqRealDiff__k6_xcmplx_0__r0_r2_rm2])). cnf(c_0_56, plain, (v1_xreal_0(X2)\|~v3_membered(X1)\|~m1_subset_1(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_44])). cnf(c_0_57, plain, (m1_subset_1(np__2,k1_numbers)), inference(split_conjunct,[status(thm)],[spc2_numerals])). cnf(c_0_58, plain, (v3_membered(k1_numbers)), inference(split_conjunct,[status(thm)],[fc3_membered])). cnf(c_0_59, plain, (m1_subset_1(np__0,k1_numbers)), inference(split_conjunct,[status(thm)],[spc0_numerals])). fof(c_0_60, plain, ![X31]:((~r1_xxreal_0(k6_numbers,X31)\|~r1_xxreal_0(X31,np__1)\|r2_hidden(X31,u1_struct_0(k17_borsuk_1))\|~v1_xreal_0(X31))&((r1_xxreal_0(k6_numbers,X31)\|~r2_hidden(X31,u1_struct_0(k17_borsuk_1))\|~v1_xreal_0(X31))&(r1_xxreal_0(X31,np__1)\|~r2_hidden(X31,u1_struct_0(k17_borsuk_1))\|~v1_xreal_0(X31)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t43_borsuk_1])])])). cnf(c_0_61, plain, (X1=k1_xboole_0\|~v1_xboole_0(X1)), inference(split_conjunct,[status(thm)],[c_0_45])). cnf(c_0_62, plain, (k6_numbers=k1_xboole_0), inference(split_conjunct,[status(thm)],[redefinition_k6_numbers])). fof(c_0_63, plain, ![X10]:(~v1_xcmplx_0(X10)\|k3_xcmplx_0(np__1,X10)=X10), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_arithm])])). fof(c_0_64, plain, ![X11, X12]:(~m1_subset_1(X11,k1_numbers)\|~v1_xreal_0(X12)\|k8_real_1(X11,X12)=k3_xcmplx_0(X11,X12)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k8_real_1])])). cnf(c_0_65, negated_conjecture, (~r2_hidden(k4_tarski(k10_real_1(np__1,np__2),k6_numbers),k8_borsuk_6)\|~r2_hidden(k4_tarski(np__1,np__1),k8_borsuk_6)), inference(split_conjunct,[status(thm)],[c_0_46])). cnf(c_0_66, plain, (k4_tarski(X1,X2)=k2_tarski(k2_tarski(X1,X2),k1_tarski(X1))), inference(split_conjunct,[status(thm)],[c_0_47])). fof(c_0_67, plain, ![X33, X34]:k2_tarski(X33,X34)=k2_tarski(X34,X33), inference(variable_rename,[status(thm)],[commutativity_k2_tarski])). fof(c_0_68, plain, ![X35, X36, X37, X38]:(v2_struct_0(X35)\|(~v2_pre_topc(X35)\|~l1_pre_topc(X35))\|(v2_struct_0(X36)\|(~v2_pre_topc(X36)\|~l1_pre_topc(X36))\|(~m1_subset_1(X37,u1_struct_0(X35))\|~m1_subset_1(X38,u1_struct_0(X36))))\|k4_borsuk_1(X35,X36,X37,X38)=k4_tarski(X37,X38)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[redefinition_k4_borsuk_1])])])). cnf(c_0_69, plain, (r2_hidden(X3,X4)\|~m1_subset_1(X1,u1_struct_0(k5_topmetr))\|~m1_subset_1(X2,u1_struct_0(k5_topmetr))\|X3!=k4_borsuk_1(k5_topmetr,k5_topmetr,X1,X2)\|~r1_xxreal_0(X2,k9_real_1(k8_real_1(np__2,X1),np__1))\|X4!=k8_borsuk_6\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr))))), inference(split_conjunct,[status(thm)],[c_0_48])). cnf(c_0_70, plain, (m1_subset_1(k8_borsuk_6,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr))))), inference(split_conjunct,[status(thm)],[dt_k8_borsuk_6])). fof(c_0_71, plain, ![X39, X40]:(~m1_subset_1(X39,k1_numbers)\|~v1_xreal_0(X40)\|k9_real_1(X39,X40)=k6_xcmplx_0(X39,X40)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k9_real_1])])). cnf(c_0_72, plain, (m1_subset_1(np__1,k1_numbers)), inference(split_conjunct,[status(thm)],[spc1_numerals])). cnf(c_0_73, plain, (r1_xxreal_0(X1,X1)\|~v1_xxreal_0(X1)\|~v1_xxreal_0(X2)), inference(split_conjunct,[status(thm)],[c_0_49])). cnf(c_0_74, plain, (v1_xxreal_0(esk6_0)), inference(split_conjunct,[status(thm)],[c_0_50])). fof(c_0_75, plain, ![X41]:(~v1_xreal_0(X41)\|v1_xxreal_0(X41)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc4_xreal_0])])). cnf(c_0_76, plain, (v1_xreal_0(k4_xcmplx_0(X1))\|~v1_xreal_0(X1)), inference(split_conjunct,[status(thm)],[c_0_51])). cnf(c_0_77, plain, (k4_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(np__1),np__2))=k7_xcmplx_0(np__1,np__2)), inference(evalgc,[status(thm)],[c_0_52])). cnf(c_0_78, plain, (k7_xcmplx_0(k4_xcmplx_0(np__1),np__2)=k7_xcmplx_0(np__1,k4_xcmplx_0(np__2))), inference(evalgc,[status(thm)],[c_0_53])). fof(c_0_79, plain, ![X42, X43]:(~v1_xreal_0(X42)\|~v1_xreal_0(X43)\|v1_xreal_0(k7_xcmplx_0(X42,X43))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc8_xreal_0])])). cnf(c_0_80, plain, (v1_xreal_0(k6_xcmplx_0(X1,X2))\|~v1_xreal_0(X2)\|~v1_xreal_0(X1)), inference(evalgc,[status(thm)],[c_0_54])). cnf(c_0_81, plain, (k6_xcmplx_0(np__0,np__2)=k4_xcmplx_0(np__2)), inference(evalgc,[status(thm)],[c_0_55])). cnf(c_0_82, plain, (v1_xreal_0(X2)\|~v3_membered(X1)\|~m1_subset_1(X2,X1)), inference(evalgc,[status(thm)],[c_0_56])). cnf(c_0_83, plain, (m1_subset_1(np__2,k1_numbers)), inference(evalgc,[status(thm)],[c_0_57])). cnf(c_0_84, plain, (v3_membered(k1_numbers)), inference(evalgc,[status(thm)],[c_0_58])). cnf(c_0_85, plain, (m1_subset_1(np__0,k1_numbers)), inference(evalgc,[status(thm)],[c_0_59])). cnf(c_0_86, plain, (r2_hidden(X1,u1_struct_0(k17_borsuk_1))\|~r1_xxreal_0(k6_numbers,X1)\|~r1_xxreal_0(X1,np__1)\|~v1_xreal_0(X1)), inference(split_conjunct,[status(thm)],[c_0_60])). cnf(c_0_87, plain, (k5_topmetr=k17_borsuk_1), inference(split_conjunct,[status(thm)],[redefinition_k5_topmetr])). cnf(c_0_88, plain, (X1=k1_xboole_0\|~v1_xboole_0(X1)), inference(evalgc,[status(thm)],[c_0_61])). cnf(c_0_89, plain, (k1_xboole_0=k6_numbers), inference(evalgc,[status(thm)],[c_0_62])). cnf(c_0_90, plain, (v1_xboole_0(np__0)), inference(split_conjunct,[status(thm)],[spc0_boole])). cnf(c_0_91, plain, (k3_xcmplx_0(np__1,X1)=X1\|~v1_xcmplx_0(X1)), inference(split_conjunct,[status(thm)],[c_0_63])). cnf(c_0_92, plain, (k8_real_1(X1,X2)=k3_xcmplx_0(X1,X2)\|~m1_subset_1(X1,k1_numbers)\|~v1_xreal_0(X2)), inference(split_conjunct,[status(thm)],[c_0_64])). fof(c_0_93, plain, ![X32]:(~v1_xreal_0(X32)\|v1_xcmplx_0(X32)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc3_xreal_0])])). cnf(c_0_94, negated_conjecture, (~r2_hidden(k2_tarski(k2_tarski(np__1,np__1),k1_tarski(np__1)),k8_borsuk_6)\|~r2_hidden(k2_tarski(k2_tarski(k10_real_1(np__1,np__2),k6_numbers),k1_tarski(k10_real_1(np__1,np__2))),k8_borsuk_6)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_65, c_0_66]), c_0_66])). cnf(c_0_95, plain, (k2_tarski(X1,X2)=k2_tarski(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_67])). cnf(c_0_96, plain, (v2_struct_0(X1)\|v2_struct_0(X2)\|k4_borsuk_1(X1,X2,X3,X4)=k4_tarski(X3,X4)\|~v2_pre_topc(X1)\|~l1_pre_topc(X1)\|~v2_pre_topc(X2)\|~l1_pre_topc(X2)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X4,u1_struct_0(X2))), inference(split_conjunct,[status(thm)],[c_0_68])). cnf(c_0_97, plain, (r2_hidden(X3,X4)\|X4!=k8_borsuk_6\|X3!=k4_borsuk_1(k5_topmetr,k5_topmetr,X1,X2)\|~m1_subset_1(X2,u1_struct_0(k5_topmetr))\|~m1_subset_1(X1,u1_struct_0(k5_topmetr))\|~r1_xxreal_0(X2,k9_real_1(k8_real_1(np__2,X1),np__1))\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr))))), inference(evalgc,[status(thm)],[c_0_69])). cnf(c_0_98, plain, (m1_subset_1(k8_borsuk_6,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr))))), inference(evalgc,[status(thm)],[c_0_70])). cnf(c_0_99, plain, (k9_real_1(X1,X2)=k6_xcmplx_0(X1,X2)\|~m1_subset_1(X1,k1_numbers)\|~v1_xreal_0(X2)), inference(split_conjunct,[status(thm)],[c_0_71])). cnf(c_0_100, plain, (m1_subset_1(np__1,k1_numbers)), inference(evalgc,[status(thm)],[c_0_72])). cnf(c_0_101, plain, (r1_xxreal_0(X1,X1)\|~v1_xxreal_0(X2)\|~v1_xxreal_0(X1)), inference(evalgc,[status(thm)],[c_0_73])). cnf(c_0_102, plain, (v1_xxreal_0(esk6_0)), inference(evalgc,[status(thm)],[c_0_74])). cnf(c_0_103, plain, (v1_xxreal_0(X1)\|~v1_xreal_0(X1)), inference(split_conjunct,[status(thm)],[c_0_75])). cnf(c_0_104, plain, (k3_xcmplx_0(np__2,k7_xcmplx_0(np__1,np__2))=np__1), inference(split_conjunct,[status(thm)],[rqRealMult__k3_xcmplx_0__r2_rn1d2_r1])). cnf(c_0_105, plain, (v1_xreal_0(k4_xcmplx_0(X1))\|~v1_xreal_0(X1)), inference(evalgc,[status(thm)],[c_0_76])). cnf(c_0_106, plain, (k4_xcmplx_0(k7_xcmplx_0(np__1,k4_xcmplx_0(np__2)))=k7_xcmplx_0(np__1,np__2)), inference(rw,[status(thm)],[c_0_77, c_0_78])). cnf(c_0_107, plain, (v1_xreal_0(k7_xcmplx_0(X1,X2))\|~v1_xreal_0(X1)\|~v1_xreal_0(X2)), inference(split_conjunct,[status(thm)],[c_0_79])). cnf(c_0_108, plain, (v1_xreal_0(k4_xcmplx_0(np__2))\|~v1_xreal_0(np__2)\|~v1_xreal_0(np__0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_80, c_0_81])])). cnf(c_0_109, plain, (v1_xreal_0(np__2)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82, c_0_83]), c_0_84])])])). cnf(c_0_110, plain, (v1_xreal_0(np__0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82, c_0_85]), c_0_84])])])). fof(c_0_111, plain, ![X46, X47]:(~r2_hidden(X46,X47)\|m1_subset_1(X46,X47)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])])). cnf(c_0_112, plain, (r2_hidden(X1,u1_struct_0(k17_borsuk_1))\|~v1_xreal_0(X1)\|~r1_xxreal_0(X1,np__1)\|~r1_xxreal_0(k6_numbers,X1)), inference(evalgc,[status(thm)],[c_0_86])). cnf(c_0_113, plain, (k17_borsuk_1=k5_topmetr), inference(evalgc,[status(thm)],[c_0_87])). cnf(c_0_114, plain, (X1=k6_numbers\|~v1_xboole_0(X1)), inference(rw,[status(thm)],[c_0_88, c_0_89])). cnf(c_0_115, plain, (v1_xboole_0(np__0)), inference(evalgc,[status(thm)],[c_0_90])). fof(c_0_116, plain, ![X44, X45]:(~m1_subset_1(X44,k1_numbers)\|~v1_xreal_0(X45)\|k8_real_1(X44,X45)=k8_real_1(X45,X44)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[commutativity_k8_real_1])])). cnf(c_0_117, plain, (k3_xcmplx_0(np__1,X1)=X1\|~v1_xcmplx_0(X1)), inference(evalgc,[status(thm)],[c_0_91])). cnf(c_0_118, plain, (k3_xcmplx_0(X1,X2)=k8_real_1(X1,X2)\|~v1_xreal_0(X2)\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[c_0_92])). cnf(c_0_119, plain, (v1_xcmplx_0(X1)\|~v1_xreal_0(X1)), inference(split_conjunct,[status(thm)],[c_0_93])). cnf(c_0_120, negated_conjecture, (~r2_hidden(k2_tarski(k2_tarski(np__1,np__1),k1_tarski(np__1)),k8_borsuk_6)\|~r2_hidden(k2_tarski(k2_tarski(k10_real_1(np__1,np__2),k6_numbers),k1_tarski(k10_real_1(np__1,np__2))),k8_borsuk_6)), inference(evalgc,[status(thm)],[c_0_94])). cnf(c_0_121, plain, (k2_tarski(X1,X2)=k2_tarski(X2,X1)), inference(evalgc,[status(thm)],[c_0_95])). cnf(c_0_122, plain, (k4_borsuk_1(X1,X2,X3,X4)=k2_tarski(k2_tarski(X3,X4),k1_tarski(X3))\|v2_struct_0(X2)\|v2_struct_0(X1)\|~v2_pre_topc(X2)\|~v2_pre_topc(X1)\|~l1_pre_topc(X2)\|~l1_pre_topc(X1)\|~m1_subset_1(X4,u1_struct_0(X2))\|~m1_subset_1(X3,u1_struct_0(X1))), inference(rw,[status(thm)],[c_0_96, c_0_66])). cnf(c_0_123, plain, (r2_hidden(X1,k8_borsuk_6)\|X1!=k4_borsuk_1(k5_topmetr,k5_topmetr,X2,X3)\|~r1_xxreal_0(X3,k9_real_1(k8_real_1(np__2,X2),np__1))\|~m1_subset_1(X3,u1_struct_0(k5_topmetr))\|~m1_subset_1(X2,u1_struct_0(k5_topmetr))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_97, c_0_98])])). cnf(c_0_124, plain, (k9_real_1(X1,X2)=k6_xcmplx_0(X1,X2)\|~v1_xreal_0(X2)\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[c_0_99])). cnf(c_0_125, plain, (v1_xreal_0(np__1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82, c_0_100]), c_0_84])])])). cnf(c_0_126, plain, (r1_xxreal_0(X1,X1)\|~v1_xxreal_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_101, c_0_102])])). cnf(c_0_127, plain, (v1_xxreal_0(X1)\|~v1_xreal_0(X1)), inference(evalgc,[status(thm)],[c_0_103])). cnf(c_0_128, plain, (k3_xcmplx_0(np__2,k7_xcmplx_0(np__1,np__2))=np__1), inference(evalgc,[status(thm)],[c_0_104])). cnf(c_0_129, plain, (v1_xreal_0(k7_xcmplx_0(np__1,np__2))\|~v1_xreal_0(k7_xcmplx_0(np__1,k4_xcmplx_0(np__2)))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_105, c_0_106])])). cnf(c_0_130, plain, (v1_xreal_0(k7_xcmplx_0(X1,X2))\|~v1_xreal_0(X2)\|~v1_xreal_0(X1)), inference(evalgc,[status(thm)],[c_0_107])). cnf(c_0_131, plain, (v1_xreal_0(k4_xcmplx_0(np__2))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_108, c_0_109]), c_0_110])])). cnf(c_0_132, plain, (m1_subset_1(X1,X2)\|~r2_hidden(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_111])). cnf(c_0_133, plain, (r2_hidden(X1,u1_struct_0(k5_topmetr))\|~r1_xxreal_0(X1,np__1)\|~r1_xxreal_0(k6_numbers,X1)\|~v1_xreal_0(X1)), inference(rw,[status(thm)],[c_0_112, c_0_113])). cnf(c_0_134, plain, (k6_numbers=np__0), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_114, c_0_115])])). cnf(c_0_135, plain, (k8_real_1(X1,X2)=k8_real_1(X2,X1)\|~m1_subset_1(X1,k1_numbers)\|~v1_xreal_0(X2)), inference(split_conjunct,[status(thm)],[c_0_116])). cnf(c_0_136, plain, (k8_real_1(np__1,X1)=X1\|~v1_xcmplx_0(X1)\|~v1_xreal_0(X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117, c_0_118]), c_0_100])])])). cnf(c_0_137, plain, (v1_xcmplx_0(X1)\|~v1_xreal_0(X1)), inference(evalgc,[status(thm)],[c_0_119])). cnf(c_0_138, negated_conjecture, (~r2_hidden(k2_tarski(k2_tarski(k6_numbers,k10_real_1(np__1,np__2)),k1_tarski(k10_real_1(np__1,np__2))),k8_borsuk_6)\|~r2_hidden(k2_tarski(k2_tarski(np__1,np__1),k1_tarski(np__1)),k8_borsuk_6)), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[c_0_120, c_0_121])])). cnf(c_0_139, plain, (k4_borsuk_1(X1,X2,X3,X4)=k2_tarski(k2_tarski(X3,X4),k1_tarski(X3))\|v2_struct_0(X2)\|v2_struct_0(X1)\|~v2_pre_topc(X2)\|~v2_pre_topc(X1)\|~l1_pre_topc(X2)\|~l1_pre_topc(X1)\|~m1_subset_1(X4,u1_struct_0(X2))\|~m1_subset_1(X3,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_122])). cnf(c_0_140, plain, (r2_hidden(X1,k8_borsuk_6)\|X1!=k4_borsuk_1(k5_topmetr,k5_topmetr,X2,X3)\|~r1_xxreal_0(X3,k6_xcmplx_0(k8_real_1(np__2,X2),np__1))\|~m1_subset_1(X3,u1_struct_0(k5_topmetr))\|~m1_subset_1(X2,u1_struct_0(k5_topmetr))\|~m1_subset_1(k8_real_1(np__2,X2),k1_numbers)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123, c_0_124]), c_0_125])])])). cnf(c_0_141, plain, (r1_xxreal_0(X1,X1)\|~v1_xreal_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_126, c_0_127])])). cnf(c_0_142, plain, (k8_real_1(np__2,k7_xcmplx_0(np__1,np__2))=np__1\|~v1_xreal_0(k7_xcmplx_0(np__1,np__2))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128, c_0_118]), c_0_83])])])). cnf(c_0_143, plain, (v1_xreal_0(k7_xcmplx_0(np__1,np__2))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129, c_0_130]), c_0_131]), c_0_125])])])). cnf(c_0_144, plain, (k6_xcmplx_0(np__1,np__1)=np__0), inference(split_conjunct,[status(thm)],[rqRealDiff__k6_xcmplx_0__r1_r1_r0])). cnf(c_0_145, plain, (m1_subset_1(X1,X2)\|~r2_hidden(X1,X2)), inference(evalgc,[status(thm)],[c_0_132])). cnf(c_0_146, plain, (r2_hidden(X1,u1_struct_0(k5_topmetr))\|~r1_xxreal_0(X1,np__1)\|~r1_xxreal_0(np__0,X1)\|~v1_xreal_0(X1)), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[c_0_133, c_0_134])])). cnf(c_0_147, plain, (r1_xxreal_0(np__0,np__1)), inference(split_conjunct,[status(thm)],[rqLessOrEqual__r1_xxreal_0__r0_r1])). cnf(c_0_148, plain, (r1_xxreal_0(np__0,np__0)), inference(split_conjunct,[status(thm)],[rqLessOrEqual__r1_xxreal_0__r0_r0])). cnf(c_0_149, plain, (r1_xxreal_0(k7_xcmplx_0(np__1,np__2),np__1)), inference(split_conjunct,[status(thm)],[rqLessOrEqual__r1_xxreal_0__rn1d2_r1])). cnf(c_0_150, plain, (r1_xxreal_0(np__0,k7_xcmplx_0(np__1,np__2))), inference(split_conjunct,[status(thm)],[rqLessOrEqual__r1_xxreal_0__r0_rn1d2])). cnf(c_0_151, plain, (k8_real_1(X1,X2)=k8_real_1(X2,X1)\|~v1_xreal_0(X2)\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[c_0_135])). cnf(c_0_152, plain, (k8_real_1(np__1,X1)=X1\|~v1_xreal_0(X1)), inference(csr,[status(thm)],[c_0_136, c_0_137])). cnf(c_0_153, plain, (k6_xcmplx_0(np__2,np__1)=np__1), inference(split_conjunct,[status(thm)],[rqRealDiff__k6_xcmplx_0__r2_r1_r1])). cnf(c_0_154, plain, (r1_xxreal_0(np__1,np__1)), inference(split_conjunct,[status(thm)],[rqLessOrEqual__r1_xxreal_0__r1_r1])). cnf(c_0_155, negated_conjecture, (~r2_hidden(k2_tarski(k2_tarski(np__0,k10_real_1(np__1,np__2)),k1_tarski(k10_real_1(np__1,np__2))),k8_borsuk_6)\|~r2_hidden(k2_tarski(k2_tarski(np__1,np__1),k1_tarski(np__1)),k8_borsuk_6)), inference(rw,[status(thm)],[c_0_138, c_0_134])). cnf(c_0_156, plain, (k4_borsuk_1(X1,X2,X3,X4)=k2_tarski(k2_tarski(X4,X3),k1_tarski(X3))\|v2_struct_0(X1)\|v2_struct_0(X2)\|~l1_pre_topc(X2)\|~l1_pre_topc(X1)\|~v2_pre_topc(X2)\|~v2_pre_topc(X1)\|~m1_subset_1(X4,u1_struct_0(X2))\|~m1_subset_1(X3,u1_struct_0(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_139, c_0_121])])). fof(c_0_157, plain, ![X49, X50]:(~m1_subset_1(X49,k1_numbers)\|~v1_xreal_0(X50)\|k10_real_1(X49,X50)=k7_xcmplx_0(X49,X50)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k10_real_1])])). cnf(c_0_158, plain, (r2_hidden(X1,k8_borsuk_6)\|X1!=k4_borsuk_1(k5_topmetr,k5_topmetr,X2,k6_xcmplx_0(k8_real_1(np__2,X2),np__1))\|~m1_subset_1(k8_real_1(np__2,X2),k1_numbers)\|~m1_subset_1(k6_xcmplx_0(k8_real_1(np__2,X2),np__1),u1_struct_0(k5_topmetr))\|~m1_subset_1(X2,u1_struct_0(k5_topmetr))\|~v1_xreal_0(k6_xcmplx_0(k8_real_1(np__2,X2),np__1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_140, c_0_141])])). cnf(c_0_159, plain, (k8_real_1(np__2,k7_xcmplx_0(np__1,np__2))=np__1), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_142, c_0_143])])])). cnf(c_0_160, plain, (k6_xcmplx_0(np__1,np__1)=np__0), inference(evalgc,[status(thm)],[c_0_144])). cnf(c_0_161, plain, (m1_subset_1(X1,u1_struct_0(k5_topmetr))\|~r1_xxreal_0(X1,np__1)\|~r1_xxreal_0(np__0,X1)\|~v1_xreal_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_145, c_0_146])])). cnf(c_0_162, plain, (r1_xxreal_0(np__0,np__1)), inference(evalgc,[status(thm)],[c_0_147])). cnf(c_0_163, plain, (r1_xxreal_0(np__0,np__0)), inference(evalgc,[status(thm)],[c_0_148])). cnf(c_0_164, plain, (r1_xxreal_0(k7_xcmplx_0(np__1,np__2),np__1)), inference(evalgc,[status(thm)],[c_0_149])). cnf(c_0_165, plain, (r1_xxreal_0(np__0,k7_xcmplx_0(np__1,np__2))), inference(evalgc,[status(thm)],[c_0_150])). fof(c_0_166, plain, (~v2_struct_0(k17_borsuk_1)&(v1_pre_topc(k17_borsuk_1)&v2_pre_topc(k17_borsuk_1))), inference(fof_simplification,[status(thm)],[fc9_borsuk_1])). cnf(c_0_167, plain, (k8_real_1(X1,np__1)=X1\|~v1_xreal_0(X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151, c_0_152]), c_0_100])])])). cnf(c_0_168, plain, (k6_xcmplx_0(np__2,np__1)=np__1), inference(evalgc,[status(thm)],[c_0_153])). cnf(c_0_169, plain, (r1_xxreal_0(np__1,np__1)), inference(evalgc,[status(thm)],[c_0_154])). cnf(c_0_170, negated_conjecture, (v2_struct_0(X2)\|v2_struct_0(X1)\|~r2_hidden(k4_borsuk_1(X1,X2,k10_real_1(np__1,np__2),np__0),k8_borsuk_6)\|~r2_hidden(k2_tarski(k2_tarski(np__1,np__1),k1_tarski(np__1)),k8_borsuk_6)\|~l1_pre_topc(X2)\|~l1_pre_topc(X1)\|~v2_pre_topc(X2)\|~v2_pre_topc(X1)\|~m1_subset_1(np__0,u1_struct_0(X2))\|~m1_subset_1(k10_real_1(np__1,np__2),u1_struct_0(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_155, c_0_156])])). cnf(c_0_171, plain, (k10_real_1(X1,X2)=k7_xcmplx_0(X1,X2)\|~m1_subset_1(X1,k1_numbers)\|~v1_xreal_0(X2)), inference(split_conjunct,[status(thm)],[c_0_157])). cnf(c_0_172, plain, (r2_hidden(X1,k8_borsuk_6)\|X1!=k4_borsuk_1(k5_topmetr,k5_topmetr,k7_xcmplx_0(np__1,np__2),np__0)\|~m1_subset_1(np__0,u1_struct_0(k5_topmetr))\|~m1_subset_1(k7_xcmplx_0(np__1,np__2),u1_struct_0(k5_topmetr))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158, c_0_159]), c_0_160]), c_0_160]), c_0_100]), c_0_160]), c_0_110])])])). cnf(c_0_173, plain, (m1_subset_1(np__0,u1_struct_0(k5_topmetr))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161, c_0_162]), c_0_163]), c_0_110])])])). cnf(c_0_174, plain, (m1_subset_1(k7_xcmplx_0(np__1,np__2),u1_struct_0(k5_topmetr))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161, c_0_164]), c_0_165]), c_0_143])])])). cnf(c_0_175, plain, (l1_pre_topc(k17_borsuk_1)), inference(split_conjunct,[status(thm)],[dt_k17_borsuk_1])). cnf(c_0_176, plain, (v2_pre_topc(k17_borsuk_1)), inference(split_conjunct,[status(thm)],[c_0_166])). cnf(c_0_177, plain, (~v2_struct_0(k17_borsuk_1)), inference(split_conjunct,[status(thm)],[c_0_166])). cnf(c_0_178, plain, (r2_hidden(X1,k8_borsuk_6)\|X1!=k4_borsuk_1(k5_topmetr,k5_topmetr,np__1,np__1)\|~m1_subset_1(np__1,u1_struct_0(k5_topmetr))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158, c_0_167]), c_0_168]), c_0_168]), c_0_83]), c_0_168]), c_0_125]), c_0_109])])])). cnf(c_0_179, plain, (m1_subset_1(np__1,u1_struct_0(k5_topmetr))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161, c_0_169]), c_0_162]), c_0_125])])])). cnf(c_0_180, negated_conjecture, (v2_struct_0(X1)\|v2_struct_0(X2)\|v2_struct_0(X3)\|v2_struct_0(X4)\|~l1_pre_topc(X2)\|~l1_pre_topc(X1)\|~v2_pre_topc(X2)\|~v2_pre_topc(X1)\|~m1_subset_1(k10_real_1(np__1,np__2),u1_struct_0(X1))\|~m1_subset_1(np__0,u1_struct_0(X2))\|~r2_hidden(k4_borsuk_1(X1,X2,k10_real_1(np__1,np__2),np__0),k8_borsuk_6)\|~r2_hidden(k4_borsuk_1(X3,X4,np__1,np__1),k8_borsuk_6)\|~l1_pre_topc(X4)\|~l1_pre_topc(X3)\|~v2_pre_topc(X4)\|~v2_pre_topc(X3)\|~m1_subset_1(np__1,u1_struct_0(X4))\|~m1_subset_1(np__1,u1_struct_0(X3))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_170, c_0_139])])). cnf(c_0_181, plain, (k10_real_1(X1,X2)=k7_xcmplx_0(X1,X2)\|~v1_xreal_0(X2)\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[c_0_171])). cnf(c_0_182, plain, (r2_hidden(X1,k8_borsuk_6)\|X1!=k4_borsuk_1(k5_topmetr,k5_topmetr,k7_xcmplx_0(np__1,np__2),np__0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_172, c_0_173]), c_0_174])])). cnf(c_0_183, plain, (l1_pre_topc(k17_borsuk_1)), inference(evalgc,[status(thm)],[c_0_175])). cnf(c_0_184, plain, (v2_pre_topc(k17_borsuk_1)), inference(evalgc,[status(thm)],[c_0_176])). cnf(c_0_185, plain, (~v2_struct_0(k17_borsuk_1)), inference(evalgc,[status(thm)],[c_0_177])). cnf(c_0_186, plain, (r2_hidden(X1,k8_borsuk_6)\|X1!=k4_borsuk_1(k5_topmetr,k5_topmetr,np__1,np__1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_178, c_0_179])])). cnf(c_0_187, negated_conjecture, (v2_struct_0(X1)\|v2_struct_0(X2)\|v2_struct_0(X3)\|v2_struct_0(X4)\|~l1_pre_topc(X3)\|~l1_pre_topc(X4)\|~l1_pre_topc(X1)\|~l1_pre_topc(X2)\|~v2_pre_topc(X3)\|~v2_pre_topc(X4)\|~v2_pre_topc(X1)\|~v2_pre_topc(X2)\|~m1_subset_1(k7_xcmplx_0(np__1,np__2),u1_struct_0(X4))\|~m1_subset_1(np__0,u1_struct_0(X3))\|~m1_subset_1(np__1,u1_struct_0(X1))\|~m1_subset_1(np__1,u1_struct_0(X2))\|~r2_hidden(k4_borsuk_1(X4,X3,k7_xcmplx_0(np__1,np__2),np__0),k8_borsuk_6)\|~r2_hidden(k4_borsuk_1(X2,X1,np__1,np__1),k8_borsuk_6)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_180, c_0_181]), c_0_100]), c_0_109])])])). cnf(c_0_188, plain, (r2_hidden(k4_borsuk_1(k5_topmetr,k5_topmetr,k7_xcmplx_0(np__1,np__2),np__0),k8_borsuk_6)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_182])])). cnf(c_0_189, plain, (l1_pre_topc(k5_topmetr)), inference(rw,[status(thm)],[c_0_183, c_0_113])). cnf(c_0_190, plain, (v2_pre_topc(k5_topmetr)), inference(rw,[status(thm)],[c_0_184, c_0_113])). cnf(c_0_191, plain, (~v2_struct_0(k5_topmetr)), inference(rw,[status(thm)],[c_0_185, c_0_113])). cnf(c_0_192, plain, (r2_hidden(k4_borsuk_1(k5_topmetr,k5_topmetr,np__1,np__1),k8_borsuk_6)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_186])])). cnf(c_0_193, plain, (k4_borsuk_1(X1,X2,X3,X4)=k4_borsuk_1(X5,X6,X3,X4)\|v2_struct_0(X1)\|v2_struct_0(X2)\|v2_struct_0(X5)\|v2_struct_0(X6)\|~l1_pre_topc(X2)\|~l1_pre_topc(X1)\|~v2_pre_topc(X2)\|~v2_pre_topc(X1)\|~m1_subset_1(X4,u1_struct_0(X2))\|~m1_subset_1(X3,u1_struct_0(X1))\|~l1_pre_topc(X6)\|~l1_pre_topc(X5)\|~v2_pre_topc(X6)\|~v2_pre_topc(X5)\|~m1_subset_1(X4,u1_struct_0(X6))\|~m1_subset_1(X3,u1_struct_0(X5))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_139, c_0_139])])). cnf(c_0_194, negated_conjecture, (v2_struct_0(X1)\|v2_struct_0(X2)\|~l1_pre_topc(X2)\|~l1_pre_topc(X1)\|~v2_pre_topc(X2)\|~v2_pre_topc(X1)\|~m1_subset_1(np__1,u1_struct_0(X2))\|~m1_subset_1(np__1,u1_struct_0(X1))\|~r2_hidden(k4_borsuk_1(X1,X2,np__1,np__1),k8_borsuk_6)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_187, c_0_188]), c_0_189]), c_0_190]), c_0_174]), c_0_173])]), c_0_191])])). cnf(c_0_195, plain, (r2_hidden(k4_borsuk_1(X1,X2,np__1,np__1),k8_borsuk_6)\|v2_struct_0(X2)\|v2_struct_0(X1)\|~l1_pre_topc(X2)\|~l1_pre_topc(X1)\|~v2_pre_topc(X2)\|~v2_pre_topc(X1)\|~m1_subset_1(np__1,u1_struct_0(X2))\|~m1_subset_1(np__1,u1_struct_0(X1))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_192, c_0_193]), c_0_189]), c_0_190]), c_0_179])]), c_0_191])])). cnf(c_0_196, negated_conjecture, (v2_struct_0(X1)\|v2_struct_0(X2)\|~l1_pre_topc(X1)\|~l1_pre_topc(X2)\|~v2_pre_topc(X1)\|~v2_pre_topc(X2)\|~m1_subset_1(np__1,u1_struct_0(X1))\|~m1_subset_1(np__1,u1_struct_0(X2))), inference(csr,[status(thm)],[c_0_194, c_0_195])). cnf(c_0_197, negated_conjecture, (v2_struct_0(X1)\|~l1_pre_topc(X1)\|~v2_pre_topc(X1)\|~m1_subset_1(np__1,u1_struct_0(X1))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_196, c_0_179]), c_0_189]), c_0_190])]), c_0_191])])). cnf(c_0_198, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_191, c_0_197]), c_0_189]), c_0_190]), c_0_179])]), ['proof']). # SZS output end CNFRefutation	reserve T for non empty TopSpace, a, b, c, d for Point of T; theorem Th66: [1/2,0] in ICC & [1,1] in ICC proof A1: 0 <= 2 * (1/2) - 1; 1/2 is Point of I[01] & 0 is Point of I[01] by BORSUK_1:43; hence [1/2,0] in ICC by A1,Def10; 1 is Point of I[01] & 1 <= 2 * 1 - 1 by BORSUK_1:43; hence thesis by Def10; end;	Convert the following ATP output trace into a readable Mizar proof.
t24_waybel23	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(dt_m2_subset_1, axiom, ![X1, X2]:((~(v1_xboole_0(X1))&(~(v1_xboole_0(X2))&m1_subset_1(X2,k1_zfmisc_1(X1))))=>![X3]:(m2_subset_1(X3,X1,X2)=>m1_subset_1(X3,X1))), file('/scratch/mptp/predsminms1/t24_waybel23__0', dt_m2_subset_1)). fof(cc1_subset_1, axiom, ![X1]:(v1_xboole_0(X1)=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(X1))=>v1_xboole_0(X2))), file('/scratch/mptp/predsminms1/t24_waybel23__0', cc1_subset_1)). fof(t24_waybel23, conjecture, ![X1]:((~(v2_struct_0(X1))&(v4_orders_2(X1)&l1_orders_2(X1)))=>![X2]:((~(v1_xboole_0(X2))&(v2_waybel23(X2,X1)&m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))))=>![X3]:(m2_subset_1(X3,u1_struct_0(X1),X2)=>![X4]:(m2_subset_1(X4,u1_struct_0(X1),X2)=>(r1_yellow_0(X1,k7_domain_1(X2,X3,X4))=>(r1_yellow_0(k5_yellow_0(X1,X2),k7_domain_1(X2,X3,X4))&k1_yellow_0(k5_yellow_0(X1,X2),k7_domain_1(X2,X3,X4))=k1_yellow_0(X1,k7_domain_1(X2,X3,X4)))))))), file('/scratch/mptp/predsminms1/t24_waybel23__0', t24_waybel23)). fof(redefinition_m2_subset_1, axiom, ![X1, X2]:((~(v1_xboole_0(X1))&(~(v1_xboole_0(X2))&m1_subset_1(X2,k1_zfmisc_1(X1))))=>![X3]:(m2_subset_1(X3,X1,X2)<=>m1_subset_1(X3,X2))), file('/scratch/mptp/predsminms1/t24_waybel23__0', redefinition_m2_subset_1)). fof(d15_yellow_0, axiom, ![X1]:(l1_orders_2(X1)=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))=>![X3]:((v1_orders_2(X3)&(v4_yellow_0(X3,X1)&m1_yellow_0(X3,X1)))=>(X3=k5_yellow_0(X1,X2)<=>u1_struct_0(X3)=X2)))), file('/scratch/mptp/predsminms1/t24_waybel23__0', d15_yellow_0)). fof(redefinition_k7_domain_1, axiom, ![X1, X2, X3]:((~(v1_xboole_0(X1))&(m1_subset_1(X2,X1)&m1_subset_1(X3,X1)))=>k7_domain_1(X1,X2,X3)=k2_tarski(X2,X3)), file('/scratch/mptp/predsminms1/t24_waybel23__0', redefinition_k7_domain_1)). fof(dt_k5_yellow_0, axiom, ![X1, X2]:((l1_orders_2(X1)&m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))))=>(v1_orders_2(k5_yellow_0(X1,X2))&(v4_yellow_0(k5_yellow_0(X1,X2),X1)&m1_yellow_0(k5_yellow_0(X1,X2),X1)))), file('/scratch/mptp/predsminms1/t24_waybel23__0', dt_k5_yellow_0)). fof(d17_yellow_0, axiom, ![X1]:((~(v2_struct_0(X1))&l1_orders_2(X1))=>![X2]:(m1_yellow_0(X2,X1)=>(v6_yellow_0(X2,X1)<=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>![X4]:(m1_subset_1(X4,u1_struct_0(X1))=>((r2_hidden(X3,u1_struct_0(X2))&(r2_hidden(X4,u1_struct_0(X2))&r1_yellow_0(X1,k7_domain_1(u1_struct_0(X1),X3,X4))))=>r2_hidden(k1_yellow_0(X1,k7_domain_1(u1_struct_0(X1),X3,X4)),u1_struct_0(X2)))))))), file('/scratch/mptp/predsminms1/t24_waybel23__0', d17_yellow_0)). fof(t66_yellow_0, axiom, ![X1]:((~(v2_struct_0(X1))&(v4_orders_2(X1)&l1_orders_2(X1)))=>![X2]:((~(v2_struct_0(X2))&(v4_yellow_0(X2,X1)&m1_yellow_0(X2,X1)))=>![X3]:(m1_subset_1(X3,u1_struct_0(X2))=>![X4]:(m1_subset_1(X4,u1_struct_0(X2))=>((r1_yellow_0(X1,k7_domain_1(u1_struct_0(X2),X3,X4))&r2_hidden(k1_yellow_0(X1,k7_domain_1(u1_struct_0(X2),X3,X4)),u1_struct_0(X2)))=>(r1_yellow_0(X2,k7_domain_1(u1_struct_0(X2),X3,X4))&k1_yellow_0(X2,k7_domain_1(u1_struct_0(X2),X3,X4))=k1_yellow_0(X1,k7_domain_1(u1_struct_0(X2),X3,X4)))))))), file('/scratch/mptp/predsminms1/t24_waybel23__0', t66_yellow_0)). fof(d2_waybel23, axiom, ![X1]:((~(v2_struct_0(X1))&l1_orders_2(X1))=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))=>(v2_waybel23(X2,X1)<=>v6_yellow_0(k5_yellow_0(X1,X2),X1)))), file('/scratch/mptp/predsminms1/t24_waybel23__0', d2_waybel23)). fof(fc1_yellow_2, axiom, ![X1, X2]:(((~(v2_struct_0(X1))&l1_orders_2(X1))&(~(v1_xboole_0(X2))&m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))))=>(~(v2_struct_0(k5_yellow_0(X1,X2)))&(v1_orders_2(k5_yellow_0(X1,X2))&v4_yellow_0(k5_yellow_0(X1,X2),X1)))), file('/scratch/mptp/predsminms1/t24_waybel23__0', fc1_yellow_2)). fof(t2_subset, axiom, ![X1, X2]:(m1_subset_1(X1,X2)=>(v1_xboole_0(X2)\|r2_hidden(X1,X2))), file('/scratch/mptp/predsminms1/t24_waybel23__0', t2_subset)). fof(c_0_12, plain, ![X26, X27, X28]:(v1_xboole_0(X26)\|(v1_xboole_0(X27)\|~m1_subset_1(X27,k1_zfmisc_1(X26)))\|(~m2_subset_1(X28,X26,X27)\|m1_subset_1(X28,X26))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_m2_subset_1])])])])). fof(c_0_13, plain, ![X11, X12]:(~v1_xboole_0(X11)\|(~m1_subset_1(X12,k1_zfmisc_1(X11))\|v1_xboole_0(X12))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_subset_1])])])). fof(c_0_14, negated_conjecture, ~(![X1]:((~(v2_struct_0(X1))&(v4_orders_2(X1)&l1_orders_2(X1)))=>![X2]:((~(v1_xboole_0(X2))&(v2_waybel23(X2,X1)&m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))))=>![X3]:(m2_subset_1(X3,u1_struct_0(X1),X2)=>![X4]:(m2_subset_1(X4,u1_struct_0(X1),X2)=>(r1_yellow_0(X1,k7_domain_1(X2,X3,X4))=>(r1_yellow_0(k5_yellow_0(X1,X2),k7_domain_1(X2,X3,X4))&k1_yellow_0(k5_yellow_0(X1,X2),k7_domain_1(X2,X3,X4))=k1_yellow_0(X1,k7_domain_1(X2,X3,X4))))))))), inference(assume_negation,[status(cth)],[t24_waybel23])). fof(c_0_15, plain, ![X13, X14, X15]:((~m2_subset_1(X15,X13,X14)\|m1_subset_1(X15,X14)\|(v1_xboole_0(X13)\|(v1_xboole_0(X14)\|~m1_subset_1(X14,k1_zfmisc_1(X13)))))&(~m1_subset_1(X15,X14)\|m2_subset_1(X15,X13,X14)\|(v1_xboole_0(X13)\|(v1_xboole_0(X14)\|~m1_subset_1(X14,k1_zfmisc_1(X13)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[redefinition_m2_subset_1])])])])])). cnf(c_0_16, plain, (v1_xboole_0(X1)\|v1_xboole_0(X2)\|m1_subset_1(X3,X1)\|~m1_subset_1(X2,k1_zfmisc_1(X1))\|~m2_subset_1(X3,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_17, plain, (v1_xboole_0(X2)\|~v1_xboole_0(X1)\|~m1_subset_1(X2,k1_zfmisc_1(X1))), inference(split_conjunct,[status(thm)],[c_0_13])). fof(c_0_18, negated_conjecture, ((~v2_struct_0(esk1_0)&(v4_orders_2(esk1_0)&l1_orders_2(esk1_0)))&((~v1_xboole_0(esk2_0)&(v2_waybel23(esk2_0,esk1_0)&m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(esk1_0)))))&(m2_subset_1(esk3_0,u1_struct_0(esk1_0),esk2_0)&(m2_subset_1(esk4_0,u1_struct_0(esk1_0),esk2_0)&(r1_yellow_0(esk1_0,k7_domain_1(esk2_0,esk3_0,esk4_0))&(~r1_yellow_0(k5_yellow_0(esk1_0,esk2_0),k7_domain_1(esk2_0,esk3_0,esk4_0))\|k1_yellow_0(k5_yellow_0(esk1_0,esk2_0),k7_domain_1(esk2_0,esk3_0,esk4_0))!=k1_yellow_0(esk1_0,k7_domain_1(esk2_0,esk3_0,esk4_0)))))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_14])])])])). cnf(c_0_19, plain, (m1_subset_1(X1,X3)\|v1_xboole_0(X2)\|v1_xboole_0(X3)\|~m2_subset_1(X1,X2,X3)\|~m1_subset_1(X3,k1_zfmisc_1(X2))), inference(split_conjunct,[status(thm)],[c_0_15])). fof(c_0_20, plain, ![X23, X24, X25]:((X25!=k5_yellow_0(X23,X24)\|u1_struct_0(X25)=X24\|(~v1_orders_2(X25)\|(~v4_yellow_0(X25,X23)\|~m1_yellow_0(X25,X23)))\|~m1_subset_1(X24,k1_zfmisc_1(u1_struct_0(X23)))\|~l1_orders_2(X23))&(u1_struct_0(X25)!=X24\|X25=k5_yellow_0(X23,X24)\|(~v1_orders_2(X25)\|(~v4_yellow_0(X25,X23)\|~m1_yellow_0(X25,X23)))\|~m1_subset_1(X24,k1_zfmisc_1(u1_struct_0(X23)))\|~l1_orders_2(X23))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d15_yellow_0])])])])). fof(c_0_21, plain, ![X16, X17, X18]:(v1_xboole_0(X16)\|(~m1_subset_1(X17,X16)\|~m1_subset_1(X18,X16))\|k7_domain_1(X16,X17,X18)=k2_tarski(X17,X18)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[redefinition_k7_domain_1])])])). cnf(c_0_22, plain, (v1_xboole_0(X2)\|v1_xboole_0(X1)\|m1_subset_1(X3,X1)\|~m2_subset_1(X3,X1,X2)\|~m1_subset_1(X2,k1_zfmisc_1(X1))), inference(evalgc,[status(thm)],[c_0_16])). cnf(c_0_23, plain, (v1_xboole_0(X2)\|~v1_xboole_0(X1)\|~m1_subset_1(X2,k1_zfmisc_1(X1))), inference(evalgc,[status(thm)],[c_0_17])). cnf(c_0_24, negated_conjecture, (m2_subset_1(esk4_0,u1_struct_0(esk1_0),esk2_0)), inference(split_conjunct,[status(thm)],[c_0_18])). cnf(c_0_25, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(esk1_0)))), inference(split_conjunct,[status(thm)],[c_0_18])). cnf(c_0_26, negated_conjecture, (~v1_xboole_0(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_18])). cnf(c_0_27, plain, (v1_xboole_0(X3)\|v1_xboole_0(X2)\|m1_subset_1(X1,X3)\|~m2_subset_1(X1,X2,X3)\|~m1_subset_1(X3,k1_zfmisc_1(X2))), inference(evalgc,[status(thm)],[c_0_19])). cnf(c_0_28, plain, (m2_subset_1(X1,X3,X2)\|v1_xboole_0(X3)\|v1_xboole_0(X2)\|~m1_subset_1(X1,X2)\|~m1_subset_1(X2,k1_zfmisc_1(X3))), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_29, plain, (u1_struct_0(X1)=X3\|X1!=k5_yellow_0(X2,X3)\|~v1_orders_2(X1)\|~v4_yellow_0(X1,X2)\|~m1_yellow_0(X1,X2)\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~l1_orders_2(X2)), inference(split_conjunct,[status(thm)],[c_0_20])). cnf(c_0_30, negated_conjecture, (l1_orders_2(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_18])). fof(c_0_31, plain, ![X9, X10]:((v1_orders_2(k5_yellow_0(X9,X10))\|(~l1_orders_2(X9)\|~m1_subset_1(X10,k1_zfmisc_1(u1_struct_0(X9)))))&((v4_yellow_0(k5_yellow_0(X9,X10),X9)\|(~l1_orders_2(X9)\|~m1_subset_1(X10,k1_zfmisc_1(u1_struct_0(X9)))))&(m1_yellow_0(k5_yellow_0(X9,X10),X9)\|(~l1_orders_2(X9)\|~m1_subset_1(X10,k1_zfmisc_1(u1_struct_0(X9))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k5_yellow_0])])])). cnf(c_0_32, plain, (v1_xboole_0(X1)\|k7_domain_1(X1,X2,X3)=k2_tarski(X2,X3)\|~m1_subset_1(X2,X1)\|~m1_subset_1(X3,X1)), inference(split_conjunct,[status(thm)],[c_0_21])). cnf(c_0_33, plain, (m1_subset_1(X1,X2)\|v1_xboole_0(X3)\|~m2_subset_1(X1,X2,X3)\|~m1_subset_1(X3,k1_zfmisc_1(X2))), inference(csr,[status(thm)],[c_0_22, c_0_23])). cnf(c_0_34, negated_conjecture, (m2_subset_1(esk4_0,u1_struct_0(esk1_0),esk2_0)), inference(evalgc,[status(thm)],[c_0_24])). cnf(c_0_35, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(esk1_0)))), inference(evalgc,[status(thm)],[c_0_25])). cnf(c_0_36, negated_conjecture, (~v1_xboole_0(esk2_0)), inference(evalgc,[status(thm)],[c_0_26])). cnf(c_0_37, plain, (m1_subset_1(X1,X2)\|v1_xboole_0(X2)\|~m2_subset_1(X1,X3,X2)\|~m1_subset_1(X2,k1_zfmisc_1(X3))), inference(csr,[status(thm)],[c_0_27, c_0_23])). cnf(c_0_38, plain, (v1_xboole_0(X3)\|v1_xboole_0(X2)\|m2_subset_1(X1,X3,X2)\|~m1_subset_1(X1,X2)\|~m1_subset_1(X2,k1_zfmisc_1(X3))), inference(evalgc,[status(thm)],[c_0_28])). cnf(c_0_39, plain, (u1_struct_0(X1)=X3\|X1!=k5_yellow_0(X2,X3)\|~l1_orders_2(X2)\|~v1_orders_2(X1)\|~v4_yellow_0(X1,X2)\|~m1_yellow_0(X1,X2)\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))), inference(evalgc,[status(thm)],[c_0_29])). cnf(c_0_40, negated_conjecture, (l1_orders_2(esk1_0)), inference(evalgc,[status(thm)],[c_0_30])). cnf(c_0_41, plain, (v1_orders_2(k5_yellow_0(X1,X2))\|~l1_orders_2(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(split_conjunct,[status(thm)],[c_0_31])). cnf(c_0_42, plain, (k7_domain_1(X1,X2,X3)=k2_tarski(X2,X3)\|v1_xboole_0(X1)\|~m1_subset_1(X3,X1)\|~m1_subset_1(X2,X1)), inference(evalgc,[status(thm)],[c_0_32])). cnf(c_0_43, negated_conjecture, (m1_subset_1(esk4_0,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33, c_0_34]), c_0_35])]), c_0_36])])). cnf(c_0_44, negated_conjecture, (~v1_xboole_0(u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23, c_0_35]), c_0_36])])). cnf(c_0_45, negated_conjecture, (m1_subset_1(esk4_0,esk2_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37, c_0_34]), c_0_35])]), c_0_36])])). cnf(c_0_46, plain, (m2_subset_1(X1,X2,X3)\|v1_xboole_0(X3)\|~m1_subset_1(X3,k1_zfmisc_1(X2))\|~m1_subset_1(X1,X3)), inference(csr,[status(thm)],[c_0_38, c_0_23])). cnf(c_0_47, negated_conjecture, (u1_struct_0(X1)=esk2_0\|X1!=k5_yellow_0(esk1_0,esk2_0)\|~m1_yellow_0(X1,esk1_0)\|~v4_yellow_0(X1,esk1_0)\|~v1_orders_2(X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39, c_0_35]), c_0_40])])])). cnf(c_0_48, plain, (v1_orders_2(k5_yellow_0(X1,X2))\|~l1_orders_2(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(evalgc,[status(thm)],[c_0_41])). cnf(c_0_49, plain, (v4_yellow_0(k5_yellow_0(X1,X2),X1)\|~l1_orders_2(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(split_conjunct,[status(thm)],[c_0_31])). fof(c_0_50, plain, ![X29, X30, X31, X32]:((~v6_yellow_0(X30,X29)\|(~m1_subset_1(X31,u1_struct_0(X29))\|(~m1_subset_1(X32,u1_struct_0(X29))\|(~r2_hidden(X31,u1_struct_0(X30))\|(~r2_hidden(X32,u1_struct_0(X30))\|~r1_yellow_0(X29,k7_domain_1(u1_struct_0(X29),X31,X32)))\|r2_hidden(k1_yellow_0(X29,k7_domain_1(u1_struct_0(X29),X31,X32)),u1_struct_0(X30)))))\|~m1_yellow_0(X30,X29)\|(v2_struct_0(X29)\|~l1_orders_2(X29)))&((m1_subset_1(esk5_2(X29,X30),u1_struct_0(X29))\|v6_yellow_0(X30,X29)\|~m1_yellow_0(X30,X29)\|(v2_struct_0(X29)\|~l1_orders_2(X29)))&((m1_subset_1(esk6_2(X29,X30),u1_struct_0(X29))\|v6_yellow_0(X30,X29)\|~m1_yellow_0(X30,X29)\|(v2_struct_0(X29)\|~l1_orders_2(X29)))&(((r2_hidden(esk5_2(X29,X30),u1_struct_0(X30))\|v6_yellow_0(X30,X29)\|~m1_yellow_0(X30,X29)\|(v2_struct_0(X29)\|~l1_orders_2(X29)))&((r2_hidden(esk6_2(X29,X30),u1_struct_0(X30))\|v6_yellow_0(X30,X29)\|~m1_yellow_0(X30,X29)\|(v2_struct_0(X29)\|~l1_orders_2(X29)))&(r1_yellow_0(X29,k7_domain_1(u1_struct_0(X29),esk5_2(X29,X30),esk6_2(X29,X30)))\|v6_yellow_0(X30,X29)\|~m1_yellow_0(X30,X29)\|(v2_struct_0(X29)\|~l1_orders_2(X29)))))&(~r2_hidden(k1_yellow_0(X29,k7_domain_1(u1_struct_0(X29),esk5_2(X29,X30),esk6_2(X29,X30))),u1_struct_0(X30))\|v6_yellow_0(X30,X29)\|~m1_yellow_0(X30,X29)\|(v2_struct_0(X29)\|~l1_orders_2(X29))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d17_yellow_0])])])])])])). cnf(c_0_51, negated_conjecture, (k2_tarski(X1,esk4_0)=k7_domain_1(u1_struct_0(esk1_0),X1,esk4_0)\|~m1_subset_1(X1,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42, c_0_43]), c_0_44])])). cnf(c_0_52, negated_conjecture, (k2_tarski(X1,esk4_0)=k7_domain_1(esk2_0,X1,esk4_0)\|~m1_subset_1(X1,esk2_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42, c_0_45]), c_0_36])])). cnf(c_0_53, plain, (m1_subset_1(X1,X2)\|v1_xboole_0(X3)\|~m1_subset_1(X3,k1_zfmisc_1(X2))\|~m1_subset_1(X1,X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_33, c_0_46])])). cnf(c_0_54, negated_conjecture, (u1_struct_0(k5_yellow_0(X1,X2))=esk2_0\|k5_yellow_0(X1,X2)!=k5_yellow_0(esk1_0,esk2_0)\|~m1_yellow_0(k5_yellow_0(X1,X2),esk1_0)\|~v4_yellow_0(k5_yellow_0(X1,X2),esk1_0)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~l1_orders_2(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_47, c_0_48])])). cnf(c_0_55, plain, (v4_yellow_0(k5_yellow_0(X1,X2),X1)\|~l1_orders_2(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(evalgc,[status(thm)],[c_0_49])). cnf(c_0_56, plain, (m1_yellow_0(k5_yellow_0(X1,X2),X1)\|~l1_orders_2(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(split_conjunct,[status(thm)],[c_0_31])). cnf(c_0_57, plain, (r2_hidden(k1_yellow_0(X2,k7_domain_1(u1_struct_0(X2),X3,X4)),u1_struct_0(X1))\|v2_struct_0(X2)\|~v6_yellow_0(X1,X2)\|~m1_subset_1(X3,u1_struct_0(X2))\|~m1_subset_1(X4,u1_struct_0(X2))\|~r2_hidden(X3,u1_struct_0(X1))\|~r2_hidden(X4,u1_struct_0(X1))\|~r1_yellow_0(X2,k7_domain_1(u1_struct_0(X2),X3,X4))\|~m1_yellow_0(X1,X2)\|~l1_orders_2(X2)), inference(split_conjunct,[status(thm)],[c_0_50])). cnf(c_0_58, negated_conjecture, (k7_domain_1(u1_struct_0(esk1_0),X1,esk4_0)=k7_domain_1(esk2_0,X1,esk4_0)\|~m1_subset_1(X1,u1_struct_0(esk1_0))\|~m1_subset_1(X1,esk2_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_51, c_0_52])])). cnf(c_0_59, negated_conjecture, (m1_subset_1(X1,u1_struct_0(esk1_0))\|~m1_subset_1(X1,esk2_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_53, c_0_35]), c_0_36])])). cnf(c_0_60, negated_conjecture, (~v2_struct_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_18])). fof(c_0_61, plain, ![X37, X38, X39, X40]:((r1_yellow_0(X38,k7_domain_1(u1_struct_0(X38),X39,X40))\|(~r1_yellow_0(X37,k7_domain_1(u1_struct_0(X38),X39,X40))\|~r2_hidden(k1_yellow_0(X37,k7_domain_1(u1_struct_0(X38),X39,X40)),u1_struct_0(X38)))\|~m1_subset_1(X40,u1_struct_0(X38))\|~m1_subset_1(X39,u1_struct_0(X38))\|(v2_struct_0(X38)\|(~v4_yellow_0(X38,X37)\|~m1_yellow_0(X38,X37)))\|(v2_struct_0(X37)\|(~v4_orders_2(X37)\|~l1_orders_2(X37))))&(k1_yellow_0(X38,k7_domain_1(u1_struct_0(X38),X39,X40))=k1_yellow_0(X37,k7_domain_1(u1_struct_0(X38),X39,X40))\|(~r1_yellow_0(X37,k7_domain_1(u1_struct_0(X38),X39,X40))\|~r2_hidden(k1_yellow_0(X37,k7_domain_1(u1_struct_0(X38),X39,X40)),u1_struct_0(X38)))\|~m1_subset_1(X40,u1_struct_0(X38))\|~m1_subset_1(X39,u1_struct_0(X38))\|(v2_struct_0(X38)\|(~v4_yellow_0(X38,X37)\|~m1_yellow_0(X38,X37)))\|(v2_struct_0(X37)\|(~v4_orders_2(X37)\|~l1_orders_2(X37))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t66_yellow_0])])])])])). cnf(c_0_62, negated_conjecture, (u1_struct_0(k5_yellow_0(esk1_0,X1))=esk2_0\|k5_yellow_0(esk1_0,X1)!=k5_yellow_0(esk1_0,esk2_0)\|~m1_yellow_0(k5_yellow_0(esk1_0,X1),esk1_0)\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(esk1_0)))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54, c_0_55]), c_0_40])])])). cnf(c_0_63, plain, (m1_yellow_0(k5_yellow_0(X1,X2),X1)\|~l1_orders_2(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(evalgc,[status(thm)],[c_0_56])). cnf(c_0_64, plain, (v2_struct_0(X2)\|r2_hidden(k1_yellow_0(X2,k7_domain_1(u1_struct_0(X2),X3,X4)),u1_struct_0(X1))\|~l1_orders_2(X2)\|~m1_yellow_0(X1,X2)\|~v6_yellow_0(X1,X2)\|~m1_subset_1(X4,u1_struct_0(X2))\|~m1_subset_1(X3,u1_struct_0(X2))\|~r2_hidden(X4,u1_struct_0(X1))\|~r2_hidden(X3,u1_struct_0(X1))\|~r1_yellow_0(X2,k7_domain_1(u1_struct_0(X2),X3,X4))), inference(evalgc,[status(thm)],[c_0_57])). cnf(c_0_65, negated_conjecture, (k7_domain_1(u1_struct_0(esk1_0),X1,esk4_0)=k7_domain_1(esk2_0,X1,esk4_0)\|~m1_subset_1(X1,esk2_0)), inference(csr,[status(thm)],[c_0_58, c_0_59])). cnf(c_0_66, negated_conjecture, (~v2_struct_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_60])). cnf(c_0_67, plain, (r1_yellow_0(X1,k7_domain_1(u1_struct_0(X1),X2,X3))\|v2_struct_0(X1)\|v2_struct_0(X4)\|~r1_yellow_0(X4,k7_domain_1(u1_struct_0(X1),X2,X3))\|~r2_hidden(k1_yellow_0(X4,k7_domain_1(u1_struct_0(X1),X2,X3)),u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~v4_yellow_0(X1,X4)\|~m1_yellow_0(X1,X4)\|~v4_orders_2(X4)\|~l1_orders_2(X4)), inference(split_conjunct,[status(thm)],[c_0_61])). cnf(c_0_68, negated_conjecture, (u1_struct_0(k5_yellow_0(esk1_0,X1))=esk2_0\|k5_yellow_0(esk1_0,X1)!=k5_yellow_0(esk1_0,esk2_0)\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(esk1_0)))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62, c_0_63]), c_0_40])])])). cnf(c_0_69, negated_conjecture, (r2_hidden(k1_yellow_0(esk1_0,k7_domain_1(esk2_0,X1,esk4_0)),u1_struct_0(X2))\|~r2_hidden(esk4_0,u1_struct_0(X2))\|~r2_hidden(X1,u1_struct_0(X2))\|~v6_yellow_0(X2,esk1_0)\|~m1_yellow_0(X2,esk1_0)\|~r1_yellow_0(esk1_0,k7_domain_1(esk2_0,X1,esk4_0))\|~m1_subset_1(X1,u1_struct_0(esk1_0))\|~m1_subset_1(X1,esk2_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64, c_0_65]), c_0_43]), c_0_40])]), c_0_66])])). cnf(c_0_70, plain, (v2_struct_0(X4)\|v2_struct_0(X1)\|r1_yellow_0(X1,k7_domain_1(u1_struct_0(X1),X2,X3))\|~v4_orders_2(X4)\|~l1_orders_2(X4)\|~v4_yellow_0(X1,X4)\|~m1_yellow_0(X1,X4)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~r1_yellow_0(X4,k7_domain_1(u1_struct_0(X1),X2,X3))\|~r2_hidden(k1_yellow_0(X4,k7_domain_1(u1_struct_0(X1),X2,X3)),u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_67])). cnf(c_0_71, negated_conjecture, (u1_struct_0(k5_yellow_0(esk1_0,esk2_0))=esk2_0), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_68, c_0_35])])). cnf(c_0_72, negated_conjecture, (r2_hidden(k1_yellow_0(esk1_0,k7_domain_1(esk2_0,X1,esk4_0)),u1_struct_0(X2))\|~r2_hidden(esk4_0,u1_struct_0(X2))\|~r2_hidden(X1,u1_struct_0(X2))\|~v6_yellow_0(X2,esk1_0)\|~m1_yellow_0(X2,esk1_0)\|~r1_yellow_0(esk1_0,k7_domain_1(esk2_0,X1,esk4_0))\|~m1_subset_1(X1,esk2_0)), inference(csr,[status(thm)],[c_0_69, c_0_59])). cnf(c_0_73, negated_conjecture, (v4_orders_2(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_18])). cnf(c_0_74, negated_conjecture, (m2_subset_1(esk3_0,u1_struct_0(esk1_0),esk2_0)), inference(split_conjunct,[status(thm)],[c_0_18])). cnf(c_0_75, plain, (k1_yellow_0(X1,k7_domain_1(u1_struct_0(X1),X2,X3))=k1_yellow_0(X4,k7_domain_1(u1_struct_0(X1),X2,X3))\|v2_struct_0(X1)\|v2_struct_0(X4)\|~r1_yellow_0(X4,k7_domain_1(u1_struct_0(X1),X2,X3))\|~r2_hidden(k1_yellow_0(X4,k7_domain_1(u1_struct_0(X1),X2,X3)),u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~v4_yellow_0(X1,X4)\|~m1_yellow_0(X1,X4)\|~v4_orders_2(X4)\|~l1_orders_2(X4)), inference(split_conjunct,[status(thm)],[c_0_61])). cnf(c_0_76, negated_conjecture, (~r1_yellow_0(k5_yellow_0(esk1_0,esk2_0),k7_domain_1(esk2_0,esk3_0,esk4_0))\|k1_yellow_0(k5_yellow_0(esk1_0,esk2_0),k7_domain_1(esk2_0,esk3_0,esk4_0))!=k1_yellow_0(esk1_0,k7_domain_1(esk2_0,esk3_0,esk4_0))), inference(split_conjunct,[status(thm)],[c_0_18])). cnf(c_0_77, negated_conjecture, (r1_yellow_0(k5_yellow_0(esk1_0,esk2_0),k7_domain_1(esk2_0,X1,X2))\|v2_struct_0(k5_yellow_0(esk1_0,esk2_0))\|v2_struct_0(X3)\|~r2_hidden(k1_yellow_0(X3,k7_domain_1(esk2_0,X1,X2)),esk2_0)\|~m1_yellow_0(k5_yellow_0(esk1_0,esk2_0),X3)\|~v4_yellow_0(k5_yellow_0(esk1_0,esk2_0),X3)\|~r1_yellow_0(X3,k7_domain_1(esk2_0,X1,X2))\|~m1_subset_1(X2,esk2_0)\|~m1_subset_1(X1,esk2_0)\|~l1_orders_2(X3)\|~v4_orders_2(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_70, c_0_71])])). cnf(c_0_78, negated_conjecture, (r2_hidden(k1_yellow_0(esk1_0,k7_domain_1(esk2_0,X1,esk4_0)),esk2_0)\|~r2_hidden(esk4_0,esk2_0)\|~r2_hidden(X1,esk2_0)\|~v6_yellow_0(k5_yellow_0(esk1_0,esk2_0),esk1_0)\|~m1_yellow_0(k5_yellow_0(esk1_0,esk2_0),esk1_0)\|~r1_yellow_0(esk1_0,k7_domain_1(esk2_0,X1,esk4_0))\|~m1_subset_1(X1,esk2_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_72, c_0_71])])). cnf(c_0_79, negated_conjecture, (v4_orders_2(esk1_0)), inference(evalgc,[status(thm)],[c_0_73])). cnf(c_0_80, negated_conjecture, (r1_yellow_0(esk1_0,k7_domain_1(esk2_0,esk3_0,esk4_0))), inference(split_conjunct,[status(thm)],[c_0_18])). cnf(c_0_81, negated_conjecture, (m2_subset_1(esk3_0,u1_struct_0(esk1_0),esk2_0)), inference(evalgc,[status(thm)],[c_0_74])). cnf(c_0_82, plain, (k1_yellow_0(X1,k7_domain_1(u1_struct_0(X1),X2,X3))=k1_yellow_0(X4,k7_domain_1(u1_struct_0(X1),X2,X3))\|v2_struct_0(X4)\|v2_struct_0(X1)\|~v4_orders_2(X4)\|~l1_orders_2(X4)\|~v4_yellow_0(X1,X4)\|~m1_yellow_0(X1,X4)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~r1_yellow_0(X4,k7_domain_1(u1_struct_0(X1),X2,X3))\|~r2_hidden(k1_yellow_0(X4,k7_domain_1(u1_struct_0(X1),X2,X3)),u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_75])). cnf(c_0_83, negated_conjecture, (k1_yellow_0(k5_yellow_0(esk1_0,esk2_0),k7_domain_1(esk2_0,esk3_0,esk4_0))!=k1_yellow_0(esk1_0,k7_domain_1(esk2_0,esk3_0,esk4_0))\|~r1_yellow_0(k5_yellow_0(esk1_0,esk2_0),k7_domain_1(esk2_0,esk3_0,esk4_0))), inference(evalgc,[status(thm)],[c_0_76])). cnf(c_0_84, negated_conjecture, (r1_yellow_0(k5_yellow_0(esk1_0,esk2_0),k7_domain_1(esk2_0,X1,esk4_0))\|v2_struct_0(k5_yellow_0(esk1_0,esk2_0))\|~m1_yellow_0(k5_yellow_0(esk1_0,esk2_0),esk1_0)\|~v4_yellow_0(k5_yellow_0(esk1_0,esk2_0),esk1_0)\|~r1_yellow_0(esk1_0,k7_domain_1(esk2_0,X1,esk4_0))\|~m1_subset_1(X1,esk2_0)\|~r2_hidden(esk4_0,esk2_0)\|~r2_hidden(X1,esk2_0)\|~v6_yellow_0(k5_yellow_0(esk1_0,esk2_0),esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77, c_0_78]), c_0_45]), c_0_40]), c_0_79])]), c_0_66])])). cnf(c_0_85, negated_conjecture, (r1_yellow_0(esk1_0,k7_domain_1(esk2_0,esk3_0,esk4_0))), inference(evalgc,[status(thm)],[c_0_80])). cnf(c_0_86, negated_conjecture, (m1_subset_1(esk3_0,esk2_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37, c_0_81]), c_0_35])]), c_0_36])])). cnf(c_0_87, negated_conjecture, (k1_yellow_0(k5_yellow_0(esk1_0,esk2_0),k7_domain_1(esk2_0,X1,X2))=k1_yellow_0(X3,k7_domain_1(esk2_0,X1,X2))\|v2_struct_0(k5_yellow_0(esk1_0,esk2_0))\|v2_struct_0(X3)\|~r2_hidden(k1_yellow_0(X3,k7_domain_1(esk2_0,X1,X2)),esk2_0)\|~m1_yellow_0(k5_yellow_0(esk1_0,esk2_0),X3)\|~v4_yellow_0(k5_yellow_0(esk1_0,esk2_0),X3)\|~r1_yellow_0(X3,k7_domain_1(esk2_0,X1,X2))\|~m1_subset_1(X2,esk2_0)\|~m1_subset_1(X1,esk2_0)\|~l1_orders_2(X3)\|~v4_orders_2(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_82, c_0_71])])). cnf(c_0_88, negated_conjecture, (v2_struct_0(k5_yellow_0(esk1_0,esk2_0))\|k1_yellow_0(k5_yellow_0(esk1_0,esk2_0),k7_domain_1(esk2_0,esk3_0,esk4_0))!=k1_yellow_0(esk1_0,k7_domain_1(esk2_0,esk3_0,esk4_0))\|~r2_hidden(esk4_0,esk2_0)\|~r2_hidden(esk3_0,esk2_0)\|~v6_yellow_0(k5_yellow_0(esk1_0,esk2_0),esk1_0)\|~m1_yellow_0(k5_yellow_0(esk1_0,esk2_0),esk1_0)\|~v4_yellow_0(k5_yellow_0(esk1_0,esk2_0),esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83, c_0_84]), c_0_85]), c_0_86])])])). cnf(c_0_89, negated_conjecture, (k1_yellow_0(k5_yellow_0(esk1_0,esk2_0),k7_domain_1(esk2_0,X1,esk4_0))=k1_yellow_0(esk1_0,k7_domain_1(esk2_0,X1,esk4_0))\|v2_struct_0(k5_yellow_0(esk1_0,esk2_0))\|~m1_yellow_0(k5_yellow_0(esk1_0,esk2_0),esk1_0)\|~v4_yellow_0(k5_yellow_0(esk1_0,esk2_0),esk1_0)\|~r1_yellow_0(esk1_0,k7_domain_1(esk2_0,X1,esk4_0))\|~m1_subset_1(X1,esk2_0)\|~r2_hidden(esk4_0,esk2_0)\|~r2_hidden(X1,esk2_0)\|~v6_yellow_0(k5_yellow_0(esk1_0,esk2_0),esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87, c_0_78]), c_0_45]), c_0_40]), c_0_79])]), c_0_66])])). fof(c_0_90, plain, ![X19, X20]:((~v2_waybel23(X20,X19)\|v6_yellow_0(k5_yellow_0(X19,X20),X19)\|~m1_subset_1(X20,k1_zfmisc_1(u1_struct_0(X19)))\|(v2_struct_0(X19)\|~l1_orders_2(X19)))&(~v6_yellow_0(k5_yellow_0(X19,X20),X19)\|v2_waybel23(X20,X19)\|~m1_subset_1(X20,k1_zfmisc_1(u1_struct_0(X19)))\|(v2_struct_0(X19)\|~l1_orders_2(X19)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d2_waybel23])])])])])). cnf(c_0_91, negated_conjecture, (v2_struct_0(k5_yellow_0(esk1_0,esk2_0))\|~r2_hidden(esk4_0,esk2_0)\|~r2_hidden(esk3_0,esk2_0)\|~v6_yellow_0(k5_yellow_0(esk1_0,esk2_0),esk1_0)\|~m1_yellow_0(k5_yellow_0(esk1_0,esk2_0),esk1_0)\|~v4_yellow_0(k5_yellow_0(esk1_0,esk2_0),esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88, c_0_89]), c_0_85]), c_0_86])])])). cnf(c_0_92, plain, (v6_yellow_0(k5_yellow_0(X2,X1),X2)\|v2_struct_0(X2)\|~v2_waybel23(X1,X2)\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X2)))\|~l1_orders_2(X2)), inference(split_conjunct,[status(thm)],[c_0_90])). cnf(c_0_93, negated_conjecture, (v2_waybel23(esk2_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_18])). fof(c_0_94, plain, ![X35, X36]:((~v2_struct_0(k5_yellow_0(X35,X36))\|(v2_struct_0(X35)\|~l1_orders_2(X35)\|(v1_xboole_0(X36)\|~m1_subset_1(X36,k1_zfmisc_1(u1_struct_0(X35))))))&((v1_orders_2(k5_yellow_0(X35,X36))\|(v2_struct_0(X35)\|~l1_orders_2(X35)\|(v1_xboole_0(X36)\|~m1_subset_1(X36,k1_zfmisc_1(u1_struct_0(X35))))))&(v4_yellow_0(k5_yellow_0(X35,X36),X35)\|(v2_struct_0(X35)\|~l1_orders_2(X35)\|(v1_xboole_0(X36)\|~m1_subset_1(X36,k1_zfmisc_1(u1_struct_0(X35)))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fc1_yellow_2])])])])). cnf(c_0_95, negated_conjecture, (v2_struct_0(k5_yellow_0(esk1_0,esk2_0))\|~r2_hidden(esk4_0,esk2_0)\|~r2_hidden(esk3_0,esk2_0)\|~v6_yellow_0(k5_yellow_0(esk1_0,esk2_0),esk1_0)\|~m1_yellow_0(k5_yellow_0(esk1_0,esk2_0),esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91, c_0_55]), c_0_35]), c_0_40])])])). cnf(c_0_96, plain, (v2_struct_0(X2)\|v6_yellow_0(k5_yellow_0(X2,X1),X2)\|~l1_orders_2(X2)\|~v2_waybel23(X1,X2)\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X2)))), inference(evalgc,[status(thm)],[c_0_92])). cnf(c_0_97, negated_conjecture, (v2_waybel23(esk2_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_93])). cnf(c_0_98, plain, (v2_struct_0(X1)\|v1_xboole_0(X2)\|~v2_struct_0(k5_yellow_0(X1,X2))\|~l1_orders_2(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(split_conjunct,[status(thm)],[c_0_94])). cnf(c_0_99, negated_conjecture, (v2_struct_0(k5_yellow_0(esk1_0,esk2_0))\|~r2_hidden(esk4_0,esk2_0)\|~r2_hidden(esk3_0,esk2_0)\|~m1_yellow_0(k5_yellow_0(esk1_0,esk2_0),esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95, c_0_96]), c_0_35]), c_0_97]), c_0_40])]), c_0_66])])). fof(c_0_100, plain, ![X21, X22]:(~m1_subset_1(X21,X22)\|(v1_xboole_0(X22)\|r2_hidden(X21,X22))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])])). cnf(c_0_101, plain, (v2_struct_0(X1)\|v1_xboole_0(X2)\|~l1_orders_2(X1)\|~v2_struct_0(k5_yellow_0(X1,X2))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(evalgc,[status(thm)],[c_0_98])). cnf(c_0_102, negated_conjecture, (v2_struct_0(k5_yellow_0(esk1_0,esk2_0))\|~r2_hidden(esk4_0,esk2_0)\|~r2_hidden(esk3_0,esk2_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99, c_0_63]), c_0_35]), c_0_40])])])). cnf(c_0_103, plain, (v1_xboole_0(X2)\|r2_hidden(X1,X2)\|~m1_subset_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_100])). cnf(c_0_104, negated_conjecture, (~r2_hidden(esk4_0,esk2_0)\|~r2_hidden(esk3_0,esk2_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101, c_0_102]), c_0_35]), c_0_40])]), c_0_36]), c_0_66])])). cnf(c_0_105, plain, (v1_xboole_0(X2)\|r2_hidden(X1,X2)\|~m1_subset_1(X1,X2)), inference(evalgc,[status(thm)],[c_0_103])). cnf(c_0_106, negated_conjecture, (~r2_hidden(esk3_0,esk2_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104, c_0_105]), c_0_45])]), c_0_36])])). cnf(c_0_107, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106, c_0_105]), c_0_86])]), c_0_36]), ['proof']). # SZS output end CNFRefutation	theorem for L be non empty transitive RelStr for S be join-closed non empty Subset of L for x,y be Element of S st ex_sup_of {x,y},L holds ex_sup_of {x,y}, subrelstr S & "\/"({x,y},subrelstr S) = "\/"({x,y},L) proof let L be non empty transitive RelStr; let S be join-closed non empty Subset of L; let x,y be Element of S; A1: x is Element of subrelstr S by YELLOW_0:def 15; A2: y is Element of subrelstr S by YELLOW_0:def 15; assume A3: ex_sup_of {x,y},L; subrelstr S is join-inheriting non empty full SubRelStr of L by Def2; then "\/"({x,y},L) in the carrier of subrelstr S by A1,A2,A3,YELLOW_0:def 17; hence thesis by A1,A2,A3,YELLOW_0:66; end;	Convert the following ATP output trace into a readable Mizar proof.
t14_cgames_1	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t13_cgames_1, axiom, ![X1]:(v3_ordinal1(X1)=>![X2]:(v2_cgames_1(X2)=>(r2_hidden(k9_cgames_1(X2),X1)<=>?[X3]:(v3_ordinal1(X3)&(r2_hidden(X3,X1)&r2_hidden(X2,k2_cgames_1(X3))))))), file('/scratch/mptp/predsminms1/t14_cgames_1__0', t13_cgames_1)). fof(t9_cgames_1, axiom, ![X1]:(v3_ordinal1(X1)=>![X2]:(v2_cgames_1(X2)=>(r2_hidden(X2,k2_cgames_1(X1))<=>![X3]:~((r2_hidden(X3,k8_cgames_1(X2))&![X4]:(v3_ordinal1(X4)=>~((r2_hidden(X4,X1)&r2_hidden(X3,k2_cgames_1(X4)))))))))), file('/scratch/mptp/predsminms1/t14_cgames_1__0', t9_cgames_1)). fof(d9_cgames_1, axiom, ![X1]:(v2_cgames_1(X1)=>![X2]:(v3_ordinal1(X2)=>(X2=k9_cgames_1(X1)<=>(r2_hidden(X1,k2_cgames_1(X2))&![X3]:(v3_ordinal1(X3)=>~((r2_hidden(X3,X2)&r2_hidden(X1,k2_cgames_1(X3))))))))), file('/scratch/mptp/predsminms1/t14_cgames_1__0', d9_cgames_1)). fof(t14_cgames_1, conjecture, ![X1]:(v2_cgames_1(X1)=>![X2]:(v2_cgames_1(X2)=>(r2_hidden(X1,k8_cgames_1(X2))=>r2_hidden(k9_cgames_1(X1),k9_cgames_1(X2))))), file('/scratch/mptp/predsminms1/t14_cgames_1__0', t14_cgames_1)). fof(dt_k9_cgames_1, axiom, ![X1]:v3_ordinal1(k9_cgames_1(X1)), file('/scratch/mptp/predsminms1/t14_cgames_1__0', dt_k9_cgames_1)). fof(c_0_5, plain, ![X18, X19, X21]:(((v3_ordinal1(esk6_2(X18,X19))\|~r2_hidden(k9_cgames_1(X19),X18)\|~v2_cgames_1(X19)\|~v3_ordinal1(X18))&((r2_hidden(esk6_2(X18,X19),X18)\|~r2_hidden(k9_cgames_1(X19),X18)\|~v2_cgames_1(X19)\|~v3_ordinal1(X18))&(r2_hidden(X19,k2_cgames_1(esk6_2(X18,X19)))\|~r2_hidden(k9_cgames_1(X19),X18)\|~v2_cgames_1(X19)\|~v3_ordinal1(X18))))&(~v3_ordinal1(X21)\|(~r2_hidden(X21,X18)\|~r2_hidden(X19,k2_cgames_1(X21)))\|r2_hidden(k9_cgames_1(X19),X18)\|~v2_cgames_1(X19)\|~v3_ordinal1(X18))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t13_cgames_1])])])])])). fof(c_0_6, plain, ![X12, X13, X14, X17]:(((v3_ordinal1(esk4_3(X12,X13,X14))\|~r2_hidden(X14,k8_cgames_1(X13))\|~r2_hidden(X13,k2_cgames_1(X12))\|~v2_cgames_1(X13)\|~v3_ordinal1(X12))&((r2_hidden(esk4_3(X12,X13,X14),X12)\|~r2_hidden(X14,k8_cgames_1(X13))\|~r2_hidden(X13,k2_cgames_1(X12))\|~v2_cgames_1(X13)\|~v3_ordinal1(X12))&(r2_hidden(X14,k2_cgames_1(esk4_3(X12,X13,X14)))\|~r2_hidden(X14,k8_cgames_1(X13))\|~r2_hidden(X13,k2_cgames_1(X12))\|~v2_cgames_1(X13)\|~v3_ordinal1(X12))))&((r2_hidden(esk5_2(X12,X13),k8_cgames_1(X13))\|r2_hidden(X13,k2_cgames_1(X12))\|~v2_cgames_1(X13)\|~v3_ordinal1(X12))&(~v3_ordinal1(X17)\|(~r2_hidden(X17,X12)\|~r2_hidden(esk5_2(X12,X13),k2_cgames_1(X17)))\|r2_hidden(X13,k2_cgames_1(X12))\|~v2_cgames_1(X13)\|~v3_ordinal1(X12)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t9_cgames_1])])])])])). cnf(c_0_7, plain, (r2_hidden(k9_cgames_1(X3),X2)\|~v3_ordinal1(X1)\|~r2_hidden(X1,X2)\|~r2_hidden(X3,k2_cgames_1(X1))\|~v2_cgames_1(X3)\|~v3_ordinal1(X2)), inference(split_conjunct,[status(thm)],[c_0_5])). cnf(c_0_8, plain, (r2_hidden(X1,k2_cgames_1(esk4_3(X2,X3,X1)))\|~r2_hidden(X1,k8_cgames_1(X3))\|~r2_hidden(X3,k2_cgames_1(X2))\|~v2_cgames_1(X3)\|~v3_ordinal1(X2)), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_9, plain, (r2_hidden(k9_cgames_1(X3),X2)\|~v2_cgames_1(X3)\|~v3_ordinal1(X2)\|~v3_ordinal1(X1)\|~r2_hidden(X1,X2)\|~r2_hidden(X3,k2_cgames_1(X1))), inference(evalgc,[status(thm)],[c_0_7])). cnf(c_0_10, plain, (r2_hidden(X1,k2_cgames_1(esk4_3(X2,X3,X1)))\|~v2_cgames_1(X3)\|~v3_ordinal1(X2)\|~r2_hidden(X3,k2_cgames_1(X2))\|~r2_hidden(X1,k8_cgames_1(X3))), inference(evalgc,[status(thm)],[c_0_8])). cnf(c_0_11, plain, (v3_ordinal1(esk4_3(X1,X2,X3))\|~r2_hidden(X3,k8_cgames_1(X2))\|~r2_hidden(X2,k2_cgames_1(X1))\|~v2_cgames_1(X2)\|~v3_ordinal1(X1)), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_12, plain, (r2_hidden(k9_cgames_1(X1),X2)\|~v3_ordinal1(X2)\|~v3_ordinal1(esk4_3(X3,X4,X1))\|~r2_hidden(esk4_3(X3,X4,X1),X2)\|~v2_cgames_1(X1)\|~v3_ordinal1(X3)\|~r2_hidden(X4,k2_cgames_1(X3))\|~r2_hidden(X1,k8_cgames_1(X4))\|~v2_cgames_1(X4)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_9, c_0_10])])). cnf(c_0_13, plain, (v3_ordinal1(esk4_3(X1,X2,X3))\|~v2_cgames_1(X2)\|~v3_ordinal1(X1)\|~r2_hidden(X3,k8_cgames_1(X2))\|~r2_hidden(X2,k2_cgames_1(X1))), inference(evalgc,[status(thm)],[c_0_11])). cnf(c_0_14, plain, (r2_hidden(esk4_3(X1,X2,X3),X1)\|~r2_hidden(X3,k8_cgames_1(X2))\|~r2_hidden(X2,k2_cgames_1(X1))\|~v2_cgames_1(X2)\|~v3_ordinal1(X1)), inference(split_conjunct,[status(thm)],[c_0_6])). fof(c_0_15, plain, ![X8, X9, X10]:(((r2_hidden(X8,k2_cgames_1(X9))\|X9!=k9_cgames_1(X8)\|~v3_ordinal1(X9)\|~v2_cgames_1(X8))&(~v3_ordinal1(X10)\|(~r2_hidden(X10,X9)\|~r2_hidden(X8,k2_cgames_1(X10)))\|X9!=k9_cgames_1(X8)\|~v3_ordinal1(X9)\|~v2_cgames_1(X8)))&((v3_ordinal1(esk3_2(X8,X9))\|~r2_hidden(X8,k2_cgames_1(X9))\|X9=k9_cgames_1(X8)\|~v3_ordinal1(X9)\|~v2_cgames_1(X8))&((r2_hidden(esk3_2(X8,X9),X9)\|~r2_hidden(X8,k2_cgames_1(X9))\|X9=k9_cgames_1(X8)\|~v3_ordinal1(X9)\|~v2_cgames_1(X8))&(r2_hidden(X8,k2_cgames_1(esk3_2(X8,X9)))\|~r2_hidden(X8,k2_cgames_1(X9))\|X9=k9_cgames_1(X8)\|~v3_ordinal1(X9)\|~v2_cgames_1(X8))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d9_cgames_1])])])])])). fof(c_0_16, negated_conjecture, ~(![X1]:(v2_cgames_1(X1)=>![X2]:(v2_cgames_1(X2)=>(r2_hidden(X1,k8_cgames_1(X2))=>r2_hidden(k9_cgames_1(X1),k9_cgames_1(X2)))))), inference(assume_negation,[status(cth)],[t14_cgames_1])). cnf(c_0_17, plain, (r2_hidden(k9_cgames_1(X1),X2)\|~v3_ordinal1(X2)\|~v3_ordinal1(X3)\|~r2_hidden(esk4_3(X3,X4,X1),X2)\|~r2_hidden(X4,k2_cgames_1(X3))\|~r2_hidden(X1,k8_cgames_1(X4))\|~v2_cgames_1(X1)\|~v2_cgames_1(X4)), inference(csr,[status(thm)],[c_0_12, c_0_13])). cnf(c_0_18, plain, (r2_hidden(esk4_3(X1,X2,X3),X1)\|~v2_cgames_1(X2)\|~v3_ordinal1(X1)\|~r2_hidden(X3,k8_cgames_1(X2))\|~r2_hidden(X2,k2_cgames_1(X1))), inference(evalgc,[status(thm)],[c_0_14])). cnf(c_0_19, plain, (r2_hidden(X1,k2_cgames_1(X2))\|X2!=k9_cgames_1(X1)\|~v3_ordinal1(X2)\|~v2_cgames_1(X1)), inference(split_conjunct,[status(thm)],[c_0_15])). fof(c_0_20, negated_conjecture, (v2_cgames_1(esk1_0)&(v2_cgames_1(esk2_0)&(r2_hidden(esk1_0,k8_cgames_1(esk2_0))&~r2_hidden(k9_cgames_1(esk1_0),k9_cgames_1(esk2_0))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])). cnf(c_0_21, plain, (r2_hidden(k9_cgames_1(X1),X2)\|~v3_ordinal1(X2)\|~r2_hidden(X3,k2_cgames_1(X2))\|~r2_hidden(X1,k8_cgames_1(X3))\|~v2_cgames_1(X1)\|~v2_cgames_1(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_17, c_0_18])])). cnf(c_0_22, plain, (r2_hidden(X1,k2_cgames_1(X2))\|X2!=k9_cgames_1(X1)\|~v2_cgames_1(X1)\|~v3_ordinal1(X2)), inference(evalgc,[status(thm)],[c_0_19])). cnf(c_0_23, negated_conjecture, (r2_hidden(esk1_0,k8_cgames_1(esk2_0))), inference(split_conjunct,[status(thm)],[c_0_20])). cnf(c_0_24, negated_conjecture, (v2_cgames_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_20])). cnf(c_0_25, negated_conjecture, (v2_cgames_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_20])). fof(c_0_26, plain, ![X7]:v3_ordinal1(k9_cgames_1(X7)), inference(variable_rename,[status(thm)],[dt_k9_cgames_1])). cnf(c_0_27, negated_conjecture, (~r2_hidden(k9_cgames_1(esk1_0),k9_cgames_1(esk2_0))), inference(split_conjunct,[status(thm)],[c_0_20])). cnf(c_0_28, plain, (r2_hidden(k9_cgames_1(X1),X2)\|~v3_ordinal1(X2)\|~r2_hidden(X1,k8_cgames_1(X3))\|~v2_cgames_1(X1)\|~v2_cgames_1(X3)\|X2!=k9_cgames_1(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_21, c_0_22])])). cnf(c_0_29, negated_conjecture, (r2_hidden(esk1_0,k8_cgames_1(esk2_0))), inference(evalgc,[status(thm)],[c_0_23])). cnf(c_0_30, negated_conjecture, (v2_cgames_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_24])). cnf(c_0_31, negated_conjecture, (v2_cgames_1(esk2_0)), inference(evalgc,[status(thm)],[c_0_25])). cnf(c_0_32, plain, (v3_ordinal1(k9_cgames_1(X1))), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_33, negated_conjecture, (~r2_hidden(k9_cgames_1(esk1_0),k9_cgames_1(esk2_0))), inference(evalgc,[status(thm)],[c_0_27])). cnf(c_0_34, negated_conjecture, (r2_hidden(k9_cgames_1(esk1_0),X1)\|X1!=k9_cgames_1(esk2_0)\|~v3_ordinal1(X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28, c_0_29]), c_0_30]), c_0_31])])])). cnf(c_0_35, plain, (v3_ordinal1(k9_cgames_1(X1))), inference(evalgc,[status(thm)],[c_0_32])). cnf(c_0_36, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33, c_0_34]), c_0_35])]), ['proof']). # SZS output end CNFRefutation	reserve x,y,y1,y2,z,e,s for set; reserve alpha,beta,gamma for Ordinal; reserve n,m,k for Nat; reserve g,g0,g1,g2,gO,gL,gR,gLL,gLR,gRL,gRR for ConwayGame; theorem Th14: gO in the_Options_of g implies ConwayRank(gO) in ConwayRank(g) proof set alpha = ConwayRank(g); A1: g in ConwayDay(alpha) by Def9; assume gO in the_Options_of g; then consider beta such that A2: beta in alpha & gO in ConwayDay(beta) by A1,Th9; ConwayRank(gO) c= beta by A2,Th12; hence thesis by A2,ORDINAL1:12; end;	Convert the following ATP output trace into a readable Mizar proof.
t15_jordan5c	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(d3_jordan5c, axiom, ![X1]:(m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))=>![X2]:(m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))=>![X3]:(m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))=>![X4]:(m1_subset_1(X4,u1_struct_0(k15_euclid(np__2)))=>![X5]:(m1_subset_1(X5,u1_struct_0(k15_euclid(np__2)))=>(r1_jordan5c(X1,X2,X3,X4,X5)<=>(r2_hidden(X4,X1)&(r2_hidden(X5,X1)&![X6]:((v1_funct_1(X6)&(v1_funct_2(X6,u1_struct_0(k5_topmetr),u1_struct_0(k1_pre_topc(k15_euclid(np__2),X1)))&m1_subset_1(X6,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_topmetr),u1_struct_0(k1_pre_topc(k15_euclid(np__2),X1)))))))=>![X7]:(m1_subset_1(X7,k1_numbers)=>![X8]:(m1_subset_1(X8,k1_numbers)=>((v3_tops_2(X6,k5_topmetr,k1_pre_topc(k15_euclid(np__2),X1))&(k1_funct_1(X6,k6_numbers)=X2&(k1_funct_1(X6,np__1)=X3&(k1_funct_1(X6,X7)=X4&(r1_xxreal_0(k6_numbers,X7)&(r1_xxreal_0(X7,np__1)&(k1_funct_1(X6,X8)=X5&(r1_xxreal_0(k6_numbers,X8)&r1_xxreal_0(X8,np__1)))))))))=>r1_xxreal_0(X7,X8))))))))))))), file('/scratch/mptp/predsminms1/t15_jordan5c__0', d3_jordan5c)). fof(t4_subset, axiom, ![X1, X2, X3]:((r2_hidden(X1,X2)&m1_subset_1(X2,k1_zfmisc_1(X3)))=>m1_subset_1(X1,X3)), file('/scratch/mptp/predsminms1/t15_jordan5c__0', t4_subset)). fof(d1_jordan5c, axiom, ![X1]:(m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))=>![X3]:(m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))=>![X4]:(m1_subset_1(X4,u1_struct_0(k15_euclid(np__2)))=>((v4_pre_topc(k9_subset_1(u1_struct_0(k15_euclid(np__2)),X1,X2),k15_euclid(np__2))&r1_topreal1(k15_euclid(np__2),X3,X4,X1))=>(r1_xboole_0(X1,X2)\|![X5]:(m1_subset_1(X5,u1_struct_0(k15_euclid(np__2)))=>(X5=k1_jordan5c(X1,X2,X3,X4)<=>(r2_hidden(X5,k9_subset_1(u1_struct_0(k15_euclid(np__2)),X1,X2))&![X6]:((v1_funct_1(X6)&(v1_funct_2(X6,u1_struct_0(k5_topmetr),u1_struct_0(k1_pre_topc(k15_euclid(np__2),X1)))&m1_subset_1(X6,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_topmetr),u1_struct_0(k1_pre_topc(k15_euclid(np__2),X1)))))))=>![X7]:(m1_subset_1(X7,k1_numbers)=>((v3_tops_2(X6,k5_topmetr,k1_pre_topc(k15_euclid(np__2),X1))&(k1_funct_1(X6,k6_numbers)=X3&(k1_funct_1(X6,np__1)=X4&(k1_funct_1(X6,X7)=X5&(r1_xxreal_0(k6_numbers,X7)&r1_xxreal_0(X7,np__1))))))=>![X8]:(m1_subset_1(X8,k1_numbers)=>~((r1_xxreal_0(k6_numbers,X8)&(~(r1_xxreal_0(X7,X8))&r2_hidden(k1_funct_1(X6,X8),X2))))))))))))))))), file('/scratch/mptp/predsminms1/t15_jordan5c__0', d1_jordan5c)). fof(t3_xboole_0, axiom, ![X1, X2]:(~((~(r1_xboole_0(X1,X2))&![X3]:~((r2_hidden(X3,X1)&r2_hidden(X3,X2)))))&~((?[X3]:(r2_hidden(X3,X1)&r2_hidden(X3,X2))&r1_xboole_0(X1,X2)))), file('/scratch/mptp/predsminms1/t15_jordan5c__0', t3_xboole_0)). fof(t15_jordan5c, conjecture, ![X1]:(m2_finseq_1(X1,u1_struct_0(k15_euclid(np__2)))=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))=>![X3]:(m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))=>((v4_topreal1(X1)&(v4_pre_topc(k9_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,X1),X2),k15_euclid(np__2))&(r2_hidden(X3,k3_topreal1(np__2,X1))&r2_hidden(X3,X2))))=>r1_jordan5c(k3_topreal1(np__2,X1),k7_partfun1(u1_struct_0(k15_euclid(np__2)),X1,np__1),k7_partfun1(u1_struct_0(k15_euclid(np__2)),X1,k3_finseq_1(X1)),k1_jordan5c(k3_topreal1(np__2,X1),X2,k7_partfun1(u1_struct_0(k15_euclid(np__2)),X1,np__1),k7_partfun1(u1_struct_0(k15_euclid(np__2)),X1,k3_finseq_1(X1))),X3))))), file('/scratch/mptp/predsminms1/t15_jordan5c__0', t15_jordan5c)). fof(t3_subset, axiom, ![X1, X2]:(m1_subset_1(X1,k1_zfmisc_1(X2))<=>r1_tarski(X1,X2)), file('/scratch/mptp/predsminms1/t15_jordan5c__0', t3_subset)). fof(t17_xboole_1, axiom, ![X1, X2]:r1_tarski(k3_xboole_0(X1,X2),X1), file('/scratch/mptp/predsminms1/t15_jordan5c__0', t17_xboole_1)). fof(redefinition_k9_subset_1, axiom, ![X1, X2, X3]:(m1_subset_1(X3,k1_zfmisc_1(X1))=>k9_subset_1(X1,X2,X3)=k3_xboole_0(X2,X3)), file('/scratch/mptp/predsminms1/t15_jordan5c__0', redefinition_k9_subset_1)). fof(t25_topreal1, axiom, ![X1]:(m2_finseq_1(X1,u1_struct_0(k15_euclid(np__2)))=>(v4_topreal1(X1)=>r1_topreal1(k15_euclid(np__2),k7_partfun1(u1_struct_0(k15_euclid(np__2)),X1,np__1),k7_partfun1(u1_struct_0(k15_euclid(np__2)),X1,k3_finseq_1(X1)),k3_topreal1(np__2,X1)))), file('/scratch/mptp/predsminms1/t15_jordan5c__0', t25_topreal1)). fof(t7_boole, axiom, ![X1, X2]:~((r2_hidden(X1,X2)&v1_xboole_0(X2))), file('/scratch/mptp/predsminms1/t15_jordan5c__0', t7_boole)). fof(t2_subset, axiom, ![X1, X2]:(m1_subset_1(X1,X2)=>(v1_xboole_0(X2)\|r2_hidden(X1,X2))), file('/scratch/mptp/predsminms1/t15_jordan5c__0', t2_subset)). fof(cc1_relset_1, axiom, ![X1, X2, X3]:(m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))=>v1_relat_1(X3)), file('/scratch/mptp/predsminms1/t15_jordan5c__0', cc1_relset_1)). fof(dt_m2_finseq_1, axiom, ![X1, X2]:(m2_finseq_1(X2,X1)=>(v1_funct_1(X2)&(v1_finseq_1(X2)&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,X1)))))), file('/scratch/mptp/predsminms1/t15_jordan5c__0', dt_m2_finseq_1)). fof(dt_k1_jordan5c, axiom, ![X1, X2, X3, X4]:((m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))&(m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))&(m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))&m1_subset_1(X4,u1_struct_0(k15_euclid(np__2))))))=>m1_subset_1(k1_jordan5c(X1,X2,X3,X4),u1_struct_0(k15_euclid(np__2)))), file('/scratch/mptp/predsminms1/t15_jordan5c__0', dt_k1_jordan5c)). fof(dt_k7_partfun1, axiom, ![X1, X2, X3]:((v1_relat_1(X2)&(v5_relat_1(X2,X1)&v1_funct_1(X2)))=>m1_subset_1(k7_partfun1(X1,X2,X3),X1)), file('/scratch/mptp/predsminms1/t15_jordan5c__0', dt_k7_partfun1)). fof(cc17_membered, axiom, ![X1]:(v6_membered(X1)=>![X2]:(m1_subset_1(X2,X1)=>v7_ordinal1(X2))), file('/scratch/mptp/predsminms1/t15_jordan5c__0', cc17_membered)). fof(fc6_membered, axiom, v6_membered(k4_ordinal1), file('/scratch/mptp/predsminms1/t15_jordan5c__0', fc6_membered)). fof(redefinition_k5_numbers, axiom, k5_numbers=k4_ordinal1, file('/scratch/mptp/predsminms1/t15_jordan5c__0', redefinition_k5_numbers)). fof(dt_k3_topreal1, axiom, ![X1, X2]:((v7_ordinal1(X1)&m1_finseq_1(X2,u1_struct_0(k15_euclid(X1))))=>m1_subset_1(k3_topreal1(X1,X2),k1_zfmisc_1(u1_struct_0(k15_euclid(X1))))), file('/scratch/mptp/predsminms1/t15_jordan5c__0', dt_k3_topreal1)). fof(spc2_numerals, axiom, ((v2_xxreal_0(np__2)&m2_subset_1(np__2,k1_numbers,k5_numbers))&(m1_subset_1(np__2,k5_numbers)&m1_subset_1(np__2,k1_numbers))), file('/scratch/mptp/predsminms1/t15_jordan5c__0', spc2_numerals)). fof(cc2_relset_1, axiom, ![X1, X2, X3]:(m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))=>(v4_relat_1(X3,X1)&v5_relat_1(X3,X2))), file('/scratch/mptp/predsminms1/t15_jordan5c__0', cc2_relset_1)). fof(redefinition_m2_finseq_1, axiom, ![X1, X2]:(m2_finseq_1(X2,X1)<=>m1_finseq_1(X2,X1)), file('/scratch/mptp/predsminms1/t15_jordan5c__0', redefinition_m2_finseq_1)). fof(c_0_22, plain, ![X23, X24, X25, X26, X27, X28, X29, X30]:(((r2_hidden(X26,X23)\|~r1_jordan5c(X23,X24,X25,X26,X27)\|~m1_subset_1(X27,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X26,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X25,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X24,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X23,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))))&((r2_hidden(X27,X23)\|~r1_jordan5c(X23,X24,X25,X26,X27)\|~m1_subset_1(X27,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X26,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X25,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X24,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X23,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))))&(~v1_funct_1(X28)\|(~v1_funct_2(X28,u1_struct_0(k5_topmetr),u1_struct_0(k1_pre_topc(k15_euclid(np__2),X23)))\|~m1_subset_1(X28,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_topmetr),u1_struct_0(k1_pre_topc(k15_euclid(np__2),X23))))))\|(~m1_subset_1(X29,k1_numbers)\|(~m1_subset_1(X30,k1_numbers)\|(~v3_tops_2(X28,k5_topmetr,k1_pre_topc(k15_euclid(np__2),X23))\|(k1_funct_1(X28,k6_numbers)!=X24\|(k1_funct_1(X28,np__1)!=X25\|(k1_funct_1(X28,X29)!=X26\|(~r1_xxreal_0(k6_numbers,X29)\|(~r1_xxreal_0(X29,np__1)\|(k1_funct_1(X28,X30)!=X27\|(~r1_xxreal_0(k6_numbers,X30)\|~r1_xxreal_0(X30,np__1))))))))\|r1_xxreal_0(X29,X30))))\|~r1_jordan5c(X23,X24,X25,X26,X27)\|~m1_subset_1(X27,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X26,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X25,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X24,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X23,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))))))&(((v1_funct_1(esk7_5(X23,X24,X25,X26,X27))\|~r2_hidden(X27,X23)\|~r2_hidden(X26,X23)\|r1_jordan5c(X23,X24,X25,X26,X27)\|~m1_subset_1(X27,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X26,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X25,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X24,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X23,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))))&((v1_funct_2(esk7_5(X23,X24,X25,X26,X27),u1_struct_0(k5_topmetr),u1_struct_0(k1_pre_topc(k15_euclid(np__2),X23)))\|~r2_hidden(X27,X23)\|~r2_hidden(X26,X23)\|r1_jordan5c(X23,X24,X25,X26,X27)\|~m1_subset_1(X27,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X26,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X25,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X24,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X23,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))))&(m1_subset_1(esk7_5(X23,X24,X25,X26,X27),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_topmetr),u1_struct_0(k1_pre_topc(k15_euclid(np__2),X23)))))\|~r2_hidden(X27,X23)\|~r2_hidden(X26,X23)\|r1_jordan5c(X23,X24,X25,X26,X27)\|~m1_subset_1(X27,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X26,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X25,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X24,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X23,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))))))&((m1_subset_1(esk8_5(X23,X24,X25,X26,X27),k1_numbers)\|~r2_hidden(X27,X23)\|~r2_hidden(X26,X23)\|r1_jordan5c(X23,X24,X25,X26,X27)\|~m1_subset_1(X27,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X26,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X25,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X24,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X23,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))))&((m1_subset_1(esk9_5(X23,X24,X25,X26,X27),k1_numbers)\|~r2_hidden(X27,X23)\|~r2_hidden(X26,X23)\|r1_jordan5c(X23,X24,X25,X26,X27)\|~m1_subset_1(X27,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X26,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X25,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X24,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X23,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))))&(((v3_tops_2(esk7_5(X23,X24,X25,X26,X27),k5_topmetr,k1_pre_topc(k15_euclid(np__2),X23))\|~r2_hidden(X27,X23)\|~r2_hidden(X26,X23)\|r1_jordan5c(X23,X24,X25,X26,X27)\|~m1_subset_1(X27,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X26,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X25,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X24,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X23,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))))&((k1_funct_1(esk7_5(X23,X24,X25,X26,X27),k6_numbers)=X24\|~r2_hidden(X27,X23)\|~r2_hidden(X26,X23)\|r1_jordan5c(X23,X24,X25,X26,X27)\|~m1_subset_1(X27,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X26,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X25,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X24,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X23,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))))&((k1_funct_1(esk7_5(X23,X24,X25,X26,X27),np__1)=X25\|~r2_hidden(X27,X23)\|~r2_hidden(X26,X23)\|r1_jordan5c(X23,X24,X25,X26,X27)\|~m1_subset_1(X27,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X26,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X25,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X24,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X23,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))))&((k1_funct_1(esk7_5(X23,X24,X25,X26,X27),esk8_5(X23,X24,X25,X26,X27))=X26\|~r2_hidden(X27,X23)\|~r2_hidden(X26,X23)\|r1_jordan5c(X23,X24,X25,X26,X27)\|~m1_subset_1(X27,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X26,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X25,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X24,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X23,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))))&((r1_xxreal_0(k6_numbers,esk8_5(X23,X24,X25,X26,X27))\|~r2_hidden(X27,X23)\|~r2_hidden(X26,X23)\|r1_jordan5c(X23,X24,X25,X26,X27)\|~m1_subset_1(X27,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X26,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X25,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X24,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X23,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))))&((r1_xxreal_0(esk8_5(X23,X24,X25,X26,X27),np__1)\|~r2_hidden(X27,X23)\|~r2_hidden(X26,X23)\|r1_jordan5c(X23,X24,X25,X26,X27)\|~m1_subset_1(X27,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X26,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X25,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X24,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X23,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))))&((k1_funct_1(esk7_5(X23,X24,X25,X26,X27),esk9_5(X23,X24,X25,X26,X27))=X27\|~r2_hidden(X27,X23)\|~r2_hidden(X26,X23)\|r1_jordan5c(X23,X24,X25,X26,X27)\|~m1_subset_1(X27,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X26,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X25,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X24,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X23,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))))&((r1_xxreal_0(k6_numbers,esk9_5(X23,X24,X25,X26,X27))\|~r2_hidden(X27,X23)\|~r2_hidden(X26,X23)\|r1_jordan5c(X23,X24,X25,X26,X27)\|~m1_subset_1(X27,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X26,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X25,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X24,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X23,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))))&(r1_xxreal_0(esk9_5(X23,X24,X25,X26,X27),np__1)\|~r2_hidden(X27,X23)\|~r2_hidden(X26,X23)\|r1_jordan5c(X23,X24,X25,X26,X27)\|~m1_subset_1(X27,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X26,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X25,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X24,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X23,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))))))))))))&(~r1_xxreal_0(esk8_5(X23,X24,X25,X26,X27),esk9_5(X23,X24,X25,X26,X27))\|~r2_hidden(X27,X23)\|~r2_hidden(X26,X23)\|r1_jordan5c(X23,X24,X25,X26,X27)\|~m1_subset_1(X27,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X26,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X25,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X24,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X23,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_jordan5c])])])])])). fof(c_0_23, plain, ![X34, X35, X36]:(~r2_hidden(X34,X35)\|~m1_subset_1(X35,k1_zfmisc_1(X36))\|m1_subset_1(X34,X36)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])])). fof(c_0_24, plain, ![X12, X13, X14, X15, X16, X17, X18, X19]:(((r2_hidden(X16,k9_subset_1(u1_struct_0(k15_euclid(np__2)),X12,X13))\|X16!=k1_jordan5c(X12,X13,X14,X15)\|~m1_subset_1(X16,u1_struct_0(k15_euclid(np__2)))\|r1_xboole_0(X12,X13)\|(~v4_pre_topc(k9_subset_1(u1_struct_0(k15_euclid(np__2)),X12,X13),k15_euclid(np__2))\|~r1_topreal1(k15_euclid(np__2),X14,X15,X12))\|~m1_subset_1(X15,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X14,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X13,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(X12,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))))&(~v1_funct_1(X17)\|(~v1_funct_2(X17,u1_struct_0(k5_topmetr),u1_struct_0(k1_pre_topc(k15_euclid(np__2),X12)))\|~m1_subset_1(X17,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_topmetr),u1_struct_0(k1_pre_topc(k15_euclid(np__2),X12))))))\|(~m1_subset_1(X18,k1_numbers)\|(~v3_tops_2(X17,k5_topmetr,k1_pre_topc(k15_euclid(np__2),X12))\|(k1_funct_1(X17,k6_numbers)!=X14\|(k1_funct_1(X17,np__1)!=X15\|(k1_funct_1(X17,X18)!=X16\|(~r1_xxreal_0(k6_numbers,X18)\|~r1_xxreal_0(X18,np__1)))))\|(~m1_subset_1(X19,k1_numbers)\|(~r1_xxreal_0(k6_numbers,X19)\|(r1_xxreal_0(X18,X19)\|~r2_hidden(k1_funct_1(X17,X19),X13))))))\|X16!=k1_jordan5c(X12,X13,X14,X15)\|~m1_subset_1(X16,u1_struct_0(k15_euclid(np__2)))\|r1_xboole_0(X12,X13)\|(~v4_pre_topc(k9_subset_1(u1_struct_0(k15_euclid(np__2)),X12,X13),k15_euclid(np__2))\|~r1_topreal1(k15_euclid(np__2),X14,X15,X12))\|~m1_subset_1(X15,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X14,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X13,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(X12,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))))&(((v1_funct_1(esk4_5(X12,X13,X14,X15,X16))\|~r2_hidden(X16,k9_subset_1(u1_struct_0(k15_euclid(np__2)),X12,X13))\|X16=k1_jordan5c(X12,X13,X14,X15)\|~m1_subset_1(X16,u1_struct_0(k15_euclid(np__2)))\|r1_xboole_0(X12,X13)\|(~v4_pre_topc(k9_subset_1(u1_struct_0(k15_euclid(np__2)),X12,X13),k15_euclid(np__2))\|~r1_topreal1(k15_euclid(np__2),X14,X15,X12))\|~m1_subset_1(X15,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X14,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X13,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(X12,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))))&((v1_funct_2(esk4_5(X12,X13,X14,X15,X16),u1_struct_0(k5_topmetr),u1_struct_0(k1_pre_topc(k15_euclid(np__2),X12)))\|~r2_hidden(X16,k9_subset_1(u1_struct_0(k15_euclid(np__2)),X12,X13))\|X16=k1_jordan5c(X12,X13,X14,X15)\|~m1_subset_1(X16,u1_struct_0(k15_euclid(np__2)))\|r1_xboole_0(X12,X13)\|(~v4_pre_topc(k9_subset_1(u1_struct_0(k15_euclid(np__2)),X12,X13),k15_euclid(np__2))\|~r1_topreal1(k15_euclid(np__2),X14,X15,X12))\|~m1_subset_1(X15,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X14,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X13,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(X12,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))))&(m1_subset_1(esk4_5(X12,X13,X14,X15,X16),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_topmetr),u1_struct_0(k1_pre_topc(k15_euclid(np__2),X12)))))\|~r2_hidden(X16,k9_subset_1(u1_struct_0(k15_euclid(np__2)),X12,X13))\|X16=k1_jordan5c(X12,X13,X14,X15)\|~m1_subset_1(X16,u1_struct_0(k15_euclid(np__2)))\|r1_xboole_0(X12,X13)\|(~v4_pre_topc(k9_subset_1(u1_struct_0(k15_euclid(np__2)),X12,X13),k15_euclid(np__2))\|~r1_topreal1(k15_euclid(np__2),X14,X15,X12))\|~m1_subset_1(X15,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X14,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X13,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(X12,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))))))&((m1_subset_1(esk5_5(X12,X13,X14,X15,X16),k1_numbers)\|~r2_hidden(X16,k9_subset_1(u1_struct_0(k15_euclid(np__2)),X12,X13))\|X16=k1_jordan5c(X12,X13,X14,X15)\|~m1_subset_1(X16,u1_struct_0(k15_euclid(np__2)))\|r1_xboole_0(X12,X13)\|(~v4_pre_topc(k9_subset_1(u1_struct_0(k15_euclid(np__2)),X12,X13),k15_euclid(np__2))\|~r1_topreal1(k15_euclid(np__2),X14,X15,X12))\|~m1_subset_1(X15,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X14,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X13,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(X12,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))))&(((v3_tops_2(esk4_5(X12,X13,X14,X15,X16),k5_topmetr,k1_pre_topc(k15_euclid(np__2),X12))\|~r2_hidden(X16,k9_subset_1(u1_struct_0(k15_euclid(np__2)),X12,X13))\|X16=k1_jordan5c(X12,X13,X14,X15)\|~m1_subset_1(X16,u1_struct_0(k15_euclid(np__2)))\|r1_xboole_0(X12,X13)\|(~v4_pre_topc(k9_subset_1(u1_struct_0(k15_euclid(np__2)),X12,X13),k15_euclid(np__2))\|~r1_topreal1(k15_euclid(np__2),X14,X15,X12))\|~m1_subset_1(X15,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X14,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X13,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(X12,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))))&((k1_funct_1(esk4_5(X12,X13,X14,X15,X16),k6_numbers)=X14\|~r2_hidden(X16,k9_subset_1(u1_struct_0(k15_euclid(np__2)),X12,X13))\|X16=k1_jordan5c(X12,X13,X14,X15)\|~m1_subset_1(X16,u1_struct_0(k15_euclid(np__2)))\|r1_xboole_0(X12,X13)\|(~v4_pre_topc(k9_subset_1(u1_struct_0(k15_euclid(np__2)),X12,X13),k15_euclid(np__2))\|~r1_topreal1(k15_euclid(np__2),X14,X15,X12))\|~m1_subset_1(X15,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X14,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X13,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(X12,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))))&((k1_funct_1(esk4_5(X12,X13,X14,X15,X16),np__1)=X15\|~r2_hidden(X16,k9_subset_1(u1_struct_0(k15_euclid(np__2)),X12,X13))\|X16=k1_jordan5c(X12,X13,X14,X15)\|~m1_subset_1(X16,u1_struct_0(k15_euclid(np__2)))\|r1_xboole_0(X12,X13)\|(~v4_pre_topc(k9_subset_1(u1_struct_0(k15_euclid(np__2)),X12,X13),k15_euclid(np__2))\|~r1_topreal1(k15_euclid(np__2),X14,X15,X12))\|~m1_subset_1(X15,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X14,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X13,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(X12,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))))&((k1_funct_1(esk4_5(X12,X13,X14,X15,X16),esk5_5(X12,X13,X14,X15,X16))=X16\|~r2_hidden(X16,k9_subset_1(u1_struct_0(k15_euclid(np__2)),X12,X13))\|X16=k1_jordan5c(X12,X13,X14,X15)\|~m1_subset_1(X16,u1_struct_0(k15_euclid(np__2)))\|r1_xboole_0(X12,X13)\|(~v4_pre_topc(k9_subset_1(u1_struct_0(k15_euclid(np__2)),X12,X13),k15_euclid(np__2))\|~r1_topreal1(k15_euclid(np__2),X14,X15,X12))\|~m1_subset_1(X15,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X14,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X13,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(X12,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))))&((r1_xxreal_0(k6_numbers,esk5_5(X12,X13,X14,X15,X16))\|~r2_hidden(X16,k9_subset_1(u1_struct_0(k15_euclid(np__2)),X12,X13))\|X16=k1_jordan5c(X12,X13,X14,X15)\|~m1_subset_1(X16,u1_struct_0(k15_euclid(np__2)))\|r1_xboole_0(X12,X13)\|(~v4_pre_topc(k9_subset_1(u1_struct_0(k15_euclid(np__2)),X12,X13),k15_euclid(np__2))\|~r1_topreal1(k15_euclid(np__2),X14,X15,X12))\|~m1_subset_1(X15,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X14,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X13,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(X12,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))))&(r1_xxreal_0(esk5_5(X12,X13,X14,X15,X16),np__1)\|~r2_hidden(X16,k9_subset_1(u1_struct_0(k15_euclid(np__2)),X12,X13))\|X16=k1_jordan5c(X12,X13,X14,X15)\|~m1_subset_1(X16,u1_struct_0(k15_euclid(np__2)))\|r1_xboole_0(X12,X13)\|(~v4_pre_topc(k9_subset_1(u1_struct_0(k15_euclid(np__2)),X12,X13),k15_euclid(np__2))\|~r1_topreal1(k15_euclid(np__2),X14,X15,X12))\|~m1_subset_1(X15,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X14,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X13,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(X12,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))))))))&((m1_subset_1(esk6_5(X12,X13,X14,X15,X16),k1_numbers)\|~r2_hidden(X16,k9_subset_1(u1_struct_0(k15_euclid(np__2)),X12,X13))\|X16=k1_jordan5c(X12,X13,X14,X15)\|~m1_subset_1(X16,u1_struct_0(k15_euclid(np__2)))\|r1_xboole_0(X12,X13)\|(~v4_pre_topc(k9_subset_1(u1_struct_0(k15_euclid(np__2)),X12,X13),k15_euclid(np__2))\|~r1_topreal1(k15_euclid(np__2),X14,X15,X12))\|~m1_subset_1(X15,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X14,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X13,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(X12,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))))&((r1_xxreal_0(k6_numbers,esk6_5(X12,X13,X14,X15,X16))\|~r2_hidden(X16,k9_subset_1(u1_struct_0(k15_euclid(np__2)),X12,X13))\|X16=k1_jordan5c(X12,X13,X14,X15)\|~m1_subset_1(X16,u1_struct_0(k15_euclid(np__2)))\|r1_xboole_0(X12,X13)\|(~v4_pre_topc(k9_subset_1(u1_struct_0(k15_euclid(np__2)),X12,X13),k15_euclid(np__2))\|~r1_topreal1(k15_euclid(np__2),X14,X15,X12))\|~m1_subset_1(X15,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X14,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X13,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(X12,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))))&((~r1_xxreal_0(esk5_5(X12,X13,X14,X15,X16),esk6_5(X12,X13,X14,X15,X16))\|~r2_hidden(X16,k9_subset_1(u1_struct_0(k15_euclid(np__2)),X12,X13))\|X16=k1_jordan5c(X12,X13,X14,X15)\|~m1_subset_1(X16,u1_struct_0(k15_euclid(np__2)))\|r1_xboole_0(X12,X13)\|(~v4_pre_topc(k9_subset_1(u1_struct_0(k15_euclid(np__2)),X12,X13),k15_euclid(np__2))\|~r1_topreal1(k15_euclid(np__2),X14,X15,X12))\|~m1_subset_1(X15,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X14,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X13,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(X12,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))))&(r2_hidden(k1_funct_1(esk4_5(X12,X13,X14,X15,X16),esk6_5(X12,X13,X14,X15,X16)),X13)\|~r2_hidden(X16,k9_subset_1(u1_struct_0(k15_euclid(np__2)),X12,X13))\|X16=k1_jordan5c(X12,X13,X14,X15)\|~m1_subset_1(X16,u1_struct_0(k15_euclid(np__2)))\|r1_xboole_0(X12,X13)\|(~v4_pre_topc(k9_subset_1(u1_struct_0(k15_euclid(np__2)),X12,X13),k15_euclid(np__2))\|~r1_topreal1(k15_euclid(np__2),X14,X15,X12))\|~m1_subset_1(X15,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X14,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X13,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(X12,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d1_jordan5c])])])])])])). cnf(c_0_25, plain, (m1_subset_1(esk7_5(X1,X2,X3,X4,X5),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_topmetr),u1_struct_0(k1_pre_topc(k15_euclid(np__2),X1)))))\|r1_jordan5c(X1,X2,X3,X4,X5)\|~r2_hidden(X5,X1)\|~r2_hidden(X4,X1)\|~m1_subset_1(X5,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X4,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_26, plain, (m1_subset_1(X1,X3)\|~r2_hidden(X1,X2)\|~m1_subset_1(X2,k1_zfmisc_1(X3))), inference(split_conjunct,[status(thm)],[c_0_23])). cnf(c_0_27, plain, (r1_xxreal_0(X3,X7)\|r1_xboole_0(X2,X8)\|~v1_funct_1(X1)\|~v1_funct_2(X1,u1_struct_0(k5_topmetr),u1_struct_0(k1_pre_topc(k15_euclid(np__2),X2)))\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_topmetr),u1_struct_0(k1_pre_topc(k15_euclid(np__2),X2)))))\|~m1_subset_1(X3,k1_numbers)\|~v3_tops_2(X1,k5_topmetr,k1_pre_topc(k15_euclid(np__2),X2))\|k1_funct_1(X1,k6_numbers)!=X4\|k1_funct_1(X1,np__1)!=X5\|k1_funct_1(X1,X3)!=X6\|~r1_xxreal_0(k6_numbers,X3)\|~r1_xxreal_0(X3,np__1)\|~m1_subset_1(X7,k1_numbers)\|~r1_xxreal_0(k6_numbers,X7)\|~r2_hidden(k1_funct_1(X1,X7),X8)\|X6!=k1_jordan5c(X2,X8,X4,X5)\|~m1_subset_1(X6,u1_struct_0(k15_euclid(np__2)))\|~v4_pre_topc(k9_subset_1(u1_struct_0(k15_euclid(np__2)),X2,X8),k15_euclid(np__2))\|~r1_topreal1(k15_euclid(np__2),X4,X5,X2)\|~m1_subset_1(X5,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X4,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X8,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))), inference(split_conjunct,[status(thm)],[c_0_24])). cnf(c_0_28, plain, (r1_jordan5c(X1,X2,X3,X4,X5)\|m1_subset_1(esk7_5(X1,X2,X3,X4,X5),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_topmetr),u1_struct_0(k1_pre_topc(k15_euclid(np__2),X1)))))\|~r2_hidden(X5,X1)\|~r2_hidden(X4,X1)\|~m1_subset_1(X5,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X4,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))), inference(evalgc,[status(thm)],[c_0_25])). cnf(c_0_29, plain, (m1_subset_1(X1,X3)\|~r2_hidden(X1,X2)\|~m1_subset_1(X2,k1_zfmisc_1(X3))), inference(evalgc,[status(thm)],[c_0_26])). cnf(c_0_30, plain, (v1_funct_1(esk7_5(X1,X2,X3,X4,X5))\|r1_jordan5c(X1,X2,X3,X4,X5)\|~r2_hidden(X5,X1)\|~r2_hidden(X4,X1)\|~m1_subset_1(X5,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X4,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_31, plain, (v1_funct_2(esk7_5(X1,X2,X3,X4,X5),u1_struct_0(k5_topmetr),u1_struct_0(k1_pre_topc(k15_euclid(np__2),X1)))\|r1_jordan5c(X1,X2,X3,X4,X5)\|~r2_hidden(X5,X1)\|~r2_hidden(X4,X1)\|~m1_subset_1(X5,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X4,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_32, plain, (v3_tops_2(esk7_5(X1,X2,X3,X4,X5),k5_topmetr,k1_pre_topc(k15_euclid(np__2),X1))\|r1_jordan5c(X1,X2,X3,X4,X5)\|~r2_hidden(X5,X1)\|~r2_hidden(X4,X1)\|~m1_subset_1(X5,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X4,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_33, plain, (r1_xboole_0(X2,X8)\|r1_xxreal_0(X3,X7)\|k1_funct_1(X1,X3)!=X6\|k1_funct_1(X1,np__1)!=X5\|k1_funct_1(X1,k6_numbers)!=X4\|X6!=k1_jordan5c(X2,X8,X4,X5)\|~v1_funct_1(X1)\|~m1_subset_1(X7,k1_numbers)\|~m1_subset_1(X3,k1_numbers)\|~r1_xxreal_0(X3,np__1)\|~r1_xxreal_0(k6_numbers,X7)\|~r1_xxreal_0(k6_numbers,X3)\|~r2_hidden(k1_funct_1(X1,X7),X8)\|~m1_subset_1(X6,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X5,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X4,u1_struct_0(k15_euclid(np__2)))\|~r1_topreal1(k15_euclid(np__2),X4,X5,X2)\|~m1_subset_1(X8,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~v3_tops_2(X1,k5_topmetr,k1_pre_topc(k15_euclid(np__2),X2))\|~v4_pre_topc(k9_subset_1(u1_struct_0(k15_euclid(np__2)),X2,X8),k15_euclid(np__2))\|~v1_funct_2(X1,u1_struct_0(k5_topmetr),u1_struct_0(k1_pre_topc(k15_euclid(np__2),X2)))\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_topmetr),u1_struct_0(k1_pre_topc(k15_euclid(np__2),X2)))))), inference(evalgc,[status(thm)],[c_0_27])). cnf(c_0_34, plain, (r1_jordan5c(X1,X2,X3,X4,X5)\|m1_subset_1(esk7_5(X1,X2,X3,X4,X5),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_topmetr),u1_struct_0(k1_pre_topc(k15_euclid(np__2),X1)))))\|~r2_hidden(X5,X1)\|~r2_hidden(X4,X1)\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_28, c_0_29]), c_0_29])). cnf(c_0_35, plain, (r1_jordan5c(X1,X2,X3,X4,X5)\|v1_funct_1(esk7_5(X1,X2,X3,X4,X5))\|~r2_hidden(X5,X1)\|~r2_hidden(X4,X1)\|~m1_subset_1(X5,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X4,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))), inference(evalgc,[status(thm)],[c_0_30])). cnf(c_0_36, plain, (r1_jordan5c(X1,X2,X3,X4,X5)\|v1_funct_2(esk7_5(X1,X2,X3,X4,X5),u1_struct_0(k5_topmetr),u1_struct_0(k1_pre_topc(k15_euclid(np__2),X1)))\|~r2_hidden(X5,X1)\|~r2_hidden(X4,X1)\|~m1_subset_1(X5,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X4,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))), inference(evalgc,[status(thm)],[c_0_31])). cnf(c_0_37, plain, (r1_jordan5c(X1,X2,X3,X4,X5)\|v3_tops_2(esk7_5(X1,X2,X3,X4,X5),k5_topmetr,k1_pre_topc(k15_euclid(np__2),X1))\|~r2_hidden(X5,X1)\|~r2_hidden(X4,X1)\|~m1_subset_1(X5,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X4,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))), inference(evalgc,[status(thm)],[c_0_32])). cnf(c_0_38, plain, (k1_funct_1(esk7_5(X1,X2,X3,X4,X5),esk9_5(X1,X2,X3,X4,X5))=X5\|r1_jordan5c(X1,X2,X3,X4,X5)\|~r2_hidden(X5,X1)\|~r2_hidden(X4,X1)\|~m1_subset_1(X5,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X4,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_39, plain, (r1_xxreal_0(X1,X2)\|r1_xboole_0(X3,X4)\|r1_jordan5c(X3,X8,X9,X10,X11)\|X5!=k1_jordan5c(X3,X4,X6,X7)\|k1_funct_1(esk7_5(X3,X8,X9,X10,X11),np__1)!=X7\|k1_funct_1(esk7_5(X3,X8,X9,X10,X11),k6_numbers)!=X6\|k1_funct_1(esk7_5(X3,X8,X9,X10,X11),X1)!=X5\|~r1_xxreal_0(X1,np__1)\|~r1_xxreal_0(k6_numbers,X2)\|~r1_xxreal_0(k6_numbers,X1)\|~v3_tops_2(esk7_5(X3,X8,X9,X10,X11),k5_topmetr,k1_pre_topc(k15_euclid(np__2),X3))\|~v1_funct_2(esk7_5(X3,X8,X9,X10,X11),u1_struct_0(k5_topmetr),u1_struct_0(k1_pre_topc(k15_euclid(np__2),X3)))\|~v1_funct_1(esk7_5(X3,X8,X9,X10,X11))\|~r1_topreal1(k15_euclid(np__2),X6,X7,X3)\|~r2_hidden(k1_funct_1(esk7_5(X3,X8,X9,X10,X11),X2),X4)\|~v4_pre_topc(k9_subset_1(u1_struct_0(k15_euclid(np__2)),X3,X4),k15_euclid(np__2))\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(X5,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X7,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X6,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X2,k1_numbers)\|~m1_subset_1(X1,k1_numbers)\|~r2_hidden(X11,X3)\|~r2_hidden(X10,X3)\|~m1_subset_1(X9,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X8,u1_struct_0(k15_euclid(np__2)))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_33, c_0_34])])). cnf(c_0_40, plain, (v1_funct_1(esk7_5(X1,X2,X3,X4,X5))\|r1_jordan5c(X1,X2,X3,X4,X5)\|~r2_hidden(X5,X1)\|~r2_hidden(X4,X1)\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_35, c_0_29]), c_0_29])). cnf(c_0_41, plain, (v1_funct_2(esk7_5(X1,X2,X3,X4,X5),u1_struct_0(k5_topmetr),u1_struct_0(k1_pre_topc(k15_euclid(np__2),X1)))\|r1_jordan5c(X1,X2,X3,X4,X5)\|~r2_hidden(X5,X1)\|~r2_hidden(X4,X1)\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_36, c_0_29]), c_0_29])). cnf(c_0_42, plain, (v3_tops_2(esk7_5(X1,X2,X3,X4,X5),k5_topmetr,k1_pre_topc(k15_euclid(np__2),X1))\|r1_jordan5c(X1,X2,X3,X4,X5)\|~r2_hidden(X5,X1)\|~r2_hidden(X4,X1)\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_37, c_0_29]), c_0_29])). cnf(c_0_43, plain, (k1_funct_1(esk7_5(X1,X2,X3,X4,X5),esk9_5(X1,X2,X3,X4,X5))=X5\|r1_jordan5c(X1,X2,X3,X4,X5)\|~r2_hidden(X5,X1)\|~r2_hidden(X4,X1)\|~m1_subset_1(X5,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X4,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))), inference(evalgc,[status(thm)],[c_0_38])). cnf(c_0_44, plain, (m1_subset_1(esk9_5(X1,X2,X3,X4,X5),k1_numbers)\|r1_jordan5c(X1,X2,X3,X4,X5)\|~r2_hidden(X5,X1)\|~r2_hidden(X4,X1)\|~m1_subset_1(X5,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X4,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_45, plain, (r1_xxreal_0(k6_numbers,esk9_5(X1,X2,X3,X4,X5))\|r1_jordan5c(X1,X2,X3,X4,X5)\|~r2_hidden(X5,X1)\|~r2_hidden(X4,X1)\|~m1_subset_1(X5,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X4,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))), inference(split_conjunct,[status(thm)],[c_0_22])). fof(c_0_46, plain, ![X37, X38, X40, X41, X42]:(((r2_hidden(esk10_2(X37,X38),X37)\|r1_xboole_0(X37,X38))&(r2_hidden(esk10_2(X37,X38),X38)\|r1_xboole_0(X37,X38)))&(~r2_hidden(X42,X40)\|~r2_hidden(X42,X41)\|~r1_xboole_0(X40,X41))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t3_xboole_0])])])])])])])). fof(c_0_47, negated_conjecture, ~(![X1]:(m2_finseq_1(X1,u1_struct_0(k15_euclid(np__2)))=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))=>![X3]:(m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))=>((v4_topreal1(X1)&(v4_pre_topc(k9_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,X1),X2),k15_euclid(np__2))&(r2_hidden(X3,k3_topreal1(np__2,X1))&r2_hidden(X3,X2))))=>r1_jordan5c(k3_topreal1(np__2,X1),k7_partfun1(u1_struct_0(k15_euclid(np__2)),X1,np__1),k7_partfun1(u1_struct_0(k15_euclid(np__2)),X1,k3_finseq_1(X1)),k1_jordan5c(k3_topreal1(np__2,X1),X2,k7_partfun1(u1_struct_0(k15_euclid(np__2)),X1,np__1),k7_partfun1(u1_struct_0(k15_euclid(np__2)),X1,k3_finseq_1(X1))),X3)))))), inference(assume_negation,[status(cth)],[t15_jordan5c])). cnf(c_0_48, plain, (r1_xxreal_0(X1,X2)\|r1_xboole_0(X3,X4)\|r1_jordan5c(X3,X5,X6,X7,X8)\|k1_funct_1(esk7_5(X3,X5,X6,X7,X8),np__1)!=X9\|k1_funct_1(esk7_5(X3,X5,X6,X7,X8),k6_numbers)!=X10\|k1_funct_1(esk7_5(X3,X5,X6,X7,X8),X1)!=X11\|X11!=k1_jordan5c(X3,X4,X10,X9)\|~r1_xxreal_0(X1,np__1)\|~r1_xxreal_0(k6_numbers,X2)\|~r1_xxreal_0(k6_numbers,X1)\|~r1_topreal1(k15_euclid(np__2),X10,X9,X3)\|~r2_hidden(k1_funct_1(esk7_5(X3,X5,X6,X7,X8),X2),X4)\|~r2_hidden(X8,X3)\|~r2_hidden(X7,X3)\|~v4_pre_topc(k9_subset_1(u1_struct_0(k15_euclid(np__2)),X3,X4),k15_euclid(np__2))\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(X11,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X9,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X10,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X6,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X5,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X2,k1_numbers)\|~m1_subset_1(X1,k1_numbers)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_39, c_0_40]), c_0_41]), c_0_42])). cnf(c_0_49, plain, (k1_funct_1(esk7_5(X1,X2,X3,X4,X5),esk9_5(X1,X2,X3,X4,X5))=X5\|r1_jordan5c(X1,X2,X3,X4,X5)\|~r2_hidden(X5,X1)\|~r2_hidden(X4,X1)\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_43, c_0_29]), c_0_29])). cnf(c_0_50, plain, (r1_jordan5c(X1,X2,X3,X4,X5)\|m1_subset_1(esk9_5(X1,X2,X3,X4,X5),k1_numbers)\|~r2_hidden(X5,X1)\|~r2_hidden(X4,X1)\|~m1_subset_1(X5,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X4,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))), inference(evalgc,[status(thm)],[c_0_44])). cnf(c_0_51, plain, (r1_jordan5c(X1,X2,X3,X4,X5)\|r1_xxreal_0(k6_numbers,esk9_5(X1,X2,X3,X4,X5))\|~r2_hidden(X5,X1)\|~r2_hidden(X4,X1)\|~m1_subset_1(X5,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X4,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))), inference(evalgc,[status(thm)],[c_0_45])). cnf(c_0_52, plain, (~r2_hidden(X1,X2)\|~r2_hidden(X1,X3)\|~r1_xboole_0(X2,X3)), inference(split_conjunct,[status(thm)],[c_0_46])). fof(c_0_53, negated_conjecture, (m2_finseq_1(esk1_0,u1_struct_0(k15_euclid(np__2)))&(m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))&(m1_subset_1(esk3_0,u1_struct_0(k15_euclid(np__2)))&((v4_topreal1(esk1_0)&(v4_pre_topc(k9_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,esk1_0),esk2_0),k15_euclid(np__2))&(r2_hidden(esk3_0,k3_topreal1(np__2,esk1_0))&r2_hidden(esk3_0,esk2_0))))&~r1_jordan5c(k3_topreal1(np__2,esk1_0),k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,np__1),k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,k3_finseq_1(esk1_0)),k1_jordan5c(k3_topreal1(np__2,esk1_0),esk2_0,k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,np__1),k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,k3_finseq_1(esk1_0))),esk3_0))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_47])])])). cnf(c_0_54, plain, (r1_xxreal_0(X1,esk9_5(X2,X3,X4,X5,X6))\|r1_xboole_0(X2,X7)\|r1_jordan5c(X2,X3,X4,X5,X6)\|k1_funct_1(esk7_5(X2,X3,X4,X5,X6),np__1)!=X8\|k1_funct_1(esk7_5(X2,X3,X4,X5,X6),k6_numbers)!=X9\|k1_funct_1(esk7_5(X2,X3,X4,X5,X6),X1)!=X10\|X10!=k1_jordan5c(X2,X7,X9,X8)\|~r1_xxreal_0(X1,np__1)\|~r1_xxreal_0(k6_numbers,esk9_5(X2,X3,X4,X5,X6))\|~r1_xxreal_0(k6_numbers,X1)\|~r1_topreal1(k15_euclid(np__2),X9,X8,X2)\|~r2_hidden(X6,X7)\|~r2_hidden(X6,X2)\|~r2_hidden(X5,X2)\|~v4_pre_topc(k9_subset_1(u1_struct_0(k15_euclid(np__2)),X2,X7),k15_euclid(np__2))\|~m1_subset_1(X7,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(X10,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X8,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X9,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X4,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(esk9_5(X2,X3,X4,X5,X6),k1_numbers)\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_48, c_0_49])])). cnf(c_0_55, plain, (r1_jordan5c(X1,X2,X3,X4,X5)\|m1_subset_1(esk9_5(X1,X2,X3,X4,X5),k1_numbers)\|~r2_hidden(X5,X1)\|~r2_hidden(X4,X1)\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_50, c_0_29]), c_0_29])). cnf(c_0_56, plain, (r1_xxreal_0(k6_numbers,esk9_5(X1,X2,X3,X4,X5))\|r1_jordan5c(X1,X2,X3,X4,X5)\|~r2_hidden(X5,X1)\|~r2_hidden(X4,X1)\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_51, c_0_29]), c_0_29])). cnf(c_0_57, plain, (~r2_hidden(X1,X3)\|~r2_hidden(X1,X2)\|~r1_xboole_0(X2,X3)), inference(evalgc,[status(thm)],[c_0_52])). cnf(c_0_58, negated_conjecture, (v4_pre_topc(k9_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,esk1_0),esk2_0),k15_euclid(np__2))), inference(split_conjunct,[status(thm)],[c_0_53])). cnf(c_0_59, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))), inference(split_conjunct,[status(thm)],[c_0_53])). cnf(c_0_60, plain, (k1_funct_1(esk7_5(X1,X2,X3,X4,X5),np__1)=X3\|r1_jordan5c(X1,X2,X3,X4,X5)\|~r2_hidden(X5,X1)\|~r2_hidden(X4,X1)\|~m1_subset_1(X5,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X4,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_61, plain, (r1_xxreal_0(X1,esk9_5(X2,X3,X4,X5,X6))\|r1_jordan5c(X2,X3,X4,X5,X6)\|k1_funct_1(esk7_5(X2,X3,X4,X5,X6),np__1)!=X7\|k1_funct_1(esk7_5(X2,X3,X4,X5,X6),k6_numbers)!=X8\|k1_funct_1(esk7_5(X2,X3,X4,X5,X6),X1)!=X9\|X9!=k1_jordan5c(X2,X10,X8,X7)\|~r1_xxreal_0(X1,np__1)\|~r1_xxreal_0(k6_numbers,X1)\|~r1_topreal1(k15_euclid(np__2),X8,X7,X2)\|~r2_hidden(X6,X10)\|~r2_hidden(X6,X2)\|~r2_hidden(X5,X2)\|~v4_pre_topc(k9_subset_1(u1_struct_0(k15_euclid(np__2)),X2,X10),k15_euclid(np__2))\|~m1_subset_1(X10,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(X9,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X7,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X8,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X4,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X1,k1_numbers)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_54, c_0_55]), c_0_56]), c_0_57])). cnf(c_0_62, negated_conjecture, (v4_pre_topc(k9_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,esk1_0),esk2_0),k15_euclid(np__2))), inference(evalgc,[status(thm)],[c_0_58])). cnf(c_0_63, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))), inference(evalgc,[status(thm)],[c_0_59])). cnf(c_0_64, plain, (k1_funct_1(esk7_5(X1,X2,X3,X4,X5),np__1)=X3\|r1_jordan5c(X1,X2,X3,X4,X5)\|~r2_hidden(X5,X1)\|~r2_hidden(X4,X1)\|~m1_subset_1(X5,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X4,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))), inference(evalgc,[status(thm)],[c_0_60])). cnf(c_0_65, plain, (k1_funct_1(esk7_5(X1,X2,X3,X4,X5),k6_numbers)=X2\|r1_jordan5c(X1,X2,X3,X4,X5)\|~r2_hidden(X5,X1)\|~r2_hidden(X4,X1)\|~m1_subset_1(X5,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X4,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_66, negated_conjecture, (r1_xxreal_0(X1,esk9_5(k3_topreal1(np__2,esk1_0),X2,X3,X4,X5))\|r1_jordan5c(k3_topreal1(np__2,esk1_0),X2,X3,X4,X5)\|k1_funct_1(esk7_5(k3_topreal1(np__2,esk1_0),X2,X3,X4,X5),np__1)!=X6\|k1_funct_1(esk7_5(k3_topreal1(np__2,esk1_0),X2,X3,X4,X5),k6_numbers)!=X7\|k1_funct_1(esk7_5(k3_topreal1(np__2,esk1_0),X2,X3,X4,X5),X1)!=X8\|X8!=k1_jordan5c(k3_topreal1(np__2,esk1_0),esk2_0,X7,X6)\|~r1_xxreal_0(X1,np__1)\|~r1_xxreal_0(k6_numbers,X1)\|~r1_topreal1(k15_euclid(np__2),X7,X6,k3_topreal1(np__2,esk1_0))\|~r2_hidden(X5,esk2_0)\|~r2_hidden(X5,k3_topreal1(np__2,esk1_0))\|~r2_hidden(X4,k3_topreal1(np__2,esk1_0))\|~m1_subset_1(k3_topreal1(np__2,esk1_0),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(X8,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X6,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X7,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61, c_0_62]), c_0_63])])])). cnf(c_0_67, plain, (k1_funct_1(esk7_5(X1,X2,X3,X4,X5),np__1)=X3\|r1_jordan5c(X1,X2,X3,X4,X5)\|~r2_hidden(X5,X1)\|~r2_hidden(X4,X1)\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_64, c_0_29]), c_0_29])). cnf(c_0_68, plain, (k1_funct_1(esk7_5(X1,X2,X3,X4,X5),k6_numbers)=X2\|r1_jordan5c(X1,X2,X3,X4,X5)\|~r2_hidden(X5,X1)\|~r2_hidden(X4,X1)\|~m1_subset_1(X5,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X4,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))), inference(evalgc,[status(thm)],[c_0_65])). cnf(c_0_69, plain, (k1_funct_1(esk7_5(X1,X2,X3,X4,X5),esk8_5(X1,X2,X3,X4,X5))=X4\|r1_jordan5c(X1,X2,X3,X4,X5)\|~r2_hidden(X5,X1)\|~r2_hidden(X4,X1)\|~m1_subset_1(X5,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X4,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))), inference(split_conjunct,[status(thm)],[c_0_22])). fof(c_0_70, plain, ![X44, X45]:((~m1_subset_1(X44,k1_zfmisc_1(X45))\|r1_tarski(X44,X45))&(~r1_tarski(X44,X45)\|m1_subset_1(X44,k1_zfmisc_1(X45)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])])). fof(c_0_71, plain, ![X46, X47]:r1_tarski(k3_xboole_0(X46,X47),X46), inference(variable_rename,[status(thm)],[t17_xboole_1])). cnf(c_0_72, negated_conjecture, (r1_xxreal_0(X1,esk9_5(k3_topreal1(np__2,esk1_0),X2,X3,X4,X5))\|r1_jordan5c(k3_topreal1(np__2,esk1_0),X2,X3,X4,X5)\|k1_funct_1(esk7_5(k3_topreal1(np__2,esk1_0),X2,X3,X4,X5),k6_numbers)!=X6\|k1_funct_1(esk7_5(k3_topreal1(np__2,esk1_0),X2,X3,X4,X5),X1)!=X7\|X7!=k1_jordan5c(k3_topreal1(np__2,esk1_0),esk2_0,X6,X3)\|~r1_xxreal_0(X1,np__1)\|~r1_xxreal_0(k6_numbers,X1)\|~r1_topreal1(k15_euclid(np__2),X6,X3,k3_topreal1(np__2,esk1_0))\|~r2_hidden(X5,k3_topreal1(np__2,esk1_0))\|~r2_hidden(X4,k3_topreal1(np__2,esk1_0))\|~r2_hidden(X5,esk2_0)\|~m1_subset_1(k3_topreal1(np__2,esk1_0),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(X7,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X6,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_66, c_0_67])])])). cnf(c_0_73, plain, (k1_funct_1(esk7_5(X1,X2,X3,X4,X5),k6_numbers)=X2\|r1_jordan5c(X1,X2,X3,X4,X5)\|~r2_hidden(X5,X1)\|~r2_hidden(X4,X1)\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_68, c_0_29]), c_0_29])). cnf(c_0_74, plain, (k1_funct_1(esk7_5(X1,X2,X3,X4,X5),esk8_5(X1,X2,X3,X4,X5))=X4\|r1_jordan5c(X1,X2,X3,X4,X5)\|~r2_hidden(X5,X1)\|~r2_hidden(X4,X1)\|~m1_subset_1(X5,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X4,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))), inference(evalgc,[status(thm)],[c_0_69])). cnf(c_0_75, plain, (m1_subset_1(esk8_5(X1,X2,X3,X4,X5),k1_numbers)\|r1_jordan5c(X1,X2,X3,X4,X5)\|~r2_hidden(X5,X1)\|~r2_hidden(X4,X1)\|~m1_subset_1(X5,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X4,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_76, plain, (r1_xxreal_0(k6_numbers,esk8_5(X1,X2,X3,X4,X5))\|r1_jordan5c(X1,X2,X3,X4,X5)\|~r2_hidden(X5,X1)\|~r2_hidden(X4,X1)\|~m1_subset_1(X5,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X4,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_77, plain, (r1_xxreal_0(esk8_5(X1,X2,X3,X4,X5),np__1)\|r1_jordan5c(X1,X2,X3,X4,X5)\|~r2_hidden(X5,X1)\|~r2_hidden(X4,X1)\|~m1_subset_1(X5,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X4,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_78, plain, (r1_jordan5c(X1,X2,X3,X4,X5)\|~r1_xxreal_0(esk8_5(X1,X2,X3,X4,X5),esk9_5(X1,X2,X3,X4,X5))\|~r2_hidden(X5,X1)\|~r2_hidden(X4,X1)\|~m1_subset_1(X5,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X4,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_79, plain, (m1_subset_1(X1,k1_zfmisc_1(X2))\|~r1_tarski(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_70])). cnf(c_0_80, plain, (r1_tarski(k3_xboole_0(X1,X2),X1)), inference(split_conjunct,[status(thm)],[c_0_71])). fof(c_0_81, plain, ![X50, X51, X52]:(~m1_subset_1(X52,k1_zfmisc_1(X50))\|k9_subset_1(X50,X51,X52)=k3_xboole_0(X51,X52)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k9_subset_1])])). cnf(c_0_82, plain, (r2_hidden(X1,k9_subset_1(u1_struct_0(k15_euclid(np__2)),X2,X3))\|r1_xboole_0(X2,X3)\|X1!=k1_jordan5c(X2,X3,X4,X5)\|~m1_subset_1(X1,u1_struct_0(k15_euclid(np__2)))\|~v4_pre_topc(k9_subset_1(u1_struct_0(k15_euclid(np__2)),X2,X3),k15_euclid(np__2))\|~r1_topreal1(k15_euclid(np__2),X4,X5,X2)\|~m1_subset_1(X5,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X4,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))), inference(split_conjunct,[status(thm)],[c_0_24])). fof(c_0_83, plain, ![X43]:(~m2_finseq_1(X43,u1_struct_0(k15_euclid(np__2)))\|(~v4_topreal1(X43)\|r1_topreal1(k15_euclid(np__2),k7_partfun1(u1_struct_0(k15_euclid(np__2)),X43,np__1),k7_partfun1(u1_struct_0(k15_euclid(np__2)),X43,k3_finseq_1(X43)),k3_topreal1(np__2,X43)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t25_topreal1])])). cnf(c_0_84, negated_conjecture, (r1_xxreal_0(X1,esk9_5(k3_topreal1(np__2,esk1_0),X2,X3,X4,X5))\|r1_jordan5c(k3_topreal1(np__2,esk1_0),X2,X3,X4,X5)\|k1_funct_1(esk7_5(k3_topreal1(np__2,esk1_0),X2,X3,X4,X5),X1)!=X6\|X6!=k1_jordan5c(k3_topreal1(np__2,esk1_0),esk2_0,X2,X3)\|~r1_xxreal_0(X1,np__1)\|~r1_xxreal_0(k6_numbers,X1)\|~r1_topreal1(k15_euclid(np__2),X2,X3,k3_topreal1(np__2,esk1_0))\|~r2_hidden(X5,k3_topreal1(np__2,esk1_0))\|~r2_hidden(X4,k3_topreal1(np__2,esk1_0))\|~r2_hidden(X5,esk2_0)\|~m1_subset_1(k3_topreal1(np__2,esk1_0),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(X6,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_72, c_0_73])])])). cnf(c_0_85, plain, (k1_funct_1(esk7_5(X1,X2,X3,X4,X5),esk8_5(X1,X2,X3,X4,X5))=X4\|r1_jordan5c(X1,X2,X3,X4,X5)\|~r2_hidden(X5,X1)\|~r2_hidden(X4,X1)\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_74, c_0_29]), c_0_29])). cnf(c_0_86, plain, (r1_jordan5c(X1,X2,X3,X4,X5)\|m1_subset_1(esk8_5(X1,X2,X3,X4,X5),k1_numbers)\|~r2_hidden(X5,X1)\|~r2_hidden(X4,X1)\|~m1_subset_1(X5,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X4,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))), inference(evalgc,[status(thm)],[c_0_75])). cnf(c_0_87, plain, (r1_jordan5c(X1,X2,X3,X4,X5)\|r1_xxreal_0(k6_numbers,esk8_5(X1,X2,X3,X4,X5))\|~r2_hidden(X5,X1)\|~r2_hidden(X4,X1)\|~m1_subset_1(X5,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X4,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))), inference(evalgc,[status(thm)],[c_0_76])). cnf(c_0_88, plain, (r1_jordan5c(X1,X2,X3,X4,X5)\|r1_xxreal_0(esk8_5(X1,X2,X3,X4,X5),np__1)\|~r2_hidden(X5,X1)\|~r2_hidden(X4,X1)\|~m1_subset_1(X5,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X4,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))), inference(evalgc,[status(thm)],[c_0_77])). cnf(c_0_89, plain, (r1_jordan5c(X1,X2,X3,X4,X5)\|~r2_hidden(X5,X1)\|~r2_hidden(X4,X1)\|~m1_subset_1(X5,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X4,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~r1_xxreal_0(esk8_5(X1,X2,X3,X4,X5),esk9_5(X1,X2,X3,X4,X5))), inference(evalgc,[status(thm)],[c_0_78])). cnf(c_0_90, plain, (m1_subset_1(X1,k1_zfmisc_1(X2))\|~r1_tarski(X1,X2)), inference(evalgc,[status(thm)],[c_0_79])). cnf(c_0_91, plain, (r1_tarski(k3_xboole_0(X1,X2),X1)), inference(evalgc,[status(thm)],[c_0_80])). cnf(c_0_92, plain, (k9_subset_1(X2,X3,X1)=k3_xboole_0(X3,X1)\|~m1_subset_1(X1,k1_zfmisc_1(X2))), inference(split_conjunct,[status(thm)],[c_0_81])). cnf(c_0_93, plain, (r1_xboole_0(X2,X3)\|r2_hidden(X1,k9_subset_1(u1_struct_0(k15_euclid(np__2)),X2,X3))\|X1!=k1_jordan5c(X2,X3,X4,X5)\|~m1_subset_1(X5,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X4,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X1,u1_struct_0(k15_euclid(np__2)))\|~r1_topreal1(k15_euclid(np__2),X4,X5,X2)\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~v4_pre_topc(k9_subset_1(u1_struct_0(k15_euclid(np__2)),X2,X3),k15_euclid(np__2))), inference(evalgc,[status(thm)],[c_0_82])). cnf(c_0_94, plain, (r1_topreal1(k15_euclid(np__2),k7_partfun1(u1_struct_0(k15_euclid(np__2)),X1,np__1),k7_partfun1(u1_struct_0(k15_euclid(np__2)),X1,k3_finseq_1(X1)),k3_topreal1(np__2,X1))\|~m2_finseq_1(X1,u1_struct_0(k15_euclid(np__2)))\|~v4_topreal1(X1)), inference(split_conjunct,[status(thm)],[c_0_83])). cnf(c_0_95, negated_conjecture, (v4_topreal1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_53])). cnf(c_0_96, negated_conjecture, (m2_finseq_1(esk1_0,u1_struct_0(k15_euclid(np__2)))), inference(split_conjunct,[status(thm)],[c_0_53])). cnf(c_0_97, negated_conjecture, (r1_xxreal_0(esk8_5(k3_topreal1(np__2,esk1_0),X1,X2,X3,X4),esk9_5(k3_topreal1(np__2,esk1_0),X1,X2,X3,X4))\|r1_jordan5c(k3_topreal1(np__2,esk1_0),X1,X2,X3,X4)\|X3!=k1_jordan5c(k3_topreal1(np__2,esk1_0),esk2_0,X1,X2)\|~r1_xxreal_0(esk8_5(k3_topreal1(np__2,esk1_0),X1,X2,X3,X4),np__1)\|~r1_xxreal_0(k6_numbers,esk8_5(k3_topreal1(np__2,esk1_0),X1,X2,X3,X4))\|~r1_topreal1(k15_euclid(np__2),X1,X2,k3_topreal1(np__2,esk1_0))\|~r2_hidden(X4,k3_topreal1(np__2,esk1_0))\|~r2_hidden(X3,k3_topreal1(np__2,esk1_0))\|~r2_hidden(X4,esk2_0)\|~m1_subset_1(k3_topreal1(np__2,esk1_0),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X1,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(esk8_5(k3_topreal1(np__2,esk1_0),X1,X2,X3,X4),k1_numbers)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_84, c_0_85])])])). cnf(c_0_98, plain, (r1_jordan5c(X1,X2,X3,X4,X5)\|m1_subset_1(esk8_5(X1,X2,X3,X4,X5),k1_numbers)\|~r2_hidden(X5,X1)\|~r2_hidden(X4,X1)\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_86, c_0_29]), c_0_29])). cnf(c_0_99, plain, (r1_xxreal_0(k6_numbers,esk8_5(X1,X2,X3,X4,X5))\|r1_jordan5c(X1,X2,X3,X4,X5)\|~r2_hidden(X5,X1)\|~r2_hidden(X4,X1)\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_87, c_0_29]), c_0_29])). cnf(c_0_100, plain, (r1_xxreal_0(esk8_5(X1,X2,X3,X4,X5),np__1)\|r1_jordan5c(X1,X2,X3,X4,X5)\|~r2_hidden(X5,X1)\|~r2_hidden(X4,X1)\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_88, c_0_29]), c_0_29])). cnf(c_0_101, plain, (r1_jordan5c(X1,X2,X3,X4,X5)\|~r1_xxreal_0(esk8_5(X1,X2,X3,X4,X5),esk9_5(X1,X2,X3,X4,X5))\|~r2_hidden(X5,X1)\|~r2_hidden(X4,X1)\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_89, c_0_29]), c_0_29])). cnf(c_0_102, plain, (m1_subset_1(k3_xboole_0(X1,X2),k1_zfmisc_1(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_90, c_0_91])])). cnf(c_0_103, plain, (k9_subset_1(X2,X3,X1)=k3_xboole_0(X3,X1)\|~m1_subset_1(X1,k1_zfmisc_1(X2))), inference(evalgc,[status(thm)],[c_0_92])). cnf(c_0_104, negated_conjecture, (r1_xboole_0(k3_topreal1(np__2,esk1_0),esk2_0)\|r2_hidden(X1,k9_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,esk1_0),esk2_0))\|X1!=k1_jordan5c(k3_topreal1(np__2,esk1_0),esk2_0,X2,X3)\|~r1_topreal1(k15_euclid(np__2),X2,X3,k3_topreal1(np__2,esk1_0))\|~m1_subset_1(k3_topreal1(np__2,esk1_0),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X1,u1_struct_0(k15_euclid(np__2)))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93, c_0_62]), c_0_63])])])). cnf(c_0_105, plain, (r1_topreal1(k15_euclid(np__2),k7_partfun1(u1_struct_0(k15_euclid(np__2)),X1,np__1),k7_partfun1(u1_struct_0(k15_euclid(np__2)),X1,k3_finseq_1(X1)),k3_topreal1(np__2,X1))\|~v4_topreal1(X1)\|~m2_finseq_1(X1,u1_struct_0(k15_euclid(np__2)))), inference(evalgc,[status(thm)],[c_0_94])). cnf(c_0_106, negated_conjecture, (v4_topreal1(esk1_0)), inference(evalgc,[status(thm)],[c_0_95])). cnf(c_0_107, negated_conjecture, (m2_finseq_1(esk1_0,u1_struct_0(k15_euclid(np__2)))), inference(evalgc,[status(thm)],[c_0_96])). fof(c_0_108, plain, ![X48, X49]:(~r2_hidden(X48,X49)\|~v1_xboole_0(X49)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])])). cnf(c_0_109, negated_conjecture, (r1_jordan5c(k3_topreal1(np__2,esk1_0),X1,X2,X3,X4)\|X3!=k1_jordan5c(k3_topreal1(np__2,esk1_0),esk2_0,X1,X2)\|~r1_topreal1(k15_euclid(np__2),X1,X2,k3_topreal1(np__2,esk1_0))\|~r2_hidden(X4,k3_topreal1(np__2,esk1_0))\|~r2_hidden(X3,k3_topreal1(np__2,esk1_0))\|~r2_hidden(X4,esk2_0)\|~m1_subset_1(k3_topreal1(np__2,esk1_0),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X1,u1_struct_0(k15_euclid(np__2)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_97, c_0_29]), c_0_98]), c_0_99]), c_0_100]), c_0_101])). fof(c_0_110, plain, ![X53, X54]:(~m1_subset_1(X53,X54)\|(v1_xboole_0(X54)\|r2_hidden(X53,X54))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])])). cnf(c_0_111, plain, (m1_subset_1(X1,X2)\|~r2_hidden(X1,k3_xboole_0(X2,X3))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_29, c_0_102])])). cnf(c_0_112, negated_conjecture, (k3_xboole_0(X1,esk2_0)=k9_subset_1(u1_struct_0(k15_euclid(np__2)),X1,esk2_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_103, c_0_63])])). cnf(c_0_113, negated_conjecture, (r1_xboole_0(k3_topreal1(np__2,esk1_0),esk2_0)\|r2_hidden(X1,k9_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,esk1_0),esk2_0))\|X1!=k1_jordan5c(k3_topreal1(np__2,esk1_0),esk2_0,k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,np__1),k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,k3_finseq_1(esk1_0)))\|~m1_subset_1(k3_topreal1(np__2,esk1_0),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,k3_finseq_1(esk1_0)),u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,np__1),u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X1,u1_struct_0(k15_euclid(np__2)))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104, c_0_105]), c_0_106]), c_0_107])])])). cnf(c_0_114, plain, (~r2_hidden(X1,X2)\|~v1_xboole_0(X2)), inference(split_conjunct,[status(thm)],[c_0_108])). cnf(c_0_115, negated_conjecture, (r2_hidden(esk3_0,k3_topreal1(np__2,esk1_0))), inference(split_conjunct,[status(thm)],[c_0_53])). cnf(c_0_116, negated_conjecture, (~r1_jordan5c(k3_topreal1(np__2,esk1_0),k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,np__1),k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,k3_finseq_1(esk1_0)),k1_jordan5c(k3_topreal1(np__2,esk1_0),esk2_0,k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,np__1),k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,k3_finseq_1(esk1_0))),esk3_0)), inference(split_conjunct,[status(thm)],[c_0_53])). cnf(c_0_117, negated_conjecture, (r1_jordan5c(k3_topreal1(np__2,esk1_0),k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,np__1),k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,k3_finseq_1(esk1_0)),X1,X2)\|X1!=k1_jordan5c(k3_topreal1(np__2,esk1_0),esk2_0,k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,np__1),k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,k3_finseq_1(esk1_0)))\|~r2_hidden(X2,k3_topreal1(np__2,esk1_0))\|~r2_hidden(X1,k3_topreal1(np__2,esk1_0))\|~r2_hidden(X2,esk2_0)\|~m1_subset_1(k3_topreal1(np__2,esk1_0),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,k3_finseq_1(esk1_0)),u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,np__1),u1_struct_0(k15_euclid(np__2)))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109, c_0_105]), c_0_106]), c_0_107])])])). cnf(c_0_118, negated_conjecture, (r2_hidden(esk3_0,esk2_0)), inference(split_conjunct,[status(thm)],[c_0_53])). cnf(c_0_119, plain, (v1_xboole_0(X2)\|r2_hidden(X1,X2)\|~m1_subset_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_110])). cnf(c_0_120, negated_conjecture, (m1_subset_1(X1,X2)\|~r2_hidden(X1,k9_subset_1(u1_struct_0(k15_euclid(np__2)),X2,esk2_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_111, c_0_112])])). cnf(c_0_121, negated_conjecture, (r1_xboole_0(k3_topreal1(np__2,esk1_0),esk2_0)\|r2_hidden(k1_jordan5c(k3_topreal1(np__2,esk1_0),esk2_0,k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,np__1),k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,k3_finseq_1(esk1_0))),k9_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,esk1_0),esk2_0))\|~m1_subset_1(k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,k3_finseq_1(esk1_0)),u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,np__1),u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(k3_topreal1(np__2,esk1_0),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(k1_jordan5c(k3_topreal1(np__2,esk1_0),esk2_0,k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,np__1),k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,k3_finseq_1(esk1_0))),u1_struct_0(k15_euclid(np__2)))), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_113])])). cnf(c_0_122, plain, (~v1_xboole_0(X2)\|~r2_hidden(X1,X2)), inference(evalgc,[status(thm)],[c_0_114])). cnf(c_0_123, negated_conjecture, (r2_hidden(esk3_0,k3_topreal1(np__2,esk1_0))), inference(evalgc,[status(thm)],[c_0_115])). fof(c_0_124, plain, ![X64, X65, X66]:(~m1_subset_1(X66,k1_zfmisc_1(k2_zfmisc_1(X64,X65)))\|v1_relat_1(X66)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relset_1])])). fof(c_0_125, plain, ![X55, X56]:((v1_funct_1(X56)\|~m2_finseq_1(X56,X55))&((v1_finseq_1(X56)\|~m2_finseq_1(X56,X55))&(m1_subset_1(X56,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,X55)))\|~m2_finseq_1(X56,X55)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m2_finseq_1])])])). cnf(c_0_126, negated_conjecture, (~r1_jordan5c(k3_topreal1(np__2,esk1_0),k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,np__1),k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,k3_finseq_1(esk1_0)),k1_jordan5c(k3_topreal1(np__2,esk1_0),esk2_0,k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,np__1),k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,k3_finseq_1(esk1_0))),esk3_0)), inference(evalgc,[status(thm)],[c_0_116])). cnf(c_0_127, negated_conjecture, (r1_jordan5c(k3_topreal1(np__2,esk1_0),k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,np__1),k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,k3_finseq_1(esk1_0)),k1_jordan5c(k3_topreal1(np__2,esk1_0),esk2_0,k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,np__1),k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,k3_finseq_1(esk1_0))),X1)\|~r2_hidden(X1,k3_topreal1(np__2,esk1_0))\|~r2_hidden(k1_jordan5c(k3_topreal1(np__2,esk1_0),esk2_0,k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,np__1),k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,k3_finseq_1(esk1_0))),k3_topreal1(np__2,esk1_0))\|~r2_hidden(X1,esk2_0)\|~m1_subset_1(k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,k3_finseq_1(esk1_0)),u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,np__1),u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(k3_topreal1(np__2,esk1_0),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_117])])). cnf(c_0_128, negated_conjecture, (r2_hidden(esk3_0,esk2_0)), inference(evalgc,[status(thm)],[c_0_118])). cnf(c_0_129, plain, (v1_xboole_0(X2)\|r2_hidden(X1,X2)\|~m1_subset_1(X1,X2)), inference(evalgc,[status(thm)],[c_0_119])). cnf(c_0_130, negated_conjecture, (m1_subset_1(k1_jordan5c(k3_topreal1(np__2,esk1_0),esk2_0,k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,np__1),k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,k3_finseq_1(esk1_0))),k3_topreal1(np__2,esk1_0))\|r1_xboole_0(k3_topreal1(np__2,esk1_0),esk2_0)\|~m1_subset_1(k1_jordan5c(k3_topreal1(np__2,esk1_0),esk2_0,k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,np__1),k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,k3_finseq_1(esk1_0))),u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,k3_finseq_1(esk1_0)),u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,np__1),u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(k3_topreal1(np__2,esk1_0),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_120, c_0_121])])). cnf(c_0_131, negated_conjecture, (~v1_xboole_0(k3_topreal1(np__2,esk1_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_122, c_0_123])])). fof(c_0_132, plain, ![X57, X58, X59, X60]:(~m1_subset_1(X57,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|(~m1_subset_1(X58,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|(~m1_subset_1(X59,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X60,u1_struct_0(k15_euclid(np__2)))))\|m1_subset_1(k1_jordan5c(X57,X58,X59,X60),u1_struct_0(k15_euclid(np__2)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_jordan5c])])). cnf(c_0_133, plain, (v1_relat_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_124])). cnf(c_0_134, plain, (m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,X2)))\|~m2_finseq_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_125])). cnf(c_0_135, negated_conjecture, (~r2_hidden(k1_jordan5c(k3_topreal1(np__2,esk1_0),esk2_0,k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,np__1),k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,k3_finseq_1(esk1_0))),k3_topreal1(np__2,esk1_0))\|~m1_subset_1(k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,k3_finseq_1(esk1_0)),u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,np__1),u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(k3_topreal1(np__2,esk1_0),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126, c_0_127]), c_0_123]), c_0_128])])])). cnf(c_0_136, negated_conjecture, (r2_hidden(k1_jordan5c(k3_topreal1(np__2,esk1_0),esk2_0,k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,np__1),k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,k3_finseq_1(esk1_0))),k3_topreal1(np__2,esk1_0))\|r1_xboole_0(k3_topreal1(np__2,esk1_0),esk2_0)\|~m1_subset_1(k1_jordan5c(k3_topreal1(np__2,esk1_0),esk2_0,k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,np__1),k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,k3_finseq_1(esk1_0))),u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,k3_finseq_1(esk1_0)),u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,np__1),u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(k3_topreal1(np__2,esk1_0),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_129, c_0_130]), c_0_131])])). cnf(c_0_137, plain, (m1_subset_1(k1_jordan5c(X1,X2,X3,X4),u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X4,u1_struct_0(k15_euclid(np__2)))), inference(split_conjunct,[status(thm)],[c_0_132])). fof(c_0_138, plain, ![X67, X68, X69]:(~v1_relat_1(X68)\|(~v5_relat_1(X68,X67)\|~v1_funct_1(X68))\|m1_subset_1(k7_partfun1(X67,X68,X69),X67)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k7_partfun1])])). cnf(c_0_139, plain, (v1_relat_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(evalgc,[status(thm)],[c_0_133])). cnf(c_0_140, plain, (m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,X2)))\|~m2_finseq_1(X1,X2)), inference(evalgc,[status(thm)],[c_0_134])). cnf(c_0_141, plain, (v1_funct_1(X1)\|~m2_finseq_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_125])). cnf(c_0_142, negated_conjecture, (r1_xboole_0(k3_topreal1(np__2,esk1_0),esk2_0)\|~m1_subset_1(k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,k3_finseq_1(esk1_0)),u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,np__1),u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(k3_topreal1(np__2,esk1_0),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(k1_jordan5c(k3_topreal1(np__2,esk1_0),esk2_0,k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,np__1),k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,k3_finseq_1(esk1_0))),u1_struct_0(k15_euclid(np__2)))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_135, c_0_136])])). cnf(c_0_143, plain, (m1_subset_1(k1_jordan5c(X1,X2,X3,X4),u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X4,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X3,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))), inference(evalgc,[status(thm)],[c_0_137])). cnf(c_0_144, plain, (m1_subset_1(k7_partfun1(X2,X1,X3),X2)\|~v1_relat_1(X1)\|~v5_relat_1(X1,X2)\|~v1_funct_1(X1)), inference(split_conjunct,[status(thm)],[c_0_138])). cnf(c_0_145, plain, (v1_relat_1(X1)\|~m2_finseq_1(X1,X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_139, c_0_140])])). cnf(c_0_146, plain, (v1_funct_1(X1)\|~m2_finseq_1(X1,X2)), inference(evalgc,[status(thm)],[c_0_141])). fof(c_0_147, plain, ![X70, X71]:(~v6_membered(X70)\|(~m1_subset_1(X71,X70)\|v7_ordinal1(X71))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc17_membered])])])). cnf(c_0_148, plain, (v6_membered(k4_ordinal1)), inference(split_conjunct,[status(thm)],[fc6_membered])). cnf(c_0_149, plain, (k5_numbers=k4_ordinal1), inference(split_conjunct,[status(thm)],[redefinition_k5_numbers])). cnf(c_0_150, negated_conjecture, (r1_xboole_0(k3_topreal1(np__2,esk1_0),esk2_0)\|~m1_subset_1(k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,k3_finseq_1(esk1_0)),u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,np__1),u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(k3_topreal1(np__2,esk1_0),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142, c_0_143]), c_0_63])])])). cnf(c_0_151, plain, (m1_subset_1(k7_partfun1(X2,X1,X3),X2)\|~v1_funct_1(X1)\|~v1_relat_1(X1)\|~v5_relat_1(X1,X2)), inference(evalgc,[status(thm)],[c_0_144])). cnf(c_0_152, negated_conjecture, (v1_relat_1(esk1_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_145, c_0_107])])). cnf(c_0_153, negated_conjecture, (v1_funct_1(esk1_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_146, c_0_107])])). fof(c_0_154, plain, ![X72, X73]:(~v7_ordinal1(X72)\|~m1_finseq_1(X73,u1_struct_0(k15_euclid(X72)))\|m1_subset_1(k3_topreal1(X72,X73),k1_zfmisc_1(u1_struct_0(k15_euclid(X72))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k3_topreal1])])). cnf(c_0_155, plain, (v7_ordinal1(X2)\|~v6_membered(X1)\|~m1_subset_1(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_147])). cnf(c_0_156, plain, (m1_subset_1(np__2,k5_numbers)), inference(split_conjunct,[status(thm)],[spc2_numerals])). cnf(c_0_157, plain, (v6_membered(k4_ordinal1)), inference(evalgc,[status(thm)],[c_0_148])). cnf(c_0_158, plain, (k4_ordinal1=k5_numbers), inference(evalgc,[status(thm)],[c_0_149])). fof(c_0_159, plain, ![X61, X62, X63]:((v4_relat_1(X63,X61)\|~m1_subset_1(X63,k1_zfmisc_1(k2_zfmisc_1(X61,X62))))&(v5_relat_1(X63,X62)\|~m1_subset_1(X63,k1_zfmisc_1(k2_zfmisc_1(X61,X62))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_relset_1])])])). cnf(c_0_160, negated_conjecture, (r1_xboole_0(k3_topreal1(np__2,esk1_0),esk2_0)\|~m1_subset_1(k7_partfun1(u1_struct_0(k15_euclid(np__2)),esk1_0,np__1),u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(k3_topreal1(np__2,esk1_0),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))\|~v5_relat_1(esk1_0,u1_struct_0(k15_euclid(np__2)))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150, c_0_151]), c_0_152]), c_0_153])])])). cnf(c_0_161, plain, (m1_subset_1(k3_topreal1(X1,X2),k1_zfmisc_1(u1_struct_0(k15_euclid(X1))))\|~v7_ordinal1(X1)\|~m1_finseq_1(X2,u1_struct_0(k15_euclid(X1)))), inference(split_conjunct,[status(thm)],[c_0_154])). cnf(c_0_162, plain, (v7_ordinal1(X2)\|~v6_membered(X1)\|~m1_subset_1(X2,X1)), inference(evalgc,[status(thm)],[c_0_155])). cnf(c_0_163, plain, (m1_subset_1(np__2,k5_numbers)), inference(evalgc,[status(thm)],[c_0_156])). cnf(c_0_164, plain, (v6_membered(k5_numbers)), inference(rw,[status(thm)],[c_0_157, c_0_158])). cnf(c_0_165, plain, (v5_relat_1(X1,X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X3,X2)))), inference(split_conjunct,[status(thm)],[c_0_159])). cnf(c_0_166, negated_conjecture, (r1_xboole_0(k3_topreal1(np__2,esk1_0),esk2_0)\|~v5_relat_1(esk1_0,u1_struct_0(k15_euclid(np__2)))\|~m1_subset_1(k3_topreal1(np__2,esk1_0),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160, c_0_151]), c_0_152]), c_0_153])])])). cnf(c_0_167, plain, (m1_subset_1(k3_topreal1(X1,X2),k1_zfmisc_1(u1_struct_0(k15_euclid(X1))))\|~v7_ordinal1(X1)\|~m1_finseq_1(X2,u1_struct_0(k15_euclid(X1)))), inference(evalgc,[status(thm)],[c_0_161])). cnf(c_0_168, plain, (v7_ordinal1(np__2)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162, c_0_163]), c_0_164])])])). cnf(c_0_169, plain, (v5_relat_1(X1,X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X3,X2)))), inference(evalgc,[status(thm)],[c_0_165])). cnf(c_0_170, negated_conjecture, (r1_xboole_0(k3_topreal1(np__2,esk1_0),esk2_0)\|~v5_relat_1(esk1_0,u1_struct_0(k15_euclid(np__2)))\|~m1_finseq_1(esk1_0,u1_struct_0(k15_euclid(np__2)))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166, c_0_167]), c_0_168])])])). cnf(c_0_171, plain, (v5_relat_1(X1,X2)\|~m2_finseq_1(X1,X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_169, c_0_140])])). fof(c_0_172, plain, ![X74, X75]:((~m2_finseq_1(X75,X74)\|m1_finseq_1(X75,X74))&(~m1_finseq_1(X75,X74)\|m2_finseq_1(X75,X74))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_finseq_1])])). cnf(c_0_173, negated_conjecture, (r1_xboole_0(k3_topreal1(np__2,esk1_0),esk2_0)\|~m1_finseq_1(esk1_0,u1_struct_0(k15_euclid(np__2)))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170, c_0_171]), c_0_107])])])). cnf(c_0_174, plain, (m1_finseq_1(X1,X2)\|~m2_finseq_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_172])). cnf(c_0_175, negated_conjecture, (~r2_hidden(X1,esk2_0)\|~r2_hidden(X1,k3_topreal1(np__2,esk1_0))\|~m1_finseq_1(esk1_0,u1_struct_0(k15_euclid(np__2)))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_57, c_0_173])])). cnf(c_0_176, plain, (m1_finseq_1(X1,X2)\|~m2_finseq_1(X1,X2)), inference(evalgc,[status(thm)],[c_0_174])). cnf(c_0_177, negated_conjecture, (~r2_hidden(X1,k3_topreal1(np__2,esk1_0))\|~r2_hidden(X1,esk2_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_175, c_0_176]), c_0_107])])])). cnf(c_0_178, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177, c_0_123]), c_0_128])]), ['proof']). # SZS output end CNFRefutation	theorem Th15: for f being FinSequence of TOP-REAL 2, Q being Subset of TOP-REAL 2, q being Point of TOP-REAL 2 st f is being_S-Seq & L~f /\ Q is closed & q in L~f & q in Q holds LE First_Point(L~f,f/.1,f/.len f,Q), q, L~f, f /.1, f/.len f proof let f be FinSequence of TOP-REAL 2, Q be Subset of TOP-REAL 2, q be Point of TOP-REAL 2; assume that A1: f is being_S-Seq and A2: L~f /\ Q is closed and A3: q in L~f and A4: q in Q; set P = L~f; A5: L~f /\ Q c= L~f by XBOOLE_1:17; set q1 = First_Point(P,f/.1,f/.len f,Q); L~f meets Q & P is_an_arc_of f/.1,f/.len f by A1,A3,A4,TOPREAL1:25,XBOOLE_0:3 ; then q1 in L~f /\ Q & for g being Function of I[01], (TOP-REAL 2)\| P, s1, s2 being Real st g is being_homeomorphism & g.0=f/.1 & g.1=f/.len f & g.s1=q1 & 0 <=s1 & s1<=1 & g.s2=q & 0<=s2 & s2<=1 holds s1<=s2 by A2,A4,Def1; hence thesis by A3,A5,Def3; end;	Convert the following ATP output trace into a readable Mizar proof.
t44_lpspace2	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t39_lpspace2, axiom, ![X1]:(~(v1_xboole_0(X1))=>![X2]:((~(v1_xboole_0(X2))&(v1_prob_1(X2,X1)&(v4_prob_1(X2,X1)&m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X1))))))=>![X3]:((v1_funct_1(X3)&(v1_funct_2(X3,X2,k7_numbers)&(v10_valued_0(X3)&(v6_supinf_2(X3)&(v4_measure1(X3,X1,X2)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X2,k7_numbers))))))))=>![X4]:((v1_funct_1(X4)&m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers))))=>![X5]:((v1_funct_1(X5)&m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers))))=>![X6]:((v2_xxreal_0(X6)&m1_subset_1(X6,k1_numbers))=>(k5_lpspace2(X1,X2,X3,X5,X6)=k5_lpspace2(X1,X2,X3,X4,X6)=>(![X7]:(m2_subset_1(X7,k1_zfmisc_1(X1),X2)=>~((k1_funct_1(X3,k3_subset_1(X1,X7))=k6_numbers&(X7=k1_relset_1(X1,X4)&r1_mesfunc6(X1,X2,X4,X7)))))\|(k5_lpspace2(X1,X2,X3,X5,X6)=k1_xboole_0\|r1_lpspace1(X1,X2,X3,X5,X4)))))))))), file('/scratch/mptp/predsminms1/t44_lpspace2__0', t39_lpspace2)). fof(t44_lpspace2, conjecture, ![X1]:(~(v1_xboole_0(X1))=>![X2]:((~(v1_xboole_0(X2))&(v1_prob_1(X2,X1)&(v4_prob_1(X2,X1)&m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X1))))))=>![X3]:((v1_funct_1(X3)&(v1_funct_2(X3,X2,k7_numbers)&(v10_valued_0(X3)&(v6_supinf_2(X3)&(v4_measure1(X3,X1,X2)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X2,k7_numbers))))))))=>![X4]:((v1_funct_1(X4)&m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers))))=>![X5]:((v1_funct_1(X5)&m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers))))=>![X6]:((v1_funct_1(X6)&m1_subset_1(X6,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers))))=>![X7]:((v1_funct_1(X7)&m1_subset_1(X7,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers))))=>![X8]:((v2_xxreal_0(X8)&m1_subset_1(X8,k1_numbers))=>((k5_lpspace2(X1,X2,X3,X4,X8)=k5_lpspace2(X1,X2,X3,X5,X8)&k5_lpspace2(X1,X2,X3,X6,X8)=k5_lpspace2(X1,X2,X3,X7,X8))=>(![X9]:(m2_subset_1(X9,k1_zfmisc_1(X1),X2)=>~((k1_funct_1(X3,k3_subset_1(X1,X9))=k6_numbers&(X9=k1_relset_1(X1,X4)&r1_mesfunc6(X1,X2,X4,X9)))))\|(![X9]:(m2_subset_1(X9,k1_zfmisc_1(X1),X2)=>~((k1_funct_1(X3,k3_subset_1(X1,X9))=k6_numbers&(X9=k1_relset_1(X1,X5)&r1_mesfunc6(X1,X2,X5,X9)))))\|(![X9]:(m2_subset_1(X9,k1_zfmisc_1(X1),X2)=>~((k1_funct_1(X3,k3_subset_1(X1,X9))=k6_numbers&(X9=k1_relset_1(X1,X6)&r1_mesfunc6(X1,X2,X6,X9)))))\|(![X9]:(m2_subset_1(X9,k1_zfmisc_1(X1),X2)=>~((k1_funct_1(X3,k3_subset_1(X1,X9))=k6_numbers&(X9=k1_relset_1(X1,X7)&r1_mesfunc6(X1,X2,X7,X9)))))\|(v1_xboole_0(k5_lpspace2(X1,X2,X3,X4,X8))\|(v1_xboole_0(k5_lpspace2(X1,X2,X3,X6,X8))\|k5_lpspace2(X1,X2,X3,k3_valued_1(X1,k1_numbers,k1_numbers,X4,X6),X8)=k5_lpspace2(X1,X2,X3,k3_valued_1(X1,k1_numbers,k1_numbers,X5,X7),X8)))))))))))))))), file('/scratch/mptp/predsminms1/t44_lpspace2__0', t44_lpspace2)). fof(t41_lpspace2, axiom, ![X1]:(~(v1_xboole_0(X1))=>![X2]:((~(v1_xboole_0(X2))&(v1_prob_1(X2,X1)&(v4_prob_1(X2,X1)&m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X1))))))=>![X3]:((v1_funct_1(X3)&(v1_funct_2(X3,X2,k7_numbers)&(v10_valued_0(X3)&(v6_supinf_2(X3)&(v4_measure1(X3,X1,X2)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X2,k7_numbers))))))))=>![X4]:((v1_funct_1(X4)&m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers))))=>![X5]:((v1_funct_1(X5)&m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers))))=>![X6]:((v2_xxreal_0(X6)&m1_subset_1(X6,k1_numbers))=>(r1_lpspace1(X1,X2,X3,X4,X5)=>k5_lpspace2(X1,X2,X3,X4,X6)=k5_lpspace2(X1,X2,X3,X5,X6)))))))), file('/scratch/mptp/predsminms1/t44_lpspace2__0', t41_lpspace2)). fof(t31_lpspace1, axiom, ![X1]:(~(v1_xboole_0(X1))=>![X2]:((~(v1_xboole_0(X2))&(v1_prob_1(X2,X1)&(v4_prob_1(X2,X1)&m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X1))))))=>![X3]:((v1_funct_1(X3)&(v1_funct_2(X3,X2,k7_numbers)&(v10_valued_0(X3)&(v6_supinf_2(X3)&(v4_measure1(X3,X1,X2)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X2,k7_numbers))))))))=>![X4]:((v1_funct_1(X4)&m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers))))=>![X5]:((v1_funct_1(X5)&m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers))))=>![X6]:((v1_funct_1(X6)&m1_subset_1(X6,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers))))=>![X7]:((v1_funct_1(X7)&m1_subset_1(X7,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers))))=>((r1_lpspace1(X1,X2,X3,X4,X5)&r1_lpspace1(X1,X2,X3,X6,X7))=>r1_lpspace1(X1,X2,X3,k3_valued_1(X1,k1_numbers,k1_numbers,X4,X6),k3_valued_1(X1,k1_numbers,k1_numbers,X5,X7)))))))))), file('/scratch/mptp/predsminms1/t44_lpspace2__0', t31_lpspace1)). fof(redefinition_k6_numbers, axiom, k6_numbers=k1_xboole_0, file('/scratch/mptp/predsminms1/t44_lpspace2__0', redefinition_k6_numbers)). fof(dt_k3_valued_1, axiom, ![X1, X2, X3, X4, X5]:((v3_membered(X2)&(v3_membered(X3)&((v1_funct_1(X4)&m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2))))&(v1_funct_1(X5)&m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))))))=>(v1_funct_1(k3_valued_1(X1,X2,X3,X4,X5))&m1_subset_1(k3_valued_1(X1,X2,X3,X4,X5),k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers))))), file('/scratch/mptp/predsminms1/t44_lpspace2__0', dt_k3_valued_1)). fof(fc3_membered, axiom, v3_membered(k1_numbers), file('/scratch/mptp/predsminms1/t44_lpspace2__0', fc3_membered)). fof(d2_xboole_0, axiom, k1_xboole_0=o_0_0_xboole_0, file('/scratch/mptp/predsminms1/t44_lpspace2__0', d2_xboole_0)). fof(dt_o_0_0_xboole_0, axiom, v1_xboole_0(o_0_0_xboole_0), file('/scratch/mptp/predsminms1/t44_lpspace2__0', dt_o_0_0_xboole_0)). fof(c_0_9, plain, ![X22, X23, X24, X25, X26, X27, X28]:(v1_xboole_0(X22)\|(v1_xboole_0(X23)\|(~v1_prob_1(X23,X22)\|(~v4_prob_1(X23,X22)\|~m1_subset_1(X23,k1_zfmisc_1(k1_zfmisc_1(X22)))))\|(~v1_funct_1(X24)\|(~v1_funct_2(X24,X23,k7_numbers)\|(~v10_valued_0(X24)\|(~v6_supinf_2(X24)\|(~v4_measure1(X24,X22,X23)\|~m1_subset_1(X24,k1_zfmisc_1(k2_zfmisc_1(X23,k7_numbers)))))))\|(~v1_funct_1(X25)\|~m1_subset_1(X25,k1_zfmisc_1(k2_zfmisc_1(X22,k1_numbers)))\|(~v1_funct_1(X26)\|~m1_subset_1(X26,k1_zfmisc_1(k2_zfmisc_1(X22,k1_numbers)))\|(~v2_xxreal_0(X27)\|~m1_subset_1(X27,k1_numbers)\|(k5_lpspace2(X22,X23,X24,X26,X27)!=k5_lpspace2(X22,X23,X24,X25,X27)\|(~m2_subset_1(X28,k1_zfmisc_1(X22),X23)\|(k1_funct_1(X24,k3_subset_1(X22,X28))!=k6_numbers\|(X28!=k1_relset_1(X22,X25)\|~r1_mesfunc6(X22,X23,X25,X28)))\|(k5_lpspace2(X22,X23,X24,X26,X27)=k1_xboole_0\|r1_lpspace1(X22,X23,X24,X26,X25)))))))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t39_lpspace2])])])])). fof(c_0_10, negated_conjecture, ~(![X1]:(~(v1_xboole_0(X1))=>![X2]:((~(v1_xboole_0(X2))&(v1_prob_1(X2,X1)&(v4_prob_1(X2,X1)&m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X1))))))=>![X3]:((v1_funct_1(X3)&(v1_funct_2(X3,X2,k7_numbers)&(v10_valued_0(X3)&(v6_supinf_2(X3)&(v4_measure1(X3,X1,X2)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X2,k7_numbers))))))))=>![X4]:((v1_funct_1(X4)&m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers))))=>![X5]:((v1_funct_1(X5)&m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers))))=>![X6]:((v1_funct_1(X6)&m1_subset_1(X6,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers))))=>![X7]:((v1_funct_1(X7)&m1_subset_1(X7,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers))))=>![X8]:((v2_xxreal_0(X8)&m1_subset_1(X8,k1_numbers))=>((k5_lpspace2(X1,X2,X3,X4,X8)=k5_lpspace2(X1,X2,X3,X5,X8)&k5_lpspace2(X1,X2,X3,X6,X8)=k5_lpspace2(X1,X2,X3,X7,X8))=>(![X9]:(m2_subset_1(X9,k1_zfmisc_1(X1),X2)=>~((k1_funct_1(X3,k3_subset_1(X1,X9))=k6_numbers&(X9=k1_relset_1(X1,X4)&r1_mesfunc6(X1,X2,X4,X9)))))\|(![X9]:(m2_subset_1(X9,k1_zfmisc_1(X1),X2)=>~((k1_funct_1(X3,k3_subset_1(X1,X9))=k6_numbers&(X9=k1_relset_1(X1,X5)&r1_mesfunc6(X1,X2,X5,X9)))))\|(![X9]:(m2_subset_1(X9,k1_zfmisc_1(X1),X2)=>~((k1_funct_1(X3,k3_subset_1(X1,X9))=k6_numbers&(X9=k1_relset_1(X1,X6)&r1_mesfunc6(X1,X2,X6,X9)))))\|(![X9]:(m2_subset_1(X9,k1_zfmisc_1(X1),X2)=>~((k1_funct_1(X3,k3_subset_1(X1,X9))=k6_numbers&(X9=k1_relset_1(X1,X7)&r1_mesfunc6(X1,X2,X7,X9)))))\|(v1_xboole_0(k5_lpspace2(X1,X2,X3,X4,X8))\|(v1_xboole_0(k5_lpspace2(X1,X2,X3,X6,X8))\|k5_lpspace2(X1,X2,X3,k3_valued_1(X1,k1_numbers,k1_numbers,X4,X6),X8)=k5_lpspace2(X1,X2,X3,k3_valued_1(X1,k1_numbers,k1_numbers,X5,X7),X8))))))))))))))))), inference(assume_negation,[status(cth)],[t44_lpspace2])). fof(c_0_11, plain, ![X29, X30, X31, X32, X33, X34]:(v1_xboole_0(X29)\|(v1_xboole_0(X30)\|(~v1_prob_1(X30,X29)\|(~v4_prob_1(X30,X29)\|~m1_subset_1(X30,k1_zfmisc_1(k1_zfmisc_1(X29)))))\|(~v1_funct_1(X31)\|(~v1_funct_2(X31,X30,k7_numbers)\|(~v10_valued_0(X31)\|(~v6_supinf_2(X31)\|(~v4_measure1(X31,X29,X30)\|~m1_subset_1(X31,k1_zfmisc_1(k2_zfmisc_1(X30,k7_numbers)))))))\|(~v1_funct_1(X32)\|~m1_subset_1(X32,k1_zfmisc_1(k2_zfmisc_1(X29,k1_numbers)))\|(~v1_funct_1(X33)\|~m1_subset_1(X33,k1_zfmisc_1(k2_zfmisc_1(X29,k1_numbers)))\|(~v2_xxreal_0(X34)\|~m1_subset_1(X34,k1_numbers)\|(~r1_lpspace1(X29,X30,X31,X32,X33)\|k5_lpspace2(X29,X30,X31,X32,X34)=k5_lpspace2(X29,X30,X31,X33,X34)))))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t41_lpspace2])])])])). fof(c_0_12, plain, ![X35, X36, X37, X38, X39, X40, X41]:(v1_xboole_0(X35)\|(v1_xboole_0(X36)\|(~v1_prob_1(X36,X35)\|(~v4_prob_1(X36,X35)\|~m1_subset_1(X36,k1_zfmisc_1(k1_zfmisc_1(X35)))))\|(~v1_funct_1(X37)\|(~v1_funct_2(X37,X36,k7_numbers)\|(~v10_valued_0(X37)\|(~v6_supinf_2(X37)\|(~v4_measure1(X37,X35,X36)\|~m1_subset_1(X37,k1_zfmisc_1(k2_zfmisc_1(X36,k7_numbers)))))))\|(~v1_funct_1(X38)\|~m1_subset_1(X38,k1_zfmisc_1(k2_zfmisc_1(X35,k1_numbers)))\|(~v1_funct_1(X39)\|~m1_subset_1(X39,k1_zfmisc_1(k2_zfmisc_1(X35,k1_numbers)))\|(~v1_funct_1(X40)\|~m1_subset_1(X40,k1_zfmisc_1(k2_zfmisc_1(X35,k1_numbers)))\|(~v1_funct_1(X41)\|~m1_subset_1(X41,k1_zfmisc_1(k2_zfmisc_1(X35,k1_numbers)))\|(~r1_lpspace1(X35,X36,X37,X38,X39)\|~r1_lpspace1(X35,X36,X37,X40,X41)\|r1_lpspace1(X35,X36,X37,k3_valued_1(X35,k1_numbers,k1_numbers,X38,X40),k3_valued_1(X35,k1_numbers,k1_numbers,X39,X41)))))))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t31_lpspace1])])])])). cnf(c_0_13, plain, (v1_xboole_0(X1)\|v1_xboole_0(X2)\|k5_lpspace2(X1,X2,X3,X5,X6)=k1_xboole_0\|r1_lpspace1(X1,X2,X3,X5,X4)\|~v1_prob_1(X2,X1)\|~v4_prob_1(X2,X1)\|~m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X1)))\|~v1_funct_1(X3)\|~v1_funct_2(X3,X2,k7_numbers)\|~v10_valued_0(X3)\|~v6_supinf_2(X3)\|~v4_measure1(X3,X1,X2)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X2,k7_numbers)))\|~v1_funct_1(X4)\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~v1_funct_1(X5)\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~v2_xxreal_0(X6)\|~m1_subset_1(X6,k1_numbers)\|k5_lpspace2(X1,X2,X3,X5,X6)!=k5_lpspace2(X1,X2,X3,X4,X6)\|~m2_subset_1(X7,k1_zfmisc_1(X1),X2)\|k1_funct_1(X3,k3_subset_1(X1,X7))!=k6_numbers\|X7!=k1_relset_1(X1,X4)\|~r1_mesfunc6(X1,X2,X4,X7)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_14, plain, (k6_numbers=k1_xboole_0), inference(split_conjunct,[status(thm)],[redefinition_k6_numbers])). fof(c_0_15, negated_conjecture, (~v1_xboole_0(esk1_0)&((~v1_xboole_0(esk2_0)&(v1_prob_1(esk2_0,esk1_0)&(v4_prob_1(esk2_0,esk1_0)&m1_subset_1(esk2_0,k1_zfmisc_1(k1_zfmisc_1(esk1_0))))))&((v1_funct_1(esk3_0)&(v1_funct_2(esk3_0,esk2_0,k7_numbers)&(v10_valued_0(esk3_0)&(v6_supinf_2(esk3_0)&(v4_measure1(esk3_0,esk1_0,esk2_0)&m1_subset_1(esk3_0,k1_zfmisc_1(k2_zfmisc_1(esk2_0,k7_numbers))))))))&((v1_funct_1(esk4_0)&m1_subset_1(esk4_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers))))&((v1_funct_1(esk5_0)&m1_subset_1(esk5_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers))))&((v1_funct_1(esk6_0)&m1_subset_1(esk6_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers))))&((v1_funct_1(esk7_0)&m1_subset_1(esk7_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers))))&((v2_xxreal_0(esk8_0)&m1_subset_1(esk8_0,k1_numbers))&((k5_lpspace2(esk1_0,esk2_0,esk3_0,esk4_0,esk8_0)=k5_lpspace2(esk1_0,esk2_0,esk3_0,esk5_0,esk8_0)&k5_lpspace2(esk1_0,esk2_0,esk3_0,esk6_0,esk8_0)=k5_lpspace2(esk1_0,esk2_0,esk3_0,esk7_0,esk8_0))&((m2_subset_1(esk9_0,k1_zfmisc_1(esk1_0),esk2_0)&(k1_funct_1(esk3_0,k3_subset_1(esk1_0,esk9_0))=k6_numbers&(esk9_0=k1_relset_1(esk1_0,esk4_0)&r1_mesfunc6(esk1_0,esk2_0,esk4_0,esk9_0))))&((m2_subset_1(esk10_0,k1_zfmisc_1(esk1_0),esk2_0)&(k1_funct_1(esk3_0,k3_subset_1(esk1_0,esk10_0))=k6_numbers&(esk10_0=k1_relset_1(esk1_0,esk5_0)&r1_mesfunc6(esk1_0,esk2_0,esk5_0,esk10_0))))&((m2_subset_1(esk11_0,k1_zfmisc_1(esk1_0),esk2_0)&(k1_funct_1(esk3_0,k3_subset_1(esk1_0,esk11_0))=k6_numbers&(esk11_0=k1_relset_1(esk1_0,esk6_0)&r1_mesfunc6(esk1_0,esk2_0,esk6_0,esk11_0))))&((m2_subset_1(esk12_0,k1_zfmisc_1(esk1_0),esk2_0)&(k1_funct_1(esk3_0,k3_subset_1(esk1_0,esk12_0))=k6_numbers&(esk12_0=k1_relset_1(esk1_0,esk7_0)&r1_mesfunc6(esk1_0,esk2_0,esk7_0,esk12_0))))&(~v1_xboole_0(k5_lpspace2(esk1_0,esk2_0,esk3_0,esk4_0,esk8_0))&(~v1_xboole_0(k5_lpspace2(esk1_0,esk2_0,esk3_0,esk6_0,esk8_0))&k5_lpspace2(esk1_0,esk2_0,esk3_0,k3_valued_1(esk1_0,k1_numbers,k1_numbers,esk4_0,esk6_0),esk8_0)!=k5_lpspace2(esk1_0,esk2_0,esk3_0,k3_valued_1(esk1_0,k1_numbers,k1_numbers,esk5_0,esk7_0),esk8_0)))))))))))))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_10])])])])). cnf(c_0_16, plain, (v1_xboole_0(X1)\|v1_xboole_0(X2)\|k5_lpspace2(X1,X2,X3,X4,X6)=k5_lpspace2(X1,X2,X3,X5,X6)\|~v1_prob_1(X2,X1)\|~v4_prob_1(X2,X1)\|~m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X1)))\|~v1_funct_1(X3)\|~v1_funct_2(X3,X2,k7_numbers)\|~v10_valued_0(X3)\|~v6_supinf_2(X3)\|~v4_measure1(X3,X1,X2)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X2,k7_numbers)))\|~v1_funct_1(X4)\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~v1_funct_1(X5)\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~v2_xxreal_0(X6)\|~m1_subset_1(X6,k1_numbers)\|~r1_lpspace1(X1,X2,X3,X4,X5)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_17, plain, (v1_xboole_0(X1)\|v1_xboole_0(X2)\|r1_lpspace1(X1,X2,X3,k3_valued_1(X1,k1_numbers,k1_numbers,X4,X6),k3_valued_1(X1,k1_numbers,k1_numbers,X5,X7))\|~v1_prob_1(X2,X1)\|~v4_prob_1(X2,X1)\|~m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X1)))\|~v1_funct_1(X3)\|~v1_funct_2(X3,X2,k7_numbers)\|~v10_valued_0(X3)\|~v6_supinf_2(X3)\|~v4_measure1(X3,X1,X2)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X2,k7_numbers)))\|~v1_funct_1(X4)\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~v1_funct_1(X5)\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~v1_funct_1(X6)\|~m1_subset_1(X6,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~v1_funct_1(X7)\|~m1_subset_1(X7,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~r1_lpspace1(X1,X2,X3,X4,X5)\|~r1_lpspace1(X1,X2,X3,X6,X7)), inference(split_conjunct,[status(thm)],[c_0_12])). fof(c_0_18, plain, ![X42, X43, X44, X45, X46]:((v1_funct_1(k3_valued_1(X42,X43,X44,X45,X46))\|(~v3_membered(X43)\|(~v3_membered(X44)\|(~v1_funct_1(X45)\|~m1_subset_1(X45,k1_zfmisc_1(k2_zfmisc_1(X42,X43)))\|(~v1_funct_1(X46)\|~m1_subset_1(X46,k1_zfmisc_1(k2_zfmisc_1(X42,X44))))))))&(m1_subset_1(k3_valued_1(X42,X43,X44,X45,X46),k1_zfmisc_1(k2_zfmisc_1(X42,k1_numbers)))\|(~v3_membered(X43)\|(~v3_membered(X44)\|(~v1_funct_1(X45)\|~m1_subset_1(X45,k1_zfmisc_1(k2_zfmisc_1(X42,X43)))\|(~v1_funct_1(X46)\|~m1_subset_1(X46,k1_zfmisc_1(k2_zfmisc_1(X42,X44))))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k3_valued_1])])])). cnf(c_0_19, plain, (k5_lpspace2(X1,X2,X3,X5,X6)=k1_xboole_0\|v1_xboole_0(X2)\|v1_xboole_0(X1)\|r1_lpspace1(X1,X2,X3,X5,X4)\|X7!=k1_relset_1(X1,X4)\|k1_funct_1(X3,k3_subset_1(X1,X7))!=k6_numbers\|k5_lpspace2(X1,X2,X3,X4,X6)!=k5_lpspace2(X1,X2,X3,X5,X6)\|~v1_funct_1(X5)\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v10_valued_0(X3)\|~v6_supinf_2(X3)\|~v2_xxreal_0(X6)\|~v1_prob_1(X2,X1)\|~v4_prob_1(X2,X1)\|~m1_subset_1(X6,k1_numbers)\|~v4_measure1(X3,X1,X2)\|~v1_funct_2(X3,X2,k7_numbers)\|~r1_mesfunc6(X1,X2,X4,X7)\|~m2_subset_1(X7,k1_zfmisc_1(X1),X2)\|~m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X1)))\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X2,k7_numbers)))), inference(evalgc,[status(thm)],[c_0_13])). cnf(c_0_20, plain, (k1_xboole_0=k6_numbers), inference(evalgc,[status(thm)],[c_0_14])). cnf(c_0_21, negated_conjecture, (m2_subset_1(esk12_0,k1_zfmisc_1(esk1_0),esk2_0)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_22, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(k1_zfmisc_1(esk1_0)))), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_23, negated_conjecture, (v4_prob_1(esk2_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_24, negated_conjecture, (v1_prob_1(esk2_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_25, negated_conjecture, (~v1_xboole_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_26, negated_conjecture, (~v1_xboole_0(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_27, plain, (k5_lpspace2(X1,X2,X3,X4,X6)=k5_lpspace2(X1,X2,X3,X5,X6)\|v1_xboole_0(X2)\|v1_xboole_0(X1)\|~v1_funct_1(X5)\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v10_valued_0(X3)\|~v6_supinf_2(X3)\|~v2_xxreal_0(X6)\|~v1_prob_1(X2,X1)\|~v4_prob_1(X2,X1)\|~m1_subset_1(X6,k1_numbers)\|~v4_measure1(X3,X1,X2)\|~v1_funct_2(X3,X2,k7_numbers)\|~r1_lpspace1(X1,X2,X3,X4,X5)\|~m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X1)))\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X2,k7_numbers)))), inference(evalgc,[status(thm)],[c_0_16])). cnf(c_0_28, plain, (v1_xboole_0(X2)\|v1_xboole_0(X1)\|r1_lpspace1(X1,X2,X3,k3_valued_1(X1,k1_numbers,k1_numbers,X4,X6),k3_valued_1(X1,k1_numbers,k1_numbers,X5,X7))\|~v1_funct_1(X7)\|~v1_funct_1(X6)\|~v1_funct_1(X5)\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v10_valued_0(X3)\|~v6_supinf_2(X3)\|~v1_prob_1(X2,X1)\|~v4_prob_1(X2,X1)\|~v4_measure1(X3,X1,X2)\|~v1_funct_2(X3,X2,k7_numbers)\|~r1_lpspace1(X1,X2,X3,X6,X7)\|~r1_lpspace1(X1,X2,X3,X4,X5)\|~m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X1)))\|~m1_subset_1(X7,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~m1_subset_1(X6,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X2,k7_numbers)))), inference(evalgc,[status(thm)],[c_0_17])). cnf(c_0_29, plain, (m1_subset_1(k3_valued_1(X1,X2,X3,X4,X5),k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~v3_membered(X2)\|~v3_membered(X3)\|~v1_funct_1(X4)\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X5)\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_18])). cnf(c_0_30, plain, (v3_membered(k1_numbers)), inference(split_conjunct,[status(thm)],[fc3_membered])). cnf(c_0_31, plain, (k5_lpspace2(X1,X2,X3,X4,X5)=k6_numbers\|r1_lpspace1(X1,X2,X3,X4,X6)\|v1_xboole_0(X1)\|v1_xboole_0(X2)\|k5_lpspace2(X1,X2,X3,X6,X5)!=k5_lpspace2(X1,X2,X3,X4,X5)\|k1_funct_1(X3,k3_subset_1(X1,X7))!=k6_numbers\|X7!=k1_relset_1(X1,X6)\|~r1_mesfunc6(X1,X2,X6,X7)\|~m2_subset_1(X7,k1_zfmisc_1(X1),X2)\|~v2_xxreal_0(X5)\|~v4_measure1(X3,X1,X2)\|~v6_supinf_2(X3)\|~v10_valued_0(X3)\|~v1_funct_2(X3,X2,k7_numbers)\|~v1_funct_1(X4)\|~v1_funct_1(X6)\|~v1_funct_1(X3)\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~m1_subset_1(X6,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X2,k7_numbers)))\|~m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X1)))\|~m1_subset_1(X5,k1_numbers)\|~v4_prob_1(X2,X1)\|~v1_prob_1(X2,X1)), inference(rw,[status(thm)],[c_0_19, c_0_20])). cnf(c_0_32, negated_conjecture, (m2_subset_1(esk12_0,k1_zfmisc_1(esk1_0),esk2_0)), inference(evalgc,[status(thm)],[c_0_21])). cnf(c_0_33, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(k1_zfmisc_1(esk1_0)))), inference(evalgc,[status(thm)],[c_0_22])). cnf(c_0_34, negated_conjecture, (v4_prob_1(esk2_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_23])). cnf(c_0_35, negated_conjecture, (v1_prob_1(esk2_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_24])). cnf(c_0_36, negated_conjecture, (~v1_xboole_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_25])). cnf(c_0_37, negated_conjecture, (~v1_xboole_0(esk2_0)), inference(evalgc,[status(thm)],[c_0_26])). cnf(c_0_38, negated_conjecture, (k1_funct_1(esk3_0,k3_subset_1(esk1_0,esk12_0))=k6_numbers), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_39, negated_conjecture, (v4_measure1(esk3_0,esk1_0,esk2_0)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_40, negated_conjecture, (v6_supinf_2(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_41, negated_conjecture, (v10_valued_0(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_42, negated_conjecture, (v1_funct_2(esk3_0,esk2_0,k7_numbers)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_43, negated_conjecture, (v1_funct_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_44, negated_conjecture, (m1_subset_1(esk3_0,k1_zfmisc_1(k2_zfmisc_1(esk2_0,k7_numbers)))), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_45, negated_conjecture, (m2_subset_1(esk10_0,k1_zfmisc_1(esk1_0),esk2_0)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_46, plain, (k5_lpspace2(X1,X2,X3,k3_valued_1(X1,k1_numbers,k1_numbers,X4,X5),X6)=k5_lpspace2(X1,X2,X3,k3_valued_1(X1,k1_numbers,k1_numbers,X7,X8),X6)\|v1_xboole_0(X1)\|v1_xboole_0(X2)\|~v2_xxreal_0(X6)\|~v4_measure1(X3,X1,X2)\|~v6_supinf_2(X3)\|~v10_valued_0(X3)\|~v1_funct_2(X3,X2,k7_numbers)\|~v1_funct_1(k3_valued_1(X1,k1_numbers,k1_numbers,X7,X8))\|~v1_funct_1(k3_valued_1(X1,k1_numbers,k1_numbers,X4,X5))\|~v1_funct_1(X3)\|~m1_subset_1(k3_valued_1(X1,k1_numbers,k1_numbers,X7,X8),k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~m1_subset_1(k3_valued_1(X1,k1_numbers,k1_numbers,X4,X5),k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X2,k7_numbers)))\|~m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X1)))\|~m1_subset_1(X6,k1_numbers)\|~v4_prob_1(X2,X1)\|~v1_prob_1(X2,X1)\|~r1_lpspace1(X1,X2,X3,X5,X8)\|~r1_lpspace1(X1,X2,X3,X4,X7)\|~v1_funct_1(X8)\|~v1_funct_1(X5)\|~v1_funct_1(X7)\|~v1_funct_1(X4)\|~m1_subset_1(X8,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~m1_subset_1(X7,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_27, c_0_28])])). cnf(c_0_47, plain, (m1_subset_1(k3_valued_1(X1,X2,X3,X4,X5),k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~v1_funct_1(X5)\|~v1_funct_1(X4)\|~v3_membered(X3)\|~v3_membered(X2)\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(evalgc,[status(thm)],[c_0_29])). cnf(c_0_48, plain, (v3_membered(k1_numbers)), inference(evalgc,[status(thm)],[c_0_30])). cnf(c_0_49, negated_conjecture, (k5_lpspace2(esk1_0,esk2_0,X1,X2,X3)=k6_numbers\|r1_lpspace1(esk1_0,esk2_0,X1,X2,X4)\|k5_lpspace2(esk1_0,esk2_0,X1,X4,X3)!=k5_lpspace2(esk1_0,esk2_0,X1,X2,X3)\|k1_funct_1(X1,k3_subset_1(esk1_0,esk12_0))!=k6_numbers\|k1_relset_1(esk1_0,X4)!=esk12_0\|~r1_mesfunc6(esk1_0,esk2_0,X4,esk12_0)\|~v2_xxreal_0(X3)\|~v4_measure1(X1,esk1_0,esk2_0)\|~v6_supinf_2(X1)\|~v10_valued_0(X1)\|~v1_funct_2(X1,esk2_0,k7_numbers)\|~v1_funct_1(X2)\|~v1_funct_1(X4)\|~v1_funct_1(X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(esk2_0,k7_numbers)))\|~m1_subset_1(X3,k1_numbers)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31, c_0_32]), c_0_33]), c_0_34]), c_0_35])]), c_0_36]), c_0_37])])). cnf(c_0_50, negated_conjecture, (k1_funct_1(esk3_0,k3_subset_1(esk1_0,esk12_0))=k6_numbers), inference(evalgc,[status(thm)],[c_0_38])). cnf(c_0_51, negated_conjecture, (v4_measure1(esk3_0,esk1_0,esk2_0)), inference(evalgc,[status(thm)],[c_0_39])). cnf(c_0_52, negated_conjecture, (v6_supinf_2(esk3_0)), inference(evalgc,[status(thm)],[c_0_40])). cnf(c_0_53, negated_conjecture, (v10_valued_0(esk3_0)), inference(evalgc,[status(thm)],[c_0_41])). cnf(c_0_54, negated_conjecture, (v1_funct_2(esk3_0,esk2_0,k7_numbers)), inference(evalgc,[status(thm)],[c_0_42])). cnf(c_0_55, negated_conjecture, (v1_funct_1(esk3_0)), inference(evalgc,[status(thm)],[c_0_43])). cnf(c_0_56, negated_conjecture, (m1_subset_1(esk3_0,k1_zfmisc_1(k2_zfmisc_1(esk2_0,k7_numbers)))), inference(evalgc,[status(thm)],[c_0_44])). cnf(c_0_57, negated_conjecture, (v2_xxreal_0(esk8_0)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_58, negated_conjecture, (m1_subset_1(esk8_0,k1_numbers)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_59, negated_conjecture, (m2_subset_1(esk10_0,k1_zfmisc_1(esk1_0),esk2_0)), inference(evalgc,[status(thm)],[c_0_45])). cnf(c_0_60, negated_conjecture, (k1_funct_1(esk3_0,k3_subset_1(esk1_0,esk10_0))=k6_numbers), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_61, plain, (k5_lpspace2(X1,X2,X3,k3_valued_1(X1,k1_numbers,k1_numbers,X4,X5),X6)=k5_lpspace2(X1,X2,X3,k3_valued_1(X1,k1_numbers,k1_numbers,X7,X8),X6)\|v1_xboole_0(X2)\|v1_xboole_0(X1)\|~r1_lpspace1(X1,X2,X3,X5,X8)\|~r1_lpspace1(X1,X2,X3,X4,X7)\|~v2_xxreal_0(X6)\|~v4_measure1(X3,X1,X2)\|~v6_supinf_2(X3)\|~v10_valued_0(X3)\|~v1_funct_2(X3,X2,k7_numbers)\|~v1_funct_1(k3_valued_1(X1,k1_numbers,k1_numbers,X7,X8))\|~v1_funct_1(k3_valued_1(X1,k1_numbers,k1_numbers,X4,X5))\|~v1_funct_1(X3)\|~v1_funct_1(X8)\|~v1_funct_1(X5)\|~v1_funct_1(X7)\|~v1_funct_1(X4)\|~m1_subset_1(k3_valued_1(X1,k1_numbers,k1_numbers,X4,X5),k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X2,k7_numbers)))\|~m1_subset_1(X8,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~m1_subset_1(X7,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X1)))\|~m1_subset_1(X6,k1_numbers)\|~v4_prob_1(X2,X1)\|~v1_prob_1(X2,X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46, c_0_47]), c_0_48])])])). cnf(c_0_62, negated_conjecture, (k5_lpspace2(esk1_0,esk2_0,esk3_0,X1,X2)=k6_numbers\|r1_lpspace1(esk1_0,esk2_0,esk3_0,X1,X3)\|k5_lpspace2(esk1_0,esk2_0,esk3_0,X3,X2)!=k5_lpspace2(esk1_0,esk2_0,esk3_0,X1,X2)\|k1_relset_1(esk1_0,X3)!=esk12_0\|~r1_mesfunc6(esk1_0,esk2_0,X3,esk12_0)\|~v2_xxreal_0(X2)\|~v1_funct_1(X1)\|~v1_funct_1(X3)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))\|~m1_subset_1(X2,k1_numbers)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49, c_0_50]), c_0_51]), c_0_52]), c_0_53]), c_0_54]), c_0_55]), c_0_56])])])). cnf(c_0_63, negated_conjecture, (v2_xxreal_0(esk8_0)), inference(evalgc,[status(thm)],[c_0_57])). cnf(c_0_64, negated_conjecture, (m1_subset_1(esk8_0,k1_numbers)), inference(evalgc,[status(thm)],[c_0_58])). cnf(c_0_65, negated_conjecture, (k5_lpspace2(esk1_0,esk2_0,X1,X2,X3)=k6_numbers\|r1_lpspace1(esk1_0,esk2_0,X1,X2,X4)\|k5_lpspace2(esk1_0,esk2_0,X1,X4,X3)!=k5_lpspace2(esk1_0,esk2_0,X1,X2,X3)\|k1_funct_1(X1,k3_subset_1(esk1_0,esk10_0))!=k6_numbers\|k1_relset_1(esk1_0,X4)!=esk10_0\|~r1_mesfunc6(esk1_0,esk2_0,X4,esk10_0)\|~v2_xxreal_0(X3)\|~v4_measure1(X1,esk1_0,esk2_0)\|~v6_supinf_2(X1)\|~v10_valued_0(X1)\|~v1_funct_2(X1,esk2_0,k7_numbers)\|~v1_funct_1(X2)\|~v1_funct_1(X4)\|~v1_funct_1(X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(esk2_0,k7_numbers)))\|~m1_subset_1(X3,k1_numbers)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31, c_0_59]), c_0_33]), c_0_34]), c_0_35])]), c_0_36]), c_0_37])])). cnf(c_0_66, negated_conjecture, (k1_funct_1(esk3_0,k3_subset_1(esk1_0,esk10_0))=k6_numbers), inference(evalgc,[status(thm)],[c_0_60])). cnf(c_0_67, plain, (k5_lpspace2(X1,X2,X3,k3_valued_1(X1,k1_numbers,k1_numbers,X4,X5),X6)=k5_lpspace2(X1,X2,X3,k3_valued_1(X1,k1_numbers,k1_numbers,X7,X8),X6)\|v1_xboole_0(X1)\|v1_xboole_0(X2)\|~r1_lpspace1(X1,X2,X3,X5,X8)\|~r1_lpspace1(X1,X2,X3,X4,X7)\|~v2_xxreal_0(X6)\|~v4_measure1(X3,X1,X2)\|~v6_supinf_2(X3)\|~v10_valued_0(X3)\|~v1_funct_2(X3,X2,k7_numbers)\|~v1_funct_1(k3_valued_1(X1,k1_numbers,k1_numbers,X7,X8))\|~v1_funct_1(k3_valued_1(X1,k1_numbers,k1_numbers,X4,X5))\|~v1_funct_1(X3)\|~v1_funct_1(X8)\|~v1_funct_1(X5)\|~v1_funct_1(X7)\|~v1_funct_1(X4)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X2,k7_numbers)))\|~m1_subset_1(X8,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~m1_subset_1(X7,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X1)))\|~m1_subset_1(X6,k1_numbers)\|~v4_prob_1(X2,X1)\|~v1_prob_1(X2,X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61, c_0_47]), c_0_48])])])). cnf(c_0_68, negated_conjecture, (k5_lpspace2(esk1_0,esk2_0,esk3_0,X1,esk8_0)=k6_numbers\|r1_lpspace1(esk1_0,esk2_0,esk3_0,X1,X2)\|k5_lpspace2(esk1_0,esk2_0,esk3_0,X2,esk8_0)!=k5_lpspace2(esk1_0,esk2_0,esk3_0,X1,esk8_0)\|k1_relset_1(esk1_0,X2)!=esk12_0\|~r1_mesfunc6(esk1_0,esk2_0,X2,esk12_0)\|~v1_funct_1(X1)\|~v1_funct_1(X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62, c_0_63]), c_0_64])])])). cnf(c_0_69, negated_conjecture, (k5_lpspace2(esk1_0,esk2_0,esk3_0,X1,X2)=k6_numbers\|r1_lpspace1(esk1_0,esk2_0,esk3_0,X1,X3)\|k5_lpspace2(esk1_0,esk2_0,esk3_0,X3,X2)!=k5_lpspace2(esk1_0,esk2_0,esk3_0,X1,X2)\|k1_relset_1(esk1_0,X3)!=esk10_0\|~r1_mesfunc6(esk1_0,esk2_0,X3,esk10_0)\|~v2_xxreal_0(X2)\|~v1_funct_1(X1)\|~v1_funct_1(X3)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))\|~m1_subset_1(X2,k1_numbers)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65, c_0_66]), c_0_51]), c_0_52]), c_0_53]), c_0_54]), c_0_55]), c_0_56])])])). cnf(c_0_70, negated_conjecture, (k5_lpspace2(esk1_0,esk2_0,esk3_0,k3_valued_1(esk1_0,k1_numbers,k1_numbers,X1,X2),X3)=k5_lpspace2(esk1_0,esk2_0,esk3_0,k3_valued_1(esk1_0,k1_numbers,k1_numbers,X4,X5),X3)\|k5_lpspace2(esk1_0,esk2_0,esk3_0,X2,esk8_0)=k6_numbers\|~r1_lpspace1(esk1_0,esk2_0,esk3_0,X1,X4)\|~v2_xxreal_0(X3)\|~v1_funct_1(k3_valued_1(esk1_0,k1_numbers,k1_numbers,X4,X5))\|~v1_funct_1(k3_valued_1(esk1_0,k1_numbers,k1_numbers,X1,X2))\|~v1_funct_1(X5)\|~v1_funct_1(X2)\|~v1_funct_1(X4)\|~v1_funct_1(X1)\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))\|~m1_subset_1(X3,k1_numbers)\|k5_lpspace2(esk1_0,esk2_0,esk3_0,X5,esk8_0)!=k5_lpspace2(esk1_0,esk2_0,esk3_0,X2,esk8_0)\|k1_relset_1(esk1_0,X5)!=esk12_0\|~r1_mesfunc6(esk1_0,esk2_0,X5,esk12_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67, c_0_68]), c_0_51]), c_0_52]), c_0_53]), c_0_54]), c_0_55]), c_0_56]), c_0_33]), c_0_34]), c_0_35])]), c_0_37]), c_0_36])])). cnf(c_0_71, negated_conjecture, (k5_lpspace2(esk1_0,esk2_0,esk3_0,X1,esk8_0)=k6_numbers\|r1_lpspace1(esk1_0,esk2_0,esk3_0,X1,X2)\|k5_lpspace2(esk1_0,esk2_0,esk3_0,X2,esk8_0)!=k5_lpspace2(esk1_0,esk2_0,esk3_0,X1,esk8_0)\|k1_relset_1(esk1_0,X2)!=esk10_0\|~r1_mesfunc6(esk1_0,esk2_0,X2,esk10_0)\|~v1_funct_1(X1)\|~v1_funct_1(X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69, c_0_63]), c_0_64])])])). cnf(c_0_72, negated_conjecture, (k5_lpspace2(esk1_0,esk2_0,esk3_0,esk6_0,esk8_0)=k5_lpspace2(esk1_0,esk2_0,esk3_0,esk7_0,esk8_0)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_73, negated_conjecture, (esk12_0=k1_relset_1(esk1_0,esk7_0)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_74, negated_conjecture, (r1_mesfunc6(esk1_0,esk2_0,esk7_0,esk12_0)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_75, negated_conjecture, (v1_funct_1(esk7_0)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_76, negated_conjecture, (m1_subset_1(esk7_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_77, negated_conjecture, (k5_lpspace2(esk1_0,esk2_0,esk3_0,k3_valued_1(esk1_0,k1_numbers,k1_numbers,X1,X2),X3)=k5_lpspace2(esk1_0,esk2_0,esk3_0,k3_valued_1(esk1_0,k1_numbers,k1_numbers,X4,X5),X3)\|k5_lpspace2(esk1_0,esk2_0,esk3_0,X2,esk8_0)=k6_numbers\|k5_lpspace2(esk1_0,esk2_0,esk3_0,X1,esk8_0)=k6_numbers\|k5_lpspace2(esk1_0,esk2_0,esk3_0,X5,esk8_0)!=k5_lpspace2(esk1_0,esk2_0,esk3_0,X2,esk8_0)\|k1_relset_1(esk1_0,X5)!=esk12_0\|~r1_mesfunc6(esk1_0,esk2_0,X5,esk12_0)\|~v2_xxreal_0(X3)\|~v1_funct_1(k3_valued_1(esk1_0,k1_numbers,k1_numbers,X4,X5))\|~v1_funct_1(k3_valued_1(esk1_0,k1_numbers,k1_numbers,X1,X2))\|~v1_funct_1(X5)\|~v1_funct_1(X2)\|~v1_funct_1(X4)\|~v1_funct_1(X1)\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))\|~m1_subset_1(X3,k1_numbers)\|k5_lpspace2(esk1_0,esk2_0,esk3_0,X4,esk8_0)!=k5_lpspace2(esk1_0,esk2_0,esk3_0,X1,esk8_0)\|k1_relset_1(esk1_0,X4)!=esk10_0\|~r1_mesfunc6(esk1_0,esk2_0,X4,esk10_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_70, c_0_71])])). cnf(c_0_78, negated_conjecture, (k5_lpspace2(esk1_0,esk2_0,esk3_0,esk7_0,esk8_0)=k5_lpspace2(esk1_0,esk2_0,esk3_0,esk6_0,esk8_0)), inference(evalgc,[status(thm)],[c_0_72])). cnf(c_0_79, negated_conjecture, (k1_relset_1(esk1_0,esk7_0)=esk12_0), inference(evalgc,[status(thm)],[c_0_73])). cnf(c_0_80, negated_conjecture, (r1_mesfunc6(esk1_0,esk2_0,esk7_0,esk12_0)), inference(evalgc,[status(thm)],[c_0_74])). cnf(c_0_81, negated_conjecture, (v1_funct_1(esk7_0)), inference(evalgc,[status(thm)],[c_0_75])). cnf(c_0_82, negated_conjecture, (m1_subset_1(esk7_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))), inference(evalgc,[status(thm)],[c_0_76])). cnf(c_0_83, negated_conjecture, (k5_lpspace2(esk1_0,esk2_0,esk3_0,esk4_0,esk8_0)=k5_lpspace2(esk1_0,esk2_0,esk3_0,esk5_0,esk8_0)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_84, negated_conjecture, (esk10_0=k1_relset_1(esk1_0,esk5_0)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_85, negated_conjecture, (r1_mesfunc6(esk1_0,esk2_0,esk5_0,esk10_0)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_86, negated_conjecture, (v1_funct_1(esk5_0)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_87, negated_conjecture, (m1_subset_1(esk5_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_88, negated_conjecture, (k5_lpspace2(esk1_0,esk2_0,esk3_0,k3_valued_1(esk1_0,k1_numbers,k1_numbers,esk4_0,esk6_0),esk8_0)!=k5_lpspace2(esk1_0,esk2_0,esk3_0,k3_valued_1(esk1_0,k1_numbers,k1_numbers,esk5_0,esk7_0),esk8_0)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_89, negated_conjecture, (k5_lpspace2(esk1_0,esk2_0,esk3_0,k3_valued_1(esk1_0,k1_numbers,k1_numbers,X1,X2),X3)=k5_lpspace2(esk1_0,esk2_0,esk3_0,k3_valued_1(esk1_0,k1_numbers,k1_numbers,X4,esk7_0),X3)\|k5_lpspace2(esk1_0,esk2_0,esk3_0,X1,esk8_0)=k6_numbers\|k5_lpspace2(esk1_0,esk2_0,esk3_0,X2,esk8_0)=k6_numbers\|k5_lpspace2(esk1_0,esk2_0,esk3_0,esk6_0,esk8_0)!=k5_lpspace2(esk1_0,esk2_0,esk3_0,X2,esk8_0)\|k5_lpspace2(esk1_0,esk2_0,esk3_0,X4,esk8_0)!=k5_lpspace2(esk1_0,esk2_0,esk3_0,X1,esk8_0)\|k1_relset_1(esk1_0,X4)!=esk10_0\|~r1_mesfunc6(esk1_0,esk2_0,X4,esk10_0)\|~v2_xxreal_0(X3)\|~v1_funct_1(k3_valued_1(esk1_0,k1_numbers,k1_numbers,X4,esk7_0))\|~v1_funct_1(k3_valued_1(esk1_0,k1_numbers,k1_numbers,X1,X2))\|~v1_funct_1(X2)\|~v1_funct_1(X4)\|~v1_funct_1(X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))\|~m1_subset_1(X3,k1_numbers)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77, c_0_78]), c_0_79]), c_0_80]), c_0_81]), c_0_82])])])). cnf(c_0_90, negated_conjecture, (k5_lpspace2(esk1_0,esk2_0,esk3_0,esk5_0,esk8_0)=k5_lpspace2(esk1_0,esk2_0,esk3_0,esk4_0,esk8_0)), inference(evalgc,[status(thm)],[c_0_83])). cnf(c_0_91, negated_conjecture, (k1_relset_1(esk1_0,esk5_0)=esk10_0), inference(evalgc,[status(thm)],[c_0_84])). cnf(c_0_92, negated_conjecture, (r1_mesfunc6(esk1_0,esk2_0,esk5_0,esk10_0)), inference(evalgc,[status(thm)],[c_0_85])). cnf(c_0_93, negated_conjecture, (v1_funct_1(esk5_0)), inference(evalgc,[status(thm)],[c_0_86])). cnf(c_0_94, negated_conjecture, (m1_subset_1(esk5_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))), inference(evalgc,[status(thm)],[c_0_87])). cnf(c_0_95, negated_conjecture, (k5_lpspace2(esk1_0,esk2_0,esk3_0,k3_valued_1(esk1_0,k1_numbers,k1_numbers,esk5_0,esk7_0),esk8_0)!=k5_lpspace2(esk1_0,esk2_0,esk3_0,k3_valued_1(esk1_0,k1_numbers,k1_numbers,esk4_0,esk6_0),esk8_0)), inference(evalgc,[status(thm)],[c_0_88])). cnf(c_0_96, negated_conjecture, (k5_lpspace2(esk1_0,esk2_0,esk3_0,k3_valued_1(esk1_0,k1_numbers,k1_numbers,X1,X2),X3)=k5_lpspace2(esk1_0,esk2_0,esk3_0,k3_valued_1(esk1_0,k1_numbers,k1_numbers,esk5_0,esk7_0),X3)\|k5_lpspace2(esk1_0,esk2_0,esk3_0,X2,esk8_0)=k6_numbers\|k5_lpspace2(esk1_0,esk2_0,esk3_0,X1,esk8_0)=k6_numbers\|k5_lpspace2(esk1_0,esk2_0,esk3_0,esk6_0,esk8_0)!=k5_lpspace2(esk1_0,esk2_0,esk3_0,X2,esk8_0)\|k5_lpspace2(esk1_0,esk2_0,esk3_0,esk4_0,esk8_0)!=k5_lpspace2(esk1_0,esk2_0,esk3_0,X1,esk8_0)\|~v2_xxreal_0(X3)\|~v1_funct_1(k3_valued_1(esk1_0,k1_numbers,k1_numbers,esk5_0,esk7_0))\|~v1_funct_1(k3_valued_1(esk1_0,k1_numbers,k1_numbers,X1,X2))\|~v1_funct_1(X2)\|~v1_funct_1(X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))\|~m1_subset_1(X3,k1_numbers)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89, c_0_90]), c_0_91]), c_0_92]), c_0_93]), c_0_94])])])). cnf(c_0_97, negated_conjecture, (v1_funct_1(esk6_0)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_98, negated_conjecture, (v1_funct_1(esk4_0)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_99, negated_conjecture, (m1_subset_1(esk6_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_100, negated_conjecture, (m1_subset_1(esk4_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_101, negated_conjecture, (k5_lpspace2(esk1_0,esk2_0,esk3_0,X1,esk8_0)=k6_numbers\|k5_lpspace2(esk1_0,esk2_0,esk3_0,X2,esk8_0)=k6_numbers\|k5_lpspace2(esk1_0,esk2_0,esk3_0,k3_valued_1(esk1_0,k1_numbers,k1_numbers,X1,X2),esk8_0)!=k5_lpspace2(esk1_0,esk2_0,esk3_0,k3_valued_1(esk1_0,k1_numbers,k1_numbers,esk4_0,esk6_0),esk8_0)\|k5_lpspace2(esk1_0,esk2_0,esk3_0,esk6_0,esk8_0)!=k5_lpspace2(esk1_0,esk2_0,esk3_0,X2,esk8_0)\|k5_lpspace2(esk1_0,esk2_0,esk3_0,esk4_0,esk8_0)!=k5_lpspace2(esk1_0,esk2_0,esk3_0,X1,esk8_0)\|~v1_funct_1(k3_valued_1(esk1_0,k1_numbers,k1_numbers,esk5_0,esk7_0))\|~v1_funct_1(k3_valued_1(esk1_0,k1_numbers,k1_numbers,X1,X2))\|~v1_funct_1(X2)\|~v1_funct_1(X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95, c_0_96]), c_0_63]), c_0_64])])])). cnf(c_0_102, negated_conjecture, (v1_funct_1(esk6_0)), inference(evalgc,[status(thm)],[c_0_97])). cnf(c_0_103, negated_conjecture, (v1_funct_1(esk4_0)), inference(evalgc,[status(thm)],[c_0_98])). cnf(c_0_104, negated_conjecture, (m1_subset_1(esk6_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))), inference(evalgc,[status(thm)],[c_0_99])). cnf(c_0_105, negated_conjecture, (m1_subset_1(esk4_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))), inference(evalgc,[status(thm)],[c_0_100])). cnf(c_0_106, plain, (v1_funct_1(k3_valued_1(X1,X2,X3,X4,X5))\|~v3_membered(X2)\|~v3_membered(X3)\|~v1_funct_1(X4)\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X5)\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_18])). cnf(c_0_107, plain, (k1_xboole_0=o_0_0_xboole_0), inference(split_conjunct,[status(thm)],[d2_xboole_0])). cnf(c_0_108, negated_conjecture, (k5_lpspace2(esk1_0,esk2_0,esk3_0,esk6_0,esk8_0)=k6_numbers\|k5_lpspace2(esk1_0,esk2_0,esk3_0,esk4_0,esk8_0)=k6_numbers\|~v1_funct_1(k3_valued_1(esk1_0,k1_numbers,k1_numbers,esk5_0,esk7_0))\|~v1_funct_1(k3_valued_1(esk1_0,k1_numbers,k1_numbers,esk4_0,esk6_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_101]), c_0_102]), c_0_103]), c_0_104]), c_0_105])])])). cnf(c_0_109, plain, (v1_funct_1(k3_valued_1(X1,X2,X3,X4,X5))\|~v1_funct_1(X5)\|~v1_funct_1(X4)\|~v3_membered(X3)\|~v3_membered(X2)\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(evalgc,[status(thm)],[c_0_106])). cnf(c_0_110, plain, (v1_xboole_0(o_0_0_xboole_0)), inference(split_conjunct,[status(thm)],[dt_o_0_0_xboole_0])). cnf(c_0_111, plain, (o_0_0_xboole_0=k1_xboole_0), inference(evalgc,[status(thm)],[c_0_107])). cnf(c_0_112, negated_conjecture, (~v1_xboole_0(k5_lpspace2(esk1_0,esk2_0,esk3_0,esk6_0,esk8_0))), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_113, negated_conjecture, (k5_lpspace2(esk1_0,esk2_0,esk3_0,esk4_0,esk8_0)=k6_numbers\|k5_lpspace2(esk1_0,esk2_0,esk3_0,esk6_0,esk8_0)=k6_numbers\|~v1_funct_1(k3_valued_1(esk1_0,k1_numbers,k1_numbers,esk4_0,esk6_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108, c_0_109]), c_0_48]), c_0_81]), c_0_93]), c_0_82]), c_0_94])])])). cnf(c_0_114, plain, (v1_xboole_0(o_0_0_xboole_0)), inference(evalgc,[status(thm)],[c_0_110])). cnf(c_0_115, plain, (o_0_0_xboole_0=k6_numbers), inference(rw,[status(thm)],[c_0_111, c_0_20])). cnf(c_0_116, negated_conjecture, (~v1_xboole_0(k5_lpspace2(esk1_0,esk2_0,esk3_0,esk4_0,esk8_0))), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_117, negated_conjecture, (~v1_xboole_0(k5_lpspace2(esk1_0,esk2_0,esk3_0,esk6_0,esk8_0))), inference(evalgc,[status(thm)],[c_0_112])). cnf(c_0_118, negated_conjecture, (k5_lpspace2(esk1_0,esk2_0,esk3_0,esk6_0,esk8_0)=k6_numbers\|k5_lpspace2(esk1_0,esk2_0,esk3_0,esk4_0,esk8_0)=k6_numbers), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113, c_0_109]), c_0_48]), c_0_102]), c_0_103]), c_0_104]), c_0_105])])])). cnf(c_0_119, plain, (v1_xboole_0(k6_numbers)), inference(rw,[status(thm)],[c_0_114, c_0_115])). cnf(c_0_120, negated_conjecture, (~v1_xboole_0(k5_lpspace2(esk1_0,esk2_0,esk3_0,esk4_0,esk8_0))), inference(evalgc,[status(thm)],[c_0_116])). cnf(c_0_121, negated_conjecture, (k5_lpspace2(esk1_0,esk2_0,esk3_0,esk4_0,esk8_0)=k6_numbers), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117, c_0_118]), c_0_119])])])). cnf(c_0_122, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_120, c_0_121]), c_0_119])]), ['proof']). # SZS output end CNFRefutation	reserve X for non empty set, x for Element of X, S for SigmaField of X, M for sigma_Measure of S, f,g,f1,g1 for PartFunc of X,REAL, l,m,n,n1,n2 for Element of NAT, a,b,c for Real; reserve k for positive Real; reserve v,u for VECTOR of RLSp_LpFunct(M,k); reserve v,u for VECTOR of RLSp_AlmostZeroLpFunct(M,k); theorem (ex E be Element of S st M.(E`)=0 & E = dom f & f is_measurable_on E) & (ex E be Element of S st M.(E`)=0 & E = dom f1 & f1 is_measurable_on E) & (ex E be Element of S st M.(E`)=0 & E = dom g & g is_measurable_on E) & (ex E be Element of S st M.(E`)=0 & E = dom g1 & g1 is_measurable_on E) & a.e-eq-class_Lp(f,M,k) is non empty & a.e-eq-class_Lp(g,M,k) is non empty & a.e-eq-class_Lp(f,M,k) = a.e-eq-class_Lp(f1,M,k) & a.e-eq-class_Lp(g,M,k) = a.e-eq-class_Lp(g1,M,k) implies a.e-eq-class_Lp(f+g,M,k) = a.e-eq-class_Lp(f1+g1,M,k) proof assume (ex E be Element of S st M.(E`)=0 & E = dom f & f is_measurable_on E) & (ex E be Element of S st M.(E`)=0 & E = dom f1 & f1 is_measurable_on E) & (ex E be Element of S st M.(E`)=0 & E = dom g & g is_measurable_on E) & (ex E be Element of S st M.(E`)=0 & E = dom g1 & g1 is_measurable_on E) & a.e-eq-class_Lp(f,M,k) is non empty & a.e-eq-class_Lp(g,M,k) is non empty & a.e-eq-class_Lp(f,M,k) = a.e-eq-class_Lp(f1,M,k) & a.e-eq-class_Lp(g,M,k) = a.e-eq-class_Lp(g1,M,k); then f a.e.= f1,M & g a.e.= g1,M by Th39; hence thesis by Th41,LPSPACE1:31; end;	Convert the following ATP output trace into a readable Mizar proof.
t115_flang_2	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(redefinition_k4_subset_1, axiom, ![X1, X2, X3]:((m1_subset_1(X2,k1_zfmisc_1(X1))&m1_subset_1(X3,k1_zfmisc_1(X1)))=>k4_subset_1(X1,X2,X3)=k2_xboole_0(X2,X3)), file('/scratch/mptp/predsminms1/t115_flang_2__0', redefinition_k4_subset_1)). fof(t76_flang_2, axiom, ![X1, X2]:(m1_subset_1(X2,k1_zfmisc_1(k8_afinsq_1(X1)))=>k2_flang_2(X1,X2)=k4_subset_1(k8_afinsq_1(X1),k4_flang_1(X1,k2_flang_1(X1)),X2)), file('/scratch/mptp/predsminms1/t115_flang_2__0', t76_flang_2)). fof(dt_k4_flang_1, axiom, ![X1, X2]:(m1_subset_1(X2,k3_catalan2(X1))=>m1_subset_1(k4_flang_1(X1,X2),k1_zfmisc_1(k3_catalan2(X1)))), file('/scratch/mptp/predsminms1/t115_flang_2__0', dt_k4_flang_1)). fof(redefinition_k3_catalan2, axiom, ![X1]:k3_catalan2(X1)=k8_afinsq_1(X1), file('/scratch/mptp/predsminms1/t115_flang_2__0', redefinition_k3_catalan2)). fof(dt_k2_flang_1, axiom, ![X1]:m1_subset_1(k2_flang_1(X1),k3_catalan2(X1)), file('/scratch/mptp/predsminms1/t115_flang_2__0', dt_k2_flang_1)). fof(t115_flang_2, conjecture, ![X1, X2]:(m1_subset_1(X2,k1_zfmisc_1(k8_afinsq_1(X1)))=>k2_flang_2(X1,X2)=k2_flang_2(X1,k7_subset_1(k8_afinsq_1(X1),X2,k4_flang_1(X1,k2_flang_1(X1))))), file('/scratch/mptp/predsminms1/t115_flang_2__0', t115_flang_2)). fof(t39_xboole_1, axiom, ![X1, X2]:k2_xboole_0(X1,k4_xboole_0(X2,X1))=k2_xboole_0(X1,X2), file('/scratch/mptp/predsminms1/t115_flang_2__0', t39_xboole_1)). fof(redefinition_k7_subset_1, axiom, ![X1, X2, X3]:(m1_subset_1(X2,k1_zfmisc_1(X1))=>k7_subset_1(X1,X2,X3)=k4_xboole_0(X2,X3)), file('/scratch/mptp/predsminms1/t115_flang_2__0', redefinition_k7_subset_1)). fof(dt_k7_subset_1, axiom, ![X1, X2, X3]:(m1_subset_1(X2,k1_zfmisc_1(X1))=>m1_subset_1(k7_subset_1(X1,X2,X3),k1_zfmisc_1(X1))), file('/scratch/mptp/predsminms1/t115_flang_2__0', dt_k7_subset_1)). fof(c_0_9, plain, ![X8, X9, X10]:(~m1_subset_1(X9,k1_zfmisc_1(X8))\|~m1_subset_1(X10,k1_zfmisc_1(X8))\|k4_subset_1(X8,X9,X10)=k2_xboole_0(X9,X10)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k4_subset_1])])). fof(c_0_10, plain, ![X14, X15]:(~m1_subset_1(X15,k1_zfmisc_1(k8_afinsq_1(X14)))\|k2_flang_2(X14,X15)=k4_subset_1(k8_afinsq_1(X14),k4_flang_1(X14,k2_flang_1(X14)),X15)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t76_flang_2])])). fof(c_0_11, plain, ![X19, X20]:(~m1_subset_1(X20,k3_catalan2(X19))\|m1_subset_1(k4_flang_1(X19,X20),k1_zfmisc_1(k3_catalan2(X19)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k4_flang_1])])). fof(c_0_12, plain, ![X21]:k3_catalan2(X21)=k8_afinsq_1(X21), inference(variable_rename,[status(thm)],[redefinition_k3_catalan2])). fof(c_0_13, plain, ![X22]:m1_subset_1(k2_flang_1(X22),k3_catalan2(X22)), inference(variable_rename,[status(thm)],[dt_k2_flang_1])). fof(c_0_14, negated_conjecture, ~(![X1, X2]:(m1_subset_1(X2,k1_zfmisc_1(k8_afinsq_1(X1)))=>k2_flang_2(X1,X2)=k2_flang_2(X1,k7_subset_1(k8_afinsq_1(X1),X2,k4_flang_1(X1,k2_flang_1(X1)))))), inference(assume_negation,[status(cth)],[t115_flang_2])). fof(c_0_15, plain, ![X6, X7]:k2_xboole_0(X6,k4_xboole_0(X7,X6))=k2_xboole_0(X6,X7), inference(variable_rename,[status(thm)],[t39_xboole_1])). fof(c_0_16, plain, ![X11, X12, X13]:(~m1_subset_1(X12,k1_zfmisc_1(X11))\|k7_subset_1(X11,X12,X13)=k4_xboole_0(X12,X13)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k7_subset_1])])). cnf(c_0_17, plain, (k4_subset_1(X2,X1,X3)=k2_xboole_0(X1,X3)\|~m1_subset_1(X1,k1_zfmisc_1(X2))\|~m1_subset_1(X3,k1_zfmisc_1(X2))), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_18, plain, (k2_flang_2(X2,X1)=k4_subset_1(k8_afinsq_1(X2),k4_flang_1(X2,k2_flang_1(X2)),X1)\|~m1_subset_1(X1,k1_zfmisc_1(k8_afinsq_1(X2)))), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_19, plain, (m1_subset_1(k4_flang_1(X2,X1),k1_zfmisc_1(k3_catalan2(X2)))\|~m1_subset_1(X1,k3_catalan2(X2))), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_20, plain, (k3_catalan2(X1)=k8_afinsq_1(X1)), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_21, plain, (m1_subset_1(k2_flang_1(X1),k3_catalan2(X1))), inference(split_conjunct,[status(thm)],[c_0_13])). fof(c_0_22, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(k8_afinsq_1(esk1_0)))&k2_flang_2(esk1_0,esk2_0)!=k2_flang_2(esk1_0,k7_subset_1(k8_afinsq_1(esk1_0),esk2_0,k4_flang_1(esk1_0,k2_flang_1(esk1_0))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])). cnf(c_0_23, plain, (k2_xboole_0(X1,k4_xboole_0(X2,X1))=k2_xboole_0(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_24, plain, (k7_subset_1(X2,X1,X3)=k4_xboole_0(X1,X3)\|~m1_subset_1(X1,k1_zfmisc_1(X2))), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_25, plain, (k4_subset_1(X2,X1,X3)=k2_xboole_0(X1,X3)\|~m1_subset_1(X3,k1_zfmisc_1(X2))\|~m1_subset_1(X1,k1_zfmisc_1(X2))), inference(evalgc,[status(thm)],[c_0_17])). cnf(c_0_26, plain, (k4_subset_1(k8_afinsq_1(X2),k4_flang_1(X2,k2_flang_1(X2)),X1)=k2_flang_2(X2,X1)\|~m1_subset_1(X1,k1_zfmisc_1(k8_afinsq_1(X2)))), inference(evalgc,[status(thm)],[c_0_18])). cnf(c_0_27, plain, (m1_subset_1(k4_flang_1(X2,X1),k1_zfmisc_1(k8_afinsq_1(X2)))\|~m1_subset_1(X1,k8_afinsq_1(X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19, c_0_20]), c_0_20])). cnf(c_0_28, plain, (m1_subset_1(k2_flang_1(X1),k8_afinsq_1(X1))), inference(rw,[status(thm)],[c_0_21, c_0_20])). cnf(c_0_29, negated_conjecture, (k2_flang_2(esk1_0,esk2_0)!=k2_flang_2(esk1_0,k7_subset_1(k8_afinsq_1(esk1_0),esk2_0,k4_flang_1(esk1_0,k2_flang_1(esk1_0))))), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_30, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(k8_afinsq_1(esk1_0)))), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_31, plain, (k2_xboole_0(X1,k4_xboole_0(X2,X1))=k2_xboole_0(X1,X2)), inference(evalgc,[status(thm)],[c_0_23])). cnf(c_0_32, plain, (k7_subset_1(X2,X1,X3)=k4_xboole_0(X1,X3)\|~m1_subset_1(X1,k1_zfmisc_1(X2))), inference(evalgc,[status(thm)],[c_0_24])). cnf(c_0_33, plain, (k2_xboole_0(k4_flang_1(X1,k2_flang_1(X1)),X2)=k2_flang_2(X1,X2)\|~m1_subset_1(X2,k1_zfmisc_1(k8_afinsq_1(X1)))\|~m1_subset_1(k4_flang_1(X1,k2_flang_1(X1)),k1_zfmisc_1(k8_afinsq_1(X1)))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_25, c_0_26])])). cnf(c_0_34, plain, (m1_subset_1(k4_flang_1(X2,X1),k1_zfmisc_1(k8_afinsq_1(X2)))\|~m1_subset_1(X1,k8_afinsq_1(X2))), inference(evalgc,[status(thm)],[c_0_27])). cnf(c_0_35, plain, (m1_subset_1(k2_flang_1(X1),k8_afinsq_1(X1))), inference(evalgc,[status(thm)],[c_0_28])). fof(c_0_36, plain, ![X16, X17, X18]:(~m1_subset_1(X17,k1_zfmisc_1(X16))\|m1_subset_1(k7_subset_1(X16,X17,X18),k1_zfmisc_1(X16))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k7_subset_1])])). cnf(c_0_37, negated_conjecture, (k2_flang_2(esk1_0,k7_subset_1(k8_afinsq_1(esk1_0),esk2_0,k4_flang_1(esk1_0,k2_flang_1(esk1_0))))!=k2_flang_2(esk1_0,esk2_0)), inference(evalgc,[status(thm)],[c_0_29])). cnf(c_0_38, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(k8_afinsq_1(esk1_0)))), inference(evalgc,[status(thm)],[c_0_30])). cnf(c_0_39, plain, (k2_xboole_0(X1,k7_subset_1(X3,X2,X1))=k2_xboole_0(X1,X2)\|~m1_subset_1(X2,k1_zfmisc_1(X3))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_31, c_0_32])])). cnf(c_0_40, plain, (k2_xboole_0(k4_flang_1(X1,k2_flang_1(X1)),X2)=k2_flang_2(X1,X2)\|~m1_subset_1(X2,k1_zfmisc_1(k8_afinsq_1(X1)))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33, c_0_34]), c_0_35])])])). cnf(c_0_41, plain, (m1_subset_1(k7_subset_1(X2,X1,X3),k1_zfmisc_1(X2))\|~m1_subset_1(X1,k1_zfmisc_1(X2))), inference(split_conjunct,[status(thm)],[c_0_36])). cnf(c_0_42, negated_conjecture, (k2_flang_2(esk1_0,k4_xboole_0(esk2_0,k4_flang_1(esk1_0,k2_flang_1(esk1_0))))!=k2_flang_2(esk1_0,esk2_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37, c_0_32]), c_0_38])])])). cnf(c_0_43, plain, (k2_flang_2(X1,k7_subset_1(X2,X3,k4_flang_1(X1,k2_flang_1(X1))))=k2_xboole_0(k4_flang_1(X1,k2_flang_1(X1)),X3)\|~m1_subset_1(X3,k1_zfmisc_1(X2))\|~m1_subset_1(k7_subset_1(X2,X3,k4_flang_1(X1,k2_flang_1(X1))),k1_zfmisc_1(k8_afinsq_1(X1)))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_39, c_0_40])])). cnf(c_0_44, plain, (m1_subset_1(k7_subset_1(X2,X1,X3),k1_zfmisc_1(X2))\|~m1_subset_1(X1,k1_zfmisc_1(X2))), inference(evalgc,[status(thm)],[c_0_41])). cnf(c_0_45, negated_conjecture, (k2_flang_2(esk1_0,k7_subset_1(X1,esk2_0,k4_flang_1(esk1_0,k2_flang_1(esk1_0))))!=k2_flang_2(esk1_0,esk2_0)\|~m1_subset_1(esk2_0,k1_zfmisc_1(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_42, c_0_32])])). cnf(c_0_46, plain, (k2_flang_2(X1,k7_subset_1(k8_afinsq_1(X1),X2,k4_flang_1(X1,k2_flang_1(X1))))=k2_xboole_0(k4_flang_1(X1,k2_flang_1(X1)),X2)\|~m1_subset_1(X2,k1_zfmisc_1(k8_afinsq_1(X1)))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_43, c_0_44])])). cnf(c_0_47, negated_conjecture, (k2_xboole_0(k4_flang_1(esk1_0,k2_flang_1(esk1_0)),esk2_0)!=k2_flang_2(esk1_0,esk2_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45, c_0_46]), c_0_38])])])). cnf(c_0_48, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47, c_0_40]), c_0_38])]), ['proof']). # SZS output end CNFRefutation	reserve E, x, y, X for set; reserve A, B, C for Subset of E^omega; reserve a, b for Element of E^omega; reserve i, k, l, kl, m, n, mn for Nat; theorem A? = (A \ {<%>E})? proof thus A? = {<%>E} \/ A by Th76 .= {<%>E} \/ (A \ {<%>E}) by XBOOLE_1:39 .= (A \ {<%>E})? by Th76; end;	Convert the following ATP output trace into a readable Mizar proof.
t13_analort	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(l49_geomtrap, axiom, ![X1]:((~(v2_struct_0(X1))&(v13_algstr_0(X1)&(v2_rlvect_1(X1)&(v3_rlvect_1(X1)&(v4_rlvect_1(X1)&(v5_rlvect_1(X1)&(v6_rlvect_1(X1)&(v7_rlvect_1(X1)&(v8_rlvect_1(X1)&l1_rlvect_1(X1))))))))))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>![X4]:(m1_subset_1(X4,u1_struct_0(X1))=>![X5]:(m1_subset_1(X5,k1_numbers)=>![X6]:(m1_subset_1(X6,k1_numbers)=>((r1_analmetr(X1,X2,X3)&X4=k3_rlvect_1(X1,k1_rlvect_1(X1,X2,X5),k1_rlvect_1(X1,X3,X6)))=>(X5=k2_geomtrap(X1,X2,X3,X4)&X6=k3_geomtrap(X1,X2,X3,X4))))))))), file('/scratch/mptp/predsminms1/t13_analort__0', l49_geomtrap)). fof(d4_geomtrap, axiom, ![X1]:((~(v2_struct_0(X1))&(v13_algstr_0(X1)&(v2_rlvect_1(X1)&(v3_rlvect_1(X1)&(v4_rlvect_1(X1)&(v5_rlvect_1(X1)&(v6_rlvect_1(X1)&(v7_rlvect_1(X1)&(v8_rlvect_1(X1)&l1_rlvect_1(X1))))))))))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>![X4]:(m1_subset_1(X4,u1_struct_0(X1))=>(r1_analmetr(X1,X2,X3)=>![X5]:(m1_subset_1(X5,k1_numbers)=>(X5=k2_geomtrap(X1,X2,X3,X4)<=>?[X6]:(m1_subset_1(X6,k1_numbers)&X4=k3_rlvect_1(X1,k1_rlvect_1(X1,X2,X5),k1_rlvect_1(X1,X3,X6)))))))))), file('/scratch/mptp/predsminms1/t13_analort__0', d4_geomtrap)). fof(d2_analort, axiom, ![X1]:((~(v2_struct_0(X1))&(v13_algstr_0(X1)&(v2_rlvect_1(X1)&(v3_rlvect_1(X1)&(v4_rlvect_1(X1)&(v5_rlvect_1(X1)&(v6_rlvect_1(X1)&(v7_rlvect_1(X1)&(v8_rlvect_1(X1)&l1_rlvect_1(X1))))))))))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>![X4]:(m1_subset_1(X4,u1_struct_0(X1))=>k2_analort(X1,X2,X3,X4)=k3_rlvect_1(X1,k1_rlvect_1(X1,X2,k3_geomtrap(X1,X2,X3,X4)),k1_rlvect_1(X1,X3,k1_real_1(k2_geomtrap(X1,X2,X3,X4)))))))), file('/scratch/mptp/predsminms1/t13_analort__0', d2_analort)). fof(dt_k1_real_1, axiom, ![X1]:(m1_subset_1(X1,k1_numbers)=>m1_subset_1(k1_real_1(X1),k1_numbers)), file('/scratch/mptp/predsminms1/t13_analort__0', dt_k1_real_1)). fof(dt_k2_geomtrap, axiom, ![X1, X2, X3, X4]:(((~(v2_struct_0(X1))&(v13_algstr_0(X1)&(v2_rlvect_1(X1)&(v3_rlvect_1(X1)&(v4_rlvect_1(X1)&(v5_rlvect_1(X1)&(v6_rlvect_1(X1)&(v7_rlvect_1(X1)&(v8_rlvect_1(X1)&l1_rlvect_1(X1))))))))))&(m1_subset_1(X2,u1_struct_0(X1))&(m1_subset_1(X3,u1_struct_0(X1))&m1_subset_1(X4,u1_struct_0(X1)))))=>m1_subset_1(k2_geomtrap(X1,X2,X3,X4),k1_numbers)), file('/scratch/mptp/predsminms1/t13_analort__0', dt_k2_geomtrap)). fof(dt_k2_analort, axiom, ![X1, X2, X3, X4]:(((~(v2_struct_0(X1))&(v13_algstr_0(X1)&(v2_rlvect_1(X1)&(v3_rlvect_1(X1)&(v4_rlvect_1(X1)&(v5_rlvect_1(X1)&(v6_rlvect_1(X1)&(v7_rlvect_1(X1)&(v8_rlvect_1(X1)&l1_rlvect_1(X1))))))))))&(m1_subset_1(X2,u1_struct_0(X1))&(m1_subset_1(X3,u1_struct_0(X1))&m1_subset_1(X4,u1_struct_0(X1)))))=>m1_subset_1(k2_analort(X1,X2,X3,X4),u1_struct_0(X1))), file('/scratch/mptp/predsminms1/t13_analort__0', dt_k2_analort)). fof(t13_analort, conjecture, ![X1]:((~(v2_struct_0(X1))&(v13_algstr_0(X1)&(v2_rlvect_1(X1)&(v3_rlvect_1(X1)&(v4_rlvect_1(X1)&(v5_rlvect_1(X1)&(v6_rlvect_1(X1)&(v7_rlvect_1(X1)&(v8_rlvect_1(X1)&l1_rlvect_1(X1))))))))))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>![X4]:(m1_subset_1(X4,u1_struct_0(X1))=>![X5]:(m1_subset_1(X5,u1_struct_0(X1))=>((r1_analmetr(X1,X2,X3)&k2_analort(X1,X2,X3,X4)=k2_analort(X1,X2,X3,X5))=>X4=X5)))))), file('/scratch/mptp/predsminms1/t13_analort__0', t13_analort)). fof(l48_geomtrap, axiom, ![X1]:((~(v2_struct_0(X1))&(v13_algstr_0(X1)&(v2_rlvect_1(X1)&(v3_rlvect_1(X1)&(v4_rlvect_1(X1)&(v5_rlvect_1(X1)&(v6_rlvect_1(X1)&(v7_rlvect_1(X1)&(v8_rlvect_1(X1)&l1_rlvect_1(X1))))))))))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>![X4]:(m1_subset_1(X4,u1_struct_0(X1))=>(r1_analmetr(X1,X2,X3)=>X4=k3_rlvect_1(X1,k1_rlvect_1(X1,X2,k2_geomtrap(X1,X2,X3,X4)),k1_rlvect_1(X1,X3,k3_geomtrap(X1,X2,X3,X4)))))))), file('/scratch/mptp/predsminms1/t13_analort__0', l48_geomtrap)). fof(involutiveness_k1_real_1, axiom, ![X1]:(m1_subset_1(X1,k1_numbers)=>k1_real_1(k1_real_1(X1))=X1), file('/scratch/mptp/predsminms1/t13_analort__0', involutiveness_k1_real_1)). fof(c_0_9, plain, ![X26, X27, X28, X29, X30, X31]:((X30=k2_geomtrap(X26,X27,X28,X29)\|(~r1_analmetr(X26,X27,X28)\|X29!=k3_rlvect_1(X26,k1_rlvect_1(X26,X27,X30),k1_rlvect_1(X26,X28,X31)))\|~m1_subset_1(X31,k1_numbers)\|~m1_subset_1(X30,k1_numbers)\|~m1_subset_1(X29,u1_struct_0(X26))\|~m1_subset_1(X28,u1_struct_0(X26))\|~m1_subset_1(X27,u1_struct_0(X26))\|(v2_struct_0(X26)\|(~v13_algstr_0(X26)\|(~v2_rlvect_1(X26)\|(~v3_rlvect_1(X26)\|(~v4_rlvect_1(X26)\|(~v5_rlvect_1(X26)\|(~v6_rlvect_1(X26)\|(~v7_rlvect_1(X26)\|(~v8_rlvect_1(X26)\|~l1_rlvect_1(X26)))))))))))&(X31=k3_geomtrap(X26,X27,X28,X29)\|(~r1_analmetr(X26,X27,X28)\|X29!=k3_rlvect_1(X26,k1_rlvect_1(X26,X27,X30),k1_rlvect_1(X26,X28,X31)))\|~m1_subset_1(X31,k1_numbers)\|~m1_subset_1(X30,k1_numbers)\|~m1_subset_1(X29,u1_struct_0(X26))\|~m1_subset_1(X28,u1_struct_0(X26))\|~m1_subset_1(X27,u1_struct_0(X26))\|(v2_struct_0(X26)\|(~v13_algstr_0(X26)\|(~v2_rlvect_1(X26)\|(~v3_rlvect_1(X26)\|(~v4_rlvect_1(X26)\|(~v5_rlvect_1(X26)\|(~v6_rlvect_1(X26)\|(~v7_rlvect_1(X26)\|(~v8_rlvect_1(X26)\|~l1_rlvect_1(X26)))))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[l49_geomtrap])])])])])). fof(c_0_10, plain, ![X36, X37, X38, X39, X40, X42]:(((m1_subset_1(esk6_5(X36,X37,X38,X39,X40),k1_numbers)\|X40!=k2_geomtrap(X36,X37,X38,X39)\|~m1_subset_1(X40,k1_numbers)\|~r1_analmetr(X36,X37,X38)\|~m1_subset_1(X39,u1_struct_0(X36))\|~m1_subset_1(X38,u1_struct_0(X36))\|~m1_subset_1(X37,u1_struct_0(X36))\|(v2_struct_0(X36)\|(~v13_algstr_0(X36)\|(~v2_rlvect_1(X36)\|(~v3_rlvect_1(X36)\|(~v4_rlvect_1(X36)\|(~v5_rlvect_1(X36)\|(~v6_rlvect_1(X36)\|(~v7_rlvect_1(X36)\|(~v8_rlvect_1(X36)\|~l1_rlvect_1(X36)))))))))))&(X39=k3_rlvect_1(X36,k1_rlvect_1(X36,X37,X40),k1_rlvect_1(X36,X38,esk6_5(X36,X37,X38,X39,X40)))\|X40!=k2_geomtrap(X36,X37,X38,X39)\|~m1_subset_1(X40,k1_numbers)\|~r1_analmetr(X36,X37,X38)\|~m1_subset_1(X39,u1_struct_0(X36))\|~m1_subset_1(X38,u1_struct_0(X36))\|~m1_subset_1(X37,u1_struct_0(X36))\|(v2_struct_0(X36)\|(~v13_algstr_0(X36)\|(~v2_rlvect_1(X36)\|(~v3_rlvect_1(X36)\|(~v4_rlvect_1(X36)\|(~v5_rlvect_1(X36)\|(~v6_rlvect_1(X36)\|(~v7_rlvect_1(X36)\|(~v8_rlvect_1(X36)\|~l1_rlvect_1(X36))))))))))))&(~m1_subset_1(X42,k1_numbers)\|X39!=k3_rlvect_1(X36,k1_rlvect_1(X36,X37,X40),k1_rlvect_1(X36,X38,X42))\|X40=k2_geomtrap(X36,X37,X38,X39)\|~m1_subset_1(X40,k1_numbers)\|~r1_analmetr(X36,X37,X38)\|~m1_subset_1(X39,u1_struct_0(X36))\|~m1_subset_1(X38,u1_struct_0(X36))\|~m1_subset_1(X37,u1_struct_0(X36))\|(v2_struct_0(X36)\|(~v13_algstr_0(X36)\|(~v2_rlvect_1(X36)\|(~v3_rlvect_1(X36)\|(~v4_rlvect_1(X36)\|(~v5_rlvect_1(X36)\|(~v6_rlvect_1(X36)\|(~v7_rlvect_1(X36)\|(~v8_rlvect_1(X36)\|~l1_rlvect_1(X36)))))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d4_geomtrap])])])])])])). cnf(c_0_11, plain, (X1=k3_geomtrap(X2,X3,X4,X5)\|v2_struct_0(X2)\|~r1_analmetr(X2,X3,X4)\|X5!=k3_rlvect_1(X2,k1_rlvect_1(X2,X3,X6),k1_rlvect_1(X2,X4,X1))\|~m1_subset_1(X1,k1_numbers)\|~m1_subset_1(X6,k1_numbers)\|~m1_subset_1(X5,u1_struct_0(X2))\|~m1_subset_1(X4,u1_struct_0(X2))\|~m1_subset_1(X3,u1_struct_0(X2))\|~v13_algstr_0(X2)\|~v2_rlvect_1(X2)\|~v3_rlvect_1(X2)\|~v4_rlvect_1(X2)\|~v5_rlvect_1(X2)\|~v6_rlvect_1(X2)\|~v7_rlvect_1(X2)\|~v8_rlvect_1(X2)\|~l1_rlvect_1(X2)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_12, plain, (X1=k3_rlvect_1(X2,k1_rlvect_1(X2,X3,X4),k1_rlvect_1(X2,X5,esk6_5(X2,X3,X5,X1,X4)))\|v2_struct_0(X2)\|X4!=k2_geomtrap(X2,X3,X5,X1)\|~m1_subset_1(X4,k1_numbers)\|~r1_analmetr(X2,X3,X5)\|~m1_subset_1(X1,u1_struct_0(X2))\|~m1_subset_1(X5,u1_struct_0(X2))\|~m1_subset_1(X3,u1_struct_0(X2))\|~v13_algstr_0(X2)\|~v2_rlvect_1(X2)\|~v3_rlvect_1(X2)\|~v4_rlvect_1(X2)\|~v5_rlvect_1(X2)\|~v6_rlvect_1(X2)\|~v7_rlvect_1(X2)\|~v8_rlvect_1(X2)\|~l1_rlvect_1(X2)), inference(split_conjunct,[status(thm)],[c_0_10])). fof(c_0_13, plain, ![X22, X23, X24, X25]:(v2_struct_0(X22)\|(~v13_algstr_0(X22)\|(~v2_rlvect_1(X22)\|(~v3_rlvect_1(X22)\|(~v4_rlvect_1(X22)\|(~v5_rlvect_1(X22)\|(~v6_rlvect_1(X22)\|(~v7_rlvect_1(X22)\|(~v8_rlvect_1(X22)\|~l1_rlvect_1(X22)))))))))\|(~m1_subset_1(X23,u1_struct_0(X22))\|(~m1_subset_1(X24,u1_struct_0(X22))\|(~m1_subset_1(X25,u1_struct_0(X22))\|k2_analort(X22,X23,X24,X25)=k3_rlvect_1(X22,k1_rlvect_1(X22,X23,k3_geomtrap(X22,X23,X24,X25)),k1_rlvect_1(X22,X24,k1_real_1(k2_geomtrap(X22,X23,X24,X25)))))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d2_analort])])])])). cnf(c_0_14, plain, (X5=k2_geomtrap(X3,X4,X6,X2)\|v2_struct_0(X3)\|~m1_subset_1(X1,k1_numbers)\|X2!=k3_rlvect_1(X3,k1_rlvect_1(X3,X4,X5),k1_rlvect_1(X3,X6,X1))\|~m1_subset_1(X5,k1_numbers)\|~r1_analmetr(X3,X4,X6)\|~m1_subset_1(X2,u1_struct_0(X3))\|~m1_subset_1(X6,u1_struct_0(X3))\|~m1_subset_1(X4,u1_struct_0(X3))\|~v13_algstr_0(X3)\|~v2_rlvect_1(X3)\|~v3_rlvect_1(X3)\|~v4_rlvect_1(X3)\|~v5_rlvect_1(X3)\|~v6_rlvect_1(X3)\|~v7_rlvect_1(X3)\|~v8_rlvect_1(X3)\|~l1_rlvect_1(X3)), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_15, plain, (X1=k3_geomtrap(X2,X3,X4,X5)\|v2_struct_0(X2)\|X5!=k3_rlvect_1(X2,k1_rlvect_1(X2,X3,X6),k1_rlvect_1(X2,X4,X1))\|~v13_algstr_0(X2)\|~v2_rlvect_1(X2)\|~v3_rlvect_1(X2)\|~v4_rlvect_1(X2)\|~v5_rlvect_1(X2)\|~v6_rlvect_1(X2)\|~v7_rlvect_1(X2)\|~v8_rlvect_1(X2)\|~l1_rlvect_1(X2)\|~m1_subset_1(X6,k1_numbers)\|~m1_subset_1(X1,k1_numbers)\|~r1_analmetr(X2,X3,X4)\|~m1_subset_1(X5,u1_struct_0(X2))\|~m1_subset_1(X4,u1_struct_0(X2))\|~m1_subset_1(X3,u1_struct_0(X2))), inference(evalgc,[status(thm)],[c_0_11])). cnf(c_0_16, plain, (k3_rlvect_1(X2,k1_rlvect_1(X2,X3,X4),k1_rlvect_1(X2,X5,esk6_5(X2,X3,X5,X1,X4)))=X1\|v2_struct_0(X2)\|X4!=k2_geomtrap(X2,X3,X5,X1)\|~v13_algstr_0(X2)\|~v2_rlvect_1(X2)\|~v3_rlvect_1(X2)\|~v4_rlvect_1(X2)\|~v5_rlvect_1(X2)\|~v6_rlvect_1(X2)\|~v7_rlvect_1(X2)\|~v8_rlvect_1(X2)\|~l1_rlvect_1(X2)\|~m1_subset_1(X4,k1_numbers)\|~r1_analmetr(X2,X3,X5)\|~m1_subset_1(X5,u1_struct_0(X2))\|~m1_subset_1(X3,u1_struct_0(X2))\|~m1_subset_1(X1,u1_struct_0(X2))), inference(evalgc,[status(thm)],[c_0_12])). cnf(c_0_17, plain, (m1_subset_1(esk6_5(X1,X2,X3,X4,X5),k1_numbers)\|v2_struct_0(X1)\|X5!=k2_geomtrap(X1,X2,X3,X4)\|~m1_subset_1(X5,k1_numbers)\|~r1_analmetr(X1,X2,X3)\|~m1_subset_1(X4,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~v13_algstr_0(X1)\|~v2_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v8_rlvect_1(X1)\|~l1_rlvect_1(X1)), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_18, plain, (v2_struct_0(X1)\|k2_analort(X1,X2,X3,X4)=k3_rlvect_1(X1,k1_rlvect_1(X1,X2,k3_geomtrap(X1,X2,X3,X4)),k1_rlvect_1(X1,X3,k1_real_1(k2_geomtrap(X1,X2,X3,X4))))\|~v13_algstr_0(X1)\|~v2_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v8_rlvect_1(X1)\|~l1_rlvect_1(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X4,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_13])). cnf(c_0_19, plain, (X5=k2_geomtrap(X3,X4,X6,X2)\|v2_struct_0(X3)\|X2!=k3_rlvect_1(X3,k1_rlvect_1(X3,X4,X5),k1_rlvect_1(X3,X6,X1))\|~v13_algstr_0(X3)\|~v2_rlvect_1(X3)\|~v3_rlvect_1(X3)\|~v4_rlvect_1(X3)\|~v5_rlvect_1(X3)\|~v6_rlvect_1(X3)\|~v7_rlvect_1(X3)\|~v8_rlvect_1(X3)\|~l1_rlvect_1(X3)\|~m1_subset_1(X5,k1_numbers)\|~m1_subset_1(X1,k1_numbers)\|~r1_analmetr(X3,X4,X6)\|~m1_subset_1(X6,u1_struct_0(X3))\|~m1_subset_1(X4,u1_struct_0(X3))\|~m1_subset_1(X2,u1_struct_0(X3))), inference(evalgc,[status(thm)],[c_0_14])). fof(c_0_20, plain, ![X17]:(~m1_subset_1(X17,k1_numbers)\|m1_subset_1(k1_real_1(X17),k1_numbers)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_real_1])])). cnf(c_0_21, plain, (esk6_5(X1,X2,X3,X4,X5)=k3_geomtrap(X1,X2,X3,X4)\|v2_struct_0(X1)\|~r1_analmetr(X1,X2,X3)\|~m1_subset_1(X4,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X5,k1_numbers)\|~m1_subset_1(esk6_5(X1,X2,X3,X4,X5),k1_numbers)\|~l1_rlvect_1(X1)\|~v8_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v13_algstr_0(X1)\|X5!=k2_geomtrap(X1,X2,X3,X4)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_15, c_0_16])])])). cnf(c_0_22, plain, (v2_struct_0(X1)\|m1_subset_1(esk6_5(X1,X2,X3,X4,X5),k1_numbers)\|X5!=k2_geomtrap(X1,X2,X3,X4)\|~v13_algstr_0(X1)\|~v2_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v8_rlvect_1(X1)\|~l1_rlvect_1(X1)\|~m1_subset_1(X5,k1_numbers)\|~r1_analmetr(X1,X2,X3)\|~m1_subset_1(X4,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_17])). cnf(c_0_23, plain, (k3_rlvect_1(X1,k1_rlvect_1(X1,X2,k3_geomtrap(X1,X2,X3,X4)),k1_rlvect_1(X1,X3,k1_real_1(k2_geomtrap(X1,X2,X3,X4))))=k2_analort(X1,X2,X3,X4)\|v2_struct_0(X1)\|~v13_algstr_0(X1)\|~v2_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v8_rlvect_1(X1)\|~l1_rlvect_1(X1)\|~m1_subset_1(X4,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_18])). cnf(c_0_24, plain, (k2_geomtrap(X2,X3,X4,k3_rlvect_1(X2,k1_rlvect_1(X2,X3,X1),k1_rlvect_1(X2,X4,X5)))=X1\|v2_struct_0(X2)\|~r1_analmetr(X2,X3,X4)\|~m1_subset_1(X4,u1_struct_0(X2))\|~m1_subset_1(X3,u1_struct_0(X2))\|~m1_subset_1(k3_rlvect_1(X2,k1_rlvect_1(X2,X3,X1),k1_rlvect_1(X2,X4,X5)),u1_struct_0(X2))\|~m1_subset_1(X1,k1_numbers)\|~m1_subset_1(X5,k1_numbers)\|~l1_rlvect_1(X2)\|~v8_rlvect_1(X2)\|~v7_rlvect_1(X2)\|~v6_rlvect_1(X2)\|~v5_rlvect_1(X2)\|~v4_rlvect_1(X2)\|~v3_rlvect_1(X2)\|~v2_rlvect_1(X2)\|~v13_algstr_0(X2)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_19])])). cnf(c_0_25, plain, (m1_subset_1(k1_real_1(X1),k1_numbers)\|~m1_subset_1(X1,k1_numbers)), inference(split_conjunct,[status(thm)],[c_0_20])). fof(c_0_26, plain, ![X32, X33, X34, X35]:(v2_struct_0(X32)\|(~v13_algstr_0(X32)\|(~v2_rlvect_1(X32)\|(~v3_rlvect_1(X32)\|(~v4_rlvect_1(X32)\|(~v5_rlvect_1(X32)\|(~v6_rlvect_1(X32)\|(~v7_rlvect_1(X32)\|(~v8_rlvect_1(X32)\|~l1_rlvect_1(X32)))))))))\|(~m1_subset_1(X33,u1_struct_0(X32))\|(~m1_subset_1(X34,u1_struct_0(X32))\|~m1_subset_1(X35,u1_struct_0(X32))))\|m1_subset_1(k2_geomtrap(X32,X33,X34,X35),k1_numbers)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k2_geomtrap])])])). cnf(c_0_27, plain, (esk6_5(X1,X2,X3,X4,X5)=k3_geomtrap(X1,X2,X3,X4)\|v2_struct_0(X1)\|X5!=k2_geomtrap(X1,X2,X3,X4)\|~r1_analmetr(X1,X2,X3)\|~m1_subset_1(X4,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X5,k1_numbers)\|~l1_rlvect_1(X1)\|~v8_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v13_algstr_0(X1)), inference(csr,[status(thm)],[c_0_21, c_0_22])). cnf(c_0_28, plain, (k3_rlvect_1(X1,k1_rlvect_1(X1,X2,k3_geomtrap(X1,X2,X3,k3_rlvect_1(X1,k1_rlvect_1(X1,X2,X4),k1_rlvect_1(X1,X3,X5)))),k1_rlvect_1(X1,X3,k1_real_1(X4)))=k2_analort(X1,X2,X3,k3_rlvect_1(X1,k1_rlvect_1(X1,X2,X4),k1_rlvect_1(X1,X3,X5)))\|v2_struct_0(X1)\|~m1_subset_1(k3_rlvect_1(X1,k1_rlvect_1(X1,X2,X4),k1_rlvect_1(X1,X3,X5)),u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l1_rlvect_1(X1)\|~v8_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v13_algstr_0(X1)\|~r1_analmetr(X1,X2,X3)\|~m1_subset_1(X4,k1_numbers)\|~m1_subset_1(X5,k1_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_23, c_0_24])])). cnf(c_0_29, plain, (k3_geomtrap(X1,X2,X3,X4)=k2_geomtrap(X1,X2,X3,X5)\|v2_struct_0(X1)\|X5!=k2_analort(X1,X2,X3,X4)\|~r1_analmetr(X1,X2,X3)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X5,u1_struct_0(X1))\|~m1_subset_1(k3_geomtrap(X1,X2,X3,X4),k1_numbers)\|~m1_subset_1(k1_real_1(k2_geomtrap(X1,X2,X3,X4)),k1_numbers)\|~l1_rlvect_1(X1)\|~v8_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v13_algstr_0(X1)\|~m1_subset_1(X4,u1_struct_0(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_19, c_0_23])])). cnf(c_0_30, plain, (m1_subset_1(k1_real_1(X1),k1_numbers)\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[c_0_25])). cnf(c_0_31, plain, (v2_struct_0(X1)\|m1_subset_1(k2_geomtrap(X1,X2,X3,X4),k1_numbers)\|~v13_algstr_0(X1)\|~v2_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v8_rlvect_1(X1)\|~l1_rlvect_1(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X4,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_32, plain, (m1_subset_1(k3_geomtrap(X1,X2,X3,X4),k1_numbers)\|v2_struct_0(X1)\|X5!=k2_geomtrap(X1,X2,X3,X4)\|~r1_analmetr(X1,X2,X3)\|~m1_subset_1(X4,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X5,k1_numbers)\|~l1_rlvect_1(X1)\|~v8_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v13_algstr_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_22, c_0_27])])). cnf(c_0_33, plain, (k3_rlvect_1(X1,k1_rlvect_1(X1,X2,k3_geomtrap(X1,X2,X3,X5)),k1_rlvect_1(X1,X3,k1_real_1(X4)))=k2_analort(X1,X2,X3,X5)\|v2_struct_0(X1)\|~r1_analmetr(X1,X2,X3)\|~m1_subset_1(X5,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X4,k1_numbers)\|~m1_subset_1(esk6_5(X1,X2,X3,X5,X4),k1_numbers)\|~l1_rlvect_1(X1)\|~v8_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v13_algstr_0(X1)\|X4!=k2_geomtrap(X1,X2,X3,X5)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_28, c_0_16])])). fof(c_0_34, plain, ![X18, X19, X20, X21]:(v2_struct_0(X18)\|(~v13_algstr_0(X18)\|(~v2_rlvect_1(X18)\|(~v3_rlvect_1(X18)\|(~v4_rlvect_1(X18)\|(~v5_rlvect_1(X18)\|(~v6_rlvect_1(X18)\|(~v7_rlvect_1(X18)\|(~v8_rlvect_1(X18)\|~l1_rlvect_1(X18)))))))))\|(~m1_subset_1(X19,u1_struct_0(X18))\|(~m1_subset_1(X20,u1_struct_0(X18))\|~m1_subset_1(X21,u1_struct_0(X18))))\|m1_subset_1(k2_analort(X18,X19,X20,X21),u1_struct_0(X18))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k2_analort])])])). cnf(c_0_35, plain, (k3_geomtrap(X1,X2,X3,X4)=k2_geomtrap(X1,X2,X3,X5)\|v2_struct_0(X1)\|X5!=k2_analort(X1,X2,X3,X4)\|~r1_analmetr(X1,X2,X3)\|~m1_subset_1(k3_geomtrap(X1,X2,X3,X4),k1_numbers)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X5,u1_struct_0(X1))\|~m1_subset_1(X4,u1_struct_0(X1))\|~l1_rlvect_1(X1)\|~v8_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v13_algstr_0(X1)\|~m1_subset_1(k2_geomtrap(X1,X2,X3,X4),k1_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_29, c_0_30])])). cnf(c_0_36, plain, (v2_struct_0(X1)\|m1_subset_1(k2_geomtrap(X1,X2,X3,X4),k1_numbers)\|~v13_algstr_0(X1)\|~v2_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v8_rlvect_1(X1)\|~l1_rlvect_1(X1)\|~m1_subset_1(X4,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_31])). cnf(c_0_37, plain, (m1_subset_1(k3_geomtrap(X1,X2,X3,X4),k1_numbers)\|v2_struct_0(X1)\|~r1_analmetr(X1,X2,X3)\|~m1_subset_1(X4,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(k2_geomtrap(X1,X2,X3,X4),k1_numbers)\|~l1_rlvect_1(X1)\|~v8_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v13_algstr_0(X1)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_32])])). cnf(c_0_38, plain, (k3_geomtrap(X2,X3,X4,k3_rlvect_1(X2,k1_rlvect_1(X2,X3,X5),k1_rlvect_1(X2,X4,X1)))=X1\|v2_struct_0(X2)\|~r1_analmetr(X2,X3,X4)\|~m1_subset_1(k3_rlvect_1(X2,k1_rlvect_1(X2,X3,X5),k1_rlvect_1(X2,X4,X1)),u1_struct_0(X2))\|~m1_subset_1(X4,u1_struct_0(X2))\|~m1_subset_1(X3,u1_struct_0(X2))\|~m1_subset_1(X5,k1_numbers)\|~m1_subset_1(X1,k1_numbers)\|~l1_rlvect_1(X2)\|~v8_rlvect_1(X2)\|~v7_rlvect_1(X2)\|~v6_rlvect_1(X2)\|~v5_rlvect_1(X2)\|~v4_rlvect_1(X2)\|~v3_rlvect_1(X2)\|~v2_rlvect_1(X2)\|~v13_algstr_0(X2)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_15])])). cnf(c_0_39, plain, (k3_rlvect_1(X1,k1_rlvect_1(X1,X2,k3_geomtrap(X1,X2,X3,X4)),k1_rlvect_1(X1,X3,k1_real_1(X5)))=k2_analort(X1,X2,X3,X4)\|v2_struct_0(X1)\|X5!=k2_geomtrap(X1,X2,X3,X4)\|~r1_analmetr(X1,X2,X3)\|~m1_subset_1(X4,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X5,k1_numbers)\|~l1_rlvect_1(X1)\|~v8_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v13_algstr_0(X1)), inference(csr,[status(thm)],[c_0_33, c_0_22])). cnf(c_0_40, plain, (v2_struct_0(X1)\|m1_subset_1(k2_analort(X1,X2,X3,X4),u1_struct_0(X1))\|~v13_algstr_0(X1)\|~v2_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v8_rlvect_1(X1)\|~l1_rlvect_1(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X4,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_34])). cnf(c_0_41, plain, (k3_geomtrap(X1,X2,X3,X4)=k2_geomtrap(X1,X2,X3,X5)\|v2_struct_0(X1)\|X5!=k2_analort(X1,X2,X3,X4)\|~r1_analmetr(X1,X2,X3)\|~m1_subset_1(k3_geomtrap(X1,X2,X3,X4),k1_numbers)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X5,u1_struct_0(X1))\|~m1_subset_1(X4,u1_struct_0(X1))\|~l1_rlvect_1(X1)\|~v8_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v13_algstr_0(X1)), inference(csr,[status(thm)],[c_0_35, c_0_36])). cnf(c_0_42, plain, (m1_subset_1(k3_geomtrap(X1,X2,X3,X4),k1_numbers)\|v2_struct_0(X1)\|~r1_analmetr(X1,X2,X3)\|~m1_subset_1(X4,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l1_rlvect_1(X1)\|~v8_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v13_algstr_0(X1)), inference(csr,[status(thm)],[c_0_37, c_0_36])). fof(c_0_43, negated_conjecture, ~(![X1]:((~(v2_struct_0(X1))&(v13_algstr_0(X1)&(v2_rlvect_1(X1)&(v3_rlvect_1(X1)&(v4_rlvect_1(X1)&(v5_rlvect_1(X1)&(v6_rlvect_1(X1)&(v7_rlvect_1(X1)&(v8_rlvect_1(X1)&l1_rlvect_1(X1))))))))))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>![X4]:(m1_subset_1(X4,u1_struct_0(X1))=>![X5]:(m1_subset_1(X5,u1_struct_0(X1))=>((r1_analmetr(X1,X2,X3)&k2_analort(X1,X2,X3,X4)=k2_analort(X1,X2,X3,X5))=>X4=X5))))))), inference(assume_negation,[status(cth)],[t13_analort])). cnf(c_0_44, plain, (k3_geomtrap(X1,X2,X3,k2_analort(X1,X2,X3,X4))=k1_real_1(X5)\|v2_struct_0(X1)\|~r1_analmetr(X1,X2,X3)\|~m1_subset_1(k2_analort(X1,X2,X3,X4),u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(k3_geomtrap(X1,X2,X3,X4),k1_numbers)\|~m1_subset_1(k1_real_1(X5),k1_numbers)\|~l1_rlvect_1(X1)\|~v8_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v13_algstr_0(X1)\|X5!=k2_geomtrap(X1,X2,X3,X4)\|~m1_subset_1(X4,u1_struct_0(X1))\|~m1_subset_1(X5,k1_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_38, c_0_39])])). cnf(c_0_45, plain, (v2_struct_0(X1)\|m1_subset_1(k2_analort(X1,X2,X3,X4),u1_struct_0(X1))\|~v13_algstr_0(X1)\|~v2_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v8_rlvect_1(X1)\|~l1_rlvect_1(X1)\|~m1_subset_1(X4,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_40])). cnf(c_0_46, plain, (k3_geomtrap(X1,X2,X3,X4)=k2_geomtrap(X1,X2,X3,X5)\|v2_struct_0(X1)\|X5!=k2_analort(X1,X2,X3,X4)\|~r1_analmetr(X1,X2,X3)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X5,u1_struct_0(X1))\|~m1_subset_1(X4,u1_struct_0(X1))\|~l1_rlvect_1(X1)\|~v8_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v13_algstr_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_41, c_0_42])])). fof(c_0_47, negated_conjecture, ((~v2_struct_0(esk1_0)&(v13_algstr_0(esk1_0)&(v2_rlvect_1(esk1_0)&(v3_rlvect_1(esk1_0)&(v4_rlvect_1(esk1_0)&(v5_rlvect_1(esk1_0)&(v6_rlvect_1(esk1_0)&(v7_rlvect_1(esk1_0)&(v8_rlvect_1(esk1_0)&l1_rlvect_1(esk1_0))))))))))&(m1_subset_1(esk2_0,u1_struct_0(esk1_0))&(m1_subset_1(esk3_0,u1_struct_0(esk1_0))&(m1_subset_1(esk4_0,u1_struct_0(esk1_0))&(m1_subset_1(esk5_0,u1_struct_0(esk1_0))&((r1_analmetr(esk1_0,esk2_0,esk3_0)&k2_analort(esk1_0,esk2_0,esk3_0,esk4_0)=k2_analort(esk1_0,esk2_0,esk3_0,esk5_0))&esk4_0!=esk5_0)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_43])])])])). cnf(c_0_48, plain, (k3_geomtrap(X1,X2,X3,k2_analort(X1,X2,X3,X4))=k1_real_1(X5)\|v2_struct_0(X1)\|X5!=k2_geomtrap(X1,X2,X3,X4)\|~r1_analmetr(X1,X2,X3)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X4,u1_struct_0(X1))\|~m1_subset_1(X5,k1_numbers)\|~l1_rlvect_1(X1)\|~v8_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v13_algstr_0(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_44, c_0_30]), c_0_42]), c_0_45])). cnf(c_0_49, plain, (k2_geomtrap(X1,X2,X3,k2_analort(X1,X2,X3,X4))=k3_geomtrap(X1,X2,X3,X4)\|v2_struct_0(X1)\|~r1_analmetr(X1,X2,X3)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(k2_analort(X1,X2,X3,X4),u1_struct_0(X1))\|~m1_subset_1(X4,u1_struct_0(X1))\|~l1_rlvect_1(X1)\|~v8_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v13_algstr_0(X1)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_46])])). cnf(c_0_50, negated_conjecture, (k2_analort(esk1_0,esk2_0,esk3_0,esk4_0)=k2_analort(esk1_0,esk2_0,esk3_0,esk5_0)), inference(split_conjunct,[status(thm)],[c_0_47])). cnf(c_0_51, negated_conjecture, (r1_analmetr(esk1_0,esk2_0,esk3_0)), inference(split_conjunct,[status(thm)],[c_0_47])). cnf(c_0_52, negated_conjecture, (m1_subset_1(esk3_0,u1_struct_0(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_47])). cnf(c_0_53, negated_conjecture, (m1_subset_1(esk2_0,u1_struct_0(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_47])). cnf(c_0_54, negated_conjecture, (m1_subset_1(esk5_0,u1_struct_0(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_47])). cnf(c_0_55, negated_conjecture, (l1_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_47])). cnf(c_0_56, negated_conjecture, (v8_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_47])). cnf(c_0_57, negated_conjecture, (v7_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_47])). cnf(c_0_58, negated_conjecture, (v6_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_47])). cnf(c_0_59, negated_conjecture, (v5_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_47])). cnf(c_0_60, negated_conjecture, (v4_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_47])). cnf(c_0_61, negated_conjecture, (v3_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_47])). cnf(c_0_62, negated_conjecture, (v2_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_47])). cnf(c_0_63, negated_conjecture, (v13_algstr_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_47])). cnf(c_0_64, negated_conjecture, (~v2_struct_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_47])). cnf(c_0_65, plain, (k3_geomtrap(X1,X2,X3,k2_analort(X1,X2,X3,X4))=k1_real_1(k2_geomtrap(X1,X2,X3,X4))\|v2_struct_0(X1)\|~r1_analmetr(X1,X2,X3)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X4,u1_struct_0(X1))\|~m1_subset_1(k2_geomtrap(X1,X2,X3,X4),k1_numbers)\|~l1_rlvect_1(X1)\|~v8_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v13_algstr_0(X1)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_48])])). fof(c_0_66, plain, ![X12, X13, X14, X15]:(v2_struct_0(X12)\|(~v13_algstr_0(X12)\|(~v2_rlvect_1(X12)\|(~v3_rlvect_1(X12)\|(~v4_rlvect_1(X12)\|(~v5_rlvect_1(X12)\|(~v6_rlvect_1(X12)\|(~v7_rlvect_1(X12)\|(~v8_rlvect_1(X12)\|~l1_rlvect_1(X12)))))))))\|(~m1_subset_1(X13,u1_struct_0(X12))\|(~m1_subset_1(X14,u1_struct_0(X12))\|(~m1_subset_1(X15,u1_struct_0(X12))\|(~r1_analmetr(X12,X13,X14)\|X15=k3_rlvect_1(X12,k1_rlvect_1(X12,X13,k2_geomtrap(X12,X13,X14,X15)),k1_rlvect_1(X12,X14,k3_geomtrap(X12,X13,X14,X15)))))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[l48_geomtrap])])])])). cnf(c_0_67, plain, (k2_geomtrap(X1,X2,X3,k2_analort(X1,X2,X3,X4))=k3_geomtrap(X1,X2,X3,X4)\|v2_struct_0(X1)\|~r1_analmetr(X1,X2,X3)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X4,u1_struct_0(X1))\|~l1_rlvect_1(X1)\|~v8_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v13_algstr_0(X1)), inference(csr,[status(thm)],[c_0_49, c_0_45])). cnf(c_0_68, negated_conjecture, (k2_analort(esk1_0,esk2_0,esk3_0,esk5_0)=k2_analort(esk1_0,esk2_0,esk3_0,esk4_0)), inference(evalgc,[status(thm)],[c_0_50])). cnf(c_0_69, negated_conjecture, (r1_analmetr(esk1_0,esk2_0,esk3_0)), inference(evalgc,[status(thm)],[c_0_51])). cnf(c_0_70, negated_conjecture, (m1_subset_1(esk3_0,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[c_0_52])). cnf(c_0_71, negated_conjecture, (m1_subset_1(esk2_0,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[c_0_53])). cnf(c_0_72, negated_conjecture, (m1_subset_1(esk5_0,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[c_0_54])). cnf(c_0_73, negated_conjecture, (l1_rlvect_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_55])). cnf(c_0_74, negated_conjecture, (v8_rlvect_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_56])). cnf(c_0_75, negated_conjecture, (v7_rlvect_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_57])). cnf(c_0_76, negated_conjecture, (v6_rlvect_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_58])). cnf(c_0_77, negated_conjecture, (v5_rlvect_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_59])). cnf(c_0_78, negated_conjecture, (v4_rlvect_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_60])). cnf(c_0_79, negated_conjecture, (v3_rlvect_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_61])). cnf(c_0_80, negated_conjecture, (v2_rlvect_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_62])). cnf(c_0_81, negated_conjecture, (v13_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_63])). cnf(c_0_82, negated_conjecture, (~v2_struct_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_64])). cnf(c_0_83, negated_conjecture, (m1_subset_1(esk4_0,u1_struct_0(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_47])). fof(c_0_84, plain, ![X16]:(~m1_subset_1(X16,k1_numbers)\|k1_real_1(k1_real_1(X16))=X16), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[involutiveness_k1_real_1])])). cnf(c_0_85, plain, (k3_geomtrap(X1,X2,X3,k2_analort(X1,X2,X3,X4))=k1_real_1(k2_geomtrap(X1,X2,X3,X4))\|v2_struct_0(X1)\|~r1_analmetr(X1,X2,X3)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X4,u1_struct_0(X1))\|~l1_rlvect_1(X1)\|~v8_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v13_algstr_0(X1)), inference(csr,[status(thm)],[c_0_65, c_0_36])). cnf(c_0_86, plain, (v2_struct_0(X1)\|X4=k3_rlvect_1(X1,k1_rlvect_1(X1,X2,k2_geomtrap(X1,X2,X3,X4)),k1_rlvect_1(X1,X3,k3_geomtrap(X1,X2,X3,X4)))\|~v13_algstr_0(X1)\|~v2_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v8_rlvect_1(X1)\|~l1_rlvect_1(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X4,u1_struct_0(X1))\|~r1_analmetr(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_66])). cnf(c_0_87, negated_conjecture, (k2_geomtrap(esk1_0,esk2_0,esk3_0,k2_analort(esk1_0,esk2_0,esk3_0,esk4_0))=k3_geomtrap(esk1_0,esk2_0,esk3_0,esk5_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67, c_0_68]), c_0_69]), c_0_70]), c_0_71]), c_0_72]), c_0_73]), c_0_74]), c_0_75]), c_0_76]), c_0_77]), c_0_78]), c_0_79]), c_0_80]), c_0_81])]), c_0_82])])). cnf(c_0_88, negated_conjecture, (m1_subset_1(esk4_0,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[c_0_83])). cnf(c_0_89, plain, (k1_real_1(k1_real_1(X1))=X1\|~m1_subset_1(X1,k1_numbers)), inference(split_conjunct,[status(thm)],[c_0_84])). cnf(c_0_90, negated_conjecture, (k3_geomtrap(esk1_0,esk2_0,esk3_0,k2_analort(esk1_0,esk2_0,esk3_0,esk4_0))=k1_real_1(k2_geomtrap(esk1_0,esk2_0,esk3_0,esk5_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85, c_0_68]), c_0_69]), c_0_70]), c_0_71]), c_0_72]), c_0_73]), c_0_74]), c_0_75]), c_0_76]), c_0_77]), c_0_78]), c_0_79]), c_0_80]), c_0_81])]), c_0_82])])). cnf(c_0_91, plain, (k3_rlvect_1(X1,k1_rlvect_1(X1,X2,k2_geomtrap(X1,X2,X3,X4)),k1_rlvect_1(X1,X3,k3_geomtrap(X1,X2,X3,X4)))=X4\|v2_struct_0(X1)\|~v13_algstr_0(X1)\|~v2_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v8_rlvect_1(X1)\|~l1_rlvect_1(X1)\|~r1_analmetr(X1,X2,X3)\|~m1_subset_1(X4,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_86])). cnf(c_0_92, negated_conjecture, (k3_geomtrap(esk1_0,esk2_0,esk3_0,esk5_0)=k3_geomtrap(esk1_0,esk2_0,esk3_0,esk4_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67, c_0_87]), c_0_69]), c_0_70]), c_0_71]), c_0_88]), c_0_73]), c_0_74]), c_0_75]), c_0_76]), c_0_77]), c_0_78]), c_0_79]), c_0_80]), c_0_81])]), c_0_82])])). cnf(c_0_93, negated_conjecture, (esk4_0!=esk5_0), inference(split_conjunct,[status(thm)],[c_0_47])). cnf(c_0_94, plain, (k1_real_1(k1_real_1(X1))=X1\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[c_0_89])). cnf(c_0_95, negated_conjecture, (k1_real_1(k2_geomtrap(esk1_0,esk2_0,esk3_0,esk5_0))=k1_real_1(k2_geomtrap(esk1_0,esk2_0,esk3_0,esk4_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85, c_0_90]), c_0_69]), c_0_70]), c_0_71]), c_0_88]), c_0_73]), c_0_74]), c_0_75]), c_0_76]), c_0_77]), c_0_78]), c_0_79]), c_0_80]), c_0_81])]), c_0_82])])). cnf(c_0_96, plain, (k3_rlvect_1(X1,k1_rlvect_1(X1,X2,X3),k1_rlvect_1(X1,X4,k3_geomtrap(X1,X2,X4,X5)))=X5\|v2_struct_0(X1)\|X3!=k2_geomtrap(X1,X2,X4,X5)\|~r1_analmetr(X1,X2,X4)\|~m1_subset_1(X4,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X5,u1_struct_0(X1))\|~m1_subset_1(X3,k1_numbers)\|~l1_rlvect_1(X1)\|~v8_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v13_algstr_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_16, c_0_27])])). cnf(c_0_97, negated_conjecture, (k3_rlvect_1(esk1_0,k1_rlvect_1(esk1_0,esk2_0,k2_geomtrap(esk1_0,esk2_0,esk3_0,esk5_0)),k1_rlvect_1(esk1_0,esk3_0,k3_geomtrap(esk1_0,esk2_0,esk3_0,esk4_0)))=esk5_0), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91, c_0_92]), c_0_69]), c_0_72]), c_0_70]), c_0_71]), c_0_73]), c_0_74]), c_0_75]), c_0_76]), c_0_77]), c_0_78]), c_0_79]), c_0_80]), c_0_81])]), c_0_82])])). cnf(c_0_98, negated_conjecture, (esk5_0!=esk4_0), inference(evalgc,[status(thm)],[c_0_93])). cnf(c_0_99, negated_conjecture, (k1_real_1(k1_real_1(k2_geomtrap(esk1_0,esk2_0,esk3_0,esk4_0)))=k2_geomtrap(esk1_0,esk2_0,esk3_0,esk5_0)\|~m1_subset_1(k2_geomtrap(esk1_0,esk2_0,esk3_0,esk5_0),k1_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_94, c_0_95])])). cnf(c_0_100, negated_conjecture, (k2_geomtrap(esk1_0,esk2_0,esk3_0,esk5_0)!=k2_geomtrap(esk1_0,esk2_0,esk3_0,esk4_0)\|~m1_subset_1(k2_geomtrap(esk1_0,esk2_0,esk3_0,esk5_0),k1_numbers)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96, c_0_97]), c_0_69]), c_0_70]), c_0_71]), c_0_88]), c_0_73]), c_0_74]), c_0_75]), c_0_76]), c_0_77]), c_0_78]), c_0_79]), c_0_80]), c_0_81])]), c_0_98]), c_0_82])])). cnf(c_0_101, negated_conjecture, (k2_geomtrap(esk1_0,esk2_0,esk3_0,esk5_0)=k2_geomtrap(esk1_0,esk2_0,esk3_0,esk4_0)\|~m1_subset_1(k2_geomtrap(esk1_0,esk2_0,esk3_0,esk4_0),k1_numbers)\|~m1_subset_1(k2_geomtrap(esk1_0,esk2_0,esk3_0,esk5_0),k1_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_94, c_0_99])])). cnf(c_0_102, negated_conjecture, (k2_geomtrap(esk1_0,esk2_0,esk3_0,esk5_0)!=k2_geomtrap(esk1_0,esk2_0,esk3_0,esk4_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100, c_0_36]), c_0_72]), c_0_70]), c_0_71]), c_0_73]), c_0_74]), c_0_75]), c_0_76]), c_0_77]), c_0_78]), c_0_79]), c_0_80]), c_0_81])]), c_0_82])])). cnf(c_0_103, negated_conjecture, (~m1_subset_1(k2_geomtrap(esk1_0,esk2_0,esk3_0,esk4_0),k1_numbers)\|~m1_subset_1(k2_geomtrap(esk1_0,esk2_0,esk3_0,esk5_0),k1_numbers)), inference(sr,[status(thm)],[c_0_101, c_0_102])). cnf(c_0_104, negated_conjecture, (~m1_subset_1(k2_geomtrap(esk1_0,esk2_0,esk3_0,esk4_0),k1_numbers)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103, c_0_36]), c_0_72]), c_0_70]), c_0_71]), c_0_73]), c_0_74]), c_0_75]), c_0_76]), c_0_77]), c_0_78]), c_0_79]), c_0_80]), c_0_81])]), c_0_82])])). cnf(c_0_105, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104, c_0_36]), c_0_88]), c_0_70]), c_0_71]), c_0_73]), c_0_74]), c_0_75]), c_0_76]), c_0_77]), c_0_78]), c_0_79]), c_0_80]), c_0_81])]), c_0_82]), ['proof']). # SZS output end CNFRefutation	reserve V for RealLinearSpace, u,u1,u2,v,v1,v2,w,w1,x,y for VECTOR of V, a,a1,a2,b,b1,b2,c1,c2,n,k1,k2 for Real; theorem Th13: Gen x,y & Orte(x,y,u)=Orte(x,y,v) implies u=v proof assume that A1: Gen x,y and A2: Orte(x,y,u)=Orte(x,y,v); pr2(x,y,u)x + (-pr1(x,y,u))y - (pr2(x,y,v)x + (-pr1(x,y,v))y) =0.V by A2,RLVECT_1:15; then pr2(x,y,u)x + (-pr1(x,y,u))y - (pr2(x,y,v)x) - (-pr1(x,y,v))y =0.V by RLVECT_1:27; then pr2(x,y,u)x + (-(pr2(x,y,v))x) + ((-pr1(x,y,u))y) - (-pr1(x,y,v))y =0.V by RLVECT_1:def 3; then pr2(x,y,u)x - pr2(x,y,v)x + ((-pr1(x,y,u))y - (-pr1(x,y,v))y) =0.V by RLVECT_1:def 3; then (pr2(x,y,u) - pr2(x,y,v))x + ((-pr1(x,y,u))y - (-pr1(x,y,v))y) =0.V by RLVECT_1:35; then A3: (pr2(x,y,u) - pr2(x,y,v))x + ((-pr1(x,y,u)) - (-pr1(x,y,v)))y =0.V by RLVECT_1:35; then A4: pr2(x,y,u) - pr2(x,y,v)=0 by A1,ANALMETR:def 1; (-pr1(x,y,u)) - (-pr1(x,y,v))=0 by A1,A3,ANALMETR:def 1; hence u=pr1(x,y,v)x + pr2(x,y,v)*y by A1,A4,Lm5 .=v by A1,Lm5; end;	Convert the following ATP output trace into a readable Mizar proof.
t63_qc_lang2	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t63_qc_lang2, conjecture, ![X1]:(m1_qc_lang1(X1)=>![X2]:(m1_subset_1(X2,k9_qc_lang1(X1))=>![X3]:(m1_subset_1(X3,k9_qc_lang1(X1))=>![X4]:(m1_subset_1(X4,k9_qc_lang1(X1))=>(~((~((r3_qc_lang2(X1,X2,X3)&r2_qc_lang2(X1,X3,X4)))&(~((r2_qc_lang2(X1,X2,X3)&r3_qc_lang2(X1,X3,X4)))&(~((r2_qc_lang2(X1,X2,X3)&r1_qc_lang2(X1,X3,X4)))&(~((r1_qc_lang2(X1,X2,X3)&r2_qc_lang2(X1,X3,X4)))&(~((r3_qc_lang2(X1,X2,X3)&r1_qc_lang2(X1,X3,X4)))&~((r1_qc_lang2(X1,X2,X3)&r3_qc_lang2(X1,X3,X4)))))))))=>r3_qc_lang2(X1,X2,X4)))))), file('/scratch/mptp/predsminms1/t63_qc_lang2__0', t63_qc_lang2)). fof(d21_qc_lang2, axiom, ![X1]:(m1_qc_lang1(X1)=>![X2]:(m1_subset_1(X2,k9_qc_lang1(X1))=>![X3]:(m1_subset_1(X3,k9_qc_lang1(X1))=>(r3_qc_lang2(X1,X2,X3)<=>(r2_qc_lang2(X1,X2,X3)&~(X2=X3)))))), file('/scratch/mptp/predsminms1/t63_qc_lang2__0', d21_qc_lang2)). fof(t52_qc_lang2, axiom, ![X1]:(m1_qc_lang1(X1)=>![X2]:(m1_subset_1(X2,k9_qc_lang1(X1))=>![X3]:(m1_subset_1(X3,k9_qc_lang1(X1))=>(r1_qc_lang2(X1,X2,X3)=>r2_qc_lang2(X1,X2,X3))))), file('/scratch/mptp/predsminms1/t63_qc_lang2__0', t52_qc_lang2)). fof(t57_qc_lang2, axiom, ![X1]:(m1_qc_lang1(X1)=>![X2]:(m1_subset_1(X2,k9_qc_lang1(X1))=>![X3]:(m1_subset_1(X3,k9_qc_lang1(X1))=>![X4]:(m1_subset_1(X4,k9_qc_lang1(X1))=>((r2_qc_lang2(X1,X2,X3)&r2_qc_lang2(X1,X3,X4))=>r2_qc_lang2(X1,X2,X4)))))), file('/scratch/mptp/predsminms1/t63_qc_lang2__0', t57_qc_lang2)). fof(t59_qc_lang2, axiom, ![X1]:(m1_qc_lang1(X1)=>![X2]:(m1_subset_1(X2,k9_qc_lang1(X1))=>![X3]:(m1_subset_1(X3,k9_qc_lang1(X1))=>~((r3_qc_lang2(X1,X2,X3)&r2_qc_lang2(X1,X3,X2)))))), file('/scratch/mptp/predsminms1/t63_qc_lang2__0', t59_qc_lang2)). fof(t61_qc_lang2, axiom, ![X1]:(m1_qc_lang1(X1)=>![X2]:(m1_subset_1(X2,k9_qc_lang1(X1))=>![X3]:(m1_subset_1(X3,k9_qc_lang1(X1))=>~((r2_qc_lang2(X1,X2,X3)&r1_qc_lang2(X1,X3,X2)))))), file('/scratch/mptp/predsminms1/t63_qc_lang2__0', t61_qc_lang2)). fof(c_0_6, plain, ![X1, X2, X3, X4]:(epred1_4(X4,X3,X2,X1)<=>(~((r2_qc_lang2(X1,X2,X3)&r3_qc_lang2(X1,X3,X4)))&(~((r2_qc_lang2(X1,X2,X3)&r1_qc_lang2(X1,X3,X4)))&(~((r1_qc_lang2(X1,X2,X3)&r2_qc_lang2(X1,X3,X4)))&(~((r3_qc_lang2(X1,X2,X3)&r1_qc_lang2(X1,X3,X4)))&~((r1_qc_lang2(X1,X2,X3)&r3_qc_lang2(X1,X3,X4)))))))), introduced(definition)). fof(c_0_7, negated_conjecture, ~(![X1]:(m1_qc_lang1(X1)=>![X2]:(m1_subset_1(X2,k9_qc_lang1(X1))=>![X3]:(m1_subset_1(X3,k9_qc_lang1(X1))=>![X4]:(m1_subset_1(X4,k9_qc_lang1(X1))=>(~((~((r3_qc_lang2(X1,X2,X3)&r2_qc_lang2(X1,X3,X4)))&epred1_4(X4,X3,X2,X1)))=>r3_qc_lang2(X1,X2,X4))))))), inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[t63_qc_lang2]), c_0_6])). fof(c_0_8, plain, ![X1, X2, X3, X4]:((~((r2_qc_lang2(X1,X2,X3)&r3_qc_lang2(X1,X3,X4)))&(~((r2_qc_lang2(X1,X2,X3)&r1_qc_lang2(X1,X3,X4)))&(~((r1_qc_lang2(X1,X2,X3)&r2_qc_lang2(X1,X3,X4)))&(~((r3_qc_lang2(X1,X2,X3)&r1_qc_lang2(X1,X3,X4)))&~((r1_qc_lang2(X1,X2,X3)&r3_qc_lang2(X1,X3,X4)))))))=>epred1_4(X4,X3,X2,X1)), inference(split_equiv,[status(thm)],[c_0_6])). fof(c_0_9, plain, ![X9, X10, X11]:(((r2_qc_lang2(X9,X10,X11)\|~r3_qc_lang2(X9,X10,X11)\|~m1_subset_1(X11,k9_qc_lang1(X9))\|~m1_subset_1(X10,k9_qc_lang1(X9))\|~m1_qc_lang1(X9))&(X10!=X11\|~r3_qc_lang2(X9,X10,X11)\|~m1_subset_1(X11,k9_qc_lang1(X9))\|~m1_subset_1(X10,k9_qc_lang1(X9))\|~m1_qc_lang1(X9)))&(~r2_qc_lang2(X9,X10,X11)\|X10=X11\|r3_qc_lang2(X9,X10,X11)\|~m1_subset_1(X11,k9_qc_lang1(X9))\|~m1_subset_1(X10,k9_qc_lang1(X9))\|~m1_qc_lang1(X9))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d21_qc_lang2])])])])])). fof(c_0_10, negated_conjecture, (m1_qc_lang1(esk1_0)&(m1_subset_1(esk2_0,k9_qc_lang1(esk1_0))&(m1_subset_1(esk3_0,k9_qc_lang1(esk1_0))&(m1_subset_1(esk4_0,k9_qc_lang1(esk1_0))&(((r3_qc_lang2(esk1_0,esk2_0,esk3_0)\|~epred1_4(esk4_0,esk3_0,esk2_0,esk1_0))&(r2_qc_lang2(esk1_0,esk3_0,esk4_0)\|~epred1_4(esk4_0,esk3_0,esk2_0,esk1_0)))&~r3_qc_lang2(esk1_0,esk2_0,esk4_0)))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])])). fof(c_0_11, plain, ![X25, X26, X27, X28]:((((((r1_qc_lang2(X25,X26,X27)\|r3_qc_lang2(X25,X26,X27)\|r1_qc_lang2(X25,X26,X27)\|r2_qc_lang2(X25,X26,X27)\|r2_qc_lang2(X25,X26,X27)\|epred1_4(X28,X27,X26,X25))&(r3_qc_lang2(X25,X27,X28)\|r3_qc_lang2(X25,X26,X27)\|r1_qc_lang2(X25,X26,X27)\|r2_qc_lang2(X25,X26,X27)\|r2_qc_lang2(X25,X26,X27)\|epred1_4(X28,X27,X26,X25)))&((r1_qc_lang2(X25,X26,X27)\|r1_qc_lang2(X25,X27,X28)\|r1_qc_lang2(X25,X26,X27)\|r2_qc_lang2(X25,X26,X27)\|r2_qc_lang2(X25,X26,X27)\|epred1_4(X28,X27,X26,X25))&(r3_qc_lang2(X25,X27,X28)\|r1_qc_lang2(X25,X27,X28)\|r1_qc_lang2(X25,X26,X27)\|r2_qc_lang2(X25,X26,X27)\|r2_qc_lang2(X25,X26,X27)\|epred1_4(X28,X27,X26,X25))))&(((r1_qc_lang2(X25,X26,X27)\|r3_qc_lang2(X25,X26,X27)\|r2_qc_lang2(X25,X27,X28)\|r2_qc_lang2(X25,X26,X27)\|r2_qc_lang2(X25,X26,X27)\|epred1_4(X28,X27,X26,X25))&(r3_qc_lang2(X25,X27,X28)\|r3_qc_lang2(X25,X26,X27)\|r2_qc_lang2(X25,X27,X28)\|r2_qc_lang2(X25,X26,X27)\|r2_qc_lang2(X25,X26,X27)\|epred1_4(X28,X27,X26,X25)))&((r1_qc_lang2(X25,X26,X27)\|r1_qc_lang2(X25,X27,X28)\|r2_qc_lang2(X25,X27,X28)\|r2_qc_lang2(X25,X26,X27)\|r2_qc_lang2(X25,X26,X27)\|epred1_4(X28,X27,X26,X25))&(r3_qc_lang2(X25,X27,X28)\|r1_qc_lang2(X25,X27,X28)\|r2_qc_lang2(X25,X27,X28)\|r2_qc_lang2(X25,X26,X27)\|r2_qc_lang2(X25,X26,X27)\|epred1_4(X28,X27,X26,X25)))))&((((r1_qc_lang2(X25,X26,X27)\|r3_qc_lang2(X25,X26,X27)\|r1_qc_lang2(X25,X26,X27)\|r1_qc_lang2(X25,X27,X28)\|r2_qc_lang2(X25,X26,X27)\|epred1_4(X28,X27,X26,X25))&(r3_qc_lang2(X25,X27,X28)\|r3_qc_lang2(X25,X26,X27)\|r1_qc_lang2(X25,X26,X27)\|r1_qc_lang2(X25,X27,X28)\|r2_qc_lang2(X25,X26,X27)\|epred1_4(X28,X27,X26,X25)))&((r1_qc_lang2(X25,X26,X27)\|r1_qc_lang2(X25,X27,X28)\|r1_qc_lang2(X25,X26,X27)\|r1_qc_lang2(X25,X27,X28)\|r2_qc_lang2(X25,X26,X27)\|epred1_4(X28,X27,X26,X25))&(r3_qc_lang2(X25,X27,X28)\|r1_qc_lang2(X25,X27,X28)\|r1_qc_lang2(X25,X26,X27)\|r1_qc_lang2(X25,X27,X28)\|r2_qc_lang2(X25,X26,X27)\|epred1_4(X28,X27,X26,X25))))&(((r1_qc_lang2(X25,X26,X27)\|r3_qc_lang2(X25,X26,X27)\|r2_qc_lang2(X25,X27,X28)\|r1_qc_lang2(X25,X27,X28)\|r2_qc_lang2(X25,X26,X27)\|epred1_4(X28,X27,X26,X25))&(r3_qc_lang2(X25,X27,X28)\|r3_qc_lang2(X25,X26,X27)\|r2_qc_lang2(X25,X27,X28)\|r1_qc_lang2(X25,X27,X28)\|r2_qc_lang2(X25,X26,X27)\|epred1_4(X28,X27,X26,X25)))&((r1_qc_lang2(X25,X26,X27)\|r1_qc_lang2(X25,X27,X28)\|r2_qc_lang2(X25,X27,X28)\|r1_qc_lang2(X25,X27,X28)\|r2_qc_lang2(X25,X26,X27)\|epred1_4(X28,X27,X26,X25))&(r3_qc_lang2(X25,X27,X28)\|r1_qc_lang2(X25,X27,X28)\|r2_qc_lang2(X25,X27,X28)\|r1_qc_lang2(X25,X27,X28)\|r2_qc_lang2(X25,X26,X27)\|epred1_4(X28,X27,X26,X25))))))&(((((r1_qc_lang2(X25,X26,X27)\|r3_qc_lang2(X25,X26,X27)\|r1_qc_lang2(X25,X26,X27)\|r2_qc_lang2(X25,X26,X27)\|r3_qc_lang2(X25,X27,X28)\|epred1_4(X28,X27,X26,X25))&(r3_qc_lang2(X25,X27,X28)\|r3_qc_lang2(X25,X26,X27)\|r1_qc_lang2(X25,X26,X27)\|r2_qc_lang2(X25,X26,X27)\|r3_qc_lang2(X25,X27,X28)\|epred1_4(X28,X27,X26,X25)))&((r1_qc_lang2(X25,X26,X27)\|r1_qc_lang2(X25,X27,X28)\|r1_qc_lang2(X25,X26,X27)\|r2_qc_lang2(X25,X26,X27)\|r3_qc_lang2(X25,X27,X28)\|epred1_4(X28,X27,X26,X25))&(r3_qc_lang2(X25,X27,X28)\|r1_qc_lang2(X25,X27,X28)\|r1_qc_lang2(X25,X26,X27)\|r2_qc_lang2(X25,X26,X27)\|r3_qc_lang2(X25,X27,X28)\|epred1_4(X28,X27,X26,X25))))&(((r1_qc_lang2(X25,X26,X27)\|r3_qc_lang2(X25,X26,X27)\|r2_qc_lang2(X25,X27,X28)\|r2_qc_lang2(X25,X26,X27)\|r3_qc_lang2(X25,X27,X28)\|epred1_4(X28,X27,X26,X25))&(r3_qc_lang2(X25,X27,X28)\|r3_qc_lang2(X25,X26,X27)\|r2_qc_lang2(X25,X27,X28)\|r2_qc_lang2(X25,X26,X27)\|r3_qc_lang2(X25,X27,X28)\|epred1_4(X28,X27,X26,X25)))&((r1_qc_lang2(X25,X26,X27)\|r1_qc_lang2(X25,X27,X28)\|r2_qc_lang2(X25,X27,X28)\|r2_qc_lang2(X25,X26,X27)\|r3_qc_lang2(X25,X27,X28)\|epred1_4(X28,X27,X26,X25))&(r3_qc_lang2(X25,X27,X28)\|r1_qc_lang2(X25,X27,X28)\|r2_qc_lang2(X25,X27,X28)\|r2_qc_lang2(X25,X26,X27)\|r3_qc_lang2(X25,X27,X28)\|epred1_4(X28,X27,X26,X25)))))&((((r1_qc_lang2(X25,X26,X27)\|r3_qc_lang2(X25,X26,X27)\|r1_qc_lang2(X25,X26,X27)\|r1_qc_lang2(X25,X27,X28)\|r3_qc_lang2(X25,X27,X28)\|epred1_4(X28,X27,X26,X25))&(r3_qc_lang2(X25,X27,X28)\|r3_qc_lang2(X25,X26,X27)\|r1_qc_lang2(X25,X26,X27)\|r1_qc_lang2(X25,X27,X28)\|r3_qc_lang2(X25,X27,X28)\|epred1_4(X28,X27,X26,X25)))&((r1_qc_lang2(X25,X26,X27)\|r1_qc_lang2(X25,X27,X28)\|r1_qc_lang2(X25,X26,X27)\|r1_qc_lang2(X25,X27,X28)\|r3_qc_lang2(X25,X27,X28)\|epred1_4(X28,X27,X26,X25))&(r3_qc_lang2(X25,X27,X28)\|r1_qc_lang2(X25,X27,X28)\|r1_qc_lang2(X25,X26,X27)\|r1_qc_lang2(X25,X27,X28)\|r3_qc_lang2(X25,X27,X28)\|epred1_4(X28,X27,X26,X25))))&(((r1_qc_lang2(X25,X26,X27)\|r3_qc_lang2(X25,X26,X27)\|r2_qc_lang2(X25,X27,X28)\|r1_qc_lang2(X25,X27,X28)\|r3_qc_lang2(X25,X27,X28)\|epred1_4(X28,X27,X26,X25))&(r3_qc_lang2(X25,X27,X28)\|r3_qc_lang2(X25,X26,X27)\|r2_qc_lang2(X25,X27,X28)\|r1_qc_lang2(X25,X27,X28)\|r3_qc_lang2(X25,X27,X28)\|epred1_4(X28,X27,X26,X25)))&((r1_qc_lang2(X25,X26,X27)\|r1_qc_lang2(X25,X27,X28)\|r2_qc_lang2(X25,X27,X28)\|r1_qc_lang2(X25,X27,X28)\|r3_qc_lang2(X25,X27,X28)\|epred1_4(X28,X27,X26,X25))&(r3_qc_lang2(X25,X27,X28)\|r1_qc_lang2(X25,X27,X28)\|r2_qc_lang2(X25,X27,X28)\|r1_qc_lang2(X25,X27,X28)\|r3_qc_lang2(X25,X27,X28)\|epred1_4(X28,X27,X26,X25))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])). cnf(c_0_12, plain, (r2_qc_lang2(X1,X2,X3)\|~r3_qc_lang2(X1,X2,X3)\|~m1_subset_1(X3,k9_qc_lang1(X1))\|~m1_subset_1(X2,k9_qc_lang1(X1))\|~m1_qc_lang1(X1)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_13, negated_conjecture, (m1_subset_1(esk4_0,k9_qc_lang1(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_14, negated_conjecture, (m1_qc_lang1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_15, plain, (r3_qc_lang2(X1,X2,X3)\|r1_qc_lang2(X1,X2,X3)\|r2_qc_lang2(X1,X2,X3)\|r1_qc_lang2(X1,X2,X3)\|r3_qc_lang2(X1,X2,X3)\|epred1_4(X3,X2,X4,X1)), inference(split_conjunct,[status(thm)],[c_0_11])). fof(c_0_16, plain, ![X12, X13, X14]:(~m1_qc_lang1(X12)\|(~m1_subset_1(X13,k9_qc_lang1(X12))\|(~m1_subset_1(X14,k9_qc_lang1(X12))\|(~r1_qc_lang2(X12,X13,X14)\|r2_qc_lang2(X12,X13,X14))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t52_qc_lang2])])])). fof(c_0_17, plain, ![X15, X16, X17, X18]:(~m1_qc_lang1(X15)\|(~m1_subset_1(X16,k9_qc_lang1(X15))\|(~m1_subset_1(X17,k9_qc_lang1(X15))\|(~m1_subset_1(X18,k9_qc_lang1(X15))\|(~r2_qc_lang2(X15,X16,X17)\|~r2_qc_lang2(X15,X17,X18)\|r2_qc_lang2(X15,X16,X18)))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t57_qc_lang2])])])). cnf(c_0_18, plain, (r2_qc_lang2(X1,X2,X3)\|~m1_qc_lang1(X1)\|~r3_qc_lang2(X1,X2,X3)\|~m1_subset_1(X3,k9_qc_lang1(X1))\|~m1_subset_1(X2,k9_qc_lang1(X1))), inference(evalgc,[status(thm)],[c_0_12])). cnf(c_0_19, negated_conjecture, (m1_subset_1(esk4_0,k9_qc_lang1(esk1_0))), inference(evalgc,[status(thm)],[c_0_13])). cnf(c_0_20, negated_conjecture, (m1_qc_lang1(esk1_0)), inference(evalgc,[status(thm)],[c_0_14])). cnf(c_0_21, negated_conjecture, (m1_subset_1(esk3_0,k9_qc_lang1(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_22, negated_conjecture, (r2_qc_lang2(esk1_0,esk3_0,esk4_0)\|~epred1_4(esk4_0,esk3_0,esk2_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_23, plain, (r3_qc_lang2(X1,X2,X3)\|r2_qc_lang2(X1,X2,X3)\|r1_qc_lang2(X1,X2,X3)\|epred1_4(X3,X2,X4,X1)), inference(cn,[status(thm)],[c_0_15])). cnf(c_0_24, plain, (r2_qc_lang2(X1,X2,X3)\|~m1_qc_lang1(X1)\|~m1_subset_1(X2,k9_qc_lang1(X1))\|~m1_subset_1(X3,k9_qc_lang1(X1))\|~r1_qc_lang2(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_25, plain, (r1_qc_lang2(X1,X2,X3)\|r3_qc_lang2(X1,X2,X3)\|r1_qc_lang2(X1,X2,X3)\|r2_qc_lang2(X1,X2,X3)\|r2_qc_lang2(X1,X2,X3)\|epred1_4(X4,X3,X2,X1)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_26, plain, (r2_qc_lang2(X1,X2,X4)\|~m1_qc_lang1(X1)\|~m1_subset_1(X2,k9_qc_lang1(X1))\|~m1_subset_1(X3,k9_qc_lang1(X1))\|~m1_subset_1(X4,k9_qc_lang1(X1))\|~r2_qc_lang2(X1,X2,X3)\|~r2_qc_lang2(X1,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_17])). cnf(c_0_27, negated_conjecture, (r2_qc_lang2(esk1_0,X1,esk4_0)\|~r3_qc_lang2(esk1_0,X1,esk4_0)\|~m1_subset_1(X1,k9_qc_lang1(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18, c_0_19]), c_0_20])])])). cnf(c_0_28, negated_conjecture, (m1_subset_1(esk3_0,k9_qc_lang1(esk1_0))), inference(evalgc,[status(thm)],[c_0_21])). cnf(c_0_29, negated_conjecture, (r2_qc_lang2(esk1_0,esk3_0,esk4_0)\|~epred1_4(esk4_0,esk3_0,esk2_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_22])). cnf(c_0_30, plain, (r3_qc_lang2(X1,X2,X3)\|r2_qc_lang2(X1,X2,X3)\|r1_qc_lang2(X1,X2,X3)\|epred1_4(X3,X2,X4,X1)), inference(evalgc,[status(thm)],[c_0_23])). cnf(c_0_31, plain, (r2_qc_lang2(X1,X2,X3)\|~m1_qc_lang1(X1)\|~r1_qc_lang2(X1,X2,X3)\|~m1_subset_1(X3,k9_qc_lang1(X1))\|~m1_subset_1(X2,k9_qc_lang1(X1))), inference(evalgc,[status(thm)],[c_0_24])). cnf(c_0_32, negated_conjecture, (m1_subset_1(esk2_0,k9_qc_lang1(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_33, negated_conjecture, (r3_qc_lang2(esk1_0,esk2_0,esk3_0)\|~epred1_4(esk4_0,esk3_0,esk2_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_34, plain, (r3_qc_lang2(X1,X2,X3)\|r2_qc_lang2(X1,X2,X3)\|r1_qc_lang2(X1,X2,X3)\|epred1_4(X4,X3,X2,X1)), inference(cn,[status(thm)],[c_0_25])). cnf(c_0_35, plain, (r2_qc_lang2(X1,X2,X4)\|~m1_qc_lang1(X1)\|~r2_qc_lang2(X1,X3,X4)\|~r2_qc_lang2(X1,X2,X3)\|~m1_subset_1(X4,k9_qc_lang1(X1))\|~m1_subset_1(X3,k9_qc_lang1(X1))\|~m1_subset_1(X2,k9_qc_lang1(X1))), inference(evalgc,[status(thm)],[c_0_26])). cnf(c_0_36, negated_conjecture, (r2_qc_lang2(esk1_0,esk3_0,esk4_0)\|~r3_qc_lang2(esk1_0,esk3_0,esk4_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_27, c_0_28])])). cnf(c_0_37, negated_conjecture, (r2_qc_lang2(esk1_0,esk3_0,esk4_0)\|r1_qc_lang2(esk1_0,esk3_0,esk4_0)\|r3_qc_lang2(esk1_0,esk3_0,esk4_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_29, c_0_30])])). cnf(c_0_38, negated_conjecture, (r2_qc_lang2(esk1_0,X1,esk4_0)\|~r1_qc_lang2(esk1_0,X1,esk4_0)\|~m1_subset_1(X1,k9_qc_lang1(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31, c_0_19]), c_0_20])])])). cnf(c_0_39, negated_conjecture, (r2_qc_lang2(esk1_0,X1,esk3_0)\|~r3_qc_lang2(esk1_0,X1,esk3_0)\|~m1_subset_1(X1,k9_qc_lang1(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18, c_0_28]), c_0_20])])])). cnf(c_0_40, negated_conjecture, (m1_subset_1(esk2_0,k9_qc_lang1(esk1_0))), inference(evalgc,[status(thm)],[c_0_32])). cnf(c_0_41, negated_conjecture, (r3_qc_lang2(esk1_0,esk2_0,esk3_0)\|~epred1_4(esk4_0,esk3_0,esk2_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_33])). cnf(c_0_42, plain, (r3_qc_lang2(X1,X2,X3)\|r2_qc_lang2(X1,X2,X3)\|r1_qc_lang2(X1,X2,X3)\|epred1_4(X4,X3,X2,X1)), inference(evalgc,[status(thm)],[c_0_34])). fof(c_0_43, plain, ![X22, X23, X24]:(~m1_qc_lang1(X22)\|(~m1_subset_1(X23,k9_qc_lang1(X22))\|(~m1_subset_1(X24,k9_qc_lang1(X22))\|(~r3_qc_lang2(X22,X23,X24)\|~r2_qc_lang2(X22,X24,X23))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t59_qc_lang2])])])). cnf(c_0_44, plain, (X2=X3\|r3_qc_lang2(X1,X2,X3)\|~r2_qc_lang2(X1,X2,X3)\|~m1_subset_1(X3,k9_qc_lang1(X1))\|~m1_subset_1(X2,k9_qc_lang1(X1))\|~m1_qc_lang1(X1)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_45, negated_conjecture, (r2_qc_lang2(esk1_0,X1,esk4_0)\|~r2_qc_lang2(esk1_0,X2,esk4_0)\|~r2_qc_lang2(esk1_0,X1,X2)\|~m1_subset_1(X2,k9_qc_lang1(esk1_0))\|~m1_subset_1(X1,k9_qc_lang1(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35, c_0_19]), c_0_20])])])). cnf(c_0_46, negated_conjecture, (r2_qc_lang2(esk1_0,esk3_0,esk4_0)\|r1_qc_lang2(esk1_0,esk3_0,esk4_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_36, c_0_37])])). cnf(c_0_47, negated_conjecture, (r2_qc_lang2(esk1_0,esk3_0,esk4_0)\|~r1_qc_lang2(esk1_0,esk3_0,esk4_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_38, c_0_28])])). cnf(c_0_48, negated_conjecture, (r2_qc_lang2(esk1_0,esk2_0,esk3_0)\|~r3_qc_lang2(esk1_0,esk2_0,esk3_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_39, c_0_40])])). cnf(c_0_49, negated_conjecture, (r3_qc_lang2(esk1_0,esk2_0,esk3_0)\|r1_qc_lang2(esk1_0,esk2_0,esk3_0)\|r2_qc_lang2(esk1_0,esk2_0,esk3_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_41, c_0_42])])). cnf(c_0_50, negated_conjecture, (r2_qc_lang2(esk1_0,X1,esk3_0)\|~r1_qc_lang2(esk1_0,X1,esk3_0)\|~m1_subset_1(X1,k9_qc_lang1(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31, c_0_28]), c_0_20])])])). cnf(c_0_51, plain, (~m1_qc_lang1(X1)\|~m1_subset_1(X2,k9_qc_lang1(X1))\|~m1_subset_1(X3,k9_qc_lang1(X1))\|~r3_qc_lang2(X1,X2,X3)\|~r2_qc_lang2(X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_43])). cnf(c_0_52, plain, (X2=X3\|r3_qc_lang2(X1,X2,X3)\|~m1_qc_lang1(X1)\|~r2_qc_lang2(X1,X2,X3)\|~m1_subset_1(X3,k9_qc_lang1(X1))\|~m1_subset_1(X2,k9_qc_lang1(X1))), inference(evalgc,[status(thm)],[c_0_44])). cnf(c_0_53, negated_conjecture, (~r3_qc_lang2(esk1_0,esk2_0,esk4_0)), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_54, negated_conjecture, (r2_qc_lang2(esk1_0,X1,esk4_0)\|~r2_qc_lang2(esk1_0,esk3_0,esk4_0)\|~r2_qc_lang2(esk1_0,X1,esk3_0)\|~m1_subset_1(X1,k9_qc_lang1(esk1_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_45, c_0_28])])). cnf(c_0_55, negated_conjecture, (r2_qc_lang2(esk1_0,esk3_0,esk4_0)), inference(csr,[status(thm)],[c_0_46, c_0_47])). cnf(c_0_56, negated_conjecture, (r2_qc_lang2(esk1_0,esk2_0,esk3_0)\|r1_qc_lang2(esk1_0,esk2_0,esk3_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_48, c_0_49])])). cnf(c_0_57, negated_conjecture, (r2_qc_lang2(esk1_0,esk2_0,esk3_0)\|~r1_qc_lang2(esk1_0,esk2_0,esk3_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_50, c_0_40])])). cnf(c_0_58, plain, (~m1_qc_lang1(X1)\|~r3_qc_lang2(X1,X2,X3)\|~r2_qc_lang2(X1,X3,X2)\|~m1_subset_1(X3,k9_qc_lang1(X1))\|~m1_subset_1(X2,k9_qc_lang1(X1))), inference(evalgc,[status(thm)],[c_0_51])). fof(c_0_59, plain, ![X19, X20, X21]:(~m1_qc_lang1(X19)\|(~m1_subset_1(X20,k9_qc_lang1(X19))\|(~m1_subset_1(X21,k9_qc_lang1(X19))\|(~r2_qc_lang2(X19,X20,X21)\|~r1_qc_lang2(X19,X21,X20))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t61_qc_lang2])])])). cnf(c_0_60, negated_conjecture, (X1=esk4_0\|r3_qc_lang2(esk1_0,X1,esk4_0)\|~r2_qc_lang2(esk1_0,X1,esk4_0)\|~m1_subset_1(X1,k9_qc_lang1(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52, c_0_19]), c_0_20])])])). cnf(c_0_61, negated_conjecture, (~r3_qc_lang2(esk1_0,esk2_0,esk4_0)), inference(evalgc,[status(thm)],[c_0_53])). cnf(c_0_62, negated_conjecture, (r2_qc_lang2(esk1_0,X1,esk4_0)\|~r2_qc_lang2(esk1_0,X1,esk3_0)\|~m1_subset_1(X1,k9_qc_lang1(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54, c_0_55])])])). cnf(c_0_63, negated_conjecture, (r2_qc_lang2(esk1_0,esk2_0,esk3_0)), inference(csr,[status(thm)],[c_0_56, c_0_57])). cnf(c_0_64, negated_conjecture, (~r2_qc_lang2(esk1_0,esk2_0,X1)\|~r3_qc_lang2(esk1_0,X1,esk2_0)\|~m1_subset_1(X1,k9_qc_lang1(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58, c_0_40]), c_0_20])])])). cnf(c_0_65, plain, (X1!=X2\|~r3_qc_lang2(X3,X1,X2)\|~m1_subset_1(X2,k9_qc_lang1(X3))\|~m1_subset_1(X1,k9_qc_lang1(X3))\|~m1_qc_lang1(X3)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_66, plain, (~m1_qc_lang1(X1)\|~m1_subset_1(X2,k9_qc_lang1(X1))\|~m1_subset_1(X3,k9_qc_lang1(X1))\|~r2_qc_lang2(X1,X2,X3)\|~r1_qc_lang2(X1,X3,X2)), inference(split_conjunct,[status(thm)],[c_0_59])). cnf(c_0_67, negated_conjecture, (esk4_0=esk2_0\|~r2_qc_lang2(esk1_0,esk2_0,esk4_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_60, c_0_40]), c_0_61])])). cnf(c_0_68, negated_conjecture, (r2_qc_lang2(esk1_0,esk2_0,esk4_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62, c_0_40]), c_0_63])])])). cnf(c_0_69, negated_conjecture, (esk4_0=esk3_0\|r3_qc_lang2(esk1_0,esk3_0,esk4_0)\|~r2_qc_lang2(esk1_0,esk3_0,esk4_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_60, c_0_28])])). cnf(c_0_70, negated_conjecture, (~r2_qc_lang2(esk1_0,esk2_0,esk3_0)\|~r3_qc_lang2(esk1_0,esk3_0,esk2_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_64, c_0_28])])). cnf(c_0_71, plain, (X1!=X2\|~m1_qc_lang1(X3)\|~r3_qc_lang2(X3,X1,X2)\|~m1_subset_1(X2,k9_qc_lang1(X3))\|~m1_subset_1(X1,k9_qc_lang1(X3))), inference(evalgc,[status(thm)],[c_0_65])). cnf(c_0_72, plain, (~m1_qc_lang1(X1)\|~r2_qc_lang2(X1,X2,X3)\|~r1_qc_lang2(X1,X3,X2)\|~m1_subset_1(X3,k9_qc_lang1(X1))\|~m1_subset_1(X2,k9_qc_lang1(X1))), inference(evalgc,[status(thm)],[c_0_66])). cnf(c_0_73, negated_conjecture, (esk4_0=esk2_0), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_67, c_0_68])])])). cnf(c_0_74, negated_conjecture, (esk4_0=esk3_0\|r3_qc_lang2(esk1_0,esk3_0,esk4_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_69, c_0_55])])])). cnf(c_0_75, negated_conjecture, (~r3_qc_lang2(esk1_0,esk3_0,esk2_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_70, c_0_63])])])). cnf(c_0_76, plain, (~r3_qc_lang2(X1,X2,X2)\|~m1_subset_1(X2,k9_qc_lang1(X1))\|~m1_qc_lang1(X1)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_71])])). cnf(c_0_77, plain, (r1_qc_lang2(X1,X2,X3)\|r1_qc_lang2(X1,X3,X4)\|r1_qc_lang2(X1,X2,X3)\|r1_qc_lang2(X1,X3,X4)\|r3_qc_lang2(X1,X3,X4)\|epred1_4(X4,X3,X2,X1)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_78, negated_conjecture, (r2_qc_lang2(esk1_0,X1,esk2_0)\|~r1_qc_lang2(esk1_0,X1,esk2_0)\|~m1_subset_1(X1,k9_qc_lang1(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31, c_0_40]), c_0_20])])])). cnf(c_0_79, negated_conjecture, (~r1_qc_lang2(esk1_0,esk2_0,X1)\|~r2_qc_lang2(esk1_0,X1,esk2_0)\|~m1_subset_1(X1,k9_qc_lang1(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72, c_0_40]), c_0_20])])])). cnf(c_0_80, negated_conjecture, (r3_qc_lang2(esk1_0,esk2_0,esk3_0)\|~epred1_4(esk2_0,esk3_0,esk2_0,esk1_0)), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[c_0_41, c_0_73])])). cnf(c_0_81, negated_conjecture, (esk3_0=esk2_0), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_74, c_0_73]), c_0_73]), c_0_75])])). cnf(c_0_82, negated_conjecture, (~r3_qc_lang2(esk1_0,esk2_0,esk2_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76, c_0_40]), c_0_20])])])). cnf(c_0_83, plain, (r3_qc_lang2(X1,X3,X4)\|r1_qc_lang2(X1,X3,X4)\|r1_qc_lang2(X1,X2,X3)\|epred1_4(X4,X3,X2,X1)), inference(cn,[status(thm)],[c_0_77])). cnf(c_0_84, negated_conjecture, (r2_qc_lang2(esk1_0,esk2_0,esk2_0)\|~r1_qc_lang2(esk1_0,esk2_0,esk2_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_78, c_0_40])])). cnf(c_0_85, negated_conjecture, (~r1_qc_lang2(esk1_0,esk2_0,esk2_0)\|~r2_qc_lang2(esk1_0,esk2_0,esk2_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_79, c_0_40])])). cnf(c_0_86, negated_conjecture, (~epred1_4(esk2_0,esk2_0,esk2_0,esk1_0)), inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_80, c_0_81]), c_0_81]), c_0_82])). cnf(c_0_87, plain, (r3_qc_lang2(X1,X3,X4)\|r1_qc_lang2(X1,X3,X4)\|r1_qc_lang2(X1,X2,X3)\|epred1_4(X4,X3,X2,X1)), inference(evalgc,[status(thm)],[c_0_83])). cnf(c_0_88, negated_conjecture, (~r1_qc_lang2(esk1_0,esk2_0,esk2_0)), inference(csr,[status(thm)],[c_0_84, c_0_85])). cnf(c_0_89, plain, ($false), inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_86, c_0_87]), c_0_88]), c_0_82]), ['proof']). # SZS output end CNFRefutation	reserve A for QC-alphabet; reserve sq for FinSequence, x,y,z for bound_QC-variable of A, p,q,p1,p2,q1 for Element of QC-WFF(A); reserve s,t for bound_QC-variable of A; reserve F,G,H,H1 for Element of QC-WFF(A); reserve x,y,z for bound_QC-variable of A, k,n,m for Element of NAT, P for ( QC-pred_symbol of k, A), V for QC-variable_list of k, A; reserve L,L9 for FinSequence; theorem Th63: F is_proper_subformula_of G & G is_subformula_of H or F is_subformula_of G & G is_proper_subformula_of H or F is_subformula_of G & G is_immediate_constituent_of H or F is_immediate_constituent_of G & G is_subformula_of H or F is_proper_subformula_of G & G is_immediate_constituent_of H or F is_immediate_constituent_of G & G is_proper_subformula_of H implies F is_proper_subformula_of H proof assume A1: F is_proper_subformula_of G & G is_subformula_of H or F is_subformula_of G & G is_proper_subformula_of H or F is_subformula_of G & G is_immediate_constituent_of H or F is_immediate_constituent_of G & G is_subformula_of H or F is_proper_subformula_of G & G is_immediate_constituent_of H or F is_immediate_constituent_of G & G is_proper_subformula_of H; then F is_subformula_of G & G is_subformula_of H by Def21,Th52; hence F is_subformula_of H by Th57; thus thesis by A1,Th59,Th61,Th62; end;	Convert the following ATP output trace into a readable Mizar proof.
t1_sfmastr3	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(rd1_extpro_1, axiom, ![X1, X2, X3, X4]:(((~(v1_xboole_0(X1))&~(v1_setfam_1(X1)))&((~(v2_struct_0(X2))&(v2_memstr_0(X2,X1)&(v3_memstr_0(X2,X1)&l1_extpro_1(X2,X1))))&((v1_relat_1(X3)&(v4_relat_1(X3,k5_numbers)&(v5_relat_1(X3,u1_compos_1(X2))&v1_funct_1(X3))))&(v1_relat_1(X4)&(v4_relat_1(X4,u1_struct_0(X2))&(v1_funct_1(X4)&(v5_funct_1(X4,k2_memstr_0(X1,X2))&v1_partfun1(X4,u1_struct_0(X2)))))))))=>k5_extpro_1(X1,X2,X3,X4,k6_numbers)=X4), file('/scratch/mptp/predsminms1/t1_sfmastr3__0', rd1_extpro_1)). fof(cc1_memstr_0, axiom, ![X1]:(~(v1_setfam_1(X1))=>~(v1_xboole_0(X1))), file('/scratch/mptp/predsminms1/t1_sfmastr3__0', cc1_memstr_0)). fof(t1_sfmastr3, conjecture, ![X1]:((v1_relat_1(X1)&(v4_relat_1(X1,u1_struct_0(k1_scmfsa_2))&(v1_funct_1(X1)&(v5_funct_1(X1,k2_memstr_0(np__3,k1_scmfsa_2))&v1_partfun1(X1,u1_struct_0(k1_scmfsa_2))))))=>![X2]:((v1_ami_2(X2)&m1_subset_1(X2,u1_struct_0(k1_scmfsa_2)))=>![X3]:((v1_relat_1(X3)&(v4_relat_1(X3,k5_numbers)&(v5_relat_1(X3,u1_compos_1(k1_scmfsa_2))&(v1_funct_1(X3)&(~(v1_xboole_0(X3))&(v1_finset_1(X3)&v1_afinsq_1(X3)))))))=>![X4]:((v1_relat_1(X4)&(v4_relat_1(X4,k5_numbers)&(v5_relat_1(X4,u1_compos_1(k1_scmfsa_2))&(v1_funct_1(X4)&v1_partfun1(X4,k5_numbers)))))=>((r5_scmfsa7b(X3,k1_scmfsa_m(X1),X4)&r6_scmfsa7b(X3,k1_scmfsa_m(X1),X4))=>(r4_scmfsa7b(X3,X2)\|k1_funct_1(k1_scmfsa6b(X3,X1,X4),X2)=k1_funct_1(k1_scmfsa_m(X1),X2))))))), file('/scratch/mptp/predsminms1/t1_sfmastr3__0', t1_sfmastr3)). fof(cc8_ordinal1, axiom, ![X1]:(m1_subset_1(X1,k4_ordinal1)=>v7_ordinal1(X1)), file('/scratch/mptp/predsminms1/t1_sfmastr3__0', cc8_ordinal1)). fof(fc10_funct_4, axiom, ![X1, X2, X3]:(((v1_relat_1(X2)&(v5_relat_1(X2,X1)&v1_funct_1(X2)))&(v1_relat_1(X3)&(v5_relat_1(X3,X1)&v1_funct_1(X3))))=>(v1_relat_1(k1_funct_4(X2,X3))&(v5_relat_1(k1_funct_4(X2,X3),X1)&v1_funct_1(k1_funct_4(X2,X3))))), file('/scratch/mptp/predsminms1/t1_sfmastr3__0', fc10_funct_4)). fof(t2_scmfsa_m, axiom, ![X1]:((v1_relat_1(X1)&(v4_relat_1(X1,u1_struct_0(k1_scmfsa_2))&(v1_funct_1(X1)&(v5_funct_1(X1,k2_memstr_0(np__3,k1_scmfsa_2))&v1_partfun1(X1,u1_struct_0(k1_scmfsa_2))))))=>![X2]:((v1_relat_1(X2)&(v4_relat_1(X2,u1_struct_0(k1_scmfsa_2))&(v1_funct_1(X2)&(v5_funct_1(X2,k2_memstr_0(np__3,k1_scmfsa_2))&v1_partfun1(X2,u1_struct_0(k1_scmfsa_2))))))=>((![X3]:((v1_ami_2(X3)&m1_subset_1(X3,u1_struct_0(k1_scmfsa_2)))=>k1_funct_1(X1,X3)=k1_funct_1(X2,X3))&![X3]:(m1_scmfsa_2(X3)=>k18_scmfsa_2(X1,X3)=k18_scmfsa_2(X2,X3)))<=>k6_memstr_0(np__3,k1_scmfsa_2,X1)=k6_memstr_0(np__3,k1_scmfsa_2,X2)))), file('/scratch/mptp/predsminms1/t1_sfmastr3__0', t2_scmfsa_m)). fof(t79_memstr_0, axiom, ![X1]:(~(v1_setfam_1(X1))=>![X2]:((~(v2_struct_0(X2))&(v2_memstr_0(X2,X1)&(v3_memstr_0(X2,X1)&l1_memstr_0(X2,X1))))=>![X3]:((v1_relat_1(X3)&(v4_relat_1(X3,u1_struct_0(X2))&(v1_funct_1(X3)&(v5_funct_1(X3,k2_memstr_0(X1,X2))&v1_partfun1(X3,u1_struct_0(X2))))))=>![X4]:(m2_subset_1(X4,k1_numbers,k5_numbers)=>k6_memstr_0(X1,X2,X3)=k6_memstr_0(X1,X2,k1_funct_4(X3,k7_memstr_0(X1,X2,X4))))))), file('/scratch/mptp/predsminms1/t1_sfmastr3__0', t79_memstr_0)). fof(d13_memstr_0, axiom, ![X1]:(~(v1_setfam_1(X1))=>![X2]:((~(v2_struct_0(X2))&(v2_memstr_0(X2,X1)&(v3_memstr_0(X2,X1)&l1_memstr_0(X2,X1))))=>![X3]:((v1_relat_1(X3)&(v4_relat_1(X3,u1_struct_0(X2))&(v1_funct_1(X3)&v5_funct_1(X3,k2_memstr_0(X1,X2)))))=>k8_memstr_0(X1,X2,X3)=k1_funct_4(X3,k7_memstr_0(X1,X2,k6_numbers))))), file('/scratch/mptp/predsminms1/t1_sfmastr3__0', d13_memstr_0)). fof(cc1_ami_3, axiom, ![X1]:((~(v1_xboole_0(X1))&v7_ordinal1(X1))=>(~(v1_xboole_0(X1))&(v7_ordinal1(X1)&~(v1_setfam_1(X1))))), file('/scratch/mptp/predsminms1/t1_sfmastr3__0', cc1_ami_3)). fof(redefinition_k5_numbers, axiom, k5_numbers=k4_ordinal1, file('/scratch/mptp/predsminms1/t1_sfmastr3__0', redefinition_k5_numbers)). fof(dt_k1_funct_4, axiom, ![X1, X2]:(((v1_relat_1(X1)&v1_funct_1(X1))&(v1_relat_1(X2)&v1_funct_1(X2)))=>(v1_relat_1(k1_funct_4(X1,X2))&v1_funct_1(k1_funct_4(X1,X2)))), file('/scratch/mptp/predsminms1/t1_sfmastr3__0', dt_k1_funct_4)). fof(dt_k6_numbers, axiom, m2_subset_1(k6_numbers,k1_numbers,k5_numbers), file('/scratch/mptp/predsminms1/t1_sfmastr3__0', dt_k6_numbers)). fof(fc1_scmfsa_2, axiom, (~(v2_struct_0(k1_scmfsa_2))&(v2_memstr_0(k1_scmfsa_2,np__3)&v1_extpro_1(k1_scmfsa_2,np__3))), file('/scratch/mptp/predsminms1/t1_sfmastr3__0', fc1_scmfsa_2)). fof(dt_l1_extpro_1, axiom, ![X1, X2]:(l1_extpro_1(X2,X1)=>(l1_memstr_0(X2,X1)&l1_compos_1(X2))), file('/scratch/mptp/predsminms1/t1_sfmastr3__0', dt_l1_extpro_1)). fof(spc3_boole, axiom, ~(v1_xboole_0(np__3)), file('/scratch/mptp/predsminms1/t1_sfmastr3__0', spc3_boole)). fof(t60_scmfsa8c, axiom, ![X1]:((v1_relat_1(X1)&(v4_relat_1(X1,k5_numbers)&(v5_relat_1(X1,u1_compos_1(k1_scmfsa_2))&(v1_funct_1(X1)&v1_partfun1(X1,k5_numbers)))))=>![X2]:((v1_relat_1(X2)&(v4_relat_1(X2,u1_struct_0(k1_scmfsa_2))&(v1_funct_1(X2)&(v5_funct_1(X2,k2_memstr_0(np__3,k1_scmfsa_2))&v1_partfun1(X2,u1_struct_0(k1_scmfsa_2))))))=>![X3]:((~(v1_xboole_0(X3))&(v1_relat_1(X3)&(v4_relat_1(X3,k5_numbers)&(v5_relat_1(X3,u1_compos_1(k1_scmfsa_2))&(v1_funct_1(X3)&(v1_finset_1(X3)&v1_afinsq_1(X3)))))))=>![X4]:((v1_ami_2(X4)&m1_subset_1(X4,u1_struct_0(k1_scmfsa_2)))=>![X5]:(m2_subset_1(X5,k1_numbers,k5_numbers)=>((r5_scmfsa7b(X3,k1_scmfsa_m(X2),X1)&r6_scmfsa7b(X3,k1_scmfsa_m(X2),X1))=>(r4_scmfsa7b(X3,X4)\|k1_funct_1(k1_scmfsa6b(X3,X2,X1),X4)=k1_funct_1(k5_extpro_1(np__3,k1_scmfsa_2,k1_funct_4(X1,X3),k8_memstr_0(np__3,k1_scmfsa_2,k1_scmfsa_m(X2)),X5),X4)))))))), file('/scratch/mptp/predsminms1/t1_sfmastr3__0', t60_scmfsa8c)). fof(fc5_scmfsa_2, axiom, (v3_memstr_0(k1_scmfsa_2,np__3)&v1_extpro_1(k1_scmfsa_2,np__3)), file('/scratch/mptp/predsminms1/t1_sfmastr3__0', fc5_scmfsa_2)). fof(dt_k1_scmfsa_2, axiom, (v1_extpro_1(k1_scmfsa_2,np__3)&l1_extpro_1(k1_scmfsa_2,np__3)), file('/scratch/mptp/predsminms1/t1_sfmastr3__0', dt_k1_scmfsa_2)). fof(spc3_numerals, axiom, ((v2_xxreal_0(np__3)&m2_subset_1(np__3,k1_numbers,k5_numbers))&(m1_subset_1(np__3,k5_numbers)&m1_subset_1(np__3,k1_numbers))), file('/scratch/mptp/predsminms1/t1_sfmastr3__0', spc3_numerals)). fof(fc7_funct_4, axiom, ![X1, X2, X3]:(((v1_relat_1(X2)&(v4_relat_1(X2,X1)&v1_funct_1(X2)))&(v1_relat_1(X3)&(v4_relat_1(X3,X1)&v1_funct_1(X3))))=>(v1_relat_1(k1_funct_4(X2,X3))&(v4_relat_1(k1_funct_4(X2,X3),X1)&v1_funct_1(k1_funct_4(X2,X3))))), file('/scratch/mptp/predsminms1/t1_sfmastr3__0', fc7_funct_4)). fof(dt_k1_scmfsa_m, axiom, ![X1]:((v1_relat_1(X1)&(v4_relat_1(X1,u1_struct_0(k1_scmfsa_2))&(v1_funct_1(X1)&v5_funct_1(X1,k2_memstr_0(np__3,k1_scmfsa_2)))))=>(v1_relat_1(k1_scmfsa_m(X1))&(v4_relat_1(k1_scmfsa_m(X1),u1_struct_0(k1_scmfsa_2))&(v1_funct_1(k1_scmfsa_m(X1))&v5_funct_1(k1_scmfsa_m(X1),k2_memstr_0(np__3,k1_scmfsa_2)))))), file('/scratch/mptp/predsminms1/t1_sfmastr3__0', dt_k1_scmfsa_m)). fof(fc4_scmfsa_m, axiom, ![X1]:((v1_relat_1(X1)&(v4_relat_1(X1,u1_struct_0(k1_scmfsa_2))&(v1_funct_1(X1)&(v5_funct_1(X1,k2_memstr_0(np__3,k1_scmfsa_2))&v1_partfun1(X1,u1_struct_0(k1_scmfsa_2))))))=>(v1_relat_1(k1_scmfsa_m(X1))&(v4_relat_1(k1_scmfsa_m(X1),u1_struct_0(k1_scmfsa_2))&(v1_funct_1(k1_scmfsa_m(X1))&(v5_funct_1(k1_scmfsa_m(X1),k2_memstr_0(np__3,k1_scmfsa_2))&v1_partfun1(k1_scmfsa_m(X1),u1_struct_0(k1_scmfsa_2))))))), file('/scratch/mptp/predsminms1/t1_sfmastr3__0', fc4_scmfsa_m)). fof(dt_k8_memstr_0, axiom, ![X1, X2, X3]:((~(v1_setfam_1(X1))&((~(v2_struct_0(X2))&(v2_memstr_0(X2,X1)&(v3_memstr_0(X2,X1)&l1_memstr_0(X2,X1))))&(v1_relat_1(X3)&(v4_relat_1(X3,u1_struct_0(X2))&(v1_funct_1(X3)&v5_funct_1(X3,k2_memstr_0(X1,X2)))))))=>(v1_relat_1(k8_memstr_0(X1,X2,X3))&(v4_relat_1(k8_memstr_0(X1,X2,X3),u1_struct_0(X2))&(v1_funct_1(k8_memstr_0(X1,X2,X3))&v5_funct_1(k8_memstr_0(X1,X2,X3),k2_memstr_0(X1,X2)))))), file('/scratch/mptp/predsminms1/t1_sfmastr3__0', dt_k8_memstr_0)). fof(fc14_memstr_0, axiom, ![X1, X2, X3]:((~(v1_setfam_1(X1))&((~(v2_struct_0(X2))&(v2_memstr_0(X2,X1)&(v3_memstr_0(X2,X1)&l1_memstr_0(X2,X1))))&(v1_relat_1(X3)&(v4_relat_1(X3,u1_struct_0(X2))&(v1_funct_1(X3)&(v5_funct_1(X3,k2_memstr_0(X1,X2))&v1_partfun1(X3,u1_struct_0(X2))))))))=>(v1_relat_1(k8_memstr_0(X1,X2,X3))&(v4_relat_1(k8_memstr_0(X1,X2,X3),u1_struct_0(X2))&(v1_funct_1(k8_memstr_0(X1,X2,X3))&(v5_funct_1(k8_memstr_0(X1,X2,X3),k2_memstr_0(X1,X2))&v1_partfun1(k8_memstr_0(X1,X2,X3),u1_struct_0(X2))))))), file('/scratch/mptp/predsminms1/t1_sfmastr3__0', fc14_memstr_0)). fof(c_0_24, plain, ![X10, X11, X12, X13]:(v1_xboole_0(X10)\|v1_setfam_1(X10)\|(v2_struct_0(X11)\|(~v2_memstr_0(X11,X10)\|(~v3_memstr_0(X11,X10)\|~l1_extpro_1(X11,X10)))\|(~v1_relat_1(X12)\|(~v4_relat_1(X12,k5_numbers)\|(~v5_relat_1(X12,u1_compos_1(X11))\|~v1_funct_1(X12)))\|(~v1_relat_1(X13)\|(~v4_relat_1(X13,u1_struct_0(X11))\|(~v1_funct_1(X13)\|(~v5_funct_1(X13,k2_memstr_0(X10,X11))\|~v1_partfun1(X13,u1_struct_0(X11))))))))\|k5_extpro_1(X10,X11,X12,X13,k6_numbers)=X13), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[rd1_extpro_1])])])). fof(c_0_25, plain, ![X14]:(v1_setfam_1(X14)\|~v1_xboole_0(X14)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[cc1_memstr_0])])])). fof(c_0_26, negated_conjecture, ~(![X1]:((v1_relat_1(X1)&(v4_relat_1(X1,u1_struct_0(k1_scmfsa_2))&(v1_funct_1(X1)&(v5_funct_1(X1,k2_memstr_0(np__3,k1_scmfsa_2))&v1_partfun1(X1,u1_struct_0(k1_scmfsa_2))))))=>![X2]:((v1_ami_2(X2)&m1_subset_1(X2,u1_struct_0(k1_scmfsa_2)))=>![X3]:((v1_relat_1(X3)&(v4_relat_1(X3,k5_numbers)&(v5_relat_1(X3,u1_compos_1(k1_scmfsa_2))&(v1_funct_1(X3)&(~(v1_xboole_0(X3))&(v1_finset_1(X3)&v1_afinsq_1(X3)))))))=>![X4]:((v1_relat_1(X4)&(v4_relat_1(X4,k5_numbers)&(v5_relat_1(X4,u1_compos_1(k1_scmfsa_2))&(v1_funct_1(X4)&v1_partfun1(X4,k5_numbers)))))=>((r5_scmfsa7b(X3,k1_scmfsa_m(X1),X4)&r6_scmfsa7b(X3,k1_scmfsa_m(X1),X4))=>(r4_scmfsa7b(X3,X2)\|k1_funct_1(k1_scmfsa6b(X3,X1,X4),X2)=k1_funct_1(k1_scmfsa_m(X1),X2)))))))), inference(assume_negation,[status(cth)],[t1_sfmastr3])). fof(c_0_27, plain, ![X51]:(~m1_subset_1(X51,k4_ordinal1)\|v7_ordinal1(X51)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc8_ordinal1])])). cnf(c_0_28, plain, (v1_xboole_0(X1)\|v1_setfam_1(X1)\|v2_struct_0(X2)\|k5_extpro_1(X1,X2,X3,X4,k6_numbers)=X4\|~v2_memstr_0(X2,X1)\|~v3_memstr_0(X2,X1)\|~l1_extpro_1(X2,X1)\|~v1_relat_1(X3)\|~v4_relat_1(X3,k5_numbers)\|~v5_relat_1(X3,u1_compos_1(X2))\|~v1_funct_1(X3)\|~v1_relat_1(X4)\|~v4_relat_1(X4,u1_struct_0(X2))\|~v1_funct_1(X4)\|~v5_funct_1(X4,k2_memstr_0(X1,X2))\|~v1_partfun1(X4,u1_struct_0(X2))), inference(split_conjunct,[status(thm)],[c_0_24])). cnf(c_0_29, plain, (v1_setfam_1(X1)\|~v1_xboole_0(X1)), inference(split_conjunct,[status(thm)],[c_0_25])). fof(c_0_30, plain, ![X15, X16, X17]:((v1_relat_1(k1_funct_4(X16,X17))\|(~v1_relat_1(X16)\|(~v5_relat_1(X16,X15)\|~v1_funct_1(X16))\|(~v1_relat_1(X17)\|(~v5_relat_1(X17,X15)\|~v1_funct_1(X17)))))&((v5_relat_1(k1_funct_4(X16,X17),X15)\|(~v1_relat_1(X16)\|(~v5_relat_1(X16,X15)\|~v1_funct_1(X16))\|(~v1_relat_1(X17)\|(~v5_relat_1(X17,X15)\|~v1_funct_1(X17)))))&(v1_funct_1(k1_funct_4(X16,X17))\|(~v1_relat_1(X16)\|(~v5_relat_1(X16,X15)\|~v1_funct_1(X16))\|(~v1_relat_1(X17)\|(~v5_relat_1(X17,X15)\|~v1_funct_1(X17))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc10_funct_4])])])). fof(c_0_31, plain, ![X20, X21, X24, X25]:(((((m1_scmfsa_2(esk6_2(X20,X21))\|v1_ami_2(esk5_2(X20,X21))\|k6_memstr_0(np__3,k1_scmfsa_2,X20)=k6_memstr_0(np__3,k1_scmfsa_2,X21)\|(~v1_relat_1(X21)\|(~v4_relat_1(X21,u1_struct_0(k1_scmfsa_2))\|(~v1_funct_1(X21)\|(~v5_funct_1(X21,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X21,u1_struct_0(k1_scmfsa_2))))))\|(~v1_relat_1(X20)\|(~v4_relat_1(X20,u1_struct_0(k1_scmfsa_2))\|(~v1_funct_1(X20)\|(~v5_funct_1(X20,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X20,u1_struct_0(k1_scmfsa_2)))))))&(k18_scmfsa_2(X20,esk6_2(X20,X21))!=k18_scmfsa_2(X21,esk6_2(X20,X21))\|v1_ami_2(esk5_2(X20,X21))\|k6_memstr_0(np__3,k1_scmfsa_2,X20)=k6_memstr_0(np__3,k1_scmfsa_2,X21)\|(~v1_relat_1(X21)\|(~v4_relat_1(X21,u1_struct_0(k1_scmfsa_2))\|(~v1_funct_1(X21)\|(~v5_funct_1(X21,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X21,u1_struct_0(k1_scmfsa_2))))))\|(~v1_relat_1(X20)\|(~v4_relat_1(X20,u1_struct_0(k1_scmfsa_2))\|(~v1_funct_1(X20)\|(~v5_funct_1(X20,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X20,u1_struct_0(k1_scmfsa_2))))))))&((m1_scmfsa_2(esk6_2(X20,X21))\|m1_subset_1(esk5_2(X20,X21),u1_struct_0(k1_scmfsa_2))\|k6_memstr_0(np__3,k1_scmfsa_2,X20)=k6_memstr_0(np__3,k1_scmfsa_2,X21)\|(~v1_relat_1(X21)\|(~v4_relat_1(X21,u1_struct_0(k1_scmfsa_2))\|(~v1_funct_1(X21)\|(~v5_funct_1(X21,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X21,u1_struct_0(k1_scmfsa_2))))))\|(~v1_relat_1(X20)\|(~v4_relat_1(X20,u1_struct_0(k1_scmfsa_2))\|(~v1_funct_1(X20)\|(~v5_funct_1(X20,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X20,u1_struct_0(k1_scmfsa_2)))))))&(k18_scmfsa_2(X20,esk6_2(X20,X21))!=k18_scmfsa_2(X21,esk6_2(X20,X21))\|m1_subset_1(esk5_2(X20,X21),u1_struct_0(k1_scmfsa_2))\|k6_memstr_0(np__3,k1_scmfsa_2,X20)=k6_memstr_0(np__3,k1_scmfsa_2,X21)\|(~v1_relat_1(X21)\|(~v4_relat_1(X21,u1_struct_0(k1_scmfsa_2))\|(~v1_funct_1(X21)\|(~v5_funct_1(X21,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X21,u1_struct_0(k1_scmfsa_2))))))\|(~v1_relat_1(X20)\|(~v4_relat_1(X20,u1_struct_0(k1_scmfsa_2))\|(~v1_funct_1(X20)\|(~v5_funct_1(X20,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X20,u1_struct_0(k1_scmfsa_2)))))))))&((m1_scmfsa_2(esk6_2(X20,X21))\|k1_funct_1(X20,esk5_2(X20,X21))!=k1_funct_1(X21,esk5_2(X20,X21))\|k6_memstr_0(np__3,k1_scmfsa_2,X20)=k6_memstr_0(np__3,k1_scmfsa_2,X21)\|(~v1_relat_1(X21)\|(~v4_relat_1(X21,u1_struct_0(k1_scmfsa_2))\|(~v1_funct_1(X21)\|(~v5_funct_1(X21,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X21,u1_struct_0(k1_scmfsa_2))))))\|(~v1_relat_1(X20)\|(~v4_relat_1(X20,u1_struct_0(k1_scmfsa_2))\|(~v1_funct_1(X20)\|(~v5_funct_1(X20,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X20,u1_struct_0(k1_scmfsa_2)))))))&(k18_scmfsa_2(X20,esk6_2(X20,X21))!=k18_scmfsa_2(X21,esk6_2(X20,X21))\|k1_funct_1(X20,esk5_2(X20,X21))!=k1_funct_1(X21,esk5_2(X20,X21))\|k6_memstr_0(np__3,k1_scmfsa_2,X20)=k6_memstr_0(np__3,k1_scmfsa_2,X21)\|(~v1_relat_1(X21)\|(~v4_relat_1(X21,u1_struct_0(k1_scmfsa_2))\|(~v1_funct_1(X21)\|(~v5_funct_1(X21,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X21,u1_struct_0(k1_scmfsa_2))))))\|(~v1_relat_1(X20)\|(~v4_relat_1(X20,u1_struct_0(k1_scmfsa_2))\|(~v1_funct_1(X20)\|(~v5_funct_1(X20,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X20,u1_struct_0(k1_scmfsa_2)))))))))&((~v1_ami_2(X24)\|~m1_subset_1(X24,u1_struct_0(k1_scmfsa_2))\|k1_funct_1(X20,X24)=k1_funct_1(X21,X24)\|k6_memstr_0(np__3,k1_scmfsa_2,X20)!=k6_memstr_0(np__3,k1_scmfsa_2,X21)\|(~v1_relat_1(X21)\|(~v4_relat_1(X21,u1_struct_0(k1_scmfsa_2))\|(~v1_funct_1(X21)\|(~v5_funct_1(X21,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X21,u1_struct_0(k1_scmfsa_2))))))\|(~v1_relat_1(X20)\|(~v4_relat_1(X20,u1_struct_0(k1_scmfsa_2))\|(~v1_funct_1(X20)\|(~v5_funct_1(X20,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X20,u1_struct_0(k1_scmfsa_2)))))))&(~m1_scmfsa_2(X25)\|k18_scmfsa_2(X20,X25)=k18_scmfsa_2(X21,X25)\|k6_memstr_0(np__3,k1_scmfsa_2,X20)!=k6_memstr_0(np__3,k1_scmfsa_2,X21)\|(~v1_relat_1(X21)\|(~v4_relat_1(X21,u1_struct_0(k1_scmfsa_2))\|(~v1_funct_1(X21)\|(~v5_funct_1(X21,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X21,u1_struct_0(k1_scmfsa_2))))))\|(~v1_relat_1(X20)\|(~v4_relat_1(X20,u1_struct_0(k1_scmfsa_2))\|(~v1_funct_1(X20)\|(~v5_funct_1(X20,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X20,u1_struct_0(k1_scmfsa_2))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_scmfsa_m])])])])])). fof(c_0_32, negated_conjecture, ((v1_relat_1(esk1_0)&(v4_relat_1(esk1_0,u1_struct_0(k1_scmfsa_2))&(v1_funct_1(esk1_0)&(v5_funct_1(esk1_0,k2_memstr_0(np__3,k1_scmfsa_2))&v1_partfun1(esk1_0,u1_struct_0(k1_scmfsa_2))))))&((v1_ami_2(esk2_0)&m1_subset_1(esk2_0,u1_struct_0(k1_scmfsa_2)))&((v1_relat_1(esk3_0)&(v4_relat_1(esk3_0,k5_numbers)&(v5_relat_1(esk3_0,u1_compos_1(k1_scmfsa_2))&(v1_funct_1(esk3_0)&(~v1_xboole_0(esk3_0)&(v1_finset_1(esk3_0)&v1_afinsq_1(esk3_0)))))))&((v1_relat_1(esk4_0)&(v4_relat_1(esk4_0,k5_numbers)&(v5_relat_1(esk4_0,u1_compos_1(k1_scmfsa_2))&(v1_funct_1(esk4_0)&v1_partfun1(esk4_0,k5_numbers)))))&((r5_scmfsa7b(esk3_0,k1_scmfsa_m(esk1_0),esk4_0)&r6_scmfsa7b(esk3_0,k1_scmfsa_m(esk1_0),esk4_0))&(~r4_scmfsa7b(esk3_0,esk2_0)&k1_funct_1(k1_scmfsa6b(esk3_0,esk1_0,esk4_0),esk2_0)!=k1_funct_1(k1_scmfsa_m(esk1_0),esk2_0))))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_26])])])])). fof(c_0_33, plain, ![X26, X27, X28, X29]:(v1_setfam_1(X26)\|(v2_struct_0(X27)\|(~v2_memstr_0(X27,X26)\|(~v3_memstr_0(X27,X26)\|~l1_memstr_0(X27,X26)))\|(~v1_relat_1(X28)\|(~v4_relat_1(X28,u1_struct_0(X27))\|(~v1_funct_1(X28)\|(~v5_funct_1(X28,k2_memstr_0(X26,X27))\|~v1_partfun1(X28,u1_struct_0(X27)))))\|(~m2_subset_1(X29,k1_numbers,k5_numbers)\|k6_memstr_0(X26,X27,X28)=k6_memstr_0(X26,X27,k1_funct_4(X28,k7_memstr_0(X26,X27,X29))))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t79_memstr_0])])])])). fof(c_0_34, plain, ![X30, X31, X32]:(v1_setfam_1(X30)\|(v2_struct_0(X31)\|(~v2_memstr_0(X31,X30)\|(~v3_memstr_0(X31,X30)\|~l1_memstr_0(X31,X30)))\|(~v1_relat_1(X32)\|(~v4_relat_1(X32,u1_struct_0(X31))\|(~v1_funct_1(X32)\|~v5_funct_1(X32,k2_memstr_0(X30,X31))))\|k8_memstr_0(X30,X31,X32)=k1_funct_4(X32,k7_memstr_0(X30,X31,k6_numbers))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d13_memstr_0])])])])). fof(c_0_35, plain, ![X52]:((~v1_xboole_0(X52)\|(v1_xboole_0(X52)\|~v7_ordinal1(X52)))&((v7_ordinal1(X52)\|(v1_xboole_0(X52)\|~v7_ordinal1(X52)))&(~v1_setfam_1(X52)\|(v1_xboole_0(X52)\|~v7_ordinal1(X52))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[cc1_ami_3])])])])). cnf(c_0_36, plain, (v7_ordinal1(X1)\|~m1_subset_1(X1,k4_ordinal1)), inference(split_conjunct,[status(thm)],[c_0_27])). cnf(c_0_37, plain, (k5_numbers=k4_ordinal1), inference(split_conjunct,[status(thm)],[redefinition_k5_numbers])). cnf(c_0_38, plain, (k5_extpro_1(X1,X2,X3,X4,k6_numbers)=X4\|v1_xboole_0(X1)\|v1_setfam_1(X1)\|v2_struct_0(X2)\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v2_memstr_0(X2,X1)\|~v3_memstr_0(X2,X1)\|~l1_extpro_1(X2,X1)\|~v4_relat_1(X3,k5_numbers)\|~v4_relat_1(X4,u1_struct_0(X2))\|~v1_partfun1(X4,u1_struct_0(X2))\|~v5_relat_1(X3,u1_compos_1(X2))\|~v5_funct_1(X4,k2_memstr_0(X1,X2))), inference(evalgc,[status(thm)],[c_0_28])). cnf(c_0_39, plain, (v1_setfam_1(X1)\|~v1_xboole_0(X1)), inference(evalgc,[status(thm)],[c_0_29])). cnf(c_0_40, plain, (v5_relat_1(k1_funct_4(X1,X2),X3)\|~v1_relat_1(X1)\|~v5_relat_1(X1,X3)\|~v1_funct_1(X1)\|~v1_relat_1(X2)\|~v5_relat_1(X2,X3)\|~v1_funct_1(X2)), inference(split_conjunct,[status(thm)],[c_0_30])). fof(c_0_41, plain, ![X18, X19]:((v1_relat_1(k1_funct_4(X18,X19))\|(~v1_relat_1(X18)\|~v1_funct_1(X18)\|(~v1_relat_1(X19)\|~v1_funct_1(X19))))&(v1_funct_1(k1_funct_4(X18,X19))\|(~v1_relat_1(X18)\|~v1_funct_1(X18)\|(~v1_relat_1(X19)\|~v1_funct_1(X19))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_funct_4])])])). cnf(c_0_42, plain, (k1_funct_1(X2,X1)=k1_funct_1(X3,X1)\|~v1_ami_2(X1)\|~m1_subset_1(X1,u1_struct_0(k1_scmfsa_2))\|k6_memstr_0(np__3,k1_scmfsa_2,X2)!=k6_memstr_0(np__3,k1_scmfsa_2,X3)\|~v1_relat_1(X3)\|~v4_relat_1(X3,u1_struct_0(k1_scmfsa_2))\|~v1_funct_1(X3)\|~v5_funct_1(X3,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X3,u1_struct_0(k1_scmfsa_2))\|~v1_relat_1(X2)\|~v4_relat_1(X2,u1_struct_0(k1_scmfsa_2))\|~v1_funct_1(X2)\|~v5_funct_1(X2,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X2,u1_struct_0(k1_scmfsa_2))), inference(split_conjunct,[status(thm)],[c_0_31])). cnf(c_0_43, negated_conjecture, (m1_subset_1(esk2_0,u1_struct_0(k1_scmfsa_2))), inference(split_conjunct,[status(thm)],[c_0_32])). cnf(c_0_44, negated_conjecture, (v1_ami_2(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_32])). cnf(c_0_45, plain, (v1_setfam_1(X1)\|v2_struct_0(X2)\|k6_memstr_0(X1,X2,X3)=k6_memstr_0(X1,X2,k1_funct_4(X3,k7_memstr_0(X1,X2,X4)))\|~v2_memstr_0(X2,X1)\|~v3_memstr_0(X2,X1)\|~l1_memstr_0(X2,X1)\|~v1_relat_1(X3)\|~v4_relat_1(X3,u1_struct_0(X2))\|~v1_funct_1(X3)\|~v5_funct_1(X3,k2_memstr_0(X1,X2))\|~v1_partfun1(X3,u1_struct_0(X2))\|~m2_subset_1(X4,k1_numbers,k5_numbers)), inference(split_conjunct,[status(thm)],[c_0_33])). cnf(c_0_46, plain, (v1_setfam_1(X1)\|v2_struct_0(X2)\|k8_memstr_0(X1,X2,X3)=k1_funct_4(X3,k7_memstr_0(X1,X2,k6_numbers))\|~v2_memstr_0(X2,X1)\|~v3_memstr_0(X2,X1)\|~l1_memstr_0(X2,X1)\|~v1_relat_1(X3)\|~v4_relat_1(X3,u1_struct_0(X2))\|~v1_funct_1(X3)\|~v5_funct_1(X3,k2_memstr_0(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_34])). cnf(c_0_47, plain, (m2_subset_1(k6_numbers,k1_numbers,k5_numbers)), inference(split_conjunct,[status(thm)],[dt_k6_numbers])). fof(c_0_48, plain, (~v2_struct_0(k1_scmfsa_2)&(v2_memstr_0(k1_scmfsa_2,np__3)&v1_extpro_1(k1_scmfsa_2,np__3))), inference(fof_simplification,[status(thm)],[fc1_scmfsa_2])). fof(c_0_49, plain, ![X33, X34]:((l1_memstr_0(X34,X33)\|~l1_extpro_1(X34,X33))&(l1_compos_1(X34)\|~l1_extpro_1(X34,X33))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_extpro_1])])])). fof(c_0_50, plain, ~v1_xboole_0(np__3), inference(fof_simplification,[status(thm)],[spc3_boole])). cnf(c_0_51, plain, (v1_xboole_0(X1)\|~v1_setfam_1(X1)\|~v7_ordinal1(X1)), inference(split_conjunct,[status(thm)],[c_0_35])). cnf(c_0_52, plain, (v7_ordinal1(X1)\|~m1_subset_1(X1,k4_ordinal1)), inference(evalgc,[status(thm)],[c_0_36])). cnf(c_0_53, plain, (k4_ordinal1=k5_numbers), inference(evalgc,[status(thm)],[c_0_37])). fof(c_0_54, plain, ![X35, X36, X37, X38, X39]:(~v1_relat_1(X35)\|(~v4_relat_1(X35,k5_numbers)\|(~v5_relat_1(X35,u1_compos_1(k1_scmfsa_2))\|(~v1_funct_1(X35)\|~v1_partfun1(X35,k5_numbers))))\|(~v1_relat_1(X36)\|(~v4_relat_1(X36,u1_struct_0(k1_scmfsa_2))\|(~v1_funct_1(X36)\|(~v5_funct_1(X36,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X36,u1_struct_0(k1_scmfsa_2)))))\|(v1_xboole_0(X37)\|(~v1_relat_1(X37)\|(~v4_relat_1(X37,k5_numbers)\|(~v5_relat_1(X37,u1_compos_1(k1_scmfsa_2))\|(~v1_funct_1(X37)\|(~v1_finset_1(X37)\|~v1_afinsq_1(X37))))))\|(~v1_ami_2(X38)\|~m1_subset_1(X38,u1_struct_0(k1_scmfsa_2))\|(~m2_subset_1(X39,k1_numbers,k5_numbers)\|(~r5_scmfsa7b(X37,k1_scmfsa_m(X36),X35)\|~r6_scmfsa7b(X37,k1_scmfsa_m(X36),X35)\|(r4_scmfsa7b(X37,X38)\|k1_funct_1(k1_scmfsa6b(X37,X36,X35),X38)=k1_funct_1(k5_extpro_1(np__3,k1_scmfsa_2,k1_funct_4(X35,X37),k8_memstr_0(np__3,k1_scmfsa_2,k1_scmfsa_m(X36)),X39),X38)))))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t60_scmfsa8c])])])])). cnf(c_0_55, plain, (k5_extpro_1(X1,X2,X3,X4,k6_numbers)=X4\|v2_struct_0(X2)\|v1_setfam_1(X1)\|~l1_extpro_1(X2,X1)\|~v3_memstr_0(X2,X1)\|~v2_memstr_0(X2,X1)\|~v5_relat_1(X3,u1_compos_1(X2))\|~v1_partfun1(X4,u1_struct_0(X2))\|~v5_funct_1(X4,k2_memstr_0(X1,X2))\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v4_relat_1(X4,u1_struct_0(X2))\|~v4_relat_1(X3,k5_numbers)\|~v1_relat_1(X4)\|~v1_relat_1(X3)), inference(csr,[status(thm)],[c_0_38, c_0_39])). cnf(c_0_56, plain, (v5_relat_1(k1_funct_4(X1,X2),X3)\|~v1_relat_1(X2)\|~v1_relat_1(X1)\|~v1_funct_1(X2)\|~v1_funct_1(X1)\|~v5_relat_1(X2,X3)\|~v5_relat_1(X1,X3)), inference(evalgc,[status(thm)],[c_0_40])). cnf(c_0_57, plain, (v1_relat_1(k1_funct_4(X1,X2))\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v1_relat_1(X2)\|~v1_funct_1(X2)), inference(split_conjunct,[status(thm)],[c_0_41])). cnf(c_0_58, plain, (v1_funct_1(k1_funct_4(X1,X2))\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v1_relat_1(X2)\|~v1_funct_1(X2)), inference(split_conjunct,[status(thm)],[c_0_41])). cnf(c_0_59, plain, (k1_funct_1(X2,X1)=k1_funct_1(X3,X1)\|k6_memstr_0(np__3,k1_scmfsa_2,X2)!=k6_memstr_0(np__3,k1_scmfsa_2,X3)\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v1_ami_2(X1)\|~v4_relat_1(X3,u1_struct_0(k1_scmfsa_2))\|~v4_relat_1(X2,u1_struct_0(k1_scmfsa_2))\|~v1_partfun1(X3,u1_struct_0(k1_scmfsa_2))\|~v1_partfun1(X2,u1_struct_0(k1_scmfsa_2))\|~m1_subset_1(X1,u1_struct_0(k1_scmfsa_2))\|~v5_funct_1(X3,k2_memstr_0(np__3,k1_scmfsa_2))\|~v5_funct_1(X2,k2_memstr_0(np__3,k1_scmfsa_2))), inference(evalgc,[status(thm)],[c_0_42])). cnf(c_0_60, negated_conjecture, (m1_subset_1(esk2_0,u1_struct_0(k1_scmfsa_2))), inference(evalgc,[status(thm)],[c_0_43])). cnf(c_0_61, negated_conjecture, (v1_ami_2(esk2_0)), inference(evalgc,[status(thm)],[c_0_44])). cnf(c_0_62, plain, (k6_memstr_0(X1,X2,k1_funct_4(X3,k7_memstr_0(X1,X2,X4)))=k6_memstr_0(X1,X2,X3)\|v1_setfam_1(X1)\|v2_struct_0(X2)\|~v1_relat_1(X3)\|~v1_funct_1(X3)\|~v2_memstr_0(X2,X1)\|~v3_memstr_0(X2,X1)\|~l1_memstr_0(X2,X1)\|~v4_relat_1(X3,u1_struct_0(X2))\|~v1_partfun1(X3,u1_struct_0(X2))\|~v5_funct_1(X3,k2_memstr_0(X1,X2))\|~m2_subset_1(X4,k1_numbers,k5_numbers)), inference(evalgc,[status(thm)],[c_0_45])). cnf(c_0_63, plain, (k1_funct_4(X3,k7_memstr_0(X1,X2,k6_numbers))=k8_memstr_0(X1,X2,X3)\|v1_setfam_1(X1)\|v2_struct_0(X2)\|~v1_relat_1(X3)\|~v1_funct_1(X3)\|~v2_memstr_0(X2,X1)\|~v3_memstr_0(X2,X1)\|~l1_memstr_0(X2,X1)\|~v4_relat_1(X3,u1_struct_0(X2))\|~v5_funct_1(X3,k2_memstr_0(X1,X2))), inference(evalgc,[status(thm)],[c_0_46])). cnf(c_0_64, plain, (m2_subset_1(k6_numbers,k1_numbers,k5_numbers)), inference(evalgc,[status(thm)],[c_0_47])). cnf(c_0_65, plain, (v3_memstr_0(k1_scmfsa_2,np__3)), inference(split_conjunct,[status(thm)],[fc5_scmfsa_2])). cnf(c_0_66, plain, (v2_memstr_0(k1_scmfsa_2,np__3)), inference(split_conjunct,[status(thm)],[c_0_48])). cnf(c_0_67, plain, (~v2_struct_0(k1_scmfsa_2)), inference(split_conjunct,[status(thm)],[c_0_48])). cnf(c_0_68, plain, (l1_memstr_0(X1,X2)\|~l1_extpro_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_49])). cnf(c_0_69, plain, (l1_extpro_1(k1_scmfsa_2,np__3)), inference(split_conjunct,[status(thm)],[dt_k1_scmfsa_2])). cnf(c_0_70, plain, (~v1_xboole_0(np__3)), inference(split_conjunct,[status(thm)],[c_0_50])). cnf(c_0_71, plain, (v1_xboole_0(X1)\|~v1_setfam_1(X1)\|~v7_ordinal1(X1)), inference(evalgc,[status(thm)],[c_0_51])). cnf(c_0_72, plain, (v7_ordinal1(X1)\|~m1_subset_1(X1,k5_numbers)), inference(rw,[status(thm)],[c_0_52, c_0_53])). cnf(c_0_73, plain, (m1_subset_1(np__3,k5_numbers)), inference(split_conjunct,[status(thm)],[spc3_numerals])). cnf(c_0_74, plain, (v1_xboole_0(X3)\|r4_scmfsa7b(X3,X4)\|k1_funct_1(k1_scmfsa6b(X3,X2,X1),X4)=k1_funct_1(k5_extpro_1(np__3,k1_scmfsa_2,k1_funct_4(X1,X3),k8_memstr_0(np__3,k1_scmfsa_2,k1_scmfsa_m(X2)),X5),X4)\|~v1_relat_1(X1)\|~v4_relat_1(X1,k5_numbers)\|~v5_relat_1(X1,u1_compos_1(k1_scmfsa_2))\|~v1_funct_1(X1)\|~v1_partfun1(X1,k5_numbers)\|~v1_relat_1(X2)\|~v4_relat_1(X2,u1_struct_0(k1_scmfsa_2))\|~v1_funct_1(X2)\|~v5_funct_1(X2,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X2,u1_struct_0(k1_scmfsa_2))\|~v1_relat_1(X3)\|~v4_relat_1(X3,k5_numbers)\|~v5_relat_1(X3,u1_compos_1(k1_scmfsa_2))\|~v1_funct_1(X3)\|~v1_finset_1(X3)\|~v1_afinsq_1(X3)\|~v1_ami_2(X4)\|~m1_subset_1(X4,u1_struct_0(k1_scmfsa_2))\|~m2_subset_1(X5,k1_numbers,k5_numbers)\|~r5_scmfsa7b(X3,k1_scmfsa_m(X2),X1)\|~r6_scmfsa7b(X3,k1_scmfsa_m(X2),X1)), inference(split_conjunct,[status(thm)],[c_0_54])). cnf(c_0_75, plain, (k5_extpro_1(X1,X2,k1_funct_4(X3,X4),X5,k6_numbers)=X5\|v2_struct_0(X2)\|v1_setfam_1(X1)\|~l1_extpro_1(X2,X1)\|~v3_memstr_0(X2,X1)\|~v2_memstr_0(X2,X1)\|~v1_partfun1(X5,u1_struct_0(X2))\|~v5_funct_1(X5,k2_memstr_0(X1,X2))\|~v1_funct_1(X5)\|~v1_funct_1(k1_funct_4(X3,X4))\|~v4_relat_1(X5,u1_struct_0(X2))\|~v4_relat_1(k1_funct_4(X3,X4),k5_numbers)\|~v1_relat_1(X5)\|~v1_relat_1(k1_funct_4(X3,X4))\|~v5_relat_1(X4,u1_compos_1(X2))\|~v5_relat_1(X3,u1_compos_1(X2))\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v1_relat_1(X4)\|~v1_relat_1(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_55, c_0_56])])). cnf(c_0_76, plain, (v1_relat_1(k1_funct_4(X1,X2))\|~v1_relat_1(X2)\|~v1_relat_1(X1)\|~v1_funct_1(X2)\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[c_0_57])). cnf(c_0_77, plain, (v1_funct_1(k1_funct_4(X1,X2))\|~v1_relat_1(X2)\|~v1_relat_1(X1)\|~v1_funct_1(X2)\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[c_0_58])). fof(c_0_78, plain, ![X40, X41, X42]:((v1_relat_1(k1_funct_4(X41,X42))\|(~v1_relat_1(X41)\|(~v4_relat_1(X41,X40)\|~v1_funct_1(X41))\|(~v1_relat_1(X42)\|(~v4_relat_1(X42,X40)\|~v1_funct_1(X42)))))&((v4_relat_1(k1_funct_4(X41,X42),X40)\|(~v1_relat_1(X41)\|(~v4_relat_1(X41,X40)\|~v1_funct_1(X41))\|(~v1_relat_1(X42)\|(~v4_relat_1(X42,X40)\|~v1_funct_1(X42)))))&(v1_funct_1(k1_funct_4(X41,X42))\|(~v1_relat_1(X41)\|(~v4_relat_1(X41,X40)\|~v1_funct_1(X41))\|(~v1_relat_1(X42)\|(~v4_relat_1(X42,X40)\|~v1_funct_1(X42))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc7_funct_4])])])). cnf(c_0_79, negated_conjecture, (k1_funct_1(X1,esk2_0)=k1_funct_1(X2,esk2_0)\|k6_memstr_0(np__3,k1_scmfsa_2,X1)!=k6_memstr_0(np__3,k1_scmfsa_2,X2)\|~v1_partfun1(X2,u1_struct_0(k1_scmfsa_2))\|~v1_partfun1(X1,u1_struct_0(k1_scmfsa_2))\|~v5_funct_1(X2,k2_memstr_0(np__3,k1_scmfsa_2))\|~v5_funct_1(X1,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_funct_1(X2)\|~v1_funct_1(X1)\|~v4_relat_1(X2,u1_struct_0(k1_scmfsa_2))\|~v4_relat_1(X1,u1_struct_0(k1_scmfsa_2))\|~v1_relat_1(X2)\|~v1_relat_1(X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59, c_0_60]), c_0_61])])])). cnf(c_0_80, plain, (k6_memstr_0(X1,X2,k8_memstr_0(X1,X2,X3))=k6_memstr_0(X1,X2,X3)\|v2_struct_0(X2)\|v1_setfam_1(X1)\|~l1_memstr_0(X2,X1)\|~v3_memstr_0(X2,X1)\|~v2_memstr_0(X2,X1)\|~v1_partfun1(X3,u1_struct_0(X2))\|~v5_funct_1(X3,k2_memstr_0(X1,X2))\|~v1_funct_1(X3)\|~v4_relat_1(X3,u1_struct_0(X2))\|~v1_relat_1(X3)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62, c_0_63]), c_0_64])])])). cnf(c_0_81, plain, (v3_memstr_0(k1_scmfsa_2,np__3)), inference(evalgc,[status(thm)],[c_0_65])). cnf(c_0_82, plain, (v2_memstr_0(k1_scmfsa_2,np__3)), inference(evalgc,[status(thm)],[c_0_66])). cnf(c_0_83, plain, (~v2_struct_0(k1_scmfsa_2)), inference(evalgc,[status(thm)],[c_0_67])). cnf(c_0_84, plain, (l1_memstr_0(X1,X2)\|~l1_extpro_1(X1,X2)), inference(evalgc,[status(thm)],[c_0_68])). cnf(c_0_85, plain, (l1_extpro_1(k1_scmfsa_2,np__3)), inference(evalgc,[status(thm)],[c_0_69])). cnf(c_0_86, plain, (~v1_xboole_0(np__3)), inference(evalgc,[status(thm)],[c_0_70])). cnf(c_0_87, plain, (v1_xboole_0(X1)\|~v1_setfam_1(X1)\|~m1_subset_1(X1,k5_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_71, c_0_72])])). cnf(c_0_88, plain, (m1_subset_1(np__3,k5_numbers)), inference(evalgc,[status(thm)],[c_0_73])). cnf(c_0_89, plain, (k1_funct_1(k5_extpro_1(np__3,k1_scmfsa_2,k1_funct_4(X1,X3),k8_memstr_0(np__3,k1_scmfsa_2,k1_scmfsa_m(X2)),X5),X4)=k1_funct_1(k1_scmfsa6b(X3,X2,X1),X4)\|v1_xboole_0(X3)\|r4_scmfsa7b(X3,X4)\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_relat_1(X1)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v1_funct_1(X1)\|~v1_ami_2(X4)\|~v1_finset_1(X3)\|~v1_afinsq_1(X3)\|~v4_relat_1(X3,k5_numbers)\|~v4_relat_1(X1,k5_numbers)\|~v1_partfun1(X1,k5_numbers)\|~v4_relat_1(X2,u1_struct_0(k1_scmfsa_2))\|~v1_partfun1(X2,u1_struct_0(k1_scmfsa_2))\|~m1_subset_1(X4,u1_struct_0(k1_scmfsa_2))\|~v5_relat_1(X3,u1_compos_1(k1_scmfsa_2))\|~v5_relat_1(X1,u1_compos_1(k1_scmfsa_2))\|~m2_subset_1(X5,k1_numbers,k5_numbers)\|~r5_scmfsa7b(X3,k1_scmfsa_m(X2),X1)\|~r6_scmfsa7b(X3,k1_scmfsa_m(X2),X1)\|~v5_funct_1(X2,k2_memstr_0(np__3,k1_scmfsa_2))), inference(evalgc,[status(thm)],[c_0_74])). cnf(c_0_90, plain, (k5_extpro_1(X1,X2,k1_funct_4(X3,X4),X5,k6_numbers)=X5\|v2_struct_0(X2)\|v1_setfam_1(X1)\|~l1_extpro_1(X2,X1)\|~v3_memstr_0(X2,X1)\|~v2_memstr_0(X2,X1)\|~v5_relat_1(X4,u1_compos_1(X2))\|~v5_relat_1(X3,u1_compos_1(X2))\|~v1_partfun1(X5,u1_struct_0(X2))\|~v5_funct_1(X5,k2_memstr_0(X1,X2))\|~v1_funct_1(X5)\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v4_relat_1(k1_funct_4(X3,X4),k5_numbers)\|~v4_relat_1(X5,u1_struct_0(X2))\|~v1_relat_1(X5)\|~v1_relat_1(X4)\|~v1_relat_1(X3)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_75, c_0_76]), c_0_77])). cnf(c_0_91, plain, (v4_relat_1(k1_funct_4(X1,X2),X3)\|~v1_relat_1(X1)\|~v4_relat_1(X1,X3)\|~v1_funct_1(X1)\|~v1_relat_1(X2)\|~v4_relat_1(X2,X3)\|~v1_funct_1(X2)), inference(split_conjunct,[status(thm)],[c_0_78])). cnf(c_0_92, negated_conjecture, (k1_funct_1(X1,esk2_0)=k1_funct_1(k8_memstr_0(np__3,k1_scmfsa_2,X2),esk2_0)\|v1_setfam_1(np__3)\|k6_memstr_0(np__3,k1_scmfsa_2,X1)!=k6_memstr_0(np__3,k1_scmfsa_2,X2)\|~v1_partfun1(k8_memstr_0(np__3,k1_scmfsa_2,X2),u1_struct_0(k1_scmfsa_2))\|~v1_partfun1(X1,u1_struct_0(k1_scmfsa_2))\|~v5_funct_1(k8_memstr_0(np__3,k1_scmfsa_2,X2),k2_memstr_0(np__3,k1_scmfsa_2))\|~v5_funct_1(X1,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_funct_1(k8_memstr_0(np__3,k1_scmfsa_2,X2))\|~v1_funct_1(X1)\|~v4_relat_1(k8_memstr_0(np__3,k1_scmfsa_2,X2),u1_struct_0(k1_scmfsa_2))\|~v4_relat_1(X1,u1_struct_0(k1_scmfsa_2))\|~v1_relat_1(k8_memstr_0(np__3,k1_scmfsa_2,X2))\|~v1_relat_1(X1)\|~l1_memstr_0(k1_scmfsa_2,np__3)\|~v1_partfun1(X2,u1_struct_0(k1_scmfsa_2))\|~v5_funct_1(X2,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_funct_1(X2)\|~v4_relat_1(X2,u1_struct_0(k1_scmfsa_2))\|~v1_relat_1(X2)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79, c_0_80]), c_0_81]), c_0_82])]), c_0_83])])). cnf(c_0_93, plain, (l1_memstr_0(k1_scmfsa_2,np__3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_84, c_0_85])])). cnf(c_0_94, plain, (~v1_setfam_1(np__3)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86, c_0_87]), c_0_88])])])). cnf(c_0_95, plain, (k1_funct_1(k8_memstr_0(np__3,k1_scmfsa_2,k1_scmfsa_m(X3)),X4)=k1_funct_1(k1_scmfsa6b(X2,X3,X1),X4)\|r4_scmfsa7b(X2,X4)\|v1_xboole_0(X2)\|v1_setfam_1(np__3)\|~r6_scmfsa7b(X2,k1_scmfsa_m(X3),X1)\|~r5_scmfsa7b(X2,k1_scmfsa_m(X3),X1)\|~v1_afinsq_1(X2)\|~v1_finset_1(X2)\|~v5_relat_1(X2,u1_compos_1(k1_scmfsa_2))\|~v5_relat_1(X1,u1_compos_1(k1_scmfsa_2))\|~m1_subset_1(X4,u1_struct_0(k1_scmfsa_2))\|~v1_ami_2(X4)\|~v1_partfun1(X3,u1_struct_0(k1_scmfsa_2))\|~v1_partfun1(X1,k5_numbers)\|~v5_funct_1(X3,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_funct_1(X2)\|~v1_funct_1(X3)\|~v1_funct_1(X1)\|~v4_relat_1(X3,u1_struct_0(k1_scmfsa_2))\|~v4_relat_1(X2,k5_numbers)\|~v4_relat_1(X1,k5_numbers)\|~v1_relat_1(X2)\|~v1_relat_1(X3)\|~v1_relat_1(X1)\|~v1_partfun1(k8_memstr_0(np__3,k1_scmfsa_2,k1_scmfsa_m(X3)),u1_struct_0(k1_scmfsa_2))\|~v5_funct_1(k8_memstr_0(np__3,k1_scmfsa_2,k1_scmfsa_m(X3)),k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_funct_1(k8_memstr_0(np__3,k1_scmfsa_2,k1_scmfsa_m(X3)))\|~v4_relat_1(k1_funct_4(X1,X2),k5_numbers)\|~v4_relat_1(k8_memstr_0(np__3,k1_scmfsa_2,k1_scmfsa_m(X3)),u1_struct_0(k1_scmfsa_2))\|~v1_relat_1(k8_memstr_0(np__3,k1_scmfsa_2,k1_scmfsa_m(X3)))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89, c_0_90]), c_0_64]), c_0_85]), c_0_81]), c_0_82])]), c_0_83])])). cnf(c_0_96, plain, (v4_relat_1(k1_funct_4(X1,X2),X3)\|~v1_relat_1(X2)\|~v1_relat_1(X1)\|~v1_funct_1(X2)\|~v1_funct_1(X1)\|~v4_relat_1(X2,X3)\|~v4_relat_1(X1,X3)), inference(evalgc,[status(thm)],[c_0_91])). cnf(c_0_97, negated_conjecture, (k1_funct_1(X1,esk2_0)=k1_funct_1(k8_memstr_0(np__3,k1_scmfsa_2,X2),esk2_0)\|k6_memstr_0(np__3,k1_scmfsa_2,X1)!=k6_memstr_0(np__3,k1_scmfsa_2,X2)\|~v1_partfun1(k8_memstr_0(np__3,k1_scmfsa_2,X2),u1_struct_0(k1_scmfsa_2))\|~v1_partfun1(X1,u1_struct_0(k1_scmfsa_2))\|~v1_partfun1(X2,u1_struct_0(k1_scmfsa_2))\|~v5_funct_1(k8_memstr_0(np__3,k1_scmfsa_2,X2),k2_memstr_0(np__3,k1_scmfsa_2))\|~v5_funct_1(X1,k2_memstr_0(np__3,k1_scmfsa_2))\|~v5_funct_1(X2,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_funct_1(k8_memstr_0(np__3,k1_scmfsa_2,X2))\|~v1_funct_1(X1)\|~v1_funct_1(X2)\|~v4_relat_1(k8_memstr_0(np__3,k1_scmfsa_2,X2),u1_struct_0(k1_scmfsa_2))\|~v4_relat_1(X1,u1_struct_0(k1_scmfsa_2))\|~v4_relat_1(X2,u1_struct_0(k1_scmfsa_2))\|~v1_relat_1(k8_memstr_0(np__3,k1_scmfsa_2,X2))\|~v1_relat_1(X1)\|~v1_relat_1(X2)), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_92, c_0_93])]), c_0_94])). fof(c_0_98, plain, ![X43]:((v1_relat_1(k1_scmfsa_m(X43))\|(~v1_relat_1(X43)\|(~v4_relat_1(X43,u1_struct_0(k1_scmfsa_2))\|(~v1_funct_1(X43)\|~v5_funct_1(X43,k2_memstr_0(np__3,k1_scmfsa_2))))))&((v4_relat_1(k1_scmfsa_m(X43),u1_struct_0(k1_scmfsa_2))\|(~v1_relat_1(X43)\|(~v4_relat_1(X43,u1_struct_0(k1_scmfsa_2))\|(~v1_funct_1(X43)\|~v5_funct_1(X43,k2_memstr_0(np__3,k1_scmfsa_2))))))&((v1_funct_1(k1_scmfsa_m(X43))\|(~v1_relat_1(X43)\|(~v4_relat_1(X43,u1_struct_0(k1_scmfsa_2))\|(~v1_funct_1(X43)\|~v5_funct_1(X43,k2_memstr_0(np__3,k1_scmfsa_2))))))&(v5_funct_1(k1_scmfsa_m(X43),k2_memstr_0(np__3,k1_scmfsa_2))\|(~v1_relat_1(X43)\|(~v4_relat_1(X43,u1_struct_0(k1_scmfsa_2))\|(~v1_funct_1(X43)\|~v5_funct_1(X43,k2_memstr_0(np__3,k1_scmfsa_2))))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_scmfsa_m])])])). fof(c_0_99, plain, ![X44]:((v1_relat_1(k1_scmfsa_m(X44))\|(~v1_relat_1(X44)\|(~v4_relat_1(X44,u1_struct_0(k1_scmfsa_2))\|(~v1_funct_1(X44)\|(~v5_funct_1(X44,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X44,u1_struct_0(k1_scmfsa_2)))))))&((v4_relat_1(k1_scmfsa_m(X44),u1_struct_0(k1_scmfsa_2))\|(~v1_relat_1(X44)\|(~v4_relat_1(X44,u1_struct_0(k1_scmfsa_2))\|(~v1_funct_1(X44)\|(~v5_funct_1(X44,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X44,u1_struct_0(k1_scmfsa_2)))))))&((v1_funct_1(k1_scmfsa_m(X44))\|(~v1_relat_1(X44)\|(~v4_relat_1(X44,u1_struct_0(k1_scmfsa_2))\|(~v1_funct_1(X44)\|(~v5_funct_1(X44,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X44,u1_struct_0(k1_scmfsa_2)))))))&((v5_funct_1(k1_scmfsa_m(X44),k2_memstr_0(np__3,k1_scmfsa_2))\|(~v1_relat_1(X44)\|(~v4_relat_1(X44,u1_struct_0(k1_scmfsa_2))\|(~v1_funct_1(X44)\|(~v5_funct_1(X44,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X44,u1_struct_0(k1_scmfsa_2)))))))&(v1_partfun1(k1_scmfsa_m(X44),u1_struct_0(k1_scmfsa_2))\|(~v1_relat_1(X44)\|(~v4_relat_1(X44,u1_struct_0(k1_scmfsa_2))\|(~v1_funct_1(X44)\|(~v5_funct_1(X44,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X44,u1_struct_0(k1_scmfsa_2))))))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc4_scmfsa_m])])])). cnf(c_0_100, plain, (k1_funct_1(k8_memstr_0(np__3,k1_scmfsa_2,k1_scmfsa_m(X1)),X2)=k1_funct_1(k1_scmfsa6b(X3,X1,X4),X2)\|v1_setfam_1(np__3)\|r4_scmfsa7b(X3,X2)\|v1_xboole_0(X3)\|~r6_scmfsa7b(X3,k1_scmfsa_m(X1),X4)\|~r5_scmfsa7b(X3,k1_scmfsa_m(X1),X4)\|~v1_afinsq_1(X3)\|~v1_finset_1(X3)\|~v5_relat_1(X3,u1_compos_1(k1_scmfsa_2))\|~v5_relat_1(X4,u1_compos_1(k1_scmfsa_2))\|~m1_subset_1(X2,u1_struct_0(k1_scmfsa_2))\|~v1_ami_2(X2)\|~v1_partfun1(k8_memstr_0(np__3,k1_scmfsa_2,k1_scmfsa_m(X1)),u1_struct_0(k1_scmfsa_2))\|~v1_partfun1(X1,u1_struct_0(k1_scmfsa_2))\|~v1_partfun1(X4,k5_numbers)\|~v5_funct_1(k8_memstr_0(np__3,k1_scmfsa_2,k1_scmfsa_m(X1)),k2_memstr_0(np__3,k1_scmfsa_2))\|~v5_funct_1(X1,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_funct_1(k8_memstr_0(np__3,k1_scmfsa_2,k1_scmfsa_m(X1)))\|~v1_funct_1(X3)\|~v1_funct_1(X1)\|~v1_funct_1(X4)\|~v4_relat_1(k8_memstr_0(np__3,k1_scmfsa_2,k1_scmfsa_m(X1)),u1_struct_0(k1_scmfsa_2))\|~v4_relat_1(X1,u1_struct_0(k1_scmfsa_2))\|~v4_relat_1(X3,k5_numbers)\|~v4_relat_1(X4,k5_numbers)\|~v1_relat_1(k8_memstr_0(np__3,k1_scmfsa_2,k1_scmfsa_m(X1)))\|~v1_relat_1(X3)\|~v1_relat_1(X1)\|~v1_relat_1(X4)), inference(csr,[status(thm)],[c_0_95, c_0_96])). cnf(c_0_101, negated_conjecture, (k1_funct_1(k8_memstr_0(np__3,k1_scmfsa_2,X1),esk2_0)=k1_funct_1(X1,esk2_0)\|~v1_partfun1(k8_memstr_0(np__3,k1_scmfsa_2,X1),u1_struct_0(k1_scmfsa_2))\|~v1_partfun1(X1,u1_struct_0(k1_scmfsa_2))\|~v5_funct_1(k8_memstr_0(np__3,k1_scmfsa_2,X1),k2_memstr_0(np__3,k1_scmfsa_2))\|~v5_funct_1(X1,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_funct_1(k8_memstr_0(np__3,k1_scmfsa_2,X1))\|~v1_funct_1(X1)\|~v4_relat_1(k8_memstr_0(np__3,k1_scmfsa_2,X1),u1_struct_0(k1_scmfsa_2))\|~v4_relat_1(X1,u1_struct_0(k1_scmfsa_2))\|~v1_relat_1(k8_memstr_0(np__3,k1_scmfsa_2,X1))\|~v1_relat_1(X1)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_97])])). cnf(c_0_102, plain, (v1_relat_1(k1_scmfsa_m(X1))\|~v1_relat_1(X1)\|~v4_relat_1(X1,u1_struct_0(k1_scmfsa_2))\|~v1_funct_1(X1)\|~v5_funct_1(X1,k2_memstr_0(np__3,k1_scmfsa_2))), inference(split_conjunct,[status(thm)],[c_0_98])). cnf(c_0_103, plain, (v4_relat_1(k1_scmfsa_m(X1),u1_struct_0(k1_scmfsa_2))\|~v1_relat_1(X1)\|~v4_relat_1(X1,u1_struct_0(k1_scmfsa_2))\|~v1_funct_1(X1)\|~v5_funct_1(X1,k2_memstr_0(np__3,k1_scmfsa_2))), inference(split_conjunct,[status(thm)],[c_0_98])). cnf(c_0_104, plain, (v1_funct_1(k1_scmfsa_m(X1))\|~v1_relat_1(X1)\|~v4_relat_1(X1,u1_struct_0(k1_scmfsa_2))\|~v1_funct_1(X1)\|~v5_funct_1(X1,k2_memstr_0(np__3,k1_scmfsa_2))), inference(split_conjunct,[status(thm)],[c_0_98])). cnf(c_0_105, plain, (v5_funct_1(k1_scmfsa_m(X1),k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_relat_1(X1)\|~v4_relat_1(X1,u1_struct_0(k1_scmfsa_2))\|~v1_funct_1(X1)\|~v5_funct_1(X1,k2_memstr_0(np__3,k1_scmfsa_2))), inference(split_conjunct,[status(thm)],[c_0_98])). cnf(c_0_106, plain, (v1_partfun1(k1_scmfsa_m(X1),u1_struct_0(k1_scmfsa_2))\|~v1_relat_1(X1)\|~v4_relat_1(X1,u1_struct_0(k1_scmfsa_2))\|~v1_funct_1(X1)\|~v5_funct_1(X1,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X1,u1_struct_0(k1_scmfsa_2))), inference(split_conjunct,[status(thm)],[c_0_99])). cnf(c_0_107, negated_conjecture, (k1_funct_1(k1_scmfsa6b(esk3_0,esk1_0,esk4_0),esk2_0)!=k1_funct_1(k1_scmfsa_m(esk1_0),esk2_0)), inference(split_conjunct,[status(thm)],[c_0_32])). cnf(c_0_108, negated_conjecture, (k1_funct_1(k1_scmfsa6b(X2,X1,X3),esk2_0)=k1_funct_1(k1_scmfsa_m(X1),esk2_0)\|r4_scmfsa7b(X2,esk2_0)\|v1_xboole_0(X2)\|~r6_scmfsa7b(X2,k1_scmfsa_m(X1),X3)\|~r5_scmfsa7b(X2,k1_scmfsa_m(X1),X3)\|~v1_afinsq_1(X2)\|~v1_finset_1(X2)\|~v5_relat_1(X2,u1_compos_1(k1_scmfsa_2))\|~v5_relat_1(X3,u1_compos_1(k1_scmfsa_2))\|~v1_partfun1(k8_memstr_0(np__3,k1_scmfsa_2,k1_scmfsa_m(X1)),u1_struct_0(k1_scmfsa_2))\|~v1_partfun1(X1,u1_struct_0(k1_scmfsa_2))\|~v1_partfun1(X3,k5_numbers)\|~v5_funct_1(k8_memstr_0(np__3,k1_scmfsa_2,k1_scmfsa_m(X1)),k2_memstr_0(np__3,k1_scmfsa_2))\|~v5_funct_1(X1,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_funct_1(k8_memstr_0(np__3,k1_scmfsa_2,k1_scmfsa_m(X1)))\|~v1_funct_1(X2)\|~v1_funct_1(X1)\|~v1_funct_1(X3)\|~v4_relat_1(k8_memstr_0(np__3,k1_scmfsa_2,k1_scmfsa_m(X1)),u1_struct_0(k1_scmfsa_2))\|~v4_relat_1(X1,u1_struct_0(k1_scmfsa_2))\|~v4_relat_1(X2,k5_numbers)\|~v4_relat_1(X3,k5_numbers)\|~v1_relat_1(k8_memstr_0(np__3,k1_scmfsa_2,k1_scmfsa_m(X1)))\|~v1_relat_1(X2)\|~v1_relat_1(X1)\|~v1_relat_1(X3)\|~v1_partfun1(k1_scmfsa_m(X1),u1_struct_0(k1_scmfsa_2))\|~v5_funct_1(k1_scmfsa_m(X1),k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_funct_1(k1_scmfsa_m(X1))\|~v4_relat_1(k1_scmfsa_m(X1),u1_struct_0(k1_scmfsa_2))\|~v1_relat_1(k1_scmfsa_m(X1))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100, c_0_101]), c_0_60]), c_0_61])]), c_0_94])])). cnf(c_0_109, plain, (v1_relat_1(k1_scmfsa_m(X1))\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v4_relat_1(X1,u1_struct_0(k1_scmfsa_2))\|~v5_funct_1(X1,k2_memstr_0(np__3,k1_scmfsa_2))), inference(evalgc,[status(thm)],[c_0_102])). cnf(c_0_110, plain, (v4_relat_1(k1_scmfsa_m(X1),u1_struct_0(k1_scmfsa_2))\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v4_relat_1(X1,u1_struct_0(k1_scmfsa_2))\|~v5_funct_1(X1,k2_memstr_0(np__3,k1_scmfsa_2))), inference(evalgc,[status(thm)],[c_0_103])). cnf(c_0_111, plain, (v1_funct_1(k1_scmfsa_m(X1))\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v4_relat_1(X1,u1_struct_0(k1_scmfsa_2))\|~v5_funct_1(X1,k2_memstr_0(np__3,k1_scmfsa_2))), inference(evalgc,[status(thm)],[c_0_104])). cnf(c_0_112, plain, (v5_funct_1(k1_scmfsa_m(X1),k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v4_relat_1(X1,u1_struct_0(k1_scmfsa_2))\|~v5_funct_1(X1,k2_memstr_0(np__3,k1_scmfsa_2))), inference(evalgc,[status(thm)],[c_0_105])). cnf(c_0_113, plain, (v1_partfun1(k1_scmfsa_m(X1),u1_struct_0(k1_scmfsa_2))\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v4_relat_1(X1,u1_struct_0(k1_scmfsa_2))\|~v1_partfun1(X1,u1_struct_0(k1_scmfsa_2))\|~v5_funct_1(X1,k2_memstr_0(np__3,k1_scmfsa_2))), inference(evalgc,[status(thm)],[c_0_106])). cnf(c_0_114, negated_conjecture, (r6_scmfsa7b(esk3_0,k1_scmfsa_m(esk1_0),esk4_0)), inference(split_conjunct,[status(thm)],[c_0_32])). cnf(c_0_115, negated_conjecture, (r5_scmfsa7b(esk3_0,k1_scmfsa_m(esk1_0),esk4_0)), inference(split_conjunct,[status(thm)],[c_0_32])). cnf(c_0_116, negated_conjecture, (v1_afinsq_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_32])). cnf(c_0_117, negated_conjecture, (v1_finset_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_32])). cnf(c_0_118, negated_conjecture, (v5_relat_1(esk3_0,u1_compos_1(k1_scmfsa_2))), inference(split_conjunct,[status(thm)],[c_0_32])). cnf(c_0_119, negated_conjecture, (v5_relat_1(esk4_0,u1_compos_1(k1_scmfsa_2))), inference(split_conjunct,[status(thm)],[c_0_32])). cnf(c_0_120, negated_conjecture, (v1_partfun1(esk1_0,u1_struct_0(k1_scmfsa_2))), inference(split_conjunct,[status(thm)],[c_0_32])). cnf(c_0_121, negated_conjecture, (v1_partfun1(esk4_0,k5_numbers)), inference(split_conjunct,[status(thm)],[c_0_32])). cnf(c_0_122, negated_conjecture, (v5_funct_1(esk1_0,k2_memstr_0(np__3,k1_scmfsa_2))), inference(split_conjunct,[status(thm)],[c_0_32])). cnf(c_0_123, negated_conjecture, (v1_funct_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_32])). cnf(c_0_124, negated_conjecture, (v1_funct_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_32])). cnf(c_0_125, negated_conjecture, (v1_funct_1(esk4_0)), inference(split_conjunct,[status(thm)],[c_0_32])). cnf(c_0_126, negated_conjecture, (v4_relat_1(esk1_0,u1_struct_0(k1_scmfsa_2))), inference(split_conjunct,[status(thm)],[c_0_32])). cnf(c_0_127, negated_conjecture, (v4_relat_1(esk3_0,k5_numbers)), inference(split_conjunct,[status(thm)],[c_0_32])). cnf(c_0_128, negated_conjecture, (v4_relat_1(esk4_0,k5_numbers)), inference(split_conjunct,[status(thm)],[c_0_32])). cnf(c_0_129, negated_conjecture, (v1_relat_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_32])). cnf(c_0_130, negated_conjecture, (v1_relat_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_32])). cnf(c_0_131, negated_conjecture, (v1_relat_1(esk4_0)), inference(split_conjunct,[status(thm)],[c_0_32])). cnf(c_0_132, negated_conjecture, (~r4_scmfsa7b(esk3_0,esk2_0)), inference(split_conjunct,[status(thm)],[c_0_32])). cnf(c_0_133, negated_conjecture, (~v1_xboole_0(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_32])). fof(c_0_134, plain, ![X48, X49, X50]:((v1_relat_1(k8_memstr_0(X48,X49,X50))\|(v1_setfam_1(X48)\|(v2_struct_0(X49)\|(~v2_memstr_0(X49,X48)\|(~v3_memstr_0(X49,X48)\|~l1_memstr_0(X49,X48)))\|(~v1_relat_1(X50)\|(~v4_relat_1(X50,u1_struct_0(X49))\|(~v1_funct_1(X50)\|~v5_funct_1(X50,k2_memstr_0(X48,X49))))))))&((v4_relat_1(k8_memstr_0(X48,X49,X50),u1_struct_0(X49))\|(v1_setfam_1(X48)\|(v2_struct_0(X49)\|(~v2_memstr_0(X49,X48)\|(~v3_memstr_0(X49,X48)\|~l1_memstr_0(X49,X48)))\|(~v1_relat_1(X50)\|(~v4_relat_1(X50,u1_struct_0(X49))\|(~v1_funct_1(X50)\|~v5_funct_1(X50,k2_memstr_0(X48,X49))))))))&((v1_funct_1(k8_memstr_0(X48,X49,X50))\|(v1_setfam_1(X48)\|(v2_struct_0(X49)\|(~v2_memstr_0(X49,X48)\|(~v3_memstr_0(X49,X48)\|~l1_memstr_0(X49,X48)))\|(~v1_relat_1(X50)\|(~v4_relat_1(X50,u1_struct_0(X49))\|(~v1_funct_1(X50)\|~v5_funct_1(X50,k2_memstr_0(X48,X49))))))))&(v5_funct_1(k8_memstr_0(X48,X49,X50),k2_memstr_0(X48,X49))\|(v1_setfam_1(X48)\|(v2_struct_0(X49)\|(~v2_memstr_0(X49,X48)\|(~v3_memstr_0(X49,X48)\|~l1_memstr_0(X49,X48)))\|(~v1_relat_1(X50)\|(~v4_relat_1(X50,u1_struct_0(X49))\|(~v1_funct_1(X50)\|~v5_funct_1(X50,k2_memstr_0(X48,X49))))))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k8_memstr_0])])])])). cnf(c_0_135, negated_conjecture, (k1_funct_1(k1_scmfsa6b(esk3_0,esk1_0,esk4_0),esk2_0)!=k1_funct_1(k1_scmfsa_m(esk1_0),esk2_0)), inference(evalgc,[status(thm)],[c_0_107])). cnf(c_0_136, negated_conjecture, (k1_funct_1(k1_scmfsa6b(X1,X2,X3),esk2_0)=k1_funct_1(k1_scmfsa_m(X2),esk2_0)\|r4_scmfsa7b(X1,esk2_0)\|v1_xboole_0(X1)\|~r6_scmfsa7b(X1,k1_scmfsa_m(X2),X3)\|~r5_scmfsa7b(X1,k1_scmfsa_m(X2),X3)\|~v1_afinsq_1(X1)\|~v1_finset_1(X1)\|~v5_relat_1(X1,u1_compos_1(k1_scmfsa_2))\|~v5_relat_1(X3,u1_compos_1(k1_scmfsa_2))\|~v1_partfun1(k8_memstr_0(np__3,k1_scmfsa_2,k1_scmfsa_m(X2)),u1_struct_0(k1_scmfsa_2))\|~v1_partfun1(X2,u1_struct_0(k1_scmfsa_2))\|~v1_partfun1(X3,k5_numbers)\|~v5_funct_1(k8_memstr_0(np__3,k1_scmfsa_2,k1_scmfsa_m(X2)),k2_memstr_0(np__3,k1_scmfsa_2))\|~v5_funct_1(X2,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_funct_1(k8_memstr_0(np__3,k1_scmfsa_2,k1_scmfsa_m(X2)))\|~v1_funct_1(X1)\|~v1_funct_1(X2)\|~v1_funct_1(X3)\|~v4_relat_1(k8_memstr_0(np__3,k1_scmfsa_2,k1_scmfsa_m(X2)),u1_struct_0(k1_scmfsa_2))\|~v4_relat_1(X2,u1_struct_0(k1_scmfsa_2))\|~v4_relat_1(X1,k5_numbers)\|~v4_relat_1(X3,k5_numbers)\|~v1_relat_1(k8_memstr_0(np__3,k1_scmfsa_2,k1_scmfsa_m(X2)))\|~v1_relat_1(X1)\|~v1_relat_1(X2)\|~v1_relat_1(X3)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_108, c_0_109]), c_0_110]), c_0_111]), c_0_112]), c_0_113])). cnf(c_0_137, negated_conjecture, (r6_scmfsa7b(esk3_0,k1_scmfsa_m(esk1_0),esk4_0)), inference(evalgc,[status(thm)],[c_0_114])). cnf(c_0_138, negated_conjecture, (r5_scmfsa7b(esk3_0,k1_scmfsa_m(esk1_0),esk4_0)), inference(evalgc,[status(thm)],[c_0_115])). cnf(c_0_139, negated_conjecture, (v1_afinsq_1(esk3_0)), inference(evalgc,[status(thm)],[c_0_116])). cnf(c_0_140, negated_conjecture, (v1_finset_1(esk3_0)), inference(evalgc,[status(thm)],[c_0_117])). cnf(c_0_141, negated_conjecture, (v5_relat_1(esk3_0,u1_compos_1(k1_scmfsa_2))), inference(evalgc,[status(thm)],[c_0_118])). cnf(c_0_142, negated_conjecture, (v5_relat_1(esk4_0,u1_compos_1(k1_scmfsa_2))), inference(evalgc,[status(thm)],[c_0_119])). cnf(c_0_143, negated_conjecture, (v1_partfun1(esk1_0,u1_struct_0(k1_scmfsa_2))), inference(evalgc,[status(thm)],[c_0_120])). cnf(c_0_144, negated_conjecture, (v1_partfun1(esk4_0,k5_numbers)), inference(evalgc,[status(thm)],[c_0_121])). cnf(c_0_145, negated_conjecture, (v5_funct_1(esk1_0,k2_memstr_0(np__3,k1_scmfsa_2))), inference(evalgc,[status(thm)],[c_0_122])). cnf(c_0_146, negated_conjecture, (v1_funct_1(esk3_0)), inference(evalgc,[status(thm)],[c_0_123])). cnf(c_0_147, negated_conjecture, (v1_funct_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_124])). cnf(c_0_148, negated_conjecture, (v1_funct_1(esk4_0)), inference(evalgc,[status(thm)],[c_0_125])). cnf(c_0_149, negated_conjecture, (v4_relat_1(esk1_0,u1_struct_0(k1_scmfsa_2))), inference(evalgc,[status(thm)],[c_0_126])). cnf(c_0_150, negated_conjecture, (v4_relat_1(esk3_0,k5_numbers)), inference(evalgc,[status(thm)],[c_0_127])). cnf(c_0_151, negated_conjecture, (v4_relat_1(esk4_0,k5_numbers)), inference(evalgc,[status(thm)],[c_0_128])). cnf(c_0_152, negated_conjecture, (v1_relat_1(esk3_0)), inference(evalgc,[status(thm)],[c_0_129])). cnf(c_0_153, negated_conjecture, (v1_relat_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_130])). cnf(c_0_154, negated_conjecture, (v1_relat_1(esk4_0)), inference(evalgc,[status(thm)],[c_0_131])). cnf(c_0_155, negated_conjecture, (~r4_scmfsa7b(esk3_0,esk2_0)), inference(evalgc,[status(thm)],[c_0_132])). cnf(c_0_156, negated_conjecture, (~v1_xboole_0(esk3_0)), inference(evalgc,[status(thm)],[c_0_133])). cnf(c_0_157, plain, (v5_funct_1(k8_memstr_0(X1,X2,X3),k2_memstr_0(X1,X2))\|v1_setfam_1(X1)\|v2_struct_0(X2)\|~v2_memstr_0(X2,X1)\|~v3_memstr_0(X2,X1)\|~l1_memstr_0(X2,X1)\|~v1_relat_1(X3)\|~v4_relat_1(X3,u1_struct_0(X2))\|~v1_funct_1(X3)\|~v5_funct_1(X3,k2_memstr_0(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_134])). fof(c_0_158, plain, ![X45, X46, X47]:((v1_relat_1(k8_memstr_0(X45,X46,X47))\|(v1_setfam_1(X45)\|(v2_struct_0(X46)\|(~v2_memstr_0(X46,X45)\|(~v3_memstr_0(X46,X45)\|~l1_memstr_0(X46,X45)))\|(~v1_relat_1(X47)\|(~v4_relat_1(X47,u1_struct_0(X46))\|(~v1_funct_1(X47)\|(~v5_funct_1(X47,k2_memstr_0(X45,X46))\|~v1_partfun1(X47,u1_struct_0(X46)))))))))&((v4_relat_1(k8_memstr_0(X45,X46,X47),u1_struct_0(X46))\|(v1_setfam_1(X45)\|(v2_struct_0(X46)\|(~v2_memstr_0(X46,X45)\|(~v3_memstr_0(X46,X45)\|~l1_memstr_0(X46,X45)))\|(~v1_relat_1(X47)\|(~v4_relat_1(X47,u1_struct_0(X46))\|(~v1_funct_1(X47)\|(~v5_funct_1(X47,k2_memstr_0(X45,X46))\|~v1_partfun1(X47,u1_struct_0(X46)))))))))&((v1_funct_1(k8_memstr_0(X45,X46,X47))\|(v1_setfam_1(X45)\|(v2_struct_0(X46)\|(~v2_memstr_0(X46,X45)\|(~v3_memstr_0(X46,X45)\|~l1_memstr_0(X46,X45)))\|(~v1_relat_1(X47)\|(~v4_relat_1(X47,u1_struct_0(X46))\|(~v1_funct_1(X47)\|(~v5_funct_1(X47,k2_memstr_0(X45,X46))\|~v1_partfun1(X47,u1_struct_0(X46)))))))))&((v5_funct_1(k8_memstr_0(X45,X46,X47),k2_memstr_0(X45,X46))\|(v1_setfam_1(X45)\|(v2_struct_0(X46)\|(~v2_memstr_0(X46,X45)\|(~v3_memstr_0(X46,X45)\|~l1_memstr_0(X46,X45)))\|(~v1_relat_1(X47)\|(~v4_relat_1(X47,u1_struct_0(X46))\|(~v1_funct_1(X47)\|(~v5_funct_1(X47,k2_memstr_0(X45,X46))\|~v1_partfun1(X47,u1_struct_0(X46)))))))))&(v1_partfun1(k8_memstr_0(X45,X46,X47),u1_struct_0(X46))\|(v1_setfam_1(X45)\|(v2_struct_0(X46)\|(~v2_memstr_0(X46,X45)\|(~v3_memstr_0(X46,X45)\|~l1_memstr_0(X46,X45)))\|(~v1_relat_1(X47)\|(~v4_relat_1(X47,u1_struct_0(X46))\|(~v1_funct_1(X47)\|(~v5_funct_1(X47,k2_memstr_0(X45,X46))\|~v1_partfun1(X47,u1_struct_0(X46))))))))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fc14_memstr_0])])])])). cnf(c_0_159, negated_conjecture, (~v1_partfun1(k8_memstr_0(np__3,k1_scmfsa_2,k1_scmfsa_m(esk1_0)),u1_struct_0(k1_scmfsa_2))\|~v5_funct_1(k8_memstr_0(np__3,k1_scmfsa_2,k1_scmfsa_m(esk1_0)),k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_funct_1(k8_memstr_0(np__3,k1_scmfsa_2,k1_scmfsa_m(esk1_0)))\|~v4_relat_1(k8_memstr_0(np__3,k1_scmfsa_2,k1_scmfsa_m(esk1_0)),u1_struct_0(k1_scmfsa_2))\|~v1_relat_1(k8_memstr_0(np__3,k1_scmfsa_2,k1_scmfsa_m(esk1_0)))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135, c_0_136]), c_0_137]), c_0_138]), c_0_139]), c_0_140]), c_0_141]), c_0_142]), c_0_143]), c_0_144]), c_0_145]), c_0_146]), c_0_147]), c_0_148]), c_0_149]), c_0_150]), c_0_151]), c_0_152]), c_0_153]), c_0_154])]), c_0_155]), c_0_156])])). cnf(c_0_160, plain, (v1_setfam_1(X1)\|v2_struct_0(X2)\|v5_funct_1(k8_memstr_0(X1,X2,X3),k2_memstr_0(X1,X2))\|~v1_relat_1(X3)\|~v1_funct_1(X3)\|~v2_memstr_0(X2,X1)\|~v3_memstr_0(X2,X1)\|~l1_memstr_0(X2,X1)\|~v4_relat_1(X3,u1_struct_0(X2))\|~v5_funct_1(X3,k2_memstr_0(X1,X2))), inference(evalgc,[status(thm)],[c_0_157])). cnf(c_0_161, negated_conjecture, (v1_funct_1(k1_scmfsa_m(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111, c_0_145]), c_0_147]), c_0_149]), c_0_153])])])). cnf(c_0_162, negated_conjecture, (v1_relat_1(k1_scmfsa_m(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109, c_0_145]), c_0_147]), c_0_149]), c_0_153])])])). cnf(c_0_163, plain, (v1_partfun1(k8_memstr_0(X1,X2,X3),u1_struct_0(X2))\|v1_setfam_1(X1)\|v2_struct_0(X2)\|~v2_memstr_0(X2,X1)\|~v3_memstr_0(X2,X1)\|~l1_memstr_0(X2,X1)\|~v1_relat_1(X3)\|~v4_relat_1(X3,u1_struct_0(X2))\|~v1_funct_1(X3)\|~v5_funct_1(X3,k2_memstr_0(X1,X2))\|~v1_partfun1(X3,u1_struct_0(X2))), inference(split_conjunct,[status(thm)],[c_0_158])). cnf(c_0_164, negated_conjecture, (~v1_partfun1(k8_memstr_0(np__3,k1_scmfsa_2,k1_scmfsa_m(esk1_0)),u1_struct_0(k1_scmfsa_2))\|~v1_funct_1(k8_memstr_0(np__3,k1_scmfsa_2,k1_scmfsa_m(esk1_0)))\|~v4_relat_1(k8_memstr_0(np__3,k1_scmfsa_2,k1_scmfsa_m(esk1_0)),u1_struct_0(k1_scmfsa_2))\|~v1_relat_1(k8_memstr_0(np__3,k1_scmfsa_2,k1_scmfsa_m(esk1_0)))\|~v5_funct_1(k1_scmfsa_m(esk1_0),k2_memstr_0(np__3,k1_scmfsa_2))\|~v4_relat_1(k1_scmfsa_m(esk1_0),u1_struct_0(k1_scmfsa_2))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159, c_0_160]), c_0_93]), c_0_81]), c_0_82]), c_0_161]), c_0_162])]), c_0_83]), c_0_94])])). cnf(c_0_165, plain, (v1_setfam_1(X1)\|v2_struct_0(X2)\|v1_partfun1(k8_memstr_0(X1,X2,X3),u1_struct_0(X2))\|~v1_relat_1(X3)\|~v1_funct_1(X3)\|~v2_memstr_0(X2,X1)\|~v3_memstr_0(X2,X1)\|~l1_memstr_0(X2,X1)\|~v4_relat_1(X3,u1_struct_0(X2))\|~v1_partfun1(X3,u1_struct_0(X2))\|~v5_funct_1(X3,k2_memstr_0(X1,X2))), inference(evalgc,[status(thm)],[c_0_163])). cnf(c_0_166, plain, (v4_relat_1(k8_memstr_0(X1,X2,X3),u1_struct_0(X2))\|v1_setfam_1(X1)\|v2_struct_0(X2)\|~v2_memstr_0(X2,X1)\|~v3_memstr_0(X2,X1)\|~l1_memstr_0(X2,X1)\|~v1_relat_1(X3)\|~v4_relat_1(X3,u1_struct_0(X2))\|~v1_funct_1(X3)\|~v5_funct_1(X3,k2_memstr_0(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_134])). cnf(c_0_167, negated_conjecture, (~v5_funct_1(k1_scmfsa_m(esk1_0),k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_funct_1(k8_memstr_0(np__3,k1_scmfsa_2,k1_scmfsa_m(esk1_0)))\|~v4_relat_1(k8_memstr_0(np__3,k1_scmfsa_2,k1_scmfsa_m(esk1_0)),u1_struct_0(k1_scmfsa_2))\|~v4_relat_1(k1_scmfsa_m(esk1_0),u1_struct_0(k1_scmfsa_2))\|~v1_relat_1(k8_memstr_0(np__3,k1_scmfsa_2,k1_scmfsa_m(esk1_0)))\|~v1_partfun1(k1_scmfsa_m(esk1_0),u1_struct_0(k1_scmfsa_2))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164, c_0_165]), c_0_93]), c_0_81]), c_0_82]), c_0_161]), c_0_162])]), c_0_83]), c_0_94])])). cnf(c_0_168, plain, (v1_setfam_1(X1)\|v2_struct_0(X2)\|v4_relat_1(k8_memstr_0(X1,X2,X3),u1_struct_0(X2))\|~v1_relat_1(X3)\|~v1_funct_1(X3)\|~v2_memstr_0(X2,X1)\|~v3_memstr_0(X2,X1)\|~l1_memstr_0(X2,X1)\|~v4_relat_1(X3,u1_struct_0(X2))\|~v5_funct_1(X3,k2_memstr_0(X1,X2))), inference(evalgc,[status(thm)],[c_0_166])). cnf(c_0_169, plain, (v1_funct_1(k8_memstr_0(X1,X2,X3))\|v1_setfam_1(X1)\|v2_struct_0(X2)\|~v2_memstr_0(X2,X1)\|~v3_memstr_0(X2,X1)\|~l1_memstr_0(X2,X1)\|~v1_relat_1(X3)\|~v4_relat_1(X3,u1_struct_0(X2))\|~v1_funct_1(X3)\|~v5_funct_1(X3,k2_memstr_0(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_134])). cnf(c_0_170, negated_conjecture, (~v1_partfun1(k1_scmfsa_m(esk1_0),u1_struct_0(k1_scmfsa_2))\|~v5_funct_1(k1_scmfsa_m(esk1_0),k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_funct_1(k8_memstr_0(np__3,k1_scmfsa_2,k1_scmfsa_m(esk1_0)))\|~v4_relat_1(k1_scmfsa_m(esk1_0),u1_struct_0(k1_scmfsa_2))\|~v1_relat_1(k8_memstr_0(np__3,k1_scmfsa_2,k1_scmfsa_m(esk1_0)))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167, c_0_168]), c_0_93]), c_0_81]), c_0_82]), c_0_161]), c_0_162])]), c_0_83]), c_0_94])])). cnf(c_0_171, plain, (v1_setfam_1(X1)\|v2_struct_0(X2)\|v1_funct_1(k8_memstr_0(X1,X2,X3))\|~v1_relat_1(X3)\|~v1_funct_1(X3)\|~v2_memstr_0(X2,X1)\|~v3_memstr_0(X2,X1)\|~l1_memstr_0(X2,X1)\|~v4_relat_1(X3,u1_struct_0(X2))\|~v5_funct_1(X3,k2_memstr_0(X1,X2))), inference(evalgc,[status(thm)],[c_0_169])). cnf(c_0_172, plain, (v1_relat_1(k8_memstr_0(X1,X2,X3))\|v1_setfam_1(X1)\|v2_struct_0(X2)\|~v2_memstr_0(X2,X1)\|~v3_memstr_0(X2,X1)\|~l1_memstr_0(X2,X1)\|~v1_relat_1(X3)\|~v4_relat_1(X3,u1_struct_0(X2))\|~v1_funct_1(X3)\|~v5_funct_1(X3,k2_memstr_0(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_134])). cnf(c_0_173, negated_conjecture, (~v1_partfun1(k1_scmfsa_m(esk1_0),u1_struct_0(k1_scmfsa_2))\|~v5_funct_1(k1_scmfsa_m(esk1_0),k2_memstr_0(np__3,k1_scmfsa_2))\|~v4_relat_1(k1_scmfsa_m(esk1_0),u1_struct_0(k1_scmfsa_2))\|~v1_relat_1(k8_memstr_0(np__3,k1_scmfsa_2,k1_scmfsa_m(esk1_0)))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170, c_0_171]), c_0_93]), c_0_81]), c_0_82]), c_0_161]), c_0_162])]), c_0_83]), c_0_94])])). cnf(c_0_174, plain, (v1_setfam_1(X1)\|v2_struct_0(X2)\|v1_relat_1(k8_memstr_0(X1,X2,X3))\|~v1_relat_1(X3)\|~v1_funct_1(X3)\|~v2_memstr_0(X2,X1)\|~v3_memstr_0(X2,X1)\|~l1_memstr_0(X2,X1)\|~v4_relat_1(X3,u1_struct_0(X2))\|~v5_funct_1(X3,k2_memstr_0(X1,X2))), inference(evalgc,[status(thm)],[c_0_172])). cnf(c_0_175, negated_conjecture, (~v1_partfun1(k1_scmfsa_m(esk1_0),u1_struct_0(k1_scmfsa_2))\|~v5_funct_1(k1_scmfsa_m(esk1_0),k2_memstr_0(np__3,k1_scmfsa_2))\|~v4_relat_1(k1_scmfsa_m(esk1_0),u1_struct_0(k1_scmfsa_2))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173, c_0_174]), c_0_93]), c_0_81]), c_0_82]), c_0_161]), c_0_162])]), c_0_83]), c_0_94])])). cnf(c_0_176, negated_conjecture, (~v1_partfun1(k1_scmfsa_m(esk1_0),u1_struct_0(k1_scmfsa_2))\|~v4_relat_1(k1_scmfsa_m(esk1_0),u1_struct_0(k1_scmfsa_2))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_175, c_0_112]), c_0_145]), c_0_147]), c_0_149]), c_0_153])])])). cnf(c_0_177, negated_conjecture, (~v4_relat_1(k1_scmfsa_m(esk1_0),u1_struct_0(k1_scmfsa_2))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176, c_0_113]), c_0_143]), c_0_145]), c_0_147]), c_0_149]), c_0_153])])])). cnf(c_0_178, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177, c_0_110]), c_0_145]), c_0_147]), c_0_149]), c_0_153])]), ['proof']). # SZS output end CNFRefutation	reserve s for State of SCM+FSA, a, c for read-write Int-Location, aa, bb, cc, dd, x for Int-Location, f for FinSeq-Location, I, J for Program of SCM+FSA, Ig for good Program of SCM+FSA, i, k for Element of NAT, p for Instruction-Sequence of SCM+FSA; theorem Th1: I is_closed_on Initialized s,p & I is_halting_on Initialized s,p & I does not destroy aa implies IExec(I,p,s).aa = (Initialized s).aa proof set a = aa; A1: DataPart Initialized s = DataPart(Initialize Initialized s) by MEMSTR_0:79; assume I is_closed_on Initialized s,p & I is_halting_on Initialized s,p & I does not destroy a; hence IExec(I,p,s).a = Comput(p+*I, Initialize Initialized s,0).a by SCMFSA8C:60 .= (Initialize Initialized s).a .= (Initialized s).a by A1,SCMFSA_M:2; end;	Convert the following ATP output trace into a readable Mizar proof.
t4_mesfunc6	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t4_mesfunc6, conjecture, ![X1]:(~(v1_xboole_0(X1))=>![X2]:((v1_funct_1(X2)&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers))))=>![X3]:(v1_xreal_0(X3)=>![X4]:(r2_hidden(X4,k12_mesfunc1(X2,X3))<=>(r2_hidden(X4,k1_relset_1(X1,X2))&?[X5]:(m1_subset_1(X5,k1_numbers)&(X5=k1_seq_1(X2,X4)&r1_xxreal_0(X5,X3)))))))), file('/scratch/mptp/predsminms1/t4_mesfunc6__0', t4_mesfunc6)). fof(cc2_relset_1, axiom, ![X1, X2, X3]:(m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))=>(v4_relat_1(X3,X1)&v5_relat_1(X3,X2))), file('/scratch/mptp/predsminms1/t4_mesfunc6__0', cc2_relset_1)). fof(cc1_relset_1, axiom, ![X1, X2, X3]:(m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))=>v1_relat_1(X3)), file('/scratch/mptp/predsminms1/t4_mesfunc6__0', cc1_relset_1)). fof(redefinition_k1_seq_1, axiom, ![X1, X2]:((v1_relat_1(X1)&(v1_funct_1(X1)&v3_valued_0(X1)))=>k1_seq_1(X1,X2)=k1_funct_1(X1,X2)), file('/scratch/mptp/predsminms1/t4_mesfunc6__0', redefinition_k1_seq_1)). fof(redefinition_k12_supinf_2, axiom, ![X1, X2]:((v1_relat_1(X1)&(v1_funct_1(X1)&v2_valued_0(X1)))=>k12_supinf_2(X1,X2)=k1_funct_1(X1,X2)), file('/scratch/mptp/predsminms1/t4_mesfunc6__0', redefinition_k12_supinf_2)). fof(cc30_valued_0, axiom, ![X1]:((v1_relat_1(X1)&v5_relat_1(X1,k1_numbers))=>(v1_relat_1(X1)&v3_valued_0(X1))), file('/scratch/mptp/predsminms1/t4_mesfunc6__0', cc30_valued_0)). fof(cc17_valued_0, axiom, ![X1, X2]:(v2_membered(X2)=>![X3]:(m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))=>v2_valued_0(X3))), file('/scratch/mptp/predsminms1/t4_mesfunc6__0', cc17_valued_0)). fof(cc4_membered, axiom, ![X1]:(v3_membered(X1)=>v2_membered(X1)), file('/scratch/mptp/predsminms1/t4_mesfunc6__0', cc4_membered)). fof(fc3_membered, axiom, v3_membered(k1_numbers), file('/scratch/mptp/predsminms1/t4_mesfunc6__0', fc3_membered)). fof(redefinition_k1_relset_1, axiom, ![X1, X2]:((v1_relat_1(X2)&v4_relat_1(X2,X1))=>k1_relset_1(X1,X2)=k9_xtuple_0(X2)), file('/scratch/mptp/predsminms1/t4_mesfunc6__0', redefinition_k1_relset_1)). fof(d12_mesfunc1, axiom, ![X1]:((v1_relat_1(X1)&(v1_funct_1(X1)&v2_valued_0(X1)))=>![X2]:(v1_xxreal_0(X2)=>![X3]:(X3=k12_mesfunc1(X1,X2)<=>![X4]:(r2_hidden(X4,X3)<=>(r2_hidden(X4,k9_xtuple_0(X1))&r1_xxreal_0(k12_supinf_2(X1,X4),X2)))))), file('/scratch/mptp/predsminms1/t4_mesfunc6__0', d12_mesfunc1)). fof(cc4_xreal_0, axiom, ![X1]:(v1_xreal_0(X1)=>v1_xxreal_0(X1)), file('/scratch/mptp/predsminms1/t4_mesfunc6__0', cc4_xreal_0)). fof(dt_k1_seq_1, axiom, ![X1, X2]:((v1_relat_1(X1)&(v1_funct_1(X1)&v3_valued_0(X1)))=>m1_subset_1(k1_seq_1(X1,X2),k1_numbers)), file('/scratch/mptp/predsminms1/t4_mesfunc6__0', dt_k1_seq_1)). fof(c_0_13, negated_conjecture, ~(![X1]:(~(v1_xboole_0(X1))=>![X2]:((v1_funct_1(X2)&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers))))=>![X3]:(v1_xreal_0(X3)=>![X4]:(r2_hidden(X4,k12_mesfunc1(X2,X3))<=>(r2_hidden(X4,k1_relset_1(X1,X2))&?[X5]:(m1_subset_1(X5,k1_numbers)&(X5=k1_seq_1(X2,X4)&r1_xxreal_0(X5,X3))))))))), inference(assume_negation,[status(cth)],[t4_mesfunc6])). fof(c_0_14, plain, ![X16, X17, X18]:((v4_relat_1(X18,X16)\|~m1_subset_1(X18,k1_zfmisc_1(k2_zfmisc_1(X16,X17))))&(v5_relat_1(X18,X17)\|~m1_subset_1(X18,k1_zfmisc_1(k2_zfmisc_1(X16,X17))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_relset_1])])])). fof(c_0_15, negated_conjecture, ![X10]:(~v1_xboole_0(esk1_0)&((v1_funct_1(esk2_0)&m1_subset_1(esk2_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers))))&(v1_xreal_0(esk3_0)&((~r2_hidden(esk4_0,k12_mesfunc1(esk2_0,esk3_0))\|(~r2_hidden(esk4_0,k1_relset_1(esk1_0,esk2_0))\|(~m1_subset_1(X10,k1_numbers)\|(X10!=k1_seq_1(esk2_0,esk4_0)\|~r1_xxreal_0(X10,esk3_0)))))&((r2_hidden(esk4_0,k1_relset_1(esk1_0,esk2_0))\|r2_hidden(esk4_0,k12_mesfunc1(esk2_0,esk3_0)))&((m1_subset_1(esk5_0,k1_numbers)\|r2_hidden(esk4_0,k12_mesfunc1(esk2_0,esk3_0)))&((esk5_0=k1_seq_1(esk2_0,esk4_0)\|r2_hidden(esk4_0,k12_mesfunc1(esk2_0,esk3_0)))&(r1_xxreal_0(esk5_0,esk3_0)\|r2_hidden(esk4_0,k12_mesfunc1(esk2_0,esk3_0)))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_13])])])])])])). fof(c_0_16, plain, ![X13, X14, X15]:(~m1_subset_1(X15,k1_zfmisc_1(k2_zfmisc_1(X13,X14)))\|v1_relat_1(X15)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relset_1])])). fof(c_0_17, plain, ![X26, X27]:(~v1_relat_1(X26)\|(~v1_funct_1(X26)\|~v3_valued_0(X26))\|k1_seq_1(X26,X27)=k1_funct_1(X26,X27)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k1_seq_1])])). fof(c_0_18, plain, ![X28, X29]:(~v1_relat_1(X28)\|(~v1_funct_1(X28)\|~v2_valued_0(X28))\|k12_supinf_2(X28,X29)=k1_funct_1(X28,X29)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k12_supinf_2])])). fof(c_0_19, plain, ![X25]:((v1_relat_1(X25)\|(~v1_relat_1(X25)\|~v5_relat_1(X25,k1_numbers)))&(v3_valued_0(X25)\|(~v1_relat_1(X25)\|~v5_relat_1(X25,k1_numbers)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc30_valued_0])])])). cnf(c_0_20, plain, (v5_relat_1(X1,X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X3,X2)))), inference(split_conjunct,[status(thm)],[c_0_14])). cnf(c_0_21, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_22, plain, (v1_relat_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_16])). fof(c_0_23, plain, ![X22, X23, X24]:(~v2_membered(X23)\|(~m1_subset_1(X24,k1_zfmisc_1(k2_zfmisc_1(X22,X23)))\|v2_valued_0(X24))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc17_valued_0])])])). cnf(c_0_24, plain, (k1_seq_1(X1,X2)=k1_funct_1(X1,X2)\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v3_valued_0(X1)), inference(split_conjunct,[status(thm)],[c_0_17])). cnf(c_0_25, plain, (k12_supinf_2(X1,X2)=k1_funct_1(X1,X2)\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v2_valued_0(X1)), inference(split_conjunct,[status(thm)],[c_0_18])). cnf(c_0_26, plain, (v3_valued_0(X1)\|~v1_relat_1(X1)\|~v5_relat_1(X1,k1_numbers)), inference(split_conjunct,[status(thm)],[c_0_19])). cnf(c_0_27, plain, (v5_relat_1(X1,X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X3,X2)))), inference(evalgc,[status(thm)],[c_0_20])). cnf(c_0_28, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))), inference(evalgc,[status(thm)],[c_0_21])). cnf(c_0_29, plain, (v1_relat_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(evalgc,[status(thm)],[c_0_22])). cnf(c_0_30, plain, (v2_valued_0(X2)\|~v2_membered(X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_23])). fof(c_0_31, plain, ![X21]:(~v3_membered(X21)\|v2_membered(X21)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc4_membered])])). cnf(c_0_32, plain, (k1_funct_1(X1,X2)=k1_seq_1(X1,X2)\|~v1_funct_1(X1)\|~v1_relat_1(X1)\|~v3_valued_0(X1)), inference(evalgc,[status(thm)],[c_0_24])). cnf(c_0_33, plain, (k1_funct_1(X1,X2)=k12_supinf_2(X1,X2)\|~v1_funct_1(X1)\|~v1_relat_1(X1)\|~v2_valued_0(X1)), inference(evalgc,[status(thm)],[c_0_25])). cnf(c_0_34, plain, (v3_valued_0(X1)\|~v1_relat_1(X1)\|~v5_relat_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[c_0_26])). cnf(c_0_35, negated_conjecture, (v5_relat_1(esk2_0,k1_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_27, c_0_28])])). cnf(c_0_36, negated_conjecture, (v1_relat_1(esk2_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_29, c_0_28])])). cnf(c_0_37, negated_conjecture, (v1_funct_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_38, plain, (v2_valued_0(X2)\|~v2_membered(X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X3,X1)))), inference(evalgc,[status(thm)],[c_0_30])). cnf(c_0_39, plain, (v2_membered(X1)\|~v3_membered(X1)), inference(split_conjunct,[status(thm)],[c_0_31])). cnf(c_0_40, plain, (v3_membered(k1_numbers)), inference(split_conjunct,[status(thm)],[fc3_membered])). cnf(c_0_41, plain, (k1_seq_1(X1,X2)=k12_supinf_2(X1,X2)\|~v3_valued_0(X1)\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v2_valued_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_32, c_0_33])])). cnf(c_0_42, negated_conjecture, (v3_valued_0(esk2_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34, c_0_35]), c_0_36])])])). cnf(c_0_43, negated_conjecture, (v1_funct_1(esk2_0)), inference(evalgc,[status(thm)],[c_0_37])). cnf(c_0_44, negated_conjecture, (v2_valued_0(esk2_0)\|~v2_membered(k1_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_38, c_0_28])])). cnf(c_0_45, plain, (v2_membered(X1)\|~v3_membered(X1)), inference(evalgc,[status(thm)],[c_0_39])). cnf(c_0_46, plain, (v3_membered(k1_numbers)), inference(evalgc,[status(thm)],[c_0_40])). fof(c_0_47, plain, ![X19, X20]:(~v1_relat_1(X20)\|~v4_relat_1(X20,X19)\|k1_relset_1(X19,X20)=k9_xtuple_0(X20)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k1_relset_1])])). cnf(c_0_48, plain, (v4_relat_1(X1,X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_14])). fof(c_0_49, plain, ![X30, X31, X32, X33, X34, X35]:((((r2_hidden(X33,k9_xtuple_0(X30))\|~r2_hidden(X33,X32)\|X32!=k12_mesfunc1(X30,X31)\|~v1_xxreal_0(X31)\|(~v1_relat_1(X30)\|(~v1_funct_1(X30)\|~v2_valued_0(X30))))&(r1_xxreal_0(k12_supinf_2(X30,X33),X31)\|~r2_hidden(X33,X32)\|X32!=k12_mesfunc1(X30,X31)\|~v1_xxreal_0(X31)\|(~v1_relat_1(X30)\|(~v1_funct_1(X30)\|~v2_valued_0(X30)))))&(~r2_hidden(X34,k9_xtuple_0(X30))\|~r1_xxreal_0(k12_supinf_2(X30,X34),X31)\|r2_hidden(X34,X32)\|X32!=k12_mesfunc1(X30,X31)\|~v1_xxreal_0(X31)\|(~v1_relat_1(X30)\|(~v1_funct_1(X30)\|~v2_valued_0(X30)))))&((~r2_hidden(esk6_3(X30,X31,X35),X35)\|(~r2_hidden(esk6_3(X30,X31,X35),k9_xtuple_0(X30))\|~r1_xxreal_0(k12_supinf_2(X30,esk6_3(X30,X31,X35)),X31))\|X35=k12_mesfunc1(X30,X31)\|~v1_xxreal_0(X31)\|(~v1_relat_1(X30)\|(~v1_funct_1(X30)\|~v2_valued_0(X30))))&((r2_hidden(esk6_3(X30,X31,X35),k9_xtuple_0(X30))\|r2_hidden(esk6_3(X30,X31,X35),X35)\|X35=k12_mesfunc1(X30,X31)\|~v1_xxreal_0(X31)\|(~v1_relat_1(X30)\|(~v1_funct_1(X30)\|~v2_valued_0(X30))))&(r1_xxreal_0(k12_supinf_2(X30,esk6_3(X30,X31,X35)),X31)\|r2_hidden(esk6_3(X30,X31,X35),X35)\|X35=k12_mesfunc1(X30,X31)\|~v1_xxreal_0(X31)\|(~v1_relat_1(X30)\|(~v1_funct_1(X30)\|~v2_valued_0(X30))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d12_mesfunc1])])])])])])). cnf(c_0_50, negated_conjecture, (esk5_0=k1_seq_1(esk2_0,esk4_0)\|r2_hidden(esk4_0,k12_mesfunc1(esk2_0,esk3_0))), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_51, negated_conjecture, (k1_seq_1(esk2_0,X1)=k12_supinf_2(esk2_0,X1)\|~v2_valued_0(esk2_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41, c_0_42]), c_0_36]), c_0_43])])])). cnf(c_0_52, negated_conjecture, (v2_valued_0(esk2_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44, c_0_45]), c_0_46])])])). cnf(c_0_53, plain, (k1_relset_1(X2,X1)=k9_xtuple_0(X1)\|~v1_relat_1(X1)\|~v4_relat_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_47])). cnf(c_0_54, plain, (v4_relat_1(X1,X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(evalgc,[status(thm)],[c_0_48])). cnf(c_0_55, plain, (r2_hidden(X1,X4)\|~r2_hidden(X1,k9_xtuple_0(X2))\|~r1_xxreal_0(k12_supinf_2(X2,X1),X3)\|X4!=k12_mesfunc1(X2,X3)\|~v1_xxreal_0(X3)\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v2_valued_0(X2)), inference(split_conjunct,[status(thm)],[c_0_49])). cnf(c_0_56, negated_conjecture, (k1_seq_1(esk2_0,esk4_0)=esk5_0\|r2_hidden(esk4_0,k12_mesfunc1(esk2_0,esk3_0))), inference(evalgc,[status(thm)],[c_0_50])). cnf(c_0_57, negated_conjecture, (k1_seq_1(esk2_0,X1)=k12_supinf_2(esk2_0,X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51, c_0_52])])). cnf(c_0_58, negated_conjecture, (r2_hidden(esk4_0,k1_relset_1(esk1_0,esk2_0))\|r2_hidden(esk4_0,k12_mesfunc1(esk2_0,esk3_0))), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_59, plain, (k1_relset_1(X2,X1)=k9_xtuple_0(X1)\|~v1_relat_1(X1)\|~v4_relat_1(X1,X2)), inference(evalgc,[status(thm)],[c_0_53])). cnf(c_0_60, negated_conjecture, (v4_relat_1(esk2_0,esk1_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_54, c_0_28])])). cnf(c_0_61, plain, (r2_hidden(X1,X4)\|X4!=k12_mesfunc1(X2,X3)\|~v1_funct_1(X2)\|~v1_xxreal_0(X3)\|~v1_relat_1(X2)\|~v2_valued_0(X2)\|~r2_hidden(X1,k9_xtuple_0(X2))\|~r1_xxreal_0(k12_supinf_2(X2,X1),X3)), inference(evalgc,[status(thm)],[c_0_55])). cnf(c_0_62, negated_conjecture, (k12_supinf_2(esk2_0,esk4_0)=esk5_0\|r2_hidden(esk4_0,k12_mesfunc1(esk2_0,esk3_0))), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[c_0_56, c_0_57])])). cnf(c_0_63, negated_conjecture, (r2_hidden(esk4_0,k12_mesfunc1(esk2_0,esk3_0))\|r2_hidden(esk4_0,k1_relset_1(esk1_0,esk2_0))), inference(evalgc,[status(thm)],[c_0_58])). cnf(c_0_64, negated_conjecture, (k1_relset_1(esk1_0,esk2_0)=k9_xtuple_0(esk2_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59, c_0_60]), c_0_36])])])). fof(c_0_65, plain, ![X12]:(~v1_xreal_0(X12)\|v1_xxreal_0(X12)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc4_xreal_0])])). cnf(c_0_66, negated_conjecture, (~r2_hidden(esk4_0,k12_mesfunc1(esk2_0,esk3_0))\|~r2_hidden(esk4_0,k1_relset_1(esk1_0,esk2_0))\|~m1_subset_1(X1,k1_numbers)\|X1!=k1_seq_1(esk2_0,esk4_0)\|~r1_xxreal_0(X1,esk3_0)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_67, negated_conjecture, (r2_hidden(esk4_0,X1)\|r2_hidden(esk4_0,k12_mesfunc1(esk2_0,esk3_0))\|X1!=k12_mesfunc1(esk2_0,X2)\|~v1_xxreal_0(X2)\|~r1_xxreal_0(esk5_0,X2)\|~r2_hidden(esk4_0,k9_xtuple_0(esk2_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61, c_0_62]), c_0_52]), c_0_36]), c_0_43])])])). cnf(c_0_68, negated_conjecture, (r2_hidden(esk4_0,k9_xtuple_0(esk2_0))\|r2_hidden(esk4_0,k12_mesfunc1(esk2_0,esk3_0))), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[c_0_63, c_0_64])])). cnf(c_0_69, plain, (v1_xxreal_0(X1)\|~v1_xreal_0(X1)), inference(split_conjunct,[status(thm)],[c_0_65])). cnf(c_0_70, negated_conjecture, (v1_xreal_0(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_71, negated_conjecture, (X1!=k1_seq_1(esk2_0,esk4_0)\|~m1_subset_1(X1,k1_numbers)\|~r1_xxreal_0(X1,esk3_0)\|~r2_hidden(esk4_0,k12_mesfunc1(esk2_0,esk3_0))\|~r2_hidden(esk4_0,k1_relset_1(esk1_0,esk2_0))), inference(evalgc,[status(thm)],[c_0_66])). cnf(c_0_72, negated_conjecture, (r2_hidden(esk4_0,k12_mesfunc1(esk2_0,esk3_0))\|r2_hidden(esk4_0,X1)\|X1!=k12_mesfunc1(esk2_0,X2)\|~v1_xxreal_0(X2)\|~r1_xxreal_0(esk5_0,X2)), inference(csr,[status(thm)],[c_0_67, c_0_68])). cnf(c_0_73, negated_conjecture, (r1_xxreal_0(esk5_0,esk3_0)\|r2_hidden(esk4_0,k12_mesfunc1(esk2_0,esk3_0))), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_74, plain, (v1_xxreal_0(X1)\|~v1_xreal_0(X1)), inference(evalgc,[status(thm)],[c_0_69])). cnf(c_0_75, negated_conjecture, (v1_xreal_0(esk3_0)), inference(evalgc,[status(thm)],[c_0_70])). cnf(c_0_76, plain, (r2_hidden(X1,k9_xtuple_0(X2))\|~r2_hidden(X1,X3)\|X3!=k12_mesfunc1(X2,X4)\|~v1_xxreal_0(X4)\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v2_valued_0(X2)), inference(split_conjunct,[status(thm)],[c_0_49])). cnf(c_0_77, negated_conjecture, (X1!=k1_seq_1(esk2_0,esk4_0)\|~r1_xxreal_0(X1,esk3_0)\|~r2_hidden(esk4_0,k12_mesfunc1(esk2_0,esk3_0))\|~r2_hidden(esk4_0,k9_xtuple_0(esk2_0))\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[c_0_71, c_0_64])])). cnf(c_0_78, negated_conjecture, (r2_hidden(esk4_0,k12_mesfunc1(esk2_0,esk3_0))\|r2_hidden(esk4_0,k12_mesfunc1(esk2_0,X1))\|~v1_xxreal_0(X1)\|~r1_xxreal_0(esk5_0,X1)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_72])])). cnf(c_0_79, negated_conjecture, (r1_xxreal_0(esk5_0,esk3_0)\|r2_hidden(esk4_0,k12_mesfunc1(esk2_0,esk3_0))), inference(evalgc,[status(thm)],[c_0_73])). cnf(c_0_80, negated_conjecture, (v1_xxreal_0(esk3_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_74, c_0_75])])). cnf(c_0_81, plain, (r2_hidden(X1,k9_xtuple_0(X2))\|X3!=k12_mesfunc1(X2,X4)\|~v1_funct_1(X2)\|~v1_xxreal_0(X4)\|~v1_relat_1(X2)\|~v2_valued_0(X2)\|~r2_hidden(X1,X3)), inference(evalgc,[status(thm)],[c_0_76])). fof(c_0_82, plain, ![X37, X38]:(~v1_relat_1(X37)\|(~v1_funct_1(X37)\|~v3_valued_0(X37))\|m1_subset_1(k1_seq_1(X37,X38),k1_numbers)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_seq_1])])). cnf(c_0_83, negated_conjecture, (X1!=k12_supinf_2(esk2_0,esk4_0)\|~r1_xxreal_0(X1,esk3_0)\|~r2_hidden(esk4_0,k12_mesfunc1(esk2_0,esk3_0))\|~r2_hidden(esk4_0,k9_xtuple_0(esk2_0))\|~m1_subset_1(X1,k1_numbers)), inference(rw,[status(thm)],[c_0_77, c_0_57])). cnf(c_0_84, negated_conjecture, (r2_hidden(esk4_0,k12_mesfunc1(esk2_0,esk3_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78, c_0_79]), c_0_80])])])). cnf(c_0_85, plain, (r2_hidden(X1,k9_xtuple_0(X2))\|~v2_valued_0(X2)\|~v1_relat_1(X2)\|~v1_xxreal_0(X3)\|~r2_hidden(X1,k12_mesfunc1(X2,X3))\|~v1_funct_1(X2)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_81])])). cnf(c_0_86, plain, (m1_subset_1(k1_seq_1(X1,X2),k1_numbers)\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v3_valued_0(X1)), inference(split_conjunct,[status(thm)],[c_0_82])). cnf(c_0_87, negated_conjecture, (X1!=k12_supinf_2(esk2_0,esk4_0)\|~r1_xxreal_0(X1,esk3_0)\|~r2_hidden(esk4_0,k9_xtuple_0(esk2_0))\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_83, c_0_84])])])). cnf(c_0_88, negated_conjecture, (r2_hidden(esk4_0,k9_xtuple_0(esk2_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85, c_0_84]), c_0_52]), c_0_36]), c_0_80]), c_0_43])])])). cnf(c_0_89, plain, (m1_subset_1(k1_seq_1(X1,X2),k1_numbers)\|~v1_funct_1(X1)\|~v1_relat_1(X1)\|~v3_valued_0(X1)), inference(evalgc,[status(thm)],[c_0_86])). cnf(c_0_90, plain, (r1_xxreal_0(k12_supinf_2(X1,X2),X3)\|~r2_hidden(X2,X4)\|X4!=k12_mesfunc1(X1,X3)\|~v1_xxreal_0(X3)\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v2_valued_0(X1)), inference(split_conjunct,[status(thm)],[c_0_49])). cnf(c_0_91, negated_conjecture, (X1!=k12_supinf_2(esk2_0,esk4_0)\|~r1_xxreal_0(X1,esk3_0)\|~m1_subset_1(X1,k1_numbers)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_87, c_0_88])])). cnf(c_0_92, negated_conjecture, (m1_subset_1(k12_supinf_2(esk2_0,X1),k1_numbers)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89, c_0_57]), c_0_42]), c_0_36]), c_0_43])])])). cnf(c_0_93, plain, (r1_xxreal_0(k12_supinf_2(X1,X2),X3)\|X4!=k12_mesfunc1(X1,X3)\|~v1_funct_1(X1)\|~v1_xxreal_0(X3)\|~v1_relat_1(X1)\|~v2_valued_0(X1)\|~r2_hidden(X2,X4)), inference(evalgc,[status(thm)],[c_0_90])). cnf(c_0_94, negated_conjecture, (~r1_xxreal_0(k12_supinf_2(esk2_0,esk4_0),esk3_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_91]), c_0_92])])])). cnf(c_0_95, plain, (r1_xxreal_0(k12_supinf_2(X1,X2),X3)\|~v2_valued_0(X1)\|~v1_relat_1(X1)\|~v1_xxreal_0(X3)\|~r2_hidden(X2,k12_mesfunc1(X1,X3))\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_93])])). cnf(c_0_96, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94, c_0_95]), c_0_52]), c_0_36]), c_0_80]), c_0_84]), c_0_43])]), ['proof']). # SZS output end CNFRefutation	reserve X for non empty set, Y for set, S for SigmaField of X, F for Function of NAT,S, f,g for PartFunc of X,REAL, A,B for Element of S, r,s for Real, a for real number, n for Nat; theorem for x be set holds x in less_eq_dom(f,a) iff x in dom f & ex y being Real st y=f.x & y <= a proof let x be set; (ex y being Real st y=f.x & y <= a) iff f.x <= R_EAL a; hence thesis by MESFUNC1:def 12; end;	Convert the following ATP output trace into a readable Mizar proof.
t5_osalg_1	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(d10_relat_1, axiom, ![X1, X2]:(v1_relat_1(X2)=>(X2=k4_relat_1(X1)<=>![X3, X4]:(r2_hidden(k4_tarski(X3,X4),X2)<=>(r2_hidden(X3,X1)&X3=X4)))), file('/scratch/mptp/predsminms1/t5_osalg_1__0', d10_relat_1)). fof(redefinition_k6_partfun1, axiom, ![X1]:k6_partfun1(X1)=k4_relat_1(X1), file('/scratch/mptp/predsminms1/t5_osalg_1__0', redefinition_k6_partfun1)). fof(d5_tarski, axiom, ![X1, X2]:k4_tarski(X1,X2)=k2_tarski(k2_tarski(X1,X2),k1_tarski(X1)), file('/scratch/mptp/predsminms1/t5_osalg_1__0', d5_tarski)). fof(d2_osalg_1, axiom, ![X1]:((~(v2_struct_0(X1))&(~(v11_struct_0(X1))&l1_osalg_1(X1)))=>![X2]:(m1_subset_1(X2,u4_struct_0(X1))=>![X3]:(m1_subset_1(X3,u4_struct_0(X1))=>(r1_osalg_1(X1,X2,X3)<=>r2_hidden(k4_tarski(X2,X3),u1_osalg_1(X1)))))), file('/scratch/mptp/predsminms1/t5_osalg_1__0', d2_osalg_1)). fof(d5_osalg_1, axiom, ![X1]:((~(v2_struct_0(X1))&(~(v11_struct_0(X1))&l1_msualg_1(X1)))=>![X2]:((~(v2_struct_0(X2))&(~(v11_struct_0(X2))&(v3_osalg_1(X2)&(v4_osalg_1(X2)&l3_osalg_1(X2)))))=>(X2=k1_osalg_1(X1)<=>(u1_struct_0(X1)=u1_struct_0(X2)&(k6_partfun1(u1_struct_0(X1))=u1_orders_2(X2)&(u4_struct_0(X1)=u4_struct_0(X2)&(k6_partfun1(u4_struct_0(X1))=u1_osalg_1(X2)&(r1_funct_2(u4_struct_0(X1),k3_finseq_2(u1_struct_0(X1)),u4_struct_0(X2),k3_finseq_2(u1_struct_0(X2)),u1_msualg_1(X1),u1_msualg_1(X2))&r1_funct_2(u4_struct_0(X1),u1_struct_0(X1),u4_struct_0(X2),u1_struct_0(X2),u2_msualg_1(X1),u2_msualg_1(X2)))))))))), file('/scratch/mptp/predsminms1/t5_osalg_1__0', d5_osalg_1)). fof(cc1_relset_1, axiom, ![X1, X2, X3]:(m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))=>v1_relat_1(X3)), file('/scratch/mptp/predsminms1/t5_osalg_1__0', cc1_relset_1)). fof(dt_u1_osalg_1, axiom, ![X1]:(l1_osalg_1(X1)=>(v3_relat_2(u1_osalg_1(X1))&(v8_relat_2(u1_osalg_1(X1))&(v1_partfun1(u1_osalg_1(X1),u4_struct_0(X1))&m1_subset_1(u1_osalg_1(X1),k1_zfmisc_1(k2_zfmisc_1(u4_struct_0(X1),u4_struct_0(X1)))))))), file('/scratch/mptp/predsminms1/t5_osalg_1__0', dt_u1_osalg_1)). fof(dt_k1_osalg_1, axiom, ![X1]:((~(v2_struct_0(X1))&(~(v11_struct_0(X1))&l1_msualg_1(X1)))=>(~(v2_struct_0(k1_osalg_1(X1)))&(~(v11_struct_0(k1_osalg_1(X1)))&(v3_osalg_1(k1_osalg_1(X1))&(v4_osalg_1(k1_osalg_1(X1))&l3_osalg_1(k1_osalg_1(X1))))))), file('/scratch/mptp/predsminms1/t5_osalg_1__0', dt_k1_osalg_1)). fof(redefinition_r2_relset_1, axiom, ![X1, X2, X3, X4]:((m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))&m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2))))=>(r2_relset_1(X1,X2,X3,X4)<=>X3=X4)), file('/scratch/mptp/predsminms1/t5_osalg_1__0', redefinition_r2_relset_1)). fof(d1_orders_3, axiom, ![X1]:(l1_orders_2(X1)=>(v1_orders_3(X1)<=>r2_relset_1(u1_struct_0(X1),u1_struct_0(X1),u1_orders_2(X1),k6_partfun1(u1_struct_0(X1))))), file('/scratch/mptp/predsminms1/t5_osalg_1__0', d1_orders_3)). fof(dt_k6_partfun1, axiom, ![X1]:(v1_partfun1(k6_partfun1(X1),X1)&m1_subset_1(k6_partfun1(X1),k1_zfmisc_1(k2_zfmisc_1(X1,X1)))), file('/scratch/mptp/predsminms1/t5_osalg_1__0', dt_k6_partfun1)). fof(t3_osalg_1, axiom, ![X1]:((~(v2_struct_0(X1))&(~(v11_struct_0(X1))&l1_osalg_1(X1)))=>(v6_osalg_1(X1)<=>![X2]:(m1_subset_1(X2,u4_struct_0(X1))=>![X3]:(m1_subset_1(X3,u4_struct_0(X1))=>(r1_osalg_1(X1,X2,X3)=>X2=X3))))), file('/scratch/mptp/predsminms1/t5_osalg_1__0', t3_osalg_1)). fof(t5_osalg_1, conjecture, ![X1]:((~(v2_struct_0(X1))&(~(v11_struct_0(X1))&l1_msualg_1(X1)))=>(v1_orders_3(k1_osalg_1(X1))&v6_osalg_1(k1_osalg_1(X1)))), file('/scratch/mptp/predsminms1/t5_osalg_1__0', t5_osalg_1)). fof(dt_l3_osalg_1, axiom, ![X1]:(l3_osalg_1(X1)=>(l1_osalg_1(X1)&l2_osalg_1(X1))), file('/scratch/mptp/predsminms1/t5_osalg_1__0', dt_l3_osalg_1)). fof(dt_l2_osalg_1, axiom, ![X1]:(l2_osalg_1(X1)=>(l1_msualg_1(X1)&l1_orders_2(X1))), file('/scratch/mptp/predsminms1/t5_osalg_1__0', dt_l2_osalg_1)). fof(c_0_15, plain, ![X23, X24, X25, X26, X27, X28]:((((r2_hidden(X25,X23)\|~r2_hidden(k4_tarski(X25,X26),X24)\|X24!=k4_relat_1(X23)\|~v1_relat_1(X24))&(X25=X26\|~r2_hidden(k4_tarski(X25,X26),X24)\|X24!=k4_relat_1(X23)\|~v1_relat_1(X24)))&(~r2_hidden(X27,X23)\|X27!=X28\|r2_hidden(k4_tarski(X27,X28),X24)\|X24!=k4_relat_1(X23)\|~v1_relat_1(X24)))&((~r2_hidden(k4_tarski(esk4_2(X23,X24),esk5_2(X23,X24)),X24)\|(~r2_hidden(esk4_2(X23,X24),X23)\|esk4_2(X23,X24)!=esk5_2(X23,X24))\|X24=k4_relat_1(X23)\|~v1_relat_1(X24))&((r2_hidden(esk4_2(X23,X24),X23)\|r2_hidden(k4_tarski(esk4_2(X23,X24),esk5_2(X23,X24)),X24)\|X24=k4_relat_1(X23)\|~v1_relat_1(X24))&(esk4_2(X23,X24)=esk5_2(X23,X24)\|r2_hidden(k4_tarski(esk4_2(X23,X24),esk5_2(X23,X24)),X24)\|X24=k4_relat_1(X23)\|~v1_relat_1(X24))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_relat_1])])])])])])). fof(c_0_16, plain, ![X22]:k6_partfun1(X22)=k4_relat_1(X22), inference(variable_rename,[status(thm)],[redefinition_k6_partfun1])). fof(c_0_17, plain, ![X14, X15]:k4_tarski(X14,X15)=k2_tarski(k2_tarski(X14,X15),k1_tarski(X14)), inference(variable_rename,[status(thm)],[d5_tarski])). fof(c_0_18, plain, ![X16, X17, X18]:((~r1_osalg_1(X16,X17,X18)\|r2_hidden(k4_tarski(X17,X18),u1_osalg_1(X16))\|~m1_subset_1(X18,u4_struct_0(X16))\|~m1_subset_1(X17,u4_struct_0(X16))\|(v2_struct_0(X16)\|(v11_struct_0(X16)\|~l1_osalg_1(X16))))&(~r2_hidden(k4_tarski(X17,X18),u1_osalg_1(X16))\|r1_osalg_1(X16,X17,X18)\|~m1_subset_1(X18,u4_struct_0(X16))\|~m1_subset_1(X17,u4_struct_0(X16))\|(v2_struct_0(X16)\|(v11_struct_0(X16)\|~l1_osalg_1(X16))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d2_osalg_1])])])])])). fof(c_0_19, plain, ![X12, X13]:(((u1_struct_0(X12)=u1_struct_0(X13)\|X13!=k1_osalg_1(X12)\|(v2_struct_0(X13)\|(v11_struct_0(X13)\|(~v3_osalg_1(X13)\|(~v4_osalg_1(X13)\|~l3_osalg_1(X13)))))\|(v2_struct_0(X12)\|(v11_struct_0(X12)\|~l1_msualg_1(X12))))&((k6_partfun1(u1_struct_0(X12))=u1_orders_2(X13)\|X13!=k1_osalg_1(X12)\|(v2_struct_0(X13)\|(v11_struct_0(X13)\|(~v3_osalg_1(X13)\|(~v4_osalg_1(X13)\|~l3_osalg_1(X13)))))\|(v2_struct_0(X12)\|(v11_struct_0(X12)\|~l1_msualg_1(X12))))&((u4_struct_0(X12)=u4_struct_0(X13)\|X13!=k1_osalg_1(X12)\|(v2_struct_0(X13)\|(v11_struct_0(X13)\|(~v3_osalg_1(X13)\|(~v4_osalg_1(X13)\|~l3_osalg_1(X13)))))\|(v2_struct_0(X12)\|(v11_struct_0(X12)\|~l1_msualg_1(X12))))&((k6_partfun1(u4_struct_0(X12))=u1_osalg_1(X13)\|X13!=k1_osalg_1(X12)\|(v2_struct_0(X13)\|(v11_struct_0(X13)\|(~v3_osalg_1(X13)\|(~v4_osalg_1(X13)\|~l3_osalg_1(X13)))))\|(v2_struct_0(X12)\|(v11_struct_0(X12)\|~l1_msualg_1(X12))))&((r1_funct_2(u4_struct_0(X12),k3_finseq_2(u1_struct_0(X12)),u4_struct_0(X13),k3_finseq_2(u1_struct_0(X13)),u1_msualg_1(X12),u1_msualg_1(X13))\|X13!=k1_osalg_1(X12)\|(v2_struct_0(X13)\|(v11_struct_0(X13)\|(~v3_osalg_1(X13)\|(~v4_osalg_1(X13)\|~l3_osalg_1(X13)))))\|(v2_struct_0(X12)\|(v11_struct_0(X12)\|~l1_msualg_1(X12))))&(r1_funct_2(u4_struct_0(X12),u1_struct_0(X12),u4_struct_0(X13),u1_struct_0(X13),u2_msualg_1(X12),u2_msualg_1(X13))\|X13!=k1_osalg_1(X12)\|(v2_struct_0(X13)\|(v11_struct_0(X13)\|(~v3_osalg_1(X13)\|(~v4_osalg_1(X13)\|~l3_osalg_1(X13)))))\|(v2_struct_0(X12)\|(v11_struct_0(X12)\|~l1_msualg_1(X12)))))))))&(u1_struct_0(X12)!=u1_struct_0(X13)\|(k6_partfun1(u1_struct_0(X12))!=u1_orders_2(X13)\|(u4_struct_0(X12)!=u4_struct_0(X13)\|(k6_partfun1(u4_struct_0(X12))!=u1_osalg_1(X13)\|(~r1_funct_2(u4_struct_0(X12),k3_finseq_2(u1_struct_0(X12)),u4_struct_0(X13),k3_finseq_2(u1_struct_0(X13)),u1_msualg_1(X12),u1_msualg_1(X13))\|~r1_funct_2(u4_struct_0(X12),u1_struct_0(X12),u4_struct_0(X13),u1_struct_0(X13),u2_msualg_1(X12),u2_msualg_1(X13))))))\|X13=k1_osalg_1(X12)\|(v2_struct_0(X13)\|(v11_struct_0(X13)\|(~v3_osalg_1(X13)\|(~v4_osalg_1(X13)\|~l3_osalg_1(X13)))))\|(v2_struct_0(X12)\|(v11_struct_0(X12)\|~l1_msualg_1(X12))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d5_osalg_1])])])])])). cnf(c_0_20, plain, (X1=X2\|~r2_hidden(k4_tarski(X1,X2),X3)\|X3!=k4_relat_1(X4)\|~v1_relat_1(X3)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_21, plain, (k6_partfun1(X1)=k4_relat_1(X1)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_22, plain, (k4_tarski(X1,X2)=k2_tarski(k2_tarski(X1,X2),k1_tarski(X1))), inference(split_conjunct,[status(thm)],[c_0_17])). cnf(c_0_23, plain, (r2_hidden(k4_tarski(X2,X3),u1_osalg_1(X1))\|v2_struct_0(X1)\|v11_struct_0(X1)\|~r1_osalg_1(X1,X2,X3)\|~m1_subset_1(X3,u4_struct_0(X1))\|~m1_subset_1(X2,u4_struct_0(X1))\|~l1_osalg_1(X1)), inference(split_conjunct,[status(thm)],[c_0_18])). fof(c_0_24, plain, ![X19, X20, X21]:(~m1_subset_1(X21,k1_zfmisc_1(k2_zfmisc_1(X19,X20)))\|v1_relat_1(X21)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relset_1])])). fof(c_0_25, plain, ![X39]:((v3_relat_2(u1_osalg_1(X39))\|~l1_osalg_1(X39))&((v8_relat_2(u1_osalg_1(X39))\|~l1_osalg_1(X39))&((v1_partfun1(u1_osalg_1(X39),u4_struct_0(X39))\|~l1_osalg_1(X39))&(m1_subset_1(u1_osalg_1(X39),k1_zfmisc_1(k2_zfmisc_1(u4_struct_0(X39),u4_struct_0(X39))))\|~l1_osalg_1(X39))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u1_osalg_1])])])). cnf(c_0_26, plain, (u1_struct_0(X1)=u1_struct_0(X2)\|v2_struct_0(X2)\|v11_struct_0(X2)\|v2_struct_0(X1)\|v11_struct_0(X1)\|X2!=k1_osalg_1(X1)\|~v3_osalg_1(X2)\|~v4_osalg_1(X2)\|~l3_osalg_1(X2)\|~l1_msualg_1(X1)), inference(split_conjunct,[status(thm)],[c_0_19])). fof(c_0_27, plain, ![X11]:((~v2_struct_0(k1_osalg_1(X11))\|(v2_struct_0(X11)\|(v11_struct_0(X11)\|~l1_msualg_1(X11))))&((~v11_struct_0(k1_osalg_1(X11))\|(v2_struct_0(X11)\|(v11_struct_0(X11)\|~l1_msualg_1(X11))))&((v3_osalg_1(k1_osalg_1(X11))\|(v2_struct_0(X11)\|(v11_struct_0(X11)\|~l1_msualg_1(X11))))&((v4_osalg_1(k1_osalg_1(X11))\|(v2_struct_0(X11)\|(v11_struct_0(X11)\|~l1_msualg_1(X11))))&(l3_osalg_1(k1_osalg_1(X11))\|(v2_struct_0(X11)\|(v11_struct_0(X11)\|~l1_msualg_1(X11)))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k1_osalg_1])])])])). fof(c_0_28, plain, ![X34, X35, X36, X37]:((~r2_relset_1(X34,X35,X36,X37)\|X36=X37\|(~m1_subset_1(X36,k1_zfmisc_1(k2_zfmisc_1(X34,X35)))\|~m1_subset_1(X37,k1_zfmisc_1(k2_zfmisc_1(X34,X35)))))&(X36!=X37\|r2_relset_1(X34,X35,X36,X37)\|(~m1_subset_1(X36,k1_zfmisc_1(k2_zfmisc_1(X34,X35)))\|~m1_subset_1(X37,k1_zfmisc_1(k2_zfmisc_1(X34,X35)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_r2_relset_1])])])). cnf(c_0_29, plain, (X1=X2\|X3!=k6_partfun1(X4)\|~v1_relat_1(X3)\|~r2_hidden(k2_tarski(k2_tarski(X1,X2),k1_tarski(X1)),X3)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20, c_0_21]), c_0_22])). cnf(c_0_30, plain, (v2_struct_0(X1)\|v11_struct_0(X1)\|r2_hidden(k2_tarski(k2_tarski(X2,X3),k1_tarski(X2)),u1_osalg_1(X1))\|~l1_osalg_1(X1)\|~r1_osalg_1(X1,X2,X3)\|~m1_subset_1(X3,u4_struct_0(X1))\|~m1_subset_1(X2,u4_struct_0(X1))), inference(rw,[status(thm)],[c_0_23, c_0_22])). cnf(c_0_31, plain, (v1_relat_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_24])). cnf(c_0_32, plain, (m1_subset_1(u1_osalg_1(X1),k1_zfmisc_1(k2_zfmisc_1(u4_struct_0(X1),u4_struct_0(X1))))\|~l1_osalg_1(X1)), inference(split_conjunct,[status(thm)],[c_0_25])). fof(c_0_33, plain, ![X38]:((~v1_orders_3(X38)\|r2_relset_1(u1_struct_0(X38),u1_struct_0(X38),u1_orders_2(X38),k6_partfun1(u1_struct_0(X38)))\|~l1_orders_2(X38))&(~r2_relset_1(u1_struct_0(X38),u1_struct_0(X38),u1_orders_2(X38),k6_partfun1(u1_struct_0(X38)))\|v1_orders_3(X38)\|~l1_orders_2(X38))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_orders_3])])])). cnf(c_0_34, plain, (u1_struct_0(X1)=u1_struct_0(X2)\|v2_struct_0(X2)\|v2_struct_0(X1)\|v11_struct_0(X2)\|v11_struct_0(X1)\|X2!=k1_osalg_1(X1)\|~l1_msualg_1(X1)\|~v3_osalg_1(X2)\|~v4_osalg_1(X2)\|~l3_osalg_1(X2)), inference(evalgc,[status(thm)],[c_0_26])). cnf(c_0_35, plain, (v3_osalg_1(k1_osalg_1(X1))\|v2_struct_0(X1)\|v11_struct_0(X1)\|~l1_msualg_1(X1)), inference(split_conjunct,[status(thm)],[c_0_27])). cnf(c_0_36, plain, (v4_osalg_1(k1_osalg_1(X1))\|v2_struct_0(X1)\|v11_struct_0(X1)\|~l1_msualg_1(X1)), inference(split_conjunct,[status(thm)],[c_0_27])). cnf(c_0_37, plain, (l3_osalg_1(k1_osalg_1(X1))\|v2_struct_0(X1)\|v11_struct_0(X1)\|~l1_msualg_1(X1)), inference(split_conjunct,[status(thm)],[c_0_27])). cnf(c_0_38, plain, (v2_struct_0(X1)\|v11_struct_0(X1)\|~v2_struct_0(k1_osalg_1(X1))\|~l1_msualg_1(X1)), inference(split_conjunct,[status(thm)],[c_0_27])). cnf(c_0_39, plain, (v2_struct_0(X1)\|v11_struct_0(X1)\|~v11_struct_0(k1_osalg_1(X1))\|~l1_msualg_1(X1)), inference(split_conjunct,[status(thm)],[c_0_27])). cnf(c_0_40, plain, (k6_partfun1(u1_struct_0(X1))=u1_orders_2(X2)\|v2_struct_0(X2)\|v11_struct_0(X2)\|v2_struct_0(X1)\|v11_struct_0(X1)\|X2!=k1_osalg_1(X1)\|~v3_osalg_1(X2)\|~v4_osalg_1(X2)\|~l3_osalg_1(X2)\|~l1_msualg_1(X1)), inference(split_conjunct,[status(thm)],[c_0_19])). cnf(c_0_41, plain, (r2_relset_1(X3,X4,X1,X2)\|X1!=X2\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X3,X4)))\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X3,X4)))), inference(split_conjunct,[status(thm)],[c_0_28])). fof(c_0_42, plain, ![X33]:(v1_partfun1(k6_partfun1(X33),X33)&m1_subset_1(k6_partfun1(X33),k1_zfmisc_1(k2_zfmisc_1(X33,X33)))), inference(variable_rename,[status(thm)],[dt_k6_partfun1])). cnf(c_0_43, plain, (X1=X2\|X3!=k6_partfun1(X4)\|~v1_relat_1(X3)\|~r2_hidden(k2_tarski(k2_tarski(X1,X2),k1_tarski(X1)),X3)), inference(evalgc,[status(thm)],[c_0_29])). cnf(c_0_44, plain, (v2_struct_0(X1)\|v11_struct_0(X1)\|r2_hidden(k2_tarski(k2_tarski(X2,X3),k1_tarski(X2)),u1_osalg_1(X1))\|~l1_osalg_1(X1)\|~r1_osalg_1(X1,X2,X3)\|~m1_subset_1(X3,u4_struct_0(X1))\|~m1_subset_1(X2,u4_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_30])). cnf(c_0_45, plain, (v1_relat_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(evalgc,[status(thm)],[c_0_31])). cnf(c_0_46, plain, (m1_subset_1(u1_osalg_1(X1),k1_zfmisc_1(k2_zfmisc_1(u4_struct_0(X1),u4_struct_0(X1))))\|~l1_osalg_1(X1)), inference(evalgc,[status(thm)],[c_0_32])). fof(c_0_47, plain, ![X6, X7, X8]:((~v6_osalg_1(X6)\|(~m1_subset_1(X7,u4_struct_0(X6))\|(~m1_subset_1(X8,u4_struct_0(X6))\|(~r1_osalg_1(X6,X7,X8)\|X7=X8)))\|(v2_struct_0(X6)\|(v11_struct_0(X6)\|~l1_osalg_1(X6))))&((m1_subset_1(esk2_1(X6),u4_struct_0(X6))\|v6_osalg_1(X6)\|(v2_struct_0(X6)\|(v11_struct_0(X6)\|~l1_osalg_1(X6))))&((m1_subset_1(esk3_1(X6),u4_struct_0(X6))\|v6_osalg_1(X6)\|(v2_struct_0(X6)\|(v11_struct_0(X6)\|~l1_osalg_1(X6))))&((r1_osalg_1(X6,esk2_1(X6),esk3_1(X6))\|v6_osalg_1(X6)\|(v2_struct_0(X6)\|(v11_struct_0(X6)\|~l1_osalg_1(X6))))&(esk2_1(X6)!=esk3_1(X6)\|v6_osalg_1(X6)\|(v2_struct_0(X6)\|(v11_struct_0(X6)\|~l1_osalg_1(X6)))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t3_osalg_1])])])])])])). fof(c_0_48, negated_conjecture, ~(![X1]:((~(v2_struct_0(X1))&(~(v11_struct_0(X1))&l1_msualg_1(X1)))=>(v1_orders_3(k1_osalg_1(X1))&v6_osalg_1(k1_osalg_1(X1))))), inference(assume_negation,[status(cth)],[t5_osalg_1])). cnf(c_0_49, plain, (v1_orders_3(X1)\|~r2_relset_1(u1_struct_0(X1),u1_struct_0(X1),u1_orders_2(X1),k6_partfun1(u1_struct_0(X1)))\|~l1_orders_2(X1)), inference(split_conjunct,[status(thm)],[c_0_33])). cnf(c_0_50, plain, (u1_struct_0(k1_osalg_1(X1))=u1_struct_0(X1)\|v11_struct_0(X1)\|v11_struct_0(k1_osalg_1(X1))\|v2_struct_0(X1)\|v2_struct_0(k1_osalg_1(X1))\|~l3_osalg_1(k1_osalg_1(X1))\|~v4_osalg_1(k1_osalg_1(X1))\|~v3_osalg_1(k1_osalg_1(X1))\|~l1_msualg_1(X1)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_34])])). cnf(c_0_51, plain, (v2_struct_0(X1)\|v11_struct_0(X1)\|v3_osalg_1(k1_osalg_1(X1))\|~l1_msualg_1(X1)), inference(evalgc,[status(thm)],[c_0_35])). cnf(c_0_52, plain, (v2_struct_0(X1)\|v11_struct_0(X1)\|v4_osalg_1(k1_osalg_1(X1))\|~l1_msualg_1(X1)), inference(evalgc,[status(thm)],[c_0_36])). cnf(c_0_53, plain, (v2_struct_0(X1)\|v11_struct_0(X1)\|l3_osalg_1(k1_osalg_1(X1))\|~l1_msualg_1(X1)), inference(evalgc,[status(thm)],[c_0_37])). cnf(c_0_54, plain, (v2_struct_0(X1)\|v11_struct_0(X1)\|~l1_msualg_1(X1)\|~v2_struct_0(k1_osalg_1(X1))), inference(evalgc,[status(thm)],[c_0_38])). cnf(c_0_55, plain, (v2_struct_0(X1)\|v11_struct_0(X1)\|~l1_msualg_1(X1)\|~v11_struct_0(k1_osalg_1(X1))), inference(evalgc,[status(thm)],[c_0_39])). cnf(c_0_56, plain, (k6_partfun1(u1_struct_0(X1))=u1_orders_2(X2)\|v2_struct_0(X2)\|v2_struct_0(X1)\|v11_struct_0(X2)\|v11_struct_0(X1)\|X2!=k1_osalg_1(X1)\|~l1_msualg_1(X1)\|~v3_osalg_1(X2)\|~v4_osalg_1(X2)\|~l3_osalg_1(X2)), inference(evalgc,[status(thm)],[c_0_40])). cnf(c_0_57, plain, (r2_relset_1(X3,X4,X1,X2)\|X1!=X2\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X3,X4)))\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X3,X4)))), inference(evalgc,[status(thm)],[c_0_41])). cnf(c_0_58, plain, (m1_subset_1(k6_partfun1(X1),k1_zfmisc_1(k2_zfmisc_1(X1,X1)))), inference(split_conjunct,[status(thm)],[c_0_42])). cnf(c_0_59, plain, (X1=X2\|v11_struct_0(X3)\|v2_struct_0(X3)\|u1_osalg_1(X3)!=k6_partfun1(X4)\|~v1_relat_1(u1_osalg_1(X3))\|~r1_osalg_1(X3,X1,X2)\|~m1_subset_1(X2,u4_struct_0(X3))\|~m1_subset_1(X1,u4_struct_0(X3))\|~l1_osalg_1(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_43, c_0_44])])). cnf(c_0_60, plain, (v1_relat_1(u1_osalg_1(X1))\|~l1_osalg_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_45, c_0_46])])). cnf(c_0_61, plain, (r1_osalg_1(X1,esk2_1(X1),esk3_1(X1))\|v6_osalg_1(X1)\|v2_struct_0(X1)\|v11_struct_0(X1)\|~l1_osalg_1(X1)), inference(split_conjunct,[status(thm)],[c_0_47])). cnf(c_0_62, plain, (k6_partfun1(u4_struct_0(X1))=u1_osalg_1(X2)\|v2_struct_0(X2)\|v11_struct_0(X2)\|v2_struct_0(X1)\|v11_struct_0(X1)\|X2!=k1_osalg_1(X1)\|~v3_osalg_1(X2)\|~v4_osalg_1(X2)\|~l3_osalg_1(X2)\|~l1_msualg_1(X1)), inference(split_conjunct,[status(thm)],[c_0_19])). fof(c_0_63, negated_conjecture, ((~v2_struct_0(esk1_0)&(~v11_struct_0(esk1_0)&l1_msualg_1(esk1_0)))&(~v1_orders_3(k1_osalg_1(esk1_0))\|~v6_osalg_1(k1_osalg_1(esk1_0)))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_48])])])])). cnf(c_0_64, plain, (v1_orders_3(X1)\|~l1_orders_2(X1)\|~r2_relset_1(u1_struct_0(X1),u1_struct_0(X1),u1_orders_2(X1),k6_partfun1(u1_struct_0(X1)))), inference(evalgc,[status(thm)],[c_0_49])). cnf(c_0_65, plain, (u1_struct_0(k1_osalg_1(X1))=u1_struct_0(X1)\|v11_struct_0(X1)\|v2_struct_0(X1)\|~l1_msualg_1(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_50, c_0_51]), c_0_52]), c_0_53]), c_0_54]), c_0_55])). cnf(c_0_66, plain, (u1_orders_2(k1_osalg_1(X1))=k6_partfun1(u1_struct_0(X1))\|v11_struct_0(X1)\|v11_struct_0(k1_osalg_1(X1))\|v2_struct_0(X1)\|v2_struct_0(k1_osalg_1(X1))\|~l3_osalg_1(k1_osalg_1(X1))\|~v4_osalg_1(k1_osalg_1(X1))\|~v3_osalg_1(k1_osalg_1(X1))\|~l1_msualg_1(X1)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_56])])). cnf(c_0_67, plain, (r2_relset_1(X1,X2,X3,X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_57])])). cnf(c_0_68, plain, (m1_subset_1(k6_partfun1(X1),k1_zfmisc_1(k2_zfmisc_1(X1,X1)))), inference(evalgc,[status(thm)],[c_0_58])). cnf(c_0_69, plain, (X1=X2\|v11_struct_0(X3)\|v2_struct_0(X3)\|u1_osalg_1(X3)!=k6_partfun1(X4)\|~r1_osalg_1(X3,X1,X2)\|~m1_subset_1(X2,u4_struct_0(X3))\|~m1_subset_1(X1,u4_struct_0(X3))\|~l1_osalg_1(X3)), inference(csr,[status(thm)],[c_0_59, c_0_60])). cnf(c_0_70, plain, (v2_struct_0(X1)\|v11_struct_0(X1)\|v6_osalg_1(X1)\|r1_osalg_1(X1,esk2_1(X1),esk3_1(X1))\|~l1_osalg_1(X1)), inference(evalgc,[status(thm)],[c_0_61])). cnf(c_0_71, plain, (m1_subset_1(esk2_1(X1),u4_struct_0(X1))\|v6_osalg_1(X1)\|v2_struct_0(X1)\|v11_struct_0(X1)\|~l1_osalg_1(X1)), inference(split_conjunct,[status(thm)],[c_0_47])). cnf(c_0_72, plain, (m1_subset_1(esk3_1(X1),u4_struct_0(X1))\|v6_osalg_1(X1)\|v2_struct_0(X1)\|v11_struct_0(X1)\|~l1_osalg_1(X1)), inference(split_conjunct,[status(thm)],[c_0_47])). cnf(c_0_73, plain, (v6_osalg_1(X1)\|v2_struct_0(X1)\|v11_struct_0(X1)\|esk2_1(X1)!=esk3_1(X1)\|~l1_osalg_1(X1)), inference(split_conjunct,[status(thm)],[c_0_47])). cnf(c_0_74, plain, (k6_partfun1(u4_struct_0(X1))=u1_osalg_1(X2)\|v2_struct_0(X2)\|v2_struct_0(X1)\|v11_struct_0(X2)\|v11_struct_0(X1)\|X2!=k1_osalg_1(X1)\|~l1_msualg_1(X1)\|~v3_osalg_1(X2)\|~v4_osalg_1(X2)\|~l3_osalg_1(X2)), inference(evalgc,[status(thm)],[c_0_62])). fof(c_0_75, plain, ![X32]:((l1_osalg_1(X32)\|~l3_osalg_1(X32))&(l2_osalg_1(X32)\|~l3_osalg_1(X32))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_osalg_1])])])). cnf(c_0_76, negated_conjecture, (~v1_orders_3(k1_osalg_1(esk1_0))\|~v6_osalg_1(k1_osalg_1(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_63])). cnf(c_0_77, plain, (v1_orders_3(k1_osalg_1(X1))\|v11_struct_0(X1)\|v2_struct_0(X1)\|~r2_relset_1(u1_struct_0(X1),u1_struct_0(X1),u1_orders_2(k1_osalg_1(X1)),k6_partfun1(u1_struct_0(X1)))\|~l1_orders_2(k1_osalg_1(X1))\|~l1_msualg_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_64, c_0_65])])). cnf(c_0_78, plain, (u1_orders_2(k1_osalg_1(X1))=k6_partfun1(u1_struct_0(X1))\|v11_struct_0(X1)\|v2_struct_0(X1)\|~l1_msualg_1(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_66, c_0_51]), c_0_52]), c_0_53]), c_0_54]), c_0_55])). cnf(c_0_79, plain, (r2_relset_1(X1,X1,k6_partfun1(X1),k6_partfun1(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_67, c_0_68])])). cnf(c_0_80, negated_conjecture, (l1_msualg_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_63])). cnf(c_0_81, negated_conjecture, (~v11_struct_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_63])). cnf(c_0_82, negated_conjecture, (~v2_struct_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_63])). fof(c_0_83, plain, ![X31]:((l1_msualg_1(X31)\|~l2_osalg_1(X31))&(l1_orders_2(X31)\|~l2_osalg_1(X31))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l2_osalg_1])])])). cnf(c_0_84, plain, (esk3_1(X1)=esk2_1(X1)\|v11_struct_0(X1)\|v2_struct_0(X1)\|v6_osalg_1(X1)\|u1_osalg_1(X1)!=k6_partfun1(X2)\|~m1_subset_1(esk3_1(X1),u4_struct_0(X1))\|~m1_subset_1(esk2_1(X1),u4_struct_0(X1))\|~l1_osalg_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_69, c_0_70])])). cnf(c_0_85, plain, (v2_struct_0(X1)\|v11_struct_0(X1)\|v6_osalg_1(X1)\|m1_subset_1(esk2_1(X1),u4_struct_0(X1))\|~l1_osalg_1(X1)), inference(evalgc,[status(thm)],[c_0_71])). cnf(c_0_86, plain, (v2_struct_0(X1)\|v11_struct_0(X1)\|v6_osalg_1(X1)\|m1_subset_1(esk3_1(X1),u4_struct_0(X1))\|~l1_osalg_1(X1)), inference(evalgc,[status(thm)],[c_0_72])). cnf(c_0_87, plain, (v2_struct_0(X1)\|v11_struct_0(X1)\|v6_osalg_1(X1)\|esk3_1(X1)!=esk2_1(X1)\|~l1_osalg_1(X1)), inference(evalgc,[status(thm)],[c_0_73])). cnf(c_0_88, plain, (u1_osalg_1(k1_osalg_1(X1))=k6_partfun1(u4_struct_0(X1))\|v11_struct_0(X1)\|v11_struct_0(k1_osalg_1(X1))\|v2_struct_0(X1)\|v2_struct_0(k1_osalg_1(X1))\|~l3_osalg_1(k1_osalg_1(X1))\|~v4_osalg_1(k1_osalg_1(X1))\|~v3_osalg_1(k1_osalg_1(X1))\|~l1_msualg_1(X1)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_74])])). cnf(c_0_89, plain, (l1_osalg_1(X1)\|~l3_osalg_1(X1)), inference(split_conjunct,[status(thm)],[c_0_75])). cnf(c_0_90, negated_conjecture, (~v1_orders_3(k1_osalg_1(esk1_0))\|~v6_osalg_1(k1_osalg_1(esk1_0))), inference(evalgc,[status(thm)],[c_0_76])). cnf(c_0_91, plain, (v1_orders_3(k1_osalg_1(X1))\|v11_struct_0(X1)\|v2_struct_0(X1)\|~l1_orders_2(k1_osalg_1(X1))\|~l1_msualg_1(X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77, c_0_78]), c_0_79])])])). cnf(c_0_92, negated_conjecture, (l1_msualg_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_80])). cnf(c_0_93, negated_conjecture, (~v11_struct_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_81])). cnf(c_0_94, negated_conjecture, (~v2_struct_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_82])). cnf(c_0_95, plain, (l1_orders_2(X1)\|~l2_osalg_1(X1)), inference(split_conjunct,[status(thm)],[c_0_83])). cnf(c_0_96, plain, (v6_osalg_1(X1)\|v11_struct_0(X1)\|v2_struct_0(X1)\|u1_osalg_1(X1)!=k6_partfun1(X2)\|~l1_osalg_1(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_84, c_0_85]), c_0_86]), c_0_87])). cnf(c_0_97, plain, (u1_osalg_1(k1_osalg_1(X1))=k6_partfun1(u4_struct_0(X1))\|v11_struct_0(X1)\|v2_struct_0(X1)\|~l1_msualg_1(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_88, c_0_51]), c_0_52]), c_0_53]), c_0_54]), c_0_55])). cnf(c_0_98, plain, (l1_osalg_1(X1)\|~l3_osalg_1(X1)), inference(evalgc,[status(thm)],[c_0_89])). cnf(c_0_99, negated_conjecture, (~v6_osalg_1(k1_osalg_1(esk1_0))\|~l1_orders_2(k1_osalg_1(esk1_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90, c_0_91]), c_0_92])]), c_0_93]), c_0_94])])). cnf(c_0_100, plain, (l1_orders_2(X1)\|~l2_osalg_1(X1)), inference(evalgc,[status(thm)],[c_0_95])). cnf(c_0_101, plain, (l2_osalg_1(X1)\|~l3_osalg_1(X1)), inference(split_conjunct,[status(thm)],[c_0_75])). cnf(c_0_102, plain, (v6_osalg_1(k1_osalg_1(X1))\|v11_struct_0(k1_osalg_1(X1))\|v2_struct_0(k1_osalg_1(X1))\|v11_struct_0(X1)\|v2_struct_0(X1)\|k6_partfun1(u4_struct_0(X1))!=k6_partfun1(X2)\|~l1_osalg_1(k1_osalg_1(X1))\|~l1_msualg_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_96, c_0_97])])). cnf(c_0_103, plain, (l1_osalg_1(k1_osalg_1(X1))\|v11_struct_0(X1)\|v2_struct_0(X1)\|~l1_msualg_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_98, c_0_53])])). cnf(c_0_104, negated_conjecture, (~v6_osalg_1(k1_osalg_1(esk1_0))\|~l2_osalg_1(k1_osalg_1(esk1_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_99, c_0_100])])). cnf(c_0_105, plain, (l2_osalg_1(X1)\|~l3_osalg_1(X1)), inference(evalgc,[status(thm)],[c_0_101])). cnf(c_0_106, plain, (v6_osalg_1(k1_osalg_1(X1))\|v11_struct_0(X1)\|v2_struct_0(X1)\|k6_partfun1(u4_struct_0(X1))!=k6_partfun1(X2)\|~l1_msualg_1(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_102, c_0_103]), c_0_54]), c_0_55])). cnf(c_0_107, negated_conjecture, (~v6_osalg_1(k1_osalg_1(esk1_0))\|~l3_osalg_1(k1_osalg_1(esk1_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_104, c_0_105])])). cnf(c_0_108, plain, (v6_osalg_1(k1_osalg_1(X1))\|v11_struct_0(X1)\|v2_struct_0(X1)\|~l1_msualg_1(X1)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_106])])). cnf(c_0_109, negated_conjecture, (~l3_osalg_1(k1_osalg_1(esk1_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107, c_0_108]), c_0_92])]), c_0_93]), c_0_94])])). cnf(c_0_110, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109, c_0_53]), c_0_92])]), c_0_93]), c_0_94]), ['proof']). # SZS output end CNFRefutation	reserve A,O for non empty set, R for Order of A, Ol for Equivalence_Relation of O, f for Function of O,A*, g for Function of O,A; reserve S for OverloadedRSSign; reserve S0 for non empty non void ManySortedSign; theorem Th5: OSSign S0 is discrete op-discrete proof set s = OSSign S0; set ol = the Overloading of s; the carrier of S0 = the carrier of OSSign S0 & id the carrier of S0 = the InternalRel of OSSign S0 by Def5; hence OSSign S0 is discrete by ORDERS_3:def 1; A1: the Overloading of OSSign S0 = id the carrier' of S0 by Def5; now let x,y be OperSymbol of s; assume x ~= y; then [x,y] in ol by Def2; hence x = y by A1,RELAT_1:def 10; end; hence thesis by Th3; end;	Convert the following ATP output trace into a readable Mizar proof.
t30_tdlat_3	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(d10_xboole_0, axiom, ![X1, X2]:(X1=X2<=>(r1_tarski(X1,X2)&r1_tarski(X2,X1))), file('/scratch/mptp/predsminms1/t30_tdlat_3__0', d10_xboole_0)). fof(t23_subset_1, axiom, ![X1, X2]:(m1_subset_1(X2,k1_zfmisc_1(X1))=>![X3]:(m1_subset_1(X3,k1_zfmisc_1(X1))=>(r1_xboole_0(X2,X3)<=>r1_tarski(X2,k3_subset_1(X1,X3))))), file('/scratch/mptp/predsminms1/t30_tdlat_3__0', t23_subset_1)). fof(t18_pre_topc, axiom, ![X1]:(l1_pre_topc(X1)=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))=>r1_tarski(X2,k2_pre_topc(X1,X2)))), file('/scratch/mptp/predsminms1/t30_tdlat_3__0', t18_pre_topc)). fof(dt_k3_subset_1, axiom, ![X1, X2]:(m1_subset_1(X2,k1_zfmisc_1(X1))=>m1_subset_1(k3_subset_1(X1,X2),k1_zfmisc_1(X1))), file('/scratch/mptp/predsminms1/t30_tdlat_3__0', dt_k3_subset_1)). fof(d1_tops_1, axiom, ![X1]:(l1_pre_topc(X1)=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))=>k1_tops_1(X1,X2)=k3_subset_1(u1_struct_0(X1),k2_pre_topc(X1,k3_subset_1(u1_struct_0(X1),X2))))), file('/scratch/mptp/predsminms1/t30_tdlat_3__0', d1_tops_1)). fof(dt_k2_pre_topc, axiom, ![X1, X2]:((l1_pre_topc(X1)&m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))))=>m1_subset_1(k2_pre_topc(X1,X2),k1_zfmisc_1(u1_struct_0(X1)))), file('/scratch/mptp/predsminms1/t30_tdlat_3__0', dt_k2_pre_topc)). fof(involutiveness_k3_subset_1, axiom, ![X1, X2]:(m1_subset_1(X2,k1_zfmisc_1(X1))=>k3_subset_1(X1,k3_subset_1(X1,X2))=X2), file('/scratch/mptp/predsminms1/t30_tdlat_3__0', involutiveness_k3_subset_1)). fof(t30_tdlat_3, conjecture, ![X1]:((~(v2_struct_0(X1))&(v2_pre_topc(X1)&l1_pre_topc(X1)))=>(v4_tdlat_3(X1)<=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))=>(v3_pre_topc(X2,X1)=>k2_pre_topc(X1,X2)=k1_tops_1(X1,k2_pre_topc(X1,X2)))))), file('/scratch/mptp/predsminms1/t30_tdlat_3__0', t30_tdlat_3)). fof(t28_tdlat_3, axiom, ![X1]:((~(v2_struct_0(X1))&(v2_pre_topc(X1)&l1_pre_topc(X1)))=>(v4_tdlat_3(X1)<=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))=>![X3]:(m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))=>((v3_pre_topc(X2,X1)&(v3_pre_topc(X3,X1)&r1_xboole_0(X2,X3)))=>r1_xboole_0(k2_pre_topc(X1,X2),k2_pre_topc(X1,X3))))))), file('/scratch/mptp/predsminms1/t30_tdlat_3__0', t28_tdlat_3)). fof(projectivity_k2_pre_topc, axiom, ![X1, X2]:((l1_pre_topc(X1)&m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))))=>k2_pre_topc(X1,k2_pre_topc(X1,X2))=k2_pre_topc(X1,X2)), file('/scratch/mptp/predsminms1/t30_tdlat_3__0', projectivity_k2_pre_topc)). fof(fc9_tops_1, axiom, ![X1, X2]:(((v2_pre_topc(X1)&l1_pre_topc(X1))&m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))))=>v3_pre_topc(k1_tops_1(X1,X2),X1)), file('/scratch/mptp/predsminms1/t30_tdlat_3__0', fc9_tops_1)). fof(d4_tdlat_3, axiom, ![X1]:((~(v2_struct_0(X1))&(v2_pre_topc(X1)&l1_pre_topc(X1)))=>(v4_tdlat_3(X1)<=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))=>(v3_pre_topc(X2,X1)=>v3_pre_topc(k2_pre_topc(X1,X2),X1))))), file('/scratch/mptp/predsminms1/t30_tdlat_3__0', d4_tdlat_3)). fof(c_0_12, plain, ![X15, X16]:(((r1_tarski(X15,X16)\|X15!=X16)&(r1_tarski(X16,X15)\|X15!=X16))&(~r1_tarski(X15,X16)\|~r1_tarski(X16,X15)\|X15=X16)), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])])). fof(c_0_13, plain, ![X17, X18, X19]:((~r1_xboole_0(X18,X19)\|r1_tarski(X18,k3_subset_1(X17,X19))\|~m1_subset_1(X19,k1_zfmisc_1(X17))\|~m1_subset_1(X18,k1_zfmisc_1(X17)))&(~r1_tarski(X18,k3_subset_1(X17,X19))\|r1_xboole_0(X18,X19)\|~m1_subset_1(X19,k1_zfmisc_1(X17))\|~m1_subset_1(X18,k1_zfmisc_1(X17)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t23_subset_1])])])])). cnf(c_0_14, plain, (r1_tarski(X1,X2)\|X2!=X1), inference(split_conjunct,[status(thm)],[c_0_12])). fof(c_0_15, plain, ![X22, X23]:(~l1_pre_topc(X22)\|(~m1_subset_1(X23,k1_zfmisc_1(u1_struct_0(X22)))\|r1_tarski(X23,k2_pre_topc(X22,X23)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t18_pre_topc])])])). fof(c_0_16, plain, ![X13, X14]:(~m1_subset_1(X14,k1_zfmisc_1(X13))\|m1_subset_1(k3_subset_1(X13,X14),k1_zfmisc_1(X13))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k3_subset_1])])). fof(c_0_17, plain, ![X9, X10]:(~l1_pre_topc(X9)\|(~m1_subset_1(X10,k1_zfmisc_1(u1_struct_0(X9)))\|k1_tops_1(X9,X10)=k3_subset_1(u1_struct_0(X9),k2_pre_topc(X9,k3_subset_1(u1_struct_0(X9),X10))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_tops_1])])])). cnf(c_0_18, plain, (r1_xboole_0(X1,X3)\|~r1_tarski(X1,k3_subset_1(X2,X3))\|~m1_subset_1(X3,k1_zfmisc_1(X2))\|~m1_subset_1(X1,k1_zfmisc_1(X2))), inference(split_conjunct,[status(thm)],[c_0_13])). cnf(c_0_19, plain, (r1_tarski(X1,X2)\|X1!=X2), inference(evalgc,[status(thm)],[c_0_14])). cnf(c_0_20, plain, (X1=X2\|~r1_tarski(X1,X2)\|~r1_tarski(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_21, plain, (r1_tarski(X2,k2_pre_topc(X1,X2))\|~l1_pre_topc(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_22, plain, (m1_subset_1(k3_subset_1(X2,X1),k1_zfmisc_1(X2))\|~m1_subset_1(X1,k1_zfmisc_1(X2))), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_23, plain, (k1_tops_1(X1,X2)=k3_subset_1(u1_struct_0(X1),k2_pre_topc(X1,k3_subset_1(u1_struct_0(X1),X2)))\|~l1_pre_topc(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(split_conjunct,[status(thm)],[c_0_17])). fof(c_0_24, plain, ![X11, X12]:(~l1_pre_topc(X11)\|~m1_subset_1(X12,k1_zfmisc_1(u1_struct_0(X11)))\|m1_subset_1(k2_pre_topc(X11,X12),k1_zfmisc_1(u1_struct_0(X11)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_pre_topc])])). fof(c_0_25, plain, ![X7, X8]:(~m1_subset_1(X8,k1_zfmisc_1(X7))\|k3_subset_1(X7,k3_subset_1(X7,X8))=X8), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[involutiveness_k3_subset_1])])). cnf(c_0_26, plain, (r1_xboole_0(X1,X3)\|~m1_subset_1(X3,k1_zfmisc_1(X2))\|~m1_subset_1(X1,k1_zfmisc_1(X2))\|~r1_tarski(X1,k3_subset_1(X2,X3))), inference(evalgc,[status(thm)],[c_0_18])). cnf(c_0_27, plain, (r1_tarski(X1,X1)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_19])])). fof(c_0_28, negated_conjecture, ~(![X1]:((~(v2_struct_0(X1))&(v2_pre_topc(X1)&l1_pre_topc(X1)))=>(v4_tdlat_3(X1)<=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))=>(v3_pre_topc(X2,X1)=>k2_pre_topc(X1,X2)=k1_tops_1(X1,k2_pre_topc(X1,X2))))))), inference(assume_negation,[status(cth)],[t30_tdlat_3])). cnf(c_0_29, plain, (X1=X2\|~r1_tarski(X2,X1)\|~r1_tarski(X1,X2)), inference(evalgc,[status(thm)],[c_0_20])). cnf(c_0_30, plain, (r1_tarski(X2,k2_pre_topc(X1,X2))\|~l1_pre_topc(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(evalgc,[status(thm)],[c_0_21])). cnf(c_0_31, plain, (r1_tarski(X1,k3_subset_1(X3,X2))\|~r1_xboole_0(X1,X2)\|~m1_subset_1(X2,k1_zfmisc_1(X3))\|~m1_subset_1(X1,k1_zfmisc_1(X3))), inference(split_conjunct,[status(thm)],[c_0_13])). fof(c_0_32, plain, ![X29, X30, X31]:((~v4_tdlat_3(X29)\|(~m1_subset_1(X30,k1_zfmisc_1(u1_struct_0(X29)))\|(~m1_subset_1(X31,k1_zfmisc_1(u1_struct_0(X29)))\|(~v3_pre_topc(X30,X29)\|(~v3_pre_topc(X31,X29)\|~r1_xboole_0(X30,X31))\|r1_xboole_0(k2_pre_topc(X29,X30),k2_pre_topc(X29,X31)))))\|(v2_struct_0(X29)\|(~v2_pre_topc(X29)\|~l1_pre_topc(X29))))&((m1_subset_1(esk4_1(X29),k1_zfmisc_1(u1_struct_0(X29)))\|v4_tdlat_3(X29)\|(v2_struct_0(X29)\|(~v2_pre_topc(X29)\|~l1_pre_topc(X29))))&((m1_subset_1(esk5_1(X29),k1_zfmisc_1(u1_struct_0(X29)))\|v4_tdlat_3(X29)\|(v2_struct_0(X29)\|(~v2_pre_topc(X29)\|~l1_pre_topc(X29))))&(((v3_pre_topc(esk4_1(X29),X29)\|v4_tdlat_3(X29)\|(v2_struct_0(X29)\|(~v2_pre_topc(X29)\|~l1_pre_topc(X29))))&((v3_pre_topc(esk5_1(X29),X29)\|v4_tdlat_3(X29)\|(v2_struct_0(X29)\|(~v2_pre_topc(X29)\|~l1_pre_topc(X29))))&(r1_xboole_0(esk4_1(X29),esk5_1(X29))\|v4_tdlat_3(X29)\|(v2_struct_0(X29)\|(~v2_pre_topc(X29)\|~l1_pre_topc(X29))))))&(~r1_xboole_0(k2_pre_topc(X29,esk4_1(X29)),k2_pre_topc(X29,esk5_1(X29)))\|v4_tdlat_3(X29)\|(v2_struct_0(X29)\|(~v2_pre_topc(X29)\|~l1_pre_topc(X29)))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t28_tdlat_3])])])])])])). fof(c_0_33, plain, ![X27, X28]:(~l1_pre_topc(X27)\|~m1_subset_1(X28,k1_zfmisc_1(u1_struct_0(X27)))\|k2_pre_topc(X27,k2_pre_topc(X27,X28))=k2_pre_topc(X27,X28)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[projectivity_k2_pre_topc])])). cnf(c_0_34, plain, (m1_subset_1(k3_subset_1(X2,X1),k1_zfmisc_1(X2))\|~m1_subset_1(X1,k1_zfmisc_1(X2))), inference(evalgc,[status(thm)],[c_0_22])). cnf(c_0_35, plain, (k3_subset_1(u1_struct_0(X1),k2_pre_topc(X1,k3_subset_1(u1_struct_0(X1),X2)))=k1_tops_1(X1,X2)\|~l1_pre_topc(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(evalgc,[status(thm)],[c_0_23])). cnf(c_0_36, plain, (m1_subset_1(k2_pre_topc(X1,X2),k1_zfmisc_1(u1_struct_0(X1)))\|~l1_pre_topc(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(split_conjunct,[status(thm)],[c_0_24])). cnf(c_0_37, plain, (k3_subset_1(X2,k3_subset_1(X2,X1))=X1\|~m1_subset_1(X1,k1_zfmisc_1(X2))), inference(split_conjunct,[status(thm)],[c_0_25])). cnf(c_0_38, plain, (r1_xboole_0(k3_subset_1(X1,X2),X2)\|~m1_subset_1(X2,k1_zfmisc_1(X1))\|~m1_subset_1(k3_subset_1(X1,X2),k1_zfmisc_1(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_26, c_0_27])])). fof(c_0_39, plain, ![X20, X21]:(~v2_pre_topc(X20)\|~l1_pre_topc(X20)\|~m1_subset_1(X21,k1_zfmisc_1(u1_struct_0(X20)))\|v3_pre_topc(k1_tops_1(X20,X21),X20)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc9_tops_1])])). fof(c_0_40, negated_conjecture, ![X6]:((~v2_struct_0(esk1_0)&(v2_pre_topc(esk1_0)&l1_pre_topc(esk1_0)))&(((m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(esk1_0)))\|~v4_tdlat_3(esk1_0))&((v3_pre_topc(esk2_0,esk1_0)\|~v4_tdlat_3(esk1_0))&(k2_pre_topc(esk1_0,esk2_0)!=k1_tops_1(esk1_0,k2_pre_topc(esk1_0,esk2_0))\|~v4_tdlat_3(esk1_0))))&(v4_tdlat_3(esk1_0)\|(~m1_subset_1(X6,k1_zfmisc_1(u1_struct_0(esk1_0)))\|(~v3_pre_topc(X6,esk1_0)\|k2_pre_topc(esk1_0,X6)=k1_tops_1(esk1_0,k2_pre_topc(esk1_0,X6))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_28])])])])])])). cnf(c_0_41, plain, (k2_pre_topc(X1,X2)=X2\|~r1_tarski(k2_pre_topc(X1,X2),X2)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~l1_pre_topc(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_29, c_0_30])])). cnf(c_0_42, plain, (r1_tarski(X1,k3_subset_1(X3,X2))\|~r1_xboole_0(X1,X2)\|~m1_subset_1(X2,k1_zfmisc_1(X3))\|~m1_subset_1(X1,k1_zfmisc_1(X3))), inference(evalgc,[status(thm)],[c_0_31])). cnf(c_0_43, plain, (r1_xboole_0(k2_pre_topc(X1,X2),k2_pre_topc(X1,X3))\|v2_struct_0(X1)\|~v4_tdlat_3(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))\|~v3_pre_topc(X2,X1)\|~v3_pre_topc(X3,X1)\|~r1_xboole_0(X2,X3)\|~v2_pre_topc(X1)\|~l1_pre_topc(X1)), inference(split_conjunct,[status(thm)],[c_0_32])). cnf(c_0_44, plain, (k2_pre_topc(X1,k2_pre_topc(X1,X2))=k2_pre_topc(X1,X2)\|~l1_pre_topc(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(split_conjunct,[status(thm)],[c_0_33])). cnf(c_0_45, plain, (m1_subset_1(k1_tops_1(X1,X2),k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(k2_pre_topc(X1,k3_subset_1(u1_struct_0(X1),X2)),k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~l1_pre_topc(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_34, c_0_35])])). cnf(c_0_46, plain, (m1_subset_1(k2_pre_topc(X1,X2),k1_zfmisc_1(u1_struct_0(X1)))\|~l1_pre_topc(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(evalgc,[status(thm)],[c_0_36])). cnf(c_0_47, plain, (k3_subset_1(X2,k3_subset_1(X2,X1))=X1\|~m1_subset_1(X1,k1_zfmisc_1(X2))), inference(evalgc,[status(thm)],[c_0_37])). cnf(c_0_48, plain, (r1_xboole_0(k3_subset_1(X1,X2),X2)\|~m1_subset_1(X2,k1_zfmisc_1(X1))), inference(csr,[status(thm)],[c_0_38, c_0_34])). fof(c_0_49, plain, ![X24, X25]:((~v4_tdlat_3(X24)\|(~m1_subset_1(X25,k1_zfmisc_1(u1_struct_0(X24)))\|(~v3_pre_topc(X25,X24)\|v3_pre_topc(k2_pre_topc(X24,X25),X24)))\|(v2_struct_0(X24)\|(~v2_pre_topc(X24)\|~l1_pre_topc(X24))))&((m1_subset_1(esk3_1(X24),k1_zfmisc_1(u1_struct_0(X24)))\|v4_tdlat_3(X24)\|(v2_struct_0(X24)\|(~v2_pre_topc(X24)\|~l1_pre_topc(X24))))&((v3_pre_topc(esk3_1(X24),X24)\|v4_tdlat_3(X24)\|(v2_struct_0(X24)\|(~v2_pre_topc(X24)\|~l1_pre_topc(X24))))&(~v3_pre_topc(k2_pre_topc(X24,esk3_1(X24)),X24)\|v4_tdlat_3(X24)\|(v2_struct_0(X24)\|(~v2_pre_topc(X24)\|~l1_pre_topc(X24))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d4_tdlat_3])])])])])])). cnf(c_0_50, plain, (v3_pre_topc(k1_tops_1(X1,X2),X1)\|~v2_pre_topc(X1)\|~l1_pre_topc(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(split_conjunct,[status(thm)],[c_0_39])). cnf(c_0_51, negated_conjecture, (v4_tdlat_3(esk1_0)\|k2_pre_topc(esk1_0,X1)=k1_tops_1(esk1_0,k2_pre_topc(esk1_0,X1))\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(esk1_0)))\|~v3_pre_topc(X1,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_40])). cnf(c_0_52, negated_conjecture, (l1_pre_topc(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_40])). cnf(c_0_53, negated_conjecture, (v2_pre_topc(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_40])). cnf(c_0_54, plain, (k2_pre_topc(X1,k3_subset_1(X2,X3))=k3_subset_1(X2,X3)\|~m1_subset_1(k3_subset_1(X2,X3),k1_zfmisc_1(u1_struct_0(X1)))\|~l1_pre_topc(X1)\|~r1_xboole_0(k2_pre_topc(X1,k3_subset_1(X2,X3)),X3)\|~m1_subset_1(X3,k1_zfmisc_1(X2))\|~m1_subset_1(k2_pre_topc(X1,k3_subset_1(X2,X3)),k1_zfmisc_1(X2))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_41, c_0_42])])). cnf(c_0_55, plain, (v2_struct_0(X1)\|r1_xboole_0(k2_pre_topc(X1,X2),k2_pre_topc(X1,X3))\|~v2_pre_topc(X1)\|~l1_pre_topc(X1)\|~v4_tdlat_3(X1)\|~v3_pre_topc(X3,X1)\|~v3_pre_topc(X2,X1)\|~r1_xboole_0(X2,X3)\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(evalgc,[status(thm)],[c_0_43])). cnf(c_0_56, plain, (k2_pre_topc(X1,k2_pre_topc(X1,X2))=k2_pre_topc(X1,X2)\|~l1_pre_topc(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(evalgc,[status(thm)],[c_0_44])). cnf(c_0_57, plain, (m1_subset_1(k1_tops_1(X1,X2),k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~l1_pre_topc(X1)\|~m1_subset_1(k3_subset_1(u1_struct_0(X1),X2),k1_zfmisc_1(u1_struct_0(X1)))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_45, c_0_46])])). cnf(c_0_58, plain, (k1_tops_1(X1,k3_subset_1(u1_struct_0(X1),X2))=k3_subset_1(u1_struct_0(X1),k2_pre_topc(X1,X2))\|~m1_subset_1(k3_subset_1(u1_struct_0(X1),X2),k1_zfmisc_1(u1_struct_0(X1)))\|~l1_pre_topc(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_35, c_0_47])])). cnf(c_0_59, plain, (r1_xboole_0(k1_tops_1(X1,X2),k2_pre_topc(X1,k3_subset_1(u1_struct_0(X1),X2)))\|~m1_subset_1(k2_pre_topc(X1,k3_subset_1(u1_struct_0(X1),X2)),k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~l1_pre_topc(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_48, c_0_35])])). cnf(c_0_60, plain, (v4_tdlat_3(X1)\|v2_struct_0(X1)\|~v3_pre_topc(k2_pre_topc(X1,esk3_1(X1)),X1)\|~v2_pre_topc(X1)\|~l1_pre_topc(X1)), inference(split_conjunct,[status(thm)],[c_0_49])). cnf(c_0_61, plain, (v3_pre_topc(k1_tops_1(X1,X2),X1)\|~v2_pre_topc(X1)\|~l1_pre_topc(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(evalgc,[status(thm)],[c_0_50])). cnf(c_0_62, negated_conjecture, (k1_tops_1(esk1_0,k2_pre_topc(esk1_0,X1))=k2_pre_topc(esk1_0,X1)\|v4_tdlat_3(esk1_0)\|~v3_pre_topc(X1,esk1_0)\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(esk1_0)))), inference(evalgc,[status(thm)],[c_0_51])). cnf(c_0_63, negated_conjecture, (l1_pre_topc(esk1_0)), inference(evalgc,[status(thm)],[c_0_52])). cnf(c_0_64, negated_conjecture, (v2_pre_topc(esk1_0)), inference(evalgc,[status(thm)],[c_0_53])). cnf(c_0_65, negated_conjecture, (~v2_struct_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_40])). cnf(c_0_66, plain, (k1_tops_1(X1,k2_pre_topc(X1,k3_subset_1(u1_struct_0(X1),X2)))=k3_subset_1(u1_struct_0(X1),k2_pre_topc(X1,k1_tops_1(X1,X2)))\|~m1_subset_1(k2_pre_topc(X1,k3_subset_1(u1_struct_0(X1),X2)),k1_zfmisc_1(u1_struct_0(X1)))\|~l1_pre_topc(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_35, c_0_35])])). cnf(c_0_67, plain, (k2_pre_topc(X1,k3_subset_1(u1_struct_0(X1),X2))=k3_subset_1(u1_struct_0(X1),X2)\|~r1_xboole_0(k2_pre_topc(X1,k3_subset_1(u1_struct_0(X1),X2)),X2)\|~m1_subset_1(k3_subset_1(u1_struct_0(X1),X2),k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~l1_pre_topc(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_54, c_0_46])])). cnf(c_0_68, plain, (r1_xboole_0(k2_pre_topc(X1,X2),k2_pre_topc(X1,X3))\|v2_struct_0(X1)\|~r1_xboole_0(X2,k2_pre_topc(X1,X3))\|~v3_pre_topc(k2_pre_topc(X1,X3),X1)\|~v3_pre_topc(X2,X1)\|~m1_subset_1(k2_pre_topc(X1,X3),k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~v4_tdlat_3(X1)\|~l1_pre_topc(X1)\|~v2_pre_topc(X1)\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_55, c_0_56])])). cnf(c_0_69, plain, (m1_subset_1(k1_tops_1(X1,X2),k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~l1_pre_topc(X1)), inference(csr,[status(thm)],[c_0_57, c_0_34])). cnf(c_0_70, plain, (k1_tops_1(X1,k3_subset_1(u1_struct_0(X1),X2))=k3_subset_1(u1_struct_0(X1),k2_pre_topc(X1,X2))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~l1_pre_topc(X1)), inference(csr,[status(thm)],[c_0_58, c_0_34])). cnf(c_0_71, plain, (r1_xboole_0(k1_tops_1(X1,k3_subset_1(u1_struct_0(X1),X2)),k2_pre_topc(X1,X2))\|~m1_subset_1(k2_pre_topc(X1,X2),k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(k3_subset_1(u1_struct_0(X1),X2),k1_zfmisc_1(u1_struct_0(X1)))\|~l1_pre_topc(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_59, c_0_47])])). cnf(c_0_72, plain, (v2_struct_0(X1)\|v4_tdlat_3(X1)\|~v2_pre_topc(X1)\|~l1_pre_topc(X1)\|~v3_pre_topc(k2_pre_topc(X1,esk3_1(X1)),X1)), inference(evalgc,[status(thm)],[c_0_60])). cnf(c_0_73, negated_conjecture, (v3_pre_topc(k2_pre_topc(esk1_0,X1),esk1_0)\|v4_tdlat_3(esk1_0)\|~m1_subset_1(k2_pre_topc(esk1_0,X1),k1_zfmisc_1(u1_struct_0(esk1_0)))\|~v3_pre_topc(X1,esk1_0)\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(esk1_0)))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61, c_0_62]), c_0_63]), c_0_64])])])). cnf(c_0_74, negated_conjecture, (~v2_struct_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_65])). cnf(c_0_75, plain, (k3_subset_1(u1_struct_0(X1),k2_pre_topc(X1,k1_tops_1(X1,k3_subset_1(u1_struct_0(X1),X2))))=k1_tops_1(X1,k2_pre_topc(X1,X2))\|~m1_subset_1(k2_pre_topc(X1,X2),k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(k3_subset_1(u1_struct_0(X1),X2),k1_zfmisc_1(u1_struct_0(X1)))\|~l1_pre_topc(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_66, c_0_47])])). cnf(c_0_76, plain, (k2_pre_topc(X1,k3_subset_1(u1_struct_0(X1),X2))=k3_subset_1(u1_struct_0(X1),X2)\|~r1_xboole_0(k2_pre_topc(X1,k3_subset_1(u1_struct_0(X1),X2)),X2)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~l1_pre_topc(X1)), inference(csr,[status(thm)],[c_0_67, c_0_34])). cnf(c_0_77, plain, (r1_xboole_0(k2_pre_topc(X1,X2),k2_pre_topc(X1,X3))\|v2_struct_0(X1)\|~r1_xboole_0(X2,k2_pre_topc(X1,X3))\|~v3_pre_topc(k2_pre_topc(X1,X3),X1)\|~v3_pre_topc(X2,X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))\|~v4_tdlat_3(X1)\|~l1_pre_topc(X1)\|~v2_pre_topc(X1)), inference(csr,[status(thm)],[c_0_68, c_0_46])). cnf(c_0_78, plain, (m1_subset_1(k3_subset_1(u1_struct_0(X1),k2_pre_topc(X1,X2)),k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(k3_subset_1(u1_struct_0(X1),X2),k1_zfmisc_1(u1_struct_0(X1)))\|~l1_pre_topc(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_69, c_0_70])])). cnf(c_0_79, plain, (v3_pre_topc(k3_subset_1(u1_struct_0(X1),k2_pre_topc(X1,X2)),X1)\|~m1_subset_1(k3_subset_1(u1_struct_0(X1),X2),k1_zfmisc_1(u1_struct_0(X1)))\|~l1_pre_topc(X1)\|~v2_pre_topc(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_61, c_0_70])])). cnf(c_0_80, plain, (r1_xboole_0(k1_tops_1(X1,k3_subset_1(u1_struct_0(X1),X2)),k2_pre_topc(X1,X2))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~l1_pre_topc(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_71, c_0_46]), c_0_34])). cnf(c_0_81, negated_conjecture, (v4_tdlat_3(esk1_0)\|~v3_pre_topc(esk3_1(esk1_0),esk1_0)\|~m1_subset_1(k2_pre_topc(esk1_0,esk3_1(esk1_0)),k1_zfmisc_1(u1_struct_0(esk1_0)))\|~m1_subset_1(esk3_1(esk1_0),k1_zfmisc_1(u1_struct_0(esk1_0)))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72, c_0_73]), c_0_63]), c_0_64])]), c_0_74])])). cnf(c_0_82, plain, (v3_pre_topc(esk3_1(X1),X1)\|v4_tdlat_3(X1)\|v2_struct_0(X1)\|~v2_pre_topc(X1)\|~l1_pre_topc(X1)), inference(split_conjunct,[status(thm)],[c_0_49])). cnf(c_0_83, plain, (k3_subset_1(u1_struct_0(X1),k2_pre_topc(X1,k1_tops_1(X1,k3_subset_1(u1_struct_0(X1),X2))))=k1_tops_1(X1,k2_pre_topc(X1,X2))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~l1_pre_topc(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_75, c_0_46]), c_0_34])). cnf(c_0_84, plain, (k2_pre_topc(X1,k3_subset_1(u1_struct_0(X1),k2_pre_topc(X1,X2)))=k3_subset_1(u1_struct_0(X1),k2_pre_topc(X1,X2))\|v2_struct_0(X1)\|~m1_subset_1(k2_pre_topc(X1,X2),k1_zfmisc_1(u1_struct_0(X1)))\|~l1_pre_topc(X1)\|~r1_xboole_0(k3_subset_1(u1_struct_0(X1),k2_pre_topc(X1,X2)),k2_pre_topc(X1,X2))\|~v3_pre_topc(k2_pre_topc(X1,X2),X1)\|~v3_pre_topc(k3_subset_1(u1_struct_0(X1),k2_pre_topc(X1,X2)),X1)\|~m1_subset_1(k3_subset_1(u1_struct_0(X1),k2_pre_topc(X1,X2)),k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~v4_tdlat_3(X1)\|~v2_pre_topc(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_76, c_0_77])])). cnf(c_0_85, plain, (m1_subset_1(k3_subset_1(u1_struct_0(X1),k2_pre_topc(X1,X2)),k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~l1_pre_topc(X1)), inference(csr,[status(thm)],[c_0_78, c_0_34])). cnf(c_0_86, plain, (v3_pre_topc(k3_subset_1(u1_struct_0(X1),k2_pre_topc(X1,X2)),X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~l1_pre_topc(X1)\|~v2_pre_topc(X1)), inference(csr,[status(thm)],[c_0_79, c_0_34])). cnf(c_0_87, plain, (r1_xboole_0(k3_subset_1(u1_struct_0(X1),k2_pre_topc(X1,X2)),k2_pre_topc(X1,X2))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~l1_pre_topc(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_80, c_0_70])])). cnf(c_0_88, negated_conjecture, (v4_tdlat_3(esk1_0)\|~v3_pre_topc(esk3_1(esk1_0),esk1_0)\|~m1_subset_1(esk3_1(esk1_0),k1_zfmisc_1(u1_struct_0(esk1_0)))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81, c_0_46]), c_0_63])])])). cnf(c_0_89, plain, (v2_struct_0(X1)\|v4_tdlat_3(X1)\|v3_pre_topc(esk3_1(X1),X1)\|~v2_pre_topc(X1)\|~l1_pre_topc(X1)), inference(evalgc,[status(thm)],[c_0_82])). cnf(c_0_90, plain, (m1_subset_1(esk3_1(X1),k1_zfmisc_1(u1_struct_0(X1)))\|v4_tdlat_3(X1)\|v2_struct_0(X1)\|~v2_pre_topc(X1)\|~l1_pre_topc(X1)), inference(split_conjunct,[status(thm)],[c_0_49])). cnf(c_0_91, plain, (k3_subset_1(u1_struct_0(X1),k2_pre_topc(X1,k3_subset_1(u1_struct_0(X1),k2_pre_topc(X1,X2))))=k1_tops_1(X1,k2_pre_topc(X1,X2))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~l1_pre_topc(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_83, c_0_70])])). cnf(c_0_92, plain, (k2_pre_topc(X1,k3_subset_1(u1_struct_0(X1),k2_pre_topc(X1,X2)))=k3_subset_1(u1_struct_0(X1),k2_pre_topc(X1,X2))\|v2_struct_0(X1)\|~v3_pre_topc(k2_pre_topc(X1,X2),X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~v4_tdlat_3(X1)\|~l1_pre_topc(X1)\|~v2_pre_topc(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_84, c_0_46]), c_0_85]), c_0_86]), c_0_87])). cnf(c_0_93, negated_conjecture, (k2_pre_topc(esk1_0,esk2_0)!=k1_tops_1(esk1_0,k2_pre_topc(esk1_0,esk2_0))\|~v4_tdlat_3(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_40])). cnf(c_0_94, negated_conjecture, (v4_tdlat_3(esk1_0)\|~m1_subset_1(esk3_1(esk1_0),k1_zfmisc_1(u1_struct_0(esk1_0)))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88, c_0_89]), c_0_63]), c_0_64])]), c_0_74])])). cnf(c_0_95, plain, (v2_struct_0(X1)\|v4_tdlat_3(X1)\|m1_subset_1(esk3_1(X1),k1_zfmisc_1(u1_struct_0(X1)))\|~v2_pre_topc(X1)\|~l1_pre_topc(X1)), inference(evalgc,[status(thm)],[c_0_90])). cnf(c_0_96, plain, (k3_subset_1(u1_struct_0(X1),k3_subset_1(u1_struct_0(X1),k2_pre_topc(X1,X2)))=k1_tops_1(X1,k2_pre_topc(X1,X2))\|v2_struct_0(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~l1_pre_topc(X1)\|~v3_pre_topc(k2_pre_topc(X1,X2),X1)\|~v4_tdlat_3(X1)\|~v2_pre_topc(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_91, c_0_92])])). cnf(c_0_97, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(esk1_0)))\|~v4_tdlat_3(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_40])). cnf(c_0_98, negated_conjecture, (k1_tops_1(esk1_0,k2_pre_topc(esk1_0,esk2_0))!=k2_pre_topc(esk1_0,esk2_0)\|~v4_tdlat_3(esk1_0)), inference(evalgc,[status(thm)],[c_0_93])). cnf(c_0_99, negated_conjecture, (v4_tdlat_3(esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94, c_0_95]), c_0_63]), c_0_64])]), c_0_74])])). cnf(c_0_100, plain, (k1_tops_1(X1,k2_pre_topc(X1,X2))=k2_pre_topc(X1,X2)\|v2_struct_0(X1)\|~m1_subset_1(k2_pre_topc(X1,X2),k1_zfmisc_1(u1_struct_0(X1)))\|~v3_pre_topc(k2_pre_topc(X1,X2),X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~v4_tdlat_3(X1)\|~l1_pre_topc(X1)\|~v2_pre_topc(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_47, c_0_96])])). cnf(c_0_101, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(esk1_0)))\|~v4_tdlat_3(esk1_0)), inference(evalgc,[status(thm)],[c_0_97])). cnf(c_0_102, negated_conjecture, (v3_pre_topc(esk2_0,esk1_0)\|~v4_tdlat_3(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_40])). cnf(c_0_103, negated_conjecture, (k1_tops_1(esk1_0,k2_pre_topc(esk1_0,esk2_0))!=k2_pre_topc(esk1_0,esk2_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_98, c_0_99])])])). cnf(c_0_104, plain, (k1_tops_1(X1,k2_pre_topc(X1,X2))=k2_pre_topc(X1,X2)\|v2_struct_0(X1)\|~v3_pre_topc(k2_pre_topc(X1,X2),X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~v4_tdlat_3(X1)\|~l1_pre_topc(X1)\|~v2_pre_topc(X1)), inference(csr,[status(thm)],[c_0_100, c_0_46])). cnf(c_0_105, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(esk1_0)))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_101, c_0_99])])])). cnf(c_0_106, plain, (v3_pre_topc(k2_pre_topc(X1,X2),X1)\|v2_struct_0(X1)\|~v4_tdlat_3(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~v3_pre_topc(X2,X1)\|~v2_pre_topc(X1)\|~l1_pre_topc(X1)), inference(split_conjunct,[status(thm)],[c_0_49])). cnf(c_0_107, negated_conjecture, (v3_pre_topc(esk2_0,esk1_0)\|~v4_tdlat_3(esk1_0)), inference(evalgc,[status(thm)],[c_0_102])). cnf(c_0_108, negated_conjecture, (~v3_pre_topc(k2_pre_topc(esk1_0,esk2_0),esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103, c_0_104]), c_0_105]), c_0_99]), c_0_63]), c_0_64])]), c_0_74])])). cnf(c_0_109, plain, (v2_struct_0(X1)\|v3_pre_topc(k2_pre_topc(X1,X2),X1)\|~v2_pre_topc(X1)\|~l1_pre_topc(X1)\|~v4_tdlat_3(X1)\|~v3_pre_topc(X2,X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(evalgc,[status(thm)],[c_0_106])). cnf(c_0_110, negated_conjecture, (v3_pre_topc(esk2_0,esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_107, c_0_99])])])). cnf(c_0_111, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108, c_0_109]), c_0_110]), c_0_105]), c_0_99]), c_0_63]), c_0_64])]), c_0_74]), ['proof']). # SZS output end CNFRefutation	reserve X for TopSpace; reserve C for Subset of X; reserve A, B for Subset of X; reserve X for non empty TopSpace; theorem Th30: X is extremally_disconnected iff for A being Subset of X st A is open holds Cl A = Int Cl A proof thus X is extremally_disconnected implies for A being Subset of X st A is open holds Cl A = Int Cl A proof assume A1: X is extremally_disconnected; let A be Subset of X; A c= Cl A by PRE_TOPC:18; then A2: A misses (Cl A)` by SUBSET_1:24; assume A is open; then (Cl A) misses Cl (Cl A)` by A1,A2,Th28; then Cl A c= (Cl (Cl A)`)` by SUBSET_1:23; then A3: Cl A c= Int Cl A by TOPS_1:def 1; Int Cl A c= Cl A by TOPS_1:16; hence thesis by A3,XBOOLE_0:def 10; end; assume A4: for A being Subset of X st A is open holds Cl A = Int Cl A; now let A be Subset of X; assume A is open; then Cl A = Int Cl A by A4; hence Cl A is open; end; hence thesis by Def4; end;	Convert the following ATP output trace into a readable Mizar proof.
t2_dynkin	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t6_boole, axiom, ![X1]:(v1_xboole_0(X1)=>X1=k1_xboole_0), file('/scratch/mptp/predsminms1/t2_dynkin__0', t6_boole)). fof(cc1_finset_1, axiom, ![X1]:(v1_xboole_0(X1)=>v1_finset_1(X1)), file('/scratch/mptp/predsminms1/t2_dynkin__0', cc1_finset_1)). fof(rc4_xreal_0, axiom, ?[X1]:(v1_xboole_0(X1)&(v1_xcmplx_0(X1)&(v1_xxreal_0(X1)&v1_xreal_0(X1)))), file('/scratch/mptp/predsminms1/t2_dynkin__0', rc4_xreal_0)). fof(redefinition_k6_numbers, axiom, k6_numbers=k1_xboole_0, file('/scratch/mptp/predsminms1/t2_dynkin__0', redefinition_k6_numbers)). fof(s1_nat_1__e3_2__dynkin, axiom, ((v1_finset_1(k6_numbers)&![X1]:(m2_subset_1(X1,k1_numbers,k5_numbers)=>(v1_finset_1(X1)=>v1_finset_1(k2_nat_1(X1,np__1)))))=>![X1]:(m2_subset_1(X1,k1_numbers,k5_numbers)=>v1_finset_1(X1))), file('/scratch/mptp/predsminms1/t2_dynkin__0', s1_nat_1__e3_2__dynkin)). fof(redefinition_k2_nat_1, axiom, ![X1, X2]:((m1_subset_1(X1,k5_numbers)&v7_ordinal1(X2))=>k2_nat_1(X1,X2)=k2_xcmplx_0(X1,X2)), file('/scratch/mptp/predsminms1/t2_dynkin__0', redefinition_k2_nat_1)). fof(redefinition_k1_nat_1, axiom, ![X1, X2]:((v7_ordinal1(X1)&m1_subset_1(X2,k5_numbers))=>k1_nat_1(X1,X2)=k2_xcmplx_0(X1,X2)), file('/scratch/mptp/predsminms1/t2_dynkin__0', redefinition_k1_nat_1)). fof(cc8_ordinal1, axiom, ![X1]:(m1_subset_1(X1,k4_ordinal1)=>v7_ordinal1(X1)), file('/scratch/mptp/predsminms1/t2_dynkin__0', cc8_ordinal1)). fof(spc1_numerals, axiom, ((v2_xxreal_0(np__1)&m2_subset_1(np__1,k1_numbers,k5_numbers))&(m1_subset_1(np__1,k5_numbers)&m1_subset_1(np__1,k1_numbers))), file('/scratch/mptp/predsminms1/t2_dynkin__0', spc1_numerals)). fof(redefinition_k5_numbers, axiom, k5_numbers=k4_ordinal1, file('/scratch/mptp/predsminms1/t2_dynkin__0', redefinition_k5_numbers)). fof(redefinition_m2_subset_1, axiom, ![X1, X2]:((~(v1_xboole_0(X1))&(~(v1_xboole_0(X2))&m1_subset_1(X2,k1_zfmisc_1(X1))))=>![X3]:(m2_subset_1(X3,X1,X2)<=>m1_subset_1(X3,X2))), file('/scratch/mptp/predsminms1/t2_dynkin__0', redefinition_m2_subset_1)). fof(cc1_subset_1, axiom, ![X1]:(v1_xboole_0(X1)=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(X1))=>v1_xboole_0(X2))), file('/scratch/mptp/predsminms1/t2_dynkin__0', cc1_subset_1)). fof(fc6_ordinal1, axiom, (~(v1_xboole_0(k4_ordinal1))&v3_ordinal1(k4_ordinal1)), file('/scratch/mptp/predsminms1/t2_dynkin__0', fc6_ordinal1)). fof(t38_nat_1, axiom, ![X1]:(v7_ordinal1(X1)=>k4_card_1(X1)=k1_nat_1(X1,np__1)), file('/scratch/mptp/predsminms1/t2_dynkin__0', t38_nat_1)). fof(redefinition_k4_card_1, axiom, ![X1]:(v7_ordinal1(X1)=>k4_card_1(X1)=k1_ordinal1(X1)), file('/scratch/mptp/predsminms1/t2_dynkin__0', redefinition_k4_card_1)). fof(d1_ordinal1, axiom, ![X1]:k1_ordinal1(X1)=k2_xboole_0(X1,k1_tarski(X1)), file('/scratch/mptp/predsminms1/t2_dynkin__0', d1_ordinal1)). fof(fc9_finset_1, axiom, ![X1, X2]:((v1_finset_1(X1)&v1_finset_1(X2))=>v1_finset_1(k2_xboole_0(X1,X2))), file('/scratch/mptp/predsminms1/t2_dynkin__0', fc9_finset_1)). fof(fc1_finset_1, axiom, ![X1]:v1_finset_1(k1_tarski(X1)), file('/scratch/mptp/predsminms1/t2_dynkin__0', fc1_finset_1)). fof(dt_k5_numbers, axiom, m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)), file('/scratch/mptp/predsminms1/t2_dynkin__0', dt_k5_numbers)). fof(t2_dynkin, conjecture, ![X1]:(m1_subset_1(X1,k5_numbers)=>v1_finset_1(X1)), file('/scratch/mptp/predsminms1/t2_dynkin__0', t2_dynkin)). fof(c_0_20, plain, ![X7]:(~v1_xboole_0(X7)\|X7=k1_xboole_0), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])])). fof(c_0_21, plain, ![X5]:(~v1_xboole_0(X5)\|v1_finset_1(X5)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_finset_1])])). fof(c_0_22, plain, (v1_xboole_0(esk2_0)&(v1_xcmplx_0(esk2_0)&(v1_xxreal_0(esk2_0)&v1_xreal_0(esk2_0)))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc4_xreal_0])])). cnf(c_0_23, plain, (X1=k1_xboole_0\|~v1_xboole_0(X1)), inference(split_conjunct,[status(thm)],[c_0_20])). cnf(c_0_24, plain, (k6_numbers=k1_xboole_0), inference(split_conjunct,[status(thm)],[redefinition_k6_numbers])). fof(c_0_25, plain, ![X14]:((m2_subset_1(esk3_0,k1_numbers,k5_numbers)\|~v1_finset_1(k6_numbers)\|(~m2_subset_1(X14,k1_numbers,k5_numbers)\|v1_finset_1(X14)))&((v1_finset_1(esk3_0)\|~v1_finset_1(k6_numbers)\|(~m2_subset_1(X14,k1_numbers,k5_numbers)\|v1_finset_1(X14)))&(~v1_finset_1(k2_nat_1(esk3_0,np__1))\|~v1_finset_1(k6_numbers)\|(~m2_subset_1(X14,k1_numbers,k5_numbers)\|v1_finset_1(X14))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[s1_nat_1__e3_2__dynkin])])])])])). fof(c_0_26, plain, ![X19, X20]:(~m1_subset_1(X19,k5_numbers)\|~v7_ordinal1(X20)\|k2_nat_1(X19,X20)=k2_xcmplx_0(X19,X20)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k2_nat_1])])). cnf(c_0_27, plain, (v1_finset_1(X1)\|~v1_xboole_0(X1)), inference(split_conjunct,[status(thm)],[c_0_21])). cnf(c_0_28, plain, (v1_xboole_0(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_29, plain, (X1=k1_xboole_0\|~v1_xboole_0(X1)), inference(evalgc,[status(thm)],[c_0_23])). cnf(c_0_30, plain, (k1_xboole_0=k6_numbers), inference(evalgc,[status(thm)],[c_0_24])). cnf(c_0_31, plain, (v1_finset_1(X1)\|~v1_finset_1(k2_nat_1(esk3_0,np__1))\|~v1_finset_1(k6_numbers)\|~m2_subset_1(X1,k1_numbers,k5_numbers)), inference(split_conjunct,[status(thm)],[c_0_25])). cnf(c_0_32, plain, (k2_nat_1(X1,X2)=k2_xcmplx_0(X1,X2)\|~m1_subset_1(X1,k5_numbers)\|~v7_ordinal1(X2)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_33, plain, (v1_finset_1(X1)\|~v1_xboole_0(X1)), inference(evalgc,[status(thm)],[c_0_27])). cnf(c_0_34, plain, (v1_xboole_0(esk2_0)), inference(evalgc,[status(thm)],[c_0_28])). cnf(c_0_35, plain, (X1=k6_numbers\|~v1_xboole_0(X1)), inference(rw,[status(thm)],[c_0_29, c_0_30])). cnf(c_0_36, plain, (v1_finset_1(X1)\|~v1_finset_1(k6_numbers)\|~m2_subset_1(X1,k1_numbers,k5_numbers)\|~v1_finset_1(k2_nat_1(esk3_0,np__1))), inference(evalgc,[status(thm)],[c_0_31])). cnf(c_0_37, plain, (k2_nat_1(X1,X2)=k2_xcmplx_0(X1,X2)\|~v7_ordinal1(X2)\|~m1_subset_1(X1,k5_numbers)), inference(evalgc,[status(thm)],[c_0_32])). cnf(c_0_38, plain, (v1_finset_1(esk2_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_33, c_0_34])])). cnf(c_0_39, plain, (esk2_0=k6_numbers), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_35, c_0_34])])). fof(c_0_40, plain, ![X16, X17]:(~v7_ordinal1(X16)\|~m1_subset_1(X17,k5_numbers)\|k1_nat_1(X16,X17)=k2_xcmplx_0(X16,X17)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k1_nat_1])])). fof(c_0_41, plain, ![X15]:(~m1_subset_1(X15,k4_ordinal1)\|v7_ordinal1(X15)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc8_ordinal1])])). cnf(c_0_42, plain, (v1_finset_1(X1)\|~m2_subset_1(X1,k1_numbers,k5_numbers)\|~v1_finset_1(k2_xcmplx_0(esk3_0,np__1))\|~v1_finset_1(k6_numbers)\|~v7_ordinal1(np__1)\|~m1_subset_1(esk3_0,k5_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_36, c_0_37])])). cnf(c_0_43, plain, (v1_finset_1(k6_numbers)), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[c_0_38, c_0_39])])). cnf(c_0_44, plain, (k1_nat_1(X1,X2)=k2_xcmplx_0(X1,X2)\|~v7_ordinal1(X1)\|~m1_subset_1(X2,k5_numbers)), inference(split_conjunct,[status(thm)],[c_0_40])). cnf(c_0_45, plain, (m1_subset_1(np__1,k5_numbers)), inference(split_conjunct,[status(thm)],[spc1_numerals])). cnf(c_0_46, plain, (v7_ordinal1(X1)\|~m1_subset_1(X1,k4_ordinal1)), inference(split_conjunct,[status(thm)],[c_0_41])). cnf(c_0_47, plain, (k5_numbers=k4_ordinal1), inference(split_conjunct,[status(thm)],[redefinition_k5_numbers])). fof(c_0_48, plain, ![X8, X9, X10]:((~m2_subset_1(X10,X8,X9)\|m1_subset_1(X10,X9)\|(v1_xboole_0(X8)\|(v1_xboole_0(X9)\|~m1_subset_1(X9,k1_zfmisc_1(X8)))))&(~m1_subset_1(X10,X9)\|m2_subset_1(X10,X8,X9)\|(v1_xboole_0(X8)\|(v1_xboole_0(X9)\|~m1_subset_1(X9,k1_zfmisc_1(X8)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[redefinition_m2_subset_1])])])])])). fof(c_0_49, plain, ![X11, X12]:(~v1_xboole_0(X11)\|(~m1_subset_1(X12,k1_zfmisc_1(X11))\|v1_xboole_0(X12))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_subset_1])])])). fof(c_0_50, plain, (~v1_xboole_0(k4_ordinal1)&v3_ordinal1(k4_ordinal1)), inference(fof_simplification,[status(thm)],[fc6_ordinal1])). cnf(c_0_51, plain, (v1_finset_1(X1)\|~v7_ordinal1(np__1)\|~m2_subset_1(X1,k1_numbers,k5_numbers)\|~v1_finset_1(k2_xcmplx_0(esk3_0,np__1))\|~m1_subset_1(esk3_0,k5_numbers)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42, c_0_43])])])). cnf(c_0_52, plain, (k2_xcmplx_0(X1,X2)=k1_nat_1(X1,X2)\|~v7_ordinal1(X1)\|~m1_subset_1(X2,k5_numbers)), inference(evalgc,[status(thm)],[c_0_44])). cnf(c_0_53, plain, (m1_subset_1(np__1,k5_numbers)), inference(evalgc,[status(thm)],[c_0_45])). cnf(c_0_54, plain, (v7_ordinal1(X1)\|~m1_subset_1(X1,k4_ordinal1)), inference(evalgc,[status(thm)],[c_0_46])). cnf(c_0_55, plain, (k4_ordinal1=k5_numbers), inference(evalgc,[status(thm)],[c_0_47])). fof(c_0_56, plain, ![X18]:(~v7_ordinal1(X18)\|k4_card_1(X18)=k1_nat_1(X18,np__1)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t38_nat_1])])). fof(c_0_57, plain, ![X24]:(~v7_ordinal1(X24)\|k4_card_1(X24)=k1_ordinal1(X24)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k4_card_1])])). fof(c_0_58, plain, ![X25]:k1_ordinal1(X25)=k2_xboole_0(X25,k1_tarski(X25)), inference(variable_rename,[status(thm)],[d1_ordinal1])). cnf(c_0_59, plain, (m2_subset_1(X1,X3,X2)\|v1_xboole_0(X3)\|v1_xboole_0(X2)\|~m1_subset_1(X1,X2)\|~m1_subset_1(X2,k1_zfmisc_1(X3))), inference(split_conjunct,[status(thm)],[c_0_48])). cnf(c_0_60, plain, (v1_xboole_0(X2)\|~v1_xboole_0(X1)\|~m1_subset_1(X2,k1_zfmisc_1(X1))), inference(split_conjunct,[status(thm)],[c_0_49])). cnf(c_0_61, plain, (~v1_xboole_0(k4_ordinal1)), inference(split_conjunct,[status(thm)],[c_0_50])). cnf(c_0_62, plain, (v1_finset_1(X1)\|~v7_ordinal1(np__1)\|~m2_subset_1(X1,k1_numbers,k5_numbers)\|~v1_finset_1(k1_nat_1(esk3_0,np__1))\|~m1_subset_1(esk3_0,k5_numbers)\|~v7_ordinal1(esk3_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51, c_0_52]), c_0_53])])])). cnf(c_0_63, plain, (v7_ordinal1(X1)\|~m1_subset_1(X1,k5_numbers)), inference(rw,[status(thm)],[c_0_54, c_0_55])). cnf(c_0_64, plain, (k4_card_1(X1)=k1_nat_1(X1,np__1)\|~v7_ordinal1(X1)), inference(split_conjunct,[status(thm)],[c_0_56])). fof(c_0_65, plain, ![X21, X22]:(~v1_finset_1(X21)\|~v1_finset_1(X22)\|v1_finset_1(k2_xboole_0(X21,X22))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc9_finset_1])])). cnf(c_0_66, plain, (k4_card_1(X1)=k1_ordinal1(X1)\|~v7_ordinal1(X1)), inference(split_conjunct,[status(thm)],[c_0_57])). cnf(c_0_67, plain, (k1_ordinal1(X1)=k2_xboole_0(X1,k1_tarski(X1))), inference(split_conjunct,[status(thm)],[c_0_58])). fof(c_0_68, plain, ![X23]:v1_finset_1(k1_tarski(X23)), inference(variable_rename,[status(thm)],[fc1_finset_1])). cnf(c_0_69, plain, (v1_finset_1(esk3_0)\|v1_finset_1(X1)\|~v1_finset_1(k6_numbers)\|~m2_subset_1(X1,k1_numbers,k5_numbers)), inference(split_conjunct,[status(thm)],[c_0_25])). cnf(c_0_70, plain, (v1_xboole_0(X3)\|v1_xboole_0(X2)\|m2_subset_1(X1,X3,X2)\|~m1_subset_1(X1,X2)\|~m1_subset_1(X2,k1_zfmisc_1(X3))), inference(evalgc,[status(thm)],[c_0_59])). cnf(c_0_71, plain, (v1_xboole_0(X2)\|~v1_xboole_0(X1)\|~m1_subset_1(X2,k1_zfmisc_1(X1))), inference(evalgc,[status(thm)],[c_0_60])). cnf(c_0_72, plain, (m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers))), inference(split_conjunct,[status(thm)],[dt_k5_numbers])). cnf(c_0_73, plain, (~v1_xboole_0(k4_ordinal1)), inference(evalgc,[status(thm)],[c_0_61])). fof(c_0_74, negated_conjecture, ~(![X1]:(m1_subset_1(X1,k5_numbers)=>v1_finset_1(X1))), inference(assume_negation,[status(cth)],[t2_dynkin])). cnf(c_0_75, plain, (m2_subset_1(esk3_0,k1_numbers,k5_numbers)\|v1_finset_1(X1)\|~v1_finset_1(k6_numbers)\|~m2_subset_1(X1,k1_numbers,k5_numbers)), inference(split_conjunct,[status(thm)],[c_0_25])). cnf(c_0_76, plain, (v1_finset_1(X1)\|~v7_ordinal1(np__1)\|~m2_subset_1(X1,k1_numbers,k5_numbers)\|~v1_finset_1(k1_nat_1(esk3_0,np__1))\|~m1_subset_1(esk3_0,k5_numbers)), inference(csr,[status(thm)],[c_0_62, c_0_63])). cnf(c_0_77, plain, (k1_nat_1(X1,np__1)=k4_card_1(X1)\|~v7_ordinal1(X1)), inference(evalgc,[status(thm)],[c_0_64])). cnf(c_0_78, plain, (v1_finset_1(k2_xboole_0(X1,X2))\|~v1_finset_1(X1)\|~v1_finset_1(X2)), inference(split_conjunct,[status(thm)],[c_0_65])). cnf(c_0_79, plain, (k2_xboole_0(X1,k1_tarski(X1))=k4_card_1(X1)\|~v7_ordinal1(X1)), inference(rw,[status(thm)],[c_0_66, c_0_67])). cnf(c_0_80, plain, (v1_finset_1(k1_tarski(X1))), inference(split_conjunct,[status(thm)],[c_0_68])). cnf(c_0_81, plain, (v1_finset_1(X1)\|v1_finset_1(esk3_0)\|~v1_finset_1(k6_numbers)\|~m2_subset_1(X1,k1_numbers,k5_numbers)), inference(evalgc,[status(thm)],[c_0_69])). cnf(c_0_82, plain, (m2_subset_1(X1,X2,X3)\|v1_xboole_0(X3)\|~m1_subset_1(X3,k1_zfmisc_1(X2))\|~m1_subset_1(X1,X3)), inference(csr,[status(thm)],[c_0_70, c_0_71])). cnf(c_0_83, plain, (m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers))), inference(evalgc,[status(thm)],[c_0_72])). cnf(c_0_84, plain, (~v1_xboole_0(k5_numbers)), inference(rw,[status(thm)],[c_0_73, c_0_55])). fof(c_0_85, negated_conjecture, (m1_subset_1(esk1_0,k5_numbers)&~v1_finset_1(esk1_0)), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_74])])])). cnf(c_0_86, plain, (m1_subset_1(X1,X3)\|v1_xboole_0(X2)\|v1_xboole_0(X3)\|~m2_subset_1(X1,X2,X3)\|~m1_subset_1(X3,k1_zfmisc_1(X2))), inference(split_conjunct,[status(thm)],[c_0_48])). cnf(c_0_87, plain, (v1_finset_1(X1)\|m2_subset_1(esk3_0,k1_numbers,k5_numbers)\|~v1_finset_1(k6_numbers)\|~m2_subset_1(X1,k1_numbers,k5_numbers)), inference(evalgc,[status(thm)],[c_0_75])). cnf(c_0_88, plain, (v1_finset_1(X1)\|~v7_ordinal1(np__1)\|~m2_subset_1(X1,k1_numbers,k5_numbers)\|~v1_finset_1(k4_card_1(esk3_0))\|~m1_subset_1(esk3_0,k5_numbers)\|~v7_ordinal1(esk3_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_76, c_0_77])])). cnf(c_0_89, plain, (v1_finset_1(k2_xboole_0(X1,X2))\|~v1_finset_1(X2)\|~v1_finset_1(X1)), inference(evalgc,[status(thm)],[c_0_78])). cnf(c_0_90, plain, (k2_xboole_0(X1,k1_tarski(X1))=k4_card_1(X1)\|~v7_ordinal1(X1)), inference(evalgc,[status(thm)],[c_0_79])). cnf(c_0_91, plain, (v1_finset_1(k1_tarski(X1))), inference(evalgc,[status(thm)],[c_0_80])). cnf(c_0_92, plain, (v1_finset_1(esk3_0)\|v1_finset_1(X1)\|~m2_subset_1(X1,k1_numbers,k5_numbers)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_81, c_0_43])])])). cnf(c_0_93, plain, (m2_subset_1(X1,k1_numbers,k5_numbers)\|~m1_subset_1(X1,k5_numbers)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_82, c_0_83]), c_0_84])])). cnf(c_0_94, negated_conjecture, (m1_subset_1(esk1_0,k5_numbers)), inference(split_conjunct,[status(thm)],[c_0_85])). cnf(c_0_95, negated_conjecture, (~v1_finset_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_85])). cnf(c_0_96, plain, (v1_xboole_0(X3)\|v1_xboole_0(X2)\|m1_subset_1(X1,X3)\|~m2_subset_1(X1,X2,X3)\|~m1_subset_1(X3,k1_zfmisc_1(X2))), inference(evalgc,[status(thm)],[c_0_86])). cnf(c_0_97, plain, (m2_subset_1(esk3_0,k1_numbers,k5_numbers)\|v1_finset_1(X1)\|~m2_subset_1(X1,k1_numbers,k5_numbers)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_87, c_0_43])])])). cnf(c_0_98, plain, (v1_finset_1(X1)\|~v7_ordinal1(np__1)\|~m2_subset_1(X1,k1_numbers,k5_numbers)\|~v1_finset_1(k4_card_1(esk3_0))\|~m1_subset_1(esk3_0,k5_numbers)), inference(csr,[status(thm)],[c_0_88, c_0_63])). cnf(c_0_99, plain, (v1_finset_1(k4_card_1(X1))\|~v1_finset_1(X1)\|~v7_ordinal1(X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89, c_0_90]), c_0_91])])])). cnf(c_0_100, plain, (v1_finset_1(esk3_0)\|v1_finset_1(X1)\|~m1_subset_1(X1,k5_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_92, c_0_93])])). cnf(c_0_101, negated_conjecture, (m1_subset_1(esk1_0,k5_numbers)), inference(evalgc,[status(thm)],[c_0_94])). cnf(c_0_102, negated_conjecture, (~v1_finset_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_95])). cnf(c_0_103, plain, (v1_xboole_0(X1)\|m1_subset_1(X2,X1)\|~m2_subset_1(X2,X3,X1)\|~m1_subset_1(X1,k1_zfmisc_1(X3))), inference(csr,[status(thm)],[c_0_96, c_0_71])). cnf(c_0_104, plain, (m2_subset_1(esk3_0,k1_numbers,k5_numbers)\|v1_finset_1(X1)\|~m1_subset_1(X1,k5_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_97, c_0_93])])). cnf(c_0_105, plain, (v1_finset_1(X1)\|~v7_ordinal1(np__1)\|~m2_subset_1(X1,k1_numbers,k5_numbers)\|~m1_subset_1(esk3_0,k5_numbers)\|~v7_ordinal1(esk3_0)\|~v1_finset_1(esk3_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_98, c_0_99])])). cnf(c_0_106, negated_conjecture, (v1_finset_1(esk3_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_100, c_0_101]), c_0_102])])). cnf(c_0_107, plain, (m1_subset_1(X1,k5_numbers)\|~m2_subset_1(X1,k1_numbers,k5_numbers)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_103, c_0_83]), c_0_84])])). cnf(c_0_108, negated_conjecture, (m2_subset_1(esk3_0,k1_numbers,k5_numbers)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_104, c_0_101]), c_0_102])])). cnf(c_0_109, plain, (v1_finset_1(X1)\|~v7_ordinal1(np__1)\|~m2_subset_1(X1,k1_numbers,k5_numbers)\|~m1_subset_1(esk3_0,k5_numbers)), inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_105, c_0_106])]), c_0_63])). cnf(c_0_110, negated_conjecture, (m1_subset_1(esk3_0,k5_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_107, c_0_108])])). cnf(c_0_111, plain, (v1_finset_1(X1)\|~v7_ordinal1(np__1)\|~m2_subset_1(X1,k1_numbers,k5_numbers)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_109, c_0_110])])])). cnf(c_0_112, plain, (v1_finset_1(X1)\|~m2_subset_1(X1,k1_numbers,k5_numbers)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111, c_0_63]), c_0_53])])])). cnf(c_0_113, plain, (v1_finset_1(X1)\|~m1_subset_1(X1,k5_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_112, c_0_93])])). cnf(c_0_114, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_113, c_0_101]), c_0_102]), ['proof']). # SZS output end CNFRefutation	reserve Omega, F for non empty set, f for SetSequence of Omega, X,A,B for Subset of Omega, D for non empty Subset-Family of Omega, n,m for Element of NAT, h,x,y,z,u,v,Y,I for set; theorem Th2: for n holds n is finite proof defpred P[Element of NAT] means $1 is finite; A1: for n st P[n] holds P[n+1] proof let n; assume P[n]; then succ n is finite; hence thesis by NAT_1:38; end; A2: P[0]; thus for n holds P[n] from NAT_1:sch 1(A2,A1); end;	Convert the following ATP output trace into a readable Mizar proof.
t59_convex4	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t6_boole, axiom, ![X1]:(v1_xboole_0(X1)=>X1=k1_xboole_0), file('/scratch/mptp/predsminms1/t59_convex4__0', t6_boole)). fof(rc2_subset_1, axiom, ![X1]:?[X2]:(m1_subset_1(X2,k1_zfmisc_1(X1))&v1_xboole_0(X2)), file('/scratch/mptp/predsminms1/t59_convex4__0', rc2_subset_1)). fof(t5_subset, axiom, ![X1, X2, X3]:~((r2_hidden(X1,X2)&(m1_subset_1(X2,k1_zfmisc_1(X3))&v1_xboole_0(X3)))), file('/scratch/mptp/predsminms1/t59_convex4__0', t5_subset)). fof(t59_convex4, conjecture, ![X1]:((~(v2_struct_0(X1))&l1_clvect_1(X1))=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))=>(X2=k1_xboole_0=>v2_convex4(X2,X1)))), file('/scratch/mptp/predsminms1/t59_convex4__0', t59_convex4)). fof(d23_convex4, axiom, ![X1]:((~(v2_struct_0(X1))&l1_clvect_1(X1))=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))=>(v2_convex4(X2,X1)<=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>![X4]:(m1_subset_1(X4,u1_struct_0(X1))=>![X5]:(v1_xcmplx_0(X5)=>((r2_hidden(X3,X2)&r2_hidden(X4,X2))=>(![X6]:(m1_subset_1(X6,k1_numbers)=>~((X5=X6&(~(r1_xxreal_0(X6,k1_xboole_0))&~(r1_xxreal_0(np__1,X6))))))\|r2_hidden(k1_algstr_0(X1,k1_clvect_1(X1,X3,X5),k1_clvect_1(X1,X4,k6_xcmplx_0(k6_complex1,X5))),X2))))))))), file('/scratch/mptp/predsminms1/t59_convex4__0', d23_convex4)). fof(c_0_5, plain, ![X19]:(~v1_xboole_0(X19)\|X19=k1_xboole_0), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])])). fof(c_0_6, plain, ![X20]:(m1_subset_1(esk7_1(X20),k1_zfmisc_1(X20))&v1_xboole_0(esk7_1(X20))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_subset_1])])). cnf(c_0_7, plain, (X1=k1_xboole_0\|~v1_xboole_0(X1)), inference(split_conjunct,[status(thm)],[c_0_5])). cnf(c_0_8, plain, (v1_xboole_0(esk7_1(X1))), inference(split_conjunct,[status(thm)],[c_0_6])). fof(c_0_9, plain, ![X22, X23, X24]:(~r2_hidden(X22,X23)\|(~m1_subset_1(X23,k1_zfmisc_1(X24))\|~v1_xboole_0(X24))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])])). cnf(c_0_10, plain, (m1_subset_1(esk7_1(X1),k1_zfmisc_1(X1))), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_11, plain, (X1=k1_xboole_0\|~v1_xboole_0(X1)), inference(evalgc,[status(thm)],[c_0_7])). cnf(c_0_12, plain, (v1_xboole_0(esk7_1(X1))), inference(evalgc,[status(thm)],[c_0_8])). fof(c_0_13, negated_conjecture, ~(![X1]:((~(v2_struct_0(X1))&l1_clvect_1(X1))=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))=>(X2=k1_xboole_0=>v2_convex4(X2,X1))))), inference(assume_negation,[status(cth)],[t59_convex4])). cnf(c_0_14, plain, (~r2_hidden(X1,X2)\|~m1_subset_1(X2,k1_zfmisc_1(X3))\|~v1_xboole_0(X3)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_15, plain, (m1_subset_1(esk7_1(X1),k1_zfmisc_1(X1))), inference(evalgc,[status(thm)],[c_0_10])). cnf(c_0_16, plain, (esk7_1(X1)=k1_xboole_0), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_11, c_0_12])])). fof(c_0_17, plain, ![X9, X10, X11, X12, X13, X14]:((~v2_convex4(X10,X9)\|(~m1_subset_1(X11,u1_struct_0(X9))\|(~m1_subset_1(X12,u1_struct_0(X9))\|(~v1_xcmplx_0(X13)\|(~r2_hidden(X11,X10)\|~r2_hidden(X12,X10)\|(~m1_subset_1(X14,k1_numbers)\|(X13!=X14\|(r1_xxreal_0(X14,k1_xboole_0)\|r1_xxreal_0(np__1,X14)))\|r2_hidden(k1_algstr_0(X9,k1_clvect_1(X9,X11,X13),k1_clvect_1(X9,X12,k6_xcmplx_0(k6_complex1,X13))),X10))))))\|~m1_subset_1(X10,k1_zfmisc_1(u1_struct_0(X9)))\|(v2_struct_0(X9)\|~l1_clvect_1(X9)))&((m1_subset_1(esk3_2(X9,X10),u1_struct_0(X9))\|v2_convex4(X10,X9)\|~m1_subset_1(X10,k1_zfmisc_1(u1_struct_0(X9)))\|(v2_struct_0(X9)\|~l1_clvect_1(X9)))&((m1_subset_1(esk4_2(X9,X10),u1_struct_0(X9))\|v2_convex4(X10,X9)\|~m1_subset_1(X10,k1_zfmisc_1(u1_struct_0(X9)))\|(v2_struct_0(X9)\|~l1_clvect_1(X9)))&((v1_xcmplx_0(esk5_2(X9,X10))\|v2_convex4(X10,X9)\|~m1_subset_1(X10,k1_zfmisc_1(u1_struct_0(X9)))\|(v2_struct_0(X9)\|~l1_clvect_1(X9)))&(((r2_hidden(esk3_2(X9,X10),X10)\|v2_convex4(X10,X9)\|~m1_subset_1(X10,k1_zfmisc_1(u1_struct_0(X9)))\|(v2_struct_0(X9)\|~l1_clvect_1(X9)))&(r2_hidden(esk4_2(X9,X10),X10)\|v2_convex4(X10,X9)\|~m1_subset_1(X10,k1_zfmisc_1(u1_struct_0(X9)))\|(v2_struct_0(X9)\|~l1_clvect_1(X9))))&(((m1_subset_1(esk6_2(X9,X10),k1_numbers)\|v2_convex4(X10,X9)\|~m1_subset_1(X10,k1_zfmisc_1(u1_struct_0(X9)))\|(v2_struct_0(X9)\|~l1_clvect_1(X9)))&((esk5_2(X9,X10)=esk6_2(X9,X10)\|v2_convex4(X10,X9)\|~m1_subset_1(X10,k1_zfmisc_1(u1_struct_0(X9)))\|(v2_struct_0(X9)\|~l1_clvect_1(X9)))&((~r1_xxreal_0(esk6_2(X9,X10),k1_xboole_0)\|v2_convex4(X10,X9)\|~m1_subset_1(X10,k1_zfmisc_1(u1_struct_0(X9)))\|(v2_struct_0(X9)\|~l1_clvect_1(X9)))&(~r1_xxreal_0(np__1,esk6_2(X9,X10))\|v2_convex4(X10,X9)\|~m1_subset_1(X10,k1_zfmisc_1(u1_struct_0(X9)))\|(v2_struct_0(X9)\|~l1_clvect_1(X9))))))&(~r2_hidden(k1_algstr_0(X9,k1_clvect_1(X9,esk3_2(X9,X10),esk5_2(X9,X10)),k1_clvect_1(X9,esk4_2(X9,X10),k6_xcmplx_0(k6_complex1,esk5_2(X9,X10)))),X10)\|v2_convex4(X10,X9)\|~m1_subset_1(X10,k1_zfmisc_1(u1_struct_0(X9)))\|(v2_struct_0(X9)\|~l1_clvect_1(X9))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d23_convex4])])])])])])). fof(c_0_18, negated_conjecture, ((~v2_struct_0(esk1_0)&l1_clvect_1(esk1_0))&(m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(esk1_0)))&(esk2_0=k1_xboole_0&~v2_convex4(esk2_0,esk1_0)))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_13])])])])). cnf(c_0_19, plain, (~v1_xboole_0(X3)\|~r2_hidden(X1,X2)\|~m1_subset_1(X2,k1_zfmisc_1(X3))), inference(evalgc,[status(thm)],[c_0_14])). cnf(c_0_20, plain, (m1_subset_1(k1_xboole_0,k1_zfmisc_1(X1))), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[c_0_15, c_0_16])])). cnf(c_0_21, plain, (r2_hidden(esk4_2(X1,X2),X2)\|v2_convex4(X2,X1)\|v2_struct_0(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~l1_clvect_1(X1)), inference(split_conjunct,[status(thm)],[c_0_17])). cnf(c_0_22, negated_conjecture, (~v2_convex4(esk2_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_18])). cnf(c_0_23, negated_conjecture, (esk2_0=k1_xboole_0), inference(split_conjunct,[status(thm)],[c_0_18])). cnf(c_0_24, plain, (~v1_xboole_0(X1)\|~r2_hidden(X2,k1_xboole_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_19, c_0_20])])). cnf(c_0_25, plain, (v2_struct_0(X1)\|v2_convex4(X2,X1)\|r2_hidden(esk4_2(X1,X2),X2)\|~l1_clvect_1(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(evalgc,[status(thm)],[c_0_21])). cnf(c_0_26, negated_conjecture, (~v2_convex4(esk2_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_22])). cnf(c_0_27, negated_conjecture, (esk2_0=k1_xboole_0), inference(evalgc,[status(thm)],[c_0_23])). cnf(c_0_28, plain, (v2_convex4(k1_xboole_0,X2)\|v2_struct_0(X2)\|~v1_xboole_0(X1)\|~l1_clvect_1(X2)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24, c_0_25]), c_0_20])])])). cnf(c_0_29, plain, (v1_xboole_0(k1_xboole_0)), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[c_0_12, c_0_16])])). cnf(c_0_30, negated_conjecture, (l1_clvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_18])). cnf(c_0_31, negated_conjecture, (~v2_struct_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_18])). cnf(c_0_32, negated_conjecture, (~v2_convex4(k1_xboole_0,esk1_0)), inference(rw,[status(thm)],[c_0_26, c_0_27])). cnf(c_0_33, plain, (v2_convex4(k1_xboole_0,X1)\|v2_struct_0(X1)\|~l1_clvect_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_28, c_0_29])])). cnf(c_0_34, negated_conjecture, (l1_clvect_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_30])). cnf(c_0_35, negated_conjecture, (~v2_struct_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_31])). cnf(c_0_36, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32, c_0_33]), c_0_34])]), c_0_35]), ['proof']). # SZS output end CNFRefutation	reserve x,y for set, i for Nat; reserve V for non empty CLSStruct, u,v,v1,v2,v3 for VECTOR of V, A for Subset of V, l, l1, l2 for C_Linear_Combination of A, x,y,y1,y2 for set, a,b for Complex, F for FinSequence of the carrier of V, f for Function of the carrier of V, COMPLEX; reserve K,L,L1,L2,L3 for C_Linear_Combination of V; reserve e,e1,e2 for Element of C_LinComb V; theorem Th59: for V being non empty CLSStruct, M being Subset of V st M = {} holds M is convex proof let V be non empty CLSStruct; let M be Subset of V; A1: for u,v being VECTOR of V, z be Complex st (ex r be Real st z=r & 0 < r & r < 1) & u in {} & v in {} holds zu + (1r-z)v in {}; assume M = {}; hence thesis by A1,Def23; end;	Convert the following ATP output trace into a readable Mizar proof.
t55_borsuk_6	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t7_mcart_1, axiom, ![X1, X2]:(k1_xtuple_0(k4_tarski(X1,X2))=X1&k2_xtuple_0(k4_tarski(X1,X2))=X2), file('/scratch/mptp/predsminms1/t55_borsuk_6__0', t7_mcart_1)). fof(d5_tarski, axiom, ![X1, X2]:k4_tarski(X1,X2)=k2_tarski(k2_tarski(X1,X2),k1_tarski(X1)), file('/scratch/mptp/predsminms1/t55_borsuk_6__0', d5_tarski)). fof(redefinition_k4_borsuk_1, axiom, ![X1, X2, X3, X4]:(((~(v2_struct_0(X1))&(v2_pre_topc(X1)&l1_pre_topc(X1)))&((~(v2_struct_0(X2))&(v2_pre_topc(X2)&l1_pre_topc(X2)))&(m1_subset_1(X3,u1_struct_0(X1))&m1_subset_1(X4,u1_struct_0(X2)))))=>k4_borsuk_1(X1,X2,X3,X4)=k4_tarski(X3,X4)), file('/scratch/mptp/predsminms1/t55_borsuk_6__0', redefinition_k4_borsuk_1)). fof(fraenkel_a_0_14_borsuk_6, axiom, ![X1]:(r2_hidden(X1,a_0_14_borsuk_6)<=>?[X2]:(m1_subset_1(X2,u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr)))&(X1=X2&r1_xxreal_0(k2_xtuple_0(X2),k9_real_1(k8_real_1(np__2,k1_xtuple_0(X2)),np__1))))), file('/scratch/mptp/predsminms1/t55_borsuk_6__0', fraenkel_a_0_14_borsuk_6)). fof(d10_borsuk_6, axiom, ![X1]:(m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr))))=>(X1=k8_borsuk_6<=>![X2]:(r2_hidden(X2,X1)<=>?[X3]:(m1_subset_1(X3,u1_struct_0(k5_topmetr))&?[X4]:(m1_subset_1(X4,u1_struct_0(k5_topmetr))&(X2=k4_borsuk_1(k5_topmetr,k5_topmetr,X3,X4)&r1_xxreal_0(X4,k9_real_1(k8_real_1(np__2,X3),np__1)))))))), file('/scratch/mptp/predsminms1/t55_borsuk_6__0', d10_borsuk_6)). fof(fc9_borsuk_1, axiom, (~(v2_struct_0(k17_borsuk_1))&(v1_pre_topc(k17_borsuk_1)&v2_pre_topc(k17_borsuk_1))), file('/scratch/mptp/predsminms1/t55_borsuk_6__0', fc9_borsuk_1)). fof(t21_mcart_1, axiom, ![X1, X2]:(v1_relat_1(X2)=>(r2_hidden(X1,X2)=>X1=k4_tarski(k1_xtuple_0(X1),k2_xtuple_0(X1)))), file('/scratch/mptp/predsminms1/t55_borsuk_6__0', t21_mcart_1)). fof(dt_k8_borsuk_6, axiom, m1_subset_1(k8_borsuk_6,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr)))), file('/scratch/mptp/predsminms1/t55_borsuk_6__0', dt_k8_borsuk_6)). fof(t27_borsuk_6, axiom, ![X1]:((~(v2_struct_0(X1))&(v2_pre_topc(X1)&l1_pre_topc(X1)))=>![X2]:((~(v2_struct_0(X2))&(v2_pre_topc(X2)&l1_pre_topc(X2)))=>![X3]:(m1_subset_1(X3,u1_struct_0(k2_borsuk_1(X1,X2)))=>(m1_subset_1(k1_xtuple_0(X3),u1_struct_0(X1))&m1_subset_1(k2_xtuple_0(X3),u1_struct_0(X2)))))), file('/scratch/mptp/predsminms1/t55_borsuk_6__0', t27_borsuk_6)). fof(dt_k17_borsuk_1, axiom, l1_pre_topc(k17_borsuk_1), file('/scratch/mptp/predsminms1/t55_borsuk_6__0', dt_k17_borsuk_1)). fof(redefinition_k5_topmetr, axiom, k5_topmetr=k17_borsuk_1, file('/scratch/mptp/predsminms1/t55_borsuk_6__0', redefinition_k5_topmetr)). fof(commutativity_k2_tarski, axiom, ![X1, X2]:k2_tarski(X1,X2)=k2_tarski(X2,X1), file('/scratch/mptp/predsminms1/t55_borsuk_6__0', commutativity_k2_tarski)). fof(d2_borsuk_1, axiom, ![X1]:((v2_pre_topc(X1)&l1_pre_topc(X1))=>![X2]:((v2_pre_topc(X2)&l1_pre_topc(X2))=>![X3]:((v1_pre_topc(X3)&(v2_pre_topc(X3)&l1_pre_topc(X3)))=>(X3=k2_borsuk_1(X1,X2)<=>(u1_struct_0(X3)=k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X2))&u1_pre_topc(X3)=a_3_0_borsuk_1(X1,X2,X3)))))), file('/scratch/mptp/predsminms1/t55_borsuk_6__0', d2_borsuk_1)). fof(t2_subset, axiom, ![X1, X2]:(m1_subset_1(X1,X2)=>(v1_xboole_0(X2)\|r2_hidden(X1,X2))), file('/scratch/mptp/predsminms1/t55_borsuk_6__0', t2_subset)). fof(d3_tarski, axiom, ![X1, X2]:(r1_tarski(X1,X2)<=>![X3]:(r2_hidden(X3,X1)=>r2_hidden(X3,X2))), file('/scratch/mptp/predsminms1/t55_borsuk_6__0', d3_tarski)). fof(t4_subset, axiom, ![X1, X2, X3]:((r2_hidden(X1,X2)&m1_subset_1(X2,k1_zfmisc_1(X3)))=>m1_subset_1(X1,X3)), file('/scratch/mptp/predsminms1/t55_borsuk_6__0', t4_subset)). fof(dt_k2_borsuk_1, axiom, ![X1, X2]:(((v2_pre_topc(X1)&l1_pre_topc(X1))&(v2_pre_topc(X2)&l1_pre_topc(X2)))=>(v1_pre_topc(k2_borsuk_1(X1,X2))&(v2_pre_topc(k2_borsuk_1(X1,X2))&l1_pre_topc(k2_borsuk_1(X1,X2))))), file('/scratch/mptp/predsminms1/t55_borsuk_6__0', dt_k2_borsuk_1)). fof(fc10_subset_1, axiom, ![X1, X2]:((~(v1_xboole_0(X1))&~(v1_xboole_0(X2)))=>~(v1_xboole_0(k2_zfmisc_1(X1,X2)))), file('/scratch/mptp/predsminms1/t55_borsuk_6__0', fc10_subset_1)). fof(t55_borsuk_6, conjecture, k8_borsuk_6=a_0_14_borsuk_6, file('/scratch/mptp/predsminms1/t55_borsuk_6__0', t55_borsuk_6)). fof(cc1_relset_1, axiom, ![X1, X2, X3]:(m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))=>v1_relat_1(X3)), file('/scratch/mptp/predsminms1/t55_borsuk_6__0', cc1_relset_1)). fof(t3_subset, axiom, ![X1, X2]:(m1_subset_1(X1,k1_zfmisc_1(X2))<=>r1_tarski(X1,X2)), file('/scratch/mptp/predsminms1/t55_borsuk_6__0', t3_subset)). fof(d10_xboole_0, axiom, ![X1, X2]:(X1=X2<=>(r1_tarski(X1,X2)&r1_tarski(X2,X1))), file('/scratch/mptp/predsminms1/t55_borsuk_6__0', d10_xboole_0)). fof(fc2_struct_0, axiom, ![X1]:((~(v2_struct_0(X1))&l1_struct_0(X1))=>~(v1_xboole_0(u1_struct_0(X1)))), file('/scratch/mptp/predsminms1/t55_borsuk_6__0', fc2_struct_0)). fof(dt_l1_pre_topc, axiom, ![X1]:(l1_pre_topc(X1)=>l1_struct_0(X1)), file('/scratch/mptp/predsminms1/t55_borsuk_6__0', dt_l1_pre_topc)). fof(c_0_24, plain, ![X9, X10]:(k1_xtuple_0(k4_tarski(X9,X10))=X9&k2_xtuple_0(k4_tarski(X9,X10))=X10), inference(variable_rename,[status(thm)],[t7_mcart_1])). fof(c_0_25, plain, ![X11, X12]:k4_tarski(X11,X12)=k2_tarski(k2_tarski(X11,X12),k1_tarski(X11)), inference(variable_rename,[status(thm)],[d5_tarski])). fof(c_0_26, plain, ![X13, X14, X15, X16]:(v2_struct_0(X13)\|(~v2_pre_topc(X13)\|~l1_pre_topc(X13))\|(v2_struct_0(X14)\|(~v2_pre_topc(X14)\|~l1_pre_topc(X14))\|(~m1_subset_1(X15,u1_struct_0(X13))\|~m1_subset_1(X16,u1_struct_0(X14))))\|k4_borsuk_1(X13,X14,X15,X16)=k4_tarski(X15,X16)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[redefinition_k4_borsuk_1])])])). fof(c_0_27, plain, ![X5, X7, X8]:(((m1_subset_1(esk1_1(X5),u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr)))\|~r2_hidden(X5,a_0_14_borsuk_6))&((X5=esk1_1(X5)\|~r2_hidden(X5,a_0_14_borsuk_6))&(r1_xxreal_0(k2_xtuple_0(esk1_1(X5)),k9_real_1(k8_real_1(np__2,k1_xtuple_0(esk1_1(X5))),np__1))\|~r2_hidden(X5,a_0_14_borsuk_6))))&(~m1_subset_1(X8,u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr)))\|(X7!=X8\|~r1_xxreal_0(k2_xtuple_0(X8),k9_real_1(k8_real_1(np__2,k1_xtuple_0(X8)),np__1)))\|r2_hidden(X7,a_0_14_borsuk_6))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fraenkel_a_0_14_borsuk_6])])])])])])). cnf(c_0_28, plain, (k2_xtuple_0(k4_tarski(X1,X2))=X2), inference(split_conjunct,[status(thm)],[c_0_24])). cnf(c_0_29, plain, (k4_tarski(X1,X2)=k2_tarski(k2_tarski(X1,X2),k1_tarski(X1))), inference(split_conjunct,[status(thm)],[c_0_25])). cnf(c_0_30, plain, (v2_struct_0(X1)\|v2_struct_0(X2)\|k4_borsuk_1(X1,X2,X3,X4)=k4_tarski(X3,X4)\|~v2_pre_topc(X1)\|~l1_pre_topc(X1)\|~v2_pre_topc(X2)\|~l1_pre_topc(X2)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X4,u1_struct_0(X2))), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_31, plain, (r2_hidden(X2,a_0_14_borsuk_6)\|~m1_subset_1(X1,u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr)))\|X2!=X1\|~r1_xxreal_0(k2_xtuple_0(X1),k9_real_1(k8_real_1(np__2,k1_xtuple_0(X1)),np__1))), inference(split_conjunct,[status(thm)],[c_0_27])). cnf(c_0_32, plain, (k2_xtuple_0(k2_tarski(k2_tarski(X1,X2),k1_tarski(X1)))=X2), inference(rw,[status(thm)],[c_0_28, c_0_29])). cnf(c_0_33, plain, (k4_borsuk_1(X1,X2,X3,X4)=k2_tarski(k2_tarski(X3,X4),k1_tarski(X3))\|v2_struct_0(X2)\|v2_struct_0(X1)\|~v2_pre_topc(X2)\|~v2_pre_topc(X1)\|~l1_pre_topc(X2)\|~l1_pre_topc(X1)\|~m1_subset_1(X4,u1_struct_0(X2))\|~m1_subset_1(X3,u1_struct_0(X1))), inference(rw,[status(thm)],[c_0_30, c_0_29])). cnf(c_0_34, plain, (k1_xtuple_0(k4_tarski(X1,X2))=X1), inference(split_conjunct,[status(thm)],[c_0_24])). fof(c_0_35, plain, ![X17, X18, X21, X22, X23, X25, X26]:((((m1_subset_1(esk2_2(X17,X18),u1_struct_0(k5_topmetr))\|~r2_hidden(X18,X17)\|X17!=k8_borsuk_6\|~m1_subset_1(X17,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr)))))&((m1_subset_1(esk3_2(X17,X18),u1_struct_0(k5_topmetr))\|~r2_hidden(X18,X17)\|X17!=k8_borsuk_6\|~m1_subset_1(X17,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr)))))&((X18=k4_borsuk_1(k5_topmetr,k5_topmetr,esk2_2(X17,X18),esk3_2(X17,X18))\|~r2_hidden(X18,X17)\|X17!=k8_borsuk_6\|~m1_subset_1(X17,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr)))))&(r1_xxreal_0(esk3_2(X17,X18),k9_real_1(k8_real_1(np__2,esk2_2(X17,X18)),np__1))\|~r2_hidden(X18,X17)\|X17!=k8_borsuk_6\|~m1_subset_1(X17,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr))))))))&(~m1_subset_1(X22,u1_struct_0(k5_topmetr))\|(~m1_subset_1(X23,u1_struct_0(k5_topmetr))\|(X21!=k4_borsuk_1(k5_topmetr,k5_topmetr,X22,X23)\|~r1_xxreal_0(X23,k9_real_1(k8_real_1(np__2,X22),np__1))))\|r2_hidden(X21,X17)\|X17!=k8_borsuk_6\|~m1_subset_1(X17,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr))))))&((~r2_hidden(esk4_1(X17),X17)\|(~m1_subset_1(X25,u1_struct_0(k5_topmetr))\|(~m1_subset_1(X26,u1_struct_0(k5_topmetr))\|(esk4_1(X17)!=k4_borsuk_1(k5_topmetr,k5_topmetr,X25,X26)\|~r1_xxreal_0(X26,k9_real_1(k8_real_1(np__2,X25),np__1)))))\|X17=k8_borsuk_6\|~m1_subset_1(X17,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr)))))&((m1_subset_1(esk5_1(X17),u1_struct_0(k5_topmetr))\|r2_hidden(esk4_1(X17),X17)\|X17=k8_borsuk_6\|~m1_subset_1(X17,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr)))))&((m1_subset_1(esk6_1(X17),u1_struct_0(k5_topmetr))\|r2_hidden(esk4_1(X17),X17)\|X17=k8_borsuk_6\|~m1_subset_1(X17,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr)))))&((esk4_1(X17)=k4_borsuk_1(k5_topmetr,k5_topmetr,esk5_1(X17),esk6_1(X17))\|r2_hidden(esk4_1(X17),X17)\|X17=k8_borsuk_6\|~m1_subset_1(X17,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr)))))&(r1_xxreal_0(esk6_1(X17),k9_real_1(k8_real_1(np__2,esk5_1(X17)),np__1))\|r2_hidden(esk4_1(X17),X17)\|X17=k8_borsuk_6\|~m1_subset_1(X17,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr)))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_borsuk_6])])])])])])). fof(c_0_36, plain, (~v2_struct_0(k17_borsuk_1)&(v1_pre_topc(k17_borsuk_1)&v2_pre_topc(k17_borsuk_1))), inference(fof_simplification,[status(thm)],[fc9_borsuk_1])). fof(c_0_37, plain, ![X32, X33]:(~v1_relat_1(X33)\|(~r2_hidden(X32,X33)\|X32=k4_tarski(k1_xtuple_0(X32),k2_xtuple_0(X32)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t21_mcart_1])])). cnf(c_0_38, plain, (r2_hidden(X2,a_0_14_borsuk_6)\|X1!=X2\|~m1_subset_1(X1,u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr)))\|~r1_xxreal_0(k2_xtuple_0(X1),k9_real_1(k8_real_1(np__2,k1_xtuple_0(X1)),np__1))), inference(evalgc,[status(thm)],[c_0_31])). cnf(c_0_39, plain, (k2_xtuple_0(k2_tarski(k2_tarski(X1,X2),k1_tarski(X1)))=X2), inference(evalgc,[status(thm)],[c_0_32])). cnf(c_0_40, plain, (k4_borsuk_1(X1,X2,X3,X4)=k2_tarski(k2_tarski(X3,X4),k1_tarski(X3))\|v2_struct_0(X2)\|v2_struct_0(X1)\|~v2_pre_topc(X2)\|~v2_pre_topc(X1)\|~l1_pre_topc(X2)\|~l1_pre_topc(X1)\|~m1_subset_1(X4,u1_struct_0(X2))\|~m1_subset_1(X3,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_33])). cnf(c_0_41, plain, (k1_xtuple_0(k2_tarski(k2_tarski(X1,X2),k1_tarski(X1)))=X1), inference(rw,[status(thm)],[c_0_34, c_0_29])). cnf(c_0_42, plain, (r2_hidden(X3,X4)\|~m1_subset_1(X1,u1_struct_0(k5_topmetr))\|~m1_subset_1(X2,u1_struct_0(k5_topmetr))\|X3!=k4_borsuk_1(k5_topmetr,k5_topmetr,X1,X2)\|~r1_xxreal_0(X2,k9_real_1(k8_real_1(np__2,X1),np__1))\|X4!=k8_borsuk_6\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr))))), inference(split_conjunct,[status(thm)],[c_0_35])). cnf(c_0_43, plain, (m1_subset_1(k8_borsuk_6,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr))))), inference(split_conjunct,[status(thm)],[dt_k8_borsuk_6])). cnf(c_0_44, plain, (r1_xxreal_0(k2_xtuple_0(esk1_1(X1)),k9_real_1(k8_real_1(np__2,k1_xtuple_0(esk1_1(X1))),np__1))\|~r2_hidden(X1,a_0_14_borsuk_6)), inference(split_conjunct,[status(thm)],[c_0_27])). cnf(c_0_45, plain, (X1=esk1_1(X1)\|~r2_hidden(X1,a_0_14_borsuk_6)), inference(split_conjunct,[status(thm)],[c_0_27])). fof(c_0_46, plain, ![X29, X30, X31]:((m1_subset_1(k1_xtuple_0(X31),u1_struct_0(X29))\|~m1_subset_1(X31,u1_struct_0(k2_borsuk_1(X29,X30)))\|(v2_struct_0(X30)\|(~v2_pre_topc(X30)\|~l1_pre_topc(X30)))\|(v2_struct_0(X29)\|(~v2_pre_topc(X29)\|~l1_pre_topc(X29))))&(m1_subset_1(k2_xtuple_0(X31),u1_struct_0(X30))\|~m1_subset_1(X31,u1_struct_0(k2_borsuk_1(X29,X30)))\|(v2_struct_0(X30)\|(~v2_pre_topc(X30)\|~l1_pre_topc(X30)))\|(v2_struct_0(X29)\|(~v2_pre_topc(X29)\|~l1_pre_topc(X29))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t27_borsuk_6])])])])])). cnf(c_0_47, plain, (m1_subset_1(esk1_1(X1),u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr)))\|~r2_hidden(X1,a_0_14_borsuk_6)), inference(split_conjunct,[status(thm)],[c_0_27])). cnf(c_0_48, plain, (l1_pre_topc(k17_borsuk_1)), inference(split_conjunct,[status(thm)],[dt_k17_borsuk_1])). cnf(c_0_49, plain, (k5_topmetr=k17_borsuk_1), inference(split_conjunct,[status(thm)],[redefinition_k5_topmetr])). cnf(c_0_50, plain, (v2_pre_topc(k17_borsuk_1)), inference(split_conjunct,[status(thm)],[c_0_36])). cnf(c_0_51, plain, (~v2_struct_0(k17_borsuk_1)), inference(split_conjunct,[status(thm)],[c_0_36])). cnf(c_0_52, plain, (X2=k4_tarski(k1_xtuple_0(X2),k2_xtuple_0(X2))\|~v1_relat_1(X1)\|~r2_hidden(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_37])). fof(c_0_53, plain, ![X34, X35]:k2_tarski(X34,X35)=k2_tarski(X35,X34), inference(variable_rename,[status(thm)],[commutativity_k2_tarski])). cnf(c_0_54, plain, (r2_hidden(X1,a_0_14_borsuk_6)\|~r1_xxreal_0(k2_xtuple_0(X1),k9_real_1(k8_real_1(np__2,k1_xtuple_0(X1)),np__1))\|~m1_subset_1(X1,u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr)))), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_38])])). cnf(c_0_55, plain, (k2_xtuple_0(k4_borsuk_1(X3,X4,X1,X2))=X2\|v2_struct_0(X3)\|v2_struct_0(X4)\|~l1_pre_topc(X4)\|~l1_pre_topc(X3)\|~v2_pre_topc(X4)\|~v2_pre_topc(X3)\|~m1_subset_1(X2,u1_struct_0(X4))\|~m1_subset_1(X1,u1_struct_0(X3))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_39, c_0_40])])). cnf(c_0_56, plain, (k1_xtuple_0(k2_tarski(k2_tarski(X1,X2),k1_tarski(X1)))=X1), inference(evalgc,[status(thm)],[c_0_41])). fof(c_0_57, plain, ![X47, X48, X49]:(((u1_struct_0(X49)=k2_zfmisc_1(u1_struct_0(X47),u1_struct_0(X48))\|X49!=k2_borsuk_1(X47,X48)\|(~v1_pre_topc(X49)\|(~v2_pre_topc(X49)\|~l1_pre_topc(X49)))\|(~v2_pre_topc(X48)\|~l1_pre_topc(X48))\|(~v2_pre_topc(X47)\|~l1_pre_topc(X47)))&(u1_pre_topc(X49)=a_3_0_borsuk_1(X47,X48,X49)\|X49!=k2_borsuk_1(X47,X48)\|(~v1_pre_topc(X49)\|(~v2_pre_topc(X49)\|~l1_pre_topc(X49)))\|(~v2_pre_topc(X48)\|~l1_pre_topc(X48))\|(~v2_pre_topc(X47)\|~l1_pre_topc(X47))))&(u1_struct_0(X49)!=k2_zfmisc_1(u1_struct_0(X47),u1_struct_0(X48))\|u1_pre_topc(X49)!=a_3_0_borsuk_1(X47,X48,X49)\|X49=k2_borsuk_1(X47,X48)\|(~v1_pre_topc(X49)\|(~v2_pre_topc(X49)\|~l1_pre_topc(X49)))\|(~v2_pre_topc(X48)\|~l1_pre_topc(X48))\|(~v2_pre_topc(X47)\|~l1_pre_topc(X47)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d2_borsuk_1])])])])). fof(c_0_58, plain, ![X42, X43]:(~m1_subset_1(X42,X43)\|(v1_xboole_0(X43)\|r2_hidden(X42,X43))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])])). cnf(c_0_59, plain, (r2_hidden(X3,X4)\|X4!=k8_borsuk_6\|X3!=k4_borsuk_1(k5_topmetr,k5_topmetr,X1,X2)\|~m1_subset_1(X2,u1_struct_0(k5_topmetr))\|~m1_subset_1(X1,u1_struct_0(k5_topmetr))\|~r1_xxreal_0(X2,k9_real_1(k8_real_1(np__2,X1),np__1))\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr))))), inference(evalgc,[status(thm)],[c_0_42])). cnf(c_0_60, plain, (m1_subset_1(k8_borsuk_6,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr))))), inference(evalgc,[status(thm)],[c_0_43])). cnf(c_0_61, plain, (r1_xxreal_0(k2_xtuple_0(esk1_1(X1)),k9_real_1(k8_real_1(np__2,k1_xtuple_0(esk1_1(X1))),np__1))\|~r2_hidden(X1,a_0_14_borsuk_6)), inference(evalgc,[status(thm)],[c_0_44])). cnf(c_0_62, plain, (esk1_1(X1)=X1\|~r2_hidden(X1,a_0_14_borsuk_6)), inference(evalgc,[status(thm)],[c_0_45])). cnf(c_0_63, plain, (m1_subset_1(k1_xtuple_0(X1),u1_struct_0(X2))\|v2_struct_0(X3)\|v2_struct_0(X2)\|~m1_subset_1(X1,u1_struct_0(k2_borsuk_1(X2,X3)))\|~v2_pre_topc(X3)\|~l1_pre_topc(X3)\|~v2_pre_topc(X2)\|~l1_pre_topc(X2)), inference(split_conjunct,[status(thm)],[c_0_46])). cnf(c_0_64, plain, (m1_subset_1(esk1_1(X1),u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr)))\|~r2_hidden(X1,a_0_14_borsuk_6)), inference(evalgc,[status(thm)],[c_0_47])). cnf(c_0_65, plain, (l1_pre_topc(k17_borsuk_1)), inference(evalgc,[status(thm)],[c_0_48])). cnf(c_0_66, plain, (k17_borsuk_1=k5_topmetr), inference(evalgc,[status(thm)],[c_0_49])). cnf(c_0_67, plain, (v2_pre_topc(k17_borsuk_1)), inference(evalgc,[status(thm)],[c_0_50])). cnf(c_0_68, plain, (~v2_struct_0(k17_borsuk_1)), inference(evalgc,[status(thm)],[c_0_51])). cnf(c_0_69, plain, (m1_subset_1(k2_xtuple_0(X1),u1_struct_0(X2))\|v2_struct_0(X2)\|v2_struct_0(X3)\|~m1_subset_1(X1,u1_struct_0(k2_borsuk_1(X3,X2)))\|~v2_pre_topc(X2)\|~l1_pre_topc(X2)\|~v2_pre_topc(X3)\|~l1_pre_topc(X3)), inference(split_conjunct,[status(thm)],[c_0_46])). cnf(c_0_70, plain, (X2=k2_tarski(k2_tarski(k1_xtuple_0(X2),k2_xtuple_0(X2)),k1_tarski(k1_xtuple_0(X2)))\|~v1_relat_1(X1)\|~r2_hidden(X2,X1)), inference(rw,[status(thm)],[c_0_52, c_0_29])). cnf(c_0_71, plain, (k2_tarski(X1,X2)=k2_tarski(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_53])). fof(c_0_72, plain, ![X36, X37, X38, X39, X40]:((~r1_tarski(X36,X37)\|(~r2_hidden(X38,X36)\|r2_hidden(X38,X37)))&((r2_hidden(esk7_2(X39,X40),X39)\|r1_tarski(X39,X40))&(~r2_hidden(esk7_2(X39,X40),X40)\|r1_tarski(X39,X40)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_tarski])])])])])])). cnf(c_0_73, plain, (r2_hidden(k4_borsuk_1(X1,X2,X3,X4),a_0_14_borsuk_6)\|v2_struct_0(X2)\|v2_struct_0(X1)\|~r1_xxreal_0(X4,k9_real_1(k8_real_1(np__2,k1_xtuple_0(k4_borsuk_1(X1,X2,X3,X4))),np__1))\|~m1_subset_1(k4_borsuk_1(X1,X2,X3,X4),u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr)))\|~l1_pre_topc(X2)\|~l1_pre_topc(X1)\|~v2_pre_topc(X2)\|~v2_pre_topc(X1)\|~m1_subset_1(X4,u1_struct_0(X2))\|~m1_subset_1(X3,u1_struct_0(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_54, c_0_55])])). cnf(c_0_74, plain, (k1_xtuple_0(k4_borsuk_1(X3,X4,X1,X2))=X1\|v2_struct_0(X3)\|v2_struct_0(X4)\|~l1_pre_topc(X4)\|~l1_pre_topc(X3)\|~v2_pre_topc(X4)\|~v2_pre_topc(X3)\|~m1_subset_1(X2,u1_struct_0(X4))\|~m1_subset_1(X1,u1_struct_0(X3))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_56, c_0_40])])). cnf(c_0_75, plain, (X1=k4_borsuk_1(k5_topmetr,k5_topmetr,esk2_2(X2,X1),esk3_2(X2,X1))\|~r2_hidden(X1,X2)\|X2!=k8_borsuk_6\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr))))), inference(split_conjunct,[status(thm)],[c_0_35])). fof(c_0_76, plain, ![X44, X45, X46]:(~r2_hidden(X44,X45)\|~m1_subset_1(X45,k1_zfmisc_1(X46))\|m1_subset_1(X44,X46)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])])). cnf(c_0_77, plain, (u1_struct_0(X1)=k2_zfmisc_1(u1_struct_0(X2),u1_struct_0(X3))\|X1!=k2_borsuk_1(X2,X3)\|~v1_pre_topc(X1)\|~v2_pre_topc(X1)\|~l1_pre_topc(X1)\|~v2_pre_topc(X3)\|~l1_pre_topc(X3)\|~v2_pre_topc(X2)\|~l1_pre_topc(X2)), inference(split_conjunct,[status(thm)],[c_0_57])). fof(c_0_78, plain, ![X50, X51]:((v1_pre_topc(k2_borsuk_1(X50,X51))\|(~v2_pre_topc(X50)\|~l1_pre_topc(X50)\|(~v2_pre_topc(X51)\|~l1_pre_topc(X51))))&((v2_pre_topc(k2_borsuk_1(X50,X51))\|(~v2_pre_topc(X50)\|~l1_pre_topc(X50)\|(~v2_pre_topc(X51)\|~l1_pre_topc(X51))))&(l1_pre_topc(k2_borsuk_1(X50,X51))\|(~v2_pre_topc(X50)\|~l1_pre_topc(X50)\|(~v2_pre_topc(X51)\|~l1_pre_topc(X51)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_borsuk_1])])])). cnf(c_0_79, plain, (v1_xboole_0(X2)\|r2_hidden(X1,X2)\|~m1_subset_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_58])). cnf(c_0_80, plain, (r2_hidden(X1,k8_borsuk_6)\|X1!=k4_borsuk_1(k5_topmetr,k5_topmetr,X2,X3)\|~r1_xxreal_0(X3,k9_real_1(k8_real_1(np__2,X2),np__1))\|~m1_subset_1(X3,u1_struct_0(k5_topmetr))\|~m1_subset_1(X2,u1_struct_0(k5_topmetr))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_59, c_0_60])])). cnf(c_0_81, plain, (r1_xxreal_0(k2_xtuple_0(X1),k9_real_1(k8_real_1(np__2,k1_xtuple_0(X1)),np__1))\|~r2_hidden(X1,a_0_14_borsuk_6)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_61, c_0_62])])). cnf(c_0_82, plain, (v2_struct_0(X3)\|v2_struct_0(X2)\|m1_subset_1(k1_xtuple_0(X1),u1_struct_0(X2))\|~v2_pre_topc(X3)\|~v2_pre_topc(X2)\|~l1_pre_topc(X3)\|~l1_pre_topc(X2)\|~m1_subset_1(X1,u1_struct_0(k2_borsuk_1(X2,X3)))), inference(evalgc,[status(thm)],[c_0_63])). cnf(c_0_83, plain, (m1_subset_1(X1,u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr)))\|~r2_hidden(X1,a_0_14_borsuk_6)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_64, c_0_62])])). cnf(c_0_84, plain, (l1_pre_topc(k5_topmetr)), inference(rw,[status(thm)],[c_0_65, c_0_66])). cnf(c_0_85, plain, (v2_pre_topc(k5_topmetr)), inference(rw,[status(thm)],[c_0_67, c_0_66])). cnf(c_0_86, plain, (~v2_struct_0(k5_topmetr)), inference(rw,[status(thm)],[c_0_68, c_0_66])). cnf(c_0_87, plain, (v2_struct_0(X3)\|v2_struct_0(X2)\|m1_subset_1(k2_xtuple_0(X1),u1_struct_0(X2))\|~v2_pre_topc(X3)\|~v2_pre_topc(X2)\|~l1_pre_topc(X3)\|~l1_pre_topc(X2)\|~m1_subset_1(X1,u1_struct_0(k2_borsuk_1(X3,X2)))), inference(evalgc,[status(thm)],[c_0_69])). cnf(c_0_88, plain, (k2_tarski(k2_tarski(k1_xtuple_0(X2),k2_xtuple_0(X2)),k1_tarski(k1_xtuple_0(X2)))=X2\|~v1_relat_1(X1)\|~r2_hidden(X2,X1)), inference(evalgc,[status(thm)],[c_0_70])). cnf(c_0_89, plain, (k2_tarski(X1,X2)=k2_tarski(X2,X1)), inference(evalgc,[status(thm)],[c_0_71])). cnf(c_0_90, plain, (r2_hidden(esk7_2(X1,X2),X1)\|r1_tarski(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_72])). cnf(c_0_91, plain, (v2_struct_0(X1)\|v2_struct_0(X2)\|r2_hidden(k4_borsuk_1(X1,X2,X3,X4),a_0_14_borsuk_6)\|~l1_pre_topc(X2)\|~l1_pre_topc(X1)\|~v2_pre_topc(X2)\|~v2_pre_topc(X1)\|~r1_xxreal_0(X4,k9_real_1(k8_real_1(np__2,X3),np__1))\|~m1_subset_1(k4_borsuk_1(X1,X2,X3,X4),u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr)))\|~m1_subset_1(X4,u1_struct_0(X2))\|~m1_subset_1(X3,u1_struct_0(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_73, c_0_74])])). cnf(c_0_92, plain, (k4_borsuk_1(k5_topmetr,k5_topmetr,esk2_2(X2,X1),esk3_2(X2,X1))=X1\|X2!=k8_borsuk_6\|~r2_hidden(X1,X2)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr))))), inference(evalgc,[status(thm)],[c_0_75])). cnf(c_0_93, plain, (m1_subset_1(esk2_2(X1,X2),u1_struct_0(k5_topmetr))\|~r2_hidden(X2,X1)\|X1!=k8_borsuk_6\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr))))), inference(split_conjunct,[status(thm)],[c_0_35])). cnf(c_0_94, plain, (m1_subset_1(esk3_2(X1,X2),u1_struct_0(k5_topmetr))\|~r2_hidden(X2,X1)\|X1!=k8_borsuk_6\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr))))), inference(split_conjunct,[status(thm)],[c_0_35])). cnf(c_0_95, plain, (m1_subset_1(X1,X3)\|~r2_hidden(X1,X2)\|~m1_subset_1(X2,k1_zfmisc_1(X3))), inference(split_conjunct,[status(thm)],[c_0_76])). cnf(c_0_96, plain, (r1_xxreal_0(esk3_2(X1,X2),k9_real_1(k8_real_1(np__2,esk2_2(X1,X2)),np__1))\|~r2_hidden(X2,X1)\|X1!=k8_borsuk_6\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr))))), inference(split_conjunct,[status(thm)],[c_0_35])). fof(c_0_97, plain, ![X52, X53]:(v1_xboole_0(X52)\|v1_xboole_0(X53)\|~v1_xboole_0(k2_zfmisc_1(X52,X53))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fc10_subset_1])])])). cnf(c_0_98, plain, (u1_struct_0(X1)=k2_zfmisc_1(u1_struct_0(X2),u1_struct_0(X3))\|X1!=k2_borsuk_1(X2,X3)\|~v1_pre_topc(X1)\|~v2_pre_topc(X3)\|~v2_pre_topc(X2)\|~v2_pre_topc(X1)\|~l1_pre_topc(X3)\|~l1_pre_topc(X2)\|~l1_pre_topc(X1)), inference(evalgc,[status(thm)],[c_0_77])). cnf(c_0_99, plain, (v1_pre_topc(k2_borsuk_1(X1,X2))\|~v2_pre_topc(X1)\|~l1_pre_topc(X1)\|~v2_pre_topc(X2)\|~l1_pre_topc(X2)), inference(split_conjunct,[status(thm)],[c_0_78])). cnf(c_0_100, plain, (v2_pre_topc(k2_borsuk_1(X1,X2))\|~v2_pre_topc(X1)\|~l1_pre_topc(X1)\|~v2_pre_topc(X2)\|~l1_pre_topc(X2)), inference(split_conjunct,[status(thm)],[c_0_78])). cnf(c_0_101, plain, (l1_pre_topc(k2_borsuk_1(X1,X2))\|~v2_pre_topc(X1)\|~l1_pre_topc(X1)\|~v2_pre_topc(X2)\|~l1_pre_topc(X2)), inference(split_conjunct,[status(thm)],[c_0_78])). cnf(c_0_102, plain, (v1_xboole_0(X2)\|r2_hidden(X1,X2)\|~m1_subset_1(X1,X2)), inference(evalgc,[status(thm)],[c_0_79])). cnf(c_0_103, plain, (r2_hidden(X1,k8_borsuk_6)\|X1!=k4_borsuk_1(k5_topmetr,k5_topmetr,k1_xtuple_0(X2),k2_xtuple_0(X2))\|~m1_subset_1(k2_xtuple_0(X2),u1_struct_0(k5_topmetr))\|~m1_subset_1(k1_xtuple_0(X2),u1_struct_0(k5_topmetr))\|~r2_hidden(X2,a_0_14_borsuk_6)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_80, c_0_81])])). cnf(c_0_104, plain, (m1_subset_1(k1_xtuple_0(X1),u1_struct_0(k5_topmetr))\|~r2_hidden(X1,a_0_14_borsuk_6)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82, c_0_83]), c_0_84]), c_0_85])]), c_0_86])])). cnf(c_0_105, plain, (m1_subset_1(k2_xtuple_0(X1),u1_struct_0(k5_topmetr))\|~r2_hidden(X1,a_0_14_borsuk_6)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87, c_0_83]), c_0_84]), c_0_85])]), c_0_86])])). cnf(c_0_106, plain, (k2_tarski(k1_tarski(k1_xtuple_0(X1)),k2_tarski(k1_xtuple_0(X1),k2_xtuple_0(X1)))=X1\|~v1_relat_1(X2)\|~r2_hidden(X1,X2)), inference(rw,[status(thm)],[c_0_88, c_0_89])). cnf(c_0_107, plain, (r1_tarski(X1,X2)\|r2_hidden(esk7_2(X1,X2),X1)), inference(evalgc,[status(thm)],[c_0_90])). cnf(c_0_108, plain, (r2_hidden(X2,a_0_14_borsuk_6)\|~r1_xxreal_0(esk3_2(X1,X2),k9_real_1(k8_real_1(np__2,esk2_2(X1,X2)),np__1))\|~m1_subset_1(X2,u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr)))\|~m1_subset_1(esk3_2(X1,X2),u1_struct_0(k5_topmetr))\|~m1_subset_1(esk2_2(X1,X2),u1_struct_0(k5_topmetr))\|X1!=k8_borsuk_6\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr))))\|~r2_hidden(X2,X1)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91, c_0_92]), c_0_84]), c_0_85])]), c_0_86])])). cnf(c_0_109, plain, (m1_subset_1(esk2_2(X1,X2),u1_struct_0(k5_topmetr))\|X1!=k8_borsuk_6\|~r2_hidden(X2,X1)\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr))))), inference(evalgc,[status(thm)],[c_0_93])). cnf(c_0_110, plain, (m1_subset_1(esk3_2(X1,X2),u1_struct_0(k5_topmetr))\|X1!=k8_borsuk_6\|~r2_hidden(X2,X1)\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr))))), inference(evalgc,[status(thm)],[c_0_94])). cnf(c_0_111, plain, (m1_subset_1(X1,X3)\|~r2_hidden(X1,X2)\|~m1_subset_1(X2,k1_zfmisc_1(X3))), inference(evalgc,[status(thm)],[c_0_95])). cnf(c_0_112, plain, (r1_xxreal_0(esk3_2(X1,X2),k9_real_1(k8_real_1(np__2,esk2_2(X1,X2)),np__1))\|X1!=k8_borsuk_6\|~r2_hidden(X2,X1)\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr))))), inference(evalgc,[status(thm)],[c_0_96])). cnf(c_0_113, plain, (v1_xboole_0(X1)\|v1_xboole_0(X2)\|~v1_xboole_0(k2_zfmisc_1(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_97])). cnf(c_0_114, plain, (k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X2))=u1_struct_0(k2_borsuk_1(X1,X2))\|~l1_pre_topc(X2)\|~l1_pre_topc(X1)\|~l1_pre_topc(k2_borsuk_1(X1,X2))\|~v2_pre_topc(X2)\|~v2_pre_topc(X1)\|~v2_pre_topc(k2_borsuk_1(X1,X2))\|~v1_pre_topc(k2_borsuk_1(X1,X2))), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_98])])). cnf(c_0_115, plain, (v1_pre_topc(k2_borsuk_1(X1,X2))\|~v2_pre_topc(X2)\|~v2_pre_topc(X1)\|~l1_pre_topc(X2)\|~l1_pre_topc(X1)), inference(evalgc,[status(thm)],[c_0_99])). cnf(c_0_116, plain, (v2_pre_topc(k2_borsuk_1(X1,X2))\|~v2_pre_topc(X2)\|~v2_pre_topc(X1)\|~l1_pre_topc(X2)\|~l1_pre_topc(X1)), inference(evalgc,[status(thm)],[c_0_100])). cnf(c_0_117, plain, (l1_pre_topc(k2_borsuk_1(X1,X2))\|~v2_pre_topc(X2)\|~v2_pre_topc(X1)\|~l1_pre_topc(X2)\|~l1_pre_topc(X1)), inference(evalgc,[status(thm)],[c_0_101])). cnf(c_0_118, plain, (r1_tarski(X1,X2)\|~r2_hidden(esk7_2(X1,X2),X2)), inference(split_conjunct,[status(thm)],[c_0_72])). cnf(c_0_119, plain, (v1_xboole_0(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr)))\|r2_hidden(X1,u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr)))\|~r2_hidden(X1,a_0_14_borsuk_6)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_102, c_0_83])])). cnf(c_0_120, plain, (r2_hidden(X1,k8_borsuk_6)\|X1!=k4_borsuk_1(k5_topmetr,k5_topmetr,k1_xtuple_0(X2),k2_xtuple_0(X2))\|~r2_hidden(X2,a_0_14_borsuk_6)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_103, c_0_104]), c_0_105])). cnf(c_0_121, plain, (k4_borsuk_1(X3,X4,X1,X2)=k2_tarski(k1_tarski(X1),k2_tarski(X1,X2))\|v2_struct_0(X3)\|v2_struct_0(X4)\|~l1_pre_topc(X4)\|~l1_pre_topc(X3)\|~v2_pre_topc(X4)\|~v2_pre_topc(X3)\|~m1_subset_1(X2,u1_struct_0(X4))\|~m1_subset_1(X1,u1_struct_0(X3))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_89, c_0_40])])). cnf(c_0_122, plain, (k2_tarski(k1_tarski(k1_xtuple_0(esk7_2(X1,X2))),k2_tarski(k1_xtuple_0(esk7_2(X1,X2)),k2_xtuple_0(esk7_2(X1,X2))))=esk7_2(X1,X2)\|r1_tarski(X1,X2)\|~v1_relat_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_106, c_0_107])])). cnf(c_0_123, plain, (r2_hidden(X1,a_0_14_borsuk_6)\|X2!=k8_borsuk_6\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr))))\|~r2_hidden(X1,X2)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_108, c_0_109]), c_0_110]), c_0_111]), c_0_112])). fof(c_0_124, negated_conjecture, ~(k8_borsuk_6=a_0_14_borsuk_6), inference(assume_negation,[status(cth)],[t55_borsuk_6])). fof(c_0_125, plain, ![X56, X57, X58]:(~m1_subset_1(X58,k1_zfmisc_1(k2_zfmisc_1(X56,X57)))\|v1_relat_1(X58)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relset_1])])). fof(c_0_126, plain, ![X54, X55]:((~m1_subset_1(X54,k1_zfmisc_1(X55))\|r1_tarski(X54,X55))&(~r1_tarski(X54,X55)\|m1_subset_1(X54,k1_zfmisc_1(X55)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])])). cnf(c_0_127, plain, (v1_xboole_0(X2)\|v1_xboole_0(X1)\|~v1_xboole_0(k2_zfmisc_1(X1,X2))), inference(evalgc,[status(thm)],[c_0_113])). cnf(c_0_128, plain, (k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X2))=u1_struct_0(k2_borsuk_1(X1,X2))\|~l1_pre_topc(X2)\|~l1_pre_topc(X1)\|~v2_pre_topc(X2)\|~v2_pre_topc(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_114, c_0_115]), c_0_116]), c_0_117])). cnf(c_0_129, plain, (r1_tarski(X1,X2)\|~r2_hidden(esk7_2(X1,X2),X2)), inference(evalgc,[status(thm)],[c_0_118])). cnf(c_0_130, plain, (v1_xboole_0(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr)))\|r2_hidden(esk7_2(a_0_14_borsuk_6,X1),u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr)))\|r1_tarski(a_0_14_borsuk_6,X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_119, c_0_107])])). cnf(c_0_131, plain, (r2_hidden(k4_borsuk_1(k5_topmetr,k5_topmetr,k1_xtuple_0(X1),k2_xtuple_0(X1)),k8_borsuk_6)\|~r2_hidden(X1,a_0_14_borsuk_6)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_120])])). cnf(c_0_132, plain, (k4_borsuk_1(X1,X2,k1_xtuple_0(esk7_2(X3,X4)),k2_xtuple_0(esk7_2(X3,X4)))=esk7_2(X3,X4)\|v2_struct_0(X2)\|v2_struct_0(X1)\|r1_tarski(X3,X4)\|~l1_pre_topc(X2)\|~l1_pre_topc(X1)\|~v2_pre_topc(X2)\|~v2_pre_topc(X1)\|~m1_subset_1(k2_xtuple_0(esk7_2(X3,X4)),u1_struct_0(X2))\|~m1_subset_1(k1_xtuple_0(esk7_2(X3,X4)),u1_struct_0(X1))\|~v1_relat_1(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_121, c_0_122])])). fof(c_0_133, plain, ![X59, X60]:(((r1_tarski(X59,X60)\|X59!=X60)&(r1_tarski(X60,X59)\|X59!=X60))&(~r1_tarski(X59,X60)\|~r1_tarski(X60,X59)\|X59=X60)), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])])). cnf(c_0_134, plain, (r2_hidden(X1,a_0_14_borsuk_6)\|~r2_hidden(X1,k8_borsuk_6)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_123, c_0_60])])). fof(c_0_135, negated_conjecture, k8_borsuk_6!=a_0_14_borsuk_6, inference(fof_simplification,[status(thm)],[c_0_124])). cnf(c_0_136, plain, (v1_relat_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_125])). cnf(c_0_137, plain, (m1_subset_1(X1,k1_zfmisc_1(X2))\|~r1_tarski(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_126])). cnf(c_0_138, plain, (v1_xboole_0(u1_struct_0(X1))\|v1_xboole_0(u1_struct_0(X2))\|~v1_xboole_0(u1_struct_0(k2_borsuk_1(X1,X2)))\|~l1_pre_topc(X2)\|~l1_pre_topc(X1)\|~v2_pre_topc(X2)\|~v2_pre_topc(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_127, c_0_128])])). cnf(c_0_139, plain, (r1_tarski(a_0_14_borsuk_6,u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr)))\|v1_xboole_0(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr)))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_129, c_0_130])])). cnf(c_0_140, plain, (r2_hidden(esk7_2(X1,X2),k8_borsuk_6)\|r1_tarski(X1,X2)\|~r2_hidden(esk7_2(X1,X2),a_0_14_borsuk_6)\|~v1_relat_1(X1)\|~m1_subset_1(k2_xtuple_0(esk7_2(X1,X2)),u1_struct_0(k5_topmetr))\|~m1_subset_1(k1_xtuple_0(esk7_2(X1,X2)),u1_struct_0(k5_topmetr))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131, c_0_132]), c_0_84]), c_0_85])]), c_0_86])])). cnf(c_0_141, plain, (X1=X2\|~r1_tarski(X1,X2)\|~r1_tarski(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_133])). cnf(c_0_142, plain, (r1_tarski(X1,a_0_14_borsuk_6)\|~r2_hidden(esk7_2(X1,a_0_14_borsuk_6),k8_borsuk_6)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_129, c_0_134])])). cnf(c_0_143, negated_conjecture, (k8_borsuk_6!=a_0_14_borsuk_6), inference(split_conjunct,[status(thm)],[c_0_135])). fof(c_0_144, plain, ![X61]:(v2_struct_0(X61)\|~l1_struct_0(X61)\|~v1_xboole_0(u1_struct_0(X61))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fc2_struct_0])])])). fof(c_0_145, plain, ![X62]:(~l1_pre_topc(X62)\|l1_struct_0(X62)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_pre_topc])])). cnf(c_0_146, plain, (v1_relat_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(evalgc,[status(thm)],[c_0_136])). cnf(c_0_147, plain, (m1_subset_1(X1,k1_zfmisc_1(X2))\|~r1_tarski(X1,X2)), inference(evalgc,[status(thm)],[c_0_137])). cnf(c_0_148, plain, (v1_xboole_0(u1_struct_0(k5_topmetr))\|r1_tarski(a_0_14_borsuk_6,u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr)))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138, c_0_139]), c_0_84]), c_0_85])])])). cnf(c_0_149, plain, (r1_tarski(X1,X2)\|r2_hidden(esk7_2(X1,X2),k8_borsuk_6)\|~v1_relat_1(X1)\|~r2_hidden(esk7_2(X1,X2),a_0_14_borsuk_6)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_140, c_0_104]), c_0_105])). cnf(c_0_150, plain, (X1=X2\|~r1_tarski(X2,X1)\|~r1_tarski(X1,X2)), inference(evalgc,[status(thm)],[c_0_141])). cnf(c_0_151, plain, (r1_tarski(k8_borsuk_6,a_0_14_borsuk_6)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_142, c_0_107])])). cnf(c_0_152, negated_conjecture, (a_0_14_borsuk_6!=k8_borsuk_6), inference(evalgc,[status(thm)],[c_0_143])). cnf(c_0_153, plain, (v2_struct_0(X1)\|~l1_struct_0(X1)\|~v1_xboole_0(u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_144])). cnf(c_0_154, plain, (l1_struct_0(X1)\|~l1_pre_topc(X1)), inference(split_conjunct,[status(thm)],[c_0_145])). cnf(c_0_155, plain, (v1_relat_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(X2,X3))))\|~l1_pre_topc(X3)\|~l1_pre_topc(X2)\|~v2_pre_topc(X3)\|~v2_pre_topc(X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_146, c_0_128])])). cnf(c_0_156, plain, (m1_subset_1(a_0_14_borsuk_6,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr))))\|v1_xboole_0(u1_struct_0(k5_topmetr))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_147, c_0_148])])). cnf(c_0_157, plain, (r1_tarski(a_0_14_borsuk_6,X1)\|r2_hidden(esk7_2(a_0_14_borsuk_6,X1),k8_borsuk_6)\|~v1_relat_1(a_0_14_borsuk_6)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_149, c_0_107])])). cnf(c_0_158, plain, (~r1_tarski(a_0_14_borsuk_6,k8_borsuk_6)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_150, c_0_151]), c_0_152])])). cnf(c_0_159, plain, (v2_struct_0(X1)\|~l1_struct_0(X1)\|~v1_xboole_0(u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_153])). cnf(c_0_160, plain, (l1_struct_0(X1)\|~l1_pre_topc(X1)), inference(evalgc,[status(thm)],[c_0_154])). cnf(c_0_161, plain, (v1_relat_1(a_0_14_borsuk_6)\|v1_xboole_0(u1_struct_0(k5_topmetr))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155, c_0_156]), c_0_84]), c_0_85])])])). cnf(c_0_162, plain, (~v1_relat_1(a_0_14_borsuk_6)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_129, c_0_157]), c_0_158])])). cnf(c_0_163, plain, (v2_struct_0(X1)\|~v1_xboole_0(u1_struct_0(X1))\|~l1_pre_topc(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_159, c_0_160])])). cnf(c_0_164, plain, (v1_xboole_0(u1_struct_0(k5_topmetr))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[c_0_161, c_0_162])])). cnf(c_0_165, plain, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163, c_0_164]), c_0_84])]), c_0_86]), ['proof']). # SZS output end CNFRefutation	reserve T for non empty TopSpace, a, b, c, d for Point of T; theorem Th55: ICC = { p where p is Point of [:I[01], I[01]:] : p`2 <= 2 * (p`1 ) - 1 } proof set P = { p where p is Point of [:I[01], I[01]:] : p`2 <= 2 * (p`1) - 1 }; thus ICC c= P proof let x be set; assume A1: x in ICC; then reconsider x9 = x as Point of [:I[01], I[01]:]; consider a, b being Point of I[01] such that A2: x = [a,b] and A3: b <= 2 * a - 1 by A1,Def10; x9`1 = a & x9`2 = b by A2,MCART_1:7; hence thesis by A3; end; let x be set; assume x in P; then consider p being Point of [:I[01], I[01]:] such that A4: p = x and A5: p`2 <= 2 * (p`1) - 1; x in the carrier of [:I[01], I[01]:] by A4; then x in [:the carrier of I[01], the carrier of I[01]:] by BORSUK_1:def 2; then A6: x = [x`1, x`2] by MCART_1:21; p`1 is Point of I[01] & p`2 is Point of I[01] by Th27; hence thesis by A4,A5,A6,Def10; end;	Convert the following ATP output trace into a readable Mizar proof.
t14_orders_1	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t3_orders_1, axiom, ![X1, X2, X3]:((v1_relat_2(X3)&(v4_relat_2(X3)&(v8_relat_2(X3)&(v1_partfun1(X3,X1)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X1)))))))=>(r2_hidden(X2,X1)=>r2_hidden(k4_tarski(X2,X2),X3))), file('/scratch/mptp/predsminms1/t14_orders_1__0', t3_orders_1)). fof(d5_tarski, axiom, ![X1, X2]:k4_tarski(X1,X2)=k2_tarski(k2_tarski(X1,X2),k1_tarski(X1)), file('/scratch/mptp/predsminms1/t14_orders_1__0', d5_tarski)). fof(t14_orders_1, conjecture, ![X1, X2]:((v1_relat_2(X2)&(v4_relat_2(X2)&(v8_relat_2(X2)&(v1_partfun1(X2,X1)&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,X1)))))))=>(k1_relset_1(X1,X2)=X1&k2_relset_1(X1,X2)=X1)), file('/scratch/mptp/predsminms1/t14_orders_1__0', t14_orders_1)). fof(d13_xtuple_0, axiom, ![X1, X2]:(X2=k10_xtuple_0(X1)<=>![X3]:(r2_hidden(X3,X2)<=>?[X4]:r2_hidden(k4_tarski(X4,X3),X1))), file('/scratch/mptp/predsminms1/t14_orders_1__0', d13_xtuple_0)). fof(d12_xtuple_0, axiom, ![X1, X2]:(X2=k9_xtuple_0(X1)<=>![X3]:(r2_hidden(X3,X2)<=>?[X4]:r2_hidden(k4_tarski(X3,X4),X1))), file('/scratch/mptp/predsminms1/t14_orders_1__0', d12_xtuple_0)). fof(dt_k2_relset_1, axiom, ![X1, X2]:((v1_relat_1(X2)&v5_relat_1(X2,X1))=>m1_subset_1(k2_relset_1(X1,X2),k1_zfmisc_1(X1))), file('/scratch/mptp/predsminms1/t14_orders_1__0', dt_k2_relset_1)). fof(redefinition_k2_relset_1, axiom, ![X1, X2]:((v1_relat_1(X2)&v5_relat_1(X2,X1))=>k2_relset_1(X1,X2)=k10_xtuple_0(X2)), file('/scratch/mptp/predsminms1/t14_orders_1__0', redefinition_k2_relset_1)). fof(d3_tarski, axiom, ![X1, X2]:(r1_tarski(X1,X2)<=>![X3]:(r2_hidden(X3,X1)=>r2_hidden(X3,X2))), file('/scratch/mptp/predsminms1/t14_orders_1__0', d3_tarski)). fof(t3_subset, axiom, ![X1, X2]:(m1_subset_1(X1,k1_zfmisc_1(X2))<=>r1_tarski(X1,X2)), file('/scratch/mptp/predsminms1/t14_orders_1__0', t3_subset)). fof(dt_k1_relset_1, axiom, ![X1, X2]:((v1_relat_1(X2)&v4_relat_1(X2,X1))=>m1_subset_1(k1_relset_1(X1,X2),k1_zfmisc_1(X1))), file('/scratch/mptp/predsminms1/t14_orders_1__0', dt_k1_relset_1)). fof(redefinition_k1_relset_1, axiom, ![X1, X2]:((v1_relat_1(X2)&v4_relat_1(X2,X1))=>k1_relset_1(X1,X2)=k9_xtuple_0(X2)), file('/scratch/mptp/predsminms1/t14_orders_1__0', redefinition_k1_relset_1)). fof(cc2_relset_1, axiom, ![X1, X2, X3]:(m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))=>(v4_relat_1(X3,X1)&v5_relat_1(X3,X2))), file('/scratch/mptp/predsminms1/t14_orders_1__0', cc2_relset_1)). fof(cc2_relat_1, axiom, ![X1]:(v1_relat_1(X1)=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(X1))=>v1_relat_1(X2))), file('/scratch/mptp/predsminms1/t14_orders_1__0', cc2_relat_1)). fof(fc6_relat_1, axiom, ![X1, X2]:v1_relat_1(k2_zfmisc_1(X1,X2)), file('/scratch/mptp/predsminms1/t14_orders_1__0', fc6_relat_1)). fof(d10_xboole_0, axiom, ![X1, X2]:(X1=X2<=>(r1_tarski(X1,X2)&r1_tarski(X2,X1))), file('/scratch/mptp/predsminms1/t14_orders_1__0', d10_xboole_0)). fof(c_0_15, plain, ![X7, X8, X9]:(~v1_relat_2(X9)\|(~v4_relat_2(X9)\|(~v8_relat_2(X9)\|(~v1_partfun1(X9,X7)\|~m1_subset_1(X9,k1_zfmisc_1(k2_zfmisc_1(X7,X7))))))\|(~r2_hidden(X8,X7)\|r2_hidden(k4_tarski(X8,X8),X9))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_orders_1])])). fof(c_0_16, plain, ![X10, X11]:k4_tarski(X10,X11)=k2_tarski(k2_tarski(X10,X11),k1_tarski(X10)), inference(variable_rename,[status(thm)],[d5_tarski])). fof(c_0_17, negated_conjecture, ~(![X1, X2]:((v1_relat_2(X2)&(v4_relat_2(X2)&(v8_relat_2(X2)&(v1_partfun1(X2,X1)&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,X1)))))))=>(k1_relset_1(X1,X2)=X1&k2_relset_1(X1,X2)=X1))), inference(assume_negation,[status(cth)],[t14_orders_1])). fof(c_0_18, plain, ![X12, X13, X14, X16, X17, X18, X19, X21]:(((~r2_hidden(X14,X13)\|r2_hidden(k4_tarski(esk3_3(X12,X13,X14),X14),X12)\|X13!=k10_xtuple_0(X12))&(~r2_hidden(k4_tarski(X17,X16),X12)\|r2_hidden(X16,X13)\|X13!=k10_xtuple_0(X12)))&((~r2_hidden(esk4_2(X18,X19),X19)\|~r2_hidden(k4_tarski(X21,esk4_2(X18,X19)),X18)\|X19=k10_xtuple_0(X18))&(r2_hidden(esk4_2(X18,X19),X19)\|r2_hidden(k4_tarski(esk5_2(X18,X19),esk4_2(X18,X19)),X18)\|X19=k10_xtuple_0(X18)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d13_xtuple_0])])])])])])). cnf(c_0_19, plain, (r2_hidden(k4_tarski(X3,X3),X1)\|~v1_relat_2(X1)\|~v4_relat_2(X1)\|~v8_relat_2(X1)\|~v1_partfun1(X1,X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X2)))\|~r2_hidden(X3,X2)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_20, plain, (k4_tarski(X1,X2)=k2_tarski(k2_tarski(X1,X2),k1_tarski(X1))), inference(split_conjunct,[status(thm)],[c_0_16])). fof(c_0_21, negated_conjecture, ((v1_relat_2(esk2_0)&(v4_relat_2(esk2_0)&(v8_relat_2(esk2_0)&(v1_partfun1(esk2_0,esk1_0)&m1_subset_1(esk2_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,esk1_0)))))))&(k1_relset_1(esk1_0,esk2_0)!=esk1_0\|k2_relset_1(esk1_0,esk2_0)!=esk1_0)), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])). cnf(c_0_22, plain, (r2_hidden(X2,X4)\|~r2_hidden(k4_tarski(X1,X2),X3)\|X4!=k10_xtuple_0(X3)), inference(split_conjunct,[status(thm)],[c_0_18])). cnf(c_0_23, plain, (r2_hidden(k2_tarski(k2_tarski(X3,X3),k1_tarski(X3)),X1)\|~v1_relat_2(X1)\|~v4_relat_2(X1)\|~v8_relat_2(X1)\|~v1_partfun1(X1,X2)\|~r2_hidden(X3,X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X2)))), inference(rw,[status(thm)],[c_0_19, c_0_20])). cnf(c_0_24, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,esk1_0)))), inference(split_conjunct,[status(thm)],[c_0_21])). cnf(c_0_25, negated_conjecture, (v1_partfun1(esk2_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_21])). cnf(c_0_26, negated_conjecture, (v8_relat_2(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_21])). cnf(c_0_27, negated_conjecture, (v4_relat_2(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_21])). cnf(c_0_28, negated_conjecture, (v1_relat_2(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_21])). fof(c_0_29, plain, ![X23, X24, X25, X27, X28, X29, X30, X32]:(((~r2_hidden(X25,X24)\|r2_hidden(k4_tarski(X25,esk6_3(X23,X24,X25)),X23)\|X24!=k9_xtuple_0(X23))&(~r2_hidden(k4_tarski(X27,X28),X23)\|r2_hidden(X27,X24)\|X24!=k9_xtuple_0(X23)))&((~r2_hidden(esk7_2(X29,X30),X30)\|~r2_hidden(k4_tarski(esk7_2(X29,X30),X32),X29)\|X30=k9_xtuple_0(X29))&(r2_hidden(esk7_2(X29,X30),X30)\|r2_hidden(k4_tarski(esk7_2(X29,X30),esk8_2(X29,X30)),X29)\|X30=k9_xtuple_0(X29)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d12_xtuple_0])])])])])])). fof(c_0_30, plain, ![X55, X56]:(~v1_relat_1(X56)\|~v5_relat_1(X56,X55)\|m1_subset_1(k2_relset_1(X55,X56),k1_zfmisc_1(X55))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_relset_1])])). fof(c_0_31, plain, ![X34, X35]:(~v1_relat_1(X35)\|~v5_relat_1(X35,X34)\|k2_relset_1(X34,X35)=k10_xtuple_0(X35)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k2_relset_1])])). cnf(c_0_32, plain, (r2_hidden(X2,X4)\|X4!=k10_xtuple_0(X3)\|~r2_hidden(k2_tarski(k2_tarski(X1,X2),k1_tarski(X1)),X3)), inference(rw,[status(thm)],[c_0_22, c_0_20])). cnf(c_0_33, plain, (r2_hidden(k2_tarski(k2_tarski(X3,X3),k1_tarski(X3)),X1)\|~v1_relat_2(X1)\|~v4_relat_2(X1)\|~v8_relat_2(X1)\|~v1_partfun1(X1,X2)\|~r2_hidden(X3,X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X2)))), inference(evalgc,[status(thm)],[c_0_23])). cnf(c_0_34, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,esk1_0)))), inference(evalgc,[status(thm)],[c_0_24])). cnf(c_0_35, negated_conjecture, (v1_partfun1(esk2_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_25])). cnf(c_0_36, negated_conjecture, (v8_relat_2(esk2_0)), inference(evalgc,[status(thm)],[c_0_26])). cnf(c_0_37, negated_conjecture, (v4_relat_2(esk2_0)), inference(evalgc,[status(thm)],[c_0_27])). cnf(c_0_38, negated_conjecture, (v1_relat_2(esk2_0)), inference(evalgc,[status(thm)],[c_0_28])). fof(c_0_39, plain, ![X36, X37, X38, X39, X40]:((~r1_tarski(X36,X37)\|(~r2_hidden(X38,X36)\|r2_hidden(X38,X37)))&((r2_hidden(esk9_2(X39,X40),X39)\|r1_tarski(X39,X40))&(~r2_hidden(esk9_2(X39,X40),X40)\|r1_tarski(X39,X40)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_tarski])])])])])])). cnf(c_0_40, plain, (r2_hidden(X1,X4)\|~r2_hidden(k4_tarski(X1,X2),X3)\|X4!=k9_xtuple_0(X3)), inference(split_conjunct,[status(thm)],[c_0_29])). fof(c_0_41, plain, ![X50, X51]:((~m1_subset_1(X50,k1_zfmisc_1(X51))\|r1_tarski(X50,X51))&(~r1_tarski(X50,X51)\|m1_subset_1(X50,k1_zfmisc_1(X51)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])])). cnf(c_0_42, plain, (m1_subset_1(k2_relset_1(X2,X1),k1_zfmisc_1(X2))\|~v1_relat_1(X1)\|~v5_relat_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_30])). cnf(c_0_43, plain, (k2_relset_1(X2,X1)=k10_xtuple_0(X1)\|~v1_relat_1(X1)\|~v5_relat_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_31])). cnf(c_0_44, plain, (r2_hidden(X2,X4)\|X4!=k10_xtuple_0(X3)\|~r2_hidden(k2_tarski(k2_tarski(X1,X2),k1_tarski(X1)),X3)), inference(evalgc,[status(thm)],[c_0_32])). cnf(c_0_45, negated_conjecture, (r2_hidden(k2_tarski(k2_tarski(X1,X1),k1_tarski(X1)),esk2_0)\|~r2_hidden(X1,esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33, c_0_34]), c_0_35]), c_0_36]), c_0_37]), c_0_38])])])). cnf(c_0_46, plain, (r2_hidden(esk9_2(X1,X2),X1)\|r1_tarski(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_39])). fof(c_0_47, plain, ![X57, X58]:(~v1_relat_1(X58)\|~v4_relat_1(X58,X57)\|m1_subset_1(k1_relset_1(X57,X58),k1_zfmisc_1(X57))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_relset_1])])). fof(c_0_48, plain, ![X42, X43]:(~v1_relat_1(X43)\|~v4_relat_1(X43,X42)\|k1_relset_1(X42,X43)=k9_xtuple_0(X43)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k1_relset_1])])). cnf(c_0_49, plain, (r2_hidden(X1,X4)\|X4!=k9_xtuple_0(X3)\|~r2_hidden(k2_tarski(k2_tarski(X1,X2),k1_tarski(X1)),X3)), inference(rw,[status(thm)],[c_0_40, c_0_20])). fof(c_0_50, plain, ![X52, X53, X54]:((v4_relat_1(X54,X52)\|~m1_subset_1(X54,k1_zfmisc_1(k2_zfmisc_1(X52,X53))))&(v5_relat_1(X54,X53)\|~m1_subset_1(X54,k1_zfmisc_1(k2_zfmisc_1(X52,X53))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_relset_1])])])). fof(c_0_51, plain, ![X44, X45]:(~v1_relat_1(X44)\|(~m1_subset_1(X45,k1_zfmisc_1(X44))\|v1_relat_1(X45))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_relat_1])])])). fof(c_0_52, plain, ![X46, X47]:v1_relat_1(k2_zfmisc_1(X46,X47)), inference(variable_rename,[status(thm)],[fc6_relat_1])). fof(c_0_53, plain, ![X48, X49]:(((r1_tarski(X48,X49)\|X48!=X49)&(r1_tarski(X49,X48)\|X48!=X49))&(~r1_tarski(X48,X49)\|~r1_tarski(X49,X48)\|X48=X49)), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])])). cnf(c_0_54, plain, (r1_tarski(X1,X2)\|~m1_subset_1(X1,k1_zfmisc_1(X2))), inference(split_conjunct,[status(thm)],[c_0_41])). cnf(c_0_55, plain, (m1_subset_1(k2_relset_1(X2,X1),k1_zfmisc_1(X2))\|~v1_relat_1(X1)\|~v5_relat_1(X1,X2)), inference(evalgc,[status(thm)],[c_0_42])). cnf(c_0_56, plain, (k2_relset_1(X2,X1)=k10_xtuple_0(X1)\|~v1_relat_1(X1)\|~v5_relat_1(X1,X2)), inference(evalgc,[status(thm)],[c_0_43])). cnf(c_0_57, plain, (r1_tarski(X1,X2)\|~r2_hidden(esk9_2(X1,X2),X2)), inference(split_conjunct,[status(thm)],[c_0_39])). cnf(c_0_58, negated_conjecture, (r2_hidden(X1,X2)\|X2!=k10_xtuple_0(esk2_0)\|~r2_hidden(X1,esk1_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_44, c_0_45])])). cnf(c_0_59, plain, (r1_tarski(X1,X2)\|r2_hidden(esk9_2(X1,X2),X1)), inference(evalgc,[status(thm)],[c_0_46])). cnf(c_0_60, plain, (m1_subset_1(k1_relset_1(X2,X1),k1_zfmisc_1(X2))\|~v1_relat_1(X1)\|~v4_relat_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_47])). cnf(c_0_61, plain, (k1_relset_1(X2,X1)=k9_xtuple_0(X1)\|~v1_relat_1(X1)\|~v4_relat_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_48])). cnf(c_0_62, plain, (r2_hidden(X1,X4)\|X4!=k9_xtuple_0(X3)\|~r2_hidden(k2_tarski(k2_tarski(X1,X2),k1_tarski(X1)),X3)), inference(evalgc,[status(thm)],[c_0_49])). cnf(c_0_63, negated_conjecture, (k1_relset_1(esk1_0,esk2_0)!=esk1_0\|k2_relset_1(esk1_0,esk2_0)!=esk1_0), inference(split_conjunct,[status(thm)],[c_0_21])). cnf(c_0_64, plain, (v5_relat_1(X1,X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X3,X2)))), inference(split_conjunct,[status(thm)],[c_0_50])). cnf(c_0_65, plain, (v1_relat_1(X2)\|~v1_relat_1(X1)\|~m1_subset_1(X2,k1_zfmisc_1(X1))), inference(split_conjunct,[status(thm)],[c_0_51])). cnf(c_0_66, plain, (v1_relat_1(k2_zfmisc_1(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_52])). cnf(c_0_67, plain, (X1=X2\|~r1_tarski(X1,X2)\|~r1_tarski(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_53])). cnf(c_0_68, plain, (r1_tarski(X1,X2)\|~m1_subset_1(X1,k1_zfmisc_1(X2))), inference(evalgc,[status(thm)],[c_0_54])). cnf(c_0_69, plain, (m1_subset_1(k10_xtuple_0(X2),k1_zfmisc_1(X1))\|~v5_relat_1(X2,X1)\|~v1_relat_1(X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_55, c_0_56])])). cnf(c_0_70, plain, (r1_tarski(X1,X2)\|~r2_hidden(esk9_2(X1,X2),X2)), inference(evalgc,[status(thm)],[c_0_57])). cnf(c_0_71, negated_conjecture, (r2_hidden(esk9_2(esk1_0,X1),X2)\|r1_tarski(esk1_0,X1)\|X2!=k10_xtuple_0(esk2_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_58, c_0_59])])). cnf(c_0_72, plain, (m1_subset_1(k1_relset_1(X2,X1),k1_zfmisc_1(X2))\|~v1_relat_1(X1)\|~v4_relat_1(X1,X2)), inference(evalgc,[status(thm)],[c_0_60])). cnf(c_0_73, plain, (k1_relset_1(X2,X1)=k9_xtuple_0(X1)\|~v1_relat_1(X1)\|~v4_relat_1(X1,X2)), inference(evalgc,[status(thm)],[c_0_61])). cnf(c_0_74, negated_conjecture, (r2_hidden(X1,X2)\|X2!=k9_xtuple_0(esk2_0)\|~r2_hidden(X1,esk1_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_62, c_0_45])])). cnf(c_0_75, negated_conjecture, (k1_relset_1(esk1_0,esk2_0)!=esk1_0\|k2_relset_1(esk1_0,esk2_0)!=esk1_0), inference(evalgc,[status(thm)],[c_0_63])). cnf(c_0_76, plain, (v5_relat_1(X1,X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X3,X2)))), inference(evalgc,[status(thm)],[c_0_64])). cnf(c_0_77, plain, (v1_relat_1(X2)\|~v1_relat_1(X1)\|~m1_subset_1(X2,k1_zfmisc_1(X1))), inference(evalgc,[status(thm)],[c_0_65])). cnf(c_0_78, plain, (v1_relat_1(k2_zfmisc_1(X1,X2))), inference(evalgc,[status(thm)],[c_0_66])). cnf(c_0_79, plain, (X1=X2\|~r1_tarski(X2,X1)\|~r1_tarski(X1,X2)), inference(evalgc,[status(thm)],[c_0_67])). cnf(c_0_80, plain, (r1_tarski(k10_xtuple_0(X1),X2)\|~v5_relat_1(X1,X2)\|~v1_relat_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_68, c_0_69])])). cnf(c_0_81, negated_conjecture, (r1_tarski(esk1_0,X1)\|X1!=k10_xtuple_0(esk2_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_70, c_0_71])])). cnf(c_0_82, plain, (m1_subset_1(k9_xtuple_0(X2),k1_zfmisc_1(X1))\|~v4_relat_1(X2,X1)\|~v1_relat_1(X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_72, c_0_73])])). cnf(c_0_83, negated_conjecture, (r2_hidden(esk9_2(esk1_0,X1),X2)\|r1_tarski(esk1_0,X1)\|X2!=k9_xtuple_0(esk2_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_74, c_0_59])])). cnf(c_0_84, plain, (v4_relat_1(X1,X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_50])). cnf(c_0_85, negated_conjecture, (k1_relset_1(esk1_0,esk2_0)!=esk1_0\|k10_xtuple_0(esk2_0)!=esk1_0\|~v5_relat_1(esk2_0,esk1_0)\|~v1_relat_1(esk2_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_75, c_0_56])])). cnf(c_0_86, negated_conjecture, (v5_relat_1(esk2_0,esk1_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_76, c_0_34])])). cnf(c_0_87, negated_conjecture, (v1_relat_1(esk2_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77, c_0_34]), c_0_78])])])). cnf(c_0_88, plain, (X1=k10_xtuple_0(X2)\|~r1_tarski(X1,k10_xtuple_0(X2))\|~v5_relat_1(X2,X1)\|~v1_relat_1(X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_79, c_0_80])])). cnf(c_0_89, negated_conjecture, (r1_tarski(esk1_0,k10_xtuple_0(esk2_0))), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_81])])). cnf(c_0_90, plain, (r1_tarski(k9_xtuple_0(X1),X2)\|~v4_relat_1(X1,X2)\|~v1_relat_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_68, c_0_82])])). cnf(c_0_91, negated_conjecture, (r1_tarski(esk1_0,X1)\|X1!=k9_xtuple_0(esk2_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_70, c_0_83])])). cnf(c_0_92, plain, (v4_relat_1(X1,X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(evalgc,[status(thm)],[c_0_84])). cnf(c_0_93, negated_conjecture, (k1_relset_1(esk1_0,esk2_0)!=esk1_0\|k10_xtuple_0(esk2_0)!=esk1_0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_85, c_0_86]), c_0_87])])). cnf(c_0_94, negated_conjecture, (k10_xtuple_0(esk2_0)=esk1_0), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88, c_0_89]), c_0_86]), c_0_87])])])). cnf(c_0_95, plain, (X1=k9_xtuple_0(X2)\|~r1_tarski(X1,k9_xtuple_0(X2))\|~v4_relat_1(X2,X1)\|~v1_relat_1(X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_79, c_0_90])])). cnf(c_0_96, negated_conjecture, (r1_tarski(esk1_0,k9_xtuple_0(esk2_0))), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_91])])). cnf(c_0_97, negated_conjecture, (v4_relat_1(esk2_0,esk1_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_92, c_0_34])])). cnf(c_0_98, negated_conjecture, (k1_relset_1(esk1_0,esk2_0)!=esk1_0), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_93, c_0_94])])])). cnf(c_0_99, negated_conjecture, (k9_xtuple_0(esk2_0)=esk1_0), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95, c_0_96]), c_0_97]), c_0_87])])])). cnf(c_0_100, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98, c_0_73]), c_0_99]), c_0_97]), c_0_87])]), ['proof']). # SZS output end CNFRefutation	reserve X,Y for set, x,x1,x2,y,y1,y2,z for set, f,g,h for Function; reserve M for non empty set; reserve D for non empty set; reserve P for Relation; reserve O for Order of X; reserve R,P for Relation, X,X1,X2,Y,Z,x,y,z,u for set, g,h for Function, O for Order of X, D for non empty set, d,d1,d2 for Element of D, A1,A2,B for Ordinal, L,L1,L2 for T-Sequence; theorem Th14: dom O = X & rng O = X proof thus dom O = X proof thus dom O c= X; let x; assume x in X; then [x,x] in O by Th3; hence thesis by XTUPLE_0:def 12; end; thus rng O c= X; let x; assume x in X; then [x,x] in O by Th3; hence thesis by XTUPLE_0:def 13; end;	Convert the following ATP output trace into a readable Mizar proof.
t8_jgraph_2	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t8_jgraph_2, conjecture, ![X1]:(m1_subset_1(X1,u1_struct_0(k15_euclid(np__2)))=>X1=k19_euclid(k3_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k4_pscomp_1,X1),k3_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k5_pscomp_1,X1))), file('/scratch/mptp/predsminms1/t8_jgraph_2__0', t8_jgraph_2)). fof(redefinition_k3_funct_2, axiom, ![X1, X2, X3, X4]:((~(v1_xboole_0(X1))&((v1_funct_1(X3)&(v1_funct_2(X3,X1,X2)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))))&m1_subset_1(X4,X1)))=>k3_funct_2(X1,X2,X3,X4)=k1_funct_1(X3,X4)), file('/scratch/mptp/predsminms1/t8_jgraph_2__0', redefinition_k3_funct_2)). fof(cc1_relset_1, axiom, ![X1, X2, X3]:(m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))=>v1_relat_1(X3)), file('/scratch/mptp/predsminms1/t8_jgraph_2__0', cc1_relset_1)). fof(cc2_relset_1, axiom, ![X1, X2, X3]:(m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))=>(v4_relat_1(X3,X1)&v5_relat_1(X3,X2))), file('/scratch/mptp/predsminms1/t8_jgraph_2__0', cc2_relset_1)). fof(dt_k5_pscomp_1, axiom, (v1_funct_1(k5_pscomp_1)&(v1_funct_2(k5_pscomp_1,u1_struct_0(k15_euclid(np__2)),k1_numbers)&m1_subset_1(k5_pscomp_1,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k15_euclid(np__2)),k1_numbers))))), file('/scratch/mptp/predsminms1/t8_jgraph_2__0', dt_k5_pscomp_1)). fof(redefinition_k1_seq_1, axiom, ![X1, X2]:((v1_relat_1(X1)&(v1_funct_1(X1)&v3_valued_0(X1)))=>k1_seq_1(X1,X2)=k1_funct_1(X1,X2)), file('/scratch/mptp/predsminms1/t8_jgraph_2__0', redefinition_k1_seq_1)). fof(cc30_valued_0, axiom, ![X1]:((v1_relat_1(X1)&v5_relat_1(X1,k1_numbers))=>(v1_relat_1(X1)&v3_valued_0(X1))), file('/scratch/mptp/predsminms1/t8_jgraph_2__0', cc30_valued_0)). fof(t5_subset, axiom, ![X1, X2, X3]:~((r2_hidden(X1,X2)&(m1_subset_1(X2,k1_zfmisc_1(X3))&v1_xboole_0(X3)))), file('/scratch/mptp/predsminms1/t8_jgraph_2__0', t5_subset)). fof(rc21_struct_0, axiom, ![X1]:((~(v2_struct_0(X1))&l1_struct_0(X1))=>?[X2]:(m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))&(~(v1_xboole_0(X2))&v1_zfmisc_1(X2)))), file('/scratch/mptp/predsminms1/t8_jgraph_2__0', rc21_struct_0)). fof(d5_pscomp_1, axiom, ![X1]:((v1_funct_1(X1)&(v1_funct_2(X1,u1_struct_0(k15_euclid(np__2)),k1_numbers)&m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k15_euclid(np__2)),k1_numbers)))))=>(X1=k4_pscomp_1<=>![X2]:(m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))=>k1_seq_1(X1,X2)=k17_euclid(X2)))), file('/scratch/mptp/predsminms1/t8_jgraph_2__0', d5_pscomp_1)). fof(t2_subset, axiom, ![X1, X2]:(m1_subset_1(X1,X2)=>(v1_xboole_0(X2)\|r2_hidden(X1,X2))), file('/scratch/mptp/predsminms1/t8_jgraph_2__0', t2_subset)). fof(dt_k4_pscomp_1, axiom, (v1_funct_1(k4_pscomp_1)&(v1_funct_2(k4_pscomp_1,u1_struct_0(k15_euclid(np__2)),k1_numbers)&m1_subset_1(k4_pscomp_1,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k15_euclid(np__2)),k1_numbers))))), file('/scratch/mptp/predsminms1/t8_jgraph_2__0', dt_k4_pscomp_1)). fof(t53_euclid, axiom, ![X1]:(m1_subset_1(X1,u1_struct_0(k15_euclid(np__2)))=>X1=k19_euclid(k17_euclid(X1),k18_euclid(X1))), file('/scratch/mptp/predsminms1/t8_jgraph_2__0', t53_euclid)). fof(d6_pscomp_1, axiom, ![X1]:((v1_funct_1(X1)&(v1_funct_2(X1,u1_struct_0(k15_euclid(np__2)),k1_numbers)&m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k15_euclid(np__2)),k1_numbers)))))=>(X1=k5_pscomp_1<=>![X2]:(m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))=>k1_seq_1(X1,X2)=k18_euclid(X2)))), file('/scratch/mptp/predsminms1/t8_jgraph_2__0', d6_pscomp_1)). fof(existence_m1_subset_1, axiom, ![X1]:?[X2]:m1_subset_1(X2,X1), file('/scratch/mptp/predsminms1/t8_jgraph_2__0', existence_m1_subset_1)). fof(dt_l1_rlvect_1, axiom, ![X1]:(l1_rlvect_1(X1)=>l2_algstr_0(X1)), file('/scratch/mptp/predsminms1/t8_jgraph_2__0', dt_l1_rlvect_1)). fof(dt_l1_rltopsp1, axiom, ![X1]:(l1_rltopsp1(X1)=>(l1_rlvect_1(X1)&l1_pre_topc(X1))), file('/scratch/mptp/predsminms1/t8_jgraph_2__0', dt_l1_rltopsp1)). fof(dt_l2_struct_0, axiom, ![X1]:(l2_struct_0(X1)=>l1_struct_0(X1)), file('/scratch/mptp/predsminms1/t8_jgraph_2__0', dt_l2_struct_0)). fof(dt_l2_algstr_0, axiom, ![X1]:(l2_algstr_0(X1)=>(l2_struct_0(X1)&l1_algstr_0(X1))), file('/scratch/mptp/predsminms1/t8_jgraph_2__0', dt_l2_algstr_0)). fof(dt_k15_euclid, axiom, ![X1]:(v7_ordinal1(X1)=>(v5_rltopsp1(k15_euclid(X1))&l1_rltopsp1(k15_euclid(X1)))), file('/scratch/mptp/predsminms1/t8_jgraph_2__0', dt_k15_euclid)). fof(fc5_euclid, axiom, ![X1]:(v7_ordinal1(X1)=>(~(v2_struct_0(k15_euclid(X1)))&v5_rltopsp1(k15_euclid(X1)))), file('/scratch/mptp/predsminms1/t8_jgraph_2__0', fc5_euclid)). fof(cc8_ordinal1, axiom, ![X1]:(m1_subset_1(X1,k4_ordinal1)=>v7_ordinal1(X1)), file('/scratch/mptp/predsminms1/t8_jgraph_2__0', cc8_ordinal1)). fof(redefinition_k5_numbers, axiom, k5_numbers=k4_ordinal1, file('/scratch/mptp/predsminms1/t8_jgraph_2__0', redefinition_k5_numbers)). fof(spc2_numerals, axiom, ((v2_xxreal_0(np__2)&m2_subset_1(np__2,k1_numbers,k5_numbers))&(m1_subset_1(np__2,k5_numbers)&m1_subset_1(np__2,k1_numbers))), file('/scratch/mptp/predsminms1/t8_jgraph_2__0', spc2_numerals)). fof(c_0_24, negated_conjecture, ~(![X1]:(m1_subset_1(X1,u1_struct_0(k15_euclid(np__2)))=>X1=k19_euclid(k3_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k4_pscomp_1,X1),k3_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k5_pscomp_1,X1)))), inference(assume_negation,[status(cth)],[t8_jgraph_2])). fof(c_0_25, negated_conjecture, (m1_subset_1(esk1_0,u1_struct_0(k15_euclid(np__2)))&esk1_0!=k19_euclid(k3_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k4_pscomp_1,esk1_0),k3_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k5_pscomp_1,esk1_0))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])])). fof(c_0_26, plain, ![X24, X25, X26, X27]:(v1_xboole_0(X24)\|(~v1_funct_1(X26)\|(~v1_funct_2(X26,X24,X25)\|~m1_subset_1(X26,k1_zfmisc_1(k2_zfmisc_1(X24,X25))))\|~m1_subset_1(X27,X24))\|k3_funct_2(X24,X25,X26,X27)=k1_funct_1(X26,X27)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[redefinition_k3_funct_2])])])). fof(c_0_27, plain, ![X7, X8, X9]:(~m1_subset_1(X9,k1_zfmisc_1(k2_zfmisc_1(X7,X8)))\|v1_relat_1(X9)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relset_1])])). fof(c_0_28, plain, ![X11, X12, X13]:((v4_relat_1(X13,X11)\|~m1_subset_1(X13,k1_zfmisc_1(k2_zfmisc_1(X11,X12))))&(v5_relat_1(X13,X12)\|~m1_subset_1(X13,k1_zfmisc_1(k2_zfmisc_1(X11,X12))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_relset_1])])])). cnf(c_0_29, negated_conjecture, (esk1_0!=k19_euclid(k3_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k4_pscomp_1,esk1_0),k3_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k5_pscomp_1,esk1_0))), inference(split_conjunct,[status(thm)],[c_0_25])). cnf(c_0_30, plain, (v1_xboole_0(X1)\|k3_funct_2(X1,X3,X2,X4)=k1_funct_1(X2,X4)\|~v1_funct_1(X2)\|~v1_funct_2(X2,X1,X3)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))\|~m1_subset_1(X4,X1)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_31, plain, (v1_funct_2(k5_pscomp_1,u1_struct_0(k15_euclid(np__2)),k1_numbers)), inference(split_conjunct,[status(thm)],[dt_k5_pscomp_1])). cnf(c_0_32, plain, (v1_funct_1(k5_pscomp_1)), inference(split_conjunct,[status(thm)],[dt_k5_pscomp_1])). cnf(c_0_33, plain, (m1_subset_1(k5_pscomp_1,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k15_euclid(np__2)),k1_numbers)))), inference(split_conjunct,[status(thm)],[dt_k5_pscomp_1])). cnf(c_0_34, negated_conjecture, (m1_subset_1(esk1_0,u1_struct_0(k15_euclid(np__2)))), inference(split_conjunct,[status(thm)],[c_0_25])). fof(c_0_35, plain, ![X14, X15]:(~v1_relat_1(X14)\|(~v1_funct_1(X14)\|~v3_valued_0(X14))\|k1_seq_1(X14,X15)=k1_funct_1(X14,X15)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k1_seq_1])])). cnf(c_0_36, plain, (v1_relat_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_27])). fof(c_0_37, plain, ![X10]:((v1_relat_1(X10)\|(~v1_relat_1(X10)\|~v5_relat_1(X10,k1_numbers)))&(v3_valued_0(X10)\|(~v1_relat_1(X10)\|~v5_relat_1(X10,k1_numbers)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc30_valued_0])])])). cnf(c_0_38, plain, (v5_relat_1(X1,X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X3,X2)))), inference(split_conjunct,[status(thm)],[c_0_28])). fof(c_0_39, plain, ![X39, X40, X41]:(~r2_hidden(X39,X40)\|(~m1_subset_1(X40,k1_zfmisc_1(X41))\|~v1_xboole_0(X41))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])])). fof(c_0_40, plain, ![X33]:((m1_subset_1(esk4_1(X33),k1_zfmisc_1(u1_struct_0(X33)))\|(v2_struct_0(X33)\|~l1_struct_0(X33)))&((~v1_xboole_0(esk4_1(X33))\|(v2_struct_0(X33)\|~l1_struct_0(X33)))&(v1_zfmisc_1(esk4_1(X33))\|(v2_struct_0(X33)\|~l1_struct_0(X33))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[rc21_struct_0])])])])])). cnf(c_0_41, negated_conjecture, (k19_euclid(k3_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k4_pscomp_1,esk1_0),k3_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k5_pscomp_1,esk1_0))!=esk1_0), inference(evalgc,[status(thm)],[c_0_29])). cnf(c_0_42, plain, (k3_funct_2(X1,X3,X2,X4)=k1_funct_1(X2,X4)\|v1_xboole_0(X1)\|~v1_funct_1(X2)\|~m1_subset_1(X4,X1)\|~v1_funct_2(X2,X1,X3)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))), inference(evalgc,[status(thm)],[c_0_30])). cnf(c_0_43, plain, (v1_funct_2(k5_pscomp_1,u1_struct_0(k15_euclid(np__2)),k1_numbers)), inference(evalgc,[status(thm)],[c_0_31])). cnf(c_0_44, plain, (v1_funct_1(k5_pscomp_1)), inference(evalgc,[status(thm)],[c_0_32])). cnf(c_0_45, plain, (m1_subset_1(k5_pscomp_1,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k15_euclid(np__2)),k1_numbers)))), inference(evalgc,[status(thm)],[c_0_33])). cnf(c_0_46, negated_conjecture, (m1_subset_1(esk1_0,u1_struct_0(k15_euclid(np__2)))), inference(evalgc,[status(thm)],[c_0_34])). cnf(c_0_47, plain, (k1_seq_1(X1,X2)=k1_funct_1(X1,X2)\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v3_valued_0(X1)), inference(split_conjunct,[status(thm)],[c_0_35])). cnf(c_0_48, plain, (v1_relat_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(evalgc,[status(thm)],[c_0_36])). cnf(c_0_49, plain, (v3_valued_0(X1)\|~v1_relat_1(X1)\|~v5_relat_1(X1,k1_numbers)), inference(split_conjunct,[status(thm)],[c_0_37])). cnf(c_0_50, plain, (v5_relat_1(X1,X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X3,X2)))), inference(evalgc,[status(thm)],[c_0_38])). fof(c_0_51, plain, ![X16, X17]:((X16!=k4_pscomp_1\|(~m1_subset_1(X17,u1_struct_0(k15_euclid(np__2)))\|k1_seq_1(X16,X17)=k17_euclid(X17))\|(~v1_funct_1(X16)\|(~v1_funct_2(X16,u1_struct_0(k15_euclid(np__2)),k1_numbers)\|~m1_subset_1(X16,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k15_euclid(np__2)),k1_numbers))))))&((m1_subset_1(esk2_1(X16),u1_struct_0(k15_euclid(np__2)))\|X16=k4_pscomp_1\|(~v1_funct_1(X16)\|(~v1_funct_2(X16,u1_struct_0(k15_euclid(np__2)),k1_numbers)\|~m1_subset_1(X16,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k15_euclid(np__2)),k1_numbers))))))&(k1_seq_1(X16,esk2_1(X16))!=k17_euclid(esk2_1(X16))\|X16=k4_pscomp_1\|(~v1_funct_1(X16)\|(~v1_funct_2(X16,u1_struct_0(k15_euclid(np__2)),k1_numbers)\|~m1_subset_1(X16,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k15_euclid(np__2)),k1_numbers)))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_pscomp_1])])])])])). cnf(c_0_52, plain, (~r2_hidden(X1,X2)\|~m1_subset_1(X2,k1_zfmisc_1(X3))\|~v1_xboole_0(X3)), inference(split_conjunct,[status(thm)],[c_0_39])). cnf(c_0_53, plain, (m1_subset_1(esk4_1(X1),k1_zfmisc_1(u1_struct_0(X1)))\|v2_struct_0(X1)\|~l1_struct_0(X1)), inference(split_conjunct,[status(thm)],[c_0_40])). fof(c_0_54, plain, ![X37, X38]:(~m1_subset_1(X37,X38)\|(v1_xboole_0(X38)\|r2_hidden(X37,X38))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])])). cnf(c_0_55, negated_conjecture, (v1_xboole_0(u1_struct_0(k15_euclid(np__2)))\|k19_euclid(k3_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k4_pscomp_1,esk1_0),k1_funct_1(k5_pscomp_1,esk1_0))!=esk1_0), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41, c_0_42]), c_0_43]), c_0_44]), c_0_45]), c_0_46])])])). cnf(c_0_56, plain, (k1_funct_1(X1,X2)=k1_seq_1(X1,X2)\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v3_valued_0(X1)), inference(evalgc,[status(thm)],[c_0_47])). cnf(c_0_57, plain, (v1_relat_1(k5_pscomp_1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_48, c_0_45])])). cnf(c_0_58, plain, (v3_valued_0(X1)\|~v1_relat_1(X1)\|~v5_relat_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[c_0_49])). cnf(c_0_59, plain, (v5_relat_1(k5_pscomp_1,k1_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_50, c_0_45])])). cnf(c_0_60, plain, (m1_subset_1(k4_pscomp_1,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k15_euclid(np__2)),k1_numbers)))), inference(split_conjunct,[status(thm)],[dt_k4_pscomp_1])). fof(c_0_61, plain, ![X6]:(~m1_subset_1(X6,u1_struct_0(k15_euclid(np__2)))\|X6=k19_euclid(k17_euclid(X6),k18_euclid(X6))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t53_euclid])])). cnf(c_0_62, plain, (k1_seq_1(X1,X2)=k17_euclid(X2)\|X1!=k4_pscomp_1\|~m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))\|~v1_funct_1(X1)\|~v1_funct_2(X1,u1_struct_0(k15_euclid(np__2)),k1_numbers)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k15_euclid(np__2)),k1_numbers)))), inference(split_conjunct,[status(thm)],[c_0_51])). cnf(c_0_63, plain, (v1_funct_2(k4_pscomp_1,u1_struct_0(k15_euclid(np__2)),k1_numbers)), inference(split_conjunct,[status(thm)],[dt_k4_pscomp_1])). cnf(c_0_64, plain, (v1_funct_1(k4_pscomp_1)), inference(split_conjunct,[status(thm)],[dt_k4_pscomp_1])). fof(c_0_65, plain, ![X19, X20]:((X19!=k5_pscomp_1\|(~m1_subset_1(X20,u1_struct_0(k15_euclid(np__2)))\|k1_seq_1(X19,X20)=k18_euclid(X20))\|(~v1_funct_1(X19)\|(~v1_funct_2(X19,u1_struct_0(k15_euclid(np__2)),k1_numbers)\|~m1_subset_1(X19,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k15_euclid(np__2)),k1_numbers))))))&((m1_subset_1(esk3_1(X19),u1_struct_0(k15_euclid(np__2)))\|X19=k5_pscomp_1\|(~v1_funct_1(X19)\|(~v1_funct_2(X19,u1_struct_0(k15_euclid(np__2)),k1_numbers)\|~m1_subset_1(X19,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k15_euclid(np__2)),k1_numbers))))))&(k1_seq_1(X19,esk3_1(X19))!=k18_euclid(esk3_1(X19))\|X19=k5_pscomp_1\|(~v1_funct_1(X19)\|(~v1_funct_2(X19,u1_struct_0(k15_euclid(np__2)),k1_numbers)\|~m1_subset_1(X19,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k15_euclid(np__2)),k1_numbers)))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d6_pscomp_1])])])])])). cnf(c_0_66, plain, (~v1_xboole_0(X3)\|~r2_hidden(X1,X2)\|~m1_subset_1(X2,k1_zfmisc_1(X3))), inference(evalgc,[status(thm)],[c_0_52])). cnf(c_0_67, plain, (v2_struct_0(X1)\|m1_subset_1(esk4_1(X1),k1_zfmisc_1(u1_struct_0(X1)))\|~l1_struct_0(X1)), inference(evalgc,[status(thm)],[c_0_53])). cnf(c_0_68, plain, (v1_xboole_0(X2)\|r2_hidden(X1,X2)\|~m1_subset_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_54])). cnf(c_0_69, negated_conjecture, (v1_xboole_0(u1_struct_0(k15_euclid(np__2)))\|k19_euclid(k3_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k4_pscomp_1,esk1_0),k1_seq_1(k5_pscomp_1,esk1_0))!=esk1_0\|~v3_valued_0(k5_pscomp_1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55, c_0_56]), c_0_44]), c_0_57])])])). cnf(c_0_70, plain, (v3_valued_0(k5_pscomp_1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58, c_0_59]), c_0_57])])])). cnf(c_0_71, plain, (m1_subset_1(k4_pscomp_1,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k15_euclid(np__2)),k1_numbers)))), inference(evalgc,[status(thm)],[c_0_60])). cnf(c_0_72, plain, (X1=k19_euclid(k17_euclid(X1),k18_euclid(X1))\|~m1_subset_1(X1,u1_struct_0(k15_euclid(np__2)))), inference(split_conjunct,[status(thm)],[c_0_61])). cnf(c_0_73, plain, (k1_seq_1(X1,X2)=k17_euclid(X2)\|X1!=k4_pscomp_1\|~v1_funct_1(X1)\|~m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))\|~v1_funct_2(X1,u1_struct_0(k15_euclid(np__2)),k1_numbers)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k15_euclid(np__2)),k1_numbers)))), inference(evalgc,[status(thm)],[c_0_62])). cnf(c_0_74, plain, (v1_funct_2(k4_pscomp_1,u1_struct_0(k15_euclid(np__2)),k1_numbers)), inference(evalgc,[status(thm)],[c_0_63])). cnf(c_0_75, plain, (v1_funct_1(k4_pscomp_1)), inference(evalgc,[status(thm)],[c_0_64])). cnf(c_0_76, plain, (k1_seq_1(X1,X2)=k18_euclid(X2)\|X1!=k5_pscomp_1\|~m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))\|~v1_funct_1(X1)\|~v1_funct_2(X1,u1_struct_0(k15_euclid(np__2)),k1_numbers)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k15_euclid(np__2)),k1_numbers)))), inference(split_conjunct,[status(thm)],[c_0_65])). cnf(c_0_77, plain, (v2_struct_0(X2)\|~r2_hidden(X1,esk4_1(X2))\|~v1_xboole_0(u1_struct_0(X2))\|~l1_struct_0(X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_66, c_0_67])])). cnf(c_0_78, plain, (v1_xboole_0(X2)\|r2_hidden(X1,X2)\|~m1_subset_1(X1,X2)), inference(evalgc,[status(thm)],[c_0_68])). cnf(c_0_79, plain, (v2_struct_0(X1)\|~v1_xboole_0(esk4_1(X1))\|~l1_struct_0(X1)), inference(split_conjunct,[status(thm)],[c_0_40])). fof(c_0_80, plain, ![X35]:m1_subset_1(esk5_1(X35),X35), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])])). cnf(c_0_81, negated_conjecture, (v1_xboole_0(u1_struct_0(k15_euclid(np__2)))\|k19_euclid(k3_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k4_pscomp_1,esk1_0),k1_seq_1(k5_pscomp_1,esk1_0))!=esk1_0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_69, c_0_70])])). cnf(c_0_82, plain, (v5_relat_1(k4_pscomp_1,k1_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_50, c_0_71])])). cnf(c_0_83, plain, (v1_relat_1(k4_pscomp_1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_48, c_0_71])])). cnf(c_0_84, plain, (k19_euclid(k17_euclid(X1),k18_euclid(X1))=X1\|~m1_subset_1(X1,u1_struct_0(k15_euclid(np__2)))), inference(evalgc,[status(thm)],[c_0_72])). cnf(c_0_85, plain, (k17_euclid(X1)=k1_seq_1(k4_pscomp_1,X1)\|~m1_subset_1(X1,u1_struct_0(k15_euclid(np__2)))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73, c_0_71]), c_0_74]), c_0_75])])])). cnf(c_0_86, plain, (k1_seq_1(X1,X2)=k18_euclid(X2)\|X1!=k5_pscomp_1\|~v1_funct_1(X1)\|~m1_subset_1(X2,u1_struct_0(k15_euclid(np__2)))\|~v1_funct_2(X1,u1_struct_0(k15_euclid(np__2)),k1_numbers)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k15_euclid(np__2)),k1_numbers)))), inference(evalgc,[status(thm)],[c_0_76])). fof(c_0_87, plain, ![X30]:(~l1_rlvect_1(X30)\|l2_algstr_0(X30)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_rlvect_1])])). fof(c_0_88, plain, ![X31]:((l1_rlvect_1(X31)\|~l1_rltopsp1(X31))&(l1_pre_topc(X31)\|~l1_rltopsp1(X31))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_rltopsp1])])])). cnf(c_0_89, plain, (v2_struct_0(X1)\|v1_xboole_0(esk4_1(X1))\|~l1_struct_0(X1)\|~v1_xboole_0(u1_struct_0(X1))\|~m1_subset_1(X2,esk4_1(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_77, c_0_78])])). cnf(c_0_90, plain, (v2_struct_0(X1)\|~l1_struct_0(X1)\|~v1_xboole_0(esk4_1(X1))), inference(evalgc,[status(thm)],[c_0_79])). cnf(c_0_91, plain, (m1_subset_1(esk5_1(X1),X1)), inference(split_conjunct,[status(thm)],[c_0_80])). cnf(c_0_92, negated_conjecture, (v1_xboole_0(u1_struct_0(k15_euclid(np__2)))\|k19_euclid(k1_funct_1(k4_pscomp_1,esk1_0),k1_seq_1(k5_pscomp_1,esk1_0))!=esk1_0), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81, c_0_42]), c_0_74]), c_0_75]), c_0_71]), c_0_46])])])). cnf(c_0_93, plain, (v3_valued_0(k4_pscomp_1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58, c_0_82]), c_0_83])])])). cnf(c_0_94, plain, (k19_euclid(k1_seq_1(k4_pscomp_1,X1),k18_euclid(X1))=X1\|~m1_subset_1(X1,u1_struct_0(k15_euclid(np__2)))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_84, c_0_85])])). cnf(c_0_95, plain, (k18_euclid(X1)=k1_seq_1(k5_pscomp_1,X1)\|~m1_subset_1(X1,u1_struct_0(k15_euclid(np__2)))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86, c_0_45]), c_0_43]), c_0_44])])])). fof(c_0_96, plain, ![X28]:(~l2_struct_0(X28)\|l1_struct_0(X28)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l2_struct_0])])). fof(c_0_97, plain, ![X29]:((l2_struct_0(X29)\|~l2_algstr_0(X29))&(l1_algstr_0(X29)\|~l2_algstr_0(X29))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l2_algstr_0])])])). cnf(c_0_98, plain, (l2_algstr_0(X1)\|~l1_rlvect_1(X1)), inference(split_conjunct,[status(thm)],[c_0_87])). cnf(c_0_99, plain, (l1_rlvect_1(X1)\|~l1_rltopsp1(X1)), inference(split_conjunct,[status(thm)],[c_0_88])). fof(c_0_100, plain, ![X32]:((v5_rltopsp1(k15_euclid(X32))\|~v7_ordinal1(X32))&(l1_rltopsp1(k15_euclid(X32))\|~v7_ordinal1(X32))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k15_euclid])])])). fof(c_0_101, plain, ![X23]:((~v2_struct_0(k15_euclid(X23))\|~v7_ordinal1(X23))&(v5_rltopsp1(k15_euclid(X23))\|~v7_ordinal1(X23))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fc5_euclid])])])])). cnf(c_0_102, plain, (v2_struct_0(X1)\|~l1_struct_0(X1)\|~v1_xboole_0(u1_struct_0(X1))\|~m1_subset_1(X2,esk4_1(X1))), inference(csr,[status(thm)],[c_0_89, c_0_90])). cnf(c_0_103, plain, (m1_subset_1(esk5_1(X1),X1)), inference(evalgc,[status(thm)],[c_0_91])). cnf(c_0_104, negated_conjecture, (v1_xboole_0(u1_struct_0(k15_euclid(np__2)))\|k19_euclid(k1_seq_1(k4_pscomp_1,esk1_0),k1_seq_1(k5_pscomp_1,esk1_0))!=esk1_0), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92, c_0_56]), c_0_93]), c_0_75]), c_0_83])])])). cnf(c_0_105, plain, (k19_euclid(k1_seq_1(k4_pscomp_1,X1),k1_seq_1(k5_pscomp_1,X1))=X1\|~m1_subset_1(X1,u1_struct_0(k15_euclid(np__2)))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_94, c_0_95])])). cnf(c_0_106, plain, (l1_struct_0(X1)\|~l2_struct_0(X1)), inference(split_conjunct,[status(thm)],[c_0_96])). cnf(c_0_107, plain, (l2_struct_0(X1)\|~l2_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_97])). cnf(c_0_108, plain, (l2_algstr_0(X1)\|~l1_rlvect_1(X1)), inference(evalgc,[status(thm)],[c_0_98])). cnf(c_0_109, plain, (l1_rlvect_1(X1)\|~l1_rltopsp1(X1)), inference(evalgc,[status(thm)],[c_0_99])). cnf(c_0_110, plain, (l1_rltopsp1(k15_euclid(X1))\|~v7_ordinal1(X1)), inference(split_conjunct,[status(thm)],[c_0_100])). cnf(c_0_111, plain, (~v2_struct_0(k15_euclid(X1))\|~v7_ordinal1(X1)), inference(split_conjunct,[status(thm)],[c_0_101])). cnf(c_0_112, plain, (v2_struct_0(X1)\|~l1_struct_0(X1)\|~v1_xboole_0(u1_struct_0(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_102, c_0_103])])). cnf(c_0_113, negated_conjecture, (v1_xboole_0(u1_struct_0(k15_euclid(np__2)))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104, c_0_105]), c_0_46])])])). cnf(c_0_114, plain, (l1_struct_0(X1)\|~l2_struct_0(X1)), inference(evalgc,[status(thm)],[c_0_106])). cnf(c_0_115, plain, (l2_struct_0(X1)\|~l2_algstr_0(X1)), inference(evalgc,[status(thm)],[c_0_107])). cnf(c_0_116, plain, (l2_algstr_0(X1)\|~l1_rltopsp1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_108, c_0_109])])). cnf(c_0_117, plain, (l1_rltopsp1(k15_euclid(X1))\|~v7_ordinal1(X1)), inference(evalgc,[status(thm)],[c_0_110])). fof(c_0_118, plain, ![X22]:(~m1_subset_1(X22,k4_ordinal1)\|v7_ordinal1(X22)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc8_ordinal1])])). cnf(c_0_119, plain, (~v7_ordinal1(X1)\|~v2_struct_0(k15_euclid(X1))), inference(evalgc,[status(thm)],[c_0_111])). cnf(c_0_120, negated_conjecture, (v2_struct_0(k15_euclid(np__2))\|~l1_struct_0(k15_euclid(np__2))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_112, c_0_113])])). cnf(c_0_121, plain, (l1_struct_0(X1)\|~l2_algstr_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_114, c_0_115])])). cnf(c_0_122, plain, (l2_algstr_0(k15_euclid(X1))\|~v7_ordinal1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_116, c_0_117])])). cnf(c_0_123, plain, (v7_ordinal1(X1)\|~m1_subset_1(X1,k4_ordinal1)), inference(split_conjunct,[status(thm)],[c_0_118])). cnf(c_0_124, plain, (k5_numbers=k4_ordinal1), inference(split_conjunct,[status(thm)],[redefinition_k5_numbers])). cnf(c_0_125, negated_conjecture, (~v7_ordinal1(np__2)\|~l1_struct_0(k15_euclid(np__2))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_119, c_0_120])])). cnf(c_0_126, plain, (l1_struct_0(k15_euclid(X1))\|~v7_ordinal1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_121, c_0_122])])). cnf(c_0_127, plain, (v7_ordinal1(X1)\|~m1_subset_1(X1,k4_ordinal1)), inference(evalgc,[status(thm)],[c_0_123])). cnf(c_0_128, plain, (k4_ordinal1=k5_numbers), inference(evalgc,[status(thm)],[c_0_124])). cnf(c_0_129, plain, (m1_subset_1(np__2,k5_numbers)), inference(split_conjunct,[status(thm)],[spc2_numerals])). cnf(c_0_130, negated_conjecture, (~v7_ordinal1(np__2)), inference(csr,[status(thm)],[c_0_125, c_0_126])). cnf(c_0_131, plain, (v7_ordinal1(X1)\|~m1_subset_1(X1,k5_numbers)), inference(rw,[status(thm)],[c_0_127, c_0_128])). cnf(c_0_132, plain, (m1_subset_1(np__2,k5_numbers)), inference(evalgc,[status(thm)],[c_0_129])). cnf(c_0_133, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130, c_0_131]), c_0_132])]), ['proof']). # SZS output end CNFRefutation	reserve T,T1,T2,S for non empty TopSpace; theorem Th8: for p being Point of TOP-REAL 2 holds p=\|[proj1.p,proj2.p]\| proof let p be Point of TOP-REAL 2; p=\|[p`1,p`2]\| & p`1=proj1.p by EUCLID:53,PSCOMP_1:def 5; hence thesis by PSCOMP_1:def 6; end;	Convert the following ATP output trace into a readable Mizar proof.
t51_scmyciel	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(d2_enumset1, axiom, ![X1, X2, X3, X4, X5]:(X5=k2_enumset1(X1,X2,X3,X4)<=>![X6]:(r2_hidden(X6,X5)<=>~((~(X6=X1)&(~(X6=X2)&(~(X6=X3)&~(X6=X4))))))), file('/scratch/mptp/predsminms1/t51_scmyciel__0', d2_enumset1)). fof(t51_scmyciel, conjecture, ![X1]:(v4_scmyciel(X1)=>![X2, X3]:((r2_hidden(X2,k3_tarski(X1))&(r2_hidden(X3,k3_tarski(X1))&r2_hidden(k2_tarski(X2,X3),X1)))=>(v4_scmyciel(k2_enumset1(k1_xboole_0,k1_tarski(X2),k1_tarski(X3),k2_tarski(X2,X3)))&(v5_scmyciel(k2_enumset1(k1_xboole_0,k1_tarski(X2),k1_tarski(X3),k2_tarski(X2,X3)))&m1_subset_1(k2_enumset1(k1_xboole_0,k1_tarski(X2),k1_tarski(X3),k2_tarski(X2,X3)),k1_zfmisc_1(X1)))))), file('/scratch/mptp/predsminms1/t51_scmyciel__0', t51_scmyciel)). fof(d3_tarski, axiom, ![X1, X2]:(r1_tarski(X1,X2)<=>![X3]:(r2_hidden(X3,X1)=>r2_hidden(X3,X2))), file('/scratch/mptp/predsminms1/t51_scmyciel__0', d3_tarski)). fof(t37_scmyciel, axiom, ![X1, X2]:k5_scmyciel(k2_tarski(X1,X2))=k2_enumset1(k1_xboole_0,k1_tarski(X1),k1_tarski(X2),k2_tarski(X1,X2)), file('/scratch/mptp/predsminms1/t51_scmyciel__0', t37_scmyciel)). fof(fc14_scmyciel, axiom, ![X1]:v5_scmyciel(k5_scmyciel(X1)), file('/scratch/mptp/predsminms1/t51_scmyciel__0', fc14_scmyciel)). fof(dt_m1_scmyciel, axiom, ![X1, X2]:(m1_scmyciel(X2,X1)=>v4_scmyciel(X2)), file('/scratch/mptp/predsminms1/t51_scmyciel__0', dt_m1_scmyciel)). fof(dt_k5_scmyciel, axiom, ![X1]:m1_scmyciel(k5_scmyciel(X1),X1), file('/scratch/mptp/predsminms1/t51_scmyciel__0', dt_k5_scmyciel)). fof(t3_subset, axiom, ![X1, X2]:(m1_subset_1(X1,k1_zfmisc_1(X2))<=>r1_tarski(X1,X2)), file('/scratch/mptp/predsminms1/t51_scmyciel__0', t3_subset)). fof(t24_scmyciel, axiom, ![X1]:(v4_scmyciel(X1)=>![X2]:(r2_hidden(X2,k3_tarski(X1))<=>r2_hidden(k1_tarski(X2),X1))), file('/scratch/mptp/predsminms1/t51_scmyciel__0', t24_scmyciel)). fof(cc4_scmyciel, axiom, ![X1]:(v4_scmyciel(X1)=>(~(v1_xboole_0(X1))&(v1_classes1(X1)&v3_scmyciel(X1,np__1)))), file('/scratch/mptp/predsminms1/t51_scmyciel__0', cc4_scmyciel)). fof(t20_scmyciel, axiom, ![X1]:((~(v1_xboole_0(X1))&v1_classes1(X1))=>r2_hidden(k1_xboole_0,X1)), file('/scratch/mptp/predsminms1/t51_scmyciel__0', t20_scmyciel)). fof(c_0_11, plain, ![X10, X11, X12, X13, X14, X15, X16, X17, X18, X19, X20, X21]:(((~r2_hidden(X15,X14)\|(X15=X10\|(X15=X11\|(X15=X12\|X15=X13)))\|X14!=k2_enumset1(X10,X11,X12,X13))&((X16!=X10\|r2_hidden(X16,X14)\|X14!=k2_enumset1(X10,X11,X12,X13))&((X16!=X11\|r2_hidden(X16,X14)\|X14!=k2_enumset1(X10,X11,X12,X13))&((X16!=X12\|r2_hidden(X16,X14)\|X14!=k2_enumset1(X10,X11,X12,X13))&(X16!=X13\|r2_hidden(X16,X14)\|X14!=k2_enumset1(X10,X11,X12,X13))))))&(((esk4_5(X17,X18,X19,X20,X21)!=X17\|~r2_hidden(esk4_5(X17,X18,X19,X20,X21),X21)\|X21=k2_enumset1(X17,X18,X19,X20))&((esk4_5(X17,X18,X19,X20,X21)!=X18\|~r2_hidden(esk4_5(X17,X18,X19,X20,X21),X21)\|X21=k2_enumset1(X17,X18,X19,X20))&((esk4_5(X17,X18,X19,X20,X21)!=X19\|~r2_hidden(esk4_5(X17,X18,X19,X20,X21),X21)\|X21=k2_enumset1(X17,X18,X19,X20))&(esk4_5(X17,X18,X19,X20,X21)!=X20\|~r2_hidden(esk4_5(X17,X18,X19,X20,X21),X21)\|X21=k2_enumset1(X17,X18,X19,X20)))))&(r2_hidden(esk4_5(X17,X18,X19,X20,X21),X21)\|(esk4_5(X17,X18,X19,X20,X21)=X17\|(esk4_5(X17,X18,X19,X20,X21)=X18\|(esk4_5(X17,X18,X19,X20,X21)=X19\|esk4_5(X17,X18,X19,X20,X21)=X20)))\|X21=k2_enumset1(X17,X18,X19,X20)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d2_enumset1])])])])])])])). fof(c_0_12, negated_conjecture, ~(![X1]:(v4_scmyciel(X1)=>![X2, X3]:((r2_hidden(X2,k3_tarski(X1))&(r2_hidden(X3,k3_tarski(X1))&r2_hidden(k2_tarski(X2,X3),X1)))=>(v4_scmyciel(k2_enumset1(k1_xboole_0,k1_tarski(X2),k1_tarski(X3),k2_tarski(X2,X3)))&(v5_scmyciel(k2_enumset1(k1_xboole_0,k1_tarski(X2),k1_tarski(X3),k2_tarski(X2,X3)))&m1_subset_1(k2_enumset1(k1_xboole_0,k1_tarski(X2),k1_tarski(X3),k2_tarski(X2,X3)),k1_zfmisc_1(X1))))))), inference(assume_negation,[status(cth)],[t51_scmyciel])). cnf(c_0_13, plain, (X1=X3\|X1=X4\|X1=X5\|X1=X6\|~r2_hidden(X1,X2)\|X2!=k2_enumset1(X3,X4,X5,X6)), inference(split_conjunct,[status(thm)],[c_0_11])). fof(c_0_14, plain, ![X23, X24, X25, X26, X27]:((~r1_tarski(X23,X24)\|(~r2_hidden(X25,X23)\|r2_hidden(X25,X24)))&((r2_hidden(esk5_2(X26,X27),X26)\|r1_tarski(X26,X27))&(~r2_hidden(esk5_2(X26,X27),X27)\|r1_tarski(X26,X27)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_tarski])])])])])])). fof(c_0_15, negated_conjecture, (v4_scmyciel(esk1_0)&((r2_hidden(esk2_0,k3_tarski(esk1_0))&(r2_hidden(esk3_0,k3_tarski(esk1_0))&r2_hidden(k2_tarski(esk2_0,esk3_0),esk1_0)))&(~v4_scmyciel(k2_enumset1(k1_xboole_0,k1_tarski(esk2_0),k1_tarski(esk3_0),k2_tarski(esk2_0,esk3_0)))\|(~v5_scmyciel(k2_enumset1(k1_xboole_0,k1_tarski(esk2_0),k1_tarski(esk3_0),k2_tarski(esk2_0,esk3_0)))\|~m1_subset_1(k2_enumset1(k1_xboole_0,k1_tarski(esk2_0),k1_tarski(esk3_0),k2_tarski(esk2_0,esk3_0)),k1_zfmisc_1(esk1_0)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])). fof(c_0_16, plain, ![X29, X30]:k5_scmyciel(k2_tarski(X29,X30))=k2_enumset1(k1_xboole_0,k1_tarski(X29),k1_tarski(X30),k2_tarski(X29,X30)), inference(variable_rename,[status(thm)],[t37_scmyciel])). fof(c_0_17, plain, ![X31]:v5_scmyciel(k5_scmyciel(X31)), inference(variable_rename,[status(thm)],[fc14_scmyciel])). fof(c_0_18, plain, ![X32, X33]:(~m1_scmyciel(X33,X32)\|v4_scmyciel(X33)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m1_scmyciel])])). fof(c_0_19, plain, ![X34]:m1_scmyciel(k5_scmyciel(X34),X34), inference(variable_rename,[status(thm)],[dt_k5_scmyciel])). cnf(c_0_20, plain, (X1=X6\|X1=X5\|X1=X4\|X1=X3\|X2!=k2_enumset1(X3,X4,X5,X6)\|~r2_hidden(X1,X2)), inference(evalgc,[status(thm)],[c_0_13])). cnf(c_0_21, plain, (r2_hidden(esk5_2(X1,X2),X1)\|r1_tarski(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_14])). cnf(c_0_22, negated_conjecture, (~v4_scmyciel(k2_enumset1(k1_xboole_0,k1_tarski(esk2_0),k1_tarski(esk3_0),k2_tarski(esk2_0,esk3_0)))\|~v5_scmyciel(k2_enumset1(k1_xboole_0,k1_tarski(esk2_0),k1_tarski(esk3_0),k2_tarski(esk2_0,esk3_0)))\|~m1_subset_1(k2_enumset1(k1_xboole_0,k1_tarski(esk2_0),k1_tarski(esk3_0),k2_tarski(esk2_0,esk3_0)),k1_zfmisc_1(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_23, plain, (k5_scmyciel(k2_tarski(X1,X2))=k2_enumset1(k1_xboole_0,k1_tarski(X1),k1_tarski(X2),k2_tarski(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_24, plain, (v5_scmyciel(k5_scmyciel(X1))), inference(split_conjunct,[status(thm)],[c_0_17])). cnf(c_0_25, plain, (v4_scmyciel(X1)\|~m1_scmyciel(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_18])). cnf(c_0_26, plain, (m1_scmyciel(k5_scmyciel(X1),X1)), inference(split_conjunct,[status(thm)],[c_0_19])). cnf(c_0_27, plain, (r1_tarski(X1,X2)\|~r2_hidden(esk5_2(X1,X2),X2)), inference(split_conjunct,[status(thm)],[c_0_14])). cnf(c_0_28, plain, (X1=X2\|X1=X3\|X1=X4\|X1=X5\|~r2_hidden(X1,k2_enumset1(X2,X3,X4,X5))), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_20])])). cnf(c_0_29, plain, (r1_tarski(X1,X2)\|r2_hidden(esk5_2(X1,X2),X1)), inference(evalgc,[status(thm)],[c_0_21])). cnf(c_0_30, negated_conjecture, (~v4_scmyciel(k2_enumset1(k1_xboole_0,k1_tarski(esk2_0),k1_tarski(esk3_0),k2_tarski(esk2_0,esk3_0)))\|~v5_scmyciel(k2_enumset1(k1_xboole_0,k1_tarski(esk2_0),k1_tarski(esk3_0),k2_tarski(esk2_0,esk3_0)))\|~m1_subset_1(k2_enumset1(k1_xboole_0,k1_tarski(esk2_0),k1_tarski(esk3_0),k2_tarski(esk2_0,esk3_0)),k1_zfmisc_1(esk1_0))), inference(evalgc,[status(thm)],[c_0_22])). cnf(c_0_31, plain, (k2_enumset1(k1_xboole_0,k1_tarski(X1),k1_tarski(X2),k2_tarski(X1,X2))=k5_scmyciel(k2_tarski(X1,X2))), inference(evalgc,[status(thm)],[c_0_23])). cnf(c_0_32, plain, (v5_scmyciel(k5_scmyciel(X1))), inference(evalgc,[status(thm)],[c_0_24])). cnf(c_0_33, plain, (v4_scmyciel(X1)\|~m1_scmyciel(X1,X2)), inference(evalgc,[status(thm)],[c_0_25])). cnf(c_0_34, plain, (m1_scmyciel(k5_scmyciel(X1),X1)), inference(evalgc,[status(thm)],[c_0_26])). fof(c_0_35, plain, ![X35, X36]:((~m1_subset_1(X35,k1_zfmisc_1(X36))\|r1_tarski(X35,X36))&(~r1_tarski(X35,X36)\|m1_subset_1(X35,k1_zfmisc_1(X36)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])])). cnf(c_0_36, plain, (r1_tarski(X1,X2)\|~r2_hidden(esk5_2(X1,X2),X2)), inference(evalgc,[status(thm)],[c_0_27])). cnf(c_0_37, plain, (esk5_2(k2_enumset1(X1,X2,X3,X4),X5)=X4\|esk5_2(k2_enumset1(X1,X2,X3,X4),X5)=X3\|esk5_2(k2_enumset1(X1,X2,X3,X4),X5)=X2\|esk5_2(k2_enumset1(X1,X2,X3,X4),X5)=X1\|r1_tarski(k2_enumset1(X1,X2,X3,X4),X5)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_28, c_0_29])])). cnf(c_0_38, negated_conjecture, (r2_hidden(k2_tarski(esk2_0,esk3_0),esk1_0)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_39, negated_conjecture, (~m1_subset_1(k5_scmyciel(k2_tarski(esk2_0,esk3_0)),k1_zfmisc_1(esk1_0))\|~v4_scmyciel(k5_scmyciel(k2_tarski(esk2_0,esk3_0)))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30, c_0_31]), c_0_31]), c_0_32]), c_0_31])])])). cnf(c_0_40, plain, (v4_scmyciel(k5_scmyciel(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_33, c_0_34])])). cnf(c_0_41, plain, (m1_subset_1(X1,k1_zfmisc_1(X2))\|~r1_tarski(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_35])). fof(c_0_42, plain, ![X37, X38]:((~r2_hidden(X38,k3_tarski(X37))\|r2_hidden(k1_tarski(X38),X37)\|~v4_scmyciel(X37))&(~r2_hidden(k1_tarski(X38),X37)\|r2_hidden(X38,k3_tarski(X37))\|~v4_scmyciel(X37))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t24_scmyciel])])])])). fof(c_0_43, plain, ![X40]:((~v1_xboole_0(X40)\|~v4_scmyciel(X40))&((v1_classes1(X40)\|~v4_scmyciel(X40))&(v3_scmyciel(X40,np__1)\|~v4_scmyciel(X40)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[cc4_scmyciel])])])])). fof(c_0_44, plain, ![X39]:(v1_xboole_0(X39)\|~v1_classes1(X39)\|r2_hidden(k1_xboole_0,X39)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t20_scmyciel])])])). cnf(c_0_45, plain, (r1_tarski(k2_enumset1(X1,X2,X3,X4),X5)\|esk5_2(k2_enumset1(X1,X2,X3,X4),X5)=X1\|esk5_2(k2_enumset1(X1,X2,X3,X4),X5)=X2\|esk5_2(k2_enumset1(X1,X2,X3,X4),X5)=X3\|~r2_hidden(X4,X5)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_36, c_0_37])])). cnf(c_0_46, negated_conjecture, (r2_hidden(k2_tarski(esk2_0,esk3_0),esk1_0)), inference(evalgc,[status(thm)],[c_0_38])). cnf(c_0_47, negated_conjecture, (~m1_subset_1(k5_scmyciel(k2_tarski(esk2_0,esk3_0)),k1_zfmisc_1(esk1_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39, c_0_40])])). cnf(c_0_48, plain, (m1_subset_1(X1,k1_zfmisc_1(X2))\|~r1_tarski(X1,X2)), inference(evalgc,[status(thm)],[c_0_41])). cnf(c_0_49, plain, (r2_hidden(k1_tarski(X1),X2)\|~r2_hidden(X1,k3_tarski(X2))\|~v4_scmyciel(X2)), inference(split_conjunct,[status(thm)],[c_0_42])). cnf(c_0_50, negated_conjecture, (r2_hidden(esk3_0,k3_tarski(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_51, negated_conjecture, (v4_scmyciel(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_52, plain, (~v1_xboole_0(X1)\|~v4_scmyciel(X1)), inference(split_conjunct,[status(thm)],[c_0_43])). cnf(c_0_53, plain, (v1_xboole_0(X1)\|r2_hidden(k1_xboole_0,X1)\|~v1_classes1(X1)), inference(split_conjunct,[status(thm)],[c_0_44])). cnf(c_0_54, negated_conjecture, (esk5_2(k2_enumset1(X1,X2,X3,k2_tarski(esk2_0,esk3_0)),esk1_0)=X3\|esk5_2(k2_enumset1(X1,X2,X3,k2_tarski(esk2_0,esk3_0)),esk1_0)=X2\|esk5_2(k2_enumset1(X1,X2,X3,k2_tarski(esk2_0,esk3_0)),esk1_0)=X1\|r1_tarski(k2_enumset1(X1,X2,X3,k2_tarski(esk2_0,esk3_0)),esk1_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_45, c_0_46])])). cnf(c_0_55, negated_conjecture, (~r1_tarski(k5_scmyciel(k2_tarski(esk2_0,esk3_0)),esk1_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_47, c_0_48])])). cnf(c_0_56, plain, (r2_hidden(k1_tarski(X1),X2)\|~v4_scmyciel(X2)\|~r2_hidden(X1,k3_tarski(X2))), inference(evalgc,[status(thm)],[c_0_49])). cnf(c_0_57, negated_conjecture, (r2_hidden(esk3_0,k3_tarski(esk1_0))), inference(evalgc,[status(thm)],[c_0_50])). cnf(c_0_58, negated_conjecture, (v4_scmyciel(esk1_0)), inference(evalgc,[status(thm)],[c_0_51])). cnf(c_0_59, negated_conjecture, (r2_hidden(esk2_0,k3_tarski(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_60, plain, (~v4_scmyciel(X1)\|~v1_xboole_0(X1)), inference(evalgc,[status(thm)],[c_0_52])). cnf(c_0_61, plain, (v1_xboole_0(X1)\|r2_hidden(k1_xboole_0,X1)\|~v1_classes1(X1)), inference(evalgc,[status(thm)],[c_0_53])). cnf(c_0_62, plain, (v1_classes1(X1)\|~v4_scmyciel(X1)), inference(split_conjunct,[status(thm)],[c_0_43])). cnf(c_0_63, negated_conjecture, (esk5_2(k5_scmyciel(k2_tarski(esk2_0,esk3_0)),esk1_0)=k1_xboole_0\|esk5_2(k5_scmyciel(k2_tarski(esk2_0,esk3_0)),esk1_0)=k1_tarski(esk2_0)\|esk5_2(k5_scmyciel(k2_tarski(esk2_0,esk3_0)),esk1_0)=k1_tarski(esk3_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_54, c_0_31]), c_0_55])])). cnf(c_0_64, negated_conjecture, (r2_hidden(k1_tarski(esk3_0),esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56, c_0_57]), c_0_58])])])). cnf(c_0_65, negated_conjecture, (r2_hidden(esk2_0,k3_tarski(esk1_0))), inference(evalgc,[status(thm)],[c_0_59])). cnf(c_0_66, plain, (r2_hidden(k1_xboole_0,X1)\|~v4_scmyciel(X1)\|~v1_classes1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_60, c_0_61])])). cnf(c_0_67, plain, (v1_classes1(X1)\|~v4_scmyciel(X1)), inference(evalgc,[status(thm)],[c_0_62])). cnf(c_0_68, negated_conjecture, (esk5_2(k5_scmyciel(k2_tarski(esk2_0,esk3_0)),esk1_0)=k1_tarski(esk2_0)\|esk5_2(k5_scmyciel(k2_tarski(esk2_0,esk3_0)),esk1_0)=k1_xboole_0), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36, c_0_63]), c_0_64])]), c_0_55])])). cnf(c_0_69, negated_conjecture, (r2_hidden(k1_tarski(esk2_0),esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56, c_0_65]), c_0_58])])])). cnf(c_0_70, plain, (r2_hidden(k1_xboole_0,X1)\|~v4_scmyciel(X1)), inference(csr,[status(thm)],[c_0_66, c_0_67])). cnf(c_0_71, negated_conjecture, (esk5_2(k5_scmyciel(k2_tarski(esk2_0,esk3_0)),esk1_0)=k1_xboole_0), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36, c_0_68]), c_0_69])]), c_0_55])])). cnf(c_0_72, negated_conjecture, (r2_hidden(k1_xboole_0,esk1_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_70, c_0_58])])). cnf(c_0_73, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36, c_0_71]), c_0_72])]), c_0_55]), ['proof']). # SZS output end CNFRefutation	theorem Cliqueon2: for G being SimpleGraph, x, y being set st x in Vertices G & y in Vertices G & {x,y} in G holds { {}, {x}, {y}, {x,y} } is Clique of G proof let G be SimpleGraph, x, y be set such that A: x in Vertices G and B: y in Vertices G and AB: {x,y} in G; set C = CompleteSGraph {x,y}; D: C = { {}, {x}, {y}, {x,y} } by P2; C c= G proof let a be set; assume A1: a in C; per cases by A1, D, ENUMSET1:def 2; suppose a = {}; hence thesis by SG1; end; suppose a = {x}; hence thesis by A, Vertices0; end; suppose a = {y}; hence thesis by B, Vertices0; end; suppose a = {x,y}; hence thesis by AB; end; end; hence { {}, {x}, {y}, {x,y} } is Clique of G by P2; end;	Convert the following ATP output trace into a readable Mizar proof.
t44_fcont_1	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t44_fcont_1, conjecture, ![X1]:((v1_funct_1(X1)&m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))))=>(![X2]:(v1_xreal_0(X2)=>(r2_hidden(X2,k1_relset_1(k1_numbers,X1))=>k1_seq_1(X1,X2)=k18_complex1(X2)))=>v1_fcont_1(X1))), file('/scratch/mptp/predsminms1/t44_fcont_1__0', t44_fcont_1)). fof(d3_fcont_1, axiom, ![X1]:((v1_funct_1(X1)&m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))))=>(v2_fcont_1(X1)<=>?[X2]:(v1_xreal_0(X2)&(~(r1_xxreal_0(X2,k6_numbers))&![X3]:(v1_xreal_0(X3)=>![X4]:(v1_xreal_0(X4)=>((r2_hidden(X3,k1_relset_1(k1_numbers,X1))&r2_hidden(X4,k1_relset_1(k1_numbers,X1)))=>r1_xxreal_0(k18_complex1(k9_real_1(k1_seq_1(X1,X3),k1_seq_1(X1,X4))),k4_real_1(X2,k18_complex1(k6_xcmplx_0(X3,X4))))))))))), file('/scratch/mptp/predsminms1/t44_fcont_1__0', d3_fcont_1)). fof(cc5_fcont_1, axiom, ![X1]:(m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))=>((v1_funct_1(X1)&v2_fcont_1(X1))=>(v1_funct_1(X1)&v1_fcont_1(X1)))), file('/scratch/mptp/predsminms1/t44_fcont_1__0', cc5_fcont_1)). fof(redefinition_k18_complex1, axiom, ![X1]:(v1_xcmplx_0(X1)=>k18_complex1(X1)=k16_complex1(X1)), file('/scratch/mptp/predsminms1/t44_fcont_1__0', redefinition_k18_complex1)). fof(redefinition_k17_complex1, axiom, ![X1]:(v1_xcmplx_0(X1)=>k17_complex1(X1)=k16_complex1(X1)), file('/scratch/mptp/predsminms1/t44_fcont_1__0', redefinition_k17_complex1)). fof(t6_boole, axiom, ![X1]:(v1_xboole_0(X1)=>X1=k1_xboole_0), file('/scratch/mptp/predsminms1/t44_fcont_1__0', t6_boole)). fof(t64_complex1, axiom, ![X1]:(v1_xcmplx_0(X1)=>![X2]:(v1_xcmplx_0(X2)=>r1_xxreal_0(k17_complex1(k9_real_1(k17_complex1(X1),k17_complex1(X2))),k17_complex1(k6_xcmplx_0(X1,X2))))), file('/scratch/mptp/predsminms1/t44_fcont_1__0', t64_complex1)). fof(redefinition_k6_numbers, axiom, k6_numbers=k1_xboole_0, file('/scratch/mptp/predsminms1/t44_fcont_1__0', redefinition_k6_numbers)). fof(t3_arithm, axiom, ![X1]:(v1_xcmplx_0(X1)=>k3_xcmplx_0(np__1,X1)=X1), file('/scratch/mptp/predsminms1/t44_fcont_1__0', t3_arithm)). fof(redefinition_k4_real_1, axiom, ![X1, X2]:((v1_xreal_0(X1)&m1_subset_1(X2,k1_numbers))=>k4_real_1(X1,X2)=k3_xcmplx_0(X1,X2)), file('/scratch/mptp/predsminms1/t44_fcont_1__0', redefinition_k4_real_1)). fof(rqLessOrEqual__r1_xxreal_0__r1_r0, axiom, ~(r1_xxreal_0(np__1,np__0)), file('/scratch/mptp/predsminms1/t44_fcont_1__0', rqLessOrEqual__r1_xxreal_0__r1_r0)). fof(spc0_boole, axiom, v1_xboole_0(np__0), file('/scratch/mptp/predsminms1/t44_fcont_1__0', spc0_boole)). fof(dt_k18_complex1, axiom, ![X1]:(v1_xcmplx_0(X1)=>m1_subset_1(k18_complex1(X1),k1_numbers)), file('/scratch/mptp/predsminms1/t44_fcont_1__0', dt_k18_complex1)). fof(cc3_xreal_0, axiom, ![X1]:(v1_xreal_0(X1)=>v1_xcmplx_0(X1)), file('/scratch/mptp/predsminms1/t44_fcont_1__0', cc3_xreal_0)). fof(cc12_membered, axiom, ![X1]:(v1_membered(X1)=>![X2]:(m1_subset_1(X2,X1)=>v1_xcmplx_0(X2))), file('/scratch/mptp/predsminms1/t44_fcont_1__0', cc12_membered)). fof(dt_k9_real_1, axiom, ![X1, X2]:((m1_subset_1(X1,k1_numbers)&v1_xreal_0(X2))=>m1_subset_1(k9_real_1(X1,X2),k1_numbers)), file('/scratch/mptp/predsminms1/t44_fcont_1__0', dt_k9_real_1)). fof(fc7_xreal_0, axiom, ![X1, X2]:((v1_xreal_0(X1)&v1_xreal_0(X2))=>v1_xreal_0(k6_xcmplx_0(X1,X2))), file('/scratch/mptp/predsminms1/t44_fcont_1__0', fc7_xreal_0)). fof(cc1_xreal_0, axiom, ![X1]:(m1_subset_1(X1,k1_numbers)=>v1_xreal_0(X1)), file('/scratch/mptp/predsminms1/t44_fcont_1__0', cc1_xreal_0)). fof(cc5_membered, axiom, ![X1]:(v3_membered(X1)=>v1_membered(X1)), file('/scratch/mptp/predsminms1/t44_fcont_1__0', cc5_membered)). fof(fc3_membered, axiom, v3_membered(k1_numbers), file('/scratch/mptp/predsminms1/t44_fcont_1__0', fc3_membered)). fof(spc1_numerals, axiom, ((v2_xxreal_0(np__1)&m2_subset_1(np__1,k1_numbers,k5_numbers))&(m1_subset_1(np__1,k5_numbers)&m1_subset_1(np__1,k1_numbers))), file('/scratch/mptp/predsminms1/t44_fcont_1__0', spc1_numerals)). fof(c_0_21, negated_conjecture, ~(![X1]:((v1_funct_1(X1)&m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))))=>(![X2]:(v1_xreal_0(X2)=>(r2_hidden(X2,k1_relset_1(k1_numbers,X1))=>k1_seq_1(X1,X2)=k18_complex1(X2)))=>v1_fcont_1(X1)))), inference(assume_negation,[status(cth)],[t44_fcont_1])). fof(c_0_22, negated_conjecture, ![X6]:((v1_funct_1(esk1_0)&m1_subset_1(esk1_0,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))))&((~v1_xreal_0(X6)\|(~r2_hidden(X6,k1_relset_1(k1_numbers,esk1_0))\|k1_seq_1(esk1_0,X6)=k18_complex1(X6)))&~v1_fcont_1(esk1_0))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])])])). fof(c_0_23, plain, ![X10, X12, X13, X14]:(((v1_xreal_0(esk2_1(X10))\|~v2_fcont_1(X10)\|(~v1_funct_1(X10)\|~m1_subset_1(X10,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))))&((~r1_xxreal_0(esk2_1(X10),k6_numbers)\|~v2_fcont_1(X10)\|(~v1_funct_1(X10)\|~m1_subset_1(X10,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))))&(~v1_xreal_0(X12)\|(~v1_xreal_0(X13)\|(~r2_hidden(X12,k1_relset_1(k1_numbers,X10))\|~r2_hidden(X13,k1_relset_1(k1_numbers,X10))\|r1_xxreal_0(k18_complex1(k9_real_1(k1_seq_1(X10,X12),k1_seq_1(X10,X13))),k4_real_1(esk2_1(X10),k18_complex1(k6_xcmplx_0(X12,X13))))))\|~v2_fcont_1(X10)\|(~v1_funct_1(X10)\|~m1_subset_1(X10,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))))))&((v1_xreal_0(esk3_2(X10,X14))\|r1_xxreal_0(X14,k6_numbers)\|~v1_xreal_0(X14)\|v2_fcont_1(X10)\|(~v1_funct_1(X10)\|~m1_subset_1(X10,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))))&((v1_xreal_0(esk4_2(X10,X14))\|r1_xxreal_0(X14,k6_numbers)\|~v1_xreal_0(X14)\|v2_fcont_1(X10)\|(~v1_funct_1(X10)\|~m1_subset_1(X10,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))))&(((r2_hidden(esk3_2(X10,X14),k1_relset_1(k1_numbers,X10))\|r1_xxreal_0(X14,k6_numbers)\|~v1_xreal_0(X14)\|v2_fcont_1(X10)\|(~v1_funct_1(X10)\|~m1_subset_1(X10,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))))&(r2_hidden(esk4_2(X10,X14),k1_relset_1(k1_numbers,X10))\|r1_xxreal_0(X14,k6_numbers)\|~v1_xreal_0(X14)\|v2_fcont_1(X10)\|(~v1_funct_1(X10)\|~m1_subset_1(X10,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))))))&(~r1_xxreal_0(k18_complex1(k9_real_1(k1_seq_1(X10,esk3_2(X10,X14)),k1_seq_1(X10,esk4_2(X10,X14)))),k4_real_1(X14,k18_complex1(k6_xcmplx_0(esk3_2(X10,X14),esk4_2(X10,X14)))))\|r1_xxreal_0(X14,k6_numbers)\|~v1_xreal_0(X14)\|v2_fcont_1(X10)\|(~v1_funct_1(X10)\|~m1_subset_1(X10,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d3_fcont_1])])])])])])). fof(c_0_24, plain, ![X9]:((v1_funct_1(X9)\|(~v1_funct_1(X9)\|~v2_fcont_1(X9))\|~m1_subset_1(X9,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))))&(v1_fcont_1(X9)\|(~v1_funct_1(X9)\|~v2_fcont_1(X9))\|~m1_subset_1(X9,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc5_fcont_1])])])). fof(c_0_25, plain, ![X32]:(~v1_xcmplx_0(X32)\|k18_complex1(X32)=k16_complex1(X32)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k18_complex1])])). fof(c_0_26, plain, ![X38]:(~v1_xcmplx_0(X38)\|k17_complex1(X38)=k16_complex1(X38)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k17_complex1])])). cnf(c_0_27, negated_conjecture, (k1_seq_1(esk1_0,X1)=k18_complex1(X1)\|~v1_xreal_0(X1)\|~r2_hidden(X1,k1_relset_1(k1_numbers,esk1_0))), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_28, plain, (r2_hidden(esk3_2(X1,X2),k1_relset_1(k1_numbers,X1))\|r1_xxreal_0(X2,k6_numbers)\|v2_fcont_1(X1)\|~v1_xreal_0(X2)\|~v1_funct_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))), inference(split_conjunct,[status(thm)],[c_0_23])). cnf(c_0_29, negated_conjecture, (m1_subset_1(esk1_0,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_30, negated_conjecture, (v1_funct_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_31, negated_conjecture, (~v1_fcont_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_32, plain, (v1_fcont_1(X1)\|~v1_funct_1(X1)\|~v2_fcont_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))), inference(split_conjunct,[status(thm)],[c_0_24])). fof(c_0_33, plain, ![X7]:(~v1_xboole_0(X7)\|X7=k1_xboole_0), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])])). fof(c_0_34, plain, ![X39, X40]:(~v1_xcmplx_0(X39)\|(~v1_xcmplx_0(X40)\|r1_xxreal_0(k17_complex1(k9_real_1(k17_complex1(X39),k17_complex1(X40))),k17_complex1(k6_xcmplx_0(X39,X40))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t64_complex1])])])). cnf(c_0_35, plain, (k18_complex1(X1)=k16_complex1(X1)\|~v1_xcmplx_0(X1)), inference(split_conjunct,[status(thm)],[c_0_25])). cnf(c_0_36, plain, (k17_complex1(X1)=k16_complex1(X1)\|~v1_xcmplx_0(X1)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_37, negated_conjecture, (k1_seq_1(esk1_0,X1)=k18_complex1(X1)\|~v1_xreal_0(X1)\|~r2_hidden(X1,k1_relset_1(k1_numbers,esk1_0))), inference(evalgc,[status(thm)],[c_0_27])). cnf(c_0_38, plain, (v2_fcont_1(X1)\|r1_xxreal_0(X2,k6_numbers)\|r2_hidden(esk3_2(X1,X2),k1_relset_1(k1_numbers,X1))\|~v1_funct_1(X1)\|~v1_xreal_0(X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))), inference(evalgc,[status(thm)],[c_0_28])). cnf(c_0_39, negated_conjecture, (m1_subset_1(esk1_0,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))), inference(evalgc,[status(thm)],[c_0_29])). cnf(c_0_40, negated_conjecture, (v1_funct_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_30])). cnf(c_0_41, negated_conjecture, (~v1_fcont_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_31])). cnf(c_0_42, plain, (v1_fcont_1(X1)\|~v1_funct_1(X1)\|~v2_fcont_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))), inference(evalgc,[status(thm)],[c_0_32])). cnf(c_0_43, plain, (r2_hidden(esk4_2(X1,X2),k1_relset_1(k1_numbers,X1))\|r1_xxreal_0(X2,k6_numbers)\|v2_fcont_1(X1)\|~v1_xreal_0(X2)\|~v1_funct_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))), inference(split_conjunct,[status(thm)],[c_0_23])). cnf(c_0_44, plain, (X1=k1_xboole_0\|~v1_xboole_0(X1)), inference(split_conjunct,[status(thm)],[c_0_33])). cnf(c_0_45, plain, (k6_numbers=k1_xboole_0), inference(split_conjunct,[status(thm)],[redefinition_k6_numbers])). cnf(c_0_46, plain, (r1_xxreal_0(k17_complex1(k9_real_1(k17_complex1(X1),k17_complex1(X2))),k17_complex1(k6_xcmplx_0(X1,X2)))\|~v1_xcmplx_0(X1)\|~v1_xcmplx_0(X2)), inference(split_conjunct,[status(thm)],[c_0_34])). cnf(c_0_47, plain, (k16_complex1(X1)=k18_complex1(X1)\|~v1_xcmplx_0(X1)), inference(evalgc,[status(thm)],[c_0_35])). cnf(c_0_48, plain, (k16_complex1(X1)=k17_complex1(X1)\|~v1_xcmplx_0(X1)), inference(evalgc,[status(thm)],[c_0_36])). cnf(c_0_49, plain, (r1_xxreal_0(X2,k6_numbers)\|v2_fcont_1(X1)\|~r1_xxreal_0(k18_complex1(k9_real_1(k1_seq_1(X1,esk3_2(X1,X2)),k1_seq_1(X1,esk4_2(X1,X2)))),k4_real_1(X2,k18_complex1(k6_xcmplx_0(esk3_2(X1,X2),esk4_2(X1,X2)))))\|~v1_xreal_0(X2)\|~v1_funct_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))), inference(split_conjunct,[status(thm)],[c_0_23])). cnf(c_0_50, negated_conjecture, (k1_seq_1(esk1_0,esk3_2(esk1_0,X1))=k18_complex1(esk3_2(esk1_0,X1))\|v2_fcont_1(esk1_0)\|r1_xxreal_0(X1,k6_numbers)\|~v1_xreal_0(esk3_2(esk1_0,X1))\|~v1_xreal_0(X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37, c_0_38]), c_0_39]), c_0_40])])])). cnf(c_0_51, negated_conjecture, (~v2_fcont_1(esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41, c_0_42]), c_0_39]), c_0_40])])])). cnf(c_0_52, plain, (v2_fcont_1(X1)\|r1_xxreal_0(X2,k6_numbers)\|r2_hidden(esk4_2(X1,X2),k1_relset_1(k1_numbers,X1))\|~v1_funct_1(X1)\|~v1_xreal_0(X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))), inference(evalgc,[status(thm)],[c_0_43])). fof(c_0_53, plain, ![X20]:(~v1_xcmplx_0(X20)\|k3_xcmplx_0(np__1,X20)=X20), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_arithm])])). fof(c_0_54, plain, ![X22, X23]:(~v1_xreal_0(X22)\|~m1_subset_1(X23,k1_numbers)\|k4_real_1(X22,X23)=k3_xcmplx_0(X22,X23)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k4_real_1])])). fof(c_0_55, plain, ~r1_xxreal_0(np__1,np__0), inference(fof_simplification,[status(thm)],[rqLessOrEqual__r1_xxreal_0__r1_r0])). cnf(c_0_56, plain, (X1=k1_xboole_0\|~v1_xboole_0(X1)), inference(evalgc,[status(thm)],[c_0_44])). cnf(c_0_57, plain, (k1_xboole_0=k6_numbers), inference(evalgc,[status(thm)],[c_0_45])). cnf(c_0_58, plain, (v1_xboole_0(np__0)), inference(split_conjunct,[status(thm)],[spc0_boole])). cnf(c_0_59, plain, (r1_xxreal_0(k17_complex1(k9_real_1(k17_complex1(X1),k17_complex1(X2))),k17_complex1(k6_xcmplx_0(X1,X2)))\|~v1_xcmplx_0(X2)\|~v1_xcmplx_0(X1)), inference(evalgc,[status(thm)],[c_0_46])). cnf(c_0_60, plain, (k17_complex1(X1)=k18_complex1(X1)\|~v1_xcmplx_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_47, c_0_48])])). cnf(c_0_61, plain, (v2_fcont_1(X1)\|r1_xxreal_0(X2,k6_numbers)\|~v1_funct_1(X1)\|~v1_xreal_0(X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))\|~r1_xxreal_0(k18_complex1(k9_real_1(k1_seq_1(X1,esk3_2(X1,X2)),k1_seq_1(X1,esk4_2(X1,X2)))),k4_real_1(X2,k18_complex1(k6_xcmplx_0(esk3_2(X1,X2),esk4_2(X1,X2)))))), inference(evalgc,[status(thm)],[c_0_49])). cnf(c_0_62, negated_conjecture, (k1_seq_1(esk1_0,esk3_2(esk1_0,X1))=k18_complex1(esk3_2(esk1_0,X1))\|r1_xxreal_0(X1,k6_numbers)\|~v1_xreal_0(esk3_2(esk1_0,X1))\|~v1_xreal_0(X1)), inference(sr,[status(thm)],[c_0_50, c_0_51])). cnf(c_0_63, negated_conjecture, (k1_seq_1(esk1_0,esk4_2(esk1_0,X1))=k18_complex1(esk4_2(esk1_0,X1))\|v2_fcont_1(esk1_0)\|r1_xxreal_0(X1,k6_numbers)\|~v1_xreal_0(esk4_2(esk1_0,X1))\|~v1_xreal_0(X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37, c_0_52]), c_0_39]), c_0_40])])])). cnf(c_0_64, plain, (k3_xcmplx_0(np__1,X1)=X1\|~v1_xcmplx_0(X1)), inference(split_conjunct,[status(thm)],[c_0_53])). cnf(c_0_65, plain, (k4_real_1(X1,X2)=k3_xcmplx_0(X1,X2)\|~v1_xreal_0(X1)\|~m1_subset_1(X2,k1_numbers)), inference(split_conjunct,[status(thm)],[c_0_54])). cnf(c_0_66, plain, (~r1_xxreal_0(np__1,np__0)), inference(split_conjunct,[status(thm)],[c_0_55])). cnf(c_0_67, plain, (X1=k6_numbers\|~v1_xboole_0(X1)), inference(rw,[status(thm)],[c_0_56, c_0_57])). cnf(c_0_68, plain, (v1_xboole_0(np__0)), inference(evalgc,[status(thm)],[c_0_58])). cnf(c_0_69, plain, (r1_xxreal_0(k17_complex1(k9_real_1(k18_complex1(X1),k17_complex1(X2))),k17_complex1(k6_xcmplx_0(X1,X2)))\|~v1_xcmplx_0(X2)\|~v1_xcmplx_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_59, c_0_60])])). cnf(c_0_70, negated_conjecture, (r1_xxreal_0(X1,k6_numbers)\|~r1_xxreal_0(k18_complex1(k9_real_1(k18_complex1(esk3_2(esk1_0,X1)),k1_seq_1(esk1_0,esk4_2(esk1_0,X1)))),k4_real_1(X1,k18_complex1(k6_xcmplx_0(esk3_2(esk1_0,X1),esk4_2(esk1_0,X1)))))\|~v1_xreal_0(X1)\|~v1_xreal_0(esk3_2(esk1_0,X1))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61, c_0_62]), c_0_39]), c_0_40])]), c_0_51])])). cnf(c_0_71, negated_conjecture, (k1_seq_1(esk1_0,esk4_2(esk1_0,X1))=k18_complex1(esk4_2(esk1_0,X1))\|r1_xxreal_0(X1,k6_numbers)\|~v1_xreal_0(esk4_2(esk1_0,X1))\|~v1_xreal_0(X1)), inference(sr,[status(thm)],[c_0_63, c_0_51])). cnf(c_0_72, plain, (k3_xcmplx_0(np__1,X1)=X1\|~v1_xcmplx_0(X1)), inference(evalgc,[status(thm)],[c_0_64])). cnf(c_0_73, plain, (k3_xcmplx_0(X1,X2)=k4_real_1(X1,X2)\|~v1_xreal_0(X1)\|~m1_subset_1(X2,k1_numbers)), inference(evalgc,[status(thm)],[c_0_65])). cnf(c_0_74, plain, (~r1_xxreal_0(np__1,np__0)), inference(evalgc,[status(thm)],[c_0_66])). cnf(c_0_75, plain, (np__0=k6_numbers), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_67, c_0_68])])). cnf(c_0_76, plain, (r1_xxreal_0(k17_complex1(k9_real_1(k18_complex1(X1),k18_complex1(X2))),k17_complex1(k6_xcmplx_0(X1,X2)))\|~v1_xcmplx_0(X2)\|~v1_xcmplx_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_69, c_0_60])])). cnf(c_0_77, negated_conjecture, (r1_xxreal_0(X1,k6_numbers)\|~r1_xxreal_0(k18_complex1(k9_real_1(k18_complex1(esk3_2(esk1_0,X1)),k18_complex1(esk4_2(esk1_0,X1)))),k4_real_1(X1,k18_complex1(k6_xcmplx_0(esk3_2(esk1_0,X1),esk4_2(esk1_0,X1)))))\|~v1_xreal_0(esk3_2(esk1_0,X1))\|~v1_xreal_0(X1)\|~v1_xreal_0(esk4_2(esk1_0,X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_70, c_0_71])])). cnf(c_0_78, plain, (k4_real_1(np__1,X1)=X1\|~v1_xcmplx_0(X1)\|~v1_xreal_0(np__1)\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_72, c_0_73])])). cnf(c_0_79, plain, (~r1_xxreal_0(np__1,k6_numbers)), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[c_0_74, c_0_75])])). cnf(c_0_80, plain, (r1_xxreal_0(k17_complex1(k9_real_1(k18_complex1(X1),k18_complex1(X2))),k18_complex1(k6_xcmplx_0(X1,X2)))\|~v1_xcmplx_0(X2)\|~v1_xcmplx_0(X1)\|~v1_xcmplx_0(k6_xcmplx_0(X1,X2))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_76, c_0_60])])). fof(c_0_81, plain, ![X21]:(~v1_xcmplx_0(X21)\|m1_subset_1(k18_complex1(X21),k1_numbers)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k18_complex1])])). fof(c_0_82, plain, ![X17]:(~v1_xreal_0(X17)\|v1_xcmplx_0(X17)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc3_xreal_0])])). fof(c_0_83, plain, ![X34, X35]:(~v1_membered(X34)\|(~m1_subset_1(X35,X34)\|v1_xcmplx_0(X35))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc12_membered])])])). fof(c_0_84, plain, ![X36, X37]:(~m1_subset_1(X36,k1_numbers)\|~v1_xreal_0(X37)\|m1_subset_1(k9_real_1(X36,X37),k1_numbers)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k9_real_1])])). cnf(c_0_85, negated_conjecture, (~r1_xxreal_0(k18_complex1(k9_real_1(k18_complex1(esk3_2(esk1_0,np__1)),k18_complex1(esk4_2(esk1_0,np__1)))),k18_complex1(k6_xcmplx_0(esk3_2(esk1_0,np__1),esk4_2(esk1_0,np__1))))\|~v1_xreal_0(esk3_2(esk1_0,np__1))\|~v1_xreal_0(esk4_2(esk1_0,np__1))\|~v1_xreal_0(np__1)\|~v1_xcmplx_0(k18_complex1(k6_xcmplx_0(esk3_2(esk1_0,np__1),esk4_2(esk1_0,np__1))))\|~m1_subset_1(k18_complex1(k6_xcmplx_0(esk3_2(esk1_0,np__1),esk4_2(esk1_0,np__1))),k1_numbers)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_77, c_0_78]), c_0_79])])). cnf(c_0_86, plain, (r1_xxreal_0(k18_complex1(k9_real_1(k18_complex1(X1),k18_complex1(X2))),k18_complex1(k6_xcmplx_0(X1,X2)))\|~v1_xcmplx_0(k6_xcmplx_0(X1,X2))\|~v1_xcmplx_0(X2)\|~v1_xcmplx_0(X1)\|~v1_xcmplx_0(k9_real_1(k18_complex1(X1),k18_complex1(X2)))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_80, c_0_60])])). cnf(c_0_87, plain, (m1_subset_1(k18_complex1(X1),k1_numbers)\|~v1_xcmplx_0(X1)), inference(split_conjunct,[status(thm)],[c_0_81])). cnf(c_0_88, plain, (v1_xcmplx_0(X1)\|~v1_xreal_0(X1)), inference(split_conjunct,[status(thm)],[c_0_82])). cnf(c_0_89, plain, (v1_xcmplx_0(X2)\|~v1_membered(X1)\|~m1_subset_1(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_83])). cnf(c_0_90, plain, (m1_subset_1(k9_real_1(X1,X2),k1_numbers)\|~m1_subset_1(X1,k1_numbers)\|~v1_xreal_0(X2)), inference(split_conjunct,[status(thm)],[c_0_84])). cnf(c_0_91, negated_conjecture, (~v1_xcmplx_0(k18_complex1(k6_xcmplx_0(esk3_2(esk1_0,np__1),esk4_2(esk1_0,np__1))))\|~v1_xreal_0(esk3_2(esk1_0,np__1))\|~v1_xreal_0(esk4_2(esk1_0,np__1))\|~v1_xreal_0(np__1)\|~m1_subset_1(k18_complex1(k6_xcmplx_0(esk3_2(esk1_0,np__1),esk4_2(esk1_0,np__1))),k1_numbers)\|~v1_xcmplx_0(k9_real_1(k18_complex1(esk3_2(esk1_0,np__1)),k18_complex1(esk4_2(esk1_0,np__1))))\|~v1_xcmplx_0(k6_xcmplx_0(esk3_2(esk1_0,np__1),esk4_2(esk1_0,np__1)))\|~v1_xcmplx_0(esk4_2(esk1_0,np__1))\|~v1_xcmplx_0(esk3_2(esk1_0,np__1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_85, c_0_86])])). cnf(c_0_92, plain, (m1_subset_1(k18_complex1(X1),k1_numbers)\|~v1_xcmplx_0(X1)), inference(evalgc,[status(thm)],[c_0_87])). cnf(c_0_93, plain, (v1_xcmplx_0(X1)\|~v1_xreal_0(X1)), inference(evalgc,[status(thm)],[c_0_88])). cnf(c_0_94, plain, (v1_xcmplx_0(X2)\|~v1_membered(X1)\|~m1_subset_1(X2,X1)), inference(evalgc,[status(thm)],[c_0_89])). cnf(c_0_95, plain, (m1_subset_1(k9_real_1(X1,X2),k1_numbers)\|~v1_xreal_0(X2)\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[c_0_90])). cnf(c_0_96, negated_conjecture, (~v1_xcmplx_0(k9_real_1(k18_complex1(esk3_2(esk1_0,np__1)),k18_complex1(esk4_2(esk1_0,np__1))))\|~v1_xcmplx_0(k18_complex1(k6_xcmplx_0(esk3_2(esk1_0,np__1),esk4_2(esk1_0,np__1))))\|~v1_xcmplx_0(k6_xcmplx_0(esk3_2(esk1_0,np__1),esk4_2(esk1_0,np__1)))\|~v1_xreal_0(esk3_2(esk1_0,np__1))\|~v1_xreal_0(esk4_2(esk1_0,np__1))\|~v1_xreal_0(np__1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_91, c_0_92]), c_0_93]), c_0_93])). cnf(c_0_97, plain, (v1_xcmplx_0(k9_real_1(X1,X2))\|~v1_membered(k1_numbers)\|~v1_xreal_0(X2)\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_94, c_0_95])])). cnf(c_0_98, negated_conjecture, (~v1_xcmplx_0(k18_complex1(k6_xcmplx_0(esk3_2(esk1_0,np__1),esk4_2(esk1_0,np__1))))\|~v1_xcmplx_0(k6_xcmplx_0(esk3_2(esk1_0,np__1),esk4_2(esk1_0,np__1)))\|~v1_xreal_0(esk3_2(esk1_0,np__1))\|~v1_xreal_0(esk4_2(esk1_0,np__1))\|~v1_xreal_0(np__1)\|~v1_membered(k1_numbers)\|~v1_xreal_0(k18_complex1(esk4_2(esk1_0,np__1)))\|~m1_subset_1(k18_complex1(esk3_2(esk1_0,np__1)),k1_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_96, c_0_97])])). cnf(c_0_99, plain, (v1_xcmplx_0(k18_complex1(X1))\|~v1_membered(k1_numbers)\|~v1_xcmplx_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_94, c_0_92])])). fof(c_0_100, plain, ![X18, X19]:(~v1_xreal_0(X18)\|~v1_xreal_0(X19)\|v1_xreal_0(k6_xcmplx_0(X18,X19))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc7_xreal_0])])). cnf(c_0_101, negated_conjecture, (~v1_membered(k1_numbers)\|~v1_xcmplx_0(k6_xcmplx_0(esk3_2(esk1_0,np__1),esk4_2(esk1_0,np__1)))\|~v1_xreal_0(k18_complex1(esk4_2(esk1_0,np__1)))\|~v1_xreal_0(esk3_2(esk1_0,np__1))\|~v1_xreal_0(esk4_2(esk1_0,np__1))\|~v1_xreal_0(np__1)\|~m1_subset_1(k18_complex1(esk3_2(esk1_0,np__1)),k1_numbers)), inference(csr,[status(thm)],[c_0_98, c_0_99])). cnf(c_0_102, plain, (v1_xreal_0(k6_xcmplx_0(X1,X2))\|~v1_xreal_0(X1)\|~v1_xreal_0(X2)), inference(split_conjunct,[status(thm)],[c_0_100])). fof(c_0_103, plain, ![X8]:(~m1_subset_1(X8,k1_numbers)\|v1_xreal_0(X8)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_xreal_0])])). cnf(c_0_104, negated_conjecture, (~v1_membered(k1_numbers)\|~v1_xreal_0(k18_complex1(esk4_2(esk1_0,np__1)))\|~v1_xreal_0(esk3_2(esk1_0,np__1))\|~v1_xreal_0(esk4_2(esk1_0,np__1))\|~v1_xreal_0(np__1)\|~m1_subset_1(k18_complex1(esk3_2(esk1_0,np__1)),k1_numbers)\|~v1_xreal_0(k6_xcmplx_0(esk3_2(esk1_0,np__1),esk4_2(esk1_0,np__1)))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_101, c_0_93])])). cnf(c_0_105, plain, (v1_xreal_0(k6_xcmplx_0(X1,X2))\|~v1_xreal_0(X2)\|~v1_xreal_0(X1)), inference(evalgc,[status(thm)],[c_0_102])). cnf(c_0_106, plain, (v1_xreal_0(X1)\|~m1_subset_1(X1,k1_numbers)), inference(split_conjunct,[status(thm)],[c_0_103])). cnf(c_0_107, negated_conjecture, (~v1_membered(k1_numbers)\|~v1_xreal_0(k18_complex1(esk4_2(esk1_0,np__1)))\|~v1_xreal_0(esk3_2(esk1_0,np__1))\|~v1_xreal_0(esk4_2(esk1_0,np__1))\|~v1_xreal_0(np__1)\|~m1_subset_1(k18_complex1(esk3_2(esk1_0,np__1)),k1_numbers)), inference(csr,[status(thm)],[c_0_104, c_0_105])). cnf(c_0_108, plain, (v1_xreal_0(X1)\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[c_0_106])). cnf(c_0_109, negated_conjecture, (~v1_membered(k1_numbers)\|~v1_xreal_0(esk3_2(esk1_0,np__1))\|~v1_xreal_0(esk4_2(esk1_0,np__1))\|~v1_xreal_0(np__1)\|~m1_subset_1(k18_complex1(esk3_2(esk1_0,np__1)),k1_numbers)\|~m1_subset_1(k18_complex1(esk4_2(esk1_0,np__1)),k1_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_107, c_0_108])])). cnf(c_0_110, negated_conjecture, (~v1_membered(k1_numbers)\|~v1_xreal_0(esk3_2(esk1_0,np__1))\|~v1_xreal_0(esk4_2(esk1_0,np__1))\|~v1_xreal_0(np__1)\|~m1_subset_1(k18_complex1(esk3_2(esk1_0,np__1)),k1_numbers)\|~v1_xcmplx_0(esk4_2(esk1_0,np__1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_109, c_0_92])])). cnf(c_0_111, negated_conjecture, (~v1_membered(k1_numbers)\|~v1_xreal_0(esk3_2(esk1_0,np__1))\|~v1_xreal_0(esk4_2(esk1_0,np__1))\|~v1_xreal_0(np__1)\|~m1_subset_1(k18_complex1(esk3_2(esk1_0,np__1)),k1_numbers)), inference(csr,[status(thm)],[c_0_110, c_0_93])). cnf(c_0_112, negated_conjecture, (~v1_membered(k1_numbers)\|~v1_xreal_0(esk3_2(esk1_0,np__1))\|~v1_xreal_0(esk4_2(esk1_0,np__1))\|~v1_xreal_0(np__1)\|~v1_xcmplx_0(esk3_2(esk1_0,np__1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_111, c_0_92])])). cnf(c_0_113, plain, (v1_xreal_0(esk4_2(X1,X2))\|r1_xxreal_0(X2,k6_numbers)\|v2_fcont_1(X1)\|~v1_xreal_0(X2)\|~v1_funct_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))), inference(split_conjunct,[status(thm)],[c_0_23])). cnf(c_0_114, negated_conjecture, (~v1_membered(k1_numbers)\|~v1_xreal_0(esk3_2(esk1_0,np__1))\|~v1_xreal_0(esk4_2(esk1_0,np__1))\|~v1_xreal_0(np__1)), inference(csr,[status(thm)],[c_0_112, c_0_93])). cnf(c_0_115, plain, (v2_fcont_1(X1)\|r1_xxreal_0(X2,k6_numbers)\|v1_xreal_0(esk4_2(X1,X2))\|~v1_funct_1(X1)\|~v1_xreal_0(X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))), inference(evalgc,[status(thm)],[c_0_113])). cnf(c_0_116, plain, (v1_xreal_0(esk3_2(X1,X2))\|r1_xxreal_0(X2,k6_numbers)\|v2_fcont_1(X1)\|~v1_xreal_0(X2)\|~v1_funct_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))), inference(split_conjunct,[status(thm)],[c_0_23])). fof(c_0_117, plain, ![X33]:(~v3_membered(X33)\|v1_membered(X33)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc5_membered])])). cnf(c_0_118, negated_conjecture, (~v1_membered(k1_numbers)\|~v1_xreal_0(esk3_2(esk1_0,np__1))\|~v1_xreal_0(np__1)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114, c_0_115]), c_0_39]), c_0_40])]), c_0_51]), c_0_79])])). cnf(c_0_119, plain, (v2_fcont_1(X1)\|r1_xxreal_0(X2,k6_numbers)\|v1_xreal_0(esk3_2(X1,X2))\|~v1_funct_1(X1)\|~v1_xreal_0(X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))), inference(evalgc,[status(thm)],[c_0_116])). cnf(c_0_120, plain, (v1_membered(X1)\|~v3_membered(X1)), inference(split_conjunct,[status(thm)],[c_0_117])). cnf(c_0_121, plain, (v3_membered(k1_numbers)), inference(split_conjunct,[status(thm)],[fc3_membered])). cnf(c_0_122, negated_conjecture, (~v1_membered(k1_numbers)\|~v1_xreal_0(np__1)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118, c_0_119]), c_0_39]), c_0_40])]), c_0_51]), c_0_79])])). cnf(c_0_123, plain, (v1_membered(X1)\|~v3_membered(X1)), inference(evalgc,[status(thm)],[c_0_120])). cnf(c_0_124, plain, (v3_membered(k1_numbers)), inference(evalgc,[status(thm)],[c_0_121])). cnf(c_0_125, plain, (m1_subset_1(np__1,k1_numbers)), inference(split_conjunct,[status(thm)],[spc1_numerals])). cnf(c_0_126, negated_conjecture, (~v1_xreal_0(np__1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122, c_0_123]), c_0_124])])])). cnf(c_0_127, plain, (m1_subset_1(np__1,k1_numbers)), inference(evalgc,[status(thm)],[c_0_125])). cnf(c_0_128, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126, c_0_108]), c_0_127])]), ['proof']). # SZS output end CNFRefutation	reserve n,m,k for Element of NAT; reserve x, X,X1,Z,Z1 for set; reserve s,g,r,p,x0,x1,x2 for real number; reserve s1,s2,q1 for Real_Sequence; reserve Y for Subset of REAL; reserve f,f1,f2 for PartFunc of REAL,REAL; theorem Th44: (for x0 st x0 in dom f holds f.x0 = abs(x0)) implies f is continuous proof assume A1: for x0 st x0 in dom f holds f.x0 = abs(x0); now let x1,x2; assume x1 in dom f & x2 in dom f; then f.x1 = abs(x1) & f.x2 = abs(x2) by A1; hence abs(f.x1-f.x2) <= 1*abs(x1-x2) by COMPLEX1:64; end; then f is Lipschitzian by Def3; hence thesis; end;	Convert the following ATP output trace into a readable Mizar proof.
t71_integra8	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(cc14_membered, axiom, ![X1]:(v3_membered(X1)=>![X2]:(m1_subset_1(X2,X1)=>v1_xreal_0(X2))), file('/scratch/mptp/predsminms1/t71_integra8__0', cc14_membered)). fof(dt_k1_real_1, axiom, ![X1]:(m1_subset_1(X1,k1_numbers)=>m1_subset_1(k1_real_1(X1),k1_numbers)), file('/scratch/mptp/predsminms1/t71_integra8__0', dt_k1_real_1)). fof(t6_boole, axiom, ![X1]:(v1_xboole_0(X1)=>X1=k1_xboole_0), file('/scratch/mptp/predsminms1/t71_integra8__0', t6_boole)). fof(cc18_valued_0, axiom, ![X1, X2]:(v3_membered(X2)=>![X3]:(m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))=>v3_valued_0(X3))), file('/scratch/mptp/predsminms1/t71_integra8__0', cc18_valued_0)). fof(dt_k32_valued_1, axiom, ![X1, X2, X3]:((v3_membered(X2)&(v1_funct_1(X3)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))))=>(v1_funct_1(k32_valued_1(X1,X2,X3))&m1_subset_1(k32_valued_1(X1,X2,X3),k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers))))), file('/scratch/mptp/predsminms1/t71_integra8__0', dt_k32_valued_1)). fof(fc3_xreal_0, axiom, ![X1]:(v1_xreal_0(X1)=>(v1_xcmplx_0(k4_xcmplx_0(X1))&v1_xreal_0(k4_xcmplx_0(X1)))), file('/scratch/mptp/predsminms1/t71_integra8__0', fc3_xreal_0)). fof(redefinition_k1_real_1, axiom, ![X1]:(m1_subset_1(X1,k1_numbers)=>k1_real_1(X1)=k4_xcmplx_0(X1)), file('/scratch/mptp/predsminms1/t71_integra8__0', redefinition_k1_real_1)). fof(fc3_membered, axiom, v3_membered(k1_numbers), file('/scratch/mptp/predsminms1/t71_integra8__0', fc3_membered)). fof(involutiveness_k1_real_1, axiom, ![X1]:(m1_subset_1(X1,k1_numbers)=>k1_real_1(k1_real_1(X1))=X1), file('/scratch/mptp/predsminms1/t71_integra8__0', involutiveness_k1_real_1)). fof(t37_integra8, axiom, ![X1]:(m1_subset_1(X1,k1_numbers)=>![X2]:(m1_subset_1(X2,k1_numbers)=>![X3]:((~(v1_xboole_0(X3))&(v2_measure5(X3)&m1_subset_1(X3,k1_zfmisc_1(k1_numbers))))=>(X3=k1_rcomp_1(X1,X2)=>(k4_seq_4(X3)=X2&k5_seq_4(X3)=X1))))), file('/scratch/mptp/predsminms1/t71_integra8__0', t37_integra8)). fof(t71_integra8, conjecture, ![X1]:((~(v1_xboole_0(X1))&(v2_measure5(X1)&m1_subset_1(X1,k1_zfmisc_1(k1_numbers))))=>(X1=k1_rcomp_1(k6_numbers,k32_sin_cos)=>k2_integra5(X1,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k19_sin_cos))=np__2)), file('/scratch/mptp/predsminms1/t71_integra8__0', t71_integra8)). fof(redefinition_k6_numbers, axiom, k6_numbers=k1_xboole_0, file('/scratch/mptp/predsminms1/t71_integra8__0', redefinition_k6_numbers)). fof(redefinition_k32_valued_1, axiom, ![X1, X2, X3]:((v3_membered(X2)&(v1_funct_1(X3)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))))=>k32_valued_1(X1,X2,X3)=k30_valued_1(X3)), file('/scratch/mptp/predsminms1/t71_integra8__0', redefinition_k32_valued_1)). fof(redefinition_k1_seq_1, axiom, ![X1, X2]:((v1_relat_1(X1)&(v1_funct_1(X1)&v3_valued_0(X1)))=>k1_seq_1(X1,X2)=k1_funct_1(X1,X2)), file('/scratch/mptp/predsminms1/t71_integra8__0', redefinition_k1_seq_1)). fof(cc1_relset_1, axiom, ![X1, X2, X3]:(m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))=>v1_relat_1(X3)), file('/scratch/mptp/predsminms1/t71_integra8__0', cc1_relset_1)). fof(cc1_funct_2, axiom, ![X1, X2, X3]:(m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))=>(v1_partfun1(X3,X1)=>v1_funct_2(X3,X1,X2))), file('/scratch/mptp/predsminms1/t71_integra8__0', cc1_funct_2)). fof(t1_arithm, axiom, ![X1]:(v1_xcmplx_0(X1)=>k2_xcmplx_0(X1,k6_numbers)=X1), file('/scratch/mptp/predsminms1/t71_integra8__0', t1_arithm)). fof(commutativity_k2_xcmplx_0, axiom, ![X1, X2]:((v1_xcmplx_0(X1)&v1_xcmplx_0(X2))=>k2_xcmplx_0(X1,X2)=k2_xcmplx_0(X2,X1)), file('/scratch/mptp/predsminms1/t71_integra8__0', commutativity_k2_xcmplx_0)). fof(rc4_xreal_0, axiom, ?[X1]:(v1_xboole_0(X1)&(v1_xcmplx_0(X1)&(v1_xxreal_0(X1)&v1_xreal_0(X1)))), file('/scratch/mptp/predsminms1/t71_integra8__0', rc4_xreal_0)). fof(spc0_boole, axiom, v1_xboole_0(np__0), file('/scratch/mptp/predsminms1/t71_integra8__0', spc0_boole)). fof(dt_k19_sin_cos, axiom, (v1_funct_1(k19_sin_cos)&(v1_funct_2(k19_sin_cos,k1_numbers,k1_numbers)&m1_subset_1(k19_sin_cos,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))))), file('/scratch/mptp/predsminms1/t71_integra8__0', dt_k19_sin_cos)). fof(fc60_valued_1, axiom, ![X1, X2, X3]:(((~(v1_xboole_0(X2))&v3_membered(X2))&(v1_funct_1(X3)&(v1_funct_2(X3,X1,X2)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2))))))=>(v1_funct_1(k30_valued_1(X3))&v1_partfun1(k30_valued_1(X3),X1))), file('/scratch/mptp/predsminms1/t71_integra8__0', fc60_valued_1)). fof(fc1_numbers, axiom, ~(v1_xboole_0(k1_numbers)), file('/scratch/mptp/predsminms1/t71_integra8__0', fc1_numbers)). fof(t69_integra8, axiom, ![X1]:((~(v1_xboole_0(X1))&(v2_measure5(X1)&m1_subset_1(X1,k1_zfmisc_1(k1_numbers))))=>k2_integra5(X1,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k19_sin_cos))=k9_real_1(k7_real_1(k9_real_1(k3_funct_2(k1_numbers,k1_numbers,k32_valued_1(k1_numbers,k1_numbers,k19_sin_cos),k4_seq_4(X1)),k3_funct_2(k1_numbers,k1_numbers,k32_valued_1(k1_numbers,k1_numbers,k19_sin_cos),k5_seq_4(X1))),k3_funct_2(k1_numbers,k1_numbers,k16_sin_cos,k4_seq_4(X1))),k3_funct_2(k1_numbers,k1_numbers,k16_sin_cos,k5_seq_4(X1)))), file('/scratch/mptp/predsminms1/t71_integra8__0', t69_integra8)). fof(dt_k32_sin_cos, axiom, m1_subset_1(k32_sin_cos,k1_numbers), file('/scratch/mptp/predsminms1/t71_integra8__0', dt_k32_sin_cos)). fof(spc0_numerals, axiom, (m2_subset_1(np__0,k1_numbers,k5_numbers)&(m1_subset_1(np__0,k5_numbers)&m1_subset_1(np__0,k1_numbers))), file('/scratch/mptp/predsminms1/t71_integra8__0', spc0_numerals)). fof(redefinition_k3_funct_2, axiom, ![X1, X2, X3, X4]:((~(v1_xboole_0(X1))&((v1_funct_1(X3)&(v1_funct_2(X3,X1,X2)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))))&m1_subset_1(X4,X1)))=>k3_funct_2(X1,X2,X3,X4)=k1_funct_1(X3,X4)), file('/scratch/mptp/predsminms1/t71_integra8__0', redefinition_k3_funct_2)). fof(cc6_valued_0, axiom, ![X1]:((v1_relat_1(X1)&v3_valued_0(X1))=>(v1_relat_1(X1)&v1_valued_0(X1))), file('/scratch/mptp/predsminms1/t71_integra8__0', cc6_valued_0)). fof(t8_valued_1, axiom, ![X1]:((v1_relat_1(X1)&(v1_funct_1(X1)&v1_valued_0(X1)))=>(k9_xtuple_0(k30_valued_1(X1))=k9_xtuple_0(X1)&![X2]:k1_funct_1(k30_valued_1(X1),X2)=k4_xcmplx_0(k1_funct_1(X1,X2)))), file('/scratch/mptp/predsminms1/t71_integra8__0', t8_valued_1)). fof(t78_sin_cos, axiom, ![X1]:(v1_xreal_0(X1)=>(k1_seq_1(k16_sin_cos,k3_real_1(X1,k8_real_1(np__2,k32_sin_cos)))=k1_seq_1(k16_sin_cos,X1)&(k1_seq_1(k19_sin_cos,k3_real_1(X1,k8_real_1(np__2,k32_sin_cos)))=k1_seq_1(k19_sin_cos,X1)&(k1_seq_1(k16_sin_cos,k9_real_1(k10_real_1(k32_sin_cos,np__2),X1))=k1_seq_1(k19_sin_cos,X1)&(k1_seq_1(k19_sin_cos,k9_real_1(k10_real_1(k32_sin_cos,np__2),X1))=k1_seq_1(k16_sin_cos,X1)&(k1_seq_1(k16_sin_cos,k7_real_1(k10_real_1(k32_sin_cos,np__2),X1))=k1_seq_1(k19_sin_cos,X1)&(k1_seq_1(k19_sin_cos,k7_real_1(k10_real_1(k32_sin_cos,np__2),X1))=k1_real_1(k1_seq_1(k16_sin_cos,X1))&(k1_seq_1(k16_sin_cos,k7_real_1(k32_sin_cos,X1))=k1_real_1(k1_seq_1(k16_sin_cos,X1))&k1_seq_1(k19_sin_cos,k7_real_1(k32_sin_cos,X1))=k1_real_1(k1_seq_1(k19_sin_cos,X1)))))))))), file('/scratch/mptp/predsminms1/t71_integra8__0', t78_sin_cos)). fof(redefinition_k3_real_1, axiom, ![X1, X2]:((v1_xreal_0(X1)&m1_subset_1(X2,k1_numbers))=>k3_real_1(X1,X2)=k2_xcmplx_0(X1,X2)), file('/scratch/mptp/predsminms1/t71_integra8__0', redefinition_k3_real_1)). fof(rqRealNeg__k4_xcmplx_0__rm1_r1, axiom, k4_xcmplx_0(k4_xcmplx_0(np__1))=np__1, file('/scratch/mptp/predsminms1/t71_integra8__0', rqRealNeg__k4_xcmplx_0__rm1_r1)). fof(t76_sin_cos, axiom, (k1_seq_1(k19_sin_cos,k10_real_1(k32_sin_cos,np__2))=k6_numbers&(k1_seq_1(k16_sin_cos,k10_real_1(k32_sin_cos,np__2))=np__1&(k1_seq_1(k19_sin_cos,k32_sin_cos)=k1_real_1(np__1)&(k1_seq_1(k16_sin_cos,k32_sin_cos)=k6_numbers&(k1_seq_1(k19_sin_cos,k7_real_1(k32_sin_cos,k10_real_1(k32_sin_cos,np__2)))=k6_numbers&(k1_seq_1(k16_sin_cos,k7_real_1(k32_sin_cos,k10_real_1(k32_sin_cos,np__2)))=k1_real_1(np__1)&(k1_seq_1(k19_sin_cos,k8_real_1(np__2,k32_sin_cos))=np__1&k1_seq_1(k16_sin_cos,k8_real_1(np__2,k32_sin_cos))=k6_numbers))))))), file('/scratch/mptp/predsminms1/t71_integra8__0', t76_sin_cos)). fof(spc1_numerals, axiom, ((v2_xxreal_0(np__1)&m2_subset_1(np__1,k1_numbers,k5_numbers))&(m1_subset_1(np__1,k5_numbers)&m1_subset_1(np__1,k1_numbers))), file('/scratch/mptp/predsminms1/t71_integra8__0', spc1_numerals)). fof(dt_k8_real_1, axiom, ![X1, X2]:((m1_subset_1(X1,k1_numbers)&v1_xreal_0(X2))=>m1_subset_1(k8_real_1(X1,X2),k1_numbers)), file('/scratch/mptp/predsminms1/t71_integra8__0', dt_k8_real_1)). fof(dt_k31_sin_cos, axiom, v1_xreal_0(k31_sin_cos), file('/scratch/mptp/predsminms1/t71_integra8__0', dt_k31_sin_cos)). fof(redefinition_k32_sin_cos, axiom, k32_sin_cos=k31_sin_cos, file('/scratch/mptp/predsminms1/t71_integra8__0', redefinition_k32_sin_cos)). fof(redefinition_k9_real_1, axiom, ![X1, X2]:((m1_subset_1(X1,k1_numbers)&v1_xreal_0(X2))=>k9_real_1(X1,X2)=k6_xcmplx_0(X1,X2)), file('/scratch/mptp/predsminms1/t71_integra8__0', redefinition_k9_real_1)). fof(rqRealDiff__k6_xcmplx_0__r1_rm1_r2, axiom, k6_xcmplx_0(np__1,k4_xcmplx_0(np__1))=np__2, file('/scratch/mptp/predsminms1/t71_integra8__0', rqRealDiff__k6_xcmplx_0__r1_rm1_r2)). fof(redefinition_k7_real_1, axiom, ![X1, X2]:((m1_subset_1(X1,k1_numbers)&v1_xreal_0(X2))=>k7_real_1(X1,X2)=k2_xcmplx_0(X1,X2)), file('/scratch/mptp/predsminms1/t71_integra8__0', redefinition_k7_real_1)). fof(spc2_numerals, axiom, ((v2_xxreal_0(np__2)&m2_subset_1(np__2,k1_numbers,k5_numbers))&(m1_subset_1(np__2,k5_numbers)&m1_subset_1(np__2,k1_numbers))), file('/scratch/mptp/predsminms1/t71_integra8__0', spc2_numerals)). fof(dt_k16_sin_cos, axiom, (v1_funct_1(k16_sin_cos)&(v1_funct_2(k16_sin_cos,k1_numbers,k1_numbers)&m1_subset_1(k16_sin_cos,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))))), file('/scratch/mptp/predsminms1/t71_integra8__0', dt_k16_sin_cos)). fof(rqRealAdd__k2_xcmplx_0__r2_r0_r2, axiom, k2_xcmplx_0(np__2,np__0)=np__2, file('/scratch/mptp/predsminms1/t71_integra8__0', rqRealAdd__k2_xcmplx_0__r2_r0_r2)). fof(rqRealDiff__k6_xcmplx_0__r2_r0_r2, axiom, k6_xcmplx_0(np__2,np__0)=np__2, file('/scratch/mptp/predsminms1/t71_integra8__0', rqRealDiff__k6_xcmplx_0__r2_r0_r2)). fof(c_0_44, plain, ![X40, X41]:(~v3_membered(X40)\|(~m1_subset_1(X41,X40)\|v1_xreal_0(X41))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc14_membered])])])). fof(c_0_45, plain, ![X21]:(~m1_subset_1(X21,k1_numbers)\|m1_subset_1(k1_real_1(X21),k1_numbers)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_real_1])])). fof(c_0_46, plain, ![X6]:(~v1_xboole_0(X6)\|X6=k1_xboole_0), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])])). fof(c_0_47, plain, ![X53, X54, X55]:(~v3_membered(X54)\|(~m1_subset_1(X55,k1_zfmisc_1(k2_zfmisc_1(X53,X54)))\|v3_valued_0(X55))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc18_valued_0])])])). fof(c_0_48, plain, ![X48, X49, X50]:((v1_funct_1(k32_valued_1(X48,X49,X50))\|(~v3_membered(X49)\|(~v1_funct_1(X50)\|~m1_subset_1(X50,k1_zfmisc_1(k2_zfmisc_1(X48,X49))))))&(m1_subset_1(k32_valued_1(X48,X49,X50),k1_zfmisc_1(k2_zfmisc_1(X48,k1_numbers)))\|(~v3_membered(X49)\|(~v1_funct_1(X50)\|~m1_subset_1(X50,k1_zfmisc_1(k2_zfmisc_1(X48,X49))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k32_valued_1])])])). fof(c_0_49, plain, ![X22]:((v1_xcmplx_0(k4_xcmplx_0(X22))\|~v1_xreal_0(X22))&(v1_xreal_0(k4_xcmplx_0(X22))\|~v1_xreal_0(X22))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc3_xreal_0])])])). fof(c_0_50, plain, ![X12]:(~m1_subset_1(X12,k1_numbers)\|k1_real_1(X12)=k4_xcmplx_0(X12)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k1_real_1])])). cnf(c_0_51, plain, (v1_xreal_0(X2)\|~v3_membered(X1)\|~m1_subset_1(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_44])). cnf(c_0_52, plain, (m1_subset_1(k1_real_1(X1),k1_numbers)\|~m1_subset_1(X1,k1_numbers)), inference(split_conjunct,[status(thm)],[c_0_45])). cnf(c_0_53, plain, (v3_membered(k1_numbers)), inference(split_conjunct,[status(thm)],[fc3_membered])). fof(c_0_54, plain, ![X18]:(~m1_subset_1(X18,k1_numbers)\|k1_real_1(k1_real_1(X18))=X18), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[involutiveness_k1_real_1])])). fof(c_0_55, plain, ![X33, X34, X35]:((k4_seq_4(X35)=X34\|X35!=k1_rcomp_1(X33,X34)\|(v1_xboole_0(X35)\|(~v2_measure5(X35)\|~m1_subset_1(X35,k1_zfmisc_1(k1_numbers))))\|~m1_subset_1(X34,k1_numbers)\|~m1_subset_1(X33,k1_numbers))&(k5_seq_4(X35)=X33\|X35!=k1_rcomp_1(X33,X34)\|(v1_xboole_0(X35)\|(~v2_measure5(X35)\|~m1_subset_1(X35,k1_zfmisc_1(k1_numbers))))\|~m1_subset_1(X34,k1_numbers)\|~m1_subset_1(X33,k1_numbers))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t37_integra8])])])])])). fof(c_0_56, negated_conjecture, ~(![X1]:((~(v1_xboole_0(X1))&(v2_measure5(X1)&m1_subset_1(X1,k1_zfmisc_1(k1_numbers))))=>(X1=k1_rcomp_1(k6_numbers,k32_sin_cos)=>k2_integra5(X1,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k19_sin_cos))=np__2))), inference(assume_negation,[status(cth)],[t71_integra8])). cnf(c_0_57, plain, (X1=k1_xboole_0\|~v1_xboole_0(X1)), inference(split_conjunct,[status(thm)],[c_0_46])). cnf(c_0_58, plain, (k6_numbers=k1_xboole_0), inference(split_conjunct,[status(thm)],[redefinition_k6_numbers])). fof(c_0_59, plain, ![X36, X37, X38]:(~v3_membered(X37)\|(~v1_funct_1(X38)\|~m1_subset_1(X38,k1_zfmisc_1(k2_zfmisc_1(X36,X37))))\|k32_valued_1(X36,X37,X38)=k30_valued_1(X38)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k32_valued_1])])). fof(c_0_60, plain, ![X16, X17]:(~v1_relat_1(X16)\|(~v1_funct_1(X16)\|~v3_valued_0(X16))\|k1_seq_1(X16,X17)=k1_funct_1(X16,X17)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k1_seq_1])])). cnf(c_0_61, plain, (v3_valued_0(X2)\|~v3_membered(X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_47])). cnf(c_0_62, plain, (m1_subset_1(k32_valued_1(X1,X2,X3),k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~v3_membered(X2)\|~v1_funct_1(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_48])). fof(c_0_63, plain, ![X13, X14, X15]:(~m1_subset_1(X15,k1_zfmisc_1(k2_zfmisc_1(X13,X14)))\|v1_relat_1(X15)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relset_1])])). fof(c_0_64, plain, ![X45, X46, X47]:(~m1_subset_1(X47,k1_zfmisc_1(k2_zfmisc_1(X45,X46)))\|(~v1_partfun1(X47,X45)\|v1_funct_2(X47,X45,X46))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_funct_2])])). fof(c_0_65, plain, ![X23]:(~v1_xcmplx_0(X23)\|k2_xcmplx_0(X23,k6_numbers)=X23), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_arithm])])). cnf(c_0_66, plain, (v1_xcmplx_0(k4_xcmplx_0(X1))\|~v1_xreal_0(X1)), inference(split_conjunct,[status(thm)],[c_0_49])). cnf(c_0_67, plain, (k1_real_1(X1)=k4_xcmplx_0(X1)\|~m1_subset_1(X1,k1_numbers)), inference(split_conjunct,[status(thm)],[c_0_50])). cnf(c_0_68, plain, (v1_xreal_0(X2)\|~v3_membered(X1)\|~m1_subset_1(X2,X1)), inference(evalgc,[status(thm)],[c_0_51])). cnf(c_0_69, plain, (m1_subset_1(k1_real_1(X1),k1_numbers)\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[c_0_52])). cnf(c_0_70, plain, (v3_membered(k1_numbers)), inference(evalgc,[status(thm)],[c_0_53])). cnf(c_0_71, plain, (k1_real_1(k1_real_1(X1))=X1\|~m1_subset_1(X1,k1_numbers)), inference(split_conjunct,[status(thm)],[c_0_54])). fof(c_0_72, plain, ![X24, X25]:(~v1_xcmplx_0(X24)\|~v1_xcmplx_0(X25)\|k2_xcmplx_0(X24,X25)=k2_xcmplx_0(X25,X24)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[commutativity_k2_xcmplx_0])])). fof(c_0_73, plain, (v1_xboole_0(esk2_0)&(v1_xcmplx_0(esk2_0)&(v1_xxreal_0(esk2_0)&v1_xreal_0(esk2_0)))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc4_xreal_0])])). cnf(c_0_74, plain, (k4_seq_4(X1)=X2\|v1_xboole_0(X1)\|X1!=k1_rcomp_1(X3,X2)\|~v2_measure5(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k1_numbers))\|~m1_subset_1(X2,k1_numbers)\|~m1_subset_1(X3,k1_numbers)), inference(split_conjunct,[status(thm)],[c_0_55])). fof(c_0_75, negated_conjecture, ((~v1_xboole_0(esk1_0)&(v2_measure5(esk1_0)&m1_subset_1(esk1_0,k1_zfmisc_1(k1_numbers))))&(esk1_0=k1_rcomp_1(k6_numbers,k32_sin_cos)&k2_integra5(esk1_0,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k19_sin_cos))!=np__2)), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_56])])])])). cnf(c_0_76, plain, (X1=k1_xboole_0\|~v1_xboole_0(X1)), inference(evalgc,[status(thm)],[c_0_57])). cnf(c_0_77, plain, (k1_xboole_0=k6_numbers), inference(evalgc,[status(thm)],[c_0_58])). cnf(c_0_78, plain, (v1_xboole_0(np__0)), inference(split_conjunct,[status(thm)],[spc0_boole])). cnf(c_0_79, plain, (k5_seq_4(X1)=X2\|v1_xboole_0(X1)\|X1!=k1_rcomp_1(X2,X3)\|~v2_measure5(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k1_numbers))\|~m1_subset_1(X3,k1_numbers)\|~m1_subset_1(X2,k1_numbers)), inference(split_conjunct,[status(thm)],[c_0_55])). cnf(c_0_80, plain, (k32_valued_1(X3,X1,X2)=k30_valued_1(X2)\|~v3_membered(X1)\|~v1_funct_1(X2)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_59])). cnf(c_0_81, plain, (m1_subset_1(k19_sin_cos,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))), inference(split_conjunct,[status(thm)],[dt_k19_sin_cos])). cnf(c_0_82, plain, (v1_funct_1(k19_sin_cos)), inference(split_conjunct,[status(thm)],[dt_k19_sin_cos])). fof(c_0_83, plain, ![X42, X43, X44]:((v1_funct_1(k30_valued_1(X44))\|(v1_xboole_0(X43)\|~v3_membered(X43)\|(~v1_funct_1(X44)\|(~v1_funct_2(X44,X42,X43)\|~m1_subset_1(X44,k1_zfmisc_1(k2_zfmisc_1(X42,X43)))))))&(v1_partfun1(k30_valued_1(X44),X42)\|(v1_xboole_0(X43)\|~v3_membered(X43)\|(~v1_funct_1(X44)\|(~v1_funct_2(X44,X42,X43)\|~m1_subset_1(X44,k1_zfmisc_1(k2_zfmisc_1(X42,X43)))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fc60_valued_1])])])])). fof(c_0_84, plain, ~v1_xboole_0(k1_numbers), inference(fof_simplification,[status(thm)],[fc1_numbers])). cnf(c_0_85, plain, (k1_seq_1(X1,X2)=k1_funct_1(X1,X2)\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v3_valued_0(X1)), inference(split_conjunct,[status(thm)],[c_0_60])). cnf(c_0_86, plain, (v3_valued_0(X2)\|~v3_membered(X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X3,X1)))), inference(evalgc,[status(thm)],[c_0_61])). cnf(c_0_87, plain, (m1_subset_1(k32_valued_1(X1,X2,X3),k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~v1_funct_1(X3)\|~v3_membered(X2)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(evalgc,[status(thm)],[c_0_62])). cnf(c_0_88, plain, (v1_relat_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_63])). cnf(c_0_89, plain, (v1_funct_2(X1,X2,X3)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))\|~v1_partfun1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_64])). cnf(c_0_90, plain, (k2_xcmplx_0(X1,k6_numbers)=X1\|~v1_xcmplx_0(X1)), inference(split_conjunct,[status(thm)],[c_0_65])). cnf(c_0_91, plain, (v1_xcmplx_0(k4_xcmplx_0(X1))\|~v1_xreal_0(X1)), inference(evalgc,[status(thm)],[c_0_66])). cnf(c_0_92, plain, (k4_xcmplx_0(X1)=k1_real_1(X1)\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[c_0_67])). cnf(c_0_93, plain, (v1_xreal_0(k1_real_1(X1))\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68, c_0_69]), c_0_70])])])). cnf(c_0_94, plain, (k1_real_1(k1_real_1(X1))=X1\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[c_0_71])). cnf(c_0_95, plain, (k2_xcmplx_0(X1,X2)=k2_xcmplx_0(X2,X1)\|~v1_xcmplx_0(X1)\|~v1_xcmplx_0(X2)), inference(split_conjunct,[status(thm)],[c_0_72])). cnf(c_0_96, plain, (v1_xboole_0(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_73])). fof(c_0_97, plain, ![X39]:(v1_xboole_0(X39)\|(~v2_measure5(X39)\|~m1_subset_1(X39,k1_zfmisc_1(k1_numbers)))\|k2_integra5(X39,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k19_sin_cos))=k9_real_1(k7_real_1(k9_real_1(k3_funct_2(k1_numbers,k1_numbers,k32_valued_1(k1_numbers,k1_numbers,k19_sin_cos),k4_seq_4(X39)),k3_funct_2(k1_numbers,k1_numbers,k32_valued_1(k1_numbers,k1_numbers,k19_sin_cos),k5_seq_4(X39))),k3_funct_2(k1_numbers,k1_numbers,k16_sin_cos,k4_seq_4(X39))),k3_funct_2(k1_numbers,k1_numbers,k16_sin_cos,k5_seq_4(X39)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t69_integra8])])])). cnf(c_0_98, plain, (k4_seq_4(X1)=X2\|v1_xboole_0(X1)\|X1!=k1_rcomp_1(X3,X2)\|~v2_measure5(X1)\|~m1_subset_1(X3,k1_numbers)\|~m1_subset_1(X2,k1_numbers)\|~m1_subset_1(X1,k1_zfmisc_1(k1_numbers))), inference(evalgc,[status(thm)],[c_0_74])). cnf(c_0_99, negated_conjecture, (esk1_0=k1_rcomp_1(k6_numbers,k32_sin_cos)), inference(split_conjunct,[status(thm)],[c_0_75])). cnf(c_0_100, negated_conjecture, (m1_subset_1(esk1_0,k1_zfmisc_1(k1_numbers))), inference(split_conjunct,[status(thm)],[c_0_75])). cnf(c_0_101, plain, (m1_subset_1(k32_sin_cos,k1_numbers)), inference(split_conjunct,[status(thm)],[dt_k32_sin_cos])). cnf(c_0_102, negated_conjecture, (v2_measure5(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_75])). cnf(c_0_103, negated_conjecture, (~v1_xboole_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_75])). cnf(c_0_104, plain, (m1_subset_1(np__0,k1_numbers)), inference(split_conjunct,[status(thm)],[spc0_numerals])). cnf(c_0_105, plain, (X1=k6_numbers\|~v1_xboole_0(X1)), inference(rw,[status(thm)],[c_0_76, c_0_77])). cnf(c_0_106, plain, (v1_xboole_0(np__0)), inference(evalgc,[status(thm)],[c_0_78])). cnf(c_0_107, plain, (k5_seq_4(X1)=X2\|v1_xboole_0(X1)\|X1!=k1_rcomp_1(X2,X3)\|~v2_measure5(X1)\|~m1_subset_1(X3,k1_numbers)\|~m1_subset_1(X2,k1_numbers)\|~m1_subset_1(X1,k1_zfmisc_1(k1_numbers))), inference(evalgc,[status(thm)],[c_0_79])). fof(c_0_108, plain, ![X29, X30, X31, X32]:(v1_xboole_0(X29)\|(~v1_funct_1(X31)\|(~v1_funct_2(X31,X29,X30)\|~m1_subset_1(X31,k1_zfmisc_1(k2_zfmisc_1(X29,X30))))\|~m1_subset_1(X32,X29))\|k3_funct_2(X29,X30,X31,X32)=k1_funct_1(X31,X32)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[redefinition_k3_funct_2])])])). cnf(c_0_109, plain, (k32_valued_1(X3,X1,X2)=k30_valued_1(X2)\|~v1_funct_1(X2)\|~v3_membered(X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X3,X1)))), inference(evalgc,[status(thm)],[c_0_80])). cnf(c_0_110, plain, (m1_subset_1(k19_sin_cos,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))), inference(evalgc,[status(thm)],[c_0_81])). cnf(c_0_111, plain, (v1_funct_1(k19_sin_cos)), inference(evalgc,[status(thm)],[c_0_82])). cnf(c_0_112, plain, (v1_funct_1(k30_valued_1(X1))\|v1_xboole_0(X2)\|~v3_membered(X2)\|~v1_funct_1(X1)\|~v1_funct_2(X1,X3,X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X3,X2)))), inference(split_conjunct,[status(thm)],[c_0_83])). cnf(c_0_113, plain, (v1_funct_2(k19_sin_cos,k1_numbers,k1_numbers)), inference(split_conjunct,[status(thm)],[dt_k19_sin_cos])). cnf(c_0_114, plain, (~v1_xboole_0(k1_numbers)), inference(split_conjunct,[status(thm)],[c_0_84])). cnf(c_0_115, plain, (k1_funct_1(X1,X2)=k1_seq_1(X1,X2)\|~v1_funct_1(X1)\|~v1_relat_1(X1)\|~v3_valued_0(X1)), inference(evalgc,[status(thm)],[c_0_85])). cnf(c_0_116, plain, (v3_valued_0(k32_valued_1(X1,X2,X3))\|~v3_membered(X2)\|~v1_funct_1(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86, c_0_87]), c_0_70])])])). cnf(c_0_117, plain, (v1_funct_1(k32_valued_1(X1,X2,X3))\|~v3_membered(X2)\|~v1_funct_1(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_48])). cnf(c_0_118, plain, (v1_relat_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(evalgc,[status(thm)],[c_0_88])). cnf(c_0_119, plain, (v1_funct_2(X1,X2,X3)\|~v1_partfun1(X1,X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(evalgc,[status(thm)],[c_0_89])). cnf(c_0_120, plain, (v1_partfun1(k30_valued_1(X1),X2)\|v1_xboole_0(X3)\|~v3_membered(X3)\|~v1_funct_1(X1)\|~v1_funct_2(X1,X2,X3)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_83])). cnf(c_0_121, plain, (k2_xcmplx_0(X1,k6_numbers)=X1\|~v1_xcmplx_0(X1)), inference(evalgc,[status(thm)],[c_0_90])). cnf(c_0_122, plain, (v1_xcmplx_0(k1_real_1(X1))\|~v1_xreal_0(X1)\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_91, c_0_92])])). cnf(c_0_123, plain, (v1_xreal_0(X1)\|~m1_subset_1(k1_real_1(X1),k1_numbers)\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_93, c_0_94])])). cnf(c_0_124, plain, (k2_xcmplx_0(X1,X2)=k2_xcmplx_0(X2,X1)\|~v1_xcmplx_0(X2)\|~v1_xcmplx_0(X1)), inference(evalgc,[status(thm)],[c_0_95])). cnf(c_0_125, plain, (v1_xcmplx_0(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_73])). cnf(c_0_126, plain, (v1_xboole_0(esk2_0)), inference(evalgc,[status(thm)],[c_0_96])). cnf(c_0_127, plain, (v1_xboole_0(X1)\|k2_integra5(X1,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k19_sin_cos))=k9_real_1(k7_real_1(k9_real_1(k3_funct_2(k1_numbers,k1_numbers,k32_valued_1(k1_numbers,k1_numbers,k19_sin_cos),k4_seq_4(X1)),k3_funct_2(k1_numbers,k1_numbers,k32_valued_1(k1_numbers,k1_numbers,k19_sin_cos),k5_seq_4(X1))),k3_funct_2(k1_numbers,k1_numbers,k16_sin_cos,k4_seq_4(X1))),k3_funct_2(k1_numbers,k1_numbers,k16_sin_cos,k5_seq_4(X1)))\|~v2_measure5(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k1_numbers))), inference(split_conjunct,[status(thm)],[c_0_97])). cnf(c_0_128, plain, (k4_seq_4(k1_rcomp_1(X1,X2))=X2\|v1_xboole_0(k1_rcomp_1(X1,X2))\|~m1_subset_1(k1_rcomp_1(X1,X2),k1_zfmisc_1(k1_numbers))\|~m1_subset_1(X1,k1_numbers)\|~m1_subset_1(X2,k1_numbers)\|~v2_measure5(k1_rcomp_1(X1,X2))), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_98])])). cnf(c_0_129, negated_conjecture, (k1_rcomp_1(k6_numbers,k32_sin_cos)=esk1_0), inference(evalgc,[status(thm)],[c_0_99])). cnf(c_0_130, negated_conjecture, (m1_subset_1(esk1_0,k1_zfmisc_1(k1_numbers))), inference(evalgc,[status(thm)],[c_0_100])). cnf(c_0_131, plain, (m1_subset_1(k32_sin_cos,k1_numbers)), inference(evalgc,[status(thm)],[c_0_101])). cnf(c_0_132, negated_conjecture, (v2_measure5(esk1_0)), inference(evalgc,[status(thm)],[c_0_102])). cnf(c_0_133, negated_conjecture, (~v1_xboole_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_103])). cnf(c_0_134, plain, (m1_subset_1(np__0,k1_numbers)), inference(evalgc,[status(thm)],[c_0_104])). cnf(c_0_135, plain, (np__0=k6_numbers), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_105, c_0_106])])). cnf(c_0_136, plain, (k5_seq_4(k1_rcomp_1(X1,X2))=X1\|v1_xboole_0(k1_rcomp_1(X1,X2))\|~m1_subset_1(k1_rcomp_1(X1,X2),k1_zfmisc_1(k1_numbers))\|~m1_subset_1(X2,k1_numbers)\|~m1_subset_1(X1,k1_numbers)\|~v2_measure5(k1_rcomp_1(X1,X2))), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_107])])). cnf(c_0_137, plain, (v1_xboole_0(X1)\|k3_funct_2(X1,X3,X2,X4)=k1_funct_1(X2,X4)\|~v1_funct_1(X2)\|~v1_funct_2(X2,X1,X3)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))\|~m1_subset_1(X4,X1)), inference(split_conjunct,[status(thm)],[c_0_108])). cnf(c_0_138, plain, (k32_valued_1(k1_numbers,k1_numbers,k19_sin_cos)=k30_valued_1(k19_sin_cos)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109, c_0_110]), c_0_70]), c_0_111])])])). cnf(c_0_139, plain, (v1_xboole_0(X2)\|v1_funct_1(k30_valued_1(X1))\|~v1_funct_1(X1)\|~v3_membered(X2)\|~v1_funct_2(X1,X3,X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X3,X2)))), inference(evalgc,[status(thm)],[c_0_112])). cnf(c_0_140, plain, (v1_funct_2(k19_sin_cos,k1_numbers,k1_numbers)), inference(evalgc,[status(thm)],[c_0_113])). cnf(c_0_141, plain, (~v1_xboole_0(k1_numbers)), inference(evalgc,[status(thm)],[c_0_114])). cnf(c_0_142, plain, (k1_funct_1(k32_valued_1(X1,X2,X3),X4)=k1_seq_1(k32_valued_1(X1,X2,X3),X4)\|~v1_relat_1(k32_valued_1(X1,X2,X3))\|~v1_funct_1(k32_valued_1(X1,X2,X3))\|~v3_membered(X2)\|~v1_funct_1(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_115, c_0_116])])). cnf(c_0_143, plain, (v1_funct_1(k32_valued_1(X1,X2,X3))\|~v1_funct_1(X3)\|~v3_membered(X2)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(evalgc,[status(thm)],[c_0_117])). cnf(c_0_144, plain, (v1_relat_1(k32_valued_1(X1,X2,X3))\|~v3_membered(X2)\|~v1_funct_1(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_118, c_0_87])])). cnf(c_0_145, plain, (v1_funct_2(k32_valued_1(X1,X2,X3),X1,k1_numbers)\|~v1_partfun1(k32_valued_1(X1,X2,X3),X1)\|~v3_membered(X2)\|~v1_funct_1(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_119, c_0_87])])). cnf(c_0_146, plain, (v1_xboole_0(X3)\|v1_partfun1(k30_valued_1(X1),X2)\|~v1_funct_1(X1)\|~v3_membered(X3)\|~v1_funct_2(X1,X2,X3)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(evalgc,[status(thm)],[c_0_120])). fof(c_0_147, plain, ![X56]:((v1_relat_1(X56)\|(~v1_relat_1(X56)\|~v3_valued_0(X56)))&(v1_valued_0(X56)\|(~v1_relat_1(X56)\|~v3_valued_0(X56)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc6_valued_0])])])). cnf(c_0_148, plain, (k2_xcmplx_0(k1_real_1(X1),k6_numbers)=k1_real_1(X1)\|~v1_xreal_0(X1)\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_121, c_0_122])])). cnf(c_0_149, plain, (v1_xreal_0(X1)\|~m1_subset_1(X1,k1_numbers)), inference(csr,[status(thm)],[c_0_123, c_0_69])). cnf(c_0_150, plain, (k2_xcmplx_0(X1,k1_real_1(X2))=k2_xcmplx_0(k1_real_1(X2),X1)\|~v1_xcmplx_0(X1)\|~v1_xreal_0(X2)\|~m1_subset_1(X2,k1_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_124, c_0_122])])). cnf(c_0_151, plain, (v1_xcmplx_0(esk2_0)), inference(evalgc,[status(thm)],[c_0_125])). cnf(c_0_152, plain, (esk2_0=k6_numbers), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_105, c_0_126])])). cnf(c_0_153, plain, (k9_real_1(k7_real_1(k9_real_1(k3_funct_2(k1_numbers,k1_numbers,k32_valued_1(k1_numbers,k1_numbers,k19_sin_cos),k4_seq_4(X1)),k3_funct_2(k1_numbers,k1_numbers,k32_valued_1(k1_numbers,k1_numbers,k19_sin_cos),k5_seq_4(X1))),k3_funct_2(k1_numbers,k1_numbers,k16_sin_cos,k4_seq_4(X1))),k3_funct_2(k1_numbers,k1_numbers,k16_sin_cos,k5_seq_4(X1)))=k2_integra5(X1,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k19_sin_cos))\|v1_xboole_0(X1)\|~v2_measure5(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k1_numbers))), inference(evalgc,[status(thm)],[c_0_127])). cnf(c_0_154, negated_conjecture, (k4_seq_4(esk1_0)=k32_sin_cos\|~m1_subset_1(k6_numbers,k1_numbers)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128, c_0_129]), c_0_130]), c_0_131]), c_0_132])]), c_0_133])])). cnf(c_0_155, plain, (m1_subset_1(k6_numbers,k1_numbers)), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[c_0_134, c_0_135])])). cnf(c_0_156, negated_conjecture, (k5_seq_4(esk1_0)=k6_numbers\|~m1_subset_1(k6_numbers,k1_numbers)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136, c_0_129]), c_0_130]), c_0_131]), c_0_132])]), c_0_133])])). cnf(c_0_157, plain, (k3_funct_2(X1,X3,X2,X4)=k1_funct_1(X2,X4)\|v1_xboole_0(X1)\|~v1_funct_1(X2)\|~m1_subset_1(X4,X1)\|~v1_funct_2(X2,X1,X3)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))), inference(evalgc,[status(thm)],[c_0_137])). cnf(c_0_158, plain, (m1_subset_1(k30_valued_1(k19_sin_cos),k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87, c_0_138]), c_0_70]), c_0_111]), c_0_110])])])). cnf(c_0_159, plain, (v1_funct_1(k30_valued_1(k19_sin_cos))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139, c_0_110]), c_0_70]), c_0_140]), c_0_111])]), c_0_141])])). cnf(c_0_160, plain, (k1_funct_1(k32_valued_1(X1,X2,X3),X4)=k1_seq_1(k32_valued_1(X1,X2,X3),X4)\|~v3_membered(X2)\|~v1_funct_1(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_142, c_0_143]), c_0_144])). cnf(c_0_161, plain, (v1_funct_2(k30_valued_1(k19_sin_cos),k1_numbers,k1_numbers)\|~v1_partfun1(k30_valued_1(k19_sin_cos),k1_numbers)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145, c_0_138]), c_0_70]), c_0_111]), c_0_110])])])). cnf(c_0_162, plain, (v1_partfun1(k30_valued_1(k19_sin_cos),k1_numbers)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146, c_0_110]), c_0_70]), c_0_140]), c_0_111])]), c_0_141])])). fof(c_0_163, plain, ![X51, X52]:((k9_xtuple_0(k30_valued_1(X51))=k9_xtuple_0(X51)\|(~v1_relat_1(X51)\|(~v1_funct_1(X51)\|~v1_valued_0(X51))))&(k1_funct_1(k30_valued_1(X51),X52)=k4_xcmplx_0(k1_funct_1(X51,X52))\|(~v1_relat_1(X51)\|(~v1_funct_1(X51)\|~v1_valued_0(X51))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_valued_1])])])])). cnf(c_0_164, plain, (v1_valued_0(X1)\|~v1_relat_1(X1)\|~v3_valued_0(X1)), inference(split_conjunct,[status(thm)],[c_0_147])). fof(c_0_165, plain, ![X28]:((k1_seq_1(k16_sin_cos,k3_real_1(X28,k8_real_1(np__2,k32_sin_cos)))=k1_seq_1(k16_sin_cos,X28)\|~v1_xreal_0(X28))&((k1_seq_1(k19_sin_cos,k3_real_1(X28,k8_real_1(np__2,k32_sin_cos)))=k1_seq_1(k19_sin_cos,X28)\|~v1_xreal_0(X28))&((k1_seq_1(k16_sin_cos,k9_real_1(k10_real_1(k32_sin_cos,np__2),X28))=k1_seq_1(k19_sin_cos,X28)\|~v1_xreal_0(X28))&((k1_seq_1(k19_sin_cos,k9_real_1(k10_real_1(k32_sin_cos,np__2),X28))=k1_seq_1(k16_sin_cos,X28)\|~v1_xreal_0(X28))&((k1_seq_1(k16_sin_cos,k7_real_1(k10_real_1(k32_sin_cos,np__2),X28))=k1_seq_1(k19_sin_cos,X28)\|~v1_xreal_0(X28))&((k1_seq_1(k19_sin_cos,k7_real_1(k10_real_1(k32_sin_cos,np__2),X28))=k1_real_1(k1_seq_1(k16_sin_cos,X28))\|~v1_xreal_0(X28))&((k1_seq_1(k16_sin_cos,k7_real_1(k32_sin_cos,X28))=k1_real_1(k1_seq_1(k16_sin_cos,X28))\|~v1_xreal_0(X28))&(k1_seq_1(k19_sin_cos,k7_real_1(k32_sin_cos,X28))=k1_real_1(k1_seq_1(k19_sin_cos,X28))\|~v1_xreal_0(X28))))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t78_sin_cos])])])). fof(c_0_166, plain, ![X26, X27]:(~v1_xreal_0(X26)\|~m1_subset_1(X27,k1_numbers)\|k3_real_1(X26,X27)=k2_xcmplx_0(X26,X27)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k3_real_1])])). cnf(c_0_167, plain, (k2_xcmplx_0(k1_real_1(X1),k6_numbers)=k1_real_1(X1)\|~m1_subset_1(X1,k1_numbers)), inference(csr,[status(thm)],[c_0_148, c_0_149])). cnf(c_0_168, plain, (k2_xcmplx_0(X1,k1_real_1(X2))=k2_xcmplx_0(k1_real_1(X2),X1)\|~v1_xcmplx_0(X1)\|~m1_subset_1(X2,k1_numbers)), inference(csr,[status(thm)],[c_0_150, c_0_149])). cnf(c_0_169, plain, (v1_xcmplx_0(k6_numbers)), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[c_0_151, c_0_152])])). cnf(c_0_170, plain, (k9_real_1(k7_real_1(k9_real_1(k3_funct_2(k1_numbers,k1_numbers,k30_valued_1(k19_sin_cos),k4_seq_4(X1)),k3_funct_2(k1_numbers,k1_numbers,k30_valued_1(k19_sin_cos),k5_seq_4(X1))),k3_funct_2(k1_numbers,k1_numbers,k16_sin_cos,k4_seq_4(X1))),k3_funct_2(k1_numbers,k1_numbers,k16_sin_cos,k5_seq_4(X1)))=k2_integra5(X1,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k19_sin_cos))\|v1_xboole_0(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k1_numbers))\|~v2_measure5(X1)), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_153, c_0_138]), c_0_138])])). cnf(c_0_171, negated_conjecture, (k4_seq_4(esk1_0)=k32_sin_cos), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_154, c_0_155])])). cnf(c_0_172, negated_conjecture, (k5_seq_4(esk1_0)=k6_numbers), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_156, c_0_155])])). cnf(c_0_173, plain, (k3_funct_2(k1_numbers,k1_numbers,k30_valued_1(k19_sin_cos),X1)=k1_funct_1(k30_valued_1(k19_sin_cos),X1)\|~v1_funct_2(k30_valued_1(k19_sin_cos),k1_numbers,k1_numbers)\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157, c_0_158]), c_0_159])]), c_0_141])])). cnf(c_0_174, plain, (k1_funct_1(k30_valued_1(k19_sin_cos),X1)=k1_seq_1(k30_valued_1(k19_sin_cos),X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160, c_0_138]), c_0_70]), c_0_111]), c_0_110])])])). cnf(c_0_175, plain, (v1_funct_2(k30_valued_1(k19_sin_cos),k1_numbers,k1_numbers)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_161, c_0_162])])). cnf(c_0_176, plain, (k1_funct_1(k30_valued_1(X1),X2)=k4_xcmplx_0(k1_funct_1(X1,X2))\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v1_valued_0(X1)), inference(split_conjunct,[status(thm)],[c_0_163])). cnf(c_0_177, plain, (v3_valued_0(k19_sin_cos)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86, c_0_110]), c_0_70])])])). cnf(c_0_178, plain, (v1_relat_1(k19_sin_cos)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_118, c_0_110])])). cnf(c_0_179, plain, (v1_valued_0(X1)\|~v1_relat_1(X1)\|~v3_valued_0(X1)), inference(evalgc,[status(thm)],[c_0_164])). cnf(c_0_180, plain, (k4_xcmplx_0(k4_xcmplx_0(np__1))=np__1), inference(split_conjunct,[status(thm)],[rqRealNeg__k4_xcmplx_0__rm1_r1])). cnf(c_0_181, plain, (k1_seq_1(k19_sin_cos,k32_sin_cos)=k1_real_1(np__1)), inference(split_conjunct,[status(thm)],[t76_sin_cos])). cnf(c_0_182, plain, (m1_subset_1(np__1,k1_numbers)), inference(split_conjunct,[status(thm)],[spc1_numerals])). cnf(c_0_183, plain, (k1_seq_1(k19_sin_cos,k3_real_1(X1,k8_real_1(np__2,k32_sin_cos)))=k1_seq_1(k19_sin_cos,X1)\|~v1_xreal_0(X1)), inference(split_conjunct,[status(thm)],[c_0_165])). cnf(c_0_184, plain, (k3_real_1(X1,X2)=k2_xcmplx_0(X1,X2)\|~v1_xreal_0(X1)\|~m1_subset_1(X2,k1_numbers)), inference(split_conjunct,[status(thm)],[c_0_166])). cnf(c_0_185, plain, (k2_xcmplx_0(k6_numbers,k1_real_1(X1))=k1_real_1(X1)\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167, c_0_168]), c_0_169])])])). cnf(c_0_186, plain, (v1_xreal_0(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_73])). cnf(c_0_187, negated_conjecture, (k9_real_1(k7_real_1(k9_real_1(k3_funct_2(k1_numbers,k1_numbers,k30_valued_1(k19_sin_cos),k32_sin_cos),k3_funct_2(k1_numbers,k1_numbers,k30_valued_1(k19_sin_cos),k6_numbers)),k3_funct_2(k1_numbers,k1_numbers,k16_sin_cos,k32_sin_cos)),k3_funct_2(k1_numbers,k1_numbers,k16_sin_cos,k6_numbers))=k2_integra5(esk1_0,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k19_sin_cos))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170, c_0_171]), c_0_172]), c_0_172]), c_0_130]), c_0_132])]), c_0_133])])). cnf(c_0_188, plain, (k3_funct_2(k1_numbers,k1_numbers,k30_valued_1(k19_sin_cos),X1)=k1_seq_1(k30_valued_1(k19_sin_cos),X1)\|~m1_subset_1(X1,k1_numbers)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_173, c_0_174]), c_0_175])])). cnf(c_0_189, plain, (k1_funct_1(k30_valued_1(X1),X2)=k4_xcmplx_0(k1_funct_1(X1,X2))\|~v1_funct_1(X1)\|~v1_relat_1(X1)\|~v1_valued_0(X1)), inference(evalgc,[status(thm)],[c_0_176])). cnf(c_0_190, plain, (k1_funct_1(k19_sin_cos,X1)=k1_seq_1(k19_sin_cos,X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115, c_0_177]), c_0_178]), c_0_111])])])). cnf(c_0_191, plain, (v1_valued_0(k19_sin_cos)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_179, c_0_177]), c_0_178])])])). cnf(c_0_192, plain, (k4_xcmplx_0(k4_xcmplx_0(np__1))=np__1), inference(evalgc,[status(thm)],[c_0_180])). cnf(c_0_193, plain, (k1_real_1(np__1)=k1_seq_1(k19_sin_cos,k32_sin_cos)), inference(evalgc,[status(thm)],[c_0_181])). cnf(c_0_194, plain, (m1_subset_1(np__1,k1_numbers)), inference(evalgc,[status(thm)],[c_0_182])). cnf(c_0_195, plain, (k1_seq_1(k19_sin_cos,k3_real_1(X1,k8_real_1(np__2,k32_sin_cos)))=k1_seq_1(k19_sin_cos,X1)\|~v1_xreal_0(X1)), inference(evalgc,[status(thm)],[c_0_183])). cnf(c_0_196, plain, (k3_real_1(X1,X2)=k2_xcmplx_0(X1,X2)\|~v1_xreal_0(X1)\|~m1_subset_1(X2,k1_numbers)), inference(evalgc,[status(thm)],[c_0_184])). cnf(c_0_197, plain, (k2_xcmplx_0(k6_numbers,X1)=X1\|~m1_subset_1(k1_real_1(X1),k1_numbers)\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_185, c_0_94])])). cnf(c_0_198, plain, (k1_seq_1(k19_sin_cos,k8_real_1(np__2,k32_sin_cos))=np__1), inference(split_conjunct,[status(thm)],[t76_sin_cos])). cnf(c_0_199, plain, (v1_xreal_0(esk2_0)), inference(evalgc,[status(thm)],[c_0_186])). fof(c_0_200, plain, ![X19, X20]:(~m1_subset_1(X19,k1_numbers)\|~v1_xreal_0(X20)\|m1_subset_1(k8_real_1(X19,X20),k1_numbers)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k8_real_1])])). cnf(c_0_201, plain, (v1_xreal_0(k31_sin_cos)), inference(split_conjunct,[status(thm)],[dt_k31_sin_cos])). cnf(c_0_202, plain, (k32_sin_cos=k31_sin_cos), inference(split_conjunct,[status(thm)],[redefinition_k32_sin_cos])). fof(c_0_203, plain, ![X8, X9]:(~m1_subset_1(X8,k1_numbers)\|~v1_xreal_0(X9)\|k9_real_1(X8,X9)=k6_xcmplx_0(X8,X9)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k9_real_1])])). cnf(c_0_204, plain, (k6_xcmplx_0(np__1,k4_xcmplx_0(np__1))=np__2), inference(split_conjunct,[status(thm)],[rqRealDiff__k6_xcmplx_0__r1_rm1_r2])). fof(c_0_205, plain, ![X10, X11]:(~m1_subset_1(X10,k1_numbers)\|~v1_xreal_0(X11)\|k7_real_1(X10,X11)=k2_xcmplx_0(X10,X11)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k7_real_1])])). cnf(c_0_206, negated_conjecture, (k9_real_1(k7_real_1(k9_real_1(k1_seq_1(k30_valued_1(k19_sin_cos),k32_sin_cos),k3_funct_2(k1_numbers,k1_numbers,k30_valued_1(k19_sin_cos),k6_numbers)),k3_funct_2(k1_numbers,k1_numbers,k16_sin_cos,k32_sin_cos)),k3_funct_2(k1_numbers,k1_numbers,k16_sin_cos,k6_numbers))=k2_integra5(esk1_0,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k19_sin_cos))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_187, c_0_188]), c_0_131])])])). cnf(c_0_207, plain, (k1_seq_1(k30_valued_1(k19_sin_cos),X1)=k4_xcmplx_0(k1_seq_1(k19_sin_cos,X1))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_189, c_0_174]), c_0_190]), c_0_191]), c_0_178]), c_0_111])])])). cnf(c_0_208, plain, (k4_xcmplx_0(k1_seq_1(k19_sin_cos,k32_sin_cos))=np__1), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_192, c_0_92]), c_0_193]), c_0_194])])])). cnf(c_0_209, plain, (k1_seq_1(k19_sin_cos,k2_xcmplx_0(X1,k8_real_1(np__2,k32_sin_cos)))=k1_seq_1(k19_sin_cos,X1)\|~v1_xreal_0(X1)\|~m1_subset_1(k8_real_1(np__2,k32_sin_cos),k1_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_195, c_0_196])])). cnf(c_0_210, plain, (k2_xcmplx_0(k6_numbers,X1)=X1\|~m1_subset_1(X1,k1_numbers)), inference(csr,[status(thm)],[c_0_197, c_0_69])). cnf(c_0_211, plain, (k1_seq_1(k19_sin_cos,k8_real_1(np__2,k32_sin_cos))=np__1), inference(evalgc,[status(thm)],[c_0_198])). cnf(c_0_212, plain, (v1_xreal_0(k6_numbers)), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[c_0_199, c_0_152])])). cnf(c_0_213, plain, (m1_subset_1(k8_real_1(X1,X2),k1_numbers)\|~m1_subset_1(X1,k1_numbers)\|~v1_xreal_0(X2)), inference(split_conjunct,[status(thm)],[c_0_200])). cnf(c_0_214, plain, (v1_xreal_0(k31_sin_cos)), inference(evalgc,[status(thm)],[c_0_201])). cnf(c_0_215, plain, (k31_sin_cos=k32_sin_cos), inference(evalgc,[status(thm)],[c_0_202])). cnf(c_0_216, plain, (m1_subset_1(np__2,k1_numbers)), inference(split_conjunct,[status(thm)],[spc2_numerals])). cnf(c_0_217, plain, (k9_real_1(X1,X2)=k6_xcmplx_0(X1,X2)\|~m1_subset_1(X1,k1_numbers)\|~v1_xreal_0(X2)), inference(split_conjunct,[status(thm)],[c_0_203])). cnf(c_0_218, plain, (k6_xcmplx_0(np__1,k4_xcmplx_0(np__1))=np__2), inference(evalgc,[status(thm)],[c_0_204])). cnf(c_0_219, plain, (m1_subset_1(k16_sin_cos,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))), inference(split_conjunct,[status(thm)],[dt_k16_sin_cos])). cnf(c_0_220, plain, (k2_xcmplx_0(np__2,np__0)=np__2), inference(split_conjunct,[status(thm)],[rqRealAdd__k2_xcmplx_0__r2_r0_r2])). cnf(c_0_221, plain, (k7_real_1(X1,X2)=k2_xcmplx_0(X1,X2)\|~m1_subset_1(X1,k1_numbers)\|~v1_xreal_0(X2)), inference(split_conjunct,[status(thm)],[c_0_205])). cnf(c_0_222, negated_conjecture, (k9_real_1(k7_real_1(k9_real_1(np__1,k3_funct_2(k1_numbers,k1_numbers,k30_valued_1(k19_sin_cos),k6_numbers)),k3_funct_2(k1_numbers,k1_numbers,k16_sin_cos,k32_sin_cos)),k3_funct_2(k1_numbers,k1_numbers,k16_sin_cos,k6_numbers))=k2_integra5(esk1_0,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k19_sin_cos))), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_206, c_0_207]), c_0_208])])). cnf(c_0_223, plain, (k3_funct_2(k1_numbers,k1_numbers,k30_valued_1(k19_sin_cos),X1)=k4_xcmplx_0(k1_seq_1(k19_sin_cos,X1))\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[c_0_188, c_0_207])])). cnf(c_0_224, plain, (k1_seq_1(k19_sin_cos,k6_numbers)=np__1\|~m1_subset_1(k8_real_1(np__2,k32_sin_cos),k1_numbers)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_209, c_0_210]), c_0_211]), c_0_212])])])). cnf(c_0_225, plain, (m1_subset_1(k8_real_1(X1,X2),k1_numbers)\|~v1_xreal_0(X2)\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[c_0_213])). cnf(c_0_226, plain, (v1_xreal_0(k32_sin_cos)), inference(rw,[status(thm)],[c_0_214, c_0_215])). cnf(c_0_227, plain, (m1_subset_1(np__2,k1_numbers)), inference(evalgc,[status(thm)],[c_0_216])). cnf(c_0_228, plain, (k6_xcmplx_0(X1,X2)=k9_real_1(X1,X2)\|~v1_xreal_0(X2)\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[c_0_217])). cnf(c_0_229, plain, (k6_xcmplx_0(np__1,k1_seq_1(k19_sin_cos,k32_sin_cos))=np__2), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_218, c_0_92]), c_0_193]), c_0_194])])])). cnf(c_0_230, plain, (m1_subset_1(k1_seq_1(k19_sin_cos,k32_sin_cos),k1_numbers)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69, c_0_193]), c_0_194])])])). cnf(c_0_231, plain, (v1_funct_2(k16_sin_cos,k1_numbers,k1_numbers)), inference(split_conjunct,[status(thm)],[dt_k16_sin_cos])). cnf(c_0_232, plain, (v1_funct_1(k16_sin_cos)), inference(split_conjunct,[status(thm)],[dt_k16_sin_cos])). cnf(c_0_233, plain, (m1_subset_1(k16_sin_cos,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))), inference(evalgc,[status(thm)],[c_0_219])). cnf(c_0_234, plain, (k2_xcmplx_0(np__2,np__0)=np__2), inference(evalgc,[status(thm)],[c_0_220])). cnf(c_0_235, plain, (k2_xcmplx_0(X1,X2)=k7_real_1(X1,X2)\|~v1_xreal_0(X2)\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[c_0_221])). cnf(c_0_236, negated_conjecture, (k9_real_1(k7_real_1(k9_real_1(np__1,k4_xcmplx_0(k1_seq_1(k19_sin_cos,k6_numbers))),k3_funct_2(k1_numbers,k1_numbers,k16_sin_cos,k32_sin_cos)),k3_funct_2(k1_numbers,k1_numbers,k16_sin_cos,k6_numbers))=k2_integra5(esk1_0,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k19_sin_cos))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_222, c_0_223]), c_0_155])])])). cnf(c_0_237, plain, (k1_seq_1(k19_sin_cos,k6_numbers)=np__1), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_224, c_0_225]), c_0_226]), c_0_227])])])). cnf(c_0_238, plain, (k9_real_1(np__1,k1_seq_1(k19_sin_cos,k32_sin_cos))=np__2\|~v1_xreal_0(k1_seq_1(k19_sin_cos,k32_sin_cos))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_228, c_0_229]), c_0_194])])])). cnf(c_0_239, plain, (v1_xreal_0(k1_seq_1(k19_sin_cos,k32_sin_cos))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68, c_0_230]), c_0_70])])])). cnf(c_0_240, plain, (v1_funct_2(k16_sin_cos,k1_numbers,k1_numbers)), inference(evalgc,[status(thm)],[c_0_231])). cnf(c_0_241, plain, (v1_funct_1(k16_sin_cos)), inference(evalgc,[status(thm)],[c_0_232])). cnf(c_0_242, plain, (v3_valued_0(k16_sin_cos)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86, c_0_233]), c_0_70])])])). cnf(c_0_243, plain, (v1_relat_1(k16_sin_cos)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_118, c_0_233])])). cnf(c_0_244, plain, (k7_real_1(np__2,np__0)=np__2\|~v1_xreal_0(np__0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_234, c_0_235]), c_0_227])])])). cnf(c_0_245, plain, (k1_seq_1(k16_sin_cos,k3_real_1(X1,k8_real_1(np__2,k32_sin_cos)))=k1_seq_1(k16_sin_cos,X1)\|~v1_xreal_0(X1)), inference(split_conjunct,[status(thm)],[c_0_165])). cnf(c_0_246, plain, (k6_xcmplx_0(np__2,np__0)=np__2), inference(split_conjunct,[status(thm)],[rqRealDiff__k6_xcmplx_0__r2_r0_r2])). cnf(c_0_247, negated_conjecture, (k9_real_1(k7_real_1(k9_real_1(np__1,k4_xcmplx_0(np__1)),k3_funct_2(k1_numbers,k1_numbers,k16_sin_cos,k32_sin_cos)),k3_funct_2(k1_numbers,k1_numbers,k16_sin_cos,k6_numbers))=k2_integra5(esk1_0,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k19_sin_cos))), inference(rw,[status(thm)],[c_0_236, c_0_237])). cnf(c_0_248, plain, (k9_real_1(np__1,k1_seq_1(k19_sin_cos,k32_sin_cos))=np__2), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_238, c_0_239])])])). cnf(c_0_249, plain, (k3_funct_2(k1_numbers,k1_numbers,k16_sin_cos,X1)=k1_funct_1(k16_sin_cos,X1)\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157, c_0_233]), c_0_240]), c_0_241])]), c_0_141])])). cnf(c_0_250, plain, (k1_funct_1(k16_sin_cos,X1)=k1_seq_1(k16_sin_cos,X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115, c_0_242]), c_0_243]), c_0_241])])])). cnf(c_0_251, plain, (k1_seq_1(k16_sin_cos,k32_sin_cos)=k6_numbers), inference(split_conjunct,[status(thm)],[t76_sin_cos])). cnf(c_0_252, plain, (k7_real_1(np__2,k6_numbers)=np__2\|~v1_xreal_0(k6_numbers)), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_244, c_0_135]), c_0_135])])). cnf(c_0_253, plain, (k1_seq_1(k16_sin_cos,k3_real_1(X1,k8_real_1(np__2,k32_sin_cos)))=k1_seq_1(k16_sin_cos,X1)\|~v1_xreal_0(X1)), inference(evalgc,[status(thm)],[c_0_245])). cnf(c_0_254, plain, (k1_seq_1(k16_sin_cos,k8_real_1(np__2,k32_sin_cos))=k6_numbers), inference(split_conjunct,[status(thm)],[t76_sin_cos])). cnf(c_0_255, plain, (k6_xcmplx_0(np__2,np__0)=np__2), inference(evalgc,[status(thm)],[c_0_246])). cnf(c_0_256, negated_conjecture, (k2_integra5(esk1_0,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k19_sin_cos))!=np__2), inference(split_conjunct,[status(thm)],[c_0_75])). cnf(c_0_257, negated_conjecture, (k9_real_1(k7_real_1(np__2,k3_funct_2(k1_numbers,k1_numbers,k16_sin_cos,k32_sin_cos)),k3_funct_2(k1_numbers,k1_numbers,k16_sin_cos,k6_numbers))=k2_integra5(esk1_0,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k19_sin_cos))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_247, c_0_92]), c_0_193]), c_0_248]), c_0_194])])])). cnf(c_0_258, plain, (k3_funct_2(k1_numbers,k1_numbers,k16_sin_cos,X1)=k1_seq_1(k16_sin_cos,X1)\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[c_0_249, c_0_250])])). cnf(c_0_259, plain, (k1_seq_1(k16_sin_cos,k32_sin_cos)=k6_numbers), inference(evalgc,[status(thm)],[c_0_251])). cnf(c_0_260, plain, (k7_real_1(np__2,k6_numbers)=np__2), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_252, c_0_212])])). cnf(c_0_261, plain, (k1_seq_1(k16_sin_cos,k2_xcmplx_0(X1,k8_real_1(np__2,k32_sin_cos)))=k1_seq_1(k16_sin_cos,X1)\|~v1_xreal_0(X1)\|~m1_subset_1(k8_real_1(np__2,k32_sin_cos),k1_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_253, c_0_196])])). cnf(c_0_262, plain, (k1_seq_1(k16_sin_cos,k8_real_1(np__2,k32_sin_cos))=k6_numbers), inference(evalgc,[status(thm)],[c_0_254])). cnf(c_0_263, plain, (k9_real_1(np__2,np__0)=np__2\|~v1_xreal_0(np__0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_255, c_0_228]), c_0_227])])])). cnf(c_0_264, negated_conjecture, (k2_integra5(esk1_0,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k19_sin_cos))!=np__2), inference(evalgc,[status(thm)],[c_0_256])). cnf(c_0_265, negated_conjecture, (k2_integra5(esk1_0,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k19_sin_cos))=k9_real_1(np__2,k3_funct_2(k1_numbers,k1_numbers,k16_sin_cos,k6_numbers))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_257, c_0_258]), c_0_259]), c_0_260]), c_0_131])])])). cnf(c_0_266, plain, (k1_seq_1(k16_sin_cos,k6_numbers)=k6_numbers\|~m1_subset_1(k8_real_1(np__2,k32_sin_cos),k1_numbers)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_261, c_0_210]), c_0_262]), c_0_212])])])). cnf(c_0_267, plain, (k9_real_1(np__2,k6_numbers)=np__2\|~v1_xreal_0(k6_numbers)), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_263, c_0_135]), c_0_135])])). cnf(c_0_268, negated_conjecture, (k9_real_1(np__2,k3_funct_2(k1_numbers,k1_numbers,k16_sin_cos,k6_numbers))!=np__2), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[c_0_264, c_0_265])])). cnf(c_0_269, plain, (k1_seq_1(k16_sin_cos,k6_numbers)=k6_numbers), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_266, c_0_225]), c_0_226]), c_0_227])])])). cnf(c_0_270, plain, (k9_real_1(np__2,k6_numbers)=np__2), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_267, c_0_212])])). cnf(c_0_271, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_268, c_0_258]), c_0_269]), c_0_270]), c_0_155])]), ['proof']). # SZS output end CNFRefutation	reserve f,f1,f2,g for PartFunc of REAL,REAL; reserve A for non empty closed_interval Subset of REAL; reserve p,r,x,x0 for Real; reserve n for Element of NAT; reserve Z for open Subset of REAL; theorem A = [.0,PI.] implies integral(sin+cos,A) = 2 proof assume A = [.0,PI.]; then upper_bound A=PI & lower_bound A=0 by Th37; then integral(sin+cos,A) = (-cos).(PI) - (-cos).0 + sin.(PI) - sin.0 by Th69 .= -(cos.(PI)) - (-cos).0 + sin.(PI) - sin.0 by VALUED_1:8 .= -(cos.(PI)) - (-cos.0) + sin.(PI) - sin.0 by VALUED_1:8 .= - (-cos.0) + 1 - sin.(0+2 * PI) by SIN_COS:76,78 .= - (-cos.(0+2*PI)) + 1 - 0 by SIN_COS:76,78 .= 2 by SIN_COS:76; hence thesis; end;	Convert the following ATP output trace into a readable Mizar proof.
t4_waybel13	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t4_waybel13, conjecture, ![X1]:((~(v2_struct_0(X1))&(v3_orders_2(X1)&(v4_orders_2(X1)&(v1_lattice3(X1)&l1_orders_2(X1)))))=>(~(v1_xboole_0(u1_struct_0(X1)))&(v1_waybel_0(u1_struct_0(X1),X1)&(v12_waybel_0(u1_struct_0(X1),X1)&m1_subset_1(u1_struct_0(X1),k1_zfmisc_1(u1_struct_0(X1))))))), file('/scratch/mptp/predsminms1/t4_waybel13__0', t4_waybel13)). fof(d3_struct_0, axiom, ![X1]:(l1_struct_0(X1)=>k2_struct_0(X1)=u1_struct_0(X1)), file('/scratch/mptp/predsminms1/t4_waybel13__0', d3_struct_0)). fof(dt_l1_orders_2, axiom, ![X1]:(l1_orders_2(X1)=>l1_struct_0(X1)), file('/scratch/mptp/predsminms1/t4_waybel13__0', dt_l1_orders_2)). fof(t3_subset, axiom, ![X1, X2]:(m1_subset_1(X1,k1_zfmisc_1(X2))<=>r1_tarski(X1,X2)), file('/scratch/mptp/predsminms1/t4_waybel13__0', t3_subset)). fof(reflexivity_r1_tarski, axiom, ![X1, X2]:r1_tarski(X1,X1), file('/scratch/mptp/predsminms1/t4_waybel13__0', reflexivity_r1_tarski)). fof(fc1_waybel_0, axiom, ![X1]:((v1_lattice3(X1)&l1_orders_2(X1))=>v1_waybel_0(k2_struct_0(X1),X1)), file('/scratch/mptp/predsminms1/t4_waybel13__0', fc1_waybel_0)). fof(cc1_subset_1, axiom, ![X1]:(v1_xboole_0(X1)=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(X1))=>v1_xboole_0(X2))), file('/scratch/mptp/predsminms1/t4_waybel13__0', cc1_subset_1)). fof(rc8_waybel_0, axiom, ![X1]:((~(v2_struct_0(X1))&l1_orders_2(X1))=>?[X2]:(m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))&(~(v1_xboole_0(X2))&(v12_waybel_0(X2,X1)&v13_waybel_0(X2,X1))))), file('/scratch/mptp/predsminms1/t4_waybel13__0', rc8_waybel_0)). fof(fc14_waybel_0, axiom, ![X1]:((~(v2_struct_0(X1))&l1_orders_2(X1))=>(v12_waybel_0(k2_struct_0(X1),X1)&v13_waybel_0(k2_struct_0(X1),X1))), file('/scratch/mptp/predsminms1/t4_waybel13__0', fc14_waybel_0)). fof(c_0_9, negated_conjecture, ~(![X1]:((~(v2_struct_0(X1))&(v3_orders_2(X1)&(v4_orders_2(X1)&(v1_lattice3(X1)&l1_orders_2(X1)))))=>(~(v1_xboole_0(u1_struct_0(X1)))&(v1_waybel_0(u1_struct_0(X1),X1)&(v12_waybel_0(u1_struct_0(X1),X1)&m1_subset_1(u1_struct_0(X1),k1_zfmisc_1(u1_struct_0(X1)))))))), inference(assume_negation,[status(cth)],[t4_waybel13])). fof(c_0_10, plain, ![X8]:(~l1_struct_0(X8)\|k2_struct_0(X8)=u1_struct_0(X8)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_struct_0])])). fof(c_0_11, plain, ![X9]:(~l1_orders_2(X9)\|l1_struct_0(X9)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_orders_2])])). fof(c_0_12, negated_conjecture, ((~v2_struct_0(esk1_0)&(v3_orders_2(esk1_0)&(v4_orders_2(esk1_0)&(v1_lattice3(esk1_0)&l1_orders_2(esk1_0)))))&(v1_xboole_0(u1_struct_0(esk1_0))\|(~v1_waybel_0(u1_struct_0(esk1_0),esk1_0)\|(~v12_waybel_0(u1_struct_0(esk1_0),esk1_0)\|~m1_subset_1(u1_struct_0(esk1_0),k1_zfmisc_1(u1_struct_0(esk1_0))))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_9])])])])). fof(c_0_13, plain, ![X4, X5]:((~m1_subset_1(X4,k1_zfmisc_1(X5))\|r1_tarski(X4,X5))&(~r1_tarski(X4,X5)\|m1_subset_1(X4,k1_zfmisc_1(X5)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])])). fof(c_0_14, plain, ![X6]:r1_tarski(X6,X6), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])])). fof(c_0_15, plain, ![X10]:(~v1_lattice3(X10)\|~l1_orders_2(X10)\|v1_waybel_0(k2_struct_0(X10),X10)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc1_waybel_0])])). cnf(c_0_16, plain, (k2_struct_0(X1)=u1_struct_0(X1)\|~l1_struct_0(X1)), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_17, plain, (l1_struct_0(X1)\|~l1_orders_2(X1)), inference(split_conjunct,[status(thm)],[c_0_11])). fof(c_0_18, plain, ![X11, X12]:(~v1_xboole_0(X11)\|(~m1_subset_1(X12,k1_zfmisc_1(X11))\|v1_xboole_0(X12))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_subset_1])])])). fof(c_0_19, plain, ![X13]:((m1_subset_1(esk2_1(X13),k1_zfmisc_1(u1_struct_0(X13)))\|(v2_struct_0(X13)\|~l1_orders_2(X13)))&((~v1_xboole_0(esk2_1(X13))\|(v2_struct_0(X13)\|~l1_orders_2(X13)))&((v12_waybel_0(esk2_1(X13),X13)\|(v2_struct_0(X13)\|~l1_orders_2(X13)))&(v13_waybel_0(esk2_1(X13),X13)\|(v2_struct_0(X13)\|~l1_orders_2(X13)))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[rc8_waybel_0])])])])])). cnf(c_0_20, negated_conjecture, (v1_xboole_0(u1_struct_0(esk1_0))\|~v1_waybel_0(u1_struct_0(esk1_0),esk1_0)\|~v12_waybel_0(u1_struct_0(esk1_0),esk1_0)\|~m1_subset_1(u1_struct_0(esk1_0),k1_zfmisc_1(u1_struct_0(esk1_0)))), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_21, plain, (m1_subset_1(X1,k1_zfmisc_1(X2))\|~r1_tarski(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_13])). cnf(c_0_22, plain, (r1_tarski(X1,X1)), inference(split_conjunct,[status(thm)],[c_0_14])). cnf(c_0_23, plain, (v1_waybel_0(k2_struct_0(X1),X1)\|~v1_lattice3(X1)\|~l1_orders_2(X1)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_24, plain, (k2_struct_0(X1)=u1_struct_0(X1)\|~l1_struct_0(X1)), inference(evalgc,[status(thm)],[c_0_16])). cnf(c_0_25, plain, (l1_struct_0(X1)\|~l1_orders_2(X1)), inference(evalgc,[status(thm)],[c_0_17])). fof(c_0_26, plain, ![X7]:((v12_waybel_0(k2_struct_0(X7),X7)\|(v2_struct_0(X7)\|~l1_orders_2(X7)))&(v13_waybel_0(k2_struct_0(X7),X7)\|(v2_struct_0(X7)\|~l1_orders_2(X7)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fc14_waybel_0])])])])). cnf(c_0_27, plain, (v1_xboole_0(X2)\|~v1_xboole_0(X1)\|~m1_subset_1(X2,k1_zfmisc_1(X1))), inference(split_conjunct,[status(thm)],[c_0_18])). cnf(c_0_28, plain, (m1_subset_1(esk2_1(X1),k1_zfmisc_1(u1_struct_0(X1)))\|v2_struct_0(X1)\|~l1_orders_2(X1)), inference(split_conjunct,[status(thm)],[c_0_19])). cnf(c_0_29, negated_conjecture, (v1_xboole_0(u1_struct_0(esk1_0))\|~v1_waybel_0(u1_struct_0(esk1_0),esk1_0)\|~v12_waybel_0(u1_struct_0(esk1_0),esk1_0)\|~m1_subset_1(u1_struct_0(esk1_0),k1_zfmisc_1(u1_struct_0(esk1_0)))), inference(evalgc,[status(thm)],[c_0_20])). cnf(c_0_30, plain, (m1_subset_1(X1,k1_zfmisc_1(X2))\|~r1_tarski(X1,X2)), inference(evalgc,[status(thm)],[c_0_21])). cnf(c_0_31, plain, (r1_tarski(X1,X1)), inference(evalgc,[status(thm)],[c_0_22])). cnf(c_0_32, plain, (v1_waybel_0(k2_struct_0(X1),X1)\|~v1_lattice3(X1)\|~l1_orders_2(X1)), inference(evalgc,[status(thm)],[c_0_23])). cnf(c_0_33, plain, (k2_struct_0(X1)=u1_struct_0(X1)\|~l1_orders_2(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_24, c_0_25])])). cnf(c_0_34, negated_conjecture, (l1_orders_2(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_35, negated_conjecture, (v1_lattice3(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_36, plain, (v12_waybel_0(k2_struct_0(X1),X1)\|v2_struct_0(X1)\|~l1_orders_2(X1)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_37, plain, (v1_xboole_0(X2)\|~v1_xboole_0(X1)\|~m1_subset_1(X2,k1_zfmisc_1(X1))), inference(evalgc,[status(thm)],[c_0_27])). cnf(c_0_38, plain, (v2_struct_0(X1)\|m1_subset_1(esk2_1(X1),k1_zfmisc_1(u1_struct_0(X1)))\|~l1_orders_2(X1)), inference(evalgc,[status(thm)],[c_0_28])). cnf(c_0_39, plain, (v2_struct_0(X1)\|~v1_xboole_0(esk2_1(X1))\|~l1_orders_2(X1)), inference(split_conjunct,[status(thm)],[c_0_19])). cnf(c_0_40, negated_conjecture, (v1_xboole_0(u1_struct_0(esk1_0))\|~v12_waybel_0(u1_struct_0(esk1_0),esk1_0)\|~v1_waybel_0(u1_struct_0(esk1_0),esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29, c_0_30]), c_0_31])])])). cnf(c_0_41, plain, (v1_waybel_0(u1_struct_0(X1),X1)\|~l1_orders_2(X1)\|~v1_lattice3(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_32, c_0_33])])). cnf(c_0_42, negated_conjecture, (l1_orders_2(esk1_0)), inference(evalgc,[status(thm)],[c_0_34])). cnf(c_0_43, negated_conjecture, (v1_lattice3(esk1_0)), inference(evalgc,[status(thm)],[c_0_35])). cnf(c_0_44, plain, (v2_struct_0(X1)\|v12_waybel_0(k2_struct_0(X1),X1)\|~l1_orders_2(X1)), inference(evalgc,[status(thm)],[c_0_36])). cnf(c_0_45, negated_conjecture, (~v2_struct_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_46, plain, (v1_xboole_0(esk2_1(X1))\|v2_struct_0(X1)\|~v1_xboole_0(u1_struct_0(X1))\|~l1_orders_2(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_37, c_0_38])])). cnf(c_0_47, plain, (v2_struct_0(X1)\|~l1_orders_2(X1)\|~v1_xboole_0(esk2_1(X1))), inference(evalgc,[status(thm)],[c_0_39])). cnf(c_0_48, negated_conjecture, (v1_xboole_0(u1_struct_0(esk1_0))\|~v12_waybel_0(u1_struct_0(esk1_0),esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40, c_0_41]), c_0_42]), c_0_43])])])). cnf(c_0_49, plain, (v12_waybel_0(u1_struct_0(X1),X1)\|v2_struct_0(X1)\|~l1_orders_2(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_44, c_0_33])])). cnf(c_0_50, negated_conjecture, (~v2_struct_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_45])). cnf(c_0_51, plain, (v2_struct_0(X1)\|~v1_xboole_0(u1_struct_0(X1))\|~l1_orders_2(X1)), inference(csr,[status(thm)],[c_0_46, c_0_47])). cnf(c_0_52, negated_conjecture, (v1_xboole_0(u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48, c_0_49]), c_0_42])]), c_0_50])])). cnf(c_0_53, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51, c_0_52]), c_0_42])]), c_0_50]), ['proof']). # SZS output end CNFRefutation	theorem Th4: for L be with_suprema non empty reflexive transitive RelStr holds the carrier of L is Ideal of L proof let L be with_suprema non empty reflexive transitive RelStr; [#]L is Ideal of L; hence thesis; end;	Convert the following ATP output trace into a readable Mizar proof.
t38_polyeq_3	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t38_polyeq_3, conjecture, ![X1]:((~(v1_xboole_0(X1))&m1_subset_1(X1,k5_numbers))=>![X2]:(v1_xcmplx_0(X2)=>![X3]:(m1_comptrig(X3,X2,X1)=>(X3=k6_numbers=>X2=k6_numbers)))), file('/scratch/mptp/predsminms1/t38_polyeq_3__0', t38_polyeq_3)). fof(dt_k2_binop_2, axiom, ![X1]:(v1_xcmplx_0(X1)=>m1_subset_1(k2_binop_2(X1),k2_numbers)), file('/scratch/mptp/predsminms1/t38_polyeq_3__0', dt_k2_binop_2)). fof(involutiveness_k2_binop_2, axiom, ![X1]:(v1_xcmplx_0(X1)=>k2_binop_2(k2_binop_2(X1))=X1), file('/scratch/mptp/predsminms1/t38_polyeq_3__0', involutiveness_k2_binop_2)). fof(cc3_xcmplx_0, axiom, ![X1]:(m1_subset_1(X1,k2_numbers)=>v1_xcmplx_0(X1)), file('/scratch/mptp/predsminms1/t38_polyeq_3__0', cc3_xcmplx_0)). fof(t60_comptrig, axiom, ![X1]:((~(v1_xboole_0(X1))&v7_ordinal1(X1))=>![X2]:(m1_subset_1(X2,k2_numbers)=>![X3]:(m1_comptrig(X3,X2,X1)=>(X3=k6_numbers=>X2=k6_numbers)))), file('/scratch/mptp/predsminms1/t38_polyeq_3__0', t60_comptrig)). fof(cc17_membered, axiom, ![X1]:(v6_membered(X1)=>![X2]:(m1_subset_1(X2,X1)=>v7_ordinal1(X2))), file('/scratch/mptp/predsminms1/t38_polyeq_3__0', cc17_membered)). fof(fc6_membered, axiom, v6_membered(k4_ordinal1), file('/scratch/mptp/predsminms1/t38_polyeq_3__0', fc6_membered)). fof(redefinition_k5_numbers, axiom, k5_numbers=k4_ordinal1, file('/scratch/mptp/predsminms1/t38_polyeq_3__0', redefinition_k5_numbers)). fof(c_0_8, negated_conjecture, ~(![X1]:((~(v1_xboole_0(X1))&m1_subset_1(X1,k5_numbers))=>![X2]:(v1_xcmplx_0(X2)=>![X3]:(m1_comptrig(X3,X2,X1)=>(X3=k6_numbers=>X2=k6_numbers))))), inference(assume_negation,[status(cth)],[t38_polyeq_3])). fof(c_0_9, plain, ![X7]:(~v1_xcmplx_0(X7)\|m1_subset_1(k2_binop_2(X7),k2_numbers)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_binop_2])])). fof(c_0_10, plain, ![X8]:(~v1_xcmplx_0(X8)\|k2_binop_2(k2_binop_2(X8))=X8), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[involutiveness_k2_binop_2])])). fof(c_0_11, negated_conjecture, ((~v1_xboole_0(esk1_0)&m1_subset_1(esk1_0,k5_numbers))&(v1_xcmplx_0(esk2_0)&(m1_comptrig(esk3_0,esk2_0,esk1_0)&(esk3_0=k6_numbers&esk2_0!=k6_numbers)))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_8])])])])). cnf(c_0_12, plain, (m1_subset_1(k2_binop_2(X1),k2_numbers)\|~v1_xcmplx_0(X1)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_13, plain, (k2_binop_2(k2_binop_2(X1))=X1\|~v1_xcmplx_0(X1)), inference(split_conjunct,[status(thm)],[c_0_10])). fof(c_0_14, plain, ![X11]:(~m1_subset_1(X11,k2_numbers)\|v1_xcmplx_0(X11)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc3_xcmplx_0])])). fof(c_0_15, plain, ![X12, X13, X14]:(v1_xboole_0(X12)\|~v7_ordinal1(X12)\|(~m1_subset_1(X13,k2_numbers)\|(~m1_comptrig(X14,X13,X12)\|(X14!=k6_numbers\|X13=k6_numbers)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t60_comptrig])])])])). cnf(c_0_16, negated_conjecture, (m1_comptrig(esk3_0,esk2_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_17, negated_conjecture, (esk3_0=k6_numbers), inference(split_conjunct,[status(thm)],[c_0_11])). fof(c_0_18, plain, ![X9, X10]:(~v6_membered(X9)\|(~m1_subset_1(X10,X9)\|v7_ordinal1(X10))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc17_membered])])])). cnf(c_0_19, plain, (v6_membered(k4_ordinal1)), inference(split_conjunct,[status(thm)],[fc6_membered])). cnf(c_0_20, plain, (k5_numbers=k4_ordinal1), inference(split_conjunct,[status(thm)],[redefinition_k5_numbers])). cnf(c_0_21, plain, (m1_subset_1(k2_binop_2(X1),k2_numbers)\|~v1_xcmplx_0(X1)), inference(evalgc,[status(thm)],[c_0_12])). cnf(c_0_22, plain, (k2_binop_2(k2_binop_2(X1))=X1\|~v1_xcmplx_0(X1)), inference(evalgc,[status(thm)],[c_0_13])). cnf(c_0_23, plain, (v1_xcmplx_0(X1)\|~m1_subset_1(X1,k2_numbers)), inference(split_conjunct,[status(thm)],[c_0_14])). cnf(c_0_24, plain, (v1_xboole_0(X1)\|X2=k6_numbers\|~v7_ordinal1(X1)\|~m1_subset_1(X2,k2_numbers)\|~m1_comptrig(X3,X2,X1)\|X3!=k6_numbers), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_25, negated_conjecture, (m1_comptrig(esk3_0,esk2_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_16])). cnf(c_0_26, negated_conjecture, (esk3_0=k6_numbers), inference(evalgc,[status(thm)],[c_0_17])). cnf(c_0_27, negated_conjecture, (esk2_0!=k6_numbers), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_28, negated_conjecture, (~v1_xboole_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_29, plain, (v7_ordinal1(X2)\|~v6_membered(X1)\|~m1_subset_1(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_18])). cnf(c_0_30, negated_conjecture, (m1_subset_1(esk1_0,k5_numbers)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_31, plain, (v6_membered(k4_ordinal1)), inference(evalgc,[status(thm)],[c_0_19])). cnf(c_0_32, plain, (k4_ordinal1=k5_numbers), inference(evalgc,[status(thm)],[c_0_20])). cnf(c_0_33, plain, (m1_subset_1(X1,k2_numbers)\|~v1_xcmplx_0(k2_binop_2(X1))\|~v1_xcmplx_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_21, c_0_22])])). cnf(c_0_34, plain, (v1_xcmplx_0(X1)\|~m1_subset_1(X1,k2_numbers)), inference(evalgc,[status(thm)],[c_0_23])). cnf(c_0_35, plain, (X2=k6_numbers\|v1_xboole_0(X1)\|X3!=k6_numbers\|~v7_ordinal1(X1)\|~m1_subset_1(X2,k2_numbers)\|~m1_comptrig(X3,X2,X1)), inference(evalgc,[status(thm)],[c_0_24])). cnf(c_0_36, negated_conjecture, (m1_comptrig(k6_numbers,esk2_0,esk1_0)), inference(rw,[status(thm)],[c_0_25, c_0_26])). cnf(c_0_37, negated_conjecture, (esk2_0!=k6_numbers), inference(evalgc,[status(thm)],[c_0_27])). cnf(c_0_38, negated_conjecture, (~v1_xboole_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_28])). cnf(c_0_39, plain, (v7_ordinal1(X2)\|~v6_membered(X1)\|~m1_subset_1(X2,X1)), inference(evalgc,[status(thm)],[c_0_29])). cnf(c_0_40, negated_conjecture, (m1_subset_1(esk1_0,k5_numbers)), inference(evalgc,[status(thm)],[c_0_30])). cnf(c_0_41, plain, (v6_membered(k5_numbers)), inference(rw,[status(thm)],[c_0_31, c_0_32])). cnf(c_0_42, plain, (m1_subset_1(X1,k2_numbers)\|~v1_xcmplx_0(X1)\|~m1_subset_1(k2_binop_2(X1),k2_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_33, c_0_34])])). cnf(c_0_43, negated_conjecture, (v1_xcmplx_0(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_44, negated_conjecture, (~v7_ordinal1(esk1_0)\|~m1_subset_1(esk2_0,k2_numbers)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35, c_0_36]), c_0_37]), c_0_38])])). cnf(c_0_45, negated_conjecture, (v7_ordinal1(esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39, c_0_40]), c_0_41])])])). cnf(c_0_46, plain, (m1_subset_1(X1,k2_numbers)\|~v1_xcmplx_0(X1)), inference(csr,[status(thm)],[c_0_42, c_0_21])). cnf(c_0_47, negated_conjecture, (v1_xcmplx_0(esk2_0)), inference(evalgc,[status(thm)],[c_0_43])). cnf(c_0_48, negated_conjecture, (~m1_subset_1(esk2_0,k2_numbers)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44, c_0_45])])). cnf(c_0_49, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_46, c_0_47]), c_0_48]), ['proof']). # SZS output end CNFRefutation	reserve a,b,c,d,a9,b9,c9,d9,y,x1,u,v for Real, s,t,h,z,z1,z2,z3,s1,s2,s3 for Element of COMPLEX; theorem for n be non empty Element of NAT, z be complex number for v be CRoot of n,z st v = 0 holds z = 0 proof let n be non empty Element of NAT, z be complex number; let v be CRoot of n,z; assume v = 0; then 0\|^ n = z by COMPTRIG:def 2; hence thesis by Lm2; end;	Convert the following ATP output trace into a readable Mizar proof.
t21_yellow_4	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(fraenkel_a_3_0_yellow_4, axiom, ![X1, X2, X3, X4]:(((~(v2_struct_0(X2))&l1_orders_2(X2))&(m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))&m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))))=>(r2_hidden(X1,a_3_0_yellow_4(X2,X3,X4))<=>?[X5, X6]:((m1_subset_1(X5,u1_struct_0(X2))&m1_subset_1(X6,u1_struct_0(X2)))&(X1=k10_lattice3(X2,X5,X6)&(r2_hidden(X5,X3)&r2_hidden(X6,X4)))))), file('/scratch/mptp/predsminms1/t21_yellow_4__0', fraenkel_a_3_0_yellow_4)). fof(t21_yellow_4, conjecture, ![X1]:((~(v2_struct_0(X1))&l1_orders_2(X1))=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))=>![X3]:(m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))=>![X4]:(m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X1)))=>![X5]:(m1_subset_1(X5,k1_zfmisc_1(u1_struct_0(X1)))=>((r1_tarski(X2,X4)&r1_tarski(X3,X5))=>r1_tarski(k1_yellow_4(X1,X2,X3),k1_yellow_4(X1,X4,X5)))))))), file('/scratch/mptp/predsminms1/t21_yellow_4__0', t21_yellow_4)). fof(d3_tarski, axiom, ![X1, X2]:(r1_tarski(X1,X2)<=>![X3]:(r2_hidden(X3,X1)=>r2_hidden(X3,X2))), file('/scratch/mptp/predsminms1/t21_yellow_4__0', d3_tarski)). fof(d3_yellow_4, axiom, ![X1]:((~(v2_struct_0(X1))&l1_orders_2(X1))=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))=>![X3]:(m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))=>k1_yellow_4(X1,X2,X3)=a_3_0_yellow_4(X1,X2,X3)))), file('/scratch/mptp/predsminms1/t21_yellow_4__0', d3_yellow_4)). fof(c_0_4, plain, ![X12, X13, X14, X15, X18, X19]:((((m1_subset_1(esk6_4(X12,X13,X14,X15),u1_struct_0(X13))\|~r2_hidden(X12,a_3_0_yellow_4(X13,X14,X15))\|(v2_struct_0(X13)\|~l1_orders_2(X13)\|(~m1_subset_1(X14,k1_zfmisc_1(u1_struct_0(X13)))\|~m1_subset_1(X15,k1_zfmisc_1(u1_struct_0(X13))))))&(m1_subset_1(esk7_4(X12,X13,X14,X15),u1_struct_0(X13))\|~r2_hidden(X12,a_3_0_yellow_4(X13,X14,X15))\|(v2_struct_0(X13)\|~l1_orders_2(X13)\|(~m1_subset_1(X14,k1_zfmisc_1(u1_struct_0(X13)))\|~m1_subset_1(X15,k1_zfmisc_1(u1_struct_0(X13)))))))&((X12=k10_lattice3(X13,esk6_4(X12,X13,X14,X15),esk7_4(X12,X13,X14,X15))\|~r2_hidden(X12,a_3_0_yellow_4(X13,X14,X15))\|(v2_struct_0(X13)\|~l1_orders_2(X13)\|(~m1_subset_1(X14,k1_zfmisc_1(u1_struct_0(X13)))\|~m1_subset_1(X15,k1_zfmisc_1(u1_struct_0(X13))))))&((r2_hidden(esk6_4(X12,X13,X14,X15),X14)\|~r2_hidden(X12,a_3_0_yellow_4(X13,X14,X15))\|(v2_struct_0(X13)\|~l1_orders_2(X13)\|(~m1_subset_1(X14,k1_zfmisc_1(u1_struct_0(X13)))\|~m1_subset_1(X15,k1_zfmisc_1(u1_struct_0(X13))))))&(r2_hidden(esk7_4(X12,X13,X14,X15),X15)\|~r2_hidden(X12,a_3_0_yellow_4(X13,X14,X15))\|(v2_struct_0(X13)\|~l1_orders_2(X13)\|(~m1_subset_1(X14,k1_zfmisc_1(u1_struct_0(X13)))\|~m1_subset_1(X15,k1_zfmisc_1(u1_struct_0(X13)))))))))&(~m1_subset_1(X18,u1_struct_0(X13))\|~m1_subset_1(X19,u1_struct_0(X13))\|(X12!=k10_lattice3(X13,X18,X19)\|(~r2_hidden(X18,X14)\|~r2_hidden(X19,X15)))\|r2_hidden(X12,a_3_0_yellow_4(X13,X14,X15))\|(v2_struct_0(X13)\|~l1_orders_2(X13)\|(~m1_subset_1(X14,k1_zfmisc_1(u1_struct_0(X13)))\|~m1_subset_1(X15,k1_zfmisc_1(u1_struct_0(X13))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fraenkel_a_3_0_yellow_4])])])])])])). fof(c_0_5, negated_conjecture, ~(![X1]:((~(v2_struct_0(X1))&l1_orders_2(X1))=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))=>![X3]:(m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))=>![X4]:(m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X1)))=>![X5]:(m1_subset_1(X5,k1_zfmisc_1(u1_struct_0(X1)))=>((r1_tarski(X2,X4)&r1_tarski(X3,X5))=>r1_tarski(k1_yellow_4(X1,X2,X3),k1_yellow_4(X1,X4,X5))))))))), inference(assume_negation,[status(cth)],[t21_yellow_4])). cnf(c_0_6, plain, (r2_hidden(X4,a_3_0_yellow_4(X2,X5,X6))\|v2_struct_0(X2)\|~m1_subset_1(X1,u1_struct_0(X2))\|~m1_subset_1(X3,u1_struct_0(X2))\|X4!=k10_lattice3(X2,X1,X3)\|~r2_hidden(X1,X5)\|~r2_hidden(X3,X6)\|~l1_orders_2(X2)\|~m1_subset_1(X5,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X6,k1_zfmisc_1(u1_struct_0(X2)))), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_7, plain, (X1=k10_lattice3(X2,esk6_4(X1,X2,X3,X4),esk7_4(X1,X2,X3,X4))\|v2_struct_0(X2)\|~r2_hidden(X1,a_3_0_yellow_4(X2,X3,X4))\|~l1_orders_2(X2)\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))), inference(split_conjunct,[status(thm)],[c_0_4])). fof(c_0_8, plain, ![X20, X21, X22, X23, X24]:((~r1_tarski(X20,X21)\|(~r2_hidden(X22,X20)\|r2_hidden(X22,X21)))&((r2_hidden(esk8_2(X23,X24),X23)\|r1_tarski(X23,X24))&(~r2_hidden(esk8_2(X23,X24),X24)\|r1_tarski(X23,X24)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_tarski])])])])])])). fof(c_0_9, negated_conjecture, ((~v2_struct_0(esk1_0)&l1_orders_2(esk1_0))&(m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(esk1_0)))&(m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(esk1_0)))&(m1_subset_1(esk4_0,k1_zfmisc_1(u1_struct_0(esk1_0)))&(m1_subset_1(esk5_0,k1_zfmisc_1(u1_struct_0(esk1_0)))&((r1_tarski(esk2_0,esk4_0)&r1_tarski(esk3_0,esk5_0))&~r1_tarski(k1_yellow_4(esk1_0,esk2_0,esk3_0),k1_yellow_4(esk1_0,esk4_0,esk5_0)))))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_5])])])])). cnf(c_0_10, plain, (v2_struct_0(X2)\|r2_hidden(X4,a_3_0_yellow_4(X2,X5,X6))\|X4!=k10_lattice3(X2,X1,X3)\|~l1_orders_2(X2)\|~r2_hidden(X3,X6)\|~r2_hidden(X1,X5)\|~m1_subset_1(X3,u1_struct_0(X2))\|~m1_subset_1(X1,u1_struct_0(X2))\|~m1_subset_1(X6,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X5,k1_zfmisc_1(u1_struct_0(X2)))), inference(evalgc,[status(thm)],[c_0_6])). cnf(c_0_11, plain, (k10_lattice3(X2,esk6_4(X1,X2,X3,X4),esk7_4(X1,X2,X3,X4))=X1\|v2_struct_0(X2)\|~l1_orders_2(X2)\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~r2_hidden(X1,a_3_0_yellow_4(X2,X3,X4))), inference(evalgc,[status(thm)],[c_0_7])). cnf(c_0_12, plain, (m1_subset_1(esk6_4(X1,X2,X3,X4),u1_struct_0(X2))\|v2_struct_0(X2)\|~r2_hidden(X1,a_3_0_yellow_4(X2,X3,X4))\|~l1_orders_2(X2)\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_13, plain, (m1_subset_1(esk7_4(X1,X2,X3,X4),u1_struct_0(X2))\|v2_struct_0(X2)\|~r2_hidden(X1,a_3_0_yellow_4(X2,X3,X4))\|~l1_orders_2(X2)\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_14, plain, (r2_hidden(X3,X2)\|~r1_tarski(X1,X2)\|~r2_hidden(X3,X1)), inference(split_conjunct,[status(thm)],[c_0_8])). cnf(c_0_15, negated_conjecture, (r1_tarski(esk3_0,esk5_0)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_16, plain, (r2_hidden(X1,a_3_0_yellow_4(X2,X3,X4))\|v2_struct_0(X2)\|~r2_hidden(esk7_4(X1,X2,X5,X6),X4)\|~r2_hidden(esk6_4(X1,X2,X5,X6),X3)\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(esk7_4(X1,X2,X5,X6),u1_struct_0(X2))\|~m1_subset_1(esk6_4(X1,X2,X5,X6),u1_struct_0(X2))\|~l1_orders_2(X2)\|~r2_hidden(X1,a_3_0_yellow_4(X2,X5,X6))\|~m1_subset_1(X6,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X5,k1_zfmisc_1(u1_struct_0(X2)))), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_10, c_0_11])])])). cnf(c_0_17, plain, (v2_struct_0(X2)\|m1_subset_1(esk6_4(X1,X2,X3,X4),u1_struct_0(X2))\|~l1_orders_2(X2)\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~r2_hidden(X1,a_3_0_yellow_4(X2,X3,X4))), inference(evalgc,[status(thm)],[c_0_12])). cnf(c_0_18, plain, (v2_struct_0(X2)\|m1_subset_1(esk7_4(X1,X2,X3,X4),u1_struct_0(X2))\|~l1_orders_2(X2)\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~r2_hidden(X1,a_3_0_yellow_4(X2,X3,X4))), inference(evalgc,[status(thm)],[c_0_13])). cnf(c_0_19, plain, (r2_hidden(X3,X2)\|~r1_tarski(X1,X2)\|~r2_hidden(X3,X1)), inference(evalgc,[status(thm)],[c_0_14])). cnf(c_0_20, negated_conjecture, (r1_tarski(esk3_0,esk5_0)), inference(evalgc,[status(thm)],[c_0_15])). cnf(c_0_21, plain, (r2_hidden(X1,a_3_0_yellow_4(X2,X3,X4))\|v2_struct_0(X2)\|~r2_hidden(esk7_4(X1,X2,X5,X6),X4)\|~r2_hidden(esk6_4(X1,X2,X5,X6),X3)\|~r2_hidden(X1,a_3_0_yellow_4(X2,X5,X6))\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X6,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X5,k1_zfmisc_1(u1_struct_0(X2)))\|~l1_orders_2(X2)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_16, c_0_17]), c_0_18])). cnf(c_0_22, negated_conjecture, (r2_hidden(X1,esk5_0)\|~r2_hidden(X1,esk3_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_19, c_0_20])])). cnf(c_0_23, plain, (r2_hidden(esk7_4(X1,X2,X3,X4),X4)\|v2_struct_0(X2)\|~r2_hidden(X1,a_3_0_yellow_4(X2,X3,X4))\|~l1_orders_2(X2)\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_24, negated_conjecture, (r1_tarski(esk2_0,esk4_0)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_25, negated_conjecture, (r2_hidden(X1,a_3_0_yellow_4(X2,X3,esk5_0))\|v2_struct_0(X2)\|~r2_hidden(esk6_4(X1,X2,X4,X5),X3)\|~r2_hidden(X1,a_3_0_yellow_4(X2,X4,X5))\|~m1_subset_1(esk5_0,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X5,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))\|~l1_orders_2(X2)\|~r2_hidden(esk7_4(X1,X2,X4,X5),esk3_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_21, c_0_22])])). cnf(c_0_26, plain, (v2_struct_0(X2)\|r2_hidden(esk7_4(X1,X2,X3,X4),X4)\|~l1_orders_2(X2)\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~r2_hidden(X1,a_3_0_yellow_4(X2,X3,X4))), inference(evalgc,[status(thm)],[c_0_23])). cnf(c_0_27, plain, (r2_hidden(esk6_4(X1,X2,X3,X4),X3)\|v2_struct_0(X2)\|~r2_hidden(X1,a_3_0_yellow_4(X2,X3,X4))\|~l1_orders_2(X2)\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_28, negated_conjecture, (r1_tarski(esk2_0,esk4_0)), inference(evalgc,[status(thm)],[c_0_24])). fof(c_0_29, plain, ![X26, X27, X28]:(v2_struct_0(X26)\|~l1_orders_2(X26)\|(~m1_subset_1(X27,k1_zfmisc_1(u1_struct_0(X26)))\|(~m1_subset_1(X28,k1_zfmisc_1(u1_struct_0(X26)))\|k1_yellow_4(X26,X27,X28)=a_3_0_yellow_4(X26,X27,X28)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d3_yellow_4])])])])). cnf(c_0_30, plain, (r1_tarski(X1,X2)\|~r2_hidden(esk8_2(X1,X2),X2)), inference(split_conjunct,[status(thm)],[c_0_8])). cnf(c_0_31, negated_conjecture, (r2_hidden(X1,a_3_0_yellow_4(X2,X3,esk5_0))\|v2_struct_0(X2)\|~r2_hidden(esk6_4(X1,X2,X4,esk3_0),X3)\|~r2_hidden(X1,a_3_0_yellow_4(X2,X4,esk3_0))\|~m1_subset_1(esk5_0,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))\|~l1_orders_2(X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_25, c_0_26])])). cnf(c_0_32, plain, (v2_struct_0(X2)\|r2_hidden(esk6_4(X1,X2,X3,X4),X3)\|~l1_orders_2(X2)\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~r2_hidden(X1,a_3_0_yellow_4(X2,X3,X4))), inference(evalgc,[status(thm)],[c_0_27])). cnf(c_0_33, plain, (r2_hidden(X1,a_3_0_yellow_4(X2,X3,X4))\|v2_struct_0(X2)\|~r2_hidden(esk6_4(X1,X2,X5,X4),X3)\|~r2_hidden(X1,a_3_0_yellow_4(X2,X5,X4))\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X5,k1_zfmisc_1(u1_struct_0(X2)))\|~l1_orders_2(X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_21, c_0_26])])). cnf(c_0_34, negated_conjecture, (r2_hidden(X1,esk4_0)\|~r2_hidden(X1,esk2_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_19, c_0_28])])). cnf(c_0_35, negated_conjecture, (~r1_tarski(k1_yellow_4(esk1_0,esk2_0,esk3_0),k1_yellow_4(esk1_0,esk4_0,esk5_0))), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_36, plain, (v2_struct_0(X1)\|k1_yellow_4(X1,X2,X3)=a_3_0_yellow_4(X1,X2,X3)\|~l1_orders_2(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))), inference(split_conjunct,[status(thm)],[c_0_29])). cnf(c_0_37, negated_conjecture, (m1_subset_1(esk5_0,k1_zfmisc_1(u1_struct_0(esk1_0)))), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_38, negated_conjecture, (m1_subset_1(esk4_0,k1_zfmisc_1(u1_struct_0(esk1_0)))), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_39, negated_conjecture, (l1_orders_2(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_40, negated_conjecture, (~v2_struct_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_41, plain, (r1_tarski(X1,X2)\|~r2_hidden(esk8_2(X1,X2),X2)), inference(evalgc,[status(thm)],[c_0_30])). cnf(c_0_42, negated_conjecture, (r2_hidden(X1,a_3_0_yellow_4(X2,X3,esk5_0))\|v2_struct_0(X2)\|~r2_hidden(X1,a_3_0_yellow_4(X2,X3,esk3_0))\|~m1_subset_1(esk5_0,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~l1_orders_2(X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_31, c_0_32])])). cnf(c_0_43, negated_conjecture, (r2_hidden(X1,a_3_0_yellow_4(X2,esk4_0,X3))\|v2_struct_0(X2)\|~r2_hidden(X1,a_3_0_yellow_4(X2,X4,X3))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(esk4_0,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))\|~l1_orders_2(X2)\|~r2_hidden(esk6_4(X1,X2,X4,X3),esk2_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_33, c_0_34])])). cnf(c_0_44, negated_conjecture, (~r1_tarski(k1_yellow_4(esk1_0,esk2_0,esk3_0),k1_yellow_4(esk1_0,esk4_0,esk5_0))), inference(evalgc,[status(thm)],[c_0_35])). cnf(c_0_45, plain, (k1_yellow_4(X1,X2,X3)=a_3_0_yellow_4(X1,X2,X3)\|v2_struct_0(X1)\|~l1_orders_2(X1)\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(evalgc,[status(thm)],[c_0_36])). cnf(c_0_46, negated_conjecture, (m1_subset_1(esk5_0,k1_zfmisc_1(u1_struct_0(esk1_0)))), inference(evalgc,[status(thm)],[c_0_37])). cnf(c_0_47, negated_conjecture, (m1_subset_1(esk4_0,k1_zfmisc_1(u1_struct_0(esk1_0)))), inference(evalgc,[status(thm)],[c_0_38])). cnf(c_0_48, negated_conjecture, (l1_orders_2(esk1_0)), inference(evalgc,[status(thm)],[c_0_39])). cnf(c_0_49, negated_conjecture, (~v2_struct_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_40])). cnf(c_0_50, negated_conjecture, (m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(esk1_0)))), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_51, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(esk1_0)))), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_52, negated_conjecture, (r1_tarski(X1,a_3_0_yellow_4(X2,X3,esk5_0))\|v2_struct_0(X2)\|~r2_hidden(esk8_2(X1,a_3_0_yellow_4(X2,X3,esk5_0)),a_3_0_yellow_4(X2,X3,esk3_0))\|~m1_subset_1(esk5_0,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~l1_orders_2(X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_41, c_0_42])])). cnf(c_0_53, negated_conjecture, (r2_hidden(X1,a_3_0_yellow_4(X2,esk4_0,X3))\|v2_struct_0(X2)\|~r2_hidden(X1,a_3_0_yellow_4(X2,esk2_0,X3))\|~m1_subset_1(esk4_0,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(X2)))\|~l1_orders_2(X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_43, c_0_32])])). cnf(c_0_54, plain, (r2_hidden(esk8_2(X1,X2),X1)\|r1_tarski(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_8])). cnf(c_0_55, negated_conjecture, (~r1_tarski(k1_yellow_4(esk1_0,esk2_0,esk3_0),a_3_0_yellow_4(esk1_0,esk4_0,esk5_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44, c_0_45]), c_0_46]), c_0_47]), c_0_48])]), c_0_49])])). cnf(c_0_56, negated_conjecture, (m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(esk1_0)))), inference(evalgc,[status(thm)],[c_0_50])). cnf(c_0_57, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(esk1_0)))), inference(evalgc,[status(thm)],[c_0_51])). cnf(c_0_58, negated_conjecture, (r1_tarski(X1,a_3_0_yellow_4(X2,esk4_0,esk5_0))\|v2_struct_0(X2)\|~m1_subset_1(esk5_0,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(esk4_0,k1_zfmisc_1(u1_struct_0(X2)))\|~l1_orders_2(X2)\|~r2_hidden(esk8_2(X1,a_3_0_yellow_4(X2,esk4_0,esk5_0)),a_3_0_yellow_4(X2,esk2_0,esk3_0))\|~m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(X2)))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_52, c_0_53])])). cnf(c_0_59, plain, (r1_tarski(X1,X2)\|r2_hidden(esk8_2(X1,X2),X1)), inference(evalgc,[status(thm)],[c_0_54])). cnf(c_0_60, negated_conjecture, (~r1_tarski(a_3_0_yellow_4(esk1_0,esk2_0,esk3_0),a_3_0_yellow_4(esk1_0,esk4_0,esk5_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55, c_0_45]), c_0_56]), c_0_57]), c_0_48])]), c_0_49])])). cnf(c_0_61, negated_conjecture, (r1_tarski(a_3_0_yellow_4(X1,esk2_0,esk3_0),a_3_0_yellow_4(X1,esk4_0,esk5_0))\|v2_struct_0(X1)\|~m1_subset_1(esk5_0,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(esk4_0,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(X1)))\|~l1_orders_2(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_58, c_0_59])])). cnf(c_0_62, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60, c_0_61]), c_0_46]), c_0_56]), c_0_47]), c_0_57]), c_0_48])]), c_0_49]), ['proof']). # SZS output end CNFRefutation	theorem for L being non empty RelStr, X1, X2, Y1, Y2 being Subset of L st X1 c= Y1 & X2 c= Y2 holds X1 "\/" X2 c= Y1 "\/" Y2 proof let L be non empty RelStr, X1, X2, Y1, Y2 be Subset of L such that A1: X1 c= Y1 & X2 c= Y2; let q be set; assume q in X1 "\/" X2; then ex x, y being Element of L st q = x "\/" y & x in X1 & y in X2; hence thesis by A1; end;	Convert the following ATP output trace into a readable Mizar proof.
t66_convex4	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(l90_convex4, axiom, ![X1]:((~(v2_struct_0(X1))&(v13_algstr_0(X1)&(v2_rlvect_1(X1)&(v3_rlvect_1(X1)&(v4_rlvect_1(X1)&(v2_clvect_1(X1)&(v3_clvect_1(X1)&(v4_clvect_1(X1)&(v5_clvect_1(X1)&l1_clvect_1(X1))))))))))=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))=>![X3]:(v1_xcmplx_0(X3)=>![X4]:(v1_xcmplx_0(X4)=>(v2_convex4(X2,X1)=>(![X5]:(m1_subset_1(X5,k1_numbers)=>![X6]:(m1_subset_1(X6,k1_numbers)=>~((X3=X5&(X4=X6&(r1_xxreal_0(k1_xboole_0,X5)&r1_xxreal_0(k1_xboole_0,X6)))))))\|r1_tarski(k7_rusub_4(X1,k19_convex4(X1,X2,X3),k19_convex4(X1,X2,X4)),k19_convex4(X1,X2,k2_xcmplx_0(X3,X4))))))))), file('/scratch/mptp/predsminms1/t66_convex4__0', l90_convex4)). fof(t61_convex4, axiom, ![X1]:((~(v2_struct_0(X1))&(v2_clvect_1(X1)&(v3_clvect_1(X1)&(v4_clvect_1(X1)&(v5_clvect_1(X1)&l1_clvect_1(X1))))))=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))=>![X3]:(v1_xcmplx_0(X3)=>![X4]:(v1_xcmplx_0(X4)=>r1_tarski(k19_convex4(X1,X2,k2_xcmplx_0(X3,X4)),k6_rusub_4(X1,k19_convex4(X1,X2,X3),k19_convex4(X1,X2,X4))))))), file('/scratch/mptp/predsminms1/t66_convex4__0', t61_convex4)). fof(redefinition_k7_rusub_4, axiom, ![X1, X2, X3]:(((~(v2_struct_0(X1))&(v2_rlvect_1(X1)&l2_algstr_0(X1)))&(m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))&m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))))=>k7_rusub_4(X1,X2,X3)=k6_rusub_4(X1,X2,X3)), file('/scratch/mptp/predsminms1/t66_convex4__0', redefinition_k7_rusub_4)). fof(d10_xboole_0, axiom, ![X1, X2]:(X1=X2<=>(r1_tarski(X1,X2)&r1_tarski(X2,X1))), file('/scratch/mptp/predsminms1/t66_convex4__0', d10_xboole_0)). fof(dt_k19_convex4, axiom, ![X1, X2, X3]:(((~(v2_struct_0(X1))&l1_clvect_1(X1))&(m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))&v1_xcmplx_0(X3)))=>m1_subset_1(k19_convex4(X1,X2,X3),k1_zfmisc_1(u1_struct_0(X1)))), file('/scratch/mptp/predsminms1/t66_convex4__0', dt_k19_convex4)). fof(dt_l1_clvect_1, axiom, ![X1]:(l1_clvect_1(X1)=>l2_algstr_0(X1)), file('/scratch/mptp/predsminms1/t66_convex4__0', dt_l1_clvect_1)). fof(t66_convex4, conjecture, ![X1]:((~(v2_struct_0(X1))&(v13_algstr_0(X1)&(v2_rlvect_1(X1)&(v3_rlvect_1(X1)&(v4_rlvect_1(X1)&(v2_clvect_1(X1)&(v3_clvect_1(X1)&(v4_clvect_1(X1)&(v5_clvect_1(X1)&l1_clvect_1(X1))))))))))=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))=>![X3]:(v1_xcmplx_0(X3)=>![X4]:(v1_xcmplx_0(X4)=>(v2_convex4(X2,X1)=>(![X5]:(m1_subset_1(X5,k1_numbers)=>![X6]:(m1_subset_1(X6,k1_numbers)=>~((X3=X5&(X4=X6&(r1_xxreal_0(k1_xboole_0,X5)&r1_xxreal_0(k1_xboole_0,X6)))))))\|k7_rusub_4(X1,k19_convex4(X1,X2,X3),k19_convex4(X1,X2,X4))=k19_convex4(X1,X2,k2_xcmplx_0(X3,X4)))))))), file('/scratch/mptp/predsminms1/t66_convex4__0', t66_convex4)). fof(c_0_7, plain, ![X13, X14, X15, X16, X17, X18]:(v2_struct_0(X13)\|(~v13_algstr_0(X13)\|(~v2_rlvect_1(X13)\|(~v3_rlvect_1(X13)\|(~v4_rlvect_1(X13)\|(~v2_clvect_1(X13)\|(~v3_clvect_1(X13)\|(~v4_clvect_1(X13)\|(~v5_clvect_1(X13)\|~l1_clvect_1(X13)))))))))\|(~m1_subset_1(X14,k1_zfmisc_1(u1_struct_0(X13)))\|(~v1_xcmplx_0(X15)\|(~v1_xcmplx_0(X16)\|(~v2_convex4(X14,X13)\|(~m1_subset_1(X17,k1_numbers)\|(~m1_subset_1(X18,k1_numbers)\|(X15!=X17\|(X16!=X18\|(~r1_xxreal_0(k1_xboole_0,X17)\|~r1_xxreal_0(k1_xboole_0,X18)))))\|r1_tarski(k7_rusub_4(X13,k19_convex4(X13,X14,X15),k19_convex4(X13,X14,X16)),k19_convex4(X13,X14,k2_xcmplx_0(X15,X16))))))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[l90_convex4])])])])). fof(c_0_8, plain, ![X19, X20, X21, X22]:(v2_struct_0(X19)\|(~v2_clvect_1(X19)\|(~v3_clvect_1(X19)\|(~v4_clvect_1(X19)\|(~v5_clvect_1(X19)\|~l1_clvect_1(X19)))))\|(~m1_subset_1(X20,k1_zfmisc_1(u1_struct_0(X19)))\|(~v1_xcmplx_0(X21)\|(~v1_xcmplx_0(X22)\|r1_tarski(k19_convex4(X19,X20,k2_xcmplx_0(X21,X22)),k6_rusub_4(X19,k19_convex4(X19,X20,X21),k19_convex4(X19,X20,X22))))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t61_convex4])])])])). fof(c_0_9, plain, ![X23, X24, X25]:(v2_struct_0(X23)\|(~v2_rlvect_1(X23)\|~l2_algstr_0(X23))\|(~m1_subset_1(X24,k1_zfmisc_1(u1_struct_0(X23)))\|~m1_subset_1(X25,k1_zfmisc_1(u1_struct_0(X23))))\|k7_rusub_4(X23,X24,X25)=k6_rusub_4(X23,X24,X25)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[redefinition_k7_rusub_4])])])). fof(c_0_10, plain, ![X26, X27]:(((r1_tarski(X26,X27)\|X26!=X27)&(r1_tarski(X27,X26)\|X26!=X27))&(~r1_tarski(X26,X27)\|~r1_tarski(X27,X26)\|X26=X27)), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])])). cnf(c_0_11, plain, (v2_struct_0(X1)\|r1_tarski(k7_rusub_4(X1,k19_convex4(X1,X2,X3),k19_convex4(X1,X2,X4)),k19_convex4(X1,X2,k2_xcmplx_0(X3,X4)))\|~v13_algstr_0(X1)\|~v2_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v2_clvect_1(X1)\|~v3_clvect_1(X1)\|~v4_clvect_1(X1)\|~v5_clvect_1(X1)\|~l1_clvect_1(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~v1_xcmplx_0(X3)\|~v1_xcmplx_0(X4)\|~v2_convex4(X2,X1)\|~m1_subset_1(X5,k1_numbers)\|~m1_subset_1(X6,k1_numbers)\|X3!=X5\|X4!=X6\|~r1_xxreal_0(k1_xboole_0,X5)\|~r1_xxreal_0(k1_xboole_0,X6)), inference(split_conjunct,[status(thm)],[c_0_7])). cnf(c_0_12, plain, (v2_struct_0(X1)\|r1_tarski(k19_convex4(X1,X2,k2_xcmplx_0(X3,X4)),k6_rusub_4(X1,k19_convex4(X1,X2,X3),k19_convex4(X1,X2,X4)))\|~v2_clvect_1(X1)\|~v3_clvect_1(X1)\|~v4_clvect_1(X1)\|~v5_clvect_1(X1)\|~l1_clvect_1(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~v1_xcmplx_0(X3)\|~v1_xcmplx_0(X4)), inference(split_conjunct,[status(thm)],[c_0_8])). cnf(c_0_13, plain, (v2_struct_0(X1)\|k7_rusub_4(X1,X2,X3)=k6_rusub_4(X1,X2,X3)\|~v2_rlvect_1(X1)\|~l2_algstr_0(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))), inference(split_conjunct,[status(thm)],[c_0_9])). fof(c_0_14, plain, ![X28, X29, X30]:(v2_struct_0(X28)\|~l1_clvect_1(X28)\|(~m1_subset_1(X29,k1_zfmisc_1(u1_struct_0(X28)))\|~v1_xcmplx_0(X30))\|m1_subset_1(k19_convex4(X28,X29,X30),k1_zfmisc_1(u1_struct_0(X28)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k19_convex4])])])). fof(c_0_15, plain, ![X31]:(~l1_clvect_1(X31)\|l2_algstr_0(X31)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_clvect_1])])). fof(c_0_16, negated_conjecture, ~(![X1]:((~(v2_struct_0(X1))&(v13_algstr_0(X1)&(v2_rlvect_1(X1)&(v3_rlvect_1(X1)&(v4_rlvect_1(X1)&(v2_clvect_1(X1)&(v3_clvect_1(X1)&(v4_clvect_1(X1)&(v5_clvect_1(X1)&l1_clvect_1(X1))))))))))=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))=>![X3]:(v1_xcmplx_0(X3)=>![X4]:(v1_xcmplx_0(X4)=>(v2_convex4(X2,X1)=>(![X5]:(m1_subset_1(X5,k1_numbers)=>![X6]:(m1_subset_1(X6,k1_numbers)=>~((X3=X5&(X4=X6&(r1_xxreal_0(k1_xboole_0,X5)&r1_xxreal_0(k1_xboole_0,X6)))))))\|k7_rusub_4(X1,k19_convex4(X1,X2,X3),k19_convex4(X1,X2,X4))=k19_convex4(X1,X2,k2_xcmplx_0(X3,X4))))))))), inference(assume_negation,[status(cth)],[t66_convex4])). cnf(c_0_17, plain, (X1=X2\|~r1_tarski(X1,X2)\|~r1_tarski(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_18, plain, (v2_struct_0(X1)\|r1_tarski(k7_rusub_4(X1,k19_convex4(X1,X2,X3),k19_convex4(X1,X2,X4)),k19_convex4(X1,X2,k2_xcmplx_0(X3,X4)))\|X4!=X6\|X3!=X5\|~v13_algstr_0(X1)\|~v2_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v2_clvect_1(X1)\|~v3_clvect_1(X1)\|~v4_clvect_1(X1)\|~v5_clvect_1(X1)\|~l1_clvect_1(X1)\|~v1_xcmplx_0(X4)\|~v1_xcmplx_0(X3)\|~v2_convex4(X2,X1)\|~m1_subset_1(X6,k1_numbers)\|~m1_subset_1(X5,k1_numbers)\|~r1_xxreal_0(k1_xboole_0,X6)\|~r1_xxreal_0(k1_xboole_0,X5)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(evalgc,[status(thm)],[c_0_11])). cnf(c_0_19, plain, (v2_struct_0(X1)\|r1_tarski(k19_convex4(X1,X2,k2_xcmplx_0(X3,X4)),k6_rusub_4(X1,k19_convex4(X1,X2,X3),k19_convex4(X1,X2,X4)))\|~v2_clvect_1(X1)\|~v3_clvect_1(X1)\|~v4_clvect_1(X1)\|~v5_clvect_1(X1)\|~l1_clvect_1(X1)\|~v1_xcmplx_0(X4)\|~v1_xcmplx_0(X3)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(evalgc,[status(thm)],[c_0_12])). cnf(c_0_20, plain, (k6_rusub_4(X1,X2,X3)=k7_rusub_4(X1,X2,X3)\|v2_struct_0(X1)\|~v2_rlvect_1(X1)\|~l2_algstr_0(X1)\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(evalgc,[status(thm)],[c_0_13])). cnf(c_0_21, plain, (v2_struct_0(X1)\|m1_subset_1(k19_convex4(X1,X2,X3),k1_zfmisc_1(u1_struct_0(X1)))\|~l1_clvect_1(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~v1_xcmplx_0(X3)), inference(split_conjunct,[status(thm)],[c_0_14])). cnf(c_0_22, plain, (l2_algstr_0(X1)\|~l1_clvect_1(X1)), inference(split_conjunct,[status(thm)],[c_0_15])). fof(c_0_23, negated_conjecture, ((~v2_struct_0(esk1_0)&(v13_algstr_0(esk1_0)&(v2_rlvect_1(esk1_0)&(v3_rlvect_1(esk1_0)&(v4_rlvect_1(esk1_0)&(v2_clvect_1(esk1_0)&(v3_clvect_1(esk1_0)&(v4_clvect_1(esk1_0)&(v5_clvect_1(esk1_0)&l1_clvect_1(esk1_0))))))))))&(m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(esk1_0)))&(v1_xcmplx_0(esk3_0)&(v1_xcmplx_0(esk4_0)&(v2_convex4(esk2_0,esk1_0)&((m1_subset_1(esk5_0,k1_numbers)&(m1_subset_1(esk6_0,k1_numbers)&(esk3_0=esk5_0&(esk4_0=esk6_0&(r1_xxreal_0(k1_xboole_0,esk5_0)&r1_xxreal_0(k1_xboole_0,esk6_0))))))&k7_rusub_4(esk1_0,k19_convex4(esk1_0,esk2_0,esk3_0),k19_convex4(esk1_0,esk2_0,esk4_0))!=k19_convex4(esk1_0,esk2_0,k2_xcmplx_0(esk3_0,esk4_0)))))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_16])])])])). cnf(c_0_24, plain, (X1=X2\|~r1_tarski(X2,X1)\|~r1_tarski(X1,X2)), inference(evalgc,[status(thm)],[c_0_17])). cnf(c_0_25, plain, (r1_tarski(k7_rusub_4(X1,k19_convex4(X1,X2,X3),k19_convex4(X1,X2,X4)),k19_convex4(X1,X2,k2_xcmplx_0(X3,X4)))\|v2_struct_0(X1)\|~r1_xxreal_0(k1_xboole_0,X4)\|~r1_xxreal_0(k1_xboole_0,X3)\|~v2_convex4(X2,X1)\|~v1_xcmplx_0(X4)\|~v1_xcmplx_0(X3)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X4,k1_numbers)\|~m1_subset_1(X3,k1_numbers)\|~l1_clvect_1(X1)\|~v5_clvect_1(X1)\|~v4_clvect_1(X1)\|~v3_clvect_1(X1)\|~v2_clvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v13_algstr_0(X1)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_18])])])). cnf(c_0_26, plain, (r1_tarski(k19_convex4(X1,X2,k2_xcmplx_0(X3,X4)),k7_rusub_4(X1,k19_convex4(X1,X2,X3),k19_convex4(X1,X2,X4)))\|v2_struct_0(X1)\|~v1_xcmplx_0(X4)\|~v1_xcmplx_0(X3)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~l1_clvect_1(X1)\|~v5_clvect_1(X1)\|~v4_clvect_1(X1)\|~v3_clvect_1(X1)\|~v2_clvect_1(X1)\|~l2_algstr_0(X1)\|~m1_subset_1(k19_convex4(X1,X2,X4),k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(k19_convex4(X1,X2,X3),k1_zfmisc_1(u1_struct_0(X1)))\|~v2_rlvect_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_19, c_0_20])])). cnf(c_0_27, plain, (v2_struct_0(X1)\|m1_subset_1(k19_convex4(X1,X2,X3),k1_zfmisc_1(u1_struct_0(X1)))\|~l1_clvect_1(X1)\|~v1_xcmplx_0(X3)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(evalgc,[status(thm)],[c_0_21])). cnf(c_0_28, plain, (l2_algstr_0(X1)\|~l1_clvect_1(X1)), inference(evalgc,[status(thm)],[c_0_22])). cnf(c_0_29, negated_conjecture, (r1_xxreal_0(k1_xboole_0,esk6_0)), inference(split_conjunct,[status(thm)],[c_0_23])). cnf(c_0_30, negated_conjecture, (esk4_0=esk6_0), inference(split_conjunct,[status(thm)],[c_0_23])). cnf(c_0_31, negated_conjecture, (r1_xxreal_0(k1_xboole_0,esk5_0)), inference(split_conjunct,[status(thm)],[c_0_23])). cnf(c_0_32, negated_conjecture, (esk3_0=esk5_0), inference(split_conjunct,[status(thm)],[c_0_23])). cnf(c_0_33, negated_conjecture, (m1_subset_1(esk6_0,k1_numbers)), inference(split_conjunct,[status(thm)],[c_0_23])). cnf(c_0_34, negated_conjecture, (m1_subset_1(esk5_0,k1_numbers)), inference(split_conjunct,[status(thm)],[c_0_23])). cnf(c_0_35, negated_conjecture, (k7_rusub_4(esk1_0,k19_convex4(esk1_0,esk2_0,esk3_0),k19_convex4(esk1_0,esk2_0,esk4_0))!=k19_convex4(esk1_0,esk2_0,k2_xcmplx_0(esk3_0,esk4_0))), inference(split_conjunct,[status(thm)],[c_0_23])). cnf(c_0_36, plain, (k7_rusub_4(X1,k19_convex4(X1,X2,X3),k19_convex4(X1,X2,X4))=k19_convex4(X1,X2,k2_xcmplx_0(X3,X4))\|v2_struct_0(X1)\|~r1_tarski(k19_convex4(X1,X2,k2_xcmplx_0(X3,X4)),k7_rusub_4(X1,k19_convex4(X1,X2,X3),k19_convex4(X1,X2,X4)))\|~r1_xxreal_0(k1_xboole_0,X4)\|~r1_xxreal_0(k1_xboole_0,X3)\|~v2_convex4(X2,X1)\|~v1_xcmplx_0(X4)\|~v1_xcmplx_0(X3)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X4,k1_numbers)\|~m1_subset_1(X3,k1_numbers)\|~l1_clvect_1(X1)\|~v5_clvect_1(X1)\|~v4_clvect_1(X1)\|~v3_clvect_1(X1)\|~v2_clvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v13_algstr_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_24, c_0_25])])). cnf(c_0_37, plain, (r1_tarski(k19_convex4(X1,X2,k2_xcmplx_0(X3,X4)),k7_rusub_4(X1,k19_convex4(X1,X2,X3),k19_convex4(X1,X2,X4)))\|v2_struct_0(X1)\|~v1_xcmplx_0(X4)\|~v1_xcmplx_0(X3)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~l1_clvect_1(X1)\|~v5_clvect_1(X1)\|~v4_clvect_1(X1)\|~v3_clvect_1(X1)\|~v2_clvect_1(X1)\|~v2_rlvect_1(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_26, c_0_27]), c_0_27]), c_0_28])). cnf(c_0_38, negated_conjecture, (r1_xxreal_0(k1_xboole_0,esk6_0)), inference(evalgc,[status(thm)],[c_0_29])). cnf(c_0_39, negated_conjecture, (esk6_0=esk4_0), inference(evalgc,[status(thm)],[c_0_30])). cnf(c_0_40, negated_conjecture, (r1_xxreal_0(k1_xboole_0,esk5_0)), inference(evalgc,[status(thm)],[c_0_31])). cnf(c_0_41, negated_conjecture, (esk5_0=esk3_0), inference(evalgc,[status(thm)],[c_0_32])). cnf(c_0_42, negated_conjecture, (v2_convex4(esk2_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_23])). cnf(c_0_43, negated_conjecture, (v1_xcmplx_0(esk4_0)), inference(split_conjunct,[status(thm)],[c_0_23])). cnf(c_0_44, negated_conjecture, (v1_xcmplx_0(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_23])). cnf(c_0_45, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(esk1_0)))), inference(split_conjunct,[status(thm)],[c_0_23])). cnf(c_0_46, negated_conjecture, (m1_subset_1(esk6_0,k1_numbers)), inference(evalgc,[status(thm)],[c_0_33])). cnf(c_0_47, negated_conjecture, (m1_subset_1(esk5_0,k1_numbers)), inference(evalgc,[status(thm)],[c_0_34])). cnf(c_0_48, negated_conjecture, (l1_clvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_23])). cnf(c_0_49, negated_conjecture, (v5_clvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_23])). cnf(c_0_50, negated_conjecture, (v4_clvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_23])). cnf(c_0_51, negated_conjecture, (v3_clvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_23])). cnf(c_0_52, negated_conjecture, (v2_clvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_23])). cnf(c_0_53, negated_conjecture, (v4_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_23])). cnf(c_0_54, negated_conjecture, (v3_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_23])). cnf(c_0_55, negated_conjecture, (v2_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_23])). cnf(c_0_56, negated_conjecture, (v13_algstr_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_23])). cnf(c_0_57, negated_conjecture, (~v2_struct_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_23])). cnf(c_0_58, negated_conjecture, (k7_rusub_4(esk1_0,k19_convex4(esk1_0,esk2_0,esk3_0),k19_convex4(esk1_0,esk2_0,esk4_0))!=k19_convex4(esk1_0,esk2_0,k2_xcmplx_0(esk3_0,esk4_0))), inference(evalgc,[status(thm)],[c_0_35])). cnf(c_0_59, plain, (k7_rusub_4(X1,k19_convex4(X1,X2,X3),k19_convex4(X1,X2,X4))=k19_convex4(X1,X2,k2_xcmplx_0(X3,X4))\|v2_struct_0(X1)\|~r1_xxreal_0(k1_xboole_0,X4)\|~r1_xxreal_0(k1_xboole_0,X3)\|~v2_convex4(X2,X1)\|~v1_xcmplx_0(X4)\|~v1_xcmplx_0(X3)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X4,k1_numbers)\|~m1_subset_1(X3,k1_numbers)\|~l1_clvect_1(X1)\|~v5_clvect_1(X1)\|~v4_clvect_1(X1)\|~v3_clvect_1(X1)\|~v2_clvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v13_algstr_0(X1)), inference(csr,[status(thm)],[c_0_36, c_0_37])). cnf(c_0_60, negated_conjecture, (r1_xxreal_0(k1_xboole_0,esk4_0)), inference(rw,[status(thm)],[c_0_38, c_0_39])). cnf(c_0_61, negated_conjecture, (r1_xxreal_0(k1_xboole_0,esk3_0)), inference(rw,[status(thm)],[c_0_40, c_0_41])). cnf(c_0_62, negated_conjecture, (v2_convex4(esk2_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_42])). cnf(c_0_63, negated_conjecture, (v1_xcmplx_0(esk4_0)), inference(evalgc,[status(thm)],[c_0_43])). cnf(c_0_64, negated_conjecture, (v1_xcmplx_0(esk3_0)), inference(evalgc,[status(thm)],[c_0_44])). cnf(c_0_65, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(esk1_0)))), inference(evalgc,[status(thm)],[c_0_45])). cnf(c_0_66, negated_conjecture, (m1_subset_1(esk4_0,k1_numbers)), inference(rw,[status(thm)],[c_0_46, c_0_39])). cnf(c_0_67, negated_conjecture, (m1_subset_1(esk3_0,k1_numbers)), inference(rw,[status(thm)],[c_0_47, c_0_41])). cnf(c_0_68, negated_conjecture, (l1_clvect_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_48])). cnf(c_0_69, negated_conjecture, (v5_clvect_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_49])). cnf(c_0_70, negated_conjecture, (v4_clvect_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_50])). cnf(c_0_71, negated_conjecture, (v3_clvect_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_51])). cnf(c_0_72, negated_conjecture, (v2_clvect_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_52])). cnf(c_0_73, negated_conjecture, (v4_rlvect_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_53])). cnf(c_0_74, negated_conjecture, (v3_rlvect_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_54])). cnf(c_0_75, negated_conjecture, (v2_rlvect_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_55])). cnf(c_0_76, negated_conjecture, (v13_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_56])). cnf(c_0_77, negated_conjecture, (~v2_struct_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_57])). cnf(c_0_78, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58, c_0_59]), c_0_60]), c_0_61]), c_0_62]), c_0_63]), c_0_64]), c_0_65]), c_0_66]), c_0_67]), c_0_68]), c_0_69]), c_0_70]), c_0_71]), c_0_72]), c_0_73]), c_0_74]), c_0_75]), c_0_76])]), c_0_77]), ['proof']). # SZS output end CNFRefutation	reserve x,y for set, i for Nat; reserve V for non empty CLSStruct, u,v,v1,v2,v3 for VECTOR of V, A for Subset of V, l, l1, l2 for C_Linear_Combination of A, x,y,y1,y2 for set, a,b for Complex, F for FinSequence of the carrier of V, f for Function of the carrier of V, COMPLEX; reserve K,L,L1,L2,L3 for C_Linear_Combination of V; reserve e,e1,e2 for Element of C_LinComb V; theorem for V being ComplexLinearSpace, M being Subset of V, z1,z2 being Complex st (ex r1,r2 being Real st z1 = r1 & z2 = r2 & r1 >= 0 & r2 >= 0) & M is convex holds z1M + z2M = (z1 + z2)M proof let V be ComplexLinearSpace, M be Subset of V, z1,z2 be Complex; assume ( ex r1,r2 being Real st z1=r1 & z2=r2 & r1 >= 0 & r2 >= 0)& M is convex; hence z1M + z2M c= (z1 + z2)M by Lm2; thus thesis by Th61; end;	Convert the following ATP output trace into a readable Mizar proof.
t5_unialg_2	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t5_unialg_2, conjecture, ![X1]:((~(v2_struct_0(X1))&(v2_unialg_1(X1)&(v3_unialg_1(X1)&(v4_unialg_1(X1)&l1_unialg_1(X1)))))=>![X2]:((~(v1_xboole_0(X2))&m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))))=>![X3]:(m5_margrel1(X3,u1_struct_0(X1),k1_unialg_2(X1))=>(r2_unialg_2(X1,X2,X3)=>k19_margrel1(k2_unialg_2(X1,X2,X3))=k19_margrel1(X3))))), file('/scratch/mptp/predsminms1/t5_unialg_2__0', t5_unialg_2)). fof(dt_m5_margrel1, axiom, ![X1, X2]:((~(v1_xboole_0(X1))&m4_margrel1(X2,X1))=>![X3]:(m5_margrel1(X3,X1,X2)=>(v1_funct_1(X3)&(~(v1_xboole_0(X3))&(v2_margrel1(X3)&(v3_margrel1(X3,X1)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k3_finseq_2(X1),X1))))))))), file('/scratch/mptp/predsminms1/t5_unialg_2__0', dt_m5_margrel1)). fof(cc1_subset_1, axiom, ![X1]:(v1_xboole_0(X1)=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(X1))=>v1_xboole_0(X2))), file('/scratch/mptp/predsminms1/t5_unialg_2__0', cc1_subset_1)). fof(dt_k18_margrel1, axiom, ![X1]:((v1_relat_1(X1)&v2_margrel1(X1))=>v7_ordinal1(k18_margrel1(X1))), file('/scratch/mptp/predsminms1/t5_unialg_2__0', dt_k18_margrel1)). fof(redefinition_k19_margrel1, axiom, ![X1]:((v1_relat_1(X1)&(v1_funct_1(X1)&v2_margrel1(X1)))=>k19_margrel1(X1)=k18_margrel1(X1)), file('/scratch/mptp/predsminms1/t5_unialg_2__0', redefinition_k19_margrel1)). fof(t22_margrel1, axiom, ![X1]:(~(v1_xboole_0(X1))=>![X2]:((v1_funct_1(X2)&(~(v1_xboole_0(X2))&(v2_margrel1(X2)&(v3_margrel1(X2,X1)&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k3_finseq_2(X1),X1)))))))=>k9_xtuple_0(X2)=k4_finseq_2(k19_margrel1(X2),X1))), file('/scratch/mptp/predsminms1/t5_unialg_2__0', t22_margrel1)). fof(dt_k2_unialg_2, axiom, ![X1, X2, X3]:(((~(v2_struct_0(X1))&(v2_unialg_1(X1)&(v3_unialg_1(X1)&(v4_unialg_1(X1)&l1_unialg_1(X1)))))&((~(v1_xboole_0(X2))&m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))))&m1_subset_1(X3,k1_unialg_2(X1))))=>(~(v1_xboole_0(k2_unialg_2(X1,X2,X3)))&(v1_funct_1(k2_unialg_2(X1,X2,X3))&(v2_margrel1(k2_unialg_2(X1,X2,X3))&(v3_margrel1(k2_unialg_2(X1,X2,X3),X2)&m1_subset_1(k2_unialg_2(X1,X2,X3),k1_zfmisc_1(k2_zfmisc_1(k3_finseq_2(X2),X2)))))))), file('/scratch/mptp/predsminms1/t5_unialg_2__0', dt_k2_unialg_2)). fof(dt_k1_unialg_2, axiom, ![X1]:((~(v2_struct_0(X1))&(v2_unialg_1(X1)&(v3_unialg_1(X1)&(v4_unialg_1(X1)&l1_unialg_1(X1)))))=>m4_margrel1(k1_unialg_2(X1),u1_struct_0(X1))), file('/scratch/mptp/predsminms1/t5_unialg_2__0', dt_k1_unialg_2)). fof(t110_finseq_2, axiom, ![X1]:(v7_ordinal1(X1)=>![X2]:(v7_ordinal1(X2)=>![X3, X4]:(~(v1_xboole_0(X4))=>(k4_finseq_2(X1,X4)=k4_finseq_2(X2,X3)=>X1=X2)))), file('/scratch/mptp/predsminms1/t5_unialg_2__0', t110_finseq_2)). fof(t21_margrel1, axiom, ![X1]:(v7_ordinal1(X1)=>![X2]:(~(v1_xboole_0(X2))=>![X3]:((~(v1_xboole_0(X3))&m1_subset_1(X3,k1_zfmisc_1(X2)))=>k3_xboole_0(k4_finseq_2(X1,X2),k4_finseq_2(X1,X3))=k4_finseq_2(X1,X3)))), file('/scratch/mptp/predsminms1/t5_unialg_2__0', t21_margrel1)). fof(cc1_relset_1, axiom, ![X1, X2, X3]:(m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))=>v1_relat_1(X3)), file('/scratch/mptp/predsminms1/t5_unialg_2__0', cc1_relset_1)). fof(redefinition_k2_partfun1, axiom, ![X1, X2, X3, X4]:((v1_funct_1(X3)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2))))=>k2_partfun1(X1,X2,X3,X4)=k5_relat_1(X3,X4)), file('/scratch/mptp/predsminms1/t5_unialg_2__0', redefinition_k2_partfun1)). fof(redefinition_m5_margrel1, axiom, ![X1, X2]:((~(v1_xboole_0(X1))&m4_margrel1(X2,X1))=>![X3]:(m5_margrel1(X3,X1,X2)<=>m1_subset_1(X3,X2))), file('/scratch/mptp/predsminms1/t5_unialg_2__0', redefinition_m5_margrel1)). fof(t61_relat_1, axiom, ![X1, X2]:(v1_relat_1(X2)=>k9_xtuple_0(k5_relat_1(X2,X1))=k3_xboole_0(k9_xtuple_0(X2),X1)), file('/scratch/mptp/predsminms1/t5_unialg_2__0', t61_relat_1)). fof(d5_unialg_2, axiom, ![X1]:((~(v2_struct_0(X1))&(v2_unialg_1(X1)&(v3_unialg_1(X1)&(v4_unialg_1(X1)&l1_unialg_1(X1)))))=>![X2]:((~(v1_xboole_0(X2))&m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))))=>![X3]:(m5_margrel1(X3,u1_struct_0(X1),k1_unialg_2(X1))=>(r2_unialg_2(X1,X2,X3)=>k2_unialg_2(X1,X2,X3)=k2_partfun1(k3_finseq_2(u1_struct_0(X1)),u1_struct_0(X1),X3,k4_finseq_2(k19_margrel1(X3),X2)))))), file('/scratch/mptp/predsminms1/t5_unialg_2__0', d5_unialg_2)). fof(c_0_15, negated_conjecture, ~(![X1]:((~(v2_struct_0(X1))&(v2_unialg_1(X1)&(v3_unialg_1(X1)&(v4_unialg_1(X1)&l1_unialg_1(X1)))))=>![X2]:((~(v1_xboole_0(X2))&m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))))=>![X3]:(m5_margrel1(X3,u1_struct_0(X1),k1_unialg_2(X1))=>(r2_unialg_2(X1,X2,X3)=>k19_margrel1(k2_unialg_2(X1,X2,X3))=k19_margrel1(X3)))))), inference(assume_negation,[status(cth)],[t5_unialg_2])). fof(c_0_16, plain, ![X13, X14, X15]:((v1_funct_1(X15)\|~m5_margrel1(X15,X13,X14)\|(v1_xboole_0(X13)\|~m4_margrel1(X14,X13)))&((~v1_xboole_0(X15)\|~m5_margrel1(X15,X13,X14)\|(v1_xboole_0(X13)\|~m4_margrel1(X14,X13)))&((v2_margrel1(X15)\|~m5_margrel1(X15,X13,X14)\|(v1_xboole_0(X13)\|~m4_margrel1(X14,X13)))&((v3_margrel1(X15,X13)\|~m5_margrel1(X15,X13,X14)\|(v1_xboole_0(X13)\|~m4_margrel1(X14,X13)))&(m1_subset_1(X15,k1_zfmisc_1(k2_zfmisc_1(k3_finseq_2(X13),X13)))\|~m5_margrel1(X15,X13,X14)\|(v1_xboole_0(X13)\|~m4_margrel1(X14,X13))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_m5_margrel1])])])])])). fof(c_0_17, negated_conjecture, ((~v2_struct_0(esk1_0)&(v2_unialg_1(esk1_0)&(v3_unialg_1(esk1_0)&(v4_unialg_1(esk1_0)&l1_unialg_1(esk1_0)))))&((~v1_xboole_0(esk2_0)&m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(esk1_0))))&(m5_margrel1(esk3_0,u1_struct_0(esk1_0),k1_unialg_2(esk1_0))&(r2_unialg_2(esk1_0,esk2_0,esk3_0)&k19_margrel1(k2_unialg_2(esk1_0,esk2_0,esk3_0))!=k19_margrel1(esk3_0))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_15])])])])). fof(c_0_18, plain, ![X11, X12]:(~v1_xboole_0(X11)\|(~m1_subset_1(X12,k1_zfmisc_1(X11))\|v1_xboole_0(X12))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_subset_1])])])). cnf(c_0_19, plain, (m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k3_finseq_2(X2),X2)))\|v1_xboole_0(X2)\|~m5_margrel1(X1,X2,X3)\|~m4_margrel1(X3,X2)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_20, negated_conjecture, (m5_margrel1(esk3_0,u1_struct_0(esk1_0),k1_unialg_2(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_17])). cnf(c_0_21, plain, (v1_xboole_0(X2)\|~v1_xboole_0(X1)\|~m1_subset_1(X2,k1_zfmisc_1(X1))), inference(split_conjunct,[status(thm)],[c_0_18])). cnf(c_0_22, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(esk1_0)))), inference(split_conjunct,[status(thm)],[c_0_17])). cnf(c_0_23, negated_conjecture, (~v1_xboole_0(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_17])). cnf(c_0_24, plain, (v2_margrel1(X1)\|v1_xboole_0(X2)\|~m5_margrel1(X1,X2,X3)\|~m4_margrel1(X3,X2)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_25, plain, (v1_funct_1(X1)\|v1_xboole_0(X2)\|~m5_margrel1(X1,X2,X3)\|~m4_margrel1(X3,X2)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_26, plain, (v1_xboole_0(X2)\|~v1_xboole_0(X1)\|~m5_margrel1(X1,X2,X3)\|~m4_margrel1(X3,X2)), inference(split_conjunct,[status(thm)],[c_0_16])). fof(c_0_27, plain, ![X17]:(~v1_relat_1(X17)\|~v2_margrel1(X17)\|v7_ordinal1(k18_margrel1(X17))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k18_margrel1])])). fof(c_0_28, plain, ![X16]:(~v1_relat_1(X16)\|(~v1_funct_1(X16)\|~v2_margrel1(X16))\|k19_margrel1(X16)=k18_margrel1(X16)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k19_margrel1])])). fof(c_0_29, plain, ![X30, X31]:(v1_xboole_0(X30)\|(~v1_funct_1(X31)\|(v1_xboole_0(X31)\|(~v2_margrel1(X31)\|(~v3_margrel1(X31,X30)\|~m1_subset_1(X31,k1_zfmisc_1(k2_zfmisc_1(k3_finseq_2(X30),X30))))))\|k9_xtuple_0(X31)=k4_finseq_2(k19_margrel1(X31),X30))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t22_margrel1])])])])). fof(c_0_30, plain, ![X18, X19, X20]:((~v1_xboole_0(k2_unialg_2(X18,X19,X20))\|(v2_struct_0(X18)\|(~v2_unialg_1(X18)\|(~v3_unialg_1(X18)\|(~v4_unialg_1(X18)\|~l1_unialg_1(X18))))\|(v1_xboole_0(X19)\|~m1_subset_1(X19,k1_zfmisc_1(u1_struct_0(X18)))\|~m1_subset_1(X20,k1_unialg_2(X18)))))&((v1_funct_1(k2_unialg_2(X18,X19,X20))\|(v2_struct_0(X18)\|(~v2_unialg_1(X18)\|(~v3_unialg_1(X18)\|(~v4_unialg_1(X18)\|~l1_unialg_1(X18))))\|(v1_xboole_0(X19)\|~m1_subset_1(X19,k1_zfmisc_1(u1_struct_0(X18)))\|~m1_subset_1(X20,k1_unialg_2(X18)))))&((v2_margrel1(k2_unialg_2(X18,X19,X20))\|(v2_struct_0(X18)\|(~v2_unialg_1(X18)\|(~v3_unialg_1(X18)\|(~v4_unialg_1(X18)\|~l1_unialg_1(X18))))\|(v1_xboole_0(X19)\|~m1_subset_1(X19,k1_zfmisc_1(u1_struct_0(X18)))\|~m1_subset_1(X20,k1_unialg_2(X18)))))&((v3_margrel1(k2_unialg_2(X18,X19,X20),X19)\|(v2_struct_0(X18)\|(~v2_unialg_1(X18)\|(~v3_unialg_1(X18)\|(~v4_unialg_1(X18)\|~l1_unialg_1(X18))))\|(v1_xboole_0(X19)\|~m1_subset_1(X19,k1_zfmisc_1(u1_struct_0(X18)))\|~m1_subset_1(X20,k1_unialg_2(X18)))))&(m1_subset_1(k2_unialg_2(X18,X19,X20),k1_zfmisc_1(k2_zfmisc_1(k3_finseq_2(X19),X19)))\|(v2_struct_0(X18)\|(~v2_unialg_1(X18)\|(~v3_unialg_1(X18)\|(~v4_unialg_1(X18)\|~l1_unialg_1(X18))))\|(v1_xboole_0(X19)\|~m1_subset_1(X19,k1_zfmisc_1(u1_struct_0(X18)))\|~m1_subset_1(X20,k1_unialg_2(X18))))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k2_unialg_2])])])])). cnf(c_0_31, plain, (v1_xboole_0(X2)\|m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k3_finseq_2(X2),X2)))\|~m4_margrel1(X3,X2)\|~m5_margrel1(X1,X2,X3)), inference(evalgc,[status(thm)],[c_0_19])). cnf(c_0_32, negated_conjecture, (m5_margrel1(esk3_0,u1_struct_0(esk1_0),k1_unialg_2(esk1_0))), inference(evalgc,[status(thm)],[c_0_20])). cnf(c_0_33, plain, (v1_xboole_0(X2)\|~v1_xboole_0(X1)\|~m1_subset_1(X2,k1_zfmisc_1(X1))), inference(evalgc,[status(thm)],[c_0_21])). cnf(c_0_34, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(esk1_0)))), inference(evalgc,[status(thm)],[c_0_22])). cnf(c_0_35, negated_conjecture, (~v1_xboole_0(esk2_0)), inference(evalgc,[status(thm)],[c_0_23])). cnf(c_0_36, plain, (v1_xboole_0(X2)\|v2_margrel1(X1)\|~m4_margrel1(X3,X2)\|~m5_margrel1(X1,X2,X3)), inference(evalgc,[status(thm)],[c_0_24])). fof(c_0_37, plain, ![X42]:(v2_struct_0(X42)\|(~v2_unialg_1(X42)\|(~v3_unialg_1(X42)\|(~v4_unialg_1(X42)\|~l1_unialg_1(X42))))\|m4_margrel1(k1_unialg_2(X42),u1_struct_0(X42))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k1_unialg_2])])])). cnf(c_0_38, plain, (v1_xboole_0(X2)\|v1_funct_1(X1)\|~m4_margrel1(X3,X2)\|~m5_margrel1(X1,X2,X3)), inference(evalgc,[status(thm)],[c_0_25])). cnf(c_0_39, plain, (v1_xboole_0(X2)\|~v1_xboole_0(X1)\|~m4_margrel1(X3,X2)\|~m5_margrel1(X1,X2,X3)), inference(evalgc,[status(thm)],[c_0_26])). cnf(c_0_40, plain, (v3_margrel1(X1,X2)\|v1_xboole_0(X2)\|~m5_margrel1(X1,X2,X3)\|~m4_margrel1(X3,X2)), inference(split_conjunct,[status(thm)],[c_0_16])). fof(c_0_41, plain, ![X35, X36, X37, X38]:(~v7_ordinal1(X35)\|(~v7_ordinal1(X36)\|(v1_xboole_0(X38)\|(k4_finseq_2(X35,X38)!=k4_finseq_2(X36,X37)\|X35=X36)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t110_finseq_2])])])])). cnf(c_0_42, plain, (v7_ordinal1(k18_margrel1(X1))\|~v1_relat_1(X1)\|~v2_margrel1(X1)), inference(split_conjunct,[status(thm)],[c_0_27])). cnf(c_0_43, plain, (k19_margrel1(X1)=k18_margrel1(X1)\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v2_margrel1(X1)), inference(split_conjunct,[status(thm)],[c_0_28])). cnf(c_0_44, plain, (v1_xboole_0(X1)\|v1_xboole_0(X2)\|k9_xtuple_0(X2)=k4_finseq_2(k19_margrel1(X2),X1)\|~v1_funct_1(X2)\|~v2_margrel1(X2)\|~v3_margrel1(X2,X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k3_finseq_2(X1),X1)))), inference(split_conjunct,[status(thm)],[c_0_29])). cnf(c_0_45, plain, (m1_subset_1(k2_unialg_2(X1,X2,X3),k1_zfmisc_1(k2_zfmisc_1(k3_finseq_2(X2),X2)))\|v2_struct_0(X1)\|v1_xboole_0(X2)\|~v2_unialg_1(X1)\|~v3_unialg_1(X1)\|~v4_unialg_1(X1)\|~l1_unialg_1(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X3,k1_unialg_2(X1))), inference(split_conjunct,[status(thm)],[c_0_30])). fof(c_0_46, plain, ![X32, X33, X34]:(~v7_ordinal1(X32)\|(v1_xboole_0(X33)\|(v1_xboole_0(X34)\|~m1_subset_1(X34,k1_zfmisc_1(X33))\|k3_xboole_0(k4_finseq_2(X32,X33),k4_finseq_2(X32,X34))=k4_finseq_2(X32,X34)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t21_margrel1])])])])). cnf(c_0_47, negated_conjecture, (m1_subset_1(esk3_0,k1_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(esk1_0)),u1_struct_0(esk1_0))))\|v1_xboole_0(u1_struct_0(esk1_0))\|~m4_margrel1(k1_unialg_2(esk1_0),u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_31, c_0_32])])). cnf(c_0_48, negated_conjecture, (~v1_xboole_0(u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33, c_0_34]), c_0_35])])). cnf(c_0_49, negated_conjecture, (v2_margrel1(esk3_0)\|v1_xboole_0(u1_struct_0(esk1_0))\|~m4_margrel1(k1_unialg_2(esk1_0),u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_36, c_0_32])])). cnf(c_0_50, plain, (v2_struct_0(X1)\|m4_margrel1(k1_unialg_2(X1),u1_struct_0(X1))\|~v2_unialg_1(X1)\|~v3_unialg_1(X1)\|~v4_unialg_1(X1)\|~l1_unialg_1(X1)), inference(split_conjunct,[status(thm)],[c_0_37])). cnf(c_0_51, negated_conjecture, (l1_unialg_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_17])). cnf(c_0_52, negated_conjecture, (v4_unialg_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_17])). cnf(c_0_53, negated_conjecture, (v3_unialg_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_17])). cnf(c_0_54, negated_conjecture, (v2_unialg_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_17])). cnf(c_0_55, negated_conjecture, (~v2_struct_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_17])). cnf(c_0_56, negated_conjecture, (v1_funct_1(esk3_0)\|v1_xboole_0(u1_struct_0(esk1_0))\|~m4_margrel1(k1_unialg_2(esk1_0),u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_38, c_0_32])])). cnf(c_0_57, negated_conjecture, (v1_xboole_0(u1_struct_0(esk1_0))\|~m4_margrel1(k1_unialg_2(esk1_0),u1_struct_0(esk1_0))\|~v1_xboole_0(esk3_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_39, c_0_32])])). cnf(c_0_58, plain, (v1_xboole_0(X2)\|v3_margrel1(X1,X2)\|~m4_margrel1(X3,X2)\|~m5_margrel1(X1,X2,X3)), inference(evalgc,[status(thm)],[c_0_40])). fof(c_0_59, plain, ![X8, X9, X10]:(~m1_subset_1(X10,k1_zfmisc_1(k2_zfmisc_1(X8,X9)))\|v1_relat_1(X10)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relset_1])])). fof(c_0_60, plain, ![X21, X22, X23, X24]:(~v1_funct_1(X23)\|~m1_subset_1(X23,k1_zfmisc_1(k2_zfmisc_1(X21,X22)))\|k2_partfun1(X21,X22,X23,X24)=k5_relat_1(X23,X24)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k2_partfun1])])). cnf(c_0_61, plain, (v1_xboole_0(X3)\|X1=X2\|~v7_ordinal1(X1)\|~v7_ordinal1(X2)\|k4_finseq_2(X1,X3)!=k4_finseq_2(X2,X4)), inference(split_conjunct,[status(thm)],[c_0_41])). cnf(c_0_62, plain, (v7_ordinal1(k18_margrel1(X1))\|~v1_relat_1(X1)\|~v2_margrel1(X1)), inference(evalgc,[status(thm)],[c_0_42])). cnf(c_0_63, plain, (k18_margrel1(X1)=k19_margrel1(X1)\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v2_margrel1(X1)), inference(evalgc,[status(thm)],[c_0_43])). cnf(c_0_64, plain, (k4_finseq_2(k19_margrel1(X2),X1)=k9_xtuple_0(X2)\|v1_xboole_0(X2)\|v1_xboole_0(X1)\|~v1_funct_1(X2)\|~v2_margrel1(X2)\|~v3_margrel1(X2,X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k3_finseq_2(X1),X1)))), inference(evalgc,[status(thm)],[c_0_44])). cnf(c_0_65, plain, (v2_struct_0(X1)\|v1_xboole_0(X2)\|m1_subset_1(k2_unialg_2(X1,X2,X3),k1_zfmisc_1(k2_zfmisc_1(k3_finseq_2(X2),X2)))\|~v2_unialg_1(X1)\|~v3_unialg_1(X1)\|~v4_unialg_1(X1)\|~l1_unialg_1(X1)\|~m1_subset_1(X3,k1_unialg_2(X1))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(evalgc,[status(thm)],[c_0_45])). cnf(c_0_66, plain, (v1_funct_1(k2_unialg_2(X1,X2,X3))\|v2_struct_0(X1)\|v1_xboole_0(X2)\|~v2_unialg_1(X1)\|~v3_unialg_1(X1)\|~v4_unialg_1(X1)\|~l1_unialg_1(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X3,k1_unialg_2(X1))), inference(split_conjunct,[status(thm)],[c_0_30])). cnf(c_0_67, plain, (v2_margrel1(k2_unialg_2(X1,X2,X3))\|v2_struct_0(X1)\|v1_xboole_0(X2)\|~v2_unialg_1(X1)\|~v3_unialg_1(X1)\|~v4_unialg_1(X1)\|~l1_unialg_1(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X3,k1_unialg_2(X1))), inference(split_conjunct,[status(thm)],[c_0_30])). cnf(c_0_68, plain, (v3_margrel1(k2_unialg_2(X1,X2,X3),X2)\|v2_struct_0(X1)\|v1_xboole_0(X2)\|~v2_unialg_1(X1)\|~v3_unialg_1(X1)\|~v4_unialg_1(X1)\|~l1_unialg_1(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X3,k1_unialg_2(X1))), inference(split_conjunct,[status(thm)],[c_0_30])). cnf(c_0_69, plain, (v2_struct_0(X1)\|v1_xboole_0(X2)\|~v1_xboole_0(k2_unialg_2(X1,X2,X3))\|~v2_unialg_1(X1)\|~v3_unialg_1(X1)\|~v4_unialg_1(X1)\|~l1_unialg_1(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X3,k1_unialg_2(X1))), inference(split_conjunct,[status(thm)],[c_0_30])). cnf(c_0_70, plain, (v1_xboole_0(X2)\|v1_xboole_0(X3)\|k3_xboole_0(k4_finseq_2(X1,X2),k4_finseq_2(X1,X3))=k4_finseq_2(X1,X3)\|~v7_ordinal1(X1)\|~m1_subset_1(X3,k1_zfmisc_1(X2))), inference(split_conjunct,[status(thm)],[c_0_46])). cnf(c_0_71, negated_conjecture, (m1_subset_1(esk3_0,k1_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(esk1_0)),u1_struct_0(esk1_0))))\|~m4_margrel1(k1_unialg_2(esk1_0),u1_struct_0(esk1_0))), inference(sr,[status(thm)],[c_0_47, c_0_48])). cnf(c_0_72, negated_conjecture, (v2_margrel1(esk3_0)\|~m4_margrel1(k1_unialg_2(esk1_0),u1_struct_0(esk1_0))), inference(sr,[status(thm)],[c_0_49, c_0_48])). cnf(c_0_73, plain, (v2_struct_0(X1)\|m4_margrel1(k1_unialg_2(X1),u1_struct_0(X1))\|~v2_unialg_1(X1)\|~v3_unialg_1(X1)\|~v4_unialg_1(X1)\|~l1_unialg_1(X1)), inference(evalgc,[status(thm)],[c_0_50])). cnf(c_0_74, negated_conjecture, (l1_unialg_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_51])). cnf(c_0_75, negated_conjecture, (v4_unialg_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_52])). cnf(c_0_76, negated_conjecture, (v3_unialg_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_53])). cnf(c_0_77, negated_conjecture, (v2_unialg_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_54])). cnf(c_0_78, negated_conjecture, (~v2_struct_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_55])). cnf(c_0_79, negated_conjecture, (v1_funct_1(esk3_0)\|~m4_margrel1(k1_unialg_2(esk1_0),u1_struct_0(esk1_0))), inference(sr,[status(thm)],[c_0_56, c_0_48])). cnf(c_0_80, negated_conjecture, (~m4_margrel1(k1_unialg_2(esk1_0),u1_struct_0(esk1_0))\|~v1_xboole_0(esk3_0)), inference(sr,[status(thm)],[c_0_57, c_0_48])). cnf(c_0_81, negated_conjecture, (v3_margrel1(esk3_0,u1_struct_0(esk1_0))\|v1_xboole_0(u1_struct_0(esk1_0))\|~m4_margrel1(k1_unialg_2(esk1_0),u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_58, c_0_32])])). cnf(c_0_82, plain, (v1_relat_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_59])). cnf(c_0_83, plain, (k2_partfun1(X2,X3,X1,X4)=k5_relat_1(X1,X4)\|~v1_funct_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_60])). fof(c_0_84, plain, ![X39, X40, X41]:((~m5_margrel1(X41,X39,X40)\|m1_subset_1(X41,X40)\|(v1_xboole_0(X39)\|~m4_margrel1(X40,X39)))&(~m1_subset_1(X41,X40)\|m5_margrel1(X41,X39,X40)\|(v1_xboole_0(X39)\|~m4_margrel1(X40,X39)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[redefinition_m5_margrel1])])])])])). cnf(c_0_85, plain, (X1=X2\|v1_xboole_0(X3)\|k4_finseq_2(X1,X3)!=k4_finseq_2(X2,X4)\|~v7_ordinal1(X2)\|~v7_ordinal1(X1)), inference(evalgc,[status(thm)],[c_0_61])). cnf(c_0_86, plain, (v7_ordinal1(k19_margrel1(X1))\|~v2_margrel1(X1)\|~v1_relat_1(X1)\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_62, c_0_63])])). cnf(c_0_87, plain, (k4_finseq_2(k19_margrel1(k2_unialg_2(X1,X2,X3)),X2)=k9_xtuple_0(k2_unialg_2(X1,X2,X3))\|v1_xboole_0(X2)\|v1_xboole_0(k2_unialg_2(X1,X2,X3))\|v2_struct_0(X1)\|~v3_margrel1(k2_unialg_2(X1,X2,X3),X2)\|~v2_margrel1(k2_unialg_2(X1,X2,X3))\|~v1_funct_1(k2_unialg_2(X1,X2,X3))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X3,k1_unialg_2(X1))\|~l1_unialg_1(X1)\|~v4_unialg_1(X1)\|~v3_unialg_1(X1)\|~v2_unialg_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_64, c_0_65])])). cnf(c_0_88, plain, (v2_struct_0(X1)\|v1_xboole_0(X2)\|v1_funct_1(k2_unialg_2(X1,X2,X3))\|~v2_unialg_1(X1)\|~v3_unialg_1(X1)\|~v4_unialg_1(X1)\|~l1_unialg_1(X1)\|~m1_subset_1(X3,k1_unialg_2(X1))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(evalgc,[status(thm)],[c_0_66])). cnf(c_0_89, plain, (v2_struct_0(X1)\|v1_xboole_0(X2)\|v2_margrel1(k2_unialg_2(X1,X2,X3))\|~v2_unialg_1(X1)\|~v3_unialg_1(X1)\|~v4_unialg_1(X1)\|~l1_unialg_1(X1)\|~m1_subset_1(X3,k1_unialg_2(X1))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(evalgc,[status(thm)],[c_0_67])). cnf(c_0_90, plain, (v2_struct_0(X1)\|v1_xboole_0(X2)\|v3_margrel1(k2_unialg_2(X1,X2,X3),X2)\|~v2_unialg_1(X1)\|~v3_unialg_1(X1)\|~v4_unialg_1(X1)\|~l1_unialg_1(X1)\|~m1_subset_1(X3,k1_unialg_2(X1))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(evalgc,[status(thm)],[c_0_68])). cnf(c_0_91, plain, (v2_struct_0(X1)\|v1_xboole_0(X2)\|~v2_unialg_1(X1)\|~v3_unialg_1(X1)\|~v4_unialg_1(X1)\|~l1_unialg_1(X1)\|~m1_subset_1(X3,k1_unialg_2(X1))\|~v1_xboole_0(k2_unialg_2(X1,X2,X3))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(evalgc,[status(thm)],[c_0_69])). fof(c_0_92, plain, ![X28, X29]:(~v1_relat_1(X29)\|k9_xtuple_0(k5_relat_1(X29,X28))=k3_xboole_0(k9_xtuple_0(X29),X28)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t61_relat_1])])). cnf(c_0_93, plain, (k3_xboole_0(k4_finseq_2(X1,X2),k4_finseq_2(X1,X3))=k4_finseq_2(X1,X3)\|v1_xboole_0(X3)\|v1_xboole_0(X2)\|~v7_ordinal1(X1)\|~m1_subset_1(X3,k1_zfmisc_1(X2))), inference(evalgc,[status(thm)],[c_0_70])). cnf(c_0_94, negated_conjecture, (k4_finseq_2(k19_margrel1(esk3_0),u1_struct_0(esk1_0))=k9_xtuple_0(esk3_0)\|v1_xboole_0(esk3_0)\|~v3_margrel1(esk3_0,u1_struct_0(esk1_0))\|~v2_margrel1(esk3_0)\|~v1_funct_1(esk3_0)\|~m4_margrel1(k1_unialg_2(esk1_0),u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_64, c_0_71]), c_0_48])])). cnf(c_0_95, negated_conjecture, (v2_margrel1(esk3_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72, c_0_73]), c_0_74]), c_0_75]), c_0_76]), c_0_77])]), c_0_78])])). cnf(c_0_96, negated_conjecture, (v1_funct_1(esk3_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79, c_0_73]), c_0_74]), c_0_75]), c_0_76]), c_0_77])]), c_0_78])])). cnf(c_0_97, negated_conjecture, (~v1_xboole_0(esk3_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80, c_0_73]), c_0_74]), c_0_75]), c_0_76]), c_0_77])]), c_0_78])])). cnf(c_0_98, negated_conjecture, (v3_margrel1(esk3_0,u1_struct_0(esk1_0))\|~m4_margrel1(k1_unialg_2(esk1_0),u1_struct_0(esk1_0))), inference(sr,[status(thm)],[c_0_81, c_0_48])). cnf(c_0_99, plain, (v1_relat_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(evalgc,[status(thm)],[c_0_82])). fof(c_0_100, plain, ![X25, X26, X27]:(v2_struct_0(X25)\|(~v2_unialg_1(X25)\|(~v3_unialg_1(X25)\|(~v4_unialg_1(X25)\|~l1_unialg_1(X25))))\|(v1_xboole_0(X26)\|~m1_subset_1(X26,k1_zfmisc_1(u1_struct_0(X25)))\|(~m5_margrel1(X27,u1_struct_0(X25),k1_unialg_2(X25))\|(~r2_unialg_2(X25,X26,X27)\|k2_unialg_2(X25,X26,X27)=k2_partfun1(k3_finseq_2(u1_struct_0(X25)),u1_struct_0(X25),X27,k4_finseq_2(k19_margrel1(X27),X26)))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d5_unialg_2])])])])). cnf(c_0_101, plain, (k2_partfun1(X2,X3,X1,X4)=k5_relat_1(X1,X4)\|~v1_funct_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(evalgc,[status(thm)],[c_0_83])). cnf(c_0_102, plain, (m1_subset_1(X1,X3)\|v1_xboole_0(X2)\|~m5_margrel1(X1,X2,X3)\|~m4_margrel1(X3,X2)), inference(split_conjunct,[status(thm)],[c_0_84])). cnf(c_0_103, plain, (X1=k19_margrel1(X2)\|v1_xboole_0(X3)\|k4_finseq_2(X1,X3)!=k4_finseq_2(k19_margrel1(X2),X4)\|~v7_ordinal1(X1)\|~v2_margrel1(X2)\|~v1_funct_1(X2)\|~v1_relat_1(X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_85, c_0_86])])). cnf(c_0_104, plain, (k4_finseq_2(k19_margrel1(k2_unialg_2(X1,X2,X3)),X2)=k9_xtuple_0(k2_unialg_2(X1,X2,X3))\|v1_xboole_0(X2)\|v2_struct_0(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X3,k1_unialg_2(X1))\|~l1_unialg_1(X1)\|~v4_unialg_1(X1)\|~v3_unialg_1(X1)\|~v2_unialg_1(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_87, c_0_88]), c_0_89]), c_0_90]), c_0_91])). cnf(c_0_105, plain, (k9_xtuple_0(k5_relat_1(X1,X2))=k3_xboole_0(k9_xtuple_0(X1),X2)\|~v1_relat_1(X1)), inference(split_conjunct,[status(thm)],[c_0_92])). cnf(c_0_106, plain, (k3_xboole_0(k4_finseq_2(X1,X2),k4_finseq_2(X1,X3))=k4_finseq_2(X1,X3)\|v1_xboole_0(X3)\|~v7_ordinal1(X1)\|~m1_subset_1(X3,k1_zfmisc_1(X2))), inference(csr,[status(thm)],[c_0_93, c_0_33])). cnf(c_0_107, negated_conjecture, (k4_finseq_2(k19_margrel1(esk3_0),u1_struct_0(esk1_0))=k9_xtuple_0(esk3_0)\|~m4_margrel1(k1_unialg_2(esk1_0),u1_struct_0(esk1_0))), inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_94, c_0_95]), c_0_96])]), c_0_97]), c_0_98])). cnf(c_0_108, negated_conjecture, (v1_relat_1(esk3_0)\|~m4_margrel1(k1_unialg_2(esk1_0),u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_99, c_0_71])])). cnf(c_0_109, plain, (v2_struct_0(X1)\|v1_xboole_0(X2)\|k2_unialg_2(X1,X2,X3)=k2_partfun1(k3_finseq_2(u1_struct_0(X1)),u1_struct_0(X1),X3,k4_finseq_2(k19_margrel1(X3),X2))\|~v2_unialg_1(X1)\|~v3_unialg_1(X1)\|~v4_unialg_1(X1)\|~l1_unialg_1(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~m5_margrel1(X3,u1_struct_0(X1),k1_unialg_2(X1))\|~r2_unialg_2(X1,X2,X3)), inference(split_conjunct,[status(thm)],[c_0_100])). cnf(c_0_110, negated_conjecture, (k2_partfun1(k3_finseq_2(u1_struct_0(esk1_0)),u1_struct_0(esk1_0),esk3_0,X1)=k5_relat_1(esk3_0,X1)\|~v1_funct_1(esk3_0)\|~m4_margrel1(k1_unialg_2(esk1_0),u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_101, c_0_71])])). cnf(c_0_111, plain, (v1_xboole_0(X2)\|m1_subset_1(X1,X3)\|~m4_margrel1(X3,X2)\|~m5_margrel1(X1,X2,X3)), inference(evalgc,[status(thm)],[c_0_102])). cnf(c_0_112, plain, (k19_margrel1(k2_unialg_2(X1,X2,X3))=k19_margrel1(X4)\|v1_xboole_0(X2)\|v2_struct_0(X1)\|k9_xtuple_0(k2_unialg_2(X1,X2,X3))!=k4_finseq_2(k19_margrel1(X4),X5)\|~v7_ordinal1(k19_margrel1(k2_unialg_2(X1,X2,X3)))\|~v2_margrel1(X4)\|~v1_funct_1(X4)\|~v1_relat_1(X4)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X3,k1_unialg_2(X1))\|~l1_unialg_1(X1)\|~v4_unialg_1(X1)\|~v3_unialg_1(X1)\|~v2_unialg_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_103, c_0_104])])). cnf(c_0_113, plain, (k3_xboole_0(k9_xtuple_0(X1),X2)=k9_xtuple_0(k5_relat_1(X1,X2))\|~v1_relat_1(X1)), inference(evalgc,[status(thm)],[c_0_105])). cnf(c_0_114, negated_conjecture, (k3_xboole_0(k9_xtuple_0(esk3_0),k4_finseq_2(k19_margrel1(esk3_0),X1))=k4_finseq_2(k19_margrel1(esk3_0),X1)\|v1_xboole_0(X1)\|~v7_ordinal1(k19_margrel1(esk3_0))\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(esk1_0)))\|~m4_margrel1(k1_unialg_2(esk1_0),u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_106, c_0_107])])). cnf(c_0_115, negated_conjecture, (v1_relat_1(esk3_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108, c_0_73]), c_0_74]), c_0_75]), c_0_76]), c_0_77])]), c_0_78])])). cnf(c_0_116, plain, (k2_partfun1(k3_finseq_2(u1_struct_0(X1)),u1_struct_0(X1),X3,k4_finseq_2(k19_margrel1(X3),X2))=k2_unialg_2(X1,X2,X3)\|v2_struct_0(X1)\|v1_xboole_0(X2)\|~v2_unialg_1(X1)\|~v3_unialg_1(X1)\|~v4_unialg_1(X1)\|~l1_unialg_1(X1)\|~r2_unialg_2(X1,X2,X3)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~m5_margrel1(X3,u1_struct_0(X1),k1_unialg_2(X1))), inference(evalgc,[status(thm)],[c_0_109])). cnf(c_0_117, negated_conjecture, (k2_partfun1(k3_finseq_2(u1_struct_0(esk1_0)),u1_struct_0(esk1_0),esk3_0,X1)=k5_relat_1(esk3_0,X1)\|~m4_margrel1(k1_unialg_2(esk1_0),u1_struct_0(esk1_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_110, c_0_96])])). cnf(c_0_118, negated_conjecture, (m1_subset_1(esk3_0,k1_unialg_2(esk1_0))\|v1_xboole_0(u1_struct_0(esk1_0))\|~m4_margrel1(k1_unialg_2(esk1_0),u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_111, c_0_32])])). cnf(c_0_119, plain, (k19_margrel1(k2_unialg_2(X1,X2,X3))=k19_margrel1(X4)\|v1_xboole_0(X2)\|v2_struct_0(X1)\|k9_xtuple_0(k2_unialg_2(X1,X2,X3))!=k4_finseq_2(k19_margrel1(X4),X5)\|~v2_margrel1(X4)\|~v1_funct_1(X4)\|~v1_relat_1(X4)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X3,k1_unialg_2(X1))\|~l1_unialg_1(X1)\|~v4_unialg_1(X1)\|~v3_unialg_1(X1)\|~v2_unialg_1(X1)\|~v2_margrel1(k2_unialg_2(X1,X2,X3))\|~v1_funct_1(k2_unialg_2(X1,X2,X3))\|~v1_relat_1(k2_unialg_2(X1,X2,X3))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_112, c_0_86])])). cnf(c_0_120, plain, (v1_relat_1(k2_unialg_2(X1,X2,X3))\|v1_xboole_0(X2)\|v2_struct_0(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X3,k1_unialg_2(X1))\|~l1_unialg_1(X1)\|~v4_unialg_1(X1)\|~v3_unialg_1(X1)\|~v2_unialg_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_99, c_0_65])])). cnf(c_0_121, negated_conjecture, (k9_xtuple_0(k5_relat_1(esk3_0,k4_finseq_2(k19_margrel1(esk3_0),X1)))=k4_finseq_2(k19_margrel1(esk3_0),X1)\|v1_xboole_0(X1)\|~v7_ordinal1(k19_margrel1(esk3_0))\|~m4_margrel1(k1_unialg_2(esk1_0),u1_struct_0(esk1_0))\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(esk1_0)))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113, c_0_114]), c_0_115])])])). cnf(c_0_122, negated_conjecture, (k5_relat_1(esk3_0,k4_finseq_2(k19_margrel1(esk3_0),X1))=k2_unialg_2(esk1_0,X1,esk3_0)\|v1_xboole_0(X1)\|~r2_unialg_2(esk1_0,X1,esk3_0)\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(esk1_0)))\|~m4_margrel1(k1_unialg_2(esk1_0),u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116, c_0_117]), c_0_32]), c_0_74]), c_0_75]), c_0_76]), c_0_77])]), c_0_78])])). cnf(c_0_123, negated_conjecture, (m1_subset_1(esk3_0,k1_unialg_2(esk1_0))\|~m4_margrel1(k1_unialg_2(esk1_0),u1_struct_0(esk1_0))), inference(sr,[status(thm)],[c_0_118, c_0_48])). cnf(c_0_124, plain, (k19_margrel1(k2_unialg_2(X1,X2,X3))=k19_margrel1(X4)\|v1_xboole_0(X2)\|v2_struct_0(X1)\|k9_xtuple_0(k2_unialg_2(X1,X2,X3))!=k4_finseq_2(k19_margrel1(X4),X5)\|~v2_margrel1(X4)\|~v1_funct_1(X4)\|~v1_relat_1(X4)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X3,k1_unialg_2(X1))\|~l1_unialg_1(X1)\|~v4_unialg_1(X1)\|~v3_unialg_1(X1)\|~v2_unialg_1(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_119, c_0_120]), c_0_88]), c_0_89])). cnf(c_0_125, negated_conjecture, (k9_xtuple_0(k2_unialg_2(esk1_0,X1,esk3_0))=k4_finseq_2(k19_margrel1(esk3_0),X1)\|v1_xboole_0(X1)\|~v7_ordinal1(k19_margrel1(esk3_0))\|~m4_margrel1(k1_unialg_2(esk1_0),u1_struct_0(esk1_0))\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(esk1_0)))\|~r2_unialg_2(esk1_0,X1,esk3_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_121, c_0_122])])). cnf(c_0_126, negated_conjecture, (m1_subset_1(esk3_0,k1_unialg_2(esk1_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123, c_0_73]), c_0_74]), c_0_75]), c_0_76]), c_0_77])]), c_0_78])])). cnf(c_0_127, negated_conjecture, (k19_margrel1(k2_unialg_2(esk1_0,X1,esk3_0))=k19_margrel1(X2)\|v1_xboole_0(X1)\|k4_finseq_2(k19_margrel1(esk3_0),X1)!=k4_finseq_2(k19_margrel1(X2),X3)\|~v2_margrel1(X2)\|~v1_funct_1(X2)\|~v1_relat_1(X2)\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(esk1_0)))\|~v7_ordinal1(k19_margrel1(esk3_0))\|~m4_margrel1(k1_unialg_2(esk1_0),u1_struct_0(esk1_0))\|~r2_unialg_2(esk1_0,X1,esk3_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124, c_0_125]), c_0_126]), c_0_74]), c_0_75]), c_0_76]), c_0_77])]), c_0_78])])). cnf(c_0_128, negated_conjecture, (k19_margrel1(k2_unialg_2(esk1_0,esk2_0,esk3_0))!=k19_margrel1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_17])). cnf(c_0_129, negated_conjecture, (k19_margrel1(k2_unialg_2(esk1_0,X1,esk3_0))=k19_margrel1(X2)\|v1_xboole_0(X1)\|k4_finseq_2(k19_margrel1(esk3_0),X1)!=k4_finseq_2(k19_margrel1(X2),X3)\|~v2_margrel1(X2)\|~v1_funct_1(X2)\|~m4_margrel1(k1_unialg_2(esk1_0),u1_struct_0(esk1_0))\|~v1_relat_1(X2)\|~r2_unialg_2(esk1_0,X1,esk3_0)\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(esk1_0)))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127, c_0_86]), c_0_95]), c_0_96]), c_0_115])])])). cnf(c_0_130, negated_conjecture, (r2_unialg_2(esk1_0,esk2_0,esk3_0)), inference(split_conjunct,[status(thm)],[c_0_17])). cnf(c_0_131, negated_conjecture, (k19_margrel1(k2_unialg_2(esk1_0,esk2_0,esk3_0))!=k19_margrel1(esk3_0)), inference(evalgc,[status(thm)],[c_0_128])). cnf(c_0_132, negated_conjecture, (k19_margrel1(k2_unialg_2(esk1_0,X1,esk3_0))=k19_margrel1(esk3_0)\|v1_xboole_0(X1)\|~m4_margrel1(k1_unialg_2(esk1_0),u1_struct_0(esk1_0))\|~r2_unialg_2(esk1_0,X1,esk3_0)\|~m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(esk1_0)))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_129]), c_0_95]), c_0_96]), c_0_115])])])). cnf(c_0_133, negated_conjecture, (r2_unialg_2(esk1_0,esk2_0,esk3_0)), inference(evalgc,[status(thm)],[c_0_130])). cnf(c_0_134, negated_conjecture, (~m4_margrel1(k1_unialg_2(esk1_0),u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131, c_0_132]), c_0_133]), c_0_34])]), c_0_35])])). cnf(c_0_135, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134, c_0_73]), c_0_74]), c_0_75]), c_0_76]), c_0_77])]), c_0_78]), ['proof']). # SZS output end CNFRefutation	reserve U0,U1,U2,U3 for Universal_Algebra, n for Nat, x,y for set; reserve A for non empty Subset of U0, o for operation of U0, x1,y1 for FinSequence of A; theorem for U1 be Universal_Algebra, A be non empty Subset of U1, o be operation of U1 st A is_closed_on o holds arity (o/.A) = arity o proof let U1 be Universal_Algebra, A be non empty Subset of U1, o be operation of U1; assume A is_closed_on o; then o/.A =o\|((arity o)-tuples_on A) by Def5; then dom (o/.A) = dom o /\ ((arity o)-tuples_on A) by RELAT_1:61; then A1: dom (o/.A) = ((arity o)-tuples_on the carrier of U1) /\ ((arity o) -tuples_on A) by MARGREL1:22 .= (arity o)-tuples_on A by MARGREL1:21; dom (o/.A)=(arity (o/.A))-tuples_on A by MARGREL1:22; hence thesis by A1,FINSEQ_2:110; end;	Convert the following ATP output trace into a readable Mizar proof.
t85_jordan2c	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(dt_k1_partfun1, axiom, ![X1, X2, X3, X4, X5, X6]:(((v1_funct_1(X5)&m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X2))))&(v1_funct_1(X6)&m1_subset_1(X6,k1_zfmisc_1(k2_zfmisc_1(X3,X4)))))=>(v1_funct_1(k1_partfun1(X1,X2,X3,X4,X5,X6))&m1_subset_1(k1_partfun1(X1,X2,X3,X4,X5,X6),k1_zfmisc_1(k2_zfmisc_1(X1,X4))))), file('/scratch/mptp/predsminms1/t85_jordan2c__0', dt_k1_partfun1)). fof(redefinition_k1_partfun1, axiom, ![X1, X2, X3, X4, X5, X6]:(((v1_funct_1(X5)&m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X2))))&(v1_funct_1(X6)&m1_subset_1(X6,k1_zfmisc_1(k2_zfmisc_1(X3,X4)))))=>k1_partfun1(X1,X2,X3,X4,X5,X6)=k3_relat_1(X5,X6)), file('/scratch/mptp/predsminms1/t85_jordan2c__0', redefinition_k1_partfun1)). fof(t84_jordan2c, axiom, ![X1]:(m2_subset_1(X1,k1_numbers,k5_numbers)=>?[X2]:((v1_funct_1(X2)&(v1_funct_2(X2,u1_struct_0(k15_euclid(X1)),u1_struct_0(k3_topmetr))&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k15_euclid(X1)),u1_struct_0(k3_topmetr))))))&(![X3]:(m1_subset_1(X3,u1_struct_0(k15_euclid(X1)))=>k1_seq_1(X2,X3)=k12_euclid(X3))&v5_pre_topc(X2,k15_euclid(X1),k3_topmetr)))), file('/scratch/mptp/predsminms1/t85_jordan2c__0', t84_jordan2c)). fof(t85_jordan2c, conjecture, ![X1]:(m2_subset_1(X1,k1_numbers,k5_numbers)=>![X2]:((v1_funct_1(X2)&(v1_funct_2(X2,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(X1)))&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(X1)))))))=>~((v5_pre_topc(X2,k5_topmetr,k15_euclid(X1))&![X3]:((v1_funct_1(X3)&(v1_funct_2(X3,u1_struct_0(k5_topmetr),u1_struct_0(k3_topmetr))&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_topmetr),u1_struct_0(k3_topmetr))))))=>~((![X4]:(m1_subset_1(X4,u1_struct_0(k5_topmetr))=>k1_seq_1(X3,X4)=k12_euclid(k3_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(X1)),X2,X4)))&v5_pre_topc(X3,k5_topmetr,k3_topmetr)))))))), file('/scratch/mptp/predsminms1/t85_jordan2c__0', t85_jordan2c)). fof(cc18_valued_0, axiom, ![X1, X2]:(v3_membered(X2)=>![X3]:(m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))=>v3_valued_0(X3))), file('/scratch/mptp/predsminms1/t85_jordan2c__0', cc18_valued_0)). fof(redefinition_k3_funct_2, axiom, ![X1, X2, X3, X4]:((~(v1_xboole_0(X1))&((v1_funct_1(X3)&(v1_funct_2(X3,X1,X2)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))))&m1_subset_1(X4,X1)))=>k3_funct_2(X1,X2,X3,X4)=k1_funct_1(X3,X4)), file('/scratch/mptp/predsminms1/t85_jordan2c__0', redefinition_k3_funct_2)). fof(redefinition_k1_seq_1, axiom, ![X1, X2]:((v1_relat_1(X1)&(v1_funct_1(X1)&v3_valued_0(X1)))=>k1_seq_1(X1,X2)=k1_funct_1(X1,X2)), file('/scratch/mptp/predsminms1/t85_jordan2c__0', redefinition_k1_seq_1)). fof(cc1_relset_1, axiom, ![X1, X2, X3]:(m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))=>v1_relat_1(X3)), file('/scratch/mptp/predsminms1/t85_jordan2c__0', cc1_relset_1)). fof(cc2_relset_1, axiom, ![X1, X2, X3]:(m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))=>(v4_relat_1(X3,X1)&v5_relat_1(X3,X2))), file('/scratch/mptp/predsminms1/t85_jordan2c__0', cc2_relset_1)). fof(d1_funct_2, axiom, ![X1, X2, X3]:(m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))=>((~(X2=k1_xboole_0)=>(v1_funct_2(X3,X1,X2)<=>X1=k1_relset_1(X1,X3)))&(X2=k1_xboole_0=>(v1_funct_2(X3,X1,X2)<=>X3=k1_xboole_0)))), file('/scratch/mptp/predsminms1/t85_jordan2c__0', d1_funct_2)). fof(redefinition_k1_relset_1, axiom, ![X1, X2]:((v1_relat_1(X2)&v4_relat_1(X2,X1))=>k1_relset_1(X1,X2)=k9_xtuple_0(X2)), file('/scratch/mptp/predsminms1/t85_jordan2c__0', redefinition_k1_relset_1)). fof(t13_funct_1, axiom, ![X1, X2]:((v1_relat_1(X2)&v1_funct_1(X2))=>![X3]:((v1_relat_1(X3)&v1_funct_1(X3))=>(r2_hidden(X1,k9_xtuple_0(X2))=>k1_funct_1(k3_relat_1(X2,X3),X1)=k1_funct_1(X3,k1_funct_1(X2,X1))))), file('/scratch/mptp/predsminms1/t85_jordan2c__0', t13_funct_1)). fof(dt_k3_funct_2, axiom, ![X1, X2, X3, X4]:((~(v1_xboole_0(X1))&((v1_funct_1(X3)&(v1_funct_2(X3,X1,X2)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))))&m1_subset_1(X4,X1)))=>m1_subset_1(k3_funct_2(X1,X2,X3,X4),X2)), file('/scratch/mptp/predsminms1/t85_jordan2c__0', dt_k3_funct_2)). fof(t2_subset, axiom, ![X1, X2]:(m1_subset_1(X1,X2)=>(v1_xboole_0(X2)\|r2_hidden(X1,X2))), file('/scratch/mptp/predsminms1/t85_jordan2c__0', t2_subset)). fof(fc1_borsuk_1, axiom, ![X1, X2, X3, X4, X5]:(((~(v2_struct_0(X1))&(v2_pre_topc(X1)&l1_pre_topc(X1)))&((~(v2_struct_0(X2))&(v2_pre_topc(X2)&l1_pre_topc(X2)))&((~(v2_struct_0(X3))&(v2_pre_topc(X3)&l1_pre_topc(X3)))&((v1_funct_1(X4)&(v1_funct_2(X4,u1_struct_0(X1),u1_struct_0(X2))&(v5_pre_topc(X4,X1,X2)&m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X2)))))))&(v1_funct_1(X5)&(v1_funct_2(X5,u1_struct_0(X2),u1_struct_0(X3))&(v5_pre_topc(X5,X2,X3)&m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X2),u1_struct_0(X3)))))))))))=>(v1_funct_1(k3_relat_1(X4,X5))&(v1_funct_2(k3_relat_1(X4,X5),u1_struct_0(X1),u1_struct_0(X3))&v5_pre_topc(k3_relat_1(X4,X5),X1,X3)))), file('/scratch/mptp/predsminms1/t85_jordan2c__0', fc1_borsuk_1)). fof(fc2_topmetr, axiom, (~(v2_struct_0(k3_topmetr))&(v1_pre_topc(k3_topmetr)&v2_pre_topc(k3_topmetr))), file('/scratch/mptp/predsminms1/t85_jordan2c__0', fc2_topmetr)). fof(dt_k3_topmetr, axiom, (v2_pre_topc(k3_topmetr)&l1_pre_topc(k3_topmetr)), file('/scratch/mptp/predsminms1/t85_jordan2c__0', dt_k3_topmetr)). fof(fc9_borsuk_1, axiom, (~(v2_struct_0(k17_borsuk_1))&(v1_pre_topc(k17_borsuk_1)&v2_pre_topc(k17_borsuk_1))), file('/scratch/mptp/predsminms1/t85_jordan2c__0', fc9_borsuk_1)). fof(dt_k17_borsuk_1, axiom, l1_pre_topc(k17_borsuk_1), file('/scratch/mptp/predsminms1/t85_jordan2c__0', dt_k17_borsuk_1)). fof(redefinition_k5_topmetr, axiom, k5_topmetr=k17_borsuk_1, file('/scratch/mptp/predsminms1/t85_jordan2c__0', redefinition_k5_topmetr)). fof(redefinition_m2_subset_1, axiom, ![X1, X2]:((~(v1_xboole_0(X1))&(~(v1_xboole_0(X2))&m1_subset_1(X2,k1_zfmisc_1(X1))))=>![X3]:(m2_subset_1(X3,X1,X2)<=>m1_subset_1(X3,X2))), file('/scratch/mptp/predsminms1/t85_jordan2c__0', redefinition_m2_subset_1)). fof(cc1_subset_1, axiom, ![X1]:(v1_xboole_0(X1)=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(X1))=>v1_xboole_0(X2))), file('/scratch/mptp/predsminms1/t85_jordan2c__0', cc1_subset_1)). fof(fc7_card_1, axiom, ~(v1_finset_1(k4_ordinal1)), file('/scratch/mptp/predsminms1/t85_jordan2c__0', fc7_card_1)). fof(redefinition_k5_numbers, axiom, k5_numbers=k4_ordinal1, file('/scratch/mptp/predsminms1/t85_jordan2c__0', redefinition_k5_numbers)). fof(cc1_finset_1, axiom, ![X1]:(v1_xboole_0(X1)=>v1_finset_1(X1)), file('/scratch/mptp/predsminms1/t85_jordan2c__0', cc1_finset_1)). fof(fc4_topmetr, axiom, ![X1]:((v3_topmetr(X1)&l1_struct_0(X1))=>v3_membered(u1_struct_0(X1))), file('/scratch/mptp/predsminms1/t85_jordan2c__0', fc4_topmetr)). fof(dt_k5_numbers, axiom, m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)), file('/scratch/mptp/predsminms1/t85_jordan2c__0', dt_k5_numbers)). fof(fc5_topmetr, axiom, (v2_pre_topc(k3_topmetr)&v3_topmetr(k3_topmetr)), file('/scratch/mptp/predsminms1/t85_jordan2c__0', fc5_topmetr)). fof(dt_l1_pre_topc, axiom, ![X1]:(l1_pre_topc(X1)=>l1_struct_0(X1)), file('/scratch/mptp/predsminms1/t85_jordan2c__0', dt_l1_pre_topc)). fof(cc17_membered, axiom, ![X1]:(v6_membered(X1)=>![X2]:(m1_subset_1(X2,X1)=>v7_ordinal1(X2))), file('/scratch/mptp/predsminms1/t85_jordan2c__0', cc17_membered)). fof(fc6_membered, axiom, v6_membered(k4_ordinal1), file('/scratch/mptp/predsminms1/t85_jordan2c__0', fc6_membered)). fof(fc5_euclid, axiom, ![X1]:(v7_ordinal1(X1)=>(~(v2_struct_0(k15_euclid(X1)))&v5_rltopsp1(k15_euclid(X1)))), file('/scratch/mptp/predsminms1/t85_jordan2c__0', fc5_euclid)). fof(dt_l1_rltopsp1, axiom, ![X1]:(l1_rltopsp1(X1)=>(l1_rlvect_1(X1)&l1_pre_topc(X1))), file('/scratch/mptp/predsminms1/t85_jordan2c__0', dt_l1_rltopsp1)). fof(dt_k15_euclid, axiom, ![X1]:(v7_ordinal1(X1)=>(v5_rltopsp1(k15_euclid(X1))&l1_rltopsp1(k15_euclid(X1)))), file('/scratch/mptp/predsminms1/t85_jordan2c__0', dt_k15_euclid)). fof(fc2_struct_0, axiom, ![X1]:((~(v2_struct_0(X1))&l1_struct_0(X1))=>~(v1_xboole_0(u1_struct_0(X1)))), file('/scratch/mptp/predsminms1/t85_jordan2c__0', fc2_struct_0)). fof(fc6_euclid, axiom, ![X1]:(v7_ordinal1(X1)=>(v2_pre_topc(k15_euclid(X1))&(v13_algstr_0(k15_euclid(X1))&(v2_rlvect_1(k15_euclid(X1))&(v3_rlvect_1(k15_euclid(X1))&(v4_rlvect_1(k15_euclid(X1))&(v5_rlvect_1(k15_euclid(X1))&(v6_rlvect_1(k15_euclid(X1))&(v7_rlvect_1(k15_euclid(X1))&(v8_rlvect_1(k15_euclid(X1))&v5_rltopsp1(k15_euclid(X1)))))))))))), file('/scratch/mptp/predsminms1/t85_jordan2c__0', fc6_euclid)). fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0), file('/scratch/mptp/predsminms1/t85_jordan2c__0', fc1_xboole_0)). fof(c_0_37, plain, ![X51, X52, X53, X54, X55, X56]:((v1_funct_1(k1_partfun1(X51,X52,X53,X54,X55,X56))\|(~v1_funct_1(X55)\|~m1_subset_1(X55,k1_zfmisc_1(k2_zfmisc_1(X51,X52)))\|(~v1_funct_1(X56)\|~m1_subset_1(X56,k1_zfmisc_1(k2_zfmisc_1(X53,X54))))))&(m1_subset_1(k1_partfun1(X51,X52,X53,X54,X55,X56),k1_zfmisc_1(k2_zfmisc_1(X51,X54)))\|(~v1_funct_1(X55)\|~m1_subset_1(X55,k1_zfmisc_1(k2_zfmisc_1(X51,X52)))\|(~v1_funct_1(X56)\|~m1_subset_1(X56,k1_zfmisc_1(k2_zfmisc_1(X53,X54))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_partfun1])])])). fof(c_0_38, plain, ![X45, X46, X47, X48, X49, X50]:(~v1_funct_1(X49)\|~m1_subset_1(X49,k1_zfmisc_1(k2_zfmisc_1(X45,X46)))\|(~v1_funct_1(X50)\|~m1_subset_1(X50,k1_zfmisc_1(k2_zfmisc_1(X47,X48))))\|k1_partfun1(X45,X46,X47,X48,X49,X50)=k3_relat_1(X49,X50)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k1_partfun1])])). cnf(c_0_39, plain, (m1_subset_1(k1_partfun1(X1,X2,X3,X4,X5,X6),k1_zfmisc_1(k2_zfmisc_1(X1,X4)))\|~v1_funct_1(X5)\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X6)\|~m1_subset_1(X6,k1_zfmisc_1(k2_zfmisc_1(X3,X4)))), inference(split_conjunct,[status(thm)],[c_0_37])). cnf(c_0_40, plain, (k1_partfun1(X2,X3,X5,X6,X1,X4)=k3_relat_1(X1,X4)\|~v1_funct_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))\|~v1_funct_1(X4)\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X5,X6)))), inference(split_conjunct,[status(thm)],[c_0_38])). fof(c_0_41, plain, ![X11, X13]:(((v1_funct_1(esk4_1(X11))\|~m2_subset_1(X11,k1_numbers,k5_numbers))&((v1_funct_2(esk4_1(X11),u1_struct_0(k15_euclid(X11)),u1_struct_0(k3_topmetr))\|~m2_subset_1(X11,k1_numbers,k5_numbers))&(m1_subset_1(esk4_1(X11),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k15_euclid(X11)),u1_struct_0(k3_topmetr))))\|~m2_subset_1(X11,k1_numbers,k5_numbers))))&((~m1_subset_1(X13,u1_struct_0(k15_euclid(X11)))\|k1_seq_1(esk4_1(X11),X13)=k12_euclid(X13)\|~m2_subset_1(X11,k1_numbers,k5_numbers))&(v5_pre_topc(esk4_1(X11),k15_euclid(X11),k3_topmetr)\|~m2_subset_1(X11,k1_numbers,k5_numbers)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t84_jordan2c])])])])])). cnf(c_0_42, plain, (m1_subset_1(k1_partfun1(X1,X2,X3,X4,X5,X6),k1_zfmisc_1(k2_zfmisc_1(X1,X4)))\|~v1_funct_1(X6)\|~v1_funct_1(X5)\|~m1_subset_1(X6,k1_zfmisc_1(k2_zfmisc_1(X3,X4)))\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(evalgc,[status(thm)],[c_0_39])). cnf(c_0_43, plain, (k1_partfun1(X2,X3,X5,X6,X1,X4)=k3_relat_1(X1,X4)\|~v1_funct_1(X4)\|~v1_funct_1(X1)\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X5,X6)))\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(evalgc,[status(thm)],[c_0_40])). cnf(c_0_44, plain, (m1_subset_1(esk4_1(X1),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k15_euclid(X1)),u1_struct_0(k3_topmetr))))\|~m2_subset_1(X1,k1_numbers,k5_numbers)), inference(split_conjunct,[status(thm)],[c_0_41])). fof(c_0_45, negated_conjecture, ~(![X1]:(m2_subset_1(X1,k1_numbers,k5_numbers)=>![X2]:((v1_funct_1(X2)&(v1_funct_2(X2,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(X1)))&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(X1)))))))=>~((v5_pre_topc(X2,k5_topmetr,k15_euclid(X1))&![X3]:((v1_funct_1(X3)&(v1_funct_2(X3,u1_struct_0(k5_topmetr),u1_struct_0(k3_topmetr))&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_topmetr),u1_struct_0(k3_topmetr))))))=>~((![X4]:(m1_subset_1(X4,u1_struct_0(k5_topmetr))=>k1_seq_1(X3,X4)=k12_euclid(k3_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(X1)),X2,X4)))&v5_pre_topc(X3,k5_topmetr,k3_topmetr))))))))), inference(assume_negation,[status(cth)],[t85_jordan2c])). cnf(c_0_46, plain, (m1_subset_1(k3_relat_1(X5,X6),k1_zfmisc_1(k2_zfmisc_1(X1,X4)))\|~m1_subset_1(X6,k1_zfmisc_1(k2_zfmisc_1(X3,X4)))\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X6)\|~v1_funct_1(X5)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_42, c_0_43])])). cnf(c_0_47, plain, (m1_subset_1(esk4_1(X1),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k15_euclid(X1)),u1_struct_0(k3_topmetr))))\|~m2_subset_1(X1,k1_numbers,k5_numbers)), inference(evalgc,[status(thm)],[c_0_44])). cnf(c_0_48, plain, (v1_funct_1(esk4_1(X1))\|~m2_subset_1(X1,k1_numbers,k5_numbers)), inference(split_conjunct,[status(thm)],[c_0_41])). fof(c_0_49, negated_conjecture, ![X9]:(m2_subset_1(esk1_0,k1_numbers,k5_numbers)&((v1_funct_1(esk2_0)&(v1_funct_2(esk2_0,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(esk1_0)))&m1_subset_1(esk2_0,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(esk1_0)))))))&(v5_pre_topc(esk2_0,k5_topmetr,k15_euclid(esk1_0))&((m1_subset_1(esk3_1(X9),u1_struct_0(k5_topmetr))\|~v5_pre_topc(X9,k5_topmetr,k3_topmetr)\|(~v1_funct_1(X9)\|(~v1_funct_2(X9,u1_struct_0(k5_topmetr),u1_struct_0(k3_topmetr))\|~m1_subset_1(X9,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_topmetr),u1_struct_0(k3_topmetr)))))))&(k1_seq_1(X9,esk3_1(X9))!=k12_euclid(k3_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(esk1_0)),esk2_0,esk3_1(X9)))\|~v5_pre_topc(X9,k5_topmetr,k3_topmetr)\|(~v1_funct_1(X9)\|(~v1_funct_2(X9,u1_struct_0(k5_topmetr),u1_struct_0(k3_topmetr))\|~m1_subset_1(X9,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_topmetr),u1_struct_0(k3_topmetr))))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_45])])])])])). cnf(c_0_50, plain, (v1_funct_1(k1_partfun1(X1,X2,X3,X4,X5,X6))\|~v1_funct_1(X5)\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X6)\|~m1_subset_1(X6,k1_zfmisc_1(k2_zfmisc_1(X3,X4)))), inference(split_conjunct,[status(thm)],[c_0_37])). fof(c_0_51, plain, ![X57, X58, X59]:(~v3_membered(X58)\|(~m1_subset_1(X59,k1_zfmisc_1(k2_zfmisc_1(X57,X58)))\|v3_valued_0(X59))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc18_valued_0])])])). cnf(c_0_52, plain, (m1_subset_1(k3_relat_1(X1,esk4_1(X2)),k1_zfmisc_1(k2_zfmisc_1(X3,u1_struct_0(k3_topmetr))))\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X3,X4)))\|~v1_funct_1(esk4_1(X2))\|~v1_funct_1(X1)\|~m2_subset_1(X2,k1_numbers,k5_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_46, c_0_47])])). cnf(c_0_53, plain, (v1_funct_1(esk4_1(X1))\|~m2_subset_1(X1,k1_numbers,k5_numbers)), inference(evalgc,[status(thm)],[c_0_48])). cnf(c_0_54, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(esk1_0)))))), inference(split_conjunct,[status(thm)],[c_0_49])). cnf(c_0_55, negated_conjecture, (v1_funct_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_49])). cnf(c_0_56, plain, (v1_funct_1(k1_partfun1(X1,X2,X3,X4,X5,X6))\|~v1_funct_1(X6)\|~v1_funct_1(X5)\|~m1_subset_1(X6,k1_zfmisc_1(k2_zfmisc_1(X3,X4)))\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(evalgc,[status(thm)],[c_0_50])). fof(c_0_57, plain, ![X19, X20, X21, X22]:(v1_xboole_0(X19)\|(~v1_funct_1(X21)\|(~v1_funct_2(X21,X19,X20)\|~m1_subset_1(X21,k1_zfmisc_1(k2_zfmisc_1(X19,X20))))\|~m1_subset_1(X22,X19))\|k3_funct_2(X19,X20,X21,X22)=k1_funct_1(X21,X22)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[redefinition_k3_funct_2])])])). fof(c_0_58, plain, ![X30, X31]:(~v1_relat_1(X30)\|(~v1_funct_1(X30)\|~v3_valued_0(X30))\|k1_seq_1(X30,X31)=k1_funct_1(X30,X31)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k1_seq_1])])). cnf(c_0_59, plain, (v3_valued_0(X2)\|~v3_membered(X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_51])). cnf(c_0_60, plain, (m1_subset_1(k3_relat_1(X1,esk4_1(X2)),k1_zfmisc_1(k2_zfmisc_1(X3,u1_struct_0(k3_topmetr))))\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X3,X4)))\|~v1_funct_1(X1)\|~m2_subset_1(X2,k1_numbers,k5_numbers)), inference(csr,[status(thm)],[c_0_52, c_0_53])). cnf(c_0_61, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(esk1_0)))))), inference(evalgc,[status(thm)],[c_0_54])). cnf(c_0_62, negated_conjecture, (v1_funct_1(esk2_0)), inference(evalgc,[status(thm)],[c_0_55])). cnf(c_0_63, plain, (v1_funct_1(k3_relat_1(X5,X6))\|~m1_subset_1(X6,k1_zfmisc_1(k2_zfmisc_1(X3,X4)))\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X6)\|~v1_funct_1(X5)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_56, c_0_43])])). fof(c_0_64, plain, ![X27, X28, X29]:(~m1_subset_1(X29,k1_zfmisc_1(k2_zfmisc_1(X27,X28)))\|v1_relat_1(X29)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relset_1])])). fof(c_0_65, plain, ![X35, X36, X37]:((v4_relat_1(X37,X35)\|~m1_subset_1(X37,k1_zfmisc_1(k2_zfmisc_1(X35,X36))))&(v5_relat_1(X37,X36)\|~m1_subset_1(X37,k1_zfmisc_1(k2_zfmisc_1(X35,X36))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_relset_1])])])). cnf(c_0_66, negated_conjecture, (k1_seq_1(X1,esk3_1(X1))!=k12_euclid(k3_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(esk1_0)),esk2_0,esk3_1(X1)))\|~v5_pre_topc(X1,k5_topmetr,k3_topmetr)\|~v1_funct_1(X1)\|~v1_funct_2(X1,u1_struct_0(k5_topmetr),u1_struct_0(k3_topmetr))\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_topmetr),u1_struct_0(k3_topmetr))))), inference(split_conjunct,[status(thm)],[c_0_49])). cnf(c_0_67, plain, (v1_xboole_0(X1)\|k3_funct_2(X1,X3,X2,X4)=k1_funct_1(X2,X4)\|~v1_funct_1(X2)\|~v1_funct_2(X2,X1,X3)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))\|~m1_subset_1(X4,X1)), inference(split_conjunct,[status(thm)],[c_0_57])). cnf(c_0_68, negated_conjecture, (v1_funct_2(esk2_0,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(esk1_0)))), inference(split_conjunct,[status(thm)],[c_0_49])). cnf(c_0_69, plain, (k1_seq_1(X1,X2)=k1_funct_1(X1,X2)\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v3_valued_0(X1)), inference(split_conjunct,[status(thm)],[c_0_58])). cnf(c_0_70, plain, (v3_valued_0(X2)\|~v3_membered(X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X3,X1)))), inference(evalgc,[status(thm)],[c_0_59])). cnf(c_0_71, negated_conjecture, (m1_subset_1(k3_relat_1(esk2_0,esk4_1(X1)),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_topmetr),u1_struct_0(k3_topmetr))))\|~m2_subset_1(X1,k1_numbers,k5_numbers)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60, c_0_61]), c_0_62])])])). cnf(c_0_72, plain, (v1_funct_1(k3_relat_1(X1,esk4_1(X2)))\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X3,X4)))\|~v1_funct_1(esk4_1(X2))\|~v1_funct_1(X1)\|~m2_subset_1(X2,k1_numbers,k5_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_63, c_0_47])])). cnf(c_0_73, plain, (v1_relat_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_64])). fof(c_0_74, plain, ![X32, X33, X34]:(((~v1_funct_2(X34,X32,X33)\|X32=k1_relset_1(X32,X34)\|X33=k1_xboole_0\|~m1_subset_1(X34,k1_zfmisc_1(k2_zfmisc_1(X32,X33))))&(X32!=k1_relset_1(X32,X34)\|v1_funct_2(X34,X32,X33)\|X33=k1_xboole_0\|~m1_subset_1(X34,k1_zfmisc_1(k2_zfmisc_1(X32,X33)))))&((~v1_funct_2(X34,X32,X33)\|X34=k1_xboole_0\|X33!=k1_xboole_0\|~m1_subset_1(X34,k1_zfmisc_1(k2_zfmisc_1(X32,X33))))&(X34!=k1_xboole_0\|v1_funct_2(X34,X32,X33)\|X33!=k1_xboole_0\|~m1_subset_1(X34,k1_zfmisc_1(k2_zfmisc_1(X32,X33)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d1_funct_2])])])])). fof(c_0_75, plain, ![X38, X39]:(~v1_relat_1(X39)\|~v4_relat_1(X39,X38)\|k1_relset_1(X38,X39)=k9_xtuple_0(X39)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k1_relset_1])])). cnf(c_0_76, plain, (v4_relat_1(X1,X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_65])). cnf(c_0_77, negated_conjecture, (k1_seq_1(X1,esk3_1(X1))!=k12_euclid(k3_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(esk1_0)),esk2_0,esk3_1(X1)))\|~v1_funct_1(X1)\|~v5_pre_topc(X1,k5_topmetr,k3_topmetr)\|~v1_funct_2(X1,u1_struct_0(k5_topmetr),u1_struct_0(k3_topmetr))\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_topmetr),u1_struct_0(k3_topmetr))))), inference(evalgc,[status(thm)],[c_0_66])). cnf(c_0_78, plain, (k3_funct_2(X1,X3,X2,X4)=k1_funct_1(X2,X4)\|v1_xboole_0(X1)\|~v1_funct_1(X2)\|~m1_subset_1(X4,X1)\|~v1_funct_2(X2,X1,X3)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))), inference(evalgc,[status(thm)],[c_0_67])). cnf(c_0_79, negated_conjecture, (v1_funct_2(esk2_0,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(esk1_0)))), inference(evalgc,[status(thm)],[c_0_68])). cnf(c_0_80, negated_conjecture, (m1_subset_1(esk3_1(X1),u1_struct_0(k5_topmetr))\|~v5_pre_topc(X1,k5_topmetr,k3_topmetr)\|~v1_funct_1(X1)\|~v1_funct_2(X1,u1_struct_0(k5_topmetr),u1_struct_0(k3_topmetr))\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_topmetr),u1_struct_0(k3_topmetr))))), inference(split_conjunct,[status(thm)],[c_0_49])). cnf(c_0_81, plain, (k1_seq_1(X1,X2)=k1_funct_1(X1,X2)\|~v1_funct_1(X1)\|~v1_relat_1(X1)\|~v3_valued_0(X1)), inference(evalgc,[status(thm)],[c_0_69])). cnf(c_0_82, negated_conjecture, (v3_valued_0(k3_relat_1(esk2_0,esk4_1(X1)))\|~v3_membered(u1_struct_0(k3_topmetr))\|~m2_subset_1(X1,k1_numbers,k5_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_70, c_0_71])])). cnf(c_0_83, plain, (v1_funct_1(k3_relat_1(X1,esk4_1(X2)))\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X3,X4)))\|~v1_funct_1(X1)\|~m2_subset_1(X2,k1_numbers,k5_numbers)), inference(csr,[status(thm)],[c_0_72, c_0_53])). cnf(c_0_84, plain, (v1_relat_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(evalgc,[status(thm)],[c_0_73])). cnf(c_0_85, plain, (X2=k1_relset_1(X2,X1)\|X3=k1_xboole_0\|~v1_funct_2(X1,X2,X3)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_74])). cnf(c_0_86, plain, (k1_relset_1(X2,X1)=k9_xtuple_0(X1)\|~v1_relat_1(X1)\|~v4_relat_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_75])). cnf(c_0_87, plain, (v4_relat_1(X1,X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(evalgc,[status(thm)],[c_0_76])). cnf(c_0_88, negated_conjecture, (v1_xboole_0(u1_struct_0(k5_topmetr))\|k1_seq_1(X1,esk3_1(X1))!=k12_euclid(k1_funct_1(esk2_0,esk3_1(X1)))\|~v5_pre_topc(X1,k5_topmetr,k3_topmetr)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_topmetr),u1_struct_0(k3_topmetr))))\|~v1_funct_2(X1,u1_struct_0(k5_topmetr),u1_struct_0(k3_topmetr))\|~v1_funct_1(X1)\|~m1_subset_1(esk3_1(X1),u1_struct_0(k5_topmetr))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77, c_0_78]), c_0_61]), c_0_79]), c_0_62])])])). cnf(c_0_89, negated_conjecture, (m1_subset_1(esk3_1(X1),u1_struct_0(k5_topmetr))\|~v1_funct_1(X1)\|~v5_pre_topc(X1,k5_topmetr,k3_topmetr)\|~v1_funct_2(X1,u1_struct_0(k5_topmetr),u1_struct_0(k3_topmetr))\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_topmetr),u1_struct_0(k3_topmetr))))), inference(evalgc,[status(thm)],[c_0_80])). cnf(c_0_90, negated_conjecture, (k1_seq_1(k3_relat_1(esk2_0,esk4_1(X1)),X2)=k1_funct_1(k3_relat_1(esk2_0,esk4_1(X1)),X2)\|~v1_relat_1(k3_relat_1(esk2_0,esk4_1(X1)))\|~v1_funct_1(k3_relat_1(esk2_0,esk4_1(X1)))\|~v3_membered(u1_struct_0(k3_topmetr))\|~m2_subset_1(X1,k1_numbers,k5_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_81, c_0_82])])). cnf(c_0_91, negated_conjecture, (v1_funct_1(k3_relat_1(esk2_0,esk4_1(X1)))\|~m2_subset_1(X1,k1_numbers,k5_numbers)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83, c_0_61]), c_0_62])])])). cnf(c_0_92, negated_conjecture, (v1_relat_1(k3_relat_1(esk2_0,esk4_1(X1)))\|~m2_subset_1(X1,k1_numbers,k5_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_84, c_0_71])])). fof(c_0_93, plain, ![X40, X41, X42]:(~v1_relat_1(X41)\|~v1_funct_1(X41)\|(~v1_relat_1(X42)\|~v1_funct_1(X42)\|(~r2_hidden(X40,k9_xtuple_0(X41))\|k1_funct_1(k3_relat_1(X41,X42),X40)=k1_funct_1(X42,k1_funct_1(X41,X40))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t13_funct_1])])])). cnf(c_0_94, plain, (X3=k1_xboole_0\|k1_relset_1(X2,X1)=X2\|~v1_funct_2(X1,X2,X3)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(evalgc,[status(thm)],[c_0_85])). cnf(c_0_95, plain, (k1_relset_1(X2,X1)=k9_xtuple_0(X1)\|~v1_relat_1(X1)\|~v4_relat_1(X1,X2)), inference(evalgc,[status(thm)],[c_0_86])). cnf(c_0_96, negated_conjecture, (v4_relat_1(esk2_0,u1_struct_0(k5_topmetr))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_87, c_0_61])])). cnf(c_0_97, negated_conjecture, (v1_relat_1(esk2_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_84, c_0_61])])). cnf(c_0_98, negated_conjecture, (v1_xboole_0(u1_struct_0(k5_topmetr))\|k1_seq_1(X1,esk3_1(X1))!=k12_euclid(k1_funct_1(esk2_0,esk3_1(X1)))\|~v5_pre_topc(X1,k5_topmetr,k3_topmetr)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_topmetr),u1_struct_0(k3_topmetr))))\|~v1_funct_2(X1,u1_struct_0(k5_topmetr),u1_struct_0(k3_topmetr))\|~v1_funct_1(X1)), inference(csr,[status(thm)],[c_0_88, c_0_89])). cnf(c_0_99, negated_conjecture, (k1_seq_1(k3_relat_1(esk2_0,esk4_1(X1)),X2)=k1_funct_1(k3_relat_1(esk2_0,esk4_1(X1)),X2)\|~v3_membered(u1_struct_0(k3_topmetr))\|~m2_subset_1(X1,k1_numbers,k5_numbers)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_90, c_0_91]), c_0_92])). cnf(c_0_100, plain, (k1_funct_1(k3_relat_1(X1,X2),X3)=k1_funct_1(X2,k1_funct_1(X1,X3))\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~r2_hidden(X3,k9_xtuple_0(X1))), inference(split_conjunct,[status(thm)],[c_0_93])). cnf(c_0_101, negated_conjecture, (k1_relset_1(u1_struct_0(k5_topmetr),esk2_0)=u1_struct_0(k5_topmetr)\|u1_struct_0(k15_euclid(esk1_0))=k1_xboole_0), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94, c_0_61]), c_0_79])])])). cnf(c_0_102, negated_conjecture, (k1_relset_1(u1_struct_0(k5_topmetr),esk2_0)=k9_xtuple_0(esk2_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95, c_0_96]), c_0_97])])])). cnf(c_0_103, negated_conjecture, (v1_xboole_0(u1_struct_0(k5_topmetr))\|k1_funct_1(k3_relat_1(esk2_0,esk4_1(X1)),esk3_1(k3_relat_1(esk2_0,esk4_1(X1))))!=k12_euclid(k1_funct_1(esk2_0,esk3_1(k3_relat_1(esk2_0,esk4_1(X1)))))\|~v5_pre_topc(k3_relat_1(esk2_0,esk4_1(X1)),k5_topmetr,k3_topmetr)\|~m1_subset_1(k3_relat_1(esk2_0,esk4_1(X1)),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_topmetr),u1_struct_0(k3_topmetr))))\|~v1_funct_2(k3_relat_1(esk2_0,esk4_1(X1)),u1_struct_0(k5_topmetr),u1_struct_0(k3_topmetr))\|~v1_funct_1(k3_relat_1(esk2_0,esk4_1(X1)))\|~v3_membered(u1_struct_0(k3_topmetr))\|~m2_subset_1(X1,k1_numbers,k5_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_98, c_0_99])])). cnf(c_0_104, plain, (k1_funct_1(k3_relat_1(X1,X2),X3)=k1_funct_1(X2,k1_funct_1(X1,X3))\|~v1_funct_1(X2)\|~v1_funct_1(X1)\|~v1_relat_1(X2)\|~v1_relat_1(X1)\|~r2_hidden(X3,k9_xtuple_0(X1))), inference(evalgc,[status(thm)],[c_0_100])). cnf(c_0_105, negated_conjecture, (k9_xtuple_0(esk2_0)=u1_struct_0(k5_topmetr)\|u1_struct_0(k15_euclid(esk1_0))=k1_xboole_0), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_101, c_0_102])])). cnf(c_0_106, plain, (v3_valued_0(esk4_1(X1))\|~v3_membered(u1_struct_0(k3_topmetr))\|~m2_subset_1(X1,k1_numbers,k5_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_70, c_0_47])])). fof(c_0_107, plain, ![X23, X24, X25, X26]:(v1_xboole_0(X23)\|(~v1_funct_1(X25)\|(~v1_funct_2(X25,X23,X24)\|~m1_subset_1(X25,k1_zfmisc_1(k2_zfmisc_1(X23,X24))))\|~m1_subset_1(X26,X23))\|m1_subset_1(k3_funct_2(X23,X24,X25,X26),X24)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k3_funct_2])])])). cnf(c_0_108, negated_conjecture, (v1_xboole_0(u1_struct_0(k5_topmetr))\|k1_funct_1(k3_relat_1(esk2_0,esk4_1(X1)),esk3_1(k3_relat_1(esk2_0,esk4_1(X1))))!=k12_euclid(k1_funct_1(esk2_0,esk3_1(k3_relat_1(esk2_0,esk4_1(X1)))))\|~v3_membered(u1_struct_0(k3_topmetr))\|~v5_pre_topc(k3_relat_1(esk2_0,esk4_1(X1)),k5_topmetr,k3_topmetr)\|~v1_funct_2(k3_relat_1(esk2_0,esk4_1(X1)),u1_struct_0(k5_topmetr),u1_struct_0(k3_topmetr))\|~m2_subset_1(X1,k1_numbers,k5_numbers)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_103, c_0_91]), c_0_71])). cnf(c_0_109, negated_conjecture, (k1_funct_1(k3_relat_1(esk2_0,X1),X2)=k1_funct_1(X1,k1_funct_1(esk2_0,X2))\|u1_struct_0(k15_euclid(esk1_0))=k1_xboole_0\|~r2_hidden(X2,u1_struct_0(k5_topmetr))\|~v1_relat_1(X1)\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104, c_0_105]), c_0_97]), c_0_62])])])). cnf(c_0_110, plain, (k1_seq_1(esk4_1(X2),X1)=k12_euclid(X1)\|~m1_subset_1(X1,u1_struct_0(k15_euclid(X2)))\|~m2_subset_1(X2,k1_numbers,k5_numbers)), inference(split_conjunct,[status(thm)],[c_0_41])). cnf(c_0_111, plain, (k1_seq_1(esk4_1(X1),X2)=k1_funct_1(esk4_1(X1),X2)\|~v1_relat_1(esk4_1(X1))\|~v1_funct_1(esk4_1(X1))\|~v3_membered(u1_struct_0(k3_topmetr))\|~m2_subset_1(X1,k1_numbers,k5_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_81, c_0_106])])). cnf(c_0_112, plain, (v1_relat_1(esk4_1(X1))\|~m2_subset_1(X1,k1_numbers,k5_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_84, c_0_47])])). cnf(c_0_113, plain, (v1_xboole_0(X1)\|m1_subset_1(k3_funct_2(X1,X3,X2,X4),X3)\|~v1_funct_1(X2)\|~v1_funct_2(X2,X1,X3)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))\|~m1_subset_1(X4,X1)), inference(split_conjunct,[status(thm)],[c_0_107])). cnf(c_0_114, negated_conjecture, (v1_xboole_0(u1_struct_0(k5_topmetr))\|u1_struct_0(k15_euclid(esk1_0))=k1_xboole_0\|k1_funct_1(esk4_1(X1),k1_funct_1(esk2_0,esk3_1(k3_relat_1(esk2_0,esk4_1(X1)))))!=k12_euclid(k1_funct_1(esk2_0,esk3_1(k3_relat_1(esk2_0,esk4_1(X1)))))\|~v3_membered(u1_struct_0(k3_topmetr))\|~v5_pre_topc(k3_relat_1(esk2_0,esk4_1(X1)),k5_topmetr,k3_topmetr)\|~v1_funct_2(k3_relat_1(esk2_0,esk4_1(X1)),u1_struct_0(k5_topmetr),u1_struct_0(k3_topmetr))\|~m2_subset_1(X1,k1_numbers,k5_numbers)\|~r2_hidden(esk3_1(k3_relat_1(esk2_0,esk4_1(X1))),u1_struct_0(k5_topmetr))\|~v1_relat_1(esk4_1(X1))\|~v1_funct_1(esk4_1(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_108, c_0_109])])). cnf(c_0_115, plain, (k1_seq_1(esk4_1(X2),X1)=k12_euclid(X1)\|~m2_subset_1(X2,k1_numbers,k5_numbers)\|~m1_subset_1(X1,u1_struct_0(k15_euclid(X2)))), inference(evalgc,[status(thm)],[c_0_110])). cnf(c_0_116, plain, (k1_seq_1(esk4_1(X1),X2)=k1_funct_1(esk4_1(X1),X2)\|~v3_membered(u1_struct_0(k3_topmetr))\|~m2_subset_1(X1,k1_numbers,k5_numbers)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_111, c_0_53]), c_0_112])). cnf(c_0_117, plain, (v1_xboole_0(X1)\|m1_subset_1(k3_funct_2(X1,X3,X2,X4),X3)\|~v1_funct_1(X2)\|~m1_subset_1(X4,X1)\|~v1_funct_2(X2,X1,X3)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))), inference(evalgc,[status(thm)],[c_0_113])). cnf(c_0_118, negated_conjecture, (u1_struct_0(k15_euclid(esk1_0))=k1_xboole_0\|v1_xboole_0(u1_struct_0(k5_topmetr))\|k1_funct_1(esk4_1(X1),k1_funct_1(esk2_0,esk3_1(k3_relat_1(esk2_0,esk4_1(X1)))))!=k12_euclid(k1_funct_1(esk2_0,esk3_1(k3_relat_1(esk2_0,esk4_1(X1)))))\|~v3_membered(u1_struct_0(k3_topmetr))\|~r2_hidden(esk3_1(k3_relat_1(esk2_0,esk4_1(X1))),u1_struct_0(k5_topmetr))\|~v5_pre_topc(k3_relat_1(esk2_0,esk4_1(X1)),k5_topmetr,k3_topmetr)\|~v1_funct_2(k3_relat_1(esk2_0,esk4_1(X1)),u1_struct_0(k5_topmetr),u1_struct_0(k3_topmetr))\|~m2_subset_1(X1,k1_numbers,k5_numbers)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_114, c_0_53]), c_0_112])). cnf(c_0_119, plain, (k1_funct_1(esk4_1(X1),X2)=k12_euclid(X2)\|~m1_subset_1(X2,u1_struct_0(k15_euclid(X1)))\|~m2_subset_1(X1,k1_numbers,k5_numbers)\|~v3_membered(u1_struct_0(k3_topmetr))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_115, c_0_116])])). cnf(c_0_120, plain, (v1_xboole_0(X1)\|m1_subset_1(k1_funct_1(X3,X4),X2)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~m1_subset_1(X4,X1)\|~v1_funct_2(X3,X1,X2)\|~v1_funct_1(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_117, c_0_78])])). cnf(c_0_121, negated_conjecture, (m2_subset_1(esk1_0,k1_numbers,k5_numbers)), inference(split_conjunct,[status(thm)],[c_0_49])). fof(c_0_122, plain, ![X43, X44]:(~m1_subset_1(X43,X44)\|(v1_xboole_0(X44)\|r2_hidden(X43,X44))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])])). fof(c_0_123, plain, ![X14, X15, X16, X17, X18]:((v1_funct_1(k3_relat_1(X17,X18))\|(v2_struct_0(X14)\|(~v2_pre_topc(X14)\|~l1_pre_topc(X14))\|(v2_struct_0(X15)\|(~v2_pre_topc(X15)\|~l1_pre_topc(X15))\|(v2_struct_0(X16)\|(~v2_pre_topc(X16)\|~l1_pre_topc(X16))\|(~v1_funct_1(X17)\|(~v1_funct_2(X17,u1_struct_0(X14),u1_struct_0(X15))\|(~v5_pre_topc(X17,X14,X15)\|~m1_subset_1(X17,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X14),u1_struct_0(X15))))))\|(~v1_funct_1(X18)\|(~v1_funct_2(X18,u1_struct_0(X15),u1_struct_0(X16))\|(~v5_pre_topc(X18,X15,X16)\|~m1_subset_1(X18,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X15),u1_struct_0(X16))))))))))))&((v1_funct_2(k3_relat_1(X17,X18),u1_struct_0(X14),u1_struct_0(X16))\|(v2_struct_0(X14)\|(~v2_pre_topc(X14)\|~l1_pre_topc(X14))\|(v2_struct_0(X15)\|(~v2_pre_topc(X15)\|~l1_pre_topc(X15))\|(v2_struct_0(X16)\|(~v2_pre_topc(X16)\|~l1_pre_topc(X16))\|(~v1_funct_1(X17)\|(~v1_funct_2(X17,u1_struct_0(X14),u1_struct_0(X15))\|(~v5_pre_topc(X17,X14,X15)\|~m1_subset_1(X17,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X14),u1_struct_0(X15))))))\|(~v1_funct_1(X18)\|(~v1_funct_2(X18,u1_struct_0(X15),u1_struct_0(X16))\|(~v5_pre_topc(X18,X15,X16)\|~m1_subset_1(X18,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X15),u1_struct_0(X16))))))))))))&(v5_pre_topc(k3_relat_1(X17,X18),X14,X16)\|(v2_struct_0(X14)\|(~v2_pre_topc(X14)\|~l1_pre_topc(X14))\|(v2_struct_0(X15)\|(~v2_pre_topc(X15)\|~l1_pre_topc(X15))\|(v2_struct_0(X16)\|(~v2_pre_topc(X16)\|~l1_pre_topc(X16))\|(~v1_funct_1(X17)\|(~v1_funct_2(X17,u1_struct_0(X14),u1_struct_0(X15))\|(~v5_pre_topc(X17,X14,X15)\|~m1_subset_1(X17,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X14),u1_struct_0(X15))))))\|(~v1_funct_1(X18)\|(~v1_funct_2(X18,u1_struct_0(X15),u1_struct_0(X16))\|(~v5_pre_topc(X18,X15,X16)\|~m1_subset_1(X18,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X15),u1_struct_0(X16)))))))))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fc1_borsuk_1])])])])). fof(c_0_124, plain, (~v2_struct_0(k3_topmetr)&(v1_pre_topc(k3_topmetr)&v2_pre_topc(k3_topmetr))), inference(fof_simplification,[status(thm)],[fc2_topmetr])). cnf(c_0_125, negated_conjecture, (u1_struct_0(k15_euclid(esk1_0))=k1_xboole_0\|v1_xboole_0(u1_struct_0(k5_topmetr))\|~v3_membered(u1_struct_0(k3_topmetr))\|~r2_hidden(esk3_1(k3_relat_1(esk2_0,esk4_1(X1))),u1_struct_0(k5_topmetr))\|~v5_pre_topc(k3_relat_1(esk2_0,esk4_1(X1)),k5_topmetr,k3_topmetr)\|~v1_funct_2(k3_relat_1(esk2_0,esk4_1(X1)),u1_struct_0(k5_topmetr),u1_struct_0(k3_topmetr))\|~m2_subset_1(X1,k1_numbers,k5_numbers)\|~m1_subset_1(k1_funct_1(esk2_0,esk3_1(k3_relat_1(esk2_0,esk4_1(X1)))),u1_struct_0(k15_euclid(X1)))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_118, c_0_119])])). cnf(c_0_126, negated_conjecture, (v1_xboole_0(u1_struct_0(k5_topmetr))\|m1_subset_1(k1_funct_1(esk2_0,X1),u1_struct_0(k15_euclid(esk1_0)))\|~m1_subset_1(X1,u1_struct_0(k5_topmetr))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120, c_0_61]), c_0_79]), c_0_62])])])). cnf(c_0_127, negated_conjecture, (m2_subset_1(esk1_0,k1_numbers,k5_numbers)), inference(evalgc,[status(thm)],[c_0_121])). cnf(c_0_128, plain, (v1_xboole_0(X2)\|r2_hidden(X1,X2)\|~m1_subset_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_122])). cnf(c_0_129, plain, (v5_pre_topc(k3_relat_1(X1,X2),X3,X4)\|v2_struct_0(X3)\|v2_struct_0(X5)\|v2_struct_0(X4)\|~v2_pre_topc(X3)\|~l1_pre_topc(X3)\|~v2_pre_topc(X5)\|~l1_pre_topc(X5)\|~v2_pre_topc(X4)\|~l1_pre_topc(X4)\|~v1_funct_1(X1)\|~v1_funct_2(X1,u1_struct_0(X3),u1_struct_0(X5))\|~v5_pre_topc(X1,X3,X5)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X3),u1_struct_0(X5))))\|~v1_funct_1(X2)\|~v1_funct_2(X2,u1_struct_0(X5),u1_struct_0(X4))\|~v5_pre_topc(X2,X5,X4)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X5),u1_struct_0(X4))))), inference(split_conjunct,[status(thm)],[c_0_123])). cnf(c_0_130, plain, (v5_pre_topc(esk4_1(X1),k15_euclid(X1),k3_topmetr)\|~m2_subset_1(X1,k1_numbers,k5_numbers)), inference(split_conjunct,[status(thm)],[c_0_41])). cnf(c_0_131, plain, (l1_pre_topc(k3_topmetr)), inference(split_conjunct,[status(thm)],[dt_k3_topmetr])). cnf(c_0_132, plain, (v2_pre_topc(k3_topmetr)), inference(split_conjunct,[status(thm)],[c_0_124])). cnf(c_0_133, plain, (~v2_struct_0(k3_topmetr)), inference(split_conjunct,[status(thm)],[c_0_124])). fof(c_0_134, plain, (~v2_struct_0(k17_borsuk_1)&(v1_pre_topc(k17_borsuk_1)&v2_pre_topc(k17_borsuk_1))), inference(fof_simplification,[status(thm)],[fc9_borsuk_1])). cnf(c_0_135, negated_conjecture, (u1_struct_0(k15_euclid(esk1_0))=k1_xboole_0\|v1_xboole_0(u1_struct_0(k5_topmetr))\|~v3_membered(u1_struct_0(k3_topmetr))\|~r2_hidden(esk3_1(k3_relat_1(esk2_0,esk4_1(esk1_0))),u1_struct_0(k5_topmetr))\|~v5_pre_topc(k3_relat_1(esk2_0,esk4_1(esk1_0)),k5_topmetr,k3_topmetr)\|~v1_funct_2(k3_relat_1(esk2_0,esk4_1(esk1_0)),u1_struct_0(k5_topmetr),u1_struct_0(k3_topmetr))\|~m1_subset_1(esk3_1(k3_relat_1(esk2_0,esk4_1(esk1_0))),u1_struct_0(k5_topmetr))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125, c_0_126]), c_0_127])])])). cnf(c_0_136, plain, (v1_xboole_0(X2)\|r2_hidden(X1,X2)\|~m1_subset_1(X1,X2)), inference(evalgc,[status(thm)],[c_0_128])). cnf(c_0_137, plain, (v2_struct_0(X5)\|v2_struct_0(X4)\|v2_struct_0(X3)\|v5_pre_topc(k3_relat_1(X1,X2),X3,X4)\|~v1_funct_1(X2)\|~v1_funct_1(X1)\|~v2_pre_topc(X5)\|~v2_pre_topc(X4)\|~v2_pre_topc(X3)\|~l1_pre_topc(X5)\|~l1_pre_topc(X4)\|~l1_pre_topc(X3)\|~v5_pre_topc(X2,X5,X4)\|~v5_pre_topc(X1,X3,X5)\|~v1_funct_2(X2,u1_struct_0(X5),u1_struct_0(X4))\|~v1_funct_2(X1,u1_struct_0(X3),u1_struct_0(X5))\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X5),u1_struct_0(X4))))\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X3),u1_struct_0(X5))))), inference(evalgc,[status(thm)],[c_0_129])). cnf(c_0_138, plain, (v5_pre_topc(esk4_1(X1),k15_euclid(X1),k3_topmetr)\|~m2_subset_1(X1,k1_numbers,k5_numbers)), inference(evalgc,[status(thm)],[c_0_130])). cnf(c_0_139, plain, (l1_pre_topc(k3_topmetr)), inference(evalgc,[status(thm)],[c_0_131])). cnf(c_0_140, plain, (v2_pre_topc(k3_topmetr)), inference(evalgc,[status(thm)],[c_0_132])). cnf(c_0_141, plain, (~v2_struct_0(k3_topmetr)), inference(evalgc,[status(thm)],[c_0_133])). cnf(c_0_142, plain, (v1_funct_2(esk4_1(X1),u1_struct_0(k15_euclid(X1)),u1_struct_0(k3_topmetr))\|~m2_subset_1(X1,k1_numbers,k5_numbers)), inference(split_conjunct,[status(thm)],[c_0_41])). cnf(c_0_143, plain, (l1_pre_topc(k17_borsuk_1)), inference(split_conjunct,[status(thm)],[dt_k17_borsuk_1])). cnf(c_0_144, plain, (k5_topmetr=k17_borsuk_1), inference(split_conjunct,[status(thm)],[redefinition_k5_topmetr])). cnf(c_0_145, plain, (v2_pre_topc(k17_borsuk_1)), inference(split_conjunct,[status(thm)],[c_0_134])). cnf(c_0_146, plain, (~v2_struct_0(k17_borsuk_1)), inference(split_conjunct,[status(thm)],[c_0_134])). cnf(c_0_147, negated_conjecture, (u1_struct_0(k15_euclid(esk1_0))=k1_xboole_0\|v1_xboole_0(u1_struct_0(k5_topmetr))\|~v3_membered(u1_struct_0(k3_topmetr))\|~v5_pre_topc(k3_relat_1(esk2_0,esk4_1(esk1_0)),k5_topmetr,k3_topmetr)\|~m1_subset_1(esk3_1(k3_relat_1(esk2_0,esk4_1(esk1_0))),u1_struct_0(k5_topmetr))\|~v1_funct_2(k3_relat_1(esk2_0,esk4_1(esk1_0)),u1_struct_0(k5_topmetr),u1_struct_0(k3_topmetr))), inference(csr,[status(thm)],[c_0_135, c_0_136])). cnf(c_0_148, plain, (v2_struct_0(X1)\|v2_struct_0(k15_euclid(X2))\|v5_pre_topc(k3_relat_1(X3,esk4_1(X2)),X1,k3_topmetr)\|~l1_pre_topc(k15_euclid(X2))\|~l1_pre_topc(X1)\|~v2_pre_topc(k15_euclid(X2))\|~v2_pre_topc(X1)\|~v5_pre_topc(X3,X1,k15_euclid(X2))\|~m1_subset_1(esk4_1(X2),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k15_euclid(X2)),u1_struct_0(k3_topmetr))))\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(k15_euclid(X2)))))\|~v1_funct_2(esk4_1(X2),u1_struct_0(k15_euclid(X2)),u1_struct_0(k3_topmetr))\|~v1_funct_2(X3,u1_struct_0(X1),u1_struct_0(k15_euclid(X2)))\|~v1_funct_1(esk4_1(X2))\|~v1_funct_1(X3)\|~m2_subset_1(X2,k1_numbers,k5_numbers)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137, c_0_138]), c_0_139]), c_0_140])]), c_0_141])])). cnf(c_0_149, plain, (v1_funct_2(esk4_1(X1),u1_struct_0(k15_euclid(X1)),u1_struct_0(k3_topmetr))\|~m2_subset_1(X1,k1_numbers,k5_numbers)), inference(evalgc,[status(thm)],[c_0_142])). cnf(c_0_150, plain, (l1_pre_topc(k17_borsuk_1)), inference(evalgc,[status(thm)],[c_0_143])). cnf(c_0_151, plain, (k17_borsuk_1=k5_topmetr), inference(evalgc,[status(thm)],[c_0_144])). cnf(c_0_152, plain, (v2_pre_topc(k17_borsuk_1)), inference(evalgc,[status(thm)],[c_0_145])). cnf(c_0_153, negated_conjecture, (v5_pre_topc(esk2_0,k5_topmetr,k15_euclid(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_49])). cnf(c_0_154, plain, (~v2_struct_0(k17_borsuk_1)), inference(evalgc,[status(thm)],[c_0_146])). cnf(c_0_155, plain, (v1_funct_2(k3_relat_1(X1,X2),u1_struct_0(X3),u1_struct_0(X4))\|v2_struct_0(X3)\|v2_struct_0(X5)\|v2_struct_0(X4)\|~v2_pre_topc(X3)\|~l1_pre_topc(X3)\|~v2_pre_topc(X5)\|~l1_pre_topc(X5)\|~v2_pre_topc(X4)\|~l1_pre_topc(X4)\|~v1_funct_1(X1)\|~v1_funct_2(X1,u1_struct_0(X3),u1_struct_0(X5))\|~v5_pre_topc(X1,X3,X5)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X3),u1_struct_0(X5))))\|~v1_funct_1(X2)\|~v1_funct_2(X2,u1_struct_0(X5),u1_struct_0(X4))\|~v5_pre_topc(X2,X5,X4)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X5),u1_struct_0(X4))))), inference(split_conjunct,[status(thm)],[c_0_123])). cnf(c_0_156, negated_conjecture, (u1_struct_0(k15_euclid(esk1_0))=k1_xboole_0\|v1_xboole_0(u1_struct_0(k5_topmetr))\|~v3_membered(u1_struct_0(k3_topmetr))\|~v5_pre_topc(k3_relat_1(esk2_0,esk4_1(esk1_0)),k5_topmetr,k3_topmetr)\|~v1_funct_2(k3_relat_1(esk2_0,esk4_1(esk1_0)),u1_struct_0(k5_topmetr),u1_struct_0(k3_topmetr))\|~m1_subset_1(k3_relat_1(esk2_0,esk4_1(esk1_0)),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_topmetr),u1_struct_0(k3_topmetr))))\|~v1_funct_1(k3_relat_1(esk2_0,esk4_1(esk1_0)))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_147, c_0_89])])). cnf(c_0_157, plain, (v2_struct_0(k15_euclid(X1))\|v2_struct_0(X2)\|v5_pre_topc(k3_relat_1(X3,esk4_1(X1)),X2,k3_topmetr)\|~l1_pre_topc(k15_euclid(X1))\|~l1_pre_topc(X2)\|~v2_pre_topc(k15_euclid(X1))\|~v2_pre_topc(X2)\|~v5_pre_topc(X3,X2,k15_euclid(X1))\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X2),u1_struct_0(k15_euclid(X1)))))\|~v1_funct_2(X3,u1_struct_0(X2),u1_struct_0(k15_euclid(X1)))\|~v1_funct_1(X3)\|~m2_subset_1(X1,k1_numbers,k5_numbers)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_148, c_0_53]), c_0_149]), c_0_47])). cnf(c_0_158, plain, (l1_pre_topc(k5_topmetr)), inference(rw,[status(thm)],[c_0_150, c_0_151])). cnf(c_0_159, plain, (v2_pre_topc(k5_topmetr)), inference(rw,[status(thm)],[c_0_152, c_0_151])). cnf(c_0_160, negated_conjecture, (v5_pre_topc(esk2_0,k5_topmetr,k15_euclid(esk1_0))), inference(evalgc,[status(thm)],[c_0_153])). cnf(c_0_161, plain, (~v2_struct_0(k5_topmetr)), inference(rw,[status(thm)],[c_0_154, c_0_151])). cnf(c_0_162, plain, (v2_struct_0(X5)\|v2_struct_0(X4)\|v2_struct_0(X3)\|v1_funct_2(k3_relat_1(X1,X2),u1_struct_0(X3),u1_struct_0(X4))\|~v1_funct_1(X2)\|~v1_funct_1(X1)\|~v2_pre_topc(X5)\|~v2_pre_topc(X4)\|~v2_pre_topc(X3)\|~l1_pre_topc(X5)\|~l1_pre_topc(X4)\|~l1_pre_topc(X3)\|~v5_pre_topc(X2,X5,X4)\|~v5_pre_topc(X1,X3,X5)\|~v1_funct_2(X2,u1_struct_0(X5),u1_struct_0(X4))\|~v1_funct_2(X1,u1_struct_0(X3),u1_struct_0(X5))\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X5),u1_struct_0(X4))))\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X3),u1_struct_0(X5))))), inference(evalgc,[status(thm)],[c_0_155])). fof(c_0_163, plain, ![X71, X72, X73]:((~m2_subset_1(X73,X71,X72)\|m1_subset_1(X73,X72)\|(v1_xboole_0(X71)\|(v1_xboole_0(X72)\|~m1_subset_1(X72,k1_zfmisc_1(X71)))))&(~m1_subset_1(X73,X72)\|m2_subset_1(X73,X71,X72)\|(v1_xboole_0(X71)\|(v1_xboole_0(X72)\|~m1_subset_1(X72,k1_zfmisc_1(X71)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[redefinition_m2_subset_1])])])])])). fof(c_0_164, plain, ![X74, X75]:(~v1_xboole_0(X74)\|(~m1_subset_1(X75,k1_zfmisc_1(X74))\|v1_xboole_0(X75))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_subset_1])])])). fof(c_0_165, plain, ~v1_finset_1(k4_ordinal1), inference(fof_simplification,[status(thm)],[fc7_card_1])). cnf(c_0_166, negated_conjecture, (u1_struct_0(k15_euclid(esk1_0))=k1_xboole_0\|v1_xboole_0(u1_struct_0(k5_topmetr))\|v2_struct_0(k15_euclid(esk1_0))\|~v3_membered(u1_struct_0(k3_topmetr))\|~m1_subset_1(k3_relat_1(esk2_0,esk4_1(esk1_0)),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_topmetr),u1_struct_0(k3_topmetr))))\|~v1_funct_2(k3_relat_1(esk2_0,esk4_1(esk1_0)),u1_struct_0(k5_topmetr),u1_struct_0(k3_topmetr))\|~v1_funct_1(k3_relat_1(esk2_0,esk4_1(esk1_0)))\|~l1_pre_topc(k15_euclid(esk1_0))\|~v2_pre_topc(k15_euclid(esk1_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156, c_0_157]), c_0_158]), c_0_159]), c_0_160]), c_0_61]), c_0_79]), c_0_62]), c_0_127])]), c_0_161])])). cnf(c_0_167, plain, (v2_struct_0(X1)\|v2_struct_0(k15_euclid(X2))\|v1_funct_2(k3_relat_1(X3,esk4_1(X2)),u1_struct_0(X1),u1_struct_0(k3_topmetr))\|~l1_pre_topc(k15_euclid(X2))\|~l1_pre_topc(X1)\|~v2_pre_topc(k15_euclid(X2))\|~v2_pre_topc(X1)\|~v5_pre_topc(X3,X1,k15_euclid(X2))\|~m1_subset_1(esk4_1(X2),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k15_euclid(X2)),u1_struct_0(k3_topmetr))))\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(k15_euclid(X2)))))\|~v1_funct_2(esk4_1(X2),u1_struct_0(k15_euclid(X2)),u1_struct_0(k3_topmetr))\|~v1_funct_2(X3,u1_struct_0(X1),u1_struct_0(k15_euclid(X2)))\|~v1_funct_1(esk4_1(X2))\|~v1_funct_1(X3)\|~m2_subset_1(X2,k1_numbers,k5_numbers)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162, c_0_138]), c_0_139]), c_0_140])]), c_0_141])])). cnf(c_0_168, plain, (m1_subset_1(X1,X3)\|v1_xboole_0(X2)\|v1_xboole_0(X3)\|~m2_subset_1(X1,X2,X3)\|~m1_subset_1(X3,k1_zfmisc_1(X2))), inference(split_conjunct,[status(thm)],[c_0_163])). cnf(c_0_169, plain, (v1_xboole_0(X2)\|~v1_xboole_0(X1)\|~m1_subset_1(X2,k1_zfmisc_1(X1))), inference(split_conjunct,[status(thm)],[c_0_164])). cnf(c_0_170, plain, (~v1_finset_1(k4_ordinal1)), inference(split_conjunct,[status(thm)],[c_0_165])). cnf(c_0_171, plain, (k5_numbers=k4_ordinal1), inference(split_conjunct,[status(thm)],[redefinition_k5_numbers])). fof(c_0_172, plain, ![X69]:(~v1_xboole_0(X69)\|v1_finset_1(X69)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_finset_1])])). cnf(c_0_173, negated_conjecture, (u1_struct_0(k15_euclid(esk1_0))=k1_xboole_0\|v1_xboole_0(u1_struct_0(k5_topmetr))\|v2_struct_0(k15_euclid(esk1_0))\|~v3_membered(u1_struct_0(k3_topmetr))\|~l1_pre_topc(k15_euclid(esk1_0))\|~v2_pre_topc(k15_euclid(esk1_0))\|~v1_funct_2(k3_relat_1(esk2_0,esk4_1(esk1_0)),u1_struct_0(k5_topmetr),u1_struct_0(k3_topmetr))\|~v1_funct_1(k3_relat_1(esk2_0,esk4_1(esk1_0)))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166, c_0_71]), c_0_127])])])). cnf(c_0_174, plain, (v2_struct_0(k15_euclid(X1))\|v2_struct_0(X2)\|v1_funct_2(k3_relat_1(X3,esk4_1(X1)),u1_struct_0(X2),u1_struct_0(k3_topmetr))\|~l1_pre_topc(k15_euclid(X1))\|~l1_pre_topc(X2)\|~v2_pre_topc(k15_euclid(X1))\|~v2_pre_topc(X2)\|~v5_pre_topc(X3,X2,k15_euclid(X1))\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X2),u1_struct_0(k15_euclid(X1)))))\|~v1_funct_2(X3,u1_struct_0(X2),u1_struct_0(k15_euclid(X1)))\|~v1_funct_1(X3)\|~m2_subset_1(X1,k1_numbers,k5_numbers)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_167, c_0_53]), c_0_149]), c_0_47])). fof(c_0_175, plain, ![X68]:(~v3_topmetr(X68)\|~l1_struct_0(X68)\|v3_membered(u1_struct_0(X68))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc4_topmetr])])). cnf(c_0_176, plain, (v1_xboole_0(X3)\|v1_xboole_0(X2)\|m1_subset_1(X1,X3)\|~m2_subset_1(X1,X2,X3)\|~m1_subset_1(X3,k1_zfmisc_1(X2))), inference(evalgc,[status(thm)],[c_0_168])). cnf(c_0_177, plain, (v1_xboole_0(X2)\|~v1_xboole_0(X1)\|~m1_subset_1(X2,k1_zfmisc_1(X1))), inference(evalgc,[status(thm)],[c_0_169])). cnf(c_0_178, plain, (m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers))), inference(split_conjunct,[status(thm)],[dt_k5_numbers])). cnf(c_0_179, plain, (~v1_finset_1(k4_ordinal1)), inference(evalgc,[status(thm)],[c_0_170])). cnf(c_0_180, plain, (k4_ordinal1=k5_numbers), inference(evalgc,[status(thm)],[c_0_171])). cnf(c_0_181, plain, (v1_finset_1(X1)\|~v1_xboole_0(X1)), inference(split_conjunct,[status(thm)],[c_0_172])). cnf(c_0_182, negated_conjecture, (u1_struct_0(k15_euclid(esk1_0))=k1_xboole_0\|v1_xboole_0(u1_struct_0(k5_topmetr))\|v2_struct_0(k15_euclid(esk1_0))\|~v3_membered(u1_struct_0(k3_topmetr))\|~l1_pre_topc(k15_euclid(esk1_0))\|~v2_pre_topc(k15_euclid(esk1_0))\|~v1_funct_1(k3_relat_1(esk2_0,esk4_1(esk1_0)))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173, c_0_174]), c_0_158]), c_0_159]), c_0_160]), c_0_61]), c_0_79]), c_0_62]), c_0_127])]), c_0_161])])). cnf(c_0_183, plain, (v3_membered(u1_struct_0(X1))\|~v3_topmetr(X1)\|~l1_struct_0(X1)), inference(split_conjunct,[status(thm)],[c_0_175])). cnf(c_0_184, plain, (v3_topmetr(k3_topmetr)), inference(split_conjunct,[status(thm)],[fc5_topmetr])). fof(c_0_185, plain, ![X67]:(~l1_pre_topc(X67)\|l1_struct_0(X67)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_pre_topc])])). fof(c_0_186, plain, ![X60, X61]:(~v6_membered(X60)\|(~m1_subset_1(X61,X60)\|v7_ordinal1(X61))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc17_membered])])])). cnf(c_0_187, plain, (v1_xboole_0(X1)\|m1_subset_1(X2,X1)\|~m1_subset_1(X1,k1_zfmisc_1(X3))\|~m2_subset_1(X2,X3,X1)), inference(csr,[status(thm)],[c_0_176, c_0_177])). cnf(c_0_188, plain, (m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers))), inference(evalgc,[status(thm)],[c_0_178])). cnf(c_0_189, plain, (~v1_finset_1(k5_numbers)), inference(rw,[status(thm)],[c_0_179, c_0_180])). cnf(c_0_190, plain, (v1_finset_1(X1)\|~v1_xboole_0(X1)), inference(evalgc,[status(thm)],[c_0_181])). cnf(c_0_191, plain, (v6_membered(k4_ordinal1)), inference(split_conjunct,[status(thm)],[fc6_membered])). fof(c_0_192, plain, ![X64]:((~v2_struct_0(k15_euclid(X64))\|~v7_ordinal1(X64))&(v5_rltopsp1(k15_euclid(X64))\|~v7_ordinal1(X64))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fc5_euclid])])])])). cnf(c_0_193, negated_conjecture, (u1_struct_0(k15_euclid(esk1_0))=k1_xboole_0\|v1_xboole_0(u1_struct_0(k5_topmetr))\|v2_struct_0(k15_euclid(esk1_0))\|~v3_membered(u1_struct_0(k3_topmetr))\|~l1_pre_topc(k15_euclid(esk1_0))\|~v2_pre_topc(k15_euclid(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_182, c_0_91]), c_0_127])])])). cnf(c_0_194, plain, (v3_membered(u1_struct_0(X1))\|~l1_struct_0(X1)\|~v3_topmetr(X1)), inference(evalgc,[status(thm)],[c_0_183])). cnf(c_0_195, plain, (v3_topmetr(k3_topmetr)), inference(evalgc,[status(thm)],[c_0_184])). cnf(c_0_196, plain, (l1_struct_0(X1)\|~l1_pre_topc(X1)), inference(split_conjunct,[status(thm)],[c_0_185])). cnf(c_0_197, plain, (v7_ordinal1(X2)\|~v6_membered(X1)\|~m1_subset_1(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_186])). cnf(c_0_198, negated_conjecture, (v1_xboole_0(k5_numbers)\|m1_subset_1(esk1_0,k5_numbers)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_187, c_0_127]), c_0_188])])])). cnf(c_0_199, plain, (~v1_xboole_0(k5_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_189, c_0_190])])). cnf(c_0_200, plain, (v6_membered(k4_ordinal1)), inference(evalgc,[status(thm)],[c_0_191])). fof(c_0_201, plain, ![X62]:((l1_rlvect_1(X62)\|~l1_rltopsp1(X62))&(l1_pre_topc(X62)\|~l1_rltopsp1(X62))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_rltopsp1])])])). fof(c_0_202, plain, ![X63]:((v5_rltopsp1(k15_euclid(X63))\|~v7_ordinal1(X63))&(l1_rltopsp1(k15_euclid(X63))\|~v7_ordinal1(X63))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k15_euclid])])])). cnf(c_0_203, plain, (~v2_struct_0(k15_euclid(X1))\|~v7_ordinal1(X1)), inference(split_conjunct,[status(thm)],[c_0_192])). cnf(c_0_204, negated_conjecture, (u1_struct_0(k15_euclid(esk1_0))=k1_xboole_0\|v1_xboole_0(u1_struct_0(k5_topmetr))\|v2_struct_0(k15_euclid(esk1_0))\|~l1_pre_topc(k15_euclid(esk1_0))\|~v2_pre_topc(k15_euclid(esk1_0))\|~l1_struct_0(k3_topmetr)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_193, c_0_194]), c_0_195])])])). cnf(c_0_205, plain, (l1_struct_0(X1)\|~l1_pre_topc(X1)), inference(evalgc,[status(thm)],[c_0_196])). cnf(c_0_206, plain, (v7_ordinal1(X2)\|~v6_membered(X1)\|~m1_subset_1(X2,X1)), inference(evalgc,[status(thm)],[c_0_197])). cnf(c_0_207, negated_conjecture, (m1_subset_1(esk1_0,k5_numbers)), inference(sr,[status(thm)],[c_0_198, c_0_199])). cnf(c_0_208, plain, (v6_membered(k5_numbers)), inference(rw,[status(thm)],[c_0_200, c_0_180])). cnf(c_0_209, plain, (l1_pre_topc(X1)\|~l1_rltopsp1(X1)), inference(split_conjunct,[status(thm)],[c_0_201])). cnf(c_0_210, plain, (l1_rltopsp1(k15_euclid(X1))\|~v7_ordinal1(X1)), inference(split_conjunct,[status(thm)],[c_0_202])). fof(c_0_211, plain, ![X65]:(v2_struct_0(X65)\|~l1_struct_0(X65)\|~v1_xboole_0(u1_struct_0(X65))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fc2_struct_0])])])). cnf(c_0_212, plain, (~v7_ordinal1(X1)\|~v2_struct_0(k15_euclid(X1))), inference(evalgc,[status(thm)],[c_0_203])). cnf(c_0_213, negated_conjecture, (u1_struct_0(k15_euclid(esk1_0))=k1_xboole_0\|v1_xboole_0(u1_struct_0(k5_topmetr))\|v2_struct_0(k15_euclid(esk1_0))\|~l1_pre_topc(k15_euclid(esk1_0))\|~v2_pre_topc(k15_euclid(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_204, c_0_205]), c_0_139])])])). cnf(c_0_214, negated_conjecture, (v7_ordinal1(esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_206, c_0_207]), c_0_208])])])). cnf(c_0_215, plain, (l1_pre_topc(X1)\|~l1_rltopsp1(X1)), inference(evalgc,[status(thm)],[c_0_209])). cnf(c_0_216, plain, (l1_rltopsp1(k15_euclid(X1))\|~v7_ordinal1(X1)), inference(evalgc,[status(thm)],[c_0_210])). fof(c_0_217, plain, ![X66]:((v2_pre_topc(k15_euclid(X66))\|~v7_ordinal1(X66))&((v13_algstr_0(k15_euclid(X66))\|~v7_ordinal1(X66))&((v2_rlvect_1(k15_euclid(X66))\|~v7_ordinal1(X66))&((v3_rlvect_1(k15_euclid(X66))\|~v7_ordinal1(X66))&((v4_rlvect_1(k15_euclid(X66))\|~v7_ordinal1(X66))&((v5_rlvect_1(k15_euclid(X66))\|~v7_ordinal1(X66))&((v6_rlvect_1(k15_euclid(X66))\|~v7_ordinal1(X66))&((v7_rlvect_1(k15_euclid(X66))\|~v7_ordinal1(X66))&((v8_rlvect_1(k15_euclid(X66))\|~v7_ordinal1(X66))&(v5_rltopsp1(k15_euclid(X66))\|~v7_ordinal1(X66))))))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc6_euclid])])])). cnf(c_0_218, plain, (v2_struct_0(X1)\|~l1_struct_0(X1)\|~v1_xboole_0(u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_211])). cnf(c_0_219, negated_conjecture, (u1_struct_0(k15_euclid(esk1_0))=k1_xboole_0\|v1_xboole_0(u1_struct_0(k5_topmetr))\|~l1_pre_topc(k15_euclid(esk1_0))\|~v2_pre_topc(k15_euclid(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_212, c_0_213]), c_0_214])])])). cnf(c_0_220, plain, (l1_pre_topc(k15_euclid(X1))\|~v7_ordinal1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_215, c_0_216])])). cnf(c_0_221, plain, (v2_pre_topc(k15_euclid(X1))\|~v7_ordinal1(X1)), inference(split_conjunct,[status(thm)],[c_0_217])). cnf(c_0_222, plain, (v2_struct_0(X1)\|~l1_struct_0(X1)\|~v1_xboole_0(u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_218])). cnf(c_0_223, negated_conjecture, (u1_struct_0(k15_euclid(esk1_0))=k1_xboole_0\|v1_xboole_0(u1_struct_0(k5_topmetr))\|~v2_pre_topc(k15_euclid(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_219, c_0_220]), c_0_214])])])). cnf(c_0_224, plain, (v2_pre_topc(k15_euclid(X1))\|~v7_ordinal1(X1)), inference(evalgc,[status(thm)],[c_0_221])). cnf(c_0_225, plain, (v2_struct_0(X1)\|~v1_xboole_0(u1_struct_0(X1))\|~l1_pre_topc(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_222, c_0_205])])). cnf(c_0_226, negated_conjecture, (u1_struct_0(k15_euclid(esk1_0))=k1_xboole_0\|v1_xboole_0(u1_struct_0(k5_topmetr))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_223, c_0_224]), c_0_214])])])). cnf(c_0_227, plain, (v1_xboole_0(k1_xboole_0)), inference(split_conjunct,[status(thm)],[fc1_xboole_0])). cnf(c_0_228, negated_conjecture, (u1_struct_0(k15_euclid(esk1_0))=k1_xboole_0), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_225, c_0_226]), c_0_158])]), c_0_161])])). cnf(c_0_229, plain, (v1_xboole_0(k1_xboole_0)), inference(evalgc,[status(thm)],[c_0_227])). cnf(c_0_230, negated_conjecture, (v2_struct_0(k15_euclid(esk1_0))\|~l1_pre_topc(k15_euclid(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_225, c_0_228]), c_0_229])])])). cnf(c_0_231, negated_conjecture, (~l1_pre_topc(k15_euclid(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_212, c_0_230]), c_0_214])])])). cnf(c_0_232, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_231, c_0_220]), c_0_214])]), ['proof']). # SZS output end CNFRefutation	reserve m,n,i,i2,j for Element of NAT, r,r1,r2,s,t for Real, x,y,z for set; reserve p,p1,p2,p3,q,q1,q2,q3,q4 for Point of TOP-REAL n; reserve u for Point of Euclid n; reserve R for Subset of TOP-REAL n; reserve P,Q for Subset of TOP-REAL n; theorem Th85: for g being Function of I[01],TOP-REAL n st g is continuous holds ex f being Function of I[01],R^1 st (for t being Point of I[01] holds f.t =\|.g.t.\|) & f is continuous proof let g be Function of I[01],TOP-REAL n; consider h being Function of TOP-REAL n,R^1 such that A1: for q holds h.q=\|.q.\| and A2: h is continuous by Th84; set f1=h*g; A3: for t being Point of I[01] holds f1.t=\|.g.t.\| proof let t be Point of I[01]; reconsider q=g.t as Point of TOP-REAL n; dom g = the carrier of I[01] by FUNCT_2:def 1; then f1.t=h.(g.t) by FUNCT_1:13 .= \|.q.\| by A1; hence thesis; end; assume g is continuous; hence thesis by A2,A3; end;	Convert the following ATP output trace into a readable Mizar proof.
t7_msualg_9	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t7_msualg_9, conjecture, ![X1, X2]:((v1_relat_1(X2)&(v2_relat_1(X2)&(v4_relat_1(X2,X1)&(v1_funct_1(X2)&v1_partfun1(X2,X1)))))=>![X3]:((v2_finset_1(X3)&m3_pboole(X3,X1,X2))=>?[X4]:((v2_relat_1(X4)&(v2_finset_1(X4)&m3_pboole(X4,X1,X2)))&r2_pboole(X1,X3,X4)))), file('/scratch/mptp/predsminms1/t7_msualg_9__0', t7_msualg_9)). fof(t14_pboole, axiom, ![X1, X2]:((v1_relat_1(X2)&(v4_relat_1(X2,X1)&(v1_funct_1(X2)&v1_partfun1(X2,X1))))=>![X3]:((v1_relat_1(X3)&(v4_relat_1(X3,X1)&(v1_funct_1(X3)&v1_partfun1(X3,X1))))=>r2_pboole(X1,X2,k2_pboole(X1,X2,X3)))), file('/scratch/mptp/predsminms1/t7_msualg_9__0', t14_pboole)). fof(dt_m3_pboole, axiom, ![X1, X2]:((v1_relat_1(X2)&(v4_relat_1(X2,X1)&(v1_funct_1(X2)&v1_partfun1(X2,X1))))=>![X3]:(m3_pboole(X3,X1,X2)=>(v1_relat_1(X3)&(v4_relat_1(X3,X1)&(v1_funct_1(X3)&v1_partfun1(X3,X1)))))), file('/scratch/mptp/predsminms1/t7_msualg_9__0', dt_m3_pboole)). fof(d18_pboole, axiom, ![X1, X2]:((v1_relat_1(X2)&(v4_relat_1(X2,X1)&(v1_funct_1(X2)&v1_partfun1(X2,X1))))=>![X3]:((v1_relat_1(X3)&(v4_relat_1(X3,X1)&(v1_funct_1(X3)&v1_partfun1(X3,X1))))=>(m3_pboole(X3,X1,X2)<=>r2_pboole(X1,X3,X2)))), file('/scratch/mptp/predsminms1/t7_msualg_9__0', d18_pboole)). fof(t16_pboole, axiom, ![X1, X2]:((v1_relat_1(X2)&(v4_relat_1(X2,X1)&(v1_funct_1(X2)&v1_partfun1(X2,X1))))=>![X3]:((v1_relat_1(X3)&(v4_relat_1(X3,X1)&(v1_funct_1(X3)&v1_partfun1(X3,X1))))=>![X4]:((v1_relat_1(X4)&(v4_relat_1(X4,X1)&(v1_funct_1(X4)&v1_partfun1(X4,X1))))=>((r2_pboole(X1,X2,X3)&r2_pboole(X1,X4,X3))=>r2_pboole(X1,k2_pboole(X1,X2,X4),X3))))), file('/scratch/mptp/predsminms1/t7_msualg_9__0', t16_pboole)). fof(t131_pboole, axiom, ![X1, X2]:((v1_relat_1(X2)&(v4_relat_1(X2,X1)&(v1_funct_1(X2)&v1_partfun1(X2,X1))))=>![X3]:((v1_relat_1(X3)&(v4_relat_1(X3,X1)&(v1_funct_1(X3)&v1_partfun1(X3,X1))))=>((v2_relat_1(X2)&r2_pboole(X1,X2,X3))=>v2_relat_1(X3)))), file('/scratch/mptp/predsminms1/t7_msualg_9__0', t131_pboole)). fof(dt_k2_pboole, axiom, ![X1, X2, X3]:(((v1_relat_1(X2)&(v4_relat_1(X2,X1)&(v1_funct_1(X2)&v1_partfun1(X2,X1))))&(v1_relat_1(X3)&(v4_relat_1(X3,X1)&(v1_funct_1(X3)&v1_partfun1(X3,X1)))))=>(v1_relat_1(k2_pboole(X1,X2,X3))&(v4_relat_1(k2_pboole(X1,X2,X3),X1)&(v1_funct_1(k2_pboole(X1,X2,X3))&v1_partfun1(k2_pboole(X1,X2,X3),X1))))), file('/scratch/mptp/predsminms1/t7_msualg_9__0', dt_k2_pboole)). fof(commutativity_k2_pboole, axiom, ![X1, X2, X3]:(((v1_relat_1(X2)&(v4_relat_1(X2,X1)&(v1_funct_1(X2)&v1_partfun1(X2,X1))))&(v1_relat_1(X3)&(v4_relat_1(X3,X1)&(v1_funct_1(X3)&v1_partfun1(X3,X1)))))=>k2_pboole(X1,X2,X3)=k2_pboole(X1,X3,X2)), file('/scratch/mptp/predsminms1/t7_msualg_9__0', commutativity_k2_pboole)). fof(rc2_msualg_9, axiom, ![X1, X2]:((v1_relat_1(X2)&(v2_relat_1(X2)&(v4_relat_1(X2,X1)&(v1_funct_1(X2)&v1_partfun1(X2,X1)))))=>?[X3]:(m3_pboole(X3,X1,X2)&(v1_relat_1(X3)&(v2_relat_1(X3)&(v4_relat_1(X3,X1)&(v1_funct_1(X3)&(v1_partfun1(X3,X1)&v2_finset_1(X3)))))))), file('/scratch/mptp/predsminms1/t7_msualg_9__0', rc2_msualg_9)). fof(fc6_mssubfam, axiom, ![X1, X2, X3]:(((v1_relat_1(X2)&(v4_relat_1(X2,X1)&(v1_funct_1(X2)&(v1_partfun1(X2,X1)&v2_finset_1(X2)))))&(v1_relat_1(X3)&(v4_relat_1(X3,X1)&(v1_funct_1(X3)&(v1_partfun1(X3,X1)&v2_finset_1(X3))))))=>(v1_relat_1(k2_pboole(X1,X2,X3))&(v4_relat_1(k2_pboole(X1,X2,X3),X1)&(v1_funct_1(k2_pboole(X1,X2,X3))&(v1_partfun1(k2_pboole(X1,X2,X3),X1)&v2_finset_1(k2_pboole(X1,X2,X3))))))), file('/scratch/mptp/predsminms1/t7_msualg_9__0', fc6_mssubfam)). fof(c_0_10, negated_conjecture, ~(![X1, X2]:((v1_relat_1(X2)&(v2_relat_1(X2)&(v4_relat_1(X2,X1)&(v1_funct_1(X2)&v1_partfun1(X2,X1)))))=>![X3]:((v2_finset_1(X3)&m3_pboole(X3,X1,X2))=>?[X4]:((v2_relat_1(X4)&(v2_finset_1(X4)&m3_pboole(X4,X1,X2)))&r2_pboole(X1,X3,X4))))), inference(assume_negation,[status(cth)],[t7_msualg_9])). fof(c_0_11, negated_conjecture, ![X8]:((v1_relat_1(esk2_0)&(v2_relat_1(esk2_0)&(v4_relat_1(esk2_0,esk1_0)&(v1_funct_1(esk2_0)&v1_partfun1(esk2_0,esk1_0)))))&((v2_finset_1(esk3_0)&m3_pboole(esk3_0,esk1_0,esk2_0))&(~v2_relat_1(X8)\|(~v2_finset_1(X8)\|~m3_pboole(X8,esk1_0,esk2_0))\|~r2_pboole(esk1_0,esk3_0,X8)))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])])). fof(c_0_12, plain, ![X22, X23, X24]:(~v1_relat_1(X23)\|(~v4_relat_1(X23,X22)\|(~v1_funct_1(X23)\|~v1_partfun1(X23,X22)))\|(~v1_relat_1(X24)\|(~v4_relat_1(X24,X22)\|(~v1_funct_1(X24)\|~v1_partfun1(X24,X22)))\|r2_pboole(X22,X23,k2_pboole(X22,X23,X24)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t14_pboole])])])). fof(c_0_13, plain, ![X9, X10, X11]:((v1_relat_1(X11)\|~m3_pboole(X11,X9,X10)\|(~v1_relat_1(X10)\|(~v4_relat_1(X10,X9)\|(~v1_funct_1(X10)\|~v1_partfun1(X10,X9)))))&((v4_relat_1(X11,X9)\|~m3_pboole(X11,X9,X10)\|(~v1_relat_1(X10)\|(~v4_relat_1(X10,X9)\|(~v1_funct_1(X10)\|~v1_partfun1(X10,X9)))))&((v1_funct_1(X11)\|~m3_pboole(X11,X9,X10)\|(~v1_relat_1(X10)\|(~v4_relat_1(X10,X9)\|(~v1_funct_1(X10)\|~v1_partfun1(X10,X9)))))&(v1_partfun1(X11,X9)\|~m3_pboole(X11,X9,X10)\|(~v1_relat_1(X10)\|(~v4_relat_1(X10,X9)\|(~v1_funct_1(X10)\|~v1_partfun1(X10,X9)))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m3_pboole])])])])). fof(c_0_14, plain, ![X12, X13, X14]:((~m3_pboole(X14,X12,X13)\|r2_pboole(X12,X14,X13)\|(~v1_relat_1(X14)\|(~v4_relat_1(X14,X12)\|(~v1_funct_1(X14)\|~v1_partfun1(X14,X12))))\|(~v1_relat_1(X13)\|(~v4_relat_1(X13,X12)\|(~v1_funct_1(X13)\|~v1_partfun1(X13,X12)))))&(~r2_pboole(X12,X14,X13)\|m3_pboole(X14,X12,X13)\|(~v1_relat_1(X14)\|(~v4_relat_1(X14,X12)\|(~v1_funct_1(X14)\|~v1_partfun1(X14,X12))))\|(~v1_relat_1(X13)\|(~v4_relat_1(X13,X12)\|(~v1_funct_1(X13)\|~v1_partfun1(X13,X12)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d18_pboole])])])])). fof(c_0_15, plain, ![X15, X16, X17, X18]:(~v1_relat_1(X16)\|(~v4_relat_1(X16,X15)\|(~v1_funct_1(X16)\|~v1_partfun1(X16,X15)))\|(~v1_relat_1(X17)\|(~v4_relat_1(X17,X15)\|(~v1_funct_1(X17)\|~v1_partfun1(X17,X15)))\|(~v1_relat_1(X18)\|(~v4_relat_1(X18,X15)\|(~v1_funct_1(X18)\|~v1_partfun1(X18,X15)))\|(~r2_pboole(X15,X16,X17)\|~r2_pboole(X15,X18,X17)\|r2_pboole(X15,k2_pboole(X15,X16,X18),X17))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t16_pboole])])])). fof(c_0_16, plain, ![X19, X20, X21]:(~v1_relat_1(X20)\|(~v4_relat_1(X20,X19)\|(~v1_funct_1(X20)\|~v1_partfun1(X20,X19)))\|(~v1_relat_1(X21)\|(~v4_relat_1(X21,X19)\|(~v1_funct_1(X21)\|~v1_partfun1(X21,X19)))\|(~v2_relat_1(X20)\|~r2_pboole(X19,X20,X21)\|v2_relat_1(X21)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t131_pboole])])])). cnf(c_0_17, negated_conjecture, (~v2_relat_1(X1)\|~v2_finset_1(X1)\|~m3_pboole(X1,esk1_0,esk2_0)\|~r2_pboole(esk1_0,esk3_0,X1)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_18, plain, (r2_pboole(X2,X1,k2_pboole(X2,X1,X3))\|~v1_relat_1(X1)\|~v4_relat_1(X1,X2)\|~v1_funct_1(X1)\|~v1_partfun1(X1,X2)\|~v1_relat_1(X3)\|~v4_relat_1(X3,X2)\|~v1_funct_1(X3)\|~v1_partfun1(X3,X2)), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_19, plain, (v1_partfun1(X1,X2)\|~m3_pboole(X1,X2,X3)\|~v1_relat_1(X3)\|~v4_relat_1(X3,X2)\|~v1_funct_1(X3)\|~v1_partfun1(X3,X2)), inference(split_conjunct,[status(thm)],[c_0_13])). cnf(c_0_20, negated_conjecture, (m3_pboole(esk3_0,esk1_0,esk2_0)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_21, negated_conjecture, (v1_partfun1(esk2_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_22, negated_conjecture, (v1_funct_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_23, negated_conjecture, (v4_relat_1(esk2_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_24, negated_conjecture, (v1_relat_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_25, plain, (v1_funct_1(X1)\|~m3_pboole(X1,X2,X3)\|~v1_relat_1(X3)\|~v4_relat_1(X3,X2)\|~v1_funct_1(X3)\|~v1_partfun1(X3,X2)), inference(split_conjunct,[status(thm)],[c_0_13])). cnf(c_0_26, plain, (v4_relat_1(X1,X2)\|~m3_pboole(X1,X2,X3)\|~v1_relat_1(X3)\|~v4_relat_1(X3,X2)\|~v1_funct_1(X3)\|~v1_partfun1(X3,X2)), inference(split_conjunct,[status(thm)],[c_0_13])). cnf(c_0_27, plain, (v1_relat_1(X1)\|~m3_pboole(X1,X2,X3)\|~v1_relat_1(X3)\|~v4_relat_1(X3,X2)\|~v1_funct_1(X3)\|~v1_partfun1(X3,X2)), inference(split_conjunct,[status(thm)],[c_0_13])). cnf(c_0_28, plain, (m3_pboole(X2,X1,X3)\|~r2_pboole(X1,X2,X3)\|~v1_relat_1(X2)\|~v4_relat_1(X2,X1)\|~v1_funct_1(X2)\|~v1_partfun1(X2,X1)\|~v1_relat_1(X3)\|~v4_relat_1(X3,X1)\|~v1_funct_1(X3)\|~v1_partfun1(X3,X1)), inference(split_conjunct,[status(thm)],[c_0_14])). cnf(c_0_29, plain, (r2_pboole(X2,k2_pboole(X2,X1,X4),X3)\|~v1_relat_1(X1)\|~v4_relat_1(X1,X2)\|~v1_funct_1(X1)\|~v1_partfun1(X1,X2)\|~v1_relat_1(X3)\|~v4_relat_1(X3,X2)\|~v1_funct_1(X3)\|~v1_partfun1(X3,X2)\|~v1_relat_1(X4)\|~v4_relat_1(X4,X2)\|~v1_funct_1(X4)\|~v1_partfun1(X4,X2)\|~r2_pboole(X2,X1,X3)\|~r2_pboole(X2,X4,X3)), inference(split_conjunct,[status(thm)],[c_0_15])). fof(c_0_30, plain, ![X25, X26, X27]:((v1_relat_1(k2_pboole(X25,X26,X27))\|(~v1_relat_1(X26)\|(~v4_relat_1(X26,X25)\|(~v1_funct_1(X26)\|~v1_partfun1(X26,X25)))\|(~v1_relat_1(X27)\|(~v4_relat_1(X27,X25)\|(~v1_funct_1(X27)\|~v1_partfun1(X27,X25))))))&((v4_relat_1(k2_pboole(X25,X26,X27),X25)\|(~v1_relat_1(X26)\|(~v4_relat_1(X26,X25)\|(~v1_funct_1(X26)\|~v1_partfun1(X26,X25)))\|(~v1_relat_1(X27)\|(~v4_relat_1(X27,X25)\|(~v1_funct_1(X27)\|~v1_partfun1(X27,X25))))))&((v1_funct_1(k2_pboole(X25,X26,X27))\|(~v1_relat_1(X26)\|(~v4_relat_1(X26,X25)\|(~v1_funct_1(X26)\|~v1_partfun1(X26,X25)))\|(~v1_relat_1(X27)\|(~v4_relat_1(X27,X25)\|(~v1_funct_1(X27)\|~v1_partfun1(X27,X25))))))&(v1_partfun1(k2_pboole(X25,X26,X27),X25)\|(~v1_relat_1(X26)\|(~v4_relat_1(X26,X25)\|(~v1_funct_1(X26)\|~v1_partfun1(X26,X25)))\|(~v1_relat_1(X27)\|(~v4_relat_1(X27,X25)\|(~v1_funct_1(X27)\|~v1_partfun1(X27,X25))))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_pboole])])])). cnf(c_0_31, plain, (v2_relat_1(X3)\|~v1_relat_1(X1)\|~v4_relat_1(X1,X2)\|~v1_funct_1(X1)\|~v1_partfun1(X1,X2)\|~v1_relat_1(X3)\|~v4_relat_1(X3,X2)\|~v1_funct_1(X3)\|~v1_partfun1(X3,X2)\|~v2_relat_1(X1)\|~r2_pboole(X2,X1,X3)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_32, negated_conjecture, (~v2_relat_1(X1)\|~v2_finset_1(X1)\|~m3_pboole(X1,esk1_0,esk2_0)\|~r2_pboole(esk1_0,esk3_0,X1)), inference(evalgc,[status(thm)],[c_0_17])). cnf(c_0_33, plain, (r2_pboole(X2,X1,k2_pboole(X2,X1,X3))\|~v1_relat_1(X3)\|~v1_relat_1(X1)\|~v1_funct_1(X3)\|~v1_funct_1(X1)\|~v4_relat_1(X3,X2)\|~v4_relat_1(X1,X2)\|~v1_partfun1(X3,X2)\|~v1_partfun1(X1,X2)), inference(evalgc,[status(thm)],[c_0_18])). cnf(c_0_34, plain, (v1_partfun1(X1,X2)\|~v1_relat_1(X3)\|~v1_funct_1(X3)\|~v4_relat_1(X3,X2)\|~v1_partfun1(X3,X2)\|~m3_pboole(X1,X2,X3)), inference(evalgc,[status(thm)],[c_0_19])). cnf(c_0_35, negated_conjecture, (m3_pboole(esk3_0,esk1_0,esk2_0)), inference(evalgc,[status(thm)],[c_0_20])). cnf(c_0_36, negated_conjecture, (v1_partfun1(esk2_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_21])). cnf(c_0_37, negated_conjecture, (v1_funct_1(esk2_0)), inference(evalgc,[status(thm)],[c_0_22])). cnf(c_0_38, negated_conjecture, (v4_relat_1(esk2_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_23])). cnf(c_0_39, negated_conjecture, (v1_relat_1(esk2_0)), inference(evalgc,[status(thm)],[c_0_24])). cnf(c_0_40, plain, (v1_funct_1(X1)\|~v1_relat_1(X3)\|~v1_funct_1(X3)\|~v4_relat_1(X3,X2)\|~v1_partfun1(X3,X2)\|~m3_pboole(X1,X2,X3)), inference(evalgc,[status(thm)],[c_0_25])). cnf(c_0_41, plain, (v4_relat_1(X1,X2)\|~v1_relat_1(X3)\|~v1_funct_1(X3)\|~v4_relat_1(X3,X2)\|~v1_partfun1(X3,X2)\|~m3_pboole(X1,X2,X3)), inference(evalgc,[status(thm)],[c_0_26])). cnf(c_0_42, plain, (v1_relat_1(X1)\|~v1_relat_1(X3)\|~v1_funct_1(X3)\|~v4_relat_1(X3,X2)\|~v1_partfun1(X3,X2)\|~m3_pboole(X1,X2,X3)), inference(evalgc,[status(thm)],[c_0_27])). cnf(c_0_43, plain, (m3_pboole(X2,X1,X3)\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v4_relat_1(X3,X1)\|~v4_relat_1(X2,X1)\|~v1_partfun1(X3,X1)\|~v1_partfun1(X2,X1)\|~r2_pboole(X1,X2,X3)), inference(evalgc,[status(thm)],[c_0_28])). cnf(c_0_44, plain, (r2_pboole(X2,k2_pboole(X2,X1,X4),X3)\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~v1_relat_1(X1)\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v1_funct_1(X1)\|~v4_relat_1(X4,X2)\|~v4_relat_1(X3,X2)\|~v4_relat_1(X1,X2)\|~v1_partfun1(X4,X2)\|~v1_partfun1(X3,X2)\|~v1_partfun1(X1,X2)\|~r2_pboole(X2,X4,X3)\|~r2_pboole(X2,X1,X3)), inference(evalgc,[status(thm)],[c_0_29])). cnf(c_0_45, plain, (v1_relat_1(k2_pboole(X1,X2,X3))\|~v1_relat_1(X2)\|~v4_relat_1(X2,X1)\|~v1_funct_1(X2)\|~v1_partfun1(X2,X1)\|~v1_relat_1(X3)\|~v4_relat_1(X3,X1)\|~v1_funct_1(X3)\|~v1_partfun1(X3,X1)), inference(split_conjunct,[status(thm)],[c_0_30])). cnf(c_0_46, plain, (v4_relat_1(k2_pboole(X1,X2,X3),X1)\|~v1_relat_1(X2)\|~v4_relat_1(X2,X1)\|~v1_funct_1(X2)\|~v1_partfun1(X2,X1)\|~v1_relat_1(X3)\|~v4_relat_1(X3,X1)\|~v1_funct_1(X3)\|~v1_partfun1(X3,X1)), inference(split_conjunct,[status(thm)],[c_0_30])). cnf(c_0_47, plain, (v1_funct_1(k2_pboole(X1,X2,X3))\|~v1_relat_1(X2)\|~v4_relat_1(X2,X1)\|~v1_funct_1(X2)\|~v1_partfun1(X2,X1)\|~v1_relat_1(X3)\|~v4_relat_1(X3,X1)\|~v1_funct_1(X3)\|~v1_partfun1(X3,X1)), inference(split_conjunct,[status(thm)],[c_0_30])). cnf(c_0_48, plain, (v1_partfun1(k2_pboole(X1,X2,X3),X1)\|~v1_relat_1(X2)\|~v4_relat_1(X2,X1)\|~v1_funct_1(X2)\|~v1_partfun1(X2,X1)\|~v1_relat_1(X3)\|~v4_relat_1(X3,X1)\|~v1_funct_1(X3)\|~v1_partfun1(X3,X1)), inference(split_conjunct,[status(thm)],[c_0_30])). cnf(c_0_49, plain, (v2_relat_1(X3)\|~v1_relat_1(X3)\|~v1_relat_1(X1)\|~v2_relat_1(X1)\|~v1_funct_1(X3)\|~v1_funct_1(X1)\|~v4_relat_1(X3,X2)\|~v4_relat_1(X1,X2)\|~v1_partfun1(X3,X2)\|~v1_partfun1(X1,X2)\|~r2_pboole(X2,X1,X3)), inference(evalgc,[status(thm)],[c_0_31])). fof(c_0_50, plain, ![X28, X29, X30]:(~v1_relat_1(X29)\|(~v4_relat_1(X29,X28)\|(~v1_funct_1(X29)\|~v1_partfun1(X29,X28)))\|(~v1_relat_1(X30)\|(~v4_relat_1(X30,X28)\|(~v1_funct_1(X30)\|~v1_partfun1(X30,X28))))\|k2_pboole(X28,X29,X30)=k2_pboole(X28,X30,X29)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[commutativity_k2_pboole])])). cnf(c_0_51, negated_conjecture, (~m3_pboole(k2_pboole(esk1_0,esk3_0,X1),esk1_0,esk2_0)\|~v2_finset_1(k2_pboole(esk1_0,esk3_0,X1))\|~v2_relat_1(k2_pboole(esk1_0,esk3_0,X1))\|~v1_partfun1(X1,esk1_0)\|~v1_partfun1(esk3_0,esk1_0)\|~v1_funct_1(X1)\|~v1_funct_1(esk3_0)\|~v4_relat_1(X1,esk1_0)\|~v4_relat_1(esk3_0,esk1_0)\|~v1_relat_1(X1)\|~v1_relat_1(esk3_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_32, c_0_33])])). cnf(c_0_52, negated_conjecture, (v1_partfun1(esk3_0,esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34, c_0_35]), c_0_36]), c_0_37]), c_0_38]), c_0_39])])])). cnf(c_0_53, negated_conjecture, (v1_funct_1(esk3_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40, c_0_35]), c_0_36]), c_0_37]), c_0_38]), c_0_39])])])). cnf(c_0_54, negated_conjecture, (v4_relat_1(esk3_0,esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41, c_0_35]), c_0_36]), c_0_37]), c_0_38]), c_0_39])])])). cnf(c_0_55, negated_conjecture, (v1_relat_1(esk3_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42, c_0_35]), c_0_36]), c_0_37]), c_0_38]), c_0_39])])])). cnf(c_0_56, plain, (m3_pboole(k2_pboole(X1,X2,X3),X1,X4)\|~v1_partfun1(X4,X1)\|~v1_partfun1(k2_pboole(X1,X2,X3),X1)\|~v1_funct_1(X4)\|~v1_funct_1(k2_pboole(X1,X2,X3))\|~v4_relat_1(X4,X1)\|~v4_relat_1(k2_pboole(X1,X2,X3),X1)\|~v1_relat_1(X4)\|~v1_relat_1(k2_pboole(X1,X2,X3))\|~r2_pboole(X1,X3,X4)\|~r2_pboole(X1,X2,X4)\|~v1_partfun1(X3,X1)\|~v1_partfun1(X2,X1)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v4_relat_1(X3,X1)\|~v4_relat_1(X2,X1)\|~v1_relat_1(X3)\|~v1_relat_1(X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_43, c_0_44])])). cnf(c_0_57, plain, (v1_relat_1(k2_pboole(X1,X2,X3))\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v4_relat_1(X3,X1)\|~v4_relat_1(X2,X1)\|~v1_partfun1(X3,X1)\|~v1_partfun1(X2,X1)), inference(evalgc,[status(thm)],[c_0_45])). cnf(c_0_58, plain, (v4_relat_1(k2_pboole(X1,X2,X3),X1)\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v4_relat_1(X3,X1)\|~v4_relat_1(X2,X1)\|~v1_partfun1(X3,X1)\|~v1_partfun1(X2,X1)), inference(evalgc,[status(thm)],[c_0_46])). cnf(c_0_59, plain, (v1_funct_1(k2_pboole(X1,X2,X3))\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v4_relat_1(X3,X1)\|~v4_relat_1(X2,X1)\|~v1_partfun1(X3,X1)\|~v1_partfun1(X2,X1)), inference(evalgc,[status(thm)],[c_0_47])). cnf(c_0_60, plain, (v1_partfun1(k2_pboole(X1,X2,X3),X1)\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v4_relat_1(X3,X1)\|~v4_relat_1(X2,X1)\|~v1_partfun1(X3,X1)\|~v1_partfun1(X2,X1)), inference(evalgc,[status(thm)],[c_0_48])). cnf(c_0_61, plain, (v2_relat_1(k2_pboole(X1,X2,X3))\|~v1_partfun1(k2_pboole(X1,X2,X3),X1)\|~v1_partfun1(X2,X1)\|~v1_funct_1(k2_pboole(X1,X2,X3))\|~v1_funct_1(X2)\|~v4_relat_1(k2_pboole(X1,X2,X3),X1)\|~v4_relat_1(X2,X1)\|~v2_relat_1(X2)\|~v1_relat_1(k2_pboole(X1,X2,X3))\|~v1_relat_1(X2)\|~v1_partfun1(X3,X1)\|~v1_funct_1(X3)\|~v4_relat_1(X3,X1)\|~v1_relat_1(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_49, c_0_33])])). cnf(c_0_62, plain, (k2_pboole(X2,X1,X3)=k2_pboole(X2,X3,X1)\|~v1_relat_1(X1)\|~v4_relat_1(X1,X2)\|~v1_funct_1(X1)\|~v1_partfun1(X1,X2)\|~v1_relat_1(X3)\|~v4_relat_1(X3,X2)\|~v1_funct_1(X3)\|~v1_partfun1(X3,X2)), inference(split_conjunct,[status(thm)],[c_0_50])). cnf(c_0_63, negated_conjecture, (~m3_pboole(k2_pboole(esk1_0,esk3_0,X1),esk1_0,esk2_0)\|~v2_finset_1(k2_pboole(esk1_0,esk3_0,X1))\|~v1_partfun1(X1,esk1_0)\|~v1_funct_1(X1)\|~v4_relat_1(X1,esk1_0)\|~v2_relat_1(k2_pboole(esk1_0,esk3_0,X1))\|~v1_relat_1(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_51, c_0_52]), c_0_53]), c_0_54]), c_0_55])])). cnf(c_0_64, plain, (m3_pboole(k2_pboole(X1,X2,X3),X1,X4)\|~r2_pboole(X1,X3,X4)\|~r2_pboole(X1,X2,X4)\|~v1_partfun1(X4,X1)\|~v1_partfun1(X3,X1)\|~v1_partfun1(X2,X1)\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v4_relat_1(X4,X1)\|~v4_relat_1(X3,X1)\|~v4_relat_1(X2,X1)\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~v1_relat_1(X2)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_56, c_0_57]), c_0_58]), c_0_59]), c_0_60])). cnf(c_0_65, plain, (v2_relat_1(k2_pboole(X1,X2,X3))\|~v1_partfun1(X2,X1)\|~v1_partfun1(X3,X1)\|~v1_funct_1(X2)\|~v1_funct_1(X3)\|~v4_relat_1(X2,X1)\|~v4_relat_1(X3,X1)\|~v2_relat_1(X2)\|~v1_relat_1(X2)\|~v1_relat_1(X3)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_61, c_0_57]), c_0_58]), c_0_59]), c_0_60])). cnf(c_0_66, plain, (k2_pboole(X2,X1,X3)=k2_pboole(X2,X3,X1)\|~v1_relat_1(X3)\|~v1_relat_1(X1)\|~v1_funct_1(X3)\|~v1_funct_1(X1)\|~v4_relat_1(X3,X2)\|~v4_relat_1(X1,X2)\|~v1_partfun1(X3,X2)\|~v1_partfun1(X1,X2)), inference(evalgc,[status(thm)],[c_0_62])). cnf(c_0_67, plain, (r2_pboole(X2,X1,X3)\|~m3_pboole(X1,X2,X3)\|~v1_relat_1(X1)\|~v4_relat_1(X1,X2)\|~v1_funct_1(X1)\|~v1_partfun1(X1,X2)\|~v1_relat_1(X3)\|~v4_relat_1(X3,X2)\|~v1_funct_1(X3)\|~v1_partfun1(X3,X2)), inference(split_conjunct,[status(thm)],[c_0_14])). cnf(c_0_68, negated_conjecture, (~v2_finset_1(k2_pboole(esk1_0,esk3_0,X1))\|~v1_partfun1(X1,esk1_0)\|~v1_funct_1(X1)\|~v4_relat_1(X1,esk1_0)\|~v2_relat_1(k2_pboole(esk1_0,esk3_0,X1))\|~v1_relat_1(X1)\|~r2_pboole(esk1_0,X1,esk2_0)\|~r2_pboole(esk1_0,esk3_0,esk2_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63, c_0_64]), c_0_36]), c_0_52]), c_0_37]), c_0_53]), c_0_38]), c_0_54]), c_0_39]), c_0_55])])])). cnf(c_0_69, plain, (v2_relat_1(k2_pboole(X1,X3,X2))\|~v1_partfun1(X2,X1)\|~v1_partfun1(X3,X1)\|~v1_funct_1(X2)\|~v1_funct_1(X3)\|~v4_relat_1(X2,X1)\|~v4_relat_1(X3,X1)\|~v2_relat_1(X2)\|~v1_relat_1(X2)\|~v1_relat_1(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_65, c_0_66])])). cnf(c_0_70, plain, (r2_pboole(X2,X1,X3)\|~v1_relat_1(X3)\|~v1_relat_1(X1)\|~v1_funct_1(X3)\|~v1_funct_1(X1)\|~v4_relat_1(X3,X2)\|~v4_relat_1(X1,X2)\|~v1_partfun1(X3,X2)\|~v1_partfun1(X1,X2)\|~m3_pboole(X1,X2,X3)), inference(evalgc,[status(thm)],[c_0_67])). cnf(c_0_71, negated_conjecture, (~r2_pboole(esk1_0,esk3_0,esk2_0)\|~r2_pboole(esk1_0,X1,esk2_0)\|~v2_finset_1(k2_pboole(esk1_0,esk3_0,X1))\|~v1_partfun1(X1,esk1_0)\|~v1_funct_1(X1)\|~v4_relat_1(X1,esk1_0)\|~v1_relat_1(X1)\|~v2_relat_1(X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68, c_0_69]), c_0_52]), c_0_53]), c_0_54]), c_0_55])])])). cnf(c_0_72, plain, (r2_pboole(X1,X2,X3)\|~m3_pboole(X2,X1,X3)\|~v1_partfun1(X3,X1)\|~v1_funct_1(X3)\|~v4_relat_1(X3,X1)\|~v1_relat_1(X3)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_70, c_0_42]), c_0_41]), c_0_40]), c_0_34])). fof(c_0_73, plain, ![X31, X32]:((m3_pboole(esk4_2(X31,X32),X31,X32)\|(~v1_relat_1(X32)\|(~v2_relat_1(X32)\|(~v4_relat_1(X32,X31)\|(~v1_funct_1(X32)\|~v1_partfun1(X32,X31))))))&((v1_relat_1(esk4_2(X31,X32))\|(~v1_relat_1(X32)\|(~v2_relat_1(X32)\|(~v4_relat_1(X32,X31)\|(~v1_funct_1(X32)\|~v1_partfun1(X32,X31))))))&((v2_relat_1(esk4_2(X31,X32))\|(~v1_relat_1(X32)\|(~v2_relat_1(X32)\|(~v4_relat_1(X32,X31)\|(~v1_funct_1(X32)\|~v1_partfun1(X32,X31))))))&((v4_relat_1(esk4_2(X31,X32),X31)\|(~v1_relat_1(X32)\|(~v2_relat_1(X32)\|(~v4_relat_1(X32,X31)\|(~v1_funct_1(X32)\|~v1_partfun1(X32,X31))))))&((v1_funct_1(esk4_2(X31,X32))\|(~v1_relat_1(X32)\|(~v2_relat_1(X32)\|(~v4_relat_1(X32,X31)\|(~v1_funct_1(X32)\|~v1_partfun1(X32,X31))))))&((v1_partfun1(esk4_2(X31,X32),X31)\|(~v1_relat_1(X32)\|(~v2_relat_1(X32)\|(~v4_relat_1(X32,X31)\|(~v1_funct_1(X32)\|~v1_partfun1(X32,X31))))))&(v2_finset_1(esk4_2(X31,X32))\|(~v1_relat_1(X32)\|(~v2_relat_1(X32)\|(~v4_relat_1(X32,X31)\|(~v1_funct_1(X32)\|~v1_partfun1(X32,X31)))))))))))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[rc2_msualg_9])])])])). cnf(c_0_74, negated_conjecture, (~r2_pboole(esk1_0,X1,esk2_0)\|~v2_finset_1(k2_pboole(esk1_0,esk3_0,X1))\|~v1_partfun1(X1,esk1_0)\|~v1_funct_1(X1)\|~v4_relat_1(X1,esk1_0)\|~v2_relat_1(X1)\|~v1_relat_1(X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71, c_0_72]), c_0_35]), c_0_36]), c_0_37]), c_0_38]), c_0_39])])])). cnf(c_0_75, plain, (m3_pboole(esk4_2(X1,X2),X1,X2)\|~v1_relat_1(X2)\|~v2_relat_1(X2)\|~v4_relat_1(X2,X1)\|~v1_funct_1(X2)\|~v1_partfun1(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_73])). cnf(c_0_76, negated_conjecture, (v2_relat_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_11])). fof(c_0_77, plain, ![X34, X35, X36]:((v1_relat_1(k2_pboole(X34,X35,X36))\|(~v1_relat_1(X35)\|(~v4_relat_1(X35,X34)\|(~v1_funct_1(X35)\|(~v1_partfun1(X35,X34)\|~v2_finset_1(X35))))\|(~v1_relat_1(X36)\|(~v4_relat_1(X36,X34)\|(~v1_funct_1(X36)\|(~v1_partfun1(X36,X34)\|~v2_finset_1(X36)))))))&((v4_relat_1(k2_pboole(X34,X35,X36),X34)\|(~v1_relat_1(X35)\|(~v4_relat_1(X35,X34)\|(~v1_funct_1(X35)\|(~v1_partfun1(X35,X34)\|~v2_finset_1(X35))))\|(~v1_relat_1(X36)\|(~v4_relat_1(X36,X34)\|(~v1_funct_1(X36)\|(~v1_partfun1(X36,X34)\|~v2_finset_1(X36)))))))&((v1_funct_1(k2_pboole(X34,X35,X36))\|(~v1_relat_1(X35)\|(~v4_relat_1(X35,X34)\|(~v1_funct_1(X35)\|(~v1_partfun1(X35,X34)\|~v2_finset_1(X35))))\|(~v1_relat_1(X36)\|(~v4_relat_1(X36,X34)\|(~v1_funct_1(X36)\|(~v1_partfun1(X36,X34)\|~v2_finset_1(X36)))))))&((v1_partfun1(k2_pboole(X34,X35,X36),X34)\|(~v1_relat_1(X35)\|(~v4_relat_1(X35,X34)\|(~v1_funct_1(X35)\|(~v1_partfun1(X35,X34)\|~v2_finset_1(X35))))\|(~v1_relat_1(X36)\|(~v4_relat_1(X36,X34)\|(~v1_funct_1(X36)\|(~v1_partfun1(X36,X34)\|~v2_finset_1(X36)))))))&(v2_finset_1(k2_pboole(X34,X35,X36))\|(~v1_relat_1(X35)\|(~v4_relat_1(X35,X34)\|(~v1_funct_1(X35)\|(~v1_partfun1(X35,X34)\|~v2_finset_1(X35))))\|(~v1_relat_1(X36)\|(~v4_relat_1(X36,X34)\|(~v1_funct_1(X36)\|(~v1_partfun1(X36,X34)\|~v2_finset_1(X36))))))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc6_mssubfam])])])). cnf(c_0_78, negated_conjecture, (~v2_finset_1(k2_pboole(esk1_0,esk3_0,X1))\|~v1_partfun1(X1,esk1_0)\|~v1_funct_1(X1)\|~v4_relat_1(X1,esk1_0)\|~v2_relat_1(X1)\|~v1_relat_1(X1)\|~m3_pboole(X1,esk1_0,esk2_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74, c_0_72]), c_0_36]), c_0_37]), c_0_38]), c_0_39])])])). cnf(c_0_79, plain, (m3_pboole(esk4_2(X1,X2),X1,X2)\|~v1_relat_1(X2)\|~v2_relat_1(X2)\|~v1_funct_1(X2)\|~v4_relat_1(X2,X1)\|~v1_partfun1(X2,X1)), inference(evalgc,[status(thm)],[c_0_75])). cnf(c_0_80, negated_conjecture, (v2_relat_1(esk2_0)), inference(evalgc,[status(thm)],[c_0_76])). cnf(c_0_81, plain, (v2_finset_1(k2_pboole(X1,X2,X3))\|~v1_relat_1(X2)\|~v4_relat_1(X2,X1)\|~v1_funct_1(X2)\|~v1_partfun1(X2,X1)\|~v2_finset_1(X2)\|~v1_relat_1(X3)\|~v4_relat_1(X3,X1)\|~v1_funct_1(X3)\|~v1_partfun1(X3,X1)\|~v2_finset_1(X3)), inference(split_conjunct,[status(thm)],[c_0_77])). cnf(c_0_82, negated_conjecture, (v2_finset_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_83, negated_conjecture, (~v2_finset_1(k2_pboole(esk1_0,esk3_0,esk4_2(esk1_0,esk2_0)))\|~v1_partfun1(esk4_2(esk1_0,esk2_0),esk1_0)\|~v1_funct_1(esk4_2(esk1_0,esk2_0))\|~v4_relat_1(esk4_2(esk1_0,esk2_0),esk1_0)\|~v2_relat_1(esk4_2(esk1_0,esk2_0))\|~v1_relat_1(esk4_2(esk1_0,esk2_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78, c_0_79]), c_0_36]), c_0_37]), c_0_38]), c_0_80]), c_0_39])])])). cnf(c_0_84, plain, (v2_finset_1(k2_pboole(X1,X2,X3))\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v2_finset_1(X3)\|~v2_finset_1(X2)\|~v4_relat_1(X3,X1)\|~v4_relat_1(X2,X1)\|~v1_partfun1(X3,X1)\|~v1_partfun1(X2,X1)), inference(evalgc,[status(thm)],[c_0_81])). cnf(c_0_85, negated_conjecture, (v2_finset_1(esk3_0)), inference(evalgc,[status(thm)],[c_0_82])). cnf(c_0_86, plain, (v2_relat_1(esk4_2(X1,X2))\|~v1_relat_1(X2)\|~v2_relat_1(X2)\|~v4_relat_1(X2,X1)\|~v1_funct_1(X2)\|~v1_partfun1(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_73])). cnf(c_0_87, negated_conjecture, (~v1_partfun1(esk4_2(esk1_0,esk2_0),esk1_0)\|~v1_funct_1(esk4_2(esk1_0,esk2_0))\|~v4_relat_1(esk4_2(esk1_0,esk2_0),esk1_0)\|~v2_relat_1(esk4_2(esk1_0,esk2_0))\|~v1_relat_1(esk4_2(esk1_0,esk2_0))\|~v2_finset_1(esk4_2(esk1_0,esk2_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83, c_0_84]), c_0_85]), c_0_52]), c_0_53]), c_0_54]), c_0_55])])])). cnf(c_0_88, plain, (v2_relat_1(esk4_2(X1,X2))\|~v1_relat_1(X2)\|~v2_relat_1(X2)\|~v1_funct_1(X2)\|~v4_relat_1(X2,X1)\|~v1_partfun1(X2,X1)), inference(evalgc,[status(thm)],[c_0_86])). cnf(c_0_89, plain, (v2_finset_1(esk4_2(X1,X2))\|~v1_relat_1(X2)\|~v2_relat_1(X2)\|~v4_relat_1(X2,X1)\|~v1_funct_1(X2)\|~v1_partfun1(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_73])). cnf(c_0_90, negated_conjecture, (~v2_finset_1(esk4_2(esk1_0,esk2_0))\|~v1_partfun1(esk4_2(esk1_0,esk2_0),esk1_0)\|~v1_funct_1(esk4_2(esk1_0,esk2_0))\|~v4_relat_1(esk4_2(esk1_0,esk2_0),esk1_0)\|~v1_relat_1(esk4_2(esk1_0,esk2_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87, c_0_88]), c_0_36]), c_0_37]), c_0_38]), c_0_80]), c_0_39])])])). cnf(c_0_91, plain, (v2_finset_1(esk4_2(X1,X2))\|~v1_relat_1(X2)\|~v2_relat_1(X2)\|~v1_funct_1(X2)\|~v4_relat_1(X2,X1)\|~v1_partfun1(X2,X1)), inference(evalgc,[status(thm)],[c_0_89])). cnf(c_0_92, plain, (v1_partfun1(esk4_2(X1,X2),X1)\|~v1_relat_1(X2)\|~v2_relat_1(X2)\|~v4_relat_1(X2,X1)\|~v1_funct_1(X2)\|~v1_partfun1(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_73])). cnf(c_0_93, negated_conjecture, (~v1_partfun1(esk4_2(esk1_0,esk2_0),esk1_0)\|~v1_funct_1(esk4_2(esk1_0,esk2_0))\|~v4_relat_1(esk4_2(esk1_0,esk2_0),esk1_0)\|~v1_relat_1(esk4_2(esk1_0,esk2_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90, c_0_91]), c_0_36]), c_0_37]), c_0_38]), c_0_80]), c_0_39])])])). cnf(c_0_94, plain, (v1_partfun1(esk4_2(X1,X2),X1)\|~v1_relat_1(X2)\|~v2_relat_1(X2)\|~v1_funct_1(X2)\|~v4_relat_1(X2,X1)\|~v1_partfun1(X2,X1)), inference(evalgc,[status(thm)],[c_0_92])). cnf(c_0_95, plain, (v4_relat_1(esk4_2(X1,X2),X1)\|~v1_relat_1(X2)\|~v2_relat_1(X2)\|~v4_relat_1(X2,X1)\|~v1_funct_1(X2)\|~v1_partfun1(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_73])). cnf(c_0_96, negated_conjecture, (~v1_funct_1(esk4_2(esk1_0,esk2_0))\|~v4_relat_1(esk4_2(esk1_0,esk2_0),esk1_0)\|~v1_relat_1(esk4_2(esk1_0,esk2_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93, c_0_94]), c_0_36]), c_0_37]), c_0_38]), c_0_80]), c_0_39])])])). cnf(c_0_97, plain, (v4_relat_1(esk4_2(X1,X2),X1)\|~v1_relat_1(X2)\|~v2_relat_1(X2)\|~v1_funct_1(X2)\|~v4_relat_1(X2,X1)\|~v1_partfun1(X2,X1)), inference(evalgc,[status(thm)],[c_0_95])). cnf(c_0_98, plain, (v1_funct_1(esk4_2(X1,X2))\|~v1_relat_1(X2)\|~v2_relat_1(X2)\|~v4_relat_1(X2,X1)\|~v1_funct_1(X2)\|~v1_partfun1(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_73])). cnf(c_0_99, negated_conjecture, (~v1_funct_1(esk4_2(esk1_0,esk2_0))\|~v1_relat_1(esk4_2(esk1_0,esk2_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96, c_0_97]), c_0_36]), c_0_37]), c_0_38]), c_0_80]), c_0_39])])])). cnf(c_0_100, plain, (v1_funct_1(esk4_2(X1,X2))\|~v1_relat_1(X2)\|~v2_relat_1(X2)\|~v1_funct_1(X2)\|~v4_relat_1(X2,X1)\|~v1_partfun1(X2,X1)), inference(evalgc,[status(thm)],[c_0_98])). cnf(c_0_101, plain, (v1_relat_1(esk4_2(X1,X2))\|~v1_relat_1(X2)\|~v2_relat_1(X2)\|~v4_relat_1(X2,X1)\|~v1_funct_1(X2)\|~v1_partfun1(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_73])). cnf(c_0_102, negated_conjecture, (~v1_relat_1(esk4_2(esk1_0,esk2_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99, c_0_100]), c_0_36]), c_0_37]), c_0_38]), c_0_80]), c_0_39])])])). cnf(c_0_103, plain, (v1_relat_1(esk4_2(X1,X2))\|~v1_relat_1(X2)\|~v2_relat_1(X2)\|~v1_funct_1(X2)\|~v4_relat_1(X2,X1)\|~v1_partfun1(X2,X1)), inference(evalgc,[status(thm)],[c_0_101])). cnf(c_0_104, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102, c_0_103]), c_0_36]), c_0_37]), c_0_38]), c_0_80]), c_0_39])]), ['proof']). # SZS output end CNFRefutation	reserve a, I for set, S for non empty non void ManySortedSign; theorem for M being non-empty ManySortedSet of I for B being finite-yielding ManySortedSubset of M ex C being non-empty finite-yielding ManySortedSubset of M st B c= C proof let M be non-empty ManySortedSet of I, B be finite-yielding ManySortedSubset of M; defpred P[set,set] means ex a being Element of M.$1 st $2 = {a} \/ B.$1; A1: now let i be set such that i in I; set a = the Element of M.i; take j = {a} \/ B.i; thus P[i,j]; end; consider C being ManySortedSet of I such that A2: for i be set st i in I holds P[i,C.i] from PBOOLE:sch 3(A1); A3: C is ManySortedSubset of M proof let i be set; assume A4: i in I; then consider a being Element of M.i such that A5: C.i = {a} \/ B.i by A2; let q be set; assume q in C.i; then A6: q in {a} or q in B.i by A5,XBOOLE_0:def 3; B c= M by PBOOLE:def 18; then B.i c= M.i by A4,PBOOLE:def 2; then A7: q = a or q in M.i by A6,TARSKI:def 1; M.i is non empty by A4; hence thesis by A7; end; A8: C is finite-yielding proof let i be set; assume A9: i in I; reconsider b = B.i as finite set; consider a being Element of M.i such that A10: C.i = {a} \/ B.i by A2,A9; thus thesis by A10; end; C is non-empty proof let i be set; assume i in I; then ex a being Element of M.i st C.i = {a} \/ B.i by A2; hence thesis; end; then reconsider C as non-empty finite-yielding ManySortedSubset of M by A3,A8 ; take C; let i be set; assume i in I; then ex a being Element of M.i st C.i = {a} \/ B.i by A2; hence thesis by XBOOLE_1:7; end;	Convert the following ATP output trace into a readable Mizar proof.
t23_morph_01	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(fraenkel_a_3_0_morph_01, axiom, ![X1, X2, X3, X4]:(((~(v2_struct_0(X2))&(v13_algstr_0(X2)&(v2_rlvect_1(X2)&(v3_rlvect_1(X2)&(v4_rlvect_1(X2)&(v5_rlvect_1(X2)&(v6_rlvect_1(X2)&(v7_rlvect_1(X2)&(v8_rlvect_1(X2)&l1_rlvect_1(X2))))))))))&(m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))&m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))))=>(r2_hidden(X1,a_3_0_morph_01(X2,X3,X4))<=>?[X5]:(m1_subset_1(X5,u1_struct_0(X2))&(X1=X5&![X6]:(m1_subset_1(X6,u1_struct_0(X2))=>(r2_hidden(X6,X4)=>r2_hidden(k5_algstr_0(X2,X5,X6),X3))))))), file('/scratch/mptp/predsminms1/t23_morph_01__0', fraenkel_a_3_0_morph_01)). fof(t4_subset, axiom, ![X1, X2, X3]:((r2_hidden(X1,X2)&m1_subset_1(X2,k1_zfmisc_1(X3)))=>m1_subset_1(X1,X3)), file('/scratch/mptp/predsminms1/t23_morph_01__0', t4_subset)). fof(t23_morph_01, conjecture, ![X1]:((~(v2_struct_0(X1))&(v13_algstr_0(X1)&(v2_rlvect_1(X1)&(v3_rlvect_1(X1)&(v4_rlvect_1(X1)&(v5_rlvect_1(X1)&(v6_rlvect_1(X1)&(v7_rlvect_1(X1)&(v8_rlvect_1(X1)&l1_rlvect_1(X1))))))))))=>![X2]:((~(v1_xboole_0(X2))&m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))))=>![X3]:((~(v1_xboole_0(X3))&m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1))))=>![X4]:((~(v1_xboole_0(X4))&m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X1))))=>(r1_tarski(X2,X3)=>r1_tarski(k1_morph_01(X1,X4,X3),k1_morph_01(X1,X4,X2))))))), file('/scratch/mptp/predsminms1/t23_morph_01__0', t23_morph_01)). fof(d3_tarski, axiom, ![X1, X2]:(r1_tarski(X1,X2)<=>![X3]:(r2_hidden(X3,X1)=>r2_hidden(X3,X2))), file('/scratch/mptp/predsminms1/t23_morph_01__0', d3_tarski)). fof(d1_morph_01, axiom, ![X1]:((~(v2_struct_0(X1))&(v13_algstr_0(X1)&(v2_rlvect_1(X1)&(v3_rlvect_1(X1)&(v4_rlvect_1(X1)&(v5_rlvect_1(X1)&(v6_rlvect_1(X1)&(v7_rlvect_1(X1)&(v8_rlvect_1(X1)&l1_rlvect_1(X1))))))))))=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))=>![X3]:(m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))=>k1_morph_01(X1,X2,X3)=a_3_0_morph_01(X1,X2,X3)))), file('/scratch/mptp/predsminms1/t23_morph_01__0', d1_morph_01)). fof(c_0_5, plain, ![X11, X12, X13, X14, X16, X17]:(((m1_subset_1(esk5_4(X11,X12,X13,X14),u1_struct_0(X12))\|~r2_hidden(X11,a_3_0_morph_01(X12,X13,X14))\|(v2_struct_0(X12)\|(~v13_algstr_0(X12)\|(~v2_rlvect_1(X12)\|(~v3_rlvect_1(X12)\|(~v4_rlvect_1(X12)\|(~v5_rlvect_1(X12)\|(~v6_rlvect_1(X12)\|(~v7_rlvect_1(X12)\|(~v8_rlvect_1(X12)\|~l1_rlvect_1(X12)))))))))\|(~m1_subset_1(X13,k1_zfmisc_1(u1_struct_0(X12)))\|~m1_subset_1(X14,k1_zfmisc_1(u1_struct_0(X12))))))&((X11=esk5_4(X11,X12,X13,X14)\|~r2_hidden(X11,a_3_0_morph_01(X12,X13,X14))\|(v2_struct_0(X12)\|(~v13_algstr_0(X12)\|(~v2_rlvect_1(X12)\|(~v3_rlvect_1(X12)\|(~v4_rlvect_1(X12)\|(~v5_rlvect_1(X12)\|(~v6_rlvect_1(X12)\|(~v7_rlvect_1(X12)\|(~v8_rlvect_1(X12)\|~l1_rlvect_1(X12)))))))))\|(~m1_subset_1(X13,k1_zfmisc_1(u1_struct_0(X12)))\|~m1_subset_1(X14,k1_zfmisc_1(u1_struct_0(X12))))))&(~m1_subset_1(X16,u1_struct_0(X12))\|(~r2_hidden(X16,X14)\|r2_hidden(k5_algstr_0(X12,esk5_4(X11,X12,X13,X14),X16),X13))\|~r2_hidden(X11,a_3_0_morph_01(X12,X13,X14))\|(v2_struct_0(X12)\|(~v13_algstr_0(X12)\|(~v2_rlvect_1(X12)\|(~v3_rlvect_1(X12)\|(~v4_rlvect_1(X12)\|(~v5_rlvect_1(X12)\|(~v6_rlvect_1(X12)\|(~v7_rlvect_1(X12)\|(~v8_rlvect_1(X12)\|~l1_rlvect_1(X12)))))))))\|(~m1_subset_1(X13,k1_zfmisc_1(u1_struct_0(X12)))\|~m1_subset_1(X14,k1_zfmisc_1(u1_struct_0(X12))))))))&((m1_subset_1(esk6_5(X11,X12,X13,X14,X17),u1_struct_0(X12))\|X11!=X17\|~m1_subset_1(X17,u1_struct_0(X12))\|r2_hidden(X11,a_3_0_morph_01(X12,X13,X14))\|(v2_struct_0(X12)\|(~v13_algstr_0(X12)\|(~v2_rlvect_1(X12)\|(~v3_rlvect_1(X12)\|(~v4_rlvect_1(X12)\|(~v5_rlvect_1(X12)\|(~v6_rlvect_1(X12)\|(~v7_rlvect_1(X12)\|(~v8_rlvect_1(X12)\|~l1_rlvect_1(X12)))))))))\|(~m1_subset_1(X13,k1_zfmisc_1(u1_struct_0(X12)))\|~m1_subset_1(X14,k1_zfmisc_1(u1_struct_0(X12))))))&((r2_hidden(esk6_5(X11,X12,X13,X14,X17),X14)\|X11!=X17\|~m1_subset_1(X17,u1_struct_0(X12))\|r2_hidden(X11,a_3_0_morph_01(X12,X13,X14))\|(v2_struct_0(X12)\|(~v13_algstr_0(X12)\|(~v2_rlvect_1(X12)\|(~v3_rlvect_1(X12)\|(~v4_rlvect_1(X12)\|(~v5_rlvect_1(X12)\|(~v6_rlvect_1(X12)\|(~v7_rlvect_1(X12)\|(~v8_rlvect_1(X12)\|~l1_rlvect_1(X12)))))))))\|(~m1_subset_1(X13,k1_zfmisc_1(u1_struct_0(X12)))\|~m1_subset_1(X14,k1_zfmisc_1(u1_struct_0(X12))))))&(~r2_hidden(k5_algstr_0(X12,X17,esk6_5(X11,X12,X13,X14,X17)),X13)\|X11!=X17\|~m1_subset_1(X17,u1_struct_0(X12))\|r2_hidden(X11,a_3_0_morph_01(X12,X13,X14))\|(v2_struct_0(X12)\|(~v13_algstr_0(X12)\|(~v2_rlvect_1(X12)\|(~v3_rlvect_1(X12)\|(~v4_rlvect_1(X12)\|(~v5_rlvect_1(X12)\|(~v6_rlvect_1(X12)\|(~v7_rlvect_1(X12)\|(~v8_rlvect_1(X12)\|~l1_rlvect_1(X12)))))))))\|(~m1_subset_1(X13,k1_zfmisc_1(u1_struct_0(X12)))\|~m1_subset_1(X14,k1_zfmisc_1(u1_struct_0(X12))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fraenkel_a_3_0_morph_01])])])])])])). fof(c_0_6, plain, ![X19, X20, X21]:(~r2_hidden(X19,X20)\|~m1_subset_1(X20,k1_zfmisc_1(X21))\|m1_subset_1(X19,X21)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])])). cnf(c_0_7, plain, (r2_hidden(X3,a_3_0_morph_01(X1,X4,X5))\|v2_struct_0(X1)\|~r2_hidden(k5_algstr_0(X1,X2,esk6_5(X3,X1,X4,X5,X2)),X4)\|X3!=X2\|~m1_subset_1(X2,u1_struct_0(X1))\|~v13_algstr_0(X1)\|~v2_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v8_rlvect_1(X1)\|~l1_rlvect_1(X1)\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X5,k1_zfmisc_1(u1_struct_0(X1)))), inference(split_conjunct,[status(thm)],[c_0_5])). cnf(c_0_8, plain, (r2_hidden(k5_algstr_0(X2,esk5_4(X4,X2,X5,X3),X1),X5)\|v2_struct_0(X2)\|~m1_subset_1(X1,u1_struct_0(X2))\|~r2_hidden(X1,X3)\|~r2_hidden(X4,a_3_0_morph_01(X2,X5,X3))\|~v13_algstr_0(X2)\|~v2_rlvect_1(X2)\|~v3_rlvect_1(X2)\|~v4_rlvect_1(X2)\|~v5_rlvect_1(X2)\|~v6_rlvect_1(X2)\|~v7_rlvect_1(X2)\|~v8_rlvect_1(X2)\|~l1_rlvect_1(X2)\|~m1_subset_1(X5,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))), inference(split_conjunct,[status(thm)],[c_0_5])). cnf(c_0_9, plain, (m1_subset_1(X1,X3)\|~r2_hidden(X1,X2)\|~m1_subset_1(X2,k1_zfmisc_1(X3))), inference(split_conjunct,[status(thm)],[c_0_6])). fof(c_0_10, negated_conjecture, ~(![X1]:((~(v2_struct_0(X1))&(v13_algstr_0(X1)&(v2_rlvect_1(X1)&(v3_rlvect_1(X1)&(v4_rlvect_1(X1)&(v5_rlvect_1(X1)&(v6_rlvect_1(X1)&(v7_rlvect_1(X1)&(v8_rlvect_1(X1)&l1_rlvect_1(X1))))))))))=>![X2]:((~(v1_xboole_0(X2))&m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))))=>![X3]:((~(v1_xboole_0(X3))&m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1))))=>![X4]:((~(v1_xboole_0(X4))&m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X1))))=>(r1_tarski(X2,X3)=>r1_tarski(k1_morph_01(X1,X4,X3),k1_morph_01(X1,X4,X2)))))))), inference(assume_negation,[status(cth)],[t23_morph_01])). cnf(c_0_11, plain, (v2_struct_0(X1)\|r2_hidden(X3,a_3_0_morph_01(X1,X4,X5))\|X2!=X3\|~v13_algstr_0(X1)\|~v2_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v8_rlvect_1(X1)\|~l1_rlvect_1(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X5,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X1)))\|~r2_hidden(k5_algstr_0(X1,X2,esk6_5(X3,X1,X4,X5,X2)),X4)), inference(evalgc,[status(thm)],[c_0_7])). cnf(c_0_12, plain, (v2_struct_0(X2)\|r2_hidden(k5_algstr_0(X2,esk5_4(X4,X2,X5,X3),X1),X5)\|~v13_algstr_0(X2)\|~v2_rlvect_1(X2)\|~v3_rlvect_1(X2)\|~v4_rlvect_1(X2)\|~v5_rlvect_1(X2)\|~v6_rlvect_1(X2)\|~v7_rlvect_1(X2)\|~v8_rlvect_1(X2)\|~l1_rlvect_1(X2)\|~r2_hidden(X1,X3)\|~m1_subset_1(X1,u1_struct_0(X2))\|~m1_subset_1(X5,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~r2_hidden(X4,a_3_0_morph_01(X2,X5,X3))), inference(evalgc,[status(thm)],[c_0_8])). cnf(c_0_13, plain, (m1_subset_1(X1,X3)\|~r2_hidden(X1,X2)\|~m1_subset_1(X2,k1_zfmisc_1(X3))), inference(evalgc,[status(thm)],[c_0_9])). fof(c_0_14, plain, ![X22, X23, X24, X25, X26]:((~r1_tarski(X22,X23)\|(~r2_hidden(X24,X22)\|r2_hidden(X24,X23)))&((r2_hidden(esk7_2(X25,X26),X25)\|r1_tarski(X25,X26))&(~r2_hidden(esk7_2(X25,X26),X26)\|r1_tarski(X25,X26)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_tarski])])])])])])). fof(c_0_15, negated_conjecture, ((~v2_struct_0(esk1_0)&(v13_algstr_0(esk1_0)&(v2_rlvect_1(esk1_0)&(v3_rlvect_1(esk1_0)&(v4_rlvect_1(esk1_0)&(v5_rlvect_1(esk1_0)&(v6_rlvect_1(esk1_0)&(v7_rlvect_1(esk1_0)&(v8_rlvect_1(esk1_0)&l1_rlvect_1(esk1_0))))))))))&((~v1_xboole_0(esk2_0)&m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(esk1_0))))&((~v1_xboole_0(esk3_0)&m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(esk1_0))))&((~v1_xboole_0(esk4_0)&m1_subset_1(esk4_0,k1_zfmisc_1(u1_struct_0(esk1_0))))&(r1_tarski(esk2_0,esk3_0)&~r1_tarski(k1_morph_01(esk1_0,esk4_0,esk3_0),k1_morph_01(esk1_0,esk4_0,esk2_0))))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_10])])])])). cnf(c_0_16, plain, (r2_hidden(X1,a_3_0_morph_01(X2,X3,X4))\|v2_struct_0(X2)\|~r2_hidden(k5_algstr_0(X2,X1,esk6_5(X1,X2,X3,X4,X1)),X3)\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X1,u1_struct_0(X2))\|~l1_rlvect_1(X2)\|~v8_rlvect_1(X2)\|~v7_rlvect_1(X2)\|~v6_rlvect_1(X2)\|~v5_rlvect_1(X2)\|~v4_rlvect_1(X2)\|~v3_rlvect_1(X2)\|~v2_rlvect_1(X2)\|~v13_algstr_0(X2)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_11])])). cnf(c_0_17, plain, (r2_hidden(k5_algstr_0(X1,esk5_4(X2,X1,X3,X4),X5),X3)\|v2_struct_0(X1)\|~r2_hidden(X2,a_3_0_morph_01(X1,X3,X4))\|~r2_hidden(X5,X4)\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X1)))\|~l1_rlvect_1(X1)\|~v8_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v13_algstr_0(X1)), inference(csr,[status(thm)],[c_0_12, c_0_13])). cnf(c_0_18, plain, (m1_subset_1(esk5_4(X1,X2,X3,X4),u1_struct_0(X2))\|v2_struct_0(X2)\|~r2_hidden(X1,a_3_0_morph_01(X2,X3,X4))\|~v13_algstr_0(X2)\|~v2_rlvect_1(X2)\|~v3_rlvect_1(X2)\|~v4_rlvect_1(X2)\|~v5_rlvect_1(X2)\|~v6_rlvect_1(X2)\|~v7_rlvect_1(X2)\|~v8_rlvect_1(X2)\|~l1_rlvect_1(X2)\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))), inference(split_conjunct,[status(thm)],[c_0_5])). cnf(c_0_19, plain, (r2_hidden(X3,X2)\|~r1_tarski(X1,X2)\|~r2_hidden(X3,X1)), inference(split_conjunct,[status(thm)],[c_0_14])). cnf(c_0_20, negated_conjecture, (r1_tarski(esk2_0,esk3_0)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_21, plain, (r2_hidden(esk5_4(X1,X2,X3,X4),a_3_0_morph_01(X2,X3,X5))\|v2_struct_0(X2)\|~m1_subset_1(X5,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(esk5_4(X1,X2,X3,X4),u1_struct_0(X2))\|~l1_rlvect_1(X2)\|~v8_rlvect_1(X2)\|~v7_rlvect_1(X2)\|~v6_rlvect_1(X2)\|~v5_rlvect_1(X2)\|~v4_rlvect_1(X2)\|~v3_rlvect_1(X2)\|~v2_rlvect_1(X2)\|~v13_algstr_0(X2)\|~r2_hidden(X1,a_3_0_morph_01(X2,X3,X4))\|~r2_hidden(esk6_5(esk5_4(X1,X2,X3,X4),X2,X3,X5,esk5_4(X1,X2,X3,X4)),X4)\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_16, c_0_17])])). cnf(c_0_22, plain, (v2_struct_0(X2)\|m1_subset_1(esk5_4(X1,X2,X3,X4),u1_struct_0(X2))\|~v13_algstr_0(X2)\|~v2_rlvect_1(X2)\|~v3_rlvect_1(X2)\|~v4_rlvect_1(X2)\|~v5_rlvect_1(X2)\|~v6_rlvect_1(X2)\|~v7_rlvect_1(X2)\|~v8_rlvect_1(X2)\|~l1_rlvect_1(X2)\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~r2_hidden(X1,a_3_0_morph_01(X2,X3,X4))), inference(evalgc,[status(thm)],[c_0_18])). cnf(c_0_23, plain, (r2_hidden(X3,X2)\|~r1_tarski(X1,X2)\|~r2_hidden(X3,X1)), inference(evalgc,[status(thm)],[c_0_19])). cnf(c_0_24, negated_conjecture, (r1_tarski(esk2_0,esk3_0)), inference(evalgc,[status(thm)],[c_0_20])). cnf(c_0_25, plain, (r2_hidden(esk6_5(X1,X2,X3,X4,X5),X4)\|r2_hidden(X1,a_3_0_morph_01(X2,X3,X4))\|v2_struct_0(X2)\|X1!=X5\|~m1_subset_1(X5,u1_struct_0(X2))\|~v13_algstr_0(X2)\|~v2_rlvect_1(X2)\|~v3_rlvect_1(X2)\|~v4_rlvect_1(X2)\|~v5_rlvect_1(X2)\|~v6_rlvect_1(X2)\|~v7_rlvect_1(X2)\|~v8_rlvect_1(X2)\|~l1_rlvect_1(X2)\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))), inference(split_conjunct,[status(thm)],[c_0_5])). cnf(c_0_26, plain, (r2_hidden(esk5_4(X1,X2,X3,X4),a_3_0_morph_01(X2,X3,X5))\|v2_struct_0(X2)\|~r2_hidden(esk6_5(esk5_4(X1,X2,X3,X4),X2,X3,X5,esk5_4(X1,X2,X3,X4)),X4)\|~r2_hidden(X1,a_3_0_morph_01(X2,X3,X4))\|~m1_subset_1(X5,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))\|~l1_rlvect_1(X2)\|~v8_rlvect_1(X2)\|~v7_rlvect_1(X2)\|~v6_rlvect_1(X2)\|~v5_rlvect_1(X2)\|~v4_rlvect_1(X2)\|~v3_rlvect_1(X2)\|~v2_rlvect_1(X2)\|~v13_algstr_0(X2)), inference(csr,[status(thm)],[c_0_21, c_0_22])). cnf(c_0_27, negated_conjecture, (r2_hidden(X1,esk3_0)\|~r2_hidden(X1,esk2_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_23, c_0_24])])). cnf(c_0_28, plain, (v2_struct_0(X2)\|r2_hidden(X1,a_3_0_morph_01(X2,X3,X4))\|r2_hidden(esk6_5(X1,X2,X3,X4,X5),X4)\|X1!=X5\|~v13_algstr_0(X2)\|~v2_rlvect_1(X2)\|~v3_rlvect_1(X2)\|~v4_rlvect_1(X2)\|~v5_rlvect_1(X2)\|~v6_rlvect_1(X2)\|~v7_rlvect_1(X2)\|~v8_rlvect_1(X2)\|~l1_rlvect_1(X2)\|~m1_subset_1(X5,u1_struct_0(X2))\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))), inference(evalgc,[status(thm)],[c_0_25])). cnf(c_0_29, negated_conjecture, (r2_hidden(esk5_4(X1,X2,X3,esk3_0),a_3_0_morph_01(X2,X3,X4))\|v2_struct_0(X2)\|~r2_hidden(X1,a_3_0_morph_01(X2,X3,esk3_0))\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(X2)))\|~l1_rlvect_1(X2)\|~v8_rlvect_1(X2)\|~v7_rlvect_1(X2)\|~v6_rlvect_1(X2)\|~v5_rlvect_1(X2)\|~v4_rlvect_1(X2)\|~v3_rlvect_1(X2)\|~v2_rlvect_1(X2)\|~v13_algstr_0(X2)\|~r2_hidden(esk6_5(esk5_4(X1,X2,X3,esk3_0),X2,X3,X4,esk5_4(X1,X2,X3,esk3_0)),esk2_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_26, c_0_27])])). cnf(c_0_30, plain, (r2_hidden(esk6_5(X1,X2,X3,X4,X1),X4)\|r2_hidden(X1,a_3_0_morph_01(X2,X3,X4))\|v2_struct_0(X2)\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X1,u1_struct_0(X2))\|~l1_rlvect_1(X2)\|~v8_rlvect_1(X2)\|~v7_rlvect_1(X2)\|~v6_rlvect_1(X2)\|~v5_rlvect_1(X2)\|~v4_rlvect_1(X2)\|~v3_rlvect_1(X2)\|~v2_rlvect_1(X2)\|~v13_algstr_0(X2)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_28])])). cnf(c_0_31, plain, (X1=esk5_4(X1,X2,X3,X4)\|v2_struct_0(X2)\|~r2_hidden(X1,a_3_0_morph_01(X2,X3,X4))\|~v13_algstr_0(X2)\|~v2_rlvect_1(X2)\|~v3_rlvect_1(X2)\|~v4_rlvect_1(X2)\|~v5_rlvect_1(X2)\|~v6_rlvect_1(X2)\|~v7_rlvect_1(X2)\|~v8_rlvect_1(X2)\|~l1_rlvect_1(X2)\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))), inference(split_conjunct,[status(thm)],[c_0_5])). cnf(c_0_32, plain, (r2_hidden(esk7_2(X1,X2),X1)\|r1_tarski(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_14])). fof(c_0_33, plain, ![X28, X29, X30]:(v2_struct_0(X28)\|(~v13_algstr_0(X28)\|(~v2_rlvect_1(X28)\|(~v3_rlvect_1(X28)\|(~v4_rlvect_1(X28)\|(~v5_rlvect_1(X28)\|(~v6_rlvect_1(X28)\|(~v7_rlvect_1(X28)\|(~v8_rlvect_1(X28)\|~l1_rlvect_1(X28)))))))))\|(~m1_subset_1(X29,k1_zfmisc_1(u1_struct_0(X28)))\|(~m1_subset_1(X30,k1_zfmisc_1(u1_struct_0(X28)))\|k1_morph_01(X28,X29,X30)=a_3_0_morph_01(X28,X29,X30)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d1_morph_01])])])])). cnf(c_0_34, negated_conjecture, (r2_hidden(esk5_4(X1,X2,X3,esk3_0),a_3_0_morph_01(X2,X3,esk2_0))\|v2_struct_0(X2)\|~r2_hidden(X1,a_3_0_morph_01(X2,X3,esk3_0))\|~m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~l1_rlvect_1(X2)\|~v8_rlvect_1(X2)\|~v7_rlvect_1(X2)\|~v6_rlvect_1(X2)\|~v5_rlvect_1(X2)\|~v4_rlvect_1(X2)\|~v3_rlvect_1(X2)\|~v2_rlvect_1(X2)\|~v13_algstr_0(X2)\|~m1_subset_1(esk5_4(X1,X2,X3,esk3_0),u1_struct_0(X2))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_29, c_0_30])])). cnf(c_0_35, plain, (esk5_4(X1,X2,X3,X4)=X1\|v2_struct_0(X2)\|~v13_algstr_0(X2)\|~v2_rlvect_1(X2)\|~v3_rlvect_1(X2)\|~v4_rlvect_1(X2)\|~v5_rlvect_1(X2)\|~v6_rlvect_1(X2)\|~v7_rlvect_1(X2)\|~v8_rlvect_1(X2)\|~l1_rlvect_1(X2)\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~r2_hidden(X1,a_3_0_morph_01(X2,X3,X4))), inference(evalgc,[status(thm)],[c_0_31])). cnf(c_0_36, plain, (r1_tarski(X1,X2)\|r2_hidden(esk7_2(X1,X2),X1)), inference(evalgc,[status(thm)],[c_0_32])). cnf(c_0_37, negated_conjecture, (~r1_tarski(k1_morph_01(esk1_0,esk4_0,esk3_0),k1_morph_01(esk1_0,esk4_0,esk2_0))), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_38, plain, (v2_struct_0(X1)\|k1_morph_01(X1,X2,X3)=a_3_0_morph_01(X1,X2,X3)\|~v13_algstr_0(X1)\|~v2_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v8_rlvect_1(X1)\|~l1_rlvect_1(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))), inference(split_conjunct,[status(thm)],[c_0_33])). cnf(c_0_39, negated_conjecture, (m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(esk1_0)))), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_40, negated_conjecture, (m1_subset_1(esk4_0,k1_zfmisc_1(u1_struct_0(esk1_0)))), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_41, negated_conjecture, (l1_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_42, negated_conjecture, (v8_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_43, negated_conjecture, (v7_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_44, negated_conjecture, (v6_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_45, negated_conjecture, (v5_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_46, negated_conjecture, (v4_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_47, negated_conjecture, (v3_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_48, negated_conjecture, (v2_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_49, negated_conjecture, (v13_algstr_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_50, negated_conjecture, (~v2_struct_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_51, negated_conjecture, (r2_hidden(esk5_4(X1,X2,X3,esk3_0),a_3_0_morph_01(X2,X3,esk2_0))\|v2_struct_0(X2)\|~r2_hidden(X1,a_3_0_morph_01(X2,X3,esk3_0))\|~m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(X2)))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X2)))\|~l1_rlvect_1(X2)\|~v8_rlvect_1(X2)\|~v7_rlvect_1(X2)\|~v6_rlvect_1(X2)\|~v5_rlvect_1(X2)\|~v4_rlvect_1(X2)\|~v3_rlvect_1(X2)\|~v2_rlvect_1(X2)\|~v13_algstr_0(X2)), inference(csr,[status(thm)],[c_0_34, c_0_22])). cnf(c_0_52, plain, (esk5_4(esk7_2(a_3_0_morph_01(X1,X2,X3),X4),X1,X2,X3)=esk7_2(a_3_0_morph_01(X1,X2,X3),X4)\|v2_struct_0(X1)\|r1_tarski(a_3_0_morph_01(X1,X2,X3),X4)\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~l1_rlvect_1(X1)\|~v8_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v13_algstr_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_35, c_0_36])])). cnf(c_0_53, negated_conjecture, (~r1_tarski(k1_morph_01(esk1_0,esk4_0,esk3_0),k1_morph_01(esk1_0,esk4_0,esk2_0))), inference(evalgc,[status(thm)],[c_0_37])). cnf(c_0_54, plain, (k1_morph_01(X1,X2,X3)=a_3_0_morph_01(X1,X2,X3)\|v2_struct_0(X1)\|~v13_algstr_0(X1)\|~v2_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v8_rlvect_1(X1)\|~l1_rlvect_1(X1)\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(evalgc,[status(thm)],[c_0_38])). cnf(c_0_55, negated_conjecture, (m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(esk1_0)))), inference(evalgc,[status(thm)],[c_0_39])). cnf(c_0_56, negated_conjecture, (m1_subset_1(esk4_0,k1_zfmisc_1(u1_struct_0(esk1_0)))), inference(evalgc,[status(thm)],[c_0_40])). cnf(c_0_57, negated_conjecture, (l1_rlvect_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_41])). cnf(c_0_58, negated_conjecture, (v8_rlvect_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_42])). cnf(c_0_59, negated_conjecture, (v7_rlvect_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_43])). cnf(c_0_60, negated_conjecture, (v6_rlvect_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_44])). cnf(c_0_61, negated_conjecture, (v5_rlvect_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_45])). cnf(c_0_62, negated_conjecture, (v4_rlvect_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_46])). cnf(c_0_63, negated_conjecture, (v3_rlvect_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_47])). cnf(c_0_64, negated_conjecture, (v2_rlvect_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_48])). cnf(c_0_65, negated_conjecture, (v13_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_49])). cnf(c_0_66, negated_conjecture, (~v2_struct_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_50])). cnf(c_0_67, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(esk1_0)))), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_68, plain, (r1_tarski(X1,X2)\|~r2_hidden(esk7_2(X1,X2),X2)), inference(split_conjunct,[status(thm)],[c_0_14])). cnf(c_0_69, negated_conjecture, (r2_hidden(esk7_2(a_3_0_morph_01(X1,X2,esk3_0),X3),a_3_0_morph_01(X1,X2,esk2_0))\|v2_struct_0(X1)\|r1_tarski(a_3_0_morph_01(X1,X2,esk3_0),X3)\|~r2_hidden(esk7_2(a_3_0_morph_01(X1,X2,esk3_0),X3),a_3_0_morph_01(X1,X2,esk3_0))\|~m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~l1_rlvect_1(X1)\|~v8_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v13_algstr_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_51, c_0_52])])). cnf(c_0_70, negated_conjecture, (~r1_tarski(a_3_0_morph_01(esk1_0,esk4_0,esk3_0),k1_morph_01(esk1_0,esk4_0,esk2_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53, c_0_54]), c_0_55]), c_0_56]), c_0_57]), c_0_58]), c_0_59]), c_0_60]), c_0_61]), c_0_62]), c_0_63]), c_0_64]), c_0_65])]), c_0_66])])). cnf(c_0_71, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(esk1_0)))), inference(evalgc,[status(thm)],[c_0_67])). cnf(c_0_72, plain, (r1_tarski(X1,X2)\|~r2_hidden(esk7_2(X1,X2),X2)), inference(evalgc,[status(thm)],[c_0_68])). cnf(c_0_73, negated_conjecture, (r2_hidden(esk7_2(a_3_0_morph_01(X1,X2,esk3_0),X3),a_3_0_morph_01(X1,X2,esk2_0))\|r1_tarski(a_3_0_morph_01(X1,X2,esk3_0),X3)\|v2_struct_0(X1)\|~m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~l1_rlvect_1(X1)\|~v8_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v13_algstr_0(X1)), inference(csr,[status(thm)],[c_0_69, c_0_36])). cnf(c_0_74, negated_conjecture, (~r1_tarski(a_3_0_morph_01(esk1_0,esk4_0,esk3_0),a_3_0_morph_01(esk1_0,esk4_0,esk2_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70, c_0_54]), c_0_71]), c_0_56]), c_0_57]), c_0_58]), c_0_59]), c_0_60]), c_0_61]), c_0_62]), c_0_63]), c_0_64]), c_0_65])]), c_0_66])])). cnf(c_0_75, negated_conjecture, (r1_tarski(a_3_0_morph_01(X1,X2,esk3_0),a_3_0_morph_01(X1,X2,esk2_0))\|v2_struct_0(X1)\|~m1_subset_1(esk3_0,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(esk2_0,k1_zfmisc_1(u1_struct_0(X1)))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))\|~l1_rlvect_1(X1)\|~v8_rlvect_1(X1)\|~v7_rlvect_1(X1)\|~v6_rlvect_1(X1)\|~v5_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v13_algstr_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_72, c_0_73])])). cnf(c_0_76, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74, c_0_75]), c_0_55]), c_0_71]), c_0_56]), c_0_57]), c_0_58]), c_0_59]), c_0_60]), c_0_61]), c_0_62]), c_0_63]), c_0_64]), c_0_65])]), c_0_66]), ['proof']). # SZS output end CNFRefutation	reserve E for RealLinearSpace; reserve A, B, C for binary-image of E; reserve a, b, v for Element of E; reserve F, G for binary-image-family of E; reserve A, B, C for non empty binary-image of E; theorem A c= B implies C(-)B c= C(-)A proof assume AS: A c= B; let x be set; assume x in C(-)B; then consider w be Element of E such that P2: x = w & for b be Element of E st b in B holds w - b in C; for a be Element of E st a in A holds w - a in C by AS, P2; hence x in C(-)A by P2; end;	Convert the following ATP output trace into a readable Mizar proof.
t27_toprealc	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t7_algstr_1, axiom, ![X1]:((~(v2_struct_0(X1))&l2_algstr_0(X1))=>((~(v2_struct_0(X1))&(v13_algstr_0(X1)&(v3_rlvect_1(X1)&(v4_rlvect_1(X1)&l2_algstr_0(X1)))))<=>(![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>k1_algstr_0(X1,X2,k4_struct_0(X1))=X2)&(![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>?[X3]:(m1_subset_1(X3,u1_struct_0(X1))&k1_algstr_0(X1,X2,X3)=k4_struct_0(X1)))&![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>![X4]:(m1_subset_1(X4,u1_struct_0(X1))=>k1_algstr_0(X1,k1_algstr_0(X1,X2,X3),X4)=k1_algstr_0(X1,X2,k1_algstr_0(X1,X3,X4))))))))), file('/scratch/mptp/predsminms1/t27_toprealc__0', t7_algstr_1)). fof(t6_rlvect_1, axiom, ![X1]:((~(v2_struct_0(X1))&(v13_algstr_0(X1)&(v3_rlvect_1(X1)&(v4_rlvect_1(X1)&l2_algstr_0(X1)))))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>(k1_algstr_0(X1,X2,X3)=k4_struct_0(X1)=>X2=k4_algstr_0(X1,X3))))), file('/scratch/mptp/predsminms1/t27_toprealc__0', t6_rlvect_1)). fof(d11_rlvect_1, axiom, ![X1]:(l2_algstr_0(X1)=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>k5_algstr_0(X1,X2,X3)=k1_algstr_0(X1,X2,k4_algstr_0(X1,X3))))), file('/scratch/mptp/predsminms1/t27_toprealc__0', d11_rlvect_1)). fof(t16_vectsp_1, axiom, ![X1]:((~(v2_struct_0(X1))&(v13_algstr_0(X1)&(v3_rlvect_1(X1)&(v4_rlvect_1(X1)&l2_algstr_0(X1)))))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>(k1_algstr_0(X1,X2,X3)=k4_struct_0(X1)<=>k4_algstr_0(X1,X2)=X3)))), file('/scratch/mptp/predsminms1/t27_toprealc__0', t16_vectsp_1)). fof(t1_ring_1, axiom, ![X1]:((~(v2_struct_0(X1))&(v13_algstr_0(X1)&(v3_rlvect_1(X1)&(v4_rlvect_1(X1)&l2_algstr_0(X1)))))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>k1_algstr_0(X1,k5_algstr_0(X1,X2,X3),X3)=X2))), file('/scratch/mptp/predsminms1/t27_toprealc__0', t1_ring_1)). fof(dt_k1_algstr_0, axiom, ![X1, X2, X3]:((l1_algstr_0(X1)&(m1_subset_1(X2,u1_struct_0(X1))&m1_subset_1(X3,u1_struct_0(X1))))=>m1_subset_1(k1_algstr_0(X1,X2,X3),u1_struct_0(X1))), file('/scratch/mptp/predsminms1/t27_toprealc__0', dt_k1_algstr_0)). fof(dt_l2_algstr_0, axiom, ![X1]:(l2_algstr_0(X1)=>(l2_struct_0(X1)&l1_algstr_0(X1))), file('/scratch/mptp/predsminms1/t27_toprealc__0', dt_l2_algstr_0)). fof(t27_toprealc, conjecture, ![X1]:((~(v2_struct_0(X1))&(v13_algstr_0(X1)&(v3_rlvect_1(X1)&(v4_rlvect_1(X1)&l2_algstr_0(X1)))))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>k5_algstr_0(X1,k1_algstr_0(X1,X2,X3),X3)=X2))), file('/scratch/mptp/predsminms1/t27_toprealc__0', t27_toprealc)). fof(c_0_8, plain, ![X1]:(epred1_1(X1)<=>((~(v2_struct_0(X1))&(v13_algstr_0(X1)&(v3_rlvect_1(X1)&(v4_rlvect_1(X1)&l2_algstr_0(X1)))))<=>(![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>k1_algstr_0(X1,X2,k4_struct_0(X1))=X2)&(![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>?[X3]:(m1_subset_1(X3,u1_struct_0(X1))&k1_algstr_0(X1,X2,X3)=k4_struct_0(X1)))&![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>![X4]:(m1_subset_1(X4,u1_struct_0(X1))=>k1_algstr_0(X1,k1_algstr_0(X1,X2,X3),X4)=k1_algstr_0(X1,X2,k1_algstr_0(X1,X3,X4))))))))), introduced(definition)). fof(c_0_9, plain, ![X1]:(epred1_1(X1)=>((~(v2_struct_0(X1))&(v13_algstr_0(X1)&(v3_rlvect_1(X1)&(v4_rlvect_1(X1)&l2_algstr_0(X1)))))<=>(![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>k1_algstr_0(X1,X2,k4_struct_0(X1))=X2)&(![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>?[X3]:(m1_subset_1(X3,u1_struct_0(X1))&k1_algstr_0(X1,X2,X3)=k4_struct_0(X1)))&![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>![X4]:(m1_subset_1(X4,u1_struct_0(X1))=>k1_algstr_0(X1,k1_algstr_0(X1,X2,X3),X4)=k1_algstr_0(X1,X2,k1_algstr_0(X1,X3,X4))))))))), inference(split_equiv,[status(thm)],[c_0_8])). fof(c_0_10, axiom, ![X1]:((~(v2_struct_0(X1))&l2_algstr_0(X1))=>epred1_1(X1)), inference(apply_def,[status(thm)],[t7_algstr_1, c_0_8])). fof(c_0_11, plain, ![X25, X26, X27, X29, X30, X31, X34]:(((~m1_subset_1(X26,u1_struct_0(X25))\|k1_algstr_0(X25,X26,k4_struct_0(X25))=X26\|(v2_struct_0(X25)\|(~v13_algstr_0(X25)\|(~v3_rlvect_1(X25)\|(~v4_rlvect_1(X25)\|~l2_algstr_0(X25)))))\|~epred1_1(X25))&(((m1_subset_1(esk4_2(X25,X27),u1_struct_0(X25))\|~m1_subset_1(X27,u1_struct_0(X25))\|(v2_struct_0(X25)\|(~v13_algstr_0(X25)\|(~v3_rlvect_1(X25)\|(~v4_rlvect_1(X25)\|~l2_algstr_0(X25)))))\|~epred1_1(X25))&(k1_algstr_0(X25,X27,esk4_2(X25,X27))=k4_struct_0(X25)\|~m1_subset_1(X27,u1_struct_0(X25))\|(v2_struct_0(X25)\|(~v13_algstr_0(X25)\|(~v3_rlvect_1(X25)\|(~v4_rlvect_1(X25)\|~l2_algstr_0(X25)))))\|~epred1_1(X25)))&(~m1_subset_1(X29,u1_struct_0(X25))\|(~m1_subset_1(X30,u1_struct_0(X25))\|(~m1_subset_1(X31,u1_struct_0(X25))\|k1_algstr_0(X25,k1_algstr_0(X25,X29,X30),X31)=k1_algstr_0(X25,X29,k1_algstr_0(X25,X30,X31))))\|(v2_struct_0(X25)\|(~v13_algstr_0(X25)\|(~v3_rlvect_1(X25)\|(~v4_rlvect_1(X25)\|~l2_algstr_0(X25)))))\|~epred1_1(X25))))&(((((~v2_struct_0(X25)\|(m1_subset_1(esk7_1(X25),u1_struct_0(X25))\|m1_subset_1(esk6_1(X25),u1_struct_0(X25))\|m1_subset_1(esk5_1(X25),u1_struct_0(X25)))\|~epred1_1(X25))&((v13_algstr_0(X25)\|(m1_subset_1(esk7_1(X25),u1_struct_0(X25))\|m1_subset_1(esk6_1(X25),u1_struct_0(X25))\|m1_subset_1(esk5_1(X25),u1_struct_0(X25)))\|~epred1_1(X25))&((v3_rlvect_1(X25)\|(m1_subset_1(esk7_1(X25),u1_struct_0(X25))\|m1_subset_1(esk6_1(X25),u1_struct_0(X25))\|m1_subset_1(esk5_1(X25),u1_struct_0(X25)))\|~epred1_1(X25))&((v4_rlvect_1(X25)\|(m1_subset_1(esk7_1(X25),u1_struct_0(X25))\|m1_subset_1(esk6_1(X25),u1_struct_0(X25))\|m1_subset_1(esk5_1(X25),u1_struct_0(X25)))\|~epred1_1(X25))&(l2_algstr_0(X25)\|(m1_subset_1(esk7_1(X25),u1_struct_0(X25))\|m1_subset_1(esk6_1(X25),u1_struct_0(X25))\|m1_subset_1(esk5_1(X25),u1_struct_0(X25)))\|~epred1_1(X25))))))&(((~v2_struct_0(X25)\|(m1_subset_1(esk8_1(X25),u1_struct_0(X25))\|m1_subset_1(esk6_1(X25),u1_struct_0(X25))\|m1_subset_1(esk5_1(X25),u1_struct_0(X25)))\|~epred1_1(X25))&((v13_algstr_0(X25)\|(m1_subset_1(esk8_1(X25),u1_struct_0(X25))\|m1_subset_1(esk6_1(X25),u1_struct_0(X25))\|m1_subset_1(esk5_1(X25),u1_struct_0(X25)))\|~epred1_1(X25))&((v3_rlvect_1(X25)\|(m1_subset_1(esk8_1(X25),u1_struct_0(X25))\|m1_subset_1(esk6_1(X25),u1_struct_0(X25))\|m1_subset_1(esk5_1(X25),u1_struct_0(X25)))\|~epred1_1(X25))&((v4_rlvect_1(X25)\|(m1_subset_1(esk8_1(X25),u1_struct_0(X25))\|m1_subset_1(esk6_1(X25),u1_struct_0(X25))\|m1_subset_1(esk5_1(X25),u1_struct_0(X25)))\|~epred1_1(X25))&(l2_algstr_0(X25)\|(m1_subset_1(esk8_1(X25),u1_struct_0(X25))\|m1_subset_1(esk6_1(X25),u1_struct_0(X25))\|m1_subset_1(esk5_1(X25),u1_struct_0(X25)))\|~epred1_1(X25))))))&(((~v2_struct_0(X25)\|(m1_subset_1(esk9_1(X25),u1_struct_0(X25))\|m1_subset_1(esk6_1(X25),u1_struct_0(X25))\|m1_subset_1(esk5_1(X25),u1_struct_0(X25)))\|~epred1_1(X25))&((v13_algstr_0(X25)\|(m1_subset_1(esk9_1(X25),u1_struct_0(X25))\|m1_subset_1(esk6_1(X25),u1_struct_0(X25))\|m1_subset_1(esk5_1(X25),u1_struct_0(X25)))\|~epred1_1(X25))&((v3_rlvect_1(X25)\|(m1_subset_1(esk9_1(X25),u1_struct_0(X25))\|m1_subset_1(esk6_1(X25),u1_struct_0(X25))\|m1_subset_1(esk5_1(X25),u1_struct_0(X25)))\|~epred1_1(X25))&((v4_rlvect_1(X25)\|(m1_subset_1(esk9_1(X25),u1_struct_0(X25))\|m1_subset_1(esk6_1(X25),u1_struct_0(X25))\|m1_subset_1(esk5_1(X25),u1_struct_0(X25)))\|~epred1_1(X25))&(l2_algstr_0(X25)\|(m1_subset_1(esk9_1(X25),u1_struct_0(X25))\|m1_subset_1(esk6_1(X25),u1_struct_0(X25))\|m1_subset_1(esk5_1(X25),u1_struct_0(X25)))\|~epred1_1(X25))))))&((~v2_struct_0(X25)\|(k1_algstr_0(X25,k1_algstr_0(X25,esk7_1(X25),esk8_1(X25)),esk9_1(X25))!=k1_algstr_0(X25,esk7_1(X25),k1_algstr_0(X25,esk8_1(X25),esk9_1(X25)))\|m1_subset_1(esk6_1(X25),u1_struct_0(X25))\|m1_subset_1(esk5_1(X25),u1_struct_0(X25)))\|~epred1_1(X25))&((v13_algstr_0(X25)\|(k1_algstr_0(X25,k1_algstr_0(X25,esk7_1(X25),esk8_1(X25)),esk9_1(X25))!=k1_algstr_0(X25,esk7_1(X25),k1_algstr_0(X25,esk8_1(X25),esk9_1(X25)))\|m1_subset_1(esk6_1(X25),u1_struct_0(X25))\|m1_subset_1(esk5_1(X25),u1_struct_0(X25)))\|~epred1_1(X25))&((v3_rlvect_1(X25)\|(k1_algstr_0(X25,k1_algstr_0(X25,esk7_1(X25),esk8_1(X25)),esk9_1(X25))!=k1_algstr_0(X25,esk7_1(X25),k1_algstr_0(X25,esk8_1(X25),esk9_1(X25)))\|m1_subset_1(esk6_1(X25),u1_struct_0(X25))\|m1_subset_1(esk5_1(X25),u1_struct_0(X25)))\|~epred1_1(X25))&((v4_rlvect_1(X25)\|(k1_algstr_0(X25,k1_algstr_0(X25,esk7_1(X25),esk8_1(X25)),esk9_1(X25))!=k1_algstr_0(X25,esk7_1(X25),k1_algstr_0(X25,esk8_1(X25),esk9_1(X25)))\|m1_subset_1(esk6_1(X25),u1_struct_0(X25))\|m1_subset_1(esk5_1(X25),u1_struct_0(X25)))\|~epred1_1(X25))&(l2_algstr_0(X25)\|(k1_algstr_0(X25,k1_algstr_0(X25,esk7_1(X25),esk8_1(X25)),esk9_1(X25))!=k1_algstr_0(X25,esk7_1(X25),k1_algstr_0(X25,esk8_1(X25),esk9_1(X25)))\|m1_subset_1(esk6_1(X25),u1_struct_0(X25))\|m1_subset_1(esk5_1(X25),u1_struct_0(X25)))\|~epred1_1(X25)))))))))&(((~v2_struct_0(X25)\|(m1_subset_1(esk7_1(X25),u1_struct_0(X25))\|(~m1_subset_1(X34,u1_struct_0(X25))\|k1_algstr_0(X25,esk6_1(X25),X34)!=k4_struct_0(X25))\|m1_subset_1(esk5_1(X25),u1_struct_0(X25)))\|~epred1_1(X25))&((v13_algstr_0(X25)\|(m1_subset_1(esk7_1(X25),u1_struct_0(X25))\|(~m1_subset_1(X34,u1_struct_0(X25))\|k1_algstr_0(X25,esk6_1(X25),X34)!=k4_struct_0(X25))\|m1_subset_1(esk5_1(X25),u1_struct_0(X25)))\|~epred1_1(X25))&((v3_rlvect_1(X25)\|(m1_subset_1(esk7_1(X25),u1_struct_0(X25))\|(~m1_subset_1(X34,u1_struct_0(X25))\|k1_algstr_0(X25,esk6_1(X25),X34)!=k4_struct_0(X25))\|m1_subset_1(esk5_1(X25),u1_struct_0(X25)))\|~epred1_1(X25))&((v4_rlvect_1(X25)\|(m1_subset_1(esk7_1(X25),u1_struct_0(X25))\|(~m1_subset_1(X34,u1_struct_0(X25))\|k1_algstr_0(X25,esk6_1(X25),X34)!=k4_struct_0(X25))\|m1_subset_1(esk5_1(X25),u1_struct_0(X25)))\|~epred1_1(X25))&(l2_algstr_0(X25)\|(m1_subset_1(esk7_1(X25),u1_struct_0(X25))\|(~m1_subset_1(X34,u1_struct_0(X25))\|k1_algstr_0(X25,esk6_1(X25),X34)!=k4_struct_0(X25))\|m1_subset_1(esk5_1(X25),u1_struct_0(X25)))\|~epred1_1(X25))))))&(((~v2_struct_0(X25)\|(m1_subset_1(esk8_1(X25),u1_struct_0(X25))\|(~m1_subset_1(X34,u1_struct_0(X25))\|k1_algstr_0(X25,esk6_1(X25),X34)!=k4_struct_0(X25))\|m1_subset_1(esk5_1(X25),u1_struct_0(X25)))\|~epred1_1(X25))&((v13_algstr_0(X25)\|(m1_subset_1(esk8_1(X25),u1_struct_0(X25))\|(~m1_subset_1(X34,u1_struct_0(X25))\|k1_algstr_0(X25,esk6_1(X25),X34)!=k4_struct_0(X25))\|m1_subset_1(esk5_1(X25),u1_struct_0(X25)))\|~epred1_1(X25))&((v3_rlvect_1(X25)\|(m1_subset_1(esk8_1(X25),u1_struct_0(X25))\|(~m1_subset_1(X34,u1_struct_0(X25))\|k1_algstr_0(X25,esk6_1(X25),X34)!=k4_struct_0(X25))\|m1_subset_1(esk5_1(X25),u1_struct_0(X25)))\|~epred1_1(X25))&((v4_rlvect_1(X25)\|(m1_subset_1(esk8_1(X25),u1_struct_0(X25))\|(~m1_subset_1(X34,u1_struct_0(X25))\|k1_algstr_0(X25,esk6_1(X25),X34)!=k4_struct_0(X25))\|m1_subset_1(esk5_1(X25),u1_struct_0(X25)))\|~epred1_1(X25))&(l2_algstr_0(X25)\|(m1_subset_1(esk8_1(X25),u1_struct_0(X25))\|(~m1_subset_1(X34,u1_struct_0(X25))\|k1_algstr_0(X25,esk6_1(X25),X34)!=k4_struct_0(X25))\|m1_subset_1(esk5_1(X25),u1_struct_0(X25)))\|~epred1_1(X25))))))&(((~v2_struct_0(X25)\|(m1_subset_1(esk9_1(X25),u1_struct_0(X25))\|(~m1_subset_1(X34,u1_struct_0(X25))\|k1_algstr_0(X25,esk6_1(X25),X34)!=k4_struct_0(X25))\|m1_subset_1(esk5_1(X25),u1_struct_0(X25)))\|~epred1_1(X25))&((v13_algstr_0(X25)\|(m1_subset_1(esk9_1(X25),u1_struct_0(X25))\|(~m1_subset_1(X34,u1_struct_0(X25))\|k1_algstr_0(X25,esk6_1(X25),X34)!=k4_struct_0(X25))\|m1_subset_1(esk5_1(X25),u1_struct_0(X25)))\|~epred1_1(X25))&((v3_rlvect_1(X25)\|(m1_subset_1(esk9_1(X25),u1_struct_0(X25))\|(~m1_subset_1(X34,u1_struct_0(X25))\|k1_algstr_0(X25,esk6_1(X25),X34)!=k4_struct_0(X25))\|m1_subset_1(esk5_1(X25),u1_struct_0(X25)))\|~epred1_1(X25))&((v4_rlvect_1(X25)\|(m1_subset_1(esk9_1(X25),u1_struct_0(X25))\|(~m1_subset_1(X34,u1_struct_0(X25))\|k1_algstr_0(X25,esk6_1(X25),X34)!=k4_struct_0(X25))\|m1_subset_1(esk5_1(X25),u1_struct_0(X25)))\|~epred1_1(X25))&(l2_algstr_0(X25)\|(m1_subset_1(esk9_1(X25),u1_struct_0(X25))\|(~m1_subset_1(X34,u1_struct_0(X25))\|k1_algstr_0(X25,esk6_1(X25),X34)!=k4_struct_0(X25))\|m1_subset_1(esk5_1(X25),u1_struct_0(X25)))\|~epred1_1(X25))))))&((~v2_struct_0(X25)\|(k1_algstr_0(X25,k1_algstr_0(X25,esk7_1(X25),esk8_1(X25)),esk9_1(X25))!=k1_algstr_0(X25,esk7_1(X25),k1_algstr_0(X25,esk8_1(X25),esk9_1(X25)))\|(~m1_subset_1(X34,u1_struct_0(X25))\|k1_algstr_0(X25,esk6_1(X25),X34)!=k4_struct_0(X25))\|m1_subset_1(esk5_1(X25),u1_struct_0(X25)))\|~epred1_1(X25))&((v13_algstr_0(X25)\|(k1_algstr_0(X25,k1_algstr_0(X25,esk7_1(X25),esk8_1(X25)),esk9_1(X25))!=k1_algstr_0(X25,esk7_1(X25),k1_algstr_0(X25,esk8_1(X25),esk9_1(X25)))\|(~m1_subset_1(X34,u1_struct_0(X25))\|k1_algstr_0(X25,esk6_1(X25),X34)!=k4_struct_0(X25))\|m1_subset_1(esk5_1(X25),u1_struct_0(X25)))\|~epred1_1(X25))&((v3_rlvect_1(X25)\|(k1_algstr_0(X25,k1_algstr_0(X25,esk7_1(X25),esk8_1(X25)),esk9_1(X25))!=k1_algstr_0(X25,esk7_1(X25),k1_algstr_0(X25,esk8_1(X25),esk9_1(X25)))\|(~m1_subset_1(X34,u1_struct_0(X25))\|k1_algstr_0(X25,esk6_1(X25),X34)!=k4_struct_0(X25))\|m1_subset_1(esk5_1(X25),u1_struct_0(X25)))\|~epred1_1(X25))&((v4_rlvect_1(X25)\|(k1_algstr_0(X25,k1_algstr_0(X25,esk7_1(X25),esk8_1(X25)),esk9_1(X25))!=k1_algstr_0(X25,esk7_1(X25),k1_algstr_0(X25,esk8_1(X25),esk9_1(X25)))\|(~m1_subset_1(X34,u1_struct_0(X25))\|k1_algstr_0(X25,esk6_1(X25),X34)!=k4_struct_0(X25))\|m1_subset_1(esk5_1(X25),u1_struct_0(X25)))\|~epred1_1(X25))&(l2_algstr_0(X25)\|(k1_algstr_0(X25,k1_algstr_0(X25,esk7_1(X25),esk8_1(X25)),esk9_1(X25))!=k1_algstr_0(X25,esk7_1(X25),k1_algstr_0(X25,esk8_1(X25),esk9_1(X25)))\|(~m1_subset_1(X34,u1_struct_0(X25))\|k1_algstr_0(X25,esk6_1(X25),X34)!=k4_struct_0(X25))\|m1_subset_1(esk5_1(X25),u1_struct_0(X25)))\|~epred1_1(X25))))))))))&((((~v2_struct_0(X25)\|(m1_subset_1(esk7_1(X25),u1_struct_0(X25))\|m1_subset_1(esk6_1(X25),u1_struct_0(X25))\|k1_algstr_0(X25,esk5_1(X25),k4_struct_0(X25))!=esk5_1(X25))\|~epred1_1(X25))&((v13_algstr_0(X25)\|(m1_subset_1(esk7_1(X25),u1_struct_0(X25))\|m1_subset_1(esk6_1(X25),u1_struct_0(X25))\|k1_algstr_0(X25,esk5_1(X25),k4_struct_0(X25))!=esk5_1(X25))\|~epred1_1(X25))&((v3_rlvect_1(X25)\|(m1_subset_1(esk7_1(X25),u1_struct_0(X25))\|m1_subset_1(esk6_1(X25),u1_struct_0(X25))\|k1_algstr_0(X25,esk5_1(X25),k4_struct_0(X25))!=esk5_1(X25))\|~epred1_1(X25))&((v4_rlvect_1(X25)\|(m1_subset_1(esk7_1(X25),u1_struct_0(X25))\|m1_subset_1(esk6_1(X25),u1_struct_0(X25))\|k1_algstr_0(X25,esk5_1(X25),k4_struct_0(X25))!=esk5_1(X25))\|~epred1_1(X25))&(l2_algstr_0(X25)\|(m1_subset_1(esk7_1(X25),u1_struct_0(X25))\|m1_subset_1(esk6_1(X25),u1_struct_0(X25))\|k1_algstr_0(X25,esk5_1(X25),k4_struct_0(X25))!=esk5_1(X25))\|~epred1_1(X25))))))&(((~v2_struct_0(X25)\|(m1_subset_1(esk8_1(X25),u1_struct_0(X25))\|m1_subset_1(esk6_1(X25),u1_struct_0(X25))\|k1_algstr_0(X25,esk5_1(X25),k4_struct_0(X25))!=esk5_1(X25))\|~epred1_1(X25))&((v13_algstr_0(X25)\|(m1_subset_1(esk8_1(X25),u1_struct_0(X25))\|m1_subset_1(esk6_1(X25),u1_struct_0(X25))\|k1_algstr_0(X25,esk5_1(X25),k4_struct_0(X25))!=esk5_1(X25))\|~epred1_1(X25))&((v3_rlvect_1(X25)\|(m1_subset_1(esk8_1(X25),u1_struct_0(X25))\|m1_subset_1(esk6_1(X25),u1_struct_0(X25))\|k1_algstr_0(X25,esk5_1(X25),k4_struct_0(X25))!=esk5_1(X25))\|~epred1_1(X25))&((v4_rlvect_1(X25)\|(m1_subset_1(esk8_1(X25),u1_struct_0(X25))\|m1_subset_1(esk6_1(X25),u1_struct_0(X25))\|k1_algstr_0(X25,esk5_1(X25),k4_struct_0(X25))!=esk5_1(X25))\|~epred1_1(X25))&(l2_algstr_0(X25)\|(m1_subset_1(esk8_1(X25),u1_struct_0(X25))\|m1_subset_1(esk6_1(X25),u1_struct_0(X25))\|k1_algstr_0(X25,esk5_1(X25),k4_struct_0(X25))!=esk5_1(X25))\|~epred1_1(X25))))))&(((~v2_struct_0(X25)\|(m1_subset_1(esk9_1(X25),u1_struct_0(X25))\|m1_subset_1(esk6_1(X25),u1_struct_0(X25))\|k1_algstr_0(X25,esk5_1(X25),k4_struct_0(X25))!=esk5_1(X25))\|~epred1_1(X25))&((v13_algstr_0(X25)\|(m1_subset_1(esk9_1(X25),u1_struct_0(X25))\|m1_subset_1(esk6_1(X25),u1_struct_0(X25))\|k1_algstr_0(X25,esk5_1(X25),k4_struct_0(X25))!=esk5_1(X25))\|~epred1_1(X25))&((v3_rlvect_1(X25)\|(m1_subset_1(esk9_1(X25),u1_struct_0(X25))\|m1_subset_1(esk6_1(X25),u1_struct_0(X25))\|k1_algstr_0(X25,esk5_1(X25),k4_struct_0(X25))!=esk5_1(X25))\|~epred1_1(X25))&((v4_rlvect_1(X25)\|(m1_subset_1(esk9_1(X25),u1_struct_0(X25))\|m1_subset_1(esk6_1(X25),u1_struct_0(X25))\|k1_algstr_0(X25,esk5_1(X25),k4_struct_0(X25))!=esk5_1(X25))\|~epred1_1(X25))&(l2_algstr_0(X25)\|(m1_subset_1(esk9_1(X25),u1_struct_0(X25))\|m1_subset_1(esk6_1(X25),u1_struct_0(X25))\|k1_algstr_0(X25,esk5_1(X25),k4_struct_0(X25))!=esk5_1(X25))\|~epred1_1(X25))))))&((~v2_struct_0(X25)\|(k1_algstr_0(X25,k1_algstr_0(X25,esk7_1(X25),esk8_1(X25)),esk9_1(X25))!=k1_algstr_0(X25,esk7_1(X25),k1_algstr_0(X25,esk8_1(X25),esk9_1(X25)))\|m1_subset_1(esk6_1(X25),u1_struct_0(X25))\|k1_algstr_0(X25,esk5_1(X25),k4_struct_0(X25))!=esk5_1(X25))\|~epred1_1(X25))&((v13_algstr_0(X25)\|(k1_algstr_0(X25,k1_algstr_0(X25,esk7_1(X25),esk8_1(X25)),esk9_1(X25))!=k1_algstr_0(X25,esk7_1(X25),k1_algstr_0(X25,esk8_1(X25),esk9_1(X25)))\|m1_subset_1(esk6_1(X25),u1_struct_0(X25))\|k1_algstr_0(X25,esk5_1(X25),k4_struct_0(X25))!=esk5_1(X25))\|~epred1_1(X25))&((v3_rlvect_1(X25)\|(k1_algstr_0(X25,k1_algstr_0(X25,esk7_1(X25),esk8_1(X25)),esk9_1(X25))!=k1_algstr_0(X25,esk7_1(X25),k1_algstr_0(X25,esk8_1(X25),esk9_1(X25)))\|m1_subset_1(esk6_1(X25),u1_struct_0(X25))\|k1_algstr_0(X25,esk5_1(X25),k4_struct_0(X25))!=esk5_1(X25))\|~epred1_1(X25))&((v4_rlvect_1(X25)\|(k1_algstr_0(X25,k1_algstr_0(X25,esk7_1(X25),esk8_1(X25)),esk9_1(X25))!=k1_algstr_0(X25,esk7_1(X25),k1_algstr_0(X25,esk8_1(X25),esk9_1(X25)))\|m1_subset_1(esk6_1(X25),u1_struct_0(X25))\|k1_algstr_0(X25,esk5_1(X25),k4_struct_0(X25))!=esk5_1(X25))\|~epred1_1(X25))&(l2_algstr_0(X25)\|(k1_algstr_0(X25,k1_algstr_0(X25,esk7_1(X25),esk8_1(X25)),esk9_1(X25))!=k1_algstr_0(X25,esk7_1(X25),k1_algstr_0(X25,esk8_1(X25),esk9_1(X25)))\|m1_subset_1(esk6_1(X25),u1_struct_0(X25))\|k1_algstr_0(X25,esk5_1(X25),k4_struct_0(X25))!=esk5_1(X25))\|~epred1_1(X25)))))))))&(((~v2_struct_0(X25)\|(m1_subset_1(esk7_1(X25),u1_struct_0(X25))\|(~m1_subset_1(X34,u1_struct_0(X25))\|k1_algstr_0(X25,esk6_1(X25),X34)!=k4_struct_0(X25))\|k1_algstr_0(X25,esk5_1(X25),k4_struct_0(X25))!=esk5_1(X25))\|~epred1_1(X25))&((v13_algstr_0(X25)\|(m1_subset_1(esk7_1(X25),u1_struct_0(X25))\|(~m1_subset_1(X34,u1_struct_0(X25))\|k1_algstr_0(X25,esk6_1(X25),X34)!=k4_struct_0(X25))\|k1_algstr_0(X25,esk5_1(X25),k4_struct_0(X25))!=esk5_1(X25))\|~epred1_1(X25))&((v3_rlvect_1(X25)\|(m1_subset_1(esk7_1(X25),u1_struct_0(X25))\|(~m1_subset_1(X34,u1_struct_0(X25))\|k1_algstr_0(X25,esk6_1(X25),X34)!=k4_struct_0(X25))\|k1_algstr_0(X25,esk5_1(X25),k4_struct_0(X25))!=esk5_1(X25))\|~epred1_1(X25))&((v4_rlvect_1(X25)\|(m1_subset_1(esk7_1(X25),u1_struct_0(X25))\|(~m1_subset_1(X34,u1_struct_0(X25))\|k1_algstr_0(X25,esk6_1(X25),X34)!=k4_struct_0(X25))\|k1_algstr_0(X25,esk5_1(X25),k4_struct_0(X25))!=esk5_1(X25))\|~epred1_1(X25))&(l2_algstr_0(X25)\|(m1_subset_1(esk7_1(X25),u1_struct_0(X25))\|(~m1_subset_1(X34,u1_struct_0(X25))\|k1_algstr_0(X25,esk6_1(X25),X34)!=k4_struct_0(X25))\|k1_algstr_0(X25,esk5_1(X25),k4_struct_0(X25))!=esk5_1(X25))\|~epred1_1(X25))))))&(((~v2_struct_0(X25)\|(m1_subset_1(esk8_1(X25),u1_struct_0(X25))\|(~m1_subset_1(X34,u1_struct_0(X25))\|k1_algstr_0(X25,esk6_1(X25),X34)!=k4_struct_0(X25))\|k1_algstr_0(X25,esk5_1(X25),k4_struct_0(X25))!=esk5_1(X25))\|~epred1_1(X25))&((v13_algstr_0(X25)\|(m1_subset_1(esk8_1(X25),u1_struct_0(X25))\|(~m1_subset_1(X34,u1_struct_0(X25))\|k1_algstr_0(X25,esk6_1(X25),X34)!=k4_struct_0(X25))\|k1_algstr_0(X25,esk5_1(X25),k4_struct_0(X25))!=esk5_1(X25))\|~epred1_1(X25))&((v3_rlvect_1(X25)\|(m1_subset_1(esk8_1(X25),u1_struct_0(X25))\|(~m1_subset_1(X34,u1_struct_0(X25))\|k1_algstr_0(X25,esk6_1(X25),X34)!=k4_struct_0(X25))\|k1_algstr_0(X25,esk5_1(X25),k4_struct_0(X25))!=esk5_1(X25))\|~epred1_1(X25))&((v4_rlvect_1(X25)\|(m1_subset_1(esk8_1(X25),u1_struct_0(X25))\|(~m1_subset_1(X34,u1_struct_0(X25))\|k1_algstr_0(X25,esk6_1(X25),X34)!=k4_struct_0(X25))\|k1_algstr_0(X25,esk5_1(X25),k4_struct_0(X25))!=esk5_1(X25))\|~epred1_1(X25))&(l2_algstr_0(X25)\|(m1_subset_1(esk8_1(X25),u1_struct_0(X25))\|(~m1_subset_1(X34,u1_struct_0(X25))\|k1_algstr_0(X25,esk6_1(X25),X34)!=k4_struct_0(X25))\|k1_algstr_0(X25,esk5_1(X25),k4_struct_0(X25))!=esk5_1(X25))\|~epred1_1(X25))))))&(((~v2_struct_0(X25)\|(m1_subset_1(esk9_1(X25),u1_struct_0(X25))\|(~m1_subset_1(X34,u1_struct_0(X25))\|k1_algstr_0(X25,esk6_1(X25),X34)!=k4_struct_0(X25))\|k1_algstr_0(X25,esk5_1(X25),k4_struct_0(X25))!=esk5_1(X25))\|~epred1_1(X25))&((v13_algstr_0(X25)\|(m1_subset_1(esk9_1(X25),u1_struct_0(X25))\|(~m1_subset_1(X34,u1_struct_0(X25))\|k1_algstr_0(X25,esk6_1(X25),X34)!=k4_struct_0(X25))\|k1_algstr_0(X25,esk5_1(X25),k4_struct_0(X25))!=esk5_1(X25))\|~epred1_1(X25))&((v3_rlvect_1(X25)\|(m1_subset_1(esk9_1(X25),u1_struct_0(X25))\|(~m1_subset_1(X34,u1_struct_0(X25))\|k1_algstr_0(X25,esk6_1(X25),X34)!=k4_struct_0(X25))\|k1_algstr_0(X25,esk5_1(X25),k4_struct_0(X25))!=esk5_1(X25))\|~epred1_1(X25))&((v4_rlvect_1(X25)\|(m1_subset_1(esk9_1(X25),u1_struct_0(X25))\|(~m1_subset_1(X34,u1_struct_0(X25))\|k1_algstr_0(X25,esk6_1(X25),X34)!=k4_struct_0(X25))\|k1_algstr_0(X25,esk5_1(X25),k4_struct_0(X25))!=esk5_1(X25))\|~epred1_1(X25))&(l2_algstr_0(X25)\|(m1_subset_1(esk9_1(X25),u1_struct_0(X25))\|(~m1_subset_1(X34,u1_struct_0(X25))\|k1_algstr_0(X25,esk6_1(X25),X34)!=k4_struct_0(X25))\|k1_algstr_0(X25,esk5_1(X25),k4_struct_0(X25))!=esk5_1(X25))\|~epred1_1(X25))))))&((~v2_struct_0(X25)\|(k1_algstr_0(X25,k1_algstr_0(X25,esk7_1(X25),esk8_1(X25)),esk9_1(X25))!=k1_algstr_0(X25,esk7_1(X25),k1_algstr_0(X25,esk8_1(X25),esk9_1(X25)))\|(~m1_subset_1(X34,u1_struct_0(X25))\|k1_algstr_0(X25,esk6_1(X25),X34)!=k4_struct_0(X25))\|k1_algstr_0(X25,esk5_1(X25),k4_struct_0(X25))!=esk5_1(X25))\|~epred1_1(X25))&((v13_algstr_0(X25)\|(k1_algstr_0(X25,k1_algstr_0(X25,esk7_1(X25),esk8_1(X25)),esk9_1(X25))!=k1_algstr_0(X25,esk7_1(X25),k1_algstr_0(X25,esk8_1(X25),esk9_1(X25)))\|(~m1_subset_1(X34,u1_struct_0(X25))\|k1_algstr_0(X25,esk6_1(X25),X34)!=k4_struct_0(X25))\|k1_algstr_0(X25,esk5_1(X25),k4_struct_0(X25))!=esk5_1(X25))\|~epred1_1(X25))&((v3_rlvect_1(X25)\|(k1_algstr_0(X25,k1_algstr_0(X25,esk7_1(X25),esk8_1(X25)),esk9_1(X25))!=k1_algstr_0(X25,esk7_1(X25),k1_algstr_0(X25,esk8_1(X25),esk9_1(X25)))\|(~m1_subset_1(X34,u1_struct_0(X25))\|k1_algstr_0(X25,esk6_1(X25),X34)!=k4_struct_0(X25))\|k1_algstr_0(X25,esk5_1(X25),k4_struct_0(X25))!=esk5_1(X25))\|~epred1_1(X25))&((v4_rlvect_1(X25)\|(k1_algstr_0(X25,k1_algstr_0(X25,esk7_1(X25),esk8_1(X25)),esk9_1(X25))!=k1_algstr_0(X25,esk7_1(X25),k1_algstr_0(X25,esk8_1(X25),esk9_1(X25)))\|(~m1_subset_1(X34,u1_struct_0(X25))\|k1_algstr_0(X25,esk6_1(X25),X34)!=k4_struct_0(X25))\|k1_algstr_0(X25,esk5_1(X25),k4_struct_0(X25))!=esk5_1(X25))\|~epred1_1(X25))&(l2_algstr_0(X25)\|(k1_algstr_0(X25,k1_algstr_0(X25,esk7_1(X25),esk8_1(X25)),esk9_1(X25))!=k1_algstr_0(X25,esk7_1(X25),k1_algstr_0(X25,esk8_1(X25),esk9_1(X25)))\|(~m1_subset_1(X34,u1_struct_0(X25))\|k1_algstr_0(X25,esk6_1(X25),X34)!=k4_struct_0(X25))\|k1_algstr_0(X25,esk5_1(X25),k4_struct_0(X25))!=esk5_1(X25))\|~epred1_1(X25)))))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_9])])])])])])). fof(c_0_12, plain, ![X8]:(v2_struct_0(X8)\|~l2_algstr_0(X8)\|epred1_1(X8)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_10])])])). fof(c_0_13, plain, ![X12, X13, X14]:(v2_struct_0(X12)\|(~v13_algstr_0(X12)\|(~v3_rlvect_1(X12)\|(~v4_rlvect_1(X12)\|~l2_algstr_0(X12))))\|(~m1_subset_1(X13,u1_struct_0(X12))\|(~m1_subset_1(X14,u1_struct_0(X12))\|(k1_algstr_0(X12,X13,X14)!=k4_struct_0(X12)\|X13=k4_algstr_0(X12,X14))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t6_rlvect_1])])])])). cnf(c_0_14, plain, (k1_algstr_0(X1,X2,esk4_2(X1,X2))=k4_struct_0(X1)\|v2_struct_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~v13_algstr_0(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~l2_algstr_0(X1)\|~epred1_1(X1)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_15, plain, (v2_struct_0(X1)\|epred1_1(X1)\|~l2_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_16, plain, (v2_struct_0(X1)\|X2=k4_algstr_0(X1,X3)\|~v13_algstr_0(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~l2_algstr_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|k1_algstr_0(X1,X2,X3)!=k4_struct_0(X1)), inference(split_conjunct,[status(thm)],[c_0_13])). cnf(c_0_17, plain, (k1_algstr_0(X1,X2,esk4_2(X1,X2))=k4_struct_0(X1)\|v2_struct_0(X1)\|~v13_algstr_0(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~l2_algstr_0(X1)\|~epred1_1(X1)\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_14])). cnf(c_0_18, plain, (v2_struct_0(X1)\|epred1_1(X1)\|~l2_algstr_0(X1)), inference(evalgc,[status(thm)],[c_0_15])). cnf(c_0_19, plain, (m1_subset_1(esk4_2(X1,X2),u1_struct_0(X1))\|v2_struct_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~v13_algstr_0(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~l2_algstr_0(X1)\|~epred1_1(X1)), inference(split_conjunct,[status(thm)],[c_0_11])). fof(c_0_20, plain, ![X15, X16, X17]:(~l2_algstr_0(X15)\|(~m1_subset_1(X16,u1_struct_0(X15))\|(~m1_subset_1(X17,u1_struct_0(X15))\|k5_algstr_0(X15,X16,X17)=k1_algstr_0(X15,X16,k4_algstr_0(X15,X17))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d11_rlvect_1])])])). cnf(c_0_21, plain, (X2=k4_algstr_0(X1,X3)\|v2_struct_0(X1)\|k1_algstr_0(X1,X2,X3)!=k4_struct_0(X1)\|~v13_algstr_0(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~l2_algstr_0(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_16])). cnf(c_0_22, plain, (k1_algstr_0(X1,X2,esk4_2(X1,X2))=k4_struct_0(X1)\|v2_struct_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~l2_algstr_0(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v13_algstr_0(X1)), inference(csr,[status(thm)],[c_0_17, c_0_18])). cnf(c_0_23, plain, (v2_struct_0(X1)\|m1_subset_1(esk4_2(X1,X2),u1_struct_0(X1))\|~v13_algstr_0(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~l2_algstr_0(X1)\|~epred1_1(X1)\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_19])). fof(c_0_24, plain, ![X9, X10, X11]:((k1_algstr_0(X9,X10,X11)!=k4_struct_0(X9)\|k4_algstr_0(X9,X10)=X11\|~m1_subset_1(X11,u1_struct_0(X9))\|~m1_subset_1(X10,u1_struct_0(X9))\|(v2_struct_0(X9)\|(~v13_algstr_0(X9)\|(~v3_rlvect_1(X9)\|(~v4_rlvect_1(X9)\|~l2_algstr_0(X9))))))&(k4_algstr_0(X9,X10)!=X11\|k1_algstr_0(X9,X10,X11)=k4_struct_0(X9)\|~m1_subset_1(X11,u1_struct_0(X9))\|~m1_subset_1(X10,u1_struct_0(X9))\|(v2_struct_0(X9)\|(~v13_algstr_0(X9)\|(~v3_rlvect_1(X9)\|(~v4_rlvect_1(X9)\|~l2_algstr_0(X9))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t16_vectsp_1])])])])])). cnf(c_0_25, plain, (k5_algstr_0(X1,X2,X3)=k1_algstr_0(X1,X2,k4_algstr_0(X1,X3))\|~l2_algstr_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_20])). cnf(c_0_26, plain, (k4_algstr_0(X2,esk4_2(X2,X1))=X1\|v2_struct_0(X2)\|~m1_subset_1(esk4_2(X2,X1),u1_struct_0(X2))\|~m1_subset_1(X1,u1_struct_0(X2))\|~l2_algstr_0(X2)\|~v4_rlvect_1(X2)\|~v3_rlvect_1(X2)\|~v13_algstr_0(X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_21, c_0_22])])). cnf(c_0_27, plain, (m1_subset_1(esk4_2(X1,X2),u1_struct_0(X1))\|v2_struct_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~l2_algstr_0(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v13_algstr_0(X1)), inference(csr,[status(thm)],[c_0_23, c_0_18])). cnf(c_0_28, plain, (k4_algstr_0(X1,X2)=X3\|v2_struct_0(X1)\|k1_algstr_0(X1,X2,X3)!=k4_struct_0(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~v13_algstr_0(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~l2_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_24])). fof(c_0_29, plain, ![X18, X19, X20]:(v2_struct_0(X18)\|(~v13_algstr_0(X18)\|(~v3_rlvect_1(X18)\|(~v4_rlvect_1(X18)\|~l2_algstr_0(X18))))\|(~m1_subset_1(X19,u1_struct_0(X18))\|(~m1_subset_1(X20,u1_struct_0(X18))\|k1_algstr_0(X18,k5_algstr_0(X18,X19,X20),X20)=X19))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t1_ring_1])])])])). cnf(c_0_30, plain, (k1_algstr_0(X1,X2,k4_algstr_0(X1,X3))=k5_algstr_0(X1,X2,X3)\|~l2_algstr_0(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_25])). cnf(c_0_31, plain, (k4_algstr_0(X1,esk4_2(X1,X2))=X2\|v2_struct_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~l2_algstr_0(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v13_algstr_0(X1)), inference(csr,[status(thm)],[c_0_26, c_0_27])). cnf(c_0_32, plain, (k4_algstr_0(X1,X2)=X3\|v2_struct_0(X1)\|k1_algstr_0(X1,X2,X3)!=k4_struct_0(X1)\|~v13_algstr_0(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~l2_algstr_0(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_28])). cnf(c_0_33, plain, (v2_struct_0(X1)\|k1_algstr_0(X1,k5_algstr_0(X1,X2,X3),X3)=X2\|~v13_algstr_0(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~l2_algstr_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_29])). cnf(c_0_34, plain, (k5_algstr_0(X1,X2,esk4_2(X1,X3))=k1_algstr_0(X1,X2,X3)\|v2_struct_0(X1)\|~m1_subset_1(esk4_2(X1,X3),u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l2_algstr_0(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v13_algstr_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_30, c_0_31])])). cnf(c_0_35, plain, (esk4_2(X1,X2)=k4_algstr_0(X1,X2)\|v2_struct_0(X1)\|~m1_subset_1(esk4_2(X1,X2),u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l2_algstr_0(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v13_algstr_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_32, c_0_22])])). fof(c_0_36, plain, ![X21, X22, X23]:(~l1_algstr_0(X21)\|(~m1_subset_1(X22,u1_struct_0(X21))\|~m1_subset_1(X23,u1_struct_0(X21)))\|m1_subset_1(k1_algstr_0(X21,X22,X23),u1_struct_0(X21))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_algstr_0])])). fof(c_0_37, plain, ![X24]:((l2_struct_0(X24)\|~l2_algstr_0(X24))&(l1_algstr_0(X24)\|~l2_algstr_0(X24))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l2_algstr_0])])])). fof(c_0_38, negated_conjecture, ~(![X1]:((~(v2_struct_0(X1))&(v13_algstr_0(X1)&(v3_rlvect_1(X1)&(v4_rlvect_1(X1)&l2_algstr_0(X1)))))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>k5_algstr_0(X1,k1_algstr_0(X1,X2,X3),X3)=X2)))), inference(assume_negation,[status(cth)],[t27_toprealc])). cnf(c_0_39, plain, (k1_algstr_0(X1,k5_algstr_0(X1,X2,X3),X3)=X2\|v2_struct_0(X1)\|~v13_algstr_0(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~l2_algstr_0(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_33])). cnf(c_0_40, plain, (k5_algstr_0(X1,X2,esk4_2(X1,X3))=k1_algstr_0(X1,X2,X3)\|v2_struct_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~l2_algstr_0(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v13_algstr_0(X1)), inference(csr,[status(thm)],[c_0_34, c_0_27])). cnf(c_0_41, plain, (esk4_2(X1,X2)=k4_algstr_0(X1,X2)\|v2_struct_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~l2_algstr_0(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v13_algstr_0(X1)), inference(csr,[status(thm)],[c_0_35, c_0_27])). cnf(c_0_42, plain, (m1_subset_1(k1_algstr_0(X1,X2,X3),u1_struct_0(X1))\|~l1_algstr_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_36])). cnf(c_0_43, plain, (l1_algstr_0(X1)\|~l2_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_37])). fof(c_0_44, negated_conjecture, ((~v2_struct_0(esk1_0)&(v13_algstr_0(esk1_0)&(v3_rlvect_1(esk1_0)&(v4_rlvect_1(esk1_0)&l2_algstr_0(esk1_0)))))&(m1_subset_1(esk2_0,u1_struct_0(esk1_0))&(m1_subset_1(esk3_0,u1_struct_0(esk1_0))&k5_algstr_0(esk1_0,k1_algstr_0(esk1_0,esk2_0,esk3_0),esk3_0)!=esk2_0))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_38])])])])). cnf(c_0_45, plain, (k5_algstr_0(X1,k5_algstr_0(X1,X2,k4_algstr_0(X1,X3)),X3)=X2\|v2_struct_0(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(k5_algstr_0(X1,X2,k4_algstr_0(X1,X3)),u1_struct_0(X1))\|~l2_algstr_0(X1)\|~m1_subset_1(k4_algstr_0(X1,X3),u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v13_algstr_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_30, c_0_39])])). cnf(c_0_46, plain, (k5_algstr_0(X1,X2,k4_algstr_0(X1,X3))=k1_algstr_0(X1,X2,X3)\|v2_struct_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~l2_algstr_0(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v13_algstr_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_40, c_0_41])])). cnf(c_0_47, plain, (m1_subset_1(k1_algstr_0(X1,X2,X3),u1_struct_0(X1))\|~l1_algstr_0(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_42])). cnf(c_0_48, plain, (l1_algstr_0(X1)\|~l2_algstr_0(X1)), inference(evalgc,[status(thm)],[c_0_43])). cnf(c_0_49, negated_conjecture, (k5_algstr_0(esk1_0,k1_algstr_0(esk1_0,esk2_0,esk3_0),esk3_0)!=esk2_0), inference(split_conjunct,[status(thm)],[c_0_44])). cnf(c_0_50, plain, (k5_algstr_0(X1,k1_algstr_0(X1,X2,X3),X3)=X2\|v2_struct_0(X1)\|~m1_subset_1(k1_algstr_0(X1,X2,X3),u1_struct_0(X1))\|~m1_subset_1(k4_algstr_0(X1,X3),u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l2_algstr_0(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v13_algstr_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_45, c_0_46])])). cnf(c_0_51, plain, (m1_subset_1(k4_algstr_0(X1,X2),u1_struct_0(X1))\|v2_struct_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~l2_algstr_0(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v13_algstr_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_27, c_0_41])])). cnf(c_0_52, plain, (m1_subset_1(k1_algstr_0(X1,X2,X3),u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l2_algstr_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_47, c_0_48])])). cnf(c_0_53, negated_conjecture, (m1_subset_1(esk3_0,u1_struct_0(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_44])). cnf(c_0_54, negated_conjecture, (m1_subset_1(esk2_0,u1_struct_0(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_44])). cnf(c_0_55, negated_conjecture, (l2_algstr_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_44])). cnf(c_0_56, negated_conjecture, (v4_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_44])). cnf(c_0_57, negated_conjecture, (v3_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_44])). cnf(c_0_58, negated_conjecture, (v13_algstr_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_44])). cnf(c_0_59, negated_conjecture, (~v2_struct_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_44])). cnf(c_0_60, negated_conjecture, (k5_algstr_0(esk1_0,k1_algstr_0(esk1_0,esk2_0,esk3_0),esk3_0)!=esk2_0), inference(evalgc,[status(thm)],[c_0_49])). cnf(c_0_61, plain, (k5_algstr_0(X1,k1_algstr_0(X1,X2,X3),X3)=X2\|v2_struct_0(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l2_algstr_0(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v13_algstr_0(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_50, c_0_51]), c_0_52])). cnf(c_0_62, negated_conjecture, (m1_subset_1(esk3_0,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[c_0_53])). cnf(c_0_63, negated_conjecture, (m1_subset_1(esk2_0,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[c_0_54])). cnf(c_0_64, negated_conjecture, (l2_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_55])). cnf(c_0_65, negated_conjecture, (v4_rlvect_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_56])). cnf(c_0_66, negated_conjecture, (v3_rlvect_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_57])). cnf(c_0_67, negated_conjecture, (v13_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_58])). cnf(c_0_68, negated_conjecture, (~v2_struct_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_59])). cnf(c_0_69, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60, c_0_61]), c_0_62]), c_0_63]), c_0_64]), c_0_65]), c_0_66]), c_0_67])]), c_0_68]), ['proof']). # SZS output end CNFRefutation	reserve x, X for set, i, n, m for Nat, r, s for real number, c, c1, c2, d for complex number, f, g for complex-valued Function, g1 for n-element complex-valued FinSequence, f1 for n-element real-valued FinSequence, T for non empty TopSpace, p for Element of TOP-REAL n; theorem for V being add-associative right_zeroed right_complementable non empty addLoopStr, v,u being Element of V holds v + u - u = v proof let V be add-associative right_zeroed right_complementable non empty addLoopStr, v,u be Element of V; thus v + u - u = v + (u-u) by RLVECT_1:28 .= v + 0.V by RLVECT_1:5 .= v by RLVECT_1:4; end;	Convert the following ATP output trace into a readable Mizar proof.
t54_mcart_1	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t54_mcart_1, conjecture, ![X1, X2]:(k4_zfmisc_1(X1,X1,X1,X1)=k4_zfmisc_1(X2,X2,X2,X2)=>X1=X2), file('/scratch/mptp/predsminms1/t54_mcart_1__0', t54_mcart_1)). fof(t50_mcart_1, axiom, ![X1, X2, X3, X4]:k3_zfmisc_1(k2_zfmisc_1(X1,X2),X3,X4)=k4_zfmisc_1(X1,X2,X3,X4), file('/scratch/mptp/predsminms1/t54_mcart_1__0', t50_mcart_1)). fof(d3_zfmisc_1, axiom, ![X1, X2, X3]:k3_zfmisc_1(X1,X2,X3)=k2_zfmisc_1(k2_zfmisc_1(X1,X2),X3), file('/scratch/mptp/predsminms1/t54_mcart_1__0', d3_zfmisc_1)). fof(t160_relat_1, axiom, ![X1, X2]:~((~(X1=k1_xboole_0)&(~(X2=k1_xboole_0)&~((k9_xtuple_0(k2_zfmisc_1(X1,X2))=X1&k10_xtuple_0(k2_zfmisc_1(X1,X2))=X2))))), file('/scratch/mptp/predsminms1/t54_mcart_1__0', t160_relat_1)). fof(t90_zfmisc_1, axiom, ![X1, X2]:(k2_zfmisc_1(X1,X2)=k1_xboole_0<=>(X1=k1_xboole_0\|X2=k1_xboole_0)), file('/scratch/mptp/predsminms1/t54_mcart_1__0', t90_zfmisc_1)). fof(t31_mcart_1, axiom, ![X1, X2, X3]:((~(X1=k1_xboole_0)&(~(X2=k1_xboole_0)&~(X3=k1_xboole_0)))<=>~(k3_zfmisc_1(X1,X2,X3)=k1_xboole_0)), file('/scratch/mptp/predsminms1/t54_mcart_1__0', t31_mcart_1)). fof(fc12_subset_1, axiom, ![X1, X2, X3, X4]:((~(v1_xboole_0(X1))&(~(v1_xboole_0(X2))&(~(v1_xboole_0(X3))&~(v1_xboole_0(X4)))))=>~(v1_xboole_0(k4_zfmisc_1(X1,X2,X3,X4)))), file('/scratch/mptp/predsminms1/t54_mcart_1__0', fc12_subset_1)). fof(t6_boole, axiom, ![X1]:(v1_xboole_0(X1)=>X1=k1_xboole_0), file('/scratch/mptp/predsminms1/t54_mcart_1__0', t6_boole)). fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0), file('/scratch/mptp/predsminms1/t54_mcart_1__0', fc1_xboole_0)). fof(c_0_9, negated_conjecture, ~(![X1, X2]:(k4_zfmisc_1(X1,X1,X1,X1)=k4_zfmisc_1(X2,X2,X2,X2)=>X1=X2)), inference(assume_negation,[status(cth)],[t54_mcart_1])). fof(c_0_10, plain, ![X7, X8, X9, X10]:k3_zfmisc_1(k2_zfmisc_1(X7,X8),X9,X10)=k4_zfmisc_1(X7,X8,X9,X10), inference(variable_rename,[status(thm)],[t50_mcart_1])). fof(c_0_11, plain, ![X11, X12, X13]:k3_zfmisc_1(X11,X12,X13)=k2_zfmisc_1(k2_zfmisc_1(X11,X12),X13), inference(variable_rename,[status(thm)],[d3_zfmisc_1])). fof(c_0_12, negated_conjecture, (k4_zfmisc_1(esk1_0,esk1_0,esk1_0,esk1_0)=k4_zfmisc_1(esk2_0,esk2_0,esk2_0,esk2_0)&esk1_0!=esk2_0), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])). cnf(c_0_13, plain, (k3_zfmisc_1(k2_zfmisc_1(X1,X2),X3,X4)=k4_zfmisc_1(X1,X2,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_14, plain, (k3_zfmisc_1(X1,X2,X3)=k2_zfmisc_1(k2_zfmisc_1(X1,X2),X3)), inference(split_conjunct,[status(thm)],[c_0_11])). fof(c_0_15, plain, ![X26, X27]:((k9_xtuple_0(k2_zfmisc_1(X26,X27))=X26\|X27=k1_xboole_0\|X26=k1_xboole_0)&(k10_xtuple_0(k2_zfmisc_1(X26,X27))=X27\|X27=k1_xboole_0\|X26=k1_xboole_0)), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t160_relat_1])])])])). cnf(c_0_16, negated_conjecture, (k4_zfmisc_1(esk1_0,esk1_0,esk1_0,esk1_0)=k4_zfmisc_1(esk2_0,esk2_0,esk2_0,esk2_0)), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_17, plain, (k2_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X2),X3),X4)=k4_zfmisc_1(X1,X2,X3,X4)), inference(rw,[status(thm)],[c_0_13, c_0_14])). cnf(c_0_18, plain, (k10_xtuple_0(k2_zfmisc_1(X1,X2))=X2\|X2=k1_xboole_0\|X1=k1_xboole_0), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_19, negated_conjecture, (k2_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(esk2_0,esk2_0),esk2_0),esk2_0)=k2_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(esk1_0,esk1_0),esk1_0),esk1_0)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16, c_0_17]), c_0_17])). fof(c_0_20, plain, ![X14, X15]:((k2_zfmisc_1(X14,X15)!=k1_xboole_0\|(X14=k1_xboole_0\|X15=k1_xboole_0))&((X14!=k1_xboole_0\|k2_zfmisc_1(X14,X15)=k1_xboole_0)&(X15!=k1_xboole_0\|k2_zfmisc_1(X14,X15)=k1_xboole_0))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t90_zfmisc_1])])])). cnf(c_0_21, plain, (X2=k1_xboole_0\|X1=k1_xboole_0\|k10_xtuple_0(k2_zfmisc_1(X1,X2))=X2), inference(evalgc,[status(thm)],[c_0_18])). cnf(c_0_22, negated_conjecture, (k2_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(esk1_0,esk1_0),esk1_0),esk1_0)=k2_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(esk2_0,esk2_0),esk2_0),esk2_0)), inference(evalgc,[status(thm)],[c_0_19])). cnf(c_0_23, plain, (k2_zfmisc_1(X2,X1)=k1_xboole_0\|X1!=k1_xboole_0), inference(split_conjunct,[status(thm)],[c_0_20])). fof(c_0_24, plain, ![X19, X20, X21]:((X19=k1_xboole_0\|(X20=k1_xboole_0\|X21=k1_xboole_0)\|k3_zfmisc_1(X19,X20,X21)!=k1_xboole_0)&((X19!=k1_xboole_0\|k3_zfmisc_1(X19,X20,X21)=k1_xboole_0)&((X20!=k1_xboole_0\|k3_zfmisc_1(X19,X20,X21)=k1_xboole_0)&(X21!=k1_xboole_0\|k3_zfmisc_1(X19,X20,X21)=k1_xboole_0)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t31_mcart_1])])])])). cnf(c_0_25, negated_conjecture, (k10_xtuple_0(k2_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(esk2_0,esk2_0),esk2_0),esk2_0))=esk1_0\|k2_zfmisc_1(k2_zfmisc_1(esk1_0,esk1_0),esk1_0)=k1_xboole_0\|esk1_0=k1_xboole_0), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_21, c_0_22])])). cnf(c_0_26, plain, (k2_zfmisc_1(X2,X1)=k1_xboole_0\|X1!=k1_xboole_0), inference(evalgc,[status(thm)],[c_0_23])). cnf(c_0_27, negated_conjecture, (esk1_0!=esk2_0), inference(split_conjunct,[status(thm)],[c_0_12])). fof(c_0_28, plain, ![X22, X23, X24, X25]:(v1_xboole_0(X22)\|(v1_xboole_0(X23)\|(v1_xboole_0(X24)\|v1_xboole_0(X25)))\|~v1_xboole_0(k4_zfmisc_1(X22,X23,X24,X25))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fc12_subset_1])])])). cnf(c_0_29, plain, (X1=k1_xboole_0\|X2=k1_xboole_0\|X3=k1_xboole_0\|k3_zfmisc_1(X1,X2,X3)!=k1_xboole_0), inference(split_conjunct,[status(thm)],[c_0_24])). cnf(c_0_30, negated_conjecture, (k10_xtuple_0(k2_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(esk2_0,esk2_0),esk2_0),esk2_0))=esk1_0\|k2_zfmisc_1(k2_zfmisc_1(esk1_0,esk1_0),esk1_0)=k1_xboole_0), inference(csr,[status(thm)],[c_0_25, c_0_26])). cnf(c_0_31, negated_conjecture, (esk1_0!=esk2_0), inference(evalgc,[status(thm)],[c_0_27])). cnf(c_0_32, plain, (v1_xboole_0(X1)\|v1_xboole_0(X2)\|v1_xboole_0(X3)\|v1_xboole_0(X4)\|~v1_xboole_0(k4_zfmisc_1(X1,X2,X3,X4))), inference(split_conjunct,[status(thm)],[c_0_28])). cnf(c_0_33, plain, (X3=k1_xboole_0\|X2=k1_xboole_0\|X1=k1_xboole_0\|k2_zfmisc_1(k2_zfmisc_1(X1,X2),X3)!=k1_xboole_0), inference(rw,[status(thm)],[c_0_29, c_0_14])). cnf(c_0_34, negated_conjecture, (k2_zfmisc_1(k2_zfmisc_1(esk2_0,esk2_0),esk2_0)=k1_xboole_0\|esk2_0=k1_xboole_0\|k2_zfmisc_1(k2_zfmisc_1(esk1_0,esk1_0),esk1_0)=k1_xboole_0), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21, c_0_30]), c_0_31])])). fof(c_0_35, plain, ![X16]:(~v1_xboole_0(X16)\|X16=k1_xboole_0), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])])). cnf(c_0_36, plain, (v1_xboole_0(X4)\|v1_xboole_0(X3)\|v1_xboole_0(X2)\|v1_xboole_0(X1)\|~v1_xboole_0(k2_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X2),X3),X4))), inference(rw,[status(thm)],[c_0_32, c_0_17])). cnf(c_0_37, plain, (v1_xboole_0(k1_xboole_0)), inference(split_conjunct,[status(thm)],[fc1_xboole_0])). cnf(c_0_38, plain, (X3=k1_xboole_0\|X2=k1_xboole_0\|X1=k1_xboole_0\|k2_zfmisc_1(k2_zfmisc_1(X1,X2),X3)!=k1_xboole_0), inference(evalgc,[status(thm)],[c_0_33])). cnf(c_0_39, plain, (k2_zfmisc_1(X1,X2)=k1_xboole_0\|X1!=k1_xboole_0), inference(split_conjunct,[status(thm)],[c_0_20])). cnf(c_0_40, negated_conjecture, (k2_zfmisc_1(k2_zfmisc_1(esk1_0,esk1_0),esk1_0)=k1_xboole_0\|k2_zfmisc_1(k2_zfmisc_1(esk2_0,esk2_0),esk2_0)=k1_xboole_0), inference(csr,[status(thm)],[c_0_34, c_0_26])). cnf(c_0_41, plain, (X1=k1_xboole_0\|~v1_xboole_0(X1)), inference(split_conjunct,[status(thm)],[c_0_35])). cnf(c_0_42, plain, (v1_xboole_0(X4)\|v1_xboole_0(X3)\|v1_xboole_0(X2)\|v1_xboole_0(X1)\|~v1_xboole_0(k2_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X2),X3),X4))), inference(evalgc,[status(thm)],[c_0_36])). cnf(c_0_43, negated_conjecture, (k2_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(esk2_0,esk2_0),esk2_0),esk2_0)=k1_xboole_0\|esk1_0!=k1_xboole_0), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_26, c_0_22])])). cnf(c_0_44, plain, (v1_xboole_0(k1_xboole_0)), inference(evalgc,[status(thm)],[c_0_37])). cnf(c_0_45, negated_conjecture, (k2_zfmisc_1(esk1_0,esk1_0)=k1_xboole_0\|esk1_0=k1_xboole_0\|k2_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(esk2_0,esk2_0),esk2_0),esk2_0)!=k1_xboole_0), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_38, c_0_22])])). cnf(c_0_46, plain, (k2_zfmisc_1(X1,X2)=k1_xboole_0\|X1!=k1_xboole_0), inference(evalgc,[status(thm)],[c_0_39])). cnf(c_0_47, negated_conjecture, (esk1_0=k1_xboole_0\|k2_zfmisc_1(k2_zfmisc_1(esk2_0,esk2_0),esk2_0)=k1_xboole_0), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_38, c_0_40])])). cnf(c_0_48, plain, (X1=k1_xboole_0\|~v1_xboole_0(X1)), inference(evalgc,[status(thm)],[c_0_41])). cnf(c_0_49, negated_conjecture, (v1_xboole_0(esk2_0)\|esk1_0!=k1_xboole_0), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42, c_0_43]), c_0_44])])])). cnf(c_0_50, plain, (X1=k1_xboole_0\|X2=k1_xboole_0\|k2_zfmisc_1(X1,X2)!=k1_xboole_0), inference(split_conjunct,[status(thm)],[c_0_20])). cnf(c_0_51, negated_conjecture, (k2_zfmisc_1(esk1_0,esk1_0)=k1_xboole_0\|k2_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(esk2_0,esk2_0),esk2_0),esk2_0)!=k1_xboole_0), inference(csr,[status(thm)],[c_0_45, c_0_46])). cnf(c_0_52, negated_conjecture, (esk2_0=k1_xboole_0\|esk1_0=k1_xboole_0), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_38, c_0_47])])). cnf(c_0_53, negated_conjecture, (esk2_0=k1_xboole_0\|esk1_0!=k1_xboole_0), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_48, c_0_49])])). cnf(c_0_54, plain, (X2=k1_xboole_0\|X1=k1_xboole_0\|k2_zfmisc_1(X1,X2)!=k1_xboole_0), inference(evalgc,[status(thm)],[c_0_50])). cnf(c_0_55, negated_conjecture, (k2_zfmisc_1(esk1_0,esk1_0)=k1_xboole_0\|esk2_0!=k1_xboole_0), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_51, c_0_26])])). cnf(c_0_56, negated_conjecture, (esk2_0=k1_xboole_0), inference(csr,[status(thm)],[c_0_52, c_0_53])). cnf(c_0_57, negated_conjecture, (esk1_0=k1_xboole_0\|esk2_0!=k1_xboole_0), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_54, c_0_55])])). cnf(c_0_58, negated_conjecture, (esk1_0!=k1_xboole_0), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[c_0_31, c_0_56])])). cnf(c_0_59, negated_conjecture, (esk1_0=k1_xboole_0), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57, c_0_56])])])). cnf(c_0_60, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_58, c_0_59])]), ['proof']). # SZS output end CNFRefutation	reserve v,x,x1,x2,x3,x4,y,y1,y2,y3,y4,z,z1,z2, X,X1,X2,X3,X4,Y,Y1,Y2,Y3,Y4,Y5, Z,Z1,Z2,Z3,Z4,Z5 for set; reserve p for pair set; reserve R for Relation; reserve xx1 for Element of X1, xx2 for Element of X2, xx3 for Element of X3; theorem [:X,X,X,X:] = [:Y,Y,Y,Y:] implies X = Y proof assume [:X,X,X,X:] = [:Y,Y,Y,Y:]; then X<>{} or Y<>{} implies thesis by Th52; hence thesis; end;	Convert the following ATP output trace into a readable Mizar proof.
t40_circtrm1	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t40_circtrm1, conjecture, ![X1]:((~(v2_struct_0(X1))&l1_msualg_1(X1))=>![X2]:((~(v2_struct_0(X2))&l1_msualg_1(X2))=>![X3]:((~(v2_struct_0(X3))&l1_msualg_1(X3))=>![X4]:((v1_relat_1(X4)&v1_funct_1(X4))=>![X5]:((v1_relat_1(X5)&v1_funct_1(X5))=>![X6]:((v1_relat_1(X6)&v1_funct_1(X6))=>![X7]:((v1_relat_1(X7)&v1_funct_1(X7))=>![X8]:((v4_msualg_1(X8,X1)&l3_msualg_1(X8,X1))=>![X9]:((v4_msualg_1(X9,X2)&l3_msualg_1(X9,X2))=>![X10]:((v4_msualg_1(X10,X3)&l3_msualg_1(X10,X3))=>((r5_circtrm1(X1,X2,X4,X5,X8,X9)&r5_circtrm1(X2,X3,X6,X7,X9,X10))=>r5_circtrm1(X1,X3,k3_relat_1(X4,X6),k3_relat_1(X5,X7),X8,X10)))))))))))), file('/scratch/mptp/predsminms1/t40_circtrm1__0', t40_circtrm1)). fof(t37_circtrm1, axiom, ![X1]:((~(v2_struct_0(X1))&l1_msualg_1(X1))=>![X2]:((~(v2_struct_0(X2))&l1_msualg_1(X2))=>![X3]:((v1_relat_1(X3)&v1_funct_1(X3))=>![X4]:((v1_relat_1(X4)&v1_funct_1(X4))=>![X5]:((v4_msualg_1(X5,X1)&l3_msualg_1(X5,X1))=>![X6]:((v4_msualg_1(X6,X2)&l3_msualg_1(X6,X2))=>(r5_circtrm1(X1,X2,X3,X4,X5,X6)<=>(r1_circtrm1(X1,X2,X3,X4)&(u3_msualg_1(X1,X5)=k3_relat_1(X3,u3_msualg_1(X2,X6))&u4_msualg_1(X1,X5)=k3_relat_1(X4,u4_msualg_1(X2,X6))))))))))), file('/scratch/mptp/predsminms1/t40_circtrm1__0', t37_circtrm1)). fof(d12_circtrm1, axiom, ![X1]:((~(v2_struct_0(X1))&l1_msualg_1(X1))=>![X2]:((~(v2_struct_0(X2))&l1_msualg_1(X2))=>![X3]:((v1_relat_1(X3)&v1_funct_1(X3))=>![X4]:((v1_relat_1(X4)&v1_funct_1(X4))=>![X5]:((v4_msualg_1(X5,X1)&l3_msualg_1(X5,X1))=>![X6]:((v4_msualg_1(X6,X2)&l3_msualg_1(X6,X2))=>(r4_circtrm1(X1,X2,X3,X4,X5,X6)<=>(v2_funct_1(X3)&(v2_funct_1(X4)&(r3_pua2mss1(X1,X2,X3,X4)&(u3_msualg_1(X1,X5)=k3_relat_1(X3,u3_msualg_1(X2,X6))&u4_msualg_1(X1,X5)=k3_relat_1(X4,u4_msualg_1(X2,X6))))))))))))), file('/scratch/mptp/predsminms1/t40_circtrm1__0', d12_circtrm1)). fof(d13_circtrm1, axiom, ![X1]:((~(v2_struct_0(X1))&l1_msualg_1(X1))=>![X2]:((~(v2_struct_0(X2))&l1_msualg_1(X2))=>![X3]:((v1_relat_1(X3)&v1_funct_1(X3))=>![X4]:((v1_relat_1(X4)&v1_funct_1(X4))=>![X5]:((v4_msualg_1(X5,X1)&l3_msualg_1(X5,X1))=>![X6]:((v4_msualg_1(X6,X2)&l3_msualg_1(X6,X2))=>(r5_circtrm1(X1,X2,X3,X4,X5,X6)<=>(r4_circtrm1(X1,X2,X3,X4,X5,X6)&r4_circtrm1(X2,X1,k2_funct_1(X3),k2_funct_1(X4),X6,X5))))))))), file('/scratch/mptp/predsminms1/t40_circtrm1__0', d13_circtrm1)). fof(t27_circtrm1, axiom, ![X1]:((~(v2_struct_0(X1))&l1_msualg_1(X1))=>![X2]:((~(v2_struct_0(X2))&l1_msualg_1(X2))=>![X3]:((~(v2_struct_0(X3))&l1_msualg_1(X3))=>![X4]:((v1_relat_1(X4)&v1_funct_1(X4))=>![X5]:((v1_relat_1(X5)&v1_funct_1(X5))=>![X6]:((v1_relat_1(X6)&v1_funct_1(X6))=>![X7]:((v1_relat_1(X7)&v1_funct_1(X7))=>((r1_circtrm1(X1,X2,X4,X5)&r1_circtrm1(X2,X3,X6,X7))=>r1_circtrm1(X1,X3,k3_relat_1(X4,X6),k3_relat_1(X5,X7)))))))))), file('/scratch/mptp/predsminms1/t40_circtrm1__0', t27_circtrm1)). fof(dt_k2_funct_1, axiom, ![X1]:((v1_relat_1(X1)&v1_funct_1(X1))=>(v1_relat_1(k2_funct_1(X1))&v1_funct_1(k2_funct_1(X1)))), file('/scratch/mptp/predsminms1/t40_circtrm1__0', dt_k2_funct_1)). fof(dt_k3_relat_1, axiom, ![X1, X2]:v1_relat_1(k3_relat_1(X1,X2)), file('/scratch/mptp/predsminms1/t40_circtrm1__0', dt_k3_relat_1)). fof(t36_relat_1, axiom, ![X1]:(v1_relat_1(X1)=>![X2]:(v1_relat_1(X2)=>![X3]:(v1_relat_1(X3)=>k3_relat_1(k3_relat_1(X1,X2),X3)=k3_relat_1(X1,k3_relat_1(X2,X3))))), file('/scratch/mptp/predsminms1/t40_circtrm1__0', t36_relat_1)). fof(fc2_funct_1, axiom, ![X1, X2]:(((v1_relat_1(X1)&v1_funct_1(X1))&(v1_relat_1(X2)&v1_funct_1(X2)))=>(v1_relat_1(k3_relat_1(X1,X2))&v1_funct_1(k3_relat_1(X1,X2)))), file('/scratch/mptp/predsminms1/t40_circtrm1__0', fc2_funct_1)). fof(c_0_9, negated_conjecture, ~(![X1]:((~(v2_struct_0(X1))&l1_msualg_1(X1))=>![X2]:((~(v2_struct_0(X2))&l1_msualg_1(X2))=>![X3]:((~(v2_struct_0(X3))&l1_msualg_1(X3))=>![X4]:((v1_relat_1(X4)&v1_funct_1(X4))=>![X5]:((v1_relat_1(X5)&v1_funct_1(X5))=>![X6]:((v1_relat_1(X6)&v1_funct_1(X6))=>![X7]:((v1_relat_1(X7)&v1_funct_1(X7))=>![X8]:((v4_msualg_1(X8,X1)&l3_msualg_1(X8,X1))=>![X9]:((v4_msualg_1(X9,X2)&l3_msualg_1(X9,X2))=>![X10]:((v4_msualg_1(X10,X3)&l3_msualg_1(X10,X3))=>((r5_circtrm1(X1,X2,X4,X5,X8,X9)&r5_circtrm1(X2,X3,X6,X7,X9,X10))=>r5_circtrm1(X1,X3,k3_relat_1(X4,X6),k3_relat_1(X5,X7),X8,X10))))))))))))), inference(assume_negation,[status(cth)],[t40_circtrm1])). fof(c_0_10, plain, ![X21, X22, X23, X24, X25, X26]:(((r1_circtrm1(X21,X22,X23,X24)\|~r5_circtrm1(X21,X22,X23,X24,X25,X26)\|(~v4_msualg_1(X26,X22)\|~l3_msualg_1(X26,X22))\|(~v4_msualg_1(X25,X21)\|~l3_msualg_1(X25,X21))\|(~v1_relat_1(X24)\|~v1_funct_1(X24))\|(~v1_relat_1(X23)\|~v1_funct_1(X23))\|(v2_struct_0(X22)\|~l1_msualg_1(X22))\|(v2_struct_0(X21)\|~l1_msualg_1(X21)))&((u3_msualg_1(X21,X25)=k3_relat_1(X23,u3_msualg_1(X22,X26))\|~r5_circtrm1(X21,X22,X23,X24,X25,X26)\|(~v4_msualg_1(X26,X22)\|~l3_msualg_1(X26,X22))\|(~v4_msualg_1(X25,X21)\|~l3_msualg_1(X25,X21))\|(~v1_relat_1(X24)\|~v1_funct_1(X24))\|(~v1_relat_1(X23)\|~v1_funct_1(X23))\|(v2_struct_0(X22)\|~l1_msualg_1(X22))\|(v2_struct_0(X21)\|~l1_msualg_1(X21)))&(u4_msualg_1(X21,X25)=k3_relat_1(X24,u4_msualg_1(X22,X26))\|~r5_circtrm1(X21,X22,X23,X24,X25,X26)\|(~v4_msualg_1(X26,X22)\|~l3_msualg_1(X26,X22))\|(~v4_msualg_1(X25,X21)\|~l3_msualg_1(X25,X21))\|(~v1_relat_1(X24)\|~v1_funct_1(X24))\|(~v1_relat_1(X23)\|~v1_funct_1(X23))\|(v2_struct_0(X22)\|~l1_msualg_1(X22))\|(v2_struct_0(X21)\|~l1_msualg_1(X21)))))&(~r1_circtrm1(X21,X22,X23,X24)\|(u3_msualg_1(X21,X25)!=k3_relat_1(X23,u3_msualg_1(X22,X26))\|u4_msualg_1(X21,X25)!=k3_relat_1(X24,u4_msualg_1(X22,X26)))\|r5_circtrm1(X21,X22,X23,X24,X25,X26)\|(~v4_msualg_1(X26,X22)\|~l3_msualg_1(X26,X22))\|(~v4_msualg_1(X25,X21)\|~l3_msualg_1(X25,X21))\|(~v1_relat_1(X24)\|~v1_funct_1(X24))\|(~v1_relat_1(X23)\|~v1_funct_1(X23))\|(v2_struct_0(X22)\|~l1_msualg_1(X22))\|(v2_struct_0(X21)\|~l1_msualg_1(X21)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t37_circtrm1])])])])])). fof(c_0_11, negated_conjecture, ((~v2_struct_0(esk1_0)&l1_msualg_1(esk1_0))&((~v2_struct_0(esk2_0)&l1_msualg_1(esk2_0))&((~v2_struct_0(esk3_0)&l1_msualg_1(esk3_0))&((v1_relat_1(esk4_0)&v1_funct_1(esk4_0))&((v1_relat_1(esk5_0)&v1_funct_1(esk5_0))&((v1_relat_1(esk6_0)&v1_funct_1(esk6_0))&((v1_relat_1(esk7_0)&v1_funct_1(esk7_0))&((v4_msualg_1(esk8_0,esk1_0)&l3_msualg_1(esk8_0,esk1_0))&((v4_msualg_1(esk9_0,esk2_0)&l3_msualg_1(esk9_0,esk2_0))&((v4_msualg_1(esk10_0,esk3_0)&l3_msualg_1(esk10_0,esk3_0))&((r5_circtrm1(esk1_0,esk2_0,esk4_0,esk5_0,esk8_0,esk9_0)&r5_circtrm1(esk2_0,esk3_0,esk6_0,esk7_0,esk9_0,esk10_0))&~r5_circtrm1(esk1_0,esk3_0,k3_relat_1(esk4_0,esk6_0),k3_relat_1(esk5_0,esk7_0),esk8_0,esk10_0)))))))))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_9])])])])). fof(c_0_12, plain, ![X38, X39, X40, X41, X42, X43]:(((v2_funct_1(X40)\|~r4_circtrm1(X38,X39,X40,X41,X42,X43)\|(~v4_msualg_1(X43,X39)\|~l3_msualg_1(X43,X39))\|(~v4_msualg_1(X42,X38)\|~l3_msualg_1(X42,X38))\|(~v1_relat_1(X41)\|~v1_funct_1(X41))\|(~v1_relat_1(X40)\|~v1_funct_1(X40))\|(v2_struct_0(X39)\|~l1_msualg_1(X39))\|(v2_struct_0(X38)\|~l1_msualg_1(X38)))&((v2_funct_1(X41)\|~r4_circtrm1(X38,X39,X40,X41,X42,X43)\|(~v4_msualg_1(X43,X39)\|~l3_msualg_1(X43,X39))\|(~v4_msualg_1(X42,X38)\|~l3_msualg_1(X42,X38))\|(~v1_relat_1(X41)\|~v1_funct_1(X41))\|(~v1_relat_1(X40)\|~v1_funct_1(X40))\|(v2_struct_0(X39)\|~l1_msualg_1(X39))\|(v2_struct_0(X38)\|~l1_msualg_1(X38)))&((r3_pua2mss1(X38,X39,X40,X41)\|~r4_circtrm1(X38,X39,X40,X41,X42,X43)\|(~v4_msualg_1(X43,X39)\|~l3_msualg_1(X43,X39))\|(~v4_msualg_1(X42,X38)\|~l3_msualg_1(X42,X38))\|(~v1_relat_1(X41)\|~v1_funct_1(X41))\|(~v1_relat_1(X40)\|~v1_funct_1(X40))\|(v2_struct_0(X39)\|~l1_msualg_1(X39))\|(v2_struct_0(X38)\|~l1_msualg_1(X38)))&((u3_msualg_1(X38,X42)=k3_relat_1(X40,u3_msualg_1(X39,X43))\|~r4_circtrm1(X38,X39,X40,X41,X42,X43)\|(~v4_msualg_1(X43,X39)\|~l3_msualg_1(X43,X39))\|(~v4_msualg_1(X42,X38)\|~l3_msualg_1(X42,X38))\|(~v1_relat_1(X41)\|~v1_funct_1(X41))\|(~v1_relat_1(X40)\|~v1_funct_1(X40))\|(v2_struct_0(X39)\|~l1_msualg_1(X39))\|(v2_struct_0(X38)\|~l1_msualg_1(X38)))&(u4_msualg_1(X38,X42)=k3_relat_1(X41,u4_msualg_1(X39,X43))\|~r4_circtrm1(X38,X39,X40,X41,X42,X43)\|(~v4_msualg_1(X43,X39)\|~l3_msualg_1(X43,X39))\|(~v4_msualg_1(X42,X38)\|~l3_msualg_1(X42,X38))\|(~v1_relat_1(X41)\|~v1_funct_1(X41))\|(~v1_relat_1(X40)\|~v1_funct_1(X40))\|(v2_struct_0(X39)\|~l1_msualg_1(X39))\|(v2_struct_0(X38)\|~l1_msualg_1(X38)))))))&(~v2_funct_1(X40)\|(~v2_funct_1(X41)\|(~r3_pua2mss1(X38,X39,X40,X41)\|(u3_msualg_1(X38,X42)!=k3_relat_1(X40,u3_msualg_1(X39,X43))\|u4_msualg_1(X38,X42)!=k3_relat_1(X41,u4_msualg_1(X39,X43)))))\|r4_circtrm1(X38,X39,X40,X41,X42,X43)\|(~v4_msualg_1(X43,X39)\|~l3_msualg_1(X43,X39))\|(~v4_msualg_1(X42,X38)\|~l3_msualg_1(X42,X38))\|(~v1_relat_1(X41)\|~v1_funct_1(X41))\|(~v1_relat_1(X40)\|~v1_funct_1(X40))\|(v2_struct_0(X39)\|~l1_msualg_1(X39))\|(v2_struct_0(X38)\|~l1_msualg_1(X38)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d12_circtrm1])])])])])). fof(c_0_13, plain, ![X44, X45, X46, X47, X48, X49]:(((r4_circtrm1(X44,X45,X46,X47,X48,X49)\|~r5_circtrm1(X44,X45,X46,X47,X48,X49)\|(~v4_msualg_1(X49,X45)\|~l3_msualg_1(X49,X45))\|(~v4_msualg_1(X48,X44)\|~l3_msualg_1(X48,X44))\|(~v1_relat_1(X47)\|~v1_funct_1(X47))\|(~v1_relat_1(X46)\|~v1_funct_1(X46))\|(v2_struct_0(X45)\|~l1_msualg_1(X45))\|(v2_struct_0(X44)\|~l1_msualg_1(X44)))&(r4_circtrm1(X45,X44,k2_funct_1(X46),k2_funct_1(X47),X49,X48)\|~r5_circtrm1(X44,X45,X46,X47,X48,X49)\|(~v4_msualg_1(X49,X45)\|~l3_msualg_1(X49,X45))\|(~v4_msualg_1(X48,X44)\|~l3_msualg_1(X48,X44))\|(~v1_relat_1(X47)\|~v1_funct_1(X47))\|(~v1_relat_1(X46)\|~v1_funct_1(X46))\|(v2_struct_0(X45)\|~l1_msualg_1(X45))\|(v2_struct_0(X44)\|~l1_msualg_1(X44))))&(~r4_circtrm1(X44,X45,X46,X47,X48,X49)\|~r4_circtrm1(X45,X44,k2_funct_1(X46),k2_funct_1(X47),X49,X48)\|r5_circtrm1(X44,X45,X46,X47,X48,X49)\|(~v4_msualg_1(X49,X45)\|~l3_msualg_1(X49,X45))\|(~v4_msualg_1(X48,X44)\|~l3_msualg_1(X48,X44))\|(~v1_relat_1(X47)\|~v1_funct_1(X47))\|(~v1_relat_1(X46)\|~v1_funct_1(X46))\|(v2_struct_0(X45)\|~l1_msualg_1(X45))\|(v2_struct_0(X44)\|~l1_msualg_1(X44)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d13_circtrm1])])])])])). fof(c_0_14, plain, ![X50, X51, X52, X53, X54, X55, X56]:(v2_struct_0(X50)\|~l1_msualg_1(X50)\|(v2_struct_0(X51)\|~l1_msualg_1(X51)\|(v2_struct_0(X52)\|~l1_msualg_1(X52)\|(~v1_relat_1(X53)\|~v1_funct_1(X53)\|(~v1_relat_1(X54)\|~v1_funct_1(X54)\|(~v1_relat_1(X55)\|~v1_funct_1(X55)\|(~v1_relat_1(X56)\|~v1_funct_1(X56)\|(~r1_circtrm1(X50,X51,X53,X54)\|~r1_circtrm1(X51,X52,X55,X56)\|r1_circtrm1(X50,X52,k3_relat_1(X53,X55),k3_relat_1(X54,X56)))))))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t27_circtrm1])])])])). cnf(c_0_15, plain, (r1_circtrm1(X1,X2,X3,X4)\|v2_struct_0(X2)\|v2_struct_0(X1)\|~r5_circtrm1(X1,X2,X3,X4,X5,X6)\|~v4_msualg_1(X6,X2)\|~l3_msualg_1(X6,X2)\|~v4_msualg_1(X5,X1)\|~l3_msualg_1(X5,X1)\|~v1_relat_1(X4)\|~v1_funct_1(X4)\|~v1_relat_1(X3)\|~v1_funct_1(X3)\|~l1_msualg_1(X2)\|~l1_msualg_1(X1)), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_16, negated_conjecture, (r5_circtrm1(esk2_0,esk3_0,esk6_0,esk7_0,esk9_0,esk10_0)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_17, negated_conjecture, (l3_msualg_1(esk10_0,esk3_0)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_18, negated_conjecture, (l3_msualg_1(esk9_0,esk2_0)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_19, negated_conjecture, (v4_msualg_1(esk10_0,esk3_0)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_20, negated_conjecture, (v4_msualg_1(esk9_0,esk2_0)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_21, negated_conjecture, (v1_funct_1(esk7_0)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_22, negated_conjecture, (v1_funct_1(esk6_0)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_23, negated_conjecture, (v1_relat_1(esk7_0)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_24, negated_conjecture, (v1_relat_1(esk6_0)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_25, negated_conjecture, (l1_msualg_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_26, negated_conjecture, (l1_msualg_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_27, negated_conjecture, (~v2_struct_0(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_28, negated_conjecture, (~v2_struct_0(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_29, plain, (u4_msualg_1(X1,X2)=k3_relat_1(X3,u4_msualg_1(X4,X5))\|v2_struct_0(X4)\|v2_struct_0(X1)\|~r4_circtrm1(X1,X4,X6,X3,X2,X5)\|~v4_msualg_1(X5,X4)\|~l3_msualg_1(X5,X4)\|~v4_msualg_1(X2,X1)\|~l3_msualg_1(X2,X1)\|~v1_relat_1(X3)\|~v1_funct_1(X3)\|~v1_relat_1(X6)\|~v1_funct_1(X6)\|~l1_msualg_1(X4)\|~l1_msualg_1(X1)), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_30, plain, (r4_circtrm1(X1,X2,k2_funct_1(X3),k2_funct_1(X4),X5,X6)\|v2_struct_0(X1)\|v2_struct_0(X2)\|~r5_circtrm1(X2,X1,X3,X4,X6,X5)\|~v4_msualg_1(X5,X1)\|~l3_msualg_1(X5,X1)\|~v4_msualg_1(X6,X2)\|~l3_msualg_1(X6,X2)\|~v1_relat_1(X4)\|~v1_funct_1(X4)\|~v1_relat_1(X3)\|~v1_funct_1(X3)\|~l1_msualg_1(X1)\|~l1_msualg_1(X2)), inference(split_conjunct,[status(thm)],[c_0_13])). fof(c_0_31, plain, ![X57]:((v1_relat_1(k2_funct_1(X57))\|(~v1_relat_1(X57)\|~v1_funct_1(X57)))&(v1_funct_1(k2_funct_1(X57))\|(~v1_relat_1(X57)\|~v1_funct_1(X57)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_funct_1])])])). cnf(c_0_32, plain, (v2_struct_0(X1)\|v2_struct_0(X2)\|v2_struct_0(X3)\|r1_circtrm1(X1,X3,k3_relat_1(X4,X6),k3_relat_1(X5,X7))\|~l1_msualg_1(X1)\|~l1_msualg_1(X2)\|~l1_msualg_1(X3)\|~v1_relat_1(X4)\|~v1_funct_1(X4)\|~v1_relat_1(X5)\|~v1_funct_1(X5)\|~v1_relat_1(X6)\|~v1_funct_1(X6)\|~v1_relat_1(X7)\|~v1_funct_1(X7)\|~r1_circtrm1(X1,X2,X4,X5)\|~r1_circtrm1(X2,X3,X6,X7)), inference(split_conjunct,[status(thm)],[c_0_14])). cnf(c_0_33, plain, (v2_struct_0(X2)\|v2_struct_0(X1)\|r1_circtrm1(X1,X2,X3,X4)\|~l1_msualg_1(X2)\|~l1_msualg_1(X1)\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v4_msualg_1(X6,X2)\|~v4_msualg_1(X5,X1)\|~l3_msualg_1(X6,X2)\|~l3_msualg_1(X5,X1)\|~r5_circtrm1(X1,X2,X3,X4,X5,X6)), inference(evalgc,[status(thm)],[c_0_15])). cnf(c_0_34, negated_conjecture, (r5_circtrm1(esk2_0,esk3_0,esk6_0,esk7_0,esk9_0,esk10_0)), inference(evalgc,[status(thm)],[c_0_16])). cnf(c_0_35, negated_conjecture, (l3_msualg_1(esk10_0,esk3_0)), inference(evalgc,[status(thm)],[c_0_17])). cnf(c_0_36, negated_conjecture, (l3_msualg_1(esk9_0,esk2_0)), inference(evalgc,[status(thm)],[c_0_18])). cnf(c_0_37, negated_conjecture, (v4_msualg_1(esk10_0,esk3_0)), inference(evalgc,[status(thm)],[c_0_19])). cnf(c_0_38, negated_conjecture, (v4_msualg_1(esk9_0,esk2_0)), inference(evalgc,[status(thm)],[c_0_20])). cnf(c_0_39, negated_conjecture, (v1_funct_1(esk7_0)), inference(evalgc,[status(thm)],[c_0_21])). cnf(c_0_40, negated_conjecture, (v1_funct_1(esk6_0)), inference(evalgc,[status(thm)],[c_0_22])). cnf(c_0_41, negated_conjecture, (v1_relat_1(esk7_0)), inference(evalgc,[status(thm)],[c_0_23])). cnf(c_0_42, negated_conjecture, (v1_relat_1(esk6_0)), inference(evalgc,[status(thm)],[c_0_24])). cnf(c_0_43, negated_conjecture, (l1_msualg_1(esk3_0)), inference(evalgc,[status(thm)],[c_0_25])). cnf(c_0_44, negated_conjecture, (l1_msualg_1(esk2_0)), inference(evalgc,[status(thm)],[c_0_26])). cnf(c_0_45, negated_conjecture, (~v2_struct_0(esk2_0)), inference(evalgc,[status(thm)],[c_0_27])). cnf(c_0_46, negated_conjecture, (~v2_struct_0(esk3_0)), inference(evalgc,[status(thm)],[c_0_28])). fof(c_0_47, plain, ![X30, X31]:v1_relat_1(k3_relat_1(X30,X31)), inference(variable_rename,[status(thm)],[dt_k3_relat_1])). cnf(c_0_48, plain, (u4_msualg_1(X1,X2)=k3_relat_1(X3,u4_msualg_1(X4,X5))\|v2_struct_0(X4)\|v2_struct_0(X1)\|~l1_msualg_1(X4)\|~l1_msualg_1(X1)\|~v1_relat_1(X6)\|~v1_relat_1(X3)\|~v1_funct_1(X6)\|~v1_funct_1(X3)\|~v4_msualg_1(X5,X4)\|~v4_msualg_1(X2,X1)\|~l3_msualg_1(X5,X4)\|~l3_msualg_1(X2,X1)\|~r4_circtrm1(X1,X4,X6,X3,X2,X5)), inference(evalgc,[status(thm)],[c_0_29])). cnf(c_0_49, plain, (v2_struct_0(X2)\|v2_struct_0(X1)\|r4_circtrm1(X1,X2,k2_funct_1(X3),k2_funct_1(X4),X5,X6)\|~l1_msualg_1(X2)\|~l1_msualg_1(X1)\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v4_msualg_1(X6,X2)\|~v4_msualg_1(X5,X1)\|~l3_msualg_1(X6,X2)\|~l3_msualg_1(X5,X1)\|~r5_circtrm1(X2,X1,X3,X4,X6,X5)), inference(evalgc,[status(thm)],[c_0_30])). cnf(c_0_50, plain, (v1_relat_1(k2_funct_1(X1))\|~v1_relat_1(X1)\|~v1_funct_1(X1)), inference(split_conjunct,[status(thm)],[c_0_31])). cnf(c_0_51, plain, (v1_funct_1(k2_funct_1(X1))\|~v1_relat_1(X1)\|~v1_funct_1(X1)), inference(split_conjunct,[status(thm)],[c_0_31])). cnf(c_0_52, plain, (u3_msualg_1(X1,X2)=k3_relat_1(X3,u3_msualg_1(X4,X5))\|v2_struct_0(X4)\|v2_struct_0(X1)\|~r4_circtrm1(X1,X4,X3,X6,X2,X5)\|~v4_msualg_1(X5,X4)\|~l3_msualg_1(X5,X4)\|~v4_msualg_1(X2,X1)\|~l3_msualg_1(X2,X1)\|~v1_relat_1(X6)\|~v1_funct_1(X6)\|~v1_relat_1(X3)\|~v1_funct_1(X3)\|~l1_msualg_1(X4)\|~l1_msualg_1(X1)), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_53, plain, (r5_circtrm1(X1,X2,X3,X4,X5,X6)\|v2_struct_0(X2)\|v2_struct_0(X1)\|~r1_circtrm1(X1,X2,X3,X4)\|u3_msualg_1(X1,X5)!=k3_relat_1(X3,u3_msualg_1(X2,X6))\|u4_msualg_1(X1,X5)!=k3_relat_1(X4,u4_msualg_1(X2,X6))\|~v4_msualg_1(X6,X2)\|~l3_msualg_1(X6,X2)\|~v4_msualg_1(X5,X1)\|~l3_msualg_1(X5,X1)\|~v1_relat_1(X4)\|~v1_funct_1(X4)\|~v1_relat_1(X3)\|~v1_funct_1(X3)\|~l1_msualg_1(X2)\|~l1_msualg_1(X1)), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_54, plain, (v2_struct_0(X3)\|v2_struct_0(X2)\|v2_struct_0(X1)\|r1_circtrm1(X1,X3,k3_relat_1(X4,X6),k3_relat_1(X5,X7))\|~l1_msualg_1(X3)\|~l1_msualg_1(X2)\|~l1_msualg_1(X1)\|~v1_relat_1(X7)\|~v1_relat_1(X6)\|~v1_relat_1(X5)\|~v1_relat_1(X4)\|~v1_funct_1(X7)\|~v1_funct_1(X6)\|~v1_funct_1(X5)\|~v1_funct_1(X4)\|~r1_circtrm1(X2,X3,X6,X7)\|~r1_circtrm1(X1,X2,X4,X5)), inference(evalgc,[status(thm)],[c_0_32])). cnf(c_0_55, negated_conjecture, (r1_circtrm1(esk2_0,esk3_0,esk6_0,esk7_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33, c_0_34]), c_0_35]), c_0_36]), c_0_37]), c_0_38]), c_0_39]), c_0_40]), c_0_41]), c_0_42]), c_0_43]), c_0_44])]), c_0_45]), c_0_46])])). cnf(c_0_56, plain, (v1_relat_1(k3_relat_1(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_47])). cnf(c_0_57, negated_conjecture, (r5_circtrm1(esk1_0,esk2_0,esk4_0,esk5_0,esk8_0,esk9_0)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_58, negated_conjecture, (l3_msualg_1(esk8_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_59, negated_conjecture, (v4_msualg_1(esk8_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_60, negated_conjecture, (v1_funct_1(esk5_0)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_61, negated_conjecture, (v1_funct_1(esk4_0)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_62, negated_conjecture, (v1_relat_1(esk5_0)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_63, negated_conjecture, (v1_relat_1(esk4_0)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_64, negated_conjecture, (l1_msualg_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_65, negated_conjecture, (~v2_struct_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_66, plain, (u4_msualg_1(X1,X2)=k3_relat_1(k2_funct_1(X3),u4_msualg_1(X4,X5))\|v2_struct_0(X1)\|v2_struct_0(X4)\|~l3_msualg_1(X5,X4)\|~l3_msualg_1(X2,X1)\|~v4_msualg_1(X5,X4)\|~v4_msualg_1(X2,X1)\|~v1_funct_1(k2_funct_1(X6))\|~v1_funct_1(k2_funct_1(X3))\|~v1_relat_1(k2_funct_1(X6))\|~v1_relat_1(k2_funct_1(X3))\|~l1_msualg_1(X4)\|~l1_msualg_1(X1)\|~r5_circtrm1(X4,X1,X6,X3,X5,X2)\|~v1_funct_1(X3)\|~v1_funct_1(X6)\|~v1_relat_1(X3)\|~v1_relat_1(X6)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_48, c_0_49])])). cnf(c_0_67, plain, (v1_relat_1(k2_funct_1(X1))\|~v1_relat_1(X1)\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[c_0_50])). cnf(c_0_68, plain, (v1_funct_1(k2_funct_1(X1))\|~v1_relat_1(X1)\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[c_0_51])). cnf(c_0_69, plain, (u3_msualg_1(X1,X2)=k3_relat_1(X3,u3_msualg_1(X4,X5))\|v2_struct_0(X4)\|v2_struct_0(X1)\|~l1_msualg_1(X4)\|~l1_msualg_1(X1)\|~v1_relat_1(X6)\|~v1_relat_1(X3)\|~v1_funct_1(X6)\|~v1_funct_1(X3)\|~v4_msualg_1(X5,X4)\|~v4_msualg_1(X2,X1)\|~l3_msualg_1(X5,X4)\|~l3_msualg_1(X2,X1)\|~r4_circtrm1(X1,X4,X3,X6,X2,X5)), inference(evalgc,[status(thm)],[c_0_52])). cnf(c_0_70, negated_conjecture, (~r5_circtrm1(esk1_0,esk3_0,k3_relat_1(esk4_0,esk6_0),k3_relat_1(esk5_0,esk7_0),esk8_0,esk10_0)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_71, plain, (v2_struct_0(X2)\|v2_struct_0(X1)\|r5_circtrm1(X1,X2,X3,X4,X5,X6)\|u3_msualg_1(X1,X5)!=k3_relat_1(X3,u3_msualg_1(X2,X6))\|u4_msualg_1(X1,X5)!=k3_relat_1(X4,u4_msualg_1(X2,X6))\|~l1_msualg_1(X2)\|~l1_msualg_1(X1)\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v4_msualg_1(X6,X2)\|~v4_msualg_1(X5,X1)\|~l3_msualg_1(X6,X2)\|~l3_msualg_1(X5,X1)\|~r1_circtrm1(X1,X2,X3,X4)), inference(evalgc,[status(thm)],[c_0_53])). cnf(c_0_72, negated_conjecture, (r1_circtrm1(X1,esk3_0,k3_relat_1(X2,esk6_0),k3_relat_1(X3,esk7_0))\|v2_struct_0(X1)\|~r1_circtrm1(X1,esk2_0,X2,X3)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~l1_msualg_1(X1)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54, c_0_55]), c_0_39]), c_0_40]), c_0_41]), c_0_42]), c_0_43]), c_0_44])]), c_0_45]), c_0_46])])). cnf(c_0_73, plain, (v1_relat_1(k3_relat_1(X1,X2))), inference(evalgc,[status(thm)],[c_0_56])). cnf(c_0_74, negated_conjecture, (r5_circtrm1(esk1_0,esk2_0,esk4_0,esk5_0,esk8_0,esk9_0)), inference(evalgc,[status(thm)],[c_0_57])). cnf(c_0_75, negated_conjecture, (l3_msualg_1(esk8_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_58])). cnf(c_0_76, negated_conjecture, (v4_msualg_1(esk8_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_59])). cnf(c_0_77, negated_conjecture, (v1_funct_1(esk5_0)), inference(evalgc,[status(thm)],[c_0_60])). cnf(c_0_78, negated_conjecture, (v1_funct_1(esk4_0)), inference(evalgc,[status(thm)],[c_0_61])). cnf(c_0_79, negated_conjecture, (v1_relat_1(esk5_0)), inference(evalgc,[status(thm)],[c_0_62])). cnf(c_0_80, negated_conjecture, (v1_relat_1(esk4_0)), inference(evalgc,[status(thm)],[c_0_63])). cnf(c_0_81, negated_conjecture, (l1_msualg_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_64])). cnf(c_0_82, negated_conjecture, (~v2_struct_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_65])). fof(c_0_83, plain, ![X27, X28, X29]:(~v1_relat_1(X27)\|(~v1_relat_1(X28)\|(~v1_relat_1(X29)\|k3_relat_1(k3_relat_1(X27,X28),X29)=k3_relat_1(X27,k3_relat_1(X28,X29))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t36_relat_1])])])). cnf(c_0_84, plain, (u4_msualg_1(X1,X2)=k3_relat_1(X3,u4_msualg_1(X4,X5))\|v2_struct_0(X4)\|v2_struct_0(X1)\|~r5_circtrm1(X1,X4,X6,X3,X2,X5)\|~v4_msualg_1(X5,X4)\|~l3_msualg_1(X5,X4)\|~v4_msualg_1(X2,X1)\|~l3_msualg_1(X2,X1)\|~v1_relat_1(X3)\|~v1_funct_1(X3)\|~v1_relat_1(X6)\|~v1_funct_1(X6)\|~l1_msualg_1(X4)\|~l1_msualg_1(X1)), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_85, plain, (u4_msualg_1(X1,X2)=k3_relat_1(k2_funct_1(X3),u4_msualg_1(X4,X5))\|v2_struct_0(X4)\|v2_struct_0(X1)\|~r5_circtrm1(X4,X1,X6,X3,X5,X2)\|~l3_msualg_1(X5,X4)\|~l3_msualg_1(X2,X1)\|~v4_msualg_1(X5,X4)\|~v4_msualg_1(X2,X1)\|~v1_funct_1(X3)\|~v1_funct_1(X6)\|~v1_relat_1(X3)\|~v1_relat_1(X6)\|~l1_msualg_1(X4)\|~l1_msualg_1(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_66, c_0_67]), c_0_67]), c_0_68]), c_0_68])). cnf(c_0_86, plain, (u3_msualg_1(X1,X2)=k3_relat_1(k2_funct_1(X3),u3_msualg_1(X4,X5))\|v2_struct_0(X1)\|v2_struct_0(X4)\|~l3_msualg_1(X5,X4)\|~l3_msualg_1(X2,X1)\|~v4_msualg_1(X5,X4)\|~v4_msualg_1(X2,X1)\|~v1_funct_1(k2_funct_1(X6))\|~v1_funct_1(k2_funct_1(X3))\|~v1_relat_1(k2_funct_1(X6))\|~v1_relat_1(k2_funct_1(X3))\|~l1_msualg_1(X4)\|~l1_msualg_1(X1)\|~r5_circtrm1(X4,X1,X3,X6,X5,X2)\|~v1_funct_1(X6)\|~v1_funct_1(X3)\|~v1_relat_1(X6)\|~v1_relat_1(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_69, c_0_49])])). cnf(c_0_87, negated_conjecture, (~r5_circtrm1(esk1_0,esk3_0,k3_relat_1(esk4_0,esk6_0),k3_relat_1(esk5_0,esk7_0),esk8_0,esk10_0)), inference(evalgc,[status(thm)],[c_0_70])). cnf(c_0_88, negated_conjecture, (r5_circtrm1(X1,esk3_0,k3_relat_1(X2,esk6_0),k3_relat_1(X3,esk7_0),X4,X5)\|v2_struct_0(X1)\|u3_msualg_1(X1,X4)!=k3_relat_1(k3_relat_1(X2,esk6_0),u3_msualg_1(esk3_0,X5))\|u4_msualg_1(X1,X4)!=k3_relat_1(k3_relat_1(X3,esk7_0),u4_msualg_1(esk3_0,X5))\|~l3_msualg_1(X5,esk3_0)\|~l3_msualg_1(X4,X1)\|~v4_msualg_1(X5,esk3_0)\|~v4_msualg_1(X4,X1)\|~v1_funct_1(k3_relat_1(X3,esk7_0))\|~v1_funct_1(k3_relat_1(X2,esk6_0))\|~l1_msualg_1(X1)\|~r1_circtrm1(X1,esk2_0,X2,X3)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v1_relat_1(X3)\|~v1_relat_1(X2)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71, c_0_72]), c_0_73]), c_0_73]), c_0_43])]), c_0_46])])). cnf(c_0_89, negated_conjecture, (r1_circtrm1(esk1_0,esk2_0,esk4_0,esk5_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33, c_0_74]), c_0_36]), c_0_75]), c_0_38]), c_0_76]), c_0_77]), c_0_78]), c_0_79]), c_0_80]), c_0_44]), c_0_81])]), c_0_82]), c_0_45])])). cnf(c_0_90, plain, (k3_relat_1(k3_relat_1(X1,X2),X3)=k3_relat_1(X1,k3_relat_1(X2,X3))\|~v1_relat_1(X1)\|~v1_relat_1(X2)\|~v1_relat_1(X3)), inference(split_conjunct,[status(thm)],[c_0_83])). cnf(c_0_91, plain, (u4_msualg_1(X1,X2)=k3_relat_1(X3,u4_msualg_1(X4,X5))\|v2_struct_0(X4)\|v2_struct_0(X1)\|~l1_msualg_1(X4)\|~l1_msualg_1(X1)\|~v1_relat_1(X6)\|~v1_relat_1(X3)\|~v1_funct_1(X6)\|~v1_funct_1(X3)\|~v4_msualg_1(X5,X4)\|~v4_msualg_1(X2,X1)\|~l3_msualg_1(X5,X4)\|~l3_msualg_1(X2,X1)\|~r5_circtrm1(X1,X4,X6,X3,X2,X5)), inference(evalgc,[status(thm)],[c_0_84])). cnf(c_0_92, negated_conjecture, (k3_relat_1(k2_funct_1(esk7_0),u4_msualg_1(esk2_0,esk9_0))=u4_msualg_1(esk3_0,esk10_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85, c_0_34]), c_0_36]), c_0_35]), c_0_38]), c_0_37]), c_0_39]), c_0_40]), c_0_41]), c_0_42]), c_0_44]), c_0_43])]), c_0_45]), c_0_46])])). cnf(c_0_93, plain, (u3_msualg_1(X1,X2)=k3_relat_1(X3,u3_msualg_1(X4,X5))\|v2_struct_0(X4)\|v2_struct_0(X1)\|~r5_circtrm1(X1,X4,X3,X6,X2,X5)\|~v4_msualg_1(X5,X4)\|~l3_msualg_1(X5,X4)\|~v4_msualg_1(X2,X1)\|~l3_msualg_1(X2,X1)\|~v1_relat_1(X6)\|~v1_funct_1(X6)\|~v1_relat_1(X3)\|~v1_funct_1(X3)\|~l1_msualg_1(X4)\|~l1_msualg_1(X1)), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_94, plain, (u3_msualg_1(X1,X2)=k3_relat_1(k2_funct_1(X3),u3_msualg_1(X4,X5))\|v2_struct_0(X4)\|v2_struct_0(X1)\|~r5_circtrm1(X4,X1,X3,X6,X5,X2)\|~l3_msualg_1(X5,X4)\|~l3_msualg_1(X2,X1)\|~v4_msualg_1(X5,X4)\|~v4_msualg_1(X2,X1)\|~v1_funct_1(X6)\|~v1_funct_1(X3)\|~v1_relat_1(X6)\|~v1_relat_1(X3)\|~l1_msualg_1(X4)\|~l1_msualg_1(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_86, c_0_67]), c_0_67]), c_0_68]), c_0_68])). cnf(c_0_95, negated_conjecture, (k3_relat_1(k3_relat_1(esk4_0,esk6_0),u3_msualg_1(esk3_0,esk10_0))!=u3_msualg_1(esk1_0,esk8_0)\|k3_relat_1(k3_relat_1(esk5_0,esk7_0),u4_msualg_1(esk3_0,esk10_0))!=u4_msualg_1(esk1_0,esk8_0)\|~v1_funct_1(k3_relat_1(esk5_0,esk7_0))\|~v1_funct_1(k3_relat_1(esk4_0,esk6_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87, c_0_88]), c_0_89]), c_0_35]), c_0_75]), c_0_37]), c_0_76]), c_0_77]), c_0_78]), c_0_79]), c_0_80]), c_0_81])]), c_0_82])])). cnf(c_0_96, plain, (k3_relat_1(k3_relat_1(X1,X2),X3)=k3_relat_1(X1,k3_relat_1(X2,X3))\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_relat_1(X1)), inference(evalgc,[status(thm)],[c_0_90])). cnf(c_0_97, negated_conjecture, (k3_relat_1(esk7_0,u4_msualg_1(esk3_0,esk10_0))=u4_msualg_1(esk2_0,esk9_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91, c_0_34]), c_0_35]), c_0_36]), c_0_37]), c_0_38]), c_0_40]), c_0_39]), c_0_42]), c_0_41]), c_0_43]), c_0_44])]), c_0_45]), c_0_46])])). cnf(c_0_98, negated_conjecture, (k3_relat_1(esk5_0,u4_msualg_1(esk2_0,esk9_0))=u4_msualg_1(esk1_0,esk8_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91, c_0_74]), c_0_36]), c_0_75]), c_0_38]), c_0_76]), c_0_78]), c_0_77]), c_0_80]), c_0_79]), c_0_44]), c_0_81])]), c_0_82]), c_0_45])])). cnf(c_0_99, negated_conjecture, (v1_relat_1(u4_msualg_1(esk3_0,esk10_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_73, c_0_92])])). cnf(c_0_100, plain, (u3_msualg_1(X1,X2)=k3_relat_1(X3,u3_msualg_1(X4,X5))\|v2_struct_0(X4)\|v2_struct_0(X1)\|~l1_msualg_1(X4)\|~l1_msualg_1(X1)\|~v1_relat_1(X6)\|~v1_relat_1(X3)\|~v1_funct_1(X6)\|~v1_funct_1(X3)\|~v4_msualg_1(X5,X4)\|~v4_msualg_1(X2,X1)\|~l3_msualg_1(X5,X4)\|~l3_msualg_1(X2,X1)\|~r5_circtrm1(X1,X4,X3,X6,X2,X5)), inference(evalgc,[status(thm)],[c_0_93])). cnf(c_0_101, negated_conjecture, (k3_relat_1(k2_funct_1(esk6_0),u3_msualg_1(esk2_0,esk9_0))=u3_msualg_1(esk3_0,esk10_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94, c_0_34]), c_0_36]), c_0_35]), c_0_38]), c_0_37]), c_0_39]), c_0_40]), c_0_41]), c_0_42]), c_0_44]), c_0_43])]), c_0_45]), c_0_46])])). fof(c_0_102, plain, ![X58, X59]:((v1_relat_1(k3_relat_1(X58,X59))\|(~v1_relat_1(X58)\|~v1_funct_1(X58)\|(~v1_relat_1(X59)\|~v1_funct_1(X59))))&(v1_funct_1(k3_relat_1(X58,X59))\|(~v1_relat_1(X58)\|~v1_funct_1(X58)\|(~v1_relat_1(X59)\|~v1_funct_1(X59))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc2_funct_1])])])). cnf(c_0_103, negated_conjecture, (k3_relat_1(k3_relat_1(esk4_0,esk6_0),u3_msualg_1(esk3_0,esk10_0))!=u3_msualg_1(esk1_0,esk8_0)\|~v1_funct_1(k3_relat_1(esk5_0,esk7_0))\|~v1_funct_1(k3_relat_1(esk4_0,esk6_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95, c_0_96]), c_0_97]), c_0_98]), c_0_99]), c_0_41]), c_0_79])])])). cnf(c_0_104, negated_conjecture, (k3_relat_1(esk6_0,u3_msualg_1(esk3_0,esk10_0))=u3_msualg_1(esk2_0,esk9_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100, c_0_34]), c_0_35]), c_0_36]), c_0_37]), c_0_38]), c_0_39]), c_0_40]), c_0_41]), c_0_42]), c_0_43]), c_0_44])]), c_0_45]), c_0_46])])). cnf(c_0_105, negated_conjecture, (k3_relat_1(esk4_0,u3_msualg_1(esk2_0,esk9_0))=u3_msualg_1(esk1_0,esk8_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100, c_0_74]), c_0_36]), c_0_75]), c_0_38]), c_0_76]), c_0_77]), c_0_78]), c_0_79]), c_0_80]), c_0_44]), c_0_81])]), c_0_82]), c_0_45])])). cnf(c_0_106, negated_conjecture, (v1_relat_1(u3_msualg_1(esk3_0,esk10_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_73, c_0_101])])). cnf(c_0_107, plain, (v1_funct_1(k3_relat_1(X1,X2))\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v1_relat_1(X2)\|~v1_funct_1(X2)), inference(split_conjunct,[status(thm)],[c_0_102])). cnf(c_0_108, negated_conjecture, (~v1_funct_1(k3_relat_1(esk5_0,esk7_0))\|~v1_funct_1(k3_relat_1(esk4_0,esk6_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103, c_0_96]), c_0_104]), c_0_105]), c_0_106]), c_0_42]), c_0_80])])])). cnf(c_0_109, plain, (v1_funct_1(k3_relat_1(X1,X2))\|~v1_relat_1(X2)\|~v1_relat_1(X1)\|~v1_funct_1(X2)\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[c_0_107])). cnf(c_0_110, negated_conjecture, (~v1_funct_1(k3_relat_1(esk4_0,esk6_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108, c_0_109]), c_0_39]), c_0_77]), c_0_41]), c_0_79])])])). cnf(c_0_111, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110, c_0_109]), c_0_40]), c_0_78]), c_0_42]), c_0_80])]), ['proof']). # SZS output end CNFRefutation	reserve S for non empty non void ManySortedSign, V for non-empty ManySortedSet of the carrier of S, A for non-empty MSAlgebra over S, X for non empty Subset of S-Terms V, t for Element of X; reserve S for non empty non void ManySortedSign, A for non-empty finite-yielding MSAlgebra over S, V for Variables of A, X for SetWithCompoundTerm of S,V; theorem for S1, S2, S3 being non empty ManySortedSign for f1, g1, f2, g2 being Function for C1 being non-empty MSAlgebra over S1 for C2 being non-empty MSAlgebra over S2 for C3 being non-empty MSAlgebra over S3 st C1, C2 are_similar_wrt f1, g1 & C2, C3 are_similar_wrt f2, g2 holds C1, C3 are_similar_wrt f2f1, g2g1 proof let S1, S2, S3 be non empty ManySortedSign; let f1,g1, f2,g2 be Function; let C1 be non-empty MSAlgebra over S1; let C2 be non-empty MSAlgebra over S2; let C3 be non-empty MSAlgebra over S3; assume that A1: f1, g1 form_embedding_of C1, C2 and A2: f1", g1" form_embedding_of C2, C1 and A3: f2, g2 form_embedding_of C2, C3 and A4: f2", g2" form_embedding_of C3, C2; thus f2f1, g2g1 form_embedding_of C1, C3 by A1,A3,Th35; A5: f1 is one-to-one by A1,Def12; A6: g1 is one-to-one by A1,Def12; A7: f2 is one-to-one by A3,Def12; A8: g2 is one-to-one by A3,Def12; A9: (f2f1)" = f1"f2" by A5,A7,FUNCT_1:44; (g2g1)" = g1"g2" by A6,A8,FUNCT_1:44; hence thesis by A2,A4,A9,Th35; end;	Convert the following ATP output trace into a readable Mizar proof.
t44_xtuple_0	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t44_xtuple_0, conjecture, ![X1, X2]:r1_tarski(k14_xtuple_0(k3_xboole_0(X1,X2)),k3_xboole_0(k14_xtuple_0(X1),k14_xtuple_0(X2))), file('/scratch/mptp/predsminms1/t44_xtuple_0__0', t44_xtuple_0)). fof(t19_xboole_1, axiom, ![X1, X2, X3]:((r1_tarski(X1,X2)&r1_tarski(X1,X3))=>r1_tarski(X1,k3_xboole_0(X2,X3))), file('/scratch/mptp/predsminms1/t44_xtuple_0__0', t19_xboole_1)). fof(t17_xboole_1, axiom, ![X1, X2]:r1_tarski(k3_xboole_0(X1,X2),X1), file('/scratch/mptp/predsminms1/t44_xtuple_0__0', t17_xboole_1)). fof(commutativity_k3_xboole_0, axiom, ![X1, X2]:k3_xboole_0(X1,X2)=k3_xboole_0(X2,X1), file('/scratch/mptp/predsminms1/t44_xtuple_0__0', commutativity_k3_xboole_0)). fof(t17_xtuple_0, axiom, ![X1, X2]:(r1_tarski(X1,X2)=>r1_tarski(k14_xtuple_0(X1),k14_xtuple_0(X2))), file('/scratch/mptp/predsminms1/t44_xtuple_0__0', t17_xtuple_0)). fof(c_0_5, negated_conjecture, ~(![X1, X2]:r1_tarski(k14_xtuple_0(k3_xboole_0(X1,X2)),k3_xboole_0(k14_xtuple_0(X1),k14_xtuple_0(X2)))), inference(assume_negation,[status(cth)],[t44_xtuple_0])). fof(c_0_6, negated_conjecture, ~r1_tarski(k14_xtuple_0(k3_xboole_0(esk1_0,esk2_0)),k3_xboole_0(k14_xtuple_0(esk1_0),k14_xtuple_0(esk2_0))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])). fof(c_0_7, plain, ![X6, X7, X8]:(~r1_tarski(X6,X7)\|~r1_tarski(X6,X8)\|r1_tarski(X6,k3_xboole_0(X7,X8))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t19_xboole_1])])). fof(c_0_8, plain, ![X9, X10]:r1_tarski(k3_xboole_0(X9,X10),X9), inference(variable_rename,[status(thm)],[t17_xboole_1])). fof(c_0_9, plain, ![X11, X12]:k3_xboole_0(X11,X12)=k3_xboole_0(X12,X11), inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0])). cnf(c_0_10, negated_conjecture, (~r1_tarski(k14_xtuple_0(k3_xboole_0(esk1_0,esk2_0)),k3_xboole_0(k14_xtuple_0(esk1_0),k14_xtuple_0(esk2_0)))), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_11, plain, (r1_tarski(X1,k3_xboole_0(X2,X3))\|~r1_tarski(X1,X2)\|~r1_tarski(X1,X3)), inference(split_conjunct,[status(thm)],[c_0_7])). fof(c_0_12, plain, ![X13, X14]:(~r1_tarski(X13,X14)\|r1_tarski(k14_xtuple_0(X13),k14_xtuple_0(X14))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t17_xtuple_0])])). cnf(c_0_13, plain, (r1_tarski(k3_xboole_0(X1,X2),X1)), inference(split_conjunct,[status(thm)],[c_0_8])). cnf(c_0_14, plain, (k3_xboole_0(X1,X2)=k3_xboole_0(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_15, negated_conjecture, (~r1_tarski(k14_xtuple_0(k3_xboole_0(esk1_0,esk2_0)),k3_xboole_0(k14_xtuple_0(esk1_0),k14_xtuple_0(esk2_0)))), inference(evalgc,[status(thm)],[c_0_10])). cnf(c_0_16, plain, (r1_tarski(X1,k3_xboole_0(X2,X3))\|~r1_tarski(X1,X3)\|~r1_tarski(X1,X2)), inference(evalgc,[status(thm)],[c_0_11])). cnf(c_0_17, plain, (r1_tarski(k14_xtuple_0(X1),k14_xtuple_0(X2))\|~r1_tarski(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_18, plain, (r1_tarski(k3_xboole_0(X1,X2),X1)), inference(evalgc,[status(thm)],[c_0_13])). cnf(c_0_19, plain, (k3_xboole_0(X1,X2)=k3_xboole_0(X2,X1)), inference(evalgc,[status(thm)],[c_0_14])). cnf(c_0_20, negated_conjecture, (~r1_tarski(k14_xtuple_0(k3_xboole_0(esk1_0,esk2_0)),k14_xtuple_0(esk2_0))\|~r1_tarski(k14_xtuple_0(k3_xboole_0(esk1_0,esk2_0)),k14_xtuple_0(esk1_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_15, c_0_16])])). cnf(c_0_21, plain, (r1_tarski(k14_xtuple_0(X1),k14_xtuple_0(X2))\|~r1_tarski(X1,X2)), inference(evalgc,[status(thm)],[c_0_17])). cnf(c_0_22, plain, (r1_tarski(k3_xboole_0(X2,X1),X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_18, c_0_19])])). cnf(c_0_23, negated_conjecture, (~r1_tarski(k14_xtuple_0(k3_xboole_0(esk1_0,esk2_0)),k14_xtuple_0(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20, c_0_21]), c_0_22])])])). cnf(c_0_24, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23, c_0_21]), c_0_18])]), ['proof']). # SZS output end CNFRefutation	reserve x,x1,x2,x3,x4,y,y1,y2,y3,y4,z,z1,z2,z2,z4 for set; reserve X,Y for set; reserve X,X1,X2,X3,X4,Y for set; theorem proj2_4(X /\ Y) c= proj2_4 X /\ proj2_4 Y proof proj2_4(X /\ Y) c= proj2_4 X & proj2_4(X /\ Y) c= proj2_4 Y by Th18,XBOOLE_1:17; hence thesis by XBOOLE_1:19; end;	Convert the following ATP output trace into a readable Mizar proof.
t1_clopban3	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t1_clopban3, conjecture, ![X1]:((~(v2_struct_0(X1))&(v13_algstr_0(X1)&(v3_rlvect_1(X1)&(v4_rlvect_1(X1)&l2_clvect_1(X1)))))=>![X2]:((v1_funct_1(X2)&(v1_funct_2(X2,k5_numbers,u1_struct_0(X1))&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,u1_struct_0(X1))))))=>(![X3]:(m2_subset_1(X3,k1_numbers,k5_numbers)=>k1_normsp_1(X1,X2,X3)=k4_struct_0(X1))=>![X3]:(m2_subset_1(X3,k1_numbers,k5_numbers)=>k1_normsp_1(X1,k1_bhsp_4(X1,X2),X3)=k4_struct_0(X1))))), file('/scratch/mptp/predsminms1/t1_clopban3__0', t1_clopban3)). fof(dt_l1_clvect_1, axiom, ![X1]:(l1_clvect_1(X1)=>l2_algstr_0(X1)), file('/scratch/mptp/predsminms1/t1_clopban3__0', dt_l1_clvect_1)). fof(dt_l2_clvect_1, axiom, ![X1]:(l2_clvect_1(X1)=>(l1_clvect_1(X1)&l2_normsp_0(X1))), file('/scratch/mptp/predsminms1/t1_clopban3__0', dt_l2_clvect_1)). fof(fc6_ordinal1, axiom, (~(v1_xboole_0(k4_ordinal1))&v3_ordinal1(k4_ordinal1)), file('/scratch/mptp/predsminms1/t1_clopban3__0', fc6_ordinal1)). fof(spc1_numerals, axiom, ((v2_xxreal_0(np__1)&m2_subset_1(np__1,k1_numbers,k5_numbers))&(m1_subset_1(np__1,k5_numbers)&m1_subset_1(np__1,k1_numbers))), file('/scratch/mptp/predsminms1/t1_clopban3__0', spc1_numerals)). fof(t4_rlvect_1, axiom, ![X1]:((~(v2_struct_0(X1))&(v13_algstr_0(X1)&(v3_rlvect_1(X1)&(v4_rlvect_1(X1)&l2_algstr_0(X1)))))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>(k1_algstr_0(X1,X2,k4_struct_0(X1))=X2&k1_algstr_0(X1,k4_struct_0(X1),X2)=X2))), file('/scratch/mptp/predsminms1/t1_clopban3__0', t4_rlvect_1)). fof(redefinition_m2_subset_1, axiom, ![X1, X2]:((~(v1_xboole_0(X1))&(~(v1_xboole_0(X2))&m1_subset_1(X2,k1_zfmisc_1(X1))))=>![X3]:(m2_subset_1(X3,X1,X2)<=>m1_subset_1(X3,X2))), file('/scratch/mptp/predsminms1/t1_clopban3__0', redefinition_m2_subset_1)). fof(redefinition_k5_numbers, axiom, k5_numbers=k4_ordinal1, file('/scratch/mptp/predsminms1/t1_clopban3__0', redefinition_k5_numbers)). fof(fc1_numbers, axiom, ~(v1_xboole_0(k1_numbers)), file('/scratch/mptp/predsminms1/t1_clopban3__0', fc1_numbers)). fof(dt_k4_struct_0, axiom, ![X1]:(l2_struct_0(X1)=>m1_subset_1(k4_struct_0(X1),u1_struct_0(X1))), file('/scratch/mptp/predsminms1/t1_clopban3__0', dt_k4_struct_0)). fof(d1_bhsp_4, axiom, ![X1]:((~(v2_struct_0(X1))&l2_algstr_0(X1))=>![X2]:((v1_funct_1(X2)&(v1_funct_2(X2,k5_numbers,u1_struct_0(X1))&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,u1_struct_0(X1))))))=>![X3]:((v1_funct_1(X3)&(v1_funct_2(X3,k5_numbers,u1_struct_0(X1))&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,u1_struct_0(X1))))))=>(X3=k1_bhsp_4(X1,X2)<=>(k1_normsp_1(X1,X3,k6_numbers)=k1_normsp_1(X1,X2,k6_numbers)&![X4]:(m2_subset_1(X4,k1_numbers,k5_numbers)=>k1_normsp_1(X1,X3,k2_nat_1(X4,np__1))=k1_algstr_0(X1,k1_normsp_1(X1,X3,X4),k1_normsp_1(X1,X2,k2_nat_1(X4,np__1))))))))), file('/scratch/mptp/predsminms1/t1_clopban3__0', d1_bhsp_4)). fof(dt_k5_numbers, axiom, m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)), file('/scratch/mptp/predsminms1/t1_clopban3__0', dt_k5_numbers)). fof(dt_l2_normsp_0, axiom, ![X1]:(l2_normsp_0(X1)=>(l1_normsp_0(X1)&l2_struct_0(X1))), file('/scratch/mptp/predsminms1/t1_clopban3__0', dt_l2_normsp_0)). fof(dt_k2_nat_1, axiom, ![X1, X2]:((m1_subset_1(X1,k5_numbers)&v7_ordinal1(X2))=>m2_subset_1(k2_nat_1(X1,X2),k1_numbers,k5_numbers)), file('/scratch/mptp/predsminms1/t1_clopban3__0', dt_k2_nat_1)). fof(cc8_ordinal1, axiom, ![X1]:(m1_subset_1(X1,k4_ordinal1)=>v7_ordinal1(X1)), file('/scratch/mptp/predsminms1/t1_clopban3__0', cc8_ordinal1)). fof(c_0_15, negated_conjecture, ~(![X1]:((~(v2_struct_0(X1))&(v13_algstr_0(X1)&(v3_rlvect_1(X1)&(v4_rlvect_1(X1)&l2_clvect_1(X1)))))=>![X2]:((v1_funct_1(X2)&(v1_funct_2(X2,k5_numbers,u1_struct_0(X1))&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,u1_struct_0(X1))))))=>(![X3]:(m2_subset_1(X3,k1_numbers,k5_numbers)=>k1_normsp_1(X1,X2,X3)=k4_struct_0(X1))=>![X3]:(m2_subset_1(X3,k1_numbers,k5_numbers)=>k1_normsp_1(X1,k1_bhsp_4(X1,X2),X3)=k4_struct_0(X1)))))), inference(assume_negation,[status(cth)],[t1_clopban3])). fof(c_0_16, negated_conjecture, ![X7]:((~v2_struct_0(esk1_0)&(v13_algstr_0(esk1_0)&(v3_rlvect_1(esk1_0)&(v4_rlvect_1(esk1_0)&l2_clvect_1(esk1_0)))))&((v1_funct_1(esk2_0)&(v1_funct_2(esk2_0,k5_numbers,u1_struct_0(esk1_0))&m1_subset_1(esk2_0,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,u1_struct_0(esk1_0))))))&((~m2_subset_1(X7,k1_numbers,k5_numbers)\|k1_normsp_1(esk1_0,esk2_0,X7)=k4_struct_0(esk1_0))&(m2_subset_1(esk3_0,k1_numbers,k5_numbers)&k1_normsp_1(esk1_0,k1_bhsp_4(esk1_0,esk2_0),esk3_0)!=k4_struct_0(esk1_0))))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_15])])])])])). fof(c_0_17, plain, ![X9]:(~l1_clvect_1(X9)\|l2_algstr_0(X9)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_clvect_1])])). fof(c_0_18, plain, ![X10]:((l1_clvect_1(X10)\|~l2_clvect_1(X10))&(l2_normsp_0(X10)\|~l2_clvect_1(X10))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l2_clvect_1])])])). fof(c_0_19, plain, (~v1_xboole_0(k4_ordinal1)&v3_ordinal1(k4_ordinal1)), inference(fof_simplification,[status(thm)],[fc6_ordinal1])). cnf(c_0_20, negated_conjecture, (k1_normsp_1(esk1_0,esk2_0,X1)=k4_struct_0(esk1_0)\|~m2_subset_1(X1,k1_numbers,k5_numbers)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_21, plain, (m2_subset_1(np__1,k1_numbers,k5_numbers)), inference(split_conjunct,[status(thm)],[spc1_numerals])). fof(c_0_22, plain, ![X13, X14]:((k1_algstr_0(X13,X14,k4_struct_0(X13))=X14\|~m1_subset_1(X14,u1_struct_0(X13))\|(v2_struct_0(X13)\|(~v13_algstr_0(X13)\|(~v3_rlvect_1(X13)\|(~v4_rlvect_1(X13)\|~l2_algstr_0(X13))))))&(k1_algstr_0(X13,k4_struct_0(X13),X14)=X14\|~m1_subset_1(X14,u1_struct_0(X13))\|(v2_struct_0(X13)\|(~v13_algstr_0(X13)\|(~v3_rlvect_1(X13)\|(~v4_rlvect_1(X13)\|~l2_algstr_0(X13))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t4_rlvect_1])])])])])). cnf(c_0_23, plain, (l2_algstr_0(X1)\|~l1_clvect_1(X1)), inference(split_conjunct,[status(thm)],[c_0_17])). cnf(c_0_24, plain, (l1_clvect_1(X1)\|~l2_clvect_1(X1)), inference(split_conjunct,[status(thm)],[c_0_18])). fof(c_0_25, plain, ![X16, X17, X18]:((~m2_subset_1(X18,X16,X17)\|m1_subset_1(X18,X17)\|(v1_xboole_0(X16)\|(v1_xboole_0(X17)\|~m1_subset_1(X17,k1_zfmisc_1(X16)))))&(~m1_subset_1(X18,X17)\|m2_subset_1(X18,X16,X17)\|(v1_xboole_0(X16)\|(v1_xboole_0(X17)\|~m1_subset_1(X17,k1_zfmisc_1(X16)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[redefinition_m2_subset_1])])])])])). cnf(c_0_26, plain, (~v1_xboole_0(k4_ordinal1)), inference(split_conjunct,[status(thm)],[c_0_19])). cnf(c_0_27, plain, (k5_numbers=k4_ordinal1), inference(split_conjunct,[status(thm)],[redefinition_k5_numbers])). fof(c_0_28, plain, ~v1_xboole_0(k1_numbers), inference(fof_simplification,[status(thm)],[fc1_numbers])). fof(c_0_29, plain, ![X12]:(~l2_struct_0(X12)\|m1_subset_1(k4_struct_0(X12),u1_struct_0(X12))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k4_struct_0])])). cnf(c_0_30, negated_conjecture, (k1_normsp_1(esk1_0,esk2_0,X1)=k4_struct_0(esk1_0)\|~m2_subset_1(X1,k1_numbers,k5_numbers)), inference(evalgc,[status(thm)],[c_0_20])). cnf(c_0_31, plain, (m2_subset_1(np__1,k1_numbers,k5_numbers)), inference(evalgc,[status(thm)],[c_0_21])). fof(c_0_32, plain, ![X23, X24, X25, X26]:(((k1_normsp_1(X23,X25,k6_numbers)=k1_normsp_1(X23,X24,k6_numbers)\|X25!=k1_bhsp_4(X23,X24)\|(~v1_funct_1(X25)\|(~v1_funct_2(X25,k5_numbers,u1_struct_0(X23))\|~m1_subset_1(X25,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,u1_struct_0(X23))))))\|(~v1_funct_1(X24)\|(~v1_funct_2(X24,k5_numbers,u1_struct_0(X23))\|~m1_subset_1(X24,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,u1_struct_0(X23))))))\|(v2_struct_0(X23)\|~l2_algstr_0(X23)))&(~m2_subset_1(X26,k1_numbers,k5_numbers)\|k1_normsp_1(X23,X25,k2_nat_1(X26,np__1))=k1_algstr_0(X23,k1_normsp_1(X23,X25,X26),k1_normsp_1(X23,X24,k2_nat_1(X26,np__1)))\|X25!=k1_bhsp_4(X23,X24)\|(~v1_funct_1(X25)\|(~v1_funct_2(X25,k5_numbers,u1_struct_0(X23))\|~m1_subset_1(X25,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,u1_struct_0(X23))))))\|(~v1_funct_1(X24)\|(~v1_funct_2(X24,k5_numbers,u1_struct_0(X23))\|~m1_subset_1(X24,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,u1_struct_0(X23))))))\|(v2_struct_0(X23)\|~l2_algstr_0(X23))))&((m2_subset_1(esk4_3(X23,X24,X25),k1_numbers,k5_numbers)\|k1_normsp_1(X23,X25,k6_numbers)!=k1_normsp_1(X23,X24,k6_numbers)\|X25=k1_bhsp_4(X23,X24)\|(~v1_funct_1(X25)\|(~v1_funct_2(X25,k5_numbers,u1_struct_0(X23))\|~m1_subset_1(X25,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,u1_struct_0(X23))))))\|(~v1_funct_1(X24)\|(~v1_funct_2(X24,k5_numbers,u1_struct_0(X23))\|~m1_subset_1(X24,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,u1_struct_0(X23))))))\|(v2_struct_0(X23)\|~l2_algstr_0(X23)))&(k1_normsp_1(X23,X25,k2_nat_1(esk4_3(X23,X24,X25),np__1))!=k1_algstr_0(X23,k1_normsp_1(X23,X25,esk4_3(X23,X24,X25)),k1_normsp_1(X23,X24,k2_nat_1(esk4_3(X23,X24,X25),np__1)))\|k1_normsp_1(X23,X25,k6_numbers)!=k1_normsp_1(X23,X24,k6_numbers)\|X25=k1_bhsp_4(X23,X24)\|(~v1_funct_1(X25)\|(~v1_funct_2(X25,k5_numbers,u1_struct_0(X23))\|~m1_subset_1(X25,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,u1_struct_0(X23))))))\|(~v1_funct_1(X24)\|(~v1_funct_2(X24,k5_numbers,u1_struct_0(X23))\|~m1_subset_1(X24,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,u1_struct_0(X23))))))\|(v2_struct_0(X23)\|~l2_algstr_0(X23))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d1_bhsp_4])])])])])])). cnf(c_0_33, plain, (k1_algstr_0(X1,X2,k4_struct_0(X1))=X2\|v2_struct_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~v13_algstr_0(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~l2_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_34, negated_conjecture, (v4_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_35, negated_conjecture, (v3_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_36, negated_conjecture, (v13_algstr_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_37, negated_conjecture, (~v2_struct_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_38, plain, (l2_algstr_0(X1)\|~l1_clvect_1(X1)), inference(evalgc,[status(thm)],[c_0_23])). cnf(c_0_39, plain, (l1_clvect_1(X1)\|~l2_clvect_1(X1)), inference(evalgc,[status(thm)],[c_0_24])). cnf(c_0_40, negated_conjecture, (l2_clvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_41, plain, (m2_subset_1(X1,X3,X2)\|v1_xboole_0(X3)\|v1_xboole_0(X2)\|~m1_subset_1(X1,X2)\|~m1_subset_1(X2,k1_zfmisc_1(X3))), inference(split_conjunct,[status(thm)],[c_0_25])). cnf(c_0_42, plain, (m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers))), inference(split_conjunct,[status(thm)],[dt_k5_numbers])). cnf(c_0_43, plain, (~v1_xboole_0(k4_ordinal1)), inference(evalgc,[status(thm)],[c_0_26])). cnf(c_0_44, plain, (k4_ordinal1=k5_numbers), inference(evalgc,[status(thm)],[c_0_27])). cnf(c_0_45, plain, (~v1_xboole_0(k1_numbers)), inference(split_conjunct,[status(thm)],[c_0_28])). cnf(c_0_46, plain, (m1_subset_1(k4_struct_0(X1),u1_struct_0(X1))\|~l2_struct_0(X1)), inference(split_conjunct,[status(thm)],[c_0_29])). fof(c_0_47, plain, ![X11]:((l1_normsp_0(X11)\|~l2_normsp_0(X11))&(l2_struct_0(X11)\|~l2_normsp_0(X11))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l2_normsp_0])])])). cnf(c_0_48, negated_conjecture, (k4_struct_0(esk1_0)=k1_normsp_1(esk1_0,esk2_0,np__1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_30, c_0_31])])). cnf(c_0_49, plain, (m2_subset_1(esk4_3(X1,X2,X3),k1_numbers,k5_numbers)\|X3=k1_bhsp_4(X1,X2)\|v2_struct_0(X1)\|k1_normsp_1(X1,X3,k6_numbers)!=k1_normsp_1(X1,X2,k6_numbers)\|~v1_funct_1(X3)\|~v1_funct_2(X3,k5_numbers,u1_struct_0(X1))\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,u1_struct_0(X1))))\|~v1_funct_1(X2)\|~v1_funct_2(X2,k5_numbers,u1_struct_0(X1))\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,u1_struct_0(X1))))\|~l2_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_32])). cnf(c_0_50, plain, (k1_algstr_0(X1,X2,k4_struct_0(X1))=X2\|v2_struct_0(X1)\|~v13_algstr_0(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~l2_algstr_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_33])). cnf(c_0_51, negated_conjecture, (v4_rlvect_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_34])). cnf(c_0_52, negated_conjecture, (v3_rlvect_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_35])). cnf(c_0_53, negated_conjecture, (v13_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_36])). cnf(c_0_54, negated_conjecture, (~v2_struct_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_37])). cnf(c_0_55, plain, (l2_algstr_0(X1)\|~l2_clvect_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_38, c_0_39])])). cnf(c_0_56, negated_conjecture, (l2_clvect_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_40])). cnf(c_0_57, plain, (v1_xboole_0(X3)\|v1_xboole_0(X2)\|m2_subset_1(X1,X3,X2)\|~m1_subset_1(X1,X2)\|~m1_subset_1(X2,k1_zfmisc_1(X3))), inference(evalgc,[status(thm)],[c_0_41])). cnf(c_0_58, plain, (m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers))), inference(evalgc,[status(thm)],[c_0_42])). cnf(c_0_59, plain, (~v1_xboole_0(k5_numbers)), inference(rw,[status(thm)],[c_0_43, c_0_44])). cnf(c_0_60, plain, (~v1_xboole_0(k1_numbers)), inference(evalgc,[status(thm)],[c_0_45])). cnf(c_0_61, plain, (m1_subset_1(k4_struct_0(X1),u1_struct_0(X1))\|~l2_struct_0(X1)), inference(evalgc,[status(thm)],[c_0_46])). cnf(c_0_62, plain, (l2_struct_0(X1)\|~l2_normsp_0(X1)), inference(split_conjunct,[status(thm)],[c_0_47])). cnf(c_0_63, plain, (X2=k1_bhsp_4(X1,X3)\|v2_struct_0(X1)\|k1_normsp_1(X1,X2,k2_nat_1(esk4_3(X1,X3,X2),np__1))!=k1_algstr_0(X1,k1_normsp_1(X1,X2,esk4_3(X1,X3,X2)),k1_normsp_1(X1,X3,k2_nat_1(esk4_3(X1,X3,X2),np__1)))\|k1_normsp_1(X1,X2,k6_numbers)!=k1_normsp_1(X1,X3,k6_numbers)\|~v1_funct_1(X2)\|~v1_funct_2(X2,k5_numbers,u1_struct_0(X1))\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,u1_struct_0(X1))))\|~v1_funct_1(X3)\|~v1_funct_2(X3,k5_numbers,u1_struct_0(X1))\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,u1_struct_0(X1))))\|~l2_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_32])). cnf(c_0_64, negated_conjecture, (k1_normsp_1(esk1_0,esk2_0,X1)=k1_normsp_1(esk1_0,esk2_0,np__1)\|~m2_subset_1(X1,k1_numbers,k5_numbers)), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[c_0_30, c_0_48])])). cnf(c_0_65, plain, (X3=k1_bhsp_4(X1,X2)\|v2_struct_0(X1)\|m2_subset_1(esk4_3(X1,X2,X3),k1_numbers,k5_numbers)\|k1_normsp_1(X1,X2,k6_numbers)!=k1_normsp_1(X1,X3,k6_numbers)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~l2_algstr_0(X1)\|~v1_funct_2(X3,k5_numbers,u1_struct_0(X1))\|~v1_funct_2(X2,k5_numbers,u1_struct_0(X1))\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,u1_struct_0(X1))))\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,u1_struct_0(X1))))), inference(evalgc,[status(thm)],[c_0_49])). cnf(c_0_66, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,u1_struct_0(esk1_0))))), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_67, negated_conjecture, (v1_funct_2(esk2_0,k5_numbers,u1_struct_0(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_68, negated_conjecture, (v1_funct_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_69, negated_conjecture, (k1_algstr_0(esk1_0,X1,k1_normsp_1(esk1_0,esk2_0,np__1))=X1\|~l2_algstr_0(esk1_0)\|~m1_subset_1(X1,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50, c_0_48]), c_0_51]), c_0_52]), c_0_53])]), c_0_54])])). cnf(c_0_70, negated_conjecture, (l2_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_55, c_0_56])])). cnf(c_0_71, plain, (m2_subset_1(X1,k1_numbers,k5_numbers)\|~m1_subset_1(X1,k5_numbers)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_57, c_0_58]), c_0_59]), c_0_60])])). cnf(c_0_72, negated_conjecture, (m1_subset_1(k1_normsp_1(esk1_0,esk2_0,np__1),u1_struct_0(esk1_0))\|~l2_struct_0(esk1_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_61, c_0_48])])). cnf(c_0_73, plain, (l2_struct_0(X1)\|~l2_normsp_0(X1)), inference(evalgc,[status(thm)],[c_0_62])). cnf(c_0_74, plain, (l2_normsp_0(X1)\|~l2_clvect_1(X1)), inference(split_conjunct,[status(thm)],[c_0_18])). fof(c_0_75, plain, ![X19, X20]:(~m1_subset_1(X19,k5_numbers)\|~v7_ordinal1(X20)\|m2_subset_1(k2_nat_1(X19,X20),k1_numbers,k5_numbers)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_nat_1])])). fof(c_0_76, plain, ![X15]:(~m1_subset_1(X15,k4_ordinal1)\|v7_ordinal1(X15)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc8_ordinal1])])). cnf(c_0_77, plain, (m1_subset_1(X1,X3)\|v1_xboole_0(X2)\|v1_xboole_0(X3)\|~m2_subset_1(X1,X2,X3)\|~m1_subset_1(X3,k1_zfmisc_1(X2))), inference(split_conjunct,[status(thm)],[c_0_25])). cnf(c_0_78, plain, (X2=k1_bhsp_4(X1,X3)\|v2_struct_0(X1)\|k1_normsp_1(X1,X2,k6_numbers)!=k1_normsp_1(X1,X3,k6_numbers)\|k1_algstr_0(X1,k1_normsp_1(X1,X2,esk4_3(X1,X3,X2)),k1_normsp_1(X1,X3,k2_nat_1(esk4_3(X1,X3,X2),np__1)))!=k1_normsp_1(X1,X2,k2_nat_1(esk4_3(X1,X3,X2),np__1))\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~l2_algstr_0(X1)\|~v1_funct_2(X3,k5_numbers,u1_struct_0(X1))\|~v1_funct_2(X2,k5_numbers,u1_struct_0(X1))\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,u1_struct_0(X1))))\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,u1_struct_0(X1))))), inference(evalgc,[status(thm)],[c_0_63])). cnf(c_0_79, negated_conjecture, (k1_normsp_1(esk1_0,esk2_0,esk4_3(X1,X2,X3))=k1_normsp_1(esk1_0,esk2_0,np__1)\|X3=k1_bhsp_4(X1,X2)\|v2_struct_0(X1)\|k1_normsp_1(X1,X2,k6_numbers)!=k1_normsp_1(X1,X3,k6_numbers)\|~l2_algstr_0(X1)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,u1_struct_0(X1))))\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,u1_struct_0(X1))))\|~v1_funct_2(X3,k5_numbers,u1_struct_0(X1))\|~v1_funct_2(X2,k5_numbers,u1_struct_0(X1))\|~v1_funct_1(X3)\|~v1_funct_1(X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_64, c_0_65])])). cnf(c_0_80, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,u1_struct_0(esk1_0))))), inference(evalgc,[status(thm)],[c_0_66])). cnf(c_0_81, negated_conjecture, (v1_funct_2(esk2_0,k5_numbers,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[c_0_67])). cnf(c_0_82, negated_conjecture, (v1_funct_1(esk2_0)), inference(evalgc,[status(thm)],[c_0_68])). cnf(c_0_83, negated_conjecture, (k1_algstr_0(esk1_0,X1,k1_normsp_1(esk1_0,esk2_0,np__1))=X1\|~m1_subset_1(X1,u1_struct_0(esk1_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_69, c_0_70])])). cnf(c_0_84, negated_conjecture, (k1_normsp_1(esk1_0,esk2_0,X1)=k1_normsp_1(esk1_0,esk2_0,np__1)\|~m1_subset_1(X1,k5_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_64, c_0_71])])). cnf(c_0_85, negated_conjecture, (m1_subset_1(k1_normsp_1(esk1_0,esk2_0,np__1),u1_struct_0(esk1_0))\|~l2_normsp_0(esk1_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_72, c_0_73])])). cnf(c_0_86, plain, (l2_normsp_0(X1)\|~l2_clvect_1(X1)), inference(evalgc,[status(thm)],[c_0_74])). cnf(c_0_87, plain, (m2_subset_1(k2_nat_1(X1,X2),k1_numbers,k5_numbers)\|~m1_subset_1(X1,k5_numbers)\|~v7_ordinal1(X2)), inference(split_conjunct,[status(thm)],[c_0_75])). cnf(c_0_88, plain, (v7_ordinal1(X1)\|~m1_subset_1(X1,k4_ordinal1)), inference(split_conjunct,[status(thm)],[c_0_76])). cnf(c_0_89, plain, (v1_xboole_0(X3)\|v1_xboole_0(X2)\|m1_subset_1(X1,X3)\|~m2_subset_1(X1,X2,X3)\|~m1_subset_1(X3,k1_zfmisc_1(X2))), inference(evalgc,[status(thm)],[c_0_77])). cnf(c_0_90, negated_conjecture, (k1_bhsp_4(esk1_0,X1)=esk2_0\|k1_algstr_0(esk1_0,k1_normsp_1(esk1_0,esk2_0,np__1),k1_normsp_1(esk1_0,X1,k2_nat_1(esk4_3(esk1_0,X1,esk2_0),np__1)))!=k1_normsp_1(esk1_0,esk2_0,k2_nat_1(esk4_3(esk1_0,X1,esk2_0),np__1))\|k1_normsp_1(esk1_0,esk2_0,k6_numbers)!=k1_normsp_1(esk1_0,X1,k6_numbers)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,u1_struct_0(esk1_0))))\|~v1_funct_2(X1,k5_numbers,u1_struct_0(esk1_0))\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78, c_0_79]), c_0_70]), c_0_80]), c_0_81]), c_0_82])]), c_0_54])])). cnf(c_0_91, negated_conjecture, (k1_algstr_0(esk1_0,X1,k1_normsp_1(esk1_0,esk2_0,X2))=X1\|~m1_subset_1(X1,u1_struct_0(esk1_0))\|~m1_subset_1(X2,k5_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_83, c_0_84])])). cnf(c_0_92, negated_conjecture, (m1_subset_1(k1_normsp_1(esk1_0,esk2_0,np__1),u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85, c_0_86]), c_0_56])])])). cnf(c_0_93, plain, (m2_subset_1(k2_nat_1(X1,X2),k1_numbers,k5_numbers)\|~v7_ordinal1(X2)\|~m1_subset_1(X1,k5_numbers)), inference(evalgc,[status(thm)],[c_0_87])). cnf(c_0_94, plain, (v7_ordinal1(X1)\|~m1_subset_1(X1,k4_ordinal1)), inference(evalgc,[status(thm)],[c_0_88])). cnf(c_0_95, plain, (m1_subset_1(esk4_3(X1,X2,X3),k5_numbers)\|X3=k1_bhsp_4(X1,X2)\|v2_struct_0(X1)\|k1_normsp_1(X1,X2,k6_numbers)!=k1_normsp_1(X1,X3,k6_numbers)\|~l2_algstr_0(X1)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,u1_struct_0(X1))))\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,u1_struct_0(X1))))\|~v1_funct_2(X3,k5_numbers,u1_struct_0(X1))\|~v1_funct_2(X2,k5_numbers,u1_struct_0(X1))\|~v1_funct_1(X3)\|~v1_funct_1(X2)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89, c_0_65]), c_0_58])]), c_0_60]), c_0_59])])). cnf(c_0_96, negated_conjecture, (k1_bhsp_4(esk1_0,esk2_0)=esk2_0\|k1_normsp_1(esk1_0,esk2_0,k2_nat_1(esk4_3(esk1_0,esk2_0,esk2_0),np__1))!=k1_normsp_1(esk1_0,esk2_0,np__1)\|~m1_subset_1(k2_nat_1(esk4_3(esk1_0,esk2_0,esk2_0),np__1),k5_numbers)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90, c_0_91]), c_0_80]), c_0_81]), c_0_82]), c_0_92])])])). cnf(c_0_97, plain, (m1_subset_1(k2_nat_1(X1,X2),k5_numbers)\|~v7_ordinal1(X2)\|~m1_subset_1(X1,k5_numbers)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89, c_0_93]), c_0_58])]), c_0_60]), c_0_59])])). cnf(c_0_98, plain, (v7_ordinal1(X1)\|~m1_subset_1(X1,k5_numbers)), inference(rw,[status(thm)],[c_0_94, c_0_44])). cnf(c_0_99, plain, (m1_subset_1(np__1,k5_numbers)), inference(split_conjunct,[status(thm)],[spc1_numerals])). cnf(c_0_100, negated_conjecture, (k1_bhsp_4(esk1_0,X1)=esk2_0\|m1_subset_1(esk4_3(esk1_0,X1,esk2_0),k5_numbers)\|k1_normsp_1(esk1_0,X1,k6_numbers)!=k1_normsp_1(esk1_0,esk2_0,k6_numbers)\|~l2_algstr_0(esk1_0)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,u1_struct_0(esk1_0))))\|~v1_funct_2(X1,k5_numbers,u1_struct_0(esk1_0))\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95, c_0_80]), c_0_81]), c_0_82])]), c_0_54])])). cnf(c_0_101, negated_conjecture, (k1_normsp_1(esk1_0,k1_bhsp_4(esk1_0,esk2_0),esk3_0)!=k4_struct_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_102, negated_conjecture, (k1_bhsp_4(esk1_0,esk2_0)=esk2_0\|~m1_subset_1(k2_nat_1(esk4_3(esk1_0,esk2_0,esk2_0),np__1),k5_numbers)), inference(csr,[status(thm)],[c_0_96, c_0_84])). cnf(c_0_103, plain, (m1_subset_1(k2_nat_1(X1,X2),k5_numbers)\|~m1_subset_1(X1,k5_numbers)\|~m1_subset_1(X2,k5_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_97, c_0_98])])). cnf(c_0_104, plain, (m1_subset_1(np__1,k5_numbers)), inference(evalgc,[status(thm)],[c_0_99])). cnf(c_0_105, negated_conjecture, (k1_bhsp_4(esk1_0,X1)=esk2_0\|m1_subset_1(esk4_3(esk1_0,X1,esk2_0),k5_numbers)\|k1_normsp_1(esk1_0,X1,k6_numbers)!=k1_normsp_1(esk1_0,esk2_0,k6_numbers)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k5_numbers,u1_struct_0(esk1_0))))\|~v1_funct_2(X1,k5_numbers,u1_struct_0(esk1_0))\|~v1_funct_1(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_100, c_0_70])])). cnf(c_0_106, negated_conjecture, (m2_subset_1(esk3_0,k1_numbers,k5_numbers)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_107, negated_conjecture, (k1_normsp_1(esk1_0,k1_bhsp_4(esk1_0,esk2_0),esk3_0)!=k4_struct_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_101])). cnf(c_0_108, negated_conjecture, (k1_bhsp_4(esk1_0,esk2_0)=esk2_0\|~m1_subset_1(esk4_3(esk1_0,esk2_0,esk2_0),k5_numbers)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102, c_0_103]), c_0_104])])])). cnf(c_0_109, negated_conjecture, (k1_bhsp_4(esk1_0,esk2_0)=esk2_0\|m1_subset_1(esk4_3(esk1_0,esk2_0,esk2_0),k5_numbers)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105, c_0_80]), c_0_81]), c_0_82])])])). cnf(c_0_110, negated_conjecture, (m2_subset_1(esk3_0,k1_numbers,k5_numbers)), inference(evalgc,[status(thm)],[c_0_106])). cnf(c_0_111, negated_conjecture, (k1_normsp_1(esk1_0,k1_bhsp_4(esk1_0,esk2_0),esk3_0)!=k1_normsp_1(esk1_0,esk2_0,np__1)), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[c_0_107, c_0_48])])). cnf(c_0_112, negated_conjecture, (k1_bhsp_4(esk1_0,esk2_0)=esk2_0), inference(csr,[status(thm)],[c_0_108, c_0_109])). cnf(c_0_113, negated_conjecture, (k1_normsp_1(esk1_0,esk2_0,esk3_0)=k1_normsp_1(esk1_0,esk2_0,np__1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_64, c_0_110])])). cnf(c_0_114, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_111, c_0_112]), c_0_113])]), ['proof']). # SZS output end CNFRefutation	theorem Th1: for X be add-associative right_zeroed right_complementable non empty CNORMSTR for seq be sequence of X st (for n be Element of NAT holds seq. n = 0.X) holds for m be Element of NAT holds (Partial_Sums seq).m = 0.X proof let X be add-associative right_zeroed right_complementable non empty CNORMSTR; let seq be sequence of X such that A1: for n be Element of NAT holds seq.n = 0.X; let m be Element of NAT; defpred P[Element of NAT] means seq.$1 = (Partial_Sums seq).$1; A2: for k be Element of NAT st P[k] holds P[k+1] proof let k be Element of NAT such that A3: P[k]; thus seq.(k+1) = 0.X + seq.(k+1) by RLVECT_1:4 .= (Partial_Sums seq).k + seq.(k+1) by A1,A3 .= (Partial_Sums seq).(k+1) by BHSP_4:def 1; end; A4: P[0] by BHSP_4:def 1; for n be Element of NAT holds P[n] from NAT_1:sch 1(A4,A2); then seq = Partial_Sums seq by FUNCT_2:63; hence thesis by A1; end;	Convert the following ATP output trace into a readable Mizar proof.
t68_matrix10	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(redefinition_k7_real_1, axiom, ![X1, X2]:((m1_subset_1(X1,k1_numbers)&v1_xreal_0(X2))=>k7_real_1(X1,X2)=k2_xcmplx_0(X1,X2)), file('/scratch/mptp/predsminms1/t68_matrix10__0', redefinition_k7_real_1)). fof(t25_matrixr1, axiom, ![X1]:((v1_matrix_1(X1)&m2_finseq_1(X1,k3_finseq_2(k1_numbers)))=>![X2]:((v1_matrix_1(X2)&m2_finseq_1(X2,k3_finseq_2(k1_numbers)))=>(k3_finseq_1(k3_matrixr1(X1,X2))=k3_finseq_1(X1)&(k1_matrix_1(k3_matrixr1(X1,X2))=k1_matrix_1(X1)&![X3]:(v7_ordinal1(X3)=>![X4]:(v7_ordinal1(X4)=>(r2_hidden(k4_tarski(X3,X4),k2_matrix_1(X1))=>k3_matrix_1(k1_numbers,k3_matrixr1(X1,X2),X3,X4)=k7_real_1(k3_matrix_1(k1_numbers,X1,X3,X4),k3_matrix_1(k1_numbers,X2,X3,X4))))))))), file('/scratch/mptp/predsminms1/t68_matrix10__0', t25_matrixr1)). fof(t31_xreal_1, axiom, ![X1]:(v1_xreal_0(X1)=>![X2]:(v1_xreal_0(X2)=>(r1_xxreal_0(k6_numbers,X1)=>r1_xxreal_0(X2,k2_xcmplx_0(X1,X2))))), file('/scratch/mptp/predsminms1/t68_matrix10__0', t31_xreal_1)). fof(cc1_xreal_0, axiom, ![X1]:(m1_subset_1(X1,k1_numbers)=>v1_xreal_0(X1)), file('/scratch/mptp/predsminms1/t68_matrix10__0', cc1_xreal_0)). fof(d6_matrix10, axiom, ![X1]:((v1_matrix_1(X1)&m2_finseq_1(X1,k3_finseq_2(k1_numbers)))=>![X2]:((v1_matrix_1(X2)&m2_finseq_1(X2,k3_finseq_2(k1_numbers)))=>(r2_matrix10(X1,X2)<=>![X3]:(v7_ordinal1(X3)=>![X4]:(v7_ordinal1(X4)=>(r2_hidden(k4_tarski(X3,X4),k2_matrix_1(X1))=>r1_xxreal_0(k3_matrix_1(k1_numbers,X1,X3,X4),k3_matrix_1(k1_numbers,X2,X3,X4)))))))), file('/scratch/mptp/predsminms1/t68_matrix10__0', d6_matrix10)). fof(t68_matrix10, conjecture, ![X1]:(v7_ordinal1(X1)=>![X2]:(m1_matrix_1(X2,k1_numbers,X1,X1)=>![X3]:(m1_matrix_1(X3,k1_numbers,X1,X1)=>(v4_matrix10(X2)=>r2_matrix10(X3,k3_matrix10(X1,X2,X3)))))), file('/scratch/mptp/predsminms1/t68_matrix10__0', t68_matrix10)). fof(cc14_membered, axiom, ![X1]:(v3_membered(X1)=>![X2]:(m1_subset_1(X2,X1)=>v1_xreal_0(X2))), file('/scratch/mptp/predsminms1/t68_matrix10__0', cc14_membered)). fof(dt_k3_matrix_1, axiom, ![X1, X2, X3, X4]:(((v1_matrix_1(X2)&m1_finseq_1(X2,k3_finseq_2(X1)))&(v7_ordinal1(X3)&v7_ordinal1(X4)))=>m1_subset_1(k3_matrix_1(X1,X2,X3,X4),X1)), file('/scratch/mptp/predsminms1/t68_matrix10__0', dt_k3_matrix_1)). fof(t24_matrix_1, axiom, ![X1]:(v7_ordinal1(X1)=>![X2]:(~(v1_xboole_0(X2))=>![X3]:(m1_matrix_1(X3,X2,X1,X1)=>(k3_finseq_1(X3)=X1&(k1_matrix_1(X3)=X1&k2_matrix_1(X3)=k2_zfmisc_1(k2_finseq_1(X1),k2_finseq_1(X1))))))), file('/scratch/mptp/predsminms1/t68_matrix10__0', t24_matrix_1)). fof(fc1_numbers, axiom, ~(v1_xboole_0(k1_numbers)), file('/scratch/mptp/predsminms1/t68_matrix10__0', fc1_numbers)). fof(dt_m1_matrix_1, axiom, ![X1, X2, X3]:((~(v1_xboole_0(X1))&(v7_ordinal1(X2)&v7_ordinal1(X3)))=>![X4]:(m1_matrix_1(X4,X1,X2,X3)=>(v1_matrix_1(X4)&m2_finseq_1(X4,k3_finseq_2(X1))))), file('/scratch/mptp/predsminms1/t68_matrix10__0', dt_m1_matrix_1)). fof(redefinition_k3_matrix10, axiom, ![X1, X2, X3]:((v7_ordinal1(X1)&(m1_matrix_1(X2,k1_numbers,X1,X1)&m1_matrix_1(X3,k1_numbers,X1,X1)))=>k3_matrix10(X1,X2,X3)=k3_matrixr1(X2,X3)), file('/scratch/mptp/predsminms1/t68_matrix10__0', redefinition_k3_matrix10)). fof(fc3_membered, axiom, v3_membered(k1_numbers), file('/scratch/mptp/predsminms1/t68_matrix10__0', fc3_membered)). fof(redefinition_m2_finseq_1, axiom, ![X1, X2]:(m2_finseq_1(X2,X1)<=>m1_finseq_1(X2,X1)), file('/scratch/mptp/predsminms1/t68_matrix10__0', redefinition_m2_finseq_1)). fof(d4_matrix10, axiom, ![X1]:((v1_matrix_1(X1)&m2_finseq_1(X1,k3_finseq_2(k1_numbers)))=>(v4_matrix10(X1)<=>![X2]:(v7_ordinal1(X2)=>![X3]:(v7_ordinal1(X3)=>(r2_hidden(k4_tarski(X2,X3),k2_matrix_1(X1))=>r1_xxreal_0(k6_numbers,k3_matrix_1(k1_numbers,X1,X2,X3))))))), file('/scratch/mptp/predsminms1/t68_matrix10__0', d4_matrix10)). fof(dt_k3_matrixr1, axiom, ![X1, X2]:(((v1_matrix_1(X1)&m1_finseq_1(X1,k3_finseq_2(k1_numbers)))&(v1_matrix_1(X2)&m1_finseq_1(X2,k3_finseq_2(k1_numbers))))=>(v1_matrix_1(k3_matrixr1(X1,X2))&m2_finseq_1(k3_matrixr1(X1,X2),k3_finseq_2(k1_numbers)))), file('/scratch/mptp/predsminms1/t68_matrix10__0', dt_k3_matrixr1)). fof(c_0_16, plain, ![X25, X26]:(~m1_subset_1(X25,k1_numbers)\|~v1_xreal_0(X26)\|k7_real_1(X25,X26)=k2_xcmplx_0(X25,X26)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k7_real_1])])). fof(c_0_17, plain, ![X21, X22, X23, X24]:((k3_finseq_1(k3_matrixr1(X21,X22))=k3_finseq_1(X21)\|(~v1_matrix_1(X22)\|~m2_finseq_1(X22,k3_finseq_2(k1_numbers)))\|(~v1_matrix_1(X21)\|~m2_finseq_1(X21,k3_finseq_2(k1_numbers))))&((k1_matrix_1(k3_matrixr1(X21,X22))=k1_matrix_1(X21)\|(~v1_matrix_1(X22)\|~m2_finseq_1(X22,k3_finseq_2(k1_numbers)))\|(~v1_matrix_1(X21)\|~m2_finseq_1(X21,k3_finseq_2(k1_numbers))))&(~v7_ordinal1(X23)\|(~v7_ordinal1(X24)\|(~r2_hidden(k4_tarski(X23,X24),k2_matrix_1(X21))\|k3_matrix_1(k1_numbers,k3_matrixr1(X21,X22),X23,X24)=k7_real_1(k3_matrix_1(k1_numbers,X21,X23,X24),k3_matrix_1(k1_numbers,X22,X23,X24))))\|(~v1_matrix_1(X22)\|~m2_finseq_1(X22,k3_finseq_2(k1_numbers)))\|(~v1_matrix_1(X21)\|~m2_finseq_1(X21,k3_finseq_2(k1_numbers)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t25_matrixr1])])])])). fof(c_0_18, plain, ![X27, X28]:(~v1_xreal_0(X27)\|(~v1_xreal_0(X28)\|(~r1_xxreal_0(k6_numbers,X27)\|r1_xxreal_0(X28,k2_xcmplx_0(X27,X28))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t31_xreal_1])])])). cnf(c_0_19, plain, (k7_real_1(X1,X2)=k2_xcmplx_0(X1,X2)\|~m1_subset_1(X1,k1_numbers)\|~v1_xreal_0(X2)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_20, plain, (k3_matrix_1(k1_numbers,k3_matrixr1(X3,X4),X1,X2)=k7_real_1(k3_matrix_1(k1_numbers,X3,X1,X2),k3_matrix_1(k1_numbers,X4,X1,X2))\|~v7_ordinal1(X1)\|~v7_ordinal1(X2)\|~r2_hidden(k4_tarski(X1,X2),k2_matrix_1(X3))\|~v1_matrix_1(X4)\|~m2_finseq_1(X4,k3_finseq_2(k1_numbers))\|~v1_matrix_1(X3)\|~m2_finseq_1(X3,k3_finseq_2(k1_numbers))), inference(split_conjunct,[status(thm)],[c_0_17])). cnf(c_0_21, plain, (r1_xxreal_0(X2,k2_xcmplx_0(X1,X2))\|~v1_xreal_0(X1)\|~v1_xreal_0(X2)\|~r1_xxreal_0(k6_numbers,X1)), inference(split_conjunct,[status(thm)],[c_0_18])). cnf(c_0_22, plain, (k7_real_1(X1,X2)=k2_xcmplx_0(X1,X2)\|~v1_xreal_0(X2)\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[c_0_19])). cnf(c_0_23, plain, (k7_real_1(k3_matrix_1(k1_numbers,X3,X1,X2),k3_matrix_1(k1_numbers,X4,X1,X2))=k3_matrix_1(k1_numbers,k3_matrixr1(X3,X4),X1,X2)\|~v7_ordinal1(X2)\|~v7_ordinal1(X1)\|~v1_matrix_1(X4)\|~v1_matrix_1(X3)\|~m2_finseq_1(X4,k3_finseq_2(k1_numbers))\|~m2_finseq_1(X3,k3_finseq_2(k1_numbers))\|~r2_hidden(k4_tarski(X1,X2),k2_matrix_1(X3))), inference(evalgc,[status(thm)],[c_0_20])). fof(c_0_24, plain, ![X37]:(~m1_subset_1(X37,k1_numbers)\|v1_xreal_0(X37)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_xreal_0])])). fof(c_0_25, plain, ![X15, X16, X17, X18]:((~r2_matrix10(X15,X16)\|(~v7_ordinal1(X17)\|(~v7_ordinal1(X18)\|(~r2_hidden(k4_tarski(X17,X18),k2_matrix_1(X15))\|r1_xxreal_0(k3_matrix_1(k1_numbers,X15,X17,X18),k3_matrix_1(k1_numbers,X16,X17,X18)))))\|(~v1_matrix_1(X16)\|~m2_finseq_1(X16,k3_finseq_2(k1_numbers)))\|(~v1_matrix_1(X15)\|~m2_finseq_1(X15,k3_finseq_2(k1_numbers))))&((v7_ordinal1(esk4_2(X15,X16))\|r2_matrix10(X15,X16)\|(~v1_matrix_1(X16)\|~m2_finseq_1(X16,k3_finseq_2(k1_numbers)))\|(~v1_matrix_1(X15)\|~m2_finseq_1(X15,k3_finseq_2(k1_numbers))))&((v7_ordinal1(esk5_2(X15,X16))\|r2_matrix10(X15,X16)\|(~v1_matrix_1(X16)\|~m2_finseq_1(X16,k3_finseq_2(k1_numbers)))\|(~v1_matrix_1(X15)\|~m2_finseq_1(X15,k3_finseq_2(k1_numbers))))&((r2_hidden(k4_tarski(esk4_2(X15,X16),esk5_2(X15,X16)),k2_matrix_1(X15))\|r2_matrix10(X15,X16)\|(~v1_matrix_1(X16)\|~m2_finseq_1(X16,k3_finseq_2(k1_numbers)))\|(~v1_matrix_1(X15)\|~m2_finseq_1(X15,k3_finseq_2(k1_numbers))))&(~r1_xxreal_0(k3_matrix_1(k1_numbers,X15,esk4_2(X15,X16),esk5_2(X15,X16)),k3_matrix_1(k1_numbers,X16,esk4_2(X15,X16),esk5_2(X15,X16)))\|r2_matrix10(X15,X16)\|(~v1_matrix_1(X16)\|~m2_finseq_1(X16,k3_finseq_2(k1_numbers)))\|(~v1_matrix_1(X15)\|~m2_finseq_1(X15,k3_finseq_2(k1_numbers)))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d6_matrix10])])])])])). cnf(c_0_26, plain, (r1_xxreal_0(X2,k2_xcmplx_0(X1,X2))\|~v1_xreal_0(X2)\|~v1_xreal_0(X1)\|~r1_xxreal_0(k6_numbers,X1)), inference(evalgc,[status(thm)],[c_0_21])). cnf(c_0_27, plain, (k2_xcmplx_0(k3_matrix_1(k1_numbers,X1,X2,X3),k3_matrix_1(k1_numbers,X4,X2,X3))=k3_matrix_1(k1_numbers,k3_matrixr1(X1,X4),X2,X3)\|~v1_xreal_0(k3_matrix_1(k1_numbers,X4,X2,X3))\|~m1_subset_1(k3_matrix_1(k1_numbers,X1,X2,X3),k1_numbers)\|~r2_hidden(k4_tarski(X2,X3),k2_matrix_1(X1))\|~m2_finseq_1(X4,k3_finseq_2(k1_numbers))\|~m2_finseq_1(X1,k3_finseq_2(k1_numbers))\|~v1_matrix_1(X4)\|~v1_matrix_1(X1)\|~v7_ordinal1(X3)\|~v7_ordinal1(X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_22, c_0_23])])). cnf(c_0_28, plain, (v1_xreal_0(X1)\|~m1_subset_1(X1,k1_numbers)), inference(split_conjunct,[status(thm)],[c_0_24])). fof(c_0_29, negated_conjecture, ~(![X1]:(v7_ordinal1(X1)=>![X2]:(m1_matrix_1(X2,k1_numbers,X1,X1)=>![X3]:(m1_matrix_1(X3,k1_numbers,X1,X1)=>(v4_matrix10(X2)=>r2_matrix10(X3,k3_matrix10(X1,X2,X3))))))), inference(assume_negation,[status(cth)],[t68_matrix10])). cnf(c_0_30, plain, (r2_matrix10(X1,X2)\|~r1_xxreal_0(k3_matrix_1(k1_numbers,X1,esk4_2(X1,X2),esk5_2(X1,X2)),k3_matrix_1(k1_numbers,X2,esk4_2(X1,X2),esk5_2(X1,X2)))\|~v1_matrix_1(X2)\|~m2_finseq_1(X2,k3_finseq_2(k1_numbers))\|~v1_matrix_1(X1)\|~m2_finseq_1(X1,k3_finseq_2(k1_numbers))), inference(split_conjunct,[status(thm)],[c_0_25])). cnf(c_0_31, plain, (r1_xxreal_0(k3_matrix_1(k1_numbers,X1,X2,X3),k3_matrix_1(k1_numbers,k3_matrixr1(X4,X1),X2,X3))\|~v1_xreal_0(k3_matrix_1(k1_numbers,X1,X2,X3))\|~v1_xreal_0(k3_matrix_1(k1_numbers,X4,X2,X3))\|~r1_xxreal_0(k6_numbers,k3_matrix_1(k1_numbers,X4,X2,X3))\|~m1_subset_1(k3_matrix_1(k1_numbers,X4,X2,X3),k1_numbers)\|~r2_hidden(k4_tarski(X2,X3),k2_matrix_1(X4))\|~m2_finseq_1(X1,k3_finseq_2(k1_numbers))\|~m2_finseq_1(X4,k3_finseq_2(k1_numbers))\|~v1_matrix_1(X1)\|~v1_matrix_1(X4)\|~v7_ordinal1(X3)\|~v7_ordinal1(X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_26, c_0_27])])). cnf(c_0_32, plain, (v1_xreal_0(X1)\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[c_0_28])). fof(c_0_33, plain, ![X42, X43]:(~v3_membered(X42)\|(~m1_subset_1(X43,X42)\|v1_xreal_0(X43))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc14_membered])])])). fof(c_0_34, plain, ![X38, X39, X40, X41]:(~v1_matrix_1(X39)\|~m1_finseq_1(X39,k3_finseq_2(X38))\|(~v7_ordinal1(X40)\|~v7_ordinal1(X41))\|m1_subset_1(k3_matrix_1(X38,X39,X40,X41),X38)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k3_matrix_1])])). fof(c_0_35, plain, ![X8, X9, X10]:((k3_finseq_1(X10)=X8\|~m1_matrix_1(X10,X9,X8,X8)\|v1_xboole_0(X9)\|~v7_ordinal1(X8))&((k1_matrix_1(X10)=X8\|~m1_matrix_1(X10,X9,X8,X8)\|v1_xboole_0(X9)\|~v7_ordinal1(X8))&(k2_matrix_1(X10)=k2_zfmisc_1(k2_finseq_1(X8),k2_finseq_1(X8))\|~m1_matrix_1(X10,X9,X8,X8)\|v1_xboole_0(X9)\|~v7_ordinal1(X8)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t24_matrix_1])])])])])). fof(c_0_36, negated_conjecture, (v7_ordinal1(esk1_0)&(m1_matrix_1(esk2_0,k1_numbers,esk1_0,esk1_0)&(m1_matrix_1(esk3_0,k1_numbers,esk1_0,esk1_0)&(v4_matrix10(esk2_0)&~r2_matrix10(esk3_0,k3_matrix10(esk1_0,esk2_0,esk3_0)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])])). fof(c_0_37, plain, ~v1_xboole_0(k1_numbers), inference(fof_simplification,[status(thm)],[fc1_numbers])). cnf(c_0_38, plain, (r2_matrix10(X1,X2)\|~v1_matrix_1(X2)\|~v1_matrix_1(X1)\|~m2_finseq_1(X2,k3_finseq_2(k1_numbers))\|~m2_finseq_1(X1,k3_finseq_2(k1_numbers))\|~r1_xxreal_0(k3_matrix_1(k1_numbers,X1,esk4_2(X1,X2),esk5_2(X1,X2)),k3_matrix_1(k1_numbers,X2,esk4_2(X1,X2),esk5_2(X1,X2)))), inference(evalgc,[status(thm)],[c_0_30])). cnf(c_0_39, plain, (r1_xxreal_0(k3_matrix_1(k1_numbers,X1,X2,X3),k3_matrix_1(k1_numbers,k3_matrixr1(X4,X1),X2,X3))\|~v1_xreal_0(k3_matrix_1(k1_numbers,X1,X2,X3))\|~m1_subset_1(k3_matrix_1(k1_numbers,X4,X2,X3),k1_numbers)\|~r1_xxreal_0(k6_numbers,k3_matrix_1(k1_numbers,X4,X2,X3))\|~r2_hidden(k4_tarski(X2,X3),k2_matrix_1(X4))\|~m2_finseq_1(X1,k3_finseq_2(k1_numbers))\|~m2_finseq_1(X4,k3_finseq_2(k1_numbers))\|~v1_matrix_1(X1)\|~v1_matrix_1(X4)\|~v7_ordinal1(X3)\|~v7_ordinal1(X2)), inference(csr,[status(thm)],[c_0_31, c_0_32])). cnf(c_0_40, plain, (v7_ordinal1(esk4_2(X1,X2))\|r2_matrix10(X1,X2)\|~v1_matrix_1(X2)\|~m2_finseq_1(X2,k3_finseq_2(k1_numbers))\|~v1_matrix_1(X1)\|~m2_finseq_1(X1,k3_finseq_2(k1_numbers))), inference(split_conjunct,[status(thm)],[c_0_25])). cnf(c_0_41, plain, (v7_ordinal1(esk5_2(X1,X2))\|r2_matrix10(X1,X2)\|~v1_matrix_1(X2)\|~m2_finseq_1(X2,k3_finseq_2(k1_numbers))\|~v1_matrix_1(X1)\|~m2_finseq_1(X1,k3_finseq_2(k1_numbers))), inference(split_conjunct,[status(thm)],[c_0_25])). cnf(c_0_42, plain, (v1_xreal_0(X2)\|~v3_membered(X1)\|~m1_subset_1(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_33])). cnf(c_0_43, plain, (m1_subset_1(k3_matrix_1(X2,X1,X3,X4),X2)\|~v1_matrix_1(X1)\|~m1_finseq_1(X1,k3_finseq_2(X2))\|~v7_ordinal1(X3)\|~v7_ordinal1(X4)), inference(split_conjunct,[status(thm)],[c_0_34])). cnf(c_0_44, plain, (k2_matrix_1(X1)=k2_zfmisc_1(k2_finseq_1(X2),k2_finseq_1(X2))\|v1_xboole_0(X3)\|~m1_matrix_1(X1,X3,X2,X2)\|~v7_ordinal1(X2)), inference(split_conjunct,[status(thm)],[c_0_35])). cnf(c_0_45, negated_conjecture, (m1_matrix_1(esk2_0,k1_numbers,esk1_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_36])). cnf(c_0_46, negated_conjecture, (v7_ordinal1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_36])). cnf(c_0_47, plain, (~v1_xboole_0(k1_numbers)), inference(split_conjunct,[status(thm)],[c_0_37])). cnf(c_0_48, negated_conjecture, (m1_matrix_1(esk3_0,k1_numbers,esk1_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_36])). fof(c_0_49, plain, ![X11, X12, X13, X14]:((v1_matrix_1(X14)\|~m1_matrix_1(X14,X11,X12,X13)\|(v1_xboole_0(X11)\|(~v7_ordinal1(X12)\|~v7_ordinal1(X13))))&(m2_finseq_1(X14,k3_finseq_2(X11))\|~m1_matrix_1(X14,X11,X12,X13)\|(v1_xboole_0(X11)\|(~v7_ordinal1(X12)\|~v7_ordinal1(X13))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_m1_matrix_1])])])])])). fof(c_0_50, plain, ![X34, X35, X36]:(~v7_ordinal1(X34)\|(~m1_matrix_1(X35,k1_numbers,X34,X34)\|~m1_matrix_1(X36,k1_numbers,X34,X34))\|k3_matrix10(X34,X35,X36)=k3_matrixr1(X35,X36)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k3_matrix10])])). cnf(c_0_51, plain, (r2_matrix10(X1,k3_matrixr1(X2,X1))\|~m2_finseq_1(k3_matrixr1(X2,X1),k3_finseq_2(k1_numbers))\|~m2_finseq_1(X1,k3_finseq_2(k1_numbers))\|~v1_matrix_1(k3_matrixr1(X2,X1))\|~v1_matrix_1(X1)\|~v1_xreal_0(k3_matrix_1(k1_numbers,X1,esk4_2(X1,k3_matrixr1(X2,X1)),esk5_2(X1,k3_matrixr1(X2,X1))))\|~m1_subset_1(k3_matrix_1(k1_numbers,X2,esk4_2(X1,k3_matrixr1(X2,X1)),esk5_2(X1,k3_matrixr1(X2,X1))),k1_numbers)\|~r1_xxreal_0(k6_numbers,k3_matrix_1(k1_numbers,X2,esk4_2(X1,k3_matrixr1(X2,X1)),esk5_2(X1,k3_matrixr1(X2,X1))))\|~r2_hidden(k4_tarski(esk4_2(X1,k3_matrixr1(X2,X1)),esk5_2(X1,k3_matrixr1(X2,X1))),k2_matrix_1(X2))\|~m2_finseq_1(X2,k3_finseq_2(k1_numbers))\|~v1_matrix_1(X2)\|~v7_ordinal1(esk5_2(X1,k3_matrixr1(X2,X1)))\|~v7_ordinal1(esk4_2(X1,k3_matrixr1(X2,X1)))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_38, c_0_39])])). cnf(c_0_52, plain, (r2_matrix10(X1,X2)\|v7_ordinal1(esk4_2(X1,X2))\|~v1_matrix_1(X2)\|~v1_matrix_1(X1)\|~m2_finseq_1(X2,k3_finseq_2(k1_numbers))\|~m2_finseq_1(X1,k3_finseq_2(k1_numbers))), inference(evalgc,[status(thm)],[c_0_40])). cnf(c_0_53, plain, (r2_matrix10(X1,X2)\|v7_ordinal1(esk5_2(X1,X2))\|~v1_matrix_1(X2)\|~v1_matrix_1(X1)\|~m2_finseq_1(X2,k3_finseq_2(k1_numbers))\|~m2_finseq_1(X1,k3_finseq_2(k1_numbers))), inference(evalgc,[status(thm)],[c_0_41])). cnf(c_0_54, plain, (v1_xreal_0(X2)\|~v3_membered(X1)\|~m1_subset_1(X2,X1)), inference(evalgc,[status(thm)],[c_0_42])). cnf(c_0_55, plain, (m1_subset_1(k3_matrix_1(X2,X1,X3,X4),X2)\|~v7_ordinal1(X4)\|~v7_ordinal1(X3)\|~v1_matrix_1(X1)\|~m1_finseq_1(X1,k3_finseq_2(X2))), inference(evalgc,[status(thm)],[c_0_43])). cnf(c_0_56, plain, (v3_membered(k1_numbers)), inference(split_conjunct,[status(thm)],[fc3_membered])). fof(c_0_57, plain, ![X46, X47]:((~m2_finseq_1(X47,X46)\|m1_finseq_1(X47,X46))&(~m1_finseq_1(X47,X46)\|m2_finseq_1(X47,X46))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_finseq_1])])). cnf(c_0_58, plain, (k2_matrix_1(X1)=k2_zfmisc_1(k2_finseq_1(X2),k2_finseq_1(X2))\|v1_xboole_0(X3)\|~v7_ordinal1(X2)\|~m1_matrix_1(X1,X3,X2,X2)), inference(evalgc,[status(thm)],[c_0_44])). cnf(c_0_59, negated_conjecture, (m1_matrix_1(esk2_0,k1_numbers,esk1_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_45])). cnf(c_0_60, negated_conjecture, (v7_ordinal1(esk1_0)), inference(evalgc,[status(thm)],[c_0_46])). cnf(c_0_61, plain, (~v1_xboole_0(k1_numbers)), inference(evalgc,[status(thm)],[c_0_47])). cnf(c_0_62, negated_conjecture, (m1_matrix_1(esk3_0,k1_numbers,esk1_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_48])). cnf(c_0_63, plain, (m2_finseq_1(X1,k3_finseq_2(X2))\|v1_xboole_0(X2)\|~m1_matrix_1(X1,X2,X3,X4)\|~v7_ordinal1(X3)\|~v7_ordinal1(X4)), inference(split_conjunct,[status(thm)],[c_0_49])). cnf(c_0_64, plain, (v1_matrix_1(X1)\|v1_xboole_0(X2)\|~m1_matrix_1(X1,X2,X3,X4)\|~v7_ordinal1(X3)\|~v7_ordinal1(X4)), inference(split_conjunct,[status(thm)],[c_0_49])). cnf(c_0_65, plain, (k3_matrix10(X1,X2,X3)=k3_matrixr1(X2,X3)\|~v7_ordinal1(X1)\|~m1_matrix_1(X2,k1_numbers,X1,X1)\|~m1_matrix_1(X3,k1_numbers,X1,X1)), inference(split_conjunct,[status(thm)],[c_0_50])). cnf(c_0_66, plain, (r2_matrix10(X1,k3_matrixr1(X2,X1))\|~v1_xreal_0(k3_matrix_1(k1_numbers,X1,esk4_2(X1,k3_matrixr1(X2,X1)),esk5_2(X1,k3_matrixr1(X2,X1))))\|~m1_subset_1(k3_matrix_1(k1_numbers,X2,esk4_2(X1,k3_matrixr1(X2,X1)),esk5_2(X1,k3_matrixr1(X2,X1))),k1_numbers)\|~r1_xxreal_0(k6_numbers,k3_matrix_1(k1_numbers,X2,esk4_2(X1,k3_matrixr1(X2,X1)),esk5_2(X1,k3_matrixr1(X2,X1))))\|~r2_hidden(k4_tarski(esk4_2(X1,k3_matrixr1(X2,X1)),esk5_2(X1,k3_matrixr1(X2,X1))),k2_matrix_1(X2))\|~m2_finseq_1(k3_matrixr1(X2,X1),k3_finseq_2(k1_numbers))\|~m2_finseq_1(X1,k3_finseq_2(k1_numbers))\|~m2_finseq_1(X2,k3_finseq_2(k1_numbers))\|~v1_matrix_1(k3_matrixr1(X2,X1))\|~v1_matrix_1(X1)\|~v1_matrix_1(X2)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_51, c_0_52]), c_0_53])). cnf(c_0_67, plain, (v1_xreal_0(k3_matrix_1(X1,X2,X3,X4))\|~v3_membered(X1)\|~m1_finseq_1(X2,k3_finseq_2(X1))\|~v1_matrix_1(X2)\|~v7_ordinal1(X4)\|~v7_ordinal1(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_54, c_0_55])])). cnf(c_0_68, plain, (v3_membered(k1_numbers)), inference(evalgc,[status(thm)],[c_0_56])). cnf(c_0_69, plain, (m2_finseq_1(X1,X2)\|~m1_finseq_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_57])). cnf(c_0_70, plain, (r2_hidden(k4_tarski(esk4_2(X1,X2),esk5_2(X1,X2)),k2_matrix_1(X1))\|r2_matrix10(X1,X2)\|~v1_matrix_1(X2)\|~m2_finseq_1(X2,k3_finseq_2(k1_numbers))\|~v1_matrix_1(X1)\|~m2_finseq_1(X1,k3_finseq_2(k1_numbers))), inference(split_conjunct,[status(thm)],[c_0_25])). cnf(c_0_71, negated_conjecture, (k2_zfmisc_1(k2_finseq_1(esk1_0),k2_finseq_1(esk1_0))=k2_matrix_1(esk2_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58, c_0_59]), c_0_60])]), c_0_61])])). cnf(c_0_72, negated_conjecture, (k2_zfmisc_1(k2_finseq_1(esk1_0),k2_finseq_1(esk1_0))=k2_matrix_1(esk3_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58, c_0_62]), c_0_60])]), c_0_61])])). cnf(c_0_73, plain, (v1_xboole_0(X2)\|m2_finseq_1(X1,k3_finseq_2(X2))\|~v7_ordinal1(X4)\|~v7_ordinal1(X3)\|~m1_matrix_1(X1,X2,X3,X4)), inference(evalgc,[status(thm)],[c_0_63])). cnf(c_0_74, plain, (v1_xboole_0(X2)\|v1_matrix_1(X1)\|~v7_ordinal1(X4)\|~v7_ordinal1(X3)\|~m1_matrix_1(X1,X2,X3,X4)), inference(evalgc,[status(thm)],[c_0_64])). cnf(c_0_75, negated_conjecture, (~r2_matrix10(esk3_0,k3_matrix10(esk1_0,esk2_0,esk3_0))), inference(split_conjunct,[status(thm)],[c_0_36])). cnf(c_0_76, plain, (k3_matrix10(X1,X2,X3)=k3_matrixr1(X2,X3)\|~v7_ordinal1(X1)\|~m1_matrix_1(X3,k1_numbers,X1,X1)\|~m1_matrix_1(X2,k1_numbers,X1,X1)), inference(evalgc,[status(thm)],[c_0_65])). cnf(c_0_77, plain, (r2_matrix10(X1,k3_matrixr1(X2,X1))\|~m1_subset_1(k3_matrix_1(k1_numbers,X2,esk4_2(X1,k3_matrixr1(X2,X1)),esk5_2(X1,k3_matrixr1(X2,X1))),k1_numbers)\|~r1_xxreal_0(k6_numbers,k3_matrix_1(k1_numbers,X2,esk4_2(X1,k3_matrixr1(X2,X1)),esk5_2(X1,k3_matrixr1(X2,X1))))\|~r2_hidden(k4_tarski(esk4_2(X1,k3_matrixr1(X2,X1)),esk5_2(X1,k3_matrixr1(X2,X1))),k2_matrix_1(X2))\|~m2_finseq_1(k3_matrixr1(X2,X1),k3_finseq_2(k1_numbers))\|~m2_finseq_1(X1,k3_finseq_2(k1_numbers))\|~m2_finseq_1(X2,k3_finseq_2(k1_numbers))\|~v1_matrix_1(k3_matrixr1(X2,X1))\|~v1_matrix_1(X1)\|~v1_matrix_1(X2)\|~m1_finseq_1(X1,k3_finseq_2(k1_numbers))\|~v7_ordinal1(esk5_2(X1,k3_matrixr1(X2,X1)))\|~v7_ordinal1(esk4_2(X1,k3_matrixr1(X2,X1)))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66, c_0_67]), c_0_68])])])). cnf(c_0_78, plain, (m2_finseq_1(X1,X2)\|~m1_finseq_1(X1,X2)), inference(evalgc,[status(thm)],[c_0_69])). cnf(c_0_79, plain, (r2_matrix10(X1,X2)\|r2_hidden(k4_tarski(esk4_2(X1,X2),esk5_2(X1,X2)),k2_matrix_1(X1))\|~v1_matrix_1(X2)\|~v1_matrix_1(X1)\|~m2_finseq_1(X2,k3_finseq_2(k1_numbers))\|~m2_finseq_1(X1,k3_finseq_2(k1_numbers))), inference(evalgc,[status(thm)],[c_0_70])). cnf(c_0_80, negated_conjecture, (k2_matrix_1(esk3_0)=k2_matrix_1(esk2_0)), inference(rw,[status(thm)],[c_0_71, c_0_72])). cnf(c_0_81, negated_conjecture, (m2_finseq_1(esk3_0,k3_finseq_2(k1_numbers))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73, c_0_62]), c_0_60])]), c_0_61])])). cnf(c_0_82, negated_conjecture, (v1_matrix_1(esk3_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74, c_0_62]), c_0_60])]), c_0_61])])). cnf(c_0_83, negated_conjecture, (~r2_matrix10(esk3_0,k3_matrix10(esk1_0,esk2_0,esk3_0))), inference(evalgc,[status(thm)],[c_0_75])). cnf(c_0_84, negated_conjecture, (k3_matrix10(esk1_0,X1,esk3_0)=k3_matrixr1(X1,esk3_0)\|~m1_matrix_1(X1,k1_numbers,esk1_0,esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76, c_0_62]), c_0_60])])])). fof(c_0_85, plain, ![X29, X30, X31]:((~v4_matrix10(X29)\|(~v7_ordinal1(X30)\|(~v7_ordinal1(X31)\|(~r2_hidden(k4_tarski(X30,X31),k2_matrix_1(X29))\|r1_xxreal_0(k6_numbers,k3_matrix_1(k1_numbers,X29,X30,X31)))))\|(~v1_matrix_1(X29)\|~m2_finseq_1(X29,k3_finseq_2(k1_numbers))))&((v7_ordinal1(esk6_1(X29))\|v4_matrix10(X29)\|(~v1_matrix_1(X29)\|~m2_finseq_1(X29,k3_finseq_2(k1_numbers))))&((v7_ordinal1(esk7_1(X29))\|v4_matrix10(X29)\|(~v1_matrix_1(X29)\|~m2_finseq_1(X29,k3_finseq_2(k1_numbers))))&((r2_hidden(k4_tarski(esk6_1(X29),esk7_1(X29)),k2_matrix_1(X29))\|v4_matrix10(X29)\|(~v1_matrix_1(X29)\|~m2_finseq_1(X29,k3_finseq_2(k1_numbers))))&(~r1_xxreal_0(k6_numbers,k3_matrix_1(k1_numbers,X29,esk6_1(X29),esk7_1(X29)))\|v4_matrix10(X29)\|(~v1_matrix_1(X29)\|~m2_finseq_1(X29,k3_finseq_2(k1_numbers)))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d4_matrix10])])])])])). cnf(c_0_86, plain, (r2_matrix10(X1,k3_matrixr1(X2,X1))\|~m1_finseq_1(X1,k3_finseq_2(k1_numbers))\|~m1_subset_1(k3_matrix_1(k1_numbers,X2,esk4_2(X1,k3_matrixr1(X2,X1)),esk5_2(X1,k3_matrixr1(X2,X1))),k1_numbers)\|~r1_xxreal_0(k6_numbers,k3_matrix_1(k1_numbers,X2,esk4_2(X1,k3_matrixr1(X2,X1)),esk5_2(X1,k3_matrixr1(X2,X1))))\|~r2_hidden(k4_tarski(esk4_2(X1,k3_matrixr1(X2,X1)),esk5_2(X1,k3_matrixr1(X2,X1))),k2_matrix_1(X2))\|~m2_finseq_1(k3_matrixr1(X2,X1),k3_finseq_2(k1_numbers))\|~m2_finseq_1(X2,k3_finseq_2(k1_numbers))\|~v1_matrix_1(k3_matrixr1(X2,X1))\|~v1_matrix_1(X1)\|~v1_matrix_1(X2)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_77, c_0_52]), c_0_53]), c_0_78])). cnf(c_0_87, negated_conjecture, (r2_hidden(k4_tarski(esk4_2(esk3_0,X1),esk5_2(esk3_0,X1)),k2_matrix_1(esk2_0))\|r2_matrix10(esk3_0,X1)\|~m2_finseq_1(X1,k3_finseq_2(k1_numbers))\|~v1_matrix_1(X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79, c_0_80]), c_0_81]), c_0_82])])])). cnf(c_0_88, negated_conjecture, (m2_finseq_1(esk2_0,k3_finseq_2(k1_numbers))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73, c_0_59]), c_0_60])]), c_0_61])])). cnf(c_0_89, negated_conjecture, (v1_matrix_1(esk2_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74, c_0_59]), c_0_60])]), c_0_61])])). cnf(c_0_90, negated_conjecture, (~r2_matrix10(esk3_0,k3_matrixr1(esk2_0,esk3_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83, c_0_84]), c_0_59])])])). cnf(c_0_91, plain, (r1_xxreal_0(k6_numbers,k3_matrix_1(k1_numbers,X1,X2,X3))\|~v4_matrix10(X1)\|~v7_ordinal1(X2)\|~v7_ordinal1(X3)\|~r2_hidden(k4_tarski(X2,X3),k2_matrix_1(X1))\|~v1_matrix_1(X1)\|~m2_finseq_1(X1,k3_finseq_2(k1_numbers))), inference(split_conjunct,[status(thm)],[c_0_85])). cnf(c_0_92, negated_conjecture, (v4_matrix10(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_36])). cnf(c_0_93, negated_conjecture, (~m1_finseq_1(esk3_0,k3_finseq_2(k1_numbers))\|~m1_subset_1(k3_matrix_1(k1_numbers,esk2_0,esk4_2(esk3_0,k3_matrixr1(esk2_0,esk3_0)),esk5_2(esk3_0,k3_matrixr1(esk2_0,esk3_0))),k1_numbers)\|~r1_xxreal_0(k6_numbers,k3_matrix_1(k1_numbers,esk2_0,esk4_2(esk3_0,k3_matrixr1(esk2_0,esk3_0)),esk5_2(esk3_0,k3_matrixr1(esk2_0,esk3_0))))\|~m2_finseq_1(k3_matrixr1(esk2_0,esk3_0),k3_finseq_2(k1_numbers))\|~v1_matrix_1(k3_matrixr1(esk2_0,esk3_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86, c_0_87]), c_0_88]), c_0_82]), c_0_89])]), c_0_90])])). cnf(c_0_94, plain, (r1_xxreal_0(k6_numbers,k3_matrix_1(k1_numbers,X1,X2,X3))\|~v7_ordinal1(X3)\|~v7_ordinal1(X2)\|~v4_matrix10(X1)\|~v1_matrix_1(X1)\|~m2_finseq_1(X1,k3_finseq_2(k1_numbers))\|~r2_hidden(k4_tarski(X2,X3),k2_matrix_1(X1))), inference(evalgc,[status(thm)],[c_0_91])). cnf(c_0_95, negated_conjecture, (v4_matrix10(esk2_0)), inference(evalgc,[status(thm)],[c_0_92])). cnf(c_0_96, negated_conjecture, (~m1_finseq_1(esk3_0,k3_finseq_2(k1_numbers))\|~r1_xxreal_0(k6_numbers,k3_matrix_1(k1_numbers,esk2_0,esk4_2(esk3_0,k3_matrixr1(esk2_0,esk3_0)),esk5_2(esk3_0,k3_matrixr1(esk2_0,esk3_0))))\|~m2_finseq_1(k3_matrixr1(esk2_0,esk3_0),k3_finseq_2(k1_numbers))\|~v1_matrix_1(k3_matrixr1(esk2_0,esk3_0))\|~m1_finseq_1(esk2_0,k3_finseq_2(k1_numbers))\|~v7_ordinal1(esk5_2(esk3_0,k3_matrixr1(esk2_0,esk3_0)))\|~v7_ordinal1(esk4_2(esk3_0,k3_matrixr1(esk2_0,esk3_0)))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93, c_0_55]), c_0_89])])])). cnf(c_0_97, negated_conjecture, (r1_xxreal_0(k6_numbers,k3_matrix_1(k1_numbers,esk2_0,esk4_2(esk3_0,X1),esk5_2(esk3_0,X1)))\|r2_matrix10(esk3_0,X1)\|~v7_ordinal1(esk5_2(esk3_0,X1))\|~v7_ordinal1(esk4_2(esk3_0,X1))\|~m2_finseq_1(X1,k3_finseq_2(k1_numbers))\|~v1_matrix_1(X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94, c_0_87]), c_0_88]), c_0_89]), c_0_95])])])). cnf(c_0_98, negated_conjecture, (~m1_finseq_1(esk3_0,k3_finseq_2(k1_numbers))\|~m1_finseq_1(esk2_0,k3_finseq_2(k1_numbers))\|~m2_finseq_1(k3_matrixr1(esk2_0,esk3_0),k3_finseq_2(k1_numbers))\|~v1_matrix_1(k3_matrixr1(esk2_0,esk3_0))\|~v7_ordinal1(esk5_2(esk3_0,k3_matrixr1(esk2_0,esk3_0)))\|~v7_ordinal1(esk4_2(esk3_0,k3_matrixr1(esk2_0,esk3_0)))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_96, c_0_97]), c_0_90])])). fof(c_0_99, plain, ![X44, X45]:((v1_matrix_1(k3_matrixr1(X44,X45))\|(~v1_matrix_1(X44)\|~m1_finseq_1(X44,k3_finseq_2(k1_numbers))\|(~v1_matrix_1(X45)\|~m1_finseq_1(X45,k3_finseq_2(k1_numbers)))))&(m2_finseq_1(k3_matrixr1(X44,X45),k3_finseq_2(k1_numbers))\|(~v1_matrix_1(X44)\|~m1_finseq_1(X44,k3_finseq_2(k1_numbers))\|(~v1_matrix_1(X45)\|~m1_finseq_1(X45,k3_finseq_2(k1_numbers)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k3_matrixr1])])])). cnf(c_0_100, negated_conjecture, (~m1_finseq_1(esk3_0,k3_finseq_2(k1_numbers))\|~m1_finseq_1(esk2_0,k3_finseq_2(k1_numbers))\|~m2_finseq_1(k3_matrixr1(esk2_0,esk3_0),k3_finseq_2(k1_numbers))\|~v1_matrix_1(k3_matrixr1(esk2_0,esk3_0))\|~v7_ordinal1(esk4_2(esk3_0,k3_matrixr1(esk2_0,esk3_0)))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98, c_0_53]), c_0_81]), c_0_82])]), c_0_90])])). cnf(c_0_101, plain, (m2_finseq_1(k3_matrixr1(X1,X2),k3_finseq_2(k1_numbers))\|~v1_matrix_1(X1)\|~m1_finseq_1(X1,k3_finseq_2(k1_numbers))\|~v1_matrix_1(X2)\|~m1_finseq_1(X2,k3_finseq_2(k1_numbers))), inference(split_conjunct,[status(thm)],[c_0_99])). cnf(c_0_102, negated_conjecture, (~m1_finseq_1(esk3_0,k3_finseq_2(k1_numbers))\|~m1_finseq_1(esk2_0,k3_finseq_2(k1_numbers))\|~m2_finseq_1(k3_matrixr1(esk2_0,esk3_0),k3_finseq_2(k1_numbers))\|~v1_matrix_1(k3_matrixr1(esk2_0,esk3_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100, c_0_52]), c_0_81]), c_0_82])]), c_0_90])])). cnf(c_0_103, plain, (m2_finseq_1(k3_matrixr1(X1,X2),k3_finseq_2(k1_numbers))\|~v1_matrix_1(X2)\|~v1_matrix_1(X1)\|~m1_finseq_1(X2,k3_finseq_2(k1_numbers))\|~m1_finseq_1(X1,k3_finseq_2(k1_numbers))), inference(evalgc,[status(thm)],[c_0_101])). cnf(c_0_104, plain, (v1_matrix_1(k3_matrixr1(X1,X2))\|~v1_matrix_1(X1)\|~m1_finseq_1(X1,k3_finseq_2(k1_numbers))\|~v1_matrix_1(X2)\|~m1_finseq_1(X2,k3_finseq_2(k1_numbers))), inference(split_conjunct,[status(thm)],[c_0_99])). cnf(c_0_105, negated_conjecture, (~m1_finseq_1(esk3_0,k3_finseq_2(k1_numbers))\|~m1_finseq_1(esk2_0,k3_finseq_2(k1_numbers))\|~v1_matrix_1(k3_matrixr1(esk2_0,esk3_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102, c_0_103]), c_0_82]), c_0_89])])])). cnf(c_0_106, plain, (v1_matrix_1(k3_matrixr1(X1,X2))\|~v1_matrix_1(X2)\|~v1_matrix_1(X1)\|~m1_finseq_1(X2,k3_finseq_2(k1_numbers))\|~m1_finseq_1(X1,k3_finseq_2(k1_numbers))), inference(evalgc,[status(thm)],[c_0_104])). cnf(c_0_107, plain, (m1_finseq_1(X1,X2)\|~m2_finseq_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_57])). cnf(c_0_108, negated_conjecture, (~m1_finseq_1(esk3_0,k3_finseq_2(k1_numbers))\|~m1_finseq_1(esk2_0,k3_finseq_2(k1_numbers))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105, c_0_106]), c_0_82]), c_0_89])])])). cnf(c_0_109, plain, (m1_finseq_1(X1,X2)\|~m2_finseq_1(X1,X2)), inference(evalgc,[status(thm)],[c_0_107])). cnf(c_0_110, negated_conjecture, (~m1_finseq_1(esk2_0,k3_finseq_2(k1_numbers))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108, c_0_109]), c_0_81])])])). cnf(c_0_111, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110, c_0_109]), c_0_88])]), ['proof']). # SZS output end CNFRefutation	reserve a,b for Element of REAL, i,j,n for Nat, M,M1,M2,M3,M4 for Matrix of n, REAL; theorem M1 is Nonnegative implies M2 is_less_or_equal_with M1+M2 proof A1: Indices M1=[:Seg n, Seg n:] & Indices M2=[:Seg n, Seg n:] by MATRIX_1:24; assume A2: M1 is Nonnegative; for i,j st [i,j] in Indices M2 holds M2(i,j)<=(M1+M2)(i,j) proof let i,j; assume A3: [i,j] in Indices M2; then M1(i,j)>=0 by A2,A1,Def4; then M2(i,j)<=M1(i,j)+M2(i,j) by XREAL_1:31; hence thesis by A1,A3,MATRIXR1:25; end; hence thesis by Def6; end;	Convert the following ATP output trace into a readable Mizar proof.
t47_bvfunc14	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t17_enumset1, axiom, ![X1, X2, X3, X4, X5, X6, X7]:k5_enumset1(X1,X2,X3,X4,X5,X6,X7)=k2_xboole_0(k2_tarski(X1,X2),k3_enumset1(X3,X4,X5,X6,X7)), file('/scratch/mptp/predsminms1/t47_bvfunc14__0', t17_enumset1)). fof(t8_enumset1, axiom, ![X1, X2, X3, X4, X5]:k3_enumset1(X1,X2,X3,X4,X5)=k2_xboole_0(k2_tarski(X1,X2),k1_enumset1(X3,X4,X5)), file('/scratch/mptp/predsminms1/t47_bvfunc14__0', t8_enumset1)). fof(t47_bvfunc14, conjecture, ![X1]:(~(v1_xboole_0(X1))=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(k1_bvfunc_2(X1)))=>![X3]:(m1_eqrel_1(X3,X1)=>![X4]:(m1_eqrel_1(X4,X1)=>![X5]:(m1_eqrel_1(X5,X1)=>![X6]:(m1_eqrel_1(X6,X1)=>![X7]:(m1_eqrel_1(X7,X1)=>![X8]:(m1_eqrel_1(X8,X1)=>![X9]:(m1_eqrel_1(X9,X1)=>(X2=k5_enumset1(X3,X4,X5,X6,X7,X8,X9)=>(X3=X4\|(X3=X5\|(X3=X6\|(X3=X7\|(X3=X8\|(X3=X9\|(X4=X5\|(X4=X6\|(X4=X7\|(X4=X8\|(X4=X9\|(X5=X6\|(X5=X7\|(X5=X8\|(X5=X9\|(X6=X7\|(X6=X8\|(X6=X9\|(X7=X8\|(X7=X9\|(X8=X9\|k5_bvfunc_2(X1,X8,X2)=k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,X3,X4),X5),X6),X7),X9)))))))))))))))))))))))))))))))), file('/scratch/mptp/predsminms1/t47_bvfunc14__0', t47_bvfunc14)). fof(t58_enumset1, axiom, ![X1, X2, X3]:k1_enumset1(X1,X2,X3)=k1_enumset1(X2,X1,X3), file('/scratch/mptp/predsminms1/t47_bvfunc14__0', t58_enumset1)). fof(t46_bvfunc14, axiom, ![X1]:(~(v1_xboole_0(X1))=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(k1_bvfunc_2(X1)))=>![X3]:(m1_eqrel_1(X3,X1)=>![X4]:(m1_eqrel_1(X4,X1)=>![X5]:(m1_eqrel_1(X5,X1)=>![X6]:(m1_eqrel_1(X6,X1)=>![X7]:(m1_eqrel_1(X7,X1)=>![X8]:(m1_eqrel_1(X8,X1)=>![X9]:(m1_eqrel_1(X9,X1)=>(X2=k5_enumset1(X3,X4,X5,X6,X7,X8,X9)=>(X3=X4\|(X3=X5\|(X3=X6\|(X3=X7\|(X3=X8\|(X3=X9\|(X4=X5\|(X4=X6\|(X4=X7\|(X4=X8\|(X4=X9\|(X5=X6\|(X5=X7\|(X5=X8\|(X5=X9\|(X6=X7\|(X6=X8\|(X6=X9\|(X7=X8\|(X7=X9\|(X8=X9\|k5_bvfunc_2(X1,X7,X2)=k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,X3,X4),X5),X6),X8),X9)))))))))))))))))))))))))))))))), file('/scratch/mptp/predsminms1/t47_bvfunc14__0', t46_bvfunc14)). fof(c_0_5, plain, ![X1, X2, X3, X4, X5, X7, X6]:(epred1_7(X6,X7,X5,X4,X3,X2,X1)<=>![X8]:(m1_eqrel_1(X8,X1)=>![X9]:(m1_eqrel_1(X9,X1)=>(X2=k5_enumset1(X3,X4,X5,X6,X7,X8,X9)=>(X3=X4\|(X3=X5\|(X3=X6\|(X3=X7\|(X3=X8\|(X3=X9\|(X4=X5\|(X4=X6\|(X4=X7\|(X4=X8\|(X4=X9\|(X5=X6\|(X5=X7\|(X5=X8\|(X5=X9\|(X6=X7\|(X6=X8\|(X6=X9\|(X7=X8\|(X7=X9\|(X8=X9\|k5_bvfunc_2(X1,X7,X2)=k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,X3,X4),X5),X6),X8),X9)))))))))))))))))))))))))), introduced(definition)). fof(c_0_6, plain, ![X1, X2, X3, X4, X5, X7, X6]:(epred1_7(X6,X7,X5,X4,X3,X2,X1)=>![X8]:(m1_eqrel_1(X8,X1)=>![X9]:(m1_eqrel_1(X9,X1)=>(X2=k5_enumset1(X3,X4,X5,X6,X7,X8,X9)=>(X3=X4\|(X3=X5\|(X3=X6\|(X3=X7\|(X3=X8\|(X3=X9\|(X4=X5\|(X4=X6\|(X4=X7\|(X4=X8\|(X4=X9\|(X5=X6\|(X5=X7\|(X5=X8\|(X5=X9\|(X6=X7\|(X6=X8\|(X6=X9\|(X7=X8\|(X7=X9\|(X8=X9\|k5_bvfunc_2(X1,X7,X2)=k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,X3,X4),X5),X6),X8),X9)))))))))))))))))))))))))), inference(split_equiv,[status(thm)],[c_0_5])). fof(c_0_7, plain, ![X19, X20, X21, X22, X23, X24, X25]:k5_enumset1(X19,X20,X21,X22,X23,X24,X25)=k2_xboole_0(k2_tarski(X19,X20),k3_enumset1(X21,X22,X23,X24,X25)), inference(variable_rename,[status(thm)],[t17_enumset1])). fof(c_0_8, plain, ![X26, X27, X28, X29, X30]:k3_enumset1(X26,X27,X28,X29,X30)=k2_xboole_0(k2_tarski(X26,X27),k1_enumset1(X28,X29,X30)), inference(variable_rename,[status(thm)],[t8_enumset1])). fof(c_0_9, plain, ![X41, X42, X43, X44, X45, X46, X47, X48, X49]:(~epred1_7(X47,X46,X45,X44,X43,X42,X41)\|(~m1_eqrel_1(X48,X41)\|(~m1_eqrel_1(X49,X41)\|(X42!=k5_enumset1(X43,X44,X45,X47,X46,X48,X49)\|(X43=X44\|(X43=X45\|(X43=X47\|(X43=X46\|(X43=X48\|(X43=X49\|(X44=X45\|(X44=X47\|(X44=X46\|(X44=X48\|(X44=X49\|(X45=X47\|(X45=X46\|(X45=X48\|(X45=X49\|(X47=X46\|(X47=X48\|(X47=X49\|(X46=X48\|(X46=X49\|(X48=X49\|k5_bvfunc_2(X41,X46,X42)=k2_partit1(X41,k2_partit1(X41,k2_partit1(X41,k2_partit1(X41,k2_partit1(X41,X43,X44),X45),X47),X48),X49)))))))))))))))))))))))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])). cnf(c_0_10, plain, (k5_enumset1(X1,X2,X3,X4,X5,X6,X7)=k2_xboole_0(k2_tarski(X1,X2),k3_enumset1(X3,X4,X5,X6,X7))), inference(split_conjunct,[status(thm)],[c_0_7])). cnf(c_0_11, plain, (k3_enumset1(X1,X2,X3,X4,X5)=k2_xboole_0(k2_tarski(X1,X2),k1_enumset1(X3,X4,X5))), inference(split_conjunct,[status(thm)],[c_0_8])). fof(c_0_12, negated_conjecture, ~(![X1]:(~(v1_xboole_0(X1))=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(k1_bvfunc_2(X1)))=>![X3]:(m1_eqrel_1(X3,X1)=>![X4]:(m1_eqrel_1(X4,X1)=>![X5]:(m1_eqrel_1(X5,X1)=>![X6]:(m1_eqrel_1(X6,X1)=>![X7]:(m1_eqrel_1(X7,X1)=>![X8]:(m1_eqrel_1(X8,X1)=>![X9]:(m1_eqrel_1(X9,X1)=>(X2=k5_enumset1(X3,X4,X5,X6,X7,X8,X9)=>(X3=X4\|(X3=X5\|(X3=X6\|(X3=X7\|(X3=X8\|(X3=X9\|(X4=X5\|(X4=X6\|(X4=X7\|(X4=X8\|(X4=X9\|(X5=X6\|(X5=X7\|(X5=X8\|(X5=X9\|(X6=X7\|(X6=X8\|(X6=X9\|(X7=X8\|(X7=X9\|(X8=X9\|k5_bvfunc_2(X1,X8,X2)=k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,X3,X4),X5),X6),X7),X9))))))))))))))))))))))))))))))))), inference(assume_negation,[status(cth)],[t47_bvfunc14])). cnf(c_0_13, plain, (X5=X4\|X5=X3\|X5=X1\|X5=X2\|X5=X8\|X5=X9\|X4=X3\|X4=X1\|X4=X2\|X4=X8\|X4=X9\|X3=X1\|X3=X2\|X3=X8\|X3=X9\|X1=X2\|X1=X8\|X1=X9\|X2=X8\|X2=X9\|X8=X9\|k5_bvfunc_2(X7,X2,X6)=k2_partit1(X7,k2_partit1(X7,k2_partit1(X7,k2_partit1(X7,k2_partit1(X7,X5,X4),X3),X1),X8),X9)\|~epred1_7(X1,X2,X3,X4,X5,X6,X7)\|~m1_eqrel_1(X8,X7)\|~m1_eqrel_1(X9,X7)\|X6!=k5_enumset1(X5,X4,X3,X1,X2,X8,X9)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_14, plain, (k5_enumset1(X1,X2,X3,X4,X5,X6,X7)=k2_xboole_0(k2_tarski(X1,X2),k2_xboole_0(k2_tarski(X3,X4),k1_enumset1(X5,X6,X7)))), inference(rw,[status(thm)],[c_0_10, c_0_11])). fof(c_0_15, plain, ![X31, X32, X33]:k1_enumset1(X31,X32,X33)=k1_enumset1(X32,X31,X33), inference(variable_rename,[status(thm)],[t58_enumset1])). fof(c_0_16, negated_conjecture, (~v1_xboole_0(esk1_0)&(m1_subset_1(esk2_0,k1_zfmisc_1(k1_bvfunc_2(esk1_0)))&(m1_eqrel_1(esk3_0,esk1_0)&(m1_eqrel_1(esk4_0,esk1_0)&(m1_eqrel_1(esk5_0,esk1_0)&(m1_eqrel_1(esk6_0,esk1_0)&(m1_eqrel_1(esk7_0,esk1_0)&(m1_eqrel_1(esk8_0,esk1_0)&(m1_eqrel_1(esk9_0,esk1_0)&(esk2_0=k5_enumset1(esk3_0,esk4_0,esk5_0,esk6_0,esk7_0,esk8_0,esk9_0)&(esk3_0!=esk4_0&(esk3_0!=esk5_0&(esk3_0!=esk6_0&(esk3_0!=esk7_0&(esk3_0!=esk8_0&(esk3_0!=esk9_0&(esk4_0!=esk5_0&(esk4_0!=esk6_0&(esk4_0!=esk7_0&(esk4_0!=esk8_0&(esk4_0!=esk9_0&(esk5_0!=esk6_0&(esk5_0!=esk7_0&(esk5_0!=esk8_0&(esk5_0!=esk9_0&(esk6_0!=esk7_0&(esk6_0!=esk8_0&(esk6_0!=esk9_0&(esk7_0!=esk8_0&(esk7_0!=esk9_0&(esk8_0!=esk9_0&k5_bvfunc_2(esk1_0,esk8_0,esk2_0)!=k2_partit1(esk1_0,k2_partit1(esk1_0,k2_partit1(esk1_0,k2_partit1(esk1_0,k2_partit1(esk1_0,esk3_0,esk4_0),esk5_0),esk6_0),esk7_0),esk9_0)))))))))))))))))))))))))))))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_12])])])])). fof(c_0_17, axiom, ![X1]:(~(v1_xboole_0(X1))=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(k1_bvfunc_2(X1)))=>![X3]:(m1_eqrel_1(X3,X1)=>![X4]:(m1_eqrel_1(X4,X1)=>![X5]:(m1_eqrel_1(X5,X1)=>![X6]:(m1_eqrel_1(X6,X1)=>![X7]:(m1_eqrel_1(X7,X1)=>epred1_7(X6,X7,X5,X4,X3,X2,X1)))))))), inference(apply_def,[status(thm)],[t46_bvfunc14, c_0_5])). cnf(c_0_18, plain, (X8=X9\|X5=X9\|X5=X8\|X4=X9\|X4=X8\|X4=X5\|X3=X9\|X3=X8\|X3=X5\|X3=X4\|X2=X9\|X2=X8\|X2=X5\|X2=X4\|X2=X3\|X1=X9\|X1=X8\|X1=X5\|X1=X4\|X1=X3\|X1=X2\|k5_bvfunc_2(X7,X2,X6)=k2_partit1(X7,k2_partit1(X7,k2_partit1(X7,k2_partit1(X7,k2_partit1(X7,X5,X4),X3),X1),X8),X9)\|X6!=k2_xboole_0(k2_tarski(X5,X4),k2_xboole_0(k2_tarski(X3,X1),k1_enumset1(X2,X8,X9)))\|~m1_eqrel_1(X9,X7)\|~m1_eqrel_1(X8,X7)\|~epred1_7(X1,X2,X3,X4,X5,X6,X7)), inference(rw,[status(thm)],[c_0_13, c_0_14])). cnf(c_0_19, plain, (k1_enumset1(X1,X2,X3)=k1_enumset1(X2,X1,X3)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_20, negated_conjecture, (esk2_0=k5_enumset1(esk3_0,esk4_0,esk5_0,esk6_0,esk7_0,esk8_0,esk9_0)), inference(split_conjunct,[status(thm)],[c_0_16])). fof(c_0_21, plain, ![X34, X35, X36, X37, X38, X39, X40]:(v1_xboole_0(X34)\|(~m1_subset_1(X35,k1_zfmisc_1(k1_bvfunc_2(X34)))\|(~m1_eqrel_1(X36,X34)\|(~m1_eqrel_1(X37,X34)\|(~m1_eqrel_1(X38,X34)\|(~m1_eqrel_1(X39,X34)\|(~m1_eqrel_1(X40,X34)\|epred1_7(X39,X40,X38,X37,X36,X35,X34)))))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_17])])])])). cnf(c_0_22, plain, (X8=X9\|X5=X9\|X5=X8\|X4=X9\|X4=X8\|X4=X5\|X3=X9\|X3=X8\|X3=X5\|X3=X4\|X2=X9\|X2=X8\|X2=X5\|X2=X4\|X2=X3\|X1=X9\|X1=X8\|X1=X5\|X1=X4\|X1=X3\|X1=X2\|k5_bvfunc_2(X7,X2,X6)=k2_partit1(X7,k2_partit1(X7,k2_partit1(X7,k2_partit1(X7,k2_partit1(X7,X5,X4),X3),X1),X8),X9)\|X6!=k2_xboole_0(k2_tarski(X5,X4),k2_xboole_0(k2_tarski(X3,X1),k1_enumset1(X2,X8,X9)))\|~m1_eqrel_1(X9,X7)\|~m1_eqrel_1(X8,X7)\|~epred1_7(X1,X2,X3,X4,X5,X6,X7)), inference(evalgc,[status(thm)],[c_0_18])). cnf(c_0_23, plain, (k1_enumset1(X1,X2,X3)=k1_enumset1(X2,X1,X3)), inference(evalgc,[status(thm)],[c_0_19])). cnf(c_0_24, negated_conjecture, (esk2_0=k2_xboole_0(k2_tarski(esk3_0,esk4_0),k2_xboole_0(k2_tarski(esk5_0,esk6_0),k1_enumset1(esk7_0,esk8_0,esk9_0)))), inference(rw,[status(thm)],[c_0_20, c_0_14])). cnf(c_0_25, negated_conjecture, (esk7_0!=esk9_0), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_26, negated_conjecture, (esk3_0!=esk9_0), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_27, negated_conjecture, (esk3_0!=esk7_0), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_28, negated_conjecture, (esk4_0!=esk9_0), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_29, negated_conjecture, (esk4_0!=esk7_0), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_30, negated_conjecture, (esk3_0!=esk4_0), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_31, negated_conjecture, (esk5_0!=esk9_0), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_32, negated_conjecture, (esk5_0!=esk7_0), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_33, negated_conjecture, (esk3_0!=esk5_0), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_34, negated_conjecture, (esk4_0!=esk5_0), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_35, negated_conjecture, (esk8_0!=esk9_0), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_36, negated_conjecture, (esk7_0!=esk8_0), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_37, negated_conjecture, (esk3_0!=esk8_0), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_38, negated_conjecture, (esk4_0!=esk8_0), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_39, negated_conjecture, (esk5_0!=esk8_0), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_40, negated_conjecture, (esk6_0!=esk9_0), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_41, negated_conjecture, (esk6_0!=esk7_0), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_42, negated_conjecture, (esk3_0!=esk6_0), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_43, negated_conjecture, (esk4_0!=esk6_0), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_44, negated_conjecture, (esk5_0!=esk6_0), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_45, negated_conjecture, (esk6_0!=esk8_0), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_46, plain, (v1_xboole_0(X1)\|epred1_7(X6,X7,X5,X4,X3,X2,X1)\|~m1_subset_1(X2,k1_zfmisc_1(k1_bvfunc_2(X1)))\|~m1_eqrel_1(X3,X1)\|~m1_eqrel_1(X4,X1)\|~m1_eqrel_1(X5,X1)\|~m1_eqrel_1(X6,X1)\|~m1_eqrel_1(X7,X1)), inference(split_conjunct,[status(thm)],[c_0_21])). cnf(c_0_47, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(k1_bvfunc_2(esk1_0)))), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_48, negated_conjecture, (~v1_xboole_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_49, plain, (k5_bvfunc_2(X1,X2,X3)=k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,X4,X5),X6),X7),X8),X9)\|X7=X2\|X7=X6\|X7=X5\|X7=X4\|X7=X8\|X7=X9\|X2=X6\|X2=X5\|X2=X4\|X2=X8\|X2=X9\|X6=X5\|X6=X4\|X6=X8\|X6=X9\|X5=X4\|X5=X8\|X5=X9\|X4=X8\|X4=X9\|X8=X9\|X3!=k2_xboole_0(k2_tarski(X4,X5),k2_xboole_0(k2_tarski(X6,X7),k1_enumset1(X8,X2,X9)))\|~epred1_7(X7,X2,X6,X5,X4,X3,X1)\|~m1_eqrel_1(X9,X1)\|~m1_eqrel_1(X8,X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_22, c_0_23])])). cnf(c_0_50, negated_conjecture, (k2_xboole_0(k2_tarski(esk3_0,esk4_0),k2_xboole_0(k2_tarski(esk5_0,esk6_0),k1_enumset1(esk7_0,esk8_0,esk9_0)))=esk2_0), inference(evalgc,[status(thm)],[c_0_24])). cnf(c_0_51, negated_conjecture, (esk9_0!=esk7_0), inference(evalgc,[status(thm)],[c_0_25])). cnf(c_0_52, negated_conjecture, (esk3_0!=esk9_0), inference(evalgc,[status(thm)],[c_0_26])). cnf(c_0_53, negated_conjecture, (esk3_0!=esk7_0), inference(evalgc,[status(thm)],[c_0_27])). cnf(c_0_54, negated_conjecture, (esk9_0!=esk4_0), inference(evalgc,[status(thm)],[c_0_28])). cnf(c_0_55, negated_conjecture, (esk7_0!=esk4_0), inference(evalgc,[status(thm)],[c_0_29])). cnf(c_0_56, negated_conjecture, (esk3_0!=esk4_0), inference(evalgc,[status(thm)],[c_0_30])). cnf(c_0_57, negated_conjecture, (esk9_0!=esk5_0), inference(evalgc,[status(thm)],[c_0_31])). cnf(c_0_58, negated_conjecture, (esk7_0!=esk5_0), inference(evalgc,[status(thm)],[c_0_32])). cnf(c_0_59, negated_conjecture, (esk3_0!=esk5_0), inference(evalgc,[status(thm)],[c_0_33])). cnf(c_0_60, negated_conjecture, (esk5_0!=esk4_0), inference(evalgc,[status(thm)],[c_0_34])). cnf(c_0_61, negated_conjecture, (esk9_0!=esk8_0), inference(evalgc,[status(thm)],[c_0_35])). cnf(c_0_62, negated_conjecture, (esk8_0!=esk7_0), inference(evalgc,[status(thm)],[c_0_36])). cnf(c_0_63, negated_conjecture, (esk3_0!=esk8_0), inference(evalgc,[status(thm)],[c_0_37])). cnf(c_0_64, negated_conjecture, (esk8_0!=esk4_0), inference(evalgc,[status(thm)],[c_0_38])). cnf(c_0_65, negated_conjecture, (esk8_0!=esk5_0), inference(evalgc,[status(thm)],[c_0_39])). cnf(c_0_66, negated_conjecture, (esk9_0!=esk6_0), inference(evalgc,[status(thm)],[c_0_40])). cnf(c_0_67, negated_conjecture, (esk7_0!=esk6_0), inference(evalgc,[status(thm)],[c_0_41])). cnf(c_0_68, negated_conjecture, (esk3_0!=esk6_0), inference(evalgc,[status(thm)],[c_0_42])). cnf(c_0_69, negated_conjecture, (esk6_0!=esk4_0), inference(evalgc,[status(thm)],[c_0_43])). cnf(c_0_70, negated_conjecture, (esk6_0!=esk5_0), inference(evalgc,[status(thm)],[c_0_44])). cnf(c_0_71, negated_conjecture, (esk8_0!=esk6_0), inference(evalgc,[status(thm)],[c_0_45])). cnf(c_0_72, plain, (v1_xboole_0(X1)\|epred1_7(X6,X7,X5,X4,X3,X2,X1)\|~m1_eqrel_1(X7,X1)\|~m1_eqrel_1(X6,X1)\|~m1_eqrel_1(X5,X1)\|~m1_eqrel_1(X4,X1)\|~m1_eqrel_1(X3,X1)\|~m1_subset_1(X2,k1_zfmisc_1(k1_bvfunc_2(X1)))), inference(evalgc,[status(thm)],[c_0_46])). cnf(c_0_73, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(k1_bvfunc_2(esk1_0)))), inference(evalgc,[status(thm)],[c_0_47])). cnf(c_0_74, negated_conjecture, (~v1_xboole_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_48])). cnf(c_0_75, negated_conjecture, (m1_eqrel_1(esk9_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_76, negated_conjecture, (m1_eqrel_1(esk7_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_77, negated_conjecture, (m1_eqrel_1(esk8_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_78, negated_conjecture, (m1_eqrel_1(esk6_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_79, negated_conjecture, (m1_eqrel_1(esk5_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_80, negated_conjecture, (m1_eqrel_1(esk4_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_81, negated_conjecture, (m1_eqrel_1(esk3_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_82, negated_conjecture, (k5_bvfunc_2(esk1_0,esk8_0,esk2_0)!=k2_partit1(esk1_0,k2_partit1(esk1_0,k2_partit1(esk1_0,k2_partit1(esk1_0,k2_partit1(esk1_0,esk3_0,esk4_0),esk5_0),esk6_0),esk7_0),esk9_0)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_83, negated_conjecture, (k5_bvfunc_2(X1,esk8_0,X2)=k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,k2_partit1(X1,esk3_0,esk4_0),esk5_0),esk6_0),esk7_0),esk9_0)\|X2!=esk2_0\|~epred1_7(esk6_0,esk8_0,esk5_0,esk4_0,esk3_0,X2,X1)\|~m1_eqrel_1(esk9_0,X1)\|~m1_eqrel_1(esk7_0,X1)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_49, c_0_50]), c_0_51]), c_0_52]), c_0_53]), c_0_54]), c_0_55]), c_0_56]), c_0_57]), c_0_58]), c_0_59]), c_0_60]), c_0_61]), c_0_62]), c_0_63]), c_0_64]), c_0_65]), c_0_66]), c_0_67]), c_0_68]), c_0_69]), c_0_70]), c_0_71])])). cnf(c_0_84, negated_conjecture, (epred1_7(X1,X2,X3,X4,X5,esk2_0,esk1_0)\|~m1_eqrel_1(X2,esk1_0)\|~m1_eqrel_1(X1,esk1_0)\|~m1_eqrel_1(X3,esk1_0)\|~m1_eqrel_1(X4,esk1_0)\|~m1_eqrel_1(X5,esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_72, c_0_73]), c_0_74])])). cnf(c_0_85, negated_conjecture, (m1_eqrel_1(esk9_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_75])). cnf(c_0_86, negated_conjecture, (m1_eqrel_1(esk7_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_76])). cnf(c_0_87, negated_conjecture, (m1_eqrel_1(esk8_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_77])). cnf(c_0_88, negated_conjecture, (m1_eqrel_1(esk6_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_78])). cnf(c_0_89, negated_conjecture, (m1_eqrel_1(esk5_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_79])). cnf(c_0_90, negated_conjecture, (m1_eqrel_1(esk4_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_80])). cnf(c_0_91, negated_conjecture, (m1_eqrel_1(esk3_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_81])). cnf(c_0_92, negated_conjecture, (k2_partit1(esk1_0,k2_partit1(esk1_0,k2_partit1(esk1_0,k2_partit1(esk1_0,k2_partit1(esk1_0,esk3_0,esk4_0),esk5_0),esk6_0),esk7_0),esk9_0)!=k5_bvfunc_2(esk1_0,esk8_0,esk2_0)), inference(evalgc,[status(thm)],[c_0_82])). cnf(c_0_93, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83, c_0_84]), c_0_85]), c_0_86]), c_0_87]), c_0_88]), c_0_89]), c_0_90]), c_0_91])]), c_0_92]), ['proof']). # SZS output end CNFRefutation	reserve Y for non empty set, G for Subset of PARTITIONS(Y), A,B,C,D,E,F for a_partition of Y; reserve Y for non empty set, G for Subset of PARTITIONS(Y), A, B, C, D, E, F, J, M for a_partition of Y, x,x1,x2,x3,x4,x5,x6,x7,x8,x9 for set; theorem Th47: G={A,B,C,D,E,F,J} & A<>B & A<>C & A<>D & A<>E & A<>F & A<>J & B <>C & B<>D & B<>E & B<>F & B<>J & C<>D & C<>E & C<>F & C<>J & D<>E & D<>F & D<> J & E<>F & E<>J & F<>J implies CompF(F,G) = A '/\' B '/\' C '/\' D '/\' E '/\' J proof {A,B,C,D,E,F,J}={A,B,C,D} \/ {E,F,J} by ENUMSET1:19 .={A,B,C,D} \/ {F,E,J} by ENUMSET1:58 .={A,B,C,D,F,E,J} by ENUMSET1:19; hence thesis by Th46; end;	Convert the following ATP output trace into a readable Mizar proof.
t120_sheffer2	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t119_sheffer2, axiom, ![X1]:((~(v2_struct_0(X1))&(v10_sheffer1(X1)&(v11_sheffer1(X1)&(v12_sheffer1(X1)&l1_sheffer1(X1)))))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>k5_sheffer1(X1,X2,k5_sheffer1(X1,X3,X2))=k5_sheffer1(X1,k5_sheffer1(X1,X3,X3),X2)))), file('/scratch/mptp/predsminms1/t120_sheffer2__0', t119_sheffer2)). fof(t120_sheffer2, conjecture, ![X1]:((~(v2_struct_0(X1))&(v10_sheffer1(X1)&(v11_sheffer1(X1)&(v12_sheffer1(X1)&l1_sheffer1(X1)))))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>k5_sheffer1(X1,k5_sheffer1(X1,X3,X2),k5_sheffer1(X1,k5_sheffer1(X1,X3,X3),X2))=k5_sheffer1(X1,k5_sheffer1(X1,X2,X2),k5_sheffer1(X1,X3,X2))))), file('/scratch/mptp/predsminms1/t120_sheffer2__0', t120_sheffer2)). fof(dt_k5_sheffer1, axiom, ![X1, X2, X3]:(((~(v2_struct_0(X1))&l1_sheffer1(X1))&(m1_subset_1(X2,u1_struct_0(X1))&m1_subset_1(X3,u1_struct_0(X1))))=>m1_subset_1(k5_sheffer1(X1,X2,X3),u1_struct_0(X1))), file('/scratch/mptp/predsminms1/t120_sheffer2__0', dt_k5_sheffer1)). fof(c_0_3, plain, ![X7, X8, X9]:(v2_struct_0(X7)\|(~v10_sheffer1(X7)\|(~v11_sheffer1(X7)\|(~v12_sheffer1(X7)\|~l1_sheffer1(X7))))\|(~m1_subset_1(X8,u1_struct_0(X7))\|(~m1_subset_1(X9,u1_struct_0(X7))\|k5_sheffer1(X7,X8,k5_sheffer1(X7,X9,X8))=k5_sheffer1(X7,k5_sheffer1(X7,X9,X9),X8)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t119_sheffer2])])])])). fof(c_0_4, negated_conjecture, ~(![X1]:((~(v2_struct_0(X1))&(v10_sheffer1(X1)&(v11_sheffer1(X1)&(v12_sheffer1(X1)&l1_sheffer1(X1)))))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>k5_sheffer1(X1,k5_sheffer1(X1,X3,X2),k5_sheffer1(X1,k5_sheffer1(X1,X3,X3),X2))=k5_sheffer1(X1,k5_sheffer1(X1,X2,X2),k5_sheffer1(X1,X3,X2)))))), inference(assume_negation,[status(cth)],[t120_sheffer2])). cnf(c_0_5, plain, (v2_struct_0(X1)\|k5_sheffer1(X1,X2,k5_sheffer1(X1,X3,X2))=k5_sheffer1(X1,k5_sheffer1(X1,X3,X3),X2)\|~v10_sheffer1(X1)\|~v11_sheffer1(X1)\|~v12_sheffer1(X1)\|~l1_sheffer1(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_3])). fof(c_0_6, plain, ![X10, X11, X12]:(v2_struct_0(X10)\|~l1_sheffer1(X10)\|(~m1_subset_1(X11,u1_struct_0(X10))\|~m1_subset_1(X12,u1_struct_0(X10)))\|m1_subset_1(k5_sheffer1(X10,X11,X12),u1_struct_0(X10))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k5_sheffer1])])])). fof(c_0_7, negated_conjecture, ((~v2_struct_0(esk1_0)&(v10_sheffer1(esk1_0)&(v11_sheffer1(esk1_0)&(v12_sheffer1(esk1_0)&l1_sheffer1(esk1_0)))))&(m1_subset_1(esk2_0,u1_struct_0(esk1_0))&(m1_subset_1(esk3_0,u1_struct_0(esk1_0))&k5_sheffer1(esk1_0,k5_sheffer1(esk1_0,esk3_0,esk2_0),k5_sheffer1(esk1_0,k5_sheffer1(esk1_0,esk3_0,esk3_0),esk2_0))!=k5_sheffer1(esk1_0,k5_sheffer1(esk1_0,esk2_0,esk2_0),k5_sheffer1(esk1_0,esk3_0,esk2_0))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_4])])])])). cnf(c_0_8, plain, (k5_sheffer1(X1,X2,k5_sheffer1(X1,X3,X2))=k5_sheffer1(X1,k5_sheffer1(X1,X3,X3),X2)\|v2_struct_0(X1)\|~v10_sheffer1(X1)\|~v11_sheffer1(X1)\|~v12_sheffer1(X1)\|~l1_sheffer1(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_5])). cnf(c_0_9, plain, (v2_struct_0(X1)\|m1_subset_1(k5_sheffer1(X1,X2,X3),u1_struct_0(X1))\|~l1_sheffer1(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_10, negated_conjecture, (k5_sheffer1(esk1_0,k5_sheffer1(esk1_0,esk3_0,esk2_0),k5_sheffer1(esk1_0,k5_sheffer1(esk1_0,esk3_0,esk3_0),esk2_0))!=k5_sheffer1(esk1_0,k5_sheffer1(esk1_0,esk2_0,esk2_0),k5_sheffer1(esk1_0,esk3_0,esk2_0))), inference(split_conjunct,[status(thm)],[c_0_7])). cnf(c_0_11, plain, (k5_sheffer1(X1,k5_sheffer1(X1,X2,X3),k5_sheffer1(X1,k5_sheffer1(X1,X2,X2),X3))=k5_sheffer1(X1,k5_sheffer1(X1,X3,X3),k5_sheffer1(X1,X2,X3))\|v2_struct_0(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(k5_sheffer1(X1,X2,X3),u1_struct_0(X1))\|~l1_sheffer1(X1)\|~v12_sheffer1(X1)\|~v11_sheffer1(X1)\|~v10_sheffer1(X1)\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_8, c_0_8])])). cnf(c_0_12, plain, (v2_struct_0(X1)\|m1_subset_1(k5_sheffer1(X1,X2,X3),u1_struct_0(X1))\|~l1_sheffer1(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_9])). cnf(c_0_13, negated_conjecture, (m1_subset_1(esk2_0,u1_struct_0(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_7])). cnf(c_0_14, negated_conjecture, (m1_subset_1(esk3_0,u1_struct_0(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_7])). cnf(c_0_15, negated_conjecture, (l1_sheffer1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_7])). cnf(c_0_16, negated_conjecture, (v12_sheffer1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_7])). cnf(c_0_17, negated_conjecture, (v11_sheffer1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_7])). cnf(c_0_18, negated_conjecture, (v10_sheffer1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_7])). cnf(c_0_19, negated_conjecture, (~v2_struct_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_7])). cnf(c_0_20, negated_conjecture, (k5_sheffer1(esk1_0,k5_sheffer1(esk1_0,esk3_0,esk2_0),k5_sheffer1(esk1_0,k5_sheffer1(esk1_0,esk3_0,esk3_0),esk2_0))!=k5_sheffer1(esk1_0,k5_sheffer1(esk1_0,esk2_0,esk2_0),k5_sheffer1(esk1_0,esk3_0,esk2_0))), inference(evalgc,[status(thm)],[c_0_10])). cnf(c_0_21, plain, (k5_sheffer1(X1,k5_sheffer1(X1,X2,X3),k5_sheffer1(X1,k5_sheffer1(X1,X2,X2),X3))=k5_sheffer1(X1,k5_sheffer1(X1,X3,X3),k5_sheffer1(X1,X2,X3))\|v2_struct_0(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l1_sheffer1(X1)\|~v12_sheffer1(X1)\|~v11_sheffer1(X1)\|~v10_sheffer1(X1)), inference(csr,[status(thm)],[c_0_11, c_0_12])). cnf(c_0_22, negated_conjecture, (m1_subset_1(esk2_0,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[c_0_13])). cnf(c_0_23, negated_conjecture, (m1_subset_1(esk3_0,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[c_0_14])). cnf(c_0_24, negated_conjecture, (l1_sheffer1(esk1_0)), inference(evalgc,[status(thm)],[c_0_15])). cnf(c_0_25, negated_conjecture, (v12_sheffer1(esk1_0)), inference(evalgc,[status(thm)],[c_0_16])). cnf(c_0_26, negated_conjecture, (v11_sheffer1(esk1_0)), inference(evalgc,[status(thm)],[c_0_17])). cnf(c_0_27, negated_conjecture, (v10_sheffer1(esk1_0)), inference(evalgc,[status(thm)],[c_0_18])). cnf(c_0_28, negated_conjecture, (~v2_struct_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_19])). cnf(c_0_29, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20, c_0_21]), c_0_22]), c_0_23]), c_0_24]), c_0_25]), c_0_26]), c_0_27])]), c_0_28]), ['proof']). # SZS output end CNFRefutation	reserve L for satisfying_Sh_1 non empty ShefferStr; reserve L for satisfying_Sheffer_1 satisfying_Sheffer_2 satisfying_Sheffer_3 non empty ShefferStr; reserve v,q,p,w,z,y,x for Element of L; theorem Th120: for p,y holds (y \| p) \| ((y \| y) \| p) = (p \| p) \| (y \| p) proof let p,y; p \| (y \| p) = (y \| y) \| p by Th119; hence thesis by Th119; end;	Convert the following ATP output trace into a readable Mizar proof.
t22_fvaluat1	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(redefinition_k3_funct_2, axiom, ![X1, X2, X3, X4]:((~(v1_xboole_0(X1))&((v1_funct_1(X3)&(v1_funct_2(X3,X1,X2)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))))&m1_subset_1(X4,X1)))=>k3_funct_2(X1,X2,X3,X4)=k1_funct_1(X3,X4)), file('/scratch/mptp/predsminms1/t22_fvaluat1__0', redefinition_k3_funct_2)). fof(dt_m1_fvaluat1, axiom, ![X1]:(l6_algstr_0(X1)=>![X2]:(m1_fvaluat1(X2,X1)=>(v1_funct_1(X2)&(v1_funct_2(X2,u1_struct_0(X1),k7_numbers)&(v2_fvaluat1(X2)&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X1),k7_numbers)))))))), file('/scratch/mptp/predsminms1/t22_fvaluat1__0', dt_m1_fvaluat1)). fof(t22_fvaluat1, conjecture, ![X1]:((~(v2_struct_0(X1))&(~(v6_struct_0(X1))&(v13_algstr_0(X1)&(v3_group_1(X1)&(v5_vectsp_1(X1)&(v2_rlvect_1(X1)&(v3_rlvect_1(X1)&(v4_rlvect_1(X1)&(v1_realset2(X1)&l6_algstr_0(X1))))))))))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>![X4]:(m1_fvaluat1(X4,X1)=>(v3_fvaluat1(X1)=>(X2=k4_struct_0(X1)\|k3_funct_2(u1_struct_0(X1),k7_numbers,X4,k1_vectsp_2(X1,X3,X2))=k4_supinf_2(k3_funct_2(u1_struct_0(X1),k7_numbers,X4,X3),k3_funct_2(u1_struct_0(X1),k7_numbers,X4,X2)))))))), file('/scratch/mptp/predsminms1/t22_fvaluat1__0', t22_fvaluat1)). fof(fc2_struct_0, axiom, ![X1]:((~(v2_struct_0(X1))&l1_struct_0(X1))=>~(v1_xboole_0(u1_struct_0(X1)))), file('/scratch/mptp/predsminms1/t22_fvaluat1__0', fc2_struct_0)). fof(dt_k3_funct_2, axiom, ![X1, X2, X3, X4]:((~(v1_xboole_0(X1))&((v1_funct_1(X3)&(v1_funct_2(X3,X1,X2)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))))&m1_subset_1(X4,X1)))=>m1_subset_1(k3_funct_2(X1,X2,X3,X4),X2)), file('/scratch/mptp/predsminms1/t22_fvaluat1__0', dt_k3_funct_2)). fof(dt_l1_algstr_0, axiom, ![X1]:(l1_algstr_0(X1)=>l1_struct_0(X1)), file('/scratch/mptp/predsminms1/t22_fvaluat1__0', dt_l1_algstr_0)). fof(t21_fvaluat1, axiom, ![X1]:((~(v2_struct_0(X1))&(~(v6_struct_0(X1))&(v13_algstr_0(X1)&(v3_group_1(X1)&(v5_vectsp_1(X1)&(v2_rlvect_1(X1)&(v3_rlvect_1(X1)&(v4_rlvect_1(X1)&(v1_realset2(X1)&l6_algstr_0(X1))))))))))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_fvaluat1(X3,X1)=>(v3_fvaluat1(X1)=>(X2=k4_struct_0(X1)\|k3_funct_2(u1_struct_0(X1),k7_numbers,X3,k11_algstr_0(X1,X2))=k2_supinf_2(k3_funct_2(u1_struct_0(X1),k7_numbers,X3,X2))))))), file('/scratch/mptp/predsminms1/t22_fvaluat1__0', t21_fvaluat1)). fof(cc2_realset2, axiom, ![X1]:(l6_algstr_0(X1)=>((~(v6_struct_0(X1))&(v13_algstr_0(X1)&(v2_rlvect_1(X1)&(v3_rlvect_1(X1)&(v4_rlvect_1(X1)&(v5_vectsp_1(X1)&v1_realset2(X1)))))))=>(~(v6_struct_0(X1))&(v33_algstr_0(X1)&(v3_group_1(X1)&(v5_group_1(X1)&v4_vectsp_1(X1))))))), file('/scratch/mptp/predsminms1/t22_fvaluat1__0', cc2_realset2)). fof(dt_l2_algstr_0, axiom, ![X1]:(l2_algstr_0(X1)=>(l2_struct_0(X1)&l1_algstr_0(X1))), file('/scratch/mptp/predsminms1/t22_fvaluat1__0', dt_l2_algstr_0)). fof(redefinition_k2_supinf_2, axiom, ![X1]:(m1_subset_1(X1,k7_numbers)=>k2_supinf_2(X1)=k2_xxreal_3(X1)), file('/scratch/mptp/predsminms1/t22_fvaluat1__0', redefinition_k2_supinf_2)). fof(dt_k11_algstr_0, axiom, ![X1, X2]:((l5_algstr_0(X1)&m1_subset_1(X2,u1_struct_0(X1)))=>m1_subset_1(k11_algstr_0(X1,X2),u1_struct_0(X1))), file('/scratch/mptp/predsminms1/t22_fvaluat1__0', dt_k11_algstr_0)). fof(redefinition_k4_supinf_2, axiom, ![X1, X2]:((m1_subset_1(X1,k7_numbers)&m1_subset_1(X2,k7_numbers))=>k4_supinf_2(X1,X2)=k3_xxreal_3(X1,X2)), file('/scratch/mptp/predsminms1/t22_fvaluat1__0', redefinition_k4_supinf_2)). fof(d4_xxreal_3, axiom, ![X1]:(v1_xxreal_0(X1)=>![X2]:(v1_xxreal_0(X2)=>k3_xxreal_3(X1,X2)=k1_xxreal_3(X1,k2_xxreal_3(X2)))), file('/scratch/mptp/predsminms1/t22_fvaluat1__0', d4_xxreal_3)). fof(dt_l6_algstr_0, axiom, ![X1]:(l6_algstr_0(X1)=>(l2_algstr_0(X1)&l5_algstr_0(X1))), file('/scratch/mptp/predsminms1/t22_fvaluat1__0', dt_l6_algstr_0)). fof(d3_vectsp_2, axiom, ![X1]:((~(v2_struct_0(X1))&(~(v6_struct_0(X1))&(v13_algstr_0(X1)&(v33_algstr_0(X1)&(v3_group_1(X1)&(v4_vectsp_1(X1)&(v5_vectsp_1(X1)&(v2_rlvect_1(X1)&(v3_rlvect_1(X1)&(v4_rlvect_1(X1)&l6_algstr_0(X1)))))))))))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>k1_vectsp_2(X1,X2,X3)=k6_algstr_0(X1,X2,k11_algstr_0(X1,X3))))), file('/scratch/mptp/predsminms1/t22_fvaluat1__0', d3_vectsp_2)). fof(cc13_membered, axiom, ![X1]:(v2_membered(X1)=>![X2]:(m1_subset_1(X2,X1)=>v1_xxreal_0(X2))), file('/scratch/mptp/predsminms1/t22_fvaluat1__0', cc13_membered)). fof(d8_fvaluat1, axiom, ![X1]:(l6_algstr_0(X1)=>(v3_fvaluat1(X1)=>![X2]:((v1_funct_1(X2)&(v1_funct_2(X2,u1_struct_0(X1),k7_numbers)&(v2_fvaluat1(X2)&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X1),k7_numbers))))))=>(m1_fvaluat1(X2,X1)<=>(k1_funct_1(X2,k4_struct_0(X1))=k1_xxreal_0&(![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>(~(X3=k4_struct_0(X1))=>r2_hidden(k1_funct_1(X2,X3),k4_numbers)))&(![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>![X4]:(m1_subset_1(X4,u1_struct_0(X1))=>k1_funct_1(X2,k6_algstr_0(X1,X3,X4))=k1_xxreal_3(k1_funct_1(X2,X3),k1_funct_1(X2,X4))))&(![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>(r1_xxreal_0(k6_numbers,k1_funct_1(X2,X3))=>r1_xxreal_0(k6_numbers,k1_funct_1(X2,k1_algstr_0(X1,k5_struct_0(X1),X3)))))&?[X3]:(m1_subset_1(X3,u1_struct_0(X1))&(~(k1_funct_1(X2,X3)=k6_numbers)&~(k1_funct_1(X2,X3)=k1_xxreal_0))))))))))), file('/scratch/mptp/predsminms1/t22_fvaluat1__0', d8_fvaluat1)). fof(dt_k1_vectsp_2, axiom, ![X1, X2, X3]:(((~(v2_struct_0(X1))&(~(v6_struct_0(X1))&(v13_algstr_0(X1)&(v33_algstr_0(X1)&(v3_group_1(X1)&(v4_vectsp_1(X1)&(v5_vectsp_1(X1)&(v2_rlvect_1(X1)&(v3_rlvect_1(X1)&(v4_rlvect_1(X1)&l6_algstr_0(X1)))))))))))&(m1_subset_1(X2,u1_struct_0(X1))&m1_subset_1(X3,u1_struct_0(X1))))=>m1_subset_1(k1_vectsp_2(X1,X2,X3),u1_struct_0(X1))), file('/scratch/mptp/predsminms1/t22_fvaluat1__0', dt_k1_vectsp_2)). fof(fc2_membered, axiom, v2_membered(k7_numbers), file('/scratch/mptp/predsminms1/t22_fvaluat1__0', fc2_membered)). fof(c_0_19, plain, ![X14, X15, X16, X17]:(v1_xboole_0(X14)\|(~v1_funct_1(X16)\|(~v1_funct_2(X16,X14,X15)\|~m1_subset_1(X16,k1_zfmisc_1(k2_zfmisc_1(X14,X15))))\|~m1_subset_1(X17,X14))\|k3_funct_2(X14,X15,X16,X17)=k1_funct_1(X16,X17)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[redefinition_k3_funct_2])])])). fof(c_0_20, plain, ![X12, X13]:((v1_funct_1(X13)\|~m1_fvaluat1(X13,X12)\|~l6_algstr_0(X12))&((v1_funct_2(X13,u1_struct_0(X12),k7_numbers)\|~m1_fvaluat1(X13,X12)\|~l6_algstr_0(X12))&((v2_fvaluat1(X13)\|~m1_fvaluat1(X13,X12)\|~l6_algstr_0(X12))&(m1_subset_1(X13,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X12),k7_numbers)))\|~m1_fvaluat1(X13,X12)\|~l6_algstr_0(X12))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m1_fvaluat1])])])])). cnf(c_0_21, plain, (v1_xboole_0(X1)\|k3_funct_2(X1,X3,X2,X4)=k1_funct_1(X2,X4)\|~v1_funct_1(X2)\|~v1_funct_2(X2,X1,X3)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))\|~m1_subset_1(X4,X1)), inference(split_conjunct,[status(thm)],[c_0_19])). cnf(c_0_22, plain, (m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X2),k7_numbers)))\|~m1_fvaluat1(X1,X2)\|~l6_algstr_0(X2)), inference(split_conjunct,[status(thm)],[c_0_20])). fof(c_0_23, negated_conjecture, ~(![X1]:((~(v2_struct_0(X1))&(~(v6_struct_0(X1))&(v13_algstr_0(X1)&(v3_group_1(X1)&(v5_vectsp_1(X1)&(v2_rlvect_1(X1)&(v3_rlvect_1(X1)&(v4_rlvect_1(X1)&(v1_realset2(X1)&l6_algstr_0(X1))))))))))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>![X4]:(m1_fvaluat1(X4,X1)=>(v3_fvaluat1(X1)=>(X2=k4_struct_0(X1)\|k3_funct_2(u1_struct_0(X1),k7_numbers,X4,k1_vectsp_2(X1,X3,X2))=k4_supinf_2(k3_funct_2(u1_struct_0(X1),k7_numbers,X4,X3),k3_funct_2(u1_struct_0(X1),k7_numbers,X4,X2))))))))), inference(assume_negation,[status(cth)],[t22_fvaluat1])). cnf(c_0_24, plain, (k3_funct_2(X1,X3,X2,X4)=k1_funct_1(X2,X4)\|v1_xboole_0(X1)\|~v1_funct_1(X2)\|~m1_subset_1(X4,X1)\|~v1_funct_2(X2,X1,X3)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))), inference(evalgc,[status(thm)],[c_0_21])). cnf(c_0_25, plain, (m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X2),k7_numbers)))\|~l6_algstr_0(X2)\|~m1_fvaluat1(X1,X2)), inference(evalgc,[status(thm)],[c_0_22])). cnf(c_0_26, plain, (v1_funct_1(X1)\|~m1_fvaluat1(X1,X2)\|~l6_algstr_0(X2)), inference(split_conjunct,[status(thm)],[c_0_20])). cnf(c_0_27, plain, (v1_funct_2(X1,u1_struct_0(X2),k7_numbers)\|~m1_fvaluat1(X1,X2)\|~l6_algstr_0(X2)), inference(split_conjunct,[status(thm)],[c_0_20])). fof(c_0_28, negated_conjecture, ((~v2_struct_0(esk1_0)&(~v6_struct_0(esk1_0)&(v13_algstr_0(esk1_0)&(v3_group_1(esk1_0)&(v5_vectsp_1(esk1_0)&(v2_rlvect_1(esk1_0)&(v3_rlvect_1(esk1_0)&(v4_rlvect_1(esk1_0)&(v1_realset2(esk1_0)&l6_algstr_0(esk1_0))))))))))&(m1_subset_1(esk2_0,u1_struct_0(esk1_0))&(m1_subset_1(esk3_0,u1_struct_0(esk1_0))&(m1_fvaluat1(esk4_0,esk1_0)&(v3_fvaluat1(esk1_0)&(esk2_0!=k4_struct_0(esk1_0)&k3_funct_2(u1_struct_0(esk1_0),k7_numbers,esk4_0,k1_vectsp_2(esk1_0,esk3_0,esk2_0))!=k4_supinf_2(k3_funct_2(u1_struct_0(esk1_0),k7_numbers,esk4_0,esk3_0),k3_funct_2(u1_struct_0(esk1_0),k7_numbers,esk4_0,esk2_0)))))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_23])])])])). cnf(c_0_29, plain, (k3_funct_2(u1_struct_0(X1),k7_numbers,X2,X3)=k1_funct_1(X2,X3)\|v1_xboole_0(u1_struct_0(X1))\|~v1_funct_2(X2,u1_struct_0(X1),k7_numbers)\|~v1_funct_1(X2)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_fvaluat1(X2,X1)\|~l6_algstr_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_24, c_0_25])])). cnf(c_0_30, plain, (v1_funct_1(X1)\|~l6_algstr_0(X2)\|~m1_fvaluat1(X1,X2)), inference(evalgc,[status(thm)],[c_0_26])). cnf(c_0_31, plain, (v1_funct_2(X1,u1_struct_0(X2),k7_numbers)\|~l6_algstr_0(X2)\|~m1_fvaluat1(X1,X2)), inference(evalgc,[status(thm)],[c_0_27])). cnf(c_0_32, negated_conjecture, (m1_subset_1(esk3_0,u1_struct_0(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_28])). cnf(c_0_33, negated_conjecture, (l6_algstr_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_28])). cnf(c_0_34, negated_conjecture, (m1_subset_1(esk2_0,u1_struct_0(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_28])). fof(c_0_35, plain, ![X43]:(v2_struct_0(X43)\|~l1_struct_0(X43)\|~v1_xboole_0(u1_struct_0(X43))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fc2_struct_0])])])). cnf(c_0_36, plain, (k3_funct_2(u1_struct_0(X1),k7_numbers,X2,X3)=k1_funct_1(X2,X3)\|v1_xboole_0(u1_struct_0(X1))\|~m1_fvaluat1(X2,X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~l6_algstr_0(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_29, c_0_30]), c_0_31])). cnf(c_0_37, negated_conjecture, (m1_subset_1(esk3_0,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[c_0_32])). cnf(c_0_38, negated_conjecture, (l6_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_33])). cnf(c_0_39, negated_conjecture, (m1_fvaluat1(esk4_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_28])). cnf(c_0_40, negated_conjecture, (m1_subset_1(esk2_0,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[c_0_34])). fof(c_0_41, plain, ![X27, X28, X29, X30]:(v1_xboole_0(X27)\|(~v1_funct_1(X29)\|(~v1_funct_2(X29,X27,X28)\|~m1_subset_1(X29,k1_zfmisc_1(k2_zfmisc_1(X27,X28))))\|~m1_subset_1(X30,X27))\|m1_subset_1(k3_funct_2(X27,X28,X29,X30),X28)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k3_funct_2])])])). cnf(c_0_42, plain, (v2_struct_0(X1)\|~l1_struct_0(X1)\|~v1_xboole_0(u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_35])). cnf(c_0_43, negated_conjecture, (k3_funct_2(u1_struct_0(esk1_0),k7_numbers,X1,esk3_0)=k1_funct_1(X1,esk3_0)\|v1_xboole_0(u1_struct_0(esk1_0))\|~m1_fvaluat1(X1,esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36, c_0_37]), c_0_38])])])). cnf(c_0_44, negated_conjecture, (m1_fvaluat1(esk4_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_39])). cnf(c_0_45, negated_conjecture, (~v2_struct_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_28])). fof(c_0_46, plain, ![X41]:(~l1_algstr_0(X41)\|l1_struct_0(X41)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_algstr_0])])). cnf(c_0_47, negated_conjecture, (k3_funct_2(u1_struct_0(esk1_0),k7_numbers,X1,esk2_0)=k1_funct_1(X1,esk2_0)\|v1_xboole_0(u1_struct_0(esk1_0))\|~m1_fvaluat1(X1,esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36, c_0_40]), c_0_38])])])). fof(c_0_48, plain, ![X9, X10, X11]:(v2_struct_0(X9)\|(v6_struct_0(X9)\|(~v13_algstr_0(X9)\|(~v3_group_1(X9)\|(~v5_vectsp_1(X9)\|(~v2_rlvect_1(X9)\|(~v3_rlvect_1(X9)\|(~v4_rlvect_1(X9)\|(~v1_realset2(X9)\|~l6_algstr_0(X9)))))))))\|(~m1_subset_1(X10,u1_struct_0(X9))\|(~m1_fvaluat1(X11,X9)\|(~v3_fvaluat1(X9)\|(X10=k4_struct_0(X9)\|k3_funct_2(u1_struct_0(X9),k7_numbers,X11,k11_algstr_0(X9,X10))=k2_supinf_2(k3_funct_2(u1_struct_0(X9),k7_numbers,X11,X10))))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t21_fvaluat1])])])])). fof(c_0_49, plain, ![X20]:((~v6_struct_0(X20)\|(v6_struct_0(X20)\|(~v13_algstr_0(X20)\|(~v2_rlvect_1(X20)\|(~v3_rlvect_1(X20)\|(~v4_rlvect_1(X20)\|(~v5_vectsp_1(X20)\|~v1_realset2(X20)))))))\|~l6_algstr_0(X20))&((v33_algstr_0(X20)\|(v6_struct_0(X20)\|(~v13_algstr_0(X20)\|(~v2_rlvect_1(X20)\|(~v3_rlvect_1(X20)\|(~v4_rlvect_1(X20)\|(~v5_vectsp_1(X20)\|~v1_realset2(X20)))))))\|~l6_algstr_0(X20))&((v3_group_1(X20)\|(v6_struct_0(X20)\|(~v13_algstr_0(X20)\|(~v2_rlvect_1(X20)\|(~v3_rlvect_1(X20)\|(~v4_rlvect_1(X20)\|(~v5_vectsp_1(X20)\|~v1_realset2(X20)))))))\|~l6_algstr_0(X20))&((v5_group_1(X20)\|(v6_struct_0(X20)\|(~v13_algstr_0(X20)\|(~v2_rlvect_1(X20)\|(~v3_rlvect_1(X20)\|(~v4_rlvect_1(X20)\|(~v5_vectsp_1(X20)\|~v1_realset2(X20)))))))\|~l6_algstr_0(X20))&(v4_vectsp_1(X20)\|(v6_struct_0(X20)\|(~v13_algstr_0(X20)\|(~v2_rlvect_1(X20)\|(~v3_rlvect_1(X20)\|(~v4_rlvect_1(X20)\|(~v5_vectsp_1(X20)\|~v1_realset2(X20)))))))\|~l6_algstr_0(X20)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[cc2_realset2])])])])). cnf(c_0_50, plain, (v1_xboole_0(X1)\|m1_subset_1(k3_funct_2(X1,X3,X2,X4),X3)\|~v1_funct_1(X2)\|~v1_funct_2(X2,X1,X3)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))\|~m1_subset_1(X4,X1)), inference(split_conjunct,[status(thm)],[c_0_41])). cnf(c_0_51, plain, (v2_struct_0(X1)\|~l1_struct_0(X1)\|~v1_xboole_0(u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_42])). cnf(c_0_52, negated_conjecture, (k3_funct_2(u1_struct_0(esk1_0),k7_numbers,esk4_0,esk3_0)=k1_funct_1(esk4_0,esk3_0)\|v1_xboole_0(u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_43, c_0_44])])). cnf(c_0_53, negated_conjecture, (~v2_struct_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_45])). cnf(c_0_54, plain, (l1_struct_0(X1)\|~l1_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_46])). fof(c_0_55, plain, ![X42]:((l2_struct_0(X42)\|~l2_algstr_0(X42))&(l1_algstr_0(X42)\|~l2_algstr_0(X42))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l2_algstr_0])])])). cnf(c_0_56, negated_conjecture, (k3_funct_2(u1_struct_0(esk1_0),k7_numbers,esk4_0,esk2_0)=k1_funct_1(esk4_0,esk2_0)\|v1_xboole_0(u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_47, c_0_44])])). fof(c_0_57, plain, ![X35]:(~m1_subset_1(X35,k7_numbers)\|k2_supinf_2(X35)=k2_xxreal_3(X35)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k2_supinf_2])])). cnf(c_0_58, plain, (v2_struct_0(X1)\|v6_struct_0(X1)\|X2=k4_struct_0(X1)\|k3_funct_2(u1_struct_0(X1),k7_numbers,X3,k11_algstr_0(X1,X2))=k2_supinf_2(k3_funct_2(u1_struct_0(X1),k7_numbers,X3,X2))\|~v13_algstr_0(X1)\|~v3_group_1(X1)\|~v5_vectsp_1(X1)\|~v2_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v1_realset2(X1)\|~l6_algstr_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_fvaluat1(X3,X1)\|~v3_fvaluat1(X1)), inference(split_conjunct,[status(thm)],[c_0_48])). cnf(c_0_59, plain, (v3_group_1(X1)\|v6_struct_0(X1)\|~v13_algstr_0(X1)\|~v2_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v5_vectsp_1(X1)\|~v1_realset2(X1)\|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_49])). fof(c_0_60, plain, ![X25, X26]:(~l5_algstr_0(X25)\|~m1_subset_1(X26,u1_struct_0(X25))\|m1_subset_1(k11_algstr_0(X25,X26),u1_struct_0(X25))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k11_algstr_0])])). cnf(c_0_61, plain, (v1_xboole_0(X1)\|m1_subset_1(k3_funct_2(X1,X3,X2,X4),X3)\|~v1_funct_1(X2)\|~m1_subset_1(X4,X1)\|~v1_funct_2(X2,X1,X3)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))), inference(evalgc,[status(thm)],[c_0_50])). cnf(c_0_62, negated_conjecture, (k3_funct_2(u1_struct_0(esk1_0),k7_numbers,esk4_0,esk3_0)=k1_funct_1(esk4_0,esk3_0)\|~l1_struct_0(esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_51, c_0_52]), c_0_53])])). cnf(c_0_63, plain, (l1_struct_0(X1)\|~l1_algstr_0(X1)), inference(evalgc,[status(thm)],[c_0_54])). cnf(c_0_64, plain, (l1_algstr_0(X1)\|~l2_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_55])). fof(c_0_65, plain, ![X31, X32]:(~m1_subset_1(X31,k7_numbers)\|~m1_subset_1(X32,k7_numbers)\|k4_supinf_2(X31,X32)=k3_xxreal_3(X31,X32)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k4_supinf_2])])). cnf(c_0_66, negated_conjecture, (k3_funct_2(u1_struct_0(esk1_0),k7_numbers,esk4_0,esk2_0)=k1_funct_1(esk4_0,esk2_0)\|~l1_struct_0(esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_51, c_0_56]), c_0_53])])). fof(c_0_67, plain, ![X1, X2]:(epred1_2(X2,X1)<=>(![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>(~(X3=k4_struct_0(X1))=>r2_hidden(k1_funct_1(X2,X3),k4_numbers)))&(![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>![X4]:(m1_subset_1(X4,u1_struct_0(X1))=>k1_funct_1(X2,k6_algstr_0(X1,X3,X4))=k1_xxreal_3(k1_funct_1(X2,X3),k1_funct_1(X2,X4))))&(![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>(r1_xxreal_0(k6_numbers,k1_funct_1(X2,X3))=>r1_xxreal_0(k6_numbers,k1_funct_1(X2,k1_algstr_0(X1,k5_struct_0(X1),X3)))))&?[X3]:(m1_subset_1(X3,u1_struct_0(X1))&(~(k1_funct_1(X2,X3)=k6_numbers)&~(k1_funct_1(X2,X3)=k1_xxreal_0))))))), introduced(definition)). fof(c_0_68, plain, ![X36, X37]:(~v1_xxreal_0(X36)\|(~v1_xxreal_0(X37)\|k3_xxreal_3(X36,X37)=k1_xxreal_3(X36,k2_xxreal_3(X37)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d4_xxreal_3])])])). cnf(c_0_69, plain, (k2_supinf_2(X1)=k2_xxreal_3(X1)\|~m1_subset_1(X1,k7_numbers)), inference(split_conjunct,[status(thm)],[c_0_57])). cnf(c_0_70, plain, (X2=k4_struct_0(X1)\|k3_funct_2(u1_struct_0(X1),k7_numbers,X3,k11_algstr_0(X1,X2))=k2_supinf_2(k3_funct_2(u1_struct_0(X1),k7_numbers,X3,X2))\|v2_struct_0(X1)\|v6_struct_0(X1)\|~v13_algstr_0(X1)\|~v3_group_1(X1)\|~v5_vectsp_1(X1)\|~v2_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v1_realset2(X1)\|~l6_algstr_0(X1)\|~v3_fvaluat1(X1)\|~m1_fvaluat1(X3,X1)\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_58])). cnf(c_0_71, plain, (v6_struct_0(X1)\|v3_group_1(X1)\|~v13_algstr_0(X1)\|~v5_vectsp_1(X1)\|~v2_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v1_realset2(X1)\|~l6_algstr_0(X1)), inference(evalgc,[status(thm)],[c_0_59])). cnf(c_0_72, plain, (m1_subset_1(k11_algstr_0(X1,X2),u1_struct_0(X1))\|~l5_algstr_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_60])). fof(c_0_73, plain, ![X24]:((l2_algstr_0(X24)\|~l6_algstr_0(X24))&(l5_algstr_0(X24)\|~l6_algstr_0(X24))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l6_algstr_0])])])). cnf(c_0_74, plain, (v1_xboole_0(u1_struct_0(X1))\|m1_subset_1(k3_funct_2(u1_struct_0(X1),k7_numbers,X2,X3),k7_numbers)\|~v1_funct_2(X2,u1_struct_0(X1),k7_numbers)\|~v1_funct_1(X2)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_fvaluat1(X2,X1)\|~l6_algstr_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_61, c_0_25])])). cnf(c_0_75, negated_conjecture, (k3_funct_2(u1_struct_0(esk1_0),k7_numbers,esk4_0,esk3_0)=k1_funct_1(esk4_0,esk3_0)\|~l1_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_62, c_0_63])])). cnf(c_0_76, plain, (l1_algstr_0(X1)\|~l2_algstr_0(X1)), inference(evalgc,[status(thm)],[c_0_64])). cnf(c_0_77, negated_conjecture, (k3_funct_2(u1_struct_0(esk1_0),k7_numbers,esk4_0,k1_vectsp_2(esk1_0,esk3_0,esk2_0))!=k4_supinf_2(k3_funct_2(u1_struct_0(esk1_0),k7_numbers,esk4_0,esk3_0),k3_funct_2(u1_struct_0(esk1_0),k7_numbers,esk4_0,esk2_0))), inference(split_conjunct,[status(thm)],[c_0_28])). cnf(c_0_78, plain, (k4_supinf_2(X1,X2)=k3_xxreal_3(X1,X2)\|~m1_subset_1(X1,k7_numbers)\|~m1_subset_1(X2,k7_numbers)), inference(split_conjunct,[status(thm)],[c_0_65])). cnf(c_0_79, negated_conjecture, (k3_funct_2(u1_struct_0(esk1_0),k7_numbers,esk4_0,esk2_0)=k1_funct_1(esk4_0,esk2_0)\|~l1_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_66, c_0_63])])). fof(c_0_80, plain, ![X44, X45, X46, X47, X48, X49, X51, X52, X57]:(((~m1_subset_1(X46,u1_struct_0(X44))\|(X46=k4_struct_0(X44)\|r2_hidden(k1_funct_1(X45,X46),k4_numbers))\|~epred1_2(X45,X44))&((~m1_subset_1(X47,u1_struct_0(X44))\|(~m1_subset_1(X48,u1_struct_0(X44))\|k1_funct_1(X45,k6_algstr_0(X44,X47,X48))=k1_xxreal_3(k1_funct_1(X45,X47),k1_funct_1(X45,X48)))\|~epred1_2(X45,X44))&((~m1_subset_1(X49,u1_struct_0(X44))\|(~r1_xxreal_0(k6_numbers,k1_funct_1(X45,X49))\|r1_xxreal_0(k6_numbers,k1_funct_1(X45,k1_algstr_0(X44,k5_struct_0(X44),X49))))\|~epred1_2(X45,X44))&((m1_subset_1(esk5_2(X44,X45),u1_struct_0(X44))\|~epred1_2(X45,X44))&((k1_funct_1(X45,esk5_2(X44,X45))!=k6_numbers\|~epred1_2(X45,X44))&(k1_funct_1(X45,esk5_2(X44,X45))!=k1_xxreal_0\|~epred1_2(X45,X44)))))))&((((m1_subset_1(esk9_2(X51,X52),u1_struct_0(X51))\|(~m1_subset_1(X57,u1_struct_0(X51))\|(k1_funct_1(X52,X57)=k6_numbers\|k1_funct_1(X52,X57)=k1_xxreal_0))\|m1_subset_1(esk7_2(X51,X52),u1_struct_0(X51))\|m1_subset_1(esk6_2(X51,X52),u1_struct_0(X51))\|epred1_2(X52,X51))&((r1_xxreal_0(k6_numbers,k1_funct_1(X52,esk9_2(X51,X52)))\|(~m1_subset_1(X57,u1_struct_0(X51))\|(k1_funct_1(X52,X57)=k6_numbers\|k1_funct_1(X52,X57)=k1_xxreal_0))\|m1_subset_1(esk7_2(X51,X52),u1_struct_0(X51))\|m1_subset_1(esk6_2(X51,X52),u1_struct_0(X51))\|epred1_2(X52,X51))&(~r1_xxreal_0(k6_numbers,k1_funct_1(X52,k1_algstr_0(X51,k5_struct_0(X51),esk9_2(X51,X52))))\|(~m1_subset_1(X57,u1_struct_0(X51))\|(k1_funct_1(X52,X57)=k6_numbers\|k1_funct_1(X52,X57)=k1_xxreal_0))\|m1_subset_1(esk7_2(X51,X52),u1_struct_0(X51))\|m1_subset_1(esk6_2(X51,X52),u1_struct_0(X51))\|epred1_2(X52,X51))))&(((m1_subset_1(esk9_2(X51,X52),u1_struct_0(X51))\|(~m1_subset_1(X57,u1_struct_0(X51))\|(k1_funct_1(X52,X57)=k6_numbers\|k1_funct_1(X52,X57)=k1_xxreal_0))\|m1_subset_1(esk8_2(X51,X52),u1_struct_0(X51))\|m1_subset_1(esk6_2(X51,X52),u1_struct_0(X51))\|epred1_2(X52,X51))&((r1_xxreal_0(k6_numbers,k1_funct_1(X52,esk9_2(X51,X52)))\|(~m1_subset_1(X57,u1_struct_0(X51))\|(k1_funct_1(X52,X57)=k6_numbers\|k1_funct_1(X52,X57)=k1_xxreal_0))\|m1_subset_1(esk8_2(X51,X52),u1_struct_0(X51))\|m1_subset_1(esk6_2(X51,X52),u1_struct_0(X51))\|epred1_2(X52,X51))&(~r1_xxreal_0(k6_numbers,k1_funct_1(X52,k1_algstr_0(X51,k5_struct_0(X51),esk9_2(X51,X52))))\|(~m1_subset_1(X57,u1_struct_0(X51))\|(k1_funct_1(X52,X57)=k6_numbers\|k1_funct_1(X52,X57)=k1_xxreal_0))\|m1_subset_1(esk8_2(X51,X52),u1_struct_0(X51))\|m1_subset_1(esk6_2(X51,X52),u1_struct_0(X51))\|epred1_2(X52,X51))))&((m1_subset_1(esk9_2(X51,X52),u1_struct_0(X51))\|(~m1_subset_1(X57,u1_struct_0(X51))\|(k1_funct_1(X52,X57)=k6_numbers\|k1_funct_1(X52,X57)=k1_xxreal_0))\|k1_funct_1(X52,k6_algstr_0(X51,esk7_2(X51,X52),esk8_2(X51,X52)))!=k1_xxreal_3(k1_funct_1(X52,esk7_2(X51,X52)),k1_funct_1(X52,esk8_2(X51,X52)))\|m1_subset_1(esk6_2(X51,X52),u1_struct_0(X51))\|epred1_2(X52,X51))&((r1_xxreal_0(k6_numbers,k1_funct_1(X52,esk9_2(X51,X52)))\|(~m1_subset_1(X57,u1_struct_0(X51))\|(k1_funct_1(X52,X57)=k6_numbers\|k1_funct_1(X52,X57)=k1_xxreal_0))\|k1_funct_1(X52,k6_algstr_0(X51,esk7_2(X51,X52),esk8_2(X51,X52)))!=k1_xxreal_3(k1_funct_1(X52,esk7_2(X51,X52)),k1_funct_1(X52,esk8_2(X51,X52)))\|m1_subset_1(esk6_2(X51,X52),u1_struct_0(X51))\|epred1_2(X52,X51))&(~r1_xxreal_0(k6_numbers,k1_funct_1(X52,k1_algstr_0(X51,k5_struct_0(X51),esk9_2(X51,X52))))\|(~m1_subset_1(X57,u1_struct_0(X51))\|(k1_funct_1(X52,X57)=k6_numbers\|k1_funct_1(X52,X57)=k1_xxreal_0))\|k1_funct_1(X52,k6_algstr_0(X51,esk7_2(X51,X52),esk8_2(X51,X52)))!=k1_xxreal_3(k1_funct_1(X52,esk7_2(X51,X52)),k1_funct_1(X52,esk8_2(X51,X52)))\|m1_subset_1(esk6_2(X51,X52),u1_struct_0(X51))\|epred1_2(X52,X51))))))&((((m1_subset_1(esk9_2(X51,X52),u1_struct_0(X51))\|(~m1_subset_1(X57,u1_struct_0(X51))\|(k1_funct_1(X52,X57)=k6_numbers\|k1_funct_1(X52,X57)=k1_xxreal_0))\|m1_subset_1(esk7_2(X51,X52),u1_struct_0(X51))\|esk6_2(X51,X52)!=k4_struct_0(X51)\|epred1_2(X52,X51))&((r1_xxreal_0(k6_numbers,k1_funct_1(X52,esk9_2(X51,X52)))\|(~m1_subset_1(X57,u1_struct_0(X51))\|(k1_funct_1(X52,X57)=k6_numbers\|k1_funct_1(X52,X57)=k1_xxreal_0))\|m1_subset_1(esk7_2(X51,X52),u1_struct_0(X51))\|esk6_2(X51,X52)!=k4_struct_0(X51)\|epred1_2(X52,X51))&(~r1_xxreal_0(k6_numbers,k1_funct_1(X52,k1_algstr_0(X51,k5_struct_0(X51),esk9_2(X51,X52))))\|(~m1_subset_1(X57,u1_struct_0(X51))\|(k1_funct_1(X52,X57)=k6_numbers\|k1_funct_1(X52,X57)=k1_xxreal_0))\|m1_subset_1(esk7_2(X51,X52),u1_struct_0(X51))\|esk6_2(X51,X52)!=k4_struct_0(X51)\|epred1_2(X52,X51))))&(((m1_subset_1(esk9_2(X51,X52),u1_struct_0(X51))\|(~m1_subset_1(X57,u1_struct_0(X51))\|(k1_funct_1(X52,X57)=k6_numbers\|k1_funct_1(X52,X57)=k1_xxreal_0))\|m1_subset_1(esk8_2(X51,X52),u1_struct_0(X51))\|esk6_2(X51,X52)!=k4_struct_0(X51)\|epred1_2(X52,X51))&((r1_xxreal_0(k6_numbers,k1_funct_1(X52,esk9_2(X51,X52)))\|(~m1_subset_1(X57,u1_struct_0(X51))\|(k1_funct_1(X52,X57)=k6_numbers\|k1_funct_1(X52,X57)=k1_xxreal_0))\|m1_subset_1(esk8_2(X51,X52),u1_struct_0(X51))\|esk6_2(X51,X52)!=k4_struct_0(X51)\|epred1_2(X52,X51))&(~r1_xxreal_0(k6_numbers,k1_funct_1(X52,k1_algstr_0(X51,k5_struct_0(X51),esk9_2(X51,X52))))\|(~m1_subset_1(X57,u1_struct_0(X51))\|(k1_funct_1(X52,X57)=k6_numbers\|k1_funct_1(X52,X57)=k1_xxreal_0))\|m1_subset_1(esk8_2(X51,X52),u1_struct_0(X51))\|esk6_2(X51,X52)!=k4_struct_0(X51)\|epred1_2(X52,X51))))&((m1_subset_1(esk9_2(X51,X52),u1_struct_0(X51))\|(~m1_subset_1(X57,u1_struct_0(X51))\|(k1_funct_1(X52,X57)=k6_numbers\|k1_funct_1(X52,X57)=k1_xxreal_0))\|k1_funct_1(X52,k6_algstr_0(X51,esk7_2(X51,X52),esk8_2(X51,X52)))!=k1_xxreal_3(k1_funct_1(X52,esk7_2(X51,X52)),k1_funct_1(X52,esk8_2(X51,X52)))\|esk6_2(X51,X52)!=k4_struct_0(X51)\|epred1_2(X52,X51))&((r1_xxreal_0(k6_numbers,k1_funct_1(X52,esk9_2(X51,X52)))\|(~m1_subset_1(X57,u1_struct_0(X51))\|(k1_funct_1(X52,X57)=k6_numbers\|k1_funct_1(X52,X57)=k1_xxreal_0))\|k1_funct_1(X52,k6_algstr_0(X51,esk7_2(X51,X52),esk8_2(X51,X52)))!=k1_xxreal_3(k1_funct_1(X52,esk7_2(X51,X52)),k1_funct_1(X52,esk8_2(X51,X52)))\|esk6_2(X51,X52)!=k4_struct_0(X51)\|epred1_2(X52,X51))&(~r1_xxreal_0(k6_numbers,k1_funct_1(X52,k1_algstr_0(X51,k5_struct_0(X51),esk9_2(X51,X52))))\|(~m1_subset_1(X57,u1_struct_0(X51))\|(k1_funct_1(X52,X57)=k6_numbers\|k1_funct_1(X52,X57)=k1_xxreal_0))\|k1_funct_1(X52,k6_algstr_0(X51,esk7_2(X51,X52),esk8_2(X51,X52)))!=k1_xxreal_3(k1_funct_1(X52,esk7_2(X51,X52)),k1_funct_1(X52,esk8_2(X51,X52)))\|esk6_2(X51,X52)!=k4_struct_0(X51)\|epred1_2(X52,X51))))))&(((m1_subset_1(esk9_2(X51,X52),u1_struct_0(X51))\|(~m1_subset_1(X57,u1_struct_0(X51))\|(k1_funct_1(X52,X57)=k6_numbers\|k1_funct_1(X52,X57)=k1_xxreal_0))\|m1_subset_1(esk7_2(X51,X52),u1_struct_0(X51))\|~r2_hidden(k1_funct_1(X52,esk6_2(X51,X52)),k4_numbers)\|epred1_2(X52,X51))&((r1_xxreal_0(k6_numbers,k1_funct_1(X52,esk9_2(X51,X52)))\|(~m1_subset_1(X57,u1_struct_0(X51))\|(k1_funct_1(X52,X57)=k6_numbers\|k1_funct_1(X52,X57)=k1_xxreal_0))\|m1_subset_1(esk7_2(X51,X52),u1_struct_0(X51))\|~r2_hidden(k1_funct_1(X52,esk6_2(X51,X52)),k4_numbers)\|epred1_2(X52,X51))&(~r1_xxreal_0(k6_numbers,k1_funct_1(X52,k1_algstr_0(X51,k5_struct_0(X51),esk9_2(X51,X52))))\|(~m1_subset_1(X57,u1_struct_0(X51))\|(k1_funct_1(X52,X57)=k6_numbers\|k1_funct_1(X52,X57)=k1_xxreal_0))\|m1_subset_1(esk7_2(X51,X52),u1_struct_0(X51))\|~r2_hidden(k1_funct_1(X52,esk6_2(X51,X52)),k4_numbers)\|epred1_2(X52,X51))))&(((m1_subset_1(esk9_2(X51,X52),u1_struct_0(X51))\|(~m1_subset_1(X57,u1_struct_0(X51))\|(k1_funct_1(X52,X57)=k6_numbers\|k1_funct_1(X52,X57)=k1_xxreal_0))\|m1_subset_1(esk8_2(X51,X52),u1_struct_0(X51))\|~r2_hidden(k1_funct_1(X52,esk6_2(X51,X52)),k4_numbers)\|epred1_2(X52,X51))&((r1_xxreal_0(k6_numbers,k1_funct_1(X52,esk9_2(X51,X52)))\|(~m1_subset_1(X57,u1_struct_0(X51))\|(k1_funct_1(X52,X57)=k6_numbers\|k1_funct_1(X52,X57)=k1_xxreal_0))\|m1_subset_1(esk8_2(X51,X52),u1_struct_0(X51))\|~r2_hidden(k1_funct_1(X52,esk6_2(X51,X52)),k4_numbers)\|epred1_2(X52,X51))&(~r1_xxreal_0(k6_numbers,k1_funct_1(X52,k1_algstr_0(X51,k5_struct_0(X51),esk9_2(X51,X52))))\|(~m1_subset_1(X57,u1_struct_0(X51))\|(k1_funct_1(X52,X57)=k6_numbers\|k1_funct_1(X52,X57)=k1_xxreal_0))\|m1_subset_1(esk8_2(X51,X52),u1_struct_0(X51))\|~r2_hidden(k1_funct_1(X52,esk6_2(X51,X52)),k4_numbers)\|epred1_2(X52,X51))))&((m1_subset_1(esk9_2(X51,X52),u1_struct_0(X51))\|(~m1_subset_1(X57,u1_struct_0(X51))\|(k1_funct_1(X52,X57)=k6_numbers\|k1_funct_1(X52,X57)=k1_xxreal_0))\|k1_funct_1(X52,k6_algstr_0(X51,esk7_2(X51,X52),esk8_2(X51,X52)))!=k1_xxreal_3(k1_funct_1(X52,esk7_2(X51,X52)),k1_funct_1(X52,esk8_2(X51,X52)))\|~r2_hidden(k1_funct_1(X52,esk6_2(X51,X52)),k4_numbers)\|epred1_2(X52,X51))&((r1_xxreal_0(k6_numbers,k1_funct_1(X52,esk9_2(X51,X52)))\|(~m1_subset_1(X57,u1_struct_0(X51))\|(k1_funct_1(X52,X57)=k6_numbers\|k1_funct_1(X52,X57)=k1_xxreal_0))\|k1_funct_1(X52,k6_algstr_0(X51,esk7_2(X51,X52),esk8_2(X51,X52)))!=k1_xxreal_3(k1_funct_1(X52,esk7_2(X51,X52)),k1_funct_1(X52,esk8_2(X51,X52)))\|~r2_hidden(k1_funct_1(X52,esk6_2(X51,X52)),k4_numbers)\|epred1_2(X52,X51))&(~r1_xxreal_0(k6_numbers,k1_funct_1(X52,k1_algstr_0(X51,k5_struct_0(X51),esk9_2(X51,X52))))\|(~m1_subset_1(X57,u1_struct_0(X51))\|(k1_funct_1(X52,X57)=k6_numbers\|k1_funct_1(X52,X57)=k1_xxreal_0))\|k1_funct_1(X52,k6_algstr_0(X51,esk7_2(X51,X52),esk8_2(X51,X52)))!=k1_xxreal_3(k1_funct_1(X52,esk7_2(X51,X52)),k1_funct_1(X52,esk8_2(X51,X52)))\|~r2_hidden(k1_funct_1(X52,esk6_2(X51,X52)),k4_numbers)\|epred1_2(X52,X51))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_67])])])])])])])). fof(c_0_81, plain, ![X21, X22, X23]:(v2_struct_0(X21)\|(v6_struct_0(X21)\|(~v13_algstr_0(X21)\|(~v33_algstr_0(X21)\|(~v3_group_1(X21)\|(~v4_vectsp_1(X21)\|(~v5_vectsp_1(X21)\|(~v2_rlvect_1(X21)\|(~v3_rlvect_1(X21)\|(~v4_rlvect_1(X21)\|~l6_algstr_0(X21))))))))))\|(~m1_subset_1(X22,u1_struct_0(X21))\|(~m1_subset_1(X23,u1_struct_0(X21))\|k1_vectsp_2(X21,X22,X23)=k6_algstr_0(X21,X22,k11_algstr_0(X21,X23))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d3_vectsp_2])])])])). cnf(c_0_82, plain, (k3_xxreal_3(X1,X2)=k1_xxreal_3(X1,k2_xxreal_3(X2))\|~v1_xxreal_0(X1)\|~v1_xxreal_0(X2)), inference(split_conjunct,[status(thm)],[c_0_68])). cnf(c_0_83, plain, (k2_supinf_2(X1)=k2_xxreal_3(X1)\|~m1_subset_1(X1,k7_numbers)), inference(evalgc,[status(thm)],[c_0_69])). cnf(c_0_84, plain, (k3_funct_2(u1_struct_0(X1),k7_numbers,X2,k11_algstr_0(X1,X3))=k2_supinf_2(k3_funct_2(u1_struct_0(X1),k7_numbers,X2,X3))\|X3=k4_struct_0(X1)\|v6_struct_0(X1)\|v2_struct_0(X1)\|~v3_fvaluat1(X1)\|~m1_fvaluat1(X2,X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~l6_algstr_0(X1)\|~v1_realset2(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v5_vectsp_1(X1)\|~v13_algstr_0(X1)), inference(csr,[status(thm)],[c_0_70, c_0_71])). cnf(c_0_85, plain, (m1_subset_1(k11_algstr_0(X1,X2),u1_struct_0(X1))\|~l5_algstr_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_72])). cnf(c_0_86, plain, (l5_algstr_0(X1)\|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_73])). fof(c_0_87, plain, ![X33, X34]:(~v2_membered(X33)\|(~m1_subset_1(X34,X33)\|v1_xxreal_0(X34))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc13_membered])])])). fof(c_0_88, axiom, ![X1]:(l6_algstr_0(X1)=>(v3_fvaluat1(X1)=>![X2]:((v1_funct_1(X2)&(v1_funct_2(X2,u1_struct_0(X1),k7_numbers)&(v2_fvaluat1(X2)&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X1),k7_numbers))))))=>(m1_fvaluat1(X2,X1)<=>(k1_funct_1(X2,k4_struct_0(X1))=k1_xxreal_0&epred1_2(X2,X1)))))), inference(apply_def,[status(thm)],[d8_fvaluat1, c_0_67])). cnf(c_0_89, plain, (v1_xboole_0(u1_struct_0(X1))\|m1_subset_1(k3_funct_2(u1_struct_0(X1),k7_numbers,X2,X3),k7_numbers)\|~m1_fvaluat1(X2,X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~l6_algstr_0(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_74, c_0_30]), c_0_31])). cnf(c_0_90, negated_conjecture, (k3_funct_2(u1_struct_0(esk1_0),k7_numbers,esk4_0,esk3_0)=k1_funct_1(esk4_0,esk3_0)\|~l2_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_75, c_0_76])])). cnf(c_0_91, negated_conjecture, (k4_supinf_2(k3_funct_2(u1_struct_0(esk1_0),k7_numbers,esk4_0,esk3_0),k3_funct_2(u1_struct_0(esk1_0),k7_numbers,esk4_0,esk2_0))!=k3_funct_2(u1_struct_0(esk1_0),k7_numbers,esk4_0,k1_vectsp_2(esk1_0,esk3_0,esk2_0))), inference(evalgc,[status(thm)],[c_0_77])). cnf(c_0_92, plain, (k4_supinf_2(X1,X2)=k3_xxreal_3(X1,X2)\|~m1_subset_1(X2,k7_numbers)\|~m1_subset_1(X1,k7_numbers)), inference(evalgc,[status(thm)],[c_0_78])). fof(c_0_93, plain, ![X38, X39, X40]:(v2_struct_0(X38)\|(v6_struct_0(X38)\|(~v13_algstr_0(X38)\|(~v33_algstr_0(X38)\|(~v3_group_1(X38)\|(~v4_vectsp_1(X38)\|(~v5_vectsp_1(X38)\|(~v2_rlvect_1(X38)\|(~v3_rlvect_1(X38)\|(~v4_rlvect_1(X38)\|~l6_algstr_0(X38))))))))))\|(~m1_subset_1(X39,u1_struct_0(X38))\|~m1_subset_1(X40,u1_struct_0(X38)))\|m1_subset_1(k1_vectsp_2(X38,X39,X40),u1_struct_0(X38))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k1_vectsp_2])])])). cnf(c_0_94, negated_conjecture, (k3_funct_2(u1_struct_0(esk1_0),k7_numbers,esk4_0,esk2_0)=k1_funct_1(esk4_0,esk2_0)\|~l2_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_79, c_0_76])])). cnf(c_0_95, plain, (k1_funct_1(X4,k6_algstr_0(X2,X1,X3))=k1_xxreal_3(k1_funct_1(X4,X1),k1_funct_1(X4,X3))\|~m1_subset_1(X1,u1_struct_0(X2))\|~m1_subset_1(X3,u1_struct_0(X2))\|~epred1_2(X4,X2)), inference(split_conjunct,[status(thm)],[c_0_80])). cnf(c_0_96, plain, (v2_struct_0(X1)\|v6_struct_0(X1)\|k1_vectsp_2(X1,X2,X3)=k6_algstr_0(X1,X2,k11_algstr_0(X1,X3))\|~v13_algstr_0(X1)\|~v33_algstr_0(X1)\|~v3_group_1(X1)\|~v4_vectsp_1(X1)\|~v5_vectsp_1(X1)\|~v2_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~l6_algstr_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_81])). cnf(c_0_97, plain, (k1_xxreal_3(X1,k2_xxreal_3(X2))=k3_xxreal_3(X1,X2)\|~v1_xxreal_0(X2)\|~v1_xxreal_0(X1)), inference(evalgc,[status(thm)],[c_0_82])). cnf(c_0_98, plain, (k3_funct_2(u1_struct_0(X1),k7_numbers,X2,k11_algstr_0(X1,X3))=k2_xxreal_3(k3_funct_2(u1_struct_0(X1),k7_numbers,X2,X3))\|X3=k4_struct_0(X1)\|v6_struct_0(X1)\|v2_struct_0(X1)\|~m1_subset_1(k3_funct_2(u1_struct_0(X1),k7_numbers,X2,X3),k7_numbers)\|~v3_fvaluat1(X1)\|~m1_fvaluat1(X2,X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~l6_algstr_0(X1)\|~v1_realset2(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v5_vectsp_1(X1)\|~v13_algstr_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_83, c_0_84])])). cnf(c_0_99, plain, (k3_funct_2(u1_struct_0(X1),k7_numbers,X2,k11_algstr_0(X1,X3))=k1_funct_1(X2,k11_algstr_0(X1,X3))\|v1_xboole_0(u1_struct_0(X1))\|~m1_fvaluat1(X2,X1)\|~l6_algstr_0(X1)\|~l5_algstr_0(X1)\|~m1_subset_1(X3,u1_struct_0(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_36, c_0_85])])). cnf(c_0_100, plain, (l5_algstr_0(X1)\|~l6_algstr_0(X1)), inference(evalgc,[status(thm)],[c_0_86])). cnf(c_0_101, plain, (v1_xxreal_0(X2)\|~v2_membered(X1)\|~m1_subset_1(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_87])). cnf(c_0_102, plain, (v2_membered(k7_numbers)), inference(split_conjunct,[status(thm)],[fc2_membered])). fof(c_0_103, plain, ![X18, X19]:(((k1_funct_1(X19,k4_struct_0(X18))=k1_xxreal_0\|~m1_fvaluat1(X19,X18)\|(~v1_funct_1(X19)\|(~v1_funct_2(X19,u1_struct_0(X18),k7_numbers)\|(~v2_fvaluat1(X19)\|~m1_subset_1(X19,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X18),k7_numbers))))))\|~v3_fvaluat1(X18)\|~l6_algstr_0(X18))&(epred1_2(X19,X18)\|~m1_fvaluat1(X19,X18)\|(~v1_funct_1(X19)\|(~v1_funct_2(X19,u1_struct_0(X18),k7_numbers)\|(~v2_fvaluat1(X19)\|~m1_subset_1(X19,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X18),k7_numbers))))))\|~v3_fvaluat1(X18)\|~l6_algstr_0(X18)))&(k1_funct_1(X19,k4_struct_0(X18))!=k1_xxreal_0\|~epred1_2(X19,X18)\|m1_fvaluat1(X19,X18)\|(~v1_funct_1(X19)\|(~v1_funct_2(X19,u1_struct_0(X18),k7_numbers)\|(~v2_fvaluat1(X19)\|~m1_subset_1(X19,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X18),k7_numbers))))))\|~v3_fvaluat1(X18)\|~l6_algstr_0(X18))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_88])])])])). cnf(c_0_104, negated_conjecture, (v1_xboole_0(u1_struct_0(esk1_0))\|m1_subset_1(k1_funct_1(esk4_0,esk3_0),k7_numbers)\|~l2_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89, c_0_90]), c_0_44]), c_0_37]), c_0_38])])])). cnf(c_0_105, negated_conjecture, (k3_xxreal_3(k3_funct_2(u1_struct_0(esk1_0),k7_numbers,esk4_0,esk3_0),k3_funct_2(u1_struct_0(esk1_0),k7_numbers,esk4_0,esk2_0))!=k3_funct_2(u1_struct_0(esk1_0),k7_numbers,esk4_0,k1_vectsp_2(esk1_0,esk3_0,esk2_0))\|~m1_subset_1(k3_funct_2(u1_struct_0(esk1_0),k7_numbers,esk4_0,esk2_0),k7_numbers)\|~m1_subset_1(k3_funct_2(u1_struct_0(esk1_0),k7_numbers,esk4_0,esk3_0),k7_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_91, c_0_92])])). cnf(c_0_106, plain, (v2_struct_0(X1)\|v6_struct_0(X1)\|m1_subset_1(k1_vectsp_2(X1,X2,X3),u1_struct_0(X1))\|~v13_algstr_0(X1)\|~v33_algstr_0(X1)\|~v3_group_1(X1)\|~v4_vectsp_1(X1)\|~v5_vectsp_1(X1)\|~v2_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~l6_algstr_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_93])). cnf(c_0_107, negated_conjecture, (v1_xboole_0(u1_struct_0(esk1_0))\|m1_subset_1(k1_funct_1(esk4_0,esk2_0),k7_numbers)\|~l2_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89, c_0_94]), c_0_44]), c_0_40]), c_0_38])])])). cnf(c_0_108, plain, (k1_funct_1(X4,k6_algstr_0(X2,X1,X3))=k1_xxreal_3(k1_funct_1(X4,X1),k1_funct_1(X4,X3))\|~epred1_2(X4,X2)\|~m1_subset_1(X3,u1_struct_0(X2))\|~m1_subset_1(X1,u1_struct_0(X2))), inference(evalgc,[status(thm)],[c_0_95])). cnf(c_0_109, plain, (k6_algstr_0(X1,X2,k11_algstr_0(X1,X3))=k1_vectsp_2(X1,X2,X3)\|v2_struct_0(X1)\|v6_struct_0(X1)\|~v13_algstr_0(X1)\|~v3_group_1(X1)\|~v5_vectsp_1(X1)\|~v2_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~l6_algstr_0(X1)\|~v33_algstr_0(X1)\|~v4_vectsp_1(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_96])). cnf(c_0_110, plain, (k1_xxreal_3(X1,k3_funct_2(u1_struct_0(X2),k7_numbers,X3,k11_algstr_0(X2,X4)))=k3_xxreal_3(X1,k3_funct_2(u1_struct_0(X2),k7_numbers,X3,X4))\|X4=k4_struct_0(X2)\|v6_struct_0(X2)\|v2_struct_0(X2)\|~v1_xxreal_0(k3_funct_2(u1_struct_0(X2),k7_numbers,X3,X4))\|~v1_xxreal_0(X1)\|~v3_fvaluat1(X2)\|~m1_fvaluat1(X3,X2)\|~m1_subset_1(k3_funct_2(u1_struct_0(X2),k7_numbers,X3,X4),k7_numbers)\|~m1_subset_1(X4,u1_struct_0(X2))\|~l6_algstr_0(X2)\|~v1_realset2(X2)\|~v4_rlvect_1(X2)\|~v3_rlvect_1(X2)\|~v2_rlvect_1(X2)\|~v5_vectsp_1(X2)\|~v13_algstr_0(X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_97, c_0_98])])). cnf(c_0_111, plain, (k3_funct_2(u1_struct_0(X1),k7_numbers,X2,k11_algstr_0(X1,X3))=k1_funct_1(X2,k11_algstr_0(X1,X3))\|v1_xboole_0(u1_struct_0(X1))\|~m1_fvaluat1(X2,X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~l6_algstr_0(X1)), inference(csr,[status(thm)],[c_0_99, c_0_100])). cnf(c_0_112, plain, (v1_xxreal_0(X2)\|~v2_membered(X1)\|~m1_subset_1(X2,X1)), inference(evalgc,[status(thm)],[c_0_101])). cnf(c_0_113, plain, (v2_membered(k7_numbers)), inference(evalgc,[status(thm)],[c_0_102])). cnf(c_0_114, plain, (epred1_2(X1,X2)\|~m1_fvaluat1(X1,X2)\|~v1_funct_1(X1)\|~v1_funct_2(X1,u1_struct_0(X2),k7_numbers)\|~v2_fvaluat1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X2),k7_numbers)))\|~v3_fvaluat1(X2)\|~l6_algstr_0(X2)), inference(split_conjunct,[status(thm)],[c_0_103])). cnf(c_0_115, plain, (v2_fvaluat1(X1)\|~m1_fvaluat1(X1,X2)\|~l6_algstr_0(X2)), inference(split_conjunct,[status(thm)],[c_0_20])). cnf(c_0_116, negated_conjecture, (m1_subset_1(k1_funct_1(esk4_0,esk3_0),k7_numbers)\|~l1_struct_0(esk1_0)\|~l2_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_51, c_0_104]), c_0_53])])). cnf(c_0_117, negated_conjecture, (k3_xxreal_3(k1_funct_1(esk4_0,esk3_0),k3_funct_2(u1_struct_0(esk1_0),k7_numbers,esk4_0,esk2_0))!=k3_funct_2(u1_struct_0(esk1_0),k7_numbers,esk4_0,k1_vectsp_2(esk1_0,esk3_0,esk2_0))\|~m1_subset_1(k3_funct_2(u1_struct_0(esk1_0),k7_numbers,esk4_0,esk2_0),k7_numbers)\|~m1_subset_1(k1_funct_1(esk4_0,esk3_0),k7_numbers)\|~l2_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_105, c_0_90])])). cnf(c_0_118, plain, (v2_struct_0(X1)\|v6_struct_0(X1)\|m1_subset_1(k1_vectsp_2(X1,X2,X3),u1_struct_0(X1))\|~v13_algstr_0(X1)\|~v3_group_1(X1)\|~v5_vectsp_1(X1)\|~v2_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~l6_algstr_0(X1)\|~v33_algstr_0(X1)\|~v4_vectsp_1(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_106])). cnf(c_0_119, negated_conjecture, (v4_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_28])). cnf(c_0_120, negated_conjecture, (v3_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_28])). cnf(c_0_121, negated_conjecture, (v2_rlvect_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_28])). cnf(c_0_122, negated_conjecture, (v5_vectsp_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_28])). cnf(c_0_123, negated_conjecture, (v3_group_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_28])). cnf(c_0_124, negated_conjecture, (v13_algstr_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_28])). cnf(c_0_125, negated_conjecture, (~v6_struct_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_28])). cnf(c_0_126, negated_conjecture, (m1_subset_1(k1_funct_1(esk4_0,esk2_0),k7_numbers)\|~l1_struct_0(esk1_0)\|~l2_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_51, c_0_107]), c_0_53])])). cnf(c_0_127, plain, (k1_xxreal_3(k1_funct_1(X1,X3),k1_funct_1(X1,k11_algstr_0(X2,X4)))=k1_funct_1(X1,k1_vectsp_2(X2,X3,X4))\|v6_struct_0(X2)\|v2_struct_0(X2)\|~epred1_2(X1,X2)\|~m1_subset_1(k11_algstr_0(X2,X4),u1_struct_0(X2))\|~m1_subset_1(X3,u1_struct_0(X2))\|~v4_vectsp_1(X2)\|~v33_algstr_0(X2)\|~m1_subset_1(X4,u1_struct_0(X2))\|~l6_algstr_0(X2)\|~v4_rlvect_1(X2)\|~v3_rlvect_1(X2)\|~v2_rlvect_1(X2)\|~v5_vectsp_1(X2)\|~v3_group_1(X2)\|~v13_algstr_0(X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_108, c_0_109])])). cnf(c_0_128, plain, (k3_xxreal_3(X1,k3_funct_2(u1_struct_0(X2),k7_numbers,X3,X4))=k1_xxreal_3(X1,k1_funct_1(X3,k11_algstr_0(X2,X4)))\|X4=k4_struct_0(X2)\|v6_struct_0(X2)\|v2_struct_0(X2)\|v1_xboole_0(u1_struct_0(X2))\|~v1_xxreal_0(k3_funct_2(u1_struct_0(X2),k7_numbers,X3,X4))\|~v1_xxreal_0(X1)\|~v3_fvaluat1(X2)\|~m1_fvaluat1(X3,X2)\|~m1_subset_1(k3_funct_2(u1_struct_0(X2),k7_numbers,X3,X4),k7_numbers)\|~m1_subset_1(X4,u1_struct_0(X2))\|~l6_algstr_0(X2)\|~v1_realset2(X2)\|~v4_rlvect_1(X2)\|~v3_rlvect_1(X2)\|~v2_rlvect_1(X2)\|~v5_vectsp_1(X2)\|~v13_algstr_0(X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_110, c_0_111])])). cnf(c_0_129, plain, (v1_xxreal_0(k3_funct_2(u1_struct_0(X1),k7_numbers,X2,X3))\|v1_xboole_0(u1_struct_0(X1))\|~m1_fvaluat1(X2,X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~l6_algstr_0(X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112, c_0_89]), c_0_113])])])). cnf(c_0_130, negated_conjecture, (v3_fvaluat1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_28])). cnf(c_0_131, negated_conjecture, (v1_realset2(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_28])). cnf(c_0_132, negated_conjecture, (esk2_0!=k4_struct_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_28])). cnf(c_0_133, plain, (epred1_2(X1,X2)\|~l6_algstr_0(X2)\|~v3_fvaluat1(X2)\|~v1_funct_1(X1)\|~v2_fvaluat1(X1)\|~m1_fvaluat1(X1,X2)\|~v1_funct_2(X1,u1_struct_0(X2),k7_numbers)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X2),k7_numbers)))), inference(evalgc,[status(thm)],[c_0_114])). cnf(c_0_134, plain, (v2_fvaluat1(X1)\|~l6_algstr_0(X2)\|~m1_fvaluat1(X1,X2)), inference(evalgc,[status(thm)],[c_0_115])). cnf(c_0_135, negated_conjecture, (m1_subset_1(k1_funct_1(esk4_0,esk3_0),k7_numbers)\|~l2_algstr_0(esk1_0)\|~l1_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_116, c_0_63])])). cnf(c_0_136, plain, (l2_algstr_0(X1)\|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_73])). cnf(c_0_137, negated_conjecture, (k3_funct_2(u1_struct_0(esk1_0),k7_numbers,esk4_0,k1_vectsp_2(esk1_0,esk3_0,esk2_0))!=k3_xxreal_3(k1_funct_1(esk4_0,esk3_0),k1_funct_1(esk4_0,esk2_0))\|~l2_algstr_0(esk1_0)\|~m1_subset_1(k1_funct_1(esk4_0,esk2_0),k7_numbers)\|~m1_subset_1(k1_funct_1(esk4_0,esk3_0),k7_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_117, c_0_94])])). cnf(c_0_138, plain, (k3_funct_2(u1_struct_0(X1),k7_numbers,X2,k1_vectsp_2(X1,X3,X4))=k1_funct_1(X2,k1_vectsp_2(X1,X3,X4))\|v1_xboole_0(u1_struct_0(X1))\|v6_struct_0(X1)\|v2_struct_0(X1)\|~m1_fvaluat1(X2,X1)\|~l6_algstr_0(X1)\|~v4_vectsp_1(X1)\|~v33_algstr_0(X1)\|~m1_subset_1(X4,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v5_vectsp_1(X1)\|~v3_group_1(X1)\|~v13_algstr_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_36, c_0_118])])). cnf(c_0_139, negated_conjecture, (v4_rlvect_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_119])). cnf(c_0_140, negated_conjecture, (v3_rlvect_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_120])). cnf(c_0_141, negated_conjecture, (v2_rlvect_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_121])). cnf(c_0_142, negated_conjecture, (v5_vectsp_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_122])). cnf(c_0_143, negated_conjecture, (v3_group_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_123])). cnf(c_0_144, negated_conjecture, (v13_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_124])). cnf(c_0_145, negated_conjecture, (~v6_struct_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_125])). cnf(c_0_146, negated_conjecture, (m1_subset_1(k1_funct_1(esk4_0,esk2_0),k7_numbers)\|~l2_algstr_0(esk1_0)\|~l1_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_126, c_0_63])])). cnf(c_0_147, plain, (k1_xxreal_3(k1_funct_1(X1,X2),k1_funct_1(X1,k11_algstr_0(X3,X4)))=k1_funct_1(X1,k1_vectsp_2(X3,X2,X4))\|v6_struct_0(X3)\|v2_struct_0(X3)\|~epred1_2(X1,X3)\|~v4_vectsp_1(X3)\|~v33_algstr_0(X3)\|~m1_subset_1(X2,u1_struct_0(X3))\|~m1_subset_1(X4,u1_struct_0(X3))\|~l6_algstr_0(X3)\|~v4_rlvect_1(X3)\|~v3_rlvect_1(X3)\|~v2_rlvect_1(X3)\|~v5_vectsp_1(X3)\|~v3_group_1(X3)\|~v13_algstr_0(X3)\|~l5_algstr_0(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_127, c_0_85])])). cnf(c_0_148, plain, (k3_xxreal_3(X1,k3_funct_2(u1_struct_0(X2),k7_numbers,X3,X4))=k1_xxreal_3(X1,k1_funct_1(X3,k11_algstr_0(X2,X4)))\|X4=k4_struct_0(X2)\|v1_xboole_0(u1_struct_0(X2))\|v6_struct_0(X2)\|v2_struct_0(X2)\|~v1_xxreal_0(X1)\|~v3_fvaluat1(X2)\|~m1_fvaluat1(X3,X2)\|~m1_subset_1(X4,u1_struct_0(X2))\|~l6_algstr_0(X2)\|~v1_realset2(X2)\|~v4_rlvect_1(X2)\|~v3_rlvect_1(X2)\|~v2_rlvect_1(X2)\|~v5_vectsp_1(X2)\|~v13_algstr_0(X2)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_128, c_0_89]), c_0_129])). cnf(c_0_149, negated_conjecture, (v3_fvaluat1(esk1_0)), inference(evalgc,[status(thm)],[c_0_130])). cnf(c_0_150, negated_conjecture, (v1_realset2(esk1_0)), inference(evalgc,[status(thm)],[c_0_131])). cnf(c_0_151, negated_conjecture, (k4_struct_0(esk1_0)!=esk2_0), inference(evalgc,[status(thm)],[c_0_132])). cnf(c_0_152, plain, (epred1_2(X1,X2)\|~v3_fvaluat1(X2)\|~m1_fvaluat1(X1,X2)\|~l6_algstr_0(X2)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_133, c_0_25]), c_0_30]), c_0_31]), c_0_134])). cnf(c_0_153, negated_conjecture, (m1_subset_1(k1_funct_1(esk4_0,esk3_0),k7_numbers)\|~l2_algstr_0(esk1_0)), inference(csr,[status(thm)],[c_0_135, c_0_76])). cnf(c_0_154, plain, (l2_algstr_0(X1)\|~l6_algstr_0(X1)), inference(evalgc,[status(thm)],[c_0_136])). cnf(c_0_155, negated_conjecture, (v1_xboole_0(u1_struct_0(esk1_0))\|k3_xxreal_3(k1_funct_1(esk4_0,esk3_0),k1_funct_1(esk4_0,esk2_0))!=k1_funct_1(esk4_0,k1_vectsp_2(esk1_0,esk3_0,esk2_0))\|~l2_algstr_0(esk1_0)\|~m1_subset_1(k1_funct_1(esk4_0,esk2_0),k7_numbers)\|~m1_subset_1(k1_funct_1(esk4_0,esk3_0),k7_numbers)\|~v4_vectsp_1(esk1_0)\|~v33_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137, c_0_138]), c_0_44]), c_0_40]), c_0_37]), c_0_38]), c_0_139]), c_0_140]), c_0_141]), c_0_142]), c_0_143]), c_0_144])]), c_0_145]), c_0_53])])). cnf(c_0_156, negated_conjecture, (m1_subset_1(k1_funct_1(esk4_0,esk2_0),k7_numbers)\|~l2_algstr_0(esk1_0)), inference(csr,[status(thm)],[c_0_146, c_0_76])). cnf(c_0_157, plain, (k1_xxreal_3(k1_funct_1(X1,X2),k1_funct_1(X1,k11_algstr_0(X3,X4)))=k1_funct_1(X1,k1_vectsp_2(X3,X2,X4))\|v6_struct_0(X3)\|v2_struct_0(X3)\|~epred1_2(X1,X3)\|~v4_vectsp_1(X3)\|~v33_algstr_0(X3)\|~m1_subset_1(X2,u1_struct_0(X3))\|~m1_subset_1(X4,u1_struct_0(X3))\|~l6_algstr_0(X3)\|~v4_rlvect_1(X3)\|~v3_rlvect_1(X3)\|~v2_rlvect_1(X3)\|~v5_vectsp_1(X3)\|~v3_group_1(X3)\|~v13_algstr_0(X3)), inference(csr,[status(thm)],[c_0_147, c_0_100])). cnf(c_0_158, negated_conjecture, (k1_xxreal_3(X1,k1_funct_1(esk4_0,k11_algstr_0(esk1_0,esk2_0)))=k3_xxreal_3(X1,k1_funct_1(esk4_0,esk2_0))\|v1_xboole_0(u1_struct_0(esk1_0))\|~v1_xxreal_0(X1)\|~l2_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148, c_0_94]), c_0_149]), c_0_44]), c_0_40]), c_0_38]), c_0_150]), c_0_139]), c_0_140]), c_0_141]), c_0_142]), c_0_144])]), c_0_151]), c_0_145]), c_0_53])])). cnf(c_0_159, negated_conjecture, (epred1_2(esk4_0,esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152, c_0_44]), c_0_149]), c_0_38])])])). cnf(c_0_160, negated_conjecture, (m1_subset_1(k1_funct_1(esk4_0,esk3_0),k7_numbers)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153, c_0_154]), c_0_38])])])). cnf(c_0_161, negated_conjecture, (v1_xboole_0(u1_struct_0(esk1_0))\|k3_xxreal_3(k1_funct_1(esk4_0,esk3_0),k1_funct_1(esk4_0,esk2_0))!=k1_funct_1(esk4_0,k1_vectsp_2(esk1_0,esk3_0,esk2_0))\|~l2_algstr_0(esk1_0)\|~v4_vectsp_1(esk1_0)\|~v33_algstr_0(esk1_0)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_155, c_0_153]), c_0_156])). cnf(c_0_162, plain, (k3_xxreal_3(k1_funct_1(esk4_0,X1),k1_funct_1(esk4_0,esk2_0))=k1_funct_1(esk4_0,k1_vectsp_2(esk1_0,X1,esk2_0))\|v1_xboole_0(u1_struct_0(esk1_0))\|~v4_vectsp_1(esk1_0)\|~v33_algstr_0(esk1_0)\|~m1_subset_1(X1,u1_struct_0(esk1_0))\|~v1_xxreal_0(k1_funct_1(esk4_0,X1))\|~l2_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157, c_0_158]), c_0_159]), c_0_40]), c_0_38]), c_0_139]), c_0_140]), c_0_141]), c_0_142]), c_0_143]), c_0_144])]), c_0_145]), c_0_53])])). cnf(c_0_163, negated_conjecture, (v1_xxreal_0(k1_funct_1(esk4_0,esk3_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112, c_0_160]), c_0_113])])])). cnf(c_0_164, negated_conjecture, (v1_xboole_0(u1_struct_0(esk1_0))\|~l2_algstr_0(esk1_0)\|~v4_vectsp_1(esk1_0)\|~v33_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161, c_0_162]), c_0_163]), c_0_37])])])). cnf(c_0_165, negated_conjecture, (~l1_struct_0(esk1_0)\|~l2_algstr_0(esk1_0)\|~v4_vectsp_1(esk1_0)\|~v33_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_51, c_0_164]), c_0_53])])). cnf(c_0_166, negated_conjecture, (~l2_algstr_0(esk1_0)\|~v4_vectsp_1(esk1_0)\|~v33_algstr_0(esk1_0)\|~l1_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_165, c_0_63])])). cnf(c_0_167, plain, (v4_vectsp_1(X1)\|v6_struct_0(X1)\|~v13_algstr_0(X1)\|~v2_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v5_vectsp_1(X1)\|~v1_realset2(X1)\|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_49])). cnf(c_0_168, negated_conjecture, (~l2_algstr_0(esk1_0)\|~v4_vectsp_1(esk1_0)\|~v33_algstr_0(esk1_0)), inference(csr,[status(thm)],[c_0_166, c_0_76])). cnf(c_0_169, plain, (v6_struct_0(X1)\|v4_vectsp_1(X1)\|~v13_algstr_0(X1)\|~v5_vectsp_1(X1)\|~v2_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v1_realset2(X1)\|~l6_algstr_0(X1)), inference(evalgc,[status(thm)],[c_0_167])). cnf(c_0_170, plain, (v33_algstr_0(X1)\|v6_struct_0(X1)\|~v13_algstr_0(X1)\|~v2_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v5_vectsp_1(X1)\|~v1_realset2(X1)\|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_49])). cnf(c_0_171, negated_conjecture, (~l2_algstr_0(esk1_0)\|~v33_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_168, c_0_169]), c_0_38]), c_0_150]), c_0_139]), c_0_140]), c_0_141]), c_0_142]), c_0_144])]), c_0_145])])). cnf(c_0_172, plain, (v6_struct_0(X1)\|v33_algstr_0(X1)\|~v13_algstr_0(X1)\|~v5_vectsp_1(X1)\|~v2_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v4_rlvect_1(X1)\|~v1_realset2(X1)\|~l6_algstr_0(X1)), inference(evalgc,[status(thm)],[c_0_170])). cnf(c_0_173, negated_conjecture, (~l2_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_171, c_0_172]), c_0_38]), c_0_150]), c_0_139]), c_0_140]), c_0_141]), c_0_142]), c_0_144])]), c_0_145])])). cnf(c_0_174, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173, c_0_154]), c_0_38])]), ['proof']). # SZS output end CNFRefutation	reserve x, y, z, s for ext-real number; reserve i, j for Integer; reserve n, m for Nat; reserve x, y, v, u for ExtInt; reserve D for non empty doubleLoopStr, A for Subset of D; reserve K for Field-like non degenerated associative add-associative right_zeroed right_complementable distributive Abelian non empty doubleLoopStr, a, b, c for Element of K; reserve v for Valuation of K; theorem Th22: K is having_valuation & b <> 0.K implies v.(a/b) = v.a - v.b proof assume A1: K is having_valuation; assume A2: b <> 0.K; thus v.(a/b) = v.a + v.(b") by A1,Def8 .= v.a - v.b by A1,A2,Th21; end;	Convert the following ATP output trace into a readable Mizar proof.
t30_mesfun7c	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(redefinition_k12_supinf_2, axiom, ![X1, X2]:((v1_relat_1(X1)&(v1_funct_1(X1)&v2_valued_0(X1)))=>k12_supinf_2(X1,X2)=k1_funct_1(X1,X2)), file('/scratch/mptp/predsminms1/t30_mesfun7c__0', redefinition_k12_supinf_2)). fof(cc29_valued_0, axiom, ![X1]:((v1_relat_1(X1)&v5_relat_1(X1,k7_numbers))=>(v1_relat_1(X1)&v2_valued_0(X1))), file('/scratch/mptp/predsminms1/t30_mesfun7c__0', cc29_valued_0)). fof(dt_k1_mesfunc5, axiom, ![X1, X2]:((~(v1_xboole_0(X1))&(v1_funct_1(X2)&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))))=>(v1_funct_1(k1_mesfunc5(X1,X2))&m1_subset_1(k1_mesfunc5(X1,X2),k1_zfmisc_1(k2_zfmisc_1(X1,k7_numbers))))), file('/scratch/mptp/predsminms1/t30_mesfun7c__0', dt_k1_mesfunc5)). fof(d7_mesfunc5, axiom, ![X1]:(~(v1_xboole_0(X1))=>![X2]:((v1_funct_1(X2)&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers))))=>k1_mesfunc5(X1,X2)=X2)), file('/scratch/mptp/predsminms1/t30_mesfun7c__0', d7_mesfunc5)). fof(t30_mesfun7c, conjecture, ![X1]:(~(v1_xboole_0(X1))=>![X2]:((v1_funct_1(X2)&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers))))=>![X3]:((v1_funct_1(X3)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers))))=>r2_relset_1(X1,k7_numbers,k5_mesfunc1(X1,k1_mesfunc5(X1,X2),k1_mesfunc5(X1,X3)),k1_mesfunc5(X1,k20_valued_1(X1,k1_numbers,k1_numbers,X2,X3)))))), file('/scratch/mptp/predsminms1/t30_mesfun7c__0', t30_mesfun7c)). fof(dt_k11_binop_2, axiom, ![X1, X2]:((v1_xreal_0(X1)&v1_xreal_0(X2))=>m1_subset_1(k11_binop_2(X1,X2),k1_numbers)), file('/scratch/mptp/predsminms1/t30_mesfun7c__0', dt_k11_binop_2)). fof(redefinition_k11_binop_2, axiom, ![X1, X2]:((v1_xreal_0(X1)&v1_xreal_0(X2))=>k11_binop_2(X1,X2)=k3_xcmplx_0(X1,X2)), file('/scratch/mptp/predsminms1/t30_mesfun7c__0', redefinition_k11_binop_2)). fof(t3_arithm, axiom, ![X1]:(v1_xcmplx_0(X1)=>k3_xcmplx_0(np__1,X1)=X1), file('/scratch/mptp/predsminms1/t30_mesfun7c__0', t3_arithm)). fof(cc3_xreal_0, axiom, ![X1]:(v1_xreal_0(X1)=>v1_xcmplx_0(X1)), file('/scratch/mptp/predsminms1/t30_mesfun7c__0', cc3_xreal_0)). fof(cc14_membered, axiom, ![X1]:(v3_membered(X1)=>![X2]:(m1_subset_1(X2,X1)=>v1_xreal_0(X2))), file('/scratch/mptp/predsminms1/t30_mesfun7c__0', cc14_membered)). fof(d5_mesfunc1, axiom, ![X1]:(~(v1_xboole_0(X1))=>![X2]:((v1_relat_1(X2)&(v4_relat_1(X2,X1)&(v5_relat_1(X2,k7_numbers)&v1_funct_1(X2))))=>![X3]:((v1_relat_1(X3)&(v4_relat_1(X3,X1)&(v5_relat_1(X3,k7_numbers)&v1_funct_1(X3))))=>![X4]:((v1_funct_1(X4)&m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,k7_numbers))))=>(X4=k5_mesfunc1(X1,X2,X3)<=>(k9_xtuple_0(X4)=k3_xboole_0(k9_xtuple_0(X2),k9_xtuple_0(X3))&![X5]:(m1_subset_1(X5,X1)=>(r2_hidden(X5,k9_xtuple_0(X4))=>k12_supinf_2(X4,X5)=k1_extreal1(k12_supinf_2(X2,X5),k12_supinf_2(X3,X5)))))))))), file('/scratch/mptp/predsminms1/t30_mesfun7c__0', d5_mesfunc1)). fof(t1_extreal1, axiom, ![X1]:(m1_subset_1(X1,k7_numbers)=>![X2]:(m1_subset_1(X2,k7_numbers)=>![X3]:(m1_subset_1(X3,k1_numbers)=>![X4]:(m1_subset_1(X4,k1_numbers)=>((X1=X3&X2=X4)=>k1_extreal1(X1,X2)=k11_binop_2(X3,X4)))))), file('/scratch/mptp/predsminms1/t30_mesfun7c__0', t1_extreal1)). fof(dt_k12_supinf_2, axiom, ![X1, X2]:((v1_relat_1(X1)&(v1_funct_1(X1)&v2_valued_0(X1)))=>m1_subset_1(k12_supinf_2(X1,X2),k7_numbers)), file('/scratch/mptp/predsminms1/t30_mesfun7c__0', dt_k12_supinf_2)). fof(spc1_numerals, axiom, ((v2_xxreal_0(np__1)&m2_subset_1(np__1,k1_numbers,k5_numbers))&(m1_subset_1(np__1,k5_numbers)&m1_subset_1(np__1,k1_numbers))), file('/scratch/mptp/predsminms1/t30_mesfun7c__0', spc1_numerals)). fof(fc3_membered, axiom, v3_membered(k1_numbers), file('/scratch/mptp/predsminms1/t30_mesfun7c__0', fc3_membered)). fof(cc17_valued_0, axiom, ![X1, X2]:(v2_membered(X2)=>![X3]:(m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))=>v2_valued_0(X3))), file('/scratch/mptp/predsminms1/t30_mesfun7c__0', cc17_valued_0)). fof(cc1_relset_1, axiom, ![X1, X2, X3]:(m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))=>v1_relat_1(X3)), file('/scratch/mptp/predsminms1/t30_mesfun7c__0', cc1_relset_1)). fof(fc63_valued_0, axiom, ![X1, X2]:((v1_relat_1(X1)&(v1_funct_1(X1)&v3_valued_0(X1)))=>v1_xreal_0(k1_funct_1(X1,X2))), file('/scratch/mptp/predsminms1/t30_mesfun7c__0', fc63_valued_0)). fof(cc18_valued_0, axiom, ![X1, X2]:(v3_membered(X2)=>![X3]:(m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))=>v3_valued_0(X3))), file('/scratch/mptp/predsminms1/t30_mesfun7c__0', cc18_valued_0)). fof(fc2_membered, axiom, v2_membered(k7_numbers), file('/scratch/mptp/predsminms1/t30_mesfun7c__0', fc2_membered)). fof(cc2_relset_1, axiom, ![X1, X2, X3]:(m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))=>(v4_relat_1(X3,X1)&v5_relat_1(X3,X2))), file('/scratch/mptp/predsminms1/t30_mesfun7c__0', cc2_relset_1)). fof(d4_valued_1, axiom, ![X1]:((v1_relat_1(X1)&(v1_funct_1(X1)&v1_valued_0(X1)))=>![X2]:((v1_relat_1(X2)&(v1_funct_1(X2)&v1_valued_0(X2)))=>![X3]:((v1_relat_1(X3)&v1_funct_1(X3))=>(X3=k18_valued_1(X1,X2)<=>(k9_xtuple_0(X3)=k3_xboole_0(k9_xtuple_0(X1),k9_xtuple_0(X2))&![X4]:(r2_hidden(X4,k9_xtuple_0(X3))=>k1_funct_1(X3,X4)=k3_xcmplx_0(k1_funct_1(X1,X4),k1_funct_1(X2,X4)))))))), file('/scratch/mptp/predsminms1/t30_mesfun7c__0', d4_valued_1)). fof(redefinition_k20_valued_1, axiom, ![X1, X2, X3, X4, X5]:((v3_membered(X2)&(v3_membered(X3)&((v1_funct_1(X4)&m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2))))&(v1_funct_1(X5)&m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))))))=>k20_valued_1(X1,X2,X3,X4,X5)=k18_valued_1(X4,X5)), file('/scratch/mptp/predsminms1/t30_mesfun7c__0', redefinition_k20_valued_1)). fof(commutativity_k20_valued_1, axiom, ![X1, X2, X3, X4, X5]:((v3_membered(X2)&(v3_membered(X3)&((v1_funct_1(X4)&m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2))))&(v1_funct_1(X5)&m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))))))=>k20_valued_1(X1,X2,X3,X4,X5)=k20_valued_1(X1,X2,X3,X5,X4)), file('/scratch/mptp/predsminms1/t30_mesfun7c__0', commutativity_k20_valued_1)). fof(cc6_valued_0, axiom, ![X1]:((v1_relat_1(X1)&v3_valued_0(X1))=>(v1_relat_1(X1)&v1_valued_0(X1))), file('/scratch/mptp/predsminms1/t30_mesfun7c__0', cc6_valued_0)). fof(dt_k20_valued_1, axiom, ![X1, X2, X3, X4, X5]:((v3_membered(X2)&(v3_membered(X3)&((v1_funct_1(X4)&m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2))))&(v1_funct_1(X5)&m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))))))=>(v1_funct_1(k20_valued_1(X1,X2,X3,X4,X5))&m1_subset_1(k20_valued_1(X1,X2,X3,X4,X5),k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers))))), file('/scratch/mptp/predsminms1/t30_mesfun7c__0', dt_k20_valued_1)). fof(dt_k18_valued_1, axiom, ![X1, X2]:(((v1_relat_1(X1)&(v1_funct_1(X1)&v1_valued_0(X1)))&(v1_relat_1(X2)&(v1_funct_1(X2)&v1_valued_0(X2))))=>(v1_relat_1(k18_valued_1(X1,X2))&v1_funct_1(k18_valued_1(X1,X2)))), file('/scratch/mptp/predsminms1/t30_mesfun7c__0', dt_k18_valued_1)). fof(commutativity_k3_xboole_0, axiom, ![X1, X2]:k3_xboole_0(X1,X2)=k3_xboole_0(X2,X1), file('/scratch/mptp/predsminms1/t30_mesfun7c__0', commutativity_k3_xboole_0)). fof(reflexivity_r2_relset_1, axiom, ![X1, X2, X3, X4]:((m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))&m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2))))=>r2_relset_1(X1,X2,X3,X3)), file('/scratch/mptp/predsminms1/t30_mesfun7c__0', reflexivity_r2_relset_1)). fof(rc1_partfun1, axiom, ![X1, X2]:?[X3]:(m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))&(v1_relat_1(X3)&(v4_relat_1(X3,X1)&(v5_relat_1(X3,X2)&v1_funct_1(X3))))), file('/scratch/mptp/predsminms1/t30_mesfun7c__0', rc1_partfun1)). fof(c_0_30, plain, ![X15, X16]:(~v1_relat_1(X15)\|(~v1_funct_1(X15)\|~v2_valued_0(X15))\|k12_supinf_2(X15,X16)=k1_funct_1(X15,X16)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k12_supinf_2])])). fof(c_0_31, plain, ![X17]:((v1_relat_1(X17)\|(~v1_relat_1(X17)\|~v5_relat_1(X17,k7_numbers)))&(v2_valued_0(X17)\|(~v1_relat_1(X17)\|~v5_relat_1(X17,k7_numbers)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc29_valued_0])])])). fof(c_0_32, plain, ![X44, X45]:((v1_funct_1(k1_mesfunc5(X44,X45))\|(v1_xboole_0(X44)\|(~v1_funct_1(X45)\|~m1_subset_1(X45,k1_zfmisc_1(k2_zfmisc_1(X44,k1_numbers))))))&(m1_subset_1(k1_mesfunc5(X44,X45),k1_zfmisc_1(k2_zfmisc_1(X44,k7_numbers)))\|(v1_xboole_0(X44)\|(~v1_funct_1(X45)\|~m1_subset_1(X45,k1_zfmisc_1(k2_zfmisc_1(X44,k1_numbers))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k1_mesfunc5])])])])). fof(c_0_33, plain, ![X68, X69]:(v1_xboole_0(X68)\|(~v1_funct_1(X69)\|~m1_subset_1(X69,k1_zfmisc_1(k2_zfmisc_1(X68,k1_numbers)))\|k1_mesfunc5(X68,X69)=X69)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d7_mesfunc5])])])])). fof(c_0_34, negated_conjecture, ~(![X1]:(~(v1_xboole_0(X1))=>![X2]:((v1_funct_1(X2)&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers))))=>![X3]:((v1_funct_1(X3)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers))))=>r2_relset_1(X1,k7_numbers,k5_mesfunc1(X1,k1_mesfunc5(X1,X2),k1_mesfunc5(X1,X3)),k1_mesfunc5(X1,k20_valued_1(X1,k1_numbers,k1_numbers,X2,X3))))))), inference(assume_negation,[status(cth)],[t30_mesfun7c])). fof(c_0_35, plain, ![X30, X31]:(~v1_xreal_0(X30)\|~v1_xreal_0(X31)\|m1_subset_1(k11_binop_2(X30,X31),k1_numbers)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k11_binop_2])])). fof(c_0_36, plain, ![X22, X23]:(~v1_xreal_0(X22)\|~v1_xreal_0(X23)\|k11_binop_2(X22,X23)=k3_xcmplx_0(X22,X23)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k11_binop_2])])). fof(c_0_37, plain, ![X39]:(~v1_xcmplx_0(X39)\|k3_xcmplx_0(np__1,X39)=X39), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_arithm])])). fof(c_0_38, plain, ![X40]:(~v1_xreal_0(X40)\|v1_xcmplx_0(X40)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc3_xreal_0])])). fof(c_0_39, plain, ![X32, X33]:(~v3_membered(X32)\|(~m1_subset_1(X33,X32)\|v1_xreal_0(X33))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc14_membered])])])). fof(c_0_40, plain, ![X9, X10, X11, X12, X13]:(((k9_xtuple_0(X12)=k3_xboole_0(k9_xtuple_0(X10),k9_xtuple_0(X11))\|X12!=k5_mesfunc1(X9,X10,X11)\|(~v1_funct_1(X12)\|~m1_subset_1(X12,k1_zfmisc_1(k2_zfmisc_1(X9,k7_numbers))))\|(~v1_relat_1(X11)\|(~v4_relat_1(X11,X9)\|(~v5_relat_1(X11,k7_numbers)\|~v1_funct_1(X11))))\|(~v1_relat_1(X10)\|(~v4_relat_1(X10,X9)\|(~v5_relat_1(X10,k7_numbers)\|~v1_funct_1(X10))))\|v1_xboole_0(X9))&(~m1_subset_1(X13,X9)\|(~r2_hidden(X13,k9_xtuple_0(X12))\|k12_supinf_2(X12,X13)=k1_extreal1(k12_supinf_2(X10,X13),k12_supinf_2(X11,X13)))\|X12!=k5_mesfunc1(X9,X10,X11)\|(~v1_funct_1(X12)\|~m1_subset_1(X12,k1_zfmisc_1(k2_zfmisc_1(X9,k7_numbers))))\|(~v1_relat_1(X11)\|(~v4_relat_1(X11,X9)\|(~v5_relat_1(X11,k7_numbers)\|~v1_funct_1(X11))))\|(~v1_relat_1(X10)\|(~v4_relat_1(X10,X9)\|(~v5_relat_1(X10,k7_numbers)\|~v1_funct_1(X10))))\|v1_xboole_0(X9)))&((m1_subset_1(esk4_4(X9,X10,X11,X12),X9)\|k9_xtuple_0(X12)!=k3_xboole_0(k9_xtuple_0(X10),k9_xtuple_0(X11))\|X12=k5_mesfunc1(X9,X10,X11)\|(~v1_funct_1(X12)\|~m1_subset_1(X12,k1_zfmisc_1(k2_zfmisc_1(X9,k7_numbers))))\|(~v1_relat_1(X11)\|(~v4_relat_1(X11,X9)\|(~v5_relat_1(X11,k7_numbers)\|~v1_funct_1(X11))))\|(~v1_relat_1(X10)\|(~v4_relat_1(X10,X9)\|(~v5_relat_1(X10,k7_numbers)\|~v1_funct_1(X10))))\|v1_xboole_0(X9))&((r2_hidden(esk4_4(X9,X10,X11,X12),k9_xtuple_0(X12))\|k9_xtuple_0(X12)!=k3_xboole_0(k9_xtuple_0(X10),k9_xtuple_0(X11))\|X12=k5_mesfunc1(X9,X10,X11)\|(~v1_funct_1(X12)\|~m1_subset_1(X12,k1_zfmisc_1(k2_zfmisc_1(X9,k7_numbers))))\|(~v1_relat_1(X11)\|(~v4_relat_1(X11,X9)\|(~v5_relat_1(X11,k7_numbers)\|~v1_funct_1(X11))))\|(~v1_relat_1(X10)\|(~v4_relat_1(X10,X9)\|(~v5_relat_1(X10,k7_numbers)\|~v1_funct_1(X10))))\|v1_xboole_0(X9))&(k12_supinf_2(X12,esk4_4(X9,X10,X11,X12))!=k1_extreal1(k12_supinf_2(X10,esk4_4(X9,X10,X11,X12)),k12_supinf_2(X11,esk4_4(X9,X10,X11,X12)))\|k9_xtuple_0(X12)!=k3_xboole_0(k9_xtuple_0(X10),k9_xtuple_0(X11))\|X12=k5_mesfunc1(X9,X10,X11)\|(~v1_funct_1(X12)\|~m1_subset_1(X12,k1_zfmisc_1(k2_zfmisc_1(X9,k7_numbers))))\|(~v1_relat_1(X11)\|(~v4_relat_1(X11,X9)\|(~v5_relat_1(X11,k7_numbers)\|~v1_funct_1(X11))))\|(~v1_relat_1(X10)\|(~v4_relat_1(X10,X9)\|(~v5_relat_1(X10,k7_numbers)\|~v1_funct_1(X10))))\|v1_xboole_0(X9))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d5_mesfunc1])])])])])])). cnf(c_0_41, plain, (k12_supinf_2(X1,X2)=k1_funct_1(X1,X2)\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v2_valued_0(X1)), inference(split_conjunct,[status(thm)],[c_0_30])). cnf(c_0_42, plain, (v2_valued_0(X1)\|~v1_relat_1(X1)\|~v5_relat_1(X1,k7_numbers)), inference(split_conjunct,[status(thm)],[c_0_31])). fof(c_0_43, plain, ![X18, X19, X20, X21]:(~m1_subset_1(X18,k7_numbers)\|(~m1_subset_1(X19,k7_numbers)\|(~m1_subset_1(X20,k1_numbers)\|(~m1_subset_1(X21,k1_numbers)\|(X18!=X20\|X19!=X21\|k1_extreal1(X18,X19)=k11_binop_2(X20,X21)))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_extreal1])])])). fof(c_0_44, plain, ![X37, X38]:(~v1_relat_1(X37)\|(~v1_funct_1(X37)\|~v2_valued_0(X37))\|m1_subset_1(k12_supinf_2(X37,X38),k7_numbers)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k12_supinf_2])])). cnf(c_0_45, plain, (m1_subset_1(k1_mesfunc5(X1,X2),k1_zfmisc_1(k2_zfmisc_1(X1,k7_numbers)))\|v1_xboole_0(X1)\|~v1_funct_1(X2)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))), inference(split_conjunct,[status(thm)],[c_0_32])). cnf(c_0_46, plain, (v1_xboole_0(X1)\|k1_mesfunc5(X1,X2)=X2\|~v1_funct_1(X2)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))), inference(split_conjunct,[status(thm)],[c_0_33])). fof(c_0_47, negated_conjecture, (~v1_xboole_0(esk1_0)&((v1_funct_1(esk2_0)&m1_subset_1(esk2_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers))))&((v1_funct_1(esk3_0)&m1_subset_1(esk3_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers))))&~r2_relset_1(esk1_0,k7_numbers,k5_mesfunc1(esk1_0,k1_mesfunc5(esk1_0,esk2_0),k1_mesfunc5(esk1_0,esk3_0)),k1_mesfunc5(esk1_0,k20_valued_1(esk1_0,k1_numbers,k1_numbers,esk2_0,esk3_0)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_34])])])])). cnf(c_0_48, plain, (m1_subset_1(k11_binop_2(X1,X2),k1_numbers)\|~v1_xreal_0(X1)\|~v1_xreal_0(X2)), inference(split_conjunct,[status(thm)],[c_0_35])). cnf(c_0_49, plain, (k11_binop_2(X1,X2)=k3_xcmplx_0(X1,X2)\|~v1_xreal_0(X1)\|~v1_xreal_0(X2)), inference(split_conjunct,[status(thm)],[c_0_36])). cnf(c_0_50, plain, (k3_xcmplx_0(np__1,X1)=X1\|~v1_xcmplx_0(X1)), inference(split_conjunct,[status(thm)],[c_0_37])). cnf(c_0_51, plain, (v1_xcmplx_0(X1)\|~v1_xreal_0(X1)), inference(split_conjunct,[status(thm)],[c_0_38])). cnf(c_0_52, plain, (v1_xreal_0(X2)\|~v3_membered(X1)\|~m1_subset_1(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_39])). cnf(c_0_53, plain, (m1_subset_1(np__1,k1_numbers)), inference(split_conjunct,[status(thm)],[spc1_numerals])). cnf(c_0_54, plain, (v3_membered(k1_numbers)), inference(split_conjunct,[status(thm)],[fc3_membered])). cnf(c_0_55, plain, (X1=k5_mesfunc1(X2,X3,X4)\|v1_xboole_0(X2)\|k12_supinf_2(X1,esk4_4(X2,X3,X4,X1))!=k1_extreal1(k12_supinf_2(X3,esk4_4(X2,X3,X4,X1)),k12_supinf_2(X4,esk4_4(X2,X3,X4,X1)))\|k9_xtuple_0(X1)!=k3_xboole_0(k9_xtuple_0(X3),k9_xtuple_0(X4))\|~v1_funct_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,k7_numbers)))\|~v1_relat_1(X4)\|~v4_relat_1(X4,X2)\|~v5_relat_1(X4,k7_numbers)\|~v1_funct_1(X4)\|~v1_relat_1(X3)\|~v4_relat_1(X3,X2)\|~v5_relat_1(X3,k7_numbers)\|~v1_funct_1(X3)), inference(split_conjunct,[status(thm)],[c_0_40])). cnf(c_0_56, plain, (k12_supinf_2(X1,X2)=k1_funct_1(X1,X2)\|~v1_funct_1(X1)\|~v1_relat_1(X1)\|~v2_valued_0(X1)), inference(evalgc,[status(thm)],[c_0_41])). cnf(c_0_57, plain, (v2_valued_0(X1)\|~v1_relat_1(X1)\|~v5_relat_1(X1,k7_numbers)), inference(evalgc,[status(thm)],[c_0_42])). cnf(c_0_58, plain, (k1_extreal1(X1,X2)=k11_binop_2(X3,X4)\|~m1_subset_1(X1,k7_numbers)\|~m1_subset_1(X2,k7_numbers)\|~m1_subset_1(X3,k1_numbers)\|~m1_subset_1(X4,k1_numbers)\|X1!=X3\|X2!=X4), inference(split_conjunct,[status(thm)],[c_0_43])). cnf(c_0_59, plain, (m1_subset_1(k12_supinf_2(X1,X2),k7_numbers)\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v2_valued_0(X1)), inference(split_conjunct,[status(thm)],[c_0_44])). fof(c_0_60, plain, ![X46, X47, X48]:(~v2_membered(X47)\|(~m1_subset_1(X48,k1_zfmisc_1(k2_zfmisc_1(X46,X47)))\|v2_valued_0(X48))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc17_valued_0])])])). cnf(c_0_61, plain, (v1_xboole_0(X1)\|m1_subset_1(k1_mesfunc5(X1,X2),k1_zfmisc_1(k2_zfmisc_1(X1,k7_numbers)))\|~v1_funct_1(X2)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))), inference(evalgc,[status(thm)],[c_0_45])). cnf(c_0_62, plain, (k1_mesfunc5(X1,X2)=X2\|v1_xboole_0(X1)\|~v1_funct_1(X2)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))), inference(evalgc,[status(thm)],[c_0_46])). cnf(c_0_63, negated_conjecture, (m1_subset_1(esk3_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))), inference(split_conjunct,[status(thm)],[c_0_47])). cnf(c_0_64, negated_conjecture, (v1_funct_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_47])). cnf(c_0_65, negated_conjecture, (~v1_xboole_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_47])). fof(c_0_66, plain, ![X34, X35, X36]:(~m1_subset_1(X36,k1_zfmisc_1(k2_zfmisc_1(X34,X35)))\|v1_relat_1(X36)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relset_1])])). cnf(c_0_67, plain, (m1_subset_1(k11_binop_2(X1,X2),k1_numbers)\|~v1_xreal_0(X2)\|~v1_xreal_0(X1)), inference(evalgc,[status(thm)],[c_0_48])). cnf(c_0_68, plain, (k11_binop_2(X1,X2)=k3_xcmplx_0(X1,X2)\|~v1_xreal_0(X2)\|~v1_xreal_0(X1)), inference(evalgc,[status(thm)],[c_0_49])). cnf(c_0_69, plain, (k3_xcmplx_0(np__1,X1)=X1\|~v1_xcmplx_0(X1)), inference(evalgc,[status(thm)],[c_0_50])). cnf(c_0_70, plain, (v1_xcmplx_0(X1)\|~v1_xreal_0(X1)), inference(evalgc,[status(thm)],[c_0_51])). cnf(c_0_71, plain, (v1_xreal_0(X2)\|~v3_membered(X1)\|~m1_subset_1(X2,X1)), inference(evalgc,[status(thm)],[c_0_52])). cnf(c_0_72, plain, (m1_subset_1(np__1,k1_numbers)), inference(evalgc,[status(thm)],[c_0_53])). cnf(c_0_73, plain, (v3_membered(k1_numbers)), inference(evalgc,[status(thm)],[c_0_54])). fof(c_0_74, plain, ![X41, X42]:(~v1_relat_1(X41)\|(~v1_funct_1(X41)\|~v3_valued_0(X41))\|v1_xreal_0(k1_funct_1(X41,X42))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc63_valued_0])])). fof(c_0_75, plain, ![X70, X71, X72]:(~v3_membered(X71)\|(~m1_subset_1(X72,k1_zfmisc_1(k2_zfmisc_1(X70,X71)))\|v3_valued_0(X72))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc18_valued_0])])])). cnf(c_0_76, plain, (X1=k5_mesfunc1(X2,X3,X4)\|v1_xboole_0(X2)\|k9_xtuple_0(X1)!=k3_xboole_0(k9_xtuple_0(X3),k9_xtuple_0(X4))\|k1_extreal1(k12_supinf_2(X3,esk4_4(X2,X3,X4,X1)),k12_supinf_2(X4,esk4_4(X2,X3,X4,X1)))!=k12_supinf_2(X1,esk4_4(X2,X3,X4,X1))\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v1_funct_1(X1)\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~v4_relat_1(X4,X2)\|~v4_relat_1(X3,X2)\|~v5_relat_1(X4,k7_numbers)\|~v5_relat_1(X3,k7_numbers)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,k7_numbers)))), inference(evalgc,[status(thm)],[c_0_55])). cnf(c_0_77, plain, (k12_supinf_2(X1,X2)=k1_funct_1(X1,X2)\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v5_relat_1(X1,k7_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_56, c_0_57])])). cnf(c_0_78, plain, (k11_binop_2(X3,X4)=k1_extreal1(X1,X2)\|X2!=X4\|X1!=X3\|~m1_subset_1(X4,k1_numbers)\|~m1_subset_1(X3,k1_numbers)\|~m1_subset_1(X2,k7_numbers)\|~m1_subset_1(X1,k7_numbers)), inference(evalgc,[status(thm)],[c_0_58])). cnf(c_0_79, plain, (m1_subset_1(k12_supinf_2(X1,X2),k7_numbers)\|~v1_funct_1(X1)\|~v1_relat_1(X1)\|~v2_valued_0(X1)), inference(evalgc,[status(thm)],[c_0_59])). cnf(c_0_80, plain, (v2_valued_0(X2)\|~v2_membered(X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_60])). cnf(c_0_81, plain, (m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,k7_numbers)))\|v1_xboole_0(X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~v1_funct_1(X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_61, c_0_62])])). cnf(c_0_82, negated_conjecture, (m1_subset_1(esk3_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))), inference(evalgc,[status(thm)],[c_0_63])). cnf(c_0_83, negated_conjecture, (v1_funct_1(esk3_0)), inference(evalgc,[status(thm)],[c_0_64])). cnf(c_0_84, negated_conjecture, (~v1_xboole_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_65])). cnf(c_0_85, plain, (v2_membered(k7_numbers)), inference(split_conjunct,[status(thm)],[fc2_membered])). cnf(c_0_86, plain, (v1_relat_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_66])). fof(c_0_87, plain, ![X73, X74, X75]:((v4_relat_1(X75,X73)\|~m1_subset_1(X75,k1_zfmisc_1(k2_zfmisc_1(X73,X74))))&(v5_relat_1(X75,X74)\|~m1_subset_1(X75,k1_zfmisc_1(k2_zfmisc_1(X73,X74))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_relset_1])])])). cnf(c_0_88, plain, (m1_subset_1(k3_xcmplx_0(X1,X2),k1_numbers)\|~v1_xreal_0(X2)\|~v1_xreal_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_67, c_0_68])])). cnf(c_0_89, plain, (k3_xcmplx_0(np__1,X1)=X1\|~v1_xreal_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_69, c_0_70])])). cnf(c_0_90, plain, (v1_xreal_0(np__1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71, c_0_72]), c_0_73])])])). cnf(c_0_91, plain, (v1_xreal_0(k1_funct_1(X1,X2))\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v3_valued_0(X1)), inference(split_conjunct,[status(thm)],[c_0_74])). cnf(c_0_92, plain, (v3_valued_0(X2)\|~v3_membered(X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_75])). cnf(c_0_93, plain, (X1=k5_mesfunc1(X2,X3,X4)\|v1_xboole_0(X2)\|k1_extreal1(k12_supinf_2(X3,esk4_4(X2,X3,X4,X1)),k1_funct_1(X4,esk4_4(X2,X3,X4,X1)))!=k12_supinf_2(X1,esk4_4(X2,X3,X4,X1))\|k9_xtuple_0(X1)!=k3_xboole_0(k9_xtuple_0(X3),k9_xtuple_0(X4))\|~v5_relat_1(X4,k7_numbers)\|~v5_relat_1(X3,k7_numbers)\|~v4_relat_1(X4,X2)\|~v4_relat_1(X3,X2)\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,k7_numbers)))\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_76, c_0_77])])). cnf(c_0_94, plain, (k1_extreal1(X1,X2)=k11_binop_2(X1,X2)\|~m1_subset_1(X2,k1_numbers)\|~m1_subset_1(X1,k1_numbers)\|~m1_subset_1(X2,k7_numbers)\|~m1_subset_1(X1,k7_numbers)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_78])])])). cnf(c_0_95, plain, (m1_subset_1(k12_supinf_2(X1,X2),k7_numbers)\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v5_relat_1(X1,k7_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_79, c_0_57])])). cnf(c_0_96, plain, (v2_valued_0(X2)\|~v2_membered(X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X3,X1)))), inference(evalgc,[status(thm)],[c_0_80])). cnf(c_0_97, negated_conjecture, (m1_subset_1(esk3_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k7_numbers)))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81, c_0_82]), c_0_83])]), c_0_84])])). cnf(c_0_98, plain, (v2_membered(k7_numbers)), inference(evalgc,[status(thm)],[c_0_85])). cnf(c_0_99, plain, (v1_relat_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(evalgc,[status(thm)],[c_0_86])). cnf(c_0_100, plain, (v5_relat_1(X1,X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X3,X2)))), inference(split_conjunct,[status(thm)],[c_0_87])). cnf(c_0_101, plain, (m1_subset_1(X1,k1_numbers)\|~v1_xreal_0(X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88, c_0_89]), c_0_90])])])). cnf(c_0_102, plain, (v1_xreal_0(k1_funct_1(X1,X2))\|~v1_funct_1(X1)\|~v1_relat_1(X1)\|~v3_valued_0(X1)), inference(evalgc,[status(thm)],[c_0_91])). cnf(c_0_103, plain, (v3_valued_0(X2)\|~v3_membered(X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X3,X1)))), inference(evalgc,[status(thm)],[c_0_92])). cnf(c_0_104, plain, (X1=k5_mesfunc1(X2,X3,X4)\|v1_xboole_0(X2)\|k11_binop_2(k12_supinf_2(X3,esk4_4(X2,X3,X4,X1)),k1_funct_1(X4,esk4_4(X2,X3,X4,X1)))!=k12_supinf_2(X1,esk4_4(X2,X3,X4,X1))\|k9_xtuple_0(X1)!=k3_xboole_0(k9_xtuple_0(X3),k9_xtuple_0(X4))\|~v5_relat_1(X4,k7_numbers)\|~v5_relat_1(X3,k7_numbers)\|~v4_relat_1(X4,X2)\|~v4_relat_1(X3,X2)\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,k7_numbers)))\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v1_funct_1(X1)\|~m1_subset_1(k1_funct_1(X4,esk4_4(X2,X3,X4,X1)),k1_numbers)\|~m1_subset_1(k12_supinf_2(X3,esk4_4(X2,X3,X4,X1)),k1_numbers)\|~m1_subset_1(k1_funct_1(X4,esk4_4(X2,X3,X4,X1)),k7_numbers)\|~m1_subset_1(k12_supinf_2(X3,esk4_4(X2,X3,X4,X1)),k7_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_93, c_0_94])])). cnf(c_0_105, plain, (m1_subset_1(k1_funct_1(X1,X2),k7_numbers)\|~v5_relat_1(X1,k7_numbers)\|~v1_relat_1(X1)\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_95, c_0_77])])). fof(c_0_106, plain, ![X25, X26, X27, X28]:(((k9_xtuple_0(X27)=k3_xboole_0(k9_xtuple_0(X25),k9_xtuple_0(X26))\|X27!=k18_valued_1(X25,X26)\|(~v1_relat_1(X27)\|~v1_funct_1(X27))\|(~v1_relat_1(X26)\|(~v1_funct_1(X26)\|~v1_valued_0(X26)))\|(~v1_relat_1(X25)\|(~v1_funct_1(X25)\|~v1_valued_0(X25))))&(~r2_hidden(X28,k9_xtuple_0(X27))\|k1_funct_1(X27,X28)=k3_xcmplx_0(k1_funct_1(X25,X28),k1_funct_1(X26,X28))\|X27!=k18_valued_1(X25,X26)\|(~v1_relat_1(X27)\|~v1_funct_1(X27))\|(~v1_relat_1(X26)\|(~v1_funct_1(X26)\|~v1_valued_0(X26)))\|(~v1_relat_1(X25)\|(~v1_funct_1(X25)\|~v1_valued_0(X25)))))&((r2_hidden(esk5_3(X25,X26,X27),k9_xtuple_0(X27))\|k9_xtuple_0(X27)!=k3_xboole_0(k9_xtuple_0(X25),k9_xtuple_0(X26))\|X27=k18_valued_1(X25,X26)\|(~v1_relat_1(X27)\|~v1_funct_1(X27))\|(~v1_relat_1(X26)\|(~v1_funct_1(X26)\|~v1_valued_0(X26)))\|(~v1_relat_1(X25)\|(~v1_funct_1(X25)\|~v1_valued_0(X25))))&(k1_funct_1(X27,esk5_3(X25,X26,X27))!=k3_xcmplx_0(k1_funct_1(X25,esk5_3(X25,X26,X27)),k1_funct_1(X26,esk5_3(X25,X26,X27)))\|k9_xtuple_0(X27)!=k3_xboole_0(k9_xtuple_0(X25),k9_xtuple_0(X26))\|X27=k18_valued_1(X25,X26)\|(~v1_relat_1(X27)\|~v1_funct_1(X27))\|(~v1_relat_1(X26)\|(~v1_funct_1(X26)\|~v1_valued_0(X26)))\|(~v1_relat_1(X25)\|(~v1_funct_1(X25)\|~v1_valued_0(X25)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d4_valued_1])])])])])). cnf(c_0_107, plain, (X1=k5_mesfunc1(X2,X3,X4)\|v1_xboole_0(X2)\|k11_binop_2(k12_supinf_2(X3,esk4_4(X2,X3,X4,X1)),k12_supinf_2(X4,esk4_4(X2,X3,X4,X1)))!=k12_supinf_2(X1,esk4_4(X2,X3,X4,X1))\|k9_xtuple_0(X1)!=k3_xboole_0(k9_xtuple_0(X3),k9_xtuple_0(X4))\|~v5_relat_1(X4,k7_numbers)\|~v5_relat_1(X3,k7_numbers)\|~v4_relat_1(X4,X2)\|~v4_relat_1(X3,X2)\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,k7_numbers)))\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v1_funct_1(X1)\|~m1_subset_1(k12_supinf_2(X4,esk4_4(X2,X3,X4,X1)),k1_numbers)\|~m1_subset_1(k12_supinf_2(X3,esk4_4(X2,X3,X4,X1)),k1_numbers)\|~m1_subset_1(k12_supinf_2(X4,esk4_4(X2,X3,X4,X1)),k7_numbers)\|~m1_subset_1(k12_supinf_2(X3,esk4_4(X2,X3,X4,X1)),k7_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_76, c_0_94])])). cnf(c_0_108, negated_conjecture, (v2_valued_0(esk3_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96, c_0_97]), c_0_98])])])). cnf(c_0_109, negated_conjecture, (v1_relat_1(esk3_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_99, c_0_82])])). cnf(c_0_110, plain, (v5_relat_1(X1,X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X3,X2)))), inference(evalgc,[status(thm)],[c_0_100])). cnf(c_0_111, plain, (m1_subset_1(k1_funct_1(X1,X2),k1_numbers)\|~v3_valued_0(X1)\|~v1_relat_1(X1)\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_101, c_0_102])])). cnf(c_0_112, negated_conjecture, (v3_valued_0(esk3_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103, c_0_82]), c_0_73])])])). fof(c_0_113, plain, ![X58, X59, X60, X61, X62]:(~v3_membered(X59)\|(~v3_membered(X60)\|(~v1_funct_1(X61)\|~m1_subset_1(X61,k1_zfmisc_1(k2_zfmisc_1(X58,X59)))\|(~v1_funct_1(X62)\|~m1_subset_1(X62,k1_zfmisc_1(k2_zfmisc_1(X58,X60))))))\|k20_valued_1(X58,X59,X60,X61,X62)=k18_valued_1(X61,X62)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k20_valued_1])])). fof(c_0_114, plain, ![X63, X64, X65, X66, X67]:(~v3_membered(X64)\|(~v3_membered(X65)\|(~v1_funct_1(X66)\|~m1_subset_1(X66,k1_zfmisc_1(k2_zfmisc_1(X63,X64)))\|(~v1_funct_1(X67)\|~m1_subset_1(X67,k1_zfmisc_1(k2_zfmisc_1(X63,X65))))))\|k20_valued_1(X63,X64,X65,X66,X67)=k20_valued_1(X63,X64,X65,X67,X66)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[commutativity_k20_valued_1])])). cnf(c_0_115, plain, (X1=k5_mesfunc1(X2,X3,X4)\|v1_xboole_0(X2)\|k11_binop_2(k12_supinf_2(X3,esk4_4(X2,X3,X4,X1)),k1_funct_1(X4,esk4_4(X2,X3,X4,X1)))!=k12_supinf_2(X1,esk4_4(X2,X3,X4,X1))\|k9_xtuple_0(X1)!=k3_xboole_0(k9_xtuple_0(X3),k9_xtuple_0(X4))\|~v5_relat_1(X4,k7_numbers)\|~v5_relat_1(X3,k7_numbers)\|~v4_relat_1(X4,X2)\|~v4_relat_1(X3,X2)\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~m1_subset_1(k1_funct_1(X4,esk4_4(X2,X3,X4,X1)),k1_numbers)\|~m1_subset_1(k12_supinf_2(X3,esk4_4(X2,X3,X4,X1)),k1_numbers)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,k7_numbers)))\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v1_funct_1(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_104, c_0_95]), c_0_105])). cnf(c_0_116, plain, (k1_funct_1(X2,X1)=k3_xcmplx_0(k1_funct_1(X3,X1),k1_funct_1(X4,X1))\|~r2_hidden(X1,k9_xtuple_0(X2))\|X2!=k18_valued_1(X3,X4)\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v1_relat_1(X4)\|~v1_funct_1(X4)\|~v1_valued_0(X4)\|~v1_relat_1(X3)\|~v1_funct_1(X3)\|~v1_valued_0(X3)), inference(split_conjunct,[status(thm)],[c_0_106])). cnf(c_0_117, plain, (r2_hidden(esk4_4(X1,X2,X3,X4),k9_xtuple_0(X4))\|X4=k5_mesfunc1(X1,X2,X3)\|v1_xboole_0(X1)\|k9_xtuple_0(X4)!=k3_xboole_0(k9_xtuple_0(X2),k9_xtuple_0(X3))\|~v1_funct_1(X4)\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,k7_numbers)))\|~v1_relat_1(X3)\|~v4_relat_1(X3,X1)\|~v5_relat_1(X3,k7_numbers)\|~v1_funct_1(X3)\|~v1_relat_1(X2)\|~v4_relat_1(X2,X1)\|~v5_relat_1(X2,k7_numbers)\|~v1_funct_1(X2)), inference(split_conjunct,[status(thm)],[c_0_40])). cnf(c_0_118, plain, (X1=k5_mesfunc1(X2,X3,X4)\|v1_xboole_0(X2)\|k11_binop_2(k12_supinf_2(X3,esk4_4(X2,X3,X4,X1)),k12_supinf_2(X4,esk4_4(X2,X3,X4,X1)))!=k12_supinf_2(X1,esk4_4(X2,X3,X4,X1))\|k9_xtuple_0(X1)!=k3_xboole_0(k9_xtuple_0(X3),k9_xtuple_0(X4))\|~v5_relat_1(X4,k7_numbers)\|~v5_relat_1(X3,k7_numbers)\|~v4_relat_1(X4,X2)\|~v4_relat_1(X3,X2)\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~m1_subset_1(k12_supinf_2(X4,esk4_4(X2,X3,X4,X1)),k1_numbers)\|~m1_subset_1(k12_supinf_2(X3,esk4_4(X2,X3,X4,X1)),k1_numbers)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,k7_numbers)))\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v1_funct_1(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_107, c_0_95]), c_0_95])). cnf(c_0_119, negated_conjecture, (k12_supinf_2(esk3_0,X1)=k1_funct_1(esk3_0,X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56, c_0_108]), c_0_109]), c_0_83])])])). cnf(c_0_120, negated_conjecture, (v5_relat_1(esk3_0,k7_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_110, c_0_97])])). cnf(c_0_121, negated_conjecture, (m1_subset_1(k1_funct_1(esk3_0,X1),k1_numbers)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111, c_0_112]), c_0_109]), c_0_83])])])). cnf(c_0_122, plain, (k20_valued_1(X4,X1,X2,X3,X5)=k18_valued_1(X3,X5)\|~v3_membered(X1)\|~v3_membered(X2)\|~v1_funct_1(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X4,X1)))\|~v1_funct_1(X5)\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X4,X2)))), inference(split_conjunct,[status(thm)],[c_0_113])). cnf(c_0_123, plain, (k20_valued_1(X4,X1,X2,X3,X5)=k20_valued_1(X4,X1,X2,X5,X3)\|~v3_membered(X1)\|~v3_membered(X2)\|~v1_funct_1(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X4,X1)))\|~v1_funct_1(X5)\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X4,X2)))), inference(split_conjunct,[status(thm)],[c_0_114])). cnf(c_0_124, plain, (X1=k5_mesfunc1(X2,X3,X4)\|v1_xboole_0(X2)\|k3_xcmplx_0(k12_supinf_2(X3,esk4_4(X2,X3,X4,X1)),k1_funct_1(X4,esk4_4(X2,X3,X4,X1)))!=k12_supinf_2(X1,esk4_4(X2,X3,X4,X1))\|k9_xtuple_0(X1)!=k3_xboole_0(k9_xtuple_0(X3),k9_xtuple_0(X4))\|~v5_relat_1(X4,k7_numbers)\|~v5_relat_1(X3,k7_numbers)\|~v4_relat_1(X4,X2)\|~v4_relat_1(X3,X2)\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~m1_subset_1(k1_funct_1(X4,esk4_4(X2,X3,X4,X1)),k1_numbers)\|~m1_subset_1(k12_supinf_2(X3,esk4_4(X2,X3,X4,X1)),k1_numbers)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,k7_numbers)))\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v1_funct_1(X1)\|~v1_xreal_0(k1_funct_1(X4,esk4_4(X2,X3,X4,X1)))\|~v1_xreal_0(k12_supinf_2(X3,esk4_4(X2,X3,X4,X1)))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_115, c_0_68])])). cnf(c_0_125, plain, (k1_funct_1(X2,X1)=k3_xcmplx_0(k1_funct_1(X3,X1),k1_funct_1(X4,X1))\|X2!=k18_valued_1(X3,X4)\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_valued_0(X4)\|~v1_valued_0(X3)\|~r2_hidden(X1,k9_xtuple_0(X2))), inference(evalgc,[status(thm)],[c_0_116])). cnf(c_0_126, plain, (X4=k5_mesfunc1(X1,X2,X3)\|v1_xboole_0(X1)\|r2_hidden(esk4_4(X1,X2,X3,X4),k9_xtuple_0(X4))\|k9_xtuple_0(X4)!=k3_xboole_0(k9_xtuple_0(X2),k9_xtuple_0(X3))\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v4_relat_1(X3,X1)\|~v4_relat_1(X2,X1)\|~v5_relat_1(X3,k7_numbers)\|~v5_relat_1(X2,k7_numbers)\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,k7_numbers)))), inference(evalgc,[status(thm)],[c_0_117])). cnf(c_0_127, negated_conjecture, (X1=k5_mesfunc1(X2,X3,esk3_0)\|v1_xboole_0(X2)\|k11_binop_2(k12_supinf_2(X3,esk4_4(X2,X3,esk3_0,X1)),k1_funct_1(esk3_0,esk4_4(X2,X3,esk3_0,X1)))!=k12_supinf_2(X1,esk4_4(X2,X3,esk3_0,X1))\|k9_xtuple_0(X1)!=k3_xboole_0(k9_xtuple_0(X3),k9_xtuple_0(esk3_0))\|~v5_relat_1(X3,k7_numbers)\|~v4_relat_1(esk3_0,X2)\|~v4_relat_1(X3,X2)\|~v1_relat_1(X3)\|~m1_subset_1(k12_supinf_2(X3,esk4_4(X2,X3,esk3_0,X1)),k1_numbers)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,k7_numbers)))\|~v1_funct_1(X3)\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118, c_0_119]), c_0_120]), c_0_109]), c_0_121]), c_0_83])])])). cnf(c_0_128, negated_conjecture, (v1_xreal_0(k1_funct_1(esk3_0,X1))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71, c_0_121]), c_0_73])])])). fof(c_0_129, plain, ![X43]:((v1_relat_1(X43)\|(~v1_relat_1(X43)\|~v3_valued_0(X43)))&(v1_valued_0(X43)\|(~v1_relat_1(X43)\|~v3_valued_0(X43)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc6_valued_0])])])). cnf(c_0_130, plain, (k20_valued_1(X4,X1,X2,X3,X5)=k18_valued_1(X3,X5)\|~v1_funct_1(X5)\|~v1_funct_1(X3)\|~v3_membered(X2)\|~v3_membered(X1)\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X4,X2)))\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X4,X1)))), inference(evalgc,[status(thm)],[c_0_122])). cnf(c_0_131, plain, (k20_valued_1(X4,X1,X2,X3,X5)=k20_valued_1(X4,X1,X2,X5,X3)\|~v1_funct_1(X5)\|~v1_funct_1(X3)\|~v3_membered(X2)\|~v3_membered(X1)\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X4,X2)))\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X4,X1)))), inference(evalgc,[status(thm)],[c_0_123])). cnf(c_0_132, plain, (X1=k5_mesfunc1(X2,X3,X4)\|v1_xboole_0(X2)\|k3_xcmplx_0(k12_supinf_2(X3,esk4_4(X2,X3,X4,X1)),k1_funct_1(X4,esk4_4(X2,X3,X4,X1)))!=k12_supinf_2(X1,esk4_4(X2,X3,X4,X1))\|k9_xtuple_0(X1)!=k3_xboole_0(k9_xtuple_0(X3),k9_xtuple_0(X4))\|~v1_xreal_0(k1_funct_1(X4,esk4_4(X2,X3,X4,X1)))\|~v1_xreal_0(k12_supinf_2(X3,esk4_4(X2,X3,X4,X1)))\|~v5_relat_1(X4,k7_numbers)\|~v5_relat_1(X3,k7_numbers)\|~v4_relat_1(X4,X2)\|~v4_relat_1(X3,X2)\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,k7_numbers)))\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v1_funct_1(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_124, c_0_101]), c_0_101])). cnf(c_0_133, plain, (k3_xcmplx_0(k1_funct_1(X5,esk4_4(X2,X3,X4,X1)),k1_funct_1(X6,esk4_4(X2,X3,X4,X1)))=k1_funct_1(X1,esk4_4(X2,X3,X4,X1))\|X1=k5_mesfunc1(X2,X3,X4)\|v1_xboole_0(X2)\|X1!=k18_valued_1(X5,X6)\|~v1_valued_0(X6)\|~v1_valued_0(X5)\|~v1_relat_1(X6)\|~v1_relat_1(X5)\|~v1_relat_1(X1)\|~v1_funct_1(X6)\|~v1_funct_1(X5)\|~v1_funct_1(X1)\|k9_xtuple_0(X1)!=k3_xboole_0(k9_xtuple_0(X3),k9_xtuple_0(X4))\|~v5_relat_1(X4,k7_numbers)\|~v5_relat_1(X3,k7_numbers)\|~v4_relat_1(X4,X2)\|~v4_relat_1(X3,X2)\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,k7_numbers)))\|~v1_funct_1(X4)\|~v1_funct_1(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_125, c_0_126])])). cnf(c_0_134, negated_conjecture, (X1=k5_mesfunc1(X2,X3,esk3_0)\|v1_xboole_0(X2)\|k3_xcmplx_0(k12_supinf_2(X3,esk4_4(X2,X3,esk3_0,X1)),k1_funct_1(esk3_0,esk4_4(X2,X3,esk3_0,X1)))!=k12_supinf_2(X1,esk4_4(X2,X3,esk3_0,X1))\|k9_xtuple_0(X1)!=k3_xboole_0(k9_xtuple_0(X3),k9_xtuple_0(esk3_0))\|~v5_relat_1(X3,k7_numbers)\|~v4_relat_1(esk3_0,X2)\|~v4_relat_1(X3,X2)\|~v1_relat_1(X3)\|~m1_subset_1(k12_supinf_2(X3,esk4_4(X2,X3,esk3_0,X1)),k1_numbers)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,k7_numbers)))\|~v1_funct_1(X3)\|~v1_funct_1(X1)\|~v1_xreal_0(k12_supinf_2(X3,esk4_4(X2,X3,esk3_0,X1)))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127, c_0_68]), c_0_128])])])). cnf(c_0_135, plain, (v1_valued_0(X1)\|~v1_relat_1(X1)\|~v3_valued_0(X1)), inference(split_conjunct,[status(thm)],[c_0_129])). cnf(c_0_136, plain, (k20_valued_1(X1,X2,X3,X5,X4)=k18_valued_1(X4,X5)\|~v3_membered(X3)\|~v3_membered(X2)\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X5)\|~v1_funct_1(X4)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_130, c_0_131])])). fof(c_0_137, plain, ![X53, X54, X55, X56, X57]:((v1_funct_1(k20_valued_1(X53,X54,X55,X56,X57))\|(~v3_membered(X54)\|(~v3_membered(X55)\|(~v1_funct_1(X56)\|~m1_subset_1(X56,k1_zfmisc_1(k2_zfmisc_1(X53,X54)))\|(~v1_funct_1(X57)\|~m1_subset_1(X57,k1_zfmisc_1(k2_zfmisc_1(X53,X55))))))))&(m1_subset_1(k20_valued_1(X53,X54,X55,X56,X57),k1_zfmisc_1(k2_zfmisc_1(X53,k1_numbers)))\|(~v3_membered(X54)\|(~v3_membered(X55)\|(~v1_funct_1(X56)\|~m1_subset_1(X56,k1_zfmisc_1(k2_zfmisc_1(X53,X54)))\|(~v1_funct_1(X57)\|~m1_subset_1(X57,k1_zfmisc_1(k2_zfmisc_1(X53,X55))))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k20_valued_1])])])). cnf(c_0_138, plain, (X1=k5_mesfunc1(X2,X3,X4)\|v1_xboole_0(X2)\|k3_xcmplx_0(k1_funct_1(X3,esk4_4(X2,X3,X4,X1)),k1_funct_1(X4,esk4_4(X2,X3,X4,X1)))!=k12_supinf_2(X1,esk4_4(X2,X3,X4,X1))\|k9_xtuple_0(X1)!=k3_xboole_0(k9_xtuple_0(X3),k9_xtuple_0(X4))\|~v1_xreal_0(k1_funct_1(X4,esk4_4(X2,X3,X4,X1)))\|~v1_xreal_0(k1_funct_1(X3,esk4_4(X2,X3,X4,X1)))\|~v5_relat_1(X4,k7_numbers)\|~v5_relat_1(X3,k7_numbers)\|~v4_relat_1(X4,X2)\|~v4_relat_1(X3,X2)\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,k7_numbers)))\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_132, c_0_77])])). cnf(c_0_139, plain, (k3_xcmplx_0(k1_funct_1(X1,esk4_4(X2,X3,X4,X5)),k1_funct_1(X6,esk4_4(X2,X3,X4,X5)))=k1_funct_1(X5,esk4_4(X2,X3,X4,X5))\|X5=k5_mesfunc1(X2,X3,X4)\|v1_xboole_0(X2)\|k9_xtuple_0(X5)!=k3_xboole_0(k9_xtuple_0(X3),k9_xtuple_0(X4))\|X5!=k18_valued_1(X1,X6)\|~v1_valued_0(X6)\|~v1_valued_0(X1)\|~v5_relat_1(X4,k7_numbers)\|~v5_relat_1(X3,k7_numbers)\|~v4_relat_1(X4,X2)\|~v4_relat_1(X3,X2)\|~v1_relat_1(X6)\|~v1_relat_1(X1)\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X2,k7_numbers)))\|~v1_funct_1(X6)\|~v1_funct_1(X1)\|~v1_funct_1(X5)\|~v1_funct_1(X4)\|~v1_funct_1(X3)), inference(csr,[status(thm)],[c_0_133, c_0_99])). cnf(c_0_140, negated_conjecture, (X1=k5_mesfunc1(X2,X3,esk3_0)\|v1_xboole_0(X2)\|k3_xcmplx_0(k12_supinf_2(X3,esk4_4(X2,X3,esk3_0,X1)),k1_funct_1(esk3_0,esk4_4(X2,X3,esk3_0,X1)))!=k12_supinf_2(X1,esk4_4(X2,X3,esk3_0,X1))\|k9_xtuple_0(X1)!=k3_xboole_0(k9_xtuple_0(X3),k9_xtuple_0(esk3_0))\|~v1_xreal_0(k12_supinf_2(X3,esk4_4(X2,X3,esk3_0,X1)))\|~v5_relat_1(X3,k7_numbers)\|~v4_relat_1(esk3_0,X2)\|~v4_relat_1(X3,X2)\|~v1_relat_1(X3)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,k7_numbers)))\|~v1_funct_1(X3)\|~v1_funct_1(X1)), inference(csr,[status(thm)],[c_0_134, c_0_101])). cnf(c_0_141, plain, (v1_valued_0(X1)\|~v1_relat_1(X1)\|~v3_valued_0(X1)), inference(evalgc,[status(thm)],[c_0_135])). cnf(c_0_142, plain, (k18_valued_1(X5,X4)=k18_valued_1(X4,X5)\|~v3_membered(X3)\|~v3_membered(X2)\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X5)\|~v1_funct_1(X4)\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_130, c_0_136])])). cnf(c_0_143, plain, (m1_subset_1(k20_valued_1(X1,X2,X3,X4,X5),k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~v3_membered(X2)\|~v3_membered(X3)\|~v1_funct_1(X4)\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X5)\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_137])). cnf(c_0_144, plain, (X1=k5_mesfunc1(X2,X3,X4)\|v1_xboole_0(X2)\|k12_supinf_2(X1,esk4_4(X2,X3,X4,X1))!=k1_funct_1(X1,esk4_4(X2,X3,X4,X1))\|k9_xtuple_0(X1)!=k3_xboole_0(k9_xtuple_0(X3),k9_xtuple_0(X4))\|~v1_xreal_0(k1_funct_1(X4,esk4_4(X2,X3,X4,X1)))\|~v1_xreal_0(k1_funct_1(X3,esk4_4(X2,X3,X4,X1)))\|~v5_relat_1(X4,k7_numbers)\|~v5_relat_1(X3,k7_numbers)\|~v4_relat_1(X4,X2)\|~v4_relat_1(X3,X2)\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,k7_numbers)))\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v1_funct_1(X1)\|X1!=k18_valued_1(X3,X4)\|~v1_valued_0(X4)\|~v1_valued_0(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_138, c_0_139])])). cnf(c_0_145, negated_conjecture, (X1=k5_mesfunc1(X2,X3,esk3_0)\|v1_xboole_0(X2)\|k3_xcmplx_0(k1_funct_1(X3,esk4_4(X2,X3,esk3_0,X1)),k1_funct_1(esk3_0,esk4_4(X2,X3,esk3_0,X1)))!=k12_supinf_2(X1,esk4_4(X2,X3,esk3_0,X1))\|k9_xtuple_0(X1)!=k3_xboole_0(k9_xtuple_0(X3),k9_xtuple_0(esk3_0))\|~v1_xreal_0(k1_funct_1(X3,esk4_4(X2,X3,esk3_0,X1)))\|~v5_relat_1(X3,k7_numbers)\|~v4_relat_1(esk3_0,X2)\|~v4_relat_1(X3,X2)\|~v1_relat_1(X3)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,k7_numbers)))\|~v1_funct_1(X3)\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_140, c_0_77])])). cnf(c_0_146, negated_conjecture, (v1_valued_0(esk3_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141, c_0_112]), c_0_109])])])). cnf(c_0_147, plain, (v1_funct_1(k20_valued_1(X1,X2,X3,X4,X5))\|~v3_membered(X2)\|~v3_membered(X3)\|~v1_funct_1(X4)\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X5)\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))), inference(split_conjunct,[status(thm)],[c_0_137])). cnf(c_0_148, plain, (k9_xtuple_0(X1)=k3_xboole_0(k9_xtuple_0(X2),k9_xtuple_0(X3))\|X1!=k18_valued_1(X2,X3)\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v1_relat_1(X3)\|~v1_funct_1(X3)\|~v1_valued_0(X3)\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v1_valued_0(X2)), inference(split_conjunct,[status(thm)],[c_0_106])). cnf(c_0_149, negated_conjecture, (k18_valued_1(esk3_0,X1)=k18_valued_1(X1,esk3_0)\|~v3_membered(X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(esk1_0,X2)))\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))\|~m1_subset_1(esk3_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,X2)))\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142, c_0_82]), c_0_73]), c_0_83])])])). cnf(c_0_150, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))), inference(split_conjunct,[status(thm)],[c_0_47])). cnf(c_0_151, negated_conjecture, (v1_funct_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_47])). cnf(c_0_152, plain, (m1_subset_1(k20_valued_1(X1,X2,X3,X4,X5),k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~v1_funct_1(X5)\|~v1_funct_1(X4)\|~v3_membered(X3)\|~v3_membered(X2)\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(evalgc,[status(thm)],[c_0_143])). cnf(c_0_153, plain, (X1=k5_mesfunc1(X2,X3,X4)\|v1_xboole_0(X2)\|k12_supinf_2(X1,esk4_4(X2,X3,X4,X1))!=k1_funct_1(X1,esk4_4(X2,X3,X4,X1))\|k9_xtuple_0(X1)!=k3_xboole_0(k9_xtuple_0(X3),k9_xtuple_0(X4))\|X1!=k18_valued_1(X3,X4)\|~v1_valued_0(X4)\|~v1_valued_0(X3)\|~v1_xreal_0(k1_funct_1(X3,esk4_4(X2,X3,X4,X1)))\|~v5_relat_1(X4,k7_numbers)\|~v5_relat_1(X3,k7_numbers)\|~v4_relat_1(X4,X2)\|~v4_relat_1(X3,X2)\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,k7_numbers)))\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v1_funct_1(X1)\|~v3_valued_0(X4)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_144, c_0_102])])). cnf(c_0_154, negated_conjecture, (X1=k5_mesfunc1(X2,X3,esk3_0)\|v1_xboole_0(X2)\|k12_supinf_2(X1,esk4_4(X2,X3,esk3_0,X1))!=k1_funct_1(X1,esk4_4(X2,X3,esk3_0,X1))\|k9_xtuple_0(X1)!=k3_xboole_0(k9_xtuple_0(X3),k9_xtuple_0(esk3_0))\|~v1_xreal_0(k1_funct_1(X3,esk4_4(X2,X3,esk3_0,X1)))\|~v5_relat_1(X3,k7_numbers)\|~v4_relat_1(esk3_0,X2)\|~v4_relat_1(X3,X2)\|~v1_relat_1(X3)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,k7_numbers)))\|~v1_funct_1(X3)\|~v1_funct_1(X1)\|X1!=k18_valued_1(X3,esk3_0)\|~v1_valued_0(X3)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145, c_0_139]), c_0_146]), c_0_120]), c_0_109]), c_0_83])])])). cnf(c_0_155, plain, (v1_funct_1(k20_valued_1(X1,X2,X3,X4,X5))\|~v1_funct_1(X5)\|~v1_funct_1(X4)\|~v3_membered(X3)\|~v3_membered(X2)\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(evalgc,[status(thm)],[c_0_147])). fof(c_0_156, plain, ![X51, X52]:((v1_relat_1(k18_valued_1(X51,X52))\|(~v1_relat_1(X51)\|(~v1_funct_1(X51)\|~v1_valued_0(X51))\|(~v1_relat_1(X52)\|(~v1_funct_1(X52)\|~v1_valued_0(X52)))))&(v1_funct_1(k18_valued_1(X51,X52))\|(~v1_relat_1(X51)\|(~v1_funct_1(X51)\|~v1_valued_0(X51))\|(~v1_relat_1(X52)\|(~v1_funct_1(X52)\|~v1_valued_0(X52)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k18_valued_1])])])). cnf(c_0_157, plain, (k9_xtuple_0(X1)=k3_xboole_0(k9_xtuple_0(X2),k9_xtuple_0(X3))\|X1!=k18_valued_1(X2,X3)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v1_funct_1(X1)\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_relat_1(X1)\|~v1_valued_0(X3)\|~v1_valued_0(X2)), inference(evalgc,[status(thm)],[c_0_148])). cnf(c_0_158, negated_conjecture, (k18_valued_1(esk3_0,X1)=k18_valued_1(X1,esk3_0)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149, c_0_82]), c_0_73])])])). cnf(c_0_159, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))), inference(evalgc,[status(thm)],[c_0_150])). cnf(c_0_160, negated_conjecture, (v1_funct_1(esk2_0)), inference(evalgc,[status(thm)],[c_0_151])). cnf(c_0_161, plain, (m1_subset_1(k18_valued_1(X4,X5),k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~v3_membered(X3)\|~v3_membered(X2)\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X5)\|~v1_funct_1(X4)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_152, c_0_130])])). cnf(c_0_162, plain, (X1=k5_mesfunc1(X2,X3,X4)\|v1_xboole_0(X2)\|k12_supinf_2(X1,esk4_4(X2,X3,X4,X1))!=k1_funct_1(X1,esk4_4(X2,X3,X4,X1))\|k9_xtuple_0(X1)!=k3_xboole_0(k9_xtuple_0(X3),k9_xtuple_0(X4))\|X1!=k18_valued_1(X3,X4)\|~v3_valued_0(X4)\|~v1_valued_0(X3)\|~v1_xreal_0(k1_funct_1(X3,esk4_4(X2,X3,X4,X1)))\|~v5_relat_1(X4,k7_numbers)\|~v5_relat_1(X3,k7_numbers)\|~v4_relat_1(X4,X2)\|~v4_relat_1(X3,X2)\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,k7_numbers)))\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v1_funct_1(X1)), inference(csr,[status(thm)],[c_0_153, c_0_141])). cnf(c_0_163, negated_conjecture, (X1=k5_mesfunc1(X2,X3,esk3_0)\|v1_xboole_0(X2)\|k12_supinf_2(X1,esk4_4(X2,X3,esk3_0,X1))!=k1_funct_1(X1,esk4_4(X2,X3,esk3_0,X1))\|k9_xtuple_0(X1)!=k3_xboole_0(k9_xtuple_0(X3),k9_xtuple_0(esk3_0))\|X1!=k18_valued_1(X3,esk3_0)\|~v1_valued_0(X3)\|~v5_relat_1(X3,k7_numbers)\|~v4_relat_1(esk3_0,X2)\|~v4_relat_1(X3,X2)\|~v1_relat_1(X3)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,k7_numbers)))\|~v1_funct_1(X3)\|~v1_funct_1(X1)\|~v3_valued_0(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_154, c_0_102])])). cnf(c_0_164, plain, (v1_funct_1(k18_valued_1(X4,X5))\|~v3_membered(X3)\|~v3_membered(X2)\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X5)\|~v1_funct_1(X4)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_155, c_0_130])])). fof(c_0_165, plain, ![X49, X50]:k3_xboole_0(X49,X50)=k3_xboole_0(X50,X49), inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0])). cnf(c_0_166, plain, (v1_funct_1(k18_valued_1(X1,X2))\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v1_valued_0(X1)\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v1_valued_0(X2)), inference(split_conjunct,[status(thm)],[c_0_156])). cnf(c_0_167, plain, (v1_relat_1(k18_valued_1(X1,X2))\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v1_valued_0(X1)\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v1_valued_0(X2)), inference(split_conjunct,[status(thm)],[c_0_156])). cnf(c_0_168, negated_conjecture, (k9_xtuple_0(X1)=k3_xboole_0(k9_xtuple_0(esk3_0),k9_xtuple_0(X2))\|X1!=k18_valued_1(X2,esk3_0)\|~v1_valued_0(X2)\|~v1_relat_1(X2)\|~v1_relat_1(X1)\|~v1_funct_1(X2)\|~v1_funct_1(X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157, c_0_158]), c_0_146]), c_0_109]), c_0_83])])])). cnf(c_0_169, negated_conjecture, (k18_valued_1(esk2_0,X1)=k18_valued_1(X1,esk2_0)\|~v3_membered(X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(esk1_0,X2)))\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))\|~m1_subset_1(esk2_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,X2)))\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142, c_0_159]), c_0_73]), c_0_160])])])). cnf(c_0_170, negated_conjecture, (v3_valued_0(esk2_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103, c_0_159]), c_0_73])])])). cnf(c_0_171, negated_conjecture, (v1_relat_1(esk2_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_99, c_0_159])])). cnf(c_0_172, negated_conjecture, (m1_subset_1(k18_valued_1(X1,esk2_0),k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))\|~v3_membered(X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(esk1_0,X2)))\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161, c_0_159]), c_0_73]), c_0_160])])])). cnf(c_0_173, plain, (X1=k5_mesfunc1(X2,X3,X4)\|v1_xboole_0(X2)\|k12_supinf_2(X1,esk4_4(X2,X3,X4,X1))!=k1_funct_1(X1,esk4_4(X2,X3,X4,X1))\|k9_xtuple_0(X1)!=k3_xboole_0(k9_xtuple_0(X3),k9_xtuple_0(X4))\|X1!=k18_valued_1(X3,X4)\|~v3_valued_0(X4)\|~v1_valued_0(X3)\|~v5_relat_1(X4,k7_numbers)\|~v5_relat_1(X3,k7_numbers)\|~v4_relat_1(X4,X2)\|~v4_relat_1(X3,X2)\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,k7_numbers)))\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v1_funct_1(X1)\|~v3_valued_0(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_162, c_0_102])])). cnf(c_0_174, negated_conjecture, (X1=k5_mesfunc1(X2,X3,esk3_0)\|v1_xboole_0(X2)\|k12_supinf_2(X1,esk4_4(X2,X3,esk3_0,X1))!=k1_funct_1(X1,esk4_4(X2,X3,esk3_0,X1))\|k9_xtuple_0(X1)!=k3_xboole_0(k9_xtuple_0(X3),k9_xtuple_0(esk3_0))\|X1!=k18_valued_1(X3,esk3_0)\|~v3_valued_0(X3)\|~v5_relat_1(X3,k7_numbers)\|~v4_relat_1(esk3_0,X2)\|~v4_relat_1(X3,X2)\|~v1_relat_1(X3)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,k7_numbers)))\|~v1_funct_1(X3)\|~v1_funct_1(X1)), inference(csr,[status(thm)],[c_0_163, c_0_141])). cnf(c_0_175, negated_conjecture, (m1_subset_1(k18_valued_1(X1,esk3_0),k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))\|~v3_membered(X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(esk1_0,X2)))\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161, c_0_82]), c_0_73]), c_0_83])])])). cnf(c_0_176, negated_conjecture, (v1_funct_1(k18_valued_1(X1,esk3_0))\|~v3_membered(X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(esk1_0,X2)))\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164, c_0_82]), c_0_73]), c_0_83])])])). cnf(c_0_177, plain, (v4_relat_1(X1,X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_87])). cnf(c_0_178, plain, (k3_xboole_0(X1,X2)=k3_xboole_0(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_165])). cnf(c_0_179, plain, (k3_xboole_0(k9_xtuple_0(X1),k9_xtuple_0(X2))=k9_xtuple_0(k18_valued_1(X1,X2))\|~v1_valued_0(X2)\|~v1_valued_0(X1)\|~v1_relat_1(X2)\|~v1_relat_1(X1)\|~v1_relat_1(k18_valued_1(X1,X2))\|~v1_funct_1(X2)\|~v1_funct_1(X1)\|~v1_funct_1(k18_valued_1(X1,X2))), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_157])])). cnf(c_0_180, plain, (v1_funct_1(k18_valued_1(X1,X2))\|~v1_funct_1(X2)\|~v1_funct_1(X1)\|~v1_relat_1(X2)\|~v1_relat_1(X1)\|~v1_valued_0(X2)\|~v1_valued_0(X1)), inference(evalgc,[status(thm)],[c_0_166])). cnf(c_0_181, plain, (v1_relat_1(k18_valued_1(X1,X2))\|~v1_funct_1(X2)\|~v1_funct_1(X1)\|~v1_relat_1(X2)\|~v1_relat_1(X1)\|~v1_valued_0(X2)\|~v1_valued_0(X1)), inference(evalgc,[status(thm)],[c_0_167])). cnf(c_0_182, negated_conjecture, (k9_xtuple_0(X1)=k3_xboole_0(k9_xtuple_0(esk3_0),k9_xtuple_0(X2))\|X1!=k18_valued_1(X2,esk3_0)\|~v1_valued_0(X2)\|~v1_relat_1(X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))\|~v1_funct_1(X2)\|~v1_funct_1(X1)), inference(csr,[status(thm)],[c_0_168, c_0_99])). cnf(c_0_183, negated_conjecture, (k18_valued_1(esk2_0,X1)=k18_valued_1(X1,esk2_0)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169, c_0_159]), c_0_73])])])). cnf(c_0_184, negated_conjecture, (v1_valued_0(esk2_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141, c_0_170]), c_0_171])])])). cnf(c_0_185, negated_conjecture, (m1_subset_1(k18_valued_1(esk3_0,esk2_0),k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_172, c_0_82]), c_0_73]), c_0_83])])])). cnf(c_0_186, negated_conjecture, (v1_funct_1(k18_valued_1(X1,esk2_0))\|~v3_membered(X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(esk1_0,X2)))\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164, c_0_159]), c_0_73]), c_0_160])])])). cnf(c_0_187, plain, (X1=k5_mesfunc1(X2,X3,X4)\|v1_xboole_0(X2)\|k12_supinf_2(X1,esk4_4(X2,X3,X4,X1))!=k1_funct_1(X1,esk4_4(X2,X3,X4,X1))\|k9_xtuple_0(X1)!=k3_xboole_0(k9_xtuple_0(X3),k9_xtuple_0(X4))\|X1!=k18_valued_1(X3,X4)\|~v3_valued_0(X4)\|~v3_valued_0(X3)\|~v5_relat_1(X4,k7_numbers)\|~v5_relat_1(X3,k7_numbers)\|~v4_relat_1(X4,X2)\|~v4_relat_1(X3,X2)\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,k7_numbers)))\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v1_funct_1(X1)), inference(csr,[status(thm)],[c_0_173, c_0_141])). cnf(c_0_188, negated_conjecture, (~r2_relset_1(esk1_0,k7_numbers,k5_mesfunc1(esk1_0,k1_mesfunc5(esk1_0,esk2_0),k1_mesfunc5(esk1_0,esk3_0)),k1_mesfunc5(esk1_0,k20_valued_1(esk1_0,k1_numbers,k1_numbers,esk2_0,esk3_0)))), inference(split_conjunct,[status(thm)],[c_0_47])). cnf(c_0_189, negated_conjecture, (X1=k5_mesfunc1(X2,X3,esk3_0)\|v1_xboole_0(X2)\|k9_xtuple_0(X1)!=k3_xboole_0(k9_xtuple_0(X3),k9_xtuple_0(esk3_0))\|X1!=k18_valued_1(X3,esk3_0)\|~v3_valued_0(X3)\|~v5_relat_1(X3,k7_numbers)\|~v4_relat_1(esk3_0,X2)\|~v4_relat_1(X3,X2)\|~v1_relat_1(X3)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,k7_numbers)))\|~v1_funct_1(X3)\|~v1_funct_1(X1)\|~v5_relat_1(X1,k7_numbers)\|~v1_relat_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_174, c_0_77])])). cnf(c_0_190, negated_conjecture, (m1_subset_1(k18_valued_1(esk2_0,esk3_0),k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_175, c_0_159]), c_0_73]), c_0_160])])])). cnf(c_0_191, negated_conjecture, (v1_funct_1(k18_valued_1(esk2_0,esk3_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176, c_0_159]), c_0_73]), c_0_160])])])). cnf(c_0_192, plain, (v4_relat_1(X1,X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(evalgc,[status(thm)],[c_0_177])). cnf(c_0_193, plain, (k3_xboole_0(X1,X2)=k3_xboole_0(X2,X1)), inference(evalgc,[status(thm)],[c_0_178])). cnf(c_0_194, plain, (k3_xboole_0(k9_xtuple_0(X1),k9_xtuple_0(X2))=k9_xtuple_0(k18_valued_1(X1,X2))\|~v1_valued_0(X2)\|~v1_valued_0(X1)\|~v1_relat_1(X2)\|~v1_relat_1(X1)\|~v1_funct_1(X2)\|~v1_funct_1(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_179, c_0_180]), c_0_181])). cnf(c_0_195, negated_conjecture, (k9_xtuple_0(X1)=k3_xboole_0(k9_xtuple_0(esk3_0),k9_xtuple_0(esk2_0))\|X1!=k18_valued_1(esk3_0,esk2_0)\|~v1_relat_1(X1)\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_182, c_0_183]), c_0_184]), c_0_159]), c_0_160]), c_0_82]), c_0_83])])])). cnf(c_0_196, negated_conjecture, (v1_relat_1(k18_valued_1(esk3_0,esk2_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_99, c_0_185])])). cnf(c_0_197, negated_conjecture, (v1_funct_1(k18_valued_1(esk3_0,esk2_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_186, c_0_82]), c_0_73]), c_0_83])])])). cnf(c_0_198, plain, (X1=k5_mesfunc1(X2,X3,X4)\|v1_xboole_0(X2)\|k9_xtuple_0(X1)!=k3_xboole_0(k9_xtuple_0(X3),k9_xtuple_0(X4))\|X1!=k18_valued_1(X3,X4)\|~v3_valued_0(X4)\|~v3_valued_0(X3)\|~v5_relat_1(X4,k7_numbers)\|~v5_relat_1(X3,k7_numbers)\|~v4_relat_1(X4,X2)\|~v4_relat_1(X3,X2)\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,k7_numbers)))\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v1_funct_1(X1)\|~v5_relat_1(X1,k7_numbers)\|~v1_relat_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_187, c_0_77])])). cnf(c_0_199, negated_conjecture, (~r2_relset_1(esk1_0,k7_numbers,k5_mesfunc1(esk1_0,k1_mesfunc5(esk1_0,esk2_0),k1_mesfunc5(esk1_0,esk3_0)),k1_mesfunc5(esk1_0,k20_valued_1(esk1_0,k1_numbers,k1_numbers,esk2_0,esk3_0)))), inference(evalgc,[status(thm)],[c_0_188])). cnf(c_0_200, negated_conjecture, (X1=k5_mesfunc1(X2,X3,esk3_0)\|v1_xboole_0(X2)\|k9_xtuple_0(X1)!=k3_xboole_0(k9_xtuple_0(X3),k9_xtuple_0(esk3_0))\|X1!=k18_valued_1(X3,esk3_0)\|~v3_valued_0(X3)\|~v5_relat_1(X3,k7_numbers)\|~v4_relat_1(esk3_0,X2)\|~v4_relat_1(X3,X2)\|~v1_relat_1(X3)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,k7_numbers)))\|~v1_funct_1(X3)\|~v1_funct_1(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_189, c_0_99]), c_0_110])). cnf(c_0_201, negated_conjecture, (m1_subset_1(k18_valued_1(esk2_0,esk3_0),k1_zfmisc_1(k2_zfmisc_1(esk1_0,k7_numbers)))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81, c_0_190]), c_0_191])]), c_0_84])])). cnf(c_0_202, negated_conjecture, (v4_relat_1(esk3_0,esk1_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_192, c_0_82])])). cnf(c_0_203, plain, (k3_xboole_0(k9_xtuple_0(X2),k9_xtuple_0(X1))=k9_xtuple_0(k18_valued_1(X1,X2))\|~v1_valued_0(X2)\|~v1_valued_0(X1)\|~v1_relat_1(X2)\|~v1_relat_1(X1)\|~v1_funct_1(X2)\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_193, c_0_194])])). cnf(c_0_204, negated_conjecture, (k3_xboole_0(k9_xtuple_0(esk3_0),k9_xtuple_0(esk2_0))=k9_xtuple_0(k18_valued_1(esk3_0,esk2_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_195]), c_0_196]), c_0_197])])])). cnf(c_0_205, plain, (X1=k5_mesfunc1(X2,X3,X4)\|v1_xboole_0(X2)\|k9_xtuple_0(X1)!=k3_xboole_0(k9_xtuple_0(X3),k9_xtuple_0(X4))\|X1!=k18_valued_1(X3,X4)\|~v3_valued_0(X4)\|~v3_valued_0(X3)\|~v5_relat_1(X4,k7_numbers)\|~v5_relat_1(X3,k7_numbers)\|~v4_relat_1(X4,X2)\|~v4_relat_1(X3,X2)\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,k7_numbers)))\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v1_funct_1(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_198, c_0_99]), c_0_110])). cnf(c_0_206, negated_conjecture, (m1_subset_1(k18_valued_1(esk3_0,esk2_0),k1_zfmisc_1(k2_zfmisc_1(esk1_0,k7_numbers)))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81, c_0_185]), c_0_197])]), c_0_84])])). cnf(c_0_207, negated_conjecture, (~r2_relset_1(esk1_0,k7_numbers,k5_mesfunc1(esk1_0,esk2_0,k1_mesfunc5(esk1_0,esk3_0)),k1_mesfunc5(esk1_0,k20_valued_1(esk1_0,k1_numbers,k1_numbers,esk2_0,esk3_0)))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_199, c_0_62]), c_0_159]), c_0_160])]), c_0_84])])). cnf(c_0_208, negated_conjecture, (k5_mesfunc1(esk1_0,X1,esk3_0)=k18_valued_1(esk2_0,esk3_0)\|k3_xboole_0(k9_xtuple_0(X1),k9_xtuple_0(esk3_0))!=k9_xtuple_0(k18_valued_1(esk2_0,esk3_0))\|k18_valued_1(esk2_0,esk3_0)!=k18_valued_1(X1,esk3_0)\|~v3_valued_0(X1)\|~v5_relat_1(X1,k7_numbers)\|~v4_relat_1(X1,esk1_0)\|~v1_relat_1(X1)\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_200, c_0_201]), c_0_202]), c_0_191])]), c_0_84])])). cnf(c_0_209, negated_conjecture, (k9_xtuple_0(k18_valued_1(esk2_0,esk3_0))=k9_xtuple_0(k18_valued_1(esk3_0,esk2_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_203, c_0_204]), c_0_146]), c_0_184]), c_0_109]), c_0_171]), c_0_83]), c_0_160])])])). cnf(c_0_210, negated_conjecture, (k5_mesfunc1(esk1_0,X1,X2)=k18_valued_1(esk3_0,esk2_0)\|k3_xboole_0(k9_xtuple_0(X1),k9_xtuple_0(X2))!=k9_xtuple_0(k18_valued_1(esk3_0,esk2_0))\|k18_valued_1(esk3_0,esk2_0)!=k18_valued_1(X1,X2)\|~v3_valued_0(X2)\|~v3_valued_0(X1)\|~v5_relat_1(X2,k7_numbers)\|~v5_relat_1(X1,k7_numbers)\|~v4_relat_1(X2,esk1_0)\|~v4_relat_1(X1,esk1_0)\|~v1_relat_1(X2)\|~v1_relat_1(X1)\|~v1_funct_1(X2)\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_205, c_0_206]), c_0_197])]), c_0_84])])). cnf(c_0_211, negated_conjecture, (~r2_relset_1(esk1_0,k7_numbers,k5_mesfunc1(esk1_0,esk2_0,esk3_0),k1_mesfunc5(esk1_0,k20_valued_1(esk1_0,k1_numbers,k1_numbers,esk2_0,esk3_0)))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_207, c_0_62]), c_0_82]), c_0_83])]), c_0_84])])). cnf(c_0_212, negated_conjecture, (k5_mesfunc1(esk1_0,X1,esk3_0)=k18_valued_1(esk2_0,esk3_0)\|k3_xboole_0(k9_xtuple_0(X1),k9_xtuple_0(esk3_0))!=k9_xtuple_0(k18_valued_1(esk3_0,esk2_0))\|k18_valued_1(esk2_0,esk3_0)!=k18_valued_1(X1,esk3_0)\|~v3_valued_0(X1)\|~v5_relat_1(X1,k7_numbers)\|~v4_relat_1(X1,esk1_0)\|~v1_relat_1(X1)\|~v1_funct_1(X1)), inference(rw,[status(thm)],[c_0_208, c_0_209])). cnf(c_0_213, negated_conjecture, (k5_mesfunc1(esk1_0,X1,X2)=k18_valued_1(esk3_0,esk2_0)\|k9_xtuple_0(k18_valued_1(X2,X1))!=k9_xtuple_0(k18_valued_1(esk3_0,esk2_0))\|k18_valued_1(esk3_0,esk2_0)!=k18_valued_1(X1,X2)\|~v3_valued_0(X2)\|~v3_valued_0(X1)\|~v5_relat_1(X2,k7_numbers)\|~v5_relat_1(X1,k7_numbers)\|~v4_relat_1(X2,esk1_0)\|~v4_relat_1(X1,esk1_0)\|~v1_relat_1(X2)\|~v1_relat_1(X1)\|~v1_funct_1(X2)\|~v1_funct_1(X1)\|~v1_valued_0(X1)\|~v1_valued_0(X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_210, c_0_203])])). cnf(c_0_214, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k7_numbers)))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81, c_0_159]), c_0_160])]), c_0_84])])). cnf(c_0_215, negated_conjecture, (~r2_relset_1(esk1_0,k7_numbers,k5_mesfunc1(esk1_0,esk2_0,esk3_0),k20_valued_1(esk1_0,k1_numbers,k1_numbers,esk2_0,esk3_0))\|~m1_subset_1(k20_valued_1(esk1_0,k1_numbers,k1_numbers,esk2_0,esk3_0),k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))\|~v1_funct_1(k20_valued_1(esk1_0,k1_numbers,k1_numbers,esk2_0,esk3_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_211, c_0_62]), c_0_84])])). cnf(c_0_216, negated_conjecture, (k5_mesfunc1(esk1_0,X1,esk3_0)=k18_valued_1(esk2_0,esk3_0)\|k9_xtuple_0(k18_valued_1(X1,esk3_0))!=k9_xtuple_0(k18_valued_1(esk3_0,esk2_0))\|k18_valued_1(esk2_0,esk3_0)!=k18_valued_1(X1,esk3_0)\|~v3_valued_0(X1)\|~v5_relat_1(X1,k7_numbers)\|~v4_relat_1(X1,esk1_0)\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v1_valued_0(X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_212, c_0_194]), c_0_146]), c_0_109]), c_0_83])])])). cnf(c_0_217, negated_conjecture, (k5_mesfunc1(esk1_0,X1,X2)=k18_valued_1(esk3_0,esk2_0)\|k9_xtuple_0(k18_valued_1(X2,X1))!=k9_xtuple_0(k18_valued_1(esk3_0,esk2_0))\|k18_valued_1(esk3_0,esk2_0)!=k18_valued_1(X1,X2)\|~v3_valued_0(X2)\|~v3_valued_0(X1)\|~v5_relat_1(X2,k7_numbers)\|~v5_relat_1(X1,k7_numbers)\|~v4_relat_1(X2,esk1_0)\|~v4_relat_1(X1,esk1_0)\|~v1_relat_1(X2)\|~v1_relat_1(X1)\|~v1_funct_1(X2)\|~v1_funct_1(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_213, c_0_141]), c_0_141])). cnf(c_0_218, negated_conjecture, (v5_relat_1(esk2_0,k7_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_110, c_0_214])])). cnf(c_0_219, negated_conjecture, (v4_relat_1(esk2_0,esk1_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_192, c_0_159])])). cnf(c_0_220, negated_conjecture, (~r2_relset_1(esk1_0,k7_numbers,k5_mesfunc1(esk1_0,esk2_0,esk3_0),k18_valued_1(esk3_0,esk2_0))\|~m1_subset_1(k18_valued_1(esk3_0,esk2_0),k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_215, c_0_136]), c_0_197]), c_0_73]), c_0_159]), c_0_82]), c_0_160]), c_0_83])])])). cnf(c_0_221, negated_conjecture, (k5_mesfunc1(esk1_0,X1,esk3_0)=k18_valued_1(esk2_0,esk3_0)\|k9_xtuple_0(k18_valued_1(X1,esk3_0))!=k9_xtuple_0(k18_valued_1(esk3_0,esk2_0))\|k18_valued_1(esk2_0,esk3_0)!=k18_valued_1(X1,esk3_0)\|~v3_valued_0(X1)\|~v5_relat_1(X1,k7_numbers)\|~v4_relat_1(X1,esk1_0)\|~v1_relat_1(X1)\|~v1_funct_1(X1)), inference(csr,[status(thm)],[c_0_216, c_0_141])). cnf(c_0_222, negated_conjecture, (k5_mesfunc1(esk1_0,esk2_0,X1)=k18_valued_1(esk3_0,esk2_0)\|k9_xtuple_0(k18_valued_1(esk2_0,X1))!=k9_xtuple_0(k18_valued_1(esk3_0,esk2_0))\|k18_valued_1(esk2_0,X1)!=k18_valued_1(esk3_0,esk2_0)\|~v3_valued_0(X1)\|~v5_relat_1(X1,k7_numbers)\|~v4_relat_1(X1,esk1_0)\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_217, c_0_183]), c_0_170]), c_0_218]), c_0_219]), c_0_171]), c_0_160])])])). fof(c_0_223, plain, ![X76, X77, X78, X79]:(~m1_subset_1(X78,k1_zfmisc_1(k2_zfmisc_1(X76,X77)))\|~m1_subset_1(X79,k1_zfmisc_1(k2_zfmisc_1(X76,X77)))\|r2_relset_1(X76,X77,X78,X78)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[reflexivity_r2_relset_1])])). fof(c_0_224, plain, ![X80, X81]:(m1_subset_1(esk6_2(X80,X81),k1_zfmisc_1(k2_zfmisc_1(X80,X81)))&(v1_relat_1(esk6_2(X80,X81))&(v4_relat_1(esk6_2(X80,X81),X80)&(v5_relat_1(esk6_2(X80,X81),X81)&v1_funct_1(esk6_2(X80,X81)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_partfun1])])). cnf(c_0_225, negated_conjecture, (~r2_relset_1(esk1_0,k7_numbers,k5_mesfunc1(esk1_0,esk2_0,esk3_0),k18_valued_1(esk3_0,esk2_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_220, c_0_185])])). cnf(c_0_226, negated_conjecture, (k5_mesfunc1(esk1_0,esk2_0,esk3_0)=k18_valued_1(esk2_0,esk3_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_221, c_0_209]), c_0_170]), c_0_218]), c_0_219]), c_0_171]), c_0_160])])])). cnf(c_0_227, negated_conjecture, (k5_mesfunc1(esk1_0,esk2_0,X1)=k18_valued_1(esk3_0,esk2_0)\|k9_xtuple_0(k18_valued_1(esk2_0,X1))!=k9_xtuple_0(k18_valued_1(esk3_0,esk2_0))\|k18_valued_1(esk2_0,X1)!=k18_valued_1(esk3_0,esk2_0)\|~v3_valued_0(X1)\|~v5_relat_1(X1,k7_numbers)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(esk1_0,k1_numbers)))\|~v1_funct_1(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_222, c_0_99]), c_0_192])). cnf(c_0_228, plain, (r2_relset_1(X2,X3,X1,X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_223])). cnf(c_0_229, plain, (m1_subset_1(esk6_2(X1,X2),k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_224])). cnf(c_0_230, negated_conjecture, (~r2_relset_1(esk1_0,k7_numbers,k18_valued_1(esk2_0,esk3_0),k18_valued_1(esk3_0,esk2_0))), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[c_0_225, c_0_226])])). cnf(c_0_231, negated_conjecture, (k18_valued_1(esk2_0,esk3_0)=k18_valued_1(esk3_0,esk2_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_227, c_0_158]), c_0_226]), c_0_112]), c_0_120]), c_0_82]), c_0_83]), c_0_159]), c_0_160])])])). cnf(c_0_232, plain, (r2_relset_1(X2,X3,X1,X1)\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(evalgc,[status(thm)],[c_0_228])). cnf(c_0_233, plain, (m1_subset_1(esk6_2(X1,X2),k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(evalgc,[status(thm)],[c_0_229])). cnf(c_0_234, negated_conjecture, (~r2_relset_1(esk1_0,k7_numbers,k18_valued_1(esk3_0,esk2_0),k18_valued_1(esk3_0,esk2_0))), inference(rw,[status(thm)],[c_0_230, c_0_231])). cnf(c_0_235, plain, (r2_relset_1(X1,X2,X3,X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_232, c_0_233])])). cnf(c_0_236, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_234, c_0_235]), c_0_206])]), ['proof']). # SZS output end CNFRefutation	reserve X for non empty set, Y for set, S for SigmaField of X, M for sigma_Measure of S, f,g for PartFunc of X,COMPLEX, r for Real, k for real number, n for Nat, E for Element of S; theorem Th30: for f,g be PartFunc of X,REAL holds (R_EAL f)(#)(R_EAL g) = R_EAL(f(#)g) proof let f,g be PartFunc of X,REAL; A1: dom ((R_EAL f)(#)(R_EAL g)) = dom(R_EAL f) /\ dom(R_EAL g) by MESFUNC1:def 5; A2: now let x be Element of X; assume A3: x in dom((R_EAL f)(#)(R_EAL g)); then x in dom(f(#)g) by A1,VALUED_1:def 4; then A4: (f(#)g).x = f.x * g.x by VALUED_1:def 4; ((R_EAL f)(#)(R_EAL g)).x = (R_EAL f).x * (R_EAL g).x by A3,MESFUNC1:def 5; hence ((R_EAL f)(#)(R_EAL g)).x = (R_EAL(f(#)g)).x by A4,EXTREAL1:1; end; dom ((R_EAL f)(#)(R_EAL g)) = dom R_EAL(f(#)g) by A1,VALUED_1:def 4; hence thesis by A2,PARTFUN1:5; end;	Convert the following ATP output trace into a readable Mizar proof.
t20_arytm_0	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t20_arytm_0, conjecture, ![X1]:(m1_subset_1(X1,k1_numbers)=>![X2]:(m1_subset_1(X2,k1_numbers)=>(~(X2=k6_numbers)=>k2_arytm_0(k2_arytm_0(X1,X2),k4_arytm_0(X2))=X1))), file('/scratch/mptp/predsminms1/t20_arytm_0__0', t20_arytm_0)). fof(t13_arytm_0, axiom, ![X1]:(m1_subset_1(X1,k1_numbers)=>![X2]:(m1_subset_1(X2,k1_numbers)=>![X3]:(m1_subset_1(X3,k1_numbers)=>k2_arytm_0(X1,k2_arytm_0(X2,X3))=k2_arytm_0(k2_arytm_0(X1,X2),X3)))), file('/scratch/mptp/predsminms1/t20_arytm_0__0', t13_arytm_0)). fof(d4_arytm_0, axiom, ![X1]:(m1_subset_1(X1,k1_numbers)=>![X2]:(m1_subset_1(X2,k1_numbers)=>((~(X1=k6_numbers)=>(X2=k4_arytm_0(X1)<=>k2_arytm_0(X1,X2)=np__1))&(X1=k6_numbers=>(X2=k4_arytm_0(X1)<=>X2=k6_numbers))))), file('/scratch/mptp/predsminms1/t20_arytm_0__0', d4_arytm_0)). fof(t19_arytm_0, axiom, ![X1]:(m1_subset_1(X1,k1_numbers)=>![X2]:(m1_subset_1(X2,k1_numbers)=>(X2=np__1=>k2_arytm_0(X1,X2)=X1))), file('/scratch/mptp/predsminms1/t20_arytm_0__0', t19_arytm_0)). fof(dt_k4_arytm_0, axiom, ![X1]:(m1_subset_1(X1,k1_numbers)=>m1_subset_1(k4_arytm_0(X1),k1_numbers)), file('/scratch/mptp/predsminms1/t20_arytm_0__0', dt_k4_arytm_0)). fof(dt_c3__arytm_0, axiom, m1_subset_1(c3__arytm_0,k1_numbers), file('/scratch/mptp/predsminms1/t20_arytm_0__0', dt_c3__arytm_0)). fof(de_c3__arytm_0, axiom, c3__arytm_0=np__1, file('/scratch/mptp/predsminms1/t20_arytm_0__0', de_c3__arytm_0)). fof(c_0_7, negated_conjecture, ~(![X1]:(m1_subset_1(X1,k1_numbers)=>![X2]:(m1_subset_1(X2,k1_numbers)=>(~(X2=k6_numbers)=>k2_arytm_0(k2_arytm_0(X1,X2),k4_arytm_0(X2))=X1)))), inference(assume_negation,[status(cth)],[t20_arytm_0])). fof(c_0_8, negated_conjecture, (m1_subset_1(esk1_0,k1_numbers)&(m1_subset_1(esk2_0,k1_numbers)&(esk2_0!=k6_numbers&k2_arytm_0(k2_arytm_0(esk1_0,esk2_0),k4_arytm_0(esk2_0))!=esk1_0))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_7])])])])). fof(c_0_9, plain, ![X8, X9, X10]:(~m1_subset_1(X8,k1_numbers)\|(~m1_subset_1(X9,k1_numbers)\|(~m1_subset_1(X10,k1_numbers)\|k2_arytm_0(X8,k2_arytm_0(X9,X10))=k2_arytm_0(k2_arytm_0(X8,X9),X10)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t13_arytm_0])])])). fof(c_0_10, plain, ![X6, X7]:(((X7!=k4_arytm_0(X6)\|k2_arytm_0(X6,X7)=np__1\|X6=k6_numbers\|~m1_subset_1(X7,k1_numbers)\|~m1_subset_1(X6,k1_numbers))&(k2_arytm_0(X6,X7)!=np__1\|X7=k4_arytm_0(X6)\|X6=k6_numbers\|~m1_subset_1(X7,k1_numbers)\|~m1_subset_1(X6,k1_numbers)))&((X7!=k4_arytm_0(X6)\|X7=k6_numbers\|X6!=k6_numbers\|~m1_subset_1(X7,k1_numbers)\|~m1_subset_1(X6,k1_numbers))&(X7!=k6_numbers\|X7=k4_arytm_0(X6)\|X6!=k6_numbers\|~m1_subset_1(X7,k1_numbers)\|~m1_subset_1(X6,k1_numbers)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d4_arytm_0])])])])])). cnf(c_0_11, negated_conjecture, (k2_arytm_0(k2_arytm_0(esk1_0,esk2_0),k4_arytm_0(esk2_0))!=esk1_0), inference(split_conjunct,[status(thm)],[c_0_8])). cnf(c_0_12, plain, (k2_arytm_0(X1,k2_arytm_0(X2,X3))=k2_arytm_0(k2_arytm_0(X1,X2),X3)\|~m1_subset_1(X1,k1_numbers)\|~m1_subset_1(X2,k1_numbers)\|~m1_subset_1(X3,k1_numbers)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_13, negated_conjecture, (m1_subset_1(esk2_0,k1_numbers)), inference(split_conjunct,[status(thm)],[c_0_8])). cnf(c_0_14, negated_conjecture, (m1_subset_1(esk1_0,k1_numbers)), inference(split_conjunct,[status(thm)],[c_0_8])). fof(c_0_15, plain, ![X12, X13]:(~m1_subset_1(X12,k1_numbers)\|(~m1_subset_1(X13,k1_numbers)\|(X13!=np__1\|k2_arytm_0(X12,X13)=X12))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t19_arytm_0])])])). cnf(c_0_16, plain, (k2_arytm_0(X2,X1)=np__1\|X2=k6_numbers\|X1!=k4_arytm_0(X2)\|~m1_subset_1(X1,k1_numbers)\|~m1_subset_1(X2,k1_numbers)), inference(split_conjunct,[status(thm)],[c_0_10])). fof(c_0_17, plain, ![X11]:(~m1_subset_1(X11,k1_numbers)\|m1_subset_1(k4_arytm_0(X11),k1_numbers)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k4_arytm_0])])). cnf(c_0_18, negated_conjecture, (k2_arytm_0(k2_arytm_0(esk1_0,esk2_0),k4_arytm_0(esk2_0))!=esk1_0), inference(evalgc,[status(thm)],[c_0_11])). cnf(c_0_19, plain, (k2_arytm_0(k2_arytm_0(X1,X2),X3)=k2_arytm_0(X1,k2_arytm_0(X2,X3))\|~m1_subset_1(X3,k1_numbers)\|~m1_subset_1(X2,k1_numbers)\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[c_0_12])). cnf(c_0_20, negated_conjecture, (m1_subset_1(esk2_0,k1_numbers)), inference(evalgc,[status(thm)],[c_0_13])). cnf(c_0_21, negated_conjecture, (m1_subset_1(esk1_0,k1_numbers)), inference(evalgc,[status(thm)],[c_0_14])). cnf(c_0_22, plain, (k2_arytm_0(X1,X2)=X1\|~m1_subset_1(X1,k1_numbers)\|~m1_subset_1(X2,k1_numbers)\|X2!=np__1), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_23, plain, (X2=k6_numbers\|k2_arytm_0(X2,X1)=np__1\|X1!=k4_arytm_0(X2)\|~m1_subset_1(X2,k1_numbers)\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[c_0_16])). cnf(c_0_24, plain, (m1_subset_1(k4_arytm_0(X1),k1_numbers)\|~m1_subset_1(X1,k1_numbers)), inference(split_conjunct,[status(thm)],[c_0_17])). cnf(c_0_25, plain, (m1_subset_1(c3__arytm_0,k1_numbers)), inference(split_conjunct,[status(thm)],[dt_c3__arytm_0])). cnf(c_0_26, plain, (c3__arytm_0=np__1), inference(split_conjunct,[status(thm)],[de_c3__arytm_0])). cnf(c_0_27, negated_conjecture, (k2_arytm_0(esk1_0,k2_arytm_0(esk2_0,k4_arytm_0(esk2_0)))!=esk1_0\|~m1_subset_1(k4_arytm_0(esk2_0),k1_numbers)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18, c_0_19]), c_0_20]), c_0_21])])])). cnf(c_0_28, plain, (k2_arytm_0(X1,X2)=X1\|X2!=np__1\|~m1_subset_1(X2,k1_numbers)\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[c_0_22])). cnf(c_0_29, plain, (k2_arytm_0(X1,k4_arytm_0(X1))=np__1\|X1=k6_numbers\|~m1_subset_1(X1,k1_numbers)\|~m1_subset_1(k4_arytm_0(X1),k1_numbers)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_23])])). cnf(c_0_30, plain, (m1_subset_1(k4_arytm_0(X1),k1_numbers)\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[c_0_24])). cnf(c_0_31, plain, (m1_subset_1(c3__arytm_0,k1_numbers)), inference(evalgc,[status(thm)],[c_0_25])). cnf(c_0_32, plain, (c3__arytm_0=np__1), inference(evalgc,[status(thm)],[c_0_26])). cnf(c_0_33, negated_conjecture, (esk2_0!=k6_numbers), inference(split_conjunct,[status(thm)],[c_0_8])). cnf(c_0_34, negated_conjecture, (~m1_subset_1(k4_arytm_0(esk2_0),k1_numbers)\|k2_arytm_0(esk2_0,k4_arytm_0(esk2_0))!=np__1\|~m1_subset_1(k2_arytm_0(esk2_0,k4_arytm_0(esk2_0)),k1_numbers)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27, c_0_28]), c_0_21])])])). cnf(c_0_35, plain, (k2_arytm_0(X1,k4_arytm_0(X1))=np__1\|X1=k6_numbers\|~m1_subset_1(X1,k1_numbers)), inference(csr,[status(thm)],[c_0_29, c_0_30])). cnf(c_0_36, plain, (m1_subset_1(np__1,k1_numbers)), inference(rw,[status(thm)],[c_0_31, c_0_32])). cnf(c_0_37, negated_conjecture, (esk2_0!=k6_numbers), inference(evalgc,[status(thm)],[c_0_33])). cnf(c_0_38, negated_conjecture, (~m1_subset_1(k4_arytm_0(esk2_0),k1_numbers)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34, c_0_35]), c_0_36]), c_0_20])]), c_0_37])])). cnf(c_0_39, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38, c_0_30]), c_0_20])]), ['proof']). # SZS output end CNFRefutation	reserve x,y for Element of REAL; reserve i,j,k for Element of NAT; reserve a,b for Element of REAL; theorem for x,y st y <> 0 holds ((x,y),inv y) = x proof let x,y such that A1: y <> 0; thus ((x,y),inv y) = (x,(y,inv y)) by Th13 .= *(x,j) by A1,Def4 .= x by Th19; end;	Convert the following ATP output trace into a readable Mizar proof.
t26_partfun1	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t26_partfun1, conjecture, ![X1, X2, X3, X4]:((v1_relat_1(X4)&v1_funct_1(X4))=>(r2_hidden(X1,k1_relset_1(X2,k3_partfun1(X4,X2,X3)))=>k1_funct_1(k3_partfun1(X4,X2,X3),X1)=k1_funct_1(X4,X1))), file('/scratch/mptp/predsminms1/t26_partfun1__0', t26_partfun1)). fof(t25_partfun1, axiom, ![X1, X2, X3, X4]:((v1_relat_1(X4)&v1_funct_1(X4))=>((r2_hidden(X1,k9_xtuple_0(X4))&(r2_hidden(X1,X2)&r2_hidden(k1_funct_1(X4,X1),X3)))=>k1_funct_1(k3_partfun1(X4,X2,X3),X1)=k1_funct_1(X4,X1))), file('/scratch/mptp/predsminms1/t26_partfun1__0', t25_partfun1)). fof(t24_partfun1, axiom, ![X1, X2, X3, X4]:((v1_relat_1(X4)&v1_funct_1(X4))=>(r2_hidden(X1,k1_relset_1(X2,k3_partfun1(X4,X2,X3)))<=>(r2_hidden(X1,k9_xtuple_0(X4))&(r2_hidden(X1,X2)&r2_hidden(k1_funct_1(X4,X1),X3))))), file('/scratch/mptp/predsminms1/t26_partfun1__0', t24_partfun1)). fof(c_0_3, negated_conjecture, ~(![X1, X2, X3, X4]:((v1_relat_1(X4)&v1_funct_1(X4))=>(r2_hidden(X1,k1_relset_1(X2,k3_partfun1(X4,X2,X3)))=>k1_funct_1(k3_partfun1(X4,X2,X3),X1)=k1_funct_1(X4,X1)))), inference(assume_negation,[status(cth)],[t26_partfun1])). fof(c_0_4, negated_conjecture, ((v1_relat_1(esk4_0)&v1_funct_1(esk4_0))&(r2_hidden(esk1_0,k1_relset_1(esk2_0,k3_partfun1(esk4_0,esk2_0,esk3_0)))&k1_funct_1(k3_partfun1(esk4_0,esk2_0,esk3_0),esk1_0)!=k1_funct_1(esk4_0,esk1_0))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])). fof(c_0_5, plain, ![X9, X10, X11, X12]:(~v1_relat_1(X12)\|~v1_funct_1(X12)\|(~r2_hidden(X9,k9_xtuple_0(X12))\|(~r2_hidden(X9,X10)\|~r2_hidden(k1_funct_1(X12,X9),X11))\|k1_funct_1(k3_partfun1(X12,X10,X11),X9)=k1_funct_1(X12,X9))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t25_partfun1])])). fof(c_0_6, plain, ![X13, X14, X15, X16]:(((r2_hidden(X13,k9_xtuple_0(X16))\|~r2_hidden(X13,k1_relset_1(X14,k3_partfun1(X16,X14,X15)))\|(~v1_relat_1(X16)\|~v1_funct_1(X16)))&((r2_hidden(X13,X14)\|~r2_hidden(X13,k1_relset_1(X14,k3_partfun1(X16,X14,X15)))\|(~v1_relat_1(X16)\|~v1_funct_1(X16)))&(r2_hidden(k1_funct_1(X16,X13),X15)\|~r2_hidden(X13,k1_relset_1(X14,k3_partfun1(X16,X14,X15)))\|(~v1_relat_1(X16)\|~v1_funct_1(X16)))))&(~r2_hidden(X13,k9_xtuple_0(X16))\|(~r2_hidden(X13,X14)\|~r2_hidden(k1_funct_1(X16,X13),X15))\|r2_hidden(X13,k1_relset_1(X14,k3_partfun1(X16,X14,X15)))\|(~v1_relat_1(X16)\|~v1_funct_1(X16)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t24_partfun1])])])). cnf(c_0_7, negated_conjecture, (k1_funct_1(k3_partfun1(esk4_0,esk2_0,esk3_0),esk1_0)!=k1_funct_1(esk4_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_8, plain, (k1_funct_1(k3_partfun1(X1,X3,X4),X2)=k1_funct_1(X1,X2)\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~r2_hidden(X2,k9_xtuple_0(X1))\|~r2_hidden(X2,X3)\|~r2_hidden(k1_funct_1(X1,X2),X4)), inference(split_conjunct,[status(thm)],[c_0_5])). cnf(c_0_9, negated_conjecture, (v1_funct_1(esk4_0)), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_10, negated_conjecture, (v1_relat_1(esk4_0)), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_11, plain, (r2_hidden(X1,k9_xtuple_0(X2))\|~r2_hidden(X1,k1_relset_1(X3,k3_partfun1(X2,X3,X4)))\|~v1_relat_1(X2)\|~v1_funct_1(X2)), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_12, negated_conjecture, (r2_hidden(esk1_0,k1_relset_1(esk2_0,k3_partfun1(esk4_0,esk2_0,esk3_0)))), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_13, plain, (r2_hidden(X1,X2)\|~r2_hidden(X1,k1_relset_1(X2,k3_partfun1(X3,X2,X4)))\|~v1_relat_1(X3)\|~v1_funct_1(X3)), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_14, plain, (r2_hidden(k1_funct_1(X1,X2),X3)\|~r2_hidden(X2,k1_relset_1(X4,k3_partfun1(X1,X4,X3)))\|~v1_relat_1(X1)\|~v1_funct_1(X1)), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_15, negated_conjecture, (k1_funct_1(k3_partfun1(esk4_0,esk2_0,esk3_0),esk1_0)!=k1_funct_1(esk4_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_7])). cnf(c_0_16, plain, (k1_funct_1(k3_partfun1(X1,X3,X4),X2)=k1_funct_1(X1,X2)\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~r2_hidden(X2,X3)\|~r2_hidden(X2,k9_xtuple_0(X1))\|~r2_hidden(k1_funct_1(X1,X2),X4)), inference(evalgc,[status(thm)],[c_0_8])). cnf(c_0_17, negated_conjecture, (v1_funct_1(esk4_0)), inference(evalgc,[status(thm)],[c_0_9])). cnf(c_0_18, negated_conjecture, (v1_relat_1(esk4_0)), inference(evalgc,[status(thm)],[c_0_10])). cnf(c_0_19, plain, (r2_hidden(X1,k9_xtuple_0(X2))\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~r2_hidden(X1,k1_relset_1(X3,k3_partfun1(X2,X3,X4)))), inference(evalgc,[status(thm)],[c_0_11])). cnf(c_0_20, negated_conjecture, (r2_hidden(esk1_0,k1_relset_1(esk2_0,k3_partfun1(esk4_0,esk2_0,esk3_0)))), inference(evalgc,[status(thm)],[c_0_12])). cnf(c_0_21, plain, (r2_hidden(X1,X2)\|~v1_relat_1(X3)\|~v1_funct_1(X3)\|~r2_hidden(X1,k1_relset_1(X2,k3_partfun1(X3,X2,X4)))), inference(evalgc,[status(thm)],[c_0_13])). cnf(c_0_22, plain, (r2_hidden(k1_funct_1(X1,X2),X3)\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~r2_hidden(X2,k1_relset_1(X4,k3_partfun1(X1,X4,X3)))), inference(evalgc,[status(thm)],[c_0_14])). cnf(c_0_23, negated_conjecture, (~r2_hidden(k1_funct_1(esk4_0,esk1_0),esk3_0)\|~r2_hidden(esk1_0,k9_xtuple_0(esk4_0))\|~r2_hidden(esk1_0,esk2_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15, c_0_16]), c_0_17]), c_0_18])])])). cnf(c_0_24, negated_conjecture, (r2_hidden(esk1_0,k9_xtuple_0(esk4_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19, c_0_20]), c_0_17]), c_0_18])])])). cnf(c_0_25, negated_conjecture, (r2_hidden(esk1_0,esk2_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21, c_0_20]), c_0_17]), c_0_18])])])). cnf(c_0_26, negated_conjecture, (r2_hidden(k1_funct_1(esk4_0,esk1_0),esk3_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22, c_0_20]), c_0_17]), c_0_18])])])). cnf(c_0_27, negated_conjecture, (~r2_hidden(k1_funct_1(esk4_0,esk1_0),esk3_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23, c_0_24]), c_0_25])])). cnf(c_0_28, negated_conjecture, ($false), inference(sr,[status(thm)],[c_0_26, c_0_27]), ['proof']). # SZS output end CNFRefutation	reserve x,x1,x2,y,y9,y1,y2,z,z1,z2,P,X,X1,X2,Y,Y1,Y2,V,Z for set; theorem Th26: for f being Function st x in dom <:f,X,Y:> holds <:f,X,Y:>.x = f .x proof let f be Function; assume A1: x in dom <:f,X,Y:>; then x in dom f & f.x in Y by Th24; hence thesis by A1,Th25; end;	Convert the following ATP output trace into a readable Mizar proof.
t8_xreal_1	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t8_xreal_1, conjecture, ![X1]:(v1_xreal_0(X1)=>![X2]:(v1_xreal_0(X2)=>![X3]:(v1_xreal_0(X3)=>![X4]:(v1_xreal_0(X4)=>~((~(r1_xxreal_0(X2,X1))&(r1_xxreal_0(X3,X4)&r1_xxreal_0(k2_xcmplx_0(X2,X4),k2_xcmplx_0(X1,X3))))))))), file('/scratch/mptp/predsminms1/t8_xreal_1__0', t8_xreal_1)). fof(l8_xreal_1, axiom, ![X1]:(v1_xreal_0(X1)=>![X2]:(v1_xreal_0(X2)=>![X3]:(v1_xreal_0(X3)=>![X4]:(v1_xreal_0(X4)=>~((~(r1_xxreal_0(X2,X1))&(r1_xxreal_0(X3,X4)&r1_xxreal_0(k2_xcmplx_0(X2,X4),k2_xcmplx_0(X1,X3))))))))), file('/scratch/mptp/predsminms1/t8_xreal_1__0', l8_xreal_1)). fof(c_0_2, negated_conjecture, ~(![X1]:(v1_xreal_0(X1)=>![X2]:(v1_xreal_0(X2)=>![X3]:(v1_xreal_0(X3)=>![X4]:(v1_xreal_0(X4)=>~((~(r1_xxreal_0(X2,X1))&(r1_xxreal_0(X3,X4)&r1_xxreal_0(k2_xcmplx_0(X2,X4),k2_xcmplx_0(X1,X3)))))))))), inference(assume_negation,[status(cth)],[t8_xreal_1])). fof(c_0_3, plain, ![X9, X10, X11, X12]:(~v1_xreal_0(X9)\|(~v1_xreal_0(X10)\|(~v1_xreal_0(X11)\|(~v1_xreal_0(X12)\|(r1_xxreal_0(X10,X9)\|(~r1_xxreal_0(X11,X12)\|~r1_xxreal_0(k2_xcmplx_0(X10,X12),k2_xcmplx_0(X9,X11)))))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[l8_xreal_1])])])])). fof(c_0_4, negated_conjecture, (v1_xreal_0(esk1_0)&(v1_xreal_0(esk2_0)&(v1_xreal_0(esk3_0)&(v1_xreal_0(esk4_0)&(~r1_xxreal_0(esk2_0,esk1_0)&(r1_xxreal_0(esk3_0,esk4_0)&r1_xxreal_0(k2_xcmplx_0(esk2_0,esk4_0),k2_xcmplx_0(esk1_0,esk3_0)))))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_2])])])])). cnf(c_0_5, plain, (r1_xxreal_0(X2,X1)\|~v1_xreal_0(X1)\|~v1_xreal_0(X2)\|~v1_xreal_0(X3)\|~v1_xreal_0(X4)\|~r1_xxreal_0(X3,X4)\|~r1_xxreal_0(k2_xcmplx_0(X2,X4),k2_xcmplx_0(X1,X3))), inference(split_conjunct,[status(thm)],[c_0_3])). cnf(c_0_6, negated_conjecture, (r1_xxreal_0(k2_xcmplx_0(esk2_0,esk4_0),k2_xcmplx_0(esk1_0,esk3_0))), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_7, negated_conjecture, (r1_xxreal_0(esk3_0,esk4_0)), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_8, negated_conjecture, (v1_xreal_0(esk4_0)), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_9, negated_conjecture, (v1_xreal_0(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_10, negated_conjecture, (v1_xreal_0(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_11, negated_conjecture, (v1_xreal_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_12, negated_conjecture, (~r1_xxreal_0(esk2_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_13, plain, (r1_xxreal_0(X2,X1)\|~v1_xreal_0(X4)\|~v1_xreal_0(X3)\|~v1_xreal_0(X2)\|~v1_xreal_0(X1)\|~r1_xxreal_0(X3,X4)\|~r1_xxreal_0(k2_xcmplx_0(X2,X4),k2_xcmplx_0(X1,X3))), inference(evalgc,[status(thm)],[c_0_5])). cnf(c_0_14, negated_conjecture, (r1_xxreal_0(k2_xcmplx_0(esk2_0,esk4_0),k2_xcmplx_0(esk1_0,esk3_0))), inference(evalgc,[status(thm)],[c_0_6])). cnf(c_0_15, negated_conjecture, (r1_xxreal_0(esk3_0,esk4_0)), inference(evalgc,[status(thm)],[c_0_7])). cnf(c_0_16, negated_conjecture, (v1_xreal_0(esk4_0)), inference(evalgc,[status(thm)],[c_0_8])). cnf(c_0_17, negated_conjecture, (v1_xreal_0(esk3_0)), inference(evalgc,[status(thm)],[c_0_9])). cnf(c_0_18, negated_conjecture, (v1_xreal_0(esk2_0)), inference(evalgc,[status(thm)],[c_0_10])). cnf(c_0_19, negated_conjecture, (v1_xreal_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_11])). cnf(c_0_20, negated_conjecture, (~r1_xxreal_0(esk2_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_12])). cnf(c_0_21, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13, c_0_14]), c_0_15]), c_0_16]), c_0_17]), c_0_18]), c_0_19])]), c_0_20]), ['proof']). # SZS output end CNFRefutation	reserve a,b,c,d for real number; reserve r,s for real number; theorem a < b & c <= d implies a+c < b+d by Lm8;	Convert the following ATP output trace into a readable Mizar proof.
t62_group_3	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(redefinition_r1_group_2, axiom, ![X1, X2, X3]:(((~(v2_struct_0(X1))&(v2_group_1(X1)&(v3_group_1(X1)&l3_algstr_0(X1))))&((v15_algstr_0(X2)&m1_group_2(X2,X1))&(v15_algstr_0(X3)&m1_group_2(X3,X1))))=>(r1_group_2(X1,X2,X3)<=>X2=X3)), file('/scratch/mptp/predsminms1/t62_group_3__0', redefinition_r1_group_2)). fof(t61_group_3, axiom, ![X1]:((~(v2_struct_0(X1))&(v2_group_1(X1)&(v3_group_1(X1)&l3_algstr_0(X1))))=>![X2]:((v15_algstr_0(X2)&m1_group_2(X2,X1))=>r1_group_2(X1,k6_group_3(X1,X2,k1_group_1(X1)),X2))), file('/scratch/mptp/predsminms1/t62_group_3__0', t61_group_3)). fof(dt_k6_group_3, axiom, ![X1, X2, X3]:(((~(v2_struct_0(X1))&(v2_group_1(X1)&(v3_group_1(X1)&l3_algstr_0(X1))))&(m1_group_2(X2,X1)&m1_subset_1(X3,u1_struct_0(X1))))=>(v15_algstr_0(k6_group_3(X1,X2,X3))&m1_group_2(k6_group_3(X1,X2,X3),X1))), file('/scratch/mptp/predsminms1/t62_group_3__0', dt_k6_group_3)). fof(dt_k6_algstr_0, axiom, ![X1, X2, X3]:((l3_algstr_0(X1)&(m1_subset_1(X2,u1_struct_0(X1))&m1_subset_1(X3,u1_struct_0(X1))))=>m1_subset_1(k6_algstr_0(X1,X2,X3),u1_struct_0(X1))), file('/scratch/mptp/predsminms1/t62_group_3__0', dt_k6_algstr_0)). fof(d5_group_1, axiom, ![X1]:((~(v2_struct_0(X1))&(v2_group_1(X1)&(v3_group_1(X1)&l3_algstr_0(X1))))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>(X3=k2_group_1(X1,X2)<=>(k6_algstr_0(X1,X2,X3)=k1_group_1(X1)&k6_algstr_0(X1,X3,X2)=k1_group_1(X1)))))), file('/scratch/mptp/predsminms1/t62_group_3__0', d5_group_1)). fof(t60_group_3, axiom, ![X1]:((~(v2_struct_0(X1))&(v2_group_1(X1)&(v3_group_1(X1)&l3_algstr_0(X1))))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>![X4]:(m1_group_2(X4,X1)=>r1_group_2(X1,k6_group_3(X1,k6_group_3(X1,X4,X2),X3),k6_group_3(X1,X4,k6_algstr_0(X1,X2,X3))))))), file('/scratch/mptp/predsminms1/t62_group_3__0', t60_group_3)). fof(dt_k2_group_1, axiom, ![X1, X2]:(((~(v2_struct_0(X1))&(v2_group_1(X1)&(v3_group_1(X1)&l3_algstr_0(X1))))&m1_subset_1(X2,u1_struct_0(X1)))=>m1_subset_1(k2_group_1(X1,X2),u1_struct_0(X1))), file('/scratch/mptp/predsminms1/t62_group_3__0', dt_k2_group_1)). fof(t62_group_3, conjecture, ![X1]:((~(v2_struct_0(X1))&(v2_group_1(X1)&(v3_group_1(X1)&l3_algstr_0(X1))))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:((v15_algstr_0(X3)&m1_group_2(X3,X1))=>(r1_group_2(X1,k6_group_3(X1,k6_group_3(X1,X3,X2),k2_group_1(X1,X2)),X3)&r1_group_2(X1,k6_group_3(X1,k6_group_3(X1,X3,k2_group_1(X1,X2)),X2),X3))))), file('/scratch/mptp/predsminms1/t62_group_3__0', t62_group_3)). fof(c_0_8, plain, ![X13, X14, X15]:((~r1_group_2(X13,X14,X15)\|X14=X15\|(v2_struct_0(X13)\|(~v2_group_1(X13)\|(~v3_group_1(X13)\|~l3_algstr_0(X13)))\|(~v15_algstr_0(X14)\|~m1_group_2(X14,X13)\|(~v15_algstr_0(X15)\|~m1_group_2(X15,X13)))))&(X14!=X15\|r1_group_2(X13,X14,X15)\|(v2_struct_0(X13)\|(~v2_group_1(X13)\|(~v3_group_1(X13)\|~l3_algstr_0(X13)))\|(~v15_algstr_0(X14)\|~m1_group_2(X14,X13)\|(~v15_algstr_0(X15)\|~m1_group_2(X15,X13)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[redefinition_r1_group_2])])])])). fof(c_0_9, plain, ![X11, X12]:(v2_struct_0(X11)\|(~v2_group_1(X11)\|(~v3_group_1(X11)\|~l3_algstr_0(X11)))\|(~v15_algstr_0(X12)\|~m1_group_2(X12,X11)\|r1_group_2(X11,k6_group_3(X11,X12,k1_group_1(X11)),X12))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t61_group_3])])])])). cnf(c_0_10, plain, (X2=X3\|v2_struct_0(X1)\|~r1_group_2(X1,X2,X3)\|~v2_group_1(X1)\|~v3_group_1(X1)\|~l3_algstr_0(X1)\|~v15_algstr_0(X2)\|~m1_group_2(X2,X1)\|~v15_algstr_0(X3)\|~m1_group_2(X3,X1)), inference(split_conjunct,[status(thm)],[c_0_8])). cnf(c_0_11, plain, (v2_struct_0(X1)\|r1_group_2(X1,k6_group_3(X1,X2,k1_group_1(X1)),X2)\|~v2_group_1(X1)\|~v3_group_1(X1)\|~l3_algstr_0(X1)\|~v15_algstr_0(X2)\|~m1_group_2(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_9])). fof(c_0_12, plain, ![X8, X9, X10]:((v15_algstr_0(k6_group_3(X8,X9,X10))\|(v2_struct_0(X8)\|(~v2_group_1(X8)\|(~v3_group_1(X8)\|~l3_algstr_0(X8)))\|(~m1_group_2(X9,X8)\|~m1_subset_1(X10,u1_struct_0(X8)))))&(m1_group_2(k6_group_3(X8,X9,X10),X8)\|(v2_struct_0(X8)\|(~v2_group_1(X8)\|(~v3_group_1(X8)\|~l3_algstr_0(X8)))\|(~m1_group_2(X9,X8)\|~m1_subset_1(X10,u1_struct_0(X8)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k6_group_3])])])])). fof(c_0_13, plain, ![X25, X26, X27]:(~l3_algstr_0(X25)\|(~m1_subset_1(X26,u1_struct_0(X25))\|~m1_subset_1(X27,u1_struct_0(X25)))\|m1_subset_1(k6_algstr_0(X25,X26,X27),u1_struct_0(X25))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k6_algstr_0])])). fof(c_0_14, plain, ![X18, X19, X20]:(((k6_algstr_0(X18,X19,X20)=k1_group_1(X18)\|X20!=k2_group_1(X18,X19)\|~m1_subset_1(X20,u1_struct_0(X18))\|~m1_subset_1(X19,u1_struct_0(X18))\|(v2_struct_0(X18)\|(~v2_group_1(X18)\|(~v3_group_1(X18)\|~l3_algstr_0(X18)))))&(k6_algstr_0(X18,X20,X19)=k1_group_1(X18)\|X20!=k2_group_1(X18,X19)\|~m1_subset_1(X20,u1_struct_0(X18))\|~m1_subset_1(X19,u1_struct_0(X18))\|(v2_struct_0(X18)\|(~v2_group_1(X18)\|(~v3_group_1(X18)\|~l3_algstr_0(X18))))))&(k6_algstr_0(X18,X19,X20)!=k1_group_1(X18)\|k6_algstr_0(X18,X20,X19)!=k1_group_1(X18)\|X20=k2_group_1(X18,X19)\|~m1_subset_1(X20,u1_struct_0(X18))\|~m1_subset_1(X19,u1_struct_0(X18))\|(v2_struct_0(X18)\|(~v2_group_1(X18)\|(~v3_group_1(X18)\|~l3_algstr_0(X18)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d5_group_1])])])])])). fof(c_0_15, plain, ![X21, X22, X23, X24]:(v2_struct_0(X21)\|(~v2_group_1(X21)\|(~v3_group_1(X21)\|~l3_algstr_0(X21)))\|(~m1_subset_1(X22,u1_struct_0(X21))\|(~m1_subset_1(X23,u1_struct_0(X21))\|(~m1_group_2(X24,X21)\|r1_group_2(X21,k6_group_3(X21,k6_group_3(X21,X24,X22),X23),k6_group_3(X21,X24,k6_algstr_0(X21,X22,X23))))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t60_group_3])])])])). cnf(c_0_16, plain, (X2=X3\|v2_struct_0(X1)\|~v2_group_1(X1)\|~v3_group_1(X1)\|~l3_algstr_0(X1)\|~v15_algstr_0(X3)\|~v15_algstr_0(X2)\|~m1_group_2(X3,X1)\|~m1_group_2(X2,X1)\|~r1_group_2(X1,X2,X3)), inference(evalgc,[status(thm)],[c_0_10])). cnf(c_0_17, plain, (v2_struct_0(X1)\|r1_group_2(X1,k6_group_3(X1,X2,k1_group_1(X1)),X2)\|~v2_group_1(X1)\|~v3_group_1(X1)\|~l3_algstr_0(X1)\|~v15_algstr_0(X2)\|~m1_group_2(X2,X1)), inference(evalgc,[status(thm)],[c_0_11])). cnf(c_0_18, plain, (m1_group_2(k6_group_3(X1,X2,X3),X1)\|v2_struct_0(X1)\|~v2_group_1(X1)\|~v3_group_1(X1)\|~l3_algstr_0(X1)\|~m1_group_2(X2,X1)\|~m1_subset_1(X3,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_19, plain, (m1_subset_1(k6_algstr_0(X1,X2,X3),u1_struct_0(X1))\|~l3_algstr_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_13])). cnf(c_0_20, plain, (k6_algstr_0(X1,X2,X3)=k1_group_1(X1)\|v2_struct_0(X1)\|X3!=k2_group_1(X1,X2)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~v2_group_1(X1)\|~v3_group_1(X1)\|~l3_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_14])). fof(c_0_21, plain, ![X16, X17]:(v2_struct_0(X16)\|(~v2_group_1(X16)\|(~v3_group_1(X16)\|~l3_algstr_0(X16)))\|~m1_subset_1(X17,u1_struct_0(X16))\|m1_subset_1(k2_group_1(X16,X17),u1_struct_0(X16))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k2_group_1])])])). cnf(c_0_22, plain, (v2_struct_0(X1)\|r1_group_2(X1,k6_group_3(X1,k6_group_3(X1,X4,X2),X3),k6_group_3(X1,X4,k6_algstr_0(X1,X2,X3)))\|~v2_group_1(X1)\|~v3_group_1(X1)\|~l3_algstr_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_group_2(X4,X1)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_23, plain, (k6_algstr_0(X1,X2,X3)=k1_group_1(X1)\|v2_struct_0(X1)\|X2!=k2_group_1(X1,X3)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~v2_group_1(X1)\|~v3_group_1(X1)\|~l3_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_14])). cnf(c_0_24, plain, (k6_group_3(X1,X2,k1_group_1(X1))=X2\|v2_struct_0(X1)\|~m1_group_2(X2,X1)\|~m1_group_2(k6_group_3(X1,X2,k1_group_1(X1)),X1)\|~v15_algstr_0(X2)\|~v15_algstr_0(k6_group_3(X1,X2,k1_group_1(X1)))\|~l3_algstr_0(X1)\|~v3_group_1(X1)\|~v2_group_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_16, c_0_17])])). cnf(c_0_25, plain, (v2_struct_0(X1)\|m1_group_2(k6_group_3(X1,X2,X3),X1)\|~v2_group_1(X1)\|~v3_group_1(X1)\|~l3_algstr_0(X1)\|~m1_group_2(X2,X1)\|~m1_subset_1(X3,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_18])). cnf(c_0_26, plain, (v15_algstr_0(k6_group_3(X1,X2,X3))\|v2_struct_0(X1)\|~v2_group_1(X1)\|~v3_group_1(X1)\|~l3_algstr_0(X1)\|~m1_group_2(X2,X1)\|~m1_subset_1(X3,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_27, plain, (m1_subset_1(k6_algstr_0(X1,X2,X3),u1_struct_0(X1))\|~l3_algstr_0(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_19])). cnf(c_0_28, plain, (k6_algstr_0(X1,X2,X3)=k1_group_1(X1)\|v2_struct_0(X1)\|X3!=k2_group_1(X1,X2)\|~v2_group_1(X1)\|~v3_group_1(X1)\|~l3_algstr_0(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_20])). cnf(c_0_29, plain, (v2_struct_0(X1)\|m1_subset_1(k2_group_1(X1,X2),u1_struct_0(X1))\|~v2_group_1(X1)\|~v3_group_1(X1)\|~l3_algstr_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_21])). fof(c_0_30, negated_conjecture, ~(![X1]:((~(v2_struct_0(X1))&(v2_group_1(X1)&(v3_group_1(X1)&l3_algstr_0(X1))))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:((v15_algstr_0(X3)&m1_group_2(X3,X1))=>(r1_group_2(X1,k6_group_3(X1,k6_group_3(X1,X3,X2),k2_group_1(X1,X2)),X3)&r1_group_2(X1,k6_group_3(X1,k6_group_3(X1,X3,k2_group_1(X1,X2)),X2),X3)))))), inference(assume_negation,[status(cth)],[t62_group_3])). cnf(c_0_31, plain, (v2_struct_0(X1)\|r1_group_2(X1,k6_group_3(X1,k6_group_3(X1,X4,X2),X3),k6_group_3(X1,X4,k6_algstr_0(X1,X2,X3)))\|~v2_group_1(X1)\|~v3_group_1(X1)\|~l3_algstr_0(X1)\|~m1_group_2(X4,X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_22])). cnf(c_0_32, plain, (k6_algstr_0(X1,X2,X3)=k1_group_1(X1)\|v2_struct_0(X1)\|X2!=k2_group_1(X1,X3)\|~v2_group_1(X1)\|~v3_group_1(X1)\|~l3_algstr_0(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_23])). cnf(c_0_33, plain, (k6_group_3(X1,X2,k1_group_1(X1))=X2\|v2_struct_0(X1)\|~m1_group_2(X2,X1)\|~v15_algstr_0(k6_group_3(X1,X2,k1_group_1(X1)))\|~v15_algstr_0(X2)\|~l3_algstr_0(X1)\|~v3_group_1(X1)\|~v2_group_1(X1)\|~m1_subset_1(k1_group_1(X1),u1_struct_0(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_24, c_0_25])])). cnf(c_0_34, plain, (v2_struct_0(X1)\|v15_algstr_0(k6_group_3(X1,X2,X3))\|~v2_group_1(X1)\|~v3_group_1(X1)\|~l3_algstr_0(X1)\|~m1_group_2(X2,X1)\|~m1_subset_1(X3,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_26])). cnf(c_0_35, plain, (m1_subset_1(k1_group_1(X1),u1_struct_0(X1))\|v2_struct_0(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l3_algstr_0(X1)\|X3!=k2_group_1(X1,X2)\|~v3_group_1(X1)\|~v2_group_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_27, c_0_28])])). cnf(c_0_36, plain, (v2_struct_0(X1)\|m1_subset_1(k2_group_1(X1,X2),u1_struct_0(X1))\|~v2_group_1(X1)\|~v3_group_1(X1)\|~l3_algstr_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_29])). fof(c_0_37, negated_conjecture, ((~v2_struct_0(esk1_0)&(v2_group_1(esk1_0)&(v3_group_1(esk1_0)&l3_algstr_0(esk1_0))))&(m1_subset_1(esk2_0,u1_struct_0(esk1_0))&((v15_algstr_0(esk3_0)&m1_group_2(esk3_0,esk1_0))&(~r1_group_2(esk1_0,k6_group_3(esk1_0,k6_group_3(esk1_0,esk3_0,esk2_0),k2_group_1(esk1_0,esk2_0)),esk3_0)\|~r1_group_2(esk1_0,k6_group_3(esk1_0,k6_group_3(esk1_0,esk3_0,k2_group_1(esk1_0,esk2_0)),esk2_0),esk3_0))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_30])])])])). cnf(c_0_38, plain, (r1_group_2(X1,k6_group_3(X1,k6_group_3(X1,X2,X3),X4),k6_group_3(X1,X2,k1_group_1(X1)))\|v2_struct_0(X1)\|~m1_group_2(X2,X1)\|~m1_subset_1(X4,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~l3_algstr_0(X1)\|~v3_group_1(X1)\|~v2_group_1(X1)\|X3!=k2_group_1(X1,X4)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_31, c_0_32])])). cnf(c_0_39, plain, (k6_group_3(X1,X2,k1_group_1(X1))=X2\|v2_struct_0(X1)\|~m1_group_2(X2,X1)\|~v15_algstr_0(X2)\|~m1_subset_1(k1_group_1(X1),u1_struct_0(X1))\|~l3_algstr_0(X1)\|~v3_group_1(X1)\|~v2_group_1(X1)), inference(csr,[status(thm)],[c_0_33, c_0_34])). cnf(c_0_40, plain, (m1_subset_1(k1_group_1(X1),u1_struct_0(X1))\|v2_struct_0(X1)\|k2_group_1(X1,X2)!=k2_group_1(X1,X3)\|~m1_subset_1(X3,u1_struct_0(X1))\|~l3_algstr_0(X1)\|~v3_group_1(X1)\|~v2_group_1(X1)\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_35, c_0_36])])). cnf(c_0_41, negated_conjecture, (~r1_group_2(esk1_0,k6_group_3(esk1_0,k6_group_3(esk1_0,esk3_0,esk2_0),k2_group_1(esk1_0,esk2_0)),esk3_0)\|~r1_group_2(esk1_0,k6_group_3(esk1_0,k6_group_3(esk1_0,esk3_0,k2_group_1(esk1_0,esk2_0)),esk2_0),esk3_0)), inference(split_conjunct,[status(thm)],[c_0_37])). cnf(c_0_42, plain, (r1_group_2(X1,k6_group_3(X1,k6_group_3(X1,X2,X3),X4),X2)\|v2_struct_0(X1)\|X3!=k2_group_1(X1,X4)\|~m1_group_2(X2,X1)\|~m1_subset_1(X4,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~l3_algstr_0(X1)\|~v3_group_1(X1)\|~v2_group_1(X1)\|~v15_algstr_0(X2)\|~m1_subset_1(k1_group_1(X1),u1_struct_0(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_38, c_0_39])])). cnf(c_0_43, plain, (m1_subset_1(k1_group_1(X1),u1_struct_0(X1))\|v2_struct_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~l3_algstr_0(X1)\|~v3_group_1(X1)\|~v2_group_1(X1)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_40])])). cnf(c_0_44, negated_conjecture, (m1_group_2(esk3_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_37])). cnf(c_0_45, negated_conjecture, (v15_algstr_0(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_37])). cnf(c_0_46, negated_conjecture, (m1_subset_1(esk2_0,u1_struct_0(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_37])). cnf(c_0_47, negated_conjecture, (l3_algstr_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_37])). cnf(c_0_48, negated_conjecture, (v3_group_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_37])). cnf(c_0_49, negated_conjecture, (v2_group_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_37])). cnf(c_0_50, negated_conjecture, (~v2_struct_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_37])). cnf(c_0_51, plain, (r1_group_2(X1,k6_group_3(X1,k6_group_3(X1,X2,X3),X4),k6_group_3(X1,X2,k1_group_1(X1)))\|v2_struct_0(X1)\|~m1_group_2(X2,X1)\|~m1_subset_1(X4,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~l3_algstr_0(X1)\|~v3_group_1(X1)\|~v2_group_1(X1)\|X4!=k2_group_1(X1,X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_31, c_0_28])])). cnf(c_0_52, negated_conjecture, (~r1_group_2(esk1_0,k6_group_3(esk1_0,k6_group_3(esk1_0,esk3_0,esk2_0),k2_group_1(esk1_0,esk2_0)),esk3_0)\|~r1_group_2(esk1_0,k6_group_3(esk1_0,k6_group_3(esk1_0,esk3_0,k2_group_1(esk1_0,esk2_0)),esk2_0),esk3_0)), inference(evalgc,[status(thm)],[c_0_41])). cnf(c_0_53, plain, (r1_group_2(X1,k6_group_3(X1,k6_group_3(X1,X2,X3),X4),X2)\|v2_struct_0(X1)\|X3!=k2_group_1(X1,X4)\|~m1_group_2(X2,X1)\|~v15_algstr_0(X2)\|~m1_subset_1(X4,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~l3_algstr_0(X1)\|~v3_group_1(X1)\|~v2_group_1(X1)), inference(csr,[status(thm)],[c_0_42, c_0_43])). cnf(c_0_54, negated_conjecture, (m1_group_2(esk3_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_44])). cnf(c_0_55, negated_conjecture, (v15_algstr_0(esk3_0)), inference(evalgc,[status(thm)],[c_0_45])). cnf(c_0_56, negated_conjecture, (m1_subset_1(esk2_0,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[c_0_46])). cnf(c_0_57, negated_conjecture, (l3_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_47])). cnf(c_0_58, negated_conjecture, (v3_group_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_48])). cnf(c_0_59, negated_conjecture, (v2_group_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_49])). cnf(c_0_60, negated_conjecture, (~v2_struct_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_50])). cnf(c_0_61, plain, (r1_group_2(X1,k6_group_3(X1,k6_group_3(X1,X2,X3),X4),X2)\|v2_struct_0(X1)\|X4!=k2_group_1(X1,X3)\|~m1_group_2(X2,X1)\|~m1_subset_1(X4,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~l3_algstr_0(X1)\|~v3_group_1(X1)\|~v2_group_1(X1)\|~v15_algstr_0(X2)\|~m1_subset_1(k1_group_1(X1),u1_struct_0(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_51, c_0_39])])). cnf(c_0_62, negated_conjecture, (~r1_group_2(esk1_0,k6_group_3(esk1_0,k6_group_3(esk1_0,esk3_0,esk2_0),k2_group_1(esk1_0,esk2_0)),esk3_0)\|~m1_subset_1(k2_group_1(esk1_0,esk2_0),u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52, c_0_53]), c_0_54]), c_0_55]), c_0_56]), c_0_57]), c_0_58]), c_0_59])]), c_0_60])])). cnf(c_0_63, plain, (r1_group_2(X1,k6_group_3(X1,k6_group_3(X1,X2,X3),X4),X2)\|v2_struct_0(X1)\|X4!=k2_group_1(X1,X3)\|~m1_group_2(X2,X1)\|~v15_algstr_0(X2)\|~m1_subset_1(X4,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~l3_algstr_0(X1)\|~v3_group_1(X1)\|~v2_group_1(X1)), inference(csr,[status(thm)],[c_0_61, c_0_43])). cnf(c_0_64, negated_conjecture, (~m1_subset_1(k2_group_1(esk1_0,esk2_0),u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62, c_0_63]), c_0_54]), c_0_55]), c_0_56]), c_0_57]), c_0_58]), c_0_59])]), c_0_60])])). cnf(c_0_65, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64, c_0_36]), c_0_56]), c_0_57]), c_0_58]), c_0_59])]), c_0_60]), ['proof']). # SZS output end CNFRefutation	reserve x,y,y1,y2 for set; reserve G for Group; reserve a,b,c,d,g,h for Element of G; reserve A,B,C,D for Subset of G; reserve H,H1,H2,H3 for Subgroup of G; reserve n for Nat; reserve i for Integer; theorem Th62: for H being strict Subgroup of G holds H \|^ a \|^ a" = H & H \|^ a " \|^ a = H proof let H be strict Subgroup of G; thus H \|^ a \|^ a" = H \|^ (a * a") by Th60 .= H \|^ 1_G by GROUP_1:def 5 .= H by Th61; thus H \|^ a" \|^ a = H \|^ (a" * a) by Th60 .= H \|^ 1_G by GROUP_1:def 5 .= H by Th61; end;	Convert the following ATP output trace into a readable Mizar proof.
t48_partfun2	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(d1_tarski, axiom, ![X1, X2]:(X2=k1_tarski(X1)<=>![X3]:(r2_hidden(X3,X2)<=>X3=X1)), file('/scratch/mptp/predsminms1/t48_partfun2__0', d1_tarski)). fof(t48_partfun2, conjecture, ![X1]:(~(v1_xboole_0(X1))=>![X2]:(~(v1_xboole_0(X2))=>![X3]:(m1_subset_1(X3,X1)=>![X4]:(m1_subset_1(X4,X2)=>![X5]:((v1_funct_1(X5)&m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X2))))=>(X5=k1_tarski(k4_tarski(X3,X4))=>k7_partfun1(X2,X5,X3)=X4)))))), file('/scratch/mptp/predsminms1/t48_partfun2__0', t48_partfun2)). fof(d6_partfun1, axiom, ![X1, X2]:((v1_relat_1(X2)&(v5_relat_1(X2,X1)&v1_funct_1(X2)))=>![X3]:(r2_hidden(X3,k9_xtuple_0(X2))=>k7_partfun1(X1,X2,X3)=k1_funct_1(X2,X3))), file('/scratch/mptp/predsminms1/t48_partfun2__0', d6_partfun1)). fof(cc2_relset_1, axiom, ![X1, X2, X3]:(m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))=>(v4_relat_1(X3,X1)&v5_relat_1(X3,X2))), file('/scratch/mptp/predsminms1/t48_partfun2__0', cc2_relset_1)). fof(cc1_relset_1, axiom, ![X1, X2, X3]:(m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))=>v1_relat_1(X3)), file('/scratch/mptp/predsminms1/t48_partfun2__0', cc1_relset_1)). fof(t1_funct_1, axiom, ![X1, X2, X3]:((v1_relat_1(X3)&v1_funct_1(X3))=>(r2_hidden(k4_tarski(X1,X2),X3)<=>(r2_hidden(X1,k9_xtuple_0(X3))&X2=k1_funct_1(X3,X1)))), file('/scratch/mptp/predsminms1/t48_partfun2__0', t1_funct_1)). fof(c_0_6, plain, ![X11, X12, X13, X14, X15, X16]:(((~r2_hidden(X13,X12)\|X13=X11\|X12!=k1_tarski(X11))&(X14!=X11\|r2_hidden(X14,X12)\|X12!=k1_tarski(X11)))&((~r2_hidden(esk6_2(X15,X16),X16)\|esk6_2(X15,X16)!=X15\|X16=k1_tarski(X15))&(r2_hidden(esk6_2(X15,X16),X16)\|esk6_2(X15,X16)=X15\|X16=k1_tarski(X15)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_tarski])])])])])])). fof(c_0_7, negated_conjecture, ~(![X1]:(~(v1_xboole_0(X1))=>![X2]:(~(v1_xboole_0(X2))=>![X3]:(m1_subset_1(X3,X1)=>![X4]:(m1_subset_1(X4,X2)=>![X5]:((v1_funct_1(X5)&m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X2))))=>(X5=k1_tarski(k4_tarski(X3,X4))=>k7_partfun1(X2,X5,X3)=X4))))))), inference(assume_negation,[status(cth)],[t48_partfun2])). cnf(c_0_8, plain, (r2_hidden(X1,X3)\|X1!=X2\|X3!=k1_tarski(X2)), inference(split_conjunct,[status(thm)],[c_0_6])). fof(c_0_9, negated_conjecture, (~v1_xboole_0(esk1_0)&(~v1_xboole_0(esk2_0)&(m1_subset_1(esk3_0,esk1_0)&(m1_subset_1(esk4_0,esk2_0)&((v1_funct_1(esk5_0)&m1_subset_1(esk5_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,esk2_0))))&(esk5_0=k1_tarski(k4_tarski(esk3_0,esk4_0))&k7_partfun1(esk2_0,esk5_0,esk3_0)!=esk4_0)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_7])])])])). fof(c_0_10, plain, ![X24, X25, X26]:(~v1_relat_1(X25)\|(~v5_relat_1(X25,X24)\|~v1_funct_1(X25))\|(~r2_hidden(X26,k9_xtuple_0(X25))\|k7_partfun1(X24,X25,X26)=k1_funct_1(X25,X26))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d6_partfun1])])])). fof(c_0_11, plain, ![X27, X28, X29]:((v4_relat_1(X29,X27)\|~m1_subset_1(X29,k1_zfmisc_1(k2_zfmisc_1(X27,X28))))&(v5_relat_1(X29,X28)\|~m1_subset_1(X29,k1_zfmisc_1(k2_zfmisc_1(X27,X28))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_relset_1])])])). fof(c_0_12, plain, ![X18, X19, X20]:(~m1_subset_1(X20,k1_zfmisc_1(k2_zfmisc_1(X18,X19)))\|v1_relat_1(X20)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relset_1])])). cnf(c_0_13, plain, (r2_hidden(X1,X3)\|X1!=X2\|X3!=k1_tarski(X2)), inference(evalgc,[status(thm)],[c_0_8])). cnf(c_0_14, negated_conjecture, (k7_partfun1(esk2_0,esk5_0,esk3_0)!=esk4_0), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_15, plain, (k7_partfun1(X2,X1,X3)=k1_funct_1(X1,X3)\|~v1_relat_1(X1)\|~v5_relat_1(X1,X2)\|~v1_funct_1(X1)\|~r2_hidden(X3,k9_xtuple_0(X1))), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_16, negated_conjecture, (v1_funct_1(esk5_0)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_17, plain, (v5_relat_1(X1,X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X3,X2)))), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_18, negated_conjecture, (m1_subset_1(esk5_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,esk2_0)))), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_19, plain, (v1_relat_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_12])). fof(c_0_20, plain, ![X21, X22, X23]:(((r2_hidden(X21,k9_xtuple_0(X23))\|~r2_hidden(k4_tarski(X21,X22),X23)\|(~v1_relat_1(X23)\|~v1_funct_1(X23)))&(X22=k1_funct_1(X23,X21)\|~r2_hidden(k4_tarski(X21,X22),X23)\|(~v1_relat_1(X23)\|~v1_funct_1(X23))))&(~r2_hidden(X21,k9_xtuple_0(X23))\|X22!=k1_funct_1(X23,X21)\|r2_hidden(k4_tarski(X21,X22),X23)\|(~v1_relat_1(X23)\|~v1_funct_1(X23)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_funct_1])])])). cnf(c_0_21, plain, (r2_hidden(X1,X2)\|X2!=k1_tarski(X1)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_13])])). cnf(c_0_22, negated_conjecture, (esk5_0=k1_tarski(k4_tarski(esk3_0,esk4_0))), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_23, negated_conjecture, (k7_partfun1(esk2_0,esk5_0,esk3_0)!=esk4_0), inference(evalgc,[status(thm)],[c_0_14])). cnf(c_0_24, plain, (k7_partfun1(X2,X1,X3)=k1_funct_1(X1,X3)\|~v1_funct_1(X1)\|~v1_relat_1(X1)\|~v5_relat_1(X1,X2)\|~r2_hidden(X3,k9_xtuple_0(X1))), inference(evalgc,[status(thm)],[c_0_15])). cnf(c_0_25, negated_conjecture, (v1_funct_1(esk5_0)), inference(evalgc,[status(thm)],[c_0_16])). cnf(c_0_26, plain, (v5_relat_1(X1,X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X3,X2)))), inference(evalgc,[status(thm)],[c_0_17])). cnf(c_0_27, negated_conjecture, (m1_subset_1(esk5_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,esk2_0)))), inference(evalgc,[status(thm)],[c_0_18])). cnf(c_0_28, plain, (v1_relat_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(evalgc,[status(thm)],[c_0_19])). cnf(c_0_29, plain, (X1=k1_funct_1(X2,X3)\|~r2_hidden(k4_tarski(X3,X1),X2)\|~v1_relat_1(X2)\|~v1_funct_1(X2)), inference(split_conjunct,[status(thm)],[c_0_20])). cnf(c_0_30, plain, (r2_hidden(X1,k1_tarski(X1))), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_21])])). cnf(c_0_31, negated_conjecture, (k1_tarski(k4_tarski(esk3_0,esk4_0))=esk5_0), inference(evalgc,[status(thm)],[c_0_22])). cnf(c_0_32, negated_conjecture, (k1_funct_1(esk5_0,esk3_0)!=esk4_0\|~v5_relat_1(esk5_0,esk2_0)\|~v1_relat_1(esk5_0)\|~r2_hidden(esk3_0,k9_xtuple_0(esk5_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23, c_0_24]), c_0_25])])])). cnf(c_0_33, negated_conjecture, (v5_relat_1(esk5_0,esk2_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_26, c_0_27])])). cnf(c_0_34, negated_conjecture, (v1_relat_1(esk5_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_28, c_0_27])])). cnf(c_0_35, plain, (X1=k1_funct_1(X2,X3)\|~v1_funct_1(X2)\|~v1_relat_1(X2)\|~r2_hidden(k4_tarski(X3,X1),X2)), inference(evalgc,[status(thm)],[c_0_29])). cnf(c_0_36, negated_conjecture, (r2_hidden(k4_tarski(esk3_0,esk4_0),esk5_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_30, c_0_31])])). cnf(c_0_37, plain, (r2_hidden(X1,k9_xtuple_0(X2))\|~r2_hidden(k4_tarski(X1,X3),X2)\|~v1_relat_1(X2)\|~v1_funct_1(X2)), inference(split_conjunct,[status(thm)],[c_0_20])). cnf(c_0_38, negated_conjecture, (k1_funct_1(esk5_0,esk3_0)!=esk4_0\|~r2_hidden(esk3_0,k9_xtuple_0(esk5_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32, c_0_33]), c_0_34])])). cnf(c_0_39, negated_conjecture, (k1_funct_1(esk5_0,esk3_0)=esk4_0), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35, c_0_36]), c_0_34]), c_0_25])])])). cnf(c_0_40, plain, (r2_hidden(X1,k9_xtuple_0(X2))\|~v1_funct_1(X2)\|~v1_relat_1(X2)\|~r2_hidden(k4_tarski(X1,X3),X2)), inference(evalgc,[status(thm)],[c_0_37])). cnf(c_0_41, negated_conjecture, (~r2_hidden(esk3_0,k9_xtuple_0(esk5_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38, c_0_39])])])). cnf(c_0_42, negated_conjecture, (r2_hidden(esk3_0,k9_xtuple_0(esk5_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40, c_0_36]), c_0_34]), c_0_25])])])). cnf(c_0_43, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41, c_0_42])]), ['proof']). # SZS output end CNFRefutation	reserve x,y,X,Y for set; reserve C,D,E for non empty set; reserve SC for Subset of C; reserve SD for Subset of D; reserve SE for Subset of E; reserve c,c1,c2 for Element of C; reserve d,d1,d2 for Element of D; reserve e for Element of E; reserve f,f1,g for PartFunc of C,D; reserve t for PartFunc of D,C; reserve s for PartFunc of D,E; reserve h for PartFunc of C,E; reserve F for PartFunc of D,D; theorem f = {[c,d]} implies f/.c = d proof assume A1: f = {[c,d]}; then [c,d] in f by TARSKI:def 1; then A2: c in dom f by FUNCT_1:1; (f qua Function).c = d by A1,GRFUNC_1:6; hence thesis by A2,PARTFUN1:def 6; end;	Convert the following ATP output trace into a readable Mizar proof.
t26_limfunc2	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(cc17_valued_0, axiom, ![X1, X2]:(v2_membered(X2)=>![X3]:(m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))=>v2_valued_0(X3))), file('/scratch/mptp/predsminms1/t26_limfunc2__0', cc17_valued_0)). fof(dt_k2_partfun1, axiom, ![X1, X2, X3, X4]:((v1_funct_1(X3)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2))))=>(v1_funct_1(k2_partfun1(X1,X2,X3,X4))&m1_subset_1(k2_partfun1(X1,X2,X3,X4),k1_zfmisc_1(k2_zfmisc_1(X1,X2))))), file('/scratch/mptp/predsminms1/t26_limfunc2__0', dt_k2_partfun1)). fof(t26_limfunc2, conjecture, ![X1]:(m1_subset_1(X1,k1_numbers)=>![X2]:((v1_funct_1(X2)&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))))=>(![X3]:(m1_subset_1(X3,k1_numbers)=>~((~(r1_xxreal_0(X1,X3))&![X4]:(m1_subset_1(X4,k1_numbers)=>~((~(r1_xxreal_0(X4,X3))&(~(r1_xxreal_0(X1,X4))&r2_hidden(X4,k1_relset_1(k1_numbers,X2)))))))))=>(![X3]:(m1_subset_1(X3,k1_numbers)=>~((~(r1_xxreal_0(X3,k6_numbers))&(v5_valued_0(k2_partfun1(k1_numbers,k1_numbers,X2,k2_rcomp_1(k9_real_1(X1,X3),X1)))&~(v1_seq_2(k2_partfun1(k1_numbers,k1_numbers,X2,k2_rcomp_1(k9_real_1(X1,X3),X1))))))))\|r2_limfunc2(X2,X1))))), file('/scratch/mptp/predsminms1/t26_limfunc2__0', t26_limfunc2)). fof(cc23_valued_0, axiom, ![X1]:((v1_relat_1(X1)&(v1_funct_1(X1)&(v2_valued_0(X1)&v5_valued_0(X1))))=>(v1_relat_1(X1)&(v1_funct_1(X1)&(v2_valued_0(X1)&v7_valued_0(X1))))), file('/scratch/mptp/predsminms1/t26_limfunc2__0', cc23_valued_0)). fof(cc1_relset_1, axiom, ![X1, X2, X3]:(m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))=>v1_relat_1(X3)), file('/scratch/mptp/predsminms1/t26_limfunc2__0', cc1_relset_1)). fof(t25_limfunc2, axiom, ![X1]:(m1_subset_1(X1,k1_numbers)=>![X2]:((v1_funct_1(X2)&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))))=>(![X3]:(m1_subset_1(X3,k1_numbers)=>~((~(r1_xxreal_0(X1,X3))&![X4]:(m1_subset_1(X4,k1_numbers)=>~((~(r1_xxreal_0(X4,X3))&(~(r1_xxreal_0(X1,X4))&r2_hidden(X4,k1_relset_1(k1_numbers,X2)))))))))=>(![X3]:(m1_subset_1(X3,k1_numbers)=>~((v7_valued_0(k2_partfun1(k1_numbers,k1_numbers,X2,k2_rcomp_1(k9_real_1(X1,X3),X1)))&~(v1_seq_2(k2_partfun1(k1_numbers,k1_numbers,X2,k2_rcomp_1(k9_real_1(X1,X3),X1)))))))\|r2_limfunc2(X2,X1))))), file('/scratch/mptp/predsminms1/t26_limfunc2__0', t25_limfunc2)). fof(cc4_membered, axiom, ![X1]:(v3_membered(X1)=>v2_membered(X1)), file('/scratch/mptp/predsminms1/t26_limfunc2__0', cc4_membered)). fof(fc3_membered, axiom, v3_membered(k1_numbers), file('/scratch/mptp/predsminms1/t26_limfunc2__0', fc3_membered)). fof(c_0_8, plain, ![X10, X11, X12]:(~v2_membered(X11)\|(~m1_subset_1(X12,k1_zfmisc_1(k2_zfmisc_1(X10,X11)))\|v2_valued_0(X12))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc17_valued_0])])])). fof(c_0_9, plain, ![X13, X14, X15, X16]:((v1_funct_1(k2_partfun1(X13,X14,X15,X16))\|(~v1_funct_1(X15)\|~m1_subset_1(X15,k1_zfmisc_1(k2_zfmisc_1(X13,X14)))))&(m1_subset_1(k2_partfun1(X13,X14,X15,X16),k1_zfmisc_1(k2_zfmisc_1(X13,X14)))\|(~v1_funct_1(X15)\|~m1_subset_1(X15,k1_zfmisc_1(k2_zfmisc_1(X13,X14)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_partfun1])])])). fof(c_0_10, negated_conjecture, ~(![X1]:(m1_subset_1(X1,k1_numbers)=>![X2]:((v1_funct_1(X2)&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))))=>(![X3]:(m1_subset_1(X3,k1_numbers)=>~((~(r1_xxreal_0(X1,X3))&![X4]:(m1_subset_1(X4,k1_numbers)=>~((~(r1_xxreal_0(X4,X3))&(~(r1_xxreal_0(X1,X4))&r2_hidden(X4,k1_relset_1(k1_numbers,X2)))))))))=>(![X3]:(m1_subset_1(X3,k1_numbers)=>~((~(r1_xxreal_0(X3,k6_numbers))&(v5_valued_0(k2_partfun1(k1_numbers,k1_numbers,X2,k2_rcomp_1(k9_real_1(X1,X3),X1)))&~(v1_seq_2(k2_partfun1(k1_numbers,k1_numbers,X2,k2_rcomp_1(k9_real_1(X1,X3),X1))))))))\|r2_limfunc2(X2,X1)))))), inference(assume_negation,[status(cth)],[t26_limfunc2])). fof(c_0_11, plain, ![X17]:((v1_relat_1(X17)\|(~v1_relat_1(X17)\|(~v1_funct_1(X17)\|(~v2_valued_0(X17)\|~v5_valued_0(X17)))))&((v1_funct_1(X17)\|(~v1_relat_1(X17)\|(~v1_funct_1(X17)\|(~v2_valued_0(X17)\|~v5_valued_0(X17)))))&((v2_valued_0(X17)\|(~v1_relat_1(X17)\|(~v1_funct_1(X17)\|(~v2_valued_0(X17)\|~v5_valued_0(X17)))))&(v7_valued_0(X17)\|(~v1_relat_1(X17)\|(~v1_funct_1(X17)\|(~v2_valued_0(X17)\|~v5_valued_0(X17)))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc23_valued_0])])])). cnf(c_0_12, plain, (v2_valued_0(X2)\|~v2_membered(X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_8])). cnf(c_0_13, plain, (m1_subset_1(k2_partfun1(X1,X2,X3,X4),k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_9])). fof(c_0_14, plain, ![X18, X19, X20]:(~m1_subset_1(X20,k1_zfmisc_1(k2_zfmisc_1(X18,X19)))\|v1_relat_1(X20)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relset_1])])). fof(c_0_15, plain, ![X21, X22, X24, X25]:((m1_subset_1(esk5_2(X21,X22),k1_numbers)\|(~m1_subset_1(X25,k1_numbers)\|(~v7_valued_0(k2_partfun1(k1_numbers,k1_numbers,X22,k2_rcomp_1(k9_real_1(X21,X25),X21)))\|v1_seq_2(k2_partfun1(k1_numbers,k1_numbers,X22,k2_rcomp_1(k9_real_1(X21,X25),X21))))\|r2_limfunc2(X22,X21))\|(~v1_funct_1(X22)\|~m1_subset_1(X22,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))))\|~m1_subset_1(X21,k1_numbers))&((~r1_xxreal_0(X21,esk5_2(X21,X22))\|(~m1_subset_1(X25,k1_numbers)\|(~v7_valued_0(k2_partfun1(k1_numbers,k1_numbers,X22,k2_rcomp_1(k9_real_1(X21,X25),X21)))\|v1_seq_2(k2_partfun1(k1_numbers,k1_numbers,X22,k2_rcomp_1(k9_real_1(X21,X25),X21))))\|r2_limfunc2(X22,X21))\|(~v1_funct_1(X22)\|~m1_subset_1(X22,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))))\|~m1_subset_1(X21,k1_numbers))&(~m1_subset_1(X24,k1_numbers)\|(r1_xxreal_0(X24,esk5_2(X21,X22))\|(r1_xxreal_0(X21,X24)\|~r2_hidden(X24,k1_relset_1(k1_numbers,X22))))\|(~m1_subset_1(X25,k1_numbers)\|(~v7_valued_0(k2_partfun1(k1_numbers,k1_numbers,X22,k2_rcomp_1(k9_real_1(X21,X25),X21)))\|v1_seq_2(k2_partfun1(k1_numbers,k1_numbers,X22,k2_rcomp_1(k9_real_1(X21,X25),X21))))\|r2_limfunc2(X22,X21))\|(~v1_funct_1(X22)\|~m1_subset_1(X22,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))))\|~m1_subset_1(X21,k1_numbers)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t25_limfunc2])])])])])])). fof(c_0_16, negated_conjecture, ![X7]:(m1_subset_1(esk1_0,k1_numbers)&((v1_funct_1(esk2_0)&m1_subset_1(esk2_0,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))))&(((m1_subset_1(esk3_1(X7),k1_numbers)\|r1_xxreal_0(esk1_0,X7)\|~m1_subset_1(X7,k1_numbers))&((~r1_xxreal_0(esk3_1(X7),X7)\|r1_xxreal_0(esk1_0,X7)\|~m1_subset_1(X7,k1_numbers))&((~r1_xxreal_0(esk1_0,esk3_1(X7))\|r1_xxreal_0(esk1_0,X7)\|~m1_subset_1(X7,k1_numbers))&(r2_hidden(esk3_1(X7),k1_relset_1(k1_numbers,esk2_0))\|r1_xxreal_0(esk1_0,X7)\|~m1_subset_1(X7,k1_numbers)))))&((m1_subset_1(esk4_0,k1_numbers)&(~r1_xxreal_0(esk4_0,k6_numbers)&(v5_valued_0(k2_partfun1(k1_numbers,k1_numbers,esk2_0,k2_rcomp_1(k9_real_1(esk1_0,esk4_0),esk1_0)))&~v1_seq_2(k2_partfun1(k1_numbers,k1_numbers,esk2_0,k2_rcomp_1(k9_real_1(esk1_0,esk4_0),esk1_0))))))&~r2_limfunc2(esk2_0,esk1_0))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_10])])])])])])). cnf(c_0_17, plain, (v7_valued_0(X1)\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v2_valued_0(X1)\|~v5_valued_0(X1)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_18, plain, (v2_valued_0(X2)\|~v2_membered(X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X3,X1)))), inference(evalgc,[status(thm)],[c_0_12])). cnf(c_0_19, plain, (m1_subset_1(k2_partfun1(X1,X2,X3,X4),k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(evalgc,[status(thm)],[c_0_13])). cnf(c_0_20, plain, (v1_relat_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_14])). cnf(c_0_21, plain, (r1_xxreal_0(X1,esk5_2(X2,X3))\|r1_xxreal_0(X2,X1)\|v1_seq_2(k2_partfun1(k1_numbers,k1_numbers,X3,k2_rcomp_1(k9_real_1(X2,X4),X2)))\|r2_limfunc2(X3,X2)\|~m1_subset_1(X1,k1_numbers)\|~r2_hidden(X1,k1_relset_1(k1_numbers,X3))\|~m1_subset_1(X4,k1_numbers)\|~v7_valued_0(k2_partfun1(k1_numbers,k1_numbers,X3,k2_rcomp_1(k9_real_1(X2,X4),X2)))\|~v1_funct_1(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))\|~m1_subset_1(X2,k1_numbers)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_22, negated_conjecture, (r2_hidden(esk3_1(X1),k1_relset_1(k1_numbers,esk2_0))\|r1_xxreal_0(esk1_0,X1)\|~m1_subset_1(X1,k1_numbers)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_23, negated_conjecture, (v1_funct_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_24, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_25, plain, (v7_valued_0(X1)\|~v1_funct_1(X1)\|~v5_valued_0(X1)\|~v2_valued_0(X1)\|~v1_relat_1(X1)), inference(evalgc,[status(thm)],[c_0_17])). cnf(c_0_26, plain, (v2_valued_0(k2_partfun1(X1,X2,X3,X4))\|~v2_membered(X2)\|~v1_funct_1(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_18, c_0_19])])). cnf(c_0_27, plain, (v1_funct_1(k2_partfun1(X1,X2,X3,X4))\|~v1_funct_1(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_28, plain, (v1_relat_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(evalgc,[status(thm)],[c_0_20])). cnf(c_0_29, plain, (r1_xxreal_0(X2,X1)\|r2_limfunc2(X3,X2)\|r1_xxreal_0(X1,esk5_2(X2,X3))\|v1_seq_2(k2_partfun1(k1_numbers,k1_numbers,X3,k2_rcomp_1(k9_real_1(X2,X4),X2)))\|~v1_funct_1(X3)\|~m1_subset_1(X4,k1_numbers)\|~m1_subset_1(X2,k1_numbers)\|~m1_subset_1(X1,k1_numbers)\|~r2_hidden(X1,k1_relset_1(k1_numbers,X3))\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))\|~v7_valued_0(k2_partfun1(k1_numbers,k1_numbers,X3,k2_rcomp_1(k9_real_1(X2,X4),X2)))), inference(evalgc,[status(thm)],[c_0_21])). cnf(c_0_30, negated_conjecture, (r1_xxreal_0(esk1_0,X1)\|r2_hidden(esk3_1(X1),k1_relset_1(k1_numbers,esk2_0))\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[c_0_22])). cnf(c_0_31, negated_conjecture, (v1_funct_1(esk2_0)), inference(evalgc,[status(thm)],[c_0_23])). cnf(c_0_32, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))), inference(evalgc,[status(thm)],[c_0_24])). cnf(c_0_33, negated_conjecture, (m1_subset_1(esk3_1(X1),k1_numbers)\|r1_xxreal_0(esk1_0,X1)\|~m1_subset_1(X1,k1_numbers)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_34, plain, (v7_valued_0(k2_partfun1(X1,X2,X3,X4))\|~v1_relat_1(k2_partfun1(X1,X2,X3,X4))\|~v5_valued_0(k2_partfun1(X1,X2,X3,X4))\|~v1_funct_1(k2_partfun1(X1,X2,X3,X4))\|~v2_membered(X2)\|~v1_funct_1(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_25, c_0_26])])). cnf(c_0_35, plain, (v1_funct_1(k2_partfun1(X1,X2,X3,X4))\|~v1_funct_1(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(evalgc,[status(thm)],[c_0_27])). cnf(c_0_36, plain, (v1_relat_1(k2_partfun1(X1,X2,X3,X4))\|~v1_funct_1(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_28, c_0_19])])). cnf(c_0_37, negated_conjecture, (v5_valued_0(k2_partfun1(k1_numbers,k1_numbers,esk2_0,k2_rcomp_1(k9_real_1(esk1_0,esk4_0),esk1_0)))), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_38, negated_conjecture, (r2_limfunc2(esk2_0,X1)\|v1_seq_2(k2_partfun1(k1_numbers,k1_numbers,esk2_0,k2_rcomp_1(k9_real_1(X1,X2),X1)))\|r1_xxreal_0(esk3_1(X3),esk5_2(X1,esk2_0))\|r1_xxreal_0(X1,esk3_1(X3))\|r1_xxreal_0(esk1_0,X3)\|~v7_valued_0(k2_partfun1(k1_numbers,k1_numbers,esk2_0,k2_rcomp_1(k9_real_1(X1,X2),X1)))\|~m1_subset_1(X2,k1_numbers)\|~m1_subset_1(X1,k1_numbers)\|~m1_subset_1(esk3_1(X3),k1_numbers)\|~m1_subset_1(X3,k1_numbers)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29, c_0_30]), c_0_31]), c_0_32])])])). cnf(c_0_39, negated_conjecture, (r1_xxreal_0(esk1_0,X1)\|m1_subset_1(esk3_1(X1),k1_numbers)\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[c_0_33])). cnf(c_0_40, plain, (v7_valued_0(k2_partfun1(X1,X2,X3,X4))\|~v2_membered(X2)\|~v5_valued_0(k2_partfun1(X1,X2,X3,X4))\|~v1_funct_1(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_34, c_0_35]), c_0_36])). cnf(c_0_41, negated_conjecture, (v5_valued_0(k2_partfun1(k1_numbers,k1_numbers,esk2_0,k2_rcomp_1(k9_real_1(esk1_0,esk4_0),esk1_0)))), inference(evalgc,[status(thm)],[c_0_37])). cnf(c_0_42, negated_conjecture, (m1_subset_1(esk4_0,k1_numbers)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_43, negated_conjecture, (m1_subset_1(esk1_0,k1_numbers)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_44, negated_conjecture, (~r2_limfunc2(esk2_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_45, negated_conjecture, (~v1_seq_2(k2_partfun1(k1_numbers,k1_numbers,esk2_0,k2_rcomp_1(k9_real_1(esk1_0,esk4_0),esk1_0)))), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_46, negated_conjecture, (r2_limfunc2(esk2_0,X1)\|v1_seq_2(k2_partfun1(k1_numbers,k1_numbers,esk2_0,k2_rcomp_1(k9_real_1(X1,X2),X1)))\|r1_xxreal_0(esk3_1(X3),esk5_2(X1,esk2_0))\|r1_xxreal_0(X1,esk3_1(X3))\|r1_xxreal_0(esk1_0,X3)\|~v7_valued_0(k2_partfun1(k1_numbers,k1_numbers,esk2_0,k2_rcomp_1(k9_real_1(X1,X2),X1)))\|~m1_subset_1(X2,k1_numbers)\|~m1_subset_1(X1,k1_numbers)\|~m1_subset_1(X3,k1_numbers)), inference(csr,[status(thm)],[c_0_38, c_0_39])). cnf(c_0_47, negated_conjecture, (v7_valued_0(k2_partfun1(k1_numbers,k1_numbers,esk2_0,k2_rcomp_1(k9_real_1(esk1_0,esk4_0),esk1_0)))\|~v2_membered(k1_numbers)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40, c_0_41]), c_0_31]), c_0_32])])])). cnf(c_0_48, negated_conjecture, (m1_subset_1(esk4_0,k1_numbers)), inference(evalgc,[status(thm)],[c_0_42])). cnf(c_0_49, negated_conjecture, (m1_subset_1(esk1_0,k1_numbers)), inference(evalgc,[status(thm)],[c_0_43])). cnf(c_0_50, negated_conjecture, (~r2_limfunc2(esk2_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_44])). cnf(c_0_51, negated_conjecture, (~v1_seq_2(k2_partfun1(k1_numbers,k1_numbers,esk2_0,k2_rcomp_1(k9_real_1(esk1_0,esk4_0),esk1_0)))), inference(evalgc,[status(thm)],[c_0_45])). cnf(c_0_52, negated_conjecture, (r1_xxreal_0(esk1_0,X1)\|~r1_xxreal_0(esk1_0,esk3_1(X1))\|~m1_subset_1(X1,k1_numbers)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_53, plain, (m1_subset_1(esk5_2(X1,X2),k1_numbers)\|v1_seq_2(k2_partfun1(k1_numbers,k1_numbers,X2,k2_rcomp_1(k9_real_1(X1,X3),X1)))\|r2_limfunc2(X2,X1)\|~m1_subset_1(X3,k1_numbers)\|~v7_valued_0(k2_partfun1(k1_numbers,k1_numbers,X2,k2_rcomp_1(k9_real_1(X1,X3),X1)))\|~v1_funct_1(X2)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))\|~m1_subset_1(X1,k1_numbers)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_54, plain, (v1_seq_2(k2_partfun1(k1_numbers,k1_numbers,X2,k2_rcomp_1(k9_real_1(X1,X3),X1)))\|r2_limfunc2(X2,X1)\|~r1_xxreal_0(X1,esk5_2(X1,X2))\|~m1_subset_1(X3,k1_numbers)\|~v7_valued_0(k2_partfun1(k1_numbers,k1_numbers,X2,k2_rcomp_1(k9_real_1(X1,X3),X1)))\|~v1_funct_1(X2)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))\|~m1_subset_1(X1,k1_numbers)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_55, negated_conjecture, (r1_xxreal_0(esk1_0,X1)\|~r1_xxreal_0(esk3_1(X1),X1)\|~m1_subset_1(X1,k1_numbers)), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_56, negated_conjecture, (r1_xxreal_0(esk3_1(X1),esk5_2(esk1_0,esk2_0))\|r1_xxreal_0(esk1_0,esk3_1(X1))\|r1_xxreal_0(esk1_0,X1)\|~m1_subset_1(X1,k1_numbers)\|~v2_membered(k1_numbers)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46, c_0_47]), c_0_48]), c_0_49])]), c_0_50]), c_0_51])])). cnf(c_0_57, negated_conjecture, (r1_xxreal_0(esk1_0,X1)\|~m1_subset_1(X1,k1_numbers)\|~r1_xxreal_0(esk1_0,esk3_1(X1))), inference(evalgc,[status(thm)],[c_0_52])). cnf(c_0_58, plain, (r2_limfunc2(X2,X1)\|m1_subset_1(esk5_2(X1,X2),k1_numbers)\|v1_seq_2(k2_partfun1(k1_numbers,k1_numbers,X2,k2_rcomp_1(k9_real_1(X1,X3),X1)))\|~v1_funct_1(X2)\|~m1_subset_1(X3,k1_numbers)\|~m1_subset_1(X1,k1_numbers)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))\|~v7_valued_0(k2_partfun1(k1_numbers,k1_numbers,X2,k2_rcomp_1(k9_real_1(X1,X3),X1)))), inference(evalgc,[status(thm)],[c_0_53])). cnf(c_0_59, plain, (r2_limfunc2(X2,X1)\|v1_seq_2(k2_partfun1(k1_numbers,k1_numbers,X2,k2_rcomp_1(k9_real_1(X1,X3),X1)))\|~v1_funct_1(X2)\|~m1_subset_1(X3,k1_numbers)\|~m1_subset_1(X1,k1_numbers)\|~r1_xxreal_0(X1,esk5_2(X1,X2))\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))\|~v7_valued_0(k2_partfun1(k1_numbers,k1_numbers,X2,k2_rcomp_1(k9_real_1(X1,X3),X1)))), inference(evalgc,[status(thm)],[c_0_54])). cnf(c_0_60, negated_conjecture, (r1_xxreal_0(esk1_0,X1)\|~m1_subset_1(X1,k1_numbers)\|~r1_xxreal_0(esk3_1(X1),X1)), inference(evalgc,[status(thm)],[c_0_55])). cnf(c_0_61, negated_conjecture, (r1_xxreal_0(esk3_1(X1),esk5_2(esk1_0,esk2_0))\|r1_xxreal_0(esk1_0,X1)\|~v2_membered(k1_numbers)\|~m1_subset_1(X1,k1_numbers)), inference(csr,[status(thm)],[c_0_56, c_0_57])). cnf(c_0_62, negated_conjecture, (m1_subset_1(esk5_2(esk1_0,esk2_0),k1_numbers)\|~v7_valued_0(k2_partfun1(k1_numbers,k1_numbers,esk2_0,k2_rcomp_1(k9_real_1(esk1_0,esk4_0),esk1_0)))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51, c_0_58]), c_0_31]), c_0_32]), c_0_48]), c_0_49])]), c_0_50])])). cnf(c_0_63, negated_conjecture, (~v7_valued_0(k2_partfun1(k1_numbers,k1_numbers,esk2_0,k2_rcomp_1(k9_real_1(esk1_0,esk4_0),esk1_0)))\|~r1_xxreal_0(esk1_0,esk5_2(esk1_0,esk2_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51, c_0_59]), c_0_31]), c_0_32]), c_0_48]), c_0_49])]), c_0_50])])). fof(c_0_64, plain, ![X26]:(~v3_membered(X26)\|v2_membered(X26)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc4_membered])])). cnf(c_0_65, negated_conjecture, (r1_xxreal_0(esk1_0,esk5_2(esk1_0,esk2_0))\|~m1_subset_1(esk5_2(esk1_0,esk2_0),k1_numbers)\|~v2_membered(k1_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_60, c_0_61])])). cnf(c_0_66, negated_conjecture, (m1_subset_1(esk5_2(esk1_0,esk2_0),k1_numbers)\|~v2_membered(k1_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_62, c_0_47])])). cnf(c_0_67, negated_conjecture, (~r1_xxreal_0(esk1_0,esk5_2(esk1_0,esk2_0))\|~v2_membered(k1_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_63, c_0_47])])). cnf(c_0_68, plain, (v2_membered(X1)\|~v3_membered(X1)), inference(split_conjunct,[status(thm)],[c_0_64])). cnf(c_0_69, plain, (v3_membered(k1_numbers)), inference(split_conjunct,[status(thm)],[fc3_membered])). cnf(c_0_70, negated_conjecture, (~v2_membered(k1_numbers)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_65, c_0_66]), c_0_67])). cnf(c_0_71, plain, (v2_membered(X1)\|~v3_membered(X1)), inference(evalgc,[status(thm)],[c_0_68])). cnf(c_0_72, plain, (v3_membered(k1_numbers)), inference(evalgc,[status(thm)],[c_0_69])). cnf(c_0_73, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70, c_0_71]), c_0_72])]), ['proof']). # SZS output end CNFRefutation	reserve r,r1,r2,g,g1,g2,x0 for Real; reserve n,k for Element of NAT; reserve seq for Real_Sequence; reserve f,f1,f2 for PartFunc of REAL,REAL; theorem (ex r st 0<r & f\|].x0-r,x0.[ is increasing & not f\|].x0-r,x0.[ is bounded_above) & (for r st r<x0 ex g st r<g & g<x0 & g in dom f) implies f is_left_divergent_to+infty_in x0 by Th25;	Convert the following ATP output trace into a readable Mizar proof.
t55_circcomb	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(d2_funcop_1, axiom, ![X1, X2]:k2_funcop_1(X1,X2)=k2_zfmisc_1(X1,k1_tarski(X2)), file('/scratch/mptp/predsminms1/t55_circcomb__0', d2_funcop_1)). fof(redefinition_k7_funcop_1, axiom, ![X1, X2]:k7_funcop_1(X1,X2)=k2_funcop_1(X1,X2), file('/scratch/mptp/predsminms1/t55_circcomb__0', redefinition_k7_funcop_1)). fof(d13_circcomb, axiom, ![X1]:(v7_ordinal1(X1)=>![X2]:(~(v1_xboole_0(X2))=>![X3]:((v1_funct_1(X3)&(v1_funct_2(X3,k4_finseq_2(X1,X2),X2)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k4_finseq_2(X1,X2),X2)))))=>![X4]:((v1_relat_1(X4)&(v1_funct_1(X4)&(v3_card_1(X4,X1)&v1_finseq_1(X4))))=>![X5]:((v3_msualg_1(X5,k5_circcomb(X3,X4))&(v4_msualg_1(X5,k5_circcomb(X3,X4))&l3_msualg_1(X5,k5_circcomb(X3,X4))))=>(X5=k7_circcomb(X1,X2,X3,X4)<=>(r8_pboole(u1_struct_0(k5_circcomb(X3,X4)),u3_msualg_1(k5_circcomb(X3,X4),X5),k7_funcop_1(u1_struct_0(k5_circcomb(X3,X4)),X2))&k1_funct_1(u4_msualg_1(k5_circcomb(X3,X4),X5),k4_tarski(X4,X3))=X3))))))), file('/scratch/mptp/predsminms1/t55_circcomb__0', d13_circcomb)). fof(t55_circcomb, conjecture, ![X1]:(v7_ordinal1(X1)=>![X2]:(~(v1_xboole_0(X2))=>![X3]:((v1_funct_1(X3)&(v1_funct_2(X3,k4_finseq_2(X1,X2),X2)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k4_finseq_2(X1,X2),X2)))))=>![X4]:((v1_relat_1(X4)&(v1_funct_1(X4)&(v3_card_1(X4,X1)&v1_finseq_1(X4))))=>![X5]:((v1_relat_1(X5)&(v1_funct_1(X5)&(v3_card_1(X5,X1)&v1_finseq_1(X5))))=>r2_circcomb(k5_circcomb(X3,X4),k5_circcomb(X3,X5),k7_circcomb(X1,X2,X3,X4),k7_circcomb(X1,X2,X3,X5))))))), file('/scratch/mptp/predsminms1/t55_circcomb__0', t55_circcomb)). fof(d7_funcop_1, axiom, ![X1, X2, X3]:k13_funcop_1(X1,X2,X3)=k7_funcop_1(k1_tarski(k4_tarski(X1,X2)),X3), file('/scratch/mptp/predsminms1/t55_circcomb__0', d7_funcop_1)). fof(d5_tarski, axiom, ![X1, X2]:k4_tarski(X1,X2)=k2_tarski(k2_tarski(X1,X2),k1_tarski(X1)), file('/scratch/mptp/predsminms1/t55_circcomb__0', d5_tarski)). fof(fc20_funcop_1, axiom, ![X1, X2]:(v1_relat_1(k2_funcop_1(X1,X2))&(v4_relat_1(k2_funcop_1(X1,X2),X1)&(v1_funct_1(k2_funcop_1(X1,X2))&v1_partfun1(k2_funcop_1(X1,X2),X1)))), file('/scratch/mptp/predsminms1/t55_circcomb__0', fc20_funcop_1)). fof(t54_circcomb, axiom, ![X1]:(v7_ordinal1(X1)=>![X2]:(~(v1_xboole_0(X2))=>![X3]:((v1_funct_1(X3)&(v1_funct_2(X3,k4_finseq_2(X1,X2),X2)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k4_finseq_2(X1,X2),X2)))))=>![X4]:((v1_relat_1(X4)&(v1_funct_1(X4)&(v3_card_1(X4,X1)&v1_finseq_1(X4))))=>(u4_msualg_1(k5_circcomb(X3,X4),k7_circcomb(X1,X2,X3,X4))=k13_funcop_1(X4,X3,X3)&![X5]:(m1_subset_1(X5,u1_struct_0(k5_circcomb(X3,X4)))=>k1_funct_1(u3_msualg_1(k5_circcomb(X3,X4),k7_circcomb(X1,X2,X3,X4)),X5)=X2)))))), file('/scratch/mptp/predsminms1/t55_circcomb__0', t54_circcomb)). fof(redefinition_r8_pboole, axiom, ![X1, X2, X3]:((~(v1_xboole_0(X1))&((v1_relat_1(X2)&(v4_relat_1(X2,X1)&(v1_funct_1(X2)&v1_partfun1(X2,X1))))&(v1_relat_1(X3)&(v4_relat_1(X3,X1)&(v1_funct_1(X3)&v1_partfun1(X3,X1))))))=>(r8_pboole(X1,X2,X3)<=>X2=X3)), file('/scratch/mptp/predsminms1/t55_circcomb__0', redefinition_r8_pboole)). fof(t87_funcop_1, axiom, ![X1, X2, X3, X4]:(r1_partfun1(k7_funcop_1(X1,X3),k7_funcop_1(X2,X4))<=>(X3=X4\|r1_xboole_0(X1,X2))), file('/scratch/mptp/predsminms1/t55_circcomb__0', t87_funcop_1)). fof(commutativity_k2_tarski, axiom, ![X1, X2]:k2_tarski(X1,X2)=k2_tarski(X2,X1), file('/scratch/mptp/predsminms1/t55_circcomb__0', commutativity_k2_tarski)). fof(dt_u3_msualg_1, axiom, ![X1, X2]:((l1_struct_0(X1)&l2_msualg_1(X2,X1))=>(v1_relat_1(u3_msualg_1(X1,X2))&(v4_relat_1(u3_msualg_1(X1,X2),u1_struct_0(X1))&(v1_funct_1(u3_msualg_1(X1,X2))&v1_partfun1(u3_msualg_1(X1,X2),u1_struct_0(X1)))))), file('/scratch/mptp/predsminms1/t55_circcomb__0', dt_u3_msualg_1)). fof(dt_k7_circcomb, axiom, ![X1, X2, X3, X4]:((v7_ordinal1(X1)&(~(v1_xboole_0(X2))&((v1_funct_1(X3)&(v1_funct_2(X3,k4_finseq_2(X1,X2),X2)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k4_finseq_2(X1,X2),X2)))))&(v1_relat_1(X4)&(v1_funct_1(X4)&(v3_card_1(X4,X1)&v1_finseq_1(X4)))))))=>(v3_msualg_1(k7_circcomb(X1,X2,X3,X4),k5_circcomb(X3,X4))&(v4_msualg_1(k7_circcomb(X1,X2,X3,X4),k5_circcomb(X3,X4))&l3_msualg_1(k7_circcomb(X1,X2,X3,X4),k5_circcomb(X3,X4))))), file('/scratch/mptp/predsminms1/t55_circcomb__0', dt_k7_circcomb)). fof(d3_circcomb, axiom, ![X1]:((~(v2_struct_0(X1))&l1_msualg_1(X1))=>![X2]:((~(v2_struct_0(X2))&l1_msualg_1(X2))=>![X3]:(l3_msualg_1(X3,X1)=>![X4]:(l3_msualg_1(X4,X2)=>(r2_circcomb(X1,X2,X3,X4)<=>(r1_circcomb(X1,X2)&(r1_partfun1(u3_msualg_1(X1,X3),u3_msualg_1(X2,X4))&r1_partfun1(u4_msualg_1(X1,X3),u4_msualg_1(X2,X4))))))))), file('/scratch/mptp/predsminms1/t55_circcomb__0', d3_circcomb)). fof(dt_l3_msualg_1, axiom, ![X1]:((~(v2_struct_0(X1))&l1_msualg_1(X1))=>![X2]:(l3_msualg_1(X2,X1)=>l2_msualg_1(X2,X1))), file('/scratch/mptp/predsminms1/t55_circcomb__0', dt_l3_msualg_1)). fof(dt_l5_struct_0, axiom, ![X1]:(l5_struct_0(X1)=>l1_struct_0(X1)), file('/scratch/mptp/predsminms1/t55_circcomb__0', dt_l5_struct_0)). fof(dt_l1_msualg_1, axiom, ![X1]:(l1_msualg_1(X1)=>l5_struct_0(X1)), file('/scratch/mptp/predsminms1/t55_circcomb__0', dt_l1_msualg_1)). fof(t43_circcomb, axiom, ![X1, X2]:((v1_relat_1(X2)&(v1_funct_1(X2)&v1_finseq_1(X2)))=>![X3]:((v1_relat_1(X3)&(v1_funct_1(X3)&v1_finseq_1(X3)))=>r1_circcomb(k5_circcomb(X1,X2),k5_circcomb(X1,X3)))), file('/scratch/mptp/predsminms1/t55_circcomb__0', t43_circcomb)). fof(dt_k5_circcomb, axiom, ![X1, X2]:((v1_relat_1(X2)&(v1_funct_1(X2)&v1_finseq_1(X2)))=>(~(v11_struct_0(k5_circcomb(X1,X2)))&(v1_msualg_1(k5_circcomb(X1,X2))&l1_msualg_1(k5_circcomb(X1,X2))))), file('/scratch/mptp/predsminms1/t55_circcomb__0', dt_k5_circcomb)). fof(fc9_circcomb, axiom, ![X1, X2]:((v1_relat_1(X2)&(v1_funct_1(X2)&v1_finseq_1(X2)))=>(~(v2_struct_0(k5_circcomb(X1,X2)))&(~(v11_struct_0(k5_circcomb(X1,X2)))&v1_msualg_1(k5_circcomb(X1,X2))))), file('/scratch/mptp/predsminms1/t55_circcomb__0', fc9_circcomb)). fof(fc2_struct_0, axiom, ![X1]:((~(v2_struct_0(X1))&l1_struct_0(X1))=>~(v1_xboole_0(u1_struct_0(X1)))), file('/scratch/mptp/predsminms1/t55_circcomb__0', fc2_struct_0)). fof(c_0_21, plain, ![X33, X34]:k2_funcop_1(X33,X34)=k2_zfmisc_1(X33,k1_tarski(X34)), inference(variable_rename,[status(thm)],[d2_funcop_1])). fof(c_0_22, plain, ![X35, X36]:k7_funcop_1(X35,X36)=k2_funcop_1(X35,X36), inference(variable_rename,[status(thm)],[redefinition_k7_funcop_1])). fof(c_0_23, plain, ![X42, X43, X44, X45, X46]:(((r8_pboole(u1_struct_0(k5_circcomb(X44,X45)),u3_msualg_1(k5_circcomb(X44,X45),X46),k7_funcop_1(u1_struct_0(k5_circcomb(X44,X45)),X43))\|X46!=k7_circcomb(X42,X43,X44,X45)\|(~v3_msualg_1(X46,k5_circcomb(X44,X45))\|(~v4_msualg_1(X46,k5_circcomb(X44,X45))\|~l3_msualg_1(X46,k5_circcomb(X44,X45))))\|(~v1_relat_1(X45)\|(~v1_funct_1(X45)\|(~v3_card_1(X45,X42)\|~v1_finseq_1(X45))))\|(~v1_funct_1(X44)\|(~v1_funct_2(X44,k4_finseq_2(X42,X43),X43)\|~m1_subset_1(X44,k1_zfmisc_1(k2_zfmisc_1(k4_finseq_2(X42,X43),X43)))))\|v1_xboole_0(X43)\|~v7_ordinal1(X42))&(k1_funct_1(u4_msualg_1(k5_circcomb(X44,X45),X46),k4_tarski(X45,X44))=X44\|X46!=k7_circcomb(X42,X43,X44,X45)\|(~v3_msualg_1(X46,k5_circcomb(X44,X45))\|(~v4_msualg_1(X46,k5_circcomb(X44,X45))\|~l3_msualg_1(X46,k5_circcomb(X44,X45))))\|(~v1_relat_1(X45)\|(~v1_funct_1(X45)\|(~v3_card_1(X45,X42)\|~v1_finseq_1(X45))))\|(~v1_funct_1(X44)\|(~v1_funct_2(X44,k4_finseq_2(X42,X43),X43)\|~m1_subset_1(X44,k1_zfmisc_1(k2_zfmisc_1(k4_finseq_2(X42,X43),X43)))))\|v1_xboole_0(X43)\|~v7_ordinal1(X42)))&(~r8_pboole(u1_struct_0(k5_circcomb(X44,X45)),u3_msualg_1(k5_circcomb(X44,X45),X46),k7_funcop_1(u1_struct_0(k5_circcomb(X44,X45)),X43))\|k1_funct_1(u4_msualg_1(k5_circcomb(X44,X45),X46),k4_tarski(X45,X44))!=X44\|X46=k7_circcomb(X42,X43,X44,X45)\|(~v3_msualg_1(X46,k5_circcomb(X44,X45))\|(~v4_msualg_1(X46,k5_circcomb(X44,X45))\|~l3_msualg_1(X46,k5_circcomb(X44,X45))))\|(~v1_relat_1(X45)\|(~v1_funct_1(X45)\|(~v3_card_1(X45,X42)\|~v1_finseq_1(X45))))\|(~v1_funct_1(X44)\|(~v1_funct_2(X44,k4_finseq_2(X42,X43),X43)\|~m1_subset_1(X44,k1_zfmisc_1(k2_zfmisc_1(k4_finseq_2(X42,X43),X43)))))\|v1_xboole_0(X43)\|~v7_ordinal1(X42))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d13_circcomb])])])])])). cnf(c_0_24, plain, (k2_funcop_1(X1,X2)=k2_zfmisc_1(X1,k1_tarski(X2))), inference(split_conjunct,[status(thm)],[c_0_21])). cnf(c_0_25, plain, (k7_funcop_1(X1,X2)=k2_funcop_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_22])). fof(c_0_26, negated_conjecture, ~(![X1]:(v7_ordinal1(X1)=>![X2]:(~(v1_xboole_0(X2))=>![X3]:((v1_funct_1(X3)&(v1_funct_2(X3,k4_finseq_2(X1,X2),X2)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k4_finseq_2(X1,X2),X2)))))=>![X4]:((v1_relat_1(X4)&(v1_funct_1(X4)&(v3_card_1(X4,X1)&v1_finseq_1(X4))))=>![X5]:((v1_relat_1(X5)&(v1_funct_1(X5)&(v3_card_1(X5,X1)&v1_finseq_1(X5))))=>r2_circcomb(k5_circcomb(X3,X4),k5_circcomb(X3,X5),k7_circcomb(X1,X2,X3,X4),k7_circcomb(X1,X2,X3,X5)))))))), inference(assume_negation,[status(cth)],[t55_circcomb])). fof(c_0_27, plain, ![X51, X52, X53]:k13_funcop_1(X51,X52,X53)=k7_funcop_1(k1_tarski(k4_tarski(X51,X52)),X53), inference(variable_rename,[status(thm)],[d7_funcop_1])). fof(c_0_28, plain, ![X49, X50]:k4_tarski(X49,X50)=k2_tarski(k2_tarski(X49,X50),k1_tarski(X49)), inference(variable_rename,[status(thm)],[d5_tarski])). cnf(c_0_29, plain, (r8_pboole(u1_struct_0(k5_circcomb(X1,X2)),u3_msualg_1(k5_circcomb(X1,X2),X3),k7_funcop_1(u1_struct_0(k5_circcomb(X1,X2)),X4))\|v1_xboole_0(X4)\|X3!=k7_circcomb(X5,X4,X1,X2)\|~v3_msualg_1(X3,k5_circcomb(X1,X2))\|~v4_msualg_1(X3,k5_circcomb(X1,X2))\|~l3_msualg_1(X3,k5_circcomb(X1,X2))\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v3_card_1(X2,X5)\|~v1_finseq_1(X2)\|~v1_funct_1(X1)\|~v1_funct_2(X1,k4_finseq_2(X5,X4),X4)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k4_finseq_2(X5,X4),X4)))\|~v7_ordinal1(X5)), inference(split_conjunct,[status(thm)],[c_0_23])). cnf(c_0_30, plain, (k7_funcop_1(X1,X2)=k2_zfmisc_1(X1,k1_tarski(X2))), inference(rw,[status(thm)],[c_0_24, c_0_25])). fof(c_0_31, negated_conjecture, (v7_ordinal1(esk1_0)&(~v1_xboole_0(esk2_0)&((v1_funct_1(esk3_0)&(v1_funct_2(esk3_0,k4_finseq_2(esk1_0,esk2_0),esk2_0)&m1_subset_1(esk3_0,k1_zfmisc_1(k2_zfmisc_1(k4_finseq_2(esk1_0,esk2_0),esk2_0)))))&((v1_relat_1(esk4_0)&(v1_funct_1(esk4_0)&(v3_card_1(esk4_0,esk1_0)&v1_finseq_1(esk4_0))))&((v1_relat_1(esk5_0)&(v1_funct_1(esk5_0)&(v3_card_1(esk5_0,esk1_0)&v1_finseq_1(esk5_0))))&~r2_circcomb(k5_circcomb(esk3_0,esk4_0),k5_circcomb(esk3_0,esk5_0),k7_circcomb(esk1_0,esk2_0,esk3_0,esk4_0),k7_circcomb(esk1_0,esk2_0,esk3_0,esk5_0))))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_26])])])])). fof(c_0_32, plain, ![X37, X38]:(v1_relat_1(k2_funcop_1(X37,X38))&(v4_relat_1(k2_funcop_1(X37,X38),X37)&(v1_funct_1(k2_funcop_1(X37,X38))&v1_partfun1(k2_funcop_1(X37,X38),X37)))), inference(variable_rename,[status(thm)],[fc20_funcop_1])). fof(c_0_33, plain, ![X54, X55, X56, X57, X58]:((u4_msualg_1(k5_circcomb(X56,X57),k7_circcomb(X54,X55,X56,X57))=k13_funcop_1(X57,X56,X56)\|(~v1_relat_1(X57)\|(~v1_funct_1(X57)\|(~v3_card_1(X57,X54)\|~v1_finseq_1(X57))))\|(~v1_funct_1(X56)\|(~v1_funct_2(X56,k4_finseq_2(X54,X55),X55)\|~m1_subset_1(X56,k1_zfmisc_1(k2_zfmisc_1(k4_finseq_2(X54,X55),X55)))))\|v1_xboole_0(X55)\|~v7_ordinal1(X54))&(~m1_subset_1(X58,u1_struct_0(k5_circcomb(X56,X57)))\|k1_funct_1(u3_msualg_1(k5_circcomb(X56,X57),k7_circcomb(X54,X55,X56,X57)),X58)=X55\|(~v1_relat_1(X57)\|(~v1_funct_1(X57)\|(~v3_card_1(X57,X54)\|~v1_finseq_1(X57))))\|(~v1_funct_1(X56)\|(~v1_funct_2(X56,k4_finseq_2(X54,X55),X55)\|~m1_subset_1(X56,k1_zfmisc_1(k2_zfmisc_1(k4_finseq_2(X54,X55),X55)))))\|v1_xboole_0(X55)\|~v7_ordinal1(X54))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t54_circcomb])])])])])). cnf(c_0_34, plain, (k13_funcop_1(X1,X2,X3)=k7_funcop_1(k1_tarski(k4_tarski(X1,X2)),X3)), inference(split_conjunct,[status(thm)],[c_0_27])). cnf(c_0_35, plain, (k4_tarski(X1,X2)=k2_tarski(k2_tarski(X1,X2),k1_tarski(X1))), inference(split_conjunct,[status(thm)],[c_0_28])). fof(c_0_36, plain, ![X39, X40, X41]:((~r8_pboole(X39,X40,X41)\|X40=X41\|(v1_xboole_0(X39)\|(~v1_relat_1(X40)\|(~v4_relat_1(X40,X39)\|(~v1_funct_1(X40)\|~v1_partfun1(X40,X39)))\|(~v1_relat_1(X41)\|(~v4_relat_1(X41,X39)\|(~v1_funct_1(X41)\|~v1_partfun1(X41,X39)))))))&(X40!=X41\|r8_pboole(X39,X40,X41)\|(v1_xboole_0(X39)\|(~v1_relat_1(X40)\|(~v4_relat_1(X40,X39)\|(~v1_funct_1(X40)\|~v1_partfun1(X40,X39)))\|(~v1_relat_1(X41)\|(~v4_relat_1(X41,X39)\|(~v1_funct_1(X41)\|~v1_partfun1(X41,X39)))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[redefinition_r8_pboole])])])])). cnf(c_0_37, plain, (v1_xboole_0(X4)\|r8_pboole(u1_struct_0(k5_circcomb(X1,X2)),u3_msualg_1(k5_circcomb(X1,X2),X3),k2_zfmisc_1(u1_struct_0(k5_circcomb(X1,X2)),k1_tarski(X4)))\|X3!=k7_circcomb(X5,X4,X1,X2)\|~v7_ordinal1(X5)\|~v1_funct_1(X2)\|~v1_funct_1(X1)\|~v1_relat_1(X2)\|~v1_finseq_1(X2)\|~v3_card_1(X2,X5)\|~l3_msualg_1(X3,k5_circcomb(X1,X2))\|~v3_msualg_1(X3,k5_circcomb(X1,X2))\|~v4_msualg_1(X3,k5_circcomb(X1,X2))\|~v1_funct_2(X1,k4_finseq_2(X5,X4),X4)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k4_finseq_2(X5,X4),X4)))), inference(rw,[status(thm)],[c_0_29, c_0_30])). cnf(c_0_38, negated_conjecture, (m1_subset_1(esk3_0,k1_zfmisc_1(k2_zfmisc_1(k4_finseq_2(esk1_0,esk2_0),esk2_0)))), inference(split_conjunct,[status(thm)],[c_0_31])). cnf(c_0_39, negated_conjecture, (v1_funct_2(esk3_0,k4_finseq_2(esk1_0,esk2_0),esk2_0)), inference(split_conjunct,[status(thm)],[c_0_31])). cnf(c_0_40, negated_conjecture, (v1_funct_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_31])). cnf(c_0_41, negated_conjecture, (v7_ordinal1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_31])). cnf(c_0_42, negated_conjecture, (~v1_xboole_0(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_31])). cnf(c_0_43, plain, (v1_partfun1(k2_funcop_1(X1,X2),X1)), inference(split_conjunct,[status(thm)],[c_0_32])). cnf(c_0_44, plain, (v4_relat_1(k2_funcop_1(X1,X2),X1)), inference(split_conjunct,[status(thm)],[c_0_32])). cnf(c_0_45, plain, (v1_relat_1(k2_funcop_1(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_32])). cnf(c_0_46, plain, (v1_funct_1(k2_funcop_1(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_32])). fof(c_0_47, plain, ![X14, X15, X16, X17]:((~r1_partfun1(k7_funcop_1(X14,X16),k7_funcop_1(X15,X17))\|(X16=X17\|r1_xboole_0(X14,X15)))&((X16!=X17\|r1_partfun1(k7_funcop_1(X14,X16),k7_funcop_1(X15,X17)))&(~r1_xboole_0(X14,X15)\|r1_partfun1(k7_funcop_1(X14,X16),k7_funcop_1(X15,X17))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t87_funcop_1])])])). cnf(c_0_48, plain, (u4_msualg_1(k5_circcomb(X1,X2),k7_circcomb(X3,X4,X1,X2))=k13_funcop_1(X2,X1,X1)\|v1_xboole_0(X4)\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v3_card_1(X2,X3)\|~v1_finseq_1(X2)\|~v1_funct_1(X1)\|~v1_funct_2(X1,k4_finseq_2(X3,X4),X4)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k4_finseq_2(X3,X4),X4)))\|~v7_ordinal1(X3)), inference(split_conjunct,[status(thm)],[c_0_33])). cnf(c_0_49, plain, (k13_funcop_1(X1,X2,X3)=k2_zfmisc_1(k1_tarski(k2_tarski(k2_tarski(X1,X2),k1_tarski(X1))),k1_tarski(X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34, c_0_30]), c_0_35])). fof(c_0_50, plain, ![X47, X48]:k2_tarski(X47,X48)=k2_tarski(X48,X47), inference(variable_rename,[status(thm)],[commutativity_k2_tarski])). cnf(c_0_51, plain, (X2=X3\|v1_xboole_0(X1)\|~r8_pboole(X1,X2,X3)\|~v1_relat_1(X2)\|~v4_relat_1(X2,X1)\|~v1_funct_1(X2)\|~v1_partfun1(X2,X1)\|~v1_relat_1(X3)\|~v4_relat_1(X3,X1)\|~v1_funct_1(X3)\|~v1_partfun1(X3,X1)), inference(split_conjunct,[status(thm)],[c_0_36])). cnf(c_0_52, plain, (v1_xboole_0(X4)\|r8_pboole(u1_struct_0(k5_circcomb(X1,X2)),u3_msualg_1(k5_circcomb(X1,X2),X3),k2_zfmisc_1(u1_struct_0(k5_circcomb(X1,X2)),k1_tarski(X4)))\|X3!=k7_circcomb(X5,X4,X1,X2)\|~v7_ordinal1(X5)\|~v1_funct_1(X2)\|~v1_funct_1(X1)\|~v1_relat_1(X2)\|~v1_finseq_1(X2)\|~v3_card_1(X2,X5)\|~l3_msualg_1(X3,k5_circcomb(X1,X2))\|~v3_msualg_1(X3,k5_circcomb(X1,X2))\|~v4_msualg_1(X3,k5_circcomb(X1,X2))\|~v1_funct_2(X1,k4_finseq_2(X5,X4),X4)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k4_finseq_2(X5,X4),X4)))), inference(evalgc,[status(thm)],[c_0_37])). cnf(c_0_53, negated_conjecture, (m1_subset_1(esk3_0,k1_zfmisc_1(k2_zfmisc_1(k4_finseq_2(esk1_0,esk2_0),esk2_0)))), inference(evalgc,[status(thm)],[c_0_38])). cnf(c_0_54, negated_conjecture, (v1_funct_2(esk3_0,k4_finseq_2(esk1_0,esk2_0),esk2_0)), inference(evalgc,[status(thm)],[c_0_39])). cnf(c_0_55, negated_conjecture, (v1_funct_1(esk3_0)), inference(evalgc,[status(thm)],[c_0_40])). cnf(c_0_56, negated_conjecture, (v7_ordinal1(esk1_0)), inference(evalgc,[status(thm)],[c_0_41])). cnf(c_0_57, negated_conjecture, (~v1_xboole_0(esk2_0)), inference(evalgc,[status(thm)],[c_0_42])). cnf(c_0_58, plain, (v1_partfun1(k2_zfmisc_1(X1,k1_tarski(X2)),X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43, c_0_25]), c_0_30])). cnf(c_0_59, plain, (v4_relat_1(k2_zfmisc_1(X1,k1_tarski(X2)),X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44, c_0_25]), c_0_30])). cnf(c_0_60, plain, (v1_relat_1(k2_zfmisc_1(X1,k1_tarski(X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45, c_0_25]), c_0_30])). cnf(c_0_61, plain, (v1_funct_1(k2_zfmisc_1(X1,k1_tarski(X2)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_46, c_0_25]), c_0_30])). fof(c_0_62, plain, ![X31, X32]:((v1_relat_1(u3_msualg_1(X31,X32))\|(~l1_struct_0(X31)\|~l2_msualg_1(X32,X31)))&((v4_relat_1(u3_msualg_1(X31,X32),u1_struct_0(X31))\|(~l1_struct_0(X31)\|~l2_msualg_1(X32,X31)))&((v1_funct_1(u3_msualg_1(X31,X32))\|(~l1_struct_0(X31)\|~l2_msualg_1(X32,X31)))&(v1_partfun1(u3_msualg_1(X31,X32),u1_struct_0(X31))\|(~l1_struct_0(X31)\|~l2_msualg_1(X32,X31)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u3_msualg_1])])])). cnf(c_0_63, plain, (r1_partfun1(k7_funcop_1(X3,X1),k7_funcop_1(X4,X2))\|X1!=X2), inference(split_conjunct,[status(thm)],[c_0_47])). cnf(c_0_64, plain, (u4_msualg_1(k5_circcomb(X1,X2),k7_circcomb(X3,X4,X1,X2))=k2_zfmisc_1(k1_tarski(k2_tarski(k2_tarski(X2,X1),k1_tarski(X2))),k1_tarski(X1))\|v1_xboole_0(X4)\|~v7_ordinal1(X3)\|~v1_funct_1(X2)\|~v1_funct_1(X1)\|~v1_relat_1(X2)\|~v1_finseq_1(X2)\|~v3_card_1(X2,X3)\|~v1_funct_2(X1,k4_finseq_2(X3,X4),X4)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k4_finseq_2(X3,X4),X4)))), inference(rw,[status(thm)],[c_0_48, c_0_49])). cnf(c_0_65, plain, (k2_tarski(X1,X2)=k2_tarski(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_50])). cnf(c_0_66, plain, (X2=X3\|v1_xboole_0(X1)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v4_relat_1(X3,X1)\|~v4_relat_1(X2,X1)\|~v1_partfun1(X3,X1)\|~v1_partfun1(X2,X1)\|~r8_pboole(X1,X2,X3)), inference(evalgc,[status(thm)],[c_0_51])). cnf(c_0_67, negated_conjecture, (r8_pboole(u1_struct_0(k5_circcomb(esk3_0,X1)),u3_msualg_1(k5_circcomb(esk3_0,X1),X2),k2_zfmisc_1(u1_struct_0(k5_circcomb(esk3_0,X1)),k1_tarski(esk2_0)))\|X2!=k7_circcomb(esk1_0,esk2_0,esk3_0,X1)\|~v4_msualg_1(X2,k5_circcomb(esk3_0,X1))\|~v3_msualg_1(X2,k5_circcomb(esk3_0,X1))\|~l3_msualg_1(X2,k5_circcomb(esk3_0,X1))\|~v1_finseq_1(X1)\|~v3_card_1(X1,esk1_0)\|~v1_relat_1(X1)\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52, c_0_53]), c_0_54]), c_0_55]), c_0_56])]), c_0_57])])). cnf(c_0_68, plain, (v1_partfun1(k2_zfmisc_1(X1,k1_tarski(X2)),X1)), inference(evalgc,[status(thm)],[c_0_58])). cnf(c_0_69, plain, (v4_relat_1(k2_zfmisc_1(X1,k1_tarski(X2)),X1)), inference(evalgc,[status(thm)],[c_0_59])). cnf(c_0_70, plain, (v1_relat_1(k2_zfmisc_1(X1,k1_tarski(X2)))), inference(evalgc,[status(thm)],[c_0_60])). cnf(c_0_71, plain, (v1_funct_1(k2_zfmisc_1(X1,k1_tarski(X2)))), inference(evalgc,[status(thm)],[c_0_61])). cnf(c_0_72, plain, (v1_partfun1(u3_msualg_1(X1,X2),u1_struct_0(X1))\|~l1_struct_0(X1)\|~l2_msualg_1(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_62])). fof(c_0_73, plain, ![X27, X28, X29, X30]:((v3_msualg_1(k7_circcomb(X27,X28,X29,X30),k5_circcomb(X29,X30))\|(~v7_ordinal1(X27)\|(v1_xboole_0(X28)\|(~v1_funct_1(X29)\|(~v1_funct_2(X29,k4_finseq_2(X27,X28),X28)\|~m1_subset_1(X29,k1_zfmisc_1(k2_zfmisc_1(k4_finseq_2(X27,X28),X28))))\|(~v1_relat_1(X30)\|(~v1_funct_1(X30)\|(~v3_card_1(X30,X27)\|~v1_finseq_1(X30))))))))&((v4_msualg_1(k7_circcomb(X27,X28,X29,X30),k5_circcomb(X29,X30))\|(~v7_ordinal1(X27)\|(v1_xboole_0(X28)\|(~v1_funct_1(X29)\|(~v1_funct_2(X29,k4_finseq_2(X27,X28),X28)\|~m1_subset_1(X29,k1_zfmisc_1(k2_zfmisc_1(k4_finseq_2(X27,X28),X28))))\|(~v1_relat_1(X30)\|(~v1_funct_1(X30)\|(~v3_card_1(X30,X27)\|~v1_finseq_1(X30))))))))&(l3_msualg_1(k7_circcomb(X27,X28,X29,X30),k5_circcomb(X29,X30))\|(~v7_ordinal1(X27)\|(v1_xboole_0(X28)\|(~v1_funct_1(X29)\|(~v1_funct_2(X29,k4_finseq_2(X27,X28),X28)\|~m1_subset_1(X29,k1_zfmisc_1(k2_zfmisc_1(k4_finseq_2(X27,X28),X28))))\|(~v1_relat_1(X30)\|(~v1_funct_1(X30)\|(~v3_card_1(X30,X27)\|~v1_finseq_1(X30)))))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k7_circcomb])])])])). cnf(c_0_74, plain, (r1_partfun1(k2_zfmisc_1(X3,k1_tarski(X1)),k2_zfmisc_1(X4,k1_tarski(X2)))\|X1!=X2), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_63, c_0_30]), c_0_30])). cnf(c_0_75, plain, (u4_msualg_1(k5_circcomb(X1,X2),k7_circcomb(X3,X4,X1,X2))=k2_zfmisc_1(k1_tarski(k2_tarski(k2_tarski(X2,X1),k1_tarski(X2))),k1_tarski(X1))\|v1_xboole_0(X4)\|~v7_ordinal1(X3)\|~v1_funct_1(X2)\|~v1_funct_1(X1)\|~v1_relat_1(X2)\|~v1_finseq_1(X2)\|~v3_card_1(X2,X3)\|~v1_funct_2(X1,k4_finseq_2(X3,X4),X4)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k4_finseq_2(X3,X4),X4)))), inference(evalgc,[status(thm)],[c_0_64])). cnf(c_0_76, plain, (k2_tarski(X1,X2)=k2_tarski(X2,X1)), inference(evalgc,[status(thm)],[c_0_65])). cnf(c_0_77, negated_conjecture, (u3_msualg_1(k5_circcomb(esk3_0,X1),X2)=k2_zfmisc_1(u1_struct_0(k5_circcomb(esk3_0,X1)),k1_tarski(esk2_0))\|v1_xboole_0(u1_struct_0(k5_circcomb(esk3_0,X1)))\|~v1_partfun1(u3_msualg_1(k5_circcomb(esk3_0,X1),X2),u1_struct_0(k5_circcomb(esk3_0,X1)))\|~v4_relat_1(u3_msualg_1(k5_circcomb(esk3_0,X1),X2),u1_struct_0(k5_circcomb(esk3_0,X1)))\|~v1_relat_1(u3_msualg_1(k5_circcomb(esk3_0,X1),X2))\|~v1_funct_1(u3_msualg_1(k5_circcomb(esk3_0,X1),X2))\|X2!=k7_circcomb(esk1_0,esk2_0,esk3_0,X1)\|~v4_msualg_1(X2,k5_circcomb(esk3_0,X1))\|~v3_msualg_1(X2,k5_circcomb(esk3_0,X1))\|~l3_msualg_1(X2,k5_circcomb(esk3_0,X1))\|~v1_finseq_1(X1)\|~v3_card_1(X1,esk1_0)\|~v1_relat_1(X1)\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66, c_0_67]), c_0_68]), c_0_69]), c_0_70]), c_0_71])])])). cnf(c_0_78, plain, (v1_partfun1(u3_msualg_1(X1,X2),u1_struct_0(X1))\|~l1_struct_0(X1)\|~l2_msualg_1(X2,X1)), inference(evalgc,[status(thm)],[c_0_72])). cnf(c_0_79, plain, (v1_funct_1(u3_msualg_1(X1,X2))\|~l1_struct_0(X1)\|~l2_msualg_1(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_62])). cnf(c_0_80, plain, (v1_relat_1(u3_msualg_1(X1,X2))\|~l1_struct_0(X1)\|~l2_msualg_1(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_62])). cnf(c_0_81, plain, (v4_relat_1(u3_msualg_1(X1,X2),u1_struct_0(X1))\|~l1_struct_0(X1)\|~l2_msualg_1(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_62])). cnf(c_0_82, plain, (v4_msualg_1(k7_circcomb(X1,X2,X3,X4),k5_circcomb(X3,X4))\|v1_xboole_0(X2)\|~v7_ordinal1(X1)\|~v1_funct_1(X3)\|~v1_funct_2(X3,k4_finseq_2(X1,X2),X2)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k4_finseq_2(X1,X2),X2)))\|~v1_relat_1(X4)\|~v1_funct_1(X4)\|~v3_card_1(X4,X1)\|~v1_finseq_1(X4)), inference(split_conjunct,[status(thm)],[c_0_73])). cnf(c_0_83, plain, (r1_partfun1(k2_zfmisc_1(X3,k1_tarski(X1)),k2_zfmisc_1(X4,k1_tarski(X2)))\|X1!=X2), inference(evalgc,[status(thm)],[c_0_74])). cnf(c_0_84, plain, (u4_msualg_1(k5_circcomb(X1,X2),k7_circcomb(X3,X4,X1,X2))=k2_zfmisc_1(k1_tarski(k2_tarski(k1_tarski(X2),k2_tarski(X2,X1))),k1_tarski(X1))\|v1_xboole_0(X4)\|~v1_finseq_1(X2)\|~v3_card_1(X2,X3)\|~v1_relat_1(X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k4_finseq_2(X3,X4),X4)))\|~v1_funct_2(X1,k4_finseq_2(X3,X4),X4)\|~v1_funct_1(X2)\|~v1_funct_1(X1)\|~v7_ordinal1(X3)), inference(rw,[status(thm)],[c_0_75, c_0_76])). cnf(c_0_85, negated_conjecture, (u3_msualg_1(k5_circcomb(esk3_0,X1),X2)=k2_zfmisc_1(u1_struct_0(k5_circcomb(esk3_0,X1)),k1_tarski(esk2_0))\|v1_xboole_0(u1_struct_0(k5_circcomb(esk3_0,X1)))\|X2!=k7_circcomb(esk1_0,esk2_0,esk3_0,X1)\|~v4_relat_1(u3_msualg_1(k5_circcomb(esk3_0,X1),X2),u1_struct_0(k5_circcomb(esk3_0,X1)))\|~v4_msualg_1(X2,k5_circcomb(esk3_0,X1))\|~v3_msualg_1(X2,k5_circcomb(esk3_0,X1))\|~l3_msualg_1(X2,k5_circcomb(esk3_0,X1))\|~v1_finseq_1(X1)\|~v3_card_1(X1,esk1_0)\|~v1_relat_1(u3_msualg_1(k5_circcomb(esk3_0,X1),X2))\|~v1_relat_1(X1)\|~v1_funct_1(u3_msualg_1(k5_circcomb(esk3_0,X1),X2))\|~v1_funct_1(X1)\|~l2_msualg_1(X2,k5_circcomb(esk3_0,X1))\|~l1_struct_0(k5_circcomb(esk3_0,X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_77, c_0_78])])). cnf(c_0_86, plain, (v1_funct_1(u3_msualg_1(X1,X2))\|~l1_struct_0(X1)\|~l2_msualg_1(X2,X1)), inference(evalgc,[status(thm)],[c_0_79])). cnf(c_0_87, plain, (v1_relat_1(u3_msualg_1(X1,X2))\|~l1_struct_0(X1)\|~l2_msualg_1(X2,X1)), inference(evalgc,[status(thm)],[c_0_80])). cnf(c_0_88, plain, (v4_relat_1(u3_msualg_1(X1,X2),u1_struct_0(X1))\|~l1_struct_0(X1)\|~l2_msualg_1(X2,X1)), inference(evalgc,[status(thm)],[c_0_81])). cnf(c_0_89, plain, (v1_xboole_0(X2)\|v4_msualg_1(k7_circcomb(X1,X2,X3,X4),k5_circcomb(X3,X4))\|~v7_ordinal1(X1)\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v1_relat_1(X4)\|~v1_finseq_1(X4)\|~v3_card_1(X4,X1)\|~v1_funct_2(X3,k4_finseq_2(X1,X2),X2)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k4_finseq_2(X1,X2),X2)))), inference(evalgc,[status(thm)],[c_0_82])). cnf(c_0_90, plain, (l3_msualg_1(k7_circcomb(X1,X2,X3,X4),k5_circcomb(X3,X4))\|v1_xboole_0(X2)\|~v7_ordinal1(X1)\|~v1_funct_1(X3)\|~v1_funct_2(X3,k4_finseq_2(X1,X2),X2)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k4_finseq_2(X1,X2),X2)))\|~v1_relat_1(X4)\|~v1_funct_1(X4)\|~v3_card_1(X4,X1)\|~v1_finseq_1(X4)), inference(split_conjunct,[status(thm)],[c_0_73])). cnf(c_0_91, plain, (v3_msualg_1(k7_circcomb(X1,X2,X3,X4),k5_circcomb(X3,X4))\|v1_xboole_0(X2)\|~v7_ordinal1(X1)\|~v1_funct_1(X3)\|~v1_funct_2(X3,k4_finseq_2(X1,X2),X2)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k4_finseq_2(X1,X2),X2)))\|~v1_relat_1(X4)\|~v1_funct_1(X4)\|~v3_card_1(X4,X1)\|~v1_finseq_1(X4)), inference(split_conjunct,[status(thm)],[c_0_73])). fof(c_0_92, plain, ![X59, X60, X61, X62]:(((r1_circcomb(X59,X60)\|~r2_circcomb(X59,X60,X61,X62)\|~l3_msualg_1(X62,X60)\|~l3_msualg_1(X61,X59)\|(v2_struct_0(X60)\|~l1_msualg_1(X60))\|(v2_struct_0(X59)\|~l1_msualg_1(X59)))&((r1_partfun1(u3_msualg_1(X59,X61),u3_msualg_1(X60,X62))\|~r2_circcomb(X59,X60,X61,X62)\|~l3_msualg_1(X62,X60)\|~l3_msualg_1(X61,X59)\|(v2_struct_0(X60)\|~l1_msualg_1(X60))\|(v2_struct_0(X59)\|~l1_msualg_1(X59)))&(r1_partfun1(u4_msualg_1(X59,X61),u4_msualg_1(X60,X62))\|~r2_circcomb(X59,X60,X61,X62)\|~l3_msualg_1(X62,X60)\|~l3_msualg_1(X61,X59)\|(v2_struct_0(X60)\|~l1_msualg_1(X60))\|(v2_struct_0(X59)\|~l1_msualg_1(X59)))))&(~r1_circcomb(X59,X60)\|(~r1_partfun1(u3_msualg_1(X59,X61),u3_msualg_1(X60,X62))\|~r1_partfun1(u4_msualg_1(X59,X61),u4_msualg_1(X60,X62)))\|r2_circcomb(X59,X60,X61,X62)\|~l3_msualg_1(X62,X60)\|~l3_msualg_1(X61,X59)\|(v2_struct_0(X60)\|~l1_msualg_1(X60))\|(v2_struct_0(X59)\|~l1_msualg_1(X59)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d3_circcomb])])])])])). cnf(c_0_93, plain, (r1_partfun1(k2_zfmisc_1(X1,k1_tarski(X2)),k2_zfmisc_1(X3,k1_tarski(X2)))), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_83])])). cnf(c_0_94, negated_conjecture, (k2_zfmisc_1(k1_tarski(k2_tarski(k1_tarski(X1),k2_tarski(X1,esk3_0))),k1_tarski(esk3_0))=u4_msualg_1(k5_circcomb(esk3_0,X1),k7_circcomb(esk1_0,esk2_0,esk3_0,X1))\|~v1_finseq_1(X1)\|~v3_card_1(X1,esk1_0)\|~v1_relat_1(X1)\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84, c_0_53]), c_0_54]), c_0_55]), c_0_56])]), c_0_57])])). cnf(c_0_95, negated_conjecture, (u3_msualg_1(k5_circcomb(esk3_0,X1),X2)=k2_zfmisc_1(u1_struct_0(k5_circcomb(esk3_0,X1)),k1_tarski(esk2_0))\|v1_xboole_0(u1_struct_0(k5_circcomb(esk3_0,X1)))\|X2!=k7_circcomb(esk1_0,esk2_0,esk3_0,X1)\|~v4_msualg_1(X2,k5_circcomb(esk3_0,X1))\|~v3_msualg_1(X2,k5_circcomb(esk3_0,X1))\|~l2_msualg_1(X2,k5_circcomb(esk3_0,X1))\|~l3_msualg_1(X2,k5_circcomb(esk3_0,X1))\|~l1_struct_0(k5_circcomb(esk3_0,X1))\|~v1_finseq_1(X1)\|~v3_card_1(X1,esk1_0)\|~v1_relat_1(X1)\|~v1_funct_1(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_85, c_0_86]), c_0_87]), c_0_88])). cnf(c_0_96, negated_conjecture, (v4_msualg_1(k7_circcomb(esk1_0,esk2_0,esk3_0,X1),k5_circcomb(esk3_0,X1))\|~v1_finseq_1(X1)\|~v3_card_1(X1,esk1_0)\|~v1_relat_1(X1)\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89, c_0_53]), c_0_54]), c_0_55]), c_0_56])]), c_0_57])])). cnf(c_0_97, plain, (v1_xboole_0(X2)\|l3_msualg_1(k7_circcomb(X1,X2,X3,X4),k5_circcomb(X3,X4))\|~v7_ordinal1(X1)\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v1_relat_1(X4)\|~v1_finseq_1(X4)\|~v3_card_1(X4,X1)\|~v1_funct_2(X3,k4_finseq_2(X1,X2),X2)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k4_finseq_2(X1,X2),X2)))), inference(evalgc,[status(thm)],[c_0_90])). cnf(c_0_98, plain, (v1_xboole_0(X2)\|v3_msualg_1(k7_circcomb(X1,X2,X3,X4),k5_circcomb(X3,X4))\|~v7_ordinal1(X1)\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v1_relat_1(X4)\|~v1_finseq_1(X4)\|~v3_card_1(X4,X1)\|~v1_funct_2(X3,k4_finseq_2(X1,X2),X2)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k4_finseq_2(X1,X2),X2)))), inference(evalgc,[status(thm)],[c_0_91])). fof(c_0_99, plain, ![X25, X26]:(v2_struct_0(X25)\|~l1_msualg_1(X25)\|(~l3_msualg_1(X26,X25)\|l2_msualg_1(X26,X25))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_l3_msualg_1])])])])). fof(c_0_100, plain, ![X20]:(~l5_struct_0(X20)\|l1_struct_0(X20)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l5_struct_0])])). fof(c_0_101, plain, ![X21]:(~l1_msualg_1(X21)\|l5_struct_0(X21)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_msualg_1])])). cnf(c_0_102, plain, (r2_circcomb(X1,X2,X3,X4)\|v2_struct_0(X2)\|v2_struct_0(X1)\|~r1_circcomb(X1,X2)\|~r1_partfun1(u3_msualg_1(X1,X3),u3_msualg_1(X2,X4))\|~r1_partfun1(u4_msualg_1(X1,X3),u4_msualg_1(X2,X4))\|~l3_msualg_1(X4,X2)\|~l3_msualg_1(X3,X1)\|~l1_msualg_1(X2)\|~l1_msualg_1(X1)), inference(split_conjunct,[status(thm)],[c_0_92])). cnf(c_0_103, negated_conjecture, (r1_partfun1(k2_zfmisc_1(X1,k1_tarski(esk3_0)),u4_msualg_1(k5_circcomb(esk3_0,X2),k7_circcomb(esk1_0,esk2_0,esk3_0,X2)))\|~v1_finseq_1(X2)\|~v3_card_1(X2,esk1_0)\|~v1_relat_1(X2)\|~v1_funct_1(X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_93, c_0_94])])). fof(c_0_104, plain, ![X11, X12, X13]:(~v1_relat_1(X12)\|(~v1_funct_1(X12)\|~v1_finseq_1(X12))\|(~v1_relat_1(X13)\|(~v1_funct_1(X13)\|~v1_finseq_1(X13))\|r1_circcomb(k5_circcomb(X11,X12),k5_circcomb(X11,X13)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t43_circcomb])])])). fof(c_0_105, plain, ![X22, X23]:((~v11_struct_0(k5_circcomb(X22,X23))\|(~v1_relat_1(X23)\|(~v1_funct_1(X23)\|~v1_finseq_1(X23))))&((v1_msualg_1(k5_circcomb(X22,X23))\|(~v1_relat_1(X23)\|(~v1_funct_1(X23)\|~v1_finseq_1(X23))))&(l1_msualg_1(k5_circcomb(X22,X23))\|(~v1_relat_1(X23)\|(~v1_funct_1(X23)\|~v1_finseq_1(X23)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k5_circcomb])])])])). fof(c_0_106, plain, ![X18, X19]:((~v2_struct_0(k5_circcomb(X18,X19))\|(~v1_relat_1(X19)\|(~v1_funct_1(X19)\|~v1_finseq_1(X19))))&((~v11_struct_0(k5_circcomb(X18,X19))\|(~v1_relat_1(X19)\|(~v1_funct_1(X19)\|~v1_finseq_1(X19))))&(v1_msualg_1(k5_circcomb(X18,X19))\|(~v1_relat_1(X19)\|(~v1_funct_1(X19)\|~v1_finseq_1(X19)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fc9_circcomb])])])])). cnf(c_0_107, negated_conjecture, (u3_msualg_1(k5_circcomb(esk3_0,X1),k7_circcomb(esk1_0,esk2_0,esk3_0,X1))=k2_zfmisc_1(u1_struct_0(k5_circcomb(esk3_0,X1)),k1_tarski(esk2_0))\|v1_xboole_0(u1_struct_0(k5_circcomb(esk3_0,X1)))\|~v3_msualg_1(k7_circcomb(esk1_0,esk2_0,esk3_0,X1),k5_circcomb(esk3_0,X1))\|~l2_msualg_1(k7_circcomb(esk1_0,esk2_0,esk3_0,X1),k5_circcomb(esk3_0,X1))\|~l3_msualg_1(k7_circcomb(esk1_0,esk2_0,esk3_0,X1),k5_circcomb(esk3_0,X1))\|~l1_struct_0(k5_circcomb(esk3_0,X1))\|~v1_finseq_1(X1)\|~v3_card_1(X1,esk1_0)\|~v1_relat_1(X1)\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_95, c_0_96])])). cnf(c_0_108, negated_conjecture, (l3_msualg_1(k7_circcomb(esk1_0,esk2_0,esk3_0,X1),k5_circcomb(esk3_0,X1))\|~v1_finseq_1(X1)\|~v3_card_1(X1,esk1_0)\|~v1_relat_1(X1)\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97, c_0_53]), c_0_54]), c_0_55]), c_0_56])]), c_0_57])])). cnf(c_0_109, negated_conjecture, (v3_msualg_1(k7_circcomb(esk1_0,esk2_0,esk3_0,X1),k5_circcomb(esk3_0,X1))\|~v1_finseq_1(X1)\|~v3_card_1(X1,esk1_0)\|~v1_relat_1(X1)\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98, c_0_53]), c_0_54]), c_0_55]), c_0_56])]), c_0_57])])). cnf(c_0_110, plain, (v2_struct_0(X1)\|l2_msualg_1(X2,X1)\|~l1_msualg_1(X1)\|~l3_msualg_1(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_99])). cnf(c_0_111, plain, (l1_struct_0(X1)\|~l5_struct_0(X1)), inference(split_conjunct,[status(thm)],[c_0_100])). cnf(c_0_112, plain, (l5_struct_0(X1)\|~l1_msualg_1(X1)), inference(split_conjunct,[status(thm)],[c_0_101])). cnf(c_0_113, plain, (v2_struct_0(X2)\|v2_struct_0(X1)\|r2_circcomb(X1,X2,X3,X4)\|~l1_msualg_1(X2)\|~l1_msualg_1(X1)\|~r1_circcomb(X1,X2)\|~l3_msualg_1(X4,X2)\|~l3_msualg_1(X3,X1)\|~r1_partfun1(u3_msualg_1(X1,X3),u3_msualg_1(X2,X4))\|~r1_partfun1(u4_msualg_1(X1,X3),u4_msualg_1(X2,X4))), inference(evalgc,[status(thm)],[c_0_102])). cnf(c_0_114, negated_conjecture, (r1_partfun1(u4_msualg_1(k5_circcomb(esk3_0,X1),k7_circcomb(esk1_0,esk2_0,esk3_0,X1)),u4_msualg_1(k5_circcomb(esk3_0,X2),k7_circcomb(esk1_0,esk2_0,esk3_0,X2)))\|~v1_finseq_1(X2)\|~v3_card_1(X2,esk1_0)\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v1_finseq_1(X1)\|~v3_card_1(X1,esk1_0)\|~v1_relat_1(X1)\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_103, c_0_94])])). cnf(c_0_115, plain, (r1_circcomb(k5_circcomb(X3,X1),k5_circcomb(X3,X2))\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v1_finseq_1(X1)\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v1_finseq_1(X2)), inference(split_conjunct,[status(thm)],[c_0_104])). cnf(c_0_116, plain, (l1_msualg_1(k5_circcomb(X1,X2))\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v1_finseq_1(X2)), inference(split_conjunct,[status(thm)],[c_0_105])). cnf(c_0_117, plain, (~v2_struct_0(k5_circcomb(X1,X2))\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v1_finseq_1(X2)), inference(split_conjunct,[status(thm)],[c_0_106])). cnf(c_0_118, negated_conjecture, (u3_msualg_1(k5_circcomb(esk3_0,X1),k7_circcomb(esk1_0,esk2_0,esk3_0,X1))=k2_zfmisc_1(u1_struct_0(k5_circcomb(esk3_0,X1)),k1_tarski(esk2_0))\|v1_xboole_0(u1_struct_0(k5_circcomb(esk3_0,X1)))\|~l2_msualg_1(k7_circcomb(esk1_0,esk2_0,esk3_0,X1),k5_circcomb(esk3_0,X1))\|~l1_struct_0(k5_circcomb(esk3_0,X1))\|~v1_finseq_1(X1)\|~v3_card_1(X1,esk1_0)\|~v1_relat_1(X1)\|~v1_funct_1(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_107, c_0_108]), c_0_109])). cnf(c_0_119, plain, (v2_struct_0(X1)\|l2_msualg_1(X2,X1)\|~l1_msualg_1(X1)\|~l3_msualg_1(X2,X1)), inference(evalgc,[status(thm)],[c_0_110])). cnf(c_0_120, plain, (l1_struct_0(X1)\|~l5_struct_0(X1)), inference(evalgc,[status(thm)],[c_0_111])). cnf(c_0_121, plain, (l5_struct_0(X1)\|~l1_msualg_1(X1)), inference(evalgc,[status(thm)],[c_0_112])). cnf(c_0_122, negated_conjecture, (v2_struct_0(k5_circcomb(esk3_0,X1))\|v2_struct_0(k5_circcomb(esk3_0,X2))\|r2_circcomb(k5_circcomb(esk3_0,X1),k5_circcomb(esk3_0,X2),k7_circcomb(esk1_0,esk2_0,esk3_0,X1),k7_circcomb(esk1_0,esk2_0,esk3_0,X2))\|~l3_msualg_1(k7_circcomb(esk1_0,esk2_0,esk3_0,X2),k5_circcomb(esk3_0,X2))\|~l3_msualg_1(k7_circcomb(esk1_0,esk2_0,esk3_0,X1),k5_circcomb(esk3_0,X1))\|~l1_msualg_1(k5_circcomb(esk3_0,X2))\|~l1_msualg_1(k5_circcomb(esk3_0,X1))\|~r1_partfun1(u3_msualg_1(k5_circcomb(esk3_0,X1),k7_circcomb(esk1_0,esk2_0,esk3_0,X1)),u3_msualg_1(k5_circcomb(esk3_0,X2),k7_circcomb(esk1_0,esk2_0,esk3_0,X2)))\|~r1_circcomb(k5_circcomb(esk3_0,X1),k5_circcomb(esk3_0,X2))\|~v1_finseq_1(X2)\|~v1_finseq_1(X1)\|~v3_card_1(X2,esk1_0)\|~v3_card_1(X1,esk1_0)\|~v1_relat_1(X2)\|~v1_relat_1(X1)\|~v1_funct_1(X2)\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_113, c_0_114])])). cnf(c_0_123, plain, (r1_circcomb(k5_circcomb(X3,X1),k5_circcomb(X3,X2))\|~v1_funct_1(X2)\|~v1_funct_1(X1)\|~v1_relat_1(X2)\|~v1_relat_1(X1)\|~v1_finseq_1(X2)\|~v1_finseq_1(X1)), inference(evalgc,[status(thm)],[c_0_115])). cnf(c_0_124, plain, (l1_msualg_1(k5_circcomb(X1,X2))\|~v1_funct_1(X2)\|~v1_relat_1(X2)\|~v1_finseq_1(X2)), inference(evalgc,[status(thm)],[c_0_116])). cnf(c_0_125, plain, (~v1_funct_1(X2)\|~v1_relat_1(X2)\|~v1_finseq_1(X2)\|~v2_struct_0(k5_circcomb(X1,X2))), inference(evalgc,[status(thm)],[c_0_117])). cnf(c_0_126, negated_conjecture, (u3_msualg_1(k5_circcomb(esk3_0,X1),k7_circcomb(esk1_0,esk2_0,esk3_0,X1))=k2_zfmisc_1(u1_struct_0(k5_circcomb(esk3_0,X1)),k1_tarski(esk2_0))\|v1_xboole_0(u1_struct_0(k5_circcomb(esk3_0,X1)))\|v2_struct_0(k5_circcomb(esk3_0,X1))\|~l1_struct_0(k5_circcomb(esk3_0,X1))\|~v1_finseq_1(X1)\|~v3_card_1(X1,esk1_0)\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~l3_msualg_1(k7_circcomb(esk1_0,esk2_0,esk3_0,X1),k5_circcomb(esk3_0,X1))\|~l1_msualg_1(k5_circcomb(esk3_0,X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_118, c_0_119])])). cnf(c_0_127, plain, (l1_struct_0(X1)\|~l1_msualg_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_120, c_0_121])])). cnf(c_0_128, negated_conjecture, (r2_circcomb(k5_circcomb(esk3_0,X1),k5_circcomb(esk3_0,X2),k7_circcomb(esk1_0,esk2_0,esk3_0,X1),k7_circcomb(esk1_0,esk2_0,esk3_0,X2))\|~r1_partfun1(u3_msualg_1(k5_circcomb(esk3_0,X1),k7_circcomb(esk1_0,esk2_0,esk3_0,X1)),u3_msualg_1(k5_circcomb(esk3_0,X2),k7_circcomb(esk1_0,esk2_0,esk3_0,X2)))\|~v1_finseq_1(X2)\|~v1_finseq_1(X1)\|~v3_card_1(X2,esk1_0)\|~v3_card_1(X1,esk1_0)\|~v1_relat_1(X2)\|~v1_relat_1(X1)\|~v1_funct_1(X2)\|~v1_funct_1(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_122, c_0_123]), c_0_124]), c_0_124]), c_0_108]), c_0_108]), c_0_125]), c_0_125])). cnf(c_0_129, negated_conjecture, (u3_msualg_1(k5_circcomb(esk3_0,X1),k7_circcomb(esk1_0,esk2_0,esk3_0,X1))=k2_zfmisc_1(u1_struct_0(k5_circcomb(esk3_0,X1)),k1_tarski(esk2_0))\|v1_xboole_0(u1_struct_0(k5_circcomb(esk3_0,X1)))\|~v1_finseq_1(X1)\|~v3_card_1(X1,esk1_0)\|~v1_relat_1(X1)\|~v1_funct_1(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_126, c_0_127]), c_0_124]), c_0_108]), c_0_125])). fof(c_0_130, plain, ![X24]:(v2_struct_0(X24)\|~l1_struct_0(X24)\|~v1_xboole_0(u1_struct_0(X24))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fc2_struct_0])])])). cnf(c_0_131, negated_conjecture, (~r2_circcomb(k5_circcomb(esk3_0,esk4_0),k5_circcomb(esk3_0,esk5_0),k7_circcomb(esk1_0,esk2_0,esk3_0,esk4_0),k7_circcomb(esk1_0,esk2_0,esk3_0,esk5_0))), inference(split_conjunct,[status(thm)],[c_0_31])). cnf(c_0_132, negated_conjecture, (r2_circcomb(k5_circcomb(esk3_0,X1),k5_circcomb(esk3_0,X2),k7_circcomb(esk1_0,esk2_0,esk3_0,X1),k7_circcomb(esk1_0,esk2_0,esk3_0,X2))\|v1_xboole_0(u1_struct_0(k5_circcomb(esk3_0,X2)))\|~r1_partfun1(u3_msualg_1(k5_circcomb(esk3_0,X1),k7_circcomb(esk1_0,esk2_0,esk3_0,X1)),k2_zfmisc_1(u1_struct_0(k5_circcomb(esk3_0,X2)),k1_tarski(esk2_0)))\|~v1_finseq_1(X2)\|~v1_finseq_1(X1)\|~v3_card_1(X2,esk1_0)\|~v3_card_1(X1,esk1_0)\|~v1_relat_1(X2)\|~v1_relat_1(X1)\|~v1_funct_1(X2)\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_128, c_0_129])])). cnf(c_0_133, negated_conjecture, (v1_finseq_1(esk5_0)), inference(split_conjunct,[status(thm)],[c_0_31])). cnf(c_0_134, negated_conjecture, (v1_finseq_1(esk4_0)), inference(split_conjunct,[status(thm)],[c_0_31])). cnf(c_0_135, negated_conjecture, (v3_card_1(esk5_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_31])). cnf(c_0_136, negated_conjecture, (v3_card_1(esk4_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_31])). cnf(c_0_137, negated_conjecture, (v1_relat_1(esk5_0)), inference(split_conjunct,[status(thm)],[c_0_31])). cnf(c_0_138, negated_conjecture, (v1_relat_1(esk4_0)), inference(split_conjunct,[status(thm)],[c_0_31])). cnf(c_0_139, negated_conjecture, (v1_funct_1(esk5_0)), inference(split_conjunct,[status(thm)],[c_0_31])). cnf(c_0_140, negated_conjecture, (v1_funct_1(esk4_0)), inference(split_conjunct,[status(thm)],[c_0_31])). cnf(c_0_141, plain, (v2_struct_0(X1)\|~l1_struct_0(X1)\|~v1_xboole_0(u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_130])). cnf(c_0_142, negated_conjecture, (~r2_circcomb(k5_circcomb(esk3_0,esk4_0),k5_circcomb(esk3_0,esk5_0),k7_circcomb(esk1_0,esk2_0,esk3_0,esk4_0),k7_circcomb(esk1_0,esk2_0,esk3_0,esk5_0))), inference(evalgc,[status(thm)],[c_0_131])). cnf(c_0_143, negated_conjecture, (r2_circcomb(k5_circcomb(esk3_0,X1),k5_circcomb(esk3_0,X2),k7_circcomb(esk1_0,esk2_0,esk3_0,X1),k7_circcomb(esk1_0,esk2_0,esk3_0,X2))\|v1_xboole_0(u1_struct_0(k5_circcomb(esk3_0,X2)))\|v1_xboole_0(u1_struct_0(k5_circcomb(esk3_0,X1)))\|~v1_finseq_1(X2)\|~v1_finseq_1(X1)\|~v3_card_1(X2,esk1_0)\|~v3_card_1(X1,esk1_0)\|~v1_relat_1(X2)\|~v1_relat_1(X1)\|~v1_funct_1(X2)\|~v1_funct_1(X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132, c_0_129]), c_0_93])])])). cnf(c_0_144, negated_conjecture, (v1_finseq_1(esk5_0)), inference(evalgc,[status(thm)],[c_0_133])). cnf(c_0_145, negated_conjecture, (v1_finseq_1(esk4_0)), inference(evalgc,[status(thm)],[c_0_134])). cnf(c_0_146, negated_conjecture, (v3_card_1(esk5_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_135])). cnf(c_0_147, negated_conjecture, (v3_card_1(esk4_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_136])). cnf(c_0_148, negated_conjecture, (v1_relat_1(esk5_0)), inference(evalgc,[status(thm)],[c_0_137])). cnf(c_0_149, negated_conjecture, (v1_relat_1(esk4_0)), inference(evalgc,[status(thm)],[c_0_138])). cnf(c_0_150, negated_conjecture, (v1_funct_1(esk5_0)), inference(evalgc,[status(thm)],[c_0_139])). cnf(c_0_151, negated_conjecture, (v1_funct_1(esk4_0)), inference(evalgc,[status(thm)],[c_0_140])). cnf(c_0_152, plain, (v2_struct_0(X1)\|~l1_struct_0(X1)\|~v1_xboole_0(u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_141])). cnf(c_0_153, negated_conjecture, (v1_xboole_0(u1_struct_0(k5_circcomb(esk3_0,esk4_0)))\|v1_xboole_0(u1_struct_0(k5_circcomb(esk3_0,esk5_0)))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142, c_0_143]), c_0_144]), c_0_145]), c_0_146]), c_0_147]), c_0_148]), c_0_149]), c_0_150]), c_0_151])])])). cnf(c_0_154, negated_conjecture, (v2_struct_0(k5_circcomb(esk3_0,esk5_0))\|v1_xboole_0(u1_struct_0(k5_circcomb(esk3_0,esk4_0)))\|~l1_struct_0(k5_circcomb(esk3_0,esk5_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_152, c_0_153])])). cnf(c_0_155, negated_conjecture, (v2_struct_0(k5_circcomb(esk3_0,esk4_0))\|v2_struct_0(k5_circcomb(esk3_0,esk5_0))\|~l1_struct_0(k5_circcomb(esk3_0,esk4_0))\|~l1_struct_0(k5_circcomb(esk3_0,esk5_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_152, c_0_154])])). cnf(c_0_156, negated_conjecture, (v2_struct_0(k5_circcomb(esk3_0,esk5_0))\|v2_struct_0(k5_circcomb(esk3_0,esk4_0))\|~l1_struct_0(k5_circcomb(esk3_0,esk4_0))\|~l1_msualg_1(k5_circcomb(esk3_0,esk5_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_155, c_0_127])])). cnf(c_0_157, negated_conjecture, (v2_struct_0(k5_circcomb(esk3_0,esk4_0))\|v2_struct_0(k5_circcomb(esk3_0,esk5_0))\|~l1_msualg_1(k5_circcomb(esk3_0,esk5_0))\|~l1_msualg_1(k5_circcomb(esk3_0,esk4_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_156, c_0_127])])). cnf(c_0_158, negated_conjecture, (v2_struct_0(k5_circcomb(esk3_0,esk4_0))\|~l1_msualg_1(k5_circcomb(esk3_0,esk5_0))\|~l1_msualg_1(k5_circcomb(esk3_0,esk4_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125, c_0_157]), c_0_144]), c_0_148]), c_0_150])])])). cnf(c_0_159, negated_conjecture, (~l1_msualg_1(k5_circcomb(esk3_0,esk5_0))\|~l1_msualg_1(k5_circcomb(esk3_0,esk4_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125, c_0_158]), c_0_145]), c_0_149]), c_0_151])])])). cnf(c_0_160, negated_conjecture, (~l1_msualg_1(k5_circcomb(esk3_0,esk4_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159, c_0_124]), c_0_144]), c_0_148]), c_0_150])])])). cnf(c_0_161, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160, c_0_124]), c_0_145]), c_0_149]), c_0_151])]), ['proof']). # SZS output end CNFRefutation	theorem for n being Nat, X being non empty set, f being Function of n -tuples_on X, X, p,q being FinSeqLen of n holds 1GateCircuit(p,f) tolerates 1GateCircuit(q,f) proof let n be Nat, X be non empty set, f be Function of n-tuples_on X, X; let p,q be FinSeqLen of n; set S1 = 1GateCircStr(p,f), S2 = 1GateCircStr(q,f); set A1 = 1GateCircuit(p,f), A2 = 1GateCircuit(q,f); thus 1GateCircStr(p,f) tolerates 1GateCircStr(q,f) by Th43; A1: the Sorts of A2 = (the carrier of S2) --> X by Def13; the Sorts of A1 = (the carrier of S1) --> X by Def13; hence the Sorts of A1 tolerates the Sorts of A2 by A1,FUNCOP_1:87; A2: the Charact of A2 = (q,f) .--> f by Th54; the Charact of A1 = (p,f) .--> f by Th54; hence thesis by A2,FUNCOP_1:87; end;	Convert the following ATP output trace into a readable Mizar proof.
t20_nat_d	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t6_boole, axiom, ![X1]:(v1_xboole_0(X1)=>X1=k1_xboole_0), file('/scratch/mptp/predsminms1/t20_nat_d__0', t6_boole)). fof(d1_nat_d, axiom, ![X1]:(v7_ordinal1(X1)=>![X2]:(v7_ordinal1(X2)=>![X3]:(v7_ordinal1(X3)=>(X3=k1_nat_d(X1,X2)<=>~((![X4]:(v7_ordinal1(X4)=>~((X1=k2_xcmplx_0(k3_xcmplx_0(X2,X3),X4)&~(r1_xxreal_0(X2,X4)))))&~((X3=k6_numbers&X2=k6_numbers)))))))), file('/scratch/mptp/predsminms1/t20_nat_d__0', d1_nat_d)). fof(cc7_ordinal1, axiom, ![X1]:(v1_xboole_0(X1)=>v7_ordinal1(X1)), file('/scratch/mptp/predsminms1/t20_nat_d__0', cc7_ordinal1)). fof(redefinition_k6_numbers, axiom, k6_numbers=k1_xboole_0, file('/scratch/mptp/predsminms1/t20_nat_d__0', redefinition_k6_numbers)). fof(t1_arithm, axiom, ![X1]:(v1_xcmplx_0(X1)=>k2_xcmplx_0(X1,k6_numbers)=X1), file('/scratch/mptp/predsminms1/t20_nat_d__0', t1_arithm)). fof(spc0_boole, axiom, v1_xboole_0(np__0), file('/scratch/mptp/predsminms1/t20_nat_d__0', spc0_boole)). fof(fc2_nat_1, axiom, ![X1, X2]:((v7_ordinal1(X1)&v7_ordinal1(X2))=>v7_ordinal1(k3_xcmplx_0(X1,X2))), file('/scratch/mptp/predsminms1/t20_nat_d__0', fc2_nat_1)). fof(cc3_xreal_0, axiom, ![X1]:(v1_xreal_0(X1)=>v1_xcmplx_0(X1)), file('/scratch/mptp/predsminms1/t20_nat_d__0', cc3_xreal_0)). fof(cc2_xreal_0, axiom, ![X1]:(v7_ordinal1(X1)=>v1_xreal_0(X1)), file('/scratch/mptp/predsminms1/t20_nat_d__0', cc2_xreal_0)). fof(commutativity_k2_xcmplx_0, axiom, ![X1, X2]:((v1_xcmplx_0(X1)&v1_xcmplx_0(X2))=>k2_xcmplx_0(X1,X2)=k2_xcmplx_0(X2,X1)), file('/scratch/mptp/predsminms1/t20_nat_d__0', commutativity_k2_xcmplx_0)). fof(cc8_ordinal1, axiom, ![X1]:(m1_subset_1(X1,k4_ordinal1)=>v7_ordinal1(X1)), file('/scratch/mptp/predsminms1/t20_nat_d__0', cc8_ordinal1)). fof(t3_arithm, axiom, ![X1]:(v1_xcmplx_0(X1)=>k3_xcmplx_0(np__1,X1)=X1), file('/scratch/mptp/predsminms1/t20_nat_d__0', t3_arithm)). fof(redefinition_k5_numbers, axiom, k5_numbers=k4_ordinal1, file('/scratch/mptp/predsminms1/t20_nat_d__0', redefinition_k5_numbers)). fof(t20_nat_d, conjecture, ![X1]:(v7_ordinal1(X1)=>![X2]:(v7_ordinal1(X2)=>(~(X1=k6_numbers)=>k3_nat_d(k3_xcmplx_0(X2,X1),X1)=X2))), file('/scratch/mptp/predsminms1/t20_nat_d__0', t20_nat_d)). fof(commutativity_k3_xcmplx_0, axiom, ![X1, X2]:((v1_xcmplx_0(X1)&v1_xcmplx_0(X2))=>k3_xcmplx_0(X1,X2)=k3_xcmplx_0(X2,X1)), file('/scratch/mptp/predsminms1/t20_nat_d__0', commutativity_k3_xcmplx_0)). fof(rqLessOrEqual__r1_xxreal_0__r1_r0, axiom, ~(r1_xxreal_0(np__1,np__0)), file('/scratch/mptp/predsminms1/t20_nat_d__0', rqLessOrEqual__r1_xxreal_0__r1_r0)). fof(spc1_numerals, axiom, ((v2_xxreal_0(np__1)&m2_subset_1(np__1,k1_numbers,k5_numbers))&(m1_subset_1(np__1,k5_numbers)&m1_subset_1(np__1,k1_numbers))), file('/scratch/mptp/predsminms1/t20_nat_d__0', spc1_numerals)). fof(redefinition_k3_nat_d, axiom, ![X1, X2]:((v7_ordinal1(X1)&v7_ordinal1(X2))=>k3_nat_d(X1,X2)=k5_int_1(X1,X2)), file('/scratch/mptp/predsminms1/t20_nat_d__0', redefinition_k3_nat_d)). fof(rc4_xxreal_0, axiom, ?[X1]:(v1_xboole_0(X1)&v1_xxreal_0(X1)), file('/scratch/mptp/predsminms1/t20_nat_d__0', rc4_xxreal_0)). fof(redefinition_k1_nat_d, axiom, ![X1, X2]:((v7_ordinal1(X1)&v7_ordinal1(X2))=>k1_nat_d(X1,X2)=k5_int_1(X1,X2)), file('/scratch/mptp/predsminms1/t20_nat_d__0', redefinition_k1_nat_d)). fof(cc3_xxreal_0, axiom, ![X1]:((v1_xxreal_0(X1)&v2_xxreal_0(X1))=>(~(v1_xboole_0(X1))&(v1_xxreal_0(X1)&~(v3_xxreal_0(X1))))), file('/scratch/mptp/predsminms1/t20_nat_d__0', cc3_xxreal_0)). fof(t1_real, axiom, ![X1]:(v1_xreal_0(X1)=>![X2]:(v1_xreal_0(X2)=>((r1_xxreal_0(X1,X2)&v2_xxreal_0(X1))=>v2_xxreal_0(X2)))), file('/scratch/mptp/predsminms1/t20_nat_d__0', t1_real)). fof(cc1_xreal_0, axiom, ![X1]:(m1_subset_1(X1,k1_numbers)=>v1_xreal_0(X1)), file('/scratch/mptp/predsminms1/t20_nat_d__0', cc1_xreal_0)). fof(c_0_23, plain, ![X24]:(~v1_xboole_0(X24)\|X24=k1_xboole_0), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])])). fof(c_0_24, plain, ![X18, X19, X20, X22]:((((X20=k6_numbers\|v7_ordinal1(esk3_3(X18,X19,X20))\|X20!=k1_nat_d(X18,X19)\|~v7_ordinal1(X20)\|~v7_ordinal1(X19)\|~v7_ordinal1(X18))&(X19=k6_numbers\|v7_ordinal1(esk3_3(X18,X19,X20))\|X20!=k1_nat_d(X18,X19)\|~v7_ordinal1(X20)\|~v7_ordinal1(X19)\|~v7_ordinal1(X18)))&(((X20=k6_numbers\|X18=k2_xcmplx_0(k3_xcmplx_0(X19,X20),esk3_3(X18,X19,X20))\|X20!=k1_nat_d(X18,X19)\|~v7_ordinal1(X20)\|~v7_ordinal1(X19)\|~v7_ordinal1(X18))&(X19=k6_numbers\|X18=k2_xcmplx_0(k3_xcmplx_0(X19,X20),esk3_3(X18,X19,X20))\|X20!=k1_nat_d(X18,X19)\|~v7_ordinal1(X20)\|~v7_ordinal1(X19)\|~v7_ordinal1(X18)))&((X20=k6_numbers\|~r1_xxreal_0(X19,esk3_3(X18,X19,X20))\|X20!=k1_nat_d(X18,X19)\|~v7_ordinal1(X20)\|~v7_ordinal1(X19)\|~v7_ordinal1(X18))&(X19=k6_numbers\|~r1_xxreal_0(X19,esk3_3(X18,X19,X20))\|X20!=k1_nat_d(X18,X19)\|~v7_ordinal1(X20)\|~v7_ordinal1(X19)\|~v7_ordinal1(X18)))))&((~v7_ordinal1(X22)\|(X18!=k2_xcmplx_0(k3_xcmplx_0(X19,X20),X22)\|r1_xxreal_0(X19,X22))\|X20=k1_nat_d(X18,X19)\|~v7_ordinal1(X20)\|~v7_ordinal1(X19)\|~v7_ordinal1(X18))&(X20!=k6_numbers\|X19!=k6_numbers\|X20=k1_nat_d(X18,X19)\|~v7_ordinal1(X20)\|~v7_ordinal1(X19)\|~v7_ordinal1(X18)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d1_nat_d])])])])])])). fof(c_0_25, plain, ![X31]:(~v1_xboole_0(X31)\|v7_ordinal1(X31)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc7_ordinal1])])). cnf(c_0_26, plain, (X1=k1_xboole_0\|~v1_xboole_0(X1)), inference(split_conjunct,[status(thm)],[c_0_23])). cnf(c_0_27, plain, (k6_numbers=k1_xboole_0), inference(split_conjunct,[status(thm)],[redefinition_k6_numbers])). cnf(c_0_28, plain, (r1_xxreal_0(X3,X1)\|X4=k1_nat_d(X2,X3)\|~v7_ordinal1(X1)\|X2!=k2_xcmplx_0(k3_xcmplx_0(X3,X4),X1)\|~v7_ordinal1(X4)\|~v7_ordinal1(X3)\|~v7_ordinal1(X2)), inference(split_conjunct,[status(thm)],[c_0_24])). fof(c_0_29, plain, ![X17]:(~v1_xcmplx_0(X17)\|k2_xcmplx_0(X17,k6_numbers)=X17), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_arithm])])). cnf(c_0_30, plain, (v7_ordinal1(X1)\|~v1_xboole_0(X1)), inference(split_conjunct,[status(thm)],[c_0_25])). cnf(c_0_31, plain, (v1_xboole_0(np__0)), inference(split_conjunct,[status(thm)],[spc0_boole])). cnf(c_0_32, plain, (X1=k1_xboole_0\|~v1_xboole_0(X1)), inference(evalgc,[status(thm)],[c_0_26])). cnf(c_0_33, plain, (k1_xboole_0=k6_numbers), inference(evalgc,[status(thm)],[c_0_27])). cnf(c_0_34, plain, (X4=k1_nat_d(X2,X3)\|r1_xxreal_0(X3,X1)\|X2!=k2_xcmplx_0(k3_xcmplx_0(X3,X4),X1)\|~v7_ordinal1(X4)\|~v7_ordinal1(X3)\|~v7_ordinal1(X2)\|~v7_ordinal1(X1)), inference(evalgc,[status(thm)],[c_0_28])). cnf(c_0_35, plain, (k2_xcmplx_0(X1,k6_numbers)=X1\|~v1_xcmplx_0(X1)), inference(split_conjunct,[status(thm)],[c_0_29])). cnf(c_0_36, plain, (v7_ordinal1(X1)\|~v1_xboole_0(X1)), inference(evalgc,[status(thm)],[c_0_30])). cnf(c_0_37, plain, (v1_xboole_0(np__0)), inference(evalgc,[status(thm)],[c_0_31])). cnf(c_0_38, plain, (X1=k6_numbers\|~v1_xboole_0(X1)), inference(rw,[status(thm)],[c_0_32, c_0_33])). fof(c_0_39, plain, ![X11, X12]:(~v7_ordinal1(X11)\|~v7_ordinal1(X12)\|v7_ordinal1(k3_xcmplx_0(X11,X12))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc2_nat_1])])). fof(c_0_40, plain, ![X7]:(~v1_xreal_0(X7)\|v1_xcmplx_0(X7)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc3_xreal_0])])). fof(c_0_41, plain, ![X8]:(~v7_ordinal1(X8)\|v1_xreal_0(X8)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_xreal_0])])). fof(c_0_42, plain, ![X32, X33]:(~v1_xcmplx_0(X32)\|~v1_xcmplx_0(X33)\|k2_xcmplx_0(X32,X33)=k2_xcmplx_0(X33,X32)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[commutativity_k2_xcmplx_0])])). fof(c_0_43, plain, ![X29]:(~m1_subset_1(X29,k4_ordinal1)\|v7_ordinal1(X29)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc8_ordinal1])])). cnf(c_0_44, plain, (k1_nat_d(k2_xcmplx_0(k3_xcmplx_0(X2,X1),X3),X2)=X1\|r1_xxreal_0(X2,X3)\|~v7_ordinal1(X1)\|~v7_ordinal1(X2)\|~v7_ordinal1(k2_xcmplx_0(k3_xcmplx_0(X2,X1),X3))\|~v7_ordinal1(X3)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_34])])). cnf(c_0_45, plain, (k2_xcmplx_0(X1,k6_numbers)=X1\|~v1_xcmplx_0(X1)), inference(evalgc,[status(thm)],[c_0_35])). cnf(c_0_46, plain, (v7_ordinal1(np__0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_36, c_0_37])])). cnf(c_0_47, plain, (np__0=k6_numbers), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_38, c_0_37])])). cnf(c_0_48, plain, (v7_ordinal1(k3_xcmplx_0(X1,X2))\|~v7_ordinal1(X1)\|~v7_ordinal1(X2)), inference(split_conjunct,[status(thm)],[c_0_39])). cnf(c_0_49, plain, (v1_xcmplx_0(X1)\|~v1_xreal_0(X1)), inference(split_conjunct,[status(thm)],[c_0_40])). cnf(c_0_50, plain, (v1_xreal_0(X1)\|~v7_ordinal1(X1)), inference(split_conjunct,[status(thm)],[c_0_41])). cnf(c_0_51, plain, (k2_xcmplx_0(X1,X2)=k2_xcmplx_0(X2,X1)\|~v1_xcmplx_0(X1)\|~v1_xcmplx_0(X2)), inference(split_conjunct,[status(thm)],[c_0_42])). fof(c_0_52, plain, ![X30]:(~v1_xcmplx_0(X30)\|k3_xcmplx_0(np__1,X30)=X30), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_arithm])])). cnf(c_0_53, plain, (v7_ordinal1(X1)\|~m1_subset_1(X1,k4_ordinal1)), inference(split_conjunct,[status(thm)],[c_0_43])). cnf(c_0_54, plain, (k5_numbers=k4_ordinal1), inference(split_conjunct,[status(thm)],[redefinition_k5_numbers])). fof(c_0_55, negated_conjecture, ~(![X1]:(v7_ordinal1(X1)=>![X2]:(v7_ordinal1(X2)=>(~(X1=k6_numbers)=>k3_nat_d(k3_xcmplx_0(X2,X1),X1)=X2)))), inference(assume_negation,[status(cth)],[t20_nat_d])). fof(c_0_56, plain, ![X9, X10]:(~v1_xcmplx_0(X9)\|~v1_xcmplx_0(X10)\|k3_xcmplx_0(X9,X10)=k3_xcmplx_0(X10,X9)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[commutativity_k3_xcmplx_0])])). cnf(c_0_57, plain, (k1_nat_d(k3_xcmplx_0(X1,X2),X1)=X2\|r1_xxreal_0(X1,k6_numbers)\|~v7_ordinal1(k3_xcmplx_0(X1,X2))\|~v7_ordinal1(X2)\|~v7_ordinal1(X1)\|~v7_ordinal1(k6_numbers)\|~v1_xcmplx_0(k3_xcmplx_0(X1,X2))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_44, c_0_45])])). cnf(c_0_58, plain, (v7_ordinal1(k6_numbers)), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[c_0_46, c_0_47])])). cnf(c_0_59, plain, (v7_ordinal1(k3_xcmplx_0(X1,X2))\|~v7_ordinal1(X2)\|~v7_ordinal1(X1)), inference(evalgc,[status(thm)],[c_0_48])). cnf(c_0_60, plain, (v1_xcmplx_0(X1)\|~v1_xreal_0(X1)), inference(evalgc,[status(thm)],[c_0_49])). cnf(c_0_61, plain, (v1_xreal_0(X1)\|~v7_ordinal1(X1)), inference(evalgc,[status(thm)],[c_0_50])). fof(c_0_62, plain, ~r1_xxreal_0(np__1,np__0), inference(fof_simplification,[status(thm)],[rqLessOrEqual__r1_xxreal_0__r1_r0])). cnf(c_0_63, plain, (k2_xcmplx_0(X1,X2)=k2_xcmplx_0(X2,X1)\|~v1_xcmplx_0(X2)\|~v1_xcmplx_0(X1)), inference(evalgc,[status(thm)],[c_0_51])). cnf(c_0_64, plain, (k3_xcmplx_0(np__1,X1)=X1\|~v1_xcmplx_0(X1)), inference(split_conjunct,[status(thm)],[c_0_52])). cnf(c_0_65, plain, (v7_ordinal1(X1)\|~m1_subset_1(X1,k4_ordinal1)), inference(evalgc,[status(thm)],[c_0_53])). cnf(c_0_66, plain, (k4_ordinal1=k5_numbers), inference(evalgc,[status(thm)],[c_0_54])). cnf(c_0_67, plain, (m1_subset_1(np__1,k5_numbers)), inference(split_conjunct,[status(thm)],[spc1_numerals])). fof(c_0_68, negated_conjecture, (v7_ordinal1(esk1_0)&(v7_ordinal1(esk2_0)&(esk1_0!=k6_numbers&k3_nat_d(k3_xcmplx_0(esk2_0,esk1_0),esk1_0)!=esk2_0))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_55])])])])). fof(c_0_69, plain, ![X13, X14]:(~v7_ordinal1(X13)\|~v7_ordinal1(X14)\|k3_nat_d(X13,X14)=k5_int_1(X13,X14)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k3_nat_d])])). cnf(c_0_70, plain, (k3_xcmplx_0(X1,X2)=k3_xcmplx_0(X2,X1)\|~v1_xcmplx_0(X1)\|~v1_xcmplx_0(X2)), inference(split_conjunct,[status(thm)],[c_0_56])). fof(c_0_71, plain, (v1_xboole_0(esk4_0)&v1_xxreal_0(esk4_0)), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc4_xxreal_0])])). cnf(c_0_72, plain, (k1_nat_d(k3_xcmplx_0(X1,X2),X1)=X2\|r1_xxreal_0(X1,k6_numbers)\|~v1_xcmplx_0(k3_xcmplx_0(X1,X2))\|~v7_ordinal1(X2)\|~v7_ordinal1(X1)), inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57, c_0_58])]), c_0_59])). cnf(c_0_73, plain, (v1_xcmplx_0(X1)\|~v7_ordinal1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_60, c_0_61])])). cnf(c_0_74, plain, (~r1_xxreal_0(np__1,np__0)), inference(split_conjunct,[status(thm)],[c_0_62])). cnf(c_0_75, plain, (k1_nat_d(k2_xcmplx_0(X3,k3_xcmplx_0(X1,X2)),X1)=X2\|r1_xxreal_0(X1,X3)\|~v7_ordinal1(k2_xcmplx_0(X3,k3_xcmplx_0(X1,X2)))\|~v7_ordinal1(X2)\|~v7_ordinal1(X1)\|~v7_ordinal1(X3)\|~v1_xcmplx_0(X3)\|~v1_xcmplx_0(k3_xcmplx_0(X1,X2))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_44, c_0_63])])). cnf(c_0_76, plain, (k3_xcmplx_0(np__1,X1)=X1\|~v1_xcmplx_0(X1)), inference(evalgc,[status(thm)],[c_0_64])). cnf(c_0_77, plain, (v7_ordinal1(X1)\|~m1_subset_1(X1,k5_numbers)), inference(rw,[status(thm)],[c_0_65, c_0_66])). cnf(c_0_78, plain, (m1_subset_1(np__1,k5_numbers)), inference(evalgc,[status(thm)],[c_0_67])). cnf(c_0_79, negated_conjecture, (k3_nat_d(k3_xcmplx_0(esk2_0,esk1_0),esk1_0)!=esk2_0), inference(split_conjunct,[status(thm)],[c_0_68])). cnf(c_0_80, plain, (k3_nat_d(X1,X2)=k5_int_1(X1,X2)\|~v7_ordinal1(X1)\|~v7_ordinal1(X2)), inference(split_conjunct,[status(thm)],[c_0_69])). cnf(c_0_81, negated_conjecture, (v7_ordinal1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_68])). fof(c_0_82, plain, ![X15, X16]:(~v7_ordinal1(X15)\|~v7_ordinal1(X16)\|k1_nat_d(X15,X16)=k5_int_1(X15,X16)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k1_nat_d])])). cnf(c_0_83, plain, (k3_xcmplx_0(X1,X2)=k3_xcmplx_0(X2,X1)\|~v1_xcmplx_0(X2)\|~v1_xcmplx_0(X1)), inference(evalgc,[status(thm)],[c_0_70])). cnf(c_0_84, plain, (v1_xboole_0(esk4_0)), inference(split_conjunct,[status(thm)],[c_0_71])). cnf(c_0_85, plain, (k1_nat_d(k3_xcmplx_0(X1,X2),X1)=X2\|r1_xxreal_0(X1,k6_numbers)\|~v7_ordinal1(X2)\|~v7_ordinal1(X1)\|~v7_ordinal1(k3_xcmplx_0(X1,X2))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_72, c_0_73])])). cnf(c_0_86, plain, (~r1_xxreal_0(np__1,np__0)), inference(evalgc,[status(thm)],[c_0_74])). cnf(c_0_87, plain, (k1_nat_d(k2_xcmplx_0(X1,k3_xcmplx_0(X2,X3)),X2)=X3\|r1_xxreal_0(X2,X1)\|~v1_xcmplx_0(k3_xcmplx_0(X2,X3))\|~v7_ordinal1(k2_xcmplx_0(X1,k3_xcmplx_0(X2,X3)))\|~v7_ordinal1(X3)\|~v7_ordinal1(X2)\|~v7_ordinal1(X1)), inference(csr,[status(thm)],[c_0_75, c_0_73])). cnf(c_0_88, plain, (k3_xcmplx_0(np__1,X1)=X1\|~v7_ordinal1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_76, c_0_73])])). cnf(c_0_89, plain, (v7_ordinal1(np__1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_77, c_0_78])])). cnf(c_0_90, negated_conjecture, (k3_nat_d(k3_xcmplx_0(esk2_0,esk1_0),esk1_0)!=esk2_0), inference(evalgc,[status(thm)],[c_0_79])). cnf(c_0_91, plain, (k3_nat_d(X1,X2)=k5_int_1(X1,X2)\|~v7_ordinal1(X2)\|~v7_ordinal1(X1)), inference(evalgc,[status(thm)],[c_0_80])). cnf(c_0_92, negated_conjecture, (v7_ordinal1(esk1_0)), inference(evalgc,[status(thm)],[c_0_81])). cnf(c_0_93, plain, (k1_nat_d(X1,X2)=k5_int_1(X1,X2)\|~v7_ordinal1(X1)\|~v7_ordinal1(X2)), inference(split_conjunct,[status(thm)],[c_0_82])). cnf(c_0_94, plain, (k3_xcmplx_0(X1,X2)=k3_xcmplx_0(X2,X1)\|~v1_xcmplx_0(X1)\|~v7_ordinal1(X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_83, c_0_73])])). fof(c_0_95, plain, ![X25]:((~v1_xboole_0(X25)\|(~v1_xxreal_0(X25)\|~v2_xxreal_0(X25)))&((v1_xxreal_0(X25)\|(~v1_xxreal_0(X25)\|~v2_xxreal_0(X25)))&(~v3_xxreal_0(X25)\|(~v1_xxreal_0(X25)\|~v2_xxreal_0(X25))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[cc3_xxreal_0])])])])). cnf(c_0_96, plain, (v1_xxreal_0(esk4_0)), inference(split_conjunct,[status(thm)],[c_0_71])). cnf(c_0_97, plain, (v1_xboole_0(esk4_0)), inference(evalgc,[status(thm)],[c_0_84])). cnf(c_0_98, plain, (k1_nat_d(k3_xcmplx_0(X1,X2),X1)=X2\|r1_xxreal_0(X1,k6_numbers)\|~v7_ordinal1(X2)\|~v7_ordinal1(X1)), inference(csr,[status(thm)],[c_0_85, c_0_59])). cnf(c_0_99, plain, (~r1_xxreal_0(np__1,k6_numbers)), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[c_0_86, c_0_47])])). cnf(c_0_100, plain, (k1_nat_d(k2_xcmplx_0(X1,X2),np__1)=X2\|r1_xxreal_0(np__1,X1)\|~v1_xcmplx_0(X2)\|~v7_ordinal1(k2_xcmplx_0(X1,X2))\|~v7_ordinal1(X2)\|~v7_ordinal1(X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87, c_0_88]), c_0_89])])])). fof(c_0_101, plain, ![X27, X28]:(~v1_xreal_0(X27)\|(~v1_xreal_0(X28)\|(~r1_xxreal_0(X27,X28)\|~v2_xxreal_0(X27)\|v2_xxreal_0(X28)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_real])])])). cnf(c_0_102, negated_conjecture, (k5_int_1(k3_xcmplx_0(esk2_0,esk1_0),esk1_0)!=esk2_0\|~v7_ordinal1(k3_xcmplx_0(esk2_0,esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90, c_0_91]), c_0_92])])])). cnf(c_0_103, plain, (k5_int_1(X1,X2)=k1_nat_d(X1,X2)\|~v7_ordinal1(X2)\|~v7_ordinal1(X1)), inference(evalgc,[status(thm)],[c_0_93])). cnf(c_0_104, plain, (k3_xcmplx_0(X1,X2)=k3_xcmplx_0(X2,X1)\|~v7_ordinal1(X2)\|~v7_ordinal1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_94, c_0_73])])). cnf(c_0_105, negated_conjecture, (v7_ordinal1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_68])). cnf(c_0_106, plain, (~v1_xboole_0(X1)\|~v1_xxreal_0(X1)\|~v2_xxreal_0(X1)), inference(split_conjunct,[status(thm)],[c_0_95])). cnf(c_0_107, plain, (v1_xxreal_0(esk4_0)), inference(evalgc,[status(thm)],[c_0_96])). cnf(c_0_108, plain, (esk4_0=k6_numbers), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_38, c_0_97])])). cnf(c_0_109, plain, (k1_nat_d(X1,np__1)=X1\|~v7_ordinal1(X1)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98, c_0_88]), c_0_89])]), c_0_99])])). cnf(c_0_110, plain, (k1_nat_d(k2_xcmplx_0(X1,X2),np__1)=X2\|r1_xxreal_0(np__1,X1)\|~v7_ordinal1(k2_xcmplx_0(X1,X2))\|~v7_ordinal1(X2)\|~v7_ordinal1(X1)), inference(csr,[status(thm)],[c_0_100, c_0_73])). fof(c_0_111, plain, ![X26]:(~m1_subset_1(X26,k1_numbers)\|v1_xreal_0(X26)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_xreal_0])])). cnf(c_0_112, plain, (v2_xxreal_0(X2)\|~v1_xreal_0(X1)\|~v1_xreal_0(X2)\|~r1_xxreal_0(X1,X2)\|~v2_xxreal_0(X1)), inference(split_conjunct,[status(thm)],[c_0_101])). cnf(c_0_113, negated_conjecture, (k1_nat_d(k3_xcmplx_0(esk2_0,esk1_0),esk1_0)!=esk2_0\|~v7_ordinal1(k3_xcmplx_0(esk2_0,esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102, c_0_103]), c_0_92])])])). cnf(c_0_114, plain, (k1_nat_d(k3_xcmplx_0(X2,X1),X1)=X2\|r1_xxreal_0(X1,k6_numbers)\|~v7_ordinal1(X2)\|~v7_ordinal1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_98, c_0_104])])). cnf(c_0_115, negated_conjecture, (v7_ordinal1(esk2_0)), inference(evalgc,[status(thm)],[c_0_105])). cnf(c_0_116, plain, (~v1_xboole_0(X1)\|~v1_xxreal_0(X1)\|~v2_xxreal_0(X1)), inference(evalgc,[status(thm)],[c_0_106])). cnf(c_0_117, plain, (v1_xxreal_0(k6_numbers)), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[c_0_107, c_0_108])])). cnf(c_0_118, plain, (v1_xboole_0(k6_numbers)), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[c_0_97, c_0_108])])). cnf(c_0_119, plain, (k2_xcmplx_0(X1,X2)=X2\|r1_xxreal_0(np__1,X1)\|~v7_ordinal1(k2_xcmplx_0(X1,X2))\|~v7_ordinal1(X2)\|~v7_ordinal1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_109, c_0_110])])). cnf(c_0_120, plain, (v1_xreal_0(X1)\|~m1_subset_1(X1,k1_numbers)), inference(split_conjunct,[status(thm)],[c_0_111])). cnf(c_0_121, plain, (m1_subset_1(np__1,k1_numbers)), inference(split_conjunct,[status(thm)],[spc1_numerals])). cnf(c_0_122, plain, (v2_xxreal_0(X2)\|~v1_xreal_0(X2)\|~v1_xreal_0(X1)\|~v2_xxreal_0(X1)\|~r1_xxreal_0(X1,X2)), inference(evalgc,[status(thm)],[c_0_112])). cnf(c_0_123, negated_conjecture, (r1_xxreal_0(esk1_0,k6_numbers)\|~v7_ordinal1(k3_xcmplx_0(esk2_0,esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113, c_0_114]), c_0_115]), c_0_92])])])). cnf(c_0_124, plain, (~v2_xxreal_0(k6_numbers)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116, c_0_117]), c_0_118])])])). cnf(c_0_125, plain, (X1=k6_numbers\|r1_xxreal_0(np__1,X1)\|~v7_ordinal1(X1)\|~v1_xcmplx_0(X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119, c_0_45]), c_0_58])])])). cnf(c_0_126, plain, (v2_xxreal_0(np__1)), inference(split_conjunct,[status(thm)],[spc1_numerals])). cnf(c_0_127, plain, (v1_xreal_0(X1)\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[c_0_120])). cnf(c_0_128, plain, (m1_subset_1(np__1,k1_numbers)), inference(evalgc,[status(thm)],[c_0_121])). cnf(c_0_129, negated_conjecture, (~v2_xxreal_0(esk1_0)\|~v1_xreal_0(k6_numbers)\|~v1_xreal_0(esk1_0)\|~v7_ordinal1(k3_xcmplx_0(esk2_0,esk1_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_122, c_0_123]), c_0_124])])). cnf(c_0_130, plain, (X1=k6_numbers\|r1_xxreal_0(np__1,X1)\|~v7_ordinal1(X1)), inference(csr,[status(thm)],[c_0_125, c_0_73])). cnf(c_0_131, plain, (v2_xxreal_0(np__1)), inference(evalgc,[status(thm)],[c_0_126])). cnf(c_0_132, plain, (v1_xreal_0(np__1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_127, c_0_128])])). cnf(c_0_133, negated_conjecture, (~v2_xxreal_0(esk1_0)\|~v1_xreal_0(k6_numbers)\|~v7_ordinal1(k3_xcmplx_0(esk2_0,esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129, c_0_61]), c_0_92])])])). cnf(c_0_134, plain, (v2_xxreal_0(X1)\|X1=k6_numbers\|~v1_xreal_0(X1)\|~v7_ordinal1(X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122, c_0_130]), c_0_131]), c_0_132])])])). cnf(c_0_135, negated_conjecture, (esk1_0!=k6_numbers), inference(split_conjunct,[status(thm)],[c_0_68])). cnf(c_0_136, negated_conjecture, (~v2_xxreal_0(esk1_0)\|~v7_ordinal1(k3_xcmplx_0(esk2_0,esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133, c_0_61]), c_0_58])])])). cnf(c_0_137, plain, (X1=k6_numbers\|v2_xxreal_0(X1)\|~v7_ordinal1(X1)), inference(csr,[status(thm)],[c_0_134, c_0_61])). cnf(c_0_138, negated_conjecture, (esk1_0!=k6_numbers), inference(evalgc,[status(thm)],[c_0_135])). cnf(c_0_139, negated_conjecture, (~v7_ordinal1(k3_xcmplx_0(esk2_0,esk1_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136, c_0_137]), c_0_92])]), c_0_138])])). cnf(c_0_140, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139, c_0_59]), c_0_92]), c_0_115])]), ['proof']). # SZS output end CNFRefutation	reserve p,k,l,m,n,s,h,i,j,t for Nat; theorem k <> 0 implies m * k div k = m proof assume k <> 0; then mk = k m + 0 & 0 < k or m = 0 & k = 0; hence thesis by Def1; end;	Convert the following ATP output trace into a readable Mizar proof.
t35_modelc_3	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t35_modelc_3, conjecture, ![X1]:(v7_ordinal1(X1)=>![X2]:((v1_relat_1(X2)&(v1_funct_1(X2)&v1_finseq_1(X2)))=>![X3]:((v1_modelc_2(X3)&m2_finseq_1(X3,k5_numbers))=>((r5_modelc_3(X3,X2)&r1_xxreal_0(np__1,X1))=>(r1_xxreal_0(k3_finseq_1(X2),X1)\|r4_modelc_3(X3,k10_modelc_3(k1_funct_1(X2,X1),X3),k10_modelc_3(k1_funct_1(X2,k1_nat_1(X1,np__1)),X3))))))), file('/scratch/mptp/predsminms1/t35_modelc_3__0', t35_modelc_3)). fof(d16_modelc_3, axiom, ![X1, X2]:((v1_modelc_2(X2)&m2_finseq_1(X2,k5_numbers))=>(((v1_modelc_3(X1,X2)&l1_modelc_3(X1,X2))=>k10_modelc_3(X1,X2)=X1)&(~((v1_modelc_3(X1,X2)&l1_modelc_3(X1,X2)))=>k10_modelc_3(X1,X2)=g1_modelc_3(X2,k7_modelc_3(X2),k7_modelc_3(X2),k7_modelc_3(X2))))), file('/scratch/mptp/predsminms1/t35_modelc_3__0', d16_modelc_3)). fof(d19_modelc_3, axiom, ![X1]:((v1_modelc_2(X1)&m2_finseq_1(X1,k5_numbers))=>![X2]:((v1_relat_1(X2)&(v1_funct_1(X2)&v1_finseq_1(X2)))=>(r5_modelc_3(X1,X2)<=>![X3]:(v7_ordinal1(X3)=>~((r1_xxreal_0(np__1,X3)&(~(r1_xxreal_0(k3_finseq_1(X2),X3))&![X4]:((v1_modelc_3(X4,X1)&l1_modelc_3(X4,X1))=>![X5]:((v1_modelc_3(X5,X1)&l1_modelc_3(X5,X1))=>~((X4=k1_funct_1(X2,X3)&(X5=k1_funct_1(X2,k1_nat_1(X3,np__1))&r4_modelc_3(X1,X4,X5))))))))))))), file('/scratch/mptp/predsminms1/t35_modelc_3__0', d19_modelc_3)). fof(c_0_3, negated_conjecture, ~(![X1]:(v7_ordinal1(X1)=>![X2]:((v1_relat_1(X2)&(v1_funct_1(X2)&v1_finseq_1(X2)))=>![X3]:((v1_modelc_2(X3)&m2_finseq_1(X3,k5_numbers))=>((r5_modelc_3(X3,X2)&r1_xxreal_0(np__1,X1))=>(r1_xxreal_0(k3_finseq_1(X2),X1)\|r4_modelc_3(X3,k10_modelc_3(k1_funct_1(X2,X1),X3),k10_modelc_3(k1_funct_1(X2,k1_nat_1(X1,np__1)),X3)))))))), inference(assume_negation,[status(cth)],[t35_modelc_3])). fof(c_0_4, negated_conjecture, (v7_ordinal1(esk1_0)&((v1_relat_1(esk2_0)&(v1_funct_1(esk2_0)&v1_finseq_1(esk2_0)))&((v1_modelc_2(esk3_0)&m2_finseq_1(esk3_0,k5_numbers))&((r5_modelc_3(esk3_0,esk2_0)&r1_xxreal_0(np__1,esk1_0))&(~r1_xxreal_0(k3_finseq_1(esk2_0),esk1_0)&~r4_modelc_3(esk3_0,k10_modelc_3(k1_funct_1(esk2_0,esk1_0),esk3_0),k10_modelc_3(k1_funct_1(esk2_0,k1_nat_1(esk1_0,np__1)),esk3_0))))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])). fof(c_0_5, plain, ![X9, X10]:((~v1_modelc_3(X9,X10)\|~l1_modelc_3(X9,X10)\|k10_modelc_3(X9,X10)=X9\|(~v1_modelc_2(X10)\|~m2_finseq_1(X10,k5_numbers)))&((v1_modelc_3(X9,X10)\|k10_modelc_3(X9,X10)=g1_modelc_3(X10,k7_modelc_3(X10),k7_modelc_3(X10),k7_modelc_3(X10))\|(~v1_modelc_2(X10)\|~m2_finseq_1(X10,k5_numbers)))&(l1_modelc_3(X9,X10)\|k10_modelc_3(X9,X10)=g1_modelc_3(X10,k7_modelc_3(X10),k7_modelc_3(X10),k7_modelc_3(X10))\|(~v1_modelc_2(X10)\|~m2_finseq_1(X10,k5_numbers))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d16_modelc_3])])])). fof(c_0_6, plain, ![X11, X12, X13, X17, X18]:((((v1_modelc_3(esk4_3(X11,X12,X13),X11)\|r1_xxreal_0(k3_finseq_1(X12),X13)\|~r1_xxreal_0(np__1,X13)\|~v7_ordinal1(X13)\|~r5_modelc_3(X11,X12)\|(~v1_relat_1(X12)\|(~v1_funct_1(X12)\|~v1_finseq_1(X12)))\|(~v1_modelc_2(X11)\|~m2_finseq_1(X11,k5_numbers)))&(l1_modelc_3(esk4_3(X11,X12,X13),X11)\|r1_xxreal_0(k3_finseq_1(X12),X13)\|~r1_xxreal_0(np__1,X13)\|~v7_ordinal1(X13)\|~r5_modelc_3(X11,X12)\|(~v1_relat_1(X12)\|(~v1_funct_1(X12)\|~v1_finseq_1(X12)))\|(~v1_modelc_2(X11)\|~m2_finseq_1(X11,k5_numbers))))&(((v1_modelc_3(esk5_3(X11,X12,X13),X11)\|r1_xxreal_0(k3_finseq_1(X12),X13)\|~r1_xxreal_0(np__1,X13)\|~v7_ordinal1(X13)\|~r5_modelc_3(X11,X12)\|(~v1_relat_1(X12)\|(~v1_funct_1(X12)\|~v1_finseq_1(X12)))\|(~v1_modelc_2(X11)\|~m2_finseq_1(X11,k5_numbers)))&(l1_modelc_3(esk5_3(X11,X12,X13),X11)\|r1_xxreal_0(k3_finseq_1(X12),X13)\|~r1_xxreal_0(np__1,X13)\|~v7_ordinal1(X13)\|~r5_modelc_3(X11,X12)\|(~v1_relat_1(X12)\|(~v1_funct_1(X12)\|~v1_finseq_1(X12)))\|(~v1_modelc_2(X11)\|~m2_finseq_1(X11,k5_numbers))))&((esk4_3(X11,X12,X13)=k1_funct_1(X12,X13)\|r1_xxreal_0(k3_finseq_1(X12),X13)\|~r1_xxreal_0(np__1,X13)\|~v7_ordinal1(X13)\|~r5_modelc_3(X11,X12)\|(~v1_relat_1(X12)\|(~v1_funct_1(X12)\|~v1_finseq_1(X12)))\|(~v1_modelc_2(X11)\|~m2_finseq_1(X11,k5_numbers)))&((esk5_3(X11,X12,X13)=k1_funct_1(X12,k1_nat_1(X13,np__1))\|r1_xxreal_0(k3_finseq_1(X12),X13)\|~r1_xxreal_0(np__1,X13)\|~v7_ordinal1(X13)\|~r5_modelc_3(X11,X12)\|(~v1_relat_1(X12)\|(~v1_funct_1(X12)\|~v1_finseq_1(X12)))\|(~v1_modelc_2(X11)\|~m2_finseq_1(X11,k5_numbers)))&(r4_modelc_3(X11,esk4_3(X11,X12,X13),esk5_3(X11,X12,X13))\|r1_xxreal_0(k3_finseq_1(X12),X13)\|~r1_xxreal_0(np__1,X13)\|~v7_ordinal1(X13)\|~r5_modelc_3(X11,X12)\|(~v1_relat_1(X12)\|(~v1_funct_1(X12)\|~v1_finseq_1(X12)))\|(~v1_modelc_2(X11)\|~m2_finseq_1(X11,k5_numbers)))))))&((v7_ordinal1(esk6_2(X11,X12))\|r5_modelc_3(X11,X12)\|(~v1_relat_1(X12)\|(~v1_funct_1(X12)\|~v1_finseq_1(X12)))\|(~v1_modelc_2(X11)\|~m2_finseq_1(X11,k5_numbers)))&((r1_xxreal_0(np__1,esk6_2(X11,X12))\|r5_modelc_3(X11,X12)\|(~v1_relat_1(X12)\|(~v1_funct_1(X12)\|~v1_finseq_1(X12)))\|(~v1_modelc_2(X11)\|~m2_finseq_1(X11,k5_numbers)))&((~r1_xxreal_0(k3_finseq_1(X12),esk6_2(X11,X12))\|r5_modelc_3(X11,X12)\|(~v1_relat_1(X12)\|(~v1_funct_1(X12)\|~v1_finseq_1(X12)))\|(~v1_modelc_2(X11)\|~m2_finseq_1(X11,k5_numbers)))&(~v1_modelc_3(X17,X11)\|~l1_modelc_3(X17,X11)\|(~v1_modelc_3(X18,X11)\|~l1_modelc_3(X18,X11)\|(X17!=k1_funct_1(X12,esk6_2(X11,X12))\|(X18!=k1_funct_1(X12,k1_nat_1(esk6_2(X11,X12),np__1))\|~r4_modelc_3(X11,X17,X18))))\|r5_modelc_3(X11,X12)\|(~v1_relat_1(X12)\|(~v1_funct_1(X12)\|~v1_finseq_1(X12)))\|(~v1_modelc_2(X11)\|~m2_finseq_1(X11,k5_numbers))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d19_modelc_3])])])])])])). cnf(c_0_7, negated_conjecture, (~r4_modelc_3(esk3_0,k10_modelc_3(k1_funct_1(esk2_0,esk1_0),esk3_0),k10_modelc_3(k1_funct_1(esk2_0,k1_nat_1(esk1_0,np__1)),esk3_0))), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_8, plain, (k10_modelc_3(X1,X2)=X1\|~v1_modelc_3(X1,X2)\|~l1_modelc_3(X1,X2)\|~v1_modelc_2(X2)\|~m2_finseq_1(X2,k5_numbers)), inference(split_conjunct,[status(thm)],[c_0_5])). cnf(c_0_9, negated_conjecture, (m2_finseq_1(esk3_0,k5_numbers)), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_10, negated_conjecture, (v1_modelc_2(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_11, plain, (r4_modelc_3(X1,esk4_3(X1,X2,X3),esk5_3(X1,X2,X3))\|r1_xxreal_0(k3_finseq_1(X2),X3)\|~r1_xxreal_0(np__1,X3)\|~v7_ordinal1(X3)\|~r5_modelc_3(X1,X2)\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v1_finseq_1(X2)\|~v1_modelc_2(X1)\|~m2_finseq_1(X1,k5_numbers)), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_12, plain, (esk5_3(X1,X2,X3)=k1_funct_1(X2,k1_nat_1(X3,np__1))\|r1_xxreal_0(k3_finseq_1(X2),X3)\|~r1_xxreal_0(np__1,X3)\|~v7_ordinal1(X3)\|~r5_modelc_3(X1,X2)\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v1_finseq_1(X2)\|~v1_modelc_2(X1)\|~m2_finseq_1(X1,k5_numbers)), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_13, negated_conjecture, (~r4_modelc_3(esk3_0,k10_modelc_3(k1_funct_1(esk2_0,esk1_0),esk3_0),k10_modelc_3(k1_funct_1(esk2_0,k1_nat_1(esk1_0,np__1)),esk3_0))), inference(evalgc,[status(thm)],[c_0_7])). cnf(c_0_14, plain, (k10_modelc_3(X1,X2)=X1\|~v1_modelc_2(X2)\|~v1_modelc_3(X1,X2)\|~l1_modelc_3(X1,X2)\|~m2_finseq_1(X2,k5_numbers)), inference(evalgc,[status(thm)],[c_0_8])). cnf(c_0_15, negated_conjecture, (m2_finseq_1(esk3_0,k5_numbers)), inference(evalgc,[status(thm)],[c_0_9])). cnf(c_0_16, negated_conjecture, (v1_modelc_2(esk3_0)), inference(evalgc,[status(thm)],[c_0_10])). cnf(c_0_17, plain, (r1_xxreal_0(k3_finseq_1(X2),X3)\|r4_modelc_3(X1,esk4_3(X1,X2,X3),esk5_3(X1,X2,X3))\|~v7_ordinal1(X3)\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v1_finseq_1(X2)\|~v1_modelc_2(X1)\|~r5_modelc_3(X1,X2)\|~m2_finseq_1(X1,k5_numbers)\|~r1_xxreal_0(np__1,X3)), inference(evalgc,[status(thm)],[c_0_11])). cnf(c_0_18, plain, (esk5_3(X1,X2,X3)=k1_funct_1(X2,k1_nat_1(X3,np__1))\|r1_xxreal_0(k3_finseq_1(X2),X3)\|~v7_ordinal1(X3)\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v1_finseq_1(X2)\|~v1_modelc_2(X1)\|~r5_modelc_3(X1,X2)\|~m2_finseq_1(X1,k5_numbers)\|~r1_xxreal_0(np__1,X3)), inference(evalgc,[status(thm)],[c_0_12])). cnf(c_0_19, plain, (esk4_3(X1,X2,X3)=k1_funct_1(X2,X3)\|r1_xxreal_0(k3_finseq_1(X2),X3)\|~r1_xxreal_0(np__1,X3)\|~v7_ordinal1(X3)\|~r5_modelc_3(X1,X2)\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v1_finseq_1(X2)\|~v1_modelc_2(X1)\|~m2_finseq_1(X1,k5_numbers)), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_20, negated_conjecture, (~r4_modelc_3(esk3_0,k1_funct_1(esk2_0,esk1_0),k10_modelc_3(k1_funct_1(esk2_0,k1_nat_1(esk1_0,np__1)),esk3_0))\|~l1_modelc_3(k1_funct_1(esk2_0,esk1_0),esk3_0)\|~v1_modelc_3(k1_funct_1(esk2_0,esk1_0),esk3_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13, c_0_14]), c_0_15]), c_0_16])])])). cnf(c_0_21, plain, (r4_modelc_3(X1,esk4_3(X1,X2,X3),k1_funct_1(X2,k1_nat_1(X3,np__1)))\|r1_xxreal_0(k3_finseq_1(X2),X3)\|~r1_xxreal_0(np__1,X3)\|~r5_modelc_3(X1,X2)\|~m2_finseq_1(X1,k5_numbers)\|~v1_modelc_2(X1)\|~v1_finseq_1(X2)\|~v1_funct_1(X2)\|~v1_relat_1(X2)\|~v7_ordinal1(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_17, c_0_18])])). cnf(c_0_22, plain, (esk4_3(X1,X2,X3)=k1_funct_1(X2,X3)\|r1_xxreal_0(k3_finseq_1(X2),X3)\|~v7_ordinal1(X3)\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v1_finseq_1(X2)\|~v1_modelc_2(X1)\|~r5_modelc_3(X1,X2)\|~m2_finseq_1(X1,k5_numbers)\|~r1_xxreal_0(np__1,X3)), inference(evalgc,[status(thm)],[c_0_19])). cnf(c_0_23, negated_conjecture, (r1_xxreal_0(np__1,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_24, negated_conjecture, (r5_modelc_3(esk3_0,esk2_0)), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_25, negated_conjecture, (v1_finseq_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_26, negated_conjecture, (v1_funct_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_27, negated_conjecture, (v1_relat_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_28, negated_conjecture, (v7_ordinal1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_29, negated_conjecture, (~r1_xxreal_0(k3_finseq_1(esk2_0),esk1_0)), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_30, plain, (l1_modelc_3(esk5_3(X1,X2,X3),X1)\|r1_xxreal_0(k3_finseq_1(X2),X3)\|~r1_xxreal_0(np__1,X3)\|~v7_ordinal1(X3)\|~r5_modelc_3(X1,X2)\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v1_finseq_1(X2)\|~v1_modelc_2(X1)\|~m2_finseq_1(X1,k5_numbers)), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_31, negated_conjecture, (~l1_modelc_3(k1_funct_1(esk2_0,esk1_0),esk3_0)\|~v1_modelc_3(k1_funct_1(esk2_0,esk1_0),esk3_0)\|~r4_modelc_3(esk3_0,k1_funct_1(esk2_0,esk1_0),k1_funct_1(esk2_0,k1_nat_1(esk1_0,np__1)))\|~l1_modelc_3(k1_funct_1(esk2_0,k1_nat_1(esk1_0,np__1)),esk3_0)\|~v1_modelc_3(k1_funct_1(esk2_0,k1_nat_1(esk1_0,np__1)),esk3_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20, c_0_14]), c_0_15]), c_0_16])])])). cnf(c_0_32, plain, (r4_modelc_3(X1,k1_funct_1(X2,X3),k1_funct_1(X2,k1_nat_1(X3,np__1)))\|r1_xxreal_0(k3_finseq_1(X2),X3)\|~r1_xxreal_0(np__1,X3)\|~r5_modelc_3(X1,X2)\|~m2_finseq_1(X1,k5_numbers)\|~v1_modelc_2(X1)\|~v1_finseq_1(X2)\|~v1_funct_1(X2)\|~v1_relat_1(X2)\|~v7_ordinal1(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_21, c_0_22])])). cnf(c_0_33, negated_conjecture, (r1_xxreal_0(np__1,esk1_0)), inference(evalgc,[status(thm)],[c_0_23])). cnf(c_0_34, negated_conjecture, (r5_modelc_3(esk3_0,esk2_0)), inference(evalgc,[status(thm)],[c_0_24])). cnf(c_0_35, negated_conjecture, (v1_finseq_1(esk2_0)), inference(evalgc,[status(thm)],[c_0_25])). cnf(c_0_36, negated_conjecture, (v1_funct_1(esk2_0)), inference(evalgc,[status(thm)],[c_0_26])). cnf(c_0_37, negated_conjecture, (v1_relat_1(esk2_0)), inference(evalgc,[status(thm)],[c_0_27])). cnf(c_0_38, negated_conjecture, (v7_ordinal1(esk1_0)), inference(evalgc,[status(thm)],[c_0_28])). cnf(c_0_39, negated_conjecture, (~r1_xxreal_0(k3_finseq_1(esk2_0),esk1_0)), inference(evalgc,[status(thm)],[c_0_29])). cnf(c_0_40, plain, (r1_xxreal_0(k3_finseq_1(X2),X3)\|l1_modelc_3(esk5_3(X1,X2,X3),X1)\|~v7_ordinal1(X3)\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v1_finseq_1(X2)\|~v1_modelc_2(X1)\|~r5_modelc_3(X1,X2)\|~m2_finseq_1(X1,k5_numbers)\|~r1_xxreal_0(np__1,X3)), inference(evalgc,[status(thm)],[c_0_30])). cnf(c_0_41, plain, (v1_modelc_3(esk5_3(X1,X2,X3),X1)\|r1_xxreal_0(k3_finseq_1(X2),X3)\|~r1_xxreal_0(np__1,X3)\|~v7_ordinal1(X3)\|~r5_modelc_3(X1,X2)\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v1_finseq_1(X2)\|~v1_modelc_2(X1)\|~m2_finseq_1(X1,k5_numbers)), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_42, negated_conjecture, (~l1_modelc_3(k1_funct_1(esk2_0,k1_nat_1(esk1_0,np__1)),esk3_0)\|~l1_modelc_3(k1_funct_1(esk2_0,esk1_0),esk3_0)\|~v1_modelc_3(k1_funct_1(esk2_0,k1_nat_1(esk1_0,np__1)),esk3_0)\|~v1_modelc_3(k1_funct_1(esk2_0,esk1_0),esk3_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31, c_0_32]), c_0_33]), c_0_34]), c_0_15]), c_0_16]), c_0_35]), c_0_36]), c_0_37]), c_0_38])]), c_0_39])])). cnf(c_0_43, plain, (l1_modelc_3(k1_funct_1(X2,k1_nat_1(X3,np__1)),X1)\|r1_xxreal_0(k3_finseq_1(X2),X3)\|~r1_xxreal_0(np__1,X3)\|~r5_modelc_3(X1,X2)\|~m2_finseq_1(X1,k5_numbers)\|~v1_modelc_2(X1)\|~v1_finseq_1(X2)\|~v1_funct_1(X2)\|~v1_relat_1(X2)\|~v7_ordinal1(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_40, c_0_18])])). cnf(c_0_44, plain, (r1_xxreal_0(k3_finseq_1(X2),X3)\|v1_modelc_3(esk5_3(X1,X2,X3),X1)\|~v7_ordinal1(X3)\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v1_finseq_1(X2)\|~v1_modelc_2(X1)\|~r5_modelc_3(X1,X2)\|~m2_finseq_1(X1,k5_numbers)\|~r1_xxreal_0(np__1,X3)), inference(evalgc,[status(thm)],[c_0_41])). cnf(c_0_45, plain, (l1_modelc_3(esk4_3(X1,X2,X3),X1)\|r1_xxreal_0(k3_finseq_1(X2),X3)\|~r1_xxreal_0(np__1,X3)\|~v7_ordinal1(X3)\|~r5_modelc_3(X1,X2)\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v1_finseq_1(X2)\|~v1_modelc_2(X1)\|~m2_finseq_1(X1,k5_numbers)), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_46, negated_conjecture, (~l1_modelc_3(k1_funct_1(esk2_0,esk1_0),esk3_0)\|~v1_modelc_3(k1_funct_1(esk2_0,k1_nat_1(esk1_0,np__1)),esk3_0)\|~v1_modelc_3(k1_funct_1(esk2_0,esk1_0),esk3_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42, c_0_43]), c_0_33]), c_0_34]), c_0_15]), c_0_16]), c_0_35]), c_0_36]), c_0_37]), c_0_38])]), c_0_39])])). cnf(c_0_47, plain, (v1_modelc_3(k1_funct_1(X2,k1_nat_1(X3,np__1)),X1)\|r1_xxreal_0(k3_finseq_1(X2),X3)\|~r1_xxreal_0(np__1,X3)\|~r5_modelc_3(X1,X2)\|~m2_finseq_1(X1,k5_numbers)\|~v1_modelc_2(X1)\|~v1_finseq_1(X2)\|~v1_funct_1(X2)\|~v1_relat_1(X2)\|~v7_ordinal1(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_44, c_0_18])])). cnf(c_0_48, plain, (r1_xxreal_0(k3_finseq_1(X2),X3)\|l1_modelc_3(esk4_3(X1,X2,X3),X1)\|~v7_ordinal1(X3)\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v1_finseq_1(X2)\|~v1_modelc_2(X1)\|~r5_modelc_3(X1,X2)\|~m2_finseq_1(X1,k5_numbers)\|~r1_xxreal_0(np__1,X3)), inference(evalgc,[status(thm)],[c_0_45])). cnf(c_0_49, plain, (v1_modelc_3(esk4_3(X1,X2,X3),X1)\|r1_xxreal_0(k3_finseq_1(X2),X3)\|~r1_xxreal_0(np__1,X3)\|~v7_ordinal1(X3)\|~r5_modelc_3(X1,X2)\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v1_finseq_1(X2)\|~v1_modelc_2(X1)\|~m2_finseq_1(X1,k5_numbers)), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_50, negated_conjecture, (~l1_modelc_3(k1_funct_1(esk2_0,esk1_0),esk3_0)\|~v1_modelc_3(k1_funct_1(esk2_0,esk1_0),esk3_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46, c_0_47]), c_0_33]), c_0_34]), c_0_15]), c_0_16]), c_0_35]), c_0_36]), c_0_37]), c_0_38])]), c_0_39])])). cnf(c_0_51, plain, (l1_modelc_3(k1_funct_1(X2,X3),X1)\|r1_xxreal_0(k3_finseq_1(X2),X3)\|~r1_xxreal_0(np__1,X3)\|~r5_modelc_3(X1,X2)\|~m2_finseq_1(X1,k5_numbers)\|~v1_modelc_2(X1)\|~v1_finseq_1(X2)\|~v1_funct_1(X2)\|~v1_relat_1(X2)\|~v7_ordinal1(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_48, c_0_22])])). cnf(c_0_52, plain, (r1_xxreal_0(k3_finseq_1(X2),X3)\|v1_modelc_3(esk4_3(X1,X2,X3),X1)\|~v7_ordinal1(X3)\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v1_finseq_1(X2)\|~v1_modelc_2(X1)\|~r5_modelc_3(X1,X2)\|~m2_finseq_1(X1,k5_numbers)\|~r1_xxreal_0(np__1,X3)), inference(evalgc,[status(thm)],[c_0_49])). cnf(c_0_53, negated_conjecture, (~v1_modelc_3(k1_funct_1(esk2_0,esk1_0),esk3_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50, c_0_51]), c_0_33]), c_0_34]), c_0_15]), c_0_16]), c_0_35]), c_0_36]), c_0_37]), c_0_38])]), c_0_39])])). cnf(c_0_54, plain, (v1_modelc_3(k1_funct_1(X2,X3),X1)\|r1_xxreal_0(k3_finseq_1(X2),X3)\|~r1_xxreal_0(np__1,X3)\|~r5_modelc_3(X1,X2)\|~m2_finseq_1(X1,k5_numbers)\|~v1_modelc_2(X1)\|~v1_finseq_1(X2)\|~v1_funct_1(X2)\|~v1_relat_1(X2)\|~v7_ordinal1(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_52, c_0_22])])). cnf(c_0_55, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53, c_0_54]), c_0_33]), c_0_34]), c_0_15]), c_0_16]), c_0_35]), c_0_36]), c_0_37]), c_0_38])]), c_0_39]), ['proof']). # SZS output end CNFRefutation	reserve k,n,n1,m,m1,m0,h,i,j for Nat, a,x,y,X,X1,X2,X3,X4,Y for set; reserve L,L1,L2 for FinSequence; reserve F,F1,G,G1,H for LTL-formula; reserve W,W1,W2 for Subset of Subformulae H; reserve v for LTL-formula; reserve N,N1,N2,N10,N20,M for strict LTLnode over v; reserve w for Element of Inf_seq(AtomicFamily); reserve R1,R2 for Real_Sequence; theorem Th35: L is_Finseq_for v & 1<= k & k<len(L) implies CastNode(L.(k+1),v) is_succ_of CastNode(L.k,v) proof assume L is_Finseq_for v & 1<= k & k<len(L); then consider N,M such that A1: N = L.k and A2: M=L.(k+1) & M is_succ_of N by Def19; CastNode(L.k,v) = N by A1,Def16; hence thesis by A2,Def16; end;	Convert the following ATP output trace into a readable Mizar proof.
t33_e_siec	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t33_e_siec, conjecture, ![X1]:((v2_e_siec(X1)&(v3_e_siec(X1)&l1_e_siec(X1)))=>(r1_tarski(k2_relat_1(k4_xboole_0(u1_e_siec(X1),k4_relat_1(u1_struct_0(X1)))),k2_zfmisc_1(k7_e_siec(X1),k8_e_siec(X1)))&r1_tarski(k2_relat_1(k4_xboole_0(u2_e_siec(X1),k4_relat_1(u1_struct_0(X1)))),k2_zfmisc_1(k7_e_siec(X1),k8_e_siec(X1))))), file('/scratch/mptp/predsminms1/t33_e_siec__0', t33_e_siec)). fof(t100_xboole_1, axiom, ![X1, X2]:k4_xboole_0(X1,X2)=k5_xboole_0(X1,k3_xboole_0(X1,X2)), file('/scratch/mptp/predsminms1/t33_e_siec__0', t100_xboole_1)). fof(t4_sysrel, axiom, ![X1, X2, X3]:(v1_relat_1(X3)=>(r1_tarski(X3,k2_zfmisc_1(X1,X2))=>r1_tarski(k2_relat_1(X3),k2_zfmisc_1(X2,X1)))), file('/scratch/mptp/predsminms1/t33_e_siec__0', t4_sysrel)). fof(t18_e_siec, axiom, ![X1]:((v2_e_siec(X1)&(v3_e_siec(X1)&l1_e_siec(X1)))=>(r1_tarski(k4_xboole_0(u1_e_siec(X1),k4_relat_1(u1_struct_0(X1))),k2_zfmisc_1(k8_e_siec(X1),k7_e_siec(X1)))&r1_tarski(k4_xboole_0(u2_e_siec(X1),k4_relat_1(u1_struct_0(X1))),k2_zfmisc_1(k8_e_siec(X1),k7_e_siec(X1))))), file('/scratch/mptp/predsminms1/t33_e_siec__0', t18_e_siec)). fof(t23_e_siec, axiom, ![X1]:((v2_e_siec(X1)&(v3_e_siec(X1)&l1_e_siec(X1)))=>(k3_relat_1(k4_relat_1(k4_xboole_0(u1_struct_0(X1),k10_xtuple_0(u2_e_siec(X1)))),k4_xboole_0(u2_e_siec(X1),k4_relat_1(u1_struct_0(X1))))=k4_xboole_0(u2_e_siec(X1),k4_relat_1(u1_struct_0(X1)))&k3_relat_1(k4_relat_1(k4_xboole_0(u1_struct_0(X1),k10_xtuple_0(u1_e_siec(X1)))),k4_xboole_0(u1_e_siec(X1),k4_relat_1(u1_struct_0(X1))))=k4_xboole_0(u1_e_siec(X1),k4_relat_1(u1_struct_0(X1))))), file('/scratch/mptp/predsminms1/t33_e_siec__0', t23_e_siec)). fof(dt_k3_relat_1, axiom, ![X1, X2]:v1_relat_1(k3_relat_1(X1,X2)), file('/scratch/mptp/predsminms1/t33_e_siec__0', dt_k3_relat_1)). fof(c_0_6, negated_conjecture, ~(![X1]:((v2_e_siec(X1)&(v3_e_siec(X1)&l1_e_siec(X1)))=>(r1_tarski(k2_relat_1(k4_xboole_0(u1_e_siec(X1),k4_relat_1(u1_struct_0(X1)))),k2_zfmisc_1(k7_e_siec(X1),k8_e_siec(X1)))&r1_tarski(k2_relat_1(k4_xboole_0(u2_e_siec(X1),k4_relat_1(u1_struct_0(X1)))),k2_zfmisc_1(k7_e_siec(X1),k8_e_siec(X1)))))), inference(assume_negation,[status(cth)],[t33_e_siec])). fof(c_0_7, negated_conjecture, ((v2_e_siec(esk1_0)&(v3_e_siec(esk1_0)&l1_e_siec(esk1_0)))&(~r1_tarski(k2_relat_1(k4_xboole_0(u1_e_siec(esk1_0),k4_relat_1(u1_struct_0(esk1_0)))),k2_zfmisc_1(k7_e_siec(esk1_0),k8_e_siec(esk1_0)))\|~r1_tarski(k2_relat_1(k4_xboole_0(u2_e_siec(esk1_0),k4_relat_1(u1_struct_0(esk1_0)))),k2_zfmisc_1(k7_e_siec(esk1_0),k8_e_siec(esk1_0))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])). fof(c_0_8, plain, ![X5, X6]:k4_xboole_0(X5,X6)=k5_xboole_0(X5,k3_xboole_0(X5,X6)), inference(variable_rename,[status(thm)],[t100_xboole_1])). cnf(c_0_9, negated_conjecture, (~r1_tarski(k2_relat_1(k4_xboole_0(u1_e_siec(esk1_0),k4_relat_1(u1_struct_0(esk1_0)))),k2_zfmisc_1(k7_e_siec(esk1_0),k8_e_siec(esk1_0)))\|~r1_tarski(k2_relat_1(k4_xboole_0(u2_e_siec(esk1_0),k4_relat_1(u1_struct_0(esk1_0)))),k2_zfmisc_1(k7_e_siec(esk1_0),k8_e_siec(esk1_0)))), inference(split_conjunct,[status(thm)],[c_0_7])). cnf(c_0_10, plain, (k4_xboole_0(X1,X2)=k5_xboole_0(X1,k3_xboole_0(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_8])). fof(c_0_11, plain, ![X9, X10, X11]:(~v1_relat_1(X11)\|(~r1_tarski(X11,k2_zfmisc_1(X9,X10))\|r1_tarski(k2_relat_1(X11),k2_zfmisc_1(X10,X9)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_sysrel])])). cnf(c_0_12, negated_conjecture, (~r1_tarski(k2_relat_1(k5_xboole_0(u1_e_siec(esk1_0),k3_xboole_0(u1_e_siec(esk1_0),k4_relat_1(u1_struct_0(esk1_0))))),k2_zfmisc_1(k7_e_siec(esk1_0),k8_e_siec(esk1_0)))\|~r1_tarski(k2_relat_1(k5_xboole_0(u2_e_siec(esk1_0),k3_xboole_0(u2_e_siec(esk1_0),k4_relat_1(u1_struct_0(esk1_0))))),k2_zfmisc_1(k7_e_siec(esk1_0),k8_e_siec(esk1_0)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9, c_0_10]), c_0_10])). cnf(c_0_13, plain, (r1_tarski(k2_relat_1(X1),k2_zfmisc_1(X3,X2))\|~v1_relat_1(X1)\|~r1_tarski(X1,k2_zfmisc_1(X2,X3))), inference(split_conjunct,[status(thm)],[c_0_11])). fof(c_0_14, plain, ![X12]:((r1_tarski(k4_xboole_0(u1_e_siec(X12),k4_relat_1(u1_struct_0(X12))),k2_zfmisc_1(k8_e_siec(X12),k7_e_siec(X12)))\|(~v2_e_siec(X12)\|(~v3_e_siec(X12)\|~l1_e_siec(X12))))&(r1_tarski(k4_xboole_0(u2_e_siec(X12),k4_relat_1(u1_struct_0(X12))),k2_zfmisc_1(k8_e_siec(X12),k7_e_siec(X12)))\|(~v2_e_siec(X12)\|(~v3_e_siec(X12)\|~l1_e_siec(X12))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t18_e_siec])])])). cnf(c_0_15, negated_conjecture, (~r1_tarski(k2_relat_1(k5_xboole_0(u1_e_siec(esk1_0),k3_xboole_0(u1_e_siec(esk1_0),k4_relat_1(u1_struct_0(esk1_0))))),k2_zfmisc_1(k7_e_siec(esk1_0),k8_e_siec(esk1_0)))\|~r1_tarski(k2_relat_1(k5_xboole_0(u2_e_siec(esk1_0),k3_xboole_0(u2_e_siec(esk1_0),k4_relat_1(u1_struct_0(esk1_0))))),k2_zfmisc_1(k7_e_siec(esk1_0),k8_e_siec(esk1_0)))), inference(evalgc,[status(thm)],[c_0_12])). cnf(c_0_16, plain, (r1_tarski(k2_relat_1(X1),k2_zfmisc_1(X3,X2))\|~v1_relat_1(X1)\|~r1_tarski(X1,k2_zfmisc_1(X2,X3))), inference(evalgc,[status(thm)],[c_0_13])). cnf(c_0_17, plain, (r1_tarski(k4_xboole_0(u1_e_siec(X1),k4_relat_1(u1_struct_0(X1))),k2_zfmisc_1(k8_e_siec(X1),k7_e_siec(X1)))\|~v2_e_siec(X1)\|~v3_e_siec(X1)\|~l1_e_siec(X1)), inference(split_conjunct,[status(thm)],[c_0_14])). fof(c_0_18, plain, ![X13]:((k3_relat_1(k4_relat_1(k4_xboole_0(u1_struct_0(X13),k10_xtuple_0(u2_e_siec(X13)))),k4_xboole_0(u2_e_siec(X13),k4_relat_1(u1_struct_0(X13))))=k4_xboole_0(u2_e_siec(X13),k4_relat_1(u1_struct_0(X13)))\|(~v2_e_siec(X13)\|(~v3_e_siec(X13)\|~l1_e_siec(X13))))&(k3_relat_1(k4_relat_1(k4_xboole_0(u1_struct_0(X13),k10_xtuple_0(u1_e_siec(X13)))),k4_xboole_0(u1_e_siec(X13),k4_relat_1(u1_struct_0(X13))))=k4_xboole_0(u1_e_siec(X13),k4_relat_1(u1_struct_0(X13)))\|(~v2_e_siec(X13)\|(~v3_e_siec(X13)\|~l1_e_siec(X13))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t23_e_siec])])])). cnf(c_0_19, negated_conjecture, (~r1_tarski(k2_relat_1(k5_xboole_0(u2_e_siec(esk1_0),k3_xboole_0(u2_e_siec(esk1_0),k4_relat_1(u1_struct_0(esk1_0))))),k2_zfmisc_1(k7_e_siec(esk1_0),k8_e_siec(esk1_0)))\|~v1_relat_1(k5_xboole_0(u1_e_siec(esk1_0),k3_xboole_0(u1_e_siec(esk1_0),k4_relat_1(u1_struct_0(esk1_0)))))\|~r1_tarski(k5_xboole_0(u1_e_siec(esk1_0),k3_xboole_0(u1_e_siec(esk1_0),k4_relat_1(u1_struct_0(esk1_0)))),k2_zfmisc_1(k8_e_siec(esk1_0),k7_e_siec(esk1_0)))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_15, c_0_16])])). cnf(c_0_20, plain, (r1_tarski(k5_xboole_0(u1_e_siec(X1),k3_xboole_0(u1_e_siec(X1),k4_relat_1(u1_struct_0(X1)))),k2_zfmisc_1(k8_e_siec(X1),k7_e_siec(X1)))\|~v2_e_siec(X1)\|~v3_e_siec(X1)\|~l1_e_siec(X1)), inference(rw,[status(thm)],[c_0_17, c_0_10])). cnf(c_0_21, negated_conjecture, (l1_e_siec(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_7])). cnf(c_0_22, negated_conjecture, (v3_e_siec(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_7])). cnf(c_0_23, negated_conjecture, (v2_e_siec(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_7])). cnf(c_0_24, plain, (r1_tarski(k4_xboole_0(u2_e_siec(X1),k4_relat_1(u1_struct_0(X1))),k2_zfmisc_1(k8_e_siec(X1),k7_e_siec(X1)))\|~v2_e_siec(X1)\|~v3_e_siec(X1)\|~l1_e_siec(X1)), inference(split_conjunct,[status(thm)],[c_0_14])). fof(c_0_25, plain, ![X14, X15]:v1_relat_1(k3_relat_1(X14,X15)), inference(variable_rename,[status(thm)],[dt_k3_relat_1])). cnf(c_0_26, plain, (k3_relat_1(k4_relat_1(k4_xboole_0(u1_struct_0(X1),k10_xtuple_0(u1_e_siec(X1)))),k4_xboole_0(u1_e_siec(X1),k4_relat_1(u1_struct_0(X1))))=k4_xboole_0(u1_e_siec(X1),k4_relat_1(u1_struct_0(X1)))\|~v2_e_siec(X1)\|~v3_e_siec(X1)\|~l1_e_siec(X1)), inference(split_conjunct,[status(thm)],[c_0_18])). cnf(c_0_27, negated_conjecture, (~v1_relat_1(k5_xboole_0(u1_e_siec(esk1_0),k3_xboole_0(u1_e_siec(esk1_0),k4_relat_1(u1_struct_0(esk1_0)))))\|~r1_tarski(k5_xboole_0(u1_e_siec(esk1_0),k3_xboole_0(u1_e_siec(esk1_0),k4_relat_1(u1_struct_0(esk1_0)))),k2_zfmisc_1(k8_e_siec(esk1_0),k7_e_siec(esk1_0)))\|~v1_relat_1(k5_xboole_0(u2_e_siec(esk1_0),k3_xboole_0(u2_e_siec(esk1_0),k4_relat_1(u1_struct_0(esk1_0)))))\|~r1_tarski(k5_xboole_0(u2_e_siec(esk1_0),k3_xboole_0(u2_e_siec(esk1_0),k4_relat_1(u1_struct_0(esk1_0)))),k2_zfmisc_1(k8_e_siec(esk1_0),k7_e_siec(esk1_0)))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_19, c_0_16])])). cnf(c_0_28, plain, (r1_tarski(k5_xboole_0(u1_e_siec(X1),k3_xboole_0(u1_e_siec(X1),k4_relat_1(u1_struct_0(X1)))),k2_zfmisc_1(k8_e_siec(X1),k7_e_siec(X1)))\|~v2_e_siec(X1)\|~v3_e_siec(X1)\|~l1_e_siec(X1)), inference(evalgc,[status(thm)],[c_0_20])). cnf(c_0_29, negated_conjecture, (l1_e_siec(esk1_0)), inference(evalgc,[status(thm)],[c_0_21])). cnf(c_0_30, negated_conjecture, (v3_e_siec(esk1_0)), inference(evalgc,[status(thm)],[c_0_22])). cnf(c_0_31, negated_conjecture, (v2_e_siec(esk1_0)), inference(evalgc,[status(thm)],[c_0_23])). cnf(c_0_32, plain, (r1_tarski(k5_xboole_0(u2_e_siec(X1),k3_xboole_0(u2_e_siec(X1),k4_relat_1(u1_struct_0(X1)))),k2_zfmisc_1(k8_e_siec(X1),k7_e_siec(X1)))\|~v2_e_siec(X1)\|~v3_e_siec(X1)\|~l1_e_siec(X1)), inference(rw,[status(thm)],[c_0_24, c_0_10])). cnf(c_0_33, plain, (v1_relat_1(k3_relat_1(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_25])). cnf(c_0_34, plain, (k3_relat_1(k4_relat_1(k5_xboole_0(u1_struct_0(X1),k3_xboole_0(u1_struct_0(X1),k10_xtuple_0(u1_e_siec(X1))))),k5_xboole_0(u1_e_siec(X1),k3_xboole_0(u1_e_siec(X1),k4_relat_1(u1_struct_0(X1)))))=k5_xboole_0(u1_e_siec(X1),k3_xboole_0(u1_e_siec(X1),k4_relat_1(u1_struct_0(X1))))\|~v2_e_siec(X1)\|~v3_e_siec(X1)\|~l1_e_siec(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26, c_0_10]), c_0_10]), c_0_10])). cnf(c_0_35, plain, (k3_relat_1(k4_relat_1(k4_xboole_0(u1_struct_0(X1),k10_xtuple_0(u2_e_siec(X1)))),k4_xboole_0(u2_e_siec(X1),k4_relat_1(u1_struct_0(X1))))=k4_xboole_0(u2_e_siec(X1),k4_relat_1(u1_struct_0(X1)))\|~v2_e_siec(X1)\|~v3_e_siec(X1)\|~l1_e_siec(X1)), inference(split_conjunct,[status(thm)],[c_0_18])). cnf(c_0_36, negated_conjecture, (~v1_relat_1(k5_xboole_0(u1_e_siec(esk1_0),k3_xboole_0(u1_e_siec(esk1_0),k4_relat_1(u1_struct_0(esk1_0)))))\|~v1_relat_1(k5_xboole_0(u2_e_siec(esk1_0),k3_xboole_0(u2_e_siec(esk1_0),k4_relat_1(u1_struct_0(esk1_0)))))\|~r1_tarski(k5_xboole_0(u2_e_siec(esk1_0),k3_xboole_0(u2_e_siec(esk1_0),k4_relat_1(u1_struct_0(esk1_0)))),k2_zfmisc_1(k8_e_siec(esk1_0),k7_e_siec(esk1_0)))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27, c_0_28]), c_0_29]), c_0_30]), c_0_31])])])). cnf(c_0_37, plain, (r1_tarski(k5_xboole_0(u2_e_siec(X1),k3_xboole_0(u2_e_siec(X1),k4_relat_1(u1_struct_0(X1)))),k2_zfmisc_1(k8_e_siec(X1),k7_e_siec(X1)))\|~v2_e_siec(X1)\|~v3_e_siec(X1)\|~l1_e_siec(X1)), inference(evalgc,[status(thm)],[c_0_32])). cnf(c_0_38, plain, (v1_relat_1(k3_relat_1(X1,X2))), inference(evalgc,[status(thm)],[c_0_33])). cnf(c_0_39, plain, (k3_relat_1(k4_relat_1(k5_xboole_0(u1_struct_0(X1),k3_xboole_0(u1_struct_0(X1),k10_xtuple_0(u1_e_siec(X1))))),k5_xboole_0(u1_e_siec(X1),k3_xboole_0(u1_e_siec(X1),k4_relat_1(u1_struct_0(X1)))))=k5_xboole_0(u1_e_siec(X1),k3_xboole_0(u1_e_siec(X1),k4_relat_1(u1_struct_0(X1))))\|~v2_e_siec(X1)\|~v3_e_siec(X1)\|~l1_e_siec(X1)), inference(evalgc,[status(thm)],[c_0_34])). cnf(c_0_40, plain, (k3_relat_1(k4_relat_1(k5_xboole_0(u1_struct_0(X1),k3_xboole_0(u1_struct_0(X1),k10_xtuple_0(u2_e_siec(X1))))),k5_xboole_0(u2_e_siec(X1),k3_xboole_0(u2_e_siec(X1),k4_relat_1(u1_struct_0(X1)))))=k5_xboole_0(u2_e_siec(X1),k3_xboole_0(u2_e_siec(X1),k4_relat_1(u1_struct_0(X1))))\|~v2_e_siec(X1)\|~v3_e_siec(X1)\|~l1_e_siec(X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35, c_0_10]), c_0_10]), c_0_10])). cnf(c_0_41, negated_conjecture, (~v1_relat_1(k5_xboole_0(u1_e_siec(esk1_0),k3_xboole_0(u1_e_siec(esk1_0),k4_relat_1(u1_struct_0(esk1_0)))))\|~v1_relat_1(k5_xboole_0(u2_e_siec(esk1_0),k3_xboole_0(u2_e_siec(esk1_0),k4_relat_1(u1_struct_0(esk1_0)))))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36, c_0_37]), c_0_29]), c_0_30]), c_0_31])])])). cnf(c_0_42, plain, (v1_relat_1(k5_xboole_0(u1_e_siec(X1),k3_xboole_0(u1_e_siec(X1),k4_relat_1(u1_struct_0(X1)))))\|~l1_e_siec(X1)\|~v3_e_siec(X1)\|~v2_e_siec(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_38, c_0_39])])). cnf(c_0_43, plain, (k3_relat_1(k4_relat_1(k5_xboole_0(u1_struct_0(X1),k3_xboole_0(u1_struct_0(X1),k10_xtuple_0(u2_e_siec(X1))))),k5_xboole_0(u2_e_siec(X1),k3_xboole_0(u2_e_siec(X1),k4_relat_1(u1_struct_0(X1)))))=k5_xboole_0(u2_e_siec(X1),k3_xboole_0(u2_e_siec(X1),k4_relat_1(u1_struct_0(X1))))\|~v2_e_siec(X1)\|~v3_e_siec(X1)\|~l1_e_siec(X1)), inference(evalgc,[status(thm)],[c_0_40])). cnf(c_0_44, negated_conjecture, (~v1_relat_1(k5_xboole_0(u2_e_siec(esk1_0),k3_xboole_0(u2_e_siec(esk1_0),k4_relat_1(u1_struct_0(esk1_0)))))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41, c_0_42]), c_0_29]), c_0_30]), c_0_31])])])). cnf(c_0_45, plain, (v1_relat_1(k5_xboole_0(u2_e_siec(X1),k3_xboole_0(u2_e_siec(X1),k4_relat_1(u1_struct_0(X1)))))\|~l1_e_siec(X1)\|~v3_e_siec(X1)\|~v2_e_siec(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_38, c_0_43])])). cnf(c_0_46, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44, c_0_45]), c_0_29]), c_0_30]), c_0_31])]), ['proof']). # SZS output end CNFRefutation	reserve x,y,z,X,Y for set; reserve N for e_net; reserve N for e_net; theorem Th33: ((the entrance of N) \ id(the carrier of N))~ c= [:e_Places(N), e_Transitions(N):] & ((the escape of N) \ id(the carrier of N))~ c= [:e_Places(N),e_Transitions(N):] proof (the entrance of N) \ id(the carrier of N) c= [:e_Transitions(N),e_Places N :] & (the escape of N) \ id(the carrier of N) c= [:e_Transitions(N),e_Places N:] by Th18; hence thesis by SYSREL:4; end;	Convert the following ATP output trace into a readable Mizar proof.
t31_groeb_1	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t31_groeb_1, conjecture, ![X1]:(m1_subset_1(X1,k5_numbers)=>![X2]:((v1_partfun1(X2,k15_pre_poly(X1))&(v1_relat_2(X2)&(v4_relat_2(X2)&(v6_relat_2(X2)&(v8_relat_2(X2)&(v2_bagorder(X2,X1)&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(X1),k15_pre_poly(X1))))))))))=>![X3]:((~(v7_struct_0(X3))&(v13_algstr_0(X3)&(v33_algstr_0(X3)&(v3_group_1(X3)&(v5_group_1(X3)&(v4_vectsp_1(X3)&(v5_vectsp_1(X3)&(v2_rlvect_1(X3)&(v3_rlvect_1(X3)&(v4_rlvect_1(X3)&l6_algstr_0(X3)))))))))))=>![X4]:((v1_funct_1(X4)&(v1_funct_2(X4,k15_pre_poly(X1),u1_struct_0(X3))&(v1_polynom1(X4,k15_pre_poly(X1),X3)&m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(X1),u1_struct_0(X3)))))))=>r2_groeb_1(X1,X2,X3,k1_groeb_1(X1,X3,X4),k7_ideal_1(k11_polynom1(X1,X3),k1_groeb_1(X1,X3,X4))))))), file('/scratch/mptp/predsminms1/t31_groeb_1__0', t31_groeb_1)). fof(fc6_ordinal1, axiom, (~(v1_xboole_0(k4_ordinal1))&v3_ordinal1(k4_ordinal1)), file('/scratch/mptp/predsminms1/t31_groeb_1__0', fc6_ordinal1)). fof(d4_groeb_1, axiom, ![X1]:(v3_ordinal1(X1)=>![X2]:((v1_partfun1(X2,k15_pre_poly(X1))&(v1_relat_2(X2)&(v4_relat_2(X2)&(v6_relat_2(X2)&(v8_relat_2(X2)&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(X1),k15_pre_poly(X1)))))))))=>![X3]:((~(v7_struct_0(X3))&(v13_algstr_0(X3)&(v33_algstr_0(X3)&(v3_group_1(X3)&(v5_group_1(X3)&(v4_vectsp_1(X3)&(v5_vectsp_1(X3)&(v3_rlvect_1(X3)&(v4_rlvect_1(X3)&l6_algstr_0(X3))))))))))=>![X4]:(m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(k11_polynom1(X1,X3))))=>![X5]:(m1_subset_1(X5,k1_zfmisc_1(u1_struct_0(k11_polynom1(X1,X3))))=>(r2_groeb_1(X1,X2,X3,X4,X5)<=>(k7_ideal_1(k11_polynom1(X1,X3),X4)=X5&v9_rewrite1(k3_polyred(X1,X2,X3,X4))))))))), file('/scratch/mptp/predsminms1/t31_groeb_1__0', d4_groeb_1)). fof(cc5_ordinal1, axiom, ![X1]:(v3_ordinal1(X1)=>![X2]:(m1_subset_1(X2,X1)=>v3_ordinal1(X2))), file('/scratch/mptp/predsminms1/t31_groeb_1__0', cc5_ordinal1)). fof(redefinition_k5_numbers, axiom, k5_numbers=k4_ordinal1, file('/scratch/mptp/predsminms1/t31_groeb_1__0', redefinition_k5_numbers)). fof(redefinition_k1_groeb_1, axiom, ![X1, X2, X3]:((v3_ordinal1(X1)&((~(v7_struct_0(X2))&(v13_algstr_0(X2)&(v4_vectsp_1(X2)&(v5_vectsp_1(X2)&(v3_rlvect_1(X2)&(v4_rlvect_1(X2)&l6_algstr_0(X2)))))))&(v1_funct_1(X3)&(v1_funct_2(X3,k15_pre_poly(X1),u1_struct_0(X2))&(v1_polynom1(X3,k15_pre_poly(X1),X2)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(X1),u1_struct_0(X2)))))))))=>k1_groeb_1(X1,X2,X3)=k1_tarski(X3)), file('/scratch/mptp/predsminms1/t31_groeb_1__0', redefinition_k1_groeb_1)). fof(t10_groeb_1, axiom, ![X1]:(m1_subset_1(X1,k5_numbers)=>![X2]:((v1_partfun1(X2,k15_pre_poly(X1))&(v1_relat_2(X2)&(v4_relat_2(X2)&(v6_relat_2(X2)&(v8_relat_2(X2)&(v2_bagorder(X2,X1)&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(X1),k15_pre_poly(X1))))))))))=>![X3]:((~(v7_struct_0(X3))&(v13_algstr_0(X3)&(v33_algstr_0(X3)&(v3_group_1(X3)&(v5_group_1(X3)&(v4_vectsp_1(X3)&(v5_vectsp_1(X3)&(v2_rlvect_1(X3)&(v3_rlvect_1(X3)&(v4_rlvect_1(X3)&l6_algstr_0(X3)))))))))))=>![X4]:((v1_funct_1(X4)&(v1_funct_2(X4,k15_pre_poly(X1),u1_struct_0(X3))&(v1_polynom1(X4,k15_pre_poly(X1),X3)&m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(X1),u1_struct_0(X3)))))))=>v9_rewrite1(k3_polyred(X1,X2,X3,k1_groeb_1(X1,X3,X4))))))), file('/scratch/mptp/predsminms1/t31_groeb_1__0', t10_groeb_1)). fof(fc2_xboole_0, axiom, ![X1]:~(v1_xboole_0(k1_tarski(X1))), file('/scratch/mptp/predsminms1/t31_groeb_1__0', fc2_xboole_0)). fof(cc1_subset_1, axiom, ![X1]:(v1_xboole_0(X1)=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(X1))=>v1_xboole_0(X2))), file('/scratch/mptp/predsminms1/t31_groeb_1__0', cc1_subset_1)). fof(dt_k1_groeb_1, axiom, ![X1, X2, X3]:((v3_ordinal1(X1)&((~(v7_struct_0(X2))&(v13_algstr_0(X2)&(v4_vectsp_1(X2)&(v5_vectsp_1(X2)&(v3_rlvect_1(X2)&(v4_rlvect_1(X2)&l6_algstr_0(X2)))))))&(v1_funct_1(X3)&(v1_funct_2(X3,k15_pre_poly(X1),u1_struct_0(X2))&(v1_polynom1(X3,k15_pre_poly(X1),X2)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(X1),u1_struct_0(X2)))))))))=>m1_subset_1(k1_groeb_1(X1,X2,X3),k1_zfmisc_1(u1_struct_0(k11_polynom1(X1,X2))))), file('/scratch/mptp/predsminms1/t31_groeb_1__0', dt_k1_groeb_1)). fof(fc1_struct_0, axiom, ![X1]:((v2_struct_0(X1)&l1_struct_0(X1))=>v1_xboole_0(u1_struct_0(X1))), file('/scratch/mptp/predsminms1/t31_groeb_1__0', fc1_struct_0)). fof(dt_l1_algstr_0, axiom, ![X1]:(l1_algstr_0(X1)=>l1_struct_0(X1)), file('/scratch/mptp/predsminms1/t31_groeb_1__0', dt_l1_algstr_0)). fof(dt_l2_algstr_0, axiom, ![X1]:(l2_algstr_0(X1)=>(l2_struct_0(X1)&l1_algstr_0(X1))), file('/scratch/mptp/predsminms1/t31_groeb_1__0', dt_l2_algstr_0)). fof(dt_k7_ideal_1, axiom, ![X1, X2]:(((~(v2_struct_0(X1))&l6_algstr_0(X1))&m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1))))=>(~(v1_xboole_0(k7_ideal_1(X1,X2)))&(v1_ideal_1(k7_ideal_1(X1,X2),X1)&(v2_ideal_1(k7_ideal_1(X1,X2),X1)&(v3_ideal_1(k7_ideal_1(X1,X2),X1)&m1_subset_1(k7_ideal_1(X1,X2),k1_zfmisc_1(u1_struct_0(X1)))))))), file('/scratch/mptp/predsminms1/t31_groeb_1__0', dt_k7_ideal_1)). fof(cc3_vectsp_1, axiom, ![X1]:(l4_algstr_0(X1)=>((~(v2_struct_0(X1))&v4_vectsp_1(X1))=>(~(v2_struct_0(X1))&(v3_vectsp_1(X1)&v6_vectsp_1(X1))))), file('/scratch/mptp/predsminms1/t31_groeb_1__0', cc3_vectsp_1)). fof(dt_l5_algstr_0, axiom, ![X1]:(l5_algstr_0(X1)=>(l4_algstr_0(X1)&l4_struct_0(X1))), file('/scratch/mptp/predsminms1/t31_groeb_1__0', dt_l5_algstr_0)). fof(dt_l6_algstr_0, axiom, ![X1]:(l6_algstr_0(X1)=>(l2_algstr_0(X1)&l5_algstr_0(X1))), file('/scratch/mptp/predsminms1/t31_groeb_1__0', dt_l6_algstr_0)). fof(cc2_struct_0, axiom, ![X1]:(l1_struct_0(X1)=>(~(v7_struct_0(X1))=>~(v2_struct_0(X1)))), file('/scratch/mptp/predsminms1/t31_groeb_1__0', cc2_struct_0)). fof(dt_k11_polynom1, axiom, ![X1, X2]:((v3_ordinal1(X1)&(~(v7_struct_0(X2))&(v13_algstr_0(X2)&(v3_vectsp_1(X2)&(v5_vectsp_1(X2)&(v3_rlvect_1(X2)&(v4_rlvect_1(X2)&l6_algstr_0(X2))))))))=>(~(v2_struct_0(k11_polynom1(X1,X2)))&(v36_algstr_0(k11_polynom1(X1,X2))&l6_algstr_0(k11_polynom1(X1,X2))))), file('/scratch/mptp/predsminms1/t31_groeb_1__0', dt_k11_polynom1)). fof(c_0_19, negated_conjecture, ~(![X1]:(m1_subset_1(X1,k5_numbers)=>![X2]:((v1_partfun1(X2,k15_pre_poly(X1))&(v1_relat_2(X2)&(v4_relat_2(X2)&(v6_relat_2(X2)&(v8_relat_2(X2)&(v2_bagorder(X2,X1)&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(X1),k15_pre_poly(X1))))))))))=>![X3]:((~(v7_struct_0(X3))&(v13_algstr_0(X3)&(v33_algstr_0(X3)&(v3_group_1(X3)&(v5_group_1(X3)&(v4_vectsp_1(X3)&(v5_vectsp_1(X3)&(v2_rlvect_1(X3)&(v3_rlvect_1(X3)&(v4_rlvect_1(X3)&l6_algstr_0(X3)))))))))))=>![X4]:((v1_funct_1(X4)&(v1_funct_2(X4,k15_pre_poly(X1),u1_struct_0(X3))&(v1_polynom1(X4,k15_pre_poly(X1),X3)&m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(X1),u1_struct_0(X3)))))))=>r2_groeb_1(X1,X2,X3,k1_groeb_1(X1,X3,X4),k7_ideal_1(k11_polynom1(X1,X3),k1_groeb_1(X1,X3,X4)))))))), inference(assume_negation,[status(cth)],[t31_groeb_1])). fof(c_0_20, plain, (~v1_xboole_0(k4_ordinal1)&v3_ordinal1(k4_ordinal1)), inference(fof_simplification,[status(thm)],[fc6_ordinal1])). fof(c_0_21, plain, ![X28, X29, X30, X31, X32]:(((k7_ideal_1(k11_polynom1(X28,X30),X31)=X32\|~r2_groeb_1(X28,X29,X30,X31,X32)\|~m1_subset_1(X32,k1_zfmisc_1(u1_struct_0(k11_polynom1(X28,X30))))\|~m1_subset_1(X31,k1_zfmisc_1(u1_struct_0(k11_polynom1(X28,X30))))\|(v7_struct_0(X30)\|(~v13_algstr_0(X30)\|(~v33_algstr_0(X30)\|(~v3_group_1(X30)\|(~v5_group_1(X30)\|(~v4_vectsp_1(X30)\|(~v5_vectsp_1(X30)\|(~v3_rlvect_1(X30)\|(~v4_rlvect_1(X30)\|~l6_algstr_0(X30))))))))))\|(~v1_partfun1(X29,k15_pre_poly(X28))\|(~v1_relat_2(X29)\|(~v4_relat_2(X29)\|(~v6_relat_2(X29)\|(~v8_relat_2(X29)\|~m1_subset_1(X29,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(X28),k15_pre_poly(X28)))))))))\|~v3_ordinal1(X28))&(v9_rewrite1(k3_polyred(X28,X29,X30,X31))\|~r2_groeb_1(X28,X29,X30,X31,X32)\|~m1_subset_1(X32,k1_zfmisc_1(u1_struct_0(k11_polynom1(X28,X30))))\|~m1_subset_1(X31,k1_zfmisc_1(u1_struct_0(k11_polynom1(X28,X30))))\|(v7_struct_0(X30)\|(~v13_algstr_0(X30)\|(~v33_algstr_0(X30)\|(~v3_group_1(X30)\|(~v5_group_1(X30)\|(~v4_vectsp_1(X30)\|(~v5_vectsp_1(X30)\|(~v3_rlvect_1(X30)\|(~v4_rlvect_1(X30)\|~l6_algstr_0(X30))))))))))\|(~v1_partfun1(X29,k15_pre_poly(X28))\|(~v1_relat_2(X29)\|(~v4_relat_2(X29)\|(~v6_relat_2(X29)\|(~v8_relat_2(X29)\|~m1_subset_1(X29,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(X28),k15_pre_poly(X28)))))))))\|~v3_ordinal1(X28)))&(k7_ideal_1(k11_polynom1(X28,X30),X31)!=X32\|~v9_rewrite1(k3_polyred(X28,X29,X30,X31))\|r2_groeb_1(X28,X29,X30,X31,X32)\|~m1_subset_1(X32,k1_zfmisc_1(u1_struct_0(k11_polynom1(X28,X30))))\|~m1_subset_1(X31,k1_zfmisc_1(u1_struct_0(k11_polynom1(X28,X30))))\|(v7_struct_0(X30)\|(~v13_algstr_0(X30)\|(~v33_algstr_0(X30)\|(~v3_group_1(X30)\|(~v5_group_1(X30)\|(~v4_vectsp_1(X30)\|(~v5_vectsp_1(X30)\|(~v3_rlvect_1(X30)\|(~v4_rlvect_1(X30)\|~l6_algstr_0(X30))))))))))\|(~v1_partfun1(X29,k15_pre_poly(X28))\|(~v1_relat_2(X29)\|(~v4_relat_2(X29)\|(~v6_relat_2(X29)\|(~v8_relat_2(X29)\|~m1_subset_1(X29,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(X28),k15_pre_poly(X28)))))))))\|~v3_ordinal1(X28))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d4_groeb_1])])])])])). fof(c_0_22, negated_conjecture, (m1_subset_1(esk1_0,k5_numbers)&((v1_partfun1(esk2_0,k15_pre_poly(esk1_0))&(v1_relat_2(esk2_0)&(v4_relat_2(esk2_0)&(v6_relat_2(esk2_0)&(v8_relat_2(esk2_0)&(v2_bagorder(esk2_0,esk1_0)&m1_subset_1(esk2_0,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(esk1_0),k15_pre_poly(esk1_0))))))))))&((~v7_struct_0(esk3_0)&(v13_algstr_0(esk3_0)&(v33_algstr_0(esk3_0)&(v3_group_1(esk3_0)&(v5_group_1(esk3_0)&(v4_vectsp_1(esk3_0)&(v5_vectsp_1(esk3_0)&(v2_rlvect_1(esk3_0)&(v3_rlvect_1(esk3_0)&(v4_rlvect_1(esk3_0)&l6_algstr_0(esk3_0)))))))))))&((v1_funct_1(esk4_0)&(v1_funct_2(esk4_0,k15_pre_poly(esk1_0),u1_struct_0(esk3_0))&(v1_polynom1(esk4_0,k15_pre_poly(esk1_0),esk3_0)&m1_subset_1(esk4_0,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(esk1_0),u1_struct_0(esk3_0)))))))&~r2_groeb_1(esk1_0,esk2_0,esk3_0,k1_groeb_1(esk1_0,esk3_0,esk4_0),k7_ideal_1(k11_polynom1(esk1_0,esk3_0),k1_groeb_1(esk1_0,esk3_0,esk4_0))))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_19])])])])). fof(c_0_23, plain, ![X10, X11]:(~v3_ordinal1(X10)\|(~m1_subset_1(X11,X10)\|v3_ordinal1(X11))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc5_ordinal1])])])). cnf(c_0_24, plain, (v3_ordinal1(k4_ordinal1)), inference(split_conjunct,[status(thm)],[c_0_20])). cnf(c_0_25, plain, (k5_numbers=k4_ordinal1), inference(split_conjunct,[status(thm)],[redefinition_k5_numbers])). fof(c_0_26, plain, ![X12, X13, X14]:(~v3_ordinal1(X12)\|(v7_struct_0(X13)\|(~v13_algstr_0(X13)\|(~v4_vectsp_1(X13)\|(~v5_vectsp_1(X13)\|(~v3_rlvect_1(X13)\|(~v4_rlvect_1(X13)\|~l6_algstr_0(X13))))))\|(~v1_funct_1(X14)\|(~v1_funct_2(X14,k15_pre_poly(X12),u1_struct_0(X13))\|(~v1_polynom1(X14,k15_pre_poly(X12),X13)\|~m1_subset_1(X14,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(X12),u1_struct_0(X13))))))))\|k1_groeb_1(X12,X13,X14)=k1_tarski(X14)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[redefinition_k1_groeb_1])])])). cnf(c_0_27, plain, (r2_groeb_1(X1,X5,X2,X3,X4)\|v7_struct_0(X2)\|k7_ideal_1(k11_polynom1(X1,X2),X3)!=X4\|~v9_rewrite1(k3_polyred(X1,X5,X2,X3))\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(k11_polynom1(X1,X2))))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(k11_polynom1(X1,X2))))\|~v13_algstr_0(X2)\|~v33_algstr_0(X2)\|~v3_group_1(X2)\|~v5_group_1(X2)\|~v4_vectsp_1(X2)\|~v5_vectsp_1(X2)\|~v3_rlvect_1(X2)\|~v4_rlvect_1(X2)\|~l6_algstr_0(X2)\|~v1_partfun1(X5,k15_pre_poly(X1))\|~v1_relat_2(X5)\|~v4_relat_2(X5)\|~v6_relat_2(X5)\|~v8_relat_2(X5)\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(X1),k15_pre_poly(X1))))\|~v3_ordinal1(X1)), inference(split_conjunct,[status(thm)],[c_0_21])). cnf(c_0_28, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(esk1_0),k15_pre_poly(esk1_0))))), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_29, negated_conjecture, (v8_relat_2(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_30, negated_conjecture, (v6_relat_2(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_31, negated_conjecture, (v4_relat_2(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_32, negated_conjecture, (v1_relat_2(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_33, negated_conjecture, (v1_partfun1(esk2_0,k15_pre_poly(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_34, plain, (v3_ordinal1(X2)\|~v3_ordinal1(X1)\|~m1_subset_1(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_23])). cnf(c_0_35, negated_conjecture, (m1_subset_1(esk1_0,k5_numbers)), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_36, plain, (v3_ordinal1(k4_ordinal1)), inference(evalgc,[status(thm)],[c_0_24])). cnf(c_0_37, plain, (k4_ordinal1=k5_numbers), inference(evalgc,[status(thm)],[c_0_25])). cnf(c_0_38, plain, (v7_struct_0(X2)\|k1_groeb_1(X1,X2,X3)=k1_tarski(X3)\|~v3_ordinal1(X1)\|~v13_algstr_0(X2)\|~v4_vectsp_1(X2)\|~v5_vectsp_1(X2)\|~v3_rlvect_1(X2)\|~v4_rlvect_1(X2)\|~l6_algstr_0(X2)\|~v1_funct_1(X3)\|~v1_funct_2(X3,k15_pre_poly(X1),u1_struct_0(X2))\|~v1_polynom1(X3,k15_pre_poly(X1),X2)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(X1),u1_struct_0(X2))))), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_39, negated_conjecture, (m1_subset_1(esk4_0,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(esk1_0),u1_struct_0(esk3_0))))), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_40, negated_conjecture, (v1_polynom1(esk4_0,k15_pre_poly(esk1_0),esk3_0)), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_41, negated_conjecture, (v1_funct_2(esk4_0,k15_pre_poly(esk1_0),u1_struct_0(esk3_0))), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_42, negated_conjecture, (v1_funct_1(esk4_0)), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_43, negated_conjecture, (l6_algstr_0(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_44, negated_conjecture, (v4_rlvect_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_45, negated_conjecture, (v3_rlvect_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_46, negated_conjecture, (v5_vectsp_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_47, negated_conjecture, (v4_vectsp_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_48, negated_conjecture, (v13_algstr_0(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_49, negated_conjecture, (~v7_struct_0(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_50, plain, (v7_struct_0(X2)\|r2_groeb_1(X1,X5,X2,X3,X4)\|k7_ideal_1(k11_polynom1(X1,X2),X3)!=X4\|~v1_relat_2(X5)\|~v4_relat_2(X5)\|~v6_relat_2(X5)\|~v8_relat_2(X5)\|~v13_algstr_0(X2)\|~v33_algstr_0(X2)\|~v3_group_1(X2)\|~v5_group_1(X2)\|~v4_vectsp_1(X2)\|~v5_vectsp_1(X2)\|~v3_rlvect_1(X2)\|~v4_rlvect_1(X2)\|~l6_algstr_0(X2)\|~v3_ordinal1(X1)\|~v1_partfun1(X5,k15_pre_poly(X1))\|~v9_rewrite1(k3_polyred(X1,X5,X2,X3))\|~m1_subset_1(X4,k1_zfmisc_1(u1_struct_0(k11_polynom1(X1,X2))))\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(k11_polynom1(X1,X2))))\|~m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(X1),k15_pre_poly(X1))))), inference(evalgc,[status(thm)],[c_0_27])). cnf(c_0_51, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(esk1_0),k15_pre_poly(esk1_0))))), inference(evalgc,[status(thm)],[c_0_28])). cnf(c_0_52, negated_conjecture, (v8_relat_2(esk2_0)), inference(evalgc,[status(thm)],[c_0_29])). cnf(c_0_53, negated_conjecture, (v6_relat_2(esk2_0)), inference(evalgc,[status(thm)],[c_0_30])). cnf(c_0_54, negated_conjecture, (v4_relat_2(esk2_0)), inference(evalgc,[status(thm)],[c_0_31])). cnf(c_0_55, negated_conjecture, (v1_relat_2(esk2_0)), inference(evalgc,[status(thm)],[c_0_32])). cnf(c_0_56, negated_conjecture, (v1_partfun1(esk2_0,k15_pre_poly(esk1_0))), inference(evalgc,[status(thm)],[c_0_33])). cnf(c_0_57, plain, (v3_ordinal1(X2)\|~v3_ordinal1(X1)\|~m1_subset_1(X2,X1)), inference(evalgc,[status(thm)],[c_0_34])). cnf(c_0_58, negated_conjecture, (m1_subset_1(esk1_0,k5_numbers)), inference(evalgc,[status(thm)],[c_0_35])). cnf(c_0_59, plain, (v3_ordinal1(k5_numbers)), inference(rw,[status(thm)],[c_0_36, c_0_37])). fof(c_0_60, plain, ![X15, X16, X17, X18]:(~m1_subset_1(X15,k5_numbers)\|(~v1_partfun1(X16,k15_pre_poly(X15))\|(~v1_relat_2(X16)\|(~v4_relat_2(X16)\|(~v6_relat_2(X16)\|(~v8_relat_2(X16)\|(~v2_bagorder(X16,X15)\|~m1_subset_1(X16,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(X15),k15_pre_poly(X15)))))))))\|(v7_struct_0(X17)\|(~v13_algstr_0(X17)\|(~v33_algstr_0(X17)\|(~v3_group_1(X17)\|(~v5_group_1(X17)\|(~v4_vectsp_1(X17)\|(~v5_vectsp_1(X17)\|(~v2_rlvect_1(X17)\|(~v3_rlvect_1(X17)\|(~v4_rlvect_1(X17)\|~l6_algstr_0(X17))))))))))\|(~v1_funct_1(X18)\|(~v1_funct_2(X18,k15_pre_poly(X15),u1_struct_0(X17))\|(~v1_polynom1(X18,k15_pre_poly(X15),X17)\|~m1_subset_1(X18,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(X15),u1_struct_0(X17))))))\|v9_rewrite1(k3_polyred(X15,X16,X17,k1_groeb_1(X15,X17,X18))))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t10_groeb_1])])])])). fof(c_0_61, plain, ![X36]:~v1_xboole_0(k1_tarski(X36)), inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fc2_xboole_0])])). cnf(c_0_62, plain, (k1_groeb_1(X1,X2,X3)=k1_tarski(X3)\|v7_struct_0(X2)\|~v13_algstr_0(X2)\|~v4_vectsp_1(X2)\|~v5_vectsp_1(X2)\|~v3_rlvect_1(X2)\|~v4_rlvect_1(X2)\|~l6_algstr_0(X2)\|~v1_funct_1(X3)\|~v3_ordinal1(X1)\|~v1_polynom1(X3,k15_pre_poly(X1),X2)\|~v1_funct_2(X3,k15_pre_poly(X1),u1_struct_0(X2))\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(X1),u1_struct_0(X2))))), inference(evalgc,[status(thm)],[c_0_38])). cnf(c_0_63, negated_conjecture, (m1_subset_1(esk4_0,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(esk1_0),u1_struct_0(esk3_0))))), inference(evalgc,[status(thm)],[c_0_39])). cnf(c_0_64, negated_conjecture, (v1_polynom1(esk4_0,k15_pre_poly(esk1_0),esk3_0)), inference(evalgc,[status(thm)],[c_0_40])). cnf(c_0_65, negated_conjecture, (v1_funct_2(esk4_0,k15_pre_poly(esk1_0),u1_struct_0(esk3_0))), inference(evalgc,[status(thm)],[c_0_41])). cnf(c_0_66, negated_conjecture, (v1_funct_1(esk4_0)), inference(evalgc,[status(thm)],[c_0_42])). cnf(c_0_67, negated_conjecture, (l6_algstr_0(esk3_0)), inference(evalgc,[status(thm)],[c_0_43])). cnf(c_0_68, negated_conjecture, (v4_rlvect_1(esk3_0)), inference(evalgc,[status(thm)],[c_0_44])). cnf(c_0_69, negated_conjecture, (v3_rlvect_1(esk3_0)), inference(evalgc,[status(thm)],[c_0_45])). cnf(c_0_70, negated_conjecture, (v5_vectsp_1(esk3_0)), inference(evalgc,[status(thm)],[c_0_46])). cnf(c_0_71, negated_conjecture, (v4_vectsp_1(esk3_0)), inference(evalgc,[status(thm)],[c_0_47])). cnf(c_0_72, negated_conjecture, (v13_algstr_0(esk3_0)), inference(evalgc,[status(thm)],[c_0_48])). cnf(c_0_73, negated_conjecture, (~v7_struct_0(esk3_0)), inference(evalgc,[status(thm)],[c_0_49])). fof(c_0_74, plain, ![X37, X38]:(~v1_xboole_0(X37)\|(~m1_subset_1(X38,k1_zfmisc_1(X37))\|v1_xboole_0(X38))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_subset_1])])])). fof(c_0_75, plain, ![X23, X24, X25]:(~v3_ordinal1(X23)\|(v7_struct_0(X24)\|(~v13_algstr_0(X24)\|(~v4_vectsp_1(X24)\|(~v5_vectsp_1(X24)\|(~v3_rlvect_1(X24)\|(~v4_rlvect_1(X24)\|~l6_algstr_0(X24))))))\|(~v1_funct_1(X25)\|(~v1_funct_2(X25,k15_pre_poly(X23),u1_struct_0(X24))\|(~v1_polynom1(X25,k15_pre_poly(X23),X24)\|~m1_subset_1(X25,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(X23),u1_struct_0(X24))))))))\|m1_subset_1(k1_groeb_1(X23,X24,X25),k1_zfmisc_1(u1_struct_0(k11_polynom1(X23,X24))))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k1_groeb_1])])])). cnf(c_0_76, negated_conjecture, (r2_groeb_1(esk1_0,esk2_0,X1,X2,X3)\|v7_struct_0(X1)\|k7_ideal_1(k11_polynom1(esk1_0,X1),X2)!=X3\|~v9_rewrite1(k3_polyred(esk1_0,esk2_0,X1,X2))\|~v3_ordinal1(esk1_0)\|~l6_algstr_0(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v5_vectsp_1(X1)\|~v4_vectsp_1(X1)\|~v5_group_1(X1)\|~v3_group_1(X1)\|~v33_algstr_0(X1)\|~v13_algstr_0(X1)\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(k11_polynom1(esk1_0,X1))))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(k11_polynom1(esk1_0,X1))))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50, c_0_51]), c_0_52]), c_0_53]), c_0_54]), c_0_55]), c_0_56])])])). cnf(c_0_77, negated_conjecture, (v3_ordinal1(esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57, c_0_58]), c_0_59])])])). cnf(c_0_78, plain, (v7_struct_0(X3)\|v9_rewrite1(k3_polyred(X1,X2,X3,k1_groeb_1(X1,X3,X4)))\|~m1_subset_1(X1,k5_numbers)\|~v1_partfun1(X2,k15_pre_poly(X1))\|~v1_relat_2(X2)\|~v4_relat_2(X2)\|~v6_relat_2(X2)\|~v8_relat_2(X2)\|~v2_bagorder(X2,X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(X1),k15_pre_poly(X1))))\|~v13_algstr_0(X3)\|~v33_algstr_0(X3)\|~v3_group_1(X3)\|~v5_group_1(X3)\|~v4_vectsp_1(X3)\|~v5_vectsp_1(X3)\|~v2_rlvect_1(X3)\|~v3_rlvect_1(X3)\|~v4_rlvect_1(X3)\|~l6_algstr_0(X3)\|~v1_funct_1(X4)\|~v1_funct_2(X4,k15_pre_poly(X1),u1_struct_0(X3))\|~v1_polynom1(X4,k15_pre_poly(X1),X3)\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(X1),u1_struct_0(X3))))), inference(split_conjunct,[status(thm)],[c_0_60])). cnf(c_0_79, negated_conjecture, (v2_bagorder(esk2_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_80, plain, (~v1_xboole_0(k1_tarski(X1))), inference(split_conjunct,[status(thm)],[c_0_61])). cnf(c_0_81, negated_conjecture, (k1_tarski(esk4_0)=k1_groeb_1(esk1_0,esk3_0,esk4_0)\|~v3_ordinal1(esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62, c_0_63]), c_0_64]), c_0_65]), c_0_66]), c_0_67]), c_0_68]), c_0_69]), c_0_70]), c_0_71]), c_0_72])]), c_0_73])])). cnf(c_0_82, plain, (v1_xboole_0(X2)\|~v1_xboole_0(X1)\|~m1_subset_1(X2,k1_zfmisc_1(X1))), inference(split_conjunct,[status(thm)],[c_0_74])). cnf(c_0_83, plain, (v7_struct_0(X2)\|m1_subset_1(k1_groeb_1(X1,X2,X3),k1_zfmisc_1(u1_struct_0(k11_polynom1(X1,X2))))\|~v3_ordinal1(X1)\|~v13_algstr_0(X2)\|~v4_vectsp_1(X2)\|~v5_vectsp_1(X2)\|~v3_rlvect_1(X2)\|~v4_rlvect_1(X2)\|~l6_algstr_0(X2)\|~v1_funct_1(X3)\|~v1_funct_2(X3,k15_pre_poly(X1),u1_struct_0(X2))\|~v1_polynom1(X3,k15_pre_poly(X1),X2)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(X1),u1_struct_0(X2))))), inference(split_conjunct,[status(thm)],[c_0_75])). cnf(c_0_84, negated_conjecture, (r2_groeb_1(esk1_0,esk2_0,X1,X2,X3)\|v7_struct_0(X1)\|k7_ideal_1(k11_polynom1(esk1_0,X1),X2)!=X3\|~v9_rewrite1(k3_polyred(esk1_0,esk2_0,X1,X2))\|~l6_algstr_0(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v5_vectsp_1(X1)\|~v4_vectsp_1(X1)\|~v5_group_1(X1)\|~v3_group_1(X1)\|~v33_algstr_0(X1)\|~v13_algstr_0(X1)\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(k11_polynom1(esk1_0,X1))))\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(k11_polynom1(esk1_0,X1))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_76, c_0_77])])). cnf(c_0_85, plain, (v7_struct_0(X3)\|v9_rewrite1(k3_polyred(X1,X2,X3,k1_groeb_1(X1,X3,X4)))\|~v1_relat_2(X2)\|~v4_relat_2(X2)\|~v6_relat_2(X2)\|~v8_relat_2(X2)\|~v13_algstr_0(X3)\|~v33_algstr_0(X3)\|~v3_group_1(X3)\|~v5_group_1(X3)\|~v4_vectsp_1(X3)\|~v5_vectsp_1(X3)\|~v2_rlvect_1(X3)\|~v3_rlvect_1(X3)\|~v4_rlvect_1(X3)\|~l6_algstr_0(X3)\|~v1_funct_1(X4)\|~v2_bagorder(X2,X1)\|~m1_subset_1(X1,k5_numbers)\|~v1_partfun1(X2,k15_pre_poly(X1))\|~v1_polynom1(X4,k15_pre_poly(X1),X3)\|~v1_funct_2(X4,k15_pre_poly(X1),u1_struct_0(X3))\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(X1),u1_struct_0(X3))))\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(X1),k15_pre_poly(X1))))), inference(evalgc,[status(thm)],[c_0_78])). cnf(c_0_86, negated_conjecture, (v2_bagorder(esk2_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_79])). cnf(c_0_87, plain, (~v1_xboole_0(k1_tarski(X1))), inference(evalgc,[status(thm)],[c_0_80])). cnf(c_0_88, negated_conjecture, (k1_tarski(esk4_0)=k1_groeb_1(esk1_0,esk3_0,esk4_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_81, c_0_77])])). cnf(c_0_89, plain, (v1_xboole_0(X2)\|~v1_xboole_0(X1)\|~m1_subset_1(X2,k1_zfmisc_1(X1))), inference(evalgc,[status(thm)],[c_0_82])). cnf(c_0_90, plain, (v7_struct_0(X2)\|m1_subset_1(k1_groeb_1(X1,X2,X3),k1_zfmisc_1(u1_struct_0(k11_polynom1(X1,X2))))\|~v13_algstr_0(X2)\|~v4_vectsp_1(X2)\|~v5_vectsp_1(X2)\|~v3_rlvect_1(X2)\|~v4_rlvect_1(X2)\|~l6_algstr_0(X2)\|~v1_funct_1(X3)\|~v3_ordinal1(X1)\|~v1_polynom1(X3,k15_pre_poly(X1),X2)\|~v1_funct_2(X3,k15_pre_poly(X1),u1_struct_0(X2))\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(X1),u1_struct_0(X2))))), inference(evalgc,[status(thm)],[c_0_83])). fof(c_0_91, plain, ![X22]:(~v2_struct_0(X22)\|~l1_struct_0(X22)\|v1_xboole_0(u1_struct_0(X22))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc1_struct_0])])). fof(c_0_92, plain, ![X19]:(~l1_algstr_0(X19)\|l1_struct_0(X19)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_algstr_0])])). fof(c_0_93, plain, ![X20]:((l2_struct_0(X20)\|~l2_algstr_0(X20))&(l1_algstr_0(X20)\|~l2_algstr_0(X20))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l2_algstr_0])])])). cnf(c_0_94, negated_conjecture, (~r2_groeb_1(esk1_0,esk2_0,esk3_0,k1_groeb_1(esk1_0,esk3_0,esk4_0),k7_ideal_1(k11_polynom1(esk1_0,esk3_0),k1_groeb_1(esk1_0,esk3_0,esk4_0)))), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_95, negated_conjecture, (r2_groeb_1(esk1_0,esk2_0,X1,k1_groeb_1(esk1_0,X1,X2),X3)\|v7_struct_0(X1)\|k7_ideal_1(k11_polynom1(esk1_0,X1),k1_groeb_1(esk1_0,X1,X2))!=X3\|~l6_algstr_0(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v5_vectsp_1(X1)\|~v4_vectsp_1(X1)\|~v5_group_1(X1)\|~v3_group_1(X1)\|~v33_algstr_0(X1)\|~v13_algstr_0(X1)\|~m1_subset_1(X3,k1_zfmisc_1(u1_struct_0(k11_polynom1(esk1_0,X1))))\|~m1_subset_1(k1_groeb_1(esk1_0,X1,X2),k1_zfmisc_1(u1_struct_0(k11_polynom1(esk1_0,X1))))\|~v1_polynom1(X2,k15_pre_poly(esk1_0),X1)\|~v1_funct_2(X2,k15_pre_poly(esk1_0),u1_struct_0(X1))\|~v1_funct_1(X2)\|~v2_rlvect_1(X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(esk1_0),u1_struct_0(X1))))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84, c_0_85]), c_0_86]), c_0_52]), c_0_53]), c_0_54]), c_0_55]), c_0_56]), c_0_51]), c_0_58])])])). cnf(c_0_96, negated_conjecture, (v2_rlvect_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_97, negated_conjecture, (v5_group_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_98, negated_conjecture, (v3_group_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_99, negated_conjecture, (v33_algstr_0(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_22])). fof(c_0_100, plain, ![X26, X27]:((~v1_xboole_0(k7_ideal_1(X26,X27))\|(v2_struct_0(X26)\|~l6_algstr_0(X26)\|~m1_subset_1(X27,k1_zfmisc_1(u1_struct_0(X26)))))&((v1_ideal_1(k7_ideal_1(X26,X27),X26)\|(v2_struct_0(X26)\|~l6_algstr_0(X26)\|~m1_subset_1(X27,k1_zfmisc_1(u1_struct_0(X26)))))&((v2_ideal_1(k7_ideal_1(X26,X27),X26)\|(v2_struct_0(X26)\|~l6_algstr_0(X26)\|~m1_subset_1(X27,k1_zfmisc_1(u1_struct_0(X26)))))&((v3_ideal_1(k7_ideal_1(X26,X27),X26)\|(v2_struct_0(X26)\|~l6_algstr_0(X26)\|~m1_subset_1(X27,k1_zfmisc_1(u1_struct_0(X26)))))&(m1_subset_1(k7_ideal_1(X26,X27),k1_zfmisc_1(u1_struct_0(X26)))\|(v2_struct_0(X26)\|~l6_algstr_0(X26)\|~m1_subset_1(X27,k1_zfmisc_1(u1_struct_0(X26))))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k7_ideal_1])])])])). cnf(c_0_101, negated_conjecture, (~v1_xboole_0(k1_groeb_1(esk1_0,esk3_0,esk4_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_87, c_0_88])])). cnf(c_0_102, plain, (v1_xboole_0(k1_groeb_1(X1,X2,X3))\|v7_struct_0(X2)\|~v1_xboole_0(u1_struct_0(k11_polynom1(X1,X2)))\|~v3_ordinal1(X1)\|~v1_polynom1(X3,k15_pre_poly(X1),X2)\|~v1_funct_2(X3,k15_pre_poly(X1),u1_struct_0(X2))\|~v1_funct_1(X3)\|~l6_algstr_0(X2)\|~v4_rlvect_1(X2)\|~v3_rlvect_1(X2)\|~v5_vectsp_1(X2)\|~v4_vectsp_1(X2)\|~v13_algstr_0(X2)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(X1),u1_struct_0(X2))))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_89, c_0_90])])). cnf(c_0_103, plain, (v1_xboole_0(u1_struct_0(X1))\|~v2_struct_0(X1)\|~l1_struct_0(X1)), inference(split_conjunct,[status(thm)],[c_0_91])). cnf(c_0_104, plain, (l1_struct_0(X1)\|~l1_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_92])). cnf(c_0_105, plain, (l1_algstr_0(X1)\|~l2_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_93])). fof(c_0_106, plain, ![X40]:((~v2_struct_0(X40)\|(v2_struct_0(X40)\|~v4_vectsp_1(X40))\|~l4_algstr_0(X40))&((v3_vectsp_1(X40)\|(v2_struct_0(X40)\|~v4_vectsp_1(X40))\|~l4_algstr_0(X40))&(v6_vectsp_1(X40)\|(v2_struct_0(X40)\|~v4_vectsp_1(X40))\|~l4_algstr_0(X40)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[cc3_vectsp_1])])])])). fof(c_0_107, plain, ![X39]:((l4_algstr_0(X39)\|~l5_algstr_0(X39))&(l4_struct_0(X39)\|~l5_algstr_0(X39))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l5_algstr_0])])])). cnf(c_0_108, negated_conjecture, (~r2_groeb_1(esk1_0,esk2_0,esk3_0,k1_groeb_1(esk1_0,esk3_0,esk4_0),k7_ideal_1(k11_polynom1(esk1_0,esk3_0),k1_groeb_1(esk1_0,esk3_0,esk4_0)))), inference(evalgc,[status(thm)],[c_0_94])). cnf(c_0_109, negated_conjecture, (r2_groeb_1(esk1_0,esk2_0,X1,k1_groeb_1(esk1_0,X1,X2),k7_ideal_1(k11_polynom1(esk1_0,X1),k1_groeb_1(esk1_0,X1,X2)))\|v7_struct_0(X1)\|~v1_polynom1(X2,k15_pre_poly(esk1_0),X1)\|~v1_funct_2(X2,k15_pre_poly(esk1_0),u1_struct_0(X1))\|~v1_funct_1(X2)\|~l6_algstr_0(X1)\|~v4_rlvect_1(X1)\|~v3_rlvect_1(X1)\|~v2_rlvect_1(X1)\|~v5_vectsp_1(X1)\|~v4_vectsp_1(X1)\|~v5_group_1(X1)\|~v3_group_1(X1)\|~v33_algstr_0(X1)\|~v13_algstr_0(X1)\|~m1_subset_1(k1_groeb_1(esk1_0,X1,X2),k1_zfmisc_1(u1_struct_0(k11_polynom1(esk1_0,X1))))\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(esk1_0),u1_struct_0(X1))))\|~m1_subset_1(k7_ideal_1(k11_polynom1(esk1_0,X1),k1_groeb_1(esk1_0,X1,X2)),k1_zfmisc_1(u1_struct_0(k11_polynom1(esk1_0,X1))))), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_95])])). cnf(c_0_110, negated_conjecture, (v2_rlvect_1(esk3_0)), inference(evalgc,[status(thm)],[c_0_96])). cnf(c_0_111, negated_conjecture, (v5_group_1(esk3_0)), inference(evalgc,[status(thm)],[c_0_97])). cnf(c_0_112, negated_conjecture, (v3_group_1(esk3_0)), inference(evalgc,[status(thm)],[c_0_98])). cnf(c_0_113, negated_conjecture, (v33_algstr_0(esk3_0)), inference(evalgc,[status(thm)],[c_0_99])). cnf(c_0_114, plain, (m1_subset_1(k7_ideal_1(X1,X2),k1_zfmisc_1(u1_struct_0(X1)))\|v2_struct_0(X1)\|~l6_algstr_0(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(split_conjunct,[status(thm)],[c_0_100])). cnf(c_0_115, negated_conjecture, (~v1_xboole_0(u1_struct_0(k11_polynom1(esk1_0,esk3_0)))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101, c_0_102]), c_0_77]), c_0_64]), c_0_65]), c_0_66]), c_0_67]), c_0_68]), c_0_69]), c_0_70]), c_0_71]), c_0_72]), c_0_63])]), c_0_73])])). cnf(c_0_116, plain, (v1_xboole_0(u1_struct_0(X1))\|~l1_struct_0(X1)\|~v2_struct_0(X1)), inference(evalgc,[status(thm)],[c_0_103])). cnf(c_0_117, plain, (l1_struct_0(X1)\|~l1_algstr_0(X1)), inference(evalgc,[status(thm)],[c_0_104])). cnf(c_0_118, plain, (l1_algstr_0(X1)\|~l2_algstr_0(X1)), inference(evalgc,[status(thm)],[c_0_105])). fof(c_0_119, plain, ![X21]:((l2_algstr_0(X21)\|~l6_algstr_0(X21))&(l5_algstr_0(X21)\|~l6_algstr_0(X21))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l6_algstr_0])])])). cnf(c_0_120, plain, (v3_vectsp_1(X1)\|v2_struct_0(X1)\|~v4_vectsp_1(X1)\|~l4_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_106])). cnf(c_0_121, plain, (l4_algstr_0(X1)\|~l5_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_107])). fof(c_0_122, plain, ![X33]:(~l1_struct_0(X33)\|(v7_struct_0(X33)\|~v2_struct_0(X33))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[cc2_struct_0])])])). cnf(c_0_123, negated_conjecture, (~m1_subset_1(k7_ideal_1(k11_polynom1(esk1_0,esk3_0),k1_groeb_1(esk1_0,esk3_0,esk4_0)),k1_zfmisc_1(u1_struct_0(k11_polynom1(esk1_0,esk3_0))))\|~m1_subset_1(k1_groeb_1(esk1_0,esk3_0,esk4_0),k1_zfmisc_1(u1_struct_0(k11_polynom1(esk1_0,esk3_0))))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108, c_0_109]), c_0_64]), c_0_65]), c_0_66]), c_0_67]), c_0_68]), c_0_69]), c_0_110]), c_0_70]), c_0_71]), c_0_111]), c_0_112]), c_0_113]), c_0_72]), c_0_63])]), c_0_73])])). cnf(c_0_124, plain, (v2_struct_0(X1)\|m1_subset_1(k7_ideal_1(X1,X2),k1_zfmisc_1(u1_struct_0(X1)))\|~l6_algstr_0(X1)\|~m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))), inference(evalgc,[status(thm)],[c_0_114])). cnf(c_0_125, negated_conjecture, (~v2_struct_0(k11_polynom1(esk1_0,esk3_0))\|~l1_struct_0(k11_polynom1(esk1_0,esk3_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_115, c_0_116])])). cnf(c_0_126, plain, (l1_struct_0(X1)\|~l2_algstr_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_117, c_0_118])])). cnf(c_0_127, plain, (l2_algstr_0(X1)\|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_119])). fof(c_0_128, plain, ![X34, X35]:((~v2_struct_0(k11_polynom1(X34,X35))\|(~v3_ordinal1(X34)\|(v7_struct_0(X35)\|(~v13_algstr_0(X35)\|(~v3_vectsp_1(X35)\|(~v5_vectsp_1(X35)\|(~v3_rlvect_1(X35)\|(~v4_rlvect_1(X35)\|~l6_algstr_0(X35)))))))))&((v36_algstr_0(k11_polynom1(X34,X35))\|(~v3_ordinal1(X34)\|(v7_struct_0(X35)\|(~v13_algstr_0(X35)\|(~v3_vectsp_1(X35)\|(~v5_vectsp_1(X35)\|(~v3_rlvect_1(X35)\|(~v4_rlvect_1(X35)\|~l6_algstr_0(X35)))))))))&(l6_algstr_0(k11_polynom1(X34,X35))\|(~v3_ordinal1(X34)\|(v7_struct_0(X35)\|(~v13_algstr_0(X35)\|(~v3_vectsp_1(X35)\|(~v5_vectsp_1(X35)\|(~v3_rlvect_1(X35)\|(~v4_rlvect_1(X35)\|~l6_algstr_0(X35))))))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k11_polynom1])])])])). cnf(c_0_129, plain, (v2_struct_0(X1)\|v3_vectsp_1(X1)\|~v4_vectsp_1(X1)\|~l4_algstr_0(X1)), inference(evalgc,[status(thm)],[c_0_120])). cnf(c_0_130, plain, (l4_algstr_0(X1)\|~l5_algstr_0(X1)), inference(evalgc,[status(thm)],[c_0_121])). cnf(c_0_131, plain, (l5_algstr_0(X1)\|~l6_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_119])). cnf(c_0_132, plain, (v7_struct_0(X1)\|~l1_struct_0(X1)\|~v2_struct_0(X1)), inference(split_conjunct,[status(thm)],[c_0_122])). cnf(c_0_133, negated_conjecture, (v2_struct_0(k11_polynom1(esk1_0,esk3_0))\|~m1_subset_1(k1_groeb_1(esk1_0,esk3_0,esk4_0),k1_zfmisc_1(u1_struct_0(k11_polynom1(esk1_0,esk3_0))))\|~l6_algstr_0(k11_polynom1(esk1_0,esk3_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_123, c_0_124])])). cnf(c_0_134, negated_conjecture, (~v2_struct_0(k11_polynom1(esk1_0,esk3_0))\|~l2_algstr_0(k11_polynom1(esk1_0,esk3_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_125, c_0_126])])). cnf(c_0_135, plain, (l2_algstr_0(X1)\|~l6_algstr_0(X1)), inference(evalgc,[status(thm)],[c_0_127])). cnf(c_0_136, plain, (l6_algstr_0(k11_polynom1(X1,X2))\|v7_struct_0(X2)\|~v3_ordinal1(X1)\|~v13_algstr_0(X2)\|~v3_vectsp_1(X2)\|~v5_vectsp_1(X2)\|~v3_rlvect_1(X2)\|~v4_rlvect_1(X2)\|~l6_algstr_0(X2)), inference(split_conjunct,[status(thm)],[c_0_128])). cnf(c_0_137, plain, (v3_vectsp_1(X1)\|v2_struct_0(X1)\|~v4_vectsp_1(X1)\|~l5_algstr_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_129, c_0_130])])). cnf(c_0_138, plain, (l5_algstr_0(X1)\|~l6_algstr_0(X1)), inference(evalgc,[status(thm)],[c_0_131])). cnf(c_0_139, plain, (v7_struct_0(X1)\|~l1_struct_0(X1)\|~v2_struct_0(X1)), inference(evalgc,[status(thm)],[c_0_132])). cnf(c_0_140, negated_conjecture, (v2_struct_0(k11_polynom1(esk1_0,esk3_0))\|~l6_algstr_0(k11_polynom1(esk1_0,esk3_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133, c_0_90]), c_0_77]), c_0_64]), c_0_65]), c_0_66]), c_0_67]), c_0_68]), c_0_69]), c_0_70]), c_0_71]), c_0_72]), c_0_63])]), c_0_73])])). cnf(c_0_141, negated_conjecture, (~v2_struct_0(k11_polynom1(esk1_0,esk3_0))\|~l6_algstr_0(k11_polynom1(esk1_0,esk3_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_134, c_0_135])])). cnf(c_0_142, plain, (v7_struct_0(X2)\|l6_algstr_0(k11_polynom1(X1,X2))\|~v13_algstr_0(X2)\|~v5_vectsp_1(X2)\|~v3_rlvect_1(X2)\|~v4_rlvect_1(X2)\|~l6_algstr_0(X2)\|~v3_ordinal1(X1)\|~v3_vectsp_1(X2)), inference(evalgc,[status(thm)],[c_0_136])). cnf(c_0_143, plain, (v3_vectsp_1(X1)\|v2_struct_0(X1)\|~v4_vectsp_1(X1)\|~l6_algstr_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_137, c_0_138])])). cnf(c_0_144, plain, (v7_struct_0(X1)\|~v2_struct_0(X1)\|~l2_algstr_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_139, c_0_126])])). cnf(c_0_145, negated_conjecture, (~l6_algstr_0(k11_polynom1(esk1_0,esk3_0))), inference(csr,[status(thm)],[c_0_140, c_0_141])). cnf(c_0_146, plain, (l6_algstr_0(k11_polynom1(X1,X2))\|v7_struct_0(X2)\|v2_struct_0(X2)\|~v3_ordinal1(X1)\|~l6_algstr_0(X2)\|~v4_rlvect_1(X2)\|~v3_rlvect_1(X2)\|~v5_vectsp_1(X2)\|~v13_algstr_0(X2)\|~v4_vectsp_1(X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_142, c_0_143])])). cnf(c_0_147, plain, (v7_struct_0(X1)\|~v2_struct_0(X1)\|~l6_algstr_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_144, c_0_135])])). cnf(c_0_148, negated_conjecture, (v2_struct_0(esk3_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145, c_0_146]), c_0_77]), c_0_67]), c_0_68]), c_0_69]), c_0_70]), c_0_71]), c_0_72])]), c_0_73])])). cnf(c_0_149, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147, c_0_148]), c_0_67])]), c_0_73]), ['proof']). # SZS output end CNFRefutation	theorem for n being Element of NAT, T being connected admissible TermOrder of n, L being add-associative right_complementable right_zeroed commutative associative well-unital distributive Abelian almost_left_invertible non trivial doubleLoopStr, p being Polynomial of n,L holds {p} is_Groebner_basis_of {p}-Ideal,T proof let n be Element of NAT, T be connected admissible TermOrder of n, L be add-associative right_complementable right_zeroed commutative associative well-unital distributive Abelian almost_left_invertible non trivial doubleLoopStr, p be Polynomial of n,L; per cases; suppose A1: p = 0_(n,L); 0_(n,L) = 0.(Polynom-Ring(n,L)) by POLYNOM1:def 10; then {p}-Ideal = {0_(n,L)} by A1,IDEAL_1:44; hence thesis by A1,Th30; end; suppose p <> 0_(n,L); then reconsider p as non-zero Polynomial of n,L by POLYNOM7:def 1; PolyRedRel({p},T) is locally-confluent by Th10; hence thesis by Def4; end; end;	Convert the following ATP output trace into a readable Mizar proof.
t41_scm_halt	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t37_scmfsa_m, axiom, ![X1]:((v1_relat_1(X1)&(v4_relat_1(X1,u1_struct_0(k1_scmfsa_2))&(v1_funct_1(X1)&(v5_funct_1(X1,k2_memstr_0(np__3,k1_scmfsa_2))&v1_partfun1(X1,u1_struct_0(k1_scmfsa_2))))))=>(![X2]:((v1_ami_2(X2)&(~(v1_scmfsa_m(X2))&m1_subset_1(X2,u1_struct_0(k1_scmfsa_2))))=>k1_funct_1(k1_scmfsa_m(X1),X2)=k1_funct_1(X1,X2))&![X2]:(m1_scmfsa_2(X2)=>k18_scmfsa_2(k1_scmfsa_m(X1),X2)=k18_scmfsa_2(X1,X2)))), file('/scratch/mptp/predsminms1/t41_scm_halt__0', t37_scmfsa_m)). fof(fc4_scmfsa_m, axiom, ![X1]:((v1_relat_1(X1)&(v4_relat_1(X1,u1_struct_0(k1_scmfsa_2))&(v1_funct_1(X1)&(v5_funct_1(X1,k2_memstr_0(np__3,k1_scmfsa_2))&v1_partfun1(X1,u1_struct_0(k1_scmfsa_2))))))=>(v1_relat_1(k1_scmfsa_m(X1))&(v4_relat_1(k1_scmfsa_m(X1),u1_struct_0(k1_scmfsa_2))&(v1_funct_1(k1_scmfsa_m(X1))&(v5_funct_1(k1_scmfsa_m(X1),k2_memstr_0(np__3,k1_scmfsa_2))&v1_partfun1(k1_scmfsa_m(X1),u1_struct_0(k1_scmfsa_2))))))), file('/scratch/mptp/predsminms1/t41_scm_halt__0', fc4_scmfsa_m)). fof(t31_scm_halt, axiom, ![X1]:((v1_relat_1(X1)&(v4_relat_1(X1,k5_numbers)&(v5_relat_1(X1,u1_compos_1(k1_scmfsa_2))&(v1_funct_1(X1)&v1_partfun1(X1,k5_numbers)))))=>![X2]:((v1_relat_1(X2)&(v4_relat_1(X2,u1_struct_0(k1_scmfsa_2))&(v1_funct_1(X2)&(v5_funct_1(X2,k2_memstr_0(np__3,k1_scmfsa_2))&v1_partfun1(X2,u1_struct_0(k1_scmfsa_2))))))=>![X3]:((~(v1_xboole_0(X3))&(v1_relat_1(X3)&(v4_relat_1(X3,k5_numbers)&(v5_relat_1(X3,u1_compos_1(k1_scmfsa_2))&(v1_funct_1(X3)&(v1_finset_1(X3)&v1_afinsq_1(X3)))))))=>(r2_scm_halt(X3,X2,X1)<=>r6_scmfsa7b(X3,k1_scmfsa_m(X2),X1))))), file('/scratch/mptp/predsminms1/t41_scm_halt__0', t31_scm_halt)). fof(t21_scmfsa8b, axiom, ![X1]:((v1_relat_1(X1)&(v4_relat_1(X1,k5_numbers)&(v5_relat_1(X1,u1_compos_1(k1_scmfsa_2))&(v1_funct_1(X1)&v1_partfun1(X1,k5_numbers)))))=>![X2]:((v1_relat_1(X2)&(v4_relat_1(X2,u1_struct_0(k1_scmfsa_2))&(v1_funct_1(X2)&(v5_funct_1(X2,k2_memstr_0(np__3,k1_scmfsa_2))&v1_partfun1(X2,u1_struct_0(k1_scmfsa_2))))))=>![X3]:((~(v1_xboole_0(X3))&(v1_relat_1(X3)&(v4_relat_1(X3,k5_numbers)&(v5_relat_1(X3,u1_compos_1(k1_scmfsa_2))&(v1_funct_1(X3)&(v1_finset_1(X3)&v1_afinsq_1(X3)))))))=>![X4]:((~(v1_xboole_0(X4))&(v1_relat_1(X4)&(v4_relat_1(X4,k5_numbers)&(v5_relat_1(X4,u1_compos_1(k1_scmfsa_2))&(v1_funct_1(X4)&(v1_finset_1(X4)&v1_afinsq_1(X4)))))))=>![X5]:((v1_ami_2(X5)&(~(v1_scmfsa_m(X5))&m1_subset_1(X5,u1_struct_0(k1_scmfsa_2))))=>((r1_xxreal_0(k1_funct_1(X2,X5),k6_numbers)&(r5_scmfsa7b(X4,X2,X1)&r6_scmfsa7b(X4,X2,X1)))=>(r5_scmfsa7b(k2_scmfsa8b(X5,X3,X4),X2,X1)&r6_scmfsa7b(k2_scmfsa8b(X5,X3,X4),X2,X1)))))))), file('/scratch/mptp/predsminms1/t41_scm_halt__0', t21_scmfsa8b)). fof(dt_k2_scmfsa8b, axiom, ![X1, X2, X3]:(((v1_ami_2(X1)&m1_subset_1(X1,u1_struct_0(k1_scmfsa_2)))&((~(v1_xboole_0(X2))&(v1_relat_1(X2)&(v4_relat_1(X2,k5_numbers)&(v5_relat_1(X2,u1_compos_1(k1_scmfsa_2))&(v1_funct_1(X2)&(v1_finset_1(X2)&v1_afinsq_1(X2)))))))&(~(v1_xboole_0(X3))&(v1_relat_1(X3)&(v4_relat_1(X3,k5_numbers)&(v5_relat_1(X3,u1_compos_1(k1_scmfsa_2))&(v1_funct_1(X3)&(v1_finset_1(X3)&v1_afinsq_1(X3)))))))))=>(~(v1_xboole_0(k2_scmfsa8b(X1,X2,X3)))&(v1_relat_1(k2_scmfsa8b(X1,X2,X3))&(v4_relat_1(k2_scmfsa8b(X1,X2,X3),k5_numbers)&(v5_relat_1(k2_scmfsa8b(X1,X2,X3),u1_compos_1(k1_scmfsa_2))&(v1_funct_1(k2_scmfsa8b(X1,X2,X3))&(v1_finset_1(k2_scmfsa8b(X1,X2,X3))&v1_afinsq_1(k2_scmfsa8b(X1,X2,X3))))))))), file('/scratch/mptp/predsminms1/t41_scm_halt__0', dt_k2_scmfsa8b)). fof(t41_scm_halt, conjecture, ![X1]:((v1_relat_1(X1)&(v4_relat_1(X1,k5_numbers)&(v5_relat_1(X1,u1_compos_1(k1_scmfsa_2))&(v1_funct_1(X1)&v1_partfun1(X1,k5_numbers)))))=>![X2]:((v1_relat_1(X2)&(v4_relat_1(X2,u1_struct_0(k1_scmfsa_2))&(v1_funct_1(X2)&(v5_funct_1(X2,k2_memstr_0(np__3,k1_scmfsa_2))&v1_partfun1(X2,u1_struct_0(k1_scmfsa_2))))))=>![X3]:((~(v1_xboole_0(X3))&(v1_relat_1(X3)&(v4_relat_1(X3,k5_numbers)&(v5_relat_1(X3,u1_compos_1(k1_scmfsa_2))&(v1_funct_1(X3)&(v1_finset_1(X3)&v1_afinsq_1(X3)))))))=>![X4]:((~(v1_xboole_0(X4))&(v1_relat_1(X4)&(v4_relat_1(X4,k5_numbers)&(v5_relat_1(X4,u1_compos_1(k1_scmfsa_2))&(v1_funct_1(X4)&(v1_finset_1(X4)&v1_afinsq_1(X4)))))))=>![X5]:((v1_ami_2(X5)&(~(v1_scmfsa_m(X5))&m1_subset_1(X5,u1_struct_0(k1_scmfsa_2))))=>((r1_xxreal_0(k1_funct_1(X2,X5),k6_numbers)&(r1_scm_halt(X4,X2,X1)&r2_scm_halt(X4,X2,X1)))=>(r1_scm_halt(k2_scmfsa8b(X5,X3,X4),X2,X1)&r2_scm_halt(k2_scmfsa8b(X5,X3,X4),X2,X1)))))))), file('/scratch/mptp/predsminms1/t41_scm_halt__0', t41_scm_halt)). fof(t30_scm_halt, axiom, ![X1]:((v1_relat_1(X1)&(v4_relat_1(X1,k5_numbers)&(v5_relat_1(X1,u1_compos_1(k1_scmfsa_2))&(v1_funct_1(X1)&v1_partfun1(X1,k5_numbers)))))=>![X2]:((v1_relat_1(X2)&(v4_relat_1(X2,u1_struct_0(k1_scmfsa_2))&(v1_funct_1(X2)&(v5_funct_1(X2,k2_memstr_0(np__3,k1_scmfsa_2))&v1_partfun1(X2,u1_struct_0(k1_scmfsa_2))))))=>![X3]:((~(v1_xboole_0(X3))&(v1_relat_1(X3)&(v4_relat_1(X3,k5_numbers)&(v5_relat_1(X3,u1_compos_1(k1_scmfsa_2))&(v1_funct_1(X3)&(v1_finset_1(X3)&v1_afinsq_1(X3)))))))=>(r1_scm_halt(X3,X2,X1)<=>r5_scmfsa7b(X3,k1_scmfsa_m(X2),X1))))), file('/scratch/mptp/predsminms1/t41_scm_halt__0', t30_scm_halt)). fof(c_0_7, plain, ![X1]:(epred1_1(X1)<=>![X2]:((v1_relat_1(X2)&(v4_relat_1(X2,u1_struct_0(k1_scmfsa_2))&(v1_funct_1(X2)&(v5_funct_1(X2,k2_memstr_0(np__3,k1_scmfsa_2))&v1_partfun1(X2,u1_struct_0(k1_scmfsa_2))))))=>![X3]:((~(v1_xboole_0(X3))&(v1_relat_1(X3)&(v4_relat_1(X3,k5_numbers)&(v5_relat_1(X3,u1_compos_1(k1_scmfsa_2))&(v1_funct_1(X3)&(v1_finset_1(X3)&v1_afinsq_1(X3)))))))=>![X4]:((~(v1_xboole_0(X4))&(v1_relat_1(X4)&(v4_relat_1(X4,k5_numbers)&(v5_relat_1(X4,u1_compos_1(k1_scmfsa_2))&(v1_funct_1(X4)&(v1_finset_1(X4)&v1_afinsq_1(X4)))))))=>![X5]:((v1_ami_2(X5)&(~(v1_scmfsa_m(X5))&m1_subset_1(X5,u1_struct_0(k1_scmfsa_2))))=>((r1_xxreal_0(k1_funct_1(X2,X5),k6_numbers)&(r5_scmfsa7b(X4,X2,X1)&r6_scmfsa7b(X4,X2,X1)))=>(r5_scmfsa7b(k2_scmfsa8b(X5,X3,X4),X2,X1)&r6_scmfsa7b(k2_scmfsa8b(X5,X3,X4),X2,X1)))))))), introduced(definition)). fof(c_0_8, plain, ![X1]:(epred1_1(X1)=>![X2]:((v1_relat_1(X2)&(v4_relat_1(X2,u1_struct_0(k1_scmfsa_2))&(v1_funct_1(X2)&(v5_funct_1(X2,k2_memstr_0(np__3,k1_scmfsa_2))&v1_partfun1(X2,u1_struct_0(k1_scmfsa_2))))))=>![X3]:((~(v1_xboole_0(X3))&(v1_relat_1(X3)&(v4_relat_1(X3,k5_numbers)&(v5_relat_1(X3,u1_compos_1(k1_scmfsa_2))&(v1_funct_1(X3)&(v1_finset_1(X3)&v1_afinsq_1(X3)))))))=>![X4]:((~(v1_xboole_0(X4))&(v1_relat_1(X4)&(v4_relat_1(X4,k5_numbers)&(v5_relat_1(X4,u1_compos_1(k1_scmfsa_2))&(v1_funct_1(X4)&(v1_finset_1(X4)&v1_afinsq_1(X4)))))))=>![X5]:((v1_ami_2(X5)&(~(v1_scmfsa_m(X5))&m1_subset_1(X5,u1_struct_0(k1_scmfsa_2))))=>((r1_xxreal_0(k1_funct_1(X2,X5),k6_numbers)&(r5_scmfsa7b(X4,X2,X1)&r6_scmfsa7b(X4,X2,X1)))=>(r5_scmfsa7b(k2_scmfsa8b(X5,X3,X4),X2,X1)&r6_scmfsa7b(k2_scmfsa8b(X5,X3,X4),X2,X1)))))))), inference(split_equiv,[status(thm)],[c_0_7])). fof(c_0_9, plain, ![X25, X26, X27, X28, X29]:((r5_scmfsa7b(k2_scmfsa8b(X29,X27,X28),X26,X25)\|(~r1_xxreal_0(k1_funct_1(X26,X29),k6_numbers)\|(~r5_scmfsa7b(X28,X26,X25)\|~r6_scmfsa7b(X28,X26,X25)))\|(~v1_ami_2(X29)\|(v1_scmfsa_m(X29)\|~m1_subset_1(X29,u1_struct_0(k1_scmfsa_2))))\|(v1_xboole_0(X28)\|(~v1_relat_1(X28)\|(~v4_relat_1(X28,k5_numbers)\|(~v5_relat_1(X28,u1_compos_1(k1_scmfsa_2))\|(~v1_funct_1(X28)\|(~v1_finset_1(X28)\|~v1_afinsq_1(X28)))))))\|(v1_xboole_0(X27)\|(~v1_relat_1(X27)\|(~v4_relat_1(X27,k5_numbers)\|(~v5_relat_1(X27,u1_compos_1(k1_scmfsa_2))\|(~v1_funct_1(X27)\|(~v1_finset_1(X27)\|~v1_afinsq_1(X27)))))))\|(~v1_relat_1(X26)\|(~v4_relat_1(X26,u1_struct_0(k1_scmfsa_2))\|(~v1_funct_1(X26)\|(~v5_funct_1(X26,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X26,u1_struct_0(k1_scmfsa_2))))))\|~epred1_1(X25))&(r6_scmfsa7b(k2_scmfsa8b(X29,X27,X28),X26,X25)\|(~r1_xxreal_0(k1_funct_1(X26,X29),k6_numbers)\|(~r5_scmfsa7b(X28,X26,X25)\|~r6_scmfsa7b(X28,X26,X25)))\|(~v1_ami_2(X29)\|(v1_scmfsa_m(X29)\|~m1_subset_1(X29,u1_struct_0(k1_scmfsa_2))))\|(v1_xboole_0(X28)\|(~v1_relat_1(X28)\|(~v4_relat_1(X28,k5_numbers)\|(~v5_relat_1(X28,u1_compos_1(k1_scmfsa_2))\|(~v1_funct_1(X28)\|(~v1_finset_1(X28)\|~v1_afinsq_1(X28)))))))\|(v1_xboole_0(X27)\|(~v1_relat_1(X27)\|(~v4_relat_1(X27,k5_numbers)\|(~v5_relat_1(X27,u1_compos_1(k1_scmfsa_2))\|(~v1_funct_1(X27)\|(~v1_finset_1(X27)\|~v1_afinsq_1(X27)))))))\|(~v1_relat_1(X26)\|(~v4_relat_1(X26,u1_struct_0(k1_scmfsa_2))\|(~v1_funct_1(X26)\|(~v5_funct_1(X26,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X26,u1_struct_0(k1_scmfsa_2))))))\|~epred1_1(X25))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_8])])])])])). fof(c_0_10, plain, ![X11, X12, X13]:((~v1_ami_2(X12)\|(v1_scmfsa_m(X12)\|~m1_subset_1(X12,u1_struct_0(k1_scmfsa_2)))\|k1_funct_1(k1_scmfsa_m(X11),X12)=k1_funct_1(X11,X12)\|(~v1_relat_1(X11)\|(~v4_relat_1(X11,u1_struct_0(k1_scmfsa_2))\|(~v1_funct_1(X11)\|(~v5_funct_1(X11,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X11,u1_struct_0(k1_scmfsa_2)))))))&(~m1_scmfsa_2(X13)\|k18_scmfsa_2(k1_scmfsa_m(X11),X13)=k18_scmfsa_2(X11,X13)\|(~v1_relat_1(X11)\|(~v4_relat_1(X11,u1_struct_0(k1_scmfsa_2))\|(~v1_funct_1(X11)\|(~v5_funct_1(X11,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X11,u1_struct_0(k1_scmfsa_2)))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t37_scmfsa_m])])])])])). cnf(c_0_11, plain, (r6_scmfsa7b(k2_scmfsa8b(X1,X2,X3),X4,X5)\|v1_scmfsa_m(X1)\|v1_xboole_0(X3)\|v1_xboole_0(X2)\|~r1_xxreal_0(k1_funct_1(X4,X1),k6_numbers)\|~r5_scmfsa7b(X3,X4,X5)\|~r6_scmfsa7b(X3,X4,X5)\|~v1_ami_2(X1)\|~m1_subset_1(X1,u1_struct_0(k1_scmfsa_2))\|~v1_relat_1(X3)\|~v4_relat_1(X3,k5_numbers)\|~v5_relat_1(X3,u1_compos_1(k1_scmfsa_2))\|~v1_funct_1(X3)\|~v1_finset_1(X3)\|~v1_afinsq_1(X3)\|~v1_relat_1(X2)\|~v4_relat_1(X2,k5_numbers)\|~v5_relat_1(X2,u1_compos_1(k1_scmfsa_2))\|~v1_funct_1(X2)\|~v1_finset_1(X2)\|~v1_afinsq_1(X2)\|~v1_relat_1(X4)\|~v4_relat_1(X4,u1_struct_0(k1_scmfsa_2))\|~v1_funct_1(X4)\|~v5_funct_1(X4,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X4,u1_struct_0(k1_scmfsa_2))\|~epred1_1(X5)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_12, plain, (v1_scmfsa_m(X1)\|k1_funct_1(k1_scmfsa_m(X2),X1)=k1_funct_1(X2,X1)\|~v1_ami_2(X1)\|~m1_subset_1(X1,u1_struct_0(k1_scmfsa_2))\|~v1_relat_1(X2)\|~v4_relat_1(X2,u1_struct_0(k1_scmfsa_2))\|~v1_funct_1(X2)\|~v5_funct_1(X2,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X2,u1_struct_0(k1_scmfsa_2))), inference(split_conjunct,[status(thm)],[c_0_10])). fof(c_0_13, plain, ![X14]:((v1_relat_1(k1_scmfsa_m(X14))\|(~v1_relat_1(X14)\|(~v4_relat_1(X14,u1_struct_0(k1_scmfsa_2))\|(~v1_funct_1(X14)\|(~v5_funct_1(X14,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X14,u1_struct_0(k1_scmfsa_2)))))))&((v4_relat_1(k1_scmfsa_m(X14),u1_struct_0(k1_scmfsa_2))\|(~v1_relat_1(X14)\|(~v4_relat_1(X14,u1_struct_0(k1_scmfsa_2))\|(~v1_funct_1(X14)\|(~v5_funct_1(X14,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X14,u1_struct_0(k1_scmfsa_2)))))))&((v1_funct_1(k1_scmfsa_m(X14))\|(~v1_relat_1(X14)\|(~v4_relat_1(X14,u1_struct_0(k1_scmfsa_2))\|(~v1_funct_1(X14)\|(~v5_funct_1(X14,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X14,u1_struct_0(k1_scmfsa_2)))))))&((v5_funct_1(k1_scmfsa_m(X14),k2_memstr_0(np__3,k1_scmfsa_2))\|(~v1_relat_1(X14)\|(~v4_relat_1(X14,u1_struct_0(k1_scmfsa_2))\|(~v1_funct_1(X14)\|(~v5_funct_1(X14,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X14,u1_struct_0(k1_scmfsa_2)))))))&(v1_partfun1(k1_scmfsa_m(X14),u1_struct_0(k1_scmfsa_2))\|(~v1_relat_1(X14)\|(~v4_relat_1(X14,u1_struct_0(k1_scmfsa_2))\|(~v1_funct_1(X14)\|(~v5_funct_1(X14,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X14,u1_struct_0(k1_scmfsa_2))))))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc4_scmfsa_m])])])). fof(c_0_14, plain, ![X15, X16, X17]:((~r2_scm_halt(X17,X16,X15)\|r6_scmfsa7b(X17,k1_scmfsa_m(X16),X15)\|(v1_xboole_0(X17)\|(~v1_relat_1(X17)\|(~v4_relat_1(X17,k5_numbers)\|(~v5_relat_1(X17,u1_compos_1(k1_scmfsa_2))\|(~v1_funct_1(X17)\|(~v1_finset_1(X17)\|~v1_afinsq_1(X17)))))))\|(~v1_relat_1(X16)\|(~v4_relat_1(X16,u1_struct_0(k1_scmfsa_2))\|(~v1_funct_1(X16)\|(~v5_funct_1(X16,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X16,u1_struct_0(k1_scmfsa_2))))))\|(~v1_relat_1(X15)\|(~v4_relat_1(X15,k5_numbers)\|(~v5_relat_1(X15,u1_compos_1(k1_scmfsa_2))\|(~v1_funct_1(X15)\|~v1_partfun1(X15,k5_numbers))))))&(~r6_scmfsa7b(X17,k1_scmfsa_m(X16),X15)\|r2_scm_halt(X17,X16,X15)\|(v1_xboole_0(X17)\|(~v1_relat_1(X17)\|(~v4_relat_1(X17,k5_numbers)\|(~v5_relat_1(X17,u1_compos_1(k1_scmfsa_2))\|(~v1_funct_1(X17)\|(~v1_finset_1(X17)\|~v1_afinsq_1(X17)))))))\|(~v1_relat_1(X16)\|(~v4_relat_1(X16,u1_struct_0(k1_scmfsa_2))\|(~v1_funct_1(X16)\|(~v5_funct_1(X16,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X16,u1_struct_0(k1_scmfsa_2))))))\|(~v1_relat_1(X15)\|(~v4_relat_1(X15,k5_numbers)\|(~v5_relat_1(X15,u1_compos_1(k1_scmfsa_2))\|(~v1_funct_1(X15)\|~v1_partfun1(X15,k5_numbers))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t31_scm_halt])])])])])). cnf(c_0_15, plain, (v1_xboole_0(X3)\|v1_xboole_0(X2)\|v1_scmfsa_m(X1)\|r6_scmfsa7b(k2_scmfsa8b(X1,X2,X3),X4,X5)\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v1_finset_1(X3)\|~v1_finset_1(X2)\|~v1_afinsq_1(X3)\|~v1_afinsq_1(X2)\|~v1_ami_2(X1)\|~epred1_1(X5)\|~v4_relat_1(X3,k5_numbers)\|~v4_relat_1(X2,k5_numbers)\|~r6_scmfsa7b(X3,X4,X5)\|~r5_scmfsa7b(X3,X4,X5)\|~v4_relat_1(X4,u1_struct_0(k1_scmfsa_2))\|~v5_relat_1(X3,u1_compos_1(k1_scmfsa_2))\|~v5_relat_1(X2,u1_compos_1(k1_scmfsa_2))\|~v1_partfun1(X4,u1_struct_0(k1_scmfsa_2))\|~m1_subset_1(X1,u1_struct_0(k1_scmfsa_2))\|~r1_xxreal_0(k1_funct_1(X4,X1),k6_numbers)\|~v5_funct_1(X4,k2_memstr_0(np__3,k1_scmfsa_2))), inference(evalgc,[status(thm)],[c_0_11])). cnf(c_0_16, plain, (k1_funct_1(k1_scmfsa_m(X2),X1)=k1_funct_1(X2,X1)\|v1_scmfsa_m(X1)\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v1_ami_2(X1)\|~v4_relat_1(X2,u1_struct_0(k1_scmfsa_2))\|~v1_partfun1(X2,u1_struct_0(k1_scmfsa_2))\|~m1_subset_1(X1,u1_struct_0(k1_scmfsa_2))\|~v5_funct_1(X2,k2_memstr_0(np__3,k1_scmfsa_2))), inference(evalgc,[status(thm)],[c_0_12])). cnf(c_0_17, plain, (v1_relat_1(k1_scmfsa_m(X1))\|~v1_relat_1(X1)\|~v4_relat_1(X1,u1_struct_0(k1_scmfsa_2))\|~v1_funct_1(X1)\|~v5_funct_1(X1,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X1,u1_struct_0(k1_scmfsa_2))), inference(split_conjunct,[status(thm)],[c_0_13])). cnf(c_0_18, plain, (v4_relat_1(k1_scmfsa_m(X1),u1_struct_0(k1_scmfsa_2))\|~v1_relat_1(X1)\|~v4_relat_1(X1,u1_struct_0(k1_scmfsa_2))\|~v1_funct_1(X1)\|~v5_funct_1(X1,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X1,u1_struct_0(k1_scmfsa_2))), inference(split_conjunct,[status(thm)],[c_0_13])). cnf(c_0_19, plain, (v1_funct_1(k1_scmfsa_m(X1))\|~v1_relat_1(X1)\|~v4_relat_1(X1,u1_struct_0(k1_scmfsa_2))\|~v1_funct_1(X1)\|~v5_funct_1(X1,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X1,u1_struct_0(k1_scmfsa_2))), inference(split_conjunct,[status(thm)],[c_0_13])). cnf(c_0_20, plain, (v1_partfun1(k1_scmfsa_m(X1),u1_struct_0(k1_scmfsa_2))\|~v1_relat_1(X1)\|~v4_relat_1(X1,u1_struct_0(k1_scmfsa_2))\|~v1_funct_1(X1)\|~v5_funct_1(X1,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X1,u1_struct_0(k1_scmfsa_2))), inference(split_conjunct,[status(thm)],[c_0_13])). cnf(c_0_21, plain, (v5_funct_1(k1_scmfsa_m(X1),k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_relat_1(X1)\|~v4_relat_1(X1,u1_struct_0(k1_scmfsa_2))\|~v1_funct_1(X1)\|~v5_funct_1(X1,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X1,u1_struct_0(k1_scmfsa_2))), inference(split_conjunct,[status(thm)],[c_0_13])). fof(c_0_22, axiom, ![X1]:((v1_relat_1(X1)&(v4_relat_1(X1,k5_numbers)&(v5_relat_1(X1,u1_compos_1(k1_scmfsa_2))&(v1_funct_1(X1)&v1_partfun1(X1,k5_numbers)))))=>epred1_1(X1)), inference(apply_def,[status(thm)],[t21_scmfsa8b, c_0_7])). cnf(c_0_23, plain, (r5_scmfsa7b(k2_scmfsa8b(X1,X2,X3),X4,X5)\|v1_scmfsa_m(X1)\|v1_xboole_0(X3)\|v1_xboole_0(X2)\|~r1_xxreal_0(k1_funct_1(X4,X1),k6_numbers)\|~r5_scmfsa7b(X3,X4,X5)\|~r6_scmfsa7b(X3,X4,X5)\|~v1_ami_2(X1)\|~m1_subset_1(X1,u1_struct_0(k1_scmfsa_2))\|~v1_relat_1(X3)\|~v4_relat_1(X3,k5_numbers)\|~v5_relat_1(X3,u1_compos_1(k1_scmfsa_2))\|~v1_funct_1(X3)\|~v1_finset_1(X3)\|~v1_afinsq_1(X3)\|~v1_relat_1(X2)\|~v4_relat_1(X2,k5_numbers)\|~v5_relat_1(X2,u1_compos_1(k1_scmfsa_2))\|~v1_funct_1(X2)\|~v1_finset_1(X2)\|~v1_afinsq_1(X2)\|~v1_relat_1(X4)\|~v4_relat_1(X4,u1_struct_0(k1_scmfsa_2))\|~v1_funct_1(X4)\|~v5_funct_1(X4,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X4,u1_struct_0(k1_scmfsa_2))\|~epred1_1(X5)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_24, plain, (r2_scm_halt(X1,X2,X3)\|v1_xboole_0(X1)\|~r6_scmfsa7b(X1,k1_scmfsa_m(X2),X3)\|~v1_relat_1(X1)\|~v4_relat_1(X1,k5_numbers)\|~v5_relat_1(X1,u1_compos_1(k1_scmfsa_2))\|~v1_funct_1(X1)\|~v1_finset_1(X1)\|~v1_afinsq_1(X1)\|~v1_relat_1(X2)\|~v4_relat_1(X2,u1_struct_0(k1_scmfsa_2))\|~v1_funct_1(X2)\|~v5_funct_1(X2,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X2,u1_struct_0(k1_scmfsa_2))\|~v1_relat_1(X3)\|~v4_relat_1(X3,k5_numbers)\|~v5_relat_1(X3,u1_compos_1(k1_scmfsa_2))\|~v1_funct_1(X3)\|~v1_partfun1(X3,k5_numbers)), inference(split_conjunct,[status(thm)],[c_0_14])). cnf(c_0_25, plain, (r6_scmfsa7b(k2_scmfsa8b(X1,X2,X3),k1_scmfsa_m(X4),X5)\|v1_scmfsa_m(X1)\|v1_xboole_0(X2)\|v1_xboole_0(X3)\|~epred1_1(X5)\|~r5_scmfsa7b(X3,k1_scmfsa_m(X4),X5)\|~r6_scmfsa7b(X3,k1_scmfsa_m(X4),X5)\|~r1_xxreal_0(k1_funct_1(X4,X1),k6_numbers)\|~m1_subset_1(X1,u1_struct_0(k1_scmfsa_2))\|~v1_ami_2(X1)\|~v1_afinsq_1(X3)\|~v1_afinsq_1(X2)\|~v1_finset_1(X3)\|~v1_finset_1(X2)\|~v5_funct_1(k1_scmfsa_m(X4),k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(k1_scmfsa_m(X4),u1_struct_0(k1_scmfsa_2))\|~v1_funct_1(k1_scmfsa_m(X4))\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v5_relat_1(X3,u1_compos_1(k1_scmfsa_2))\|~v5_relat_1(X2,u1_compos_1(k1_scmfsa_2))\|~v4_relat_1(k1_scmfsa_m(X4),u1_struct_0(k1_scmfsa_2))\|~v4_relat_1(X3,k5_numbers)\|~v4_relat_1(X2,k5_numbers)\|~v1_relat_1(k1_scmfsa_m(X4))\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v5_funct_1(X4,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X4,u1_struct_0(k1_scmfsa_2))\|~v1_funct_1(X4)\|~v4_relat_1(X4,u1_struct_0(k1_scmfsa_2))\|~v1_relat_1(X4)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_15, c_0_16])])). cnf(c_0_26, plain, (v1_relat_1(k1_scmfsa_m(X1))\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v4_relat_1(X1,u1_struct_0(k1_scmfsa_2))\|~v1_partfun1(X1,u1_struct_0(k1_scmfsa_2))\|~v5_funct_1(X1,k2_memstr_0(np__3,k1_scmfsa_2))), inference(evalgc,[status(thm)],[c_0_17])). cnf(c_0_27, plain, (v4_relat_1(k1_scmfsa_m(X1),u1_struct_0(k1_scmfsa_2))\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v4_relat_1(X1,u1_struct_0(k1_scmfsa_2))\|~v1_partfun1(X1,u1_struct_0(k1_scmfsa_2))\|~v5_funct_1(X1,k2_memstr_0(np__3,k1_scmfsa_2))), inference(evalgc,[status(thm)],[c_0_18])). cnf(c_0_28, plain, (v1_funct_1(k1_scmfsa_m(X1))\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v4_relat_1(X1,u1_struct_0(k1_scmfsa_2))\|~v1_partfun1(X1,u1_struct_0(k1_scmfsa_2))\|~v5_funct_1(X1,k2_memstr_0(np__3,k1_scmfsa_2))), inference(evalgc,[status(thm)],[c_0_19])). cnf(c_0_29, plain, (v1_partfun1(k1_scmfsa_m(X1),u1_struct_0(k1_scmfsa_2))\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v4_relat_1(X1,u1_struct_0(k1_scmfsa_2))\|~v1_partfun1(X1,u1_struct_0(k1_scmfsa_2))\|~v5_funct_1(X1,k2_memstr_0(np__3,k1_scmfsa_2))), inference(evalgc,[status(thm)],[c_0_20])). cnf(c_0_30, plain, (v5_funct_1(k1_scmfsa_m(X1),k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v4_relat_1(X1,u1_struct_0(k1_scmfsa_2))\|~v1_partfun1(X1,u1_struct_0(k1_scmfsa_2))\|~v5_funct_1(X1,k2_memstr_0(np__3,k1_scmfsa_2))), inference(evalgc,[status(thm)],[c_0_21])). fof(c_0_31, plain, ![X19, X20, X21]:((~v1_xboole_0(k2_scmfsa8b(X19,X20,X21))\|(~v1_ami_2(X19)\|~m1_subset_1(X19,u1_struct_0(k1_scmfsa_2))\|(v1_xboole_0(X20)\|(~v1_relat_1(X20)\|(~v4_relat_1(X20,k5_numbers)\|(~v5_relat_1(X20,u1_compos_1(k1_scmfsa_2))\|(~v1_funct_1(X20)\|(~v1_finset_1(X20)\|~v1_afinsq_1(X20))))))\|(v1_xboole_0(X21)\|(~v1_relat_1(X21)\|(~v4_relat_1(X21,k5_numbers)\|(~v5_relat_1(X21,u1_compos_1(k1_scmfsa_2))\|(~v1_funct_1(X21)\|(~v1_finset_1(X21)\|~v1_afinsq_1(X21))))))))))&((v1_relat_1(k2_scmfsa8b(X19,X20,X21))\|(~v1_ami_2(X19)\|~m1_subset_1(X19,u1_struct_0(k1_scmfsa_2))\|(v1_xboole_0(X20)\|(~v1_relat_1(X20)\|(~v4_relat_1(X20,k5_numbers)\|(~v5_relat_1(X20,u1_compos_1(k1_scmfsa_2))\|(~v1_funct_1(X20)\|(~v1_finset_1(X20)\|~v1_afinsq_1(X20))))))\|(v1_xboole_0(X21)\|(~v1_relat_1(X21)\|(~v4_relat_1(X21,k5_numbers)\|(~v5_relat_1(X21,u1_compos_1(k1_scmfsa_2))\|(~v1_funct_1(X21)\|(~v1_finset_1(X21)\|~v1_afinsq_1(X21))))))))))&((v4_relat_1(k2_scmfsa8b(X19,X20,X21),k5_numbers)\|(~v1_ami_2(X19)\|~m1_subset_1(X19,u1_struct_0(k1_scmfsa_2))\|(v1_xboole_0(X20)\|(~v1_relat_1(X20)\|(~v4_relat_1(X20,k5_numbers)\|(~v5_relat_1(X20,u1_compos_1(k1_scmfsa_2))\|(~v1_funct_1(X20)\|(~v1_finset_1(X20)\|~v1_afinsq_1(X20))))))\|(v1_xboole_0(X21)\|(~v1_relat_1(X21)\|(~v4_relat_1(X21,k5_numbers)\|(~v5_relat_1(X21,u1_compos_1(k1_scmfsa_2))\|(~v1_funct_1(X21)\|(~v1_finset_1(X21)\|~v1_afinsq_1(X21))))))))))&((v5_relat_1(k2_scmfsa8b(X19,X20,X21),u1_compos_1(k1_scmfsa_2))\|(~v1_ami_2(X19)\|~m1_subset_1(X19,u1_struct_0(k1_scmfsa_2))\|(v1_xboole_0(X20)\|(~v1_relat_1(X20)\|(~v4_relat_1(X20,k5_numbers)\|(~v5_relat_1(X20,u1_compos_1(k1_scmfsa_2))\|(~v1_funct_1(X20)\|(~v1_finset_1(X20)\|~v1_afinsq_1(X20))))))\|(v1_xboole_0(X21)\|(~v1_relat_1(X21)\|(~v4_relat_1(X21,k5_numbers)\|(~v5_relat_1(X21,u1_compos_1(k1_scmfsa_2))\|(~v1_funct_1(X21)\|(~v1_finset_1(X21)\|~v1_afinsq_1(X21))))))))))&((v1_funct_1(k2_scmfsa8b(X19,X20,X21))\|(~v1_ami_2(X19)\|~m1_subset_1(X19,u1_struct_0(k1_scmfsa_2))\|(v1_xboole_0(X20)\|(~v1_relat_1(X20)\|(~v4_relat_1(X20,k5_numbers)\|(~v5_relat_1(X20,u1_compos_1(k1_scmfsa_2))\|(~v1_funct_1(X20)\|(~v1_finset_1(X20)\|~v1_afinsq_1(X20))))))\|(v1_xboole_0(X21)\|(~v1_relat_1(X21)\|(~v4_relat_1(X21,k5_numbers)\|(~v5_relat_1(X21,u1_compos_1(k1_scmfsa_2))\|(~v1_funct_1(X21)\|(~v1_finset_1(X21)\|~v1_afinsq_1(X21))))))))))&((v1_finset_1(k2_scmfsa8b(X19,X20,X21))\|(~v1_ami_2(X19)\|~m1_subset_1(X19,u1_struct_0(k1_scmfsa_2))\|(v1_xboole_0(X20)\|(~v1_relat_1(X20)\|(~v4_relat_1(X20,k5_numbers)\|(~v5_relat_1(X20,u1_compos_1(k1_scmfsa_2))\|(~v1_funct_1(X20)\|(~v1_finset_1(X20)\|~v1_afinsq_1(X20))))))\|(v1_xboole_0(X21)\|(~v1_relat_1(X21)\|(~v4_relat_1(X21,k5_numbers)\|(~v5_relat_1(X21,u1_compos_1(k1_scmfsa_2))\|(~v1_funct_1(X21)\|(~v1_finset_1(X21)\|~v1_afinsq_1(X21))))))))))&(v1_afinsq_1(k2_scmfsa8b(X19,X20,X21))\|(~v1_ami_2(X19)\|~m1_subset_1(X19,u1_struct_0(k1_scmfsa_2))\|(v1_xboole_0(X20)\|(~v1_relat_1(X20)\|(~v4_relat_1(X20,k5_numbers)\|(~v5_relat_1(X20,u1_compos_1(k1_scmfsa_2))\|(~v1_funct_1(X20)\|(~v1_finset_1(X20)\|~v1_afinsq_1(X20))))))\|(v1_xboole_0(X21)\|(~v1_relat_1(X21)\|(~v4_relat_1(X21,k5_numbers)\|(~v5_relat_1(X21,u1_compos_1(k1_scmfsa_2))\|(~v1_funct_1(X21)\|(~v1_finset_1(X21)\|~v1_afinsq_1(X21)))))))))))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k2_scmfsa8b])])])])). fof(c_0_32, plain, ![X18]:(~v1_relat_1(X18)\|(~v4_relat_1(X18,k5_numbers)\|(~v5_relat_1(X18,u1_compos_1(k1_scmfsa_2))\|(~v1_funct_1(X18)\|~v1_partfun1(X18,k5_numbers))))\|epred1_1(X18)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])). fof(c_0_33, negated_conjecture, ~(![X1]:((v1_relat_1(X1)&(v4_relat_1(X1,k5_numbers)&(v5_relat_1(X1,u1_compos_1(k1_scmfsa_2))&(v1_funct_1(X1)&v1_partfun1(X1,k5_numbers)))))=>![X2]:((v1_relat_1(X2)&(v4_relat_1(X2,u1_struct_0(k1_scmfsa_2))&(v1_funct_1(X2)&(v5_funct_1(X2,k2_memstr_0(np__3,k1_scmfsa_2))&v1_partfun1(X2,u1_struct_0(k1_scmfsa_2))))))=>![X3]:((~(v1_xboole_0(X3))&(v1_relat_1(X3)&(v4_relat_1(X3,k5_numbers)&(v5_relat_1(X3,u1_compos_1(k1_scmfsa_2))&(v1_funct_1(X3)&(v1_finset_1(X3)&v1_afinsq_1(X3)))))))=>![X4]:((~(v1_xboole_0(X4))&(v1_relat_1(X4)&(v4_relat_1(X4,k5_numbers)&(v5_relat_1(X4,u1_compos_1(k1_scmfsa_2))&(v1_funct_1(X4)&(v1_finset_1(X4)&v1_afinsq_1(X4)))))))=>![X5]:((v1_ami_2(X5)&(~(v1_scmfsa_m(X5))&m1_subset_1(X5,u1_struct_0(k1_scmfsa_2))))=>((r1_xxreal_0(k1_funct_1(X2,X5),k6_numbers)&(r1_scm_halt(X4,X2,X1)&r2_scm_halt(X4,X2,X1)))=>(r1_scm_halt(k2_scmfsa8b(X5,X3,X4),X2,X1)&r2_scm_halt(k2_scmfsa8b(X5,X3,X4),X2,X1))))))))), inference(assume_negation,[status(cth)],[t41_scm_halt])). fof(c_0_34, plain, ![X22, X23, X24]:((~r1_scm_halt(X24,X23,X22)\|r5_scmfsa7b(X24,k1_scmfsa_m(X23),X22)\|(v1_xboole_0(X24)\|(~v1_relat_1(X24)\|(~v4_relat_1(X24,k5_numbers)\|(~v5_relat_1(X24,u1_compos_1(k1_scmfsa_2))\|(~v1_funct_1(X24)\|(~v1_finset_1(X24)\|~v1_afinsq_1(X24)))))))\|(~v1_relat_1(X23)\|(~v4_relat_1(X23,u1_struct_0(k1_scmfsa_2))\|(~v1_funct_1(X23)\|(~v5_funct_1(X23,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X23,u1_struct_0(k1_scmfsa_2))))))\|(~v1_relat_1(X22)\|(~v4_relat_1(X22,k5_numbers)\|(~v5_relat_1(X22,u1_compos_1(k1_scmfsa_2))\|(~v1_funct_1(X22)\|~v1_partfun1(X22,k5_numbers))))))&(~r5_scmfsa7b(X24,k1_scmfsa_m(X23),X22)\|r1_scm_halt(X24,X23,X22)\|(v1_xboole_0(X24)\|(~v1_relat_1(X24)\|(~v4_relat_1(X24,k5_numbers)\|(~v5_relat_1(X24,u1_compos_1(k1_scmfsa_2))\|(~v1_funct_1(X24)\|(~v1_finset_1(X24)\|~v1_afinsq_1(X24)))))))\|(~v1_relat_1(X23)\|(~v4_relat_1(X23,u1_struct_0(k1_scmfsa_2))\|(~v1_funct_1(X23)\|(~v5_funct_1(X23,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X23,u1_struct_0(k1_scmfsa_2))))))\|(~v1_relat_1(X22)\|(~v4_relat_1(X22,k5_numbers)\|(~v5_relat_1(X22,u1_compos_1(k1_scmfsa_2))\|(~v1_funct_1(X22)\|~v1_partfun1(X22,k5_numbers))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t30_scm_halt])])])])])). cnf(c_0_35, plain, (v1_xboole_0(X3)\|v1_xboole_0(X2)\|v1_scmfsa_m(X1)\|r5_scmfsa7b(k2_scmfsa8b(X1,X2,X3),X4,X5)\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v1_finset_1(X3)\|~v1_finset_1(X2)\|~v1_afinsq_1(X3)\|~v1_afinsq_1(X2)\|~v1_ami_2(X1)\|~epred1_1(X5)\|~v4_relat_1(X3,k5_numbers)\|~v4_relat_1(X2,k5_numbers)\|~r6_scmfsa7b(X3,X4,X5)\|~r5_scmfsa7b(X3,X4,X5)\|~v4_relat_1(X4,u1_struct_0(k1_scmfsa_2))\|~v5_relat_1(X3,u1_compos_1(k1_scmfsa_2))\|~v5_relat_1(X2,u1_compos_1(k1_scmfsa_2))\|~v1_partfun1(X4,u1_struct_0(k1_scmfsa_2))\|~m1_subset_1(X1,u1_struct_0(k1_scmfsa_2))\|~r1_xxreal_0(k1_funct_1(X4,X1),k6_numbers)\|~v5_funct_1(X4,k2_memstr_0(np__3,k1_scmfsa_2))), inference(evalgc,[status(thm)],[c_0_23])). cnf(c_0_36, plain, (v1_xboole_0(X1)\|r2_scm_halt(X1,X2,X3)\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_relat_1(X1)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v1_funct_1(X1)\|~v1_finset_1(X1)\|~v1_afinsq_1(X1)\|~v4_relat_1(X3,k5_numbers)\|~v4_relat_1(X1,k5_numbers)\|~v1_partfun1(X3,k5_numbers)\|~v4_relat_1(X2,u1_struct_0(k1_scmfsa_2))\|~v5_relat_1(X3,u1_compos_1(k1_scmfsa_2))\|~v5_relat_1(X1,u1_compos_1(k1_scmfsa_2))\|~v1_partfun1(X2,u1_struct_0(k1_scmfsa_2))\|~r6_scmfsa7b(X1,k1_scmfsa_m(X2),X3)\|~v5_funct_1(X2,k2_memstr_0(np__3,k1_scmfsa_2))), inference(evalgc,[status(thm)],[c_0_24])). cnf(c_0_37, plain, (r6_scmfsa7b(k2_scmfsa8b(X1,X2,X3),k1_scmfsa_m(X4),X5)\|v1_scmfsa_m(X1)\|v1_xboole_0(X3)\|v1_xboole_0(X2)\|~epred1_1(X5)\|~r5_scmfsa7b(X3,k1_scmfsa_m(X4),X5)\|~r6_scmfsa7b(X3,k1_scmfsa_m(X4),X5)\|~r1_xxreal_0(k1_funct_1(X4,X1),k6_numbers)\|~m1_subset_1(X1,u1_struct_0(k1_scmfsa_2))\|~v1_ami_2(X1)\|~v1_afinsq_1(X3)\|~v1_afinsq_1(X2)\|~v1_finset_1(X3)\|~v1_finset_1(X2)\|~v5_funct_1(X4,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X4,u1_struct_0(k1_scmfsa_2))\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v1_funct_1(X4)\|~v5_relat_1(X3,u1_compos_1(k1_scmfsa_2))\|~v5_relat_1(X2,u1_compos_1(k1_scmfsa_2))\|~v4_relat_1(X4,u1_struct_0(k1_scmfsa_2))\|~v4_relat_1(X3,k5_numbers)\|~v4_relat_1(X2,k5_numbers)\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_relat_1(X4)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_25, c_0_26]), c_0_27]), c_0_28]), c_0_29]), c_0_30])). cnf(c_0_38, plain, (v1_relat_1(k2_scmfsa8b(X1,X2,X3))\|v1_xboole_0(X2)\|v1_xboole_0(X3)\|~v1_ami_2(X1)\|~m1_subset_1(X1,u1_struct_0(k1_scmfsa_2))\|~v1_relat_1(X2)\|~v4_relat_1(X2,k5_numbers)\|~v5_relat_1(X2,u1_compos_1(k1_scmfsa_2))\|~v1_funct_1(X2)\|~v1_finset_1(X2)\|~v1_afinsq_1(X2)\|~v1_relat_1(X3)\|~v4_relat_1(X3,k5_numbers)\|~v5_relat_1(X3,u1_compos_1(k1_scmfsa_2))\|~v1_funct_1(X3)\|~v1_finset_1(X3)\|~v1_afinsq_1(X3)), inference(split_conjunct,[status(thm)],[c_0_31])). cnf(c_0_39, plain, (v4_relat_1(k2_scmfsa8b(X1,X2,X3),k5_numbers)\|v1_xboole_0(X2)\|v1_xboole_0(X3)\|~v1_ami_2(X1)\|~m1_subset_1(X1,u1_struct_0(k1_scmfsa_2))\|~v1_relat_1(X2)\|~v4_relat_1(X2,k5_numbers)\|~v5_relat_1(X2,u1_compos_1(k1_scmfsa_2))\|~v1_funct_1(X2)\|~v1_finset_1(X2)\|~v1_afinsq_1(X2)\|~v1_relat_1(X3)\|~v4_relat_1(X3,k5_numbers)\|~v5_relat_1(X3,u1_compos_1(k1_scmfsa_2))\|~v1_funct_1(X3)\|~v1_finset_1(X3)\|~v1_afinsq_1(X3)), inference(split_conjunct,[status(thm)],[c_0_31])). cnf(c_0_40, plain, (v5_relat_1(k2_scmfsa8b(X1,X2,X3),u1_compos_1(k1_scmfsa_2))\|v1_xboole_0(X2)\|v1_xboole_0(X3)\|~v1_ami_2(X1)\|~m1_subset_1(X1,u1_struct_0(k1_scmfsa_2))\|~v1_relat_1(X2)\|~v4_relat_1(X2,k5_numbers)\|~v5_relat_1(X2,u1_compos_1(k1_scmfsa_2))\|~v1_funct_1(X2)\|~v1_finset_1(X2)\|~v1_afinsq_1(X2)\|~v1_relat_1(X3)\|~v4_relat_1(X3,k5_numbers)\|~v5_relat_1(X3,u1_compos_1(k1_scmfsa_2))\|~v1_funct_1(X3)\|~v1_finset_1(X3)\|~v1_afinsq_1(X3)), inference(split_conjunct,[status(thm)],[c_0_31])). cnf(c_0_41, plain, (v1_funct_1(k2_scmfsa8b(X1,X2,X3))\|v1_xboole_0(X2)\|v1_xboole_0(X3)\|~v1_ami_2(X1)\|~m1_subset_1(X1,u1_struct_0(k1_scmfsa_2))\|~v1_relat_1(X2)\|~v4_relat_1(X2,k5_numbers)\|~v5_relat_1(X2,u1_compos_1(k1_scmfsa_2))\|~v1_funct_1(X2)\|~v1_finset_1(X2)\|~v1_afinsq_1(X2)\|~v1_relat_1(X3)\|~v4_relat_1(X3,k5_numbers)\|~v5_relat_1(X3,u1_compos_1(k1_scmfsa_2))\|~v1_funct_1(X3)\|~v1_finset_1(X3)\|~v1_afinsq_1(X3)), inference(split_conjunct,[status(thm)],[c_0_31])). cnf(c_0_42, plain, (v1_finset_1(k2_scmfsa8b(X1,X2,X3))\|v1_xboole_0(X2)\|v1_xboole_0(X3)\|~v1_ami_2(X1)\|~m1_subset_1(X1,u1_struct_0(k1_scmfsa_2))\|~v1_relat_1(X2)\|~v4_relat_1(X2,k5_numbers)\|~v5_relat_1(X2,u1_compos_1(k1_scmfsa_2))\|~v1_funct_1(X2)\|~v1_finset_1(X2)\|~v1_afinsq_1(X2)\|~v1_relat_1(X3)\|~v4_relat_1(X3,k5_numbers)\|~v5_relat_1(X3,u1_compos_1(k1_scmfsa_2))\|~v1_funct_1(X3)\|~v1_finset_1(X3)\|~v1_afinsq_1(X3)), inference(split_conjunct,[status(thm)],[c_0_31])). cnf(c_0_43, plain, (v1_afinsq_1(k2_scmfsa8b(X1,X2,X3))\|v1_xboole_0(X2)\|v1_xboole_0(X3)\|~v1_ami_2(X1)\|~m1_subset_1(X1,u1_struct_0(k1_scmfsa_2))\|~v1_relat_1(X2)\|~v4_relat_1(X2,k5_numbers)\|~v5_relat_1(X2,u1_compos_1(k1_scmfsa_2))\|~v1_funct_1(X2)\|~v1_finset_1(X2)\|~v1_afinsq_1(X2)\|~v1_relat_1(X3)\|~v4_relat_1(X3,k5_numbers)\|~v5_relat_1(X3,u1_compos_1(k1_scmfsa_2))\|~v1_funct_1(X3)\|~v1_finset_1(X3)\|~v1_afinsq_1(X3)), inference(split_conjunct,[status(thm)],[c_0_31])). cnf(c_0_44, plain, (epred1_1(X1)\|~v1_relat_1(X1)\|~v4_relat_1(X1,k5_numbers)\|~v5_relat_1(X1,u1_compos_1(k1_scmfsa_2))\|~v1_funct_1(X1)\|~v1_partfun1(X1,k5_numbers)), inference(split_conjunct,[status(thm)],[c_0_32])). cnf(c_0_45, plain, (v1_xboole_0(X2)\|v1_xboole_0(X3)\|~v1_xboole_0(k2_scmfsa8b(X1,X2,X3))\|~v1_ami_2(X1)\|~m1_subset_1(X1,u1_struct_0(k1_scmfsa_2))\|~v1_relat_1(X2)\|~v4_relat_1(X2,k5_numbers)\|~v5_relat_1(X2,u1_compos_1(k1_scmfsa_2))\|~v1_funct_1(X2)\|~v1_finset_1(X2)\|~v1_afinsq_1(X2)\|~v1_relat_1(X3)\|~v4_relat_1(X3,k5_numbers)\|~v5_relat_1(X3,u1_compos_1(k1_scmfsa_2))\|~v1_funct_1(X3)\|~v1_finset_1(X3)\|~v1_afinsq_1(X3)), inference(split_conjunct,[status(thm)],[c_0_31])). fof(c_0_46, negated_conjecture, ((v1_relat_1(esk1_0)&(v4_relat_1(esk1_0,k5_numbers)&(v5_relat_1(esk1_0,u1_compos_1(k1_scmfsa_2))&(v1_funct_1(esk1_0)&v1_partfun1(esk1_0,k5_numbers)))))&((v1_relat_1(esk2_0)&(v4_relat_1(esk2_0,u1_struct_0(k1_scmfsa_2))&(v1_funct_1(esk2_0)&(v5_funct_1(esk2_0,k2_memstr_0(np__3,k1_scmfsa_2))&v1_partfun1(esk2_0,u1_struct_0(k1_scmfsa_2))))))&((~v1_xboole_0(esk3_0)&(v1_relat_1(esk3_0)&(v4_relat_1(esk3_0,k5_numbers)&(v5_relat_1(esk3_0,u1_compos_1(k1_scmfsa_2))&(v1_funct_1(esk3_0)&(v1_finset_1(esk3_0)&v1_afinsq_1(esk3_0)))))))&((~v1_xboole_0(esk4_0)&(v1_relat_1(esk4_0)&(v4_relat_1(esk4_0,k5_numbers)&(v5_relat_1(esk4_0,u1_compos_1(k1_scmfsa_2))&(v1_funct_1(esk4_0)&(v1_finset_1(esk4_0)&v1_afinsq_1(esk4_0)))))))&((v1_ami_2(esk5_0)&(~v1_scmfsa_m(esk5_0)&m1_subset_1(esk5_0,u1_struct_0(k1_scmfsa_2))))&((r1_xxreal_0(k1_funct_1(esk2_0,esk5_0),k6_numbers)&(r1_scm_halt(esk4_0,esk2_0,esk1_0)&r2_scm_halt(esk4_0,esk2_0,esk1_0)))&(~r1_scm_halt(k2_scmfsa8b(esk5_0,esk3_0,esk4_0),esk2_0,esk1_0)\|~r2_scm_halt(k2_scmfsa8b(esk5_0,esk3_0,esk4_0),esk2_0,esk1_0)))))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_33])])])])). cnf(c_0_47, plain, (r1_scm_halt(X1,X2,X3)\|v1_xboole_0(X1)\|~r5_scmfsa7b(X1,k1_scmfsa_m(X2),X3)\|~v1_relat_1(X1)\|~v4_relat_1(X1,k5_numbers)\|~v5_relat_1(X1,u1_compos_1(k1_scmfsa_2))\|~v1_funct_1(X1)\|~v1_finset_1(X1)\|~v1_afinsq_1(X1)\|~v1_relat_1(X2)\|~v4_relat_1(X2,u1_struct_0(k1_scmfsa_2))\|~v1_funct_1(X2)\|~v5_funct_1(X2,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X2,u1_struct_0(k1_scmfsa_2))\|~v1_relat_1(X3)\|~v4_relat_1(X3,k5_numbers)\|~v5_relat_1(X3,u1_compos_1(k1_scmfsa_2))\|~v1_funct_1(X3)\|~v1_partfun1(X3,k5_numbers)), inference(split_conjunct,[status(thm)],[c_0_34])). cnf(c_0_48, plain, (r5_scmfsa7b(k2_scmfsa8b(X1,X2,X3),k1_scmfsa_m(X4),X5)\|v1_scmfsa_m(X1)\|v1_xboole_0(X2)\|v1_xboole_0(X3)\|~epred1_1(X5)\|~r5_scmfsa7b(X3,k1_scmfsa_m(X4),X5)\|~r6_scmfsa7b(X3,k1_scmfsa_m(X4),X5)\|~r1_xxreal_0(k1_funct_1(X4,X1),k6_numbers)\|~m1_subset_1(X1,u1_struct_0(k1_scmfsa_2))\|~v1_ami_2(X1)\|~v1_afinsq_1(X3)\|~v1_afinsq_1(X2)\|~v1_finset_1(X3)\|~v1_finset_1(X2)\|~v5_funct_1(k1_scmfsa_m(X4),k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(k1_scmfsa_m(X4),u1_struct_0(k1_scmfsa_2))\|~v1_funct_1(k1_scmfsa_m(X4))\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v5_relat_1(X3,u1_compos_1(k1_scmfsa_2))\|~v5_relat_1(X2,u1_compos_1(k1_scmfsa_2))\|~v4_relat_1(k1_scmfsa_m(X4),u1_struct_0(k1_scmfsa_2))\|~v4_relat_1(X3,k5_numbers)\|~v4_relat_1(X2,k5_numbers)\|~v1_relat_1(k1_scmfsa_m(X4))\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v5_funct_1(X4,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X4,u1_struct_0(k1_scmfsa_2))\|~v1_funct_1(X4)\|~v4_relat_1(X4,u1_struct_0(k1_scmfsa_2))\|~v1_relat_1(X4)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_35, c_0_16])])). cnf(c_0_49, plain, (r2_scm_halt(k2_scmfsa8b(X1,X2,X3),X4,X5)\|v1_xboole_0(k2_scmfsa8b(X1,X2,X3))\|v1_scmfsa_m(X1)\|v1_xboole_0(X3)\|v1_xboole_0(X2)\|~v1_afinsq_1(k2_scmfsa8b(X1,X2,X3))\|~v1_finset_1(k2_scmfsa8b(X1,X2,X3))\|~v5_funct_1(X4,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X4,u1_struct_0(k1_scmfsa_2))\|~v1_partfun1(X5,k5_numbers)\|~v1_funct_1(X5)\|~v1_funct_1(X4)\|~v1_funct_1(k2_scmfsa8b(X1,X2,X3))\|~v5_relat_1(X5,u1_compos_1(k1_scmfsa_2))\|~v5_relat_1(k2_scmfsa8b(X1,X2,X3),u1_compos_1(k1_scmfsa_2))\|~v4_relat_1(X4,u1_struct_0(k1_scmfsa_2))\|~v4_relat_1(X5,k5_numbers)\|~v4_relat_1(k2_scmfsa8b(X1,X2,X3),k5_numbers)\|~v1_relat_1(X5)\|~v1_relat_1(X4)\|~v1_relat_1(k2_scmfsa8b(X1,X2,X3))\|~epred1_1(X5)\|~r5_scmfsa7b(X3,k1_scmfsa_m(X4),X5)\|~r6_scmfsa7b(X3,k1_scmfsa_m(X4),X5)\|~r1_xxreal_0(k1_funct_1(X4,X1),k6_numbers)\|~m1_subset_1(X1,u1_struct_0(k1_scmfsa_2))\|~v1_ami_2(X1)\|~v1_afinsq_1(X3)\|~v1_afinsq_1(X2)\|~v1_finset_1(X3)\|~v1_finset_1(X2)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v5_relat_1(X3,u1_compos_1(k1_scmfsa_2))\|~v5_relat_1(X2,u1_compos_1(k1_scmfsa_2))\|~v4_relat_1(X3,k5_numbers)\|~v4_relat_1(X2,k5_numbers)\|~v1_relat_1(X3)\|~v1_relat_1(X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_36, c_0_37])])). cnf(c_0_50, plain, (v1_xboole_0(X3)\|v1_xboole_0(X2)\|v1_relat_1(k2_scmfsa8b(X1,X2,X3))\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v1_finset_1(X3)\|~v1_finset_1(X2)\|~v1_afinsq_1(X3)\|~v1_afinsq_1(X2)\|~v1_ami_2(X1)\|~v4_relat_1(X3,k5_numbers)\|~v4_relat_1(X2,k5_numbers)\|~v5_relat_1(X3,u1_compos_1(k1_scmfsa_2))\|~v5_relat_1(X2,u1_compos_1(k1_scmfsa_2))\|~m1_subset_1(X1,u1_struct_0(k1_scmfsa_2))), inference(evalgc,[status(thm)],[c_0_38])). cnf(c_0_51, plain, (v1_xboole_0(X3)\|v1_xboole_0(X2)\|v4_relat_1(k2_scmfsa8b(X1,X2,X3),k5_numbers)\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v1_finset_1(X3)\|~v1_finset_1(X2)\|~v1_afinsq_1(X3)\|~v1_afinsq_1(X2)\|~v1_ami_2(X1)\|~v4_relat_1(X3,k5_numbers)\|~v4_relat_1(X2,k5_numbers)\|~v5_relat_1(X3,u1_compos_1(k1_scmfsa_2))\|~v5_relat_1(X2,u1_compos_1(k1_scmfsa_2))\|~m1_subset_1(X1,u1_struct_0(k1_scmfsa_2))), inference(evalgc,[status(thm)],[c_0_39])). cnf(c_0_52, plain, (v1_xboole_0(X3)\|v1_xboole_0(X2)\|v5_relat_1(k2_scmfsa8b(X1,X2,X3),u1_compos_1(k1_scmfsa_2))\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v1_finset_1(X3)\|~v1_finset_1(X2)\|~v1_afinsq_1(X3)\|~v1_afinsq_1(X2)\|~v1_ami_2(X1)\|~v4_relat_1(X3,k5_numbers)\|~v4_relat_1(X2,k5_numbers)\|~v5_relat_1(X3,u1_compos_1(k1_scmfsa_2))\|~v5_relat_1(X2,u1_compos_1(k1_scmfsa_2))\|~m1_subset_1(X1,u1_struct_0(k1_scmfsa_2))), inference(evalgc,[status(thm)],[c_0_40])). cnf(c_0_53, plain, (v1_xboole_0(X3)\|v1_xboole_0(X2)\|v1_funct_1(k2_scmfsa8b(X1,X2,X3))\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v1_finset_1(X3)\|~v1_finset_1(X2)\|~v1_afinsq_1(X3)\|~v1_afinsq_1(X2)\|~v1_ami_2(X1)\|~v4_relat_1(X3,k5_numbers)\|~v4_relat_1(X2,k5_numbers)\|~v5_relat_1(X3,u1_compos_1(k1_scmfsa_2))\|~v5_relat_1(X2,u1_compos_1(k1_scmfsa_2))\|~m1_subset_1(X1,u1_struct_0(k1_scmfsa_2))), inference(evalgc,[status(thm)],[c_0_41])). cnf(c_0_54, plain, (v1_xboole_0(X3)\|v1_xboole_0(X2)\|v1_finset_1(k2_scmfsa8b(X1,X2,X3))\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v1_finset_1(X3)\|~v1_finset_1(X2)\|~v1_afinsq_1(X3)\|~v1_afinsq_1(X2)\|~v1_ami_2(X1)\|~v4_relat_1(X3,k5_numbers)\|~v4_relat_1(X2,k5_numbers)\|~v5_relat_1(X3,u1_compos_1(k1_scmfsa_2))\|~v5_relat_1(X2,u1_compos_1(k1_scmfsa_2))\|~m1_subset_1(X1,u1_struct_0(k1_scmfsa_2))), inference(evalgc,[status(thm)],[c_0_42])). cnf(c_0_55, plain, (v1_xboole_0(X3)\|v1_xboole_0(X2)\|v1_afinsq_1(k2_scmfsa8b(X1,X2,X3))\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v1_finset_1(X3)\|~v1_finset_1(X2)\|~v1_afinsq_1(X3)\|~v1_afinsq_1(X2)\|~v1_ami_2(X1)\|~v4_relat_1(X3,k5_numbers)\|~v4_relat_1(X2,k5_numbers)\|~v5_relat_1(X3,u1_compos_1(k1_scmfsa_2))\|~v5_relat_1(X2,u1_compos_1(k1_scmfsa_2))\|~m1_subset_1(X1,u1_struct_0(k1_scmfsa_2))), inference(evalgc,[status(thm)],[c_0_43])). cnf(c_0_56, plain, (epred1_1(X1)\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v4_relat_1(X1,k5_numbers)\|~v1_partfun1(X1,k5_numbers)\|~v5_relat_1(X1,u1_compos_1(k1_scmfsa_2))), inference(evalgc,[status(thm)],[c_0_44])). cnf(c_0_57, plain, (v1_xboole_0(X3)\|v1_xboole_0(X2)\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v1_finset_1(X3)\|~v1_finset_1(X2)\|~v1_afinsq_1(X3)\|~v1_afinsq_1(X2)\|~v1_ami_2(X1)\|~v4_relat_1(X3,k5_numbers)\|~v4_relat_1(X2,k5_numbers)\|~v1_xboole_0(k2_scmfsa8b(X1,X2,X3))\|~v5_relat_1(X3,u1_compos_1(k1_scmfsa_2))\|~v5_relat_1(X2,u1_compos_1(k1_scmfsa_2))\|~m1_subset_1(X1,u1_struct_0(k1_scmfsa_2))), inference(evalgc,[status(thm)],[c_0_45])). cnf(c_0_58, negated_conjecture, (r1_xxreal_0(k1_funct_1(esk2_0,esk5_0),k6_numbers)), inference(split_conjunct,[status(thm)],[c_0_46])). cnf(c_0_59, negated_conjecture, (m1_subset_1(esk5_0,u1_struct_0(k1_scmfsa_2))), inference(split_conjunct,[status(thm)],[c_0_46])). cnf(c_0_60, negated_conjecture, (v1_ami_2(esk5_0)), inference(split_conjunct,[status(thm)],[c_0_46])). cnf(c_0_61, negated_conjecture, (v5_funct_1(esk2_0,k2_memstr_0(np__3,k1_scmfsa_2))), inference(split_conjunct,[status(thm)],[c_0_46])). cnf(c_0_62, negated_conjecture, (v1_partfun1(esk2_0,u1_struct_0(k1_scmfsa_2))), inference(split_conjunct,[status(thm)],[c_0_46])). cnf(c_0_63, negated_conjecture, (v1_funct_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_46])). cnf(c_0_64, negated_conjecture, (v4_relat_1(esk2_0,u1_struct_0(k1_scmfsa_2))), inference(split_conjunct,[status(thm)],[c_0_46])). cnf(c_0_65, negated_conjecture, (v1_relat_1(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_46])). cnf(c_0_66, negated_conjecture, (~v1_scmfsa_m(esk5_0)), inference(split_conjunct,[status(thm)],[c_0_46])). cnf(c_0_67, plain, (v1_xboole_0(X1)\|r1_scm_halt(X1,X2,X3)\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_relat_1(X1)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v1_funct_1(X1)\|~v1_finset_1(X1)\|~v1_afinsq_1(X1)\|~v4_relat_1(X3,k5_numbers)\|~v4_relat_1(X1,k5_numbers)\|~v1_partfun1(X3,k5_numbers)\|~v4_relat_1(X2,u1_struct_0(k1_scmfsa_2))\|~v5_relat_1(X3,u1_compos_1(k1_scmfsa_2))\|~v5_relat_1(X1,u1_compos_1(k1_scmfsa_2))\|~v1_partfun1(X2,u1_struct_0(k1_scmfsa_2))\|~r5_scmfsa7b(X1,k1_scmfsa_m(X2),X3)\|~v5_funct_1(X2,k2_memstr_0(np__3,k1_scmfsa_2))), inference(evalgc,[status(thm)],[c_0_47])). cnf(c_0_68, plain, (r5_scmfsa7b(k2_scmfsa8b(X1,X2,X3),k1_scmfsa_m(X4),X5)\|v1_scmfsa_m(X1)\|v1_xboole_0(X3)\|v1_xboole_0(X2)\|~epred1_1(X5)\|~r5_scmfsa7b(X3,k1_scmfsa_m(X4),X5)\|~r6_scmfsa7b(X3,k1_scmfsa_m(X4),X5)\|~r1_xxreal_0(k1_funct_1(X4,X1),k6_numbers)\|~m1_subset_1(X1,u1_struct_0(k1_scmfsa_2))\|~v1_ami_2(X1)\|~v1_afinsq_1(X3)\|~v1_afinsq_1(X2)\|~v1_finset_1(X3)\|~v1_finset_1(X2)\|~v5_funct_1(X4,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X4,u1_struct_0(k1_scmfsa_2))\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v1_funct_1(X4)\|~v5_relat_1(X3,u1_compos_1(k1_scmfsa_2))\|~v5_relat_1(X2,u1_compos_1(k1_scmfsa_2))\|~v4_relat_1(X4,u1_struct_0(k1_scmfsa_2))\|~v4_relat_1(X3,k5_numbers)\|~v4_relat_1(X2,k5_numbers)\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_relat_1(X4)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_48, c_0_26]), c_0_27]), c_0_28]), c_0_29]), c_0_30])). cnf(c_0_69, negated_conjecture, (~r1_scm_halt(k2_scmfsa8b(esk5_0,esk3_0,esk4_0),esk2_0,esk1_0)\|~r2_scm_halt(k2_scmfsa8b(esk5_0,esk3_0,esk4_0),esk2_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_46])). cnf(c_0_70, plain, (r2_scm_halt(k2_scmfsa8b(X1,X2,X3),X4,X5)\|v1_scmfsa_m(X1)\|v1_xboole_0(X2)\|v1_xboole_0(X3)\|~r5_scmfsa7b(X3,k1_scmfsa_m(X4),X5)\|~r6_scmfsa7b(X3,k1_scmfsa_m(X4),X5)\|~r1_xxreal_0(k1_funct_1(X4,X1),k6_numbers)\|~m1_subset_1(X1,u1_struct_0(k1_scmfsa_2))\|~v1_ami_2(X1)\|~v1_afinsq_1(X3)\|~v1_afinsq_1(X2)\|~v1_finset_1(X3)\|~v1_finset_1(X2)\|~v5_funct_1(X4,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X4,u1_struct_0(k1_scmfsa_2))\|~v1_partfun1(X5,k5_numbers)\|~v1_funct_1(X5)\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v5_relat_1(X5,u1_compos_1(k1_scmfsa_2))\|~v5_relat_1(X3,u1_compos_1(k1_scmfsa_2))\|~v5_relat_1(X2,u1_compos_1(k1_scmfsa_2))\|~v4_relat_1(X4,u1_struct_0(k1_scmfsa_2))\|~v4_relat_1(X5,k5_numbers)\|~v4_relat_1(X3,k5_numbers)\|~v4_relat_1(X2,k5_numbers)\|~v1_relat_1(X5)\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~v1_relat_1(X2)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_49, c_0_50]), c_0_51]), c_0_52]), c_0_53]), c_0_54]), c_0_55]), c_0_56]), c_0_57])). cnf(c_0_71, negated_conjecture, (r1_xxreal_0(k1_funct_1(esk2_0,esk5_0),k6_numbers)), inference(evalgc,[status(thm)],[c_0_58])). cnf(c_0_72, negated_conjecture, (m1_subset_1(esk5_0,u1_struct_0(k1_scmfsa_2))), inference(evalgc,[status(thm)],[c_0_59])). cnf(c_0_73, negated_conjecture, (v1_ami_2(esk5_0)), inference(evalgc,[status(thm)],[c_0_60])). cnf(c_0_74, negated_conjecture, (v5_funct_1(esk2_0,k2_memstr_0(np__3,k1_scmfsa_2))), inference(evalgc,[status(thm)],[c_0_61])). cnf(c_0_75, negated_conjecture, (v1_partfun1(esk2_0,u1_struct_0(k1_scmfsa_2))), inference(evalgc,[status(thm)],[c_0_62])). cnf(c_0_76, negated_conjecture, (v1_funct_1(esk2_0)), inference(evalgc,[status(thm)],[c_0_63])). cnf(c_0_77, negated_conjecture, (v4_relat_1(esk2_0,u1_struct_0(k1_scmfsa_2))), inference(evalgc,[status(thm)],[c_0_64])). cnf(c_0_78, negated_conjecture, (v1_relat_1(esk2_0)), inference(evalgc,[status(thm)],[c_0_65])). cnf(c_0_79, negated_conjecture, (~v1_scmfsa_m(esk5_0)), inference(evalgc,[status(thm)],[c_0_66])). cnf(c_0_80, negated_conjecture, (v1_afinsq_1(esk4_0)), inference(split_conjunct,[status(thm)],[c_0_46])). cnf(c_0_81, negated_conjecture, (v1_afinsq_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_46])). cnf(c_0_82, negated_conjecture, (v1_finset_1(esk4_0)), inference(split_conjunct,[status(thm)],[c_0_46])). cnf(c_0_83, negated_conjecture, (v1_finset_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_46])). cnf(c_0_84, negated_conjecture, (v1_partfun1(esk1_0,k5_numbers)), inference(split_conjunct,[status(thm)],[c_0_46])). cnf(c_0_85, negated_conjecture, (v1_funct_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_46])). cnf(c_0_86, negated_conjecture, (v1_funct_1(esk4_0)), inference(split_conjunct,[status(thm)],[c_0_46])). cnf(c_0_87, negated_conjecture, (v1_funct_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_46])). cnf(c_0_88, negated_conjecture, (v5_relat_1(esk1_0,u1_compos_1(k1_scmfsa_2))), inference(split_conjunct,[status(thm)],[c_0_46])). cnf(c_0_89, negated_conjecture, (v5_relat_1(esk4_0,u1_compos_1(k1_scmfsa_2))), inference(split_conjunct,[status(thm)],[c_0_46])). cnf(c_0_90, negated_conjecture, (v5_relat_1(esk3_0,u1_compos_1(k1_scmfsa_2))), inference(split_conjunct,[status(thm)],[c_0_46])). cnf(c_0_91, negated_conjecture, (v4_relat_1(esk1_0,k5_numbers)), inference(split_conjunct,[status(thm)],[c_0_46])). cnf(c_0_92, negated_conjecture, (v4_relat_1(esk4_0,k5_numbers)), inference(split_conjunct,[status(thm)],[c_0_46])). cnf(c_0_93, negated_conjecture, (v4_relat_1(esk3_0,k5_numbers)), inference(split_conjunct,[status(thm)],[c_0_46])). cnf(c_0_94, negated_conjecture, (v1_relat_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_46])). cnf(c_0_95, negated_conjecture, (v1_relat_1(esk4_0)), inference(split_conjunct,[status(thm)],[c_0_46])). cnf(c_0_96, negated_conjecture, (v1_relat_1(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_46])). cnf(c_0_97, negated_conjecture, (~v1_xboole_0(esk4_0)), inference(split_conjunct,[status(thm)],[c_0_46])). cnf(c_0_98, negated_conjecture, (~v1_xboole_0(esk3_0)), inference(split_conjunct,[status(thm)],[c_0_46])). cnf(c_0_99, plain, (r1_scm_halt(k2_scmfsa8b(X1,X2,X3),X4,X5)\|v1_xboole_0(k2_scmfsa8b(X1,X2,X3))\|v1_scmfsa_m(X1)\|v1_xboole_0(X3)\|v1_xboole_0(X2)\|~v1_afinsq_1(k2_scmfsa8b(X1,X2,X3))\|~v1_finset_1(k2_scmfsa8b(X1,X2,X3))\|~v5_funct_1(X4,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X4,u1_struct_0(k1_scmfsa_2))\|~v1_partfun1(X5,k5_numbers)\|~v1_funct_1(X5)\|~v1_funct_1(X4)\|~v1_funct_1(k2_scmfsa8b(X1,X2,X3))\|~v5_relat_1(X5,u1_compos_1(k1_scmfsa_2))\|~v5_relat_1(k2_scmfsa8b(X1,X2,X3),u1_compos_1(k1_scmfsa_2))\|~v4_relat_1(X4,u1_struct_0(k1_scmfsa_2))\|~v4_relat_1(X5,k5_numbers)\|~v4_relat_1(k2_scmfsa8b(X1,X2,X3),k5_numbers)\|~v1_relat_1(X5)\|~v1_relat_1(X4)\|~v1_relat_1(k2_scmfsa8b(X1,X2,X3))\|~epred1_1(X5)\|~r5_scmfsa7b(X3,k1_scmfsa_m(X4),X5)\|~r6_scmfsa7b(X3,k1_scmfsa_m(X4),X5)\|~r1_xxreal_0(k1_funct_1(X4,X1),k6_numbers)\|~m1_subset_1(X1,u1_struct_0(k1_scmfsa_2))\|~v1_ami_2(X1)\|~v1_afinsq_1(X3)\|~v1_afinsq_1(X2)\|~v1_finset_1(X3)\|~v1_finset_1(X2)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v5_relat_1(X3,u1_compos_1(k1_scmfsa_2))\|~v5_relat_1(X2,u1_compos_1(k1_scmfsa_2))\|~v4_relat_1(X3,k5_numbers)\|~v4_relat_1(X2,k5_numbers)\|~v1_relat_1(X3)\|~v1_relat_1(X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_67, c_0_68])])). cnf(c_0_100, negated_conjecture, (~r1_scm_halt(k2_scmfsa8b(esk5_0,esk3_0,esk4_0),esk2_0,esk1_0)\|~r2_scm_halt(k2_scmfsa8b(esk5_0,esk3_0,esk4_0),esk2_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_69])). cnf(c_0_101, negated_conjecture, (r2_scm_halt(k2_scmfsa8b(esk5_0,X1,X2),esk2_0,X3)\|v1_xboole_0(X1)\|v1_xboole_0(X2)\|~r5_scmfsa7b(X2,k1_scmfsa_m(esk2_0),X3)\|~r6_scmfsa7b(X2,k1_scmfsa_m(esk2_0),X3)\|~v1_afinsq_1(X2)\|~v1_afinsq_1(X1)\|~v1_finset_1(X2)\|~v1_finset_1(X1)\|~v1_partfun1(X3,k5_numbers)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v1_funct_1(X1)\|~v5_relat_1(X3,u1_compos_1(k1_scmfsa_2))\|~v5_relat_1(X2,u1_compos_1(k1_scmfsa_2))\|~v5_relat_1(X1,u1_compos_1(k1_scmfsa_2))\|~v4_relat_1(X3,k5_numbers)\|~v4_relat_1(X2,k5_numbers)\|~v4_relat_1(X1,k5_numbers)\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_relat_1(X1)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70, c_0_71]), c_0_72]), c_0_73]), c_0_74]), c_0_75]), c_0_76]), c_0_77]), c_0_78])]), c_0_79])])). cnf(c_0_102, negated_conjecture, (v1_afinsq_1(esk4_0)), inference(evalgc,[status(thm)],[c_0_80])). cnf(c_0_103, negated_conjecture, (v1_afinsq_1(esk3_0)), inference(evalgc,[status(thm)],[c_0_81])). cnf(c_0_104, negated_conjecture, (v1_finset_1(esk4_0)), inference(evalgc,[status(thm)],[c_0_82])). cnf(c_0_105, negated_conjecture, (v1_finset_1(esk3_0)), inference(evalgc,[status(thm)],[c_0_83])). cnf(c_0_106, negated_conjecture, (v1_partfun1(esk1_0,k5_numbers)), inference(evalgc,[status(thm)],[c_0_84])). cnf(c_0_107, negated_conjecture, (v1_funct_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_85])). cnf(c_0_108, negated_conjecture, (v1_funct_1(esk4_0)), inference(evalgc,[status(thm)],[c_0_86])). cnf(c_0_109, negated_conjecture, (v1_funct_1(esk3_0)), inference(evalgc,[status(thm)],[c_0_87])). cnf(c_0_110, negated_conjecture, (v5_relat_1(esk1_0,u1_compos_1(k1_scmfsa_2))), inference(evalgc,[status(thm)],[c_0_88])). cnf(c_0_111, negated_conjecture, (v5_relat_1(esk4_0,u1_compos_1(k1_scmfsa_2))), inference(evalgc,[status(thm)],[c_0_89])). cnf(c_0_112, negated_conjecture, (v5_relat_1(esk3_0,u1_compos_1(k1_scmfsa_2))), inference(evalgc,[status(thm)],[c_0_90])). cnf(c_0_113, negated_conjecture, (v4_relat_1(esk1_0,k5_numbers)), inference(evalgc,[status(thm)],[c_0_91])). cnf(c_0_114, negated_conjecture, (v4_relat_1(esk4_0,k5_numbers)), inference(evalgc,[status(thm)],[c_0_92])). cnf(c_0_115, negated_conjecture, (v4_relat_1(esk3_0,k5_numbers)), inference(evalgc,[status(thm)],[c_0_93])). cnf(c_0_116, negated_conjecture, (v1_relat_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_94])). cnf(c_0_117, negated_conjecture, (v1_relat_1(esk4_0)), inference(evalgc,[status(thm)],[c_0_95])). cnf(c_0_118, negated_conjecture, (v1_relat_1(esk3_0)), inference(evalgc,[status(thm)],[c_0_96])). cnf(c_0_119, negated_conjecture, (~v1_xboole_0(esk4_0)), inference(evalgc,[status(thm)],[c_0_97])). cnf(c_0_120, negated_conjecture, (~v1_xboole_0(esk3_0)), inference(evalgc,[status(thm)],[c_0_98])). cnf(c_0_121, plain, (r1_scm_halt(k2_scmfsa8b(X1,X2,X3),X4,X5)\|v1_scmfsa_m(X1)\|v1_xboole_0(X2)\|v1_xboole_0(X3)\|~r5_scmfsa7b(X3,k1_scmfsa_m(X4),X5)\|~r6_scmfsa7b(X3,k1_scmfsa_m(X4),X5)\|~r1_xxreal_0(k1_funct_1(X4,X1),k6_numbers)\|~m1_subset_1(X1,u1_struct_0(k1_scmfsa_2))\|~v1_ami_2(X1)\|~v1_afinsq_1(X3)\|~v1_afinsq_1(X2)\|~v1_finset_1(X3)\|~v1_finset_1(X2)\|~v5_funct_1(X4,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X4,u1_struct_0(k1_scmfsa_2))\|~v1_partfun1(X5,k5_numbers)\|~v1_funct_1(X5)\|~v1_funct_1(X4)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v5_relat_1(X5,u1_compos_1(k1_scmfsa_2))\|~v5_relat_1(X3,u1_compos_1(k1_scmfsa_2))\|~v5_relat_1(X2,u1_compos_1(k1_scmfsa_2))\|~v4_relat_1(X4,u1_struct_0(k1_scmfsa_2))\|~v4_relat_1(X5,k5_numbers)\|~v4_relat_1(X3,k5_numbers)\|~v4_relat_1(X2,k5_numbers)\|~v1_relat_1(X5)\|~v1_relat_1(X4)\|~v1_relat_1(X3)\|~v1_relat_1(X2)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_99, c_0_50]), c_0_51]), c_0_52]), c_0_53]), c_0_54]), c_0_55]), c_0_56]), c_0_57])). cnf(c_0_122, negated_conjecture, (~r1_scm_halt(k2_scmfsa8b(esk5_0,esk3_0,esk4_0),esk2_0,esk1_0)\|~r5_scmfsa7b(esk4_0,k1_scmfsa_m(esk2_0),esk1_0)\|~r6_scmfsa7b(esk4_0,k1_scmfsa_m(esk2_0),esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100, c_0_101]), c_0_102]), c_0_103]), c_0_104]), c_0_105]), c_0_106]), c_0_107]), c_0_108]), c_0_109]), c_0_110]), c_0_111]), c_0_112]), c_0_113]), c_0_114]), c_0_115]), c_0_116]), c_0_117]), c_0_118])]), c_0_119]), c_0_120])])). cnf(c_0_123, negated_conjecture, (r1_scm_halt(k2_scmfsa8b(esk5_0,X1,X2),esk2_0,X3)\|v1_xboole_0(X1)\|v1_xboole_0(X2)\|~r5_scmfsa7b(X2,k1_scmfsa_m(esk2_0),X3)\|~r6_scmfsa7b(X2,k1_scmfsa_m(esk2_0),X3)\|~v1_afinsq_1(X2)\|~v1_afinsq_1(X1)\|~v1_finset_1(X2)\|~v1_finset_1(X1)\|~v1_partfun1(X3,k5_numbers)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v1_funct_1(X1)\|~v5_relat_1(X3,u1_compos_1(k1_scmfsa_2))\|~v5_relat_1(X2,u1_compos_1(k1_scmfsa_2))\|~v5_relat_1(X1,u1_compos_1(k1_scmfsa_2))\|~v4_relat_1(X3,k5_numbers)\|~v4_relat_1(X2,k5_numbers)\|~v4_relat_1(X1,k5_numbers)\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_relat_1(X1)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121, c_0_71]), c_0_72]), c_0_73]), c_0_74]), c_0_75]), c_0_76]), c_0_77]), c_0_78])]), c_0_79])])). cnf(c_0_124, plain, (r6_scmfsa7b(X1,k1_scmfsa_m(X2),X3)\|v1_xboole_0(X1)\|~r2_scm_halt(X1,X2,X3)\|~v1_relat_1(X1)\|~v4_relat_1(X1,k5_numbers)\|~v5_relat_1(X1,u1_compos_1(k1_scmfsa_2))\|~v1_funct_1(X1)\|~v1_finset_1(X1)\|~v1_afinsq_1(X1)\|~v1_relat_1(X2)\|~v4_relat_1(X2,u1_struct_0(k1_scmfsa_2))\|~v1_funct_1(X2)\|~v5_funct_1(X2,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X2,u1_struct_0(k1_scmfsa_2))\|~v1_relat_1(X3)\|~v4_relat_1(X3,k5_numbers)\|~v5_relat_1(X3,u1_compos_1(k1_scmfsa_2))\|~v1_funct_1(X3)\|~v1_partfun1(X3,k5_numbers)), inference(split_conjunct,[status(thm)],[c_0_14])). cnf(c_0_125, negated_conjecture, (r2_scm_halt(esk4_0,esk2_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_46])). cnf(c_0_126, negated_conjecture, (~r5_scmfsa7b(esk4_0,k1_scmfsa_m(esk2_0),esk1_0)\|~r6_scmfsa7b(esk4_0,k1_scmfsa_m(esk2_0),esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122, c_0_123]), c_0_102]), c_0_103]), c_0_104]), c_0_105]), c_0_106]), c_0_107]), c_0_108]), c_0_109]), c_0_110]), c_0_111]), c_0_112]), c_0_113]), c_0_114]), c_0_115]), c_0_116]), c_0_117]), c_0_118])]), c_0_119]), c_0_120])])). cnf(c_0_127, plain, (v1_xboole_0(X1)\|r6_scmfsa7b(X1,k1_scmfsa_m(X2),X3)\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_relat_1(X1)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v1_funct_1(X1)\|~v1_finset_1(X1)\|~v1_afinsq_1(X1)\|~v4_relat_1(X3,k5_numbers)\|~v4_relat_1(X1,k5_numbers)\|~v1_partfun1(X3,k5_numbers)\|~r2_scm_halt(X1,X2,X3)\|~v4_relat_1(X2,u1_struct_0(k1_scmfsa_2))\|~v5_relat_1(X3,u1_compos_1(k1_scmfsa_2))\|~v5_relat_1(X1,u1_compos_1(k1_scmfsa_2))\|~v1_partfun1(X2,u1_struct_0(k1_scmfsa_2))\|~v5_funct_1(X2,k2_memstr_0(np__3,k1_scmfsa_2))), inference(evalgc,[status(thm)],[c_0_124])). cnf(c_0_128, negated_conjecture, (r2_scm_halt(esk4_0,esk2_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_125])). cnf(c_0_129, plain, (r5_scmfsa7b(X1,k1_scmfsa_m(X2),X3)\|v1_xboole_0(X1)\|~r1_scm_halt(X1,X2,X3)\|~v1_relat_1(X1)\|~v4_relat_1(X1,k5_numbers)\|~v5_relat_1(X1,u1_compos_1(k1_scmfsa_2))\|~v1_funct_1(X1)\|~v1_finset_1(X1)\|~v1_afinsq_1(X1)\|~v1_relat_1(X2)\|~v4_relat_1(X2,u1_struct_0(k1_scmfsa_2))\|~v1_funct_1(X2)\|~v5_funct_1(X2,k2_memstr_0(np__3,k1_scmfsa_2))\|~v1_partfun1(X2,u1_struct_0(k1_scmfsa_2))\|~v1_relat_1(X3)\|~v4_relat_1(X3,k5_numbers)\|~v5_relat_1(X3,u1_compos_1(k1_scmfsa_2))\|~v1_funct_1(X3)\|~v1_partfun1(X3,k5_numbers)), inference(split_conjunct,[status(thm)],[c_0_34])). cnf(c_0_130, negated_conjecture, (r1_scm_halt(esk4_0,esk2_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_46])). cnf(c_0_131, negated_conjecture, (~r5_scmfsa7b(esk4_0,k1_scmfsa_m(esk2_0),esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126, c_0_127]), c_0_128]), c_0_102]), c_0_104]), c_0_74]), c_0_75]), c_0_106]), c_0_107]), c_0_76]), c_0_108]), c_0_110]), c_0_111]), c_0_77]), c_0_113]), c_0_114]), c_0_116]), c_0_78]), c_0_117])]), c_0_119])])). cnf(c_0_132, plain, (v1_xboole_0(X1)\|r5_scmfsa7b(X1,k1_scmfsa_m(X2),X3)\|~v1_relat_1(X3)\|~v1_relat_1(X2)\|~v1_relat_1(X1)\|~v1_funct_1(X3)\|~v1_funct_1(X2)\|~v1_funct_1(X1)\|~v1_finset_1(X1)\|~v1_afinsq_1(X1)\|~v4_relat_1(X3,k5_numbers)\|~v4_relat_1(X1,k5_numbers)\|~v1_partfun1(X3,k5_numbers)\|~r1_scm_halt(X1,X2,X3)\|~v4_relat_1(X2,u1_struct_0(k1_scmfsa_2))\|~v5_relat_1(X3,u1_compos_1(k1_scmfsa_2))\|~v5_relat_1(X1,u1_compos_1(k1_scmfsa_2))\|~v1_partfun1(X2,u1_struct_0(k1_scmfsa_2))\|~v5_funct_1(X2,k2_memstr_0(np__3,k1_scmfsa_2))), inference(evalgc,[status(thm)],[c_0_129])). cnf(c_0_133, negated_conjecture, (r1_scm_halt(esk4_0,esk2_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_130])). cnf(c_0_134, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131, c_0_132]), c_0_133]), c_0_102]), c_0_104]), c_0_74]), c_0_75]), c_0_106]), c_0_107]), c_0_76]), c_0_108]), c_0_110]), c_0_111]), c_0_77]), c_0_113]), c_0_114]), c_0_116]), c_0_78]), c_0_117])]), c_0_119]), ['proof']). # SZS output end CNFRefutation	reserve m,n for Element of NAT, I for Program of SCM+FSA, s,s1,s2 for State of SCM+FSA, a for Int-Location, f for FinSeq-Location, p,p1,p2 for Instruction-Sequence of SCM+FSA; theorem Th41: for s being State of SCM+FSA, I,J being Program of SCM+FSA, a being read-write Int-Location st s.a <= 0 & J is_closed_onInit s,p & J is_halting_onInit s,p holds if>0(a,I,J) is_closed_onInit s,p & if>0(a,I,J) is_halting_onInit s,p proof let s be State of SCM+FSA; let I,J be Program of SCM+FSA; let a be read-write Int-Location; set Is = Initialized s; assume s.a <= 0; then A1: Is.a <= 0 by SCMFSA_M:37; assume J is_closed_onInit s,p; then A2: J is_closed_on Is,p by Th30; assume J is_halting_onInit s,p; then J is_halting_on Is,p by Th31; then if>0(a,I,J) is_closed_on Is,p & if>0(a,I,J) is_halting_on Is,p by A1,A2, SCMFSA8B:21; hence thesis by Th30,Th31; end;	Convert the following ATP output trace into a readable Mizar proof.
t3_prvect_1	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(d3_binop_1, axiom, ![X1, X2]:((v1_funct_1(X2)&(v1_funct_2(X2,k2_zfmisc_1(X1,X1),X1)&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X1),X1)))))=>(v2_binop_1(X2,X1)<=>![X3]:(m1_subset_1(X3,X1)=>![X4]:(m1_subset_1(X4,X1)=>![X5]:(m1_subset_1(X5,X1)=>k3_binop_1(X1,X2,X3,k3_binop_1(X1,X2,X4,X5))=k3_binop_1(X1,X2,k3_binop_1(X1,X2,X3,X4),X5)))))), file('/scratch/mptp/predsminms1/t3_prvect_1__0', d3_binop_1)). fof(dt_u1_algstr_0, axiom, ![X1]:(l1_algstr_0(X1)=>(v1_funct_1(u1_algstr_0(X1))&(v1_funct_2(u1_algstr_0(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))&m1_subset_1(u1_algstr_0(X1),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))))))), file('/scratch/mptp/predsminms1/t3_prvect_1__0', dt_u1_algstr_0)). fof(redefinition_k3_binop_1, axiom, ![X1, X2, X3, X4]:(((v1_funct_1(X2)&(v1_funct_2(X2,k2_zfmisc_1(X1,X1),X1)&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X1),X1)))))&(m1_subset_1(X3,X1)&m1_subset_1(X4,X1)))=>k3_binop_1(X1,X2,X3,X4)=k1_binop_1(X2,X3,X4)), file('/scratch/mptp/predsminms1/t3_prvect_1__0', redefinition_k3_binop_1)). fof(redefinition_k5_binop_1, axiom, ![X1, X2, X3, X4]:(((v1_funct_1(X2)&(v1_funct_2(X2,k2_zfmisc_1(X1,X1),X1)&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X1),X1)))))&(m1_subset_1(X3,X1)&m1_subset_1(X4,X1)))=>k5_binop_1(X1,X2,X3,X4)=k1_binop_1(X2,X3,X4)), file('/scratch/mptp/predsminms1/t3_prvect_1__0', redefinition_k5_binop_1)). fof(d1_algstr_0, axiom, ![X1]:(l1_algstr_0(X1)=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>k1_algstr_0(X1,X2,X3)=k5_binop_1(u1_struct_0(X1),u1_algstr_0(X1),X2,X3)))), file('/scratch/mptp/predsminms1/t3_prvect_1__0', d1_algstr_0)). fof(d1_finseqop, axiom, ![X1]:(~(v1_xboole_0(X1))=>![X2]:((v1_funct_1(X2)&(v1_funct_2(X2,X1,X1)&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,X1)))))=>![X3]:((v1_funct_1(X3)&(v1_funct_2(X3,k2_zfmisc_1(X1,X1),X1)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X1),X1)))))=>(r1_finseqop(X1,X2,X3)<=>![X4]:(m1_subset_1(X4,X1)=>(k5_binop_1(X1,X3,X4,k3_funct_2(X1,X1,X2,X4))=k4_binop_1(X1,X3)&k5_binop_1(X1,X3,k3_funct_2(X1,X1,X2,X4),X4)=k4_binop_1(X1,X3))))))), file('/scratch/mptp/predsminms1/t3_prvect_1__0', d1_finseqop)). fof(dt_k3_funct_2, axiom, ![X1, X2, X3, X4]:((~(v1_xboole_0(X1))&((v1_funct_1(X3)&(v1_funct_2(X3,X1,X2)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))))&m1_subset_1(X4,X1)))=>m1_subset_1(k3_funct_2(X1,X2,X3,X4),X2)), file('/scratch/mptp/predsminms1/t3_prvect_1__0', dt_k3_funct_2)). fof(d11_algstr_0, axiom, ![X1]:(l2_algstr_0(X1)=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>(v10_algstr_0(X2,X1)<=>?[X3]:(m1_subset_1(X3,u1_struct_0(X1))&k1_algstr_0(X1,X2,X3)=k4_struct_0(X1))))), file('/scratch/mptp/predsminms1/t3_prvect_1__0', d11_algstr_0)). fof(dt_l2_algstr_0, axiom, ![X1]:(l2_algstr_0(X1)=>(l2_struct_0(X1)&l1_algstr_0(X1))), file('/scratch/mptp/predsminms1/t3_prvect_1__0', dt_l2_algstr_0)). fof(t3_prvect_1, conjecture, ![X1]:((~(v2_struct_0(X1))&l2_algstr_0(X1))=>((v1_binop_1(u1_algstr_0(X1),u1_struct_0(X1))&(v2_binop_1(u1_algstr_0(X1),u1_struct_0(X1))&(r3_binop_1(u1_struct_0(X1),k4_struct_0(X1),u1_algstr_0(X1))&r1_finseqop(u1_struct_0(X1),k5_vectsp_1(X1),u1_algstr_0(X1)))))=>(~(v2_struct_0(X1))&(v13_algstr_0(X1)&(v2_rlvect_1(X1)&(v3_rlvect_1(X1)&(v4_rlvect_1(X1)&l2_algstr_0(X1)))))))), file('/scratch/mptp/predsminms1/t3_prvect_1__0', t3_prvect_1)). fof(d8_binop_1, axiom, ![X1, X2]:((v1_funct_1(X2)&(v1_funct_2(X2,k2_zfmisc_1(X1,X1),X1)&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X1),X1)))))=>(?[X3]:(m1_subset_1(X3,X1)&r3_binop_1(X1,X3,X2))=>![X3]:(m1_subset_1(X3,X1)=>(X3=k4_binop_1(X1,X2)<=>r3_binop_1(X1,X3,X2))))), file('/scratch/mptp/predsminms1/t3_prvect_1__0', d8_binop_1)). fof(t3_binop_1, axiom, ![X1, X2]:((v1_funct_1(X2)&(v1_funct_2(X2,k2_zfmisc_1(X1,X1),X1)&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X1),X1)))))=>![X3]:(m1_subset_1(X3,X1)=>(r3_binop_1(X1,X3,X2)<=>![X4]:(m1_subset_1(X4,X1)=>(k3_binop_1(X1,X2,X3,X4)=X4&k3_binop_1(X1,X2,X4,X3)=X4))))), file('/scratch/mptp/predsminms1/t3_prvect_1__0', t3_binop_1)). fof(dt_k5_vectsp_1, axiom, ![X1]:((~(v2_struct_0(X1))&l2_algstr_0(X1))=>(v1_funct_1(k5_vectsp_1(X1))&(v1_funct_2(k5_vectsp_1(X1),u1_struct_0(X1),u1_struct_0(X1))&m1_subset_1(k5_vectsp_1(X1),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1))))))), file('/scratch/mptp/predsminms1/t3_prvect_1__0', dt_k5_vectsp_1)). fof(d2_binop_1, axiom, ![X1, X2]:((v1_funct_1(X2)&(v1_funct_2(X2,k2_zfmisc_1(X1,X1),X1)&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X1),X1)))))=>(v1_binop_1(X2,X1)<=>![X3]:(m1_subset_1(X3,X1)=>![X4]:(m1_subset_1(X4,X1)=>k3_binop_1(X1,X2,X3,X4)=k3_binop_1(X1,X2,X4,X3))))), file('/scratch/mptp/predsminms1/t3_prvect_1__0', d2_binop_1)). fof(dt_k1_algstr_0, axiom, ![X1, X2, X3]:((l1_algstr_0(X1)&(m1_subset_1(X2,u1_struct_0(X1))&m1_subset_1(X3,u1_struct_0(X1))))=>m1_subset_1(k1_algstr_0(X1,X2,X3),u1_struct_0(X1))), file('/scratch/mptp/predsminms1/t3_prvect_1__0', dt_k1_algstr_0)). fof(d4_rlvect_1, axiom, ![X1]:(l2_algstr_0(X1)=>(v4_rlvect_1(X1)<=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>k1_algstr_0(X1,X2,k4_struct_0(X1))=X2))), file('/scratch/mptp/predsminms1/t3_prvect_1__0', d4_rlvect_1)). fof(dt_k4_struct_0, axiom, ![X1]:(l2_struct_0(X1)=>m1_subset_1(k4_struct_0(X1),u1_struct_0(X1))), file('/scratch/mptp/predsminms1/t3_prvect_1__0', dt_k4_struct_0)). fof(d2_rlvect_1, axiom, ![X1]:(l1_algstr_0(X1)=>(v2_rlvect_1(X1)<=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>k1_algstr_0(X1,X2,X3)=k1_algstr_0(X1,X3,X2))))), file('/scratch/mptp/predsminms1/t3_prvect_1__0', d2_rlvect_1)). fof(d16_algstr_0, axiom, ![X1]:(l2_algstr_0(X1)=>(v13_algstr_0(X1)<=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>v10_algstr_0(X2,X1)))), file('/scratch/mptp/predsminms1/t3_prvect_1__0', d16_algstr_0)). fof(fc2_struct_0, axiom, ![X1]:((~(v2_struct_0(X1))&l1_struct_0(X1))=>~(v1_xboole_0(u1_struct_0(X1)))), file('/scratch/mptp/predsminms1/t3_prvect_1__0', fc2_struct_0)). fof(dt_l1_algstr_0, axiom, ![X1]:(l1_algstr_0(X1)=>l1_struct_0(X1)), file('/scratch/mptp/predsminms1/t3_prvect_1__0', dt_l1_algstr_0)). fof(d3_rlvect_1, axiom, ![X1]:(l1_algstr_0(X1)=>(v3_rlvect_1(X1)<=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>![X4]:(m1_subset_1(X4,u1_struct_0(X1))=>k1_algstr_0(X1,k1_algstr_0(X1,X2,X3),X4)=k1_algstr_0(X1,X2,k1_algstr_0(X1,X3,X4))))))), file('/scratch/mptp/predsminms1/t3_prvect_1__0', d3_rlvect_1)). fof(c_0_22, plain, ![X62, X63, X64, X65, X66]:((~v2_binop_1(X63,X62)\|(~m1_subset_1(X64,X62)\|(~m1_subset_1(X65,X62)\|(~m1_subset_1(X66,X62)\|k3_binop_1(X62,X63,X64,k3_binop_1(X62,X63,X65,X66))=k3_binop_1(X62,X63,k3_binop_1(X62,X63,X64,X65),X66))))\|(~v1_funct_1(X63)\|(~v1_funct_2(X63,k2_zfmisc_1(X62,X62),X62)\|~m1_subset_1(X63,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X62,X62),X62))))))&((m1_subset_1(esk12_2(X62,X63),X62)\|v2_binop_1(X63,X62)\|(~v1_funct_1(X63)\|(~v1_funct_2(X63,k2_zfmisc_1(X62,X62),X62)\|~m1_subset_1(X63,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X62,X62),X62))))))&((m1_subset_1(esk13_2(X62,X63),X62)\|v2_binop_1(X63,X62)\|(~v1_funct_1(X63)\|(~v1_funct_2(X63,k2_zfmisc_1(X62,X62),X62)\|~m1_subset_1(X63,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X62,X62),X62))))))&((m1_subset_1(esk14_2(X62,X63),X62)\|v2_binop_1(X63,X62)\|(~v1_funct_1(X63)\|(~v1_funct_2(X63,k2_zfmisc_1(X62,X62),X62)\|~m1_subset_1(X63,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X62,X62),X62))))))&(k3_binop_1(X62,X63,esk12_2(X62,X63),k3_binop_1(X62,X63,esk13_2(X62,X63),esk14_2(X62,X63)))!=k3_binop_1(X62,X63,k3_binop_1(X62,X63,esk12_2(X62,X63),esk13_2(X62,X63)),esk14_2(X62,X63))\|v2_binop_1(X63,X62)\|(~v1_funct_1(X63)\|(~v1_funct_2(X63,k2_zfmisc_1(X62,X62),X62)\|~m1_subset_1(X63,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X62,X62),X62)))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_binop_1])])])])])). fof(c_0_23, plain, ![X38]:((v1_funct_1(u1_algstr_0(X38))\|~l1_algstr_0(X38))&((v1_funct_2(u1_algstr_0(X38),k2_zfmisc_1(u1_struct_0(X38),u1_struct_0(X38)),u1_struct_0(X38))\|~l1_algstr_0(X38))&(m1_subset_1(u1_algstr_0(X38),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(X38),u1_struct_0(X38)),u1_struct_0(X38))))\|~l1_algstr_0(X38)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_u1_algstr_0])])])). fof(c_0_24, plain, ![X52, X53, X54, X55]:(~v1_funct_1(X53)\|(~v1_funct_2(X53,k2_zfmisc_1(X52,X52),X52)\|~m1_subset_1(X53,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X52,X52),X52))))\|(~m1_subset_1(X54,X52)\|~m1_subset_1(X55,X52))\|k3_binop_1(X52,X53,X54,X55)=k1_binop_1(X53,X54,X55)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k3_binop_1])])). fof(c_0_25, plain, ![X48, X49, X50, X51]:(~v1_funct_1(X49)\|(~v1_funct_2(X49,k2_zfmisc_1(X48,X48),X48)\|~m1_subset_1(X49,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X48,X48),X48))))\|(~m1_subset_1(X50,X48)\|~m1_subset_1(X51,X48))\|k5_binop_1(X48,X49,X50,X51)=k1_binop_1(X49,X50,X51)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k5_binop_1])])). cnf(c_0_26, plain, (k3_binop_1(X2,X1,X3,k3_binop_1(X2,X1,X4,X5))=k3_binop_1(X2,X1,k3_binop_1(X2,X1,X3,X4),X5)\|~v2_binop_1(X1,X2)\|~m1_subset_1(X3,X2)\|~m1_subset_1(X4,X2)\|~m1_subset_1(X5,X2)\|~v1_funct_1(X1)\|~v1_funct_2(X1,k2_zfmisc_1(X2,X2),X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X2,X2),X2)))), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_27, plain, (m1_subset_1(u1_algstr_0(X1),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))))\|~l1_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_23])). cnf(c_0_28, plain, (k3_binop_1(X2,X1,X3,X4)=k1_binop_1(X1,X3,X4)\|~v1_funct_1(X1)\|~v1_funct_2(X1,k2_zfmisc_1(X2,X2),X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X2,X2),X2)))\|~m1_subset_1(X3,X2)\|~m1_subset_1(X4,X2)), inference(split_conjunct,[status(thm)],[c_0_24])). cnf(c_0_29, plain, (k5_binop_1(X2,X1,X3,X4)=k1_binop_1(X1,X3,X4)\|~v1_funct_1(X1)\|~v1_funct_2(X1,k2_zfmisc_1(X2,X2),X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X2,X2),X2)))\|~m1_subset_1(X3,X2)\|~m1_subset_1(X4,X2)), inference(split_conjunct,[status(thm)],[c_0_25])). fof(c_0_30, plain, ![X11, X12, X13]:(~l1_algstr_0(X11)\|(~m1_subset_1(X12,u1_struct_0(X11))\|(~m1_subset_1(X13,u1_struct_0(X11))\|k1_algstr_0(X11,X12,X13)=k5_binop_1(u1_struct_0(X11),u1_algstr_0(X11),X12,X13)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_algstr_0])])])). fof(c_0_31, plain, ![X43, X44, X45, X46]:(((k5_binop_1(X43,X45,X46,k3_funct_2(X43,X43,X44,X46))=k4_binop_1(X43,X45)\|~m1_subset_1(X46,X43)\|~r1_finseqop(X43,X44,X45)\|(~v1_funct_1(X45)\|(~v1_funct_2(X45,k2_zfmisc_1(X43,X43),X43)\|~m1_subset_1(X45,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X43,X43),X43)))))\|(~v1_funct_1(X44)\|(~v1_funct_2(X44,X43,X43)\|~m1_subset_1(X44,k1_zfmisc_1(k2_zfmisc_1(X43,X43)))))\|v1_xboole_0(X43))&(k5_binop_1(X43,X45,k3_funct_2(X43,X43,X44,X46),X46)=k4_binop_1(X43,X45)\|~m1_subset_1(X46,X43)\|~r1_finseqop(X43,X44,X45)\|(~v1_funct_1(X45)\|(~v1_funct_2(X45,k2_zfmisc_1(X43,X43),X43)\|~m1_subset_1(X45,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X43,X43),X43)))))\|(~v1_funct_1(X44)\|(~v1_funct_2(X44,X43,X43)\|~m1_subset_1(X44,k1_zfmisc_1(k2_zfmisc_1(X43,X43)))))\|v1_xboole_0(X43)))&((m1_subset_1(esk9_3(X43,X44,X45),X43)\|r1_finseqop(X43,X44,X45)\|(~v1_funct_1(X45)\|(~v1_funct_2(X45,k2_zfmisc_1(X43,X43),X43)\|~m1_subset_1(X45,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X43,X43),X43)))))\|(~v1_funct_1(X44)\|(~v1_funct_2(X44,X43,X43)\|~m1_subset_1(X44,k1_zfmisc_1(k2_zfmisc_1(X43,X43)))))\|v1_xboole_0(X43))&(k5_binop_1(X43,X45,esk9_3(X43,X44,X45),k3_funct_2(X43,X43,X44,esk9_3(X43,X44,X45)))!=k4_binop_1(X43,X45)\|k5_binop_1(X43,X45,k3_funct_2(X43,X43,X44,esk9_3(X43,X44,X45)),esk9_3(X43,X44,X45))!=k4_binop_1(X43,X45)\|r1_finseqop(X43,X44,X45)\|(~v1_funct_1(X45)\|(~v1_funct_2(X45,k2_zfmisc_1(X43,X43),X43)\|~m1_subset_1(X45,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X43,X43),X43)))))\|(~v1_funct_1(X44)\|(~v1_funct_2(X44,X43,X43)\|~m1_subset_1(X44,k1_zfmisc_1(k2_zfmisc_1(X43,X43)))))\|v1_xboole_0(X43)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d1_finseqop])])])])])])). cnf(c_0_32, plain, (k3_binop_1(X2,X1,k3_binop_1(X2,X1,X3,X4),X5)=k3_binop_1(X2,X1,X3,k3_binop_1(X2,X1,X4,X5))\|~v1_funct_1(X1)\|~v2_binop_1(X1,X2)\|~m1_subset_1(X5,X2)\|~m1_subset_1(X4,X2)\|~m1_subset_1(X3,X2)\|~v1_funct_2(X1,k2_zfmisc_1(X2,X2),X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X2,X2),X2)))), inference(evalgc,[status(thm)],[c_0_26])). cnf(c_0_33, plain, (m1_subset_1(u1_algstr_0(X1),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))))\|~l1_algstr_0(X1)), inference(evalgc,[status(thm)],[c_0_27])). cnf(c_0_34, plain, (v1_funct_1(u1_algstr_0(X1))\|~l1_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_23])). cnf(c_0_35, plain, (v1_funct_2(u1_algstr_0(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))\|~l1_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_23])). cnf(c_0_36, plain, (k3_binop_1(X2,X1,X3,X4)=k1_binop_1(X1,X3,X4)\|~v1_funct_1(X1)\|~m1_subset_1(X4,X2)\|~m1_subset_1(X3,X2)\|~v1_funct_2(X1,k2_zfmisc_1(X2,X2),X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X2,X2),X2)))), inference(evalgc,[status(thm)],[c_0_28])). cnf(c_0_37, plain, (k5_binop_1(X2,X1,X3,X4)=k1_binop_1(X1,X3,X4)\|~v1_funct_1(X1)\|~m1_subset_1(X4,X2)\|~m1_subset_1(X3,X2)\|~v1_funct_2(X1,k2_zfmisc_1(X2,X2),X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X2,X2),X2)))), inference(evalgc,[status(thm)],[c_0_29])). cnf(c_0_38, plain, (k1_algstr_0(X1,X2,X3)=k5_binop_1(u1_struct_0(X1),u1_algstr_0(X1),X2,X3)\|~l1_algstr_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_30])). cnf(c_0_39, plain, (k5_binop_1(X1,X2,X3,k3_funct_2(X1,X1,X4,X3))=k4_binop_1(X1,X2)\|v1_xboole_0(X1)\|~m1_subset_1(X3,X1)\|~r1_finseqop(X1,X4,X2)\|~v1_funct_1(X2)\|~v1_funct_2(X2,k2_zfmisc_1(X1,X1),X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X1),X1)))\|~v1_funct_1(X4)\|~v1_funct_2(X4,X1,X1)\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X1)))), inference(split_conjunct,[status(thm)],[c_0_31])). fof(c_0_40, plain, ![X24, X25, X26, X27]:(v1_xboole_0(X24)\|(~v1_funct_1(X26)\|(~v1_funct_2(X26,X24,X25)\|~m1_subset_1(X26,k1_zfmisc_1(k2_zfmisc_1(X24,X25))))\|~m1_subset_1(X27,X24))\|m1_subset_1(k3_funct_2(X24,X25,X26,X27),X25)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k3_funct_2])])])). cnf(c_0_41, plain, (k3_binop_1(u1_struct_0(X1),u1_algstr_0(X1),k3_binop_1(u1_struct_0(X1),u1_algstr_0(X1),X2,X3),X4)=k3_binop_1(u1_struct_0(X1),u1_algstr_0(X1),X2,k3_binop_1(u1_struct_0(X1),u1_algstr_0(X1),X3,X4))\|~v1_funct_2(u1_algstr_0(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))\|~v1_funct_1(u1_algstr_0(X1))\|~m1_subset_1(X4,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~v2_binop_1(u1_algstr_0(X1),u1_struct_0(X1))\|~l1_algstr_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_32, c_0_33])])). cnf(c_0_42, plain, (v1_funct_1(u1_algstr_0(X1))\|~l1_algstr_0(X1)), inference(evalgc,[status(thm)],[c_0_34])). cnf(c_0_43, plain, (v1_funct_2(u1_algstr_0(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))\|~l1_algstr_0(X1)), inference(evalgc,[status(thm)],[c_0_35])). cnf(c_0_44, plain, (k3_binop_1(u1_struct_0(X1),u1_algstr_0(X1),X2,X3)=k1_binop_1(u1_algstr_0(X1),X2,X3)\|~v1_funct_2(u1_algstr_0(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))\|~v1_funct_1(u1_algstr_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l1_algstr_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_36, c_0_33])])). cnf(c_0_45, plain, (k5_binop_1(u1_struct_0(X1),u1_algstr_0(X1),X2,X3)=k1_binop_1(u1_algstr_0(X1),X2,X3)\|~v1_funct_2(u1_algstr_0(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))\|~v1_funct_1(u1_algstr_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l1_algstr_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_37, c_0_33])])). fof(c_0_46, plain, ![X19, X20, X22]:(((m1_subset_1(esk5_2(X19,X20),u1_struct_0(X19))\|~v10_algstr_0(X20,X19)\|~m1_subset_1(X20,u1_struct_0(X19))\|~l2_algstr_0(X19))&(k1_algstr_0(X19,X20,esk5_2(X19,X20))=k4_struct_0(X19)\|~v10_algstr_0(X20,X19)\|~m1_subset_1(X20,u1_struct_0(X19))\|~l2_algstr_0(X19)))&(~m1_subset_1(X22,u1_struct_0(X19))\|k1_algstr_0(X19,X20,X22)!=k4_struct_0(X19)\|v10_algstr_0(X20,X19)\|~m1_subset_1(X20,u1_struct_0(X19))\|~l2_algstr_0(X19))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d11_algstr_0])])])])])). cnf(c_0_47, plain, (k5_binop_1(u1_struct_0(X1),u1_algstr_0(X1),X2,X3)=k1_algstr_0(X1,X2,X3)\|~l1_algstr_0(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_38])). cnf(c_0_48, plain, (k5_binop_1(X1,X2,X3,k3_funct_2(X1,X1,X4,X3))=k4_binop_1(X1,X2)\|v1_xboole_0(X1)\|~v1_funct_1(X4)\|~v1_funct_1(X2)\|~m1_subset_1(X3,X1)\|~r1_finseqop(X1,X4,X2)\|~v1_funct_2(X4,X1,X1)\|~v1_funct_2(X2,k2_zfmisc_1(X1,X1),X1)\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X1,X1)))\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X1),X1)))), inference(evalgc,[status(thm)],[c_0_39])). cnf(c_0_49, plain, (v1_xboole_0(X1)\|m1_subset_1(k3_funct_2(X1,X3,X2,X4),X3)\|~v1_funct_1(X2)\|~v1_funct_2(X2,X1,X3)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))\|~m1_subset_1(X4,X1)), inference(split_conjunct,[status(thm)],[c_0_40])). cnf(c_0_50, plain, (k3_binop_1(u1_struct_0(X1),u1_algstr_0(X1),k3_binop_1(u1_struct_0(X1),u1_algstr_0(X1),X2,X3),X4)=k3_binop_1(u1_struct_0(X1),u1_algstr_0(X1),X2,k3_binop_1(u1_struct_0(X1),u1_algstr_0(X1),X3,X4))\|~m1_subset_1(X4,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l1_algstr_0(X1)\|~v2_binop_1(u1_algstr_0(X1),u1_struct_0(X1))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_41, c_0_42]), c_0_43])). cnf(c_0_51, plain, (k3_binop_1(u1_struct_0(X1),u1_algstr_0(X1),X2,X3)=k1_binop_1(u1_algstr_0(X1),X2,X3)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l1_algstr_0(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_44, c_0_42]), c_0_43])). cnf(c_0_52, plain, (k5_binop_1(u1_struct_0(X1),u1_algstr_0(X1),X2,X3)=k1_binop_1(u1_algstr_0(X1),X2,X3)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l1_algstr_0(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_45, c_0_42]), c_0_43])). cnf(c_0_53, plain, (v10_algstr_0(X3,X2)\|~m1_subset_1(X1,u1_struct_0(X2))\|k1_algstr_0(X2,X3,X1)!=k4_struct_0(X2)\|~m1_subset_1(X3,u1_struct_0(X2))\|~l2_algstr_0(X2)), inference(split_conjunct,[status(thm)],[c_0_46])). cnf(c_0_54, plain, (k1_algstr_0(X1,X2,k3_funct_2(u1_struct_0(X1),u1_struct_0(X1),X3,X2))=k4_binop_1(u1_struct_0(X1),u1_algstr_0(X1))\|v1_xboole_0(u1_struct_0(X1))\|~m1_subset_1(k3_funct_2(u1_struct_0(X1),u1_struct_0(X1),X3,X2),u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l1_algstr_0(X1)\|~v1_funct_2(u1_algstr_0(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))\|~v1_funct_2(X3,u1_struct_0(X1),u1_struct_0(X1))\|~v1_funct_1(X3)\|~v1_funct_1(u1_algstr_0(X1))\|~m1_subset_1(u1_algstr_0(X1),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))))\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1))))\|~r1_finseqop(u1_struct_0(X1),X3,u1_algstr_0(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_47, c_0_48])])). cnf(c_0_55, plain, (v1_xboole_0(X1)\|m1_subset_1(k3_funct_2(X1,X3,X2,X4),X3)\|~v1_funct_1(X2)\|~m1_subset_1(X4,X1)\|~v1_funct_2(X2,X1,X3)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))), inference(evalgc,[status(thm)],[c_0_49])). fof(c_0_56, plain, ![X7]:((l2_struct_0(X7)\|~l2_algstr_0(X7))&(l1_algstr_0(X7)\|~l2_algstr_0(X7))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l2_algstr_0])])])). fof(c_0_57, negated_conjecture, ~(![X1]:((~(v2_struct_0(X1))&l2_algstr_0(X1))=>((v1_binop_1(u1_algstr_0(X1),u1_struct_0(X1))&(v2_binop_1(u1_algstr_0(X1),u1_struct_0(X1))&(r3_binop_1(u1_struct_0(X1),k4_struct_0(X1),u1_algstr_0(X1))&r1_finseqop(u1_struct_0(X1),k5_vectsp_1(X1),u1_algstr_0(X1)))))=>(~(v2_struct_0(X1))&(v13_algstr_0(X1)&(v2_rlvect_1(X1)&(v3_rlvect_1(X1)&(v4_rlvect_1(X1)&l2_algstr_0(X1))))))))), inference(assume_negation,[status(cth)],[t3_prvect_1])). fof(c_0_58, plain, ![X39, X40, X41, X42]:((X42!=k4_binop_1(X39,X40)\|r3_binop_1(X39,X42,X40)\|~m1_subset_1(X42,X39)\|(~m1_subset_1(X41,X39)\|~r3_binop_1(X39,X41,X40))\|(~v1_funct_1(X40)\|(~v1_funct_2(X40,k2_zfmisc_1(X39,X39),X39)\|~m1_subset_1(X40,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X39,X39),X39))))))&(~r3_binop_1(X39,X42,X40)\|X42=k4_binop_1(X39,X40)\|~m1_subset_1(X42,X39)\|(~m1_subset_1(X41,X39)\|~r3_binop_1(X39,X41,X40))\|(~v1_funct_1(X40)\|(~v1_funct_2(X40,k2_zfmisc_1(X39,X39),X39)\|~m1_subset_1(X40,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X39,X39),X39))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_binop_1])])])])). cnf(c_0_59, plain, (k3_binop_1(u1_struct_0(X1),u1_algstr_0(X1),k1_binop_1(u1_algstr_0(X1),X2,X3),X4)=k3_binop_1(u1_struct_0(X1),u1_algstr_0(X1),X2,k3_binop_1(u1_struct_0(X1),u1_algstr_0(X1),X3,X4))\|~m1_subset_1(X4,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l1_algstr_0(X1)\|~v2_binop_1(u1_algstr_0(X1),u1_struct_0(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_50, c_0_51])])). cnf(c_0_60, plain, (k1_binop_1(u1_algstr_0(X1),X2,X3)=k1_algstr_0(X1,X2,X3)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l1_algstr_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_47, c_0_52])])). cnf(c_0_61, plain, (v10_algstr_0(X3,X2)\|k1_algstr_0(X2,X3,X1)!=k4_struct_0(X2)\|~l2_algstr_0(X2)\|~m1_subset_1(X3,u1_struct_0(X2))\|~m1_subset_1(X1,u1_struct_0(X2))), inference(evalgc,[status(thm)],[c_0_53])). cnf(c_0_62, plain, (k1_algstr_0(X1,X2,k3_funct_2(u1_struct_0(X1),u1_struct_0(X1),X3,X2))=k4_binop_1(u1_struct_0(X1),u1_algstr_0(X1))\|v1_xboole_0(u1_struct_0(X1))\|~v1_funct_2(X3,u1_struct_0(X1),u1_struct_0(X1))\|~v1_funct_1(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1))))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l1_algstr_0(X1)\|~r1_finseqop(u1_struct_0(X1),X3,u1_algstr_0(X1))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_54, c_0_55]), c_0_33]), c_0_42]), c_0_43])). cnf(c_0_63, plain, (l1_algstr_0(X1)\|~l2_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_56])). fof(c_0_64, negated_conjecture, ((~v2_struct_0(esk1_0)&l2_algstr_0(esk1_0))&((v1_binop_1(u1_algstr_0(esk1_0),u1_struct_0(esk1_0))&(v2_binop_1(u1_algstr_0(esk1_0),u1_struct_0(esk1_0))&(r3_binop_1(u1_struct_0(esk1_0),k4_struct_0(esk1_0),u1_algstr_0(esk1_0))&r1_finseqop(u1_struct_0(esk1_0),k5_vectsp_1(esk1_0),u1_algstr_0(esk1_0)))))&(v2_struct_0(esk1_0)\|(~v13_algstr_0(esk1_0)\|(~v2_rlvect_1(esk1_0)\|(~v3_rlvect_1(esk1_0)\|(~v4_rlvect_1(esk1_0)\|~l2_algstr_0(esk1_0)))))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_57])])])])). cnf(c_0_65, plain, (X2=k4_binop_1(X1,X3)\|~r3_binop_1(X1,X2,X3)\|~m1_subset_1(X2,X1)\|~m1_subset_1(X4,X1)\|~r3_binop_1(X1,X4,X3)\|~v1_funct_1(X3)\|~v1_funct_2(X3,k2_zfmisc_1(X1,X1),X1)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X1),X1)))), inference(split_conjunct,[status(thm)],[c_0_58])). cnf(c_0_66, plain, (k3_binop_1(u1_struct_0(X1),u1_algstr_0(X1),X2,k3_binop_1(u1_struct_0(X1),u1_algstr_0(X1),X3,X4))=k3_binop_1(u1_struct_0(X1),u1_algstr_0(X1),k1_algstr_0(X1,X2,X3),X4)\|~m1_subset_1(X4,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l1_algstr_0(X1)\|~v2_binop_1(u1_algstr_0(X1),u1_struct_0(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_59, c_0_60])])). fof(c_0_67, plain, ![X74, X75, X76, X77]:(((k3_binop_1(X74,X75,X76,X77)=X77\|~m1_subset_1(X77,X74)\|~r3_binop_1(X74,X76,X75)\|~m1_subset_1(X76,X74)\|(~v1_funct_1(X75)\|(~v1_funct_2(X75,k2_zfmisc_1(X74,X74),X74)\|~m1_subset_1(X75,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X74,X74),X74))))))&(k3_binop_1(X74,X75,X77,X76)=X77\|~m1_subset_1(X77,X74)\|~r3_binop_1(X74,X76,X75)\|~m1_subset_1(X76,X74)\|(~v1_funct_1(X75)\|(~v1_funct_2(X75,k2_zfmisc_1(X74,X74),X74)\|~m1_subset_1(X75,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X74,X74),X74)))))))&((m1_subset_1(esk16_3(X74,X75,X76),X74)\|r3_binop_1(X74,X76,X75)\|~m1_subset_1(X76,X74)\|(~v1_funct_1(X75)\|(~v1_funct_2(X75,k2_zfmisc_1(X74,X74),X74)\|~m1_subset_1(X75,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X74,X74),X74))))))&(k3_binop_1(X74,X75,X76,esk16_3(X74,X75,X76))!=esk16_3(X74,X75,X76)\|k3_binop_1(X74,X75,esk16_3(X74,X75,X76),X76)!=esk16_3(X74,X75,X76)\|r3_binop_1(X74,X76,X75)\|~m1_subset_1(X76,X74)\|(~v1_funct_1(X75)\|(~v1_funct_2(X75,k2_zfmisc_1(X74,X74),X74)\|~m1_subset_1(X75,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X74,X74),X74)))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_binop_1])])])])])). cnf(c_0_68, plain, (v10_algstr_0(X1,X2)\|v1_xboole_0(u1_struct_0(X2))\|k4_binop_1(u1_struct_0(X2),u1_algstr_0(X2))!=k4_struct_0(X2)\|~m1_subset_1(X1,u1_struct_0(X2))\|~m1_subset_1(k3_funct_2(u1_struct_0(X2),u1_struct_0(X2),X3,X1),u1_struct_0(X2))\|~l2_algstr_0(X2)\|~v1_funct_2(X3,u1_struct_0(X2),u1_struct_0(X2))\|~v1_funct_1(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X2),u1_struct_0(X2))))\|~l1_algstr_0(X2)\|~r1_finseqop(u1_struct_0(X2),X3,u1_algstr_0(X2))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_61, c_0_62])])). cnf(c_0_69, plain, (l1_algstr_0(X1)\|~l2_algstr_0(X1)), inference(evalgc,[status(thm)],[c_0_63])). cnf(c_0_70, negated_conjecture, (r1_finseqop(u1_struct_0(esk1_0),k5_vectsp_1(esk1_0),u1_algstr_0(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_64])). cnf(c_0_71, negated_conjecture, (l2_algstr_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_64])). fof(c_0_72, plain, ![X23]:((v1_funct_1(k5_vectsp_1(X23))\|(v2_struct_0(X23)\|~l2_algstr_0(X23)))&((v1_funct_2(k5_vectsp_1(X23),u1_struct_0(X23),u1_struct_0(X23))\|(v2_struct_0(X23)\|~l2_algstr_0(X23)))&(m1_subset_1(k5_vectsp_1(X23),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X23),u1_struct_0(X23))))\|(v2_struct_0(X23)\|~l2_algstr_0(X23))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k5_vectsp_1])])])])). cnf(c_0_73, plain, (X2=k4_binop_1(X1,X3)\|~v1_funct_1(X3)\|~m1_subset_1(X4,X1)\|~m1_subset_1(X2,X1)\|~r3_binop_1(X1,X4,X3)\|~r3_binop_1(X1,X2,X3)\|~v1_funct_2(X3,k2_zfmisc_1(X1,X1),X1)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X1),X1)))), inference(evalgc,[status(thm)],[c_0_65])). cnf(c_0_74, plain, (k3_binop_1(u1_struct_0(X1),u1_algstr_0(X1),X2,k1_binop_1(u1_algstr_0(X1),X3,X4))=k3_binop_1(u1_struct_0(X1),u1_algstr_0(X1),k1_algstr_0(X1,X2,X3),X4)\|~m1_subset_1(X4,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l1_algstr_0(X1)\|~v2_binop_1(u1_algstr_0(X1),u1_struct_0(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_66, c_0_51])])). cnf(c_0_75, plain, (k3_binop_1(X1,X2,X3,X4)=X3\|~m1_subset_1(X3,X1)\|~r3_binop_1(X1,X4,X2)\|~m1_subset_1(X4,X1)\|~v1_funct_1(X2)\|~v1_funct_2(X2,k2_zfmisc_1(X1,X1),X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X1),X1)))), inference(split_conjunct,[status(thm)],[c_0_67])). fof(c_0_76, plain, ![X56, X57, X58, X59]:((~v1_binop_1(X57,X56)\|(~m1_subset_1(X58,X56)\|(~m1_subset_1(X59,X56)\|k3_binop_1(X56,X57,X58,X59)=k3_binop_1(X56,X57,X59,X58)))\|(~v1_funct_1(X57)\|(~v1_funct_2(X57,k2_zfmisc_1(X56,X56),X56)\|~m1_subset_1(X57,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X56,X56),X56))))))&((m1_subset_1(esk10_2(X56,X57),X56)\|v1_binop_1(X57,X56)\|(~v1_funct_1(X57)\|(~v1_funct_2(X57,k2_zfmisc_1(X56,X56),X56)\|~m1_subset_1(X57,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X56,X56),X56))))))&((m1_subset_1(esk11_2(X56,X57),X56)\|v1_binop_1(X57,X56)\|(~v1_funct_1(X57)\|(~v1_funct_2(X57,k2_zfmisc_1(X56,X56),X56)\|~m1_subset_1(X57,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X56,X56),X56))))))&(k3_binop_1(X56,X57,esk10_2(X56,X57),esk11_2(X56,X57))!=k3_binop_1(X56,X57,esk11_2(X56,X57),esk10_2(X56,X57))\|v1_binop_1(X57,X56)\|(~v1_funct_1(X57)\|(~v1_funct_2(X57,k2_zfmisc_1(X56,X56),X56)\|~m1_subset_1(X57,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X56,X56),X56))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d2_binop_1])])])])])). cnf(c_0_77, plain, (v1_xboole_0(u1_struct_0(X1))\|v10_algstr_0(X2,X1)\|k4_binop_1(u1_struct_0(X1),u1_algstr_0(X1))!=k4_struct_0(X1)\|~v1_funct_2(X3,u1_struct_0(X1),u1_struct_0(X1))\|~v1_funct_1(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1))))\|~m1_subset_1(X2,u1_struct_0(X1))\|~r1_finseqop(u1_struct_0(X1),X3,u1_algstr_0(X1))\|~l2_algstr_0(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_68, c_0_69]), c_0_55])). cnf(c_0_78, negated_conjecture, (r1_finseqop(u1_struct_0(esk1_0),k5_vectsp_1(esk1_0),u1_algstr_0(esk1_0))), inference(evalgc,[status(thm)],[c_0_70])). cnf(c_0_79, negated_conjecture, (l2_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_71])). cnf(c_0_80, plain, (m1_subset_1(k5_vectsp_1(X1),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1))))\|v2_struct_0(X1)\|~l2_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_72])). cnf(c_0_81, negated_conjecture, (~v2_struct_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_64])). cnf(c_0_82, plain, (X1=k4_binop_1(u1_struct_0(X2),u1_algstr_0(X2))\|~v1_funct_2(u1_algstr_0(X2),k2_zfmisc_1(u1_struct_0(X2),u1_struct_0(X2)),u1_struct_0(X2))\|~v1_funct_1(u1_algstr_0(X2))\|~m1_subset_1(X3,u1_struct_0(X2))\|~m1_subset_1(X1,u1_struct_0(X2))\|~r3_binop_1(u1_struct_0(X2),X3,u1_algstr_0(X2))\|~r3_binop_1(u1_struct_0(X2),X1,u1_algstr_0(X2))\|~l1_algstr_0(X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_73, c_0_33])])). cnf(c_0_83, negated_conjecture, (r3_binop_1(u1_struct_0(esk1_0),k4_struct_0(esk1_0),u1_algstr_0(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_64])). cnf(c_0_84, plain, (k3_binop_1(u1_struct_0(X1),u1_algstr_0(X1),X2,k5_binop_1(u1_struct_0(X1),u1_algstr_0(X1),X3,X4))=k3_binop_1(u1_struct_0(X1),u1_algstr_0(X1),k1_algstr_0(X1,X2,X3),X4)\|~m1_subset_1(X4,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l1_algstr_0(X1)\|~v2_binop_1(u1_algstr_0(X1),u1_struct_0(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_74, c_0_52])])). fof(c_0_85, plain, ![X35, X36, X37]:(~l1_algstr_0(X35)\|(~m1_subset_1(X36,u1_struct_0(X35))\|~m1_subset_1(X37,u1_struct_0(X35)))\|m1_subset_1(k1_algstr_0(X35,X36,X37),u1_struct_0(X35))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_algstr_0])])). cnf(c_0_86, plain, (k3_binop_1(X1,X2,X3,X4)=X3\|~v1_funct_1(X2)\|~m1_subset_1(X4,X1)\|~m1_subset_1(X3,X1)\|~r3_binop_1(X1,X4,X2)\|~v1_funct_2(X2,k2_zfmisc_1(X1,X1),X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X1,X1),X1)))), inference(evalgc,[status(thm)],[c_0_75])). cnf(c_0_87, plain, (k3_binop_1(X2,X1,X3,X4)=k3_binop_1(X2,X1,X4,X3)\|~v1_binop_1(X1,X2)\|~m1_subset_1(X3,X2)\|~m1_subset_1(X4,X2)\|~v1_funct_1(X1)\|~v1_funct_2(X1,k2_zfmisc_1(X2,X2),X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X2,X2),X2)))), inference(split_conjunct,[status(thm)],[c_0_76])). cnf(c_0_88, negated_conjecture, (v1_xboole_0(u1_struct_0(esk1_0))\|v10_algstr_0(X1,esk1_0)\|k4_binop_1(u1_struct_0(esk1_0),u1_algstr_0(esk1_0))!=k4_struct_0(esk1_0)\|~v1_funct_2(k5_vectsp_1(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0))\|~v1_funct_1(k5_vectsp_1(esk1_0))\|~m1_subset_1(k5_vectsp_1(esk1_0),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(esk1_0),u1_struct_0(esk1_0))))\|~m1_subset_1(X1,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77, c_0_78]), c_0_79])])])). cnf(c_0_89, plain, (v2_struct_0(X1)\|m1_subset_1(k5_vectsp_1(X1),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1))))\|~l2_algstr_0(X1)), inference(evalgc,[status(thm)],[c_0_80])). cnf(c_0_90, negated_conjecture, (~v2_struct_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_81])). cnf(c_0_91, plain, (v1_funct_2(k5_vectsp_1(X1),u1_struct_0(X1),u1_struct_0(X1))\|v2_struct_0(X1)\|~l2_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_72])). cnf(c_0_92, plain, (X1=k4_binop_1(u1_struct_0(X2),u1_algstr_0(X2))\|~m1_subset_1(X3,u1_struct_0(X2))\|~m1_subset_1(X1,u1_struct_0(X2))\|~l1_algstr_0(X2)\|~r3_binop_1(u1_struct_0(X2),X3,u1_algstr_0(X2))\|~r3_binop_1(u1_struct_0(X2),X1,u1_algstr_0(X2))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_82, c_0_42]), c_0_43])). cnf(c_0_93, negated_conjecture, (r3_binop_1(u1_struct_0(esk1_0),k4_struct_0(esk1_0),u1_algstr_0(esk1_0))), inference(evalgc,[status(thm)],[c_0_83])). cnf(c_0_94, plain, (k3_binop_1(u1_struct_0(X1),u1_algstr_0(X1),k1_algstr_0(X1,X2,X3),X4)=k3_binop_1(u1_struct_0(X1),u1_algstr_0(X1),X2,k1_algstr_0(X1,X3,X4))\|~m1_subset_1(X4,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l1_algstr_0(X1)\|~v2_binop_1(u1_algstr_0(X1),u1_struct_0(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_84, c_0_47])])). cnf(c_0_95, plain, (m1_subset_1(k1_algstr_0(X1,X2,X3),u1_struct_0(X1))\|~l1_algstr_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_85])). cnf(c_0_96, plain, (k3_binop_1(u1_struct_0(X1),u1_algstr_0(X1),X2,X3)=X2\|~v1_funct_2(u1_algstr_0(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))\|~v1_funct_1(u1_algstr_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~r3_binop_1(u1_struct_0(X1),X3,u1_algstr_0(X1))\|~l1_algstr_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_86, c_0_33])])). cnf(c_0_97, plain, (k3_binop_1(X2,X1,X3,X4)=k3_binop_1(X2,X1,X4,X3)\|~v1_funct_1(X1)\|~v1_binop_1(X1,X2)\|~m1_subset_1(X4,X2)\|~m1_subset_1(X3,X2)\|~v1_funct_2(X1,k2_zfmisc_1(X2,X2),X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(X2,X2),X2)))), inference(evalgc,[status(thm)],[c_0_87])). cnf(c_0_98, negated_conjecture, (v1_xboole_0(u1_struct_0(esk1_0))\|v10_algstr_0(X1,esk1_0)\|k4_binop_1(u1_struct_0(esk1_0),u1_algstr_0(esk1_0))!=k4_struct_0(esk1_0)\|~v1_funct_2(k5_vectsp_1(esk1_0),u1_struct_0(esk1_0),u1_struct_0(esk1_0))\|~v1_funct_1(k5_vectsp_1(esk1_0))\|~m1_subset_1(X1,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88, c_0_89]), c_0_79])]), c_0_90])])). cnf(c_0_99, plain, (v2_struct_0(X1)\|v1_funct_2(k5_vectsp_1(X1),u1_struct_0(X1),u1_struct_0(X1))\|~l2_algstr_0(X1)), inference(evalgc,[status(thm)],[c_0_91])). cnf(c_0_100, negated_conjecture, (X1=k4_binop_1(u1_struct_0(esk1_0),u1_algstr_0(esk1_0))\|~m1_subset_1(k4_struct_0(esk1_0),u1_struct_0(esk1_0))\|~m1_subset_1(X1,u1_struct_0(esk1_0))\|~l1_algstr_0(esk1_0)\|~r3_binop_1(u1_struct_0(esk1_0),X1,u1_algstr_0(esk1_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_92, c_0_93])])). cnf(c_0_101, plain, (k5_binop_1(u1_struct_0(X1),u1_algstr_0(X1),X2,X3)=k3_binop_1(u1_struct_0(X1),u1_algstr_0(X1),X2,X3)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l1_algstr_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_51, c_0_52])])). cnf(c_0_102, plain, (k3_binop_1(u1_struct_0(X1),u1_algstr_0(X1),X2,k1_algstr_0(X1,X3,X4))=k1_binop_1(u1_algstr_0(X1),k1_algstr_0(X1,X2,X3),X4)\|~m1_subset_1(X4,u1_struct_0(X1))\|~m1_subset_1(k1_algstr_0(X1,X2,X3),u1_struct_0(X1))\|~l1_algstr_0(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~v2_binop_1(u1_algstr_0(X1),u1_struct_0(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_51, c_0_94])])). cnf(c_0_103, plain, (m1_subset_1(k1_algstr_0(X1,X2,X3),u1_struct_0(X1))\|~l1_algstr_0(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_95])). fof(c_0_104, plain, ![X70, X71]:((~v4_rlvect_1(X70)\|(~m1_subset_1(X71,u1_struct_0(X70))\|k1_algstr_0(X70,X71,k4_struct_0(X70))=X71)\|~l2_algstr_0(X70))&((m1_subset_1(esk15_1(X70),u1_struct_0(X70))\|v4_rlvect_1(X70)\|~l2_algstr_0(X70))&(k1_algstr_0(X70,esk15_1(X70),k4_struct_0(X70))!=esk15_1(X70)\|v4_rlvect_1(X70)\|~l2_algstr_0(X70)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d4_rlvect_1])])])])])). cnf(c_0_105, plain, (k3_binop_1(u1_struct_0(X1),u1_algstr_0(X1),X2,X3)=X2\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l1_algstr_0(X1)\|~r3_binop_1(u1_struct_0(X1),X3,u1_algstr_0(X1))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_96, c_0_42]), c_0_43])). cnf(c_0_106, plain, (k3_binop_1(u1_struct_0(X1),u1_algstr_0(X1),X2,X3)=k3_binop_1(u1_struct_0(X1),u1_algstr_0(X1),X3,X2)\|~v1_funct_2(u1_algstr_0(X1),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_struct_0(X1))\|~v1_funct_1(u1_algstr_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~v1_binop_1(u1_algstr_0(X1),u1_struct_0(X1))\|~l1_algstr_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_97, c_0_33])])). cnf(c_0_107, negated_conjecture, (v1_binop_1(u1_algstr_0(esk1_0),u1_struct_0(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_64])). cnf(c_0_108, negated_conjecture, (v1_xboole_0(u1_struct_0(esk1_0))\|v10_algstr_0(X1,esk1_0)\|k4_binop_1(u1_struct_0(esk1_0),u1_algstr_0(esk1_0))!=k4_struct_0(esk1_0)\|~v1_funct_1(k5_vectsp_1(esk1_0))\|~m1_subset_1(X1,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98, c_0_99]), c_0_79])]), c_0_90])])). cnf(c_0_109, negated_conjecture, (k4_binop_1(u1_struct_0(esk1_0),u1_algstr_0(esk1_0))=k4_struct_0(esk1_0)\|~m1_subset_1(k4_struct_0(esk1_0),u1_struct_0(esk1_0))\|~l1_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_100, c_0_93])])). cnf(c_0_110, plain, (v1_funct_1(k5_vectsp_1(X1))\|v2_struct_0(X1)\|~l2_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_72])). fof(c_0_111, plain, ![X73]:(~l2_struct_0(X73)\|m1_subset_1(k4_struct_0(X73),u1_struct_0(X73))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k4_struct_0])])). cnf(c_0_112, plain, (k3_binop_1(u1_struct_0(X1),u1_algstr_0(X1),X2,X3)=k1_algstr_0(X1,X2,X3)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l1_algstr_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_47, c_0_101])])). cnf(c_0_113, plain, (k3_binop_1(u1_struct_0(X1),u1_algstr_0(X1),X2,k1_algstr_0(X1,X3,X4))=k1_binop_1(u1_algstr_0(X1),k1_algstr_0(X1,X2,X3),X4)\|~m1_subset_1(X4,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l1_algstr_0(X1)\|~v2_binop_1(u1_algstr_0(X1),u1_struct_0(X1))), inference(csr,[status(thm)],[c_0_102, c_0_103])). cnf(c_0_114, plain, (v4_rlvect_1(X1)\|k1_algstr_0(X1,esk15_1(X1),k4_struct_0(X1))!=esk15_1(X1)\|~l2_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_104])). cnf(c_0_115, negated_conjecture, (k3_binop_1(u1_struct_0(esk1_0),u1_algstr_0(esk1_0),X1,k4_struct_0(esk1_0))=X1\|~m1_subset_1(k4_struct_0(esk1_0),u1_struct_0(esk1_0))\|~m1_subset_1(X1,u1_struct_0(esk1_0))\|~l1_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_105, c_0_93])])). cnf(c_0_116, plain, (k3_binop_1(u1_struct_0(X1),u1_algstr_0(X1),X2,X3)=k3_binop_1(u1_struct_0(X1),u1_algstr_0(X1),X3,X2)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l1_algstr_0(X1)\|~v1_binop_1(u1_algstr_0(X1),u1_struct_0(X1))), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_106, c_0_42]), c_0_43])). cnf(c_0_117, negated_conjecture, (v1_binop_1(u1_algstr_0(esk1_0),u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[c_0_107])). cnf(c_0_118, negated_conjecture, (v1_xboole_0(u1_struct_0(esk1_0))\|v10_algstr_0(X1,esk1_0)\|~v1_funct_1(k5_vectsp_1(esk1_0))\|~m1_subset_1(X1,u1_struct_0(esk1_0))\|~m1_subset_1(k4_struct_0(esk1_0),u1_struct_0(esk1_0))\|~l1_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_108, c_0_109])])). cnf(c_0_119, plain, (v2_struct_0(X1)\|v1_funct_1(k5_vectsp_1(X1))\|~l2_algstr_0(X1)), inference(evalgc,[status(thm)],[c_0_110])). cnf(c_0_120, plain, (m1_subset_1(k4_struct_0(X1),u1_struct_0(X1))\|~l2_struct_0(X1)), inference(split_conjunct,[status(thm)],[c_0_111])). cnf(c_0_121, plain, (k1_binop_1(u1_algstr_0(X1),k1_algstr_0(X1,X2,X3),X4)=k1_algstr_0(X1,X2,k1_algstr_0(X1,X3,X4))\|~m1_subset_1(k1_algstr_0(X1,X3,X4),u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l1_algstr_0(X1)\|~m1_subset_1(X4,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~v2_binop_1(u1_algstr_0(X1),u1_struct_0(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_112, c_0_113])])). cnf(c_0_122, plain, (v4_rlvect_1(X1)\|k1_algstr_0(X1,esk15_1(X1),k4_struct_0(X1))!=esk15_1(X1)\|~l2_algstr_0(X1)), inference(evalgc,[status(thm)],[c_0_114])). cnf(c_0_123, negated_conjecture, (k1_algstr_0(esk1_0,X1,k4_struct_0(esk1_0))=X1\|~m1_subset_1(k4_struct_0(esk1_0),u1_struct_0(esk1_0))\|~m1_subset_1(X1,u1_struct_0(esk1_0))\|~l1_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_115, c_0_112])])). cnf(c_0_124, plain, (m1_subset_1(esk15_1(X1),u1_struct_0(X1))\|v4_rlvect_1(X1)\|~l2_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_104])). cnf(c_0_125, negated_conjecture, (k3_binop_1(u1_struct_0(esk1_0),u1_algstr_0(esk1_0),X1,X2)=k3_binop_1(u1_struct_0(esk1_0),u1_algstr_0(esk1_0),X2,X1)\|~m1_subset_1(X2,u1_struct_0(esk1_0))\|~m1_subset_1(X1,u1_struct_0(esk1_0))\|~l1_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_116, c_0_117])])). cnf(c_0_126, negated_conjecture, (v1_xboole_0(u1_struct_0(esk1_0))\|v10_algstr_0(X1,esk1_0)\|~m1_subset_1(k4_struct_0(esk1_0),u1_struct_0(esk1_0))\|~m1_subset_1(X1,u1_struct_0(esk1_0))\|~l1_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118, c_0_119]), c_0_79])]), c_0_90])])). cnf(c_0_127, plain, (m1_subset_1(k4_struct_0(X1),u1_struct_0(X1))\|~l2_struct_0(X1)), inference(evalgc,[status(thm)],[c_0_120])). cnf(c_0_128, plain, (l2_struct_0(X1)\|~l2_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_56])). cnf(c_0_129, plain, (k1_binop_1(u1_algstr_0(X1),k1_algstr_0(X1,X2,X3),X4)=k1_algstr_0(X1,X2,k1_algstr_0(X1,X3,X4))\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X4,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~l1_algstr_0(X1)\|~v2_binop_1(u1_algstr_0(X1),u1_struct_0(X1))), inference(csr,[status(thm)],[c_0_121, c_0_103])). cnf(c_0_130, negated_conjecture, (v4_rlvect_1(esk1_0)\|~m1_subset_1(k4_struct_0(esk1_0),u1_struct_0(esk1_0))\|~m1_subset_1(esk15_1(esk1_0),u1_struct_0(esk1_0))\|~l1_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122, c_0_123]), c_0_79])])])). cnf(c_0_131, plain, (v4_rlvect_1(X1)\|m1_subset_1(esk15_1(X1),u1_struct_0(X1))\|~l2_algstr_0(X1)), inference(evalgc,[status(thm)],[c_0_124])). fof(c_0_132, plain, ![X14, X15, X16]:((~v2_rlvect_1(X14)\|(~m1_subset_1(X15,u1_struct_0(X14))\|(~m1_subset_1(X16,u1_struct_0(X14))\|k1_algstr_0(X14,X15,X16)=k1_algstr_0(X14,X16,X15)))\|~l1_algstr_0(X14))&((m1_subset_1(esk3_1(X14),u1_struct_0(X14))\|v2_rlvect_1(X14)\|~l1_algstr_0(X14))&((m1_subset_1(esk4_1(X14),u1_struct_0(X14))\|v2_rlvect_1(X14)\|~l1_algstr_0(X14))&(k1_algstr_0(X14,esk3_1(X14),esk4_1(X14))!=k1_algstr_0(X14,esk4_1(X14),esk3_1(X14))\|v2_rlvect_1(X14)\|~l1_algstr_0(X14))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d2_rlvect_1])])])])])). cnf(c_0_133, negated_conjecture, (k3_binop_1(u1_struct_0(esk1_0),u1_algstr_0(esk1_0),X1,X2)=k1_algstr_0(esk1_0,X2,X1)\|~m1_subset_1(X2,u1_struct_0(esk1_0))\|~m1_subset_1(X1,u1_struct_0(esk1_0))\|~l1_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_125, c_0_112])])). cnf(c_0_134, negated_conjecture, (v1_xboole_0(u1_struct_0(esk1_0))\|v10_algstr_0(X1,esk1_0)\|~m1_subset_1(X1,u1_struct_0(esk1_0))\|~l1_algstr_0(esk1_0)\|~l2_struct_0(esk1_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_126, c_0_127])])). cnf(c_0_135, plain, (l2_struct_0(X1)\|~l2_algstr_0(X1)), inference(evalgc,[status(thm)],[c_0_128])). fof(c_0_136, plain, ![X8, X9]:((~v13_algstr_0(X8)\|(~m1_subset_1(X9,u1_struct_0(X8))\|v10_algstr_0(X9,X8))\|~l2_algstr_0(X8))&((m1_subset_1(esk2_1(X8),u1_struct_0(X8))\|v13_algstr_0(X8)\|~l2_algstr_0(X8))&(~v10_algstr_0(esk2_1(X8),X8)\|v13_algstr_0(X8)\|~l2_algstr_0(X8)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d16_algstr_0])])])])])). cnf(c_0_137, plain, (k5_binop_1(u1_struct_0(X1),u1_algstr_0(X1),k1_algstr_0(X1,X2,X3),X4)=k1_algstr_0(X1,X2,k1_algstr_0(X1,X3,X4))\|~m1_subset_1(X4,u1_struct_0(X1))\|~m1_subset_1(k1_algstr_0(X1,X2,X3),u1_struct_0(X1))\|~l1_algstr_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~v2_binop_1(u1_algstr_0(X1),u1_struct_0(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_52, c_0_129])])). cnf(c_0_138, negated_conjecture, (v2_struct_0(esk1_0)\|~v13_algstr_0(esk1_0)\|~v2_rlvect_1(esk1_0)\|~v3_rlvect_1(esk1_0)\|~v4_rlvect_1(esk1_0)\|~l2_algstr_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_64])). cnf(c_0_139, negated_conjecture, (v4_rlvect_1(esk1_0)\|~m1_subset_1(k4_struct_0(esk1_0),u1_struct_0(esk1_0))\|~l1_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130, c_0_131]), c_0_79])])])). cnf(c_0_140, plain, (v2_rlvect_1(X1)\|k1_algstr_0(X1,esk3_1(X1),esk4_1(X1))!=k1_algstr_0(X1,esk4_1(X1),esk3_1(X1))\|~l1_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_132])). cnf(c_0_141, negated_conjecture, (k1_algstr_0(esk1_0,X2,X1)=k1_algstr_0(esk1_0,X1,X2)\|~m1_subset_1(X2,u1_struct_0(esk1_0))\|~m1_subset_1(X1,u1_struct_0(esk1_0))\|~l1_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_112, c_0_133])])). fof(c_0_142, plain, ![X80]:(v2_struct_0(X80)\|~l1_struct_0(X80)\|~v1_xboole_0(u1_struct_0(X80))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fc2_struct_0])])])). fof(c_0_143, plain, ![X79]:(~l1_algstr_0(X79)\|l1_struct_0(X79)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_algstr_0])])). cnf(c_0_144, negated_conjecture, (v1_xboole_0(u1_struct_0(esk1_0))\|v10_algstr_0(X1,esk1_0)\|~m1_subset_1(X1,u1_struct_0(esk1_0))\|~l1_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134, c_0_135]), c_0_79])])])). cnf(c_0_145, plain, (m1_subset_1(esk2_1(X1),u1_struct_0(X1))\|v13_algstr_0(X1)\|~l2_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_136])). cnf(c_0_146, plain, (k5_binop_1(u1_struct_0(X1),u1_algstr_0(X1),k1_algstr_0(X1,X2,X3),X4)=k1_algstr_0(X1,X2,k1_algstr_0(X1,X3,X4))\|~m1_subset_1(X4,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~l1_algstr_0(X1)\|~v2_binop_1(u1_algstr_0(X1),u1_struct_0(X1))), inference(csr,[status(thm)],[c_0_137, c_0_103])). cnf(c_0_147, negated_conjecture, (v2_struct_0(esk1_0)\|~l2_algstr_0(esk1_0)\|~v13_algstr_0(esk1_0)\|~v2_rlvect_1(esk1_0)\|~v3_rlvect_1(esk1_0)\|~v4_rlvect_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_138])). cnf(c_0_148, negated_conjecture, (v4_rlvect_1(esk1_0)\|~l1_algstr_0(esk1_0)\|~l2_struct_0(esk1_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_139, c_0_127])])). cnf(c_0_149, plain, (v2_rlvect_1(X1)\|k1_algstr_0(X1,esk4_1(X1),esk3_1(X1))!=k1_algstr_0(X1,esk3_1(X1),esk4_1(X1))\|~l1_algstr_0(X1)), inference(evalgc,[status(thm)],[c_0_140])). cnf(c_0_150, negated_conjecture, (k1_algstr_0(esk1_0,X1,X2)=k1_algstr_0(esk1_0,X2,X1)\|~m1_subset_1(X1,u1_struct_0(esk1_0))\|~m1_subset_1(X2,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141, c_0_69]), c_0_79])])])). cnf(c_0_151, plain, (m1_subset_1(esk4_1(X1),u1_struct_0(X1))\|v2_rlvect_1(X1)\|~l1_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_132])). cnf(c_0_152, plain, (m1_subset_1(esk3_1(X1),u1_struct_0(X1))\|v2_rlvect_1(X1)\|~l1_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_132])). cnf(c_0_153, plain, (v2_struct_0(X1)\|~l1_struct_0(X1)\|~v1_xboole_0(u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_142])). cnf(c_0_154, plain, (l1_struct_0(X1)\|~l1_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_143])). cnf(c_0_155, plain, (v13_algstr_0(X1)\|~v10_algstr_0(esk2_1(X1),X1)\|~l2_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_136])). cnf(c_0_156, negated_conjecture, (v1_xboole_0(u1_struct_0(esk1_0))\|v10_algstr_0(X1,esk1_0)\|~m1_subset_1(X1,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144, c_0_69]), c_0_79])])])). cnf(c_0_157, plain, (v13_algstr_0(X1)\|m1_subset_1(esk2_1(X1),u1_struct_0(X1))\|~l2_algstr_0(X1)), inference(evalgc,[status(thm)],[c_0_145])). fof(c_0_158, plain, ![X28, X29, X30, X31]:((~v3_rlvect_1(X28)\|(~m1_subset_1(X29,u1_struct_0(X28))\|(~m1_subset_1(X30,u1_struct_0(X28))\|(~m1_subset_1(X31,u1_struct_0(X28))\|k1_algstr_0(X28,k1_algstr_0(X28,X29,X30),X31)=k1_algstr_0(X28,X29,k1_algstr_0(X28,X30,X31)))))\|~l1_algstr_0(X28))&((m1_subset_1(esk6_1(X28),u1_struct_0(X28))\|v3_rlvect_1(X28)\|~l1_algstr_0(X28))&((m1_subset_1(esk7_1(X28),u1_struct_0(X28))\|v3_rlvect_1(X28)\|~l1_algstr_0(X28))&((m1_subset_1(esk8_1(X28),u1_struct_0(X28))\|v3_rlvect_1(X28)\|~l1_algstr_0(X28))&(k1_algstr_0(X28,k1_algstr_0(X28,esk6_1(X28),esk7_1(X28)),esk8_1(X28))!=k1_algstr_0(X28,esk6_1(X28),k1_algstr_0(X28,esk7_1(X28),esk8_1(X28)))\|v3_rlvect_1(X28)\|~l1_algstr_0(X28)))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_rlvect_1])])])])])). cnf(c_0_159, plain, (k1_algstr_0(X1,k1_algstr_0(X1,X2,X3),X4)=k1_algstr_0(X1,X2,k1_algstr_0(X1,X3,X4))\|~m1_subset_1(X4,u1_struct_0(X1))\|~m1_subset_1(k1_algstr_0(X1,X2,X3),u1_struct_0(X1))\|~l1_algstr_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~v2_binop_1(u1_algstr_0(X1),u1_struct_0(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_47, c_0_146])])). cnf(c_0_160, negated_conjecture, (v2_binop_1(u1_algstr_0(esk1_0),u1_struct_0(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_64])). cnf(c_0_161, negated_conjecture, (~v4_rlvect_1(esk1_0)\|~v3_rlvect_1(esk1_0)\|~v2_rlvect_1(esk1_0)\|~v13_algstr_0(esk1_0)), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_147, c_0_79])]), c_0_90])). cnf(c_0_162, negated_conjecture, (v4_rlvect_1(esk1_0)\|~l1_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148, c_0_135]), c_0_79])])])). cnf(c_0_163, negated_conjecture, (v2_rlvect_1(esk1_0)\|~l1_algstr_0(esk1_0)\|~m1_subset_1(esk3_1(esk1_0),u1_struct_0(esk1_0))\|~m1_subset_1(esk4_1(esk1_0),u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_149, c_0_150])])). cnf(c_0_164, plain, (v2_rlvect_1(X1)\|m1_subset_1(esk4_1(X1),u1_struct_0(X1))\|~l1_algstr_0(X1)), inference(evalgc,[status(thm)],[c_0_151])). cnf(c_0_165, plain, (v2_rlvect_1(X1)\|m1_subset_1(esk3_1(X1),u1_struct_0(X1))\|~l1_algstr_0(X1)), inference(evalgc,[status(thm)],[c_0_152])). cnf(c_0_166, plain, (v2_struct_0(X1)\|~l1_struct_0(X1)\|~v1_xboole_0(u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_153])). cnf(c_0_167, plain, (l1_struct_0(X1)\|~l1_algstr_0(X1)), inference(evalgc,[status(thm)],[c_0_154])). cnf(c_0_168, plain, (v13_algstr_0(X1)\|~l2_algstr_0(X1)\|~v10_algstr_0(esk2_1(X1),X1)), inference(evalgc,[status(thm)],[c_0_155])). cnf(c_0_169, negated_conjecture, (v1_xboole_0(u1_struct_0(esk1_0))\|v10_algstr_0(esk2_1(esk1_0),esk1_0)\|v13_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156, c_0_157]), c_0_79])])])). cnf(c_0_170, plain, (v3_rlvect_1(X1)\|k1_algstr_0(X1,k1_algstr_0(X1,esk6_1(X1),esk7_1(X1)),esk8_1(X1))!=k1_algstr_0(X1,esk6_1(X1),k1_algstr_0(X1,esk7_1(X1),esk8_1(X1)))\|~l1_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_158])). cnf(c_0_171, plain, (k1_algstr_0(X1,k1_algstr_0(X1,X2,X3),X4)=k1_algstr_0(X1,X2,k1_algstr_0(X1,X3,X4))\|~m1_subset_1(X4,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~l1_algstr_0(X1)\|~v2_binop_1(u1_algstr_0(X1),u1_struct_0(X1))), inference(csr,[status(thm)],[c_0_159, c_0_103])). cnf(c_0_172, negated_conjecture, (v2_binop_1(u1_algstr_0(esk1_0),u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[c_0_160])). cnf(c_0_173, negated_conjecture, (~v3_rlvect_1(esk1_0)\|~v2_rlvect_1(esk1_0)\|~v13_algstr_0(esk1_0)\|~l1_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_161, c_0_162])])). cnf(c_0_174, negated_conjecture, (v2_rlvect_1(esk1_0)\|~l1_algstr_0(esk1_0)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_163, c_0_164]), c_0_165])). cnf(c_0_175, plain, (v2_struct_0(X1)\|~v1_xboole_0(u1_struct_0(X1))\|~l1_algstr_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_166, c_0_167])])). cnf(c_0_176, negated_conjecture, (v13_algstr_0(esk1_0)\|v1_xboole_0(u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_168, c_0_169]), c_0_79])])])). cnf(c_0_177, plain, (v3_rlvect_1(X1)\|k1_algstr_0(X1,k1_algstr_0(X1,esk6_1(X1),esk7_1(X1)),esk8_1(X1))!=k1_algstr_0(X1,esk6_1(X1),k1_algstr_0(X1,esk7_1(X1),esk8_1(X1)))\|~l1_algstr_0(X1)), inference(evalgc,[status(thm)],[c_0_170])). cnf(c_0_178, negated_conjecture, (k1_algstr_0(esk1_0,k1_algstr_0(esk1_0,X1,X2),X3)=k1_algstr_0(esk1_0,X1,k1_algstr_0(esk1_0,X2,X3))\|~m1_subset_1(X3,u1_struct_0(esk1_0))\|~m1_subset_1(X1,u1_struct_0(esk1_0))\|~m1_subset_1(X2,u1_struct_0(esk1_0))\|~l1_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_171, c_0_172])])). cnf(c_0_179, plain, (m1_subset_1(esk7_1(X1),u1_struct_0(X1))\|v3_rlvect_1(X1)\|~l1_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_158])). cnf(c_0_180, plain, (m1_subset_1(esk6_1(X1),u1_struct_0(X1))\|v3_rlvect_1(X1)\|~l1_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_158])). cnf(c_0_181, plain, (m1_subset_1(esk8_1(X1),u1_struct_0(X1))\|v3_rlvect_1(X1)\|~l1_algstr_0(X1)), inference(split_conjunct,[status(thm)],[c_0_158])). cnf(c_0_182, negated_conjecture, (~l1_algstr_0(esk1_0)\|~v3_rlvect_1(esk1_0)\|~v13_algstr_0(esk1_0)), inference(csr,[status(thm)],[c_0_173, c_0_174])). cnf(c_0_183, negated_conjecture, (v13_algstr_0(esk1_0)\|~l1_algstr_0(esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_175, c_0_176]), c_0_90])])). cnf(c_0_184, negated_conjecture, (v3_rlvect_1(esk1_0)\|~l1_algstr_0(esk1_0)\|~m1_subset_1(esk8_1(esk1_0),u1_struct_0(esk1_0))\|~m1_subset_1(esk6_1(esk1_0),u1_struct_0(esk1_0))\|~m1_subset_1(esk7_1(esk1_0),u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_177, c_0_178])])). cnf(c_0_185, plain, (v3_rlvect_1(X1)\|m1_subset_1(esk7_1(X1),u1_struct_0(X1))\|~l1_algstr_0(X1)), inference(evalgc,[status(thm)],[c_0_179])). cnf(c_0_186, plain, (v3_rlvect_1(X1)\|m1_subset_1(esk6_1(X1),u1_struct_0(X1))\|~l1_algstr_0(X1)), inference(evalgc,[status(thm)],[c_0_180])). cnf(c_0_187, plain, (v3_rlvect_1(X1)\|m1_subset_1(esk8_1(X1),u1_struct_0(X1))\|~l1_algstr_0(X1)), inference(evalgc,[status(thm)],[c_0_181])). cnf(c_0_188, negated_conjecture, (~l1_algstr_0(esk1_0)\|~v3_rlvect_1(esk1_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_182, c_0_183])])). cnf(c_0_189, negated_conjecture, (~l1_algstr_0(esk1_0)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_184, c_0_185]), c_0_186]), c_0_187]), c_0_188])). cnf(c_0_190, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_189, c_0_69]), c_0_79])]), ['proof']). # SZS output end CNFRefutation	reserve G for Abelian add-associative right_complementable right_zeroed non empty addLoopStr; reserve GS for non empty addLoopStr; theorem the addF of GS is commutative associative & 0.GS is_a_unity_wrt the addF of GS & comp GS is_an_inverseOp_wrt the addF of GS implies GS is AbGroup proof assume that A1: the addF of GS is commutative & the addF of GS is associative and A2: 0.GS is_a_unity_wrt the addF of GS and A3: comp GS is_an_inverseOp_wrt the addF of GS; A4: GS is right_complementable proof let x be Element of GS; reconsider b = (comp GS).x as Element of GS; take b; thus x+b = the_unity_wrt the addF of GS by A3,FINSEQOP:def 1 .= (0.GS) by A2,BINOP_1:def 8; end; for x,y,z being Element of GS holds x+y = y+x & (x+y)+z = x+(y+z) & x+( 0.GS) = x by A1,A2,BINOP_1:3,def 2,def 3; hence thesis by A4,RLVECT_1:def 2,def 3,def 4; end;	Convert the following ATP output trace into a readable Mizar proof.
t74_glib_000	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(redefinition_k24_glib_000, axiom, ![X1, X2]:(((v1_relat_1(X1)&(v4_relat_1(X1,k5_numbers)&(v1_funct_1(X1)&(v1_finset_1(X1)&v1_glib_000(X1)))))&m1_glib_000(X2,X1))=>k24_glib_000(X1,X2)=k6_glib_000(X2)), file('/scratch/mptp/predsminms1/t74_glib_000__0', redefinition_k24_glib_000)). fof(d33_glib_000, axiom, ![X1]:((v1_relat_1(X1)&(v4_relat_1(X1,k5_numbers)&(v1_funct_1(X1)&(v1_finset_1(X1)&v1_glib_000(X1)))))=>![X2]:(m1_glib_000(X2,X1)=>(v9_glib_000(X2,X1)<=>k24_glib_000(X1,X2)=k6_glib_000(X1)))), file('/scratch/mptp/predsminms1/t74_glib_000__0', d33_glib_000)). fof(t74_glib_000, conjecture, ![X1]:((v1_relat_1(X1)&(v4_relat_1(X1,k5_numbers)&(v1_funct_1(X1)&(v1_finset_1(X1)&v1_glib_000(X1)))))=>![X2]:((v9_glib_000(X2,X1)&m1_glib_000(X2,X1))=>![X3]:((v9_glib_000(X3,X2)&m1_glib_000(X3,X2))=>(v9_glib_000(X3,X1)&m1_glib_000(X3,X1))))), file('/scratch/mptp/predsminms1/t74_glib_000__0', t74_glib_000)). fof(t43_glib_000, axiom, ![X1]:((v1_relat_1(X1)&(v4_relat_1(X1,k5_numbers)&(v1_funct_1(X1)&(v1_finset_1(X1)&v1_glib_000(X1)))))=>![X2]:(m1_glib_000(X2,X1)=>![X3]:(m1_glib_000(X3,X2)=>m1_glib_000(X3,X1)))), file('/scratch/mptp/predsminms1/t74_glib_000__0', t43_glib_000)). fof(dt_m1_glib_000, axiom, ![X1]:((v1_relat_1(X1)&(v4_relat_1(X1,k5_numbers)&(v1_funct_1(X1)&(v1_finset_1(X1)&v1_glib_000(X1)))))=>![X2]:(m1_glib_000(X2,X1)=>(v1_relat_1(X2)&(v4_relat_1(X2,k5_numbers)&(v1_funct_1(X2)&(v1_finset_1(X2)&v1_glib_000(X2))))))), file('/scratch/mptp/predsminms1/t74_glib_000__0', dt_m1_glib_000)). fof(c_0_5, plain, ![X7, X8]:(~v1_relat_1(X7)\|(~v4_relat_1(X7,k5_numbers)\|(~v1_funct_1(X7)\|(~v1_finset_1(X7)\|~v1_glib_000(X7))))\|~m1_glib_000(X8,X7)\|k24_glib_000(X7,X8)=k6_glib_000(X8)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k24_glib_000])])). fof(c_0_6, plain, ![X9, X10]:((~v9_glib_000(X10,X9)\|k24_glib_000(X9,X10)=k6_glib_000(X9)\|~m1_glib_000(X10,X9)\|(~v1_relat_1(X9)\|(~v4_relat_1(X9,k5_numbers)\|(~v1_funct_1(X9)\|(~v1_finset_1(X9)\|~v1_glib_000(X9))))))&(k24_glib_000(X9,X10)!=k6_glib_000(X9)\|v9_glib_000(X10,X9)\|~m1_glib_000(X10,X9)\|(~v1_relat_1(X9)\|(~v4_relat_1(X9,k5_numbers)\|(~v1_funct_1(X9)\|(~v1_finset_1(X9)\|~v1_glib_000(X9))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d33_glib_000])])])])). fof(c_0_7, negated_conjecture, ~(![X1]:((v1_relat_1(X1)&(v4_relat_1(X1,k5_numbers)&(v1_funct_1(X1)&(v1_finset_1(X1)&v1_glib_000(X1)))))=>![X2]:((v9_glib_000(X2,X1)&m1_glib_000(X2,X1))=>![X3]:((v9_glib_000(X3,X2)&m1_glib_000(X3,X2))=>(v9_glib_000(X3,X1)&m1_glib_000(X3,X1)))))), inference(assume_negation,[status(cth)],[t74_glib_000])). cnf(c_0_8, plain, (k24_glib_000(X1,X2)=k6_glib_000(X2)\|~v1_relat_1(X1)\|~v4_relat_1(X1,k5_numbers)\|~v1_funct_1(X1)\|~v1_finset_1(X1)\|~v1_glib_000(X1)\|~m1_glib_000(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_5])). cnf(c_0_9, plain, (k24_glib_000(X2,X1)=k6_glib_000(X2)\|~v9_glib_000(X1,X2)\|~m1_glib_000(X1,X2)\|~v1_relat_1(X2)\|~v4_relat_1(X2,k5_numbers)\|~v1_funct_1(X2)\|~v1_finset_1(X2)\|~v1_glib_000(X2)), inference(split_conjunct,[status(thm)],[c_0_6])). fof(c_0_10, negated_conjecture, ((v1_relat_1(esk1_0)&(v4_relat_1(esk1_0,k5_numbers)&(v1_funct_1(esk1_0)&(v1_finset_1(esk1_0)&v1_glib_000(esk1_0)))))&((v9_glib_000(esk2_0,esk1_0)&m1_glib_000(esk2_0,esk1_0))&((v9_glib_000(esk3_0,esk2_0)&m1_glib_000(esk3_0,esk2_0))&(~v9_glib_000(esk3_0,esk1_0)\|~m1_glib_000(esk3_0,esk1_0))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])). fof(c_0_11, plain, ![X13, X14, X15]:(~v1_relat_1(X13)\|(~v4_relat_1(X13,k5_numbers)\|(~v1_funct_1(X13)\|(~v1_finset_1(X13)\|~v1_glib_000(X13))))\|(~m1_glib_000(X14,X13)\|(~m1_glib_000(X15,X14)\|m1_glib_000(X15,X13)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t43_glib_000])])])). cnf(c_0_12, plain, (k24_glib_000(X1,X2)=k6_glib_000(X2)\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v1_finset_1(X1)\|~v1_glib_000(X1)\|~m1_glib_000(X2,X1)\|~v4_relat_1(X1,k5_numbers)), inference(evalgc,[status(thm)],[c_0_8])). cnf(c_0_13, plain, (k24_glib_000(X2,X1)=k6_glib_000(X2)\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v1_finset_1(X2)\|~v1_glib_000(X2)\|~v9_glib_000(X1,X2)\|~m1_glib_000(X1,X2)\|~v4_relat_1(X2,k5_numbers)), inference(evalgc,[status(thm)],[c_0_9])). cnf(c_0_14, negated_conjecture, (v9_glib_000(esk3_0,esk2_0)), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_15, negated_conjecture, (m1_glib_000(esk3_0,esk2_0)), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_16, negated_conjecture, (v9_glib_000(esk2_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_17, negated_conjecture, (m1_glib_000(esk2_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_18, negated_conjecture, (v1_glib_000(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_19, negated_conjecture, (v1_finset_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_20, negated_conjecture, (v1_funct_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_21, negated_conjecture, (v4_relat_1(esk1_0,k5_numbers)), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_22, negated_conjecture, (v1_relat_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_23, plain, (m1_glib_000(X3,X1)\|~v1_relat_1(X1)\|~v4_relat_1(X1,k5_numbers)\|~v1_funct_1(X1)\|~v1_finset_1(X1)\|~v1_glib_000(X1)\|~m1_glib_000(X2,X1)\|~m1_glib_000(X3,X2)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_24, plain, (v9_glib_000(X2,X1)\|k24_glib_000(X1,X2)!=k6_glib_000(X1)\|~m1_glib_000(X2,X1)\|~v1_relat_1(X1)\|~v4_relat_1(X1,k5_numbers)\|~v1_funct_1(X1)\|~v1_finset_1(X1)\|~v1_glib_000(X1)), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_25, plain, (k6_glib_000(X1)=k6_glib_000(X2)\|~m1_glib_000(X2,X1)\|~v1_glib_000(X1)\|~v1_finset_1(X1)\|~v1_funct_1(X1)\|~v4_relat_1(X1,k5_numbers)\|~v1_relat_1(X1)\|~v9_glib_000(X2,X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_12, c_0_13])])). cnf(c_0_26, negated_conjecture, (v9_glib_000(esk3_0,esk2_0)), inference(evalgc,[status(thm)],[c_0_14])). cnf(c_0_27, negated_conjecture, (m1_glib_000(esk3_0,esk2_0)), inference(evalgc,[status(thm)],[c_0_15])). cnf(c_0_28, negated_conjecture, (v9_glib_000(esk2_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_16])). cnf(c_0_29, negated_conjecture, (m1_glib_000(esk2_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_17])). cnf(c_0_30, negated_conjecture, (v1_glib_000(esk1_0)), inference(evalgc,[status(thm)],[c_0_18])). cnf(c_0_31, negated_conjecture, (v1_finset_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_19])). cnf(c_0_32, negated_conjecture, (v1_funct_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_20])). cnf(c_0_33, negated_conjecture, (v4_relat_1(esk1_0,k5_numbers)), inference(evalgc,[status(thm)],[c_0_21])). cnf(c_0_34, negated_conjecture, (v1_relat_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_22])). cnf(c_0_35, plain, (m1_glib_000(X3,X1)\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v1_finset_1(X1)\|~v1_glib_000(X1)\|~m1_glib_000(X3,X2)\|~m1_glib_000(X2,X1)\|~v4_relat_1(X1,k5_numbers)), inference(evalgc,[status(thm)],[c_0_23])). cnf(c_0_36, plain, (v9_glib_000(X2,X1)\|k24_glib_000(X1,X2)!=k6_glib_000(X1)\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v1_finset_1(X1)\|~v1_glib_000(X1)\|~m1_glib_000(X2,X1)\|~v4_relat_1(X1,k5_numbers)), inference(evalgc,[status(thm)],[c_0_24])). cnf(c_0_37, negated_conjecture, (k6_glib_000(esk3_0)=k6_glib_000(esk2_0)\|~v1_glib_000(esk2_0)\|~v1_finset_1(esk2_0)\|~v1_funct_1(esk2_0)\|~v4_relat_1(esk2_0,k5_numbers)\|~v1_relat_1(esk2_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25, c_0_26]), c_0_27])])])). cnf(c_0_38, negated_conjecture, (k6_glib_000(esk2_0)=k6_glib_000(esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25, c_0_28]), c_0_29]), c_0_30]), c_0_31]), c_0_32]), c_0_33]), c_0_34])])])). cnf(c_0_39, negated_conjecture, (m1_glib_000(X1,esk1_0)\|~m1_glib_000(X1,X2)\|~m1_glib_000(X2,esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35, c_0_33]), c_0_30]), c_0_31]), c_0_32]), c_0_34])])])). cnf(c_0_40, plain, (v9_glib_000(X1,X2)\|k6_glib_000(X1)!=k6_glib_000(X2)\|~m1_glib_000(X1,X2)\|~v1_glib_000(X2)\|~v1_finset_1(X2)\|~v1_funct_1(X2)\|~v4_relat_1(X2,k5_numbers)\|~v1_relat_1(X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_36, c_0_12])])). cnf(c_0_41, negated_conjecture, (k6_glib_000(esk3_0)=k6_glib_000(esk1_0)\|~v1_glib_000(esk2_0)\|~v1_finset_1(esk2_0)\|~v1_funct_1(esk2_0)\|~v4_relat_1(esk2_0,k5_numbers)\|~v1_relat_1(esk2_0)), inference(rw,[status(thm)],[c_0_37, c_0_38])). cnf(c_0_42, negated_conjecture, (m1_glib_000(X1,esk1_0)\|~m1_glib_000(X1,esk2_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_39, c_0_29])])). cnf(c_0_43, negated_conjecture, (~v9_glib_000(esk3_0,esk1_0)\|~m1_glib_000(esk3_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_10])). fof(c_0_44, plain, ![X11, X12]:((v1_relat_1(X12)\|~m1_glib_000(X12,X11)\|(~v1_relat_1(X11)\|(~v4_relat_1(X11,k5_numbers)\|(~v1_funct_1(X11)\|(~v1_finset_1(X11)\|~v1_glib_000(X11))))))&((v4_relat_1(X12,k5_numbers)\|~m1_glib_000(X12,X11)\|(~v1_relat_1(X11)\|(~v4_relat_1(X11,k5_numbers)\|(~v1_funct_1(X11)\|(~v1_finset_1(X11)\|~v1_glib_000(X11))))))&((v1_funct_1(X12)\|~m1_glib_000(X12,X11)\|(~v1_relat_1(X11)\|(~v4_relat_1(X11,k5_numbers)\|(~v1_funct_1(X11)\|(~v1_finset_1(X11)\|~v1_glib_000(X11))))))&((v1_finset_1(X12)\|~m1_glib_000(X12,X11)\|(~v1_relat_1(X11)\|(~v4_relat_1(X11,k5_numbers)\|(~v1_funct_1(X11)\|(~v1_finset_1(X11)\|~v1_glib_000(X11))))))&(v1_glib_000(X12)\|~m1_glib_000(X12,X11)\|(~v1_relat_1(X11)\|(~v4_relat_1(X11,k5_numbers)\|(~v1_funct_1(X11)\|(~v1_finset_1(X11)\|~v1_glib_000(X11)))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m1_glib_000])])])])). cnf(c_0_45, negated_conjecture, (v9_glib_000(esk3_0,X1)\|k6_glib_000(esk1_0)!=k6_glib_000(X1)\|~m1_glib_000(esk3_0,X1)\|~v1_glib_000(X1)\|~v1_finset_1(X1)\|~v1_funct_1(X1)\|~v4_relat_1(X1,k5_numbers)\|~v1_relat_1(X1)\|~v1_glib_000(esk2_0)\|~v1_finset_1(esk2_0)\|~v1_funct_1(esk2_0)\|~v4_relat_1(esk2_0,k5_numbers)\|~v1_relat_1(esk2_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_40, c_0_41])])). cnf(c_0_46, negated_conjecture, (m1_glib_000(esk3_0,esk1_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_42, c_0_27])])). cnf(c_0_47, negated_conjecture, (~v9_glib_000(esk3_0,esk1_0)\|~m1_glib_000(esk3_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_43])). cnf(c_0_48, plain, (v4_relat_1(X1,k5_numbers)\|~m1_glib_000(X1,X2)\|~v1_relat_1(X2)\|~v4_relat_1(X2,k5_numbers)\|~v1_funct_1(X2)\|~v1_finset_1(X2)\|~v1_glib_000(X2)), inference(split_conjunct,[status(thm)],[c_0_44])). cnf(c_0_49, negated_conjecture, (v9_glib_000(esk3_0,esk1_0)\|~v1_glib_000(esk2_0)\|~v1_finset_1(esk2_0)\|~v1_funct_1(esk2_0)\|~v4_relat_1(esk2_0,k5_numbers)\|~v1_relat_1(esk2_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_45]), c_0_46]), c_0_30]), c_0_31]), c_0_32]), c_0_33]), c_0_34])])])). cnf(c_0_50, negated_conjecture, (~v9_glib_000(esk3_0,esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47, c_0_46])])])). cnf(c_0_51, plain, (v4_relat_1(X1,k5_numbers)\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v1_finset_1(X2)\|~v1_glib_000(X2)\|~m1_glib_000(X1,X2)\|~v4_relat_1(X2,k5_numbers)), inference(evalgc,[status(thm)],[c_0_48])). cnf(c_0_52, plain, (v1_glib_000(X1)\|~m1_glib_000(X1,X2)\|~v1_relat_1(X2)\|~v4_relat_1(X2,k5_numbers)\|~v1_funct_1(X2)\|~v1_finset_1(X2)\|~v1_glib_000(X2)), inference(split_conjunct,[status(thm)],[c_0_44])). cnf(c_0_53, negated_conjecture, (~v1_glib_000(esk2_0)\|~v1_finset_1(esk2_0)\|~v1_funct_1(esk2_0)\|~v4_relat_1(esk2_0,k5_numbers)\|~v1_relat_1(esk2_0)), inference(sr,[status(thm)],[c_0_49, c_0_50])). cnf(c_0_54, negated_conjecture, (v4_relat_1(X1,k5_numbers)\|~m1_glib_000(X1,esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51, c_0_33]), c_0_30]), c_0_31]), c_0_32]), c_0_34])])])). cnf(c_0_55, plain, (v1_glib_000(X1)\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v1_finset_1(X2)\|~v1_glib_000(X2)\|~m1_glib_000(X1,X2)\|~v4_relat_1(X2,k5_numbers)), inference(evalgc,[status(thm)],[c_0_52])). cnf(c_0_56, plain, (v1_finset_1(X1)\|~m1_glib_000(X1,X2)\|~v1_relat_1(X2)\|~v4_relat_1(X2,k5_numbers)\|~v1_funct_1(X2)\|~v1_finset_1(X2)\|~v1_glib_000(X2)), inference(split_conjunct,[status(thm)],[c_0_44])). cnf(c_0_57, negated_conjecture, (~v1_glib_000(esk2_0)\|~v1_finset_1(esk2_0)\|~v1_funct_1(esk2_0)\|~v1_relat_1(esk2_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53, c_0_54]), c_0_29])])])). cnf(c_0_58, negated_conjecture, (v1_glib_000(X1)\|~m1_glib_000(X1,esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55, c_0_33]), c_0_30]), c_0_31]), c_0_32]), c_0_34])])])). cnf(c_0_59, plain, (v1_finset_1(X1)\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v1_finset_1(X2)\|~v1_glib_000(X2)\|~m1_glib_000(X1,X2)\|~v4_relat_1(X2,k5_numbers)), inference(evalgc,[status(thm)],[c_0_56])). cnf(c_0_60, plain, (v1_funct_1(X1)\|~m1_glib_000(X1,X2)\|~v1_relat_1(X2)\|~v4_relat_1(X2,k5_numbers)\|~v1_funct_1(X2)\|~v1_finset_1(X2)\|~v1_glib_000(X2)), inference(split_conjunct,[status(thm)],[c_0_44])). cnf(c_0_61, negated_conjecture, (~v1_finset_1(esk2_0)\|~v1_funct_1(esk2_0)\|~v1_relat_1(esk2_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57, c_0_58]), c_0_29])])])). cnf(c_0_62, negated_conjecture, (v1_finset_1(X1)\|~m1_glib_000(X1,esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59, c_0_33]), c_0_30]), c_0_31]), c_0_32]), c_0_34])])])). cnf(c_0_63, plain, (v1_funct_1(X1)\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v1_finset_1(X2)\|~v1_glib_000(X2)\|~m1_glib_000(X1,X2)\|~v4_relat_1(X2,k5_numbers)), inference(evalgc,[status(thm)],[c_0_60])). cnf(c_0_64, plain, (v1_relat_1(X1)\|~m1_glib_000(X1,X2)\|~v1_relat_1(X2)\|~v4_relat_1(X2,k5_numbers)\|~v1_funct_1(X2)\|~v1_finset_1(X2)\|~v1_glib_000(X2)), inference(split_conjunct,[status(thm)],[c_0_44])). cnf(c_0_65, negated_conjecture, (~v1_funct_1(esk2_0)\|~v1_relat_1(esk2_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61, c_0_62]), c_0_29])])])). cnf(c_0_66, negated_conjecture, (v1_funct_1(X1)\|~m1_glib_000(X1,esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63, c_0_33]), c_0_30]), c_0_31]), c_0_32]), c_0_34])])])). cnf(c_0_67, plain, (v1_relat_1(X1)\|~v1_relat_1(X2)\|~v1_funct_1(X2)\|~v1_finset_1(X2)\|~v1_glib_000(X2)\|~m1_glib_000(X1,X2)\|~v4_relat_1(X2,k5_numbers)), inference(evalgc,[status(thm)],[c_0_64])). cnf(c_0_68, negated_conjecture, (~v1_relat_1(esk2_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65, c_0_66]), c_0_29])])])). cnf(c_0_69, negated_conjecture, (v1_relat_1(X1)\|~m1_glib_000(X1,esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67, c_0_33]), c_0_30]), c_0_31]), c_0_32]), c_0_34])])])). cnf(c_0_70, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68, c_0_69]), c_0_29])]), ['proof']). # SZS output end CNFRefutation	reserve GS for GraphStruct; reserve G,G1,G2,G3 for _Graph; reserve e,x,x1,x2,y,y1,y2,E,V,X,Y for set; reserve n,n1,n2 for Nat; reserve v,v1,v2 for Vertex of G; theorem for G1 being _Graph, G2 being spanning Subgraph of G1, G3 being spanning Subgraph of G2 holds G3 is spanning Subgraph of G1 proof let G1 be _Graph, G2 be spanning Subgraph of G1, G3 be spanning Subgraph of G2; the_Vertices_of G3 = the_Vertices_of G2 by Def33 .= the_Vertices_of G1 by Def33; hence thesis by Def33,Th43; end;	Convert the following ATP output trace into a readable Mizar proof.
t43_orders_1	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t43_orders_1, conjecture, ![X1, X2]:((v1_relat_2(X2)&(v4_relat_2(X2)&(v8_relat_2(X2)&(v1_partfun1(X2,X1)&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,X1)))))))=>r1_orders_1(X2,X1)), file('/scratch/mptp/predsminms1/t43_orders_1__0', t43_orders_1)). fof(l6_orders_1, axiom, ![X1, X2]:((v1_partfun1(X2,X1)&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,X1))))=>k1_relat_1(X2)=X1), file('/scratch/mptp/predsminms1/t43_orders_1__0', l6_orders_1)). fof(cc2_relat_1, axiom, ![X1]:(v1_relat_1(X1)=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(X1))=>v1_relat_1(X2))), file('/scratch/mptp/predsminms1/t43_orders_1__0', cc2_relat_1)). fof(fc6_relat_1, axiom, ![X1, X2]:v1_relat_1(k2_zfmisc_1(X1,X2)), file('/scratch/mptp/predsminms1/t43_orders_1__0', fc6_relat_1)). fof(d16_relat_2, axiom, ![X1]:(v1_relat_1(X1)=>(v8_relat_2(X1)<=>r8_relat_2(X1,k1_relat_1(X1)))), file('/scratch/mptp/predsminms1/t43_orders_1__0', d16_relat_2)). fof(d9_relat_2, axiom, ![X1]:(v1_relat_1(X1)=>(v1_relat_2(X1)<=>r1_relat_2(X1,k1_relat_1(X1)))), file('/scratch/mptp/predsminms1/t43_orders_1__0', d9_relat_2)). fof(d6_orders_1, axiom, ![X1]:(v1_relat_1(X1)=>![X2]:(r1_orders_1(X1,X2)<=>(r1_relat_2(X1,X2)&r8_relat_2(X1,X2)))), file('/scratch/mptp/predsminms1/t43_orders_1__0', d6_orders_1)). fof(c_0_7, negated_conjecture, ~(![X1, X2]:((v1_relat_2(X2)&(v4_relat_2(X2)&(v8_relat_2(X2)&(v1_partfun1(X2,X1)&m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,X1)))))))=>r1_orders_1(X2,X1))), inference(assume_negation,[status(cth)],[t43_orders_1])). fof(c_0_8, plain, ![X8, X9]:(~v1_partfun1(X9,X8)\|~m1_subset_1(X9,k1_zfmisc_1(k2_zfmisc_1(X8,X8)))\|k1_relat_1(X9)=X8), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l6_orders_1])])). fof(c_0_9, negated_conjecture, ((v1_relat_2(esk2_0)&(v4_relat_2(esk2_0)&(v8_relat_2(esk2_0)&(v1_partfun1(esk2_0,esk1_0)&m1_subset_1(esk2_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,esk1_0)))))))&~r1_orders_1(esk2_0,esk1_0)), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])). fof(c_0_10, plain, ![X10, X11]:(~v1_relat_1(X10)\|(~m1_subset_1(X11,k1_zfmisc_1(X10))\|v1_relat_1(X11))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_relat_1])])])). fof(c_0_11, plain, ![X12, X13]:v1_relat_1(k2_zfmisc_1(X12,X13)), inference(variable_rename,[status(thm)],[fc6_relat_1])). fof(c_0_12, plain, ![X14]:((~v8_relat_2(X14)\|r8_relat_2(X14,k1_relat_1(X14))\|~v1_relat_1(X14))&(~r8_relat_2(X14,k1_relat_1(X14))\|v8_relat_2(X14)\|~v1_relat_1(X14))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d16_relat_2])])])). cnf(c_0_13, plain, (k1_relat_1(X1)=X2\|~v1_partfun1(X1,X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X2)))), inference(split_conjunct,[status(thm)],[c_0_8])). cnf(c_0_14, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,esk1_0)))), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_15, negated_conjecture, (v1_partfun1(esk2_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_16, plain, (v1_relat_1(X2)\|~v1_relat_1(X1)\|~m1_subset_1(X2,k1_zfmisc_1(X1))), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_17, plain, (v1_relat_1(k2_zfmisc_1(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_11])). fof(c_0_18, plain, ![X7]:((~v1_relat_2(X7)\|r1_relat_2(X7,k1_relat_1(X7))\|~v1_relat_1(X7))&(~r1_relat_2(X7,k1_relat_1(X7))\|v1_relat_2(X7)\|~v1_relat_1(X7))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d9_relat_2])])])). fof(c_0_19, plain, ![X5, X6]:(((r1_relat_2(X5,X6)\|~r1_orders_1(X5,X6)\|~v1_relat_1(X5))&(r8_relat_2(X5,X6)\|~r1_orders_1(X5,X6)\|~v1_relat_1(X5)))&(~r1_relat_2(X5,X6)\|~r8_relat_2(X5,X6)\|r1_orders_1(X5,X6)\|~v1_relat_1(X5))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d6_orders_1])])])])). cnf(c_0_20, plain, (r8_relat_2(X1,k1_relat_1(X1))\|~v8_relat_2(X1)\|~v1_relat_1(X1)), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_21, plain, (k1_relat_1(X1)=X2\|~v1_partfun1(X1,X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X2)))), inference(evalgc,[status(thm)],[c_0_13])). cnf(c_0_22, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,esk1_0)))), inference(evalgc,[status(thm)],[c_0_14])). cnf(c_0_23, negated_conjecture, (v1_partfun1(esk2_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_15])). cnf(c_0_24, plain, (v1_relat_1(X2)\|~v1_relat_1(X1)\|~m1_subset_1(X2,k1_zfmisc_1(X1))), inference(evalgc,[status(thm)],[c_0_16])). cnf(c_0_25, plain, (v1_relat_1(k2_zfmisc_1(X1,X2))), inference(evalgc,[status(thm)],[c_0_17])). cnf(c_0_26, negated_conjecture, (v8_relat_2(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_27, plain, (r1_relat_2(X1,k1_relat_1(X1))\|~v1_relat_2(X1)\|~v1_relat_1(X1)), inference(split_conjunct,[status(thm)],[c_0_18])). cnf(c_0_28, negated_conjecture, (v1_relat_2(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_29, plain, (r1_orders_1(X1,X2)\|~r1_relat_2(X1,X2)\|~r8_relat_2(X1,X2)\|~v1_relat_1(X1)), inference(split_conjunct,[status(thm)],[c_0_19])). cnf(c_0_30, plain, (r8_relat_2(X1,k1_relat_1(X1))\|~v8_relat_2(X1)\|~v1_relat_1(X1)), inference(evalgc,[status(thm)],[c_0_20])). cnf(c_0_31, negated_conjecture, (k1_relat_1(esk2_0)=esk1_0), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21, c_0_22]), c_0_23])])])). cnf(c_0_32, negated_conjecture, (v1_relat_1(esk2_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24, c_0_22]), c_0_25])])])). cnf(c_0_33, negated_conjecture, (v8_relat_2(esk2_0)), inference(evalgc,[status(thm)],[c_0_26])). cnf(c_0_34, plain, (r1_relat_2(X1,k1_relat_1(X1))\|~v1_relat_2(X1)\|~v1_relat_1(X1)), inference(evalgc,[status(thm)],[c_0_27])). cnf(c_0_35, negated_conjecture, (v1_relat_2(esk2_0)), inference(evalgc,[status(thm)],[c_0_28])). cnf(c_0_36, negated_conjecture, (~r1_orders_1(esk2_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_9])). cnf(c_0_37, plain, (r1_orders_1(X1,X2)\|~v1_relat_1(X1)\|~r1_relat_2(X1,X2)\|~r8_relat_2(X1,X2)), inference(evalgc,[status(thm)],[c_0_29])). cnf(c_0_38, negated_conjecture, (r8_relat_2(esk2_0,esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30, c_0_31]), c_0_32]), c_0_33])])])). cnf(c_0_39, negated_conjecture, (r1_relat_2(esk2_0,esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34, c_0_31]), c_0_32]), c_0_35])])])). cnf(c_0_40, negated_conjecture, (~r1_orders_1(esk2_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_36])). cnf(c_0_41, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37, c_0_38]), c_0_39]), c_0_32])]), c_0_40]), ['proof']). # SZS output end CNFRefutation	reserve X,Y for set, x,x1,x2,y,y1,y2,z for set, f,g,h for Function; reserve M for non empty set; reserve D for non empty set; reserve P for Relation; reserve O for Order of X; reserve R,P for Relation, X,X1,X2,Y,Z,x,y,z,u for set, g,h for Function, O for Order of X, D for non empty set, d,d1,d2 for Element of D, A1,A2,B for Ordinal, L,L1,L2 for T-Sequence; theorem O quasi_orders X proof A1: field O = X by Lm2; then A2: O is_transitive_in X by RELAT_2:def 16; O is_reflexive_in X by A1,RELAT_2:def 9; hence thesis by A2,Def6; end;	Convert the following ATP output trace into a readable Mizar proof.
t3_pencil_1	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t3_pencil_1, conjecture, ![X1]:(r1_ordinal1(np__2,k1_card_1(X1))=>![X2]:?[X3]:(r2_hidden(X3,X1)&~(X2=X3))), file('/scratch/mptp/predsminms1/t3_pencil_1__0', t3_pencil_1)). fof(t2_pencil_1, axiom, ![X1]:(r1_ordinal1(np__2,k1_card_1(X1))<=>?[X2, X3]:(r2_hidden(X2,X1)&(r2_hidden(X3,X1)&~(X2=X3)))), file('/scratch/mptp/predsminms1/t3_pencil_1__0', t2_pencil_1)). fof(c_0_2, negated_conjecture, ~(![X1]:(r1_ordinal1(np__2,k1_card_1(X1))=>![X2]:?[X3]:(r2_hidden(X3,X1)&~(X2=X3)))), inference(assume_negation,[status(cth)],[t3_pencil_1])). fof(c_0_3, plain, ![X7, X10, X11, X12]:(((r2_hidden(esk3_1(X7),X7)\|~r1_ordinal1(np__2,k1_card_1(X7)))&((r2_hidden(esk4_1(X7),X7)\|~r1_ordinal1(np__2,k1_card_1(X7)))&(esk3_1(X7)!=esk4_1(X7)\|~r1_ordinal1(np__2,k1_card_1(X7)))))&(~r2_hidden(X11,X10)\|(~r2_hidden(X12,X10)\|X11=X12)\|r1_ordinal1(np__2,k1_card_1(X10)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t2_pencil_1])])])])])])])). fof(c_0_4, negated_conjecture, ![X6]:(r1_ordinal1(np__2,k1_card_1(esk1_0))&(~r2_hidden(X6,esk1_0)\|esk2_0=X6)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_2])])])])])). cnf(c_0_5, plain, (esk3_1(X1)!=esk4_1(X1)\|~r1_ordinal1(np__2,k1_card_1(X1))), inference(split_conjunct,[status(thm)],[c_0_3])). cnf(c_0_6, negated_conjecture, (r1_ordinal1(np__2,k1_card_1(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_7, negated_conjecture, (esk2_0=X1\|~r2_hidden(X1,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_8, plain, (r2_hidden(esk4_1(X1),X1)\|~r1_ordinal1(np__2,k1_card_1(X1))), inference(split_conjunct,[status(thm)],[c_0_3])). cnf(c_0_9, plain, (r2_hidden(esk3_1(X1),X1)\|~r1_ordinal1(np__2,k1_card_1(X1))), inference(split_conjunct,[status(thm)],[c_0_3])). cnf(c_0_10, plain, (esk4_1(X1)!=esk3_1(X1)\|~r1_ordinal1(np__2,k1_card_1(X1))), inference(evalgc,[status(thm)],[c_0_5])). cnf(c_0_11, negated_conjecture, (r1_ordinal1(np__2,k1_card_1(esk1_0))), inference(evalgc,[status(thm)],[c_0_6])). cnf(c_0_12, negated_conjecture, (esk2_0=X1\|~r2_hidden(X1,esk1_0)), inference(evalgc,[status(thm)],[c_0_7])). cnf(c_0_13, plain, (r2_hidden(esk4_1(X1),X1)\|~r1_ordinal1(np__2,k1_card_1(X1))), inference(evalgc,[status(thm)],[c_0_8])). cnf(c_0_14, plain, (r2_hidden(esk3_1(X1),X1)\|~r1_ordinal1(np__2,k1_card_1(X1))), inference(evalgc,[status(thm)],[c_0_9])). cnf(c_0_15, negated_conjecture, (esk4_1(esk1_0)!=esk3_1(esk1_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_10, c_0_11])])). cnf(c_0_16, negated_conjecture, (esk4_1(esk1_0)=esk2_0), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12, c_0_13]), c_0_11])])])). cnf(c_0_17, negated_conjecture, (esk3_1(esk1_0)=esk2_0), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12, c_0_14]), c_0_11])])])). cnf(c_0_18, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15, c_0_16]), c_0_17])]), ['proof']). # SZS output end CNFRefutation	theorem Th3: for X being set st 2 c= card X for x being set ex y being set st y in X & x<>y proof let X be set; assume 2 c= card X; then consider a,b being set such that A1: a in X and A2: b in X & a <> b by Th2; let x be set; per cases; suppose A3: x=a; take b; thus thesis by A2,A3; end; suppose A4: x <> a; take a; thus thesis by A1,A4; end; end;	Convert the following ATP output trace into a readable Mizar proof.
t10_euclid_3	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t10_euclid_3, conjecture, ![X1]:(v1_xcmplx_0(X1)=>k19_euclid(k3_complex1(k4_xcmplx_0(X1)),k4_complex1(k4_xcmplx_0(X1)))=k19_euclid(k1_real_1(k3_complex1(X1)),k1_real_1(k4_complex1(X1)))), file('/scratch/mptp/predsminms1/t10_euclid_3__0', t10_euclid_3)). fof(t17_complex1, axiom, ![X1]:(v1_xcmplx_0(X1)=>(k3_complex1(k4_xcmplx_0(X1))=k1_real_1(k3_complex1(X1))&k4_complex1(k4_xcmplx_0(X1))=k1_real_1(k4_complex1(X1)))), file('/scratch/mptp/predsminms1/t10_euclid_3__0', t17_complex1)). fof(c_0_2, negated_conjecture, ~(![X1]:(v1_xcmplx_0(X1)=>k19_euclid(k3_complex1(k4_xcmplx_0(X1)),k4_complex1(k4_xcmplx_0(X1)))=k19_euclid(k1_real_1(k3_complex1(X1)),k1_real_1(k4_complex1(X1))))), inference(assume_negation,[status(cth)],[t10_euclid_3])). fof(c_0_3, negated_conjecture, (v1_xcmplx_0(esk1_0)&k19_euclid(k3_complex1(k4_xcmplx_0(esk1_0)),k4_complex1(k4_xcmplx_0(esk1_0)))!=k19_euclid(k1_real_1(k3_complex1(esk1_0)),k1_real_1(k4_complex1(esk1_0)))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])])])). fof(c_0_4, plain, ![X3]:((k3_complex1(k4_xcmplx_0(X3))=k1_real_1(k3_complex1(X3))\|~v1_xcmplx_0(X3))&(k4_complex1(k4_xcmplx_0(X3))=k1_real_1(k4_complex1(X3))\|~v1_xcmplx_0(X3))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t17_complex1])])])). cnf(c_0_5, negated_conjecture, (k19_euclid(k3_complex1(k4_xcmplx_0(esk1_0)),k4_complex1(k4_xcmplx_0(esk1_0)))!=k19_euclid(k1_real_1(k3_complex1(esk1_0)),k1_real_1(k4_complex1(esk1_0)))), inference(split_conjunct,[status(thm)],[c_0_3])). cnf(c_0_6, plain, (k3_complex1(k4_xcmplx_0(X1))=k1_real_1(k3_complex1(X1))\|~v1_xcmplx_0(X1)), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_7, negated_conjecture, (v1_xcmplx_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_3])). cnf(c_0_8, negated_conjecture, (k19_euclid(k1_real_1(k3_complex1(esk1_0)),k1_real_1(k4_complex1(esk1_0)))!=k19_euclid(k3_complex1(k4_xcmplx_0(esk1_0)),k4_complex1(k4_xcmplx_0(esk1_0)))), inference(evalgc,[status(thm)],[c_0_5])). cnf(c_0_9, plain, (k1_real_1(k3_complex1(X1))=k3_complex1(k4_xcmplx_0(X1))\|~v1_xcmplx_0(X1)), inference(evalgc,[status(thm)],[c_0_6])). cnf(c_0_10, negated_conjecture, (v1_xcmplx_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_7])). cnf(c_0_11, plain, (k4_complex1(k4_xcmplx_0(X1))=k1_real_1(k4_complex1(X1))\|~v1_xcmplx_0(X1)), inference(split_conjunct,[status(thm)],[c_0_4])). cnf(c_0_12, negated_conjecture, (k19_euclid(k3_complex1(k4_xcmplx_0(esk1_0)),k4_complex1(k4_xcmplx_0(esk1_0)))!=k19_euclid(k3_complex1(k4_xcmplx_0(esk1_0)),k1_real_1(k4_complex1(esk1_0)))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8, c_0_9]), c_0_10])])])). cnf(c_0_13, plain, (k4_complex1(k4_xcmplx_0(X1))=k1_real_1(k4_complex1(X1))\|~v1_xcmplx_0(X1)), inference(evalgc,[status(thm)],[c_0_11])). cnf(c_0_14, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12, c_0_13]), c_0_10])]), ['proof']). # SZS output end CNFRefutation	reserve z,z1,z2 for complex number; reserve r,x1,x2 for Real; reserve p0,p,p1,p2,p3,q for Point of TOP-REAL 2; theorem Th10: \|[Re (-z),Im (-z)]\|=\|[-(Re z), -(Im z)]\| proof (\|[Re (-z),Im (-z)]\|)`2=Im (-z) by EUCLID:52; then A1: (\|[Re (-z),Im (-z)]\|)`2=-(Im z) by COMPLEX1:17; (\|[Re (-z),Im (-z)]\|)`1=Re (-z) by EUCLID:52; then (\|[Re (-z),Im (-z)]\|)`1=-(Re z) by COMPLEX1:17; hence thesis by A1,EUCLID:53; end;	Convert the following ATP output trace into a readable Mizar proof.
t10_finseq_1	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(d1_tarski, axiom, ![X1, X2]:(X2=k1_tarski(X1)<=>![X3]:(r2_hidden(X3,X2)<=>X3=X1)), file('/scratch/mptp/predsminms1/t10_finseq_1__0', d1_tarski)). fof(d4_xboole_0, axiom, ![X1, X2, X3]:(X3=k3_xboole_0(X1,X2)<=>![X4]:(r2_hidden(X4,X3)<=>(r2_hidden(X4,X1)&r2_hidden(X4,X2)))), file('/scratch/mptp/predsminms1/t10_finseq_1__0', d4_xboole_0)). fof(t29_xreal_1, axiom, ![X1]:(v1_xreal_0(X1)=>![X2]:(v1_xreal_0(X2)=>~((~(r1_xxreal_0(X1,k6_numbers))&r1_xxreal_0(k2_xcmplx_0(X2,X1),X2))))), file('/scratch/mptp/predsminms1/t10_finseq_1__0', t29_xreal_1)). fof(t10_finseq_1, conjecture, ![X1]:(v7_ordinal1(X1)=>k2_finseq_1(X1)=k7_subset_1(k5_numbers,k2_finseq_1(k1_nat_1(X1,np__1)),k1_tarski(k1_nat_1(X1,np__1)))), file('/scratch/mptp/predsminms1/t10_finseq_1__0', t10_finseq_1)). fof(redefinition_k7_subset_1, axiom, ![X1, X2, X3]:(m1_subset_1(X2,k1_zfmisc_1(X1))=>k7_subset_1(X1,X2,X3)=k4_xboole_0(X2,X3)), file('/scratch/mptp/predsminms1/t10_finseq_1__0', redefinition_k7_subset_1)). fof(dt_k2_finseq_1, axiom, ![X1]:(v7_ordinal1(X1)=>m1_subset_1(k2_finseq_1(X1),k1_zfmisc_1(k5_numbers))), file('/scratch/mptp/predsminms1/t10_finseq_1__0', dt_k2_finseq_1)). fof(t7_boole, axiom, ![X1, X2]:~((r2_hidden(X1,X2)&v1_xboole_0(X2))), file('/scratch/mptp/predsminms1/t10_finseq_1__0', t7_boole)). fof(redefinition_k6_numbers, axiom, k6_numbers=k1_xboole_0, file('/scratch/mptp/predsminms1/t10_finseq_1__0', redefinition_k6_numbers)). fof(redefinition_k1_nat_1, axiom, ![X1, X2]:((v7_ordinal1(X1)&m1_subset_1(X2,k5_numbers))=>k1_nat_1(X1,X2)=k2_xcmplx_0(X1,X2)), file('/scratch/mptp/predsminms1/t10_finseq_1__0', redefinition_k1_nat_1)). fof(t88_xboole_1, axiom, ![X1, X2]:(r1_xboole_0(X1,X2)=>k4_xboole_0(k2_xboole_0(X1,X2),X2)=X1), file('/scratch/mptp/predsminms1/t10_finseq_1__0', t88_xboole_1)). fof(t9_finseq_1, axiom, ![X1]:(v7_ordinal1(X1)=>k2_xboole_0(k2_finseq_1(X1),k1_tarski(k1_nat_1(X1,np__1)))=k2_finseq_1(k1_nat_1(X1,np__1))), file('/scratch/mptp/predsminms1/t10_finseq_1__0', t9_finseq_1)). fof(t6_boole, axiom, ![X1]:(v1_xboole_0(X1)=>X1=k1_xboole_0), file('/scratch/mptp/predsminms1/t10_finseq_1__0', t6_boole)). fof(cc2_xreal_0, axiom, ![X1]:(v7_ordinal1(X1)=>v1_xreal_0(X1)), file('/scratch/mptp/predsminms1/t10_finseq_1__0', cc2_xreal_0)). fof(fc1_nat_1, axiom, ![X1, X2]:((v7_ordinal1(X1)&v7_ordinal1(X2))=>v7_ordinal1(k2_xcmplx_0(X1,X2))), file('/scratch/mptp/predsminms1/t10_finseq_1__0', fc1_nat_1)). fof(cc8_ordinal1, axiom, ![X1]:(m1_subset_1(X1,k4_ordinal1)=>v7_ordinal1(X1)), file('/scratch/mptp/predsminms1/t10_finseq_1__0', cc8_ordinal1)). fof(spc0_boole, axiom, v1_xboole_0(np__0), file('/scratch/mptp/predsminms1/t10_finseq_1__0', spc0_boole)). fof(t1_finseq_1, axiom, ![X1]:(v7_ordinal1(X1)=>![X2]:(v7_ordinal1(X2)=>(r2_hidden(X1,k2_finseq_1(X2))<=>(r1_xxreal_0(np__1,X1)&r1_xxreal_0(X1,X2))))), file('/scratch/mptp/predsminms1/t10_finseq_1__0', t1_finseq_1)). fof(redefinition_k5_numbers, axiom, k5_numbers=k4_ordinal1, file('/scratch/mptp/predsminms1/t10_finseq_1__0', redefinition_k5_numbers)). fof(d7_xboole_0, axiom, ![X1, X2]:(r1_xboole_0(X1,X2)<=>k3_xboole_0(X1,X2)=k1_xboole_0), file('/scratch/mptp/predsminms1/t10_finseq_1__0', d7_xboole_0)). fof(rqLessOrEqual__r1_xxreal_0__r1_r0, axiom, ~(r1_xxreal_0(np__1,np__0)), file('/scratch/mptp/predsminms1/t10_finseq_1__0', rqLessOrEqual__r1_xxreal_0__r1_r0)). fof(spc1_numerals, axiom, ((v2_xxreal_0(np__1)&m2_subset_1(np__1,k1_numbers,k5_numbers))&(m1_subset_1(np__1,k5_numbers)&m1_subset_1(np__1,k1_numbers))), file('/scratch/mptp/predsminms1/t10_finseq_1__0', spc1_numerals)). fof(c_0_21, plain, ![X22, X23, X24, X25, X26, X27]:(((~r2_hidden(X24,X23)\|X24=X22\|X23!=k1_tarski(X22))&(X25!=X22\|r2_hidden(X25,X23)\|X23!=k1_tarski(X22)))&((~r2_hidden(esk2_2(X26,X27),X27)\|esk2_2(X26,X27)!=X26\|X27=k1_tarski(X26))&(r2_hidden(esk2_2(X26,X27),X27)\|esk2_2(X26,X27)=X26\|X27=k1_tarski(X26)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_tarski])])])])])])). fof(c_0_22, plain, ![X31, X32, X33, X34, X35, X36, X37, X38]:((((r2_hidden(X34,X31)\|~r2_hidden(X34,X33)\|X33!=k3_xboole_0(X31,X32))&(r2_hidden(X34,X32)\|~r2_hidden(X34,X33)\|X33!=k3_xboole_0(X31,X32)))&(~r2_hidden(X35,X31)\|~r2_hidden(X35,X32)\|r2_hidden(X35,X33)\|X33!=k3_xboole_0(X31,X32)))&((~r2_hidden(esk3_3(X36,X37,X38),X38)\|(~r2_hidden(esk3_3(X36,X37,X38),X36)\|~r2_hidden(esk3_3(X36,X37,X38),X37))\|X38=k3_xboole_0(X36,X37))&((r2_hidden(esk3_3(X36,X37,X38),X36)\|r2_hidden(esk3_3(X36,X37,X38),X38)\|X38=k3_xboole_0(X36,X37))&(r2_hidden(esk3_3(X36,X37,X38),X37)\|r2_hidden(esk3_3(X36,X37,X38),X38)\|X38=k3_xboole_0(X36,X37))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d4_xboole_0])])])])])])). cnf(c_0_23, plain, (X1=X3\|~r2_hidden(X1,X2)\|X2!=k1_tarski(X3)), inference(split_conjunct,[status(thm)],[c_0_21])). cnf(c_0_24, plain, (r2_hidden(esk3_3(X1,X2,X3),X2)\|r2_hidden(esk3_3(X1,X2,X3),X3)\|X3=k3_xboole_0(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_22])). fof(c_0_25, plain, ![X20, X21]:(~v1_xreal_0(X20)\|(~v1_xreal_0(X21)\|(r1_xxreal_0(X20,k6_numbers)\|~r1_xxreal_0(k2_xcmplx_0(X21,X20),X21)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t29_xreal_1])])])])). fof(c_0_26, negated_conjecture, ~(![X1]:(v7_ordinal1(X1)=>k2_finseq_1(X1)=k7_subset_1(k5_numbers,k2_finseq_1(k1_nat_1(X1,np__1)),k1_tarski(k1_nat_1(X1,np__1))))), inference(assume_negation,[status(cth)],[t10_finseq_1])). fof(c_0_27, plain, ![X12, X13, X14]:(~m1_subset_1(X13,k1_zfmisc_1(X12))\|k7_subset_1(X12,X13,X14)=k4_xboole_0(X13,X14)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k7_subset_1])])). fof(c_0_28, plain, ![X11]:(~v7_ordinal1(X11)\|m1_subset_1(k2_finseq_1(X11),k1_zfmisc_1(k5_numbers))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_finseq_1])])). fof(c_0_29, plain, ![X29, X30]:(~r2_hidden(X29,X30)\|~v1_xboole_0(X30)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])])). cnf(c_0_30, plain, (X1=X3\|X2!=k1_tarski(X3)\|~r2_hidden(X1,X2)), inference(evalgc,[status(thm)],[c_0_23])). cnf(c_0_31, plain, (X3=k3_xboole_0(X1,X2)\|r2_hidden(esk3_3(X1,X2,X3),X3)\|r2_hidden(esk3_3(X1,X2,X3),X2)), inference(evalgc,[status(thm)],[c_0_24])). cnf(c_0_32, plain, (r1_xxreal_0(X1,k6_numbers)\|~v1_xreal_0(X1)\|~v1_xreal_0(X2)\|~r1_xxreal_0(k2_xcmplx_0(X2,X1),X2)), inference(split_conjunct,[status(thm)],[c_0_25])). cnf(c_0_33, plain, (k6_numbers=k1_xboole_0), inference(split_conjunct,[status(thm)],[redefinition_k6_numbers])). fof(c_0_34, plain, ![X7, X8]:(~v7_ordinal1(X7)\|~m1_subset_1(X8,k5_numbers)\|k1_nat_1(X7,X8)=k2_xcmplx_0(X7,X8)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k1_nat_1])])). fof(c_0_35, negated_conjecture, (v7_ordinal1(esk1_0)&k2_finseq_1(esk1_0)!=k7_subset_1(k5_numbers,k2_finseq_1(k1_nat_1(esk1_0,np__1)),k1_tarski(k1_nat_1(esk1_0,np__1)))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])])). cnf(c_0_36, plain, (k7_subset_1(X2,X1,X3)=k4_xboole_0(X1,X3)\|~m1_subset_1(X1,k1_zfmisc_1(X2))), inference(split_conjunct,[status(thm)],[c_0_27])). cnf(c_0_37, plain, (m1_subset_1(k2_finseq_1(X1),k1_zfmisc_1(k5_numbers))\|~v7_ordinal1(X1)), inference(split_conjunct,[status(thm)],[c_0_28])). fof(c_0_38, plain, ![X16, X17]:(~r1_xboole_0(X16,X17)\|k4_xboole_0(k2_xboole_0(X16,X17),X17)=X16), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t88_xboole_1])])). fof(c_0_39, plain, ![X15]:(~v7_ordinal1(X15)\|k2_xboole_0(k2_finseq_1(X15),k1_tarski(k1_nat_1(X15,np__1)))=k2_finseq_1(k1_nat_1(X15,np__1))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t9_finseq_1])])). cnf(c_0_40, plain, (~r2_hidden(X1,X2)\|~v1_xboole_0(X2)), inference(split_conjunct,[status(thm)],[c_0_29])). cnf(c_0_41, plain, (esk3_3(X1,X2,X3)=X4\|X3=k3_xboole_0(X1,X2)\|r2_hidden(esk3_3(X1,X2,X3),X3)\|X2!=k1_tarski(X4)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_30, c_0_31])])). fof(c_0_42, plain, ![X19]:(~v1_xboole_0(X19)\|X19=k1_xboole_0), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])])). cnf(c_0_43, plain, (r1_xxreal_0(X1,k6_numbers)\|~v1_xreal_0(X2)\|~v1_xreal_0(X1)\|~r1_xxreal_0(k2_xcmplx_0(X2,X1),X2)), inference(evalgc,[status(thm)],[c_0_32])). cnf(c_0_44, plain, (k6_numbers=k1_xboole_0), inference(evalgc,[status(thm)],[c_0_33])). cnf(c_0_45, plain, (k1_nat_1(X1,X2)=k2_xcmplx_0(X1,X2)\|~v7_ordinal1(X1)\|~m1_subset_1(X2,k5_numbers)), inference(split_conjunct,[status(thm)],[c_0_34])). fof(c_0_46, plain, ![X18]:(~v7_ordinal1(X18)\|v1_xreal_0(X18)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_xreal_0])])). fof(c_0_47, plain, ![X9, X10]:(~v7_ordinal1(X9)\|~v7_ordinal1(X10)\|v7_ordinal1(k2_xcmplx_0(X9,X10))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc1_nat_1])])). fof(c_0_48, plain, ![X6]:(~m1_subset_1(X6,k4_ordinal1)\|v7_ordinal1(X6)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc8_ordinal1])])). cnf(c_0_49, negated_conjecture, (k2_finseq_1(esk1_0)!=k7_subset_1(k5_numbers,k2_finseq_1(k1_nat_1(esk1_0,np__1)),k1_tarski(k1_nat_1(esk1_0,np__1)))), inference(split_conjunct,[status(thm)],[c_0_35])). cnf(c_0_50, plain, (k7_subset_1(X2,X1,X3)=k4_xboole_0(X1,X3)\|~m1_subset_1(X1,k1_zfmisc_1(X2))), inference(evalgc,[status(thm)],[c_0_36])). cnf(c_0_51, plain, (m1_subset_1(k2_finseq_1(X1),k1_zfmisc_1(k5_numbers))\|~v7_ordinal1(X1)), inference(evalgc,[status(thm)],[c_0_37])). cnf(c_0_52, plain, (k4_xboole_0(k2_xboole_0(X1,X2),X2)=X1\|~r1_xboole_0(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_38])). cnf(c_0_53, plain, (k2_xboole_0(k2_finseq_1(X1),k1_tarski(k1_nat_1(X1,np__1)))=k2_finseq_1(k1_nat_1(X1,np__1))\|~v7_ordinal1(X1)), inference(split_conjunct,[status(thm)],[c_0_39])). cnf(c_0_54, plain, (r2_hidden(esk3_3(X1,X2,X3),X1)\|r2_hidden(esk3_3(X1,X2,X3),X3)\|X3=k3_xboole_0(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_55, plain, (~v1_xboole_0(X2)\|~r2_hidden(X1,X2)), inference(evalgc,[status(thm)],[c_0_40])). cnf(c_0_56, plain, (esk3_3(X1,k1_tarski(X2),X3)=X2\|X3=k3_xboole_0(X1,k1_tarski(X2))\|r2_hidden(esk3_3(X1,k1_tarski(X2),X3),X3)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[c_0_41])])). cnf(c_0_57, plain, (X1=k1_xboole_0\|~v1_xboole_0(X1)), inference(split_conjunct,[status(thm)],[c_0_42])). cnf(c_0_58, plain, (v1_xboole_0(np__0)), inference(split_conjunct,[status(thm)],[spc0_boole])). cnf(c_0_59, plain, (r1_xxreal_0(X1,k1_xboole_0)\|~r1_xxreal_0(k2_xcmplx_0(X2,X1),X2)\|~v1_xreal_0(X2)\|~v1_xreal_0(X1)), inference(rw,[status(thm)],[c_0_43, c_0_44])). cnf(c_0_60, plain, (k2_xcmplx_0(X1,X2)=k1_nat_1(X1,X2)\|~v7_ordinal1(X1)\|~m1_subset_1(X2,k5_numbers)), inference(evalgc,[status(thm)],[c_0_45])). cnf(c_0_61, plain, (v1_xreal_0(X1)\|~v7_ordinal1(X1)), inference(split_conjunct,[status(thm)],[c_0_46])). fof(c_0_62, plain, ![X40, X41]:(((r1_xxreal_0(np__1,X40)\|~r2_hidden(X40,k2_finseq_1(X41))\|~v7_ordinal1(X41)\|~v7_ordinal1(X40))&(r1_xxreal_0(X40,X41)\|~r2_hidden(X40,k2_finseq_1(X41))\|~v7_ordinal1(X41)\|~v7_ordinal1(X40)))&(~r1_xxreal_0(np__1,X40)\|~r1_xxreal_0(X40,X41)\|r2_hidden(X40,k2_finseq_1(X41))\|~v7_ordinal1(X41)\|~v7_ordinal1(X40))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_finseq_1])])])])). cnf(c_0_63, plain, (v7_ordinal1(k2_xcmplx_0(X1,X2))\|~v7_ordinal1(X1)\|~v7_ordinal1(X2)), inference(split_conjunct,[status(thm)],[c_0_47])). cnf(c_0_64, plain, (v7_ordinal1(X1)\|~m1_subset_1(X1,k4_ordinal1)), inference(split_conjunct,[status(thm)],[c_0_48])). cnf(c_0_65, plain, (k5_numbers=k4_ordinal1), inference(split_conjunct,[status(thm)],[redefinition_k5_numbers])). cnf(c_0_66, negated_conjecture, (k7_subset_1(k5_numbers,k2_finseq_1(k1_nat_1(esk1_0,np__1)),k1_tarski(k1_nat_1(esk1_0,np__1)))!=k2_finseq_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_49])). cnf(c_0_67, plain, (k7_subset_1(k5_numbers,k2_finseq_1(X1),X2)=k4_xboole_0(k2_finseq_1(X1),X2)\|~v7_ordinal1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_50, c_0_51])])). cnf(c_0_68, plain, (k4_xboole_0(k2_xboole_0(X1,X2),X2)=X1\|~r1_xboole_0(X1,X2)), inference(evalgc,[status(thm)],[c_0_52])). cnf(c_0_69, plain, (k2_xboole_0(k2_finseq_1(X1),k1_tarski(k1_nat_1(X1,np__1)))=k2_finseq_1(k1_nat_1(X1,np__1))\|~v7_ordinal1(X1)), inference(evalgc,[status(thm)],[c_0_53])). cnf(c_0_70, negated_conjecture, (v7_ordinal1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_35])). fof(c_0_71, plain, ![X44, X45]:((~r1_xboole_0(X44,X45)\|k3_xboole_0(X44,X45)=k1_xboole_0)&(k3_xboole_0(X44,X45)!=k1_xboole_0\|r1_xboole_0(X44,X45))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_xboole_0])])). cnf(c_0_72, plain, (X3=k3_xboole_0(X1,X2)\|r2_hidden(esk3_3(X1,X2,X3),X3)\|r2_hidden(esk3_3(X1,X2,X3),X1)), inference(evalgc,[status(thm)],[c_0_54])). cnf(c_0_73, plain, (esk3_3(X1,k1_tarski(X2),X3)=X2\|X3=k3_xboole_0(X1,k1_tarski(X2))\|~v1_xboole_0(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_55, c_0_56])])). cnf(c_0_74, plain, (X1=k1_xboole_0\|~v1_xboole_0(X1)), inference(evalgc,[status(thm)],[c_0_57])). cnf(c_0_75, plain, (v1_xboole_0(np__0)), inference(evalgc,[status(thm)],[c_0_58])). cnf(c_0_76, plain, (r1_xxreal_0(X1,k1_xboole_0)\|~r1_xxreal_0(k1_nat_1(X2,X1),X2)\|~v1_xreal_0(X2)\|~v1_xreal_0(X1)\|~m1_subset_1(X1,k5_numbers)\|~v7_ordinal1(X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_59, c_0_60])])). cnf(c_0_77, plain, (v1_xreal_0(X1)\|~v7_ordinal1(X1)), inference(evalgc,[status(thm)],[c_0_61])). cnf(c_0_78, plain, (r1_xxreal_0(X1,X2)\|~r2_hidden(X1,k2_finseq_1(X2))\|~v7_ordinal1(X2)\|~v7_ordinal1(X1)), inference(split_conjunct,[status(thm)],[c_0_62])). cnf(c_0_79, plain, (v7_ordinal1(k2_xcmplx_0(X1,X2))\|~v7_ordinal1(X2)\|~v7_ordinal1(X1)), inference(evalgc,[status(thm)],[c_0_63])). cnf(c_0_80, plain, (v7_ordinal1(X1)\|~m1_subset_1(X1,k4_ordinal1)), inference(evalgc,[status(thm)],[c_0_64])). cnf(c_0_81, plain, (k4_ordinal1=k5_numbers), inference(evalgc,[status(thm)],[c_0_65])). cnf(c_0_82, negated_conjecture, (k4_xboole_0(k2_finseq_1(k1_nat_1(esk1_0,np__1)),k1_tarski(k1_nat_1(esk1_0,np__1)))!=k2_finseq_1(esk1_0)\|~v7_ordinal1(k1_nat_1(esk1_0,np__1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_66, c_0_67])])). cnf(c_0_83, plain, (k4_xboole_0(k2_finseq_1(k1_nat_1(X1,np__1)),k1_tarski(k1_nat_1(X1,np__1)))=k2_finseq_1(X1)\|~r1_xboole_0(k2_finseq_1(X1),k1_tarski(k1_nat_1(X1,np__1)))\|~v7_ordinal1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_68, c_0_69])])). cnf(c_0_84, negated_conjecture, (v7_ordinal1(esk1_0)), inference(evalgc,[status(thm)],[c_0_70])). cnf(c_0_85, plain, (r1_xboole_0(X1,X2)\|k3_xboole_0(X1,X2)!=k1_xboole_0), inference(split_conjunct,[status(thm)],[c_0_71])). cnf(c_0_86, plain, (X1=k3_xboole_0(X2,k1_tarski(X3))\|r2_hidden(X3,X2)\|r2_hidden(X3,X1)\|~v1_xboole_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_72, c_0_73])])). cnf(c_0_87, plain, (np__0=k1_xboole_0), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_74, c_0_75])])). fof(c_0_88, plain, ~r1_xxreal_0(np__1,np__0), inference(fof_simplification,[status(thm)],[rqLessOrEqual__r1_xxreal_0__r1_r0])). cnf(c_0_89, plain, (r1_xxreal_0(X1,k1_xboole_0)\|~r1_xxreal_0(k1_nat_1(X2,X1),X2)\|~v1_xreal_0(X1)\|~m1_subset_1(X1,k5_numbers)\|~v7_ordinal1(X2)), inference(csr,[status(thm)],[c_0_76, c_0_77])). cnf(c_0_90, plain, (r1_xxreal_0(X1,X2)\|~v7_ordinal1(X2)\|~v7_ordinal1(X1)\|~r2_hidden(X1,k2_finseq_1(X2))), inference(evalgc,[status(thm)],[c_0_78])). cnf(c_0_91, plain, (v7_ordinal1(k1_nat_1(X1,X2))\|~v7_ordinal1(X2)\|~v7_ordinal1(X1)\|~m1_subset_1(X2,k5_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_79, c_0_60])])). cnf(c_0_92, plain, (v7_ordinal1(X1)\|~m1_subset_1(X1,k5_numbers)), inference(rw,[status(thm)],[c_0_80, c_0_81])). cnf(c_0_93, negated_conjecture, (~v7_ordinal1(k1_nat_1(esk1_0,np__1))\|~r1_xboole_0(k2_finseq_1(esk1_0),k1_tarski(k1_nat_1(esk1_0,np__1)))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82, c_0_83]), c_0_84])])])). cnf(c_0_94, plain, (r1_xboole_0(X1,X2)\|k3_xboole_0(X1,X2)!=k1_xboole_0), inference(evalgc,[status(thm)],[c_0_85])). cnf(c_0_95, plain, (X1=k3_xboole_0(X2,k1_tarski(X3))\|r2_hidden(X3,X2)\|~v1_xboole_0(X1)), inference(csr,[status(thm)],[c_0_86, c_0_55])). cnf(c_0_96, plain, (v1_xboole_0(k1_xboole_0)), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[c_0_75, c_0_87])])). cnf(c_0_97, plain, (~r1_xxreal_0(np__1,np__0)), inference(split_conjunct,[status(thm)],[c_0_88])). cnf(c_0_98, plain, (r1_xxreal_0(X1,k1_xboole_0)\|~v1_xreal_0(X1)\|~m1_subset_1(X1,k5_numbers)\|~v7_ordinal1(X2)\|~r2_hidden(k1_nat_1(X2,X1),k2_finseq_1(X2))\|~v7_ordinal1(k1_nat_1(X2,X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_89, c_0_90])])). cnf(c_0_99, plain, (v7_ordinal1(k1_nat_1(X1,X2))\|~m1_subset_1(X2,k5_numbers)\|~v7_ordinal1(X1)), inference(csr,[status(thm)],[c_0_91, c_0_92])). cnf(c_0_100, negated_conjecture, (~v7_ordinal1(k1_nat_1(esk1_0,np__1))\|k3_xboole_0(k2_finseq_1(esk1_0),k1_tarski(k1_nat_1(esk1_0,np__1)))!=k1_xboole_0), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_93, c_0_94])])). cnf(c_0_101, plain, (k3_xboole_0(X1,k1_tarski(X2))=k1_xboole_0\|r2_hidden(X2,X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_95, c_0_96])])). cnf(c_0_102, plain, (m1_subset_1(np__1,k5_numbers)), inference(split_conjunct,[status(thm)],[spc1_numerals])). cnf(c_0_103, plain, (~r1_xxreal_0(np__1,np__0)), inference(evalgc,[status(thm)],[c_0_97])). cnf(c_0_104, plain, (r1_xxreal_0(X1,k1_xboole_0)\|~r2_hidden(k1_nat_1(X2,X1),k2_finseq_1(X2))\|~v1_xreal_0(X1)\|~m1_subset_1(X1,k5_numbers)\|~v7_ordinal1(X2)), inference(csr,[status(thm)],[c_0_98, c_0_99])). cnf(c_0_105, negated_conjecture, (r2_hidden(k1_nat_1(esk1_0,np__1),k2_finseq_1(esk1_0))\|~v7_ordinal1(k1_nat_1(esk1_0,np__1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_100, c_0_101])])). cnf(c_0_106, plain, (m1_subset_1(np__1,k5_numbers)), inference(evalgc,[status(thm)],[c_0_102])). cnf(c_0_107, plain, (~r1_xxreal_0(np__1,k1_xboole_0)), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[c_0_103, c_0_87])])). cnf(c_0_108, negated_conjecture, (~v1_xreal_0(np__1)\|~v7_ordinal1(k1_nat_1(esk1_0,np__1))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104, c_0_105]), c_0_106]), c_0_84])]), c_0_107])])). cnf(c_0_109, negated_conjecture, (~v1_xreal_0(np__1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108, c_0_99]), c_0_106]), c_0_84])])])). cnf(c_0_110, plain, (v7_ordinal1(np__1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_92, c_0_106])])). cnf(c_0_111, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109, c_0_77]), c_0_110])]), ['proof']). # SZS output end CNFRefutation	reserve k,l,m,n,k1,a,b,c,i for Nat, x,y,z,y1,y2,X,Y for set, f,g for Function; theorem for k being Nat holds Seg k = Seg(k + 1) \ {k + 1} proof let k be Nat; A1: Seg(k + 1) = Seg k \/ {k + 1} by Th9; Seg k misses {k + 1} proof assume not thesis; then A2: Seg k /\ {k + 1} <> {} by XBOOLE_0:def 7; set x = the Element of Seg k /\ {k + 1}; A3: x in Seg k by A2,XBOOLE_0:def 4; then reconsider x as Element of NAT; x in {k + 1} by A2,XBOOLE_0:def 4; then A4: x = k + 1 by TARSKI:def 1; x <= k by A3,Th1; hence thesis by A4,XREAL_1:29; end; hence thesis by A1,XBOOLE_1:88; end;	Convert the following ATP output trace into a readable Mizar proof.
t10_anproj_2	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(fc6_ordinal1, axiom, (~(v1_xboole_0(k4_ordinal1))&v3_ordinal1(k4_ordinal1)), file('/scratch/mptp/predsminms1/t10_anproj_2__0', fc6_ordinal1)). fof(s5_funct_2__e2_44__anproj_2, axiom, ![X1, X2]:((~(v1_xboole_0(X1))&m1_subset_1(X2,X1))=>(![X3]:(r2_hidden(X3,X1)=>((X3=X2=>r2_hidden(np__1,k1_numbers))&(~(X3=X2)=>r2_hidden(k6_numbers,k1_numbers))))=>?[X3]:((v1_funct_1(X3)&(v1_funct_2(X3,X1,k1_numbers)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))))&![X4]:(r2_hidden(X4,X1)=>((X4=X2=>k1_funct_1(X3,X4)=np__1)&(~(X4=X2)=>k1_funct_1(X3,X4)=k6_numbers)))))), file('/scratch/mptp/predsminms1/t10_anproj_2__0', s5_funct_2__e2_44__anproj_2)). fof(t7_boole, axiom, ![X1, X2]:~((r2_hidden(X1,X2)&v1_xboole_0(X2))), file('/scratch/mptp/predsminms1/t10_anproj_2__0', t7_boole)). fof(t2_subset, axiom, ![X1, X2]:(m1_subset_1(X1,X2)=>(v1_xboole_0(X2)\|r2_hidden(X1,X2))), file('/scratch/mptp/predsminms1/t10_anproj_2__0', t2_subset)). fof(fc1_numbers, axiom, ~(v1_xboole_0(k1_numbers)), file('/scratch/mptp/predsminms1/t10_anproj_2__0', fc1_numbers)). fof(dt_m2_subset_1, axiom, ![X1, X2]:((~(v1_xboole_0(X1))&(~(v1_xboole_0(X2))&m1_subset_1(X2,k1_zfmisc_1(X1))))=>![X3]:(m2_subset_1(X3,X1,X2)=>m1_subset_1(X3,X1))), file('/scratch/mptp/predsminms1/t10_anproj_2__0', dt_m2_subset_1)). fof(redefinition_k5_numbers, axiom, k5_numbers=k4_ordinal1, file('/scratch/mptp/predsminms1/t10_anproj_2__0', redefinition_k5_numbers)). fof(t10_anproj_2, conjecture, ![X1]:(~(v1_xboole_0(X1))=>![X2]:(m1_subset_1(X2,X1)=>?[X3]:(m2_funct_2(X3,X1,k1_numbers,k9_funct_2(X1,k1_numbers))&(k3_funct_2(X1,k1_numbers,X3,X2)=np__1&![X4]:(r2_hidden(X4,X1)=>(X4=X2\|k1_funct_1(X3,X4)=k6_numbers)))))), file('/scratch/mptp/predsminms1/t10_anproj_2__0', t10_anproj_2)). fof(redefinition_m2_funct_2, axiom, ![X1, X2, X3]:((~(v1_xboole_0(X2))&m1_funct_2(X3,X1,X2))=>![X4]:(m2_funct_2(X4,X1,X2,X3)<=>m1_subset_1(X4,X3))), file('/scratch/mptp/predsminms1/t10_anproj_2__0', redefinition_m2_funct_2)). fof(dt_k9_funct_2, axiom, ![X1, X2]:(~(v1_xboole_0(X2))=>m1_funct_2(k9_funct_2(X1,X2),X1,X2)), file('/scratch/mptp/predsminms1/t10_anproj_2__0', dt_k9_funct_2)). fof(spc1_numerals, axiom, ((v2_xxreal_0(np__1)&m2_subset_1(np__1,k1_numbers,k5_numbers))&(m1_subset_1(np__1,k5_numbers)&m1_subset_1(np__1,k1_numbers))), file('/scratch/mptp/predsminms1/t10_anproj_2__0', spc1_numerals)). fof(dt_k6_numbers, axiom, m2_subset_1(k6_numbers,k1_numbers,k5_numbers), file('/scratch/mptp/predsminms1/t10_anproj_2__0', dt_k6_numbers)). fof(dt_k5_numbers, axiom, m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)), file('/scratch/mptp/predsminms1/t10_anproj_2__0', dt_k5_numbers)). fof(t8_funct_2, axiom, ![X1, X2, X3]:((v1_funct_1(X3)&(v1_funct_2(X3,X1,X2)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))))=>((X2=k1_xboole_0=>X1=k1_xboole_0)=>r2_hidden(X3,k1_funct_2(X1,X2)))), file('/scratch/mptp/predsminms1/t10_anproj_2__0', t8_funct_2)). fof(redefinition_k3_funct_2, axiom, ![X1, X2, X3, X4]:((~(v1_xboole_0(X1))&((v1_funct_1(X3)&(v1_funct_2(X3,X1,X2)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))))&m1_subset_1(X4,X1)))=>k3_funct_2(X1,X2,X3,X4)=k1_funct_1(X3,X4)), file('/scratch/mptp/predsminms1/t10_anproj_2__0', redefinition_k3_funct_2)). fof(redefinition_k6_numbers, axiom, k6_numbers=k1_xboole_0, file('/scratch/mptp/predsminms1/t10_anproj_2__0', redefinition_k6_numbers)). fof(t1_subset, axiom, ![X1, X2]:(r2_hidden(X1,X2)=>m1_subset_1(X1,X2)), file('/scratch/mptp/predsminms1/t10_anproj_2__0', t1_subset)). fof(redefinition_k9_funct_2, axiom, ![X1, X2]:(~(v1_xboole_0(X2))=>k9_funct_2(X1,X2)=k1_funct_2(X1,X2)), file('/scratch/mptp/predsminms1/t10_anproj_2__0', redefinition_k9_funct_2)). fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0), file('/scratch/mptp/predsminms1/t10_anproj_2__0', fc1_xboole_0)). fof(c_0_19, plain, (~v1_xboole_0(k4_ordinal1)&v3_ordinal1(k4_ordinal1)), inference(fof_simplification,[status(thm)],[fc6_ordinal1])). fof(c_0_20, plain, ![X11, X12, X15]:((((v1_funct_1(esk5_2(X11,X12))\|r2_hidden(esk4_2(X11,X12),X11)\|(v1_xboole_0(X11)\|~m1_subset_1(X12,X11)))&((v1_funct_2(esk5_2(X11,X12),X11,k1_numbers)\|r2_hidden(esk4_2(X11,X12),X11)\|(v1_xboole_0(X11)\|~m1_subset_1(X12,X11)))&(m1_subset_1(esk5_2(X11,X12),k1_zfmisc_1(k2_zfmisc_1(X11,k1_numbers)))\|r2_hidden(esk4_2(X11,X12),X11)\|(v1_xboole_0(X11)\|~m1_subset_1(X12,X11)))))&((X15!=X12\|k1_funct_1(esk5_2(X11,X12),X15)=np__1\|~r2_hidden(X15,X11)\|r2_hidden(esk4_2(X11,X12),X11)\|(v1_xboole_0(X11)\|~m1_subset_1(X12,X11)))&(X15=X12\|k1_funct_1(esk5_2(X11,X12),X15)=k6_numbers\|~r2_hidden(X15,X11)\|r2_hidden(esk4_2(X11,X12),X11)\|(v1_xboole_0(X11)\|~m1_subset_1(X12,X11)))))&(((((v1_funct_1(esk5_2(X11,X12))\|(esk4_2(X11,X12)!=X12\|esk4_2(X11,X12)=X12)\|(v1_xboole_0(X11)\|~m1_subset_1(X12,X11)))&((v1_funct_2(esk5_2(X11,X12),X11,k1_numbers)\|(esk4_2(X11,X12)!=X12\|esk4_2(X11,X12)=X12)\|(v1_xboole_0(X11)\|~m1_subset_1(X12,X11)))&(m1_subset_1(esk5_2(X11,X12),k1_zfmisc_1(k2_zfmisc_1(X11,k1_numbers)))\|(esk4_2(X11,X12)!=X12\|esk4_2(X11,X12)=X12)\|(v1_xboole_0(X11)\|~m1_subset_1(X12,X11)))))&((X15!=X12\|k1_funct_1(esk5_2(X11,X12),X15)=np__1\|~r2_hidden(X15,X11)\|(esk4_2(X11,X12)!=X12\|esk4_2(X11,X12)=X12)\|(v1_xboole_0(X11)\|~m1_subset_1(X12,X11)))&(X15=X12\|k1_funct_1(esk5_2(X11,X12),X15)=k6_numbers\|~r2_hidden(X15,X11)\|(esk4_2(X11,X12)!=X12\|esk4_2(X11,X12)=X12)\|(v1_xboole_0(X11)\|~m1_subset_1(X12,X11)))))&(((v1_funct_1(esk5_2(X11,X12))\|(~r2_hidden(k6_numbers,k1_numbers)\|esk4_2(X11,X12)=X12)\|(v1_xboole_0(X11)\|~m1_subset_1(X12,X11)))&((v1_funct_2(esk5_2(X11,X12),X11,k1_numbers)\|(~r2_hidden(k6_numbers,k1_numbers)\|esk4_2(X11,X12)=X12)\|(v1_xboole_0(X11)\|~m1_subset_1(X12,X11)))&(m1_subset_1(esk5_2(X11,X12),k1_zfmisc_1(k2_zfmisc_1(X11,k1_numbers)))\|(~r2_hidden(k6_numbers,k1_numbers)\|esk4_2(X11,X12)=X12)\|(v1_xboole_0(X11)\|~m1_subset_1(X12,X11)))))&((X15!=X12\|k1_funct_1(esk5_2(X11,X12),X15)=np__1\|~r2_hidden(X15,X11)\|(~r2_hidden(k6_numbers,k1_numbers)\|esk4_2(X11,X12)=X12)\|(v1_xboole_0(X11)\|~m1_subset_1(X12,X11)))&(X15=X12\|k1_funct_1(esk5_2(X11,X12),X15)=k6_numbers\|~r2_hidden(X15,X11)\|(~r2_hidden(k6_numbers,k1_numbers)\|esk4_2(X11,X12)=X12)\|(v1_xboole_0(X11)\|~m1_subset_1(X12,X11))))))&((((v1_funct_1(esk5_2(X11,X12))\|(esk4_2(X11,X12)!=X12\|~r2_hidden(np__1,k1_numbers))\|(v1_xboole_0(X11)\|~m1_subset_1(X12,X11)))&((v1_funct_2(esk5_2(X11,X12),X11,k1_numbers)\|(esk4_2(X11,X12)!=X12\|~r2_hidden(np__1,k1_numbers))\|(v1_xboole_0(X11)\|~m1_subset_1(X12,X11)))&(m1_subset_1(esk5_2(X11,X12),k1_zfmisc_1(k2_zfmisc_1(X11,k1_numbers)))\|(esk4_2(X11,X12)!=X12\|~r2_hidden(np__1,k1_numbers))\|(v1_xboole_0(X11)\|~m1_subset_1(X12,X11)))))&((X15!=X12\|k1_funct_1(esk5_2(X11,X12),X15)=np__1\|~r2_hidden(X15,X11)\|(esk4_2(X11,X12)!=X12\|~r2_hidden(np__1,k1_numbers))\|(v1_xboole_0(X11)\|~m1_subset_1(X12,X11)))&(X15=X12\|k1_funct_1(esk5_2(X11,X12),X15)=k6_numbers\|~r2_hidden(X15,X11)\|(esk4_2(X11,X12)!=X12\|~r2_hidden(np__1,k1_numbers))\|(v1_xboole_0(X11)\|~m1_subset_1(X12,X11)))))&(((v1_funct_1(esk5_2(X11,X12))\|(~r2_hidden(k6_numbers,k1_numbers)\|~r2_hidden(np__1,k1_numbers))\|(v1_xboole_0(X11)\|~m1_subset_1(X12,X11)))&((v1_funct_2(esk5_2(X11,X12),X11,k1_numbers)\|(~r2_hidden(k6_numbers,k1_numbers)\|~r2_hidden(np__1,k1_numbers))\|(v1_xboole_0(X11)\|~m1_subset_1(X12,X11)))&(m1_subset_1(esk5_2(X11,X12),k1_zfmisc_1(k2_zfmisc_1(X11,k1_numbers)))\|(~r2_hidden(k6_numbers,k1_numbers)\|~r2_hidden(np__1,k1_numbers))\|(v1_xboole_0(X11)\|~m1_subset_1(X12,X11)))))&((X15!=X12\|k1_funct_1(esk5_2(X11,X12),X15)=np__1\|~r2_hidden(X15,X11)\|(~r2_hidden(k6_numbers,k1_numbers)\|~r2_hidden(np__1,k1_numbers))\|(v1_xboole_0(X11)\|~m1_subset_1(X12,X11)))&(X15=X12\|k1_funct_1(esk5_2(X11,X12),X15)=k6_numbers\|~r2_hidden(X15,X11)\|(~r2_hidden(k6_numbers,k1_numbers)\|~r2_hidden(np__1,k1_numbers))\|(v1_xboole_0(X11)\|~m1_subset_1(X12,X11)))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[s5_funct_2__e2_44__anproj_2])])])])])])). fof(c_0_21, plain, ![X9, X10]:(~r2_hidden(X9,X10)\|~v1_xboole_0(X10)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])])). fof(c_0_22, plain, ![X24, X25]:(~m1_subset_1(X24,X25)\|(v1_xboole_0(X25)\|r2_hidden(X24,X25))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])])). fof(c_0_23, plain, ~v1_xboole_0(k1_numbers), inference(fof_simplification,[status(thm)],[fc1_numbers])). fof(c_0_24, plain, ![X35, X36, X37]:(v1_xboole_0(X35)\|(v1_xboole_0(X36)\|~m1_subset_1(X36,k1_zfmisc_1(X35)))\|(~m2_subset_1(X37,X35,X36)\|m1_subset_1(X37,X35))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_m2_subset_1])])])])). cnf(c_0_25, plain, (~v1_xboole_0(k4_ordinal1)), inference(split_conjunct,[status(thm)],[c_0_19])). cnf(c_0_26, plain, (k5_numbers=k4_ordinal1), inference(split_conjunct,[status(thm)],[redefinition_k5_numbers])). fof(c_0_27, negated_conjecture, ~(![X1]:(~(v1_xboole_0(X1))=>![X2]:(m1_subset_1(X2,X1)=>?[X3]:(m2_funct_2(X3,X1,k1_numbers,k9_funct_2(X1,k1_numbers))&(k3_funct_2(X1,k1_numbers,X3,X2)=np__1&![X4]:(r2_hidden(X4,X1)=>(X4=X2\|k1_funct_1(X3,X4)=k6_numbers))))))), inference(assume_negation,[status(cth)],[t10_anproj_2])). fof(c_0_28, plain, ![X20, X21, X22, X23]:((~m2_funct_2(X23,X20,X21,X22)\|m1_subset_1(X23,X22)\|(v1_xboole_0(X21)\|~m1_funct_2(X22,X20,X21)))&(~m1_subset_1(X23,X22)\|m2_funct_2(X23,X20,X21,X22)\|(v1_xboole_0(X21)\|~m1_funct_2(X22,X20,X21)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[redefinition_m2_funct_2])])])])])). fof(c_0_29, plain, ![X18, X19]:(v1_xboole_0(X19)\|m1_funct_2(k9_funct_2(X18,X19),X18,X19)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k9_funct_2])])])). cnf(c_0_30, plain, (X1=X2\|k1_funct_1(esk5_2(X3,X2),X1)=k6_numbers\|v1_xboole_0(X3)\|~r2_hidden(X1,X3)\|~r2_hidden(k6_numbers,k1_numbers)\|~r2_hidden(np__1,k1_numbers)\|~m1_subset_1(X2,X3)), inference(split_conjunct,[status(thm)],[c_0_20])). cnf(c_0_31, plain, (~r2_hidden(X1,X2)\|~v1_xboole_0(X2)), inference(split_conjunct,[status(thm)],[c_0_21])). cnf(c_0_32, plain, (v1_xboole_0(X2)\|r2_hidden(X1,X2)\|~m1_subset_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_33, plain, (m1_subset_1(np__1,k1_numbers)), inference(split_conjunct,[status(thm)],[spc1_numerals])). cnf(c_0_34, plain, (~v1_xboole_0(k1_numbers)), inference(split_conjunct,[status(thm)],[c_0_23])). cnf(c_0_35, plain, (v1_xboole_0(X1)\|v1_xboole_0(X2)\|m1_subset_1(X3,X1)\|~m1_subset_1(X2,k1_zfmisc_1(X1))\|~m2_subset_1(X3,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_24])). cnf(c_0_36, plain, (m2_subset_1(k6_numbers,k1_numbers,k5_numbers)), inference(split_conjunct,[status(thm)],[dt_k6_numbers])). cnf(c_0_37, plain, (m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers))), inference(split_conjunct,[status(thm)],[dt_k5_numbers])). cnf(c_0_38, plain, (~v1_xboole_0(k4_ordinal1)), inference(evalgc,[status(thm)],[c_0_25])). cnf(c_0_39, plain, (k4_ordinal1=k5_numbers), inference(evalgc,[status(thm)],[c_0_26])). fof(c_0_40, negated_conjecture, ![X7]:(~v1_xboole_0(esk1_0)&(m1_subset_1(esk2_0,esk1_0)&((r2_hidden(esk3_1(X7),esk1_0)\|k3_funct_2(esk1_0,k1_numbers,X7,esk2_0)!=np__1\|~m2_funct_2(X7,esk1_0,k1_numbers,k9_funct_2(esk1_0,k1_numbers)))&((esk3_1(X7)!=esk2_0\|k3_funct_2(esk1_0,k1_numbers,X7,esk2_0)!=np__1\|~m2_funct_2(X7,esk1_0,k1_numbers,k9_funct_2(esk1_0,k1_numbers)))&(k1_funct_1(X7,esk3_1(X7))!=k6_numbers\|k3_funct_2(esk1_0,k1_numbers,X7,esk2_0)!=np__1\|~m2_funct_2(X7,esk1_0,k1_numbers,k9_funct_2(esk1_0,k1_numbers))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_27])])])])])])). cnf(c_0_41, plain, (m2_funct_2(X1,X3,X4,X2)\|v1_xboole_0(X4)\|~m1_subset_1(X1,X2)\|~m1_funct_2(X2,X3,X4)), inference(split_conjunct,[status(thm)],[c_0_28])). cnf(c_0_42, plain, (v1_xboole_0(X1)\|m1_funct_2(k9_funct_2(X2,X1),X2,X1)), inference(split_conjunct,[status(thm)],[c_0_29])). cnf(c_0_43, plain, (X1=X2\|k1_funct_1(esk5_2(X3,X2),X1)=k6_numbers\|v1_xboole_0(X3)\|~m1_subset_1(X2,X3)\|~r2_hidden(X1,X3)\|~r2_hidden(np__1,k1_numbers)\|~r2_hidden(k6_numbers,k1_numbers)), inference(evalgc,[status(thm)],[c_0_30])). cnf(c_0_44, plain, (~v1_xboole_0(X2)\|~r2_hidden(X1,X2)), inference(evalgc,[status(thm)],[c_0_31])). cnf(c_0_45, plain, (v1_xboole_0(X2)\|r2_hidden(X1,X2)\|~m1_subset_1(X1,X2)), inference(evalgc,[status(thm)],[c_0_32])). cnf(c_0_46, plain, (m1_subset_1(np__1,k1_numbers)), inference(evalgc,[status(thm)],[c_0_33])). cnf(c_0_47, plain, (~v1_xboole_0(k1_numbers)), inference(evalgc,[status(thm)],[c_0_34])). cnf(c_0_48, plain, (v1_xboole_0(X2)\|v1_xboole_0(X1)\|m1_subset_1(X3,X1)\|~m2_subset_1(X3,X1,X2)\|~m1_subset_1(X2,k1_zfmisc_1(X1))), inference(evalgc,[status(thm)],[c_0_35])). cnf(c_0_49, plain, (m2_subset_1(k6_numbers,k1_numbers,k5_numbers)), inference(evalgc,[status(thm)],[c_0_36])). cnf(c_0_50, plain, (m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers))), inference(evalgc,[status(thm)],[c_0_37])). cnf(c_0_51, plain, (~v1_xboole_0(k5_numbers)), inference(rw,[status(thm)],[c_0_38, c_0_39])). cnf(c_0_52, plain, (m1_subset_1(esk5_2(X1,X2),k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|v1_xboole_0(X1)\|~r2_hidden(k6_numbers,k1_numbers)\|~r2_hidden(np__1,k1_numbers)\|~m1_subset_1(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_20])). fof(c_0_53, plain, ![X32, X33, X34]:((X33=k1_xboole_0\|r2_hidden(X34,k1_funct_2(X32,X33))\|(~v1_funct_1(X34)\|(~v1_funct_2(X34,X32,X33)\|~m1_subset_1(X34,k1_zfmisc_1(k2_zfmisc_1(X32,X33))))))&(X32!=k1_xboole_0\|r2_hidden(X34,k1_funct_2(X32,X33))\|(~v1_funct_1(X34)\|(~v1_funct_2(X34,X32,X33)\|~m1_subset_1(X34,k1_zfmisc_1(k2_zfmisc_1(X32,X33))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_funct_2])])])). cnf(c_0_54, negated_conjecture, (k1_funct_1(X1,esk3_1(X1))!=k6_numbers\|k3_funct_2(esk1_0,k1_numbers,X1,esk2_0)!=np__1\|~m2_funct_2(X1,esk1_0,k1_numbers,k9_funct_2(esk1_0,k1_numbers))), inference(split_conjunct,[status(thm)],[c_0_40])). cnf(c_0_55, plain, (v1_xboole_0(X4)\|m2_funct_2(X1,X3,X4,X2)\|~m1_subset_1(X1,X2)\|~m1_funct_2(X2,X3,X4)), inference(evalgc,[status(thm)],[c_0_41])). cnf(c_0_56, plain, (v1_xboole_0(X1)\|m1_funct_2(k9_funct_2(X2,X1),X2,X1)), inference(evalgc,[status(thm)],[c_0_42])). cnf(c_0_57, plain, (k1_funct_1(esk5_2(X1,X2),X3)=k6_numbers\|X3=X2\|~r2_hidden(np__1,k1_numbers)\|~r2_hidden(k6_numbers,k1_numbers)\|~r2_hidden(X3,X1)\|~m1_subset_1(X2,X1)), inference(csr,[status(thm)],[c_0_43, c_0_44])). cnf(c_0_58, plain, (r2_hidden(np__1,k1_numbers)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_45, c_0_46]), c_0_47])])). cnf(c_0_59, plain, (m1_subset_1(k6_numbers,k1_numbers)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48, c_0_49]), c_0_50])]), c_0_47]), c_0_51])])). fof(c_0_60, plain, ![X26, X27, X28, X29]:(v1_xboole_0(X26)\|(~v1_funct_1(X28)\|(~v1_funct_2(X28,X26,X27)\|~m1_subset_1(X28,k1_zfmisc_1(k2_zfmisc_1(X26,X27))))\|~m1_subset_1(X29,X26))\|k3_funct_2(X26,X27,X28,X29)=k1_funct_1(X28,X29)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[redefinition_k3_funct_2])])])). cnf(c_0_61, plain, (v1_xboole_0(X1)\|m1_subset_1(esk5_2(X1,X2),k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|~m1_subset_1(X2,X1)\|~r2_hidden(np__1,k1_numbers)\|~r2_hidden(k6_numbers,k1_numbers)), inference(evalgc,[status(thm)],[c_0_52])). cnf(c_0_62, plain, (v1_funct_1(esk5_2(X1,X2))\|v1_xboole_0(X1)\|~r2_hidden(k6_numbers,k1_numbers)\|~r2_hidden(np__1,k1_numbers)\|~m1_subset_1(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_20])). cnf(c_0_63, plain, (v1_funct_2(esk5_2(X1,X2),X1,k1_numbers)\|v1_xboole_0(X1)\|~r2_hidden(k6_numbers,k1_numbers)\|~r2_hidden(np__1,k1_numbers)\|~m1_subset_1(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_20])). cnf(c_0_64, plain, (X1=k1_xboole_0\|r2_hidden(X2,k1_funct_2(X3,X1))\|~v1_funct_1(X2)\|~v1_funct_2(X2,X3,X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_53])). cnf(c_0_65, plain, (k6_numbers=k1_xboole_0), inference(split_conjunct,[status(thm)],[redefinition_k6_numbers])). cnf(c_0_66, negated_conjecture, (k1_funct_1(X1,esk3_1(X1))!=k6_numbers\|k3_funct_2(esk1_0,k1_numbers,X1,esk2_0)!=np__1\|~m2_funct_2(X1,esk1_0,k1_numbers,k9_funct_2(esk1_0,k1_numbers))), inference(evalgc,[status(thm)],[c_0_54])). cnf(c_0_67, plain, (m2_funct_2(X1,X2,X3,k9_funct_2(X2,X3))\|v1_xboole_0(X3)\|~m1_subset_1(X1,k9_funct_2(X2,X3))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_55, c_0_56])])). cnf(c_0_68, plain, (k1_funct_1(esk5_2(X1,X2),X3)=k6_numbers\|X3=X2\|~r2_hidden(k6_numbers,k1_numbers)\|~r2_hidden(X3,X1)\|~m1_subset_1(X2,X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57, c_0_58])])])). cnf(c_0_69, plain, (r2_hidden(k6_numbers,k1_numbers)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_45, c_0_59]), c_0_47])])). fof(c_0_70, plain, ![X16, X17]:(~r2_hidden(X16,X17)\|m1_subset_1(X16,X17)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])])). cnf(c_0_71, negated_conjecture, (r2_hidden(esk3_1(X1),esk1_0)\|k3_funct_2(esk1_0,k1_numbers,X1,esk2_0)!=np__1\|~m2_funct_2(X1,esk1_0,k1_numbers,k9_funct_2(esk1_0,k1_numbers))), inference(split_conjunct,[status(thm)],[c_0_40])). cnf(c_0_72, negated_conjecture, (esk3_1(X1)!=esk2_0\|k3_funct_2(esk1_0,k1_numbers,X1,esk2_0)!=np__1\|~m2_funct_2(X1,esk1_0,k1_numbers,k9_funct_2(esk1_0,k1_numbers))), inference(split_conjunct,[status(thm)],[c_0_40])). cnf(c_0_73, plain, (v1_xboole_0(X1)\|k3_funct_2(X1,X3,X2,X4)=k1_funct_1(X2,X4)\|~v1_funct_1(X2)\|~v1_funct_2(X2,X1,X3)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))\|~m1_subset_1(X4,X1)), inference(split_conjunct,[status(thm)],[c_0_60])). cnf(c_0_74, plain, (m1_subset_1(esk5_2(X1,X2),k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|v1_xboole_0(X1)\|~r2_hidden(k6_numbers,k1_numbers)\|~m1_subset_1(X2,X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_61, c_0_58])])])). cnf(c_0_75, plain, (v1_xboole_0(X1)\|v1_funct_1(esk5_2(X1,X2))\|~m1_subset_1(X2,X1)\|~r2_hidden(np__1,k1_numbers)\|~r2_hidden(k6_numbers,k1_numbers)), inference(evalgc,[status(thm)],[c_0_62])). cnf(c_0_76, plain, (v1_xboole_0(X1)\|v1_funct_2(esk5_2(X1,X2),X1,k1_numbers)\|~m1_subset_1(X2,X1)\|~r2_hidden(np__1,k1_numbers)\|~r2_hidden(k6_numbers,k1_numbers)), inference(evalgc,[status(thm)],[c_0_63])). cnf(c_0_77, plain, (X1=k1_xboole_0\|r2_hidden(X2,k1_funct_2(X3,X1))\|~v1_funct_1(X2)\|~v1_funct_2(X2,X3,X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X3,X1)))), inference(evalgc,[status(thm)],[c_0_64])). cnf(c_0_78, plain, (k1_xboole_0=k6_numbers), inference(evalgc,[status(thm)],[c_0_65])). cnf(c_0_79, negated_conjecture, (k3_funct_2(esk1_0,k1_numbers,X1,esk2_0)!=np__1\|k1_funct_1(X1,esk3_1(X1))!=k6_numbers\|~m1_subset_1(X1,k9_funct_2(esk1_0,k1_numbers))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_66, c_0_67]), c_0_47])])). cnf(c_0_80, plain, (k1_funct_1(esk5_2(X1,X2),X3)=k6_numbers\|X3=X2\|~r2_hidden(X3,X1)\|~m1_subset_1(X2,X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_68, c_0_69])])])). cnf(c_0_81, plain, (m1_subset_1(X1,X2)\|~r2_hidden(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_70])). cnf(c_0_82, negated_conjecture, (r2_hidden(esk3_1(X1),esk1_0)\|k3_funct_2(esk1_0,k1_numbers,X1,esk2_0)!=np__1\|~m2_funct_2(X1,esk1_0,k1_numbers,k9_funct_2(esk1_0,k1_numbers))), inference(evalgc,[status(thm)],[c_0_71])). cnf(c_0_83, negated_conjecture, (esk3_1(X1)!=esk2_0\|k3_funct_2(esk1_0,k1_numbers,X1,esk2_0)!=np__1\|~m2_funct_2(X1,esk1_0,k1_numbers,k9_funct_2(esk1_0,k1_numbers))), inference(evalgc,[status(thm)],[c_0_72])). cnf(c_0_84, plain, (k3_funct_2(X1,X3,X2,X4)=k1_funct_1(X2,X4)\|v1_xboole_0(X1)\|~v1_funct_1(X2)\|~m1_subset_1(X4,X1)\|~v1_funct_2(X2,X1,X3)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,X3)))), inference(evalgc,[status(thm)],[c_0_73])). cnf(c_0_85, plain, (m1_subset_1(esk5_2(X1,X2),k1_zfmisc_1(k2_zfmisc_1(X1,k1_numbers)))\|v1_xboole_0(X1)\|~m1_subset_1(X2,X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_74, c_0_69])])). cnf(c_0_86, plain, (v1_funct_1(esk5_2(X1,X2))\|v1_xboole_0(X1)\|~r2_hidden(k6_numbers,k1_numbers)\|~m1_subset_1(X2,X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_75, c_0_58])])])). cnf(c_0_87, plain, (v1_funct_2(esk5_2(X1,X2),X1,k1_numbers)\|v1_xboole_0(X1)\|~r2_hidden(k6_numbers,k1_numbers)\|~m1_subset_1(X2,X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_76, c_0_58])])])). cnf(c_0_88, plain, (X1=k6_numbers\|r2_hidden(X2,k1_funct_2(X3,X1))\|~v1_funct_2(X2,X3,X1)\|~v1_funct_1(X2)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X3,X1)))), inference(rw,[status(thm)],[c_0_77, c_0_78])). fof(c_0_89, plain, ![X30, X31]:(v1_xboole_0(X31)\|k9_funct_2(X30,X31)=k1_funct_2(X30,X31)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[redefinition_k9_funct_2])])])). cnf(c_0_90, negated_conjecture, (esk3_1(esk5_2(X1,X2))=X2\|k3_funct_2(esk1_0,k1_numbers,esk5_2(X1,X2),esk2_0)!=np__1\|~m1_subset_1(esk5_2(X1,X2),k9_funct_2(esk1_0,k1_numbers))\|~r2_hidden(esk3_1(esk5_2(X1,X2)),X1)\|~m1_subset_1(X2,X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_79, c_0_80])])). cnf(c_0_91, plain, (m1_subset_1(X1,X2)\|~r2_hidden(X1,X2)), inference(evalgc,[status(thm)],[c_0_81])). cnf(c_0_92, negated_conjecture, (r2_hidden(esk3_1(X1),esk1_0)\|k3_funct_2(esk1_0,k1_numbers,X1,esk2_0)!=np__1\|~m1_subset_1(X1,k9_funct_2(esk1_0,k1_numbers))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_82, c_0_67]), c_0_47])])). cnf(c_0_93, plain, (k1_funct_1(esk5_2(X3,X2),X1)=np__1\|v1_xboole_0(X3)\|X1!=X2\|~r2_hidden(X1,X3)\|esk4_2(X3,X2)!=X2\|~r2_hidden(np__1,k1_numbers)\|~m1_subset_1(X2,X3)), inference(split_conjunct,[status(thm)],[c_0_20])). cnf(c_0_94, negated_conjecture, (k3_funct_2(esk1_0,k1_numbers,X1,esk2_0)!=np__1\|esk3_1(X1)!=esk2_0\|~m1_subset_1(X1,k9_funct_2(esk1_0,k1_numbers))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_83, c_0_67]), c_0_47])])). cnf(c_0_95, plain, (k3_funct_2(X1,k1_numbers,esk5_2(X1,X2),X3)=k1_funct_1(esk5_2(X1,X2),X3)\|v1_xboole_0(X1)\|~v1_funct_2(esk5_2(X1,X2),X1,k1_numbers)\|~v1_funct_1(esk5_2(X1,X2))\|~m1_subset_1(X3,X1)\|~m1_subset_1(X2,X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_84, c_0_85])])). cnf(c_0_96, plain, (v1_funct_1(esk5_2(X1,X2))\|v1_xboole_0(X1)\|~m1_subset_1(X2,X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_86, c_0_69])])). cnf(c_0_97, plain, (v1_funct_2(esk5_2(X1,X2),X1,k1_numbers)\|v1_xboole_0(X1)\|~m1_subset_1(X2,X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_87, c_0_69])])])). cnf(c_0_98, negated_conjecture, (m1_subset_1(esk2_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_40])). cnf(c_0_99, negated_conjecture, (~v1_xboole_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_40])). cnf(c_0_100, plain, (k6_numbers=k1_numbers\|r2_hidden(esk5_2(X1,X2),k1_funct_2(X1,k1_numbers))\|v1_xboole_0(X1)\|~v1_funct_2(esk5_2(X1,X2),X1,k1_numbers)\|~v1_funct_1(esk5_2(X1,X2))\|~m1_subset_1(X2,X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_88, c_0_85])])). cnf(c_0_101, plain, (v1_xboole_0(X1)\|k9_funct_2(X2,X1)=k1_funct_2(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_89])). cnf(c_0_102, negated_conjecture, (esk3_1(esk5_2(X1,X2))=X2\|k3_funct_2(esk1_0,k1_numbers,esk5_2(X1,X2),esk2_0)!=np__1\|~r2_hidden(esk3_1(esk5_2(X1,X2)),X1)\|~m1_subset_1(X2,X1)\|~r2_hidden(esk5_2(X1,X2),k9_funct_2(esk1_0,k1_numbers))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_90, c_0_91])])). cnf(c_0_103, negated_conjecture, (r2_hidden(esk3_1(X1),esk1_0)\|k3_funct_2(esk1_0,k1_numbers,X1,esk2_0)!=np__1\|~r2_hidden(X1,k9_funct_2(esk1_0,k1_numbers))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_92, c_0_91])])). cnf(c_0_104, plain, (k1_funct_1(esk5_2(X3,X2),X1)=np__1\|esk4_2(X3,X2)=X2\|v1_xboole_0(X3)\|X1!=X2\|~r2_hidden(X1,X3)\|~r2_hidden(k6_numbers,k1_numbers)\|~m1_subset_1(X2,X3)), inference(split_conjunct,[status(thm)],[c_0_20])). cnf(c_0_105, plain, (k1_funct_1(esk5_2(X3,X2),X1)=np__1\|v1_xboole_0(X3)\|X1!=X2\|esk4_2(X3,X2)!=X2\|~m1_subset_1(X2,X3)\|~r2_hidden(X1,X3)\|~r2_hidden(np__1,k1_numbers)), inference(evalgc,[status(thm)],[c_0_93])). cnf(c_0_106, negated_conjecture, (k3_funct_2(esk1_0,k1_numbers,X1,esk2_0)!=np__1\|esk3_1(X1)!=esk2_0\|~r2_hidden(X1,k9_funct_2(esk1_0,k1_numbers))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_94, c_0_91])])). cnf(c_0_107, plain, (k3_funct_2(X1,k1_numbers,esk5_2(X1,X2),X3)=k1_funct_1(esk5_2(X1,X2),X3)\|v1_xboole_0(X1)\|~m1_subset_1(X3,X1)\|~m1_subset_1(X2,X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_95, c_0_96]), c_0_97])). cnf(c_0_108, negated_conjecture, (m1_subset_1(esk2_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_98])). cnf(c_0_109, negated_conjecture, (~v1_xboole_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_99])). cnf(c_0_110, plain, (k6_numbers=k1_numbers\|r2_hidden(esk5_2(X1,X2),k1_funct_2(X1,k1_numbers))\|v1_xboole_0(X1)\|~m1_subset_1(X2,X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_100, c_0_96]), c_0_97])). cnf(c_0_111, plain, (k1_funct_2(X2,X1)=k9_funct_2(X2,X1)\|v1_xboole_0(X1)), inference(evalgc,[status(thm)],[c_0_101])). cnf(c_0_112, negated_conjecture, (esk3_1(esk5_2(esk1_0,X1))=X1\|k3_funct_2(esk1_0,k1_numbers,esk5_2(esk1_0,X1),esk2_0)!=np__1\|~r2_hidden(esk5_2(esk1_0,X1),k9_funct_2(esk1_0,k1_numbers))\|~m1_subset_1(X1,esk1_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_102, c_0_103])])). cnf(c_0_113, plain, (esk4_2(X3,X2)=X2\|k1_funct_1(esk5_2(X3,X2),X1)=np__1\|v1_xboole_0(X3)\|X1!=X2\|~m1_subset_1(X2,X3)\|~r2_hidden(X1,X3)\|~r2_hidden(k6_numbers,k1_numbers)), inference(evalgc,[status(thm)],[c_0_104])). cnf(c_0_114, plain, (k1_funct_1(esk5_2(X1,X2),X2)=np__1\|esk4_2(X1,X2)!=X2\|~r2_hidden(np__1,k1_numbers)\|~r2_hidden(X2,X1)\|~m1_subset_1(X2,X1)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[inference(csr,[status(thm)],[c_0_105, c_0_44])])])). cnf(c_0_115, negated_conjecture, (k1_funct_1(esk5_2(esk1_0,X1),esk2_0)!=np__1\|esk3_1(esk5_2(esk1_0,X1))!=esk2_0\|~r2_hidden(esk5_2(esk1_0,X1),k9_funct_2(esk1_0,k1_numbers))\|~m1_subset_1(X1,esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106, c_0_107]), c_0_108])]), c_0_109])])). cnf(c_0_116, plain, (k6_numbers=k1_numbers\|r2_hidden(esk5_2(X1,X2),k9_funct_2(X1,k1_numbers))\|v1_xboole_0(X1)\|~m1_subset_1(X2,X1)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_110, c_0_111]), c_0_47])])). cnf(c_0_117, negated_conjecture, (esk3_1(esk5_2(esk1_0,X1))=X1\|k1_funct_1(esk5_2(esk1_0,X1),esk2_0)!=np__1\|~r2_hidden(esk5_2(esk1_0,X1),k9_funct_2(esk1_0,k1_numbers))\|~m1_subset_1(X1,esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112, c_0_107]), c_0_108])]), c_0_109])])). cnf(c_0_118, plain, (k1_funct_1(esk5_2(X1,X2),X2)=np__1\|esk4_2(X1,X2)=X2\|~r2_hidden(k6_numbers,k1_numbers)\|~r2_hidden(X2,X1)\|~m1_subset_1(X2,X1)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[inference(csr,[status(thm)],[c_0_113, c_0_44])])])). cnf(c_0_119, plain, (k1_funct_1(esk5_2(X1,X2),X2)=np__1\|esk4_2(X1,X2)!=X2\|~r2_hidden(X2,X1)), inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_114, c_0_58])]), c_0_91])). cnf(c_0_120, plain, (v1_xboole_0(k1_xboole_0)), inference(split_conjunct,[status(thm)],[fc1_xboole_0])). cnf(c_0_121, negated_conjecture, (k6_numbers=k1_numbers\|k1_funct_1(esk5_2(esk1_0,X1),esk2_0)!=np__1\|esk3_1(esk5_2(esk1_0,X1))!=esk2_0\|~m1_subset_1(X1,esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_115, c_0_116]), c_0_109])])). cnf(c_0_122, negated_conjecture, (esk3_1(esk5_2(esk1_0,X1))=X1\|k6_numbers=k1_numbers\|k1_funct_1(esk5_2(esk1_0,X1),esk2_0)!=np__1\|~m1_subset_1(X1,esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_117, c_0_116]), c_0_109])])). cnf(c_0_123, plain, (k1_funct_1(esk5_2(X1,X2),X2)=np__1\|~r2_hidden(k6_numbers,k1_numbers)\|~r2_hidden(X2,X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_118, c_0_91]), c_0_119])). cnf(c_0_124, plain, (v1_xboole_0(k1_xboole_0)), inference(evalgc,[status(thm)],[c_0_120])). cnf(c_0_125, negated_conjecture, (k6_numbers=k1_numbers\|k1_funct_1(esk5_2(esk1_0,X1),esk2_0)!=np__1\|X1!=esk2_0\|~m1_subset_1(X1,esk1_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_121, c_0_122])])). cnf(c_0_126, plain, (k1_funct_1(esk5_2(X1,X2),X2)=np__1\|~r2_hidden(X2,X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_123, c_0_69])])])). cnf(c_0_127, negated_conjecture, (r2_hidden(esk2_0,esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_45, c_0_108]), c_0_109])])). cnf(c_0_128, plain, (v1_xboole_0(k6_numbers)), inference(rw,[status(thm)],[c_0_124, c_0_78])). cnf(c_0_129, negated_conjecture, (k6_numbers=k1_numbers), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125, c_0_126]), c_0_108]), c_0_127])])])). cnf(c_0_130, plain, ($false), inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_128, c_0_129]), c_0_47]), ['proof']). # SZS output end CNFRefutation	reserve V for RealLinearSpace, o,p,q,r,s,u,v,w,y,y1,u1,v1,w1,u2,v2,w2 for Element of V, a,b,c,d,a1,b1,c1,d1,a2,b2,c2,d2,a3,b3,c3,d3 for Real, z for set; reserve A for non empty set; reserve f,g,h,f1 for Element of Funcs(A,REAL); reserve x1,x2,x3,x4 for Element of A; theorem Th10: ex f st f.x1 = 1 & for z st z in A & z<>x1 holds f.z = 0 proof deffunc G(set) = 0; deffunc F(set) = 1; defpred P[set] means $1 = x1; A1: for z st z in A holds (P[z] implies F(z) in REAL) & (not P[z] implies G( z) in REAL); consider f being Function of A,REAL such that A2: for z st z in A holds (P[z] implies f.z = F(z)) & (not P[z] implies f.z = G(z)) from FUNCT_2:sch 5(A1); reconsider f as Element of Funcs(A,REAL) by FUNCT_2:8; take f; thus thesis by A2; end;	Convert the following ATP output trace into a readable Mizar proof.
t57_sincos10	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(redefinition_k2_partfun1, axiom, ![X1, X2, X3, X4]:((v1_funct_1(X3)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2))))=>k2_partfun1(X1,X2,X3,X4)=k5_relat_1(X3,X4)), file('/scratch/mptp/predsminms1/t57_sincos10__0', redefinition_k2_partfun1)). fof(dt_k2_partfun2, axiom, ![X1, X2, X3]:((v1_funct_1(X3)&(v2_funct_1(X3)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))))=>(v1_funct_1(k2_partfun2(X1,X2,X3))&m1_subset_1(k2_partfun2(X1,X2,X3),k1_zfmisc_1(k2_zfmisc_1(X2,X1))))), file('/scratch/mptp/predsminms1/t57_sincos10__0', dt_k2_partfun2)). fof(dt_k1_fdiff_9, axiom, (v1_funct_1(k1_fdiff_9)&m1_subset_1(k1_fdiff_9,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))), file('/scratch/mptp/predsminms1/t57_sincos10__0', dt_k1_fdiff_9)). fof(t49_sincos10, axiom, k2_partfun1(k1_numbers,k1_numbers,k1_sincos10,k1_rcomp_1(np__1,k7_square_1(np__2)))=k2_partfun2(k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4)))), file('/scratch/mptp/predsminms1/t57_sincos10__0', t49_sincos10)). fof(fc9_sincos10, axiom, (v1_relat_1(k5_relat_1(k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))))&v2_funct_1(k5_relat_1(k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))))), file('/scratch/mptp/predsminms1/t57_sincos10__0', fc9_sincos10)). fof(cc2_relset_1, axiom, ![X1, X2, X3]:(m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))=>(v4_relat_1(X3,X1)&v5_relat_1(X3,X2))), file('/scratch/mptp/predsminms1/t57_sincos10__0', cc2_relset_1)). fof(dt_k2_partfun1, axiom, ![X1, X2, X3, X4]:((v1_funct_1(X3)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2))))=>(v1_funct_1(k2_partfun1(X1,X2,X3,X4))&m1_subset_1(k2_partfun1(X1,X2,X3,X4),k1_zfmisc_1(k2_zfmisc_1(X1,X2))))), file('/scratch/mptp/predsminms1/t57_sincos10__0', dt_k2_partfun1)). fof(t57_sincos10, conjecture, k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k1_sincos10,k1_rcomp_1(np__1,k7_square_1(np__2))),k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))))=k1_partfun2(k1_numbers,k1_rcomp_1(np__1,k7_square_1(np__2))), file('/scratch/mptp/predsminms1/t57_sincos10__0', t57_sincos10)). fof(redefinition_k2_relset_1, axiom, ![X1, X2]:((v1_relat_1(X2)&v5_relat_1(X2,X1))=>k2_relset_1(X1,X2)=k10_xtuple_0(X2)), file('/scratch/mptp/predsminms1/t57_sincos10__0', redefinition_k2_relset_1)). fof(cc1_relset_1, axiom, ![X1, X2, X3]:(m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))=>v1_relat_1(X3)), file('/scratch/mptp/predsminms1/t57_sincos10__0', cc1_relset_1)). fof(redefinition_k1_partfun1, axiom, ![X1, X2, X3, X4, X5, X6]:(((v1_funct_1(X5)&m1_subset_1(X5,k1_zfmisc_1(k2_zfmisc_1(X1,X2))))&(v1_funct_1(X6)&m1_subset_1(X6,k1_zfmisc_1(k2_zfmisc_1(X3,X4)))))=>k1_partfun1(X1,X2,X3,X4,X5,X6)=k3_relat_1(X5,X6)), file('/scratch/mptp/predsminms1/t57_sincos10__0', redefinition_k1_partfun1)). fof(redefinition_k2_partfun2, axiom, ![X1, X2, X3]:((v1_funct_1(X3)&(v2_funct_1(X3)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))))=>k2_partfun2(X1,X2,X3)=k2_funct_1(X3)), file('/scratch/mptp/predsminms1/t57_sincos10__0', redefinition_k2_partfun2)). fof(t39_funct_1, axiom, ![X1]:((v1_relat_1(X1)&v1_funct_1(X1))=>(v2_funct_1(X1)=>(k3_relat_1(X1,k2_funct_1(X1))=k4_relat_1(k9_xtuple_0(X1))&k3_relat_1(k2_funct_1(X1),X1)=k4_relat_1(k10_xtuple_0(X1))))), file('/scratch/mptp/predsminms1/t57_sincos10__0', t39_funct_1)). fof(t41_sincos10, axiom, k2_relset_1(k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))))=k1_rcomp_1(np__1,k7_square_1(np__2)), file('/scratch/mptp/predsminms1/t57_sincos10__0', t41_sincos10)). fof(redefinition_k1_partfun2, axiom, ![X1, X2]:((~(v1_xboole_0(X1))&m1_subset_1(X2,k1_zfmisc_1(X1)))=>k1_partfun2(X1,X2)=k4_relat_1(X2)), file('/scratch/mptp/predsminms1/t57_sincos10__0', redefinition_k1_partfun2)). fof(fc1_numbers, axiom, ~(v1_xboole_0(k1_numbers)), file('/scratch/mptp/predsminms1/t57_sincos10__0', fc1_numbers)). fof(dt_k6_square_1, axiom, ![X1]:(v1_xreal_0(X1)=>v1_xreal_0(k6_square_1(X1))), file('/scratch/mptp/predsminms1/t57_sincos10__0', dt_k6_square_1)). fof(redefinition_k7_square_1, axiom, ![X1]:(m1_subset_1(X1,k1_numbers)=>k7_square_1(X1)=k6_square_1(X1)), file('/scratch/mptp/predsminms1/t57_sincos10__0', redefinition_k7_square_1)). fof(dt_k1_rcomp_1, axiom, ![X1, X2]:((v1_xreal_0(X1)&v1_xreal_0(X2))=>m1_subset_1(k1_rcomp_1(X1,X2),k1_zfmisc_1(k1_numbers))), file('/scratch/mptp/predsminms1/t57_sincos10__0', dt_k1_rcomp_1)). fof(cc1_xreal_0, axiom, ![X1]:(m1_subset_1(X1,k1_numbers)=>v1_xreal_0(X1)), file('/scratch/mptp/predsminms1/t57_sincos10__0', cc1_xreal_0)). fof(spc2_numerals, axiom, ((v2_xxreal_0(np__2)&m2_subset_1(np__2,k1_numbers,k5_numbers))&(m1_subset_1(np__2,k5_numbers)&m1_subset_1(np__2,k1_numbers))), file('/scratch/mptp/predsminms1/t57_sincos10__0', spc2_numerals)). fof(spc1_numerals, axiom, ((v2_xxreal_0(np__1)&m2_subset_1(np__1,k1_numbers,k5_numbers))&(m1_subset_1(np__1,k5_numbers)&m1_subset_1(np__1,k1_numbers))), file('/scratch/mptp/predsminms1/t57_sincos10__0', spc1_numerals)). fof(c_0_22, plain, ![X7, X8, X9, X10]:(~v1_funct_1(X9)\|~m1_subset_1(X9,k1_zfmisc_1(k2_zfmisc_1(X7,X8)))\|k2_partfun1(X7,X8,X9,X10)=k5_relat_1(X9,X10)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k2_partfun1])])). fof(c_0_23, plain, ![X27, X28, X29]:((v1_funct_1(k2_partfun2(X27,X28,X29))\|(~v1_funct_1(X29)\|(~v2_funct_1(X29)\|~m1_subset_1(X29,k1_zfmisc_1(k2_zfmisc_1(X27,X28))))))&(m1_subset_1(k2_partfun2(X27,X28,X29),k1_zfmisc_1(k2_zfmisc_1(X28,X27)))\|(~v1_funct_1(X29)\|(~v2_funct_1(X29)\|~m1_subset_1(X29,k1_zfmisc_1(k2_zfmisc_1(X27,X28))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_partfun2])])])). cnf(c_0_24, plain, (k2_partfun1(X2,X3,X1,X4)=k5_relat_1(X1,X4)\|~v1_funct_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_25, plain, (m1_subset_1(k1_fdiff_9,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))), inference(split_conjunct,[status(thm)],[dt_k1_fdiff_9])). cnf(c_0_26, plain, (v1_funct_1(k1_fdiff_9)), inference(split_conjunct,[status(thm)],[dt_k1_fdiff_9])). cnf(c_0_27, plain, (v1_funct_1(k2_partfun2(X1,X2,X3))\|~v1_funct_1(X3)\|~v2_funct_1(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_23])). cnf(c_0_28, plain, (k2_partfun1(k1_numbers,k1_numbers,k1_sincos10,k1_rcomp_1(np__1,k7_square_1(np__2)))=k2_partfun2(k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))))), inference(split_conjunct,[status(thm)],[t49_sincos10])). cnf(c_0_29, plain, (v2_funct_1(k5_relat_1(k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))))), inference(split_conjunct,[status(thm)],[fc9_sincos10])). cnf(c_0_30, plain, (k2_partfun1(X2,X3,X1,X4)=k5_relat_1(X1,X4)\|~v1_funct_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(evalgc,[status(thm)],[c_0_24])). cnf(c_0_31, plain, (m1_subset_1(k1_fdiff_9,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))), inference(evalgc,[status(thm)],[c_0_25])). cnf(c_0_32, plain, (v1_funct_1(k1_fdiff_9)), inference(evalgc,[status(thm)],[c_0_26])). fof(c_0_33, plain, ![X20, X21, X22]:((v4_relat_1(X22,X20)\|~m1_subset_1(X22,k1_zfmisc_1(k2_zfmisc_1(X20,X21))))&(v5_relat_1(X22,X21)\|~m1_subset_1(X22,k1_zfmisc_1(k2_zfmisc_1(X20,X21))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_relset_1])])])). fof(c_0_34, plain, ![X14, X15, X16, X17]:((v1_funct_1(k2_partfun1(X14,X15,X16,X17))\|(~v1_funct_1(X16)\|~m1_subset_1(X16,k1_zfmisc_1(k2_zfmisc_1(X14,X15)))))&(m1_subset_1(k2_partfun1(X14,X15,X16,X17),k1_zfmisc_1(k2_zfmisc_1(X14,X15)))\|(~v1_funct_1(X16)\|~m1_subset_1(X16,k1_zfmisc_1(k2_zfmisc_1(X14,X15)))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_partfun1])])])). fof(c_0_35, negated_conjecture, ~(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k1_sincos10,k1_rcomp_1(np__1,k7_square_1(np__2))),k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))))=k1_partfun2(k1_numbers,k1_rcomp_1(np__1,k7_square_1(np__2)))), inference(assume_negation,[status(cth)],[t57_sincos10])). cnf(c_0_36, plain, (v1_funct_1(k2_partfun2(X1,X2,X3))\|~v1_funct_1(X3)\|~v2_funct_1(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(evalgc,[status(thm)],[c_0_27])). cnf(c_0_37, plain, (k2_partfun2(k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))))=k2_partfun1(k1_numbers,k1_numbers,k1_sincos10,k1_rcomp_1(np__1,k7_square_1(np__2)))), inference(evalgc,[status(thm)],[c_0_28])). cnf(c_0_38, plain, (v2_funct_1(k5_relat_1(k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))))), inference(evalgc,[status(thm)],[c_0_29])). cnf(c_0_39, plain, (k5_relat_1(k1_fdiff_9,X1)=k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30, c_0_31]), c_0_32])])])). fof(c_0_40, plain, ![X18, X19]:(~v1_relat_1(X19)\|~v5_relat_1(X19,X18)\|k2_relset_1(X18,X19)=k10_xtuple_0(X19)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k2_relset_1])])). cnf(c_0_41, plain, (v5_relat_1(X1,X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X3,X2)))), inference(split_conjunct,[status(thm)],[c_0_33])). cnf(c_0_42, plain, (m1_subset_1(k2_partfun1(X1,X2,X3,X4),k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_34])). fof(c_0_43, plain, ![X11, X12, X13]:(~m1_subset_1(X13,k1_zfmisc_1(k2_zfmisc_1(X11,X12)))\|v1_relat_1(X13)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relset_1])])). fof(c_0_44, negated_conjecture, k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k1_sincos10,k1_rcomp_1(np__1,k7_square_1(np__2))),k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))))!=k1_partfun2(k1_numbers,k1_rcomp_1(np__1,k7_square_1(np__2))), inference(fof_simplification,[status(thm)],[c_0_35])). fof(c_0_45, plain, ![X30, X31, X32, X33, X34, X35]:(~v1_funct_1(X34)\|~m1_subset_1(X34,k1_zfmisc_1(k2_zfmisc_1(X30,X31)))\|(~v1_funct_1(X35)\|~m1_subset_1(X35,k1_zfmisc_1(k2_zfmisc_1(X32,X33))))\|k1_partfun1(X30,X31,X32,X33,X34,X35)=k3_relat_1(X34,X35)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k1_partfun1])])). cnf(c_0_46, plain, (v1_funct_1(k2_partfun1(k1_numbers,k1_numbers,k1_sincos10,k1_rcomp_1(np__1,k7_square_1(np__2))))\|~v2_funct_1(k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))))\|~m1_subset_1(k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))),k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))\|~v1_funct_1(k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_36, c_0_37])])). cnf(c_0_47, plain, (v2_funct_1(k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))))), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[c_0_38, c_0_39])])). cnf(c_0_48, plain, (m1_subset_1(k2_partfun2(X1,X2,X3),k1_zfmisc_1(k2_zfmisc_1(X2,X1)))\|~v1_funct_1(X3)\|~v2_funct_1(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_23])). fof(c_0_49, plain, ![X24, X25, X26]:(~v1_funct_1(X26)\|(~v2_funct_1(X26)\|~m1_subset_1(X26,k1_zfmisc_1(k2_zfmisc_1(X24,X25))))\|k2_partfun2(X24,X25,X26)=k2_funct_1(X26)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k2_partfun2])])). cnf(c_0_50, plain, (k2_relset_1(X2,X1)=k10_xtuple_0(X1)\|~v1_relat_1(X1)\|~v5_relat_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_40])). cnf(c_0_51, plain, (v5_relat_1(X1,X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X3,X2)))), inference(evalgc,[status(thm)],[c_0_41])). cnf(c_0_52, plain, (m1_subset_1(k2_partfun1(X1,X2,X3,X4),k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(evalgc,[status(thm)],[c_0_42])). cnf(c_0_53, plain, (v1_relat_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_43])). cnf(c_0_54, negated_conjecture, (k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k1_sincos10,k1_rcomp_1(np__1,k7_square_1(np__2))),k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))))!=k1_partfun2(k1_numbers,k1_rcomp_1(np__1,k7_square_1(np__2)))), inference(split_conjunct,[status(thm)],[c_0_44])). cnf(c_0_55, plain, (k1_partfun1(X2,X3,X5,X6,X1,X4)=k3_relat_1(X1,X4)\|~v1_funct_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))\|~v1_funct_1(X4)\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X5,X6)))), inference(split_conjunct,[status(thm)],[c_0_45])). cnf(c_0_56, plain, (v1_funct_1(k2_partfun1(k1_numbers,k1_numbers,k1_sincos10,k1_rcomp_1(np__1,k7_square_1(np__2))))\|~m1_subset_1(k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))),k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))\|~v1_funct_1(k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46, c_0_47])])])). cnf(c_0_57, plain, (v1_funct_1(k2_partfun1(X1,X2,X3,X4))\|~v1_funct_1(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(split_conjunct,[status(thm)],[c_0_34])). cnf(c_0_58, plain, (m1_subset_1(k2_partfun2(X1,X2,X3),k1_zfmisc_1(k2_zfmisc_1(X2,X1)))\|~v1_funct_1(X3)\|~v2_funct_1(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(evalgc,[status(thm)],[c_0_48])). cnf(c_0_59, plain, (k2_partfun2(X2,X3,X1)=k2_funct_1(X1)\|~v1_funct_1(X1)\|~v2_funct_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_49])). cnf(c_0_60, plain, (k2_relset_1(X2,X1)=k10_xtuple_0(X1)\|~v1_relat_1(X1)\|~v5_relat_1(X1,X2)), inference(evalgc,[status(thm)],[c_0_50])). cnf(c_0_61, plain, (v5_relat_1(k2_partfun1(X1,X2,X3,X4),X2)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_51, c_0_52])])). cnf(c_0_62, plain, (v1_relat_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(evalgc,[status(thm)],[c_0_53])). cnf(c_0_63, negated_conjecture, (k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k1_sincos10,k1_rcomp_1(np__1,k7_square_1(np__2))),k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))))!=k1_partfun2(k1_numbers,k1_rcomp_1(np__1,k7_square_1(np__2)))), inference(evalgc,[status(thm)],[c_0_54])). cnf(c_0_64, plain, (k1_partfun1(X2,X3,X5,X6,X1,X4)=k3_relat_1(X1,X4)\|~v1_funct_1(X4)\|~v1_funct_1(X1)\|~m1_subset_1(X4,k1_zfmisc_1(k2_zfmisc_1(X5,X6)))\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(evalgc,[status(thm)],[c_0_55])). cnf(c_0_65, plain, (v1_funct_1(k2_partfun1(k1_numbers,k1_numbers,k1_sincos10,k1_rcomp_1(np__1,k7_square_1(np__2))))\|~v1_funct_1(k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56, c_0_52]), c_0_31]), c_0_32])])])). cnf(c_0_66, plain, (v1_funct_1(k2_partfun1(X1,X2,X3,X4))\|~v1_funct_1(X3)\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))), inference(evalgc,[status(thm)],[c_0_57])). cnf(c_0_67, plain, (m1_subset_1(k2_partfun1(k1_numbers,k1_numbers,k1_sincos10,k1_rcomp_1(np__1,k7_square_1(np__2))),k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))\|~v2_funct_1(k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))))\|~m1_subset_1(k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))),k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))\|~v1_funct_1(k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_58, c_0_37])])). fof(c_0_68, plain, ![X23]:((k3_relat_1(X23,k2_funct_1(X23))=k4_relat_1(k9_xtuple_0(X23))\|~v2_funct_1(X23)\|(~v1_relat_1(X23)\|~v1_funct_1(X23)))&(k3_relat_1(k2_funct_1(X23),X23)=k4_relat_1(k10_xtuple_0(X23))\|~v2_funct_1(X23)\|(~v1_relat_1(X23)\|~v1_funct_1(X23)))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t39_funct_1])])])). cnf(c_0_69, plain, (k2_partfun2(X2,X3,X1)=k2_funct_1(X1)\|~v1_funct_1(X1)\|~v2_funct_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(evalgc,[status(thm)],[c_0_59])). cnf(c_0_70, plain, (k2_relset_1(k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))))=k1_rcomp_1(np__1,k7_square_1(np__2))), inference(split_conjunct,[status(thm)],[t41_sincos10])). cnf(c_0_71, plain, (k2_relset_1(X1,k2_partfun1(X2,X1,X3,X4))=k10_xtuple_0(k2_partfun1(X2,X1,X3,X4))\|~v1_relat_1(k2_partfun1(X2,X1,X3,X4))\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X2,X1)))\|~v1_funct_1(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_60, c_0_61])])). cnf(c_0_72, plain, (v1_relat_1(k2_partfun1(X1,X2,X3,X4))\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))\|~v1_funct_1(X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_62, c_0_52])])). cnf(c_0_73, plain, (v1_relat_1(k5_relat_1(k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))))), inference(split_conjunct,[status(thm)],[fc9_sincos10])). cnf(c_0_74, negated_conjecture, (k3_relat_1(k2_partfun1(k1_numbers,k1_numbers,k1_sincos10,k1_rcomp_1(np__1,k7_square_1(np__2))),k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))))!=k1_partfun2(k1_numbers,k1_rcomp_1(np__1,k7_square_1(np__2)))\|~m1_subset_1(k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))),k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))\|~m1_subset_1(k2_partfun1(k1_numbers,k1_numbers,k1_sincos10,k1_rcomp_1(np__1,k7_square_1(np__2))),k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))\|~v1_funct_1(k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))))\|~v1_funct_1(k2_partfun1(k1_numbers,k1_numbers,k1_sincos10,k1_rcomp_1(np__1,k7_square_1(np__2))))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_63, c_0_64])])). cnf(c_0_75, plain, (v1_funct_1(k2_partfun1(k1_numbers,k1_numbers,k1_sincos10,k1_rcomp_1(np__1,k7_square_1(np__2))))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65, c_0_66]), c_0_31]), c_0_32])])])). cnf(c_0_76, plain, (m1_subset_1(k2_partfun1(k1_numbers,k1_numbers,k1_sincos10,k1_rcomp_1(np__1,k7_square_1(np__2))),k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))\|~m1_subset_1(k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))),k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))\|~v1_funct_1(k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_67, c_0_47])])])). cnf(c_0_77, plain, (k3_relat_1(k2_funct_1(X1),X1)=k4_relat_1(k10_xtuple_0(X1))\|~v2_funct_1(X1)\|~v1_relat_1(X1)\|~v1_funct_1(X1)), inference(split_conjunct,[status(thm)],[c_0_68])). cnf(c_0_78, plain, (k2_funct_1(k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))))=k2_partfun1(k1_numbers,k1_numbers,k1_sincos10,k1_rcomp_1(np__1,k7_square_1(np__2)))\|~v2_funct_1(k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))))\|~m1_subset_1(k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))),k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))\|~v1_funct_1(k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_69, c_0_37])])). cnf(c_0_79, plain, (k2_relset_1(k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))))=k1_rcomp_1(np__1,k7_square_1(np__2))), inference(evalgc,[status(thm)],[c_0_70])). cnf(c_0_80, plain, (k2_relset_1(X1,k2_partfun1(X2,X1,X3,X4))=k10_xtuple_0(k2_partfun1(X2,X1,X3,X4))\|~m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X2,X1)))\|~v1_funct_1(X3)), inference(csr,[status(thm)],[c_0_71, c_0_72])). cnf(c_0_81, plain, (v1_relat_1(k5_relat_1(k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))))), inference(evalgc,[status(thm)],[c_0_73])). cnf(c_0_82, negated_conjecture, (k3_relat_1(k2_partfun1(k1_numbers,k1_numbers,k1_sincos10,k1_rcomp_1(np__1,k7_square_1(np__2))),k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))))!=k1_partfun2(k1_numbers,k1_rcomp_1(np__1,k7_square_1(np__2)))\|~m1_subset_1(k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))),k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))\|~m1_subset_1(k2_partfun1(k1_numbers,k1_numbers,k1_sincos10,k1_rcomp_1(np__1,k7_square_1(np__2))),k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))\|~v1_funct_1(k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_74, c_0_75])])])). cnf(c_0_83, plain, (m1_subset_1(k2_partfun1(k1_numbers,k1_numbers,k1_sincos10,k1_rcomp_1(np__1,k7_square_1(np__2))),k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))\|~v1_funct_1(k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76, c_0_52]), c_0_31]), c_0_32])])])). cnf(c_0_84, plain, (k3_relat_1(k2_funct_1(X1),X1)=k4_relat_1(k10_xtuple_0(X1))\|~v1_funct_1(X1)\|~v1_relat_1(X1)\|~v2_funct_1(X1)), inference(evalgc,[status(thm)],[c_0_77])). cnf(c_0_85, plain, (k2_funct_1(k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))))=k2_partfun1(k1_numbers,k1_numbers,k1_sincos10,k1_rcomp_1(np__1,k7_square_1(np__2)))\|~m1_subset_1(k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))),k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))\|~v1_funct_1(k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_78, c_0_47])])])). cnf(c_0_86, plain, (k10_xtuple_0(k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))))=k1_rcomp_1(np__1,k7_square_1(np__2))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79, c_0_80]), c_0_31]), c_0_32])])])). cnf(c_0_87, plain, (v1_relat_1(k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))))), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[c_0_81, c_0_39])])). cnf(c_0_88, negated_conjecture, (k3_relat_1(k2_partfun1(k1_numbers,k1_numbers,k1_sincos10,k1_rcomp_1(np__1,k7_square_1(np__2))),k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))))!=k1_partfun2(k1_numbers,k1_rcomp_1(np__1,k7_square_1(np__2)))\|~m1_subset_1(k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))),k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))\|~v1_funct_1(k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))))), inference(csr,[status(thm)],[c_0_82, c_0_83])). cnf(c_0_89, plain, (k3_relat_1(k2_partfun1(k1_numbers,k1_numbers,k1_sincos10,k1_rcomp_1(np__1,k7_square_1(np__2))),k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))))=k4_relat_1(k1_rcomp_1(np__1,k7_square_1(np__2)))\|~v1_funct_1(k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))))\|~m1_subset_1(k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))),k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84, c_0_85]), c_0_86]), c_0_47]), c_0_87])])])). cnf(c_0_90, negated_conjecture, (k1_partfun2(k1_numbers,k1_rcomp_1(np__1,k7_square_1(np__2)))!=k4_relat_1(k1_rcomp_1(np__1,k7_square_1(np__2)))\|~m1_subset_1(k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))),k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers)))\|~v1_funct_1(k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_88, c_0_89])])). fof(c_0_91, plain, ![X41, X42]:(v1_xboole_0(X41)\|~m1_subset_1(X42,k1_zfmisc_1(X41))\|k1_partfun2(X41,X42)=k4_relat_1(X42)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[redefinition_k1_partfun2])])])). fof(c_0_92, plain, ~v1_xboole_0(k1_numbers), inference(fof_simplification,[status(thm)],[fc1_numbers])). fof(c_0_93, plain, ![X38]:(~v1_xreal_0(X38)\|v1_xreal_0(k6_square_1(X38))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k6_square_1])])). fof(c_0_94, plain, ![X37]:(~m1_subset_1(X37,k1_numbers)\|k7_square_1(X37)=k6_square_1(X37)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k7_square_1])])). cnf(c_0_95, negated_conjecture, (k1_partfun2(k1_numbers,k1_rcomp_1(np__1,k7_square_1(np__2)))!=k4_relat_1(k1_rcomp_1(np__1,k7_square_1(np__2)))\|~v1_funct_1(k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k6_numbers,k10_real_1(k32_sin_cos,np__4))))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90, c_0_52]), c_0_31]), c_0_32])])])). cnf(c_0_96, plain, (v1_xboole_0(X1)\|k1_partfun2(X1,X2)=k4_relat_1(X2)\|~m1_subset_1(X2,k1_zfmisc_1(X1))), inference(split_conjunct,[status(thm)],[c_0_91])). cnf(c_0_97, plain, (~v1_xboole_0(k1_numbers)), inference(split_conjunct,[status(thm)],[c_0_92])). fof(c_0_98, plain, ![X39, X40]:(~v1_xreal_0(X39)\|~v1_xreal_0(X40)\|m1_subset_1(k1_rcomp_1(X39,X40),k1_zfmisc_1(k1_numbers))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_rcomp_1])])). cnf(c_0_99, plain, (v1_xreal_0(k6_square_1(X1))\|~v1_xreal_0(X1)), inference(split_conjunct,[status(thm)],[c_0_93])). cnf(c_0_100, plain, (k7_square_1(X1)=k6_square_1(X1)\|~m1_subset_1(X1,k1_numbers)), inference(split_conjunct,[status(thm)],[c_0_94])). fof(c_0_101, plain, ![X36]:(~m1_subset_1(X36,k1_numbers)\|v1_xreal_0(X36)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_xreal_0])])). cnf(c_0_102, negated_conjecture, (k1_partfun2(k1_numbers,k1_rcomp_1(np__1,k7_square_1(np__2)))!=k4_relat_1(k1_rcomp_1(np__1,k7_square_1(np__2)))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95, c_0_66]), c_0_31]), c_0_32])])])). cnf(c_0_103, plain, (k1_partfun2(X1,X2)=k4_relat_1(X2)\|v1_xboole_0(X1)\|~m1_subset_1(X2,k1_zfmisc_1(X1))), inference(evalgc,[status(thm)],[c_0_96])). cnf(c_0_104, plain, (~v1_xboole_0(k1_numbers)), inference(evalgc,[status(thm)],[c_0_97])). cnf(c_0_105, plain, (m1_subset_1(k1_rcomp_1(X1,X2),k1_zfmisc_1(k1_numbers))\|~v1_xreal_0(X1)\|~v1_xreal_0(X2)), inference(split_conjunct,[status(thm)],[c_0_98])). cnf(c_0_106, plain, (v1_xreal_0(k6_square_1(X1))\|~v1_xreal_0(X1)), inference(evalgc,[status(thm)],[c_0_99])). cnf(c_0_107, plain, (k6_square_1(X1)=k7_square_1(X1)\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[c_0_100])). cnf(c_0_108, plain, (v1_xreal_0(X1)\|~m1_subset_1(X1,k1_numbers)), inference(split_conjunct,[status(thm)],[c_0_101])). cnf(c_0_109, negated_conjecture, (~m1_subset_1(k1_rcomp_1(np__1,k7_square_1(np__2)),k1_zfmisc_1(k1_numbers))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_102, c_0_103]), c_0_104])])). cnf(c_0_110, plain, (m1_subset_1(k1_rcomp_1(X1,X2),k1_zfmisc_1(k1_numbers))\|~v1_xreal_0(X2)\|~v1_xreal_0(X1)), inference(evalgc,[status(thm)],[c_0_105])). cnf(c_0_111, plain, (v1_xreal_0(k7_square_1(X1))\|~v1_xreal_0(X1)\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_106, c_0_107])])). cnf(c_0_112, plain, (v1_xreal_0(X1)\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[c_0_108])). cnf(c_0_113, plain, (m1_subset_1(np__2,k1_numbers)), inference(split_conjunct,[status(thm)],[spc2_numerals])). cnf(c_0_114, negated_conjecture, (~v1_xreal_0(k7_square_1(np__2))\|~v1_xreal_0(np__1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_109, c_0_110])])). cnf(c_0_115, plain, (v1_xreal_0(k7_square_1(X1))\|~m1_subset_1(X1,k1_numbers)), inference(csr,[status(thm)],[c_0_111, c_0_112])). cnf(c_0_116, plain, (m1_subset_1(np__2,k1_numbers)), inference(evalgc,[status(thm)],[c_0_113])). cnf(c_0_117, plain, (m1_subset_1(np__1,k1_numbers)), inference(split_conjunct,[status(thm)],[spc1_numerals])). cnf(c_0_118, negated_conjecture, (~v1_xreal_0(np__1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114, c_0_115]), c_0_116])])])). cnf(c_0_119, plain, (m1_subset_1(np__1,k1_numbers)), inference(evalgc,[status(thm)],[c_0_117])). cnf(c_0_120, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118, c_0_112]), c_0_119])]), ['proof']). # SZS output end CNFRefutation	reserve x, r for Real, th for real number, rr for set, rseq for Real_Sequence; theorem (sec \| [.0,PI/4.]) * (arcsec1 \| [.1,sqrt 2.]) = id [.1,sqrt 2.] by Th41,Th49,	Convert the following ATP output trace into a readable Mizar proof.
t21_robbins1	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(d4_robbins1, axiom, ![X1]:((~(v2_struct_0(X1))&l2_robbins1(X1))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>k4_robbins1(X1,X2,X3)=k3_robbins1(X1,k1_lattices(X1,k3_robbins1(X1,X2),k3_robbins1(X1,X3)))))), file('/scratch/mptp/predsminms1/t21_robbins1__0', d4_robbins1)). fof(t3_robbins1, axiom, ![X1]:((~(v2_struct_0(X1))&(v4_lattices(X1)&(v5_lattices(X1)&(v6_robbins1(X1)&l2_robbins1(X1)))))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>k3_robbins1(X1,k3_robbins1(X1,X2))=X2)), file('/scratch/mptp/predsminms1/t21_robbins1__0', t3_robbins1)). fof(dt_k3_robbins1, axiom, ![X1, X2]:(((~(v2_struct_0(X1))&l1_robbins1(X1))&m1_subset_1(X2,u1_struct_0(X1)))=>m1_subset_1(k3_robbins1(X1,X2),u1_struct_0(X1))), file('/scratch/mptp/predsminms1/t21_robbins1__0', dt_k3_robbins1)). fof(dt_l2_robbins1, axiom, ![X1]:(l2_robbins1(X1)=>(l2_lattices(X1)&l1_robbins1(X1))), file('/scratch/mptp/predsminms1/t21_robbins1__0', dt_l2_robbins1)). fof(t17_robbins1, axiom, ![X1]:((~(v2_struct_0(X1))&(v4_lattices(X1)&(v5_lattices(X1)&(v6_robbins1(X1)&l2_robbins1(X1)))))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>k5_robbins1(X1,X2,X3)=k3_robbins1(X1,k6_robbins1(X1,k3_robbins1(X1,X2),k3_robbins1(X1,X3)))))), file('/scratch/mptp/predsminms1/t21_robbins1__0', t17_robbins1)). fof(dt_k6_robbins1, axiom, ![X1, X2, X3]:(((~(v2_struct_0(X1))&(v4_lattices(X1)&(v5_lattices(X1)&l2_robbins1(X1))))&(m1_subset_1(X2,u1_struct_0(X1))&m1_subset_1(X3,u1_struct_0(X1))))=>m1_subset_1(k6_robbins1(X1,X2,X3),u1_struct_0(X1))), file('/scratch/mptp/predsminms1/t21_robbins1__0', dt_k6_robbins1)). fof(redefinition_k6_robbins1, axiom, ![X1, X2, X3]:(((~(v2_struct_0(X1))&(v4_lattices(X1)&(v5_lattices(X1)&l2_robbins1(X1))))&(m1_subset_1(X2,u1_struct_0(X1))&m1_subset_1(X3,u1_struct_0(X1))))=>k6_robbins1(X1,X2,X3)=k4_robbins1(X1,X2,X3)), file('/scratch/mptp/predsminms1/t21_robbins1__0', redefinition_k6_robbins1)). fof(redefinition_k5_robbins1, axiom, ![X1, X2, X3]:(((~(v2_struct_0(X1))&(v4_lattices(X1)&l2_robbins1(X1)))&(m1_subset_1(X2,u1_struct_0(X1))&m1_subset_1(X3,u1_struct_0(X1))))=>k5_robbins1(X1,X2,X3)=k1_lattices(X1,X2,X3)), file('/scratch/mptp/predsminms1/t21_robbins1__0', redefinition_k5_robbins1)). fof(t20_robbins1, axiom, ![X1]:((~(v2_struct_0(X1))&(v4_lattices(X1)&(v5_lattices(X1)&(v6_robbins1(X1)&l2_robbins1(X1)))))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>k5_robbins1(X1,X2,k6_robbins1(X1,X2,X3))=X2))), file('/scratch/mptp/predsminms1/t21_robbins1__0', t20_robbins1)). fof(t21_robbins1, conjecture, ![X1]:((~(v2_struct_0(X1))&(v4_lattices(X1)&(v5_lattices(X1)&(v6_robbins1(X1)&l2_robbins1(X1)))))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>k6_robbins1(X1,X2,k5_robbins1(X1,X2,X3))=X2))), file('/scratch/mptp/predsminms1/t21_robbins1__0', t21_robbins1)). fof(c_0_10, plain, ![X21, X22, X23]:(v2_struct_0(X21)\|~l2_robbins1(X21)\|(~m1_subset_1(X22,u1_struct_0(X21))\|(~m1_subset_1(X23,u1_struct_0(X21))\|k4_robbins1(X21,X22,X23)=k3_robbins1(X21,k1_lattices(X21,k3_robbins1(X21,X22),k3_robbins1(X21,X23)))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d4_robbins1])])])])). fof(c_0_11, plain, ![X7, X8]:(v2_struct_0(X7)\|(~v4_lattices(X7)\|(~v5_lattices(X7)\|(~v6_robbins1(X7)\|~l2_robbins1(X7))))\|(~m1_subset_1(X8,u1_struct_0(X7))\|k3_robbins1(X7,k3_robbins1(X7,X8))=X8)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t3_robbins1])])])])). fof(c_0_12, plain, ![X13, X14]:(v2_struct_0(X13)\|~l1_robbins1(X13)\|~m1_subset_1(X14,u1_struct_0(X13))\|m1_subset_1(k3_robbins1(X13,X14),u1_struct_0(X13))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k3_robbins1])])])). fof(c_0_13, plain, ![X12]:((l2_lattices(X12)\|~l2_robbins1(X12))&(l1_robbins1(X12)\|~l2_robbins1(X12))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l2_robbins1])])])). cnf(c_0_14, plain, (v2_struct_0(X1)\|k4_robbins1(X1,X2,X3)=k3_robbins1(X1,k1_lattices(X1,k3_robbins1(X1,X2),k3_robbins1(X1,X3)))\|~l2_robbins1(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_10])). cnf(c_0_15, plain, (v2_struct_0(X1)\|k3_robbins1(X1,k3_robbins1(X1,X2))=X2\|~v4_lattices(X1)\|~v5_lattices(X1)\|~v6_robbins1(X1)\|~l2_robbins1(X1)\|~m1_subset_1(X2,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_16, plain, (v2_struct_0(X1)\|m1_subset_1(k3_robbins1(X1,X2),u1_struct_0(X1))\|~l1_robbins1(X1)\|~m1_subset_1(X2,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_17, plain, (l1_robbins1(X1)\|~l2_robbins1(X1)), inference(split_conjunct,[status(thm)],[c_0_13])). cnf(c_0_18, plain, (k3_robbins1(X1,k1_lattices(X1,k3_robbins1(X1,X2),k3_robbins1(X1,X3)))=k4_robbins1(X1,X2,X3)\|v2_struct_0(X1)\|~l2_robbins1(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_14])). cnf(c_0_19, plain, (k3_robbins1(X1,k3_robbins1(X1,X2))=X2\|v2_struct_0(X1)\|~v4_lattices(X1)\|~v5_lattices(X1)\|~v6_robbins1(X1)\|~l2_robbins1(X1)\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_15])). cnf(c_0_20, plain, (v2_struct_0(X1)\|m1_subset_1(k3_robbins1(X1,X2),u1_struct_0(X1))\|~l1_robbins1(X1)\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_16])). cnf(c_0_21, plain, (l1_robbins1(X1)\|~l2_robbins1(X1)), inference(evalgc,[status(thm)],[c_0_17])). fof(c_0_22, plain, ![X9, X10, X11]:(v2_struct_0(X9)\|(~v4_lattices(X9)\|(~v5_lattices(X9)\|(~v6_robbins1(X9)\|~l2_robbins1(X9))))\|(~m1_subset_1(X10,u1_struct_0(X9))\|(~m1_subset_1(X11,u1_struct_0(X9))\|k5_robbins1(X9,X10,X11)=k3_robbins1(X9,k6_robbins1(X9,k3_robbins1(X9,X10),k3_robbins1(X9,X11)))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t17_robbins1])])])])). cnf(c_0_23, plain, (k3_robbins1(X1,k1_lattices(X1,X2,k3_robbins1(X1,X3)))=k4_robbins1(X1,k3_robbins1(X1,X2),X3)\|v2_struct_0(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(k3_robbins1(X1,X2),u1_struct_0(X1))\|~l2_robbins1(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~v6_robbins1(X1)\|~v5_lattices(X1)\|~v4_lattices(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_18, c_0_19])])). cnf(c_0_24, plain, (m1_subset_1(k3_robbins1(X1,X2),u1_struct_0(X1))\|v2_struct_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~l2_robbins1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_20, c_0_21])])). cnf(c_0_25, plain, (v2_struct_0(X1)\|k5_robbins1(X1,X2,X3)=k3_robbins1(X1,k6_robbins1(X1,k3_robbins1(X1,X2),k3_robbins1(X1,X3)))\|~v4_lattices(X1)\|~v5_lattices(X1)\|~v6_robbins1(X1)\|~l2_robbins1(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_22])). fof(c_0_26, plain, ![X27, X28, X29]:(v2_struct_0(X27)\|(~v4_lattices(X27)\|(~v5_lattices(X27)\|~l2_robbins1(X27)))\|(~m1_subset_1(X28,u1_struct_0(X27))\|~m1_subset_1(X29,u1_struct_0(X27)))\|m1_subset_1(k6_robbins1(X27,X28,X29),u1_struct_0(X27))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k6_robbins1])])])). fof(c_0_27, plain, ![X24, X25, X26]:(v2_struct_0(X24)\|(~v4_lattices(X24)\|(~v5_lattices(X24)\|~l2_robbins1(X24)))\|(~m1_subset_1(X25,u1_struct_0(X24))\|~m1_subset_1(X26,u1_struct_0(X24)))\|k6_robbins1(X24,X25,X26)=k4_robbins1(X24,X25,X26)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[redefinition_k6_robbins1])])])). cnf(c_0_28, plain, (k3_robbins1(X1,k1_lattices(X1,X2,k3_robbins1(X1,X3)))=k4_robbins1(X1,k3_robbins1(X1,X2),X3)\|v2_struct_0(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l2_robbins1(X1)\|~v6_robbins1(X1)\|~v5_lattices(X1)\|~v4_lattices(X1)), inference(csr,[status(thm)],[c_0_23, c_0_24])). cnf(c_0_29, plain, (k3_robbins1(X1,k6_robbins1(X1,k3_robbins1(X1,X2),k3_robbins1(X1,X3)))=k5_robbins1(X1,X2,X3)\|v2_struct_0(X1)\|~v4_lattices(X1)\|~v5_lattices(X1)\|~v6_robbins1(X1)\|~l2_robbins1(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_25])). cnf(c_0_30, plain, (v2_struct_0(X1)\|m1_subset_1(k6_robbins1(X1,X2,X3),u1_struct_0(X1))\|~v4_lattices(X1)\|~v5_lattices(X1)\|~l2_robbins1(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_26])). fof(c_0_31, plain, ![X18, X19, X20]:(v2_struct_0(X18)\|(~v4_lattices(X18)\|~l2_robbins1(X18))\|(~m1_subset_1(X19,u1_struct_0(X18))\|~m1_subset_1(X20,u1_struct_0(X18)))\|k5_robbins1(X18,X19,X20)=k1_lattices(X18,X19,X20)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[redefinition_k5_robbins1])])])). cnf(c_0_32, plain, (v2_struct_0(X1)\|k6_robbins1(X1,X2,X3)=k4_robbins1(X1,X2,X3)\|~v4_lattices(X1)\|~v5_lattices(X1)\|~l2_robbins1(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_27])). cnf(c_0_33, plain, (k4_robbins1(X1,k3_robbins1(X1,X2),k3_robbins1(X1,X3))=k3_robbins1(X1,k1_lattices(X1,X2,X3))\|v2_struct_0(X1)\|~m1_subset_1(k3_robbins1(X1,X3),u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l2_robbins1(X1)\|~v6_robbins1(X1)\|~v5_lattices(X1)\|~v4_lattices(X1)\|~m1_subset_1(X3,u1_struct_0(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_28, c_0_19])])). cnf(c_0_34, plain, (k6_robbins1(X1,k3_robbins1(X1,X2),k3_robbins1(X1,X3))=k3_robbins1(X1,k5_robbins1(X1,X2,X3))\|v2_struct_0(X1)\|~m1_subset_1(k6_robbins1(X1,k3_robbins1(X1,X2),k3_robbins1(X1,X3)),u1_struct_0(X1))\|~l2_robbins1(X1)\|~v6_robbins1(X1)\|~v5_lattices(X1)\|~v4_lattices(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_19, c_0_29])])). cnf(c_0_35, plain, (v2_struct_0(X1)\|m1_subset_1(k6_robbins1(X1,X2,X3),u1_struct_0(X1))\|~v4_lattices(X1)\|~v5_lattices(X1)\|~l2_robbins1(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_30])). cnf(c_0_36, plain, (v2_struct_0(X1)\|k5_robbins1(X1,X2,X3)=k1_lattices(X1,X2,X3)\|~v4_lattices(X1)\|~l2_robbins1(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_31])). fof(c_0_37, plain, ![X15, X16, X17]:(v2_struct_0(X15)\|(~v4_lattices(X15)\|(~v5_lattices(X15)\|(~v6_robbins1(X15)\|~l2_robbins1(X15))))\|(~m1_subset_1(X16,u1_struct_0(X15))\|(~m1_subset_1(X17,u1_struct_0(X15))\|k5_robbins1(X15,X16,k6_robbins1(X15,X16,X17))=X16))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t20_robbins1])])])])). cnf(c_0_38, plain, (k4_robbins1(X1,X2,X3)=k6_robbins1(X1,X2,X3)\|v2_struct_0(X1)\|~v4_lattices(X1)\|~v5_lattices(X1)\|~l2_robbins1(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_32])). cnf(c_0_39, plain, (k4_robbins1(X1,k3_robbins1(X1,X2),k3_robbins1(X1,X3))=k3_robbins1(X1,k1_lattices(X1,X2,X3))\|v2_struct_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~l2_robbins1(X1)\|~v6_robbins1(X1)\|~v5_lattices(X1)\|~v4_lattices(X1)), inference(csr,[status(thm)],[c_0_33, c_0_24])). cnf(c_0_40, plain, (k6_robbins1(X1,k3_robbins1(X1,X2),k3_robbins1(X1,X3))=k3_robbins1(X1,k5_robbins1(X1,X2,X3))\|v2_struct_0(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l2_robbins1(X1)\|~v6_robbins1(X1)\|~v5_lattices(X1)\|~v4_lattices(X1)\|~m1_subset_1(k3_robbins1(X1,X3),u1_struct_0(X1))\|~m1_subset_1(k3_robbins1(X1,X2),u1_struct_0(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_34, c_0_35])])). cnf(c_0_41, plain, (k1_lattices(X1,X2,X3)=k5_robbins1(X1,X2,X3)\|v2_struct_0(X1)\|~v4_lattices(X1)\|~l2_robbins1(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_36])). cnf(c_0_42, plain, (k3_robbins1(X1,k6_robbins1(X1,X2,k3_robbins1(X1,X3)))=k5_robbins1(X1,k3_robbins1(X1,X2),X3)\|v2_struct_0(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(k3_robbins1(X1,X2),u1_struct_0(X1))\|~l2_robbins1(X1)\|~v6_robbins1(X1)\|~v5_lattices(X1)\|~v4_lattices(X1)\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_29, c_0_19])])). cnf(c_0_43, plain, (v2_struct_0(X1)\|k5_robbins1(X1,X2,k6_robbins1(X1,X2,X3))=X2\|~v4_lattices(X1)\|~v5_lattices(X1)\|~v6_robbins1(X1)\|~l2_robbins1(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_37])). cnf(c_0_44, plain, (k6_robbins1(X1,k3_robbins1(X1,X2),k3_robbins1(X1,X3))=k3_robbins1(X1,k1_lattices(X1,X2,X3))\|v2_struct_0(X1)\|~m1_subset_1(k3_robbins1(X1,X3),u1_struct_0(X1))\|~m1_subset_1(k3_robbins1(X1,X2),u1_struct_0(X1))\|~l2_robbins1(X1)\|~v5_lattices(X1)\|~v4_lattices(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~v6_robbins1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_38, c_0_39])])). cnf(c_0_45, plain, (k6_robbins1(X1,k3_robbins1(X1,X2),k3_robbins1(X1,X3))=k3_robbins1(X1,k5_robbins1(X1,X2,X3))\|v2_struct_0(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l2_robbins1(X1)\|~v6_robbins1(X1)\|~v5_lattices(X1)\|~v4_lattices(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_40, c_0_24]), c_0_24])). cnf(c_0_46, plain, (k3_robbins1(X1,k5_robbins1(X1,k3_robbins1(X1,X2),k3_robbins1(X1,X3)))=k4_robbins1(X1,X2,X3)\|v2_struct_0(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l2_robbins1(X1)\|~m1_subset_1(k3_robbins1(X1,X3),u1_struct_0(X1))\|~m1_subset_1(k3_robbins1(X1,X2),u1_struct_0(X1))\|~v4_lattices(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_18, c_0_41])])). cnf(c_0_47, plain, (k3_robbins1(X1,k6_robbins1(X1,X2,k3_robbins1(X1,X3)))=k5_robbins1(X1,k3_robbins1(X1,X2),X3)\|v2_struct_0(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l2_robbins1(X1)\|~v6_robbins1(X1)\|~v5_lattices(X1)\|~v4_lattices(X1)), inference(csr,[status(thm)],[c_0_42, c_0_24])). cnf(c_0_48, plain, (k5_robbins1(X1,X2,k6_robbins1(X1,X2,X3))=X2\|v2_struct_0(X1)\|~v4_lattices(X1)\|~v5_lattices(X1)\|~v6_robbins1(X1)\|~l2_robbins1(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_43])). cnf(c_0_49, plain, (k6_robbins1(X1,k3_robbins1(X1,X2),k3_robbins1(X1,X3))=k3_robbins1(X1,k1_lattices(X1,X2,X3))\|v2_struct_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~l2_robbins1(X1)\|~v6_robbins1(X1)\|~v5_lattices(X1)\|~v4_lattices(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_44, c_0_24]), c_0_24])). cnf(c_0_50, plain, (k3_robbins1(X1,k3_robbins1(X1,k5_robbins1(X1,X2,X3)))=k5_robbins1(X1,X2,X3)\|v2_struct_0(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l2_robbins1(X1)\|~v6_robbins1(X1)\|~v5_lattices(X1)\|~v4_lattices(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_29, c_0_45])])). cnf(c_0_51, plain, (k3_robbins1(X1,k5_robbins1(X1,k3_robbins1(X1,X2),k3_robbins1(X1,X3)))=k4_robbins1(X1,X2,X3)\|v2_struct_0(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l2_robbins1(X1)\|~v4_lattices(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_46, c_0_24]), c_0_24])). cnf(c_0_52, plain, (k5_robbins1(X1,k3_robbins1(X1,X2),k3_robbins1(X1,X3))=k3_robbins1(X1,k6_robbins1(X1,X2,X3))\|v2_struct_0(X1)\|~m1_subset_1(k3_robbins1(X1,X3),u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l2_robbins1(X1)\|~v6_robbins1(X1)\|~v5_lattices(X1)\|~v4_lattices(X1)\|~m1_subset_1(X3,u1_struct_0(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_47, c_0_19])])). cnf(c_0_53, plain, (k5_robbins1(X1,k3_robbins1(X1,X2),k3_robbins1(X1,k1_lattices(X1,X2,X3)))=k3_robbins1(X1,X2)\|v2_struct_0(X1)\|~m1_subset_1(k3_robbins1(X1,X3),u1_struct_0(X1))\|~m1_subset_1(k3_robbins1(X1,X2),u1_struct_0(X1))\|~l2_robbins1(X1)\|~v6_robbins1(X1)\|~v5_lattices(X1)\|~v4_lattices(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_48, c_0_49])])). cnf(c_0_54, plain, (k5_robbins1(X1,k3_robbins1(X1,X2),k3_robbins1(X1,X3))=k3_robbins1(X1,k4_robbins1(X1,X2,X3))\|v2_struct_0(X1)\|~m1_subset_1(k3_robbins1(X1,X3),u1_struct_0(X1))\|~m1_subset_1(k3_robbins1(X1,X2),u1_struct_0(X1))\|~l2_robbins1(X1)\|~v6_robbins1(X1)\|~v5_lattices(X1)\|~v4_lattices(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_50, c_0_51])])). cnf(c_0_55, plain, (k5_robbins1(X1,k3_robbins1(X1,X2),k3_robbins1(X1,X3))=k3_robbins1(X1,k6_robbins1(X1,X2,X3))\|v2_struct_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~l2_robbins1(X1)\|~v6_robbins1(X1)\|~v5_lattices(X1)\|~v4_lattices(X1)), inference(csr,[status(thm)],[c_0_52, c_0_24])). cnf(c_0_56, plain, (k5_robbins1(X1,k3_robbins1(X1,X2),k3_robbins1(X1,k1_lattices(X1,X2,X3)))=k3_robbins1(X1,X2)\|v2_struct_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~l2_robbins1(X1)\|~v6_robbins1(X1)\|~v5_lattices(X1)\|~v4_lattices(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_53, c_0_24]), c_0_24])). cnf(c_0_57, plain, (m1_subset_1(k5_robbins1(X1,X2,X3),u1_struct_0(X1))\|v2_struct_0(X1)\|~m1_subset_1(k6_robbins1(X1,k3_robbins1(X1,X2),k3_robbins1(X1,X3)),u1_struct_0(X1))\|~l2_robbins1(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~v6_robbins1(X1)\|~v5_lattices(X1)\|~v4_lattices(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_24, c_0_29])])). cnf(c_0_58, plain, (k5_robbins1(X1,k3_robbins1(X1,X2),k3_robbins1(X1,X3))=k3_robbins1(X1,k4_robbins1(X1,X2,X3))\|v2_struct_0(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l2_robbins1(X1)\|~v6_robbins1(X1)\|~v5_lattices(X1)\|~v4_lattices(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_54, c_0_24]), c_0_24])). cnf(c_0_59, plain, (k3_robbins1(X1,k6_robbins1(X1,X2,k1_lattices(X1,X2,X3)))=k3_robbins1(X1,X2)\|v2_struct_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(k1_lattices(X1,X2,X3),u1_struct_0(X1))\|~l2_robbins1(X1)\|~v6_robbins1(X1)\|~v5_lattices(X1)\|~v4_lattices(X1)\|~m1_subset_1(X3,u1_struct_0(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_55, c_0_56])])). cnf(c_0_60, plain, (m1_subset_1(k5_robbins1(X1,X2,X3),u1_struct_0(X1))\|v2_struct_0(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l2_robbins1(X1)\|~v6_robbins1(X1)\|~v5_lattices(X1)\|~v4_lattices(X1)\|~m1_subset_1(k3_robbins1(X1,X3),u1_struct_0(X1))\|~m1_subset_1(k3_robbins1(X1,X2),u1_struct_0(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_57, c_0_35])])). fof(c_0_61, negated_conjecture, ~(![X1]:((~(v2_struct_0(X1))&(v4_lattices(X1)&(v5_lattices(X1)&(v6_robbins1(X1)&l2_robbins1(X1)))))=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>k6_robbins1(X1,X2,k5_robbins1(X1,X2,X3))=X2)))), inference(assume_negation,[status(cth)],[t21_robbins1])). cnf(c_0_62, plain, (k3_robbins1(X1,k3_robbins1(X1,k4_robbins1(X1,X2,X3)))=k4_robbins1(X1,X2,X3)\|v2_struct_0(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l2_robbins1(X1)\|~v4_lattices(X1)\|~v6_robbins1(X1)\|~v5_lattices(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_51, c_0_58])])). cnf(c_0_63, plain, (k3_robbins1(X1,k6_robbins1(X1,X2,k5_robbins1(X1,X2,X3)))=k3_robbins1(X1,X2)\|v2_struct_0(X1)\|~m1_subset_1(k5_robbins1(X1,X2,X3),u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~l2_robbins1(X1)\|~v6_robbins1(X1)\|~v5_lattices(X1)\|~v4_lattices(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_59, c_0_41])])). cnf(c_0_64, plain, (m1_subset_1(k5_robbins1(X1,X2,X3),u1_struct_0(X1))\|v2_struct_0(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l2_robbins1(X1)\|~v6_robbins1(X1)\|~v5_lattices(X1)\|~v4_lattices(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_60, c_0_24]), c_0_24])). fof(c_0_65, negated_conjecture, ((~v2_struct_0(esk1_0)&(v4_lattices(esk1_0)&(v5_lattices(esk1_0)&(v6_robbins1(esk1_0)&l2_robbins1(esk1_0)))))&(m1_subset_1(esk2_0,u1_struct_0(esk1_0))&(m1_subset_1(esk3_0,u1_struct_0(esk1_0))&k6_robbins1(esk1_0,esk2_0,k5_robbins1(esk1_0,esk2_0,esk3_0))!=esk2_0))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_61])])])])). cnf(c_0_66, plain, (k3_robbins1(X1,k3_robbins1(X1,k6_robbins1(X1,X2,X3)))=k6_robbins1(X1,X2,X3)\|v2_struct_0(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l2_robbins1(X1)\|~v6_robbins1(X1)\|~v5_lattices(X1)\|~v4_lattices(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_62, c_0_38])])). cnf(c_0_67, plain, (k3_robbins1(X1,k6_robbins1(X1,X2,k5_robbins1(X1,X2,X3)))=k3_robbins1(X1,X2)\|v2_struct_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~l2_robbins1(X1)\|~v6_robbins1(X1)\|~v5_lattices(X1)\|~v4_lattices(X1)), inference(csr,[status(thm)],[c_0_63, c_0_64])). cnf(c_0_68, negated_conjecture, (k6_robbins1(esk1_0,esk2_0,k5_robbins1(esk1_0,esk2_0,esk3_0))!=esk2_0), inference(split_conjunct,[status(thm)],[c_0_65])). cnf(c_0_69, plain, (k6_robbins1(X1,X2,k5_robbins1(X1,X2,X3))=k3_robbins1(X1,k3_robbins1(X1,X2))\|v2_struct_0(X1)\|~m1_subset_1(k5_robbins1(X1,X2,X3),u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~l2_robbins1(X1)\|~v6_robbins1(X1)\|~v5_lattices(X1)\|~v4_lattices(X1)\|~m1_subset_1(X3,u1_struct_0(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_66, c_0_67])])). cnf(c_0_70, negated_conjecture, (m1_subset_1(esk2_0,u1_struct_0(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_65])). cnf(c_0_71, negated_conjecture, (m1_subset_1(esk3_0,u1_struct_0(esk1_0))), inference(split_conjunct,[status(thm)],[c_0_65])). cnf(c_0_72, negated_conjecture, (l2_robbins1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_65])). cnf(c_0_73, negated_conjecture, (v6_robbins1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_65])). cnf(c_0_74, negated_conjecture, (v5_lattices(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_65])). cnf(c_0_75, negated_conjecture, (v4_lattices(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_65])). cnf(c_0_76, negated_conjecture, (~v2_struct_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_65])). cnf(c_0_77, negated_conjecture, (k6_robbins1(esk1_0,esk2_0,k5_robbins1(esk1_0,esk2_0,esk3_0))!=esk2_0), inference(evalgc,[status(thm)],[c_0_68])). cnf(c_0_78, plain, (k6_robbins1(X1,X2,k5_robbins1(X1,X2,X3))=k3_robbins1(X1,k3_robbins1(X1,X2))\|v2_struct_0(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~l2_robbins1(X1)\|~v6_robbins1(X1)\|~v5_lattices(X1)\|~v4_lattices(X1)), inference(csr,[status(thm)],[c_0_69, c_0_64])). cnf(c_0_79, negated_conjecture, (m1_subset_1(esk2_0,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[c_0_70])). cnf(c_0_80, negated_conjecture, (m1_subset_1(esk3_0,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[c_0_71])). cnf(c_0_81, negated_conjecture, (l2_robbins1(esk1_0)), inference(evalgc,[status(thm)],[c_0_72])). cnf(c_0_82, negated_conjecture, (v6_robbins1(esk1_0)), inference(evalgc,[status(thm)],[c_0_73])). cnf(c_0_83, negated_conjecture, (v5_lattices(esk1_0)), inference(evalgc,[status(thm)],[c_0_74])). cnf(c_0_84, negated_conjecture, (v4_lattices(esk1_0)), inference(evalgc,[status(thm)],[c_0_75])). cnf(c_0_85, negated_conjecture, (~v2_struct_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_76])). cnf(c_0_86, negated_conjecture, (k3_robbins1(esk1_0,k3_robbins1(esk1_0,esk2_0))!=esk2_0), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77, c_0_78]), c_0_79]), c_0_80]), c_0_81]), c_0_82]), c_0_83]), c_0_84])]), c_0_85])])). cnf(c_0_87, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86, c_0_19]), c_0_79]), c_0_81]), c_0_82]), c_0_83]), c_0_84])]), c_0_85]), ['proof']). # SZS output end CNFRefutation	theorem Th21: :: 4.25 for L being join-commutative join-associative Huntington non empty ComplLLattStr, a, b being Element of L holds a ' (a + b) = a proof let L be join-commutative join-associative Huntington non empty ComplLLattStr, a,b be Element of L; thus a ' (a + b) = (a` + (a` ' b`)``)` by Th17 .= (a` + (a` ' b`))` by Th3 .= a`` by Th20 .= a by Th3; end;	Convert the following ATP output trace into a readable Mizar proof.
t50_altcat_4	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t50_altcat_4, conjecture, ![X1]:((~(v2_struct_0(X1))&(v2_altcat_1(X1)&(v11_altcat_1(X1)&(v12_altcat_1(X1)&l2_altcat_1(X1)))))=>![X2]:(m1_subset_1(X2,u1_struct_0(k1_altcat_4(X1)))=>![X3]:(m1_subset_1(X3,u1_struct_0(k1_altcat_4(X1)))=>![X4]:(m1_subset_1(X4,k1_altcat_1(k1_altcat_4(X1),X2,X3))=>(~(k1_altcat_1(k1_altcat_4(X1),X2,X3)=k1_xboole_0)=>v4_altcat_3(X4,k1_altcat_4(X1),X2,X3)))))), file('/scratch/mptp/predsminms1/t50_altcat_4__0', t50_altcat_4)). fof(t2_subset, axiom, ![X1, X2]:(m1_subset_1(X1,X2)=>(v1_xboole_0(X2)\|r2_hidden(X1,X2))), file('/scratch/mptp/predsminms1/t50_altcat_4__0', t2_subset)). fof(d1_altcat_4, axiom, ![X1]:((~(v2_struct_0(X1))&(v2_altcat_1(X1)&(v11_altcat_1(X1)&(v12_altcat_1(X1)&l2_altcat_1(X1)))))=>![X2]:((~(v2_struct_0(X2))&(v2_altcat_1(X2)&(v6_altcat_1(X2)&m1_altcat_2(X2,X1))))=>(X2=k1_altcat_4(X1)<=>(u1_struct_0(X2)=u1_struct_0(X1)&(r2_altcat_2(k2_zfmisc_1(u1_struct_0(X2),u1_struct_0(X2)),k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)),u1_altcat_1(X2),u1_altcat_1(X1))&![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>![X4]:(m1_subset_1(X4,u1_struct_0(X1))=>![X5]:(m1_subset_1(X5,k1_altcat_1(X1,X3,X4))=>(r2_hidden(X5,k1_binop_1(u1_altcat_1(X2),X3,X4))<=>(~(k1_altcat_1(X1,X3,X4)=k1_xboole_0)&v4_altcat_3(X5,X1,X3,X4))))))))))), file('/scratch/mptp/predsminms1/t50_altcat_4__0', d1_altcat_4)). fof(d1_altcat_1, axiom, ![X1]:(l1_altcat_1(X1)=>![X2]:(m1_subset_1(X2,u1_struct_0(X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>k1_altcat_1(X1,X2,X3)=k1_binop_1(u1_altcat_1(X1),X2,X3)))), file('/scratch/mptp/predsminms1/t50_altcat_4__0', d1_altcat_1)). fof(t6_boole, axiom, ![X1]:(v1_xboole_0(X1)=>X1=k1_xboole_0), file('/scratch/mptp/predsminms1/t50_altcat_4__0', t6_boole)). fof(t33_altcat_2, axiom, ![X1]:((~(v2_struct_0(X1))&l2_altcat_1(X1))=>![X2]:((~(v2_struct_0(X2))&m1_altcat_2(X2,X1))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>![X4]:(m1_subset_1(X4,u1_struct_0(X1))=>![X5]:(m1_subset_1(X5,u1_struct_0(X2))=>![X6]:(m1_subset_1(X6,u1_struct_0(X2))=>((X3=X5&X4=X6)=>(k1_altcat_1(X2,X5,X6)=k1_xboole_0\|![X7]:(m1_subset_1(X7,k1_altcat_1(X2,X5,X6))=>m1_subset_1(X7,k1_altcat_1(X1,X3,X4))))))))))), file('/scratch/mptp/predsminms1/t50_altcat_4__0', t33_altcat_2)). fof(dt_l2_altcat_1, axiom, ![X1]:(l2_altcat_1(X1)=>l1_altcat_1(X1)), file('/scratch/mptp/predsminms1/t50_altcat_4__0', dt_l2_altcat_1)). fof(dt_m1_altcat_2, axiom, ![X1]:(l2_altcat_1(X1)=>![X2]:(m1_altcat_2(X2,X1)=>l2_altcat_1(X2))), file('/scratch/mptp/predsminms1/t50_altcat_4__0', dt_m1_altcat_2)). fof(dt_k1_altcat_4, axiom, ![X1]:((~(v2_struct_0(X1))&(v2_altcat_1(X1)&(v11_altcat_1(X1)&(v12_altcat_1(X1)&l2_altcat_1(X1)))))=>(~(v2_struct_0(k1_altcat_4(X1)))&(v2_altcat_1(k1_altcat_4(X1))&(v6_altcat_1(k1_altcat_4(X1))&m1_altcat_2(k1_altcat_4(X1),X1))))), file('/scratch/mptp/predsminms1/t50_altcat_4__0', dt_k1_altcat_4)). fof(t37_altcat_4, axiom, ![X1]:((~(v2_struct_0(X1))&(v2_altcat_1(X1)&l2_altcat_1(X1)))=>![X2]:((~(v2_struct_0(X2))&(v2_altcat_1(X2)&m1_altcat_2(X2,X1)))=>![X3]:(m1_subset_1(X3,u1_struct_0(X1))=>![X4]:(m1_subset_1(X4,u1_struct_0(X1))=>![X5]:(m1_subset_1(X5,u1_struct_0(X2))=>![X6]:(m1_subset_1(X6,u1_struct_0(X2))=>![X7]:(m1_subset_1(X7,k1_altcat_1(X1,X3,X4))=>![X8]:(m1_subset_1(X8,k1_altcat_1(X2,X5,X6))=>((X5=X3&(X6=X4&X7=X8))=>(k1_altcat_1(X2,X5,X6)=k1_xboole_0\|((v4_altcat_3(X7,X1,X3,X4)=>v4_altcat_3(X8,X2,X5,X6))&(v5_altcat_3(X7,X1,X3,X4)=>v5_altcat_3(X8,X2,X5,X6))))))))))))), file('/scratch/mptp/predsminms1/t50_altcat_4__0', t37_altcat_4)). fof(c_0_10, negated_conjecture, ~(![X1]:((~(v2_struct_0(X1))&(v2_altcat_1(X1)&(v11_altcat_1(X1)&(v12_altcat_1(X1)&l2_altcat_1(X1)))))=>![X2]:(m1_subset_1(X2,u1_struct_0(k1_altcat_4(X1)))=>![X3]:(m1_subset_1(X3,u1_struct_0(k1_altcat_4(X1)))=>![X4]:(m1_subset_1(X4,k1_altcat_1(k1_altcat_4(X1),X2,X3))=>(~(k1_altcat_1(k1_altcat_4(X1),X2,X3)=k1_xboole_0)=>v4_altcat_3(X4,k1_altcat_4(X1),X2,X3))))))), inference(assume_negation,[status(cth)],[t50_altcat_4])). fof(c_0_11, plain, ![X25, X26]:(~m1_subset_1(X25,X26)\|(v1_xboole_0(X26)\|r2_hidden(X25,X26))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])])). fof(c_0_12, negated_conjecture, ((~v2_struct_0(esk1_0)&(v2_altcat_1(esk1_0)&(v11_altcat_1(esk1_0)&(v12_altcat_1(esk1_0)&l2_altcat_1(esk1_0)))))&(m1_subset_1(esk2_0,u1_struct_0(k1_altcat_4(esk1_0)))&(m1_subset_1(esk3_0,u1_struct_0(k1_altcat_4(esk1_0)))&(m1_subset_1(esk4_0,k1_altcat_1(k1_altcat_4(esk1_0),esk2_0,esk3_0))&(k1_altcat_1(k1_altcat_4(esk1_0),esk2_0,esk3_0)!=k1_xboole_0&~v4_altcat_3(esk4_0,k1_altcat_4(esk1_0),esk2_0,esk3_0)))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_10])])])])). fof(c_0_13, plain, ![X13, X14, X15, X16, X17]:(((u1_struct_0(X14)=u1_struct_0(X13)\|X14!=k1_altcat_4(X13)\|(v2_struct_0(X14)\|(~v2_altcat_1(X14)\|(~v6_altcat_1(X14)\|~m1_altcat_2(X14,X13))))\|(v2_struct_0(X13)\|(~v2_altcat_1(X13)\|(~v11_altcat_1(X13)\|(~v12_altcat_1(X13)\|~l2_altcat_1(X13))))))&((r2_altcat_2(k2_zfmisc_1(u1_struct_0(X14),u1_struct_0(X14)),k2_zfmisc_1(u1_struct_0(X13),u1_struct_0(X13)),u1_altcat_1(X14),u1_altcat_1(X13))\|X14!=k1_altcat_4(X13)\|(v2_struct_0(X14)\|(~v2_altcat_1(X14)\|(~v6_altcat_1(X14)\|~m1_altcat_2(X14,X13))))\|(v2_struct_0(X13)\|(~v2_altcat_1(X13)\|(~v11_altcat_1(X13)\|(~v12_altcat_1(X13)\|~l2_altcat_1(X13))))))&(((k1_altcat_1(X13,X15,X16)!=k1_xboole_0\|~r2_hidden(X17,k1_binop_1(u1_altcat_1(X14),X15,X16))\|~m1_subset_1(X17,k1_altcat_1(X13,X15,X16))\|~m1_subset_1(X16,u1_struct_0(X13))\|~m1_subset_1(X15,u1_struct_0(X13))\|X14!=k1_altcat_4(X13)\|(v2_struct_0(X14)\|(~v2_altcat_1(X14)\|(~v6_altcat_1(X14)\|~m1_altcat_2(X14,X13))))\|(v2_struct_0(X13)\|(~v2_altcat_1(X13)\|(~v11_altcat_1(X13)\|(~v12_altcat_1(X13)\|~l2_altcat_1(X13))))))&(v4_altcat_3(X17,X13,X15,X16)\|~r2_hidden(X17,k1_binop_1(u1_altcat_1(X14),X15,X16))\|~m1_subset_1(X17,k1_altcat_1(X13,X15,X16))\|~m1_subset_1(X16,u1_struct_0(X13))\|~m1_subset_1(X15,u1_struct_0(X13))\|X14!=k1_altcat_4(X13)\|(v2_struct_0(X14)\|(~v2_altcat_1(X14)\|(~v6_altcat_1(X14)\|~m1_altcat_2(X14,X13))))\|(v2_struct_0(X13)\|(~v2_altcat_1(X13)\|(~v11_altcat_1(X13)\|(~v12_altcat_1(X13)\|~l2_altcat_1(X13)))))))&(k1_altcat_1(X13,X15,X16)=k1_xboole_0\|~v4_altcat_3(X17,X13,X15,X16)\|r2_hidden(X17,k1_binop_1(u1_altcat_1(X14),X15,X16))\|~m1_subset_1(X17,k1_altcat_1(X13,X15,X16))\|~m1_subset_1(X16,u1_struct_0(X13))\|~m1_subset_1(X15,u1_struct_0(X13))\|X14!=k1_altcat_4(X13)\|(v2_struct_0(X14)\|(~v2_altcat_1(X14)\|(~v6_altcat_1(X14)\|~m1_altcat_2(X14,X13))))\|(v2_struct_0(X13)\|(~v2_altcat_1(X13)\|(~v11_altcat_1(X13)\|(~v12_altcat_1(X13)\|~l2_altcat_1(X13)))))))))&((m1_subset_1(esk5_2(X13,X14),u1_struct_0(X13))\|~r2_altcat_2(k2_zfmisc_1(u1_struct_0(X14),u1_struct_0(X14)),k2_zfmisc_1(u1_struct_0(X13),u1_struct_0(X13)),u1_altcat_1(X14),u1_altcat_1(X13))\|u1_struct_0(X14)!=u1_struct_0(X13)\|X14=k1_altcat_4(X13)\|(v2_struct_0(X14)\|(~v2_altcat_1(X14)\|(~v6_altcat_1(X14)\|~m1_altcat_2(X14,X13))))\|(v2_struct_0(X13)\|(~v2_altcat_1(X13)\|(~v11_altcat_1(X13)\|(~v12_altcat_1(X13)\|~l2_altcat_1(X13))))))&((m1_subset_1(esk6_2(X13,X14),u1_struct_0(X13))\|~r2_altcat_2(k2_zfmisc_1(u1_struct_0(X14),u1_struct_0(X14)),k2_zfmisc_1(u1_struct_0(X13),u1_struct_0(X13)),u1_altcat_1(X14),u1_altcat_1(X13))\|u1_struct_0(X14)!=u1_struct_0(X13)\|X14=k1_altcat_4(X13)\|(v2_struct_0(X14)\|(~v2_altcat_1(X14)\|(~v6_altcat_1(X14)\|~m1_altcat_2(X14,X13))))\|(v2_struct_0(X13)\|(~v2_altcat_1(X13)\|(~v11_altcat_1(X13)\|(~v12_altcat_1(X13)\|~l2_altcat_1(X13))))))&((m1_subset_1(esk7_2(X13,X14),k1_altcat_1(X13,esk5_2(X13,X14),esk6_2(X13,X14)))\|~r2_altcat_2(k2_zfmisc_1(u1_struct_0(X14),u1_struct_0(X14)),k2_zfmisc_1(u1_struct_0(X13),u1_struct_0(X13)),u1_altcat_1(X14),u1_altcat_1(X13))\|u1_struct_0(X14)!=u1_struct_0(X13)\|X14=k1_altcat_4(X13)\|(v2_struct_0(X14)\|(~v2_altcat_1(X14)\|(~v6_altcat_1(X14)\|~m1_altcat_2(X14,X13))))\|(v2_struct_0(X13)\|(~v2_altcat_1(X13)\|(~v11_altcat_1(X13)\|(~v12_altcat_1(X13)\|~l2_altcat_1(X13))))))&((~r2_hidden(esk7_2(X13,X14),k1_binop_1(u1_altcat_1(X14),esk5_2(X13,X14),esk6_2(X13,X14)))\|(k1_altcat_1(X13,esk5_2(X13,X14),esk6_2(X13,X14))=k1_xboole_0\|~v4_altcat_3(esk7_2(X13,X14),X13,esk5_2(X13,X14),esk6_2(X13,X14)))\|~r2_altcat_2(k2_zfmisc_1(u1_struct_0(X14),u1_struct_0(X14)),k2_zfmisc_1(u1_struct_0(X13),u1_struct_0(X13)),u1_altcat_1(X14),u1_altcat_1(X13))\|u1_struct_0(X14)!=u1_struct_0(X13)\|X14=k1_altcat_4(X13)\|(v2_struct_0(X14)\|(~v2_altcat_1(X14)\|(~v6_altcat_1(X14)\|~m1_altcat_2(X14,X13))))\|(v2_struct_0(X13)\|(~v2_altcat_1(X13)\|(~v11_altcat_1(X13)\|(~v12_altcat_1(X13)\|~l2_altcat_1(X13))))))&((k1_altcat_1(X13,esk5_2(X13,X14),esk6_2(X13,X14))!=k1_xboole_0\|r2_hidden(esk7_2(X13,X14),k1_binop_1(u1_altcat_1(X14),esk5_2(X13,X14),esk6_2(X13,X14)))\|~r2_altcat_2(k2_zfmisc_1(u1_struct_0(X14),u1_struct_0(X14)),k2_zfmisc_1(u1_struct_0(X13),u1_struct_0(X13)),u1_altcat_1(X14),u1_altcat_1(X13))\|u1_struct_0(X14)!=u1_struct_0(X13)\|X14=k1_altcat_4(X13)\|(v2_struct_0(X14)\|(~v2_altcat_1(X14)\|(~v6_altcat_1(X14)\|~m1_altcat_2(X14,X13))))\|(v2_struct_0(X13)\|(~v2_altcat_1(X13)\|(~v11_altcat_1(X13)\|(~v12_altcat_1(X13)\|~l2_altcat_1(X13))))))&(v4_altcat_3(esk7_2(X13,X14),X13,esk5_2(X13,X14),esk6_2(X13,X14))\|r2_hidden(esk7_2(X13,X14),k1_binop_1(u1_altcat_1(X14),esk5_2(X13,X14),esk6_2(X13,X14)))\|~r2_altcat_2(k2_zfmisc_1(u1_struct_0(X14),u1_struct_0(X14)),k2_zfmisc_1(u1_struct_0(X13),u1_struct_0(X13)),u1_altcat_1(X14),u1_altcat_1(X13))\|u1_struct_0(X14)!=u1_struct_0(X13)\|X14=k1_altcat_4(X13)\|(v2_struct_0(X14)\|(~v2_altcat_1(X14)\|(~v6_altcat_1(X14)\|~m1_altcat_2(X14,X13))))\|(v2_struct_0(X13)\|(~v2_altcat_1(X13)\|(~v11_altcat_1(X13)\|(~v12_altcat_1(X13)\|~l2_altcat_1(X13)))))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[d1_altcat_4])])])])])])). fof(c_0_14, plain, ![X22, X23, X24]:(~l1_altcat_1(X22)\|(~m1_subset_1(X23,u1_struct_0(X22))\|(~m1_subset_1(X24,u1_struct_0(X22))\|k1_altcat_1(X22,X23,X24)=k1_binop_1(u1_altcat_1(X22),X23,X24)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_altcat_1])])])). fof(c_0_15, plain, ![X45]:(~v1_xboole_0(X45)\|X45=k1_xboole_0), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])])). cnf(c_0_16, plain, (v1_xboole_0(X2)\|r2_hidden(X1,X2)\|~m1_subset_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_17, negated_conjecture, (m1_subset_1(esk4_0,k1_altcat_1(k1_altcat_4(esk1_0),esk2_0,esk3_0))), inference(split_conjunct,[status(thm)],[c_0_12])). fof(c_0_18, plain, ![X27, X28, X29, X30, X31, X32, X33]:(v2_struct_0(X27)\|~l2_altcat_1(X27)\|(v2_struct_0(X28)\|~m1_altcat_2(X28,X27)\|(~m1_subset_1(X29,u1_struct_0(X27))\|(~m1_subset_1(X30,u1_struct_0(X27))\|(~m1_subset_1(X31,u1_struct_0(X28))\|(~m1_subset_1(X32,u1_struct_0(X28))\|(X29!=X31\|X30!=X32\|(k1_altcat_1(X28,X31,X32)=k1_xboole_0\|(~m1_subset_1(X33,k1_altcat_1(X28,X31,X32))\|m1_subset_1(X33,k1_altcat_1(X27,X29,X30))))))))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t33_altcat_2])])])])). cnf(c_0_19, plain, (v4_altcat_3(X1,X2,X3,X4)\|v2_struct_0(X5)\|v2_struct_0(X2)\|~r2_hidden(X1,k1_binop_1(u1_altcat_1(X5),X3,X4))\|~m1_subset_1(X1,k1_altcat_1(X2,X3,X4))\|~m1_subset_1(X4,u1_struct_0(X2))\|~m1_subset_1(X3,u1_struct_0(X2))\|X5!=k1_altcat_4(X2)\|~v2_altcat_1(X5)\|~v6_altcat_1(X5)\|~m1_altcat_2(X5,X2)\|~v2_altcat_1(X2)\|~v11_altcat_1(X2)\|~v12_altcat_1(X2)\|~l2_altcat_1(X2)), inference(split_conjunct,[status(thm)],[c_0_13])). cnf(c_0_20, plain, (k1_altcat_1(X1,X2,X3)=k1_binop_1(u1_altcat_1(X1),X2,X3)\|~l1_altcat_1(X1)\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))), inference(split_conjunct,[status(thm)],[c_0_14])). cnf(c_0_21, plain, (X1=k1_xboole_0\|~v1_xboole_0(X1)), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_22, plain, (v1_xboole_0(X2)\|r2_hidden(X1,X2)\|~m1_subset_1(X1,X2)), inference(evalgc,[status(thm)],[c_0_16])). cnf(c_0_23, negated_conjecture, (m1_subset_1(esk4_0,k1_altcat_1(k1_altcat_4(esk1_0),esk2_0,esk3_0))), inference(evalgc,[status(thm)],[c_0_17])). cnf(c_0_24, negated_conjecture, (k1_altcat_1(k1_altcat_4(esk1_0),esk2_0,esk3_0)!=k1_xboole_0), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_25, plain, (v2_struct_0(X1)\|v2_struct_0(X2)\|k1_altcat_1(X2,X5,X6)=k1_xboole_0\|m1_subset_1(X7,k1_altcat_1(X1,X3,X4))\|~l2_altcat_1(X1)\|~m1_altcat_2(X2,X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X4,u1_struct_0(X1))\|~m1_subset_1(X5,u1_struct_0(X2))\|~m1_subset_1(X6,u1_struct_0(X2))\|X3!=X5\|X4!=X6\|~m1_subset_1(X7,k1_altcat_1(X2,X5,X6))), inference(split_conjunct,[status(thm)],[c_0_18])). cnf(c_0_26, plain, (v2_struct_0(X5)\|v2_struct_0(X2)\|v4_altcat_3(X1,X2,X3,X4)\|X5!=k1_altcat_4(X2)\|~v2_altcat_1(X5)\|~v2_altcat_1(X2)\|~v11_altcat_1(X2)\|~v12_altcat_1(X2)\|~l2_altcat_1(X2)\|~v6_altcat_1(X5)\|~m1_altcat_2(X5,X2)\|~m1_subset_1(X4,u1_struct_0(X2))\|~m1_subset_1(X3,u1_struct_0(X2))\|~m1_subset_1(X1,k1_altcat_1(X2,X3,X4))\|~r2_hidden(X1,k1_binop_1(u1_altcat_1(X5),X3,X4))), inference(evalgc,[status(thm)],[c_0_19])). cnf(c_0_27, plain, (k1_binop_1(u1_altcat_1(X1),X2,X3)=k1_altcat_1(X1,X2,X3)\|~l1_altcat_1(X1)\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))), inference(evalgc,[status(thm)],[c_0_20])). cnf(c_0_28, plain, (X1=k1_xboole_0\|~v1_xboole_0(X1)), inference(evalgc,[status(thm)],[c_0_21])). cnf(c_0_29, negated_conjecture, (v1_xboole_0(k1_altcat_1(k1_altcat_4(esk1_0),esk2_0,esk3_0))\|r2_hidden(esk4_0,k1_altcat_1(k1_altcat_4(esk1_0),esk2_0,esk3_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_22, c_0_23])])). cnf(c_0_30, negated_conjecture, (k1_altcat_1(k1_altcat_4(esk1_0),esk2_0,esk3_0)!=k1_xboole_0), inference(evalgc,[status(thm)],[c_0_24])). cnf(c_0_31, negated_conjecture, (m1_subset_1(esk3_0,u1_struct_0(k1_altcat_4(esk1_0)))), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_32, negated_conjecture, (m1_subset_1(esk2_0,u1_struct_0(k1_altcat_4(esk1_0)))), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_33, plain, (k1_altcat_1(X2,X5,X6)=k1_xboole_0\|v2_struct_0(X2)\|v2_struct_0(X1)\|m1_subset_1(X7,k1_altcat_1(X1,X3,X4))\|X4!=X6\|X3!=X5\|~l2_altcat_1(X1)\|~m1_altcat_2(X2,X1)\|~m1_subset_1(X6,u1_struct_0(X2))\|~m1_subset_1(X5,u1_struct_0(X2))\|~m1_subset_1(X4,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X7,k1_altcat_1(X2,X5,X6))), inference(evalgc,[status(thm)],[c_0_25])). cnf(c_0_34, plain, (v4_altcat_3(X1,X2,X3,X4)\|v2_struct_0(X2)\|v2_struct_0(X5)\|X5!=k1_altcat_4(X2)\|~r2_hidden(X1,k1_altcat_1(X5,X3,X4))\|~m1_altcat_2(X5,X2)\|~v6_altcat_1(X5)\|~m1_subset_1(X1,k1_altcat_1(X2,X3,X4))\|~m1_subset_1(X4,u1_struct_0(X2))\|~m1_subset_1(X3,u1_struct_0(X2))\|~l2_altcat_1(X2)\|~v12_altcat_1(X2)\|~v11_altcat_1(X2)\|~v2_altcat_1(X5)\|~v2_altcat_1(X2)\|~l1_altcat_1(X5)\|~m1_subset_1(X4,u1_struct_0(X5))\|~m1_subset_1(X3,u1_struct_0(X5))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_26, c_0_27])])). cnf(c_0_35, negated_conjecture, (r2_hidden(esk4_0,k1_altcat_1(k1_altcat_4(esk1_0),esk2_0,esk3_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28, c_0_29]), c_0_30])])). cnf(c_0_36, negated_conjecture, (m1_subset_1(esk3_0,u1_struct_0(k1_altcat_4(esk1_0)))), inference(evalgc,[status(thm)],[c_0_31])). cnf(c_0_37, negated_conjecture, (m1_subset_1(esk2_0,u1_struct_0(k1_altcat_4(esk1_0)))), inference(evalgc,[status(thm)],[c_0_32])). cnf(c_0_38, plain, (k1_altcat_1(X1,X2,X3)=k1_xboole_0\|m1_subset_1(X4,k1_altcat_1(X5,X2,X3))\|v2_struct_0(X5)\|v2_struct_0(X1)\|~m1_altcat_2(X1,X5)\|~m1_subset_1(X4,k1_altcat_1(X1,X2,X3))\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X5))\|~m1_subset_1(X2,u1_struct_0(X5))\|~l2_altcat_1(X5)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_33])])])). fof(c_0_39, plain, ![X34]:(~l2_altcat_1(X34)\|l1_altcat_1(X34)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l2_altcat_1])])). cnf(c_0_40, negated_conjecture, (v4_altcat_3(esk4_0,X1,esk2_0,esk3_0)\|v2_struct_0(k1_altcat_4(esk1_0))\|v2_struct_0(X1)\|k1_altcat_4(esk1_0)!=k1_altcat_4(X1)\|~l1_altcat_1(k1_altcat_4(esk1_0))\|~m1_altcat_2(k1_altcat_4(esk1_0),X1)\|~v6_altcat_1(k1_altcat_4(esk1_0))\|~m1_subset_1(esk4_0,k1_altcat_1(X1,esk2_0,esk3_0))\|~m1_subset_1(esk3_0,u1_struct_0(X1))\|~m1_subset_1(esk2_0,u1_struct_0(X1))\|~l2_altcat_1(X1)\|~v12_altcat_1(X1)\|~v11_altcat_1(X1)\|~v2_altcat_1(k1_altcat_4(esk1_0))\|~v2_altcat_1(X1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34, c_0_35]), c_0_36]), c_0_37])])])). cnf(c_0_41, negated_conjecture, (m1_subset_1(esk4_0,k1_altcat_1(X1,esk2_0,esk3_0))\|v2_struct_0(k1_altcat_4(esk1_0))\|v2_struct_0(X1)\|~m1_altcat_2(k1_altcat_4(esk1_0),X1)\|~m1_subset_1(esk3_0,u1_struct_0(X1))\|~m1_subset_1(esk2_0,u1_struct_0(X1))\|~l2_altcat_1(X1)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38, c_0_23]), c_0_36]), c_0_37])]), c_0_30])])). cnf(c_0_42, plain, (l1_altcat_1(X1)\|~l2_altcat_1(X1)), inference(split_conjunct,[status(thm)],[c_0_39])). fof(c_0_43, plain, ![X35, X36]:(~l2_altcat_1(X35)\|(~m1_altcat_2(X36,X35)\|l2_altcat_1(X36))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m1_altcat_2])])])). fof(c_0_44, plain, ![X21]:((~v2_struct_0(k1_altcat_4(X21))\|(v2_struct_0(X21)\|(~v2_altcat_1(X21)\|(~v11_altcat_1(X21)\|(~v12_altcat_1(X21)\|~l2_altcat_1(X21))))))&((v2_altcat_1(k1_altcat_4(X21))\|(v2_struct_0(X21)\|(~v2_altcat_1(X21)\|(~v11_altcat_1(X21)\|(~v12_altcat_1(X21)\|~l2_altcat_1(X21))))))&((v6_altcat_1(k1_altcat_4(X21))\|(v2_struct_0(X21)\|(~v2_altcat_1(X21)\|(~v11_altcat_1(X21)\|(~v12_altcat_1(X21)\|~l2_altcat_1(X21))))))&(m1_altcat_2(k1_altcat_4(X21),X21)\|(v2_struct_0(X21)\|(~v2_altcat_1(X21)\|(~v11_altcat_1(X21)\|(~v12_altcat_1(X21)\|~l2_altcat_1(X21))))))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k1_altcat_4])])])])). fof(c_0_45, plain, ![X37, X38, X39, X40, X41, X42, X43, X44]:((~v4_altcat_3(X43,X37,X39,X40)\|v4_altcat_3(X44,X38,X41,X42)\|k1_altcat_1(X38,X41,X42)=k1_xboole_0\|(X41!=X39\|(X42!=X40\|X43!=X44))\|~m1_subset_1(X44,k1_altcat_1(X38,X41,X42))\|~m1_subset_1(X43,k1_altcat_1(X37,X39,X40))\|~m1_subset_1(X42,u1_struct_0(X38))\|~m1_subset_1(X41,u1_struct_0(X38))\|~m1_subset_1(X40,u1_struct_0(X37))\|~m1_subset_1(X39,u1_struct_0(X37))\|(v2_struct_0(X38)\|(~v2_altcat_1(X38)\|~m1_altcat_2(X38,X37)))\|(v2_struct_0(X37)\|(~v2_altcat_1(X37)\|~l2_altcat_1(X37))))&(~v5_altcat_3(X43,X37,X39,X40)\|v5_altcat_3(X44,X38,X41,X42)\|k1_altcat_1(X38,X41,X42)=k1_xboole_0\|(X41!=X39\|(X42!=X40\|X43!=X44))\|~m1_subset_1(X44,k1_altcat_1(X38,X41,X42))\|~m1_subset_1(X43,k1_altcat_1(X37,X39,X40))\|~m1_subset_1(X42,u1_struct_0(X38))\|~m1_subset_1(X41,u1_struct_0(X38))\|~m1_subset_1(X40,u1_struct_0(X37))\|~m1_subset_1(X39,u1_struct_0(X37))\|(v2_struct_0(X38)\|(~v2_altcat_1(X38)\|~m1_altcat_2(X38,X37)))\|(v2_struct_0(X37)\|(~v2_altcat_1(X37)\|~l2_altcat_1(X37))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t37_altcat_4])])])])])). cnf(c_0_46, negated_conjecture, (v4_altcat_3(esk4_0,X1,esk2_0,esk3_0)\|v2_struct_0(k1_altcat_4(esk1_0))\|v2_struct_0(X1)\|k1_altcat_4(esk1_0)!=k1_altcat_4(X1)\|~l1_altcat_1(k1_altcat_4(esk1_0))\|~m1_altcat_2(k1_altcat_4(esk1_0),X1)\|~v6_altcat_1(k1_altcat_4(esk1_0))\|~m1_subset_1(esk3_0,u1_struct_0(X1))\|~m1_subset_1(esk2_0,u1_struct_0(X1))\|~l2_altcat_1(X1)\|~v12_altcat_1(X1)\|~v11_altcat_1(X1)\|~v2_altcat_1(k1_altcat_4(esk1_0))\|~v2_altcat_1(X1)), inference(csr,[status(thm)],[c_0_40, c_0_41])). cnf(c_0_47, plain, (l1_altcat_1(X1)\|~l2_altcat_1(X1)), inference(evalgc,[status(thm)],[c_0_42])). cnf(c_0_48, plain, (l2_altcat_1(X2)\|~l2_altcat_1(X1)\|~m1_altcat_2(X2,X1)), inference(split_conjunct,[status(thm)],[c_0_43])). cnf(c_0_49, plain, (u1_struct_0(X1)=u1_struct_0(X2)\|v2_struct_0(X1)\|v2_struct_0(X2)\|X1!=k1_altcat_4(X2)\|~v2_altcat_1(X1)\|~v6_altcat_1(X1)\|~m1_altcat_2(X1,X2)\|~v2_altcat_1(X2)\|~v11_altcat_1(X2)\|~v12_altcat_1(X2)\|~l2_altcat_1(X2)), inference(split_conjunct,[status(thm)],[c_0_13])). cnf(c_0_50, plain, (m1_altcat_2(k1_altcat_4(X1),X1)\|v2_struct_0(X1)\|~v2_altcat_1(X1)\|~v11_altcat_1(X1)\|~v12_altcat_1(X1)\|~l2_altcat_1(X1)), inference(split_conjunct,[status(thm)],[c_0_44])). cnf(c_0_51, plain, (v4_altcat_3(X5,X6,X7,X8)\|k1_altcat_1(X6,X7,X8)=k1_xboole_0\|v2_struct_0(X6)\|v2_struct_0(X2)\|~v4_altcat_3(X1,X2,X3,X4)\|X7!=X3\|X8!=X4\|X1!=X5\|~m1_subset_1(X5,k1_altcat_1(X6,X7,X8))\|~m1_subset_1(X1,k1_altcat_1(X2,X3,X4))\|~m1_subset_1(X8,u1_struct_0(X6))\|~m1_subset_1(X7,u1_struct_0(X6))\|~m1_subset_1(X4,u1_struct_0(X2))\|~m1_subset_1(X3,u1_struct_0(X2))\|~v2_altcat_1(X6)\|~m1_altcat_2(X6,X2)\|~v2_altcat_1(X2)\|~l2_altcat_1(X2)), inference(split_conjunct,[status(thm)],[c_0_45])). cnf(c_0_52, negated_conjecture, (v4_altcat_3(esk4_0,X1,esk2_0,esk3_0)\|v2_struct_0(k1_altcat_4(esk1_0))\|v2_struct_0(X1)\|k1_altcat_4(esk1_0)!=k1_altcat_4(X1)\|~m1_altcat_2(k1_altcat_4(esk1_0),X1)\|~v6_altcat_1(k1_altcat_4(esk1_0))\|~m1_subset_1(esk3_0,u1_struct_0(X1))\|~m1_subset_1(esk2_0,u1_struct_0(X1))\|~l2_altcat_1(X1)\|~v12_altcat_1(X1)\|~v11_altcat_1(X1)\|~v2_altcat_1(k1_altcat_4(esk1_0))\|~v2_altcat_1(X1)\|~l2_altcat_1(k1_altcat_4(esk1_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_46, c_0_47])])). cnf(c_0_53, plain, (l2_altcat_1(X2)\|~l2_altcat_1(X1)\|~m1_altcat_2(X2,X1)), inference(evalgc,[status(thm)],[c_0_48])). cnf(c_0_54, plain, (v6_altcat_1(k1_altcat_4(X1))\|v2_struct_0(X1)\|~v2_altcat_1(X1)\|~v11_altcat_1(X1)\|~v12_altcat_1(X1)\|~l2_altcat_1(X1)), inference(split_conjunct,[status(thm)],[c_0_44])). cnf(c_0_55, negated_conjecture, (l2_altcat_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_56, negated_conjecture, (v12_altcat_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_57, negated_conjecture, (v11_altcat_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_58, negated_conjecture, (v2_altcat_1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_59, negated_conjecture, (~v2_struct_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_60, plain, (u1_struct_0(X1)=u1_struct_0(X2)\|v2_struct_0(X2)\|v2_struct_0(X1)\|X1!=k1_altcat_4(X2)\|~v2_altcat_1(X2)\|~v2_altcat_1(X1)\|~v11_altcat_1(X2)\|~v12_altcat_1(X2)\|~l2_altcat_1(X2)\|~v6_altcat_1(X1)\|~m1_altcat_2(X1,X2)), inference(evalgc,[status(thm)],[c_0_49])). cnf(c_0_61, plain, (v2_struct_0(X1)\|m1_altcat_2(k1_altcat_4(X1),X1)\|~v2_altcat_1(X1)\|~v11_altcat_1(X1)\|~v12_altcat_1(X1)\|~l2_altcat_1(X1)), inference(evalgc,[status(thm)],[c_0_50])). cnf(c_0_62, plain, (v2_altcat_1(k1_altcat_4(X1))\|v2_struct_0(X1)\|~v2_altcat_1(X1)\|~v11_altcat_1(X1)\|~v12_altcat_1(X1)\|~l2_altcat_1(X1)), inference(split_conjunct,[status(thm)],[c_0_44])). cnf(c_0_63, plain, (v2_struct_0(X1)\|~v2_struct_0(k1_altcat_4(X1))\|~v2_altcat_1(X1)\|~v11_altcat_1(X1)\|~v12_altcat_1(X1)\|~l2_altcat_1(X1)), inference(split_conjunct,[status(thm)],[c_0_44])). cnf(c_0_64, plain, (k1_altcat_1(X6,X7,X8)=k1_xboole_0\|v2_struct_0(X6)\|v2_struct_0(X2)\|v4_altcat_3(X5,X6,X7,X8)\|X4!=X8\|X3!=X7\|X1!=X5\|~v2_altcat_1(X6)\|~v2_altcat_1(X2)\|~l2_altcat_1(X2)\|~m1_altcat_2(X6,X2)\|~m1_subset_1(X8,u1_struct_0(X6))\|~m1_subset_1(X7,u1_struct_0(X6))\|~m1_subset_1(X4,u1_struct_0(X2))\|~m1_subset_1(X3,u1_struct_0(X2))\|~v4_altcat_3(X1,X2,X3,X4)\|~m1_subset_1(X5,k1_altcat_1(X6,X7,X8))\|~m1_subset_1(X1,k1_altcat_1(X2,X3,X4))), inference(evalgc,[status(thm)],[c_0_51])). cnf(c_0_65, negated_conjecture, (v4_altcat_3(esk4_0,X1,esk2_0,esk3_0)\|v2_struct_0(k1_altcat_4(esk1_0))\|v2_struct_0(X1)\|k1_altcat_4(esk1_0)!=k1_altcat_4(X1)\|~m1_altcat_2(k1_altcat_4(esk1_0),X1)\|~v6_altcat_1(k1_altcat_4(esk1_0))\|~m1_subset_1(esk3_0,u1_struct_0(X1))\|~m1_subset_1(esk2_0,u1_struct_0(X1))\|~l2_altcat_1(X1)\|~v12_altcat_1(X1)\|~v11_altcat_1(X1)\|~v2_altcat_1(k1_altcat_4(esk1_0))\|~v2_altcat_1(X1)), inference(csr,[status(thm)],[c_0_52, c_0_53])). cnf(c_0_66, plain, (v2_struct_0(X1)\|v6_altcat_1(k1_altcat_4(X1))\|~v2_altcat_1(X1)\|~v11_altcat_1(X1)\|~v12_altcat_1(X1)\|~l2_altcat_1(X1)), inference(evalgc,[status(thm)],[c_0_54])). cnf(c_0_67, negated_conjecture, (l2_altcat_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_55])). cnf(c_0_68, negated_conjecture, (v12_altcat_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_56])). cnf(c_0_69, negated_conjecture, (v11_altcat_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_57])). cnf(c_0_70, negated_conjecture, (v2_altcat_1(esk1_0)), inference(evalgc,[status(thm)],[c_0_58])). cnf(c_0_71, negated_conjecture, (~v2_struct_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_59])). cnf(c_0_72, plain, (u1_struct_0(k1_altcat_4(X1))=u1_struct_0(X1)\|v2_struct_0(k1_altcat_4(X1))\|v2_struct_0(X1)\|~v6_altcat_1(k1_altcat_4(X1))\|~l2_altcat_1(X1)\|~v12_altcat_1(X1)\|~v11_altcat_1(X1)\|~v2_altcat_1(X1)\|~v2_altcat_1(k1_altcat_4(X1))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_60, c_0_61])])). cnf(c_0_73, plain, (v2_struct_0(X1)\|v2_altcat_1(k1_altcat_4(X1))\|~v2_altcat_1(X1)\|~v11_altcat_1(X1)\|~v12_altcat_1(X1)\|~l2_altcat_1(X1)), inference(evalgc,[status(thm)],[c_0_62])). cnf(c_0_74, plain, (v2_struct_0(X1)\|~v2_altcat_1(X1)\|~v11_altcat_1(X1)\|~v12_altcat_1(X1)\|~l2_altcat_1(X1)\|~v2_struct_0(k1_altcat_4(X1))), inference(evalgc,[status(thm)],[c_0_63])). cnf(c_0_75, plain, (k1_altcat_1(X1,X2,X3)=k1_xboole_0\|v4_altcat_3(X4,X1,X2,X3)\|v2_struct_0(X5)\|v2_struct_0(X1)\|~m1_altcat_2(X1,X5)\|~v4_altcat_3(X4,X5,X2,X3)\|~m1_subset_1(X4,k1_altcat_1(X1,X2,X3))\|~m1_subset_1(X4,k1_altcat_1(X5,X2,X3))\|~m1_subset_1(X3,u1_struct_0(X1))\|~m1_subset_1(X2,u1_struct_0(X1))\|~m1_subset_1(X3,u1_struct_0(X5))\|~m1_subset_1(X2,u1_struct_0(X5))\|~l2_altcat_1(X5)\|~v2_altcat_1(X1)\|~v2_altcat_1(X5)), inference(evalgc,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_64])])])])). cnf(c_0_76, negated_conjecture, (v4_altcat_3(esk4_0,X1,esk2_0,esk3_0)\|v2_struct_0(k1_altcat_4(esk1_0))\|v2_struct_0(X1)\|k1_altcat_4(esk1_0)!=k1_altcat_4(X1)\|~m1_altcat_2(k1_altcat_4(esk1_0),X1)\|~m1_subset_1(esk3_0,u1_struct_0(X1))\|~m1_subset_1(esk2_0,u1_struct_0(X1))\|~l2_altcat_1(X1)\|~v12_altcat_1(X1)\|~v11_altcat_1(X1)\|~v2_altcat_1(k1_altcat_4(esk1_0))\|~v2_altcat_1(X1)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65, c_0_66]), c_0_67]), c_0_68]), c_0_69]), c_0_70])]), c_0_71])])). cnf(c_0_77, plain, (u1_struct_0(k1_altcat_4(X1))=u1_struct_0(X1)\|v2_struct_0(X1)\|~l2_altcat_1(X1)\|~v12_altcat_1(X1)\|~v11_altcat_1(X1)\|~v2_altcat_1(X1)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_72, c_0_73]), c_0_66]), c_0_74])). cnf(c_0_78, negated_conjecture, (k1_altcat_1(X1,esk2_0,esk3_0)=k1_xboole_0\|v4_altcat_3(esk4_0,X1,esk2_0,esk3_0)\|v2_struct_0(X1)\|v2_struct_0(X2)\|v2_struct_0(k1_altcat_4(esk1_0))\|~m1_altcat_2(X1,X2)\|~m1_subset_1(esk4_0,k1_altcat_1(X1,esk2_0,esk3_0))\|~m1_subset_1(esk4_0,k1_altcat_1(X2,esk2_0,esk3_0))\|~m1_subset_1(esk3_0,u1_struct_0(X1))\|~m1_subset_1(esk2_0,u1_struct_0(X1))\|~m1_subset_1(esk3_0,u1_struct_0(X2))\|~m1_subset_1(esk2_0,u1_struct_0(X2))\|~l2_altcat_1(X2)\|~v2_altcat_1(X1)\|~v2_altcat_1(X2)\|k1_altcat_4(esk1_0)!=k1_altcat_4(X2)\|~m1_altcat_2(k1_altcat_4(esk1_0),X2)\|~v12_altcat_1(X2)\|~v11_altcat_1(X2)\|~v2_altcat_1(k1_altcat_4(esk1_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_75, c_0_76])])). cnf(c_0_79, negated_conjecture, (u1_struct_0(k1_altcat_4(esk1_0))=u1_struct_0(esk1_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77, c_0_68]), c_0_67]), c_0_69]), c_0_70])]), c_0_71])])). cnf(c_0_80, negated_conjecture, (~v4_altcat_3(esk4_0,k1_altcat_4(esk1_0),esk2_0,esk3_0)), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_81, negated_conjecture, (k1_altcat_1(X1,esk2_0,esk3_0)=k1_xboole_0\|v4_altcat_3(esk4_0,X1,esk2_0,esk3_0)\|v2_struct_0(k1_altcat_4(esk1_0))\|v2_struct_0(X2)\|v2_struct_0(X1)\|k1_altcat_4(esk1_0)!=k1_altcat_4(X2)\|~m1_altcat_2(k1_altcat_4(esk1_0),X2)\|~m1_altcat_2(X1,X2)\|~m1_subset_1(esk4_0,k1_altcat_1(X1,esk2_0,esk3_0))\|~m1_subset_1(esk3_0,u1_struct_0(X1))\|~m1_subset_1(esk2_0,u1_struct_0(X1))\|~m1_subset_1(esk3_0,u1_struct_0(X2))\|~m1_subset_1(esk2_0,u1_struct_0(X2))\|~l2_altcat_1(X2)\|~v12_altcat_1(X2)\|~v11_altcat_1(X2)\|~v2_altcat_1(k1_altcat_4(esk1_0))\|~v2_altcat_1(X1)\|~v2_altcat_1(X2)), inference(csr,[status(thm)],[c_0_78, c_0_38])). cnf(c_0_82, negated_conjecture, (m1_subset_1(esk3_0,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[c_0_36, c_0_79])])). cnf(c_0_83, negated_conjecture, (m1_subset_1(esk2_0,u1_struct_0(esk1_0))), inference(evalgc,[status(thm)],[inference(rw,[status(thm)],[c_0_37, c_0_79])])). cnf(c_0_84, negated_conjecture, (~v4_altcat_3(esk4_0,k1_altcat_4(esk1_0),esk2_0,esk3_0)), inference(evalgc,[status(thm)],[c_0_80])). cnf(c_0_85, negated_conjecture, (k1_altcat_1(X1,esk2_0,esk3_0)=k1_xboole_0\|v4_altcat_3(esk4_0,X1,esk2_0,esk3_0)\|v2_struct_0(k1_altcat_4(esk1_0))\|v2_struct_0(X1)\|~m1_altcat_2(X1,esk1_0)\|~m1_subset_1(esk4_0,k1_altcat_1(X1,esk2_0,esk3_0))\|~m1_subset_1(esk3_0,u1_struct_0(X1))\|~m1_subset_1(esk2_0,u1_struct_0(X1))\|~v2_altcat_1(k1_altcat_4(esk1_0))\|~v2_altcat_1(X1)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81, c_0_61]), c_0_82]), c_0_83]), c_0_67]), c_0_68]), c_0_69]), c_0_70])]), c_0_71])])). cnf(c_0_86, negated_conjecture, (v2_struct_0(k1_altcat_4(esk1_0))\|~m1_altcat_2(k1_altcat_4(esk1_0),esk1_0)\|~v2_altcat_1(k1_altcat_4(esk1_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84, c_0_85]), c_0_23]), c_0_79]), c_0_82]), c_0_79]), c_0_83])]), c_0_30])])). cnf(c_0_87, negated_conjecture, (v2_struct_0(k1_altcat_4(esk1_0))\|~v2_altcat_1(k1_altcat_4(esk1_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86, c_0_61]), c_0_67]), c_0_68]), c_0_69]), c_0_70])]), c_0_71])])). cnf(c_0_88, negated_conjecture, (v2_struct_0(k1_altcat_4(esk1_0))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87, c_0_73]), c_0_67]), c_0_68]), c_0_69]), c_0_70])]), c_0_71])])). cnf(c_0_89, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74, c_0_88]), c_0_67]), c_0_68]), c_0_69]), c_0_70])]), c_0_71]), ['proof']). # SZS output end CNFRefutation	reserve C for category, o1, o2, o3 for object of C; theorem Th50: for o1, o2 being object of AllMono C for m being Morphism of o1, o2 st <^o1,o2^> <> {} holds m is mono proof let o1, o2 be object of AllMono C, m be Morphism of o1, o2 such that A1: <^o1,o2^> <> {}; reconsider p1 = o1, p2 = o2 as object of C by Def1; reconsider p = m as Morphism of p1, p2 by A1,ALTCAT_2:33; p is mono by A1,Def1; hence thesis by A1,Th37; end;	Convert the following ATP output trace into a readable Mizar proof.
t20_qc_lang3	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(d31_qc_lang1, axiom, ![X1]:(m1_qc_lang1(X1)=>![X2]:(m1_subset_1(X2,k9_qc_lang1(X1))=>(v6_qc_lang1(X2,X1)<=>k24_qc_lang1(X1,X2)=k1_xboole_0))), file('/scratch/mptp/predsminms1/t20_qc_lang3__0', d31_qc_lang1)). fof(dt_k1_qc_lang2, axiom, ![X1]:(m1_qc_lang1(X1)=>m1_subset_1(k1_qc_lang2(X1),k9_qc_lang1(X1))), file('/scratch/mptp/predsminms1/t20_qc_lang3__0', dt_k1_qc_lang2)). fof(t20_qc_lang3, conjecture, ![X1]:(m1_qc_lang1(X1)=>(v6_qc_lang1(k12_qc_lang1(X1),X1)&v6_qc_lang1(k1_qc_lang2(X1),X1))), file('/scratch/mptp/predsminms1/t20_qc_lang3__0', t20_qc_lang3)). fof(t8_qc_lang3, axiom, ![X1]:(m1_qc_lang1(X1)=>k24_qc_lang1(X1,k1_qc_lang2(X1))=k1_xboole_0), file('/scratch/mptp/predsminms1/t20_qc_lang3__0', t8_qc_lang3)). fof(dt_k12_qc_lang1, axiom, ![X1]:(m1_qc_lang1(X1)=>m1_subset_1(k12_qc_lang1(X1),k9_qc_lang1(X1))), file('/scratch/mptp/predsminms1/t20_qc_lang3__0', dt_k12_qc_lang1)). fof(t3_qc_lang3, axiom, ![X1]:(m1_qc_lang1(X1)=>k24_qc_lang1(X1,k12_qc_lang1(X1))=k1_xboole_0), file('/scratch/mptp/predsminms1/t20_qc_lang3__0', t3_qc_lang3)). fof(c_0_6, plain, ![X4, X5]:((~v6_qc_lang1(X5,X4)\|k24_qc_lang1(X4,X5)=k1_xboole_0\|~m1_subset_1(X5,k9_qc_lang1(X4))\|~m1_qc_lang1(X4))&(k24_qc_lang1(X4,X5)!=k1_xboole_0\|v6_qc_lang1(X5,X4)\|~m1_subset_1(X5,k9_qc_lang1(X4))\|~m1_qc_lang1(X4))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d31_qc_lang1])])])])). fof(c_0_7, plain, ![X7]:(~m1_qc_lang1(X7)\|m1_subset_1(k1_qc_lang2(X7),k9_qc_lang1(X7))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_qc_lang2])])). fof(c_0_8, negated_conjecture, ~(![X1]:(m1_qc_lang1(X1)=>(v6_qc_lang1(k12_qc_lang1(X1),X1)&v6_qc_lang1(k1_qc_lang2(X1),X1)))), inference(assume_negation,[status(cth)],[t20_qc_lang3])). cnf(c_0_9, plain, (v6_qc_lang1(X2,X1)\|k24_qc_lang1(X1,X2)!=k1_xboole_0\|~m1_subset_1(X2,k9_qc_lang1(X1))\|~m1_qc_lang1(X1)), inference(split_conjunct,[status(thm)],[c_0_6])). cnf(c_0_10, plain, (m1_subset_1(k1_qc_lang2(X1),k9_qc_lang1(X1))\|~m1_qc_lang1(X1)), inference(split_conjunct,[status(thm)],[c_0_7])). fof(c_0_11, plain, ![X6]:(~m1_qc_lang1(X6)\|k24_qc_lang1(X6,k1_qc_lang2(X6))=k1_xboole_0), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_qc_lang3])])). fof(c_0_12, plain, ![X9]:(~m1_qc_lang1(X9)\|m1_subset_1(k12_qc_lang1(X9),k9_qc_lang1(X9))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k12_qc_lang1])])). fof(c_0_13, negated_conjecture, (m1_qc_lang1(esk1_0)&(~v6_qc_lang1(k12_qc_lang1(esk1_0),esk1_0)\|~v6_qc_lang1(k1_qc_lang2(esk1_0),esk1_0))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])). cnf(c_0_14, plain, (v6_qc_lang1(X2,X1)\|k24_qc_lang1(X1,X2)!=k1_xboole_0\|~m1_qc_lang1(X1)\|~m1_subset_1(X2,k9_qc_lang1(X1))), inference(evalgc,[status(thm)],[c_0_9])). cnf(c_0_15, plain, (m1_subset_1(k1_qc_lang2(X1),k9_qc_lang1(X1))\|~m1_qc_lang1(X1)), inference(evalgc,[status(thm)],[c_0_10])). cnf(c_0_16, plain, (k24_qc_lang1(X1,k1_qc_lang2(X1))=k1_xboole_0\|~m1_qc_lang1(X1)), inference(split_conjunct,[status(thm)],[c_0_11])). cnf(c_0_17, plain, (m1_subset_1(k12_qc_lang1(X1),k9_qc_lang1(X1))\|~m1_qc_lang1(X1)), inference(split_conjunct,[status(thm)],[c_0_12])). fof(c_0_18, plain, ![X8]:(~m1_qc_lang1(X8)\|k24_qc_lang1(X8,k12_qc_lang1(X8))=k1_xboole_0), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_qc_lang3])])). cnf(c_0_19, negated_conjecture, (~v6_qc_lang1(k12_qc_lang1(esk1_0),esk1_0)\|~v6_qc_lang1(k1_qc_lang2(esk1_0),esk1_0)), inference(split_conjunct,[status(thm)],[c_0_13])). cnf(c_0_20, plain, (v6_qc_lang1(k1_qc_lang2(X1),X1)\|k24_qc_lang1(X1,k1_qc_lang2(X1))!=k1_xboole_0\|~m1_qc_lang1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_14, c_0_15])])). cnf(c_0_21, plain, (k24_qc_lang1(X1,k1_qc_lang2(X1))=k1_xboole_0\|~m1_qc_lang1(X1)), inference(evalgc,[status(thm)],[c_0_16])). cnf(c_0_22, negated_conjecture, (m1_qc_lang1(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_13])). cnf(c_0_23, plain, (m1_subset_1(k12_qc_lang1(X1),k9_qc_lang1(X1))\|~m1_qc_lang1(X1)), inference(evalgc,[status(thm)],[c_0_17])). cnf(c_0_24, plain, (k24_qc_lang1(X1,k12_qc_lang1(X1))=k1_xboole_0\|~m1_qc_lang1(X1)), inference(split_conjunct,[status(thm)],[c_0_18])). cnf(c_0_25, negated_conjecture, (~v6_qc_lang1(k12_qc_lang1(esk1_0),esk1_0)\|~v6_qc_lang1(k1_qc_lang2(esk1_0),esk1_0)), inference(evalgc,[status(thm)],[c_0_19])). cnf(c_0_26, plain, (v6_qc_lang1(k1_qc_lang2(X1),X1)\|~m1_qc_lang1(X1)), inference(csr,[status(thm)],[c_0_20, c_0_21])). cnf(c_0_27, negated_conjecture, (m1_qc_lang1(esk1_0)), inference(evalgc,[status(thm)],[c_0_22])). cnf(c_0_28, plain, (v6_qc_lang1(k12_qc_lang1(X1),X1)\|k24_qc_lang1(X1,k12_qc_lang1(X1))!=k1_xboole_0\|~m1_qc_lang1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_14, c_0_23])])). cnf(c_0_29, plain, (k24_qc_lang1(X1,k12_qc_lang1(X1))=k1_xboole_0\|~m1_qc_lang1(X1)), inference(evalgc,[status(thm)],[c_0_24])). cnf(c_0_30, negated_conjecture, (~v6_qc_lang1(k12_qc_lang1(esk1_0),esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25, c_0_26]), c_0_27])])])). cnf(c_0_31, plain, (v6_qc_lang1(k12_qc_lang1(X1),X1)\|~m1_qc_lang1(X1)), inference(csr,[status(thm)],[c_0_28, c_0_29])). cnf(c_0_32, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30, c_0_31]), c_0_27])]), ['proof']). # SZS output end CNFRefutation	reserve i,k for Element of NAT; reserve A for QC-alphabet; reserve x for bound_QC-variable of A; reserve a for free_QC-variable of A; reserve p,q for Element of QC-WFF(A); reserve l for FinSequence of QC-variables(A); reserve P,Q for QC-pred_symbol of A; reserve V for non empty Subset of QC-variables(A); reserve s,t for QC-symbol of A; theorem VERUM(A) is closed & FALSUM(A) is closed ::by Th7,Th12,QC_LANG1:def 30; proof still_not-bound_in VERUM(A) = {} & still_not-bound_in FALSUM(A) = {} by Th3,Th8; hence VERUM(A) is closed & FALSUM(A) is closed by QC_LANG1:def 31; end;	Convert the following ATP output trace into a readable Mizar proof.
t15_prob_2	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t15_prob_2, conjecture, ![X1]:(~(v1_xboole_0(X1))=>![X2]:((~(v1_xboole_0(X2))&(v1_prob_1(X2,X1)&(v4_prob_1(X2,X1)&m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X1))))))=>![X3]:(m1_prob_1(X3,X1,X2)=>![X4]:(m1_prob_1(X4,X1,X2)=>![X5]:(m2_prob_1(X5,X1,X2)=>r1_xxreal_0(k9_real_1(k7_real_1(k1_seq_1(X5,X3),k1_seq_1(X5,X4)),np__1),k1_seq_1(X5,k5_prob_1(X1,X2,X3,X4)))))))), file('/scratch/mptp/predsminms1/t15_prob_2__0', t15_prob_2)). fof(redefinition_k9_real_1, axiom, ![X1, X2]:((m1_subset_1(X1,k1_numbers)&v1_xreal_0(X2))=>k9_real_1(X1,X2)=k6_xcmplx_0(X1,X2)), file('/scratch/mptp/predsminms1/t15_prob_2__0', redefinition_k9_real_1)). fof(t38_prob_1, axiom, ![X1]:(~(v1_xboole_0(X1))=>![X2]:((~(v1_xboole_0(X2))&(v1_prob_1(X2,X1)&(v4_prob_1(X2,X1)&m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X1))))))=>![X3]:(m1_prob_1(X3,X1,X2)=>![X4]:(m1_prob_1(X4,X1,X2)=>![X5]:(m2_prob_1(X5,X1,X2)=>k1_seq_1(X5,k6_prob_1(X1,X2,X3,X4))=k9_real_1(k7_real_1(k1_seq_1(X5,X3),k1_seq_1(X5,X4)),k1_seq_1(X5,k5_prob_1(X1,X2,X3,X4)))))))), file('/scratch/mptp/predsminms1/t15_prob_2__0', t38_prob_1)). fof(redefinition_k5_prob_1, axiom, ![X1, X2, X3, X4]:(((~(v1_xboole_0(X2))&(v1_prob_1(X2,X1)&(v4_prob_1(X2,X1)&m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X1))))))&(m1_subset_1(X3,X2)&m1_subset_1(X4,X2)))=>k5_prob_1(X1,X2,X3,X4)=k3_xboole_0(X3,X4)), file('/scratch/mptp/predsminms1/t15_prob_2__0', redefinition_k5_prob_1)). fof(t20_xreal_1, axiom, ![X1]:(v1_xreal_0(X1)=>![X2]:(v1_xreal_0(X2)=>![X3]:(v1_xreal_0(X3)=>(r1_xxreal_0(X1,k2_xcmplx_0(X2,X3))<=>r1_xxreal_0(k6_xcmplx_0(X1,X2),X3))))), file('/scratch/mptp/predsminms1/t15_prob_2__0', t20_xreal_1)). fof(commutativity_k2_xcmplx_0, axiom, ![X1, X2]:((v1_xcmplx_0(X1)&v1_xcmplx_0(X2))=>k2_xcmplx_0(X1,X2)=k2_xcmplx_0(X2,X1)), file('/scratch/mptp/predsminms1/t15_prob_2__0', commutativity_k2_xcmplx_0)). fof(cc3_xreal_0, axiom, ![X1]:(v1_xreal_0(X1)=>v1_xcmplx_0(X1)), file('/scratch/mptp/predsminms1/t15_prob_2__0', cc3_xreal_0)). fof(t35_prob_1, axiom, ![X1]:(~(v1_xboole_0(X1))=>![X2]:((~(v1_xboole_0(X2))&(v1_prob_1(X2,X1)&(v4_prob_1(X2,X1)&m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X1))))))=>![X3]:(m1_prob_1(X3,X1,X2)=>![X4]:(m2_prob_1(X4,X1,X2)=>r1_xxreal_0(k1_seq_1(X4,X3),np__1))))), file('/scratch/mptp/predsminms1/t15_prob_2__0', t35_prob_1)). fof(redefinition_m1_prob_1, axiom, ![X1, X2]:((~(v1_xboole_0(X2))&(v1_prob_1(X2,X1)&(v4_prob_1(X2,X1)&m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X1))))))=>![X3]:(m1_prob_1(X3,X1,X2)<=>m1_subset_1(X3,X2))), file('/scratch/mptp/predsminms1/t15_prob_2__0', redefinition_m1_prob_1)). fof(cc1_xreal_0, axiom, ![X1]:(m1_subset_1(X1,k1_numbers)=>v1_xreal_0(X1)), file('/scratch/mptp/predsminms1/t15_prob_2__0', cc1_xreal_0)). fof(dt_k6_prob_1, axiom, ![X1, X2, X3, X4]:(((~(v1_xboole_0(X2))&(v1_prob_1(X2,X1)&(v4_prob_1(X2,X1)&m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X1))))))&(m1_subset_1(X3,X2)&m1_subset_1(X4,X2)))=>m1_prob_1(k6_prob_1(X1,X2,X3,X4),X1,X2)), file('/scratch/mptp/predsminms1/t15_prob_2__0', dt_k6_prob_1)). fof(dt_m2_prob_1, axiom, ![X1, X2]:((~(v1_xboole_0(X1))&(~(v1_xboole_0(X2))&(v1_prob_1(X2,X1)&(v4_prob_1(X2,X1)&m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X1)))))))=>![X3]:(m2_prob_1(X3,X1,X2)=>(v1_funct_1(X3)&(v1_funct_2(X3,X2,k1_numbers)&m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X2,k1_numbers))))))), file('/scratch/mptp/predsminms1/t15_prob_2__0', dt_m2_prob_1)). fof(dt_k1_seq_1, axiom, ![X1, X2]:((v1_relat_1(X1)&(v1_funct_1(X1)&v3_valued_0(X1)))=>m1_subset_1(k1_seq_1(X1,X2),k1_numbers)), file('/scratch/mptp/predsminms1/t15_prob_2__0', dt_k1_seq_1)). fof(cc18_valued_0, axiom, ![X1, X2]:(v3_membered(X2)=>![X3]:(m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))=>v3_valued_0(X3))), file('/scratch/mptp/predsminms1/t15_prob_2__0', cc18_valued_0)). fof(cc1_relset_1, axiom, ![X1, X2, X3]:(m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))=>v1_relat_1(X3)), file('/scratch/mptp/predsminms1/t15_prob_2__0', cc1_relset_1)). fof(fc3_membered, axiom, v3_membered(k1_numbers), file('/scratch/mptp/predsminms1/t15_prob_2__0', fc3_membered)). fof(dt_k7_real_1, axiom, ![X1, X2]:((m1_subset_1(X1,k1_numbers)&v1_xreal_0(X2))=>m1_subset_1(k7_real_1(X1,X2),k1_numbers)), file('/scratch/mptp/predsminms1/t15_prob_2__0', dt_k7_real_1)). fof(spc1_numerals, axiom, ((v2_xxreal_0(np__1)&m2_subset_1(np__1,k1_numbers,k5_numbers))&(m1_subset_1(np__1,k5_numbers)&m1_subset_1(np__1,k1_numbers))), file('/scratch/mptp/predsminms1/t15_prob_2__0', spc1_numerals)). fof(c_0_18, negated_conjecture, ~(![X1]:(~(v1_xboole_0(X1))=>![X2]:((~(v1_xboole_0(X2))&(v1_prob_1(X2,X1)&(v4_prob_1(X2,X1)&m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X1))))))=>![X3]:(m1_prob_1(X3,X1,X2)=>![X4]:(m1_prob_1(X4,X1,X2)=>![X5]:(m2_prob_1(X5,X1,X2)=>r1_xxreal_0(k9_real_1(k7_real_1(k1_seq_1(X5,X3),k1_seq_1(X5,X4)),np__1),k1_seq_1(X5,k5_prob_1(X1,X2,X3,X4))))))))), inference(assume_negation,[status(cth)],[t15_prob_2])). fof(c_0_19, plain, ![X22, X23]:(~m1_subset_1(X22,k1_numbers)\|~v1_xreal_0(X23)\|k9_real_1(X22,X23)=k6_xcmplx_0(X22,X23)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k9_real_1])])). fof(c_0_20, plain, ![X47, X48, X49, X50, X51]:(v1_xboole_0(X47)\|(v1_xboole_0(X48)\|(~v1_prob_1(X48,X47)\|(~v4_prob_1(X48,X47)\|~m1_subset_1(X48,k1_zfmisc_1(k1_zfmisc_1(X47)))))\|(~m1_prob_1(X49,X47,X48)\|(~m1_prob_1(X50,X47,X48)\|(~m2_prob_1(X51,X47,X48)\|k1_seq_1(X51,k6_prob_1(X47,X48,X49,X50))=k9_real_1(k7_real_1(k1_seq_1(X51,X49),k1_seq_1(X51,X50)),k1_seq_1(X51,k5_prob_1(X47,X48,X49,X50)))))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t38_prob_1])])])])). fof(c_0_21, plain, ![X27, X28, X29, X30]:(v1_xboole_0(X28)\|(~v1_prob_1(X28,X27)\|(~v4_prob_1(X28,X27)\|~m1_subset_1(X28,k1_zfmisc_1(k1_zfmisc_1(X27)))))\|(~m1_subset_1(X29,X28)\|~m1_subset_1(X30,X28))\|k5_prob_1(X27,X28,X29,X30)=k3_xboole_0(X29,X30)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[redefinition_k5_prob_1])])])). fof(c_0_22, negated_conjecture, (~v1_xboole_0(esk1_0)&((~v1_xboole_0(esk2_0)&(v1_prob_1(esk2_0,esk1_0)&(v4_prob_1(esk2_0,esk1_0)&m1_subset_1(esk2_0,k1_zfmisc_1(k1_zfmisc_1(esk1_0))))))&(m1_prob_1(esk3_0,esk1_0,esk2_0)&(m1_prob_1(esk4_0,esk1_0,esk2_0)&(m2_prob_1(esk5_0,esk1_0,esk2_0)&~r1_xxreal_0(k9_real_1(k7_real_1(k1_seq_1(esk5_0,esk3_0),k1_seq_1(esk5_0,esk4_0)),np__1),k1_seq_1(esk5_0,k5_prob_1(esk1_0,esk2_0,esk3_0,esk4_0)))))))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_18])])])])). fof(c_0_23, plain, ![X31, X32, X33]:((~r1_xxreal_0(X31,k2_xcmplx_0(X32,X33))\|r1_xxreal_0(k6_xcmplx_0(X31,X32),X33)\|~v1_xreal_0(X33)\|~v1_xreal_0(X32)\|~v1_xreal_0(X31))&(~r1_xxreal_0(k6_xcmplx_0(X31,X32),X33)\|r1_xxreal_0(X31,k2_xcmplx_0(X32,X33))\|~v1_xreal_0(X33)\|~v1_xreal_0(X32)\|~v1_xreal_0(X31))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t20_xreal_1])])])])). cnf(c_0_24, plain, (k9_real_1(X1,X2)=k6_xcmplx_0(X1,X2)\|~m1_subset_1(X1,k1_numbers)\|~v1_xreal_0(X2)), inference(split_conjunct,[status(thm)],[c_0_19])). cnf(c_0_25, plain, (v1_xboole_0(X1)\|v1_xboole_0(X2)\|k1_seq_1(X5,k6_prob_1(X1,X2,X3,X4))=k9_real_1(k7_real_1(k1_seq_1(X5,X3),k1_seq_1(X5,X4)),k1_seq_1(X5,k5_prob_1(X1,X2,X3,X4)))\|~v1_prob_1(X2,X1)\|~v4_prob_1(X2,X1)\|~m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X1)))\|~m1_prob_1(X3,X1,X2)\|~m1_prob_1(X4,X1,X2)\|~m2_prob_1(X5,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_20])). fof(c_0_26, plain, ![X43, X44]:(~v1_xcmplx_0(X43)\|~v1_xcmplx_0(X44)\|k2_xcmplx_0(X43,X44)=k2_xcmplx_0(X44,X43)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[commutativity_k2_xcmplx_0])])). fof(c_0_27, plain, ![X42]:(~v1_xreal_0(X42)\|v1_xcmplx_0(X42)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc3_xreal_0])])). fof(c_0_28, plain, ![X38, X39, X40, X41]:(v1_xboole_0(X38)\|(v1_xboole_0(X39)\|(~v1_prob_1(X39,X38)\|(~v4_prob_1(X39,X38)\|~m1_subset_1(X39,k1_zfmisc_1(k1_zfmisc_1(X38)))))\|(~m1_prob_1(X40,X38,X39)\|(~m2_prob_1(X41,X38,X39)\|r1_xxreal_0(k1_seq_1(X41,X40),np__1))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[t35_prob_1])])])])). cnf(c_0_29, plain, (v1_xboole_0(X1)\|k5_prob_1(X2,X1,X3,X4)=k3_xboole_0(X3,X4)\|~v1_prob_1(X1,X2)\|~v4_prob_1(X1,X2)\|~m1_subset_1(X1,k1_zfmisc_1(k1_zfmisc_1(X2)))\|~m1_subset_1(X3,X1)\|~m1_subset_1(X4,X1)), inference(split_conjunct,[status(thm)],[c_0_21])). fof(c_0_30, plain, ![X24, X25, X26]:((~m1_prob_1(X26,X24,X25)\|m1_subset_1(X26,X25)\|(v1_xboole_0(X25)\|(~v1_prob_1(X25,X24)\|(~v4_prob_1(X25,X24)\|~m1_subset_1(X25,k1_zfmisc_1(k1_zfmisc_1(X24)))))))&(~m1_subset_1(X26,X25)\|m1_prob_1(X26,X24,X25)\|(v1_xboole_0(X25)\|(~v1_prob_1(X25,X24)\|(~v4_prob_1(X25,X24)\|~m1_subset_1(X25,k1_zfmisc_1(k1_zfmisc_1(X24)))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[redefinition_m1_prob_1])])])])])). cnf(c_0_31, negated_conjecture, (~r1_xxreal_0(k9_real_1(k7_real_1(k1_seq_1(esk5_0,esk3_0),k1_seq_1(esk5_0,esk4_0)),np__1),k1_seq_1(esk5_0,k5_prob_1(esk1_0,esk2_0,esk3_0,esk4_0)))), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_32, plain, (r1_xxreal_0(X1,k2_xcmplx_0(X2,X3))\|~r1_xxreal_0(k6_xcmplx_0(X1,X2),X3)\|~v1_xreal_0(X3)\|~v1_xreal_0(X2)\|~v1_xreal_0(X1)), inference(split_conjunct,[status(thm)],[c_0_23])). cnf(c_0_33, plain, (k9_real_1(X1,X2)=k6_xcmplx_0(X1,X2)\|~v1_xreal_0(X2)\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[c_0_24])). cnf(c_0_34, plain, (k9_real_1(k7_real_1(k1_seq_1(X5,X3),k1_seq_1(X5,X4)),k1_seq_1(X5,k5_prob_1(X1,X2,X3,X4)))=k1_seq_1(X5,k6_prob_1(X1,X2,X3,X4))\|v1_xboole_0(X2)\|v1_xboole_0(X1)\|~v1_prob_1(X2,X1)\|~v4_prob_1(X2,X1)\|~m1_prob_1(X4,X1,X2)\|~m1_prob_1(X3,X1,X2)\|~m2_prob_1(X5,X1,X2)\|~m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X1)))), inference(evalgc,[status(thm)],[c_0_25])). fof(c_0_35, plain, ![X11]:(~m1_subset_1(X11,k1_numbers)\|v1_xreal_0(X11)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_xreal_0])])). cnf(c_0_36, plain, (k2_xcmplx_0(X1,X2)=k2_xcmplx_0(X2,X1)\|~v1_xcmplx_0(X1)\|~v1_xcmplx_0(X2)), inference(split_conjunct,[status(thm)],[c_0_26])). cnf(c_0_37, plain, (v1_xcmplx_0(X1)\|~v1_xreal_0(X1)), inference(split_conjunct,[status(thm)],[c_0_27])). cnf(c_0_38, plain, (v1_xboole_0(X1)\|v1_xboole_0(X2)\|r1_xxreal_0(k1_seq_1(X4,X3),np__1)\|~v1_prob_1(X2,X1)\|~v4_prob_1(X2,X1)\|~m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X1)))\|~m1_prob_1(X3,X1,X2)\|~m2_prob_1(X4,X1,X2)), inference(split_conjunct,[status(thm)],[c_0_28])). cnf(c_0_39, negated_conjecture, (m2_prob_1(esk5_0,esk1_0,esk2_0)), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_40, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(k1_zfmisc_1(esk1_0)))), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_41, negated_conjecture, (v4_prob_1(esk2_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_42, negated_conjecture, (v1_prob_1(esk2_0,esk1_0)), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_43, negated_conjecture, (~v1_xboole_0(esk1_0)), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_44, negated_conjecture, (~v1_xboole_0(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_45, plain, (k5_prob_1(X2,X1,X3,X4)=k3_xboole_0(X3,X4)\|v1_xboole_0(X1)\|~v1_prob_1(X1,X2)\|~v4_prob_1(X1,X2)\|~m1_subset_1(X4,X1)\|~m1_subset_1(X3,X1)\|~m1_subset_1(X1,k1_zfmisc_1(k1_zfmisc_1(X2)))), inference(evalgc,[status(thm)],[c_0_29])). cnf(c_0_46, plain, (m1_subset_1(X1,X3)\|v1_xboole_0(X3)\|~m1_prob_1(X1,X2,X3)\|~v1_prob_1(X3,X2)\|~v4_prob_1(X3,X2)\|~m1_subset_1(X3,k1_zfmisc_1(k1_zfmisc_1(X2)))), inference(split_conjunct,[status(thm)],[c_0_30])). cnf(c_0_47, negated_conjecture, (~r1_xxreal_0(k9_real_1(k7_real_1(k1_seq_1(esk5_0,esk3_0),k1_seq_1(esk5_0,esk4_0)),np__1),k1_seq_1(esk5_0,k5_prob_1(esk1_0,esk2_0,esk3_0,esk4_0)))), inference(evalgc,[status(thm)],[c_0_31])). cnf(c_0_48, plain, (r1_xxreal_0(k6_xcmplx_0(X1,X2),X3)\|~r1_xxreal_0(X1,k2_xcmplx_0(X2,X3))\|~v1_xreal_0(X3)\|~v1_xreal_0(X2)\|~v1_xreal_0(X1)), inference(split_conjunct,[status(thm)],[c_0_23])). cnf(c_0_49, plain, (r1_xxreal_0(X1,k2_xcmplx_0(X2,X3))\|~v1_xreal_0(X3)\|~v1_xreal_0(X2)\|~v1_xreal_0(X1)\|~r1_xxreal_0(k6_xcmplx_0(X1,X2),X3)), inference(evalgc,[status(thm)],[c_0_32])). cnf(c_0_50, plain, (k6_xcmplx_0(k7_real_1(k1_seq_1(X1,X2),k1_seq_1(X1,X3)),k1_seq_1(X1,k5_prob_1(X4,X5,X2,X3)))=k1_seq_1(X1,k6_prob_1(X4,X5,X2,X3))\|v1_xboole_0(X4)\|v1_xboole_0(X5)\|~v1_xreal_0(k1_seq_1(X1,k5_prob_1(X4,X5,X2,X3)))\|~m1_subset_1(k7_real_1(k1_seq_1(X1,X2),k1_seq_1(X1,X3)),k1_numbers)\|~m2_prob_1(X1,X4,X5)\|~m1_prob_1(X3,X4,X5)\|~m1_prob_1(X2,X4,X5)\|~m1_subset_1(X5,k1_zfmisc_1(k1_zfmisc_1(X4)))\|~v4_prob_1(X5,X4)\|~v1_prob_1(X5,X4)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_33, c_0_34])])). cnf(c_0_51, plain, (v1_xreal_0(X1)\|~m1_subset_1(X1,k1_numbers)), inference(split_conjunct,[status(thm)],[c_0_35])). cnf(c_0_52, plain, (k2_xcmplx_0(X1,X2)=k2_xcmplx_0(X2,X1)\|~v1_xcmplx_0(X2)\|~v1_xcmplx_0(X1)), inference(evalgc,[status(thm)],[c_0_36])). cnf(c_0_53, plain, (v1_xcmplx_0(X1)\|~v1_xreal_0(X1)), inference(evalgc,[status(thm)],[c_0_37])). cnf(c_0_54, plain, (v1_xboole_0(X2)\|v1_xboole_0(X1)\|r1_xxreal_0(k1_seq_1(X4,X3),np__1)\|~v1_prob_1(X2,X1)\|~v4_prob_1(X2,X1)\|~m1_prob_1(X3,X1,X2)\|~m2_prob_1(X4,X1,X2)\|~m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X1)))), inference(evalgc,[status(thm)],[c_0_38])). cnf(c_0_55, negated_conjecture, (m2_prob_1(esk5_0,esk1_0,esk2_0)), inference(evalgc,[status(thm)],[c_0_39])). cnf(c_0_56, negated_conjecture, (m1_subset_1(esk2_0,k1_zfmisc_1(k1_zfmisc_1(esk1_0)))), inference(evalgc,[status(thm)],[c_0_40])). cnf(c_0_57, negated_conjecture, (v4_prob_1(esk2_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_41])). cnf(c_0_58, negated_conjecture, (v1_prob_1(esk2_0,esk1_0)), inference(evalgc,[status(thm)],[c_0_42])). cnf(c_0_59, negated_conjecture, (~v1_xboole_0(esk1_0)), inference(evalgc,[status(thm)],[c_0_43])). cnf(c_0_60, negated_conjecture, (~v1_xboole_0(esk2_0)), inference(evalgc,[status(thm)],[c_0_44])). cnf(c_0_61, plain, (k9_real_1(k7_real_1(k1_seq_1(X1,X2),k1_seq_1(X1,X3)),k1_seq_1(X1,k3_xboole_0(X2,X3)))=k1_seq_1(X1,k6_prob_1(X4,X5,X2,X3))\|v1_xboole_0(X4)\|v1_xboole_0(X5)\|~m2_prob_1(X1,X4,X5)\|~m1_prob_1(X3,X4,X5)\|~m1_prob_1(X2,X4,X5)\|~m1_subset_1(X5,k1_zfmisc_1(k1_zfmisc_1(X4)))\|~v4_prob_1(X5,X4)\|~v1_prob_1(X5,X4)\|~m1_subset_1(X3,X5)\|~m1_subset_1(X2,X5)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_34, c_0_45])])). cnf(c_0_62, plain, (v1_xboole_0(X3)\|m1_subset_1(X1,X3)\|~v1_prob_1(X3,X2)\|~v4_prob_1(X3,X2)\|~m1_prob_1(X1,X2,X3)\|~m1_subset_1(X3,k1_zfmisc_1(k1_zfmisc_1(X2)))), inference(evalgc,[status(thm)],[c_0_46])). fof(c_0_63, plain, ![X34, X35, X36, X37]:(v1_xboole_0(X35)\|(~v1_prob_1(X35,X34)\|(~v4_prob_1(X35,X34)\|~m1_subset_1(X35,k1_zfmisc_1(k1_zfmisc_1(X34)))))\|(~m1_subset_1(X36,X35)\|~m1_subset_1(X37,X35))\|m1_prob_1(k6_prob_1(X34,X35,X36,X37),X34,X35)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_k6_prob_1])])])). fof(c_0_64, plain, ![X12, X13, X14]:((v1_funct_1(X14)\|~m2_prob_1(X14,X12,X13)\|(v1_xboole_0(X12)\|(v1_xboole_0(X13)\|(~v1_prob_1(X13,X12)\|(~v4_prob_1(X13,X12)\|~m1_subset_1(X13,k1_zfmisc_1(k1_zfmisc_1(X12))))))))&((v1_funct_2(X14,X13,k1_numbers)\|~m2_prob_1(X14,X12,X13)\|(v1_xboole_0(X12)\|(v1_xboole_0(X13)\|(~v1_prob_1(X13,X12)\|(~v4_prob_1(X13,X12)\|~m1_subset_1(X13,k1_zfmisc_1(k1_zfmisc_1(X12))))))))&(m1_subset_1(X14,k1_zfmisc_1(k2_zfmisc_1(X13,k1_numbers)))\|~m2_prob_1(X14,X12,X13)\|(v1_xboole_0(X12)\|(v1_xboole_0(X13)\|(~v1_prob_1(X13,X12)\|(~v4_prob_1(X13,X12)\|~m1_subset_1(X13,k1_zfmisc_1(k1_zfmisc_1(X12)))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[dt_m2_prob_1])])])])])). cnf(c_0_65, negated_conjecture, (~r1_xxreal_0(k6_xcmplx_0(k7_real_1(k1_seq_1(esk5_0,esk3_0),k1_seq_1(esk5_0,esk4_0)),np__1),k1_seq_1(esk5_0,k5_prob_1(esk1_0,esk2_0,esk3_0,esk4_0)))\|~v1_xreal_0(np__1)\|~m1_subset_1(k7_real_1(k1_seq_1(esk5_0,esk3_0),k1_seq_1(esk5_0,esk4_0)),k1_numbers)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_47, c_0_33])])). cnf(c_0_66, plain, (r1_xxreal_0(k6_xcmplx_0(X1,X2),X3)\|~v1_xreal_0(X3)\|~v1_xreal_0(X2)\|~v1_xreal_0(X1)\|~r1_xxreal_0(X1,k2_xcmplx_0(X2,X3))), inference(evalgc,[status(thm)],[c_0_48])). cnf(c_0_67, plain, (r1_xxreal_0(k7_real_1(k1_seq_1(X1,X2),k1_seq_1(X1,X3)),k2_xcmplx_0(k1_seq_1(X1,k5_prob_1(X4,X5,X2,X3)),X6))\|v1_xboole_0(X5)\|v1_xboole_0(X4)\|~v1_xreal_0(X6)\|~v1_xreal_0(k1_seq_1(X1,k5_prob_1(X4,X5,X2,X3)))\|~v1_xreal_0(k7_real_1(k1_seq_1(X1,X2),k1_seq_1(X1,X3)))\|~r1_xxreal_0(k1_seq_1(X1,k6_prob_1(X4,X5,X2,X3)),X6)\|~m2_prob_1(X1,X4,X5)\|~m1_prob_1(X3,X4,X5)\|~m1_prob_1(X2,X4,X5)\|~m1_subset_1(k7_real_1(k1_seq_1(X1,X2),k1_seq_1(X1,X3)),k1_numbers)\|~m1_subset_1(X5,k1_zfmisc_1(k1_zfmisc_1(X4)))\|~v4_prob_1(X5,X4)\|~v1_prob_1(X5,X4)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_49, c_0_50])])). cnf(c_0_68, plain, (v1_xreal_0(X1)\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[c_0_51])). cnf(c_0_69, plain, (k2_xcmplx_0(X1,X2)=k2_xcmplx_0(X2,X1)\|~v1_xcmplx_0(X1)\|~v1_xreal_0(X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_52, c_0_53])])). cnf(c_0_70, negated_conjecture, (r1_xxreal_0(k1_seq_1(esk5_0,X1),np__1)\|~m1_prob_1(X1,esk1_0,esk2_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54, c_0_55]), c_0_56]), c_0_57]), c_0_58])]), c_0_59]), c_0_60])])). cnf(c_0_71, plain, (k9_real_1(k7_real_1(k1_seq_1(X1,X2),k1_seq_1(X1,X3)),k1_seq_1(X1,k3_xboole_0(X2,X3)))=k1_seq_1(X1,k6_prob_1(X4,X5,X2,X3))\|v1_xboole_0(X5)\|v1_xboole_0(X4)\|~m2_prob_1(X1,X4,X5)\|~m1_prob_1(X3,X4,X5)\|~m1_prob_1(X2,X4,X5)\|~m1_subset_1(X5,k1_zfmisc_1(k1_zfmisc_1(X4)))\|~v4_prob_1(X5,X4)\|~v1_prob_1(X5,X4)), inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_61, c_0_62]), c_0_62])). cnf(c_0_72, plain, (v1_xboole_0(X1)\|m1_prob_1(k6_prob_1(X2,X1,X3,X4),X2,X1)\|~v1_prob_1(X1,X2)\|~v4_prob_1(X1,X2)\|~m1_subset_1(X1,k1_zfmisc_1(k1_zfmisc_1(X2)))\|~m1_subset_1(X3,X1)\|~m1_subset_1(X4,X1)), inference(split_conjunct,[status(thm)],[c_0_63])). fof(c_0_73, plain, ![X18, X19]:(~v1_relat_1(X18)\|(~v1_funct_1(X18)\|~v3_valued_0(X18))\|m1_subset_1(k1_seq_1(X18,X19),k1_numbers)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_seq_1])])). cnf(c_0_74, plain, (v1_funct_1(X1)\|v1_xboole_0(X2)\|v1_xboole_0(X3)\|~m2_prob_1(X1,X2,X3)\|~v1_prob_1(X3,X2)\|~v4_prob_1(X3,X2)\|~m1_subset_1(X3,k1_zfmisc_1(k1_zfmisc_1(X2)))), inference(split_conjunct,[status(thm)],[c_0_64])). fof(c_0_75, plain, ![X52, X53, X54]:(~v3_membered(X53)\|(~m1_subset_1(X54,k1_zfmisc_1(k2_zfmisc_1(X52,X53)))\|v3_valued_0(X54))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc18_valued_0])])])). cnf(c_0_76, plain, (m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,k1_numbers)))\|v1_xboole_0(X3)\|v1_xboole_0(X2)\|~m2_prob_1(X1,X3,X2)\|~v1_prob_1(X2,X3)\|~v4_prob_1(X2,X3)\|~m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X3)))), inference(split_conjunct,[status(thm)],[c_0_64])). fof(c_0_77, plain, ![X15, X16, X17]:(~m1_subset_1(X17,k1_zfmisc_1(k2_zfmisc_1(X15,X16)))\|v1_relat_1(X17)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relset_1])])). cnf(c_0_78, negated_conjecture, (~v1_xreal_0(np__1)\|~m1_subset_1(k7_real_1(k1_seq_1(esk5_0,esk3_0),k1_seq_1(esk5_0,esk4_0)),k1_numbers)\|~v1_xreal_0(k1_seq_1(esk5_0,k5_prob_1(esk1_0,esk2_0,esk3_0,esk4_0)))\|~v1_xreal_0(k7_real_1(k1_seq_1(esk5_0,esk3_0),k1_seq_1(esk5_0,esk4_0)))\|~r1_xxreal_0(k7_real_1(k1_seq_1(esk5_0,esk3_0),k1_seq_1(esk5_0,esk4_0)),k2_xcmplx_0(np__1,k1_seq_1(esk5_0,k5_prob_1(esk1_0,esk2_0,esk3_0,esk4_0))))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_65, c_0_66])])). cnf(c_0_79, plain, (r1_xxreal_0(k7_real_1(k1_seq_1(X1,X2),k1_seq_1(X1,X3)),k2_xcmplx_0(k1_seq_1(X1,k5_prob_1(X4,X5,X2,X3)),X6))\|v1_xboole_0(X4)\|v1_xboole_0(X5)\|~v1_xreal_0(k1_seq_1(X1,k5_prob_1(X4,X5,X2,X3)))\|~v1_xreal_0(X6)\|~r1_xxreal_0(k1_seq_1(X1,k6_prob_1(X4,X5,X2,X3)),X6)\|~m2_prob_1(X1,X4,X5)\|~m1_prob_1(X3,X4,X5)\|~m1_prob_1(X2,X4,X5)\|~m1_subset_1(k7_real_1(k1_seq_1(X1,X2),k1_seq_1(X1,X3)),k1_numbers)\|~m1_subset_1(X5,k1_zfmisc_1(k1_zfmisc_1(X4)))\|~v4_prob_1(X5,X4)\|~v1_prob_1(X5,X4)), inference(csr,[status(thm)],[c_0_67, c_0_68])). cnf(c_0_80, plain, (k2_xcmplx_0(X1,X2)=k2_xcmplx_0(X2,X1)\|~v1_xreal_0(X2)\|~v1_xreal_0(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_69, c_0_53])])). cnf(c_0_81, negated_conjecture, (m1_prob_1(esk4_0,esk1_0,esk2_0)), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_82, negated_conjecture, (m1_prob_1(esk3_0,esk1_0,esk2_0)), inference(split_conjunct,[status(thm)],[c_0_22])). cnf(c_0_83, negated_conjecture, (r1_xxreal_0(k9_real_1(k7_real_1(k1_seq_1(esk5_0,X3),k1_seq_1(esk5_0,X4)),k1_seq_1(esk5_0,k3_xboole_0(X3,X4))),np__1)\|v1_xboole_0(X2)\|v1_xboole_0(X1)\|~m1_prob_1(k6_prob_1(X1,X2,X3,X4),esk1_0,esk2_0)\|~m2_prob_1(esk5_0,X1,X2)\|~m1_prob_1(X4,X1,X2)\|~m1_prob_1(X3,X1,X2)\|~m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X1)))\|~v4_prob_1(X2,X1)\|~v1_prob_1(X2,X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_70, c_0_71])])). cnf(c_0_84, plain, (v1_xboole_0(X1)\|m1_prob_1(k6_prob_1(X2,X1,X3,X4),X2,X1)\|~v1_prob_1(X1,X2)\|~v4_prob_1(X1,X2)\|~m1_subset_1(X4,X1)\|~m1_subset_1(X3,X1)\|~m1_subset_1(X1,k1_zfmisc_1(k1_zfmisc_1(X2)))), inference(evalgc,[status(thm)],[c_0_72])). cnf(c_0_85, plain, (m1_subset_1(k1_seq_1(X1,X2),k1_numbers)\|~v1_relat_1(X1)\|~v1_funct_1(X1)\|~v3_valued_0(X1)), inference(split_conjunct,[status(thm)],[c_0_73])). cnf(c_0_86, plain, (v1_xboole_0(X3)\|v1_xboole_0(X2)\|v1_funct_1(X1)\|~v1_prob_1(X3,X2)\|~v4_prob_1(X3,X2)\|~m2_prob_1(X1,X2,X3)\|~m1_subset_1(X3,k1_zfmisc_1(k1_zfmisc_1(X2)))), inference(evalgc,[status(thm)],[c_0_74])). cnf(c_0_87, plain, (v3_valued_0(X2)\|~v3_membered(X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X3,X1)))), inference(split_conjunct,[status(thm)],[c_0_75])). cnf(c_0_88, plain, (v1_xboole_0(X3)\|v1_xboole_0(X2)\|m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,k1_numbers)))\|~v1_prob_1(X2,X3)\|~v4_prob_1(X2,X3)\|~m2_prob_1(X1,X3,X2)\|~m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X3)))), inference(evalgc,[status(thm)],[c_0_76])). cnf(c_0_89, plain, (v3_membered(k1_numbers)), inference(split_conjunct,[status(thm)],[fc3_membered])). cnf(c_0_90, plain, (v1_relat_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_77])). cnf(c_0_91, negated_conjecture, (~v1_xreal_0(k1_seq_1(esk5_0,k5_prob_1(esk1_0,esk2_0,esk3_0,esk4_0)))\|~v1_xreal_0(np__1)\|~r1_xxreal_0(k7_real_1(k1_seq_1(esk5_0,esk3_0),k1_seq_1(esk5_0,esk4_0)),k2_xcmplx_0(np__1,k1_seq_1(esk5_0,k5_prob_1(esk1_0,esk2_0,esk3_0,esk4_0))))\|~m1_subset_1(k7_real_1(k1_seq_1(esk5_0,esk3_0),k1_seq_1(esk5_0,esk4_0)),k1_numbers)), inference(csr,[status(thm)],[c_0_78, c_0_68])). cnf(c_0_92, plain, (r1_xxreal_0(k7_real_1(k1_seq_1(X1,X2),k1_seq_1(X1,X3)),k2_xcmplx_0(X6,k1_seq_1(X1,k5_prob_1(X4,X5,X2,X3))))\|v1_xboole_0(X4)\|v1_xboole_0(X5)\|~v1_xreal_0(k1_seq_1(X1,k5_prob_1(X4,X5,X2,X3)))\|~v1_xreal_0(X6)\|~r1_xxreal_0(k1_seq_1(X1,k6_prob_1(X4,X5,X2,X3)),X6)\|~m2_prob_1(X1,X4,X5)\|~m1_prob_1(X3,X4,X5)\|~m1_prob_1(X2,X4,X5)\|~m1_subset_1(k7_real_1(k1_seq_1(X1,X2),k1_seq_1(X1,X3)),k1_numbers)\|~m1_subset_1(X5,k1_zfmisc_1(k1_zfmisc_1(X4)))\|~v4_prob_1(X5,X4)\|~v1_prob_1(X5,X4)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_79, c_0_80])])). cnf(c_0_93, negated_conjecture, (m1_prob_1(esk4_0,esk1_0,esk2_0)), inference(evalgc,[status(thm)],[c_0_81])). cnf(c_0_94, negated_conjecture, (m1_prob_1(esk3_0,esk1_0,esk2_0)), inference(evalgc,[status(thm)],[c_0_82])). cnf(c_0_95, negated_conjecture, (r1_xxreal_0(k9_real_1(k7_real_1(k1_seq_1(esk5_0,X1),k1_seq_1(esk5_0,X2)),k1_seq_1(esk5_0,k3_xboole_0(X1,X2))),np__1)\|~m1_prob_1(X2,esk1_0,esk2_0)\|~m1_prob_1(X1,esk1_0,esk2_0)\|~m1_subset_1(X2,esk2_0)\|~m1_subset_1(X1,esk2_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83, c_0_84]), c_0_55]), c_0_56]), c_0_57]), c_0_58])]), c_0_59]), c_0_60])])). fof(c_0_96, plain, ![X20, X21]:(~m1_subset_1(X20,k1_numbers)\|~v1_xreal_0(X21)\|m1_subset_1(k7_real_1(X20,X21),k1_numbers)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k7_real_1])])). cnf(c_0_97, plain, (m1_subset_1(k1_seq_1(X1,X2),k1_numbers)\|~v1_funct_1(X1)\|~v1_relat_1(X1)\|~v3_valued_0(X1)), inference(evalgc,[status(thm)],[c_0_85])). cnf(c_0_98, negated_conjecture, (v1_funct_1(esk5_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86, c_0_55]), c_0_56]), c_0_57]), c_0_58])]), c_0_59]), c_0_60])])). cnf(c_0_99, plain, (v3_valued_0(X2)\|~v3_membered(X1)\|~m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X3,X1)))), inference(evalgc,[status(thm)],[c_0_87])). cnf(c_0_100, negated_conjecture, (m1_subset_1(esk5_0,k1_zfmisc_1(k2_zfmisc_1(esk2_0,k1_numbers)))), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88, c_0_55]), c_0_56]), c_0_57]), c_0_58])]), c_0_60]), c_0_59])])). cnf(c_0_101, plain, (v3_membered(k1_numbers)), inference(evalgc,[status(thm)],[c_0_89])). cnf(c_0_102, plain, (v1_relat_1(X1)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(evalgc,[status(thm)],[c_0_90])). cnf(c_0_103, negated_conjecture, (~v1_xreal_0(k1_seq_1(esk5_0,k5_prob_1(esk1_0,esk2_0,esk3_0,esk4_0)))\|~v1_xreal_0(np__1)\|~m1_subset_1(k7_real_1(k1_seq_1(esk5_0,esk3_0),k1_seq_1(esk5_0,esk4_0)),k1_numbers)\|~r1_xxreal_0(k1_seq_1(esk5_0,k6_prob_1(esk1_0,esk2_0,esk3_0,esk4_0)),np__1)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91, c_0_92]), c_0_55]), c_0_93]), c_0_94]), c_0_56]), c_0_57]), c_0_58])]), c_0_60]), c_0_59])])). cnf(c_0_104, negated_conjecture, (r1_xxreal_0(k1_seq_1(esk5_0,k6_prob_1(X3,X4,X1,X2)),np__1)\|v1_xboole_0(X4)\|v1_xboole_0(X3)\|~m1_prob_1(X2,esk1_0,esk2_0)\|~m1_prob_1(X1,esk1_0,esk2_0)\|~m1_subset_1(X2,esk2_0)\|~m1_subset_1(X1,esk2_0)\|~m2_prob_1(esk5_0,X3,X4)\|~m1_prob_1(X2,X3,X4)\|~m1_prob_1(X1,X3,X4)\|~m1_subset_1(X4,k1_zfmisc_1(k1_zfmisc_1(X3)))\|~v4_prob_1(X4,X3)\|~v1_prob_1(X4,X3)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_95, c_0_71])])). cnf(c_0_105, negated_conjecture, (m1_subset_1(esk4_0,esk2_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62, c_0_93]), c_0_56]), c_0_57]), c_0_58])]), c_0_60])])). cnf(c_0_106, negated_conjecture, (m1_subset_1(esk3_0,esk2_0)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62, c_0_94]), c_0_56]), c_0_57]), c_0_58])]), c_0_60])])). cnf(c_0_107, plain, (m1_subset_1(k7_real_1(X1,X2),k1_numbers)\|~m1_subset_1(X1,k1_numbers)\|~v1_xreal_0(X2)), inference(split_conjunct,[status(thm)],[c_0_96])). cnf(c_0_108, negated_conjecture, (m1_subset_1(k1_seq_1(esk5_0,X1),k1_numbers)\|~v3_valued_0(esk5_0)\|~v1_relat_1(esk5_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_97, c_0_98])])). cnf(c_0_109, negated_conjecture, (v3_valued_0(esk5_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99, c_0_100]), c_0_101])])])). cnf(c_0_110, negated_conjecture, (v1_relat_1(esk5_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_102, c_0_100])])). cnf(c_0_111, negated_conjecture, (~v1_xreal_0(k1_seq_1(esk5_0,k5_prob_1(esk1_0,esk2_0,esk3_0,esk4_0)))\|~v1_xreal_0(np__1)\|~m1_subset_1(k7_real_1(k1_seq_1(esk5_0,esk3_0),k1_seq_1(esk5_0,esk4_0)),k1_numbers)), inference(evalgc,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103, c_0_104]), c_0_55]), c_0_93]), c_0_94]), c_0_56]), c_0_105]), c_0_106]), c_0_57]), c_0_58])]), c_0_59]), c_0_60])])). cnf(c_0_112, plain, (m1_subset_1(k7_real_1(X1,X2),k1_numbers)\|~v1_xreal_0(X2)\|~m1_subset_1(X1,k1_numbers)), inference(evalgc,[status(thm)],[c_0_107])). cnf(c_0_113, negated_conjecture, (m1_subset_1(k1_seq_1(esk5_0,X1),k1_numbers)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_108, c_0_109]), c_0_110])])). cnf(c_0_114, negated_conjecture, (~v1_xreal_0(k1_seq_1(esk5_0,k5_prob_1(esk1_0,esk2_0,esk3_0,esk4_0)))\|~v1_xreal_0(np__1)\|~v1_xreal_0(k1_seq_1(esk5_0,esk4_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111, c_0_112]), c_0_113])])])). cnf(c_0_115, negated_conjecture, (~v1_xreal_0(k1_seq_1(esk5_0,esk4_0))\|~v1_xreal_0(np__1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114, c_0_68]), c_0_113])])])). cnf(c_0_116, plain, (m1_subset_1(np__1,k1_numbers)), inference(split_conjunct,[status(thm)],[spc1_numerals])). cnf(c_0_117, negated_conjecture, (~v1_xreal_0(np__1)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115, c_0_68]), c_0_113])])])). cnf(c_0_118, plain, (m1_subset_1(np__1,k1_numbers)), inference(evalgc,[status(thm)],[c_0_116])). cnf(c_0_119, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117, c_0_68]), c_0_118])]), ['proof']). # SZS output end CNFRefutation	reserve Omega for set; reserve m,n,k for Element of NAT; reserve x,y for set; reserve r,r1,r2,r3 for Real; reserve seq,seq1 for Real_Sequence; reserve Sigma for SigmaField of Omega; reserve ASeq,BSeq for SetSequence of Sigma; reserve A, B, C, A1, A2, A3 for Event of Sigma; reserve Omega for non empty set; reserve Sigma for SigmaField of Omega; reserve A, B, C, A1, A2, A3 for Event of Sigma; reserve ASeq,BSeq for SetSequence of Sigma; reserve P,P1,P2 for Probability of Sigma; theorem Th15: P.A + P.B - 1 <= P.(A /\ B) proof P.A + P.B - P.(A /\ B) = P.(A \/ B) by PROB_1:38; then P.A + P.B - P.(A /\ B) <= 1 by PROB_1:35; then P.A + P.B <= P.(A /\ B) + 1 by XREAL_1:20; hence thesis by XREAL_1:20; end;	Convert the following ATP output trace into a readable Mizar proof.
t8_relset_1	Proof found! # SZS status Theorem # SZS output start CNFRefutation fof(t8_relset_1, conjecture, ![X1, X2, X3]:(m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))=>r1_tarski(k1_relat_1(X3),k2_xboole_0(X1,X2))), file('/scratch/mptp/predsminms1/t8_relset_1__0', t8_relset_1)). fof(t13_xboole_1, axiom, ![X1, X2, X3, X4]:((r1_tarski(X1,X2)&r1_tarski(X3,X4))=>r1_tarski(k2_xboole_0(X1,X3),k2_xboole_0(X2,X4))), file('/scratch/mptp/predsminms1/t8_relset_1__0', t13_xboole_1)). fof(d6_relat_1, axiom, ![X1]:(v1_relat_1(X1)=>k1_relat_1(X1)=k2_xboole_0(k9_xtuple_0(X1),k10_xtuple_0(X1))), file('/scratch/mptp/predsminms1/t8_relset_1__0', d6_relat_1)). fof(cc2_relat_1, axiom, ![X1]:(v1_relat_1(X1)=>![X2]:(m1_subset_1(X2,k1_zfmisc_1(X1))=>v1_relat_1(X2))), file('/scratch/mptp/predsminms1/t8_relset_1__0', cc2_relat_1)). fof(fc6_relat_1, axiom, ![X1, X2]:v1_relat_1(k2_zfmisc_1(X1,X2)), file('/scratch/mptp/predsminms1/t8_relset_1__0', fc6_relat_1)). fof(t3_subset, axiom, ![X1, X2]:(m1_subset_1(X1,k1_zfmisc_1(X2))<=>r1_tarski(X1,X2)), file('/scratch/mptp/predsminms1/t8_relset_1__0', t3_subset)). fof(dt_k2_relset_1, axiom, ![X1, X2]:((v1_relat_1(X2)&v5_relat_1(X2,X1))=>m1_subset_1(k2_relset_1(X1,X2),k1_zfmisc_1(X1))), file('/scratch/mptp/predsminms1/t8_relset_1__0', dt_k2_relset_1)). fof(redefinition_k2_relset_1, axiom, ![X1, X2]:((v1_relat_1(X2)&v5_relat_1(X2,X1))=>k2_relset_1(X1,X2)=k10_xtuple_0(X2)), file('/scratch/mptp/predsminms1/t8_relset_1__0', redefinition_k2_relset_1)). fof(cc2_relset_1, axiom, ![X1, X2, X3]:(m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))=>(v4_relat_1(X3,X1)&v5_relat_1(X3,X2))), file('/scratch/mptp/predsminms1/t8_relset_1__0', cc2_relset_1)). fof(dt_k1_relset_1, axiom, ![X1, X2]:((v1_relat_1(X2)&v4_relat_1(X2,X1))=>m1_subset_1(k1_relset_1(X1,X2),k1_zfmisc_1(X1))), file('/scratch/mptp/predsminms1/t8_relset_1__0', dt_k1_relset_1)). fof(redefinition_k1_relset_1, axiom, ![X1, X2]:((v1_relat_1(X2)&v4_relat_1(X2,X1))=>k1_relset_1(X1,X2)=k9_xtuple_0(X2)), file('/scratch/mptp/predsminms1/t8_relset_1__0', redefinition_k1_relset_1)). fof(c_0_11, negated_conjecture, ~(![X1, X2, X3]:(m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))=>r1_tarski(k1_relat_1(X3),k2_xboole_0(X1,X2)))), inference(assume_negation,[status(cth)],[t8_relset_1])). fof(c_0_12, plain, ![X23, X24, X25, X26]:(~r1_tarski(X23,X24)\|~r1_tarski(X25,X26)\|r1_tarski(k2_xboole_0(X23,X25),k2_xboole_0(X24,X26))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t13_xboole_1])])). fof(c_0_13, plain, ![X27]:(~v1_relat_1(X27)\|k1_relat_1(X27)=k2_xboole_0(k9_xtuple_0(X27),k10_xtuple_0(X27))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d6_relat_1])])). fof(c_0_14, plain, ![X15, X16]:(~v1_relat_1(X15)\|(~m1_subset_1(X16,k1_zfmisc_1(X15))\|v1_relat_1(X16))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_relat_1])])])). fof(c_0_15, negated_conjecture, (m1_subset_1(esk3_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,esk2_0)))&~r1_tarski(k1_relat_1(esk3_0),k2_xboole_0(esk1_0,esk2_0))), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])). fof(c_0_16, plain, ![X17, X18]:v1_relat_1(k2_zfmisc_1(X17,X18)), inference(variable_rename,[status(thm)],[fc6_relat_1])). cnf(c_0_17, plain, (r1_tarski(k2_xboole_0(X1,X3),k2_xboole_0(X2,X4))\|~r1_tarski(X1,X2)\|~r1_tarski(X3,X4)), inference(split_conjunct,[status(thm)],[c_0_12])). cnf(c_0_18, plain, (k1_relat_1(X1)=k2_xboole_0(k9_xtuple_0(X1),k10_xtuple_0(X1))\|~v1_relat_1(X1)), inference(split_conjunct,[status(thm)],[c_0_13])). cnf(c_0_19, plain, (v1_relat_1(X2)\|~v1_relat_1(X1)\|~m1_subset_1(X2,k1_zfmisc_1(X1))), inference(split_conjunct,[status(thm)],[c_0_14])). cnf(c_0_20, negated_conjecture, (m1_subset_1(esk3_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,esk2_0)))), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_21, plain, (v1_relat_1(k2_zfmisc_1(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_16])). cnf(c_0_22, negated_conjecture, (~r1_tarski(k1_relat_1(esk3_0),k2_xboole_0(esk1_0,esk2_0))), inference(split_conjunct,[status(thm)],[c_0_15])). cnf(c_0_23, plain, (r1_tarski(k2_xboole_0(X1,X3),k2_xboole_0(X2,X4))\|~r1_tarski(X3,X4)\|~r1_tarski(X1,X2)), inference(evalgc,[status(thm)],[c_0_17])). cnf(c_0_24, plain, (k2_xboole_0(k9_xtuple_0(X1),k10_xtuple_0(X1))=k1_relat_1(X1)\|~v1_relat_1(X1)), inference(evalgc,[status(thm)],[c_0_18])). cnf(c_0_25, plain, (v1_relat_1(X2)\|~v1_relat_1(X1)\|~m1_subset_1(X2,k1_zfmisc_1(X1))), inference(evalgc,[status(thm)],[c_0_19])). cnf(c_0_26, negated_conjecture, (m1_subset_1(esk3_0,k1_zfmisc_1(k2_zfmisc_1(esk1_0,esk2_0)))), inference(evalgc,[status(thm)],[c_0_20])). cnf(c_0_27, plain, (v1_relat_1(k2_zfmisc_1(X1,X2))), inference(evalgc,[status(thm)],[c_0_21])). fof(c_0_28, plain, ![X28, X29]:((~m1_subset_1(X28,k1_zfmisc_1(X29))\|r1_tarski(X28,X29))&(~r1_tarski(X28,X29)\|m1_subset_1(X28,k1_zfmisc_1(X29)))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])])). cnf(c_0_29, negated_conjecture, (~r1_tarski(k1_relat_1(esk3_0),k2_xboole_0(esk1_0,esk2_0))), inference(evalgc,[status(thm)],[c_0_22])). cnf(c_0_30, plain, (r1_tarski(k1_relat_1(X1),k2_xboole_0(X2,X3))\|~r1_tarski(k10_xtuple_0(X1),X3)\|~r1_tarski(k9_xtuple_0(X1),X2)\|~v1_relat_1(X1)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_23, c_0_24])])). cnf(c_0_31, negated_conjecture, (v1_relat_1(esk3_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25, c_0_26]), c_0_27])])])). cnf(c_0_32, plain, (r1_tarski(X1,X2)\|~m1_subset_1(X1,k1_zfmisc_1(X2))), inference(split_conjunct,[status(thm)],[c_0_28])). fof(c_0_33, plain, ![X8, X9]:(~v1_relat_1(X9)\|~v5_relat_1(X9,X8)\|m1_subset_1(k2_relset_1(X8,X9),k1_zfmisc_1(X8))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_relset_1])])). fof(c_0_34, plain, ![X10, X11]:(~v1_relat_1(X11)\|~v5_relat_1(X11,X10)\|k2_relset_1(X10,X11)=k10_xtuple_0(X11)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k2_relset_1])])). fof(c_0_35, plain, ![X12, X13, X14]:((v4_relat_1(X14,X12)\|~m1_subset_1(X14,k1_zfmisc_1(k2_zfmisc_1(X12,X13))))&(v5_relat_1(X14,X13)\|~m1_subset_1(X14,k1_zfmisc_1(k2_zfmisc_1(X12,X13))))), inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_relset_1])])])). cnf(c_0_36, negated_conjecture, (~r1_tarski(k10_xtuple_0(esk3_0),esk2_0)\|~r1_tarski(k9_xtuple_0(esk3_0),esk1_0)), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29, c_0_30]), c_0_31])])])). cnf(c_0_37, plain, (r1_tarski(X1,X2)\|~m1_subset_1(X1,k1_zfmisc_1(X2))), inference(evalgc,[status(thm)],[c_0_32])). cnf(c_0_38, plain, (m1_subset_1(k2_relset_1(X2,X1),k1_zfmisc_1(X2))\|~v1_relat_1(X1)\|~v5_relat_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_33])). cnf(c_0_39, plain, (k2_relset_1(X2,X1)=k10_xtuple_0(X1)\|~v1_relat_1(X1)\|~v5_relat_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_34])). cnf(c_0_40, plain, (v5_relat_1(X1,X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X3,X2)))), inference(split_conjunct,[status(thm)],[c_0_35])). fof(c_0_41, plain, ![X19, X20]:(~v1_relat_1(X20)\|~v4_relat_1(X20,X19)\|m1_subset_1(k1_relset_1(X19,X20),k1_zfmisc_1(X19))), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_relset_1])])). fof(c_0_42, plain, ![X21, X22]:(~v1_relat_1(X22)\|~v4_relat_1(X22,X21)\|k1_relset_1(X21,X22)=k9_xtuple_0(X22)), inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k1_relset_1])])). cnf(c_0_43, negated_conjecture, (~r1_tarski(k9_xtuple_0(esk3_0),esk1_0)\|~m1_subset_1(k10_xtuple_0(esk3_0),k1_zfmisc_1(esk2_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_36, c_0_37])])). cnf(c_0_44, plain, (m1_subset_1(k2_relset_1(X2,X1),k1_zfmisc_1(X2))\|~v1_relat_1(X1)\|~v5_relat_1(X1,X2)), inference(evalgc,[status(thm)],[c_0_38])). cnf(c_0_45, plain, (k2_relset_1(X2,X1)=k10_xtuple_0(X1)\|~v1_relat_1(X1)\|~v5_relat_1(X1,X2)), inference(evalgc,[status(thm)],[c_0_39])). cnf(c_0_46, plain, (v5_relat_1(X1,X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X3,X2)))), inference(evalgc,[status(thm)],[c_0_40])). cnf(c_0_47, plain, (m1_subset_1(k1_relset_1(X2,X1),k1_zfmisc_1(X2))\|~v1_relat_1(X1)\|~v4_relat_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_41])). cnf(c_0_48, plain, (k1_relset_1(X2,X1)=k9_xtuple_0(X1)\|~v1_relat_1(X1)\|~v4_relat_1(X1,X2)), inference(split_conjunct,[status(thm)],[c_0_42])). cnf(c_0_49, plain, (v4_relat_1(X1,X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(split_conjunct,[status(thm)],[c_0_35])). cnf(c_0_50, negated_conjecture, (~m1_subset_1(k10_xtuple_0(esk3_0),k1_zfmisc_1(esk2_0))\|~m1_subset_1(k9_xtuple_0(esk3_0),k1_zfmisc_1(esk1_0))), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_43, c_0_37])])). cnf(c_0_51, plain, (m1_subset_1(k10_xtuple_0(X2),k1_zfmisc_1(X1))\|~v5_relat_1(X2,X1)\|~v1_relat_1(X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_44, c_0_45])])). cnf(c_0_52, negated_conjecture, (v5_relat_1(esk3_0,esk2_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_46, c_0_26])])). cnf(c_0_53, plain, (m1_subset_1(k1_relset_1(X2,X1),k1_zfmisc_1(X2))\|~v1_relat_1(X1)\|~v4_relat_1(X1,X2)), inference(evalgc,[status(thm)],[c_0_47])). cnf(c_0_54, plain, (k1_relset_1(X2,X1)=k9_xtuple_0(X1)\|~v1_relat_1(X1)\|~v4_relat_1(X1,X2)), inference(evalgc,[status(thm)],[c_0_48])). cnf(c_0_55, plain, (v4_relat_1(X1,X2)\|~m1_subset_1(X1,k1_zfmisc_1(k2_zfmisc_1(X2,X3)))), inference(evalgc,[status(thm)],[c_0_49])). cnf(c_0_56, negated_conjecture, (~m1_subset_1(k9_xtuple_0(esk3_0),k1_zfmisc_1(esk1_0))), inference(evalgc,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50, c_0_51]), c_0_52]), c_0_31])])])). cnf(c_0_57, plain, (m1_subset_1(k9_xtuple_0(X2),k1_zfmisc_1(X1))\|~v4_relat_1(X2,X1)\|~v1_relat_1(X2)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_53, c_0_54])])). cnf(c_0_58, negated_conjecture, (v4_relat_1(esk3_0,esk1_0)), inference(evalgc,[status(thm)],[inference(spm,[status(thm)],[c_0_55, c_0_26])])). cnf(c_0_59, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56, c_0_57]), c_0_58]), c_0_31])]), ['proof']). # SZS output end CNFRefutation	reserve A,B,X,X1,Y,Y1,Y2,Z,a,x,y,z for set; reserve P,R for Relation of X,Y; theorem field R c= X \/ Y proof dom R \/ rng R c= X \/ Y by XBOOLE_1:13; hence thesis; end;	Convert the following ATP output trace into a readable Mizar proof.

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