[{"premise_expression": "\\frac{- M + v}{D}", "variable": "M", "positive": "\\frac{M (- M + 2 v)}{2 D}", "negatives": ["\\frac{v (- 2 M + v)}{2 D}", "\\frac{M (- M + 2 v^{D})}{2}", "\\frac{M (2 D + M)}{2 v}", "(- M + v) \\log{(D)}"], "srepr_premise_expression": "Mul(Pow(Symbol('D', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('M', commutative=True)), Symbol('v', commutative=True)))", "srepr_variable": "Symbol('M', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(-1)), Symbol('M', commutative=True), Add(Mul(Integer(-1), Symbol('M', commutative=True)), Mul(Integer(2), Symbol('v', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(-1)), Symbol('v', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('M', commutative=True)), Symbol('v', commutative=True)))", "Mul(Rational(1, 2), Symbol('M', commutative=True), Add(Mul(Integer(-1), Symbol('M', commutative=True)), Mul(Integer(2), Pow(Symbol('v', commutative=True), Symbol('D', commutative=True)))))", "Mul(Rational(1, 2), Symbol('M', commutative=True), Pow(Symbol('v', commutative=True), Integer(-1)), Add(Mul(Integer(2), Symbol('D', commutative=True)), Symbol('M', commutative=True)))", "Mul(Add(Mul(Integer(-1), Symbol('M', commutative=True)), Symbol('v', commutative=True)), log(Symbol('D', commutative=True)))"]}, {"premise_expression": "K + M - R", "variable": "K", "positive": "K (\\frac{K}{2} + M - R)", "negatives": ["\\frac{K (- K + 2 M + 2 R)}{2}", "\\frac{M (2 K + M - 2 R)}{2}", "\\frac{R (2 K + 2 M - R)}{2}", "\\frac{K (K M + 2 R)}{2}"], "srepr_premise_expression": "Add(Symbol('K', commutative=True), Symbol('M', commutative=True), Mul(Integer(-1), Symbol('R', commutative=True)))", "srepr_variable": "Symbol('K', commutative=True)", "srepr_positive": "Mul(Symbol('K', commutative=True), Add(Mul(Rational(1, 2), Symbol('K', commutative=True)), Symbol('M', commutative=True), Mul(Integer(-1), Symbol('R', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Mul(Integer(-1), Symbol('K', commutative=True)), Mul(Integer(2), Symbol('M', commutative=True)), Mul(Integer(2), Symbol('R', commutative=True))))", "Mul(Rational(1, 2), Symbol('M', commutative=True), Add(Mul(Integer(2), Symbol('K', commutative=True)), Symbol('M', commutative=True), Mul(Integer(-1), Integer(2), Symbol('R', commutative=True))))", "Mul(Rational(1, 2), Symbol('R', commutative=True), Add(Mul(Integer(2), Symbol('K', commutative=True)), Mul(Integer(2), Symbol('M', commutative=True)), Mul(Integer(-1), Symbol('R', commutative=True))))", "Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Mul(Symbol('K', commutative=True), Symbol('M', commutative=True)), Mul(Integer(2), Symbol('R', commutative=True))))"]}, {"premise_expression": "J + \\sin{(V)}", "variable": "J", "positive": "\\frac{J (J + 2 \\sin{(V)})}{2}", "negatives": ["\\frac{J (J + 2 e^{V})}{2}", "\\frac{J (J - 2 V)}{2}", "J V + \\sin{(J)}", "\\frac{J^{2} e^{V}}{2}"], "srepr_premise_expression": "Add(Symbol('J', commutative=True), sin(Symbol('V', commutative=True)))", "srepr_variable": "Symbol('J', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('J', commutative=True), Add(Symbol('J', commutative=True), Mul(Integer(2), sin(Symbol('V', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('J', commutative=True), Add(Symbol('J', commutative=True), Mul(Integer(2), exp(Symbol('V', commutative=True)))))", "Mul(Rational(1, 2), Symbol('J', commutative=True), Add(Symbol('J', commutative=True), Mul(Integer(-1), Integer(2), Symbol('V', commutative=True))))", "Add(Mul(Symbol('J', commutative=True), Symbol('V', commutative=True)), sin(Symbol('J', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('J', commutative=True), Integer(2)), exp(Symbol('V', commutative=True)))"]}, {"premise_expression": "E N", "variable": "E", "positive": "\\frac{E^{2} N}{2}", "negatives": ["\\frac{E N^{2}}{2}", "\\frac{E^{2} \\log{(N)}}{2}", "\\frac{E (E - 2 N)}{2}", "N \\log{(E)}"], "srepr_premise_expression": "Mul(Symbol('E', commutative=True), Symbol('N', commutative=True))", "srepr_variable": "Symbol('E', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('E', commutative=True), Integer(2)), Symbol('N', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('E', commutative=True), Pow(Symbol('N', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('E', commutative=True), Integer(2)), log(Symbol('N', commutative=True)))", "Mul(Rational(1, 2), Symbol('E', commutative=True), Add(Symbol('E', commutative=True), Mul(Integer(-1), Integer(2), Symbol('N', commutative=True))))", "Mul(Symbol('N', commutative=True), log(Symbol('E', commutative=True)))"]}, {"premise_expression": "- C + \\log{(K)}", "variable": "K", "positive": "K (- C + \\log{(K)} - 1)", "negatives": ["K (\\log{(\\frac{K}{C})} - 1)", "\\frac{C (- C + 2 \\log{(K)})}{2}", "\\frac{K (K + 2 \\log{(C)})}{2}", "e^{C} \\log{(K)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('C', commutative=True)), log(Symbol('K', commutative=True)))", "srepr_variable": "Symbol('K', commutative=True)", "srepr_positive": "Mul(Symbol('K', commutative=True), Add(Mul(Integer(-1), Symbol('C', commutative=True)), log(Symbol('K', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('K', commutative=True), Add(log(Mul(Pow(Symbol('C', commutative=True), Integer(-1)), Symbol('K', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Mul(Integer(-1), Symbol('C', commutative=True)), Mul(Integer(2), log(Symbol('K', commutative=True)))))", "Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Symbol('K', commutative=True), Mul(Integer(2), log(Symbol('C', commutative=True)))))", "Mul(exp(Symbol('C', commutative=True)), log(Symbol('K', commutative=True)))"]}, {"premise_expression": "\\log{(- P + V)}", "variable": "V", "positive": "- P \\log{(- P + V)} + V \\log{(- P + V)} - V", "negatives": ["P \\log{(- P + V)} - P - V \\log{(P - V)}", "P V (\\log{(V)} - 1)", "V (- P + \\sin{(P)})", "V (\\log{(\\frac{V}{P})} - 1)"], "srepr_premise_expression": "log(Add(Mul(Integer(-1), Symbol('P', commutative=True)), Symbol('V', commutative=True)))", "srepr_variable": "Symbol('V', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('P', commutative=True), log(Add(Mul(Integer(-1), Symbol('P', commutative=True)), Symbol('V', commutative=True)))), Mul(Symbol('V', commutative=True), log(Add(Mul(Integer(-1), Symbol('P', commutative=True)), Symbol('V', commutative=True)))), Mul(Integer(-1), Symbol('V', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('P', commutative=True), log(Add(Mul(Integer(-1), Symbol('P', commutative=True)), Symbol('V', commutative=True)))), Mul(Integer(-1), Symbol('P', commutative=True)), Mul(Integer(-1), Symbol('V', commutative=True), log(Add(Symbol('P', commutative=True), Mul(Integer(-1), Symbol('V', commutative=True))))))", "Mul(Symbol('P', commutative=True), Symbol('V', commutative=True), Add(log(Symbol('V', commutative=True)), Integer(-1)))", "Mul(Symbol('V', commutative=True), Add(Mul(Integer(-1), Symbol('P', commutative=True)), sin(Symbol('P', commutative=True))))", "Mul(Symbol('V', commutative=True), Add(log(Mul(Pow(Symbol('P', commutative=True), Integer(-1)), Symbol('V', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\log{(I + o)}", "variable": "o", "positive": "I \\log{(I + o)} + o \\log{(I + o)} - o", "negatives": ["I \\log{(I + o)} - I + o \\log{(I + o)}", "o (\\log{(\\frac{I}{o})} + 1)", "\\frac{o (o + 2 \\sin{(I)})}{2}", "o (- I + \\log{(o^{I})})"], "srepr_premise_expression": "log(Add(Symbol('I', commutative=True), Symbol('o', commutative=True)))", "srepr_variable": "Symbol('o', commutative=True)", "srepr_positive": "Add(Mul(Symbol('I', commutative=True), log(Add(Symbol('I', commutative=True), Symbol('o', commutative=True)))), Mul(Symbol('o', commutative=True), log(Add(Symbol('I', commutative=True), Symbol('o', commutative=True)))), Mul(Integer(-1), Symbol('o', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('I', commutative=True), log(Add(Symbol('I', commutative=True), Symbol('o', commutative=True)))), Mul(Integer(-1), Symbol('I', commutative=True)), Mul(Symbol('o', commutative=True), log(Add(Symbol('I', commutative=True), Symbol('o', commutative=True)))))", "Mul(Symbol('o', commutative=True), Add(log(Mul(Symbol('I', commutative=True), Pow(Symbol('o', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Symbol('o', commutative=True), Mul(Integer(2), sin(Symbol('I', commutative=True)))))", "Mul(Symbol('o', commutative=True), Add(Mul(Integer(-1), Symbol('I', commutative=True)), log(Pow(Symbol('o', commutative=True), Symbol('I', commutative=True)))))"]}, {"premise_expression": "\\frac{\\cos{(E)}}{g}", "variable": "g", "positive": "\\log{(g)} \\cos{(E)}", "negatives": ["E g + \\sin{(g)}", "\\cos{(E - g)}", "\\frac{\\sin{(E)}}{g}", "g (\\log{(\\frac{E}{g})} + 1)"], "srepr_premise_expression": "Mul(Pow(Symbol('g', commutative=True), Integer(-1)), cos(Symbol('E', commutative=True)))", "srepr_variable": "Symbol('g', commutative=True)", "srepr_positive": "Mul(log(Symbol('g', commutative=True)), cos(Symbol('E', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('E', commutative=True), Symbol('g', commutative=True)), sin(Symbol('g', commutative=True)))", "cos(Add(Symbol('E', commutative=True), Mul(Integer(-1), Symbol('g', commutative=True))))", "Mul(Pow(Symbol('g', commutative=True), Integer(-1)), sin(Symbol('E', commutative=True)))", "Mul(Symbol('g', commutative=True), Add(log(Mul(Symbol('E', commutative=True), Pow(Symbol('g', commutative=True), Integer(-1)))), Integer(1)))"]}, {"premise_expression": "C - F", "variable": "C", "positive": "\\frac{C (C - 2 F)}{2}", "negatives": ["\\frac{F (2 C - F)}{2}", "\\frac{C^{2}}{2 F}", "\\frac{C^{2} \\log{(F)}}{2}", "C F + e^{C}"], "srepr_premise_expression": "Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('F', commutative=True)))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Symbol('C', commutative=True), Mul(Integer(-1), Integer(2), Symbol('F', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Mul(Integer(2), Symbol('C', commutative=True)), Mul(Integer(-1), Symbol('F', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2)), Pow(Symbol('F', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2)), log(Symbol('F', commutative=True)))", "Add(Mul(Symbol('C', commutative=True), Symbol('F', commutative=True)), exp(Symbol('C', commutative=True)))"]}, {"premise_expression": "\\frac{K}{J f}", "variable": "J", "positive": "\\frac{K \\log{(J)}}{f}", "negatives": ["\\frac{K \\log{(f)}}{J}", "K f \\log{(J)}", "f^{K} \\log{(J)}", "\\frac{K^{2}}{2 J f}"], "srepr_premise_expression": "Mul(Pow(Symbol('J', commutative=True), Integer(-1)), Symbol('K', commutative=True), Pow(Symbol('f', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('J', commutative=True)", "srepr_positive": "Mul(Symbol('K', commutative=True), Pow(Symbol('f', commutative=True), Integer(-1)), log(Symbol('J', commutative=True)))", "srepr_negatives": ["Mul(Pow(Symbol('J', commutative=True), Integer(-1)), Symbol('K', commutative=True), log(Symbol('f', commutative=True)))", "Mul(Symbol('K', commutative=True), Symbol('f', commutative=True), log(Symbol('J', commutative=True)))", "Mul(Pow(Symbol('f', commutative=True), Symbol('K', commutative=True)), log(Symbol('J', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('J', commutative=True), Integer(-1)), Pow(Symbol('K', commutative=True), Integer(2)), Pow(Symbol('f', commutative=True), Integer(-1)))"]}, {"premise_expression": "- \\sin{(D - J)}", "variable": "D", "positive": "\\cos{(D - J)}", "negatives": ["- \\cos{(D - J)}", "J \\log{(D)}", "\\frac{D (\\log{(D)} - 1)}{J}", "\\frac{D^{2} J}{2}"], "srepr_premise_expression": "Mul(Integer(-1), sin(Add(Symbol('D', commutative=True), Mul(Integer(-1), Symbol('J', commutative=True)))))", "srepr_variable": "Symbol('D', commutative=True)", "srepr_positive": "cos(Add(Symbol('D', commutative=True), Mul(Integer(-1), Symbol('J', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('D', commutative=True), Mul(Integer(-1), Symbol('J', commutative=True)))))", "Mul(Symbol('J', commutative=True), log(Symbol('D', commutative=True)))", "Mul(Symbol('D', commutative=True), Pow(Symbol('J', commutative=True), Integer(-1)), Add(log(Symbol('D', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(2)), Symbol('J', commutative=True))"]}, {"premise_expression": "\\frac{B + M}{B}", "variable": "M", "positive": "M + \\frac{M^{2}}{2 B}", "negatives": ["B + M \\log{(B)}", "\\frac{B M^{2}}{2}", "\\frac{B M^{3}}{3}", "- B M + e^{M}"], "srepr_premise_expression": "Mul(Pow(Symbol('B', commutative=True), Integer(-1)), Add(Symbol('B', commutative=True), Symbol('M', commutative=True)))", "srepr_variable": "Symbol('M', commutative=True)", "srepr_positive": "Add(Symbol('M', commutative=True), Mul(Rational(1, 2), Pow(Symbol('B', commutative=True), Integer(-1)), Pow(Symbol('M', commutative=True), Integer(2))))", "srepr_negatives": ["Add(Symbol('B', commutative=True), Mul(Symbol('M', commutative=True), log(Symbol('B', commutative=True))))", "Mul(Rational(1, 2), Symbol('B', commutative=True), Pow(Symbol('M', commutative=True), Integer(2)))", "Mul(Rational(1, 3), Symbol('B', commutative=True), Pow(Symbol('M', commutative=True), Integer(3)))", "Add(Mul(Integer(-1), Symbol('B', commutative=True), Symbol('M', commutative=True)), exp(Symbol('M', commutative=True)))"]}, {"premise_expression": "U - x", "variable": "U", "positive": "\\frac{U (U - 2 x)}{2}", "negatives": ["\\frac{x (2 U - x)}{2}", "\\sin{(U - x)}", "e^{U + x}", "- \\cos{(U - x)}"], "srepr_premise_expression": "Add(Symbol('U', commutative=True), Mul(Integer(-1), Symbol('x', commutative=True)))", "srepr_variable": "Symbol('U', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('U', commutative=True), Add(Symbol('U', commutative=True), Mul(Integer(-1), Integer(2), Symbol('x', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('x', commutative=True), Add(Mul(Integer(2), Symbol('U', commutative=True)), Mul(Integer(-1), Symbol('x', commutative=True))))", "sin(Add(Symbol('U', commutative=True), Mul(Integer(-1), Symbol('x', commutative=True))))", "exp(Add(Symbol('U', commutative=True), Symbol('x', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('U', commutative=True), Mul(Integer(-1), Symbol('x', commutative=True)))))"]}, {"premise_expression": "P a^{j}", "variable": "P", "positive": "\\frac{P^{2} a^{j}}{2}", "negatives": ["\\frac{P^{2} a j}{2}", "\\frac{P^{2} a^{2}}{2}", "\\frac{P^{2}}{2 a} + P", "\\frac{P (P j + 2 a)}{2}"], "srepr_premise_expression": "Mul(Symbol('P', commutative=True), Pow(Symbol('a', commutative=True), Symbol('j', commutative=True)))", "srepr_variable": "Symbol('P', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2)), Pow(Symbol('a', commutative=True), Symbol('j', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2)), Symbol('a', commutative=True), Symbol('j', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2)), Pow(Symbol('a', commutative=True), Integer(2)))", "Add(Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2)), Pow(Symbol('a', commutative=True), Integer(-1))), Symbol('P', commutative=True))", "Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Mul(Symbol('P', commutative=True), Symbol('j', commutative=True)), Mul(Integer(2), Symbol('a', commutative=True))))"]}, {"premise_expression": "\\cos{(\\frac{h}{Y})}", "variable": "Y", "positive": "Y \\cos{(\\frac{h}{Y})} + h \\operatorname{Si}{(\\frac{h}{Y})}", "negatives": ["Y (\\log{(\\frac{h}{Y})} + 1)", "\\frac{Y (\\log{(Y)} - 1)}{h}", "Y h - \\cos{(Y)}", "\\frac{Y (Y + 2 \\cos{(h)})}{2}"], "srepr_premise_expression": "cos(Mul(Pow(Symbol('Y', commutative=True), Integer(-1)), Symbol('h', commutative=True)))", "srepr_variable": "Symbol('Y', commutative=True)", "srepr_positive": "Add(Mul(Symbol('Y', commutative=True), cos(Mul(Pow(Symbol('Y', commutative=True), Integer(-1)), Symbol('h', commutative=True)))), Mul(Symbol('h', commutative=True), Si(Mul(Pow(Symbol('Y', commutative=True), Integer(-1)), Symbol('h', commutative=True)))))", "srepr_negatives": ["Mul(Symbol('Y', commutative=True), Add(log(Mul(Pow(Symbol('Y', commutative=True), Integer(-1)), Symbol('h', commutative=True))), Integer(1)))", "Mul(Symbol('Y', commutative=True), Pow(Symbol('h', commutative=True), Integer(-1)), Add(log(Symbol('Y', commutative=True)), Integer(-1)))", "Add(Mul(Symbol('Y', commutative=True), Symbol('h', commutative=True)), Mul(Integer(-1), cos(Symbol('Y', commutative=True))))", "Mul(Rational(1, 2), Symbol('Y', commutative=True), Add(Symbol('Y', commutative=True), Mul(Integer(2), cos(Symbol('h', commutative=True)))))"]}, {"premise_expression": "\\frac{- X + q}{p}", "variable": "X", "positive": "\\frac{X (- X + 2 q)}{2 p}", "negatives": ["\\frac{q (- 2 X + q)}{2 p}", "\\frac{X (X + 2 p q)}{2}", "\\frac{X q (X + 2 p)}{2}", "(- X + q) \\log{(p)}"], "srepr_premise_expression": "Mul(Pow(Symbol('p', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('X', commutative=True)), Symbol('q', commutative=True)))", "srepr_variable": "Symbol('X', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('X', commutative=True), Pow(Symbol('p', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('X', commutative=True)), Mul(Integer(2), Symbol('q', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('p', commutative=True), Integer(-1)), Symbol('q', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('X', commutative=True)), Symbol('q', commutative=True)))", "Mul(Rational(1, 2), Symbol('X', commutative=True), Add(Symbol('X', commutative=True), Mul(Integer(2), Symbol('p', commutative=True), Symbol('q', commutative=True))))", "Mul(Rational(1, 2), Symbol('X', commutative=True), Symbol('q', commutative=True), Add(Symbol('X', commutative=True), Mul(Integer(2), Symbol('p', commutative=True))))", "Mul(Add(Mul(Integer(-1), Symbol('X', commutative=True)), Symbol('q', commutative=True)), log(Symbol('p', commutative=True)))"]}, {"premise_expression": "\\log{(\\frac{F}{z})}", "variable": "F", "positive": "F (\\log{(\\frac{F}{z})} - 1)", "negatives": ["F (\\log{(F z)} - 1)", "z (\\log{(\\frac{F}{z})} + 1)", "F (\\log{(\\frac{z}{F})} + 1)", "F (- z + \\log{(F)} - 1)"], "srepr_premise_expression": "log(Mul(Symbol('F', commutative=True), Pow(Symbol('z', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('F', commutative=True)", "srepr_positive": "Mul(Symbol('F', commutative=True), Add(log(Mul(Symbol('F', commutative=True), Pow(Symbol('z', commutative=True), Integer(-1)))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('F', commutative=True), Add(log(Mul(Symbol('F', commutative=True), Symbol('z', commutative=True))), Integer(-1)))", "Mul(Symbol('z', commutative=True), Add(log(Mul(Symbol('F', commutative=True), Pow(Symbol('z', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Symbol('F', commutative=True), Add(log(Mul(Pow(Symbol('F', commutative=True), Integer(-1)), Symbol('z', commutative=True))), Integer(1)))", "Mul(Symbol('F', commutative=True), Add(Mul(Integer(-1), Symbol('z', commutative=True)), log(Symbol('F', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\cos{(G + q)}", "variable": "q", "positive": "\\sin{(G + q)}", "negatives": ["e^{G + q}", "q \\sin{(1)}", "\\frac{q (2 G - q)}{2}", "\\frac{G q^{2}}{2}"], "srepr_premise_expression": "cos(Add(Symbol('G', commutative=True), Symbol('q', commutative=True)))", "srepr_variable": "Symbol('q', commutative=True)", "srepr_positive": "sin(Add(Symbol('G', commutative=True), Symbol('q', commutative=True)))", "srepr_negatives": ["exp(Add(Symbol('G', commutative=True), Symbol('q', commutative=True)))", "Mul(Symbol('q', commutative=True), sin(Integer(1)))", "Mul(Rational(1, 2), Symbol('q', commutative=True), Add(Mul(Integer(2), Symbol('G', commutative=True)), Mul(Integer(-1), Symbol('q', commutative=True))))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Pow(Symbol('q', commutative=True), Integer(2)))"]}, {"premise_expression": "\\frac{g}{n}", "variable": "g", "positive": "\\frac{g^{2}}{2 n}", "negatives": ["g \\log{(n)}", "n e^{g}", "\\frac{g (- g + 2 n)}{2}", "- \\cos{(g - n)}"], "srepr_premise_expression": "Mul(Symbol('g', commutative=True), Pow(Symbol('n', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('g', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('g', commutative=True), Integer(2)), Pow(Symbol('n', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('g', commutative=True), log(Symbol('n', commutative=True)))", "Mul(Symbol('n', commutative=True), exp(Symbol('g', commutative=True)))", "Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Mul(Integer(-1), Symbol('g', commutative=True)), Mul(Integer(2), Symbol('n', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('g', commutative=True), Mul(Integer(-1), Symbol('n', commutative=True)))))"]}, {"premise_expression": "- Z + \\sin{(k)}", "variable": "k", "positive": "- Z k - \\cos{(k)}", "negatives": ["\\log{(Z)} \\log{(k)}", "e^{Z + k}", "Z k (\\log{(k)} - 1)", "\\frac{k^{2}}{2 Z}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('Z', commutative=True)), sin(Symbol('k', commutative=True)))", "srepr_variable": "Symbol('k', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('Z', commutative=True), Symbol('k', commutative=True)), Mul(Integer(-1), cos(Symbol('k', commutative=True))))", "srepr_negatives": ["Mul(log(Symbol('Z', commutative=True)), log(Symbol('k', commutative=True)))", "exp(Add(Symbol('Z', commutative=True), Symbol('k', commutative=True)))", "Mul(Symbol('Z', commutative=True), Symbol('k', commutative=True), Add(log(Symbol('k', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('Z', commutative=True), Integer(-1)), Pow(Symbol('k', commutative=True), Integer(2)))"]}, {"premise_expression": "l + q", "variable": "l", "positive": "\\frac{l (l + 2 q)}{2}", "negatives": ["\\frac{l (- l + 2 q)}{2}", "\\frac{q (2 l + q)}{2}", "\\frac{l^{2} \\log{(q)}}{2}", "q \\log{(l)}"], "srepr_premise_expression": "Add(Symbol('l', commutative=True), Symbol('q', commutative=True))", "srepr_variable": "Symbol('l', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('l', commutative=True), Add(Symbol('l', commutative=True), Mul(Integer(2), Symbol('q', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('l', commutative=True), Add(Mul(Integer(-1), Symbol('l', commutative=True)), Mul(Integer(2), Symbol('q', commutative=True))))", "Mul(Rational(1, 2), Symbol('q', commutative=True), Add(Mul(Integer(2), Symbol('l', commutative=True)), Symbol('q', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('l', commutative=True), Integer(2)), log(Symbol('q', commutative=True)))", "Mul(Symbol('q', commutative=True), log(Symbol('l', commutative=True)))"]}, {"premise_expression": "a + \\cos{(f)}", "variable": "f", "positive": "a f + \\sin{(f)}", "negatives": ["- a \\cos{(f)}", "\\log{(f)} \\sin{(a)}", "\\frac{f (f + 2 \\sin{(a)})}{2}", "\\frac{f (- f + 2 \\sin{(a)})}{2}"], "srepr_premise_expression": "Add(Symbol('a', commutative=True), cos(Symbol('f', commutative=True)))", "srepr_variable": "Symbol('f', commutative=True)", "srepr_positive": "Add(Mul(Symbol('a', commutative=True), Symbol('f', commutative=True)), sin(Symbol('f', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Symbol('a', commutative=True), cos(Symbol('f', commutative=True)))", "Mul(log(Symbol('f', commutative=True)), sin(Symbol('a', commutative=True)))", "Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Symbol('f', commutative=True), Mul(Integer(2), sin(Symbol('a', commutative=True)))))", "Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Mul(Integer(-1), Symbol('f', commutative=True)), Mul(Integer(2), sin(Symbol('a', commutative=True)))))"]}, {"premise_expression": "\\frac{n}{Y}", "variable": "Y", "positive": "n \\log{(Y)}", "negatives": ["\\frac{n^{2}}{2 Y}", "\\frac{Y^{2} n}{2}", "\\frac{Y^{2} \\log{(n)}}{2}", "\\frac{Y (\\log{(Y)} - 1)}{n}"], "srepr_premise_expression": "Mul(Pow(Symbol('Y', commutative=True), Integer(-1)), Symbol('n', commutative=True))", "srepr_variable": "Symbol('Y', commutative=True)", "srepr_positive": "Mul(Symbol('n', commutative=True), log(Symbol('Y', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('Y', commutative=True), Integer(-1)), Pow(Symbol('n', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('Y', commutative=True), Integer(2)), Symbol('n', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('Y', commutative=True), Integer(2)), log(Symbol('n', commutative=True)))", "Mul(Symbol('Y', commutative=True), Pow(Symbol('n', commutative=True), Integer(-1)), Add(log(Symbol('Y', commutative=True)), Integer(-1)))"]}, {"premise_expression": "E + f", "variable": "f", "positive": "\\frac{f (2 E + f)}{2}", "negatives": ["\\frac{E (E + 2 f)}{2}", "\\frac{f^{2} e^{E}}{2}", "e^{- E + f}", "\\frac{f (\\log{(f)} - 1)}{E}"], "srepr_premise_expression": "Add(Symbol('E', commutative=True), Symbol('f', commutative=True))", "srepr_variable": "Symbol('f', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Mul(Integer(2), Symbol('E', commutative=True)), Symbol('f', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('E', commutative=True), Add(Symbol('E', commutative=True), Mul(Integer(2), Symbol('f', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('f', commutative=True), Integer(2)), exp(Symbol('E', commutative=True)))", "exp(Add(Mul(Integer(-1), Symbol('E', commutative=True)), Symbol('f', commutative=True)))", "Mul(Pow(Symbol('E', commutative=True), Integer(-1)), Symbol('f', commutative=True), Add(log(Symbol('f', commutative=True)), Integer(-1)))"]}, {"premise_expression": "- S + x", "variable": "x", "positive": "\\frac{x (- 2 S + x)}{2}", "negatives": ["\\frac{S (- S + 2 x)}{2}", "\\frac{x^{2} \\sin{(S)}}{2}", "\\sin{(S + x)}", "- \\sin{(S - x)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('S', commutative=True)), Symbol('x', commutative=True))", "srepr_variable": "Symbol('x', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('x', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('S', commutative=True)), Symbol('x', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Mul(Integer(-1), Symbol('S', commutative=True)), Mul(Integer(2), Symbol('x', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('x', commutative=True), Integer(2)), sin(Symbol('S', commutative=True)))", "sin(Add(Symbol('S', commutative=True), Symbol('x', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('x', commutative=True)))))"]}, {"premise_expression": "\\frac{L}{o}", "variable": "L", "positive": "\\frac{L^{2}}{2 o}", "negatives": ["L \\log{(o)}", "\\frac{L^{2} \\sin{(o)}}{2}", "\\cos{(L - o)}", "\\frac{L^{2} (o - 1)}{2}"], "srepr_premise_expression": "Mul(Symbol('L', commutative=True), Pow(Symbol('o', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('L', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(2)), Pow(Symbol('o', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('L', commutative=True), log(Symbol('o', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(2)), sin(Symbol('o', commutative=True)))", "cos(Add(Symbol('L', commutative=True), Mul(Integer(-1), Symbol('o', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(2)), Add(Symbol('o', commutative=True), Integer(-1)))"]}, {"premise_expression": "\\frac{\\sin{(k)}}{H}", "variable": "H", "positive": "\\log{(H)} \\sin{(k)}", "negatives": ["- \\frac{\\cos{(H)}}{k}", "e^{H - k}", "H (\\log{(H k)} - 1)", "- \\frac{\\cos{(k)}}{H}"], "srepr_premise_expression": "Mul(Pow(Symbol('H', commutative=True), Integer(-1)), sin(Symbol('k', commutative=True)))", "srepr_variable": "Symbol('H', commutative=True)", "srepr_positive": "Mul(log(Symbol('H', commutative=True)), sin(Symbol('k', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Pow(Symbol('k', commutative=True), Integer(-1)), cos(Symbol('H', commutative=True)))", "exp(Add(Symbol('H', commutative=True), Mul(Integer(-1), Symbol('k', commutative=True))))", "Mul(Symbol('H', commutative=True), Add(log(Mul(Symbol('H', commutative=True), Symbol('k', commutative=True))), Integer(-1)))", "Mul(Integer(-1), Pow(Symbol('H', commutative=True), Integer(-1)), cos(Symbol('k', commutative=True)))"]}, {"premise_expression": "\\cos{(C - j)}", "variable": "j", "positive": "- \\sin{(C - j)}", "negatives": ["\\sin{(C - j)}", "- \\cos{(C - j)}", "e^{C + j}", "C j + e^{j}"], "srepr_premise_expression": "cos(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('j', commutative=True))))", "srepr_variable": "Symbol('j', commutative=True)", "srepr_positive": "Mul(Integer(-1), sin(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('j', commutative=True)))))", "srepr_negatives": ["sin(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('j', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('j', commutative=True)))))", "exp(Add(Symbol('C', commutative=True), Symbol('j', commutative=True)))", "Add(Mul(Symbol('C', commutative=True), Symbol('j', commutative=True)), exp(Symbol('j', commutative=True)))"]}, {"premise_expression": "e^{\\frac{L}{g}}", "variable": "L", "positive": "g e^{\\frac{L}{g}}", "negatives": ["e^{L - g}", "- e^{- L + g}", "\\frac{\\sin{(L)}}{g}", "\\frac{L (L + 2 g)}{2}"], "srepr_premise_expression": "exp(Mul(Symbol('L', commutative=True), Pow(Symbol('g', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('L', commutative=True)", "srepr_positive": "Mul(Symbol('g', commutative=True), exp(Mul(Symbol('L', commutative=True), Pow(Symbol('g', commutative=True), Integer(-1)))))", "srepr_negatives": ["exp(Add(Symbol('L', commutative=True), Mul(Integer(-1), Symbol('g', commutative=True))))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('L', commutative=True)), Symbol('g', commutative=True))))", "Mul(Pow(Symbol('g', commutative=True), Integer(-1)), sin(Symbol('L', commutative=True)))", "Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Symbol('L', commutative=True), Mul(Integer(2), Symbol('g', commutative=True))))"]}, {"premise_expression": "N W", "variable": "N", "positive": "\\frac{N^{2} W}{2}", "negatives": ["\\frac{N W^{2}}{2}", "\\frac{N (N + 2 W)}{2}", "W e^{N}", "e^{N - W}"], "srepr_premise_expression": "Mul(Symbol('N', commutative=True), Symbol('W', commutative=True))", "srepr_variable": "Symbol('N', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('N', commutative=True), Integer(2)), Symbol('W', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('N', commutative=True), Pow(Symbol('W', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Symbol('N', commutative=True), Mul(Integer(2), Symbol('W', commutative=True))))", "Mul(Symbol('W', commutative=True), exp(Symbol('N', commutative=True)))", "exp(Add(Symbol('N', commutative=True), Mul(Integer(-1), Symbol('W', commutative=True))))"]}, {"premise_expression": "R + y", "variable": "y", "positive": "\\frac{y (2 R + y)}{2}", "negatives": ["\\frac{R (R + 2 y)}{2}", "\\frac{y^{2} \\log{(R)}}{2}", "- \\cos{(R - y)}", "\\frac{R y^{2}}{2}"], "srepr_premise_expression": "Add(Symbol('R', commutative=True), Symbol('y', commutative=True))", "srepr_variable": "Symbol('y', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('y', commutative=True), Add(Mul(Integer(2), Symbol('R', commutative=True)), Symbol('y', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('R', commutative=True), Add(Symbol('R', commutative=True), Mul(Integer(2), Symbol('y', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('y', commutative=True), Integer(2)), log(Symbol('R', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('R', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True)))))", "Mul(Rational(1, 2), Symbol('R', commutative=True), Pow(Symbol('y', commutative=True), Integer(2)))"]}, {"premise_expression": "e^{E + h}", "variable": "h", "positive": "e^{E + h}", "negatives": ["\\frac{h (2 E - h)}{2}", "E h + e^{h}", "\\log{(E)} \\log{(h)}", "\\frac{h^{2} e^{E}}{2}"], "srepr_premise_expression": "exp(Add(Symbol('E', commutative=True), Symbol('h', commutative=True)))", "srepr_variable": "Symbol('h', commutative=True)", "srepr_positive": "exp(Add(Symbol('E', commutative=True), Symbol('h', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('h', commutative=True), Add(Mul(Integer(2), Symbol('E', commutative=True)), Mul(Integer(-1), Symbol('h', commutative=True))))", "Add(Mul(Symbol('E', commutative=True), Symbol('h', commutative=True)), exp(Symbol('h', commutative=True)))", "Mul(log(Symbol('E', commutative=True)), log(Symbol('h', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('h', commutative=True), Integer(2)), exp(Symbol('E', commutative=True)))"]}, {"premise_expression": "\\frac{\\cos{(n)}}{x}", "variable": "n", "positive": "\\frac{\\sin{(n)}}{x}", "negatives": ["\\frac{n^{3} x}{3}", "x \\log{(n)}", "- \\cos{(n + x)}", "\\frac{n (n - 2 x)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('x', commutative=True), Integer(-1)), cos(Symbol('n', commutative=True)))", "srepr_variable": "Symbol('n', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('x', commutative=True), Integer(-1)), sin(Symbol('n', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 3), Pow(Symbol('n', commutative=True), Integer(3)), Symbol('x', commutative=True))", "Mul(Symbol('x', commutative=True), log(Symbol('n', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('n', commutative=True), Symbol('x', commutative=True))))", "Mul(Rational(1, 2), Symbol('n', commutative=True), Add(Symbol('n', commutative=True), Mul(Integer(-1), Integer(2), Symbol('x', commutative=True))))"]}, {"premise_expression": "v e^{p}", "variable": "v", "positive": "\\frac{v^{2} e^{p}}{2}", "negatives": ["\\frac{v^{2} \\log{(p)}}{2}", "v e^{p}", "\\frac{v (2 p + v)}{2}", "e^{p + v}"], "srepr_premise_expression": "Mul(Symbol('v', commutative=True), exp(Symbol('p', commutative=True)))", "srepr_variable": "Symbol('v', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('v', commutative=True), Integer(2)), exp(Symbol('p', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('v', commutative=True), Integer(2)), log(Symbol('p', commutative=True)))", "Mul(Symbol('v', commutative=True), exp(Symbol('p', commutative=True)))", "Mul(Rational(1, 2), Symbol('v', commutative=True), Add(Mul(Integer(2), Symbol('p', commutative=True)), Symbol('v', commutative=True)))", "exp(Add(Symbol('p', commutative=True), Symbol('v', commutative=True)))"]}, {"premise_expression": "B + \\log{(Z)}", "variable": "Z", "positive": "Z (B + \\log{(Z)} - 1)", "negatives": ["\\frac{Z (\\log{(Z)} - 1)}{B}", "Z (\\log{(\\frac{B}{Z})} + 1)", "\\frac{B (B + 2 \\log{(Z)})}{2}", "B Z - \\cos{(Z)}"], "srepr_premise_expression": "Add(Symbol('B', commutative=True), log(Symbol('Z', commutative=True)))", "srepr_variable": "Symbol('Z', commutative=True)", "srepr_positive": "Mul(Symbol('Z', commutative=True), Add(Symbol('B', commutative=True), log(Symbol('Z', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Pow(Symbol('B', commutative=True), Integer(-1)), Symbol('Z', commutative=True), Add(log(Symbol('Z', commutative=True)), Integer(-1)))", "Mul(Symbol('Z', commutative=True), Add(log(Mul(Symbol('B', commutative=True), Pow(Symbol('Z', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Rational(1, 2), Symbol('B', commutative=True), Add(Symbol('B', commutative=True), Mul(Integer(2), log(Symbol('Z', commutative=True)))))", "Add(Mul(Symbol('B', commutative=True), Symbol('Z', commutative=True)), Mul(Integer(-1), cos(Symbol('Z', commutative=True))))"]}, {"premise_expression": "- R + e^{b}", "variable": "b", "positive": "- R b + e^{b}", "negatives": ["R b + e^{b}", "R e^{\\frac{b}{R}}", "\\frac{R (- R + 2 e^{b})}{2}", "\\frac{b (b + 2 e^{R})}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('R', commutative=True)), exp(Symbol('b', commutative=True)))", "srepr_variable": "Symbol('b', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('R', commutative=True), Symbol('b', commutative=True)), exp(Symbol('b', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('R', commutative=True), Symbol('b', commutative=True)), exp(Symbol('b', commutative=True)))", "Mul(Symbol('R', commutative=True), exp(Mul(Pow(Symbol('R', commutative=True), Integer(-1)), Symbol('b', commutative=True))))", "Mul(Rational(1, 2), Symbol('R', commutative=True), Add(Mul(Integer(-1), Symbol('R', commutative=True)), Mul(Integer(2), exp(Symbol('b', commutative=True)))))", "Mul(Rational(1, 2), Symbol('b', commutative=True), Add(Symbol('b', commutative=True), Mul(Integer(2), exp(Symbol('R', commutative=True)))))"]}, {"premise_expression": "- V + c", "variable": "c", "positive": "\\frac{c (- 2 V + c)}{2}", "negatives": ["\\frac{V (- V + 2 c)}{2}", "\\frac{c^{2} e^{V}}{2}", "\\frac{c^{2} \\log{(V)}}{2}", "- \\sin{(V - c)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('V', commutative=True)), Symbol('c', commutative=True))", "srepr_variable": "Symbol('c', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('c', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('V', commutative=True)), Symbol('c', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('V', commutative=True), Add(Mul(Integer(-1), Symbol('V', commutative=True)), Mul(Integer(2), Symbol('c', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('c', commutative=True), Integer(2)), exp(Symbol('V', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('c', commutative=True), Integer(2)), log(Symbol('V', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('V', commutative=True), Mul(Integer(-1), Symbol('c', commutative=True)))))"]}, {"premise_expression": "\\frac{H}{s}", "variable": "s", "positive": "H \\log{(s)}", "negatives": ["H \\sin{(s)}", "H e^{s}", "\\frac{H^{2}}{2 s}", "H s - \\cos{(s)}"], "srepr_premise_expression": "Mul(Symbol('H', commutative=True), Pow(Symbol('s', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('s', commutative=True)", "srepr_positive": "Mul(Symbol('H', commutative=True), log(Symbol('s', commutative=True)))", "srepr_negatives": ["Mul(Symbol('H', commutative=True), sin(Symbol('s', commutative=True)))", "Mul(Symbol('H', commutative=True), exp(Symbol('s', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('H', commutative=True), Integer(2)), Pow(Symbol('s', commutative=True), Integer(-1)))", "Add(Mul(Symbol('H', commutative=True), Symbol('s', commutative=True)), Mul(Integer(-1), cos(Symbol('s', commutative=True))))"]}, {"premise_expression": "\\log{(r + w)}", "variable": "w", "positive": "r \\log{(r + w)} + w \\log{(r + w)} - w", "negatives": ["r \\log{(r + w)} - r + w \\log{(r + w)}", "\\frac{w (- w + 2 \\log{(r)})}{2}", "\\frac{w (w + 2 \\sin{(r)})}{2}", "r \\log{(w)}"], "srepr_premise_expression": "log(Add(Symbol('r', commutative=True), Symbol('w', commutative=True)))", "srepr_variable": "Symbol('w', commutative=True)", "srepr_positive": "Add(Mul(Symbol('r', commutative=True), log(Add(Symbol('r', commutative=True), Symbol('w', commutative=True)))), Mul(Symbol('w', commutative=True), log(Add(Symbol('r', commutative=True), Symbol('w', commutative=True)))), Mul(Integer(-1), Symbol('w', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('r', commutative=True), log(Add(Symbol('r', commutative=True), Symbol('w', commutative=True)))), Mul(Integer(-1), Symbol('r', commutative=True)), Mul(Symbol('w', commutative=True), log(Add(Symbol('r', commutative=True), Symbol('w', commutative=True)))))", "Mul(Rational(1, 2), Symbol('w', commutative=True), Add(Mul(Integer(-1), Symbol('w', commutative=True)), Mul(Integer(2), log(Symbol('r', commutative=True)))))", "Mul(Rational(1, 2), Symbol('w', commutative=True), Add(Symbol('w', commutative=True), Mul(Integer(2), sin(Symbol('r', commutative=True)))))", "Mul(Symbol('r', commutative=True), log(Symbol('w', commutative=True)))"]}, {"premise_expression": "M u + p", "variable": "M", "positive": "\\frac{M (M u + 2 p)}{2}", "negatives": ["\\frac{u (M u + 2 p)}{2}", "\\frac{M (M u - 2 p)}{2}", "\\frac{p (2 M u + p)}{2}", "\\frac{M (- M - 2 p + 2 u)}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('M', commutative=True), Symbol('u', commutative=True)), Symbol('p', commutative=True))", "srepr_variable": "Symbol('M', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('M', commutative=True), Add(Mul(Symbol('M', commutative=True), Symbol('u', commutative=True)), Mul(Integer(2), Symbol('p', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Symbol('M', commutative=True), Symbol('u', commutative=True)), Mul(Integer(2), Symbol('p', commutative=True))))", "Mul(Rational(1, 2), Symbol('M', commutative=True), Add(Mul(Symbol('M', commutative=True), Symbol('u', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('p', commutative=True))))", "Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Mul(Integer(2), Symbol('M', commutative=True), Symbol('u', commutative=True)), Symbol('p', commutative=True)))", "Mul(Rational(1, 2), Symbol('M', commutative=True), Add(Mul(Integer(-1), Symbol('M', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('p', commutative=True)), Mul(Integer(2), Symbol('u', commutative=True))))"]}, {"premise_expression": "\\frac{\\log{(A)}}{E}", "variable": "A", "positive": "\\frac{A (\\log{(A)} - 1)}{E}", "negatives": ["A E (\\log{(A)} - 1)", "A (\\log{(\\frac{E}{A})} + 1)", "\\cos{(A - E)}", "\\log{(A)} \\log{(E)}"], "srepr_premise_expression": "Mul(Pow(Symbol('E', commutative=True), Integer(-1)), log(Symbol('A', commutative=True)))", "srepr_variable": "Symbol('A', commutative=True)", "srepr_positive": "Mul(Symbol('A', commutative=True), Pow(Symbol('E', commutative=True), Integer(-1)), Add(log(Symbol('A', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('A', commutative=True), Symbol('E', commutative=True), Add(log(Symbol('A', commutative=True)), Integer(-1)))", "Mul(Symbol('A', commutative=True), Add(log(Mul(Pow(Symbol('A', commutative=True), Integer(-1)), Symbol('E', commutative=True))), Integer(1)))", "cos(Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('E', commutative=True))))", "Mul(log(Symbol('A', commutative=True)), log(Symbol('E', commutative=True)))"]}, {"premise_expression": "S - Y", "variable": "S", "positive": "\\frac{S (S - 2 Y)}{2}", "negatives": ["\\frac{Y (2 S - Y)}{2}", "\\frac{S (S + 2 \\sin{(Y)})}{2}", "\\frac{S^{2} \\log{(Y)}}{2}", "S (\\log{(S Y)} - 1)"], "srepr_premise_expression": "Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('Y', commutative=True)))", "srepr_variable": "Symbol('S', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Symbol('S', commutative=True), Mul(Integer(-1), Integer(2), Symbol('Y', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('Y', commutative=True), Add(Mul(Integer(2), Symbol('S', commutative=True)), Mul(Integer(-1), Symbol('Y', commutative=True))))", "Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Symbol('S', commutative=True), Mul(Integer(2), sin(Symbol('Y', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('S', commutative=True), Integer(2)), log(Symbol('Y', commutative=True)))", "Mul(Symbol('S', commutative=True), Add(log(Mul(Symbol('S', commutative=True), Symbol('Y', commutative=True))), Integer(-1)))"]}, {"premise_expression": "I - S", "variable": "S", "positive": "\\frac{S (2 I - S)}{2}", "negatives": ["\\frac{I (I - 2 S)}{2}", "\\frac{S^{2} \\cos{(I)}}{2}", "\\frac{S^{2} e^{I}}{2}", "\\cos{(I - S)}"], "srepr_premise_expression": "Add(Symbol('I', commutative=True), Mul(Integer(-1), Symbol('S', commutative=True)))", "srepr_variable": "Symbol('S', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Mul(Integer(2), Symbol('I', commutative=True)), Mul(Integer(-1), Symbol('S', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('I', commutative=True), Add(Symbol('I', commutative=True), Mul(Integer(-1), Integer(2), Symbol('S', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('S', commutative=True), Integer(2)), cos(Symbol('I', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('S', commutative=True), Integer(2)), exp(Symbol('I', commutative=True)))", "cos(Add(Symbol('I', commutative=True), Mul(Integer(-1), Symbol('S', commutative=True))))"]}, {"premise_expression": "e^{C^{F}}", "variable": "C", "positive": "\\frac{e^{- \\frac{i \\pi}{F}} \\gamma(\\frac{1}{F}, C^{F} e^{i \\pi})}{F}", "negatives": ["C \\log{(C + F)} - C + F \\log{(C + F)}", "\\frac{C (\\log{(C)} - 1)}{F}", "\\frac{C (C + 2 \\sin{(F)})}{2}", "- e^{- C + F}"], "srepr_premise_expression": "exp(Pow(Symbol('C', commutative=True), Symbol('F', commutative=True)))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('F', commutative=True), Integer(-1)), exp(Mul(Integer(-1), I, pi, Pow(Symbol('F', commutative=True), Integer(-1)))), lowergamma(Pow(Symbol('F', commutative=True), Integer(-1)), Mul(Pow(Symbol('C', commutative=True), Symbol('F', commutative=True)), exp_polar(Mul(I, pi)))))", "srepr_negatives": ["Add(Mul(Symbol('C', commutative=True), log(Add(Symbol('C', commutative=True), Symbol('F', commutative=True)))), Mul(Integer(-1), Symbol('C', commutative=True)), Mul(Symbol('F', commutative=True), log(Add(Symbol('C', commutative=True), Symbol('F', commutative=True)))))", "Mul(Symbol('C', commutative=True), Pow(Symbol('F', commutative=True), Integer(-1)), Add(log(Symbol('C', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Symbol('C', commutative=True), Mul(Integer(2), sin(Symbol('F', commutative=True)))))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('C', commutative=True)), Symbol('F', commutative=True))))"]}, {"premise_expression": "\\frac{J S}{z}", "variable": "S", "positive": "\\frac{J S^{2}}{2 z}", "negatives": ["\\frac{J^{2} S}{2 z}", "J S \\log{(z)}", "\\frac{S (S + 2 z)}{2 J}", "\\frac{S (J S - 2 z)}{2}"], "srepr_premise_expression": "Mul(Symbol('J', commutative=True), Symbol('S', commutative=True), Pow(Symbol('z', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('S', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('J', commutative=True), Pow(Symbol('S', commutative=True), Integer(2)), Pow(Symbol('z', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('J', commutative=True), Integer(2)), Symbol('S', commutative=True), Pow(Symbol('z', commutative=True), Integer(-1)))", "Mul(Symbol('J', commutative=True), Symbol('S', commutative=True), log(Symbol('z', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('J', commutative=True), Integer(-1)), Symbol('S', commutative=True), Add(Symbol('S', commutative=True), Mul(Integer(2), Symbol('z', commutative=True))))", "Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Mul(Symbol('J', commutative=True), Symbol('S', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('z', commutative=True))))"]}, {"premise_expression": "- X + t w", "variable": "w", "positive": "\\frac{w (- 2 X + t w)}{2}", "negatives": ["\\frac{t (- 2 X + t w)}{2}", "\\frac{X (- X + 2 t w)}{2}", "\\frac{w^{2} (X + t)}{2}", "\\frac{w^{2}}{2} + \\frac{t w}{X}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('X', commutative=True)), Mul(Symbol('t', commutative=True), Symbol('w', commutative=True)))", "srepr_variable": "Symbol('w', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('w', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('X', commutative=True)), Mul(Symbol('t', commutative=True), Symbol('w', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('t', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('X', commutative=True)), Mul(Symbol('t', commutative=True), Symbol('w', commutative=True))))", "Mul(Rational(1, 2), Symbol('X', commutative=True), Add(Mul(Integer(-1), Symbol('X', commutative=True)), Mul(Integer(2), Symbol('t', commutative=True), Symbol('w', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('w', commutative=True), Integer(2)), Add(Symbol('X', commutative=True), Symbol('t', commutative=True)))", "Add(Mul(Rational(1, 2), Pow(Symbol('w', commutative=True), Integer(2))), Mul(Pow(Symbol('X', commutative=True), Integer(-1)), Symbol('t', commutative=True), Symbol('w', commutative=True)))"]}, {"premise_expression": "\\frac{D F}{R}", "variable": "D", "positive": "\\frac{D^{2} F}{2 R}", "negatives": ["\\frac{D F^{2}}{2 R}", "D F \\log{(R)}", "\\frac{D (D F - 2 R)}{2}", "\\frac{D (D R + 2 F)}{2}"], "srepr_premise_expression": "Mul(Symbol('D', commutative=True), Symbol('F', commutative=True), Pow(Symbol('R', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('D', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(2)), Symbol('F', commutative=True), Pow(Symbol('R', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('D', commutative=True), Pow(Symbol('F', commutative=True), Integer(2)), Pow(Symbol('R', commutative=True), Integer(-1)))", "Mul(Symbol('D', commutative=True), Symbol('F', commutative=True), log(Symbol('R', commutative=True)))", "Mul(Rational(1, 2), Symbol('D', commutative=True), Add(Mul(Symbol('D', commutative=True), Symbol('F', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('R', commutative=True))))", "Mul(Rational(1, 2), Symbol('D', commutative=True), Add(Mul(Symbol('D', commutative=True), Symbol('R', commutative=True)), Mul(Integer(2), Symbol('F', commutative=True))))"]}, {"premise_expression": "e^{\\frac{a}{u}}", "variable": "u", "positive": "- a \\operatorname{Ei}{(\\frac{a}{u})} + u e^{\\frac{a}{u}}", "negatives": ["a \\operatorname{Si}{(\\frac{a}{u})} + u \\cos{(\\frac{a}{u})}", "u e^{\\frac{a}{u}}", "\\frac{u (2 a + u)}{2}", "\\frac{u (2 a - u)}{2}"], "srepr_premise_expression": "exp(Mul(Symbol('a', commutative=True), Pow(Symbol('u', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('a', commutative=True), Ei(Mul(Symbol('a', commutative=True), Pow(Symbol('u', commutative=True), Integer(-1))))), Mul(Symbol('u', commutative=True), exp(Mul(Symbol('a', commutative=True), Pow(Symbol('u', commutative=True), Integer(-1))))))", "srepr_negatives": ["Add(Mul(Symbol('a', commutative=True), Si(Mul(Symbol('a', commutative=True), Pow(Symbol('u', commutative=True), Integer(-1))))), Mul(Symbol('u', commutative=True), cos(Mul(Symbol('a', commutative=True), Pow(Symbol('u', commutative=True), Integer(-1))))))", "Mul(Symbol('u', commutative=True), exp(Mul(Symbol('a', commutative=True), Pow(Symbol('u', commutative=True), Integer(-1)))))", "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(2), Symbol('a', commutative=True)), Symbol('u', commutative=True)))", "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(2), Symbol('a', commutative=True)), Mul(Integer(-1), Symbol('u', commutative=True))))"]}, {"premise_expression": "N + o", "variable": "o", "positive": "\\frac{o (2 N + o)}{2}", "negatives": ["\\frac{N (N + 2 o)}{2}", "\\frac{o^{2} e^{N}}{2}", "\\frac{o^{2} \\cos{(N)}}{2}", "o \\cos{(2 N)}"], "srepr_premise_expression": "Add(Symbol('N', commutative=True), Symbol('o', commutative=True))", "srepr_variable": "Symbol('o', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Mul(Integer(2), Symbol('N', commutative=True)), Symbol('o', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Symbol('N', commutative=True), Mul(Integer(2), Symbol('o', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('o', commutative=True), Integer(2)), exp(Symbol('N', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('o', commutative=True), Integer(2)), cos(Symbol('N', commutative=True)))", "Mul(Symbol('o', commutative=True), cos(Mul(Integer(2), Symbol('N', commutative=True))))"]}, {"premise_expression": "G + y", "variable": "G", "positive": "\\frac{G (G + 2 y)}{2}", "negatives": ["\\frac{y (2 G + y)}{2}", "\\frac{G (G + 2 \\sin{(y)})}{2}", "\\frac{G (G + 2 e^{y})}{2}", "\\frac{G (- G + 2 \\cos{(y)})}{2}"], "srepr_premise_expression": "Add(Symbol('G', commutative=True), Symbol('y', commutative=True))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Symbol('G', commutative=True), Mul(Integer(2), Symbol('y', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('y', commutative=True), Add(Mul(Integer(2), Symbol('G', commutative=True)), Symbol('y', commutative=True)))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Symbol('G', commutative=True), Mul(Integer(2), sin(Symbol('y', commutative=True)))))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Symbol('G', commutative=True), Mul(Integer(2), exp(Symbol('y', commutative=True)))))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Mul(Integer(-1), Symbol('G', commutative=True)), Mul(Integer(2), cos(Symbol('y', commutative=True)))))"]}, {"premise_expression": "- A + R", "variable": "R", "positive": "\\frac{R (- 2 A + R)}{2}", "negatives": ["\\frac{R (2 A + R)}{2}", "\\frac{A (- A + 2 R)}{2}", "\\frac{R^{2} \\cos{(A)}}{2}", "\\frac{R (- R + 2 \\sin{(A)})}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('A', commutative=True)), Symbol('R', commutative=True))", "srepr_variable": "Symbol('R', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('R', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('A', commutative=True)), Symbol('R', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('R', commutative=True), Add(Mul(Integer(2), Symbol('A', commutative=True)), Symbol('R', commutative=True)))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Mul(Integer(-1), Symbol('A', commutative=True)), Mul(Integer(2), Symbol('R', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('R', commutative=True), Integer(2)), cos(Symbol('A', commutative=True)))", "Mul(Rational(1, 2), Symbol('R', commutative=True), Add(Mul(Integer(-1), Symbol('R', commutative=True)), Mul(Integer(2), sin(Symbol('A', commutative=True)))))"]}, {"premise_expression": "K - p", "variable": "p", "positive": "\\frac{p (2 K - p)}{2}", "negatives": ["\\frac{K (K - 2 p)}{2}", "\\frac{p (\\log{(p)} - 1)}{K}", "\\frac{p^{2}}{2} - \\cos{(p)}", "e^{K} \\log{(p)}"], "srepr_premise_expression": "Add(Symbol('K', commutative=True), Mul(Integer(-1), Symbol('p', commutative=True)))", "srepr_variable": "Symbol('p', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Mul(Integer(2), Symbol('K', commutative=True)), Mul(Integer(-1), Symbol('p', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Symbol('K', commutative=True), Mul(Integer(-1), Integer(2), Symbol('p', commutative=True))))", "Mul(Pow(Symbol('K', commutative=True), Integer(-1)), Symbol('p', commutative=True), Add(log(Symbol('p', commutative=True)), Integer(-1)))", "Add(Mul(Rational(1, 2), Pow(Symbol('p', commutative=True), Integer(2))), Mul(Integer(-1), cos(Symbol('p', commutative=True))))", "Mul(exp(Symbol('K', commutative=True)), log(Symbol('p', commutative=True)))"]}, {"premise_expression": "F - p", "variable": "p", "positive": "\\frac{p (2 F - p)}{2}", "negatives": ["\\frac{p (2 F + p)}{2}", "\\frac{F (F - 2 p)}{2}", "\\frac{p^{2} \\sin{(F)}}{2}", "\\frac{p^{2} e^{F}}{2}"], "srepr_premise_expression": "Add(Symbol('F', commutative=True), Mul(Integer(-1), Symbol('p', commutative=True)))", "srepr_variable": "Symbol('p', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Mul(Integer(2), Symbol('F', commutative=True)), Mul(Integer(-1), Symbol('p', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Mul(Integer(2), Symbol('F', commutative=True)), Symbol('p', commutative=True)))", "Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Symbol('F', commutative=True), Mul(Integer(-1), Integer(2), Symbol('p', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('p', commutative=True), Integer(2)), sin(Symbol('F', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('p', commutative=True), Integer(2)), exp(Symbol('F', commutative=True)))"]}, {"premise_expression": "g + r", "variable": "r", "positive": "\\frac{r (2 g + r)}{2}", "negatives": ["\\frac{g (g + 2 r)}{2}", "\\frac{r^{2} e^{g}}{2}", "g \\log{(r)}", "r (\\log{(\\frac{g}{r})} + 1)"], "srepr_premise_expression": "Add(Symbol('g', commutative=True), Symbol('r', commutative=True))", "srepr_variable": "Symbol('r', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(2), Symbol('g', commutative=True)), Symbol('r', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Symbol('g', commutative=True), Mul(Integer(2), Symbol('r', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('r', commutative=True), Integer(2)), exp(Symbol('g', commutative=True)))", "Mul(Symbol('g', commutative=True), log(Symbol('r', commutative=True)))", "Mul(Symbol('r', commutative=True), Add(log(Mul(Symbol('g', commutative=True), Pow(Symbol('r', commutative=True), Integer(-1)))), Integer(1)))"]}, {"premise_expression": "\\log{(I^{p})}", "variable": "I", "positive": "I (- p + \\log{(I^{p})})", "negatives": ["I (\\log{(I p)} - 1)", "\\frac{I^{2} \\log{(p)}}{2}", "I (\\log{(\\frac{I}{p})} - 1)", "\\frac{p^{2} \\log{(I)}}{2}"], "srepr_premise_expression": "log(Pow(Symbol('I', commutative=True), Symbol('p', commutative=True)))", "srepr_variable": "Symbol('I', commutative=True)", "srepr_positive": "Mul(Symbol('I', commutative=True), Add(Mul(Integer(-1), Symbol('p', commutative=True)), log(Pow(Symbol('I', commutative=True), Symbol('p', commutative=True)))))", "srepr_negatives": ["Mul(Symbol('I', commutative=True), Add(log(Mul(Symbol('I', commutative=True), Symbol('p', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(2)), log(Symbol('p', commutative=True)))", "Mul(Symbol('I', commutative=True), Add(log(Mul(Symbol('I', commutative=True), Pow(Symbol('p', commutative=True), Integer(-1)))), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('p', commutative=True), Integer(2)), log(Symbol('I', commutative=True)))"]}, {"premise_expression": "\\frac{D}{W}", "variable": "W", "positive": "D \\log{(W)}", "negatives": ["\\frac{D^{2}}{2 W}", "D W + e^{W}", "D W + \\sin{(W)}", "- D W + \\sin{(W)}"], "srepr_premise_expression": "Mul(Symbol('D', commutative=True), Pow(Symbol('W', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('W', commutative=True)", "srepr_positive": "Mul(Symbol('D', commutative=True), log(Symbol('W', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(2)), Pow(Symbol('W', commutative=True), Integer(-1)))", "Add(Mul(Symbol('D', commutative=True), Symbol('W', commutative=True)), exp(Symbol('W', commutative=True)))", "Add(Mul(Symbol('D', commutative=True), Symbol('W', commutative=True)), sin(Symbol('W', commutative=True)))", "Add(Mul(Integer(-1), Symbol('D', commutative=True), Symbol('W', commutative=True)), sin(Symbol('W', commutative=True)))"]}, {"premise_expression": "\\frac{\\sin{(L)}}{Q}", "variable": "L", "positive": "- \\frac{\\cos{(L)}}{Q}", "negatives": ["- \\cos{(L - Q)}", "- Q \\cos{(L)}", "\\frac{L^{2} \\cos{(Q)}}{2}", "- e^{- L + Q}"], "srepr_premise_expression": "Mul(Pow(Symbol('Q', commutative=True), Integer(-1)), sin(Symbol('L', commutative=True)))", "srepr_variable": "Symbol('L', commutative=True)", "srepr_positive": "Mul(Integer(-1), Pow(Symbol('Q', commutative=True), Integer(-1)), cos(Symbol('L', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('L', commutative=True), Mul(Integer(-1), Symbol('Q', commutative=True)))))", "Mul(Integer(-1), Symbol('Q', commutative=True), cos(Symbol('L', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(2)), cos(Symbol('Q', commutative=True)))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('L', commutative=True)), Symbol('Q', commutative=True))))"]}, {"premise_expression": "A - b", "variable": "A", "positive": "\\frac{A (A - 2 b)}{2}", "negatives": ["\\frac{b (2 A - b)}{2}", "\\sin{(A - b)}", "\\cos{(A - b)}", "- A b - \\cos{(A)}"], "srepr_premise_expression": "Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('b', commutative=True)))", "srepr_variable": "Symbol('A', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Symbol('A', commutative=True), Mul(Integer(-1), Integer(2), Symbol('b', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('b', commutative=True), Add(Mul(Integer(2), Symbol('A', commutative=True)), Mul(Integer(-1), Symbol('b', commutative=True))))", "sin(Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('b', commutative=True))))", "cos(Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('b', commutative=True))))", "Add(Mul(Integer(-1), Symbol('A', commutative=True), Symbol('b', commutative=True)), Mul(Integer(-1), cos(Symbol('A', commutative=True))))"]}, {"premise_expression": "\\frac{\\cos{(M)}}{f}", "variable": "M", "positive": "\\frac{\\sin{(M)}}{f}", "negatives": ["\\frac{M^{2} f}{2}", "\\frac{M^{2} \\sin{(f)}}{2}", "e^{M - f}", "e^{M + f}"], "srepr_premise_expression": "Mul(Pow(Symbol('f', commutative=True), Integer(-1)), cos(Symbol('M', commutative=True)))", "srepr_variable": "Symbol('M', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('f', commutative=True), Integer(-1)), sin(Symbol('M', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('M', commutative=True), Integer(2)), Symbol('f', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('M', commutative=True), Integer(2)), sin(Symbol('f', commutative=True)))", "exp(Add(Symbol('M', commutative=True), Mul(Integer(-1), Symbol('f', commutative=True))))", "exp(Add(Symbol('M', commutative=True), Symbol('f', commutative=True)))"]}, {"premise_expression": "R + o + x", "variable": "R", "positive": "R (\\frac{R}{2} + o + x)", "negatives": ["\\frac{R (- R + 2 o - 2 x)}{2}", "\\frac{o (2 R + o + 2 x)}{2}", "\\frac{x (2 R + 2 o + x)}{2}", "\\frac{R^{2} (o - x)}{2}"], "srepr_premise_expression": "Add(Symbol('R', commutative=True), Symbol('o', commutative=True), Symbol('x', commutative=True))", "srepr_variable": "Symbol('R', commutative=True)", "srepr_positive": "Mul(Symbol('R', commutative=True), Add(Mul(Rational(1, 2), Symbol('R', commutative=True)), Symbol('o', commutative=True), Symbol('x', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('R', commutative=True), Add(Mul(Integer(-1), Symbol('R', commutative=True)), Mul(Integer(2), Symbol('o', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('x', commutative=True))))", "Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Mul(Integer(2), Symbol('R', commutative=True)), Symbol('o', commutative=True), Mul(Integer(2), Symbol('x', commutative=True))))", "Mul(Rational(1, 2), Symbol('x', commutative=True), Add(Mul(Integer(2), Symbol('R', commutative=True)), Mul(Integer(2), Symbol('o', commutative=True)), Symbol('x', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('R', commutative=True), Integer(2)), Add(Symbol('o', commutative=True), Mul(Integer(-1), Symbol('x', commutative=True))))"]}, {"premise_expression": "\\cos{(x + y)}", "variable": "y", "positive": "\\sin{(x + y)}", "negatives": ["- \\sin{(x - y)}", "- \\cos{(x + y)}", "e^{- x + y}", "x \\sin{(y)}"], "srepr_premise_expression": "cos(Add(Symbol('x', commutative=True), Symbol('y', commutative=True)))", "srepr_variable": "Symbol('y', commutative=True)", "srepr_positive": "sin(Add(Symbol('x', commutative=True), Symbol('y', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('x', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('x', commutative=True), Symbol('y', commutative=True))))", "exp(Add(Mul(Integer(-1), Symbol('x', commutative=True)), Symbol('y', commutative=True)))", "Mul(Symbol('x', commutative=True), sin(Symbol('y', commutative=True)))"]}, {"premise_expression": "f n", "variable": "n", "positive": "\\frac{f n^{2}}{2}", "negatives": ["\\frac{f^{2} n}{2}", "\\sin{(f + n)}", "\\frac{n (- 2 f + n)}{2}", "- f n - \\cos{(n)}"], "srepr_premise_expression": "Mul(Symbol('f', commutative=True), Symbol('n', commutative=True))", "srepr_variable": "Symbol('n', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('f', commutative=True), Pow(Symbol('n', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('f', commutative=True), Integer(2)), Symbol('n', commutative=True))", "sin(Add(Symbol('f', commutative=True), Symbol('n', commutative=True)))", "Mul(Rational(1, 2), Symbol('n', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('f', commutative=True)), Symbol('n', commutative=True)))", "Add(Mul(Integer(-1), Symbol('f', commutative=True), Symbol('n', commutative=True)), Mul(Integer(-1), cos(Symbol('n', commutative=True))))"]}, {"premise_expression": "\\frac{n}{V}", "variable": "n", "positive": "\\frac{n^{2}}{2 V}", "negatives": ["n \\log{(V)}", "\\frac{n^{2} \\log{(V)}}{2}", "\\frac{n (2 V + n)}{2}", "- \\cos{(V + n)}"], "srepr_premise_expression": "Mul(Pow(Symbol('V', commutative=True), Integer(-1)), Symbol('n', commutative=True))", "srepr_variable": "Symbol('n', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('V', commutative=True), Integer(-1)), Pow(Symbol('n', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('n', commutative=True), log(Symbol('V', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('n', commutative=True), Integer(2)), log(Symbol('V', commutative=True)))", "Mul(Rational(1, 2), Symbol('n', commutative=True), Add(Mul(Integer(2), Symbol('V', commutative=True)), Symbol('n', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('V', commutative=True), Symbol('n', commutative=True))))"]}, {"premise_expression": "s + w", "variable": "w", "positive": "\\frac{w (2 s + w)}{2}", "negatives": ["\\frac{s (s + 2 w)}{2}", "\\frac{w^{2} \\sin{(s)}}{2}", "\\frac{w (\\log{(w)} - 1)}{s}", "- \\frac{\\cos{(w)}}{s}"], "srepr_premise_expression": "Add(Symbol('s', commutative=True), Symbol('w', commutative=True))", "srepr_variable": "Symbol('w', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('w', commutative=True), Add(Mul(Integer(2), Symbol('s', commutative=True)), Symbol('w', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('s', commutative=True), Add(Symbol('s', commutative=True), Mul(Integer(2), Symbol('w', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('w', commutative=True), Integer(2)), sin(Symbol('s', commutative=True)))", "Mul(Pow(Symbol('s', commutative=True), Integer(-1)), Symbol('w', commutative=True), Add(log(Symbol('w', commutative=True)), Integer(-1)))", "Mul(Integer(-1), Pow(Symbol('s', commutative=True), Integer(-1)), cos(Symbol('w', commutative=True)))"]}, {"premise_expression": "e^{- p + y}", "variable": "y", "positive": "e^{- p + y}", "negatives": ["- e^{- p + y}", "p e^{\\frac{y}{p}}", "p y - \\cos{(y)}", "- p y - \\cos{(y)}"], "srepr_premise_expression": "exp(Add(Mul(Integer(-1), Symbol('p', commutative=True)), Symbol('y', commutative=True)))", "srepr_variable": "Symbol('y', commutative=True)", "srepr_positive": "exp(Add(Mul(Integer(-1), Symbol('p', commutative=True)), Symbol('y', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('p', commutative=True)), Symbol('y', commutative=True))))", "Mul(Symbol('p', commutative=True), exp(Mul(Pow(Symbol('p', commutative=True), Integer(-1)), Symbol('y', commutative=True))))", "Add(Mul(Symbol('p', commutative=True), Symbol('y', commutative=True)), Mul(Integer(-1), cos(Symbol('y', commutative=True))))", "Add(Mul(Integer(-1), Symbol('p', commutative=True), Symbol('y', commutative=True)), Mul(Integer(-1), cos(Symbol('y', commutative=True))))"]}, {"premise_expression": "\\frac{s}{r}", "variable": "r", "positive": "s \\log{(r)}", "negatives": ["- s \\cos{(r)}", "\\frac{s^{2}}{2 r}", "\\frac{r^{2}}{2 s}", "- \\cos{(r - s)}"], "srepr_premise_expression": "Mul(Pow(Symbol('r', commutative=True), Integer(-1)), Symbol('s', commutative=True))", "srepr_variable": "Symbol('r', commutative=True)", "srepr_positive": "Mul(Symbol('s', commutative=True), log(Symbol('r', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Symbol('s', commutative=True), cos(Symbol('r', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('r', commutative=True), Integer(-1)), Pow(Symbol('s', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('r', commutative=True), Integer(2)), Pow(Symbol('s', commutative=True), Integer(-1)))", "Mul(Integer(-1), cos(Add(Symbol('r', commutative=True), Mul(Integer(-1), Symbol('s', commutative=True)))))"]}, {"premise_expression": "\\frac{- W + o}{P}", "variable": "P", "positive": "(- W + o) \\log{(P)}", "negatives": ["\\frac{W (- W + 2 o)}{2 P}", "\\frac{o (- 2 W + o)}{2 P}", "\\frac{P (- P + 2 W^{o})}{2}", "\\frac{P W (P + 2 o)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('P', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('W', commutative=True)), Symbol('o', commutative=True)))", "srepr_variable": "Symbol('P', commutative=True)", "srepr_positive": "Mul(Add(Mul(Integer(-1), Symbol('W', commutative=True)), Symbol('o', commutative=True)), log(Symbol('P', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(-1)), Symbol('W', commutative=True), Add(Mul(Integer(-1), Symbol('W', commutative=True)), Mul(Integer(2), Symbol('o', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(-1)), Symbol('o', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('W', commutative=True)), Symbol('o', commutative=True)))", "Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Mul(Integer(-1), Symbol('P', commutative=True)), Mul(Integer(2), Pow(Symbol('W', commutative=True), Symbol('o', commutative=True)))))", "Mul(Rational(1, 2), Symbol('P', commutative=True), Symbol('W', commutative=True), Add(Symbol('P', commutative=True), Mul(Integer(2), Symbol('o', commutative=True))))"]}, {"premise_expression": "W e^{Y}", "variable": "W", "positive": "\\frac{W^{2} e^{Y}}{2}", "negatives": ["\\frac{W^{2} \\log{(Y)}}{2}", "W e^{Y}", "\\frac{W Y (W + 2 Y)}{2}", "W Y + \\sin{(W)}"], "srepr_premise_expression": "Mul(Symbol('W', commutative=True), exp(Symbol('Y', commutative=True)))", "srepr_variable": "Symbol('W', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('W', commutative=True), Integer(2)), exp(Symbol('Y', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('W', commutative=True), Integer(2)), log(Symbol('Y', commutative=True)))", "Mul(Symbol('W', commutative=True), exp(Symbol('Y', commutative=True)))", "Mul(Rational(1, 2), Symbol('W', commutative=True), Symbol('Y', commutative=True), Add(Symbol('W', commutative=True), Mul(Integer(2), Symbol('Y', commutative=True))))", "Add(Mul(Symbol('W', commutative=True), Symbol('Y', commutative=True)), sin(Symbol('W', commutative=True)))"]}, {"premise_expression": "r (o - p)", "variable": "o", "positive": "\\frac{o r (o - 2 p)}{2}", "negatives": ["\\frac{o r (o + 2 p)}{2}", "\\frac{p r (2 o - p)}{2}", "\\frac{r^{2} (o - p)}{2}", "\\frac{o (o r + 2 p)}{2}"], "srepr_premise_expression": "Mul(Symbol('r', commutative=True), Add(Symbol('o', commutative=True), Mul(Integer(-1), Symbol('p', commutative=True))))", "srepr_variable": "Symbol('o', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('o', commutative=True), Symbol('r', commutative=True), Add(Symbol('o', commutative=True), Mul(Integer(-1), Integer(2), Symbol('p', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('o', commutative=True), Symbol('r', commutative=True), Add(Symbol('o', commutative=True), Mul(Integer(2), Symbol('p', commutative=True))))", "Mul(Rational(1, 2), Symbol('p', commutative=True), Symbol('r', commutative=True), Add(Mul(Integer(2), Symbol('o', commutative=True)), Mul(Integer(-1), Symbol('p', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('r', commutative=True), Integer(2)), Add(Symbol('o', commutative=True), Mul(Integer(-1), Symbol('p', commutative=True))))", "Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Mul(Symbol('o', commutative=True), Symbol('r', commutative=True)), Mul(Integer(2), Symbol('p', commutative=True))))"]}, {"premise_expression": "\\cos{(G - V)}", "variable": "G", "positive": "\\sin{(G - V)}", "negatives": ["- \\sin{(G - V)}", "\\frac{\\sin{(G)}}{V}", "e^{G + V}", "\\frac{G (G - 2 V)}{2}"], "srepr_premise_expression": "cos(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('V', commutative=True))))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "sin(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('V', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('V', commutative=True)))))", "Mul(Pow(Symbol('V', commutative=True), Integer(-1)), sin(Symbol('G', commutative=True)))", "exp(Add(Symbol('G', commutative=True), Symbol('V', commutative=True)))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Symbol('G', commutative=True), Mul(Integer(-1), Integer(2), Symbol('V', commutative=True))))"]}, {"premise_expression": "\\frac{C}{y}", "variable": "C", "positive": "\\frac{C^{2}}{2 y}", "negatives": ["C \\log{(y)}", "\\frac{C (C + 2 y)}{2}", "\\sin{(C - y)}", "\\frac{C (- C + 4 y)}{2}"], "srepr_premise_expression": "Mul(Symbol('C', commutative=True), Pow(Symbol('y', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2)), Pow(Symbol('y', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('C', commutative=True), log(Symbol('y', commutative=True)))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Symbol('C', commutative=True), Mul(Integer(2), Symbol('y', commutative=True))))", "sin(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True))))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Mul(Integer(-1), Symbol('C', commutative=True)), Mul(Integer(4), Symbol('y', commutative=True))))"]}, {"premise_expression": "- T + \\log{(m)}", "variable": "T", "positive": "\\frac{T (- T + 2 \\log{(m)})}{2}", "negatives": ["m (- T + \\log{(m)} - 1)", "m \\log{(T)}", "T (\\log{(T m)} - 1)", "T \\log{(T + m)} - T + m \\log{(T + m)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('T', commutative=True)), log(Symbol('m', commutative=True)))", "srepr_variable": "Symbol('T', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('T', commutative=True), Add(Mul(Integer(-1), Symbol('T', commutative=True)), Mul(Integer(2), log(Symbol('m', commutative=True)))))", "srepr_negatives": ["Mul(Symbol('m', commutative=True), Add(Mul(Integer(-1), Symbol('T', commutative=True)), log(Symbol('m', commutative=True)), Integer(-1)))", "Mul(Symbol('m', commutative=True), log(Symbol('T', commutative=True)))", "Mul(Symbol('T', commutative=True), Add(log(Mul(Symbol('T', commutative=True), Symbol('m', commutative=True))), Integer(-1)))", "Add(Mul(Symbol('T', commutative=True), log(Add(Symbol('T', commutative=True), Symbol('m', commutative=True)))), Mul(Integer(-1), Symbol('T', commutative=True)), Mul(Symbol('m', commutative=True), log(Add(Symbol('T', commutative=True), Symbol('m', commutative=True)))))"]}, {"premise_expression": "\\log{(\\frac{n}{w})}", "variable": "n", "positive": "n (\\log{(\\frac{n}{w})} - 1)", "negatives": ["n (\\log{(n w)} - 1)", "w (\\log{(\\frac{n}{w})} + 1)", "n (- w + \\log{(n)} - 1)", "\\log{(n)} \\log{(w)}"], "srepr_premise_expression": "log(Mul(Symbol('n', commutative=True), Pow(Symbol('w', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('n', commutative=True)", "srepr_positive": "Mul(Symbol('n', commutative=True), Add(log(Mul(Symbol('n', commutative=True), Pow(Symbol('w', commutative=True), Integer(-1)))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('n', commutative=True), Add(log(Mul(Symbol('n', commutative=True), Symbol('w', commutative=True))), Integer(-1)))", "Mul(Symbol('w', commutative=True), Add(log(Mul(Symbol('n', commutative=True), Pow(Symbol('w', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Symbol('n', commutative=True), Add(Mul(Integer(-1), Symbol('w', commutative=True)), log(Symbol('n', commutative=True)), Integer(-1)))", "Mul(log(Symbol('n', commutative=True)), log(Symbol('w', commutative=True)))"]}, {"premise_expression": "\\frac{j}{Z}", "variable": "j", "positive": "\\frac{j^{2}}{2 Z}", "negatives": ["j \\log{(Z)}", "\\frac{Z j^{2}}{2}", "Z \\sin{(j)}", "Z j - \\cos{(j)}"], "srepr_premise_expression": "Mul(Pow(Symbol('Z', commutative=True), Integer(-1)), Symbol('j', commutative=True))", "srepr_variable": "Symbol('j', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('Z', commutative=True), Integer(-1)), Pow(Symbol('j', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('j', commutative=True), log(Symbol('Z', commutative=True)))", "Mul(Rational(1, 2), Symbol('Z', commutative=True), Pow(Symbol('j', commutative=True), Integer(2)))", "Mul(Symbol('Z', commutative=True), sin(Symbol('j', commutative=True)))", "Add(Mul(Symbol('Z', commutative=True), Symbol('j', commutative=True)), Mul(Integer(-1), cos(Symbol('j', commutative=True))))"]}, {"premise_expression": "M + b", "variable": "M", "positive": "\\frac{M (M + 2 b)}{2}", "negatives": ["\\frac{b (2 M + b)}{2}", "\\frac{M^{2} (b + 1)}{2}", "\\sin{(M + b)}", "\\cos{(M - b)}"], "srepr_premise_expression": "Add(Symbol('M', commutative=True), Symbol('b', commutative=True))", "srepr_variable": "Symbol('M', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('M', commutative=True), Add(Symbol('M', commutative=True), Mul(Integer(2), Symbol('b', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('b', commutative=True), Add(Mul(Integer(2), Symbol('M', commutative=True)), Symbol('b', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('M', commutative=True), Integer(2)), Add(Symbol('b', commutative=True), Integer(1)))", "sin(Add(Symbol('M', commutative=True), Symbol('b', commutative=True)))", "cos(Add(Symbol('M', commutative=True), Mul(Integer(-1), Symbol('b', commutative=True))))"]}, {"premise_expression": "e^{\\frac{W}{h}}", "variable": "h", "positive": "- W \\operatorname{Ei}{(\\frac{W}{h})} + h e^{\\frac{W}{h}}", "negatives": ["\\frac{h (h + 2 e^{W})}{2}", "h e^{\\frac{W}{h}}", "\\frac{h (- h + 2 \\sin{(W)})}{2}", "\\frac{h (h + 2 \\sin{(W)})}{2}"], "srepr_premise_expression": "exp(Mul(Symbol('W', commutative=True), Pow(Symbol('h', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('h', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('W', commutative=True), Ei(Mul(Symbol('W', commutative=True), Pow(Symbol('h', commutative=True), Integer(-1))))), Mul(Symbol('h', commutative=True), exp(Mul(Symbol('W', commutative=True), Pow(Symbol('h', commutative=True), Integer(-1))))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('h', commutative=True), Add(Symbol('h', commutative=True), Mul(Integer(2), exp(Symbol('W', commutative=True)))))", "Mul(Symbol('h', commutative=True), exp(Mul(Symbol('W', commutative=True), Pow(Symbol('h', commutative=True), Integer(-1)))))", "Mul(Rational(1, 2), Symbol('h', commutative=True), Add(Mul(Integer(-1), Symbol('h', commutative=True)), Mul(Integer(2), sin(Symbol('W', commutative=True)))))", "Mul(Rational(1, 2), Symbol('h', commutative=True), Add(Symbol('h', commutative=True), Mul(Integer(2), sin(Symbol('W', commutative=True)))))"]}, {"premise_expression": "\\log{(S - W)}", "variable": "W", "positive": "- S \\log{(- S + W)} + W \\log{(S - W)} - W", "negatives": ["S \\log{(S - W)} - S - W \\log{(S - W)}", "\\frac{W (- W + 2 \\log{(S)})}{2}", "\\frac{W (W + 2 \\cos{(S)})}{2}", "- \\cos{(S - W)}"], "srepr_premise_expression": "log(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('W', commutative=True))))", "srepr_variable": "Symbol('W', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('S', commutative=True), log(Add(Mul(Integer(-1), Symbol('S', commutative=True)), Symbol('W', commutative=True)))), Mul(Symbol('W', commutative=True), log(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('W', commutative=True))))), Mul(Integer(-1), Symbol('W', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('S', commutative=True), log(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('W', commutative=True))))), Mul(Integer(-1), Symbol('S', commutative=True)), Mul(Integer(-1), Symbol('W', commutative=True), log(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('W', commutative=True))))))", "Mul(Rational(1, 2), Symbol('W', commutative=True), Add(Mul(Integer(-1), Symbol('W', commutative=True)), Mul(Integer(2), log(Symbol('S', commutative=True)))))", "Mul(Rational(1, 2), Symbol('W', commutative=True), Add(Symbol('W', commutative=True), Mul(Integer(2), cos(Symbol('S', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('W', commutative=True)))))"]}, {"premise_expression": "e^{f - n}", "variable": "f", "positive": "e^{f - n}", "negatives": ["- e^{f - n}", "- \\cos{(f + n)}", "\\frac{f (f + 2 n)}{2}", "f n + e^{f}"], "srepr_premise_expression": "exp(Add(Symbol('f', commutative=True), Mul(Integer(-1), Symbol('n', commutative=True))))", "srepr_variable": "Symbol('f', commutative=True)", "srepr_positive": "exp(Add(Symbol('f', commutative=True), Mul(Integer(-1), Symbol('n', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Symbol('f', commutative=True), Mul(Integer(-1), Symbol('n', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('f', commutative=True), Symbol('n', commutative=True))))", "Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Symbol('f', commutative=True), Mul(Integer(2), Symbol('n', commutative=True))))", "Add(Mul(Symbol('f', commutative=True), Symbol('n', commutative=True)), exp(Symbol('f', commutative=True)))"]}, {"premise_expression": "P \\cos{(b)}", "variable": "P", "positive": "\\frac{P^{2} \\cos{(b)}}{2}", "negatives": ["\\frac{P^{2} \\log{(b)}}{2}", "\\frac{P^{2} b}{2}", "\\frac{P^{2}}{2 b}", "P \\sin{(b)}"], "srepr_premise_expression": "Mul(Symbol('P', commutative=True), cos(Symbol('b', commutative=True)))", "srepr_variable": "Symbol('P', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2)), cos(Symbol('b', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2)), log(Symbol('b', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2)), Symbol('b', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2)), Pow(Symbol('b', commutative=True), Integer(-1)))", "Mul(Symbol('P', commutative=True), sin(Symbol('b', commutative=True)))"]}, {"premise_expression": "\\frac{N}{T} - p", "variable": "p", "positive": "\\frac{N p}{T} - \\frac{p^{2}}{2}", "negatives": ["\\frac{N T p^{2}}{2}", "- N p + \\frac{p^{2}}{2 T}", "p (T + T^{N})", "N \\log{(T)} - T p"], "srepr_premise_expression": "Add(Mul(Symbol('N', commutative=True), Pow(Symbol('T', commutative=True), Integer(-1))), Mul(Integer(-1), Symbol('p', commutative=True)))", "srepr_variable": "Symbol('p', commutative=True)", "srepr_positive": "Add(Mul(Symbol('N', commutative=True), Pow(Symbol('T', commutative=True), Integer(-1)), Symbol('p', commutative=True)), Mul(Integer(-1), Rational(1, 2), Pow(Symbol('p', commutative=True), Integer(2))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('N', commutative=True), Symbol('T', commutative=True), Pow(Symbol('p', commutative=True), Integer(2)))", "Add(Mul(Integer(-1), Symbol('N', commutative=True), Symbol('p', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('T', commutative=True), Integer(-1)), Pow(Symbol('p', commutative=True), Integer(2))))", "Mul(Symbol('p', commutative=True), Add(Symbol('T', commutative=True), Pow(Symbol('T', commutative=True), Symbol('N', commutative=True))))", "Add(Mul(Symbol('N', commutative=True), log(Symbol('T', commutative=True))), Mul(Integer(-1), Symbol('T', commutative=True), Symbol('p', commutative=True)))"]}, {"premise_expression": "U \\sin{(x)}", "variable": "x", "positive": "- U \\cos{(x)}", "negatives": ["- \\cos{(U + x)}", "\\cos{(U - x)}", "\\frac{U^{2} \\sin{(x)}}{2}", "e^{U + x}"], "srepr_premise_expression": "Mul(Symbol('U', commutative=True), sin(Symbol('x', commutative=True)))", "srepr_variable": "Symbol('x', commutative=True)", "srepr_positive": "Mul(Integer(-1), Symbol('U', commutative=True), cos(Symbol('x', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('U', commutative=True), Symbol('x', commutative=True))))", "cos(Add(Symbol('U', commutative=True), Mul(Integer(-1), Symbol('x', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('U', commutative=True), Integer(2)), sin(Symbol('x', commutative=True)))", "exp(Add(Symbol('U', commutative=True), Symbol('x', commutative=True)))"]}, {"premise_expression": "\\log{(Q + p)}", "variable": "p", "positive": "Q \\log{(Q + p)} + p \\log{(Q + p)} - p", "negatives": ["Q \\log{(Q + p)} - Q + p \\log{(Q + p)}", "\\log{(p)} \\cos{(Q)}", "Q p + e^{p}", "\\frac{p (2 Q + p)}{2}"], "srepr_premise_expression": "log(Add(Symbol('Q', commutative=True), Symbol('p', commutative=True)))", "srepr_variable": "Symbol('p', commutative=True)", "srepr_positive": "Add(Mul(Symbol('Q', commutative=True), log(Add(Symbol('Q', commutative=True), Symbol('p', commutative=True)))), Mul(Symbol('p', commutative=True), log(Add(Symbol('Q', commutative=True), Symbol('p', commutative=True)))), Mul(Integer(-1), Symbol('p', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('Q', commutative=True), log(Add(Symbol('Q', commutative=True), Symbol('p', commutative=True)))), Mul(Integer(-1), Symbol('Q', commutative=True)), Mul(Symbol('p', commutative=True), log(Add(Symbol('Q', commutative=True), Symbol('p', commutative=True)))))", "Mul(log(Symbol('p', commutative=True)), cos(Symbol('Q', commutative=True)))", "Add(Mul(Symbol('Q', commutative=True), Symbol('p', commutative=True)), exp(Symbol('p', commutative=True)))", "Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Mul(Integer(2), Symbol('Q', commutative=True)), Symbol('p', commutative=True)))"]}, {"premise_expression": "M \\cos{(g)}", "variable": "g", "positive": "M \\sin{(g)}", "negatives": ["M e^{g}", "- M g + \\sin{(g)}", "\\frac{M g^{2}}{2}", "\\frac{M^{2} \\cos{(g)}}{2}"], "srepr_premise_expression": "Mul(Symbol('M', commutative=True), cos(Symbol('g', commutative=True)))", "srepr_variable": "Symbol('g', commutative=True)", "srepr_positive": "Mul(Symbol('M', commutative=True), sin(Symbol('g', commutative=True)))", "srepr_negatives": ["Mul(Symbol('M', commutative=True), exp(Symbol('g', commutative=True)))", "Add(Mul(Integer(-1), Symbol('M', commutative=True), Symbol('g', commutative=True)), sin(Symbol('g', commutative=True)))", "Mul(Rational(1, 2), Symbol('M', commutative=True), Pow(Symbol('g', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('M', commutative=True), Integer(2)), cos(Symbol('g', commutative=True)))"]}, {"premise_expression": "T X", "variable": "X", "positive": "\\frac{T X^{2}}{2}", "negatives": ["\\frac{T^{2} X}{2}", "T \\log{(X)}", "T e^{\\frac{X}{T}}", "\\frac{X^{2} \\cos{(T)}}{2}"], "srepr_premise_expression": "Mul(Symbol('T', commutative=True), Symbol('X', commutative=True))", "srepr_variable": "Symbol('X', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('T', commutative=True), Pow(Symbol('X', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('T', commutative=True), Integer(2)), Symbol('X', commutative=True))", "Mul(Symbol('T', commutative=True), log(Symbol('X', commutative=True)))", "Mul(Symbol('T', commutative=True), exp(Mul(Pow(Symbol('T', commutative=True), Integer(-1)), Symbol('X', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('X', commutative=True), Integer(2)), cos(Symbol('T', commutative=True)))"]}, {"premise_expression": "\\frac{w}{m}", "variable": "w", "positive": "\\frac{w^{2}}{2 m}", "negatives": ["w \\log{(m)}", "\\frac{w^{2} \\log{(m)}}{2}", "- m \\cos{(w)}", "\\frac{\\sin{(w)}}{m}"], "srepr_premise_expression": "Mul(Pow(Symbol('m', commutative=True), Integer(-1)), Symbol('w', commutative=True))", "srepr_variable": "Symbol('w', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('m', commutative=True), Integer(-1)), Pow(Symbol('w', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('w', commutative=True), log(Symbol('m', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('w', commutative=True), Integer(2)), log(Symbol('m', commutative=True)))", "Mul(Integer(-1), Symbol('m', commutative=True), cos(Symbol('w', commutative=True)))", "Mul(Pow(Symbol('m', commutative=True), Integer(-1)), sin(Symbol('w', commutative=True)))"]}, {"premise_expression": "\\log{(c^{B})}", "variable": "B", "positive": "\\frac{B^{2} \\log{(c)}}{2}", "negatives": ["B c - \\cos{(B)}", "\\frac{B (- B + 2 \\cos{(c)})}{2}", "B c + e^{B}", "\\sin{(B + c)}"], "srepr_premise_expression": "log(Pow(Symbol('c', commutative=True), Symbol('B', commutative=True)))", "srepr_variable": "Symbol('B', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('B', commutative=True), Integer(2)), log(Symbol('c', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('B', commutative=True), Symbol('c', commutative=True)), Mul(Integer(-1), cos(Symbol('B', commutative=True))))", "Mul(Rational(1, 2), Symbol('B', commutative=True), Add(Mul(Integer(-1), Symbol('B', commutative=True)), Mul(Integer(2), cos(Symbol('c', commutative=True)))))", "Add(Mul(Symbol('B', commutative=True), Symbol('c', commutative=True)), exp(Symbol('B', commutative=True)))", "sin(Add(Symbol('B', commutative=True), Symbol('c', commutative=True)))"]}, {"premise_expression": "K l", "variable": "l", "positive": "\\frac{K l^{2}}{2}", "negatives": ["\\frac{K^{2} l}{2}", "K \\sin{(l)}", "\\frac{l (- 2 K + l)}{2}", "- K l - \\cos{(l)}"], "srepr_premise_expression": "Mul(Symbol('K', commutative=True), Symbol('l', commutative=True))", "srepr_variable": "Symbol('l', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('K', commutative=True), Pow(Symbol('l', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('K', commutative=True), Integer(2)), Symbol('l', commutative=True))", "Mul(Symbol('K', commutative=True), sin(Symbol('l', commutative=True)))", "Mul(Rational(1, 2), Symbol('l', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('K', commutative=True)), Symbol('l', commutative=True)))", "Add(Mul(Integer(-1), Symbol('K', commutative=True), Symbol('l', commutative=True)), Mul(Integer(-1), cos(Symbol('l', commutative=True))))"]}, {"premise_expression": "e^{- W + n}", "variable": "n", "positive": "e^{- W + n}", "negatives": ["- e^{- W + n}", "- \\cos{(W - n)}", "n (- W + \\log{(W)})", "W n + \\sin{(n)}"], "srepr_premise_expression": "exp(Add(Mul(Integer(-1), Symbol('W', commutative=True)), Symbol('n', commutative=True)))", "srepr_variable": "Symbol('n', commutative=True)", "srepr_positive": "exp(Add(Mul(Integer(-1), Symbol('W', commutative=True)), Symbol('n', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('W', commutative=True)), Symbol('n', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('W', commutative=True), Mul(Integer(-1), Symbol('n', commutative=True)))))", "Mul(Symbol('n', commutative=True), Add(Mul(Integer(-1), Symbol('W', commutative=True)), log(Symbol('W', commutative=True))))", "Add(Mul(Symbol('W', commutative=True), Symbol('n', commutative=True)), sin(Symbol('n', commutative=True)))"]}, {"premise_expression": "M - T", "variable": "T", "positive": "\\frac{T (2 M - T)}{2}", "negatives": ["\\frac{M (M - 2 T)}{2}", "\\frac{T^{2} \\sin{(M)}}{2}", "- e^{M - T}", "\\frac{T (\\log{(T)} - 1)}{M}"], "srepr_premise_expression": "Add(Symbol('M', commutative=True), Mul(Integer(-1), Symbol('T', commutative=True)))", "srepr_variable": "Symbol('T', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('T', commutative=True), Add(Mul(Integer(2), Symbol('M', commutative=True)), Mul(Integer(-1), Symbol('T', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('M', commutative=True), Add(Symbol('M', commutative=True), Mul(Integer(-1), Integer(2), Symbol('T', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('T', commutative=True), Integer(2)), sin(Symbol('M', commutative=True)))", "Mul(Integer(-1), exp(Add(Symbol('M', commutative=True), Mul(Integer(-1), Symbol('T', commutative=True)))))", "Mul(Pow(Symbol('M', commutative=True), Integer(-1)), Symbol('T', commutative=True), Add(log(Symbol('T', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\sin^{v}{(q)}", "variable": "q", "positive": "\\int \\sin^{v}{(q)} dq", "negatives": ["\\int (\\frac{q}{v})^{q} dq", "\\sin{(q + v)}", "q v + \\sin{(q)}", "\\log{(q)} \\log{(v)}"], "srepr_premise_expression": "Pow(sin(Symbol('q', commutative=True)), Symbol('v', commutative=True))", "srepr_variable": "Symbol('q', commutative=True)", "srepr_positive": "Integral(Pow(sin(Symbol('q', commutative=True)), Symbol('v', commutative=True)), Tuple(Symbol('q', commutative=True)))", "srepr_negatives": ["NonElementaryIntegral(Pow(Mul(Symbol('q', commutative=True), Pow(Symbol('v', commutative=True), Integer(-1))), Symbol('q', commutative=True)), Tuple(Symbol('q', commutative=True)))", "sin(Add(Symbol('q', commutative=True), Symbol('v', commutative=True)))", "Add(Mul(Symbol('q', commutative=True), Symbol('v', commutative=True)), sin(Symbol('q', commutative=True)))", "Mul(log(Symbol('q', commutative=True)), log(Symbol('v', commutative=True)))"]}, {"premise_expression": "q \\log{(w)}", "variable": "w", "positive": "q w (\\log{(w)} - 1)", "negatives": ["\\frac{q^{2} \\log{(w)}}{2}", "\\frac{q w (w + 2)}{2}", "- \\cos{(q - w)}", "\\cos{(q - w)}"], "srepr_premise_expression": "Mul(Symbol('q', commutative=True), log(Symbol('w', commutative=True)))", "srepr_variable": "Symbol('w', commutative=True)", "srepr_positive": "Mul(Symbol('q', commutative=True), Symbol('w', commutative=True), Add(log(Symbol('w', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('q', commutative=True), Integer(2)), log(Symbol('w', commutative=True)))", "Mul(Rational(1, 2), Symbol('q', commutative=True), Symbol('w', commutative=True), Add(Symbol('w', commutative=True), Integer(2)))", "Mul(Integer(-1), cos(Add(Symbol('q', commutative=True), Mul(Integer(-1), Symbol('w', commutative=True)))))", "cos(Add(Symbol('q', commutative=True), Mul(Integer(-1), Symbol('w', commutative=True))))"]}, {"premise_expression": "B H p", "variable": "H", "positive": "\\frac{B H^{2} p}{2}", "negatives": ["\\frac{B H p^{2}}{2}", "\\frac{B^{2} H p}{2}", "\\frac{H^{2} p}{2 B}", "B p \\log{(H)}"], "srepr_premise_expression": "Mul(Symbol('B', commutative=True), Symbol('H', commutative=True), Symbol('p', commutative=True))", "srepr_variable": "Symbol('H', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('B', commutative=True), Pow(Symbol('H', commutative=True), Integer(2)), Symbol('p', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('B', commutative=True), Symbol('H', commutative=True), Pow(Symbol('p', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('B', commutative=True), Integer(2)), Symbol('H', commutative=True), Symbol('p', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('B', commutative=True), Integer(-1)), Pow(Symbol('H', commutative=True), Integer(2)), Symbol('p', commutative=True))", "Mul(Symbol('B', commutative=True), Symbol('p', commutative=True), log(Symbol('H', commutative=True)))"]}, {"premise_expression": "b r", "variable": "r", "positive": "\\frac{b r^{2}}{2}", "negatives": ["\\frac{b^{2} r}{2}", "b e^{r}", "b r e^{b}", "\\frac{r (2 b + r)}{2}"], "srepr_premise_expression": "Mul(Symbol('b', commutative=True), Symbol('r', commutative=True))", "srepr_variable": "Symbol('r', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('b', commutative=True), Pow(Symbol('r', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('b', commutative=True), Integer(2)), Symbol('r', commutative=True))", "Mul(Symbol('b', commutative=True), exp(Symbol('r', commutative=True)))", "Mul(Symbol('b', commutative=True), Symbol('r', commutative=True), exp(Symbol('b', commutative=True)))", "Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(2), Symbol('b', commutative=True)), Symbol('r', commutative=True)))"]}, {"premise_expression": "\\frac{M}{Z} - l", "variable": "Z", "positive": "M \\log{(Z)} - Z l", "negatives": ["\\frac{M^{2}}{2 Z} - M l", "\\frac{M l}{Z} - \\frac{l^{2}}{2}", "\\frac{Z^{2}}{2} + \\frac{Z l}{M}", "\\frac{Z (2 M l - Z)}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('M', commutative=True), Pow(Symbol('Z', commutative=True), Integer(-1))), Mul(Integer(-1), Symbol('l', commutative=True)))", "srepr_variable": "Symbol('Z', commutative=True)", "srepr_positive": "Add(Mul(Symbol('M', commutative=True), log(Symbol('Z', commutative=True))), Mul(Integer(-1), Symbol('Z', commutative=True), Symbol('l', commutative=True)))", "srepr_negatives": ["Add(Mul(Rational(1, 2), Pow(Symbol('M', commutative=True), Integer(2)), Pow(Symbol('Z', commutative=True), Integer(-1))), Mul(Integer(-1), Symbol('M', commutative=True), Symbol('l', commutative=True)))", "Add(Mul(Symbol('M', commutative=True), Pow(Symbol('Z', commutative=True), Integer(-1)), Symbol('l', commutative=True)), Mul(Integer(-1), Rational(1, 2), Pow(Symbol('l', commutative=True), Integer(2))))", "Add(Mul(Rational(1, 2), Pow(Symbol('Z', commutative=True), Integer(2))), Mul(Pow(Symbol('M', commutative=True), Integer(-1)), Symbol('Z', commutative=True), Symbol('l', commutative=True)))", "Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Mul(Integer(2), Symbol('M', commutative=True), Symbol('l', commutative=True)), Mul(Integer(-1), Symbol('Z', commutative=True))))"]}, {"premise_expression": "P Q", "variable": "P", "positive": "\\frac{P^{2} Q}{2}", "negatives": ["\\frac{P Q^{2}}{2}", "\\frac{P (P - 2 Q)}{2}", "\\frac{P (- P + 2 Q)}{2}", "Q e^{\\frac{P}{Q}}"], "srepr_premise_expression": "Mul(Symbol('P', commutative=True), Symbol('Q', commutative=True))", "srepr_variable": "Symbol('P', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2)), Symbol('Q', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('P', commutative=True), Pow(Symbol('Q', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Symbol('P', commutative=True), Mul(Integer(-1), Integer(2), Symbol('Q', commutative=True))))", "Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Mul(Integer(-1), Symbol('P', commutative=True)), Mul(Integer(2), Symbol('Q', commutative=True))))", "Mul(Symbol('Q', commutative=True), exp(Mul(Symbol('P', commutative=True), Pow(Symbol('Q', commutative=True), Integer(-1)))))"]}, {"premise_expression": "- g + \\log{(I)}", "variable": "g", "positive": "\\frac{g (- g + 2 \\log{(I)})}{2}", "negatives": ["\\frac{g (g + 2 \\log{(I)})}{2}", "I (- g + \\log{(I)} - 1)", "\\log{(I)} \\log{(g)}", "\\frac{I^{2} g^{2}}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('g', commutative=True)), log(Symbol('I', commutative=True)))", "srepr_variable": "Symbol('g', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Mul(Integer(-1), Symbol('g', commutative=True)), Mul(Integer(2), log(Symbol('I', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Symbol('g', commutative=True), Mul(Integer(2), log(Symbol('I', commutative=True)))))", "Mul(Symbol('I', commutative=True), Add(Mul(Integer(-1), Symbol('g', commutative=True)), log(Symbol('I', commutative=True)), Integer(-1)))", "Mul(log(Symbol('I', commutative=True)), log(Symbol('g', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(2)), Pow(Symbol('g', commutative=True), Integer(2)))"]}, {"premise_expression": "G + P k", "variable": "G", "positive": "\\frac{G (G + 2 P k)}{2}", "negatives": ["\\frac{G k (G + 2 P)}{2}", "\\frac{P (2 G + P k)}{2}", "\\frac{k (2 G + P k)}{2}", "\\frac{G^{2} P k}{2}"], "srepr_premise_expression": "Add(Symbol('G', commutative=True), Mul(Symbol('P', commutative=True), Symbol('k', commutative=True)))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Symbol('G', commutative=True), Mul(Integer(2), Symbol('P', commutative=True), Symbol('k', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('G', commutative=True), Symbol('k', commutative=True), Add(Symbol('G', commutative=True), Mul(Integer(2), Symbol('P', commutative=True))))", "Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Mul(Integer(2), Symbol('G', commutative=True)), Mul(Symbol('P', commutative=True), Symbol('k', commutative=True))))", "Mul(Rational(1, 2), Symbol('k', commutative=True), Add(Mul(Integer(2), Symbol('G', commutative=True)), Mul(Symbol('P', commutative=True), Symbol('k', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(2)), Symbol('P', commutative=True), Symbol('k', commutative=True))"]}, {"premise_expression": "\\frac{H}{g}", "variable": "g", "positive": "H \\log{(g)}", "negatives": ["\\frac{H^{2}}{2 g}", "- \\cos{(H - g)}", "\\log{(g)} \\cos{(H)}", "\\frac{g (\\log{(g)} - 1)}{H}"], "srepr_premise_expression": "Mul(Symbol('H', commutative=True), Pow(Symbol('g', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('g', commutative=True)", "srepr_positive": "Mul(Symbol('H', commutative=True), log(Symbol('g', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('H', commutative=True), Integer(2)), Pow(Symbol('g', commutative=True), Integer(-1)))", "Mul(Integer(-1), cos(Add(Symbol('H', commutative=True), Mul(Integer(-1), Symbol('g', commutative=True)))))", "Mul(log(Symbol('g', commutative=True)), cos(Symbol('H', commutative=True)))", "Mul(Pow(Symbol('H', commutative=True), Integer(-1)), Symbol('g', commutative=True), Add(log(Symbol('g', commutative=True)), Integer(-1)))"]}, {"premise_expression": "U + \\log{(u)}", "variable": "u", "positive": "u (U + \\log{(u)} - 1)", "negatives": ["u (- U + \\log{(u^{U})})", "\\frac{U (U + 2 \\log{(u)})}{2}", "\\frac{u (u + 2 \\log{(U)})}{2}", "U \\log{(u)}"], "srepr_premise_expression": "Add(Symbol('U', commutative=True), log(Symbol('u', commutative=True)))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "Mul(Symbol('u', commutative=True), Add(Symbol('U', commutative=True), log(Symbol('u', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('u', commutative=True), Add(Mul(Integer(-1), Symbol('U', commutative=True)), log(Pow(Symbol('u', commutative=True), Symbol('U', commutative=True)))))", "Mul(Rational(1, 2), Symbol('U', commutative=True), Add(Symbol('U', commutative=True), Mul(Integer(2), log(Symbol('u', commutative=True)))))", "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Symbol('u', commutative=True), Mul(Integer(2), log(Symbol('U', commutative=True)))))", "Mul(Symbol('U', commutative=True), log(Symbol('u', commutative=True)))"]}, {"premise_expression": "e^{l + r}", "variable": "l", "positive": "e^{l + r}", "negatives": ["- \\cos{(l + r)}", "\\sin{(l - r)}", "- l r - \\cos{(l)}", "\\frac{l (l + 2 e^{r})}{2}"], "srepr_premise_expression": "exp(Add(Symbol('l', commutative=True), Symbol('r', commutative=True)))", "srepr_variable": "Symbol('l', commutative=True)", "srepr_positive": "exp(Add(Symbol('l', commutative=True), Symbol('r', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('l', commutative=True), Symbol('r', commutative=True))))", "sin(Add(Symbol('l', commutative=True), Mul(Integer(-1), Symbol('r', commutative=True))))", "Add(Mul(Integer(-1), Symbol('l', commutative=True), Symbol('r', commutative=True)), Mul(Integer(-1), cos(Symbol('l', commutative=True))))", "Mul(Rational(1, 2), Symbol('l', commutative=True), Add(Symbol('l', commutative=True), Mul(Integer(2), exp(Symbol('r', commutative=True)))))"]}, {"premise_expression": "- k + x", "variable": "k", "positive": "\\frac{k (- k + 2 x)}{2}", "negatives": ["\\frac{x (- 2 k + x)}{2}", "\\frac{k^{2} x}{2}", "\\sin{(k + x)}", "\\frac{k^{2} \\sin{(x)}}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('k', commutative=True)), Symbol('x', commutative=True))", "srepr_variable": "Symbol('k', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('k', commutative=True), Add(Mul(Integer(-1), Symbol('k', commutative=True)), Mul(Integer(2), Symbol('x', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('x', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('k', commutative=True)), Symbol('x', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('k', commutative=True), Integer(2)), Symbol('x', commutative=True))", "sin(Add(Symbol('k', commutative=True), Symbol('x', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('k', commutative=True), Integer(2)), sin(Symbol('x', commutative=True)))"]}, {"premise_expression": "M - W", "variable": "W", "positive": "\\frac{W (2 M - W)}{2}", "negatives": ["\\frac{M (M - 2 W)}{2}", "- \\cos{(M - W)}", "- e^{M - W}", "\\frac{W (W + 2 e^{M})}{2}"], "srepr_premise_expression": "Add(Symbol('M', commutative=True), Mul(Integer(-1), Symbol('W', commutative=True)))", "srepr_variable": "Symbol('W', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('W', commutative=True), Add(Mul(Integer(2), Symbol('M', commutative=True)), Mul(Integer(-1), Symbol('W', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('M', commutative=True), Add(Symbol('M', commutative=True), Mul(Integer(-1), Integer(2), Symbol('W', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('M', commutative=True), Mul(Integer(-1), Symbol('W', commutative=True)))))", "Mul(Integer(-1), exp(Add(Symbol('M', commutative=True), Mul(Integer(-1), Symbol('W', commutative=True)))))", "Mul(Rational(1, 2), Symbol('W', commutative=True), Add(Symbol('W', commutative=True), Mul(Integer(2), exp(Symbol('M', commutative=True)))))"]}, {"premise_expression": "- C + M", "variable": "C", "positive": "\\frac{C (- C + 2 M)}{2}", "negatives": ["\\frac{C (C + 2 M)}{2}", "\\frac{C (C - 2 M)}{2}", "\\frac{M (- 2 C + M)}{2}", "\\frac{C (- C + 2 \\sin{(M)})}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('C', commutative=True)), Symbol('M', commutative=True))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Mul(Integer(-1), Symbol('C', commutative=True)), Mul(Integer(2), Symbol('M', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Symbol('C', commutative=True), Mul(Integer(2), Symbol('M', commutative=True))))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Symbol('C', commutative=True), Mul(Integer(-1), Integer(2), Symbol('M', commutative=True))))", "Mul(Rational(1, 2), Symbol('M', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('C', commutative=True)), Symbol('M', commutative=True)))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Mul(Integer(-1), Symbol('C', commutative=True)), Mul(Integer(2), sin(Symbol('M', commutative=True)))))"]}, {"premise_expression": "W (Y - j)", "variable": "j", "positive": "\\frac{W j (2 Y - j)}{2}", "negatives": ["\\frac{W^{2} (Y - j)}{2}", "\\frac{W Y (Y - 2 j)}{2}", "\\frac{j (2 W^{Y} - j)}{2}", "\\frac{j (2 W^{Y} + j)}{2}"], "srepr_premise_expression": "Mul(Symbol('W', commutative=True), Add(Symbol('Y', commutative=True), Mul(Integer(-1), Symbol('j', commutative=True))))", "srepr_variable": "Symbol('j', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('W', commutative=True), Symbol('j', commutative=True), Add(Mul(Integer(2), Symbol('Y', commutative=True)), Mul(Integer(-1), Symbol('j', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('W', commutative=True), Integer(2)), Add(Symbol('Y', commutative=True), Mul(Integer(-1), Symbol('j', commutative=True))))", "Mul(Rational(1, 2), Symbol('W', commutative=True), Symbol('Y', commutative=True), Add(Symbol('Y', commutative=True), Mul(Integer(-1), Integer(2), Symbol('j', commutative=True))))", "Mul(Rational(1, 2), Symbol('j', commutative=True), Add(Mul(Integer(2), Pow(Symbol('W', commutative=True), Symbol('Y', commutative=True))), Mul(Integer(-1), Symbol('j', commutative=True))))", "Mul(Rational(1, 2), Symbol('j', commutative=True), Add(Mul(Integer(2), Pow(Symbol('W', commutative=True), Symbol('Y', commutative=True))), Symbol('j', commutative=True)))"]}, {"premise_expression": "W + s", "variable": "W", "positive": "\\frac{W (W + 2 s)}{2}", "negatives": ["\\frac{W (W - 2 s)}{2}", "\\frac{s (2 W + s)}{2}", "\\frac{W (W + 2 \\log{(s)})}{2}", "\\frac{W (- W + 2 \\sin{(s)})}{2}"], "srepr_premise_expression": "Add(Symbol('W', commutative=True), Symbol('s', commutative=True))", "srepr_variable": "Symbol('W', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('W', commutative=True), Add(Symbol('W', commutative=True), Mul(Integer(2), Symbol('s', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('W', commutative=True), Add(Symbol('W', commutative=True), Mul(Integer(-1), Integer(2), Symbol('s', commutative=True))))", "Mul(Rational(1, 2), Symbol('s', commutative=True), Add(Mul(Integer(2), Symbol('W', commutative=True)), Symbol('s', commutative=True)))", "Mul(Rational(1, 2), Symbol('W', commutative=True), Add(Symbol('W', commutative=True), Mul(Integer(2), log(Symbol('s', commutative=True)))))", "Mul(Rational(1, 2), Symbol('W', commutative=True), Add(Mul(Integer(-1), Symbol('W', commutative=True)), Mul(Integer(2), sin(Symbol('s', commutative=True)))))"]}, {"premise_expression": "B W + u", "variable": "W", "positive": "\\frac{W (B W + 2 u)}{2}", "negatives": ["\\frac{B (B W + 2 u)}{2}", "\\frac{u (2 B W + u)}{2}", "\\frac{W (W + 2 u^{u})}{2}", "\\frac{B W^{2} u}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('B', commutative=True), Symbol('W', commutative=True)), Symbol('u', commutative=True))", "srepr_variable": "Symbol('W', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('W', commutative=True), Add(Mul(Symbol('B', commutative=True), Symbol('W', commutative=True)), Mul(Integer(2), Symbol('u', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('B', commutative=True), Add(Mul(Symbol('B', commutative=True), Symbol('W', commutative=True)), Mul(Integer(2), Symbol('u', commutative=True))))", "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(2), Symbol('B', commutative=True), Symbol('W', commutative=True)), Symbol('u', commutative=True)))", "Mul(Rational(1, 2), Symbol('W', commutative=True), Add(Symbol('W', commutative=True), Mul(Integer(2), Pow(Symbol('u', commutative=True), Symbol('u', commutative=True)))))", "Mul(Rational(1, 2), Symbol('B', commutative=True), Pow(Symbol('W', commutative=True), Integer(2)), Symbol('u', commutative=True))"]}, {"premise_expression": "\\sin{(H + P)}", "variable": "H", "positive": "- \\cos{(H + P)}", "negatives": ["\\log{(H)} \\log{(P)}", "H", "H P^{2}", "H (- P + e^{P})"], "srepr_premise_expression": "sin(Add(Symbol('H', commutative=True), Symbol('P', commutative=True)))", "srepr_variable": "Symbol('H', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('H', commutative=True), Symbol('P', commutative=True))))", "srepr_negatives": ["Mul(log(Symbol('H', commutative=True)), log(Symbol('P', commutative=True)))", "Symbol('H', commutative=True)", "Mul(Symbol('H', commutative=True), Pow(Symbol('P', commutative=True), Integer(2)))", "Mul(Symbol('H', commutative=True), Add(Mul(Integer(-1), Symbol('P', commutative=True)), exp(Symbol('P', commutative=True))))"]}, {"premise_expression": "D w", "variable": "D", "positive": "\\frac{D^{2} w}{2}", "negatives": ["\\frac{D w^{2}}{2}", "e^{D - w}", "- D w - \\cos{(D)}", "e^{w} \\log{(D)}"], "srepr_premise_expression": "Mul(Symbol('D', commutative=True), Symbol('w', commutative=True))", "srepr_variable": "Symbol('D', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(2)), Symbol('w', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('D', commutative=True), Pow(Symbol('w', commutative=True), Integer(2)))", "exp(Add(Symbol('D', commutative=True), Mul(Integer(-1), Symbol('w', commutative=True))))", "Add(Mul(Integer(-1), Symbol('D', commutative=True), Symbol('w', commutative=True)), Mul(Integer(-1), cos(Symbol('D', commutative=True))))", "Mul(exp(Symbol('w', commutative=True)), log(Symbol('D', commutative=True)))"]}, {"premise_expression": "- m - t + u", "variable": "m", "positive": "\\frac{m (- m - 2 t + 2 u)}{2}", "negatives": ["\\frac{t (- 2 m - t + 2 u)}{2}", "\\frac{u (- 2 m - 2 t + u)}{2}", "\\frac{m (- m + 2 t + 2 u)}{2}", "\\frac{m^{2} (t + u)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('m', commutative=True)), Mul(Integer(-1), Symbol('t', commutative=True)), Symbol('u', commutative=True))", "srepr_variable": "Symbol('m', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Mul(Integer(-1), Symbol('m', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('t', commutative=True)), Mul(Integer(2), Symbol('u', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('t', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('m', commutative=True)), Mul(Integer(-1), Symbol('t', commutative=True)), Mul(Integer(2), Symbol('u', commutative=True))))", "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('m', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('t', commutative=True)), Symbol('u', commutative=True)))", "Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Mul(Integer(-1), Symbol('m', commutative=True)), Mul(Integer(2), Symbol('t', commutative=True)), Mul(Integer(2), Symbol('u', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('m', commutative=True), Integer(2)), Add(Symbol('t', commutative=True), Symbol('u', commutative=True)))"]}, {"premise_expression": "V - Y", "variable": "V", "positive": "\\frac{V (V - 2 Y)}{2}", "negatives": ["\\frac{Y (2 V - Y)}{2}", "\\frac{V (- V + 2 \\sin{(Y)})}{2}", "\\frac{V^{2}}{2 Y}", "- \\cos{(V - Y)}"], "srepr_premise_expression": "Add(Symbol('V', commutative=True), Mul(Integer(-1), Symbol('Y', commutative=True)))", "srepr_variable": "Symbol('V', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('V', commutative=True), Add(Symbol('V', commutative=True), Mul(Integer(-1), Integer(2), Symbol('Y', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('Y', commutative=True), Add(Mul(Integer(2), Symbol('V', commutative=True)), Mul(Integer(-1), Symbol('Y', commutative=True))))", "Mul(Rational(1, 2), Symbol('V', commutative=True), Add(Mul(Integer(-1), Symbol('V', commutative=True)), Mul(Integer(2), sin(Symbol('Y', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('V', commutative=True), Integer(2)), Pow(Symbol('Y', commutative=True), Integer(-1)))", "Mul(Integer(-1), cos(Add(Symbol('V', commutative=True), Mul(Integer(-1), Symbol('Y', commutative=True)))))"]}, {"premise_expression": "- M - X + b", "variable": "M", "positive": "\\frac{M (- M - 2 X + 2 b)}{2}", "negatives": ["\\frac{X (- 2 M - X + 2 b)}{2}", "\\frac{b (- 2 M - 2 X + b)}{2}", "\\frac{M (M b + 2 X)}{2}", "\\frac{M (- M + 2 b^{X})}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('M', commutative=True)), Mul(Integer(-1), Symbol('X', commutative=True)), Symbol('b', commutative=True))", "srepr_variable": "Symbol('M', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('M', commutative=True), Add(Mul(Integer(-1), Symbol('M', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('X', commutative=True)), Mul(Integer(2), Symbol('b', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('X', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('M', commutative=True)), Mul(Integer(-1), Symbol('X', commutative=True)), Mul(Integer(2), Symbol('b', commutative=True))))", "Mul(Rational(1, 2), Symbol('b', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('M', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('X', commutative=True)), Symbol('b', commutative=True)))", "Mul(Rational(1, 2), Symbol('M', commutative=True), Add(Mul(Symbol('M', commutative=True), Symbol('b', commutative=True)), Mul(Integer(2), Symbol('X', commutative=True))))", "Mul(Rational(1, 2), Symbol('M', commutative=True), Add(Mul(Integer(-1), Symbol('M', commutative=True)), Mul(Integer(2), Pow(Symbol('b', commutative=True), Symbol('X', commutative=True)))))"]}, {"premise_expression": "\\frac{w}{a}", "variable": "w", "positive": "\\frac{w^{2}}{2 a}", "negatives": ["w \\log{(a)}", "a e^{w}", "\\frac{w^{2} e^{a}}{2}", "e^{a + w}"], "srepr_premise_expression": "Mul(Pow(Symbol('a', commutative=True), Integer(-1)), Symbol('w', commutative=True))", "srepr_variable": "Symbol('w', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('a', commutative=True), Integer(-1)), Pow(Symbol('w', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('w', commutative=True), log(Symbol('a', commutative=True)))", "Mul(Symbol('a', commutative=True), exp(Symbol('w', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('w', commutative=True), Integer(2)), exp(Symbol('a', commutative=True)))", "exp(Add(Symbol('a', commutative=True), Symbol('w', commutative=True)))"]}, {"premise_expression": "\\log{(B u)}", "variable": "u", "positive": "u (\\log{(B u)} - 1)", "negatives": ["B (\\log{(B u)} - 1)", "u (\\log{(\\frac{u}{B})} - 1)", "B u (\\log{(u)} - 1)", "- \\cos{(B - u)}"], "srepr_premise_expression": "log(Mul(Symbol('B', commutative=True), Symbol('u', commutative=True)))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "Mul(Symbol('u', commutative=True), Add(log(Mul(Symbol('B', commutative=True), Symbol('u', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('B', commutative=True), Add(log(Mul(Symbol('B', commutative=True), Symbol('u', commutative=True))), Integer(-1)))", "Mul(Symbol('u', commutative=True), Add(log(Mul(Pow(Symbol('B', commutative=True), Integer(-1)), Symbol('u', commutative=True))), Integer(-1)))", "Mul(Symbol('B', commutative=True), Symbol('u', commutative=True), Add(log(Symbol('u', commutative=True)), Integer(-1)))", "Mul(Integer(-1), cos(Add(Symbol('B', commutative=True), Mul(Integer(-1), Symbol('u', commutative=True)))))"]}, {"premise_expression": "Q T", "variable": "Q", "positive": "\\frac{Q^{2} T}{2}", "negatives": ["\\frac{Q T^{2}}{2}", "\\frac{Q^{2} \\log{(T)}}{2}", "\\frac{Q^{2} (T - 1)}{2}", "\\frac{Q (- Q + 2 \\log{(T)})}{2}"], "srepr_premise_expression": "Mul(Symbol('Q', commutative=True), Symbol('T', commutative=True))", "srepr_variable": "Symbol('Q', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(2)), Symbol('T', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('Q', commutative=True), Pow(Symbol('T', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(2)), log(Symbol('T', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(2)), Add(Symbol('T', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Mul(Integer(-1), Symbol('Q', commutative=True)), Mul(Integer(2), log(Symbol('T', commutative=True)))))"]}, {"premise_expression": "D - N", "variable": "N", "positive": "\\frac{N (2 D - N)}{2}", "negatives": ["\\frac{D (D - 2 N)}{2}", "\\frac{N^{2} \\sin{(D)}}{2}", "\\frac{D N (N + 2)}{2}", "\\frac{N^{2}}{2 D}"], "srepr_premise_expression": "Add(Symbol('D', commutative=True), Mul(Integer(-1), Symbol('N', commutative=True)))", "srepr_variable": "Symbol('N', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Mul(Integer(2), Symbol('D', commutative=True)), Mul(Integer(-1), Symbol('N', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('D', commutative=True), Add(Symbol('D', commutative=True), Mul(Integer(-1), Integer(2), Symbol('N', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('N', commutative=True), Integer(2)), sin(Symbol('D', commutative=True)))", "Mul(Rational(1, 2), Symbol('D', commutative=True), Symbol('N', commutative=True), Add(Symbol('N', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(-1)), Pow(Symbol('N', commutative=True), Integer(2)))"]}, {"premise_expression": "B \\sin{(z)}", "variable": "B", "positive": "\\frac{B^{2} \\sin{(z)}}{2}", "negatives": ["\\frac{B^{2} z^{2}}{2}", "- B \\cos{(z)}", "z \\log{(B)}", "e^{B - z}"], "srepr_premise_expression": "Mul(Symbol('B', commutative=True), sin(Symbol('z', commutative=True)))", "srepr_variable": "Symbol('B', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('B', commutative=True), Integer(2)), sin(Symbol('z', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('B', commutative=True), Integer(2)), Pow(Symbol('z', commutative=True), Integer(2)))", "Mul(Integer(-1), Symbol('B', commutative=True), cos(Symbol('z', commutative=True)))", "Mul(Symbol('z', commutative=True), log(Symbol('B', commutative=True)))", "exp(Add(Symbol('B', commutative=True), Mul(Integer(-1), Symbol('z', commutative=True))))"]}, {"premise_expression": "Y s", "variable": "s", "positive": "\\frac{Y s^{2}}{2}", "negatives": ["\\frac{Y^{2} s}{2}", "\\frac{s (2 Y - s)}{2}", "\\frac{s^{2} \\sin{(Y)}}{2}", "\\frac{s (- 2 Y + s)}{2}"], "srepr_premise_expression": "Mul(Symbol('Y', commutative=True), Symbol('s', commutative=True))", "srepr_variable": "Symbol('s', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('Y', commutative=True), Pow(Symbol('s', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('Y', commutative=True), Integer(2)), Symbol('s', commutative=True))", "Mul(Rational(1, 2), Symbol('s', commutative=True), Add(Mul(Integer(2), Symbol('Y', commutative=True)), Mul(Integer(-1), Symbol('s', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('s', commutative=True), Integer(2)), sin(Symbol('Y', commutative=True)))", "Mul(Rational(1, 2), Symbol('s', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('Y', commutative=True)), Symbol('s', commutative=True)))"]}, {"premise_expression": "\\frac{F + G}{U}", "variable": "G", "positive": "\\frac{G (2 F + G)}{2 U}", "negatives": ["- \\frac{G (2 F - G)}{2 U}", "\\frac{F (F + 2 G)}{2 U}", "\\frac{G (2 F + G U)}{2}", "\\frac{G (2 F + G + 2 U)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('U', commutative=True), Integer(-1)), Add(Symbol('F', commutative=True), Symbol('G', commutative=True)))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('G', commutative=True), Pow(Symbol('U', commutative=True), Integer(-1)), Add(Mul(Integer(2), Symbol('F', commutative=True)), Symbol('G', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Rational(1, 2), Symbol('G', commutative=True), Pow(Symbol('U', commutative=True), Integer(-1)), Add(Mul(Integer(2), Symbol('F', commutative=True)), Mul(Integer(-1), Symbol('G', commutative=True))))", "Mul(Rational(1, 2), Symbol('F', commutative=True), Pow(Symbol('U', commutative=True), Integer(-1)), Add(Symbol('F', commutative=True), Mul(Integer(2), Symbol('G', commutative=True))))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Mul(Integer(2), Symbol('F', commutative=True)), Mul(Symbol('G', commutative=True), Symbol('U', commutative=True))))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Mul(Integer(2), Symbol('F', commutative=True)), Symbol('G', commutative=True), Mul(Integer(2), Symbol('U', commutative=True))))"]}, {"premise_expression": "I + \\frac{W}{Z}", "variable": "W", "positive": "I W + \\frac{W^{2}}{2 Z}", "negatives": ["I Z + W \\log{(Z)}", "\\frac{W (2 I - W)}{2 Z}", "\\frac{W (2 I + W + 2 Z)}{2}", "\\frac{I^{2}}{2} + \\frac{I W}{Z}"], "srepr_premise_expression": "Add(Symbol('I', commutative=True), Mul(Symbol('W', commutative=True), Pow(Symbol('Z', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('W', commutative=True)", "srepr_positive": "Add(Mul(Symbol('I', commutative=True), Symbol('W', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('W', commutative=True), Integer(2)), Pow(Symbol('Z', commutative=True), Integer(-1))))", "srepr_negatives": ["Add(Mul(Symbol('I', commutative=True), Symbol('Z', commutative=True)), Mul(Symbol('W', commutative=True), log(Symbol('Z', commutative=True))))", "Mul(Rational(1, 2), Symbol('W', commutative=True), Pow(Symbol('Z', commutative=True), Integer(-1)), Add(Mul(Integer(2), Symbol('I', commutative=True)), Mul(Integer(-1), Symbol('W', commutative=True))))", "Mul(Rational(1, 2), Symbol('W', commutative=True), Add(Mul(Integer(2), Symbol('I', commutative=True)), Symbol('W', commutative=True), Mul(Integer(2), Symbol('Z', commutative=True))))", "Add(Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(2))), Mul(Symbol('I', commutative=True), Symbol('W', commutative=True), Pow(Symbol('Z', commutative=True), Integer(-1))))"]}, {"premise_expression": "e^{- M + W}", "variable": "M", "positive": "- e^{- M + W}", "negatives": ["e^{- M + W}", "\\frac{\\sin{(M)}}{W}", "\\log{(M)} \\cos{(W)}", "M W + e^{M}"], "srepr_premise_expression": "exp(Add(Mul(Integer(-1), Symbol('M', commutative=True)), Symbol('W', commutative=True)))", "srepr_variable": "Symbol('M', commutative=True)", "srepr_positive": "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('M', commutative=True)), Symbol('W', commutative=True))))", "srepr_negatives": ["exp(Add(Mul(Integer(-1), Symbol('M', commutative=True)), Symbol('W', commutative=True)))", "Mul(Pow(Symbol('W', commutative=True), Integer(-1)), sin(Symbol('M', commutative=True)))", "Mul(log(Symbol('M', commutative=True)), cos(Symbol('W', commutative=True)))", "Add(Mul(Symbol('M', commutative=True), Symbol('W', commutative=True)), exp(Symbol('M', commutative=True)))"]}, {"premise_expression": "- m + \\cos{(u)}", "variable": "m", "positive": "\\frac{m (- m + 2 \\cos{(u)})}{2}", "negatives": ["- m u + \\sin{(u)}", "\\frac{m^{2}}{2 u}", "\\frac{m^{2}}{2} + \\sin{(m)}", "\\frac{m^{2} u^{2}}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('m', commutative=True)), cos(Symbol('u', commutative=True)))", "srepr_variable": "Symbol('m', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Mul(Integer(-1), Symbol('m', commutative=True)), Mul(Integer(2), cos(Symbol('u', commutative=True)))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('m', commutative=True), Symbol('u', commutative=True)), sin(Symbol('u', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('m', commutative=True), Integer(2)), Pow(Symbol('u', commutative=True), Integer(-1)))", "Add(Mul(Rational(1, 2), Pow(Symbol('m', commutative=True), Integer(2))), sin(Symbol('m', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('m', commutative=True), Integer(2)), Pow(Symbol('u', commutative=True), Integer(2)))"]}, {"premise_expression": "\\cos{(F - j)}", "variable": "j", "positive": "- \\sin{(F - j)}", "negatives": ["\\sin{(F - j)}", "\\sin{(F + j)}", "F \\sin{(j)}", "\\frac{j (- 2 F + j)}{2}"], "srepr_premise_expression": "cos(Add(Symbol('F', commutative=True), Mul(Integer(-1), Symbol('j', commutative=True))))", "srepr_variable": "Symbol('j', commutative=True)", "srepr_positive": "Mul(Integer(-1), sin(Add(Symbol('F', commutative=True), Mul(Integer(-1), Symbol('j', commutative=True)))))", "srepr_negatives": ["sin(Add(Symbol('F', commutative=True), Mul(Integer(-1), Symbol('j', commutative=True))))", "sin(Add(Symbol('F', commutative=True), Symbol('j', commutative=True)))", "Mul(Symbol('F', commutative=True), sin(Symbol('j', commutative=True)))", "Mul(Rational(1, 2), Symbol('j', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('F', commutative=True)), Symbol('j', commutative=True)))"]}, {"premise_expression": "- L + \\cos{(l)}", "variable": "L", "positive": "\\frac{L (- L + 2 \\cos{(l)})}{2}", "negatives": ["\\frac{L (L + 2 e^{l})}{2}", "\\frac{L (- L + 2 l)}{2}", "\\frac{L^{2} \\log{(l)}}{2}", "\\frac{L^{2} \\sin{(l)}}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('L', commutative=True)), cos(Symbol('l', commutative=True)))", "srepr_variable": "Symbol('L', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Mul(Integer(-1), Symbol('L', commutative=True)), Mul(Integer(2), cos(Symbol('l', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Symbol('L', commutative=True), Mul(Integer(2), exp(Symbol('l', commutative=True)))))", "Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Mul(Integer(-1), Symbol('L', commutative=True)), Mul(Integer(2), Symbol('l', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(2)), log(Symbol('l', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(2)), sin(Symbol('l', commutative=True)))"]}, {"premise_expression": "- H + \\sin{(C)}", "variable": "C", "positive": "- C H - \\cos{(C)}", "negatives": ["- C H + e^{C}", "- H \\cos{(C)}", "e^{C - H}", "\\cos{(C - H)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('H', commutative=True)), sin(Symbol('C', commutative=True)))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('C', commutative=True), Symbol('H', commutative=True)), Mul(Integer(-1), cos(Symbol('C', commutative=True))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('C', commutative=True), Symbol('H', commutative=True)), exp(Symbol('C', commutative=True)))", "Mul(Integer(-1), Symbol('H', commutative=True), cos(Symbol('C', commutative=True)))", "exp(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('H', commutative=True))))", "cos(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('H', commutative=True))))"]}, {"premise_expression": "- X + g", "variable": "X", "positive": "\\frac{X (- X + 2 g)}{2}", "negatives": ["\\frac{g (- 2 X + g)}{2}", "\\frac{X (X + 2 e^{g})}{2}", "e^{X + g}", "\\frac{X^{2}}{2 g}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('X', commutative=True)), Symbol('g', commutative=True))", "srepr_variable": "Symbol('X', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('X', commutative=True), Add(Mul(Integer(-1), Symbol('X', commutative=True)), Mul(Integer(2), Symbol('g', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('X', commutative=True)), Symbol('g', commutative=True)))", "Mul(Rational(1, 2), Symbol('X', commutative=True), Add(Symbol('X', commutative=True), Mul(Integer(2), exp(Symbol('g', commutative=True)))))", "exp(Add(Symbol('X', commutative=True), Symbol('g', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('X', commutative=True), Integer(2)), Pow(Symbol('g', commutative=True), Integer(-1)))"]}, {"premise_expression": "\\frac{\\sin{(g)}}{A}", "variable": "g", "positive": "- \\frac{\\cos{(g)}}{A}", "negatives": ["A e^{g}", "- A g + \\sin{(g)}", "\\log{(A)} \\sin{(g)}", "\\log{(A)} \\log{(g)}"], "srepr_premise_expression": "Mul(Pow(Symbol('A', commutative=True), Integer(-1)), sin(Symbol('g', commutative=True)))", "srepr_variable": "Symbol('g', commutative=True)", "srepr_positive": "Mul(Integer(-1), Pow(Symbol('A', commutative=True), Integer(-1)), cos(Symbol('g', commutative=True)))", "srepr_negatives": ["Mul(Symbol('A', commutative=True), exp(Symbol('g', commutative=True)))", "Add(Mul(Integer(-1), Symbol('A', commutative=True), Symbol('g', commutative=True)), sin(Symbol('g', commutative=True)))", "Mul(log(Symbol('A', commutative=True)), sin(Symbol('g', commutative=True)))", "Mul(log(Symbol('A', commutative=True)), log(Symbol('g', commutative=True)))"]}, {"premise_expression": "\\log{(\\frac{D}{Z})}", "variable": "D", "positive": "D (\\log{(\\frac{D}{Z})} - 1)", "negatives": ["Z (\\log{(\\frac{D}{Z})} + 1)", "\\frac{D (\\log{(D)} - 1)}{Z}", "D (Z + \\log{(D)} - 1)", "- \\cos{(D - Z)}"], "srepr_premise_expression": "log(Mul(Symbol('D', commutative=True), Pow(Symbol('Z', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('D', commutative=True)", "srepr_positive": "Mul(Symbol('D', commutative=True), Add(log(Mul(Symbol('D', commutative=True), Pow(Symbol('Z', commutative=True), Integer(-1)))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('Z', commutative=True), Add(log(Mul(Symbol('D', commutative=True), Pow(Symbol('Z', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Symbol('D', commutative=True), Pow(Symbol('Z', commutative=True), Integer(-1)), Add(log(Symbol('D', commutative=True)), Integer(-1)))", "Mul(Symbol('D', commutative=True), Add(Symbol('Z', commutative=True), log(Symbol('D', commutative=True)), Integer(-1)))", "Mul(Integer(-1), cos(Add(Symbol('D', commutative=True), Mul(Integer(-1), Symbol('Z', commutative=True)))))"]}, {"premise_expression": "- N + e^{f}", "variable": "f", "positive": "- N f + e^{f}", "negatives": ["N f + e^{f}", "\\frac{N (- N + 2 e^{f})}{2}", "\\log{(f)} \\cos{(N)}", "\\frac{f^{2}}{2 N}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('N', commutative=True)), exp(Symbol('f', commutative=True)))", "srepr_variable": "Symbol('f', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('N', commutative=True), Symbol('f', commutative=True)), exp(Symbol('f', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('N', commutative=True), Symbol('f', commutative=True)), exp(Symbol('f', commutative=True)))", "Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Mul(Integer(-1), Symbol('N', commutative=True)), Mul(Integer(2), exp(Symbol('f', commutative=True)))))", "Mul(log(Symbol('f', commutative=True)), cos(Symbol('N', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('N', commutative=True), Integer(-1)), Pow(Symbol('f', commutative=True), Integer(2)))"]}, {"premise_expression": "\\frac{b}{o} - p", "variable": "p", "positive": "\\frac{b p}{o} - \\frac{p^{2}}{2}", "negatives": ["\\frac{b p (2 o - p)}{2}", "\\frac{p^{2}}{2} + \\frac{o p}{b}", "b \\log{(o)} - o p", "\\frac{p (2 b + 2 o - p)}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('b', commutative=True), Pow(Symbol('o', commutative=True), Integer(-1))), Mul(Integer(-1), Symbol('p', commutative=True)))", "srepr_variable": "Symbol('p', commutative=True)", "srepr_positive": "Add(Mul(Symbol('b', commutative=True), Pow(Symbol('o', commutative=True), Integer(-1)), Symbol('p', commutative=True)), Mul(Integer(-1), Rational(1, 2), Pow(Symbol('p', commutative=True), Integer(2))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('b', commutative=True), Symbol('p', commutative=True), Add(Mul(Integer(2), Symbol('o', commutative=True)), Mul(Integer(-1), Symbol('p', commutative=True))))", "Add(Mul(Rational(1, 2), Pow(Symbol('p', commutative=True), Integer(2))), Mul(Pow(Symbol('b', commutative=True), Integer(-1)), Symbol('o', commutative=True), Symbol('p', commutative=True)))", "Add(Mul(Symbol('b', commutative=True), log(Symbol('o', commutative=True))), Mul(Integer(-1), Symbol('o', commutative=True), Symbol('p', commutative=True)))", "Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Mul(Integer(2), Symbol('b', commutative=True)), Mul(Integer(2), Symbol('o', commutative=True)), Mul(Integer(-1), Symbol('p', commutative=True))))"]}, {"premise_expression": "M a", "variable": "a", "positive": "\\frac{M a^{2}}{2}", "negatives": ["\\frac{M^{2} a}{2}", "- M \\cos{(a)}", "\\frac{\\sin{(a)}}{M}", "- \\sin{(M - a)}"], "srepr_premise_expression": "Mul(Symbol('M', commutative=True), Symbol('a', commutative=True))", "srepr_variable": "Symbol('a', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('M', commutative=True), Pow(Symbol('a', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('M', commutative=True), Integer(2)), Symbol('a', commutative=True))", "Mul(Integer(-1), Symbol('M', commutative=True), cos(Symbol('a', commutative=True)))", "Mul(Pow(Symbol('M', commutative=True), Integer(-1)), sin(Symbol('a', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('M', commutative=True), Mul(Integer(-1), Symbol('a', commutative=True)))))"]}, {"premise_expression": "\\cos{(M + Z)}", "variable": "Z", "positive": "\\sin{(M + Z)}", "negatives": ["M \\log{(Z)}", "M e^{\\frac{Z}{M}}", "\\frac{Z^{2}}{2 M}", "Z (- M + \\log{(Z^{M})})"], "srepr_premise_expression": "cos(Add(Symbol('M', commutative=True), Symbol('Z', commutative=True)))", "srepr_variable": "Symbol('Z', commutative=True)", "srepr_positive": "sin(Add(Symbol('M', commutative=True), Symbol('Z', commutative=True)))", "srepr_negatives": ["Mul(Symbol('M', commutative=True), log(Symbol('Z', commutative=True)))", "Mul(Symbol('M', commutative=True), exp(Mul(Pow(Symbol('M', commutative=True), Integer(-1)), Symbol('Z', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('M', commutative=True), Integer(-1)), Pow(Symbol('Z', commutative=True), Integer(2)))", "Mul(Symbol('Z', commutative=True), Add(Mul(Integer(-1), Symbol('M', commutative=True)), log(Pow(Symbol('Z', commutative=True), Symbol('M', commutative=True)))))"]}, {"premise_expression": "\\frac{v}{Q}", "variable": "v", "positive": "\\frac{v^{2}}{2 Q}", "negatives": ["v \\log{(Q)}", "\\frac{v^{2} \\log{(Q)}}{2}", "\\frac{v^{2} \\sin{(Q)}}{2}", "\\frac{v (2 Q - v)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('Q', commutative=True), Integer(-1)), Symbol('v', commutative=True))", "srepr_variable": "Symbol('v', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(-1)), Pow(Symbol('v', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('v', commutative=True), log(Symbol('Q', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('v', commutative=True), Integer(2)), log(Symbol('Q', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('v', commutative=True), Integer(2)), sin(Symbol('Q', commutative=True)))", "Mul(Rational(1, 2), Symbol('v', commutative=True), Add(Mul(Integer(2), Symbol('Q', commutative=True)), Mul(Integer(-1), Symbol('v', commutative=True))))"]}, {"premise_expression": "- \\sin{(I - Q)}", "variable": "I", "positive": "\\cos{(I - Q)}", "negatives": ["- \\cos{(I - Q)}", "- \\frac{\\cos{(I)}}{Q}", "\\frac{I (I - 2 Q)}{2}", "I Q - \\cos{(I)}"], "srepr_premise_expression": "Mul(Integer(-1), sin(Add(Symbol('I', commutative=True), Mul(Integer(-1), Symbol('Q', commutative=True)))))", "srepr_variable": "Symbol('I', commutative=True)", "srepr_positive": "cos(Add(Symbol('I', commutative=True), Mul(Integer(-1), Symbol('Q', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('I', commutative=True), Mul(Integer(-1), Symbol('Q', commutative=True)))))", "Mul(Integer(-1), Pow(Symbol('Q', commutative=True), Integer(-1)), cos(Symbol('I', commutative=True)))", "Mul(Rational(1, 2), Symbol('I', commutative=True), Add(Symbol('I', commutative=True), Mul(Integer(-1), Integer(2), Symbol('Q', commutative=True))))", "Add(Mul(Symbol('I', commutative=True), Symbol('Q', commutative=True)), Mul(Integer(-1), cos(Symbol('I', commutative=True))))"]}, {"premise_expression": "Q + \\log{(Y)}", "variable": "Q", "positive": "\\frac{Q (Q + 2 \\log{(Y)})}{2}", "negatives": ["\\frac{Q (- Q + 2 \\log{(Y)})}{2}", "Y (Q + \\log{(Y)} - 1)", "\\frac{Q^{2} \\cos{(Y)}}{2}", "\\frac{Q^{2} e^{Y}}{2}"], "srepr_premise_expression": "Add(Symbol('Q', commutative=True), log(Symbol('Y', commutative=True)))", "srepr_variable": "Symbol('Q', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Symbol('Q', commutative=True), Mul(Integer(2), log(Symbol('Y', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Mul(Integer(-1), Symbol('Q', commutative=True)), Mul(Integer(2), log(Symbol('Y', commutative=True)))))", "Mul(Symbol('Y', commutative=True), Add(Symbol('Q', commutative=True), log(Symbol('Y', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(2)), cos(Symbol('Y', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(2)), exp(Symbol('Y', commutative=True)))"]}, {"premise_expression": "U - g", "variable": "U", "positive": "\\frac{U (U - 2 g)}{2}", "negatives": ["\\frac{U (- U + 2 g)}{2}", "\\frac{g (2 U - g)}{2}", "\\frac{U^{2} \\log{(g)}}{2}", "e^{U - g}"], "srepr_premise_expression": "Add(Symbol('U', commutative=True), Mul(Integer(-1), Symbol('g', commutative=True)))", "srepr_variable": "Symbol('U', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('U', commutative=True), Add(Symbol('U', commutative=True), Mul(Integer(-1), Integer(2), Symbol('g', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('U', commutative=True), Add(Mul(Integer(-1), Symbol('U', commutative=True)), Mul(Integer(2), Symbol('g', commutative=True))))", "Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Mul(Integer(2), Symbol('U', commutative=True)), Mul(Integer(-1), Symbol('g', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('U', commutative=True), Integer(2)), log(Symbol('g', commutative=True)))", "exp(Add(Symbol('U', commutative=True), Mul(Integer(-1), Symbol('g', commutative=True))))"]}, {"premise_expression": "r \\cos{(z)}", "variable": "r", "positive": "\\frac{r^{2} \\cos{(z)}}{2}", "negatives": ["\\frac{r^{2} \\sin{(z)}}{2}", "r z \\sin{(z)}", "r \\sin{(z)}", "\\frac{r (- r + 2 \\log{(z)})}{2}"], "srepr_premise_expression": "Mul(Symbol('r', commutative=True), cos(Symbol('z', commutative=True)))", "srepr_variable": "Symbol('r', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('r', commutative=True), Integer(2)), cos(Symbol('z', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('r', commutative=True), Integer(2)), sin(Symbol('z', commutative=True)))", "Mul(Symbol('r', commutative=True), Symbol('z', commutative=True), sin(Symbol('z', commutative=True)))", "Mul(Symbol('r', commutative=True), sin(Symbol('z', commutative=True)))", "Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(-1), Symbol('r', commutative=True)), Mul(Integer(2), log(Symbol('z', commutative=True)))))"]}, {"premise_expression": "F I", "variable": "F", "positive": "\\frac{F^{2} I}{2}", "negatives": ["\\frac{F I^{2}}{2}", "0", "\\log{(F)} \\cos{(I)}", "- \\cos{(F + I)}"], "srepr_premise_expression": "Mul(Symbol('F', commutative=True), Symbol('I', commutative=True))", "srepr_variable": "Symbol('F', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('F', commutative=True), Integer(2)), Symbol('I', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('F', commutative=True), Pow(Symbol('I', commutative=True), Integer(2)))", "Integer(0)", "Mul(log(Symbol('F', commutative=True)), cos(Symbol('I', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('F', commutative=True), Symbol('I', commutative=True))))"]}, {"premise_expression": "\\cos^{Y}{(G)}", "variable": "G", "positive": "\\int \\cos^{Y}{(G)} dG", "negatives": ["G (\\log{(\\frac{G}{Y})} - 1)", "\\frac{G (- G + 2 \\cos{(Y)})}{2}", "\\frac{G (G + 2 Y)}{2}", "\\frac{G (- G + 2 \\log{(Y)})}{2}"], "srepr_premise_expression": "Pow(cos(Symbol('G', commutative=True)), Symbol('Y', commutative=True))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Integral(Pow(cos(Symbol('G', commutative=True)), Symbol('Y', commutative=True)), Tuple(Symbol('G', commutative=True)))", "srepr_negatives": ["Mul(Symbol('G', commutative=True), Add(log(Mul(Symbol('G', commutative=True), Pow(Symbol('Y', commutative=True), Integer(-1)))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Mul(Integer(-1), Symbol('G', commutative=True)), Mul(Integer(2), cos(Symbol('Y', commutative=True)))))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Symbol('G', commutative=True), Mul(Integer(2), Symbol('Y', commutative=True))))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Mul(Integer(-1), Symbol('G', commutative=True)), Mul(Integer(2), log(Symbol('Y', commutative=True)))))"]}, {"premise_expression": "T \\sin{(W)}", "variable": "W", "positive": "- T \\cos{(W)}", "negatives": ["T \\sin{(W)}", "- T W + \\sin{(W)}", "\\frac{T W^{2}}{2}", "\\frac{T^{2} \\sin{(W)}}{2}"], "srepr_premise_expression": "Mul(Symbol('T', commutative=True), sin(Symbol('W', commutative=True)))", "srepr_variable": "Symbol('W', commutative=True)", "srepr_positive": "Mul(Integer(-1), Symbol('T', commutative=True), cos(Symbol('W', commutative=True)))", "srepr_negatives": ["Mul(Symbol('T', commutative=True), sin(Symbol('W', commutative=True)))", "Add(Mul(Integer(-1), Symbol('T', commutative=True), Symbol('W', commutative=True)), sin(Symbol('W', commutative=True)))", "Mul(Rational(1, 2), Symbol('T', commutative=True), Pow(Symbol('W', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('T', commutative=True), Integer(2)), sin(Symbol('W', commutative=True)))"]}, {"premise_expression": "A + \\frac{L}{p}", "variable": "A", "positive": "\\frac{A^{2}}{2} + \\frac{A L}{p}", "negatives": ["\\frac{A (A L + 2 p)}{2}", "\\frac{A (- A + 2 L + 2 p)}{2}", "\\frac{A (A p - 2 L)}{2}", "\\frac{A^{2} L p}{2}"], "srepr_premise_expression": "Add(Symbol('A', commutative=True), Mul(Symbol('L', commutative=True), Pow(Symbol('p', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('A', commutative=True)", "srepr_positive": "Add(Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2))), Mul(Symbol('A', commutative=True), Symbol('L', commutative=True), Pow(Symbol('p', commutative=True), Integer(-1))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Mul(Symbol('A', commutative=True), Symbol('L', commutative=True)), Mul(Integer(2), Symbol('p', commutative=True))))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Mul(Integer(-1), Symbol('A', commutative=True)), Mul(Integer(2), Symbol('L', commutative=True)), Mul(Integer(2), Symbol('p', commutative=True))))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Mul(Symbol('A', commutative=True), Symbol('p', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('L', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2)), Symbol('L', commutative=True), Symbol('p', commutative=True))"]}, {"premise_expression": "\\frac{\\sin{(r)}}{C}", "variable": "r", "positive": "- \\frac{\\cos{(r)}}{C}", "negatives": ["\\frac{C r^{2}}{2}", "- \\sin{(C - r)}", "\\frac{r^{2} \\log{(C)}}{2}", "\\frac{r (2 C - r)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('C', commutative=True), Integer(-1)), sin(Symbol('r', commutative=True)))", "srepr_variable": "Symbol('r', commutative=True)", "srepr_positive": "Mul(Integer(-1), Pow(Symbol('C', commutative=True), Integer(-1)), cos(Symbol('r', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('C', commutative=True), Pow(Symbol('r', commutative=True), Integer(2)))", "Mul(Integer(-1), sin(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('r', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('r', commutative=True), Integer(2)), log(Symbol('C', commutative=True)))", "Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(2), Symbol('C', commutative=True)), Mul(Integer(-1), Symbol('r', commutative=True))))"]}, {"premise_expression": "Q \\cos{(t)}", "variable": "Q", "positive": "\\frac{Q^{2} \\cos{(t)}}{2}", "negatives": ["\\frac{Q^{2} \\log{(t)}}{2}", "\\frac{Q (- Q + 2 \\cos{(t)})}{2}", "- \\frac{\\cos{(Q)}}{t}", "Q \\sin{(t)}"], "srepr_premise_expression": "Mul(Symbol('Q', commutative=True), cos(Symbol('t', commutative=True)))", "srepr_variable": "Symbol('Q', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(2)), cos(Symbol('t', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(2)), log(Symbol('t', commutative=True)))", "Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Mul(Integer(-1), Symbol('Q', commutative=True)), Mul(Integer(2), cos(Symbol('t', commutative=True)))))", "Mul(Integer(-1), Pow(Symbol('t', commutative=True), Integer(-1)), cos(Symbol('Q', commutative=True)))", "Mul(Symbol('Q', commutative=True), sin(Symbol('t', commutative=True)))"]}, {"premise_expression": "J h", "variable": "J", "positive": "\\frac{J^{2} h}{2}", "negatives": ["\\frac{J h^{2}}{2}", "\\frac{J^{2} \\log{(h)}}{2}", "\\frac{J (- J + 2 h)}{2}", "J h + e^{J}"], "srepr_premise_expression": "Mul(Symbol('J', commutative=True), Symbol('h', commutative=True))", "srepr_variable": "Symbol('J', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('J', commutative=True), Integer(2)), Symbol('h', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('J', commutative=True), Pow(Symbol('h', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('J', commutative=True), Integer(2)), log(Symbol('h', commutative=True)))", "Mul(Rational(1, 2), Symbol('J', commutative=True), Add(Mul(Integer(-1), Symbol('J', commutative=True)), Mul(Integer(2), Symbol('h', commutative=True))))", "Add(Mul(Symbol('J', commutative=True), Symbol('h', commutative=True)), exp(Symbol('J', commutative=True)))"]}, {"premise_expression": "I - L", "variable": "I", "positive": "\\frac{I (I - 2 L)}{2}", "negatives": ["\\frac{L (2 I - L)}{2}", "\\frac{I^{2} L}{2}", "\\sin{(I - L)}", "\\cos{(I - L)}"], "srepr_premise_expression": "Add(Symbol('I', commutative=True), Mul(Integer(-1), Symbol('L', commutative=True)))", "srepr_variable": "Symbol('I', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('I', commutative=True), Add(Symbol('I', commutative=True), Mul(Integer(-1), Integer(2), Symbol('L', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Mul(Integer(2), Symbol('I', commutative=True)), Mul(Integer(-1), Symbol('L', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(2)), Symbol('L', commutative=True))", "sin(Add(Symbol('I', commutative=True), Mul(Integer(-1), Symbol('L', commutative=True))))", "cos(Add(Symbol('I', commutative=True), Mul(Integer(-1), Symbol('L', commutative=True))))"]}, {"premise_expression": "- F + X + z", "variable": "z", "positive": "z (- F + X + \\frac{z}{2})", "negatives": ["\\frac{X (- 2 F + X + 2 z)}{2}", "\\frac{F (- F + 2 X + 2 z)}{2}", "\\frac{z^{2} (F + X)}{2}", "\\frac{z (F z + 2 X)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('F', commutative=True)), Symbol('X', commutative=True), Symbol('z', commutative=True))", "srepr_variable": "Symbol('z', commutative=True)", "srepr_positive": "Mul(Symbol('z', commutative=True), Add(Mul(Integer(-1), Symbol('F', commutative=True)), Symbol('X', commutative=True), Mul(Rational(1, 2), Symbol('z', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('X', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('F', commutative=True)), Symbol('X', commutative=True), Mul(Integer(2), Symbol('z', commutative=True))))", "Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Mul(Integer(-1), Symbol('F', commutative=True)), Mul(Integer(2), Symbol('X', commutative=True)), Mul(Integer(2), Symbol('z', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('z', commutative=True), Integer(2)), Add(Symbol('F', commutative=True), Symbol('X', commutative=True)))", "Mul(Rational(1, 2), Symbol('z', commutative=True), Add(Mul(Symbol('F', commutative=True), Symbol('z', commutative=True)), Mul(Integer(2), Symbol('X', commutative=True))))"]}, {"premise_expression": "X w", "variable": "w", "positive": "\\frac{X w^{2}}{2}", "negatives": ["\\frac{X^{2} w}{2}", "X \\sin{(w)}", "\\frac{w^{2} \\cos{(X)}}{2}", "\\cos{(X - w)}"], "srepr_premise_expression": "Mul(Symbol('X', commutative=True), Symbol('w', commutative=True))", "srepr_variable": "Symbol('w', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('X', commutative=True), Pow(Symbol('w', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('X', commutative=True), Integer(2)), Symbol('w', commutative=True))", "Mul(Symbol('X', commutative=True), sin(Symbol('w', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('w', commutative=True), Integer(2)), cos(Symbol('X', commutative=True)))", "cos(Add(Symbol('X', commutative=True), Mul(Integer(-1), Symbol('w', commutative=True))))"]}, {"premise_expression": "S + s", "variable": "S", "positive": "\\frac{S (S + 2 s)}{2}", "negatives": ["\\frac{S (S - 2 s)}{2}", "\\frac{s (2 S + s)}{2}", "\\frac{S (- S + 2 \\log{(s)})}{2}", "\\frac{S^{2} \\sin{(s)}}{2}"], "srepr_premise_expression": "Add(Symbol('S', commutative=True), Symbol('s', commutative=True))", "srepr_variable": "Symbol('S', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Symbol('S', commutative=True), Mul(Integer(2), Symbol('s', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Symbol('S', commutative=True), Mul(Integer(-1), Integer(2), Symbol('s', commutative=True))))", "Mul(Rational(1, 2), Symbol('s', commutative=True), Add(Mul(Integer(2), Symbol('S', commutative=True)), Symbol('s', commutative=True)))", "Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Mul(Integer(-1), Symbol('S', commutative=True)), Mul(Integer(2), log(Symbol('s', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('S', commutative=True), Integer(2)), sin(Symbol('s', commutative=True)))"]}, {"premise_expression": "\\frac{e^{V}}{T}", "variable": "T", "positive": "e^{V} \\log{(T)}", "negatives": ["V e^{T}", "T (e^{V})^{V}", "- e^{- T + V}", "- T V - \\cos{(T)}"], "srepr_premise_expression": "Mul(Pow(Symbol('T', commutative=True), Integer(-1)), exp(Symbol('V', commutative=True)))", "srepr_variable": "Symbol('T', commutative=True)", "srepr_positive": "Mul(exp(Symbol('V', commutative=True)), log(Symbol('T', commutative=True)))", "srepr_negatives": ["Mul(Symbol('V', commutative=True), exp(Symbol('T', commutative=True)))", "Mul(Symbol('T', commutative=True), Pow(exp(Symbol('V', commutative=True)), Symbol('V', commutative=True)))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('T', commutative=True)), Symbol('V', commutative=True))))", "Add(Mul(Integer(-1), Symbol('T', commutative=True), Symbol('V', commutative=True)), Mul(Integer(-1), cos(Symbol('T', commutative=True))))"]}, {"premise_expression": "\\frac{x}{a u}", "variable": "x", "positive": "\\frac{x^{2}}{2 a u}", "negatives": ["\\frac{a x^{2}}{2 u}", "\\frac{u x^{2}}{2 a}", "\\frac{x \\log{(a)}}{u}", "\\frac{x \\log{(u)}}{a}"], "srepr_premise_expression": "Mul(Pow(Symbol('a', commutative=True), Integer(-1)), Pow(Symbol('u', commutative=True), Integer(-1)), Symbol('x', commutative=True))", "srepr_variable": "Symbol('x', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('a', commutative=True), Integer(-1)), Pow(Symbol('u', commutative=True), Integer(-1)), Pow(Symbol('x', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('a', commutative=True), Pow(Symbol('u', commutative=True), Integer(-1)), Pow(Symbol('x', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('a', commutative=True), Integer(-1)), Symbol('u', commutative=True), Pow(Symbol('x', commutative=True), Integer(2)))", "Mul(Pow(Symbol('u', commutative=True), Integer(-1)), Symbol('x', commutative=True), log(Symbol('a', commutative=True)))", "Mul(Pow(Symbol('a', commutative=True), Integer(-1)), Symbol('x', commutative=True), log(Symbol('u', commutative=True)))"]}, {"premise_expression": "\\frac{L}{c} + m", "variable": "c", "positive": "L \\log{(c)} + c m", "negatives": ["\\frac{L^{2}}{2 c} + L m", "\\frac{L m}{c} + \\frac{m^{2}}{2}", "(L + m) \\log{(c)}", "\\frac{c (- 2 L + c)}{2 m}"], "srepr_premise_expression": "Add(Mul(Symbol('L', commutative=True), Pow(Symbol('c', commutative=True), Integer(-1))), Symbol('m', commutative=True))", "srepr_variable": "Symbol('c', commutative=True)", "srepr_positive": "Add(Mul(Symbol('L', commutative=True), log(Symbol('c', commutative=True))), Mul(Symbol('c', commutative=True), Symbol('m', commutative=True)))", "srepr_negatives": ["Add(Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(2)), Pow(Symbol('c', commutative=True), Integer(-1))), Mul(Symbol('L', commutative=True), Symbol('m', commutative=True)))", "Add(Mul(Symbol('L', commutative=True), Pow(Symbol('c', commutative=True), Integer(-1)), Symbol('m', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('m', commutative=True), Integer(2))))", "Mul(Add(Symbol('L', commutative=True), Symbol('m', commutative=True)), log(Symbol('c', commutative=True)))", "Mul(Rational(1, 2), Symbol('c', commutative=True), Pow(Symbol('m', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Integer(2), Symbol('L', commutative=True)), Symbol('c', commutative=True)))"]}, {"premise_expression": "Q \\cos{(m)}", "variable": "Q", "positive": "\\frac{Q^{2} \\cos{(m)}}{2}", "negatives": ["\\frac{Q^{2} \\log{(m)}}{2}", "\\frac{Q^{2} m}{2}", "Q \\sin{(m)}", "\\frac{Q (Q + 2 \\sin{(m)})}{2}"], "srepr_premise_expression": "Mul(Symbol('Q', commutative=True), cos(Symbol('m', commutative=True)))", "srepr_variable": "Symbol('Q', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(2)), cos(Symbol('m', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(2)), log(Symbol('m', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(2)), Symbol('m', commutative=True))", "Mul(Symbol('Q', commutative=True), sin(Symbol('m', commutative=True)))", "Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Symbol('Q', commutative=True), Mul(Integer(2), sin(Symbol('m', commutative=True)))))"]}, {"premise_expression": "A - S", "variable": "S", "positive": "\\frac{S (2 A - S)}{2}", "negatives": ["\\frac{A (A - 2 S)}{2}", "\\frac{S^{2} \\log{(A)}}{2}", "A S + e^{S}", "- A S - \\cos{(S)}"], "srepr_premise_expression": "Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('S', commutative=True)))", "srepr_variable": "Symbol('S', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Mul(Integer(2), Symbol('A', commutative=True)), Mul(Integer(-1), Symbol('S', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Symbol('A', commutative=True), Mul(Integer(-1), Integer(2), Symbol('S', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('S', commutative=True), Integer(2)), log(Symbol('A', commutative=True)))", "Add(Mul(Symbol('A', commutative=True), Symbol('S', commutative=True)), exp(Symbol('S', commutative=True)))", "Add(Mul(Integer(-1), Symbol('A', commutative=True), Symbol('S', commutative=True)), Mul(Integer(-1), cos(Symbol('S', commutative=True))))"]}, {"premise_expression": "\\frac{t}{E}", "variable": "t", "positive": "\\frac{t^{2}}{2 E}", "negatives": ["t \\log{(E)}", "- \\frac{\\cos{(t)}}{E}", "\\frac{\\sin{(t)}}{E}", "e^{- E + t}"], "srepr_premise_expression": "Mul(Pow(Symbol('E', commutative=True), Integer(-1)), Symbol('t', commutative=True))", "srepr_variable": "Symbol('t', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('E', commutative=True), Integer(-1)), Pow(Symbol('t', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('t', commutative=True), log(Symbol('E', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('E', commutative=True), Integer(-1)), cos(Symbol('t', commutative=True)))", "Mul(Pow(Symbol('E', commutative=True), Integer(-1)), sin(Symbol('t', commutative=True)))", "exp(Add(Mul(Integer(-1), Symbol('E', commutative=True)), Symbol('t', commutative=True)))"]}, {"premise_expression": "- F + \\sin{(g)}", "variable": "F", "positive": "\\frac{F (- F + 2 \\sin{(g)})}{2}", "negatives": ["F g + \\sin{(F)}", "\\frac{F g (F - 2)}{2}", "- F g - \\cos{(g)}", "\\frac{F^{2} g}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('F', commutative=True)), sin(Symbol('g', commutative=True)))", "srepr_variable": "Symbol('F', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Mul(Integer(-1), Symbol('F', commutative=True)), Mul(Integer(2), sin(Symbol('g', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('F', commutative=True), Symbol('g', commutative=True)), sin(Symbol('F', commutative=True)))", "Mul(Rational(1, 2), Symbol('F', commutative=True), Symbol('g', commutative=True), Add(Symbol('F', commutative=True), Integer(-2)))", "Add(Mul(Integer(-1), Symbol('F', commutative=True), Symbol('g', commutative=True)), Mul(Integer(-1), cos(Symbol('g', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('F', commutative=True), Integer(2)), Symbol('g', commutative=True))"]}, {"premise_expression": "H K", "variable": "H", "positive": "\\frac{H^{2} K}{2}", "negatives": ["\\frac{H K^{2}}{2}", "K \\sin{(H)}", "\\frac{H^{2} (K + 1)}{2 K}", "\\log{(H)} \\log{(K)}"], "srepr_premise_expression": "Mul(Symbol('H', commutative=True), Symbol('K', commutative=True))", "srepr_variable": "Symbol('H', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('H', commutative=True), Integer(2)), Symbol('K', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('H', commutative=True), Pow(Symbol('K', commutative=True), Integer(2)))", "Mul(Symbol('K', commutative=True), sin(Symbol('H', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('H', commutative=True), Integer(2)), Pow(Symbol('K', commutative=True), Integer(-1)), Add(Symbol('K', commutative=True), Integer(1)))", "Mul(log(Symbol('H', commutative=True)), log(Symbol('K', commutative=True)))"]}, {"premise_expression": "G - R", "variable": "R", "positive": "\\frac{R (2 G - R)}{2}", "negatives": ["\\frac{G (G - 2 R)}{2}", "\\frac{R^{2} \\cos{(G)}}{2}", "- \\sin{(G - R)}", "- \\cos{(G - R)}"], "srepr_premise_expression": "Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('R', commutative=True)))", "srepr_variable": "Symbol('R', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('R', commutative=True), Add(Mul(Integer(2), Symbol('G', commutative=True)), Mul(Integer(-1), Symbol('R', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Symbol('G', commutative=True), Mul(Integer(-1), Integer(2), Symbol('R', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('R', commutative=True), Integer(2)), cos(Symbol('G', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('R', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('R', commutative=True)))))"]}, {"premise_expression": "\\frac{w}{F}", "variable": "F", "positive": "w \\log{(F)}", "negatives": ["\\frac{w^{2}}{2 F}", "w e^{\\frac{F}{w}}", "F w (\\log{(F)} - 1)", "e^{F - w}"], "srepr_premise_expression": "Mul(Pow(Symbol('F', commutative=True), Integer(-1)), Symbol('w', commutative=True))", "srepr_variable": "Symbol('F', commutative=True)", "srepr_positive": "Mul(Symbol('w', commutative=True), log(Symbol('F', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('F', commutative=True), Integer(-1)), Pow(Symbol('w', commutative=True), Integer(2)))", "Mul(Symbol('w', commutative=True), exp(Mul(Symbol('F', commutative=True), Pow(Symbol('w', commutative=True), Integer(-1)))))", "Mul(Symbol('F', commutative=True), Symbol('w', commutative=True), Add(log(Symbol('F', commutative=True)), Integer(-1)))", "exp(Add(Symbol('F', commutative=True), Mul(Integer(-1), Symbol('w', commutative=True))))"]}, {"premise_expression": "U e^{a}", "variable": "U", "positive": "\\frac{U^{2} e^{a}}{2}", "negatives": ["U e^{a}", "\\frac{U^{2} a}{2}", "\\frac{U (U + 2 a)}{2}", "\\frac{U (- U + 2 \\log{(a)})}{2}"], "srepr_premise_expression": "Mul(Symbol('U', commutative=True), exp(Symbol('a', commutative=True)))", "srepr_variable": "Symbol('U', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('U', commutative=True), Integer(2)), exp(Symbol('a', commutative=True)))", "srepr_negatives": ["Mul(Symbol('U', commutative=True), exp(Symbol('a', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('U', commutative=True), Integer(2)), Symbol('a', commutative=True))", "Mul(Rational(1, 2), Symbol('U', commutative=True), Add(Symbol('U', commutative=True), Mul(Integer(2), Symbol('a', commutative=True))))", "Mul(Rational(1, 2), Symbol('U', commutative=True), Add(Mul(Integer(-1), Symbol('U', commutative=True)), Mul(Integer(2), log(Symbol('a', commutative=True)))))"]}, {"premise_expression": "X + e^{m}", "variable": "m", "positive": "X m + e^{m}", "negatives": ["X m + \\sin{(m)}", "\\frac{X (X + 2 e^{m})}{2}", "\\frac{m^{2} e^{X}}{2}", "\\frac{m^{2}}{2 X}"], "srepr_premise_expression": "Add(Symbol('X', commutative=True), exp(Symbol('m', commutative=True)))", "srepr_variable": "Symbol('m', commutative=True)", "srepr_positive": "Add(Mul(Symbol('X', commutative=True), Symbol('m', commutative=True)), exp(Symbol('m', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('X', commutative=True), Symbol('m', commutative=True)), sin(Symbol('m', commutative=True)))", "Mul(Rational(1, 2), Symbol('X', commutative=True), Add(Symbol('X', commutative=True), Mul(Integer(2), exp(Symbol('m', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('m', commutative=True), Integer(2)), exp(Symbol('X', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('X', commutative=True), Integer(-1)), Pow(Symbol('m', commutative=True), Integer(2)))"]}, {"premise_expression": "\\frac{h}{I}", "variable": "h", "positive": "\\frac{h^{2}}{2 I}", "negatives": ["h \\log{(I)}", "\\frac{I h^{2}}{2}", "\\frac{h (h + 2 \\log{(I)})}{2}", "\\frac{h (- h + 2 \\cos{(I)})}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('I', commutative=True), Integer(-1)), Symbol('h', commutative=True))", "srepr_variable": "Symbol('h', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(-1)), Pow(Symbol('h', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('h', commutative=True), log(Symbol('I', commutative=True)))", "Mul(Rational(1, 2), Symbol('I', commutative=True), Pow(Symbol('h', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('h', commutative=True), Add(Symbol('h', commutative=True), Mul(Integer(2), log(Symbol('I', commutative=True)))))", "Mul(Rational(1, 2), Symbol('h', commutative=True), Add(Mul(Integer(-1), Symbol('h', commutative=True)), Mul(Integer(2), cos(Symbol('I', commutative=True)))))"]}, {"premise_expression": "- q + x", "variable": "q", "positive": "\\frac{q (- q + 2 x)}{2}", "negatives": ["\\frac{x (- 2 q + x)}{2}", "\\frac{q (- q + 2 \\sin{(x)})}{2}", "\\frac{q (q + 2 e^{x})}{2}", "q \\sin{(2 x)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('q', commutative=True)), Symbol('x', commutative=True))", "srepr_variable": "Symbol('q', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('q', commutative=True), Add(Mul(Integer(-1), Symbol('q', commutative=True)), Mul(Integer(2), Symbol('x', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('x', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('q', commutative=True)), Symbol('x', commutative=True)))", "Mul(Rational(1, 2), Symbol('q', commutative=True), Add(Mul(Integer(-1), Symbol('q', commutative=True)), Mul(Integer(2), sin(Symbol('x', commutative=True)))))", "Mul(Rational(1, 2), Symbol('q', commutative=True), Add(Symbol('q', commutative=True), Mul(Integer(2), exp(Symbol('x', commutative=True)))))", "Mul(Symbol('q', commutative=True), sin(Mul(Integer(2), Symbol('x', commutative=True))))"]}, {"premise_expression": "- A + Q - m", "variable": "m", "positive": "\\frac{m (- 2 A + 2 Q - m)}{2}", "negatives": ["\\frac{m (2 A^{Q} - m)}{2}", "\\frac{m (2 Q^{A} - m)}{2}", "\\frac{Q (- 2 A + Q - 2 m)}{2}", "\\frac{A (- A + 2 Q - 2 m)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('A', commutative=True)), Symbol('Q', commutative=True), Mul(Integer(-1), Symbol('m', commutative=True)))", "srepr_variable": "Symbol('m', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('A', commutative=True)), Mul(Integer(2), Symbol('Q', commutative=True)), Mul(Integer(-1), Symbol('m', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Mul(Integer(2), Pow(Symbol('A', commutative=True), Symbol('Q', commutative=True))), Mul(Integer(-1), Symbol('m', commutative=True))))", "Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Mul(Integer(2), Pow(Symbol('Q', commutative=True), Symbol('A', commutative=True))), Mul(Integer(-1), Symbol('m', commutative=True))))", "Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('A', commutative=True)), Symbol('Q', commutative=True), Mul(Integer(-1), Integer(2), Symbol('m', commutative=True))))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Mul(Integer(-1), Symbol('A', commutative=True)), Mul(Integer(2), Symbol('Q', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('m', commutative=True))))"]}, {"premise_expression": "\\frac{e^{C}}{D}", "variable": "D", "positive": "e^{C} \\log{(D)}", "negatives": ["- C D + e^{D}", "\\frac{D (2 C + D)}{2}", "\\frac{D (2 C - D)}{2}", "D (- C + \\log{(D)} - 1)"], "srepr_premise_expression": "Mul(Pow(Symbol('D', commutative=True), Integer(-1)), exp(Symbol('C', commutative=True)))", "srepr_variable": "Symbol('D', commutative=True)", "srepr_positive": "Mul(exp(Symbol('C', commutative=True)), log(Symbol('D', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('C', commutative=True), Symbol('D', commutative=True)), exp(Symbol('D', commutative=True)))", "Mul(Rational(1, 2), Symbol('D', commutative=True), Add(Mul(Integer(2), Symbol('C', commutative=True)), Symbol('D', commutative=True)))", "Mul(Rational(1, 2), Symbol('D', commutative=True), Add(Mul(Integer(2), Symbol('C', commutative=True)), Mul(Integer(-1), Symbol('D', commutative=True))))", "Mul(Symbol('D', commutative=True), Add(Mul(Integer(-1), Symbol('C', commutative=True)), log(Symbol('D', commutative=True)), Integer(-1)))"]}, {"premise_expression": "C M", "variable": "M", "positive": "\\frac{C M^{2}}{2}", "negatives": ["\\frac{C^{2} M}{2}", "C e^{M}", "- \\frac{\\cos{(M)}}{C}", "\\frac{M^{2} \\log{(C)}}{2}"], "srepr_premise_expression": "Mul(Symbol('C', commutative=True), Symbol('M', commutative=True))", "srepr_variable": "Symbol('M', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('C', commutative=True), Pow(Symbol('M', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2)), Symbol('M', commutative=True))", "Mul(Symbol('C', commutative=True), exp(Symbol('M', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('C', commutative=True), Integer(-1)), cos(Symbol('M', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('M', commutative=True), Integer(2)), log(Symbol('C', commutative=True)))"]}, {"premise_expression": "e^{S^{B}}", "variable": "S", "positive": "\\frac{e^{- \\frac{i \\pi}{B}} \\gamma(\\frac{1}{B}, S^{B} e^{i \\pi})}{B}", "negatives": ["S (- B + \\log{(S^{B})})", "\\frac{S (S + 2 \\log{(B)})}{2}", "\\frac{S^{2} e^{B}}{2}", "\\int \\cos^{B}{(S)} dS"], "srepr_premise_expression": "exp(Pow(Symbol('S', commutative=True), Symbol('B', commutative=True)))", "srepr_variable": "Symbol('S', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('B', commutative=True), Integer(-1)), exp(Mul(Integer(-1), I, pi, Pow(Symbol('B', commutative=True), Integer(-1)))), lowergamma(Pow(Symbol('B', commutative=True), Integer(-1)), Mul(Pow(Symbol('S', commutative=True), Symbol('B', commutative=True)), exp_polar(Mul(I, pi)))))", "srepr_negatives": ["Mul(Symbol('S', commutative=True), Add(Mul(Integer(-1), Symbol('B', commutative=True)), log(Pow(Symbol('S', commutative=True), Symbol('B', commutative=True)))))", "Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Symbol('S', commutative=True), Mul(Integer(2), log(Symbol('B', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('S', commutative=True), Integer(2)), exp(Symbol('B', commutative=True)))", "Integral(Pow(cos(Symbol('S', commutative=True)), Symbol('B', commutative=True)), Tuple(Symbol('S', commutative=True)))"]}, {"premise_expression": "D + e^{a}", "variable": "a", "positive": "D a + e^{a}", "negatives": ["D e^{a}", "D a - \\cos{(a)}", "\\frac{D (D + 2 e^{a})}{2}", "e^{D} \\log{(a)}"], "srepr_premise_expression": "Add(Symbol('D', commutative=True), exp(Symbol('a', commutative=True)))", "srepr_variable": "Symbol('a', commutative=True)", "srepr_positive": "Add(Mul(Symbol('D', commutative=True), Symbol('a', commutative=True)), exp(Symbol('a', commutative=True)))", "srepr_negatives": ["Mul(Symbol('D', commutative=True), exp(Symbol('a', commutative=True)))", "Add(Mul(Symbol('D', commutative=True), Symbol('a', commutative=True)), Mul(Integer(-1), cos(Symbol('a', commutative=True))))", "Mul(Rational(1, 2), Symbol('D', commutative=True), Add(Symbol('D', commutative=True), Mul(Integer(2), exp(Symbol('a', commutative=True)))))", "Mul(exp(Symbol('D', commutative=True)), log(Symbol('a', commutative=True)))"]}, {"premise_expression": "\\sin{(Z - o)}", "variable": "o", "positive": "\\cos{(Z - o)}", "negatives": ["- \\cos{(Z - o)}", "e^{- Z + o}", "- \\frac{\\cos{(o)}}{Z}", "Z \\sin{(o)}"], "srepr_premise_expression": "sin(Add(Symbol('Z', commutative=True), Mul(Integer(-1), Symbol('o', commutative=True))))", "srepr_variable": "Symbol('o', commutative=True)", "srepr_positive": "cos(Add(Symbol('Z', commutative=True), Mul(Integer(-1), Symbol('o', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('Z', commutative=True), Mul(Integer(-1), Symbol('o', commutative=True)))))", "exp(Add(Mul(Integer(-1), Symbol('Z', commutative=True)), Symbol('o', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('Z', commutative=True), Integer(-1)), cos(Symbol('o', commutative=True)))", "Mul(Symbol('Z', commutative=True), sin(Symbol('o', commutative=True)))"]}, {"premise_expression": "\\frac{J}{k}", "variable": "k", "positive": "J \\log{(k)}", "negatives": ["\\frac{J^{2}}{2 k}", "e^{J} \\log{(k)}", "k", "\\frac{k^{2} \\log{(J)}}{2}"], "srepr_premise_expression": "Mul(Symbol('J', commutative=True), Pow(Symbol('k', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('k', commutative=True)", "srepr_positive": "Mul(Symbol('J', commutative=True), log(Symbol('k', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('J', commutative=True), Integer(2)), Pow(Symbol('k', commutative=True), Integer(-1)))", "Mul(exp(Symbol('J', commutative=True)), log(Symbol('k', commutative=True)))", "Symbol('k', commutative=True)", "Mul(Rational(1, 2), Pow(Symbol('k', commutative=True), Integer(2)), log(Symbol('J', commutative=True)))"]}, {"premise_expression": "e^{- E + T}", "variable": "T", "positive": "e^{- E + T}", "negatives": ["- e^{- E + T}", "- \\cos{(E + T)}", "- \\sin{(E - T)}", "\\frac{T^{2} \\log{(E)}}{2}"], "srepr_premise_expression": "exp(Add(Mul(Integer(-1), Symbol('E', commutative=True)), Symbol('T', commutative=True)))", "srepr_variable": "Symbol('T', commutative=True)", "srepr_positive": "exp(Add(Mul(Integer(-1), Symbol('E', commutative=True)), Symbol('T', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('E', commutative=True)), Symbol('T', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('E', commutative=True), Symbol('T', commutative=True))))", "Mul(Integer(-1), sin(Add(Symbol('E', commutative=True), Mul(Integer(-1), Symbol('T', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('T', commutative=True), Integer(2)), log(Symbol('E', commutative=True)))"]}, {"premise_expression": "\\log{(V b)}", "variable": "b", "positive": "b (\\log{(V b)} - 1)", "negatives": ["V (\\log{(V b)} - 1)", "\\frac{b (2 V - b)}{2}", "e^{V} \\log{(b)}", "\\frac{b (b + 2 \\log{(V)})}{2}"], "srepr_premise_expression": "log(Mul(Symbol('V', commutative=True), Symbol('b', commutative=True)))", "srepr_variable": "Symbol('b', commutative=True)", "srepr_positive": "Mul(Symbol('b', commutative=True), Add(log(Mul(Symbol('V', commutative=True), Symbol('b', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('V', commutative=True), Add(log(Mul(Symbol('V', commutative=True), Symbol('b', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('b', commutative=True), Add(Mul(Integer(2), Symbol('V', commutative=True)), Mul(Integer(-1), Symbol('b', commutative=True))))", "Mul(exp(Symbol('V', commutative=True)), log(Symbol('b', commutative=True)))", "Mul(Rational(1, 2), Symbol('b', commutative=True), Add(Symbol('b', commutative=True), Mul(Integer(2), log(Symbol('V', commutative=True)))))"]}, {"premise_expression": "\\log{(L v)}", "variable": "L", "positive": "L (\\log{(L v)} - 1)", "negatives": ["v (\\log{(L v)} - 1)", "\\frac{L (\\log{(L)} - 1)}{v}", "- \\cos{(L + v)}", "\\sin{(L + v)}"], "srepr_premise_expression": "log(Mul(Symbol('L', commutative=True), Symbol('v', commutative=True)))", "srepr_variable": "Symbol('L', commutative=True)", "srepr_positive": "Mul(Symbol('L', commutative=True), Add(log(Mul(Symbol('L', commutative=True), Symbol('v', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('v', commutative=True), Add(log(Mul(Symbol('L', commutative=True), Symbol('v', commutative=True))), Integer(-1)))", "Mul(Symbol('L', commutative=True), Pow(Symbol('v', commutative=True), Integer(-1)), Add(log(Symbol('L', commutative=True)), Integer(-1)))", "Mul(Integer(-1), cos(Add(Symbol('L', commutative=True), Symbol('v', commutative=True))))", "sin(Add(Symbol('L', commutative=True), Symbol('v', commutative=True)))"]}, {"premise_expression": "\\log{(m - t)}", "variable": "m", "positive": "m \\log{(m - t)} - m - t \\log{(m - t)}", "negatives": ["- m \\log{(- m + t)} + t \\log{(m - t)} - t", "\\frac{m (- m + 2 \\log{(t)})}{2}", "m \\cos{(\\frac{t}{m})} + t \\operatorname{Si}{(\\frac{t}{m})}", "- e^{- m + t}"], "srepr_premise_expression": "log(Add(Symbol('m', commutative=True), Mul(Integer(-1), Symbol('t', commutative=True))))", "srepr_variable": "Symbol('m', commutative=True)", "srepr_positive": "Add(Mul(Symbol('m', commutative=True), log(Add(Symbol('m', commutative=True), Mul(Integer(-1), Symbol('t', commutative=True))))), Mul(Integer(-1), Symbol('m', commutative=True)), Mul(Integer(-1), Symbol('t', commutative=True), log(Add(Symbol('m', commutative=True), Mul(Integer(-1), Symbol('t', commutative=True))))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('m', commutative=True), log(Add(Mul(Integer(-1), Symbol('m', commutative=True)), Symbol('t', commutative=True)))), Mul(Symbol('t', commutative=True), log(Add(Symbol('m', commutative=True), Mul(Integer(-1), Symbol('t', commutative=True))))), Mul(Integer(-1), Symbol('t', commutative=True)))", "Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Mul(Integer(-1), Symbol('m', commutative=True)), Mul(Integer(2), log(Symbol('t', commutative=True)))))", "Add(Mul(Symbol('m', commutative=True), cos(Mul(Pow(Symbol('m', commutative=True), Integer(-1)), Symbol('t', commutative=True)))), Mul(Symbol('t', commutative=True), Si(Mul(Pow(Symbol('m', commutative=True), Integer(-1)), Symbol('t', commutative=True)))))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('m', commutative=True)), Symbol('t', commutative=True))))"]}, {"premise_expression": "e^{\\frac{n}{s}}", "variable": "n", "positive": "s e^{\\frac{n}{s}}", "negatives": ["\\sin{(n - s)}", "\\frac{n^{2} \\log{(s)}}{2}", "n (\\log{(n s)} - 1)", "\\log{(n)} \\cos{(s)}"], "srepr_premise_expression": "exp(Mul(Symbol('n', commutative=True), Pow(Symbol('s', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('n', commutative=True)", "srepr_positive": "Mul(Symbol('s', commutative=True), exp(Mul(Symbol('n', commutative=True), Pow(Symbol('s', commutative=True), Integer(-1)))))", "srepr_negatives": ["sin(Add(Symbol('n', commutative=True), Mul(Integer(-1), Symbol('s', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('n', commutative=True), Integer(2)), log(Symbol('s', commutative=True)))", "Mul(Symbol('n', commutative=True), Add(log(Mul(Symbol('n', commutative=True), Symbol('s', commutative=True))), Integer(-1)))", "Mul(log(Symbol('n', commutative=True)), cos(Symbol('s', commutative=True)))"]}, {"premise_expression": "f + v", "variable": "f", "positive": "\\frac{f (f + 2 v)}{2}", "negatives": ["\\frac{f (- f + 2 v)}{2}", "\\frac{v (2 f + v)}{2}", "\\frac{f (- f + 2 e^{v})}{2}", "\\frac{f (- f + 2 \\sin{(v)})}{2}"], "srepr_premise_expression": "Add(Symbol('f', commutative=True), Symbol('v', commutative=True))", "srepr_variable": "Symbol('f', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Symbol('f', commutative=True), Mul(Integer(2), Symbol('v', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Mul(Integer(-1), Symbol('f', commutative=True)), Mul(Integer(2), Symbol('v', commutative=True))))", "Mul(Rational(1, 2), Symbol('v', commutative=True), Add(Mul(Integer(2), Symbol('f', commutative=True)), Symbol('v', commutative=True)))", "Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Mul(Integer(-1), Symbol('f', commutative=True)), Mul(Integer(2), exp(Symbol('v', commutative=True)))))", "Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Mul(Integer(-1), Symbol('f', commutative=True)), Mul(Integer(2), sin(Symbol('v', commutative=True)))))"]}, {"premise_expression": "\\log{(J V)}", "variable": "V", "positive": "V (\\log{(J V)} - 1)", "negatives": ["J (\\log{(J V)} - 1)", "V (\\log{(\\frac{J}{V})} + 1)", "V (\\log{(\\frac{V}{J})} - 1)", "- \\cos{(J + V)}"], "srepr_premise_expression": "log(Mul(Symbol('J', commutative=True), Symbol('V', commutative=True)))", "srepr_variable": "Symbol('V', commutative=True)", "srepr_positive": "Mul(Symbol('V', commutative=True), Add(log(Mul(Symbol('J', commutative=True), Symbol('V', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('J', commutative=True), Add(log(Mul(Symbol('J', commutative=True), Symbol('V', commutative=True))), Integer(-1)))", "Mul(Symbol('V', commutative=True), Add(log(Mul(Symbol('J', commutative=True), Pow(Symbol('V', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Symbol('V', commutative=True), Add(log(Mul(Pow(Symbol('J', commutative=True), Integer(-1)), Symbol('V', commutative=True))), Integer(-1)))", "Mul(Integer(-1), cos(Add(Symbol('J', commutative=True), Symbol('V', commutative=True))))"]}, {"premise_expression": "\\log{(\\frac{o}{M})}", "variable": "o", "positive": "o (\\log{(\\frac{o}{M})} - 1)", "negatives": ["M (\\log{(\\frac{o}{M})} + 1)", "\\log{(o)} \\sin{(M)}", "M e^{\\frac{o}{M}}", "\\frac{o^{2} \\log{(M)}}{2}"], "srepr_premise_expression": "log(Mul(Pow(Symbol('M', commutative=True), Integer(-1)), Symbol('o', commutative=True)))", "srepr_variable": "Symbol('o', commutative=True)", "srepr_positive": "Mul(Symbol('o', commutative=True), Add(log(Mul(Pow(Symbol('M', commutative=True), Integer(-1)), Symbol('o', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('M', commutative=True), Add(log(Mul(Pow(Symbol('M', commutative=True), Integer(-1)), Symbol('o', commutative=True))), Integer(1)))", "Mul(log(Symbol('o', commutative=True)), sin(Symbol('M', commutative=True)))", "Mul(Symbol('M', commutative=True), exp(Mul(Pow(Symbol('M', commutative=True), Integer(-1)), Symbol('o', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('o', commutative=True), Integer(2)), log(Symbol('M', commutative=True)))"]}, {"premise_expression": "S - n", "variable": "S", "positive": "\\frac{S (S - 2 n)}{2}", "negatives": ["\\frac{n (2 S - n)}{2}", "\\frac{S^{2}}{2 n}", "\\cos{(S - n)}", "\\frac{S (- S + 2 e^{n})}{2}"], "srepr_premise_expression": "Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('n', commutative=True)))", "srepr_variable": "Symbol('S', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Symbol('S', commutative=True), Mul(Integer(-1), Integer(2), Symbol('n', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('n', commutative=True), Add(Mul(Integer(2), Symbol('S', commutative=True)), Mul(Integer(-1), Symbol('n', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('S', commutative=True), Integer(2)), Pow(Symbol('n', commutative=True), Integer(-1)))", "cos(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('n', commutative=True))))", "Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Mul(Integer(-1), Symbol('S', commutative=True)), Mul(Integer(2), exp(Symbol('n', commutative=True)))))"]}, {"premise_expression": "e^{o - r}", "variable": "o", "positive": "e^{o - r}", "negatives": ["- e^{o - r}", "\\frac{o r (o + 2)}{2}", "\\frac{o^{2} \\log{(r)}}{2}", "o \\log{(- o + r)} - o - r \\log{(o - r)}"], "srepr_premise_expression": "exp(Add(Symbol('o', commutative=True), Mul(Integer(-1), Symbol('r', commutative=True))))", "srepr_variable": "Symbol('o', commutative=True)", "srepr_positive": "exp(Add(Symbol('o', commutative=True), Mul(Integer(-1), Symbol('r', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Symbol('o', commutative=True), Mul(Integer(-1), Symbol('r', commutative=True)))))", "Mul(Rational(1, 2), Symbol('o', commutative=True), Symbol('r', commutative=True), Add(Symbol('o', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('o', commutative=True), Integer(2)), log(Symbol('r', commutative=True)))", "Add(Mul(Symbol('o', commutative=True), log(Add(Mul(Integer(-1), Symbol('o', commutative=True)), Symbol('r', commutative=True)))), Mul(Integer(-1), Symbol('o', commutative=True)), Mul(Integer(-1), Symbol('r', commutative=True), log(Add(Symbol('o', commutative=True), Mul(Integer(-1), Symbol('r', commutative=True))))))"]}, {"premise_expression": "\\sin^{j}{(B)}", "variable": "B", "positive": "\\int \\sin^{j}{(B)} dB", "negatives": ["e^{j} \\log{(B)}", "B \\log{(j^{j})}", "B (\\log{(\\frac{B}{j})} - 1)", "j e^{B}"], "srepr_premise_expression": "Pow(sin(Symbol('B', commutative=True)), Symbol('j', commutative=True))", "srepr_variable": "Symbol('B', commutative=True)", "srepr_positive": "Integral(Pow(sin(Symbol('B', commutative=True)), Symbol('j', commutative=True)), Tuple(Symbol('B', commutative=True)))", "srepr_negatives": ["Mul(exp(Symbol('j', commutative=True)), log(Symbol('B', commutative=True)))", "Mul(Symbol('B', commutative=True), log(Pow(Symbol('j', commutative=True), Symbol('j', commutative=True))))", "Mul(Symbol('B', commutative=True), Add(log(Mul(Symbol('B', commutative=True), Pow(Symbol('j', commutative=True), Integer(-1)))), Integer(-1)))", "Mul(Symbol('j', commutative=True), exp(Symbol('B', commutative=True)))"]}, {"premise_expression": "b + c", "variable": "b", "positive": "\\frac{b (b + 2 c)}{2}", "negatives": ["\\frac{c (2 b + c)}{2}", "\\cos{(b - c)}", "c e^{\\frac{b}{c}}", "b e^{\\frac{c}{b}} - c \\operatorname{Ei}{(\\frac{c}{b})}"], "srepr_premise_expression": "Add(Symbol('b', commutative=True), Symbol('c', commutative=True))", "srepr_variable": "Symbol('b', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('b', commutative=True), Add(Symbol('b', commutative=True), Mul(Integer(2), Symbol('c', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('c', commutative=True), Add(Mul(Integer(2), Symbol('b', commutative=True)), Symbol('c', commutative=True)))", "cos(Add(Symbol('b', commutative=True), Mul(Integer(-1), Symbol('c', commutative=True))))", "Mul(Symbol('c', commutative=True), exp(Mul(Symbol('b', commutative=True), Pow(Symbol('c', commutative=True), Integer(-1)))))", "Add(Mul(Symbol('b', commutative=True), exp(Mul(Pow(Symbol('b', commutative=True), Integer(-1)), Symbol('c', commutative=True)))), Mul(Integer(-1), Symbol('c', commutative=True), Ei(Mul(Pow(Symbol('b', commutative=True), Integer(-1)), Symbol('c', commutative=True)))))"]}, {"premise_expression": "J + \\log{(B)}", "variable": "J", "positive": "\\frac{J (J + 2 \\log{(B)})}{2}", "negatives": ["\\frac{J (- J + 2 e^{B})}{2}", "\\frac{J^{2} \\log{(B)}}{2}", "B (J + \\log{(B)} - 1)", "\\frac{J^{2} \\sin{(B)}}{2}"], "srepr_premise_expression": "Add(Symbol('J', commutative=True), log(Symbol('B', commutative=True)))", "srepr_variable": "Symbol('J', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('J', commutative=True), Add(Symbol('J', commutative=True), Mul(Integer(2), log(Symbol('B', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('J', commutative=True), Add(Mul(Integer(-1), Symbol('J', commutative=True)), Mul(Integer(2), exp(Symbol('B', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('J', commutative=True), Integer(2)), log(Symbol('B', commutative=True)))", "Mul(Symbol('B', commutative=True), Add(Symbol('J', commutative=True), log(Symbol('B', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('J', commutative=True), Integer(2)), sin(Symbol('B', commutative=True)))"]}, {"premise_expression": "\\frac{\\log{(l)}}{u}", "variable": "l", "positive": "\\frac{l (\\log{(l)} - 1)}{u}", "negatives": ["l (\\log{(l u)} - 1)", "\\log{(l)} \\log{(u)}", "\\frac{l^{2} \\log{(u)}}{2}", "\\frac{l (- l + 2 u)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('u', commutative=True), Integer(-1)), log(Symbol('l', commutative=True)))", "srepr_variable": "Symbol('l', commutative=True)", "srepr_positive": "Mul(Symbol('l', commutative=True), Pow(Symbol('u', commutative=True), Integer(-1)), Add(log(Symbol('l', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('l', commutative=True), Add(log(Mul(Symbol('l', commutative=True), Symbol('u', commutative=True))), Integer(-1)))", "Mul(log(Symbol('l', commutative=True)), log(Symbol('u', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('l', commutative=True), Integer(2)), log(Symbol('u', commutative=True)))", "Mul(Rational(1, 2), Symbol('l', commutative=True), Add(Mul(Integer(-1), Symbol('l', commutative=True)), Mul(Integer(2), Symbol('u', commutative=True))))"]}, {"premise_expression": "\\cos{(\\frac{z}{v})}", "variable": "v", "positive": "v \\cos{(\\frac{z}{v})} + z \\operatorname{Si}{(\\frac{z}{v})}", "negatives": ["v e^{\\frac{z}{v}} - z \\operatorname{Ei}{(\\frac{z}{v})}", "v (\\log{(\\frac{z}{v})} + 1)", "\\frac{v (v + 2 z)}{2}", "\\frac{v (v + 2 \\log{(z)})}{2}"], "srepr_premise_expression": "cos(Mul(Pow(Symbol('v', commutative=True), Integer(-1)), Symbol('z', commutative=True)))", "srepr_variable": "Symbol('v', commutative=True)", "srepr_positive": "Add(Mul(Symbol('v', commutative=True), cos(Mul(Pow(Symbol('v', commutative=True), Integer(-1)), Symbol('z', commutative=True)))), Mul(Symbol('z', commutative=True), Si(Mul(Pow(Symbol('v', commutative=True), Integer(-1)), Symbol('z', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('v', commutative=True), exp(Mul(Pow(Symbol('v', commutative=True), Integer(-1)), Symbol('z', commutative=True)))), Mul(Integer(-1), Symbol('z', commutative=True), Ei(Mul(Pow(Symbol('v', commutative=True), Integer(-1)), Symbol('z', commutative=True)))))", "Mul(Symbol('v', commutative=True), Add(log(Mul(Pow(Symbol('v', commutative=True), Integer(-1)), Symbol('z', commutative=True))), Integer(1)))", "Mul(Rational(1, 2), Symbol('v', commutative=True), Add(Symbol('v', commutative=True), Mul(Integer(2), Symbol('z', commutative=True))))", "Mul(Rational(1, 2), Symbol('v', commutative=True), Add(Symbol('v', commutative=True), Mul(Integer(2), log(Symbol('z', commutative=True)))))"]}, {"premise_expression": "- l + e^{P}", "variable": "l", "positive": "\\frac{l (- l + 2 e^{P})}{2}", "negatives": ["\\frac{l (l + 2 \\log{(P)})}{2}", "- P l + e^{P}", "\\frac{l (4 P + l)}{2}", "e^{P + l}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('l', commutative=True)), exp(Symbol('P', commutative=True)))", "srepr_variable": "Symbol('l', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('l', commutative=True), Add(Mul(Integer(-1), Symbol('l', commutative=True)), Mul(Integer(2), exp(Symbol('P', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('l', commutative=True), Add(Symbol('l', commutative=True), Mul(Integer(2), log(Symbol('P', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('P', commutative=True), Symbol('l', commutative=True)), exp(Symbol('P', commutative=True)))", "Mul(Rational(1, 2), Symbol('l', commutative=True), Add(Mul(Integer(4), Symbol('P', commutative=True)), Symbol('l', commutative=True)))", "exp(Add(Symbol('P', commutative=True), Symbol('l', commutative=True)))"]}, {"premise_expression": "- L + \\frac{Z}{T}", "variable": "T", "positive": "- L T + Z \\log{(T)}", "negatives": ["L Z \\log{(T)}", "- L Z + \\frac{Z^{2}}{2 T}", "Z^{L} \\log{(T)}", "- T Z + \\frac{T^{2}}{2 L}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('L', commutative=True)), Mul(Pow(Symbol('T', commutative=True), Integer(-1)), Symbol('Z', commutative=True)))", "srepr_variable": "Symbol('T', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('L', commutative=True), Symbol('T', commutative=True)), Mul(Symbol('Z', commutative=True), log(Symbol('T', commutative=True))))", "srepr_negatives": ["Mul(Symbol('L', commutative=True), Symbol('Z', commutative=True), log(Symbol('T', commutative=True)))", "Add(Mul(Integer(-1), Symbol('L', commutative=True), Symbol('Z', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('T', commutative=True), Integer(-1)), Pow(Symbol('Z', commutative=True), Integer(2))))", "Mul(Pow(Symbol('Z', commutative=True), Symbol('L', commutative=True)), log(Symbol('T', commutative=True)))", "Add(Mul(Integer(-1), Symbol('T', commutative=True), Symbol('Z', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(-1)), Pow(Symbol('T', commutative=True), Integer(2))))"]}, {"premise_expression": "- S + \\frac{c}{z}", "variable": "c", "positive": "- S c + \\frac{c^{2}}{2 z}", "negatives": ["- S z + c \\log{(z)}", "\\frac{c (c + 2 z)}{2 S}", "\\frac{S^{2} c^{2}}{2}", "\\frac{S^{z} c^{2}}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('S', commutative=True)), Mul(Symbol('c', commutative=True), Pow(Symbol('z', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('c', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('S', commutative=True), Symbol('c', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('c', commutative=True), Integer(2)), Pow(Symbol('z', commutative=True), Integer(-1))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('S', commutative=True), Symbol('z', commutative=True)), Mul(Symbol('c', commutative=True), log(Symbol('z', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('S', commutative=True), Integer(-1)), Symbol('c', commutative=True), Add(Symbol('c', commutative=True), Mul(Integer(2), Symbol('z', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('S', commutative=True), Integer(2)), Pow(Symbol('c', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('S', commutative=True), Symbol('z', commutative=True)), Pow(Symbol('c', commutative=True), Integer(2)))"]}, {"premise_expression": "Q \\cos{(m)}", "variable": "Q", "positive": "\\frac{Q^{2} \\cos{(m)}}{2}", "negatives": ["Q \\sin{(m)}", "\\log{(Q)} \\cos{(m)}", "\\log{(Q)} \\log{(m)}", "- Q m + e^{Q}"], "srepr_premise_expression": "Mul(Symbol('Q', commutative=True), cos(Symbol('m', commutative=True)))", "srepr_variable": "Symbol('Q', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(2)), cos(Symbol('m', commutative=True)))", "srepr_negatives": ["Mul(Symbol('Q', commutative=True), sin(Symbol('m', commutative=True)))", "Mul(log(Symbol('Q', commutative=True)), cos(Symbol('m', commutative=True)))", "Mul(log(Symbol('Q', commutative=True)), log(Symbol('m', commutative=True)))", "Add(Mul(Integer(-1), Symbol('Q', commutative=True), Symbol('m', commutative=True)), exp(Symbol('Q', commutative=True)))"]}, {"premise_expression": "- \\sin{(C - X)}", "variable": "C", "positive": "\\cos{(C - X)}", "negatives": ["- \\cos{(C - X)}", "- e^{- C + X}", "C X + \\sin{(C)}", "\\frac{C^{2} X}{2}"], "srepr_premise_expression": "Mul(Integer(-1), sin(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('X', commutative=True)))))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "cos(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('X', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('X', commutative=True)))))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('C', commutative=True)), Symbol('X', commutative=True))))", "Add(Mul(Symbol('C', commutative=True), Symbol('X', commutative=True)), sin(Symbol('C', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2)), Symbol('X', commutative=True))"]}, {"premise_expression": "Y t", "variable": "t", "positive": "\\frac{Y t^{2}}{2}", "negatives": ["\\frac{Y^{2} t}{2}", "\\frac{t (2 Y - t)}{2}", "- Y t + \\sin{(t)}", "e^{Y + t}"], "srepr_premise_expression": "Mul(Symbol('Y', commutative=True), Symbol('t', commutative=True))", "srepr_variable": "Symbol('t', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('Y', commutative=True), Pow(Symbol('t', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('Y', commutative=True), Integer(2)), Symbol('t', commutative=True))", "Mul(Rational(1, 2), Symbol('t', commutative=True), Add(Mul(Integer(2), Symbol('Y', commutative=True)), Mul(Integer(-1), Symbol('t', commutative=True))))", "Add(Mul(Integer(-1), Symbol('Y', commutative=True), Symbol('t', commutative=True)), sin(Symbol('t', commutative=True)))", "exp(Add(Symbol('Y', commutative=True), Symbol('t', commutative=True)))"]}, {"premise_expression": "\\frac{L}{z}", "variable": "z", "positive": "L \\log{(z)}", "negatives": ["\\frac{L^{2}}{2 z}", "\\log{(L)} \\log{(z)}", "L z - \\cos{(z)}", "\\frac{z^{2}}{2 L}"], "srepr_premise_expression": "Mul(Symbol('L', commutative=True), Pow(Symbol('z', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('z', commutative=True)", "srepr_positive": "Mul(Symbol('L', commutative=True), log(Symbol('z', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(2)), Pow(Symbol('z', commutative=True), Integer(-1)))", "Mul(log(Symbol('L', commutative=True)), log(Symbol('z', commutative=True)))", "Add(Mul(Symbol('L', commutative=True), Symbol('z', commutative=True)), Mul(Integer(-1), cos(Symbol('z', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(-1)), Pow(Symbol('z', commutative=True), Integer(2)))"]}, {"premise_expression": "L k", "variable": "L", "positive": "\\frac{L^{2} k}{2}", "negatives": ["\\frac{L k^{2}}{2}", "\\frac{L^{2}}{2 k}", "\\frac{L (- L + 2 k)}{2}", "\\sin{(L - k)}"], "srepr_premise_expression": "Mul(Symbol('L', commutative=True), Symbol('k', commutative=True))", "srepr_variable": "Symbol('L', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(2)), Symbol('k', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('L', commutative=True), Pow(Symbol('k', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(2)), Pow(Symbol('k', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Mul(Integer(-1), Symbol('L', commutative=True)), Mul(Integer(2), Symbol('k', commutative=True))))", "sin(Add(Symbol('L', commutative=True), Mul(Integer(-1), Symbol('k', commutative=True))))"]}, {"premise_expression": "e^{f - u}", "variable": "f", "positive": "e^{f - u}", "negatives": ["- e^{f - u}", "u e^{\\frac{f}{u}}", "\\frac{f (f - 2 u)}{2}", "f u e^{u}"], "srepr_premise_expression": "exp(Add(Symbol('f', commutative=True), Mul(Integer(-1), Symbol('u', commutative=True))))", "srepr_variable": "Symbol('f', commutative=True)", "srepr_positive": "exp(Add(Symbol('f', commutative=True), Mul(Integer(-1), Symbol('u', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Symbol('f', commutative=True), Mul(Integer(-1), Symbol('u', commutative=True)))))", "Mul(Symbol('u', commutative=True), exp(Mul(Symbol('f', commutative=True), Pow(Symbol('u', commutative=True), Integer(-1)))))", "Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Symbol('f', commutative=True), Mul(Integer(-1), Integer(2), Symbol('u', commutative=True))))", "Mul(Symbol('f', commutative=True), Symbol('u', commutative=True), exp(Symbol('u', commutative=True)))"]}, {"premise_expression": "c \\cos{(Q)}", "variable": "Q", "positive": "c \\sin{(Q)}", "negatives": ["c \\log{(Q)}", "- c \\cos{(Q)}", "c e^{\\frac{Q}{c}}", "\\frac{c^{2} \\cos{(Q)}}{2}"], "srepr_premise_expression": "Mul(Symbol('c', commutative=True), cos(Symbol('Q', commutative=True)))", "srepr_variable": "Symbol('Q', commutative=True)", "srepr_positive": "Mul(Symbol('c', commutative=True), sin(Symbol('Q', commutative=True)))", "srepr_negatives": ["Mul(Symbol('c', commutative=True), log(Symbol('Q', commutative=True)))", "Mul(Integer(-1), Symbol('c', commutative=True), cos(Symbol('Q', commutative=True)))", "Mul(Symbol('c', commutative=True), exp(Mul(Symbol('Q', commutative=True), Pow(Symbol('c', commutative=True), Integer(-1)))))", "Mul(Rational(1, 2), Pow(Symbol('c', commutative=True), Integer(2)), cos(Symbol('Q', commutative=True)))"]}, {"premise_expression": "L + r", "variable": "r", "positive": "\\frac{r (2 L + r)}{2}", "negatives": ["\\frac{L (L + 2 r)}{2}", "\\frac{r^{2} e^{L}}{2}", "e^{- L + r}", "\\frac{r (\\log{(r)} - 1)}{L}"], "srepr_premise_expression": "Add(Symbol('L', commutative=True), Symbol('r', commutative=True))", "srepr_variable": "Symbol('r', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(2), Symbol('L', commutative=True)), Symbol('r', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Symbol('L', commutative=True), Mul(Integer(2), Symbol('r', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('r', commutative=True), Integer(2)), exp(Symbol('L', commutative=True)))", "exp(Add(Mul(Integer(-1), Symbol('L', commutative=True)), Symbol('r', commutative=True)))", "Mul(Pow(Symbol('L', commutative=True), Integer(-1)), Symbol('r', commutative=True), Add(log(Symbol('r', commutative=True)), Integer(-1)))"]}, {"premise_expression": "Q Z", "variable": "Q", "positive": "\\frac{Q^{2} Z}{2}", "negatives": ["\\frac{Q Z^{2}}{2}", "\\frac{Q^{2}}{2 Z}", "\\frac{Q (Q - 2 Z)}{2}", "\\frac{Q (Q + 2 Z)}{2}"], "srepr_premise_expression": "Mul(Symbol('Q', commutative=True), Symbol('Z', commutative=True))", "srepr_variable": "Symbol('Q', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(2)), Symbol('Z', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('Q', commutative=True), Pow(Symbol('Z', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(2)), Pow(Symbol('Z', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Symbol('Q', commutative=True), Mul(Integer(-1), Integer(2), Symbol('Z', commutative=True))))", "Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Symbol('Q', commutative=True), Mul(Integer(2), Symbol('Z', commutative=True))))"]}, {"premise_expression": "\\frac{- Z + c}{S}", "variable": "c", "positive": "\\frac{c (- 2 Z + c)}{2 S}", "negatives": ["\\frac{c (2 S + c)}{2 Z}", "\\frac{Z (- Z + 2 c)}{2 S}", "\\frac{c (- 2 S + 2 Z + c)}{2}", "(- Z + c) \\log{(S)}"], "srepr_premise_expression": "Mul(Pow(Symbol('S', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('Z', commutative=True)), Symbol('c', commutative=True)))", "srepr_variable": "Symbol('c', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('S', commutative=True), Integer(-1)), Symbol('c', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('Z', commutative=True)), Symbol('c', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('Z', commutative=True), Integer(-1)), Symbol('c', commutative=True), Add(Mul(Integer(2), Symbol('S', commutative=True)), Symbol('c', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('S', commutative=True), Integer(-1)), Symbol('Z', commutative=True), Add(Mul(Integer(-1), Symbol('Z', commutative=True)), Mul(Integer(2), Symbol('c', commutative=True))))", "Mul(Rational(1, 2), Symbol('c', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('S', commutative=True)), Mul(Integer(2), Symbol('Z', commutative=True)), Symbol('c', commutative=True)))", "Mul(Add(Mul(Integer(-1), Symbol('Z', commutative=True)), Symbol('c', commutative=True)), log(Symbol('S', commutative=True)))"]}, {"premise_expression": "\\frac{g}{N}", "variable": "N", "positive": "g \\log{(N)}", "negatives": ["\\frac{g^{2}}{2 N}", "N g - \\cos{(N)}", "- \\cos{(N + g)}", "N (\\log{(\\frac{g}{N})} + 1)"], "srepr_premise_expression": "Mul(Pow(Symbol('N', commutative=True), Integer(-1)), Symbol('g', commutative=True))", "srepr_variable": "Symbol('N', commutative=True)", "srepr_positive": "Mul(Symbol('g', commutative=True), log(Symbol('N', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('N', commutative=True), Integer(-1)), Pow(Symbol('g', commutative=True), Integer(2)))", "Add(Mul(Symbol('N', commutative=True), Symbol('g', commutative=True)), Mul(Integer(-1), cos(Symbol('N', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('N', commutative=True), Symbol('g', commutative=True))))", "Mul(Symbol('N', commutative=True), Add(log(Mul(Pow(Symbol('N', commutative=True), Integer(-1)), Symbol('g', commutative=True))), Integer(1)))"]}, {"premise_expression": "A p", "variable": "A", "positive": "\\frac{A^{2} p}{2}", "negatives": ["\\frac{A p^{2}}{2}", "\\frac{A^{2} (p - 1)}{2}", "p e^{\\frac{A}{p}}", "\\frac{A (A + 2 \\log{(p)})}{2}"], "srepr_premise_expression": "Mul(Symbol('A', commutative=True), Symbol('p', commutative=True))", "srepr_variable": "Symbol('A', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2)), Symbol('p', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('A', commutative=True), Pow(Symbol('p', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2)), Add(Symbol('p', commutative=True), Integer(-1)))", "Mul(Symbol('p', commutative=True), exp(Mul(Symbol('A', commutative=True), Pow(Symbol('p', commutative=True), Integer(-1)))))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Symbol('A', commutative=True), Mul(Integer(2), log(Symbol('p', commutative=True)))))"]}, {"premise_expression": "h v", "variable": "v", "positive": "\\frac{h v^{2}}{2}", "negatives": ["\\frac{h^{2} v}{2}", "h v + \\sin{(v)}", "\\frac{v (2 h + v)}{2}", "\\frac{v (2 h - v)}{2}"], "srepr_premise_expression": "Mul(Symbol('h', commutative=True), Symbol('v', commutative=True))", "srepr_variable": "Symbol('v', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('h', commutative=True), Pow(Symbol('v', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('h', commutative=True), Integer(2)), Symbol('v', commutative=True))", "Add(Mul(Symbol('h', commutative=True), Symbol('v', commutative=True)), sin(Symbol('v', commutative=True)))", "Mul(Rational(1, 2), Symbol('v', commutative=True), Add(Mul(Integer(2), Symbol('h', commutative=True)), Symbol('v', commutative=True)))", "Mul(Rational(1, 2), Symbol('v', commutative=True), Add(Mul(Integer(2), Symbol('h', commutative=True)), Mul(Integer(-1), Symbol('v', commutative=True))))"]}, {"premise_expression": "\\frac{W}{c}", "variable": "c", "positive": "W \\log{(c)}", "negatives": ["\\frac{W^{2}}{2 c}", "c (W + c)", "- \\frac{\\cos{(c)}}{W}", "\\sin{(W + c)}"], "srepr_premise_expression": "Mul(Symbol('W', commutative=True), Pow(Symbol('c', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('c', commutative=True)", "srepr_positive": "Mul(Symbol('W', commutative=True), log(Symbol('c', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('W', commutative=True), Integer(2)), Pow(Symbol('c', commutative=True), Integer(-1)))", "Mul(Symbol('c', commutative=True), Add(Symbol('W', commutative=True), Symbol('c', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('W', commutative=True), Integer(-1)), cos(Symbol('c', commutative=True)))", "sin(Add(Symbol('W', commutative=True), Symbol('c', commutative=True)))"]}, {"premise_expression": "Q S", "variable": "Q", "positive": "\\frac{Q^{2} S}{2}", "negatives": ["\\frac{Q S^{2}}{2}", "\\frac{Q^{2} \\log{(S)}}{2}", "\\frac{Q (Q - 2 S)}{2}", "S e^{Q}"], "srepr_premise_expression": "Mul(Symbol('Q', commutative=True), Symbol('S', commutative=True))", "srepr_variable": "Symbol('Q', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(2)), Symbol('S', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('Q', commutative=True), Pow(Symbol('S', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(2)), log(Symbol('S', commutative=True)))", "Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Symbol('Q', commutative=True), Mul(Integer(-1), Integer(2), Symbol('S', commutative=True))))", "Mul(Symbol('S', commutative=True), exp(Symbol('Q', commutative=True)))"]}, {"premise_expression": "\\frac{S}{V}", "variable": "V", "positive": "S \\log{(V)}", "negatives": ["\\frac{S^{2}}{2 V}", "S V - \\cos{(V)}", "V (\\log{(\\frac{V}{S})} - 1)", "V (\\log{(S V)} - 1)"], "srepr_premise_expression": "Mul(Symbol('S', commutative=True), Pow(Symbol('V', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('V', commutative=True)", "srepr_positive": "Mul(Symbol('S', commutative=True), log(Symbol('V', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('S', commutative=True), Integer(2)), Pow(Symbol('V', commutative=True), Integer(-1)))", "Add(Mul(Symbol('S', commutative=True), Symbol('V', commutative=True)), Mul(Integer(-1), cos(Symbol('V', commutative=True))))", "Mul(Symbol('V', commutative=True), Add(log(Mul(Pow(Symbol('S', commutative=True), Integer(-1)), Symbol('V', commutative=True))), Integer(-1)))", "Mul(Symbol('V', commutative=True), Add(log(Mul(Symbol('S', commutative=True), Symbol('V', commutative=True))), Integer(-1)))"]}, {"premise_expression": "- R + v", "variable": "R", "positive": "\\frac{R (- R + 2 v)}{2}", "negatives": ["\\frac{v (- 2 R + v)}{2}", "\\frac{R (- R + 2 \\log{(v)})}{2}", "\\frac{R^{2} e^{v}}{2}", "- R v + e^{R}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('R', commutative=True)), Symbol('v', commutative=True))", "srepr_variable": "Symbol('R', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('R', commutative=True), Add(Mul(Integer(-1), Symbol('R', commutative=True)), Mul(Integer(2), Symbol('v', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('v', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('R', commutative=True)), Symbol('v', commutative=True)))", "Mul(Rational(1, 2), Symbol('R', commutative=True), Add(Mul(Integer(-1), Symbol('R', commutative=True)), Mul(Integer(2), log(Symbol('v', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('R', commutative=True), Integer(2)), exp(Symbol('v', commutative=True)))", "Add(Mul(Integer(-1), Symbol('R', commutative=True), Symbol('v', commutative=True)), exp(Symbol('R', commutative=True)))"]}, {"premise_expression": "\\frac{s}{x}", "variable": "x", "positive": "s \\log{(x)}", "negatives": ["- s \\cos{(x)}", "\\frac{s^{2}}{2 x}", "\\frac{s x^{2}}{2}", "s x + \\sin{(x)}"], "srepr_premise_expression": "Mul(Symbol('s', commutative=True), Pow(Symbol('x', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('x', commutative=True)", "srepr_positive": "Mul(Symbol('s', commutative=True), log(Symbol('x', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Symbol('s', commutative=True), cos(Symbol('x', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('s', commutative=True), Integer(2)), Pow(Symbol('x', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Symbol('s', commutative=True), Pow(Symbol('x', commutative=True), Integer(2)))", "Add(Mul(Symbol('s', commutative=True), Symbol('x', commutative=True)), sin(Symbol('x', commutative=True)))"]}, {"premise_expression": "N x", "variable": "N", "positive": "\\frac{N^{2} x}{2}", "negatives": ["\\frac{N x^{2}}{2}", "\\frac{N^{2}}{2 x}", "- \\cos{(N - x)}", "- \\cos{(N + x)}"], "srepr_premise_expression": "Mul(Symbol('N', commutative=True), Symbol('x', commutative=True))", "srepr_variable": "Symbol('N', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('N', commutative=True), Integer(2)), Symbol('x', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('N', commutative=True), Pow(Symbol('x', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('N', commutative=True), Integer(2)), Pow(Symbol('x', commutative=True), Integer(-1)))", "Mul(Integer(-1), cos(Add(Symbol('N', commutative=True), Mul(Integer(-1), Symbol('x', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('N', commutative=True), Symbol('x', commutative=True))))"]}, {"premise_expression": "e^{F + V}", "variable": "F", "positive": "e^{F + V}", "negatives": ["e^{F - V}", "\\cos{(F - V)}", "\\frac{F (- F + 2 V)}{2}", "F V (\\log{(F)} - 1)"], "srepr_premise_expression": "exp(Add(Symbol('F', commutative=True), Symbol('V', commutative=True)))", "srepr_variable": "Symbol('F', commutative=True)", "srepr_positive": "exp(Add(Symbol('F', commutative=True), Symbol('V', commutative=True)))", "srepr_negatives": ["exp(Add(Symbol('F', commutative=True), Mul(Integer(-1), Symbol('V', commutative=True))))", "cos(Add(Symbol('F', commutative=True), Mul(Integer(-1), Symbol('V', commutative=True))))", "Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Mul(Integer(-1), Symbol('F', commutative=True)), Mul(Integer(2), Symbol('V', commutative=True))))", "Mul(Symbol('F', commutative=True), Symbol('V', commutative=True), Add(log(Symbol('F', commutative=True)), Integer(-1)))"]}, {"premise_expression": "c \\sin{(W)}", "variable": "c", "positive": "\\frac{c^{2} \\sin{(W)}}{2}", "negatives": ["\\frac{c (- 2 W + c)}{2}", "- c \\cos{(W)}", "e^{- W + c}", "c (- W + \\log{(c^{W})})"], "srepr_premise_expression": "Mul(Symbol('c', commutative=True), sin(Symbol('W', commutative=True)))", "srepr_variable": "Symbol('c', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('c', commutative=True), Integer(2)), sin(Symbol('W', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('c', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('W', commutative=True)), Symbol('c', commutative=True)))", "Mul(Integer(-1), Symbol('c', commutative=True), cos(Symbol('W', commutative=True)))", "exp(Add(Mul(Integer(-1), Symbol('W', commutative=True)), Symbol('c', commutative=True)))", "Mul(Symbol('c', commutative=True), Add(Mul(Integer(-1), Symbol('W', commutative=True)), log(Pow(Symbol('c', commutative=True), Symbol('W', commutative=True)))))"]}, {"premise_expression": "\\log{(f x)}", "variable": "x", "positive": "x (\\log{(f x)} - 1)", "negatives": ["f (\\log{(f x)} - 1)", "f \\log{(x)}", "- \\sin{(f - x)}", "- e^{f - x}"], "srepr_premise_expression": "log(Mul(Symbol('f', commutative=True), Symbol('x', commutative=True)))", "srepr_variable": "Symbol('x', commutative=True)", "srepr_positive": "Mul(Symbol('x', commutative=True), Add(log(Mul(Symbol('f', commutative=True), Symbol('x', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('f', commutative=True), Add(log(Mul(Symbol('f', commutative=True), Symbol('x', commutative=True))), Integer(-1)))", "Mul(Symbol('f', commutative=True), log(Symbol('x', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('f', commutative=True), Mul(Integer(-1), Symbol('x', commutative=True)))))", "Mul(Integer(-1), exp(Add(Symbol('f', commutative=True), Mul(Integer(-1), Symbol('x', commutative=True)))))"]}, {"premise_expression": "A - T", "variable": "T", "positive": "\\frac{T (2 A - T)}{2}", "negatives": ["\\frac{A (A - 2 T)}{2}", "\\frac{A T^{2}}{2}", "T (\\log{(A T)} - 1)", "A \\sin{(T)}"], "srepr_premise_expression": "Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('T', commutative=True)))", "srepr_variable": "Symbol('T', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('T', commutative=True), Add(Mul(Integer(2), Symbol('A', commutative=True)), Mul(Integer(-1), Symbol('T', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Symbol('A', commutative=True), Mul(Integer(-1), Integer(2), Symbol('T', commutative=True))))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Pow(Symbol('T', commutative=True), Integer(2)))", "Mul(Symbol('T', commutative=True), Add(log(Mul(Symbol('A', commutative=True), Symbol('T', commutative=True))), Integer(-1)))", "Mul(Symbol('A', commutative=True), sin(Symbol('T', commutative=True)))"]}, {"premise_expression": "B + G", "variable": "G", "positive": "\\frac{G (2 B + G)}{2}", "negatives": ["\\frac{G (- 2 B + G)}{2}", "\\frac{B (B + 2 G)}{2}", "e^{- B + G}", "e^{B + G}"], "srepr_premise_expression": "Add(Symbol('B', commutative=True), Symbol('G', commutative=True))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Mul(Integer(2), Symbol('B', commutative=True)), Symbol('G', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('B', commutative=True)), Symbol('G', commutative=True)))", "Mul(Rational(1, 2), Symbol('B', commutative=True), Add(Symbol('B', commutative=True), Mul(Integer(2), Symbol('G', commutative=True))))", "exp(Add(Mul(Integer(-1), Symbol('B', commutative=True)), Symbol('G', commutative=True)))", "exp(Add(Symbol('B', commutative=True), Symbol('G', commutative=True)))"]}, {"premise_expression": "\\frac{\\log{(N)}}{S}", "variable": "S", "positive": "\\log{(N)} \\log{(S)}", "negatives": ["\\log{(S)} \\cos{(N)}", "e^{N + S}", "\\frac{N (\\log{(N)} - 1)}{S}", "\\frac{S^{2} \\cos{(N)}}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('S', commutative=True), Integer(-1)), log(Symbol('N', commutative=True)))", "srepr_variable": "Symbol('S', commutative=True)", "srepr_positive": "Mul(log(Symbol('N', commutative=True)), log(Symbol('S', commutative=True)))", "srepr_negatives": ["Mul(log(Symbol('S', commutative=True)), cos(Symbol('N', commutative=True)))", "exp(Add(Symbol('N', commutative=True), Symbol('S', commutative=True)))", "Mul(Symbol('N', commutative=True), Pow(Symbol('S', commutative=True), Integer(-1)), Add(log(Symbol('N', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('S', commutative=True), Integer(2)), cos(Symbol('N', commutative=True)))"]}, {"premise_expression": "\\frac{\\sin{(K)}}{h}", "variable": "K", "positive": "- \\frac{\\cos{(K)}}{h}", "negatives": ["- K h - \\cos{(K)}", "\\frac{K^{2} \\log{(h)}}{2}", "\\frac{K^{2} \\sin{(h)}}{2}", "\\log{(h)} \\sin{(K)}"], "srepr_premise_expression": "Mul(Pow(Symbol('h', commutative=True), Integer(-1)), sin(Symbol('K', commutative=True)))", "srepr_variable": "Symbol('K', commutative=True)", "srepr_positive": "Mul(Integer(-1), Pow(Symbol('h', commutative=True), Integer(-1)), cos(Symbol('K', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('K', commutative=True), Symbol('h', commutative=True)), Mul(Integer(-1), cos(Symbol('K', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('K', commutative=True), Integer(2)), log(Symbol('h', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('K', commutative=True), Integer(2)), sin(Symbol('h', commutative=True)))", "Mul(log(Symbol('h', commutative=True)), sin(Symbol('K', commutative=True)))"]}, {"premise_expression": "L + \\log{(b)}", "variable": "L", "positive": "\\frac{L (L + 2 \\log{(b)})}{2}", "negatives": ["\\frac{L (L + 2 \\sin{(b)})}{2}", "\\frac{L (L - 2 b)}{2}", "b (L + \\log{(b)} - 1)", "L (b + e^{b})"], "srepr_premise_expression": "Add(Symbol('L', commutative=True), log(Symbol('b', commutative=True)))", "srepr_variable": "Symbol('L', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Symbol('L', commutative=True), Mul(Integer(2), log(Symbol('b', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Symbol('L', commutative=True), Mul(Integer(2), sin(Symbol('b', commutative=True)))))", "Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Symbol('L', commutative=True), Mul(Integer(-1), Integer(2), Symbol('b', commutative=True))))", "Mul(Symbol('b', commutative=True), Add(Symbol('L', commutative=True), log(Symbol('b', commutative=True)), Integer(-1)))", "Mul(Symbol('L', commutative=True), Add(Symbol('b', commutative=True), exp(Symbol('b', commutative=True))))"]}, {"premise_expression": "\\sin{(M - t)}", "variable": "t", "positive": "\\cos{(M - t)}", "negatives": ["- \\cos{(M - t)}", "- \\sin{(M - t)}", "\\frac{t (2 M + t)}{2}", "M t + \\sin{(t)}"], "srepr_premise_expression": "sin(Add(Symbol('M', commutative=True), Mul(Integer(-1), Symbol('t', commutative=True))))", "srepr_variable": "Symbol('t', commutative=True)", "srepr_positive": "cos(Add(Symbol('M', commutative=True), Mul(Integer(-1), Symbol('t', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('M', commutative=True), Mul(Integer(-1), Symbol('t', commutative=True)))))", "Mul(Integer(-1), sin(Add(Symbol('M', commutative=True), Mul(Integer(-1), Symbol('t', commutative=True)))))", "Mul(Rational(1, 2), Symbol('t', commutative=True), Add(Mul(Integer(2), Symbol('M', commutative=True)), Symbol('t', commutative=True)))", "Add(Mul(Symbol('M', commutative=True), Symbol('t', commutative=True)), sin(Symbol('t', commutative=True)))"]}, {"premise_expression": "K v", "variable": "v", "positive": "\\frac{K v^{2}}{2}", "negatives": ["\\frac{K^{2} v}{2}", "v \\cos{(1)}", "0", "\\frac{v^{2} \\log{(K)}}{2}"], "srepr_premise_expression": "Mul(Symbol('K', commutative=True), Symbol('v', commutative=True))", "srepr_variable": "Symbol('v', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('K', commutative=True), Pow(Symbol('v', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('K', commutative=True), Integer(2)), Symbol('v', commutative=True))", "Mul(Symbol('v', commutative=True), cos(Integer(1)))", "Integer(0)", "Mul(Rational(1, 2), Pow(Symbol('v', commutative=True), Integer(2)), log(Symbol('K', commutative=True)))"]}, {"premise_expression": "e^{- D + N}", "variable": "N", "positive": "e^{- D + N}", "negatives": ["- e^{- D + N}", "D e^{N}", "D \\log{(N)}", "\\frac{\\sin{(N)}}{D}"], "srepr_premise_expression": "exp(Add(Mul(Integer(-1), Symbol('D', commutative=True)), Symbol('N', commutative=True)))", "srepr_variable": "Symbol('N', commutative=True)", "srepr_positive": "exp(Add(Mul(Integer(-1), Symbol('D', commutative=True)), Symbol('N', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('D', commutative=True)), Symbol('N', commutative=True))))", "Mul(Symbol('D', commutative=True), exp(Symbol('N', commutative=True)))", "Mul(Symbol('D', commutative=True), log(Symbol('N', commutative=True)))", "Mul(Pow(Symbol('D', commutative=True), Integer(-1)), sin(Symbol('N', commutative=True)))"]}, {"premise_expression": "e^{\\frac{U}{p}}", "variable": "U", "positive": "p e^{\\frac{U}{p}}", "negatives": ["e^{U + p}", "\\frac{U^{2}}{2 p}", "\\frac{U^{2} e^{p}}{2}", "\\frac{U^{2} p}{2}"], "srepr_premise_expression": "exp(Mul(Symbol('U', commutative=True), Pow(Symbol('p', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('U', commutative=True)", "srepr_positive": "Mul(Symbol('p', commutative=True), exp(Mul(Symbol('U', commutative=True), Pow(Symbol('p', commutative=True), Integer(-1)))))", "srepr_negatives": ["exp(Add(Symbol('U', commutative=True), Symbol('p', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('U', commutative=True), Integer(2)), Pow(Symbol('p', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('U', commutative=True), Integer(2)), exp(Symbol('p', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('U', commutative=True), Integer(2)), Symbol('p', commutative=True))"]}, {"premise_expression": "L - r", "variable": "r", "positive": "\\frac{r (2 L - r)}{2}", "negatives": ["\\frac{L r (- 2 L + r)}{2}", "\\frac{L (L - 2 r)}{2}", "\\frac{r^{2} \\log{(L)}}{2}", "e^{L + r}"], "srepr_premise_expression": "Add(Symbol('L', commutative=True), Mul(Integer(-1), Symbol('r', commutative=True)))", "srepr_variable": "Symbol('r', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(2), Symbol('L', commutative=True)), Mul(Integer(-1), Symbol('r', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('L', commutative=True), Symbol('r', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('L', commutative=True)), Symbol('r', commutative=True)))", "Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Symbol('L', commutative=True), Mul(Integer(-1), Integer(2), Symbol('r', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('r', commutative=True), Integer(2)), log(Symbol('L', commutative=True)))", "exp(Add(Symbol('L', commutative=True), Symbol('r', commutative=True)))"]}, {"premise_expression": "\\log{(T + t)}", "variable": "T", "positive": "T \\log{(T + t)} - T + t \\log{(T + t)}", "negatives": ["T \\log{(- T + t)} - T - t \\log{(T - t)}", "T \\log{(T + t)} + t \\log{(T + t)} - t", "T (- t + \\log{(T^{t})})", "\\frac{T (- T + 2 \\cos{(t)})}{2}"], "srepr_premise_expression": "log(Add(Symbol('T', commutative=True), Symbol('t', commutative=True)))", "srepr_variable": "Symbol('T', commutative=True)", "srepr_positive": "Add(Mul(Symbol('T', commutative=True), log(Add(Symbol('T', commutative=True), Symbol('t', commutative=True)))), Mul(Integer(-1), Symbol('T', commutative=True)), Mul(Symbol('t', commutative=True), log(Add(Symbol('T', commutative=True), Symbol('t', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('T', commutative=True), log(Add(Mul(Integer(-1), Symbol('T', commutative=True)), Symbol('t', commutative=True)))), Mul(Integer(-1), Symbol('T', commutative=True)), Mul(Integer(-1), Symbol('t', commutative=True), log(Add(Symbol('T', commutative=True), Mul(Integer(-1), Symbol('t', commutative=True))))))", "Add(Mul(Symbol('T', commutative=True), log(Add(Symbol('T', commutative=True), Symbol('t', commutative=True)))), Mul(Symbol('t', commutative=True), log(Add(Symbol('T', commutative=True), Symbol('t', commutative=True)))), Mul(Integer(-1), Symbol('t', commutative=True)))", "Mul(Symbol('T', commutative=True), Add(Mul(Integer(-1), Symbol('t', commutative=True)), log(Pow(Symbol('T', commutative=True), Symbol('t', commutative=True)))))", "Mul(Rational(1, 2), Symbol('T', commutative=True), Add(Mul(Integer(-1), Symbol('T', commutative=True)), Mul(Integer(2), cos(Symbol('t', commutative=True)))))"]}, {"premise_expression": "o - s + u", "variable": "o", "positive": "o (\\frac{o}{2} - s + u)", "negatives": ["\\frac{o (o + 2 s + 2 u)}{2}", "\\frac{u (2 o - 2 s + u)}{2}", "\\frac{s (2 o - s + 2 u)}{2}", "\\frac{o (o u - 2 s)}{2}"], "srepr_premise_expression": "Add(Symbol('o', commutative=True), Mul(Integer(-1), Symbol('s', commutative=True)), Symbol('u', commutative=True))", "srepr_variable": "Symbol('o', commutative=True)", "srepr_positive": "Mul(Symbol('o', commutative=True), Add(Mul(Rational(1, 2), Symbol('o', commutative=True)), Mul(Integer(-1), Symbol('s', commutative=True)), Symbol('u', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Symbol('o', commutative=True), Mul(Integer(2), Symbol('s', commutative=True)), Mul(Integer(2), Symbol('u', commutative=True))))", "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(2), Symbol('o', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('s', commutative=True)), Symbol('u', commutative=True)))", "Mul(Rational(1, 2), Symbol('s', commutative=True), Add(Mul(Integer(2), Symbol('o', commutative=True)), Mul(Integer(-1), Symbol('s', commutative=True)), Mul(Integer(2), Symbol('u', commutative=True))))", "Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Mul(Symbol('o', commutative=True), Symbol('u', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('s', commutative=True))))"]}, {"premise_expression": "- A + W", "variable": "W", "positive": "\\frac{W (- 2 A + W)}{2}", "negatives": ["\\frac{A (- A + 2 W)}{2}", "\\frac{W (\\log{(W)} - 1)}{A}", "\\frac{W (- W + 2 \\log{(A)})}{2}", "A W + e^{W}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('A', commutative=True)), Symbol('W', commutative=True))", "srepr_variable": "Symbol('W', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('W', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('A', commutative=True)), Symbol('W', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Mul(Integer(-1), Symbol('A', commutative=True)), Mul(Integer(2), Symbol('W', commutative=True))))", "Mul(Pow(Symbol('A', commutative=True), Integer(-1)), Symbol('W', commutative=True), Add(log(Symbol('W', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('W', commutative=True), Add(Mul(Integer(-1), Symbol('W', commutative=True)), Mul(Integer(2), log(Symbol('A', commutative=True)))))", "Add(Mul(Symbol('A', commutative=True), Symbol('W', commutative=True)), exp(Symbol('W', commutative=True)))"]}, {"premise_expression": "- m + o", "variable": "m", "positive": "\\frac{m (- m + 2 o)}{2}", "negatives": ["\\frac{o (- 2 m + o)}{2}", "e^{m + o}", "\\frac{m^{2} \\log{(o)}}{2}", "\\frac{m (\\log{(m)} - 1)}{o}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('m', commutative=True)), Symbol('o', commutative=True))", "srepr_variable": "Symbol('m', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Mul(Integer(-1), Symbol('m', commutative=True)), Mul(Integer(2), Symbol('o', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('m', commutative=True)), Symbol('o', commutative=True)))", "exp(Add(Symbol('m', commutative=True), Symbol('o', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('m', commutative=True), Integer(2)), log(Symbol('o', commutative=True)))", "Mul(Symbol('m', commutative=True), Pow(Symbol('o', commutative=True), Integer(-1)), Add(log(Symbol('m', commutative=True)), Integer(-1)))"]}, {"premise_expression": "P k", "variable": "P", "positive": "\\frac{P^{2} k}{2}", "negatives": ["\\frac{P k^{2}}{2}", "\\frac{P^{2} \\sin{(k)}}{2}", "\\frac{P^{2} \\log{(k)}}{2}", "k \\log{(P)}"], "srepr_premise_expression": "Mul(Symbol('P', commutative=True), Symbol('k', commutative=True))", "srepr_variable": "Symbol('P', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2)), Symbol('k', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('P', commutative=True), Pow(Symbol('k', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2)), sin(Symbol('k', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2)), log(Symbol('k', commutative=True)))", "Mul(Symbol('k', commutative=True), log(Symbol('P', commutative=True)))"]}, {"premise_expression": "\\log{(\\frac{H}{Q})}", "variable": "H", "positive": "H (\\log{(\\frac{H}{Q})} - 1)", "negatives": ["Q (\\log{(\\frac{H}{Q})} + 1)", "H (\\log{(\\frac{Q}{H})} + 1)", "H Q (\\log{(H)} - 1)", "e^{H - Q}"], "srepr_premise_expression": "log(Mul(Symbol('H', commutative=True), Pow(Symbol('Q', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('H', commutative=True)", "srepr_positive": "Mul(Symbol('H', commutative=True), Add(log(Mul(Symbol('H', commutative=True), Pow(Symbol('Q', commutative=True), Integer(-1)))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('Q', commutative=True), Add(log(Mul(Symbol('H', commutative=True), Pow(Symbol('Q', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Symbol('H', commutative=True), Add(log(Mul(Pow(Symbol('H', commutative=True), Integer(-1)), Symbol('Q', commutative=True))), Integer(1)))", "Mul(Symbol('H', commutative=True), Symbol('Q', commutative=True), Add(log(Symbol('H', commutative=True)), Integer(-1)))", "exp(Add(Symbol('H', commutative=True), Mul(Integer(-1), Symbol('Q', commutative=True))))"]}, {"premise_expression": "Y + g", "variable": "Y", "positive": "\\frac{Y (Y + 2 g)}{2}", "negatives": ["\\frac{g (2 Y + g)}{2}", "\\frac{Y (Y + 2 \\sin{(g)})}{2}", "\\frac{Y^{2}}{2 g}", "e^{Y + g}"], "srepr_premise_expression": "Add(Symbol('Y', commutative=True), Symbol('g', commutative=True))", "srepr_variable": "Symbol('Y', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('Y', commutative=True), Add(Symbol('Y', commutative=True), Mul(Integer(2), Symbol('g', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Mul(Integer(2), Symbol('Y', commutative=True)), Symbol('g', commutative=True)))", "Mul(Rational(1, 2), Symbol('Y', commutative=True), Add(Symbol('Y', commutative=True), Mul(Integer(2), sin(Symbol('g', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('Y', commutative=True), Integer(2)), Pow(Symbol('g', commutative=True), Integer(-1)))", "exp(Add(Symbol('Y', commutative=True), Symbol('g', commutative=True)))"]}, {"premise_expression": "C t", "variable": "C", "positive": "\\frac{C^{2} t}{2}", "negatives": ["\\frac{C t^{2}}{2}", "\\frac{C (- C + 2 t)}{2}", "- \\frac{\\cos{(C)}}{t}", "e^{C - t}"], "srepr_premise_expression": "Mul(Symbol('C', commutative=True), Symbol('t', commutative=True))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2)), Symbol('t', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('C', commutative=True), Pow(Symbol('t', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Mul(Integer(-1), Symbol('C', commutative=True)), Mul(Integer(2), Symbol('t', commutative=True))))", "Mul(Integer(-1), Pow(Symbol('t', commutative=True), Integer(-1)), cos(Symbol('C', commutative=True)))", "exp(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('t', commutative=True))))"]}, {"premise_expression": "\\log{(R^{W})}", "variable": "W", "positive": "\\frac{W^{2} \\log{(R)}}{2}", "negatives": ["\\frac{W (2 R + W)}{2}", "\\frac{W (- 2 R + W)}{2}", "- R W - \\cos{(W)}", "R (- W + \\log{(R^{W})})"], "srepr_premise_expression": "log(Pow(Symbol('R', commutative=True), Symbol('W', commutative=True)))", "srepr_variable": "Symbol('W', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('W', commutative=True), Integer(2)), log(Symbol('R', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('W', commutative=True), Add(Mul(Integer(2), Symbol('R', commutative=True)), Symbol('W', commutative=True)))", "Mul(Rational(1, 2), Symbol('W', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('R', commutative=True)), Symbol('W', commutative=True)))", "Add(Mul(Integer(-1), Symbol('R', commutative=True), Symbol('W', commutative=True)), Mul(Integer(-1), cos(Symbol('W', commutative=True))))", "Mul(Symbol('R', commutative=True), Add(Mul(Integer(-1), Symbol('W', commutative=True)), log(Pow(Symbol('R', commutative=True), Symbol('W', commutative=True)))))"]}, {"premise_expression": "e^{D - H}", "variable": "H", "positive": "- e^{D - H}", "negatives": ["e^{D - H}", "D \\log{(H)}", "H \\sin{(D^{D})}", "D \\sin{(H)}"], "srepr_premise_expression": "exp(Add(Symbol('D', commutative=True), Mul(Integer(-1), Symbol('H', commutative=True))))", "srepr_variable": "Symbol('H', commutative=True)", "srepr_positive": "Mul(Integer(-1), exp(Add(Symbol('D', commutative=True), Mul(Integer(-1), Symbol('H', commutative=True)))))", "srepr_negatives": ["exp(Add(Symbol('D', commutative=True), Mul(Integer(-1), Symbol('H', commutative=True))))", "Mul(Symbol('D', commutative=True), log(Symbol('H', commutative=True)))", "Mul(Symbol('H', commutative=True), sin(Pow(Symbol('D', commutative=True), Symbol('D', commutative=True))))", "Mul(Symbol('D', commutative=True), sin(Symbol('H', commutative=True)))"]}, {"premise_expression": "\\log{(M^{j})}", "variable": "M", "positive": "M (- j + \\log{(M^{j})})", "negatives": ["M (- j + \\log{(M)} - 1)", "M j + e^{M}", "\\frac{j^{2} \\log{(M)}}{2}", "M (\\log{(\\frac{j}{M})} + 1)"], "srepr_premise_expression": "log(Pow(Symbol('M', commutative=True), Symbol('j', commutative=True)))", "srepr_variable": "Symbol('M', commutative=True)", "srepr_positive": "Mul(Symbol('M', commutative=True), Add(Mul(Integer(-1), Symbol('j', commutative=True)), log(Pow(Symbol('M', commutative=True), Symbol('j', commutative=True)))))", "srepr_negatives": ["Mul(Symbol('M', commutative=True), Add(Mul(Integer(-1), Symbol('j', commutative=True)), log(Symbol('M', commutative=True)), Integer(-1)))", "Add(Mul(Symbol('M', commutative=True), Symbol('j', commutative=True)), exp(Symbol('M', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('j', commutative=True), Integer(2)), log(Symbol('M', commutative=True)))", "Mul(Symbol('M', commutative=True), Add(log(Mul(Pow(Symbol('M', commutative=True), Integer(-1)), Symbol('j', commutative=True))), Integer(1)))"]}, {"premise_expression": "H^{E} Z", "variable": "Z", "positive": "\\frac{H^{E} Z^{2}}{2}", "negatives": ["\\frac{E H Z^{2}}{2}", "\\frac{H Z^{2}}{2 E}", "\\frac{E Z^{2}}{2 H}", "E Z + \\frac{Z^{2}}{2 H}"], "srepr_premise_expression": "Mul(Pow(Symbol('H', commutative=True), Symbol('E', commutative=True)), Symbol('Z', commutative=True))", "srepr_variable": "Symbol('Z', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('H', commutative=True), Symbol('E', commutative=True)), Pow(Symbol('Z', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('E', commutative=True), Symbol('H', commutative=True), Pow(Symbol('Z', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('E', commutative=True), Integer(-1)), Symbol('H', commutative=True), Pow(Symbol('Z', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('E', commutative=True), Pow(Symbol('H', commutative=True), Integer(-1)), Pow(Symbol('Z', commutative=True), Integer(2)))", "Add(Mul(Symbol('E', commutative=True), Symbol('Z', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('H', commutative=True), Integer(-1)), Pow(Symbol('Z', commutative=True), Integer(2))))"]}, {"premise_expression": "- U + \\log{(t)}", "variable": "t", "positive": "t (- U + \\log{(t)} - 1)", "negatives": ["t (\\log{(\\frac{t}{U})} - 1)", "\\frac{U (- U + 2 \\log{(t)})}{2}", "U \\log{(t)}", "e^{U + t}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('U', commutative=True)), log(Symbol('t', commutative=True)))", "srepr_variable": "Symbol('t', commutative=True)", "srepr_positive": "Mul(Symbol('t', commutative=True), Add(Mul(Integer(-1), Symbol('U', commutative=True)), log(Symbol('t', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('t', commutative=True), Add(log(Mul(Pow(Symbol('U', commutative=True), Integer(-1)), Symbol('t', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('U', commutative=True), Add(Mul(Integer(-1), Symbol('U', commutative=True)), Mul(Integer(2), log(Symbol('t', commutative=True)))))", "Mul(Symbol('U', commutative=True), log(Symbol('t', commutative=True)))", "exp(Add(Symbol('U', commutative=True), Symbol('t', commutative=True)))"]}, {"premise_expression": "\\sin{(\\frac{B}{w})}", "variable": "w", "positive": "B \\log{(\\frac{B}{w})} - \\frac{B \\log{(\\frac{B^{2}}{w^{2}})}}{2} - B \\operatorname{Ci}{(\\frac{B}{w})} + w \\sin{(\\frac{B}{w})}", "negatives": ["B \\log{(B + w)} + w \\log{(B + w)} - w", "(- \\log{(w)})^{- B} \\log{(w)}^{B} \\Gamma(B + 1, - \\log{(w)})", "w (\\log{(B w)} - 1)", "w (\\log{(\\frac{B}{w})} + 1)"], "srepr_premise_expression": "sin(Mul(Symbol('B', commutative=True), Pow(Symbol('w', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('w', commutative=True)", "srepr_positive": "Add(Mul(Symbol('B', commutative=True), log(Mul(Symbol('B', commutative=True), Pow(Symbol('w', commutative=True), Integer(-1))))), Mul(Integer(-1), Rational(1, 2), Symbol('B', commutative=True), log(Mul(Pow(Symbol('B', commutative=True), Integer(2)), Pow(Symbol('w', commutative=True), Integer(-2))))), Mul(Integer(-1), Symbol('B', commutative=True), Ci(Mul(Symbol('B', commutative=True), Pow(Symbol('w', commutative=True), Integer(-1))))), Mul(Symbol('w', commutative=True), sin(Mul(Symbol('B', commutative=True), Pow(Symbol('w', commutative=True), Integer(-1))))))", "srepr_negatives": ["Add(Mul(Symbol('B', commutative=True), log(Add(Symbol('B', commutative=True), Symbol('w', commutative=True)))), Mul(Symbol('w', commutative=True), log(Add(Symbol('B', commutative=True), Symbol('w', commutative=True)))), Mul(Integer(-1), Symbol('w', commutative=True)))", "Mul(Pow(Mul(Integer(-1), log(Symbol('w', commutative=True))), Mul(Integer(-1), Symbol('B', commutative=True))), Pow(log(Symbol('w', commutative=True)), Symbol('B', commutative=True)), uppergamma(Add(Symbol('B', commutative=True), Integer(1)), Mul(Integer(-1), log(Symbol('w', commutative=True)))))", "Mul(Symbol('w', commutative=True), Add(log(Mul(Symbol('B', commutative=True), Symbol('w', commutative=True))), Integer(-1)))", "Mul(Symbol('w', commutative=True), Add(log(Mul(Symbol('B', commutative=True), Pow(Symbol('w', commutative=True), Integer(-1)))), Integer(1)))"]}, {"premise_expression": "b h", "variable": "h", "positive": "\\frac{b h^{2}}{2}", "negatives": ["\\frac{b^{2} h}{2}", "b \\log{(h)}", "b h + \\sin{(h)}", "\\frac{h^{2} \\log{(b)}}{2}"], "srepr_premise_expression": "Mul(Symbol('b', commutative=True), Symbol('h', commutative=True))", "srepr_variable": "Symbol('h', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('b', commutative=True), Pow(Symbol('h', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('b', commutative=True), Integer(2)), Symbol('h', commutative=True))", "Mul(Symbol('b', commutative=True), log(Symbol('h', commutative=True)))", "Add(Mul(Symbol('b', commutative=True), Symbol('h', commutative=True)), sin(Symbol('h', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('h', commutative=True), Integer(2)), log(Symbol('b', commutative=True)))"]}, {"premise_expression": "\\cos{(B + H)}", "variable": "B", "positive": "\\sin{(B + H)}", "negatives": ["\\sin{(B - H)}", "\\frac{B (- B + 2 H)}{2}", "\\frac{B^{2} H}{2}", "\\frac{B (\\log{(B)} - 1)}{H}"], "srepr_premise_expression": "cos(Add(Symbol('B', commutative=True), Symbol('H', commutative=True)))", "srepr_variable": "Symbol('B', commutative=True)", "srepr_positive": "sin(Add(Symbol('B', commutative=True), Symbol('H', commutative=True)))", "srepr_negatives": ["sin(Add(Symbol('B', commutative=True), Mul(Integer(-1), Symbol('H', commutative=True))))", "Mul(Rational(1, 2), Symbol('B', commutative=True), Add(Mul(Integer(-1), Symbol('B', commutative=True)), Mul(Integer(2), Symbol('H', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('B', commutative=True), Integer(2)), Symbol('H', commutative=True))", "Mul(Symbol('B', commutative=True), Pow(Symbol('H', commutative=True), Integer(-1)), Add(log(Symbol('B', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\frac{L}{X b}", "variable": "L", "positive": "\\frac{L^{2}}{2 X b}", "negatives": ["\\frac{L^{2}}{2 X} - L b", "\\frac{L^{2} (X + b)}{2}", "\\frac{L \\log{(X)}}{b}", "\\frac{L \\log{(b)}}{X}"], "srepr_premise_expression": "Mul(Symbol('L', commutative=True), Pow(Symbol('X', commutative=True), Integer(-1)), Pow(Symbol('b', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('L', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(2)), Pow(Symbol('X', commutative=True), Integer(-1)), Pow(Symbol('b', commutative=True), Integer(-1)))", "srepr_negatives": ["Add(Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(2)), Pow(Symbol('X', commutative=True), Integer(-1))), Mul(Integer(-1), Symbol('L', commutative=True), Symbol('b', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(2)), Add(Symbol('X', commutative=True), Symbol('b', commutative=True)))", "Mul(Symbol('L', commutative=True), Pow(Symbol('b', commutative=True), Integer(-1)), log(Symbol('X', commutative=True)))", "Mul(Symbol('L', commutative=True), Pow(Symbol('X', commutative=True), Integer(-1)), log(Symbol('b', commutative=True)))"]}, {"premise_expression": "- s + \\sin{(V)}", "variable": "s", "positive": "\\frac{s (- s + 2 \\sin{(V)})}{2}", "negatives": ["\\frac{s (s + 2 e^{V})}{2}", "- V s - \\cos{(V)}", "V s - \\cos{(s)}", "s (\\log{(2 s)} - 1)"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('s', commutative=True)), sin(Symbol('V', commutative=True)))", "srepr_variable": "Symbol('s', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('s', commutative=True), Add(Mul(Integer(-1), Symbol('s', commutative=True)), Mul(Integer(2), sin(Symbol('V', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('s', commutative=True), Add(Symbol('s', commutative=True), Mul(Integer(2), exp(Symbol('V', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('V', commutative=True), Symbol('s', commutative=True)), Mul(Integer(-1), cos(Symbol('V', commutative=True))))", "Add(Mul(Symbol('V', commutative=True), Symbol('s', commutative=True)), Mul(Integer(-1), cos(Symbol('s', commutative=True))))", "Mul(Symbol('s', commutative=True), Add(log(Mul(Integer(2), Symbol('s', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\frac{s}{x}", "variable": "s", "positive": "\\frac{s^{2}}{2 x}", "negatives": ["s \\log{(x)}", "x e^{\\frac{s}{x}}", "\\sin{(s + x)}", "\\frac{s (s + 2 x)}{2}"], "srepr_premise_expression": "Mul(Symbol('s', commutative=True), Pow(Symbol('x', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('s', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('s', commutative=True), Integer(2)), Pow(Symbol('x', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('s', commutative=True), log(Symbol('x', commutative=True)))", "Mul(Symbol('x', commutative=True), exp(Mul(Symbol('s', commutative=True), Pow(Symbol('x', commutative=True), Integer(-1)))))", "sin(Add(Symbol('s', commutative=True), Symbol('x', commutative=True)))", "Mul(Rational(1, 2), Symbol('s', commutative=True), Add(Symbol('s', commutative=True), Mul(Integer(2), Symbol('x', commutative=True))))"]}, {"premise_expression": "e^{L + m}", "variable": "L", "positive": "e^{L + m}", "negatives": ["\\cos{(L - m)}", "\\sin{(L - m)}", "\\frac{L (L + 2 m)}{2}", "\\log{(L)} \\cos{(m)}"], "srepr_premise_expression": "exp(Add(Symbol('L', commutative=True), Symbol('m', commutative=True)))", "srepr_variable": "Symbol('L', commutative=True)", "srepr_positive": "exp(Add(Symbol('L', commutative=True), Symbol('m', commutative=True)))", "srepr_negatives": ["cos(Add(Symbol('L', commutative=True), Mul(Integer(-1), Symbol('m', commutative=True))))", "sin(Add(Symbol('L', commutative=True), Mul(Integer(-1), Symbol('m', commutative=True))))", "Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Symbol('L', commutative=True), Mul(Integer(2), Symbol('m', commutative=True))))", "Mul(log(Symbol('L', commutative=True)), cos(Symbol('m', commutative=True)))"]}, {"premise_expression": "\\cos^{V}{(o)}", "variable": "o", "positive": "\\int \\cos^{V}{(o)} do", "negatives": ["- \\frac{\\cos{(o)}}{V}", "V e^{\\frac{o}{V}}", "o (\\log{(V o)} - 1)", "\\frac{o^{2} \\log{(V)}}{2}"], "srepr_premise_expression": "Pow(cos(Symbol('o', commutative=True)), Symbol('V', commutative=True))", "srepr_variable": "Symbol('o', commutative=True)", "srepr_positive": "Integral(Pow(cos(Symbol('o', commutative=True)), Symbol('V', commutative=True)), Tuple(Symbol('o', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Pow(Symbol('V', commutative=True), Integer(-1)), cos(Symbol('o', commutative=True)))", "Mul(Symbol('V', commutative=True), exp(Mul(Pow(Symbol('V', commutative=True), Integer(-1)), Symbol('o', commutative=True))))", "Mul(Symbol('o', commutative=True), Add(log(Mul(Symbol('V', commutative=True), Symbol('o', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('o', commutative=True), Integer(2)), log(Symbol('V', commutative=True)))"]}, {"premise_expression": "e^{\\frac{V}{s}}", "variable": "V", "positive": "s e^{\\frac{V}{s}}", "negatives": ["s e^{V}", "- e^{- V + s}", "\\frac{V^{2}}{2 s}", "- \\frac{\\cos{(V)}}{s}"], "srepr_premise_expression": "exp(Mul(Symbol('V', commutative=True), Pow(Symbol('s', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('V', commutative=True)", "srepr_positive": "Mul(Symbol('s', commutative=True), exp(Mul(Symbol('V', commutative=True), Pow(Symbol('s', commutative=True), Integer(-1)))))", "srepr_negatives": ["Mul(Symbol('s', commutative=True), exp(Symbol('V', commutative=True)))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('V', commutative=True)), Symbol('s', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('V', commutative=True), Integer(2)), Pow(Symbol('s', commutative=True), Integer(-1)))", "Mul(Integer(-1), Pow(Symbol('s', commutative=True), Integer(-1)), cos(Symbol('V', commutative=True)))"]}, {"premise_expression": "- \\sin{(C - P)}", "variable": "P", "positive": "- \\cos{(C - P)}", "negatives": ["\\cos{(C - P)}", "e^{C + P}", "- C P - \\cos{(P)}", "P (\\log{(\\frac{C}{P})} + 1)"], "srepr_premise_expression": "Mul(Integer(-1), sin(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('P', commutative=True)))))", "srepr_variable": "Symbol('P', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('P', commutative=True)))))", "srepr_negatives": ["cos(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('P', commutative=True))))", "exp(Add(Symbol('C', commutative=True), Symbol('P', commutative=True)))", "Add(Mul(Integer(-1), Symbol('C', commutative=True), Symbol('P', commutative=True)), Mul(Integer(-1), cos(Symbol('P', commutative=True))))", "Mul(Symbol('P', commutative=True), Add(log(Mul(Symbol('C', commutative=True), Pow(Symbol('P', commutative=True), Integer(-1)))), Integer(1)))"]}, {"premise_expression": "p t", "variable": "p", "positive": "\\frac{p^{2} t}{2}", "negatives": ["\\frac{p t^{2}}{2}", "\\frac{p^{2} \\log{(t)}}{2}", "t \\log{(p)}", "e^{t} \\log{(p)}"], "srepr_premise_expression": "Mul(Symbol('p', commutative=True), Symbol('t', commutative=True))", "srepr_variable": "Symbol('p', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('p', commutative=True), Integer(2)), Symbol('t', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('p', commutative=True), Pow(Symbol('t', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('p', commutative=True), Integer(2)), log(Symbol('t', commutative=True)))", "Mul(Symbol('t', commutative=True), log(Symbol('p', commutative=True)))", "Mul(exp(Symbol('t', commutative=True)), log(Symbol('p', commutative=True)))"]}, {"premise_expression": "\\cos^{Q}{(a)}", "variable": "a", "positive": "\\int \\cos^{Q}{(a)} da", "negatives": ["- \\cos{(Q + a)}", "- \\cos{(Q - a)}", "\\frac{a^{2}}{2 Q}", "\\frac{a (2 Q - a)}{2}"], "srepr_premise_expression": "Pow(cos(Symbol('a', commutative=True)), Symbol('Q', commutative=True))", "srepr_variable": "Symbol('a', commutative=True)", "srepr_positive": "Integral(Pow(cos(Symbol('a', commutative=True)), Symbol('Q', commutative=True)), Tuple(Symbol('a', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('Q', commutative=True), Symbol('a', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('Q', commutative=True), Mul(Integer(-1), Symbol('a', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(-1)), Pow(Symbol('a', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('a', commutative=True), Add(Mul(Integer(2), Symbol('Q', commutative=True)), Mul(Integer(-1), Symbol('a', commutative=True))))"]}, {"premise_expression": "\\frac{S + T}{Q}", "variable": "T", "positive": "\\frac{T (2 S + T)}{2 Q}", "negatives": ["\\frac{T (2 S - T)}{2 Q}", "\\frac{S (S + 2 T)}{2 Q}", "\\frac{T (2 S^{Q} + T)}{2}", "(S + T) \\log{(Q)}"], "srepr_premise_expression": "Mul(Pow(Symbol('Q', commutative=True), Integer(-1)), Add(Symbol('S', commutative=True), Symbol('T', commutative=True)))", "srepr_variable": "Symbol('T', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(-1)), Symbol('T', commutative=True), Add(Mul(Integer(2), Symbol('S', commutative=True)), Symbol('T', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(-1)), Symbol('T', commutative=True), Add(Mul(Integer(2), Symbol('S', commutative=True)), Mul(Integer(-1), Symbol('T', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(-1)), Symbol('S', commutative=True), Add(Symbol('S', commutative=True), Mul(Integer(2), Symbol('T', commutative=True))))", "Mul(Rational(1, 2), Symbol('T', commutative=True), Add(Mul(Integer(2), Pow(Symbol('S', commutative=True), Symbol('Q', commutative=True))), Symbol('T', commutative=True)))", "Mul(Add(Symbol('S', commutative=True), Symbol('T', commutative=True)), log(Symbol('Q', commutative=True)))"]}, {"premise_expression": "\\cos^{X}{(z)}", "variable": "z", "positive": "\\int \\cos^{X}{(z)} dz", "negatives": ["\\log{(X)} \\log{(z)}", "- \\frac{\\cos{(z)}}{X}", "- X z - \\cos{(z)}", "X z - \\cos{(z)}"], "srepr_premise_expression": "Pow(cos(Symbol('z', commutative=True)), Symbol('X', commutative=True))", "srepr_variable": "Symbol('z', commutative=True)", "srepr_positive": "Integral(Pow(cos(Symbol('z', commutative=True)), Symbol('X', commutative=True)), Tuple(Symbol('z', commutative=True)))", "srepr_negatives": ["Mul(log(Symbol('X', commutative=True)), log(Symbol('z', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('X', commutative=True), Integer(-1)), cos(Symbol('z', commutative=True)))", "Add(Mul(Integer(-1), Symbol('X', commutative=True), Symbol('z', commutative=True)), Mul(Integer(-1), cos(Symbol('z', commutative=True))))", "Add(Mul(Symbol('X', commutative=True), Symbol('z', commutative=True)), Mul(Integer(-1), cos(Symbol('z', commutative=True))))"]}, {"premise_expression": "\\log{(G^{M})}", "variable": "G", "positive": "G (- M + \\log{(G^{M})})", "negatives": ["\\frac{G (- G + 2 \\sin{(M)})}{2}", "- G M - \\cos{(G)}", "M \\log{(G)}", "\\frac{M^{2} \\log{(G)}}{2}"], "srepr_premise_expression": "log(Pow(Symbol('G', commutative=True), Symbol('M', commutative=True)))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Mul(Symbol('G', commutative=True), Add(Mul(Integer(-1), Symbol('M', commutative=True)), log(Pow(Symbol('G', commutative=True), Symbol('M', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Mul(Integer(-1), Symbol('G', commutative=True)), Mul(Integer(2), sin(Symbol('M', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('G', commutative=True), Symbol('M', commutative=True)), Mul(Integer(-1), cos(Symbol('G', commutative=True))))", "Mul(Symbol('M', commutative=True), log(Symbol('G', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('M', commutative=True), Integer(2)), log(Symbol('G', commutative=True)))"]}, {"premise_expression": "\\frac{R t}{h}", "variable": "R", "positive": "\\frac{R^{2} t}{2 h}", "negatives": ["\\frac{R t^{2}}{2 h}", "\\frac{R^{2}}{2 h t}", "R t \\log{(h)}", "\\frac{R (- R + 2 t)}{2 h}"], "srepr_premise_expression": "Mul(Symbol('R', commutative=True), Pow(Symbol('h', commutative=True), Integer(-1)), Symbol('t', commutative=True))", "srepr_variable": "Symbol('R', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('R', commutative=True), Integer(2)), Pow(Symbol('h', commutative=True), Integer(-1)), Symbol('t', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('R', commutative=True), Pow(Symbol('h', commutative=True), Integer(-1)), Pow(Symbol('t', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('R', commutative=True), Integer(2)), Pow(Symbol('h', commutative=True), Integer(-1)), Pow(Symbol('t', commutative=True), Integer(-1)))", "Mul(Symbol('R', commutative=True), Symbol('t', commutative=True), log(Symbol('h', commutative=True)))", "Mul(Rational(1, 2), Symbol('R', commutative=True), Pow(Symbol('h', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('R', commutative=True)), Mul(Integer(2), Symbol('t', commutative=True))))"]}, {"premise_expression": "e^{N - a}", "variable": "a", "positive": "- e^{N - a}", "negatives": ["e^{N - a}", "- \\cos{(N + a)}", "\\frac{a (- 2 N + a)}{2}", "N a - \\cos{(a)}"], "srepr_premise_expression": "exp(Add(Symbol('N', commutative=True), Mul(Integer(-1), Symbol('a', commutative=True))))", "srepr_variable": "Symbol('a', commutative=True)", "srepr_positive": "Mul(Integer(-1), exp(Add(Symbol('N', commutative=True), Mul(Integer(-1), Symbol('a', commutative=True)))))", "srepr_negatives": ["exp(Add(Symbol('N', commutative=True), Mul(Integer(-1), Symbol('a', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('N', commutative=True), Symbol('a', commutative=True))))", "Mul(Rational(1, 2), Symbol('a', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('N', commutative=True)), Symbol('a', commutative=True)))", "Add(Mul(Symbol('N', commutative=True), Symbol('a', commutative=True)), Mul(Integer(-1), cos(Symbol('a', commutative=True))))"]}, {"premise_expression": "- n + \\log{(C)}", "variable": "n", "positive": "\\frac{n (- n + 2 \\log{(C)})}{2}", "negatives": ["\\frac{n (- n + 2 \\sin{(C)})}{2}", "C (- n + \\log{(C)} - 1)", "\\frac{n (2 C - n)}{2}", "\\frac{C n^{2}}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('n', commutative=True)), log(Symbol('C', commutative=True)))", "srepr_variable": "Symbol('n', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('n', commutative=True), Add(Mul(Integer(-1), Symbol('n', commutative=True)), Mul(Integer(2), log(Symbol('C', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('n', commutative=True), Add(Mul(Integer(-1), Symbol('n', commutative=True)), Mul(Integer(2), sin(Symbol('C', commutative=True)))))", "Mul(Symbol('C', commutative=True), Add(Mul(Integer(-1), Symbol('n', commutative=True)), log(Symbol('C', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('n', commutative=True), Add(Mul(Integer(2), Symbol('C', commutative=True)), Mul(Integer(-1), Symbol('n', commutative=True))))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Pow(Symbol('n', commutative=True), Integer(2)))"]}, {"premise_expression": "\\frac{X}{q}", "variable": "q", "positive": "X \\log{(q)}", "negatives": ["\\frac{X^{2}}{2 q}", "\\frac{\\sin{(q)}}{X}", "\\frac{\\sin{(2 q)}}{2}", "q (\\log{(\\frac{q}{X})} - 1)"], "srepr_premise_expression": "Mul(Symbol('X', commutative=True), Pow(Symbol('q', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('q', commutative=True)", "srepr_positive": "Mul(Symbol('X', commutative=True), log(Symbol('q', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('X', commutative=True), Integer(2)), Pow(Symbol('q', commutative=True), Integer(-1)))", "Mul(Pow(Symbol('X', commutative=True), Integer(-1)), sin(Symbol('q', commutative=True)))", "Mul(Rational(1, 2), sin(Mul(Integer(2), Symbol('q', commutative=True))))", "Mul(Symbol('q', commutative=True), Add(log(Mul(Pow(Symbol('X', commutative=True), Integer(-1)), Symbol('q', commutative=True))), Integer(-1)))"]}, {"premise_expression": "P + k", "variable": "k", "positive": "\\frac{k (2 P + k)}{2}", "negatives": ["\\frac{P (P + 2 k)}{2}", "\\frac{k^{2} \\log{(P)}}{2}", "- \\cos{(P + k)}", "P \\log{(k)} + k"], "srepr_premise_expression": "Add(Symbol('P', commutative=True), Symbol('k', commutative=True))", "srepr_variable": "Symbol('k', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('k', commutative=True), Add(Mul(Integer(2), Symbol('P', commutative=True)), Symbol('k', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Symbol('P', commutative=True), Mul(Integer(2), Symbol('k', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('k', commutative=True), Integer(2)), log(Symbol('P', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('P', commutative=True), Symbol('k', commutative=True))))", "Add(Mul(Symbol('P', commutative=True), log(Symbol('k', commutative=True))), Symbol('k', commutative=True))"]}, {"premise_expression": "\\sin{(S + j)}", "variable": "j", "positive": "- \\cos{(S + j)}", "negatives": ["- \\cos{(S - j)}", "e^{S + j}", "S \\log{(j)}", "S j + e^{j}"], "srepr_premise_expression": "sin(Add(Symbol('S', commutative=True), Symbol('j', commutative=True)))", "srepr_variable": "Symbol('j', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('S', commutative=True), Symbol('j', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('j', commutative=True)))))", "exp(Add(Symbol('S', commutative=True), Symbol('j', commutative=True)))", "Mul(Symbol('S', commutative=True), log(Symbol('j', commutative=True)))", "Add(Mul(Symbol('S', commutative=True), Symbol('j', commutative=True)), exp(Symbol('j', commutative=True)))"]}, {"premise_expression": "\\log{(A - m)}", "variable": "A", "positive": "A \\log{(A - m)} - A - m \\log{(A - m)}", "negatives": ["- A \\log{(- A + m)} + m \\log{(A - m)} - m", "\\log{(A)} \\log{(m)}", "e^{m} \\log{(A)}", "- A m - \\cos{(A)}"], "srepr_premise_expression": "log(Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('m', commutative=True))))", "srepr_variable": "Symbol('A', commutative=True)", "srepr_positive": "Add(Mul(Symbol('A', commutative=True), log(Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('m', commutative=True))))), Mul(Integer(-1), Symbol('A', commutative=True)), Mul(Integer(-1), Symbol('m', commutative=True), log(Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('m', commutative=True))))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('A', commutative=True), log(Add(Mul(Integer(-1), Symbol('A', commutative=True)), Symbol('m', commutative=True)))), Mul(Symbol('m', commutative=True), log(Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('m', commutative=True))))), Mul(Integer(-1), Symbol('m', commutative=True)))", "Mul(log(Symbol('A', commutative=True)), log(Symbol('m', commutative=True)))", "Mul(exp(Symbol('m', commutative=True)), log(Symbol('A', commutative=True)))", "Add(Mul(Integer(-1), Symbol('A', commutative=True), Symbol('m', commutative=True)), Mul(Integer(-1), cos(Symbol('A', commutative=True))))"]}, {"premise_expression": "- \\sin{(Y - b)}", "variable": "Y", "positive": "\\cos{(Y - b)}", "negatives": ["- \\cos{(Y - b)}", "- \\cos{(Y + b)}", "\\sin{(Y - b)}", "- b \\cos{(Y)}"], "srepr_premise_expression": "Mul(Integer(-1), sin(Add(Symbol('Y', commutative=True), Mul(Integer(-1), Symbol('b', commutative=True)))))", "srepr_variable": "Symbol('Y', commutative=True)", "srepr_positive": "cos(Add(Symbol('Y', commutative=True), Mul(Integer(-1), Symbol('b', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('Y', commutative=True), Mul(Integer(-1), Symbol('b', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('Y', commutative=True), Symbol('b', commutative=True))))", "sin(Add(Symbol('Y', commutative=True), Mul(Integer(-1), Symbol('b', commutative=True))))", "Mul(Integer(-1), Symbol('b', commutative=True), cos(Symbol('Y', commutative=True)))"]}, {"premise_expression": "D + S", "variable": "S", "positive": "\\frac{S (2 D + S)}{2}", "negatives": ["\\frac{D (D + 2 S)}{2}", "\\frac{S^{2} e^{D}}{2}", "- \\cos{(D - S)}", "\\frac{\\sin{(S)}}{D}"], "srepr_premise_expression": "Add(Symbol('D', commutative=True), Symbol('S', commutative=True))", "srepr_variable": "Symbol('S', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Mul(Integer(2), Symbol('D', commutative=True)), Symbol('S', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('D', commutative=True), Add(Symbol('D', commutative=True), Mul(Integer(2), Symbol('S', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('S', commutative=True), Integer(2)), exp(Symbol('D', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('D', commutative=True), Mul(Integer(-1), Symbol('S', commutative=True)))))", "Mul(Pow(Symbol('D', commutative=True), Integer(-1)), sin(Symbol('S', commutative=True)))"]}, {"premise_expression": "\\frac{e^{w}}{n}", "variable": "n", "positive": "e^{w} \\log{(n)}", "negatives": ["\\log{(n)} \\cos{(w)}", "e^{n + w}", "n (w + w^{w})", "\\frac{\\sin{(n)}}{w}"], "srepr_premise_expression": "Mul(Pow(Symbol('n', commutative=True), Integer(-1)), exp(Symbol('w', commutative=True)))", "srepr_variable": "Symbol('n', commutative=True)", "srepr_positive": "Mul(exp(Symbol('w', commutative=True)), log(Symbol('n', commutative=True)))", "srepr_negatives": ["Mul(log(Symbol('n', commutative=True)), cos(Symbol('w', commutative=True)))", "exp(Add(Symbol('n', commutative=True), Symbol('w', commutative=True)))", "Mul(Symbol('n', commutative=True), Add(Symbol('w', commutative=True), Pow(Symbol('w', commutative=True), Symbol('w', commutative=True))))", "Mul(Pow(Symbol('w', commutative=True), Integer(-1)), sin(Symbol('n', commutative=True)))"]}, {"premise_expression": "\\sin{(F - K)}", "variable": "F", "positive": "- \\cos{(F - K)}", "negatives": ["\\cos{(F - K)}", "- \\frac{\\cos{(F)}}{K}", "\\frac{F^{2}}{2 K}", "F (\\log{(\\frac{K}{F})} + 1)"], "srepr_premise_expression": "sin(Add(Symbol('F', commutative=True), Mul(Integer(-1), Symbol('K', commutative=True))))", "srepr_variable": "Symbol('F', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('F', commutative=True), Mul(Integer(-1), Symbol('K', commutative=True)))))", "srepr_negatives": ["cos(Add(Symbol('F', commutative=True), Mul(Integer(-1), Symbol('K', commutative=True))))", "Mul(Integer(-1), Pow(Symbol('K', commutative=True), Integer(-1)), cos(Symbol('F', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('F', commutative=True), Integer(2)), Pow(Symbol('K', commutative=True), Integer(-1)))", "Mul(Symbol('F', commutative=True), Add(log(Mul(Pow(Symbol('F', commutative=True), Integer(-1)), Symbol('K', commutative=True))), Integer(1)))"]}, {"premise_expression": "\\frac{- F + R}{l}", "variable": "R", "positive": "\\frac{R (- 2 F + R)}{2 l}", "negatives": ["- \\frac{F (F - 2 R)}{2 l}", "\\frac{R (2 F + R + 2 l)}{2}", "(- F + R) \\log{(l)}", "\\frac{R^{2} (F - l)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('l', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('F', commutative=True)), Symbol('R', commutative=True)))", "srepr_variable": "Symbol('R', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('R', commutative=True), Pow(Symbol('l', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Integer(2), Symbol('F', commutative=True)), Symbol('R', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Rational(1, 2), Symbol('F', commutative=True), Pow(Symbol('l', commutative=True), Integer(-1)), Add(Symbol('F', commutative=True), Mul(Integer(-1), Integer(2), Symbol('R', commutative=True))))", "Mul(Rational(1, 2), Symbol('R', commutative=True), Add(Mul(Integer(2), Symbol('F', commutative=True)), Symbol('R', commutative=True), Mul(Integer(2), Symbol('l', commutative=True))))", "Mul(Add(Mul(Integer(-1), Symbol('F', commutative=True)), Symbol('R', commutative=True)), log(Symbol('l', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('R', commutative=True), Integer(2)), Add(Symbol('F', commutative=True), Mul(Integer(-1), Symbol('l', commutative=True))))"]}, {"premise_expression": "\\log{(- A + z)}", "variable": "z", "positive": "- A \\log{(- A + z)} + z \\log{(- A + z)} - z", "negatives": ["A \\log{(- A + z)} - A - z \\log{(A - z)}", "- A \\operatorname{Ei}{(\\frac{A}{z})} + z e^{\\frac{A}{z}}", "\\log{(A)} \\log{(z)}", "\\log{(z)} \\cos{(A)}"], "srepr_premise_expression": "log(Add(Mul(Integer(-1), Symbol('A', commutative=True)), Symbol('z', commutative=True)))", "srepr_variable": "Symbol('z', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('A', commutative=True), log(Add(Mul(Integer(-1), Symbol('A', commutative=True)), Symbol('z', commutative=True)))), Mul(Symbol('z', commutative=True), log(Add(Mul(Integer(-1), Symbol('A', commutative=True)), Symbol('z', commutative=True)))), Mul(Integer(-1), Symbol('z', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('A', commutative=True), log(Add(Mul(Integer(-1), Symbol('A', commutative=True)), Symbol('z', commutative=True)))), Mul(Integer(-1), Symbol('A', commutative=True)), Mul(Integer(-1), Symbol('z', commutative=True), log(Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('z', commutative=True))))))", "Add(Mul(Integer(-1), Symbol('A', commutative=True), Ei(Mul(Symbol('A', commutative=True), Pow(Symbol('z', commutative=True), Integer(-1))))), Mul(Symbol('z', commutative=True), exp(Mul(Symbol('A', commutative=True), Pow(Symbol('z', commutative=True), Integer(-1))))))", "Mul(log(Symbol('A', commutative=True)), log(Symbol('z', commutative=True)))", "Mul(log(Symbol('z', commutative=True)), cos(Symbol('A', commutative=True)))"]}, {"premise_expression": "D + \\cos{(g)}", "variable": "D", "positive": "\\frac{D (D + 2 \\cos{(g)})}{2}", "negatives": ["\\frac{D (D + 2 \\log{(g)})}{2}", "\\frac{D (- D + 2 e^{g})}{2}", "\\frac{D (- D + 2 g)}{2}", "D g + \\sin{(g)}"], "srepr_premise_expression": "Add(Symbol('D', commutative=True), cos(Symbol('g', commutative=True)))", "srepr_variable": "Symbol('D', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('D', commutative=True), Add(Symbol('D', commutative=True), Mul(Integer(2), cos(Symbol('g', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('D', commutative=True), Add(Symbol('D', commutative=True), Mul(Integer(2), log(Symbol('g', commutative=True)))))", "Mul(Rational(1, 2), Symbol('D', commutative=True), Add(Mul(Integer(-1), Symbol('D', commutative=True)), Mul(Integer(2), exp(Symbol('g', commutative=True)))))", "Mul(Rational(1, 2), Symbol('D', commutative=True), Add(Mul(Integer(-1), Symbol('D', commutative=True)), Mul(Integer(2), Symbol('g', commutative=True))))", "Add(Mul(Symbol('D', commutative=True), Symbol('g', commutative=True)), sin(Symbol('g', commutative=True)))"]}, {"premise_expression": "- Y - r + s", "variable": "r", "positive": "\\frac{r (- 2 Y - r + 2 s)}{2}", "negatives": ["\\frac{Y (- Y - 2 r + 2 s)}{2}", "\\frac{r (- 2 Y + r s)}{2}", "\\frac{s (- 2 Y - 2 r + s)}{2}", "\\frac{r (2 Y + r)}{2 s}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('Y', commutative=True)), Mul(Integer(-1), Symbol('r', commutative=True)), Symbol('s', commutative=True))", "srepr_variable": "Symbol('r', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('Y', commutative=True)), Mul(Integer(-1), Symbol('r', commutative=True)), Mul(Integer(2), Symbol('s', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('Y', commutative=True), Add(Mul(Integer(-1), Symbol('Y', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('r', commutative=True)), Mul(Integer(2), Symbol('s', commutative=True))))", "Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('Y', commutative=True)), Mul(Symbol('r', commutative=True), Symbol('s', commutative=True))))", "Mul(Rational(1, 2), Symbol('s', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('Y', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('r', commutative=True)), Symbol('s', commutative=True)))", "Mul(Rational(1, 2), Symbol('r', commutative=True), Pow(Symbol('s', commutative=True), Integer(-1)), Add(Mul(Integer(2), Symbol('Y', commutative=True)), Symbol('r', commutative=True)))"]}, {"premise_expression": "j + o + s", "variable": "o", "positive": "o (j + \\frac{o}{2} + s)", "negatives": ["\\frac{o (2 j - o - 2 s)}{2}", "\\frac{s (2 j + 2 o + s)}{2}", "\\frac{j (j + 2 o + 2 s)}{2}", "\\frac{o (2 j + o)}{2 s}"], "srepr_premise_expression": "Add(Symbol('j', commutative=True), Symbol('o', commutative=True), Symbol('s', commutative=True))", "srepr_variable": "Symbol('o', commutative=True)", "srepr_positive": "Mul(Symbol('o', commutative=True), Add(Symbol('j', commutative=True), Mul(Rational(1, 2), Symbol('o', commutative=True)), Symbol('s', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Mul(Integer(2), Symbol('j', commutative=True)), Mul(Integer(-1), Symbol('o', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('s', commutative=True))))", "Mul(Rational(1, 2), Symbol('s', commutative=True), Add(Mul(Integer(2), Symbol('j', commutative=True)), Mul(Integer(2), Symbol('o', commutative=True)), Symbol('s', commutative=True)))", "Mul(Rational(1, 2), Symbol('j', commutative=True), Add(Symbol('j', commutative=True), Mul(Integer(2), Symbol('o', commutative=True)), Mul(Integer(2), Symbol('s', commutative=True))))", "Mul(Rational(1, 2), Symbol('o', commutative=True), Pow(Symbol('s', commutative=True), Integer(-1)), Add(Mul(Integer(2), Symbol('j', commutative=True)), Symbol('o', commutative=True)))"]}, {"premise_expression": "r (W + n)", "variable": "r", "positive": "\\frac{r^{2} (W + n)}{2}", "negatives": ["\\frac{n r (2 W + n)}{2}", "\\frac{W r (W + 2 n)}{2}", "\\frac{r (2 W n - r)}{2}", "\\frac{W r (2 n + r)}{2}"], "srepr_premise_expression": "Mul(Symbol('r', commutative=True), Add(Symbol('W', commutative=True), Symbol('n', commutative=True)))", "srepr_variable": "Symbol('r', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('r', commutative=True), Integer(2)), Add(Symbol('W', commutative=True), Symbol('n', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('n', commutative=True), Symbol('r', commutative=True), Add(Mul(Integer(2), Symbol('W', commutative=True)), Symbol('n', commutative=True)))", "Mul(Rational(1, 2), Symbol('W', commutative=True), Symbol('r', commutative=True), Add(Symbol('W', commutative=True), Mul(Integer(2), Symbol('n', commutative=True))))", "Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(2), Symbol('W', commutative=True), Symbol('n', commutative=True)), Mul(Integer(-1), Symbol('r', commutative=True))))", "Mul(Rational(1, 2), Symbol('W', commutative=True), Symbol('r', commutative=True), Add(Mul(Integer(2), Symbol('n', commutative=True)), Symbol('r', commutative=True)))"]}, {"premise_expression": "L + c", "variable": "L", "positive": "\\frac{L (L + 2 c)}{2}", "negatives": ["\\frac{c (2 L + c)}{2}", "\\frac{L^{2} c}{2}", "\\frac{L^{2} \\log{(c)}}{2}", "e^{L - c}"], "srepr_premise_expression": "Add(Symbol('L', commutative=True), Symbol('c', commutative=True))", "srepr_variable": "Symbol('L', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Symbol('L', commutative=True), Mul(Integer(2), Symbol('c', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('c', commutative=True), Add(Mul(Integer(2), Symbol('L', commutative=True)), Symbol('c', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(2)), Symbol('c', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(2)), log(Symbol('c', commutative=True)))", "exp(Add(Symbol('L', commutative=True), Mul(Integer(-1), Symbol('c', commutative=True))))"]}, {"premise_expression": "e^{X - Z}", "variable": "X", "positive": "e^{X - Z}", "negatives": ["- e^{X - Z}", "- e^{- X + Z}", "Z e^{X}", "\\frac{X (X - 2 Z)}{2}"], "srepr_premise_expression": "exp(Add(Symbol('X', commutative=True), Mul(Integer(-1), Symbol('Z', commutative=True))))", "srepr_variable": "Symbol('X', commutative=True)", "srepr_positive": "exp(Add(Symbol('X', commutative=True), Mul(Integer(-1), Symbol('Z', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Symbol('X', commutative=True), Mul(Integer(-1), Symbol('Z', commutative=True)))))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('X', commutative=True)), Symbol('Z', commutative=True))))", "Mul(Symbol('Z', commutative=True), exp(Symbol('X', commutative=True)))", "Mul(Rational(1, 2), Symbol('X', commutative=True), Add(Symbol('X', commutative=True), Mul(Integer(-1), Integer(2), Symbol('Z', commutative=True))))"]}, {"premise_expression": "\\log{(Q - y)}", "variable": "Q", "positive": "Q \\log{(Q - y)} - Q - y \\log{(Q - y)}", "negatives": ["- Q \\log{(- Q + y)} + y \\log{(Q - y)} - y", "Q (- y + \\log{(Q)} - 1)", "\\frac{Q (- Q + 2 \\log{(y)})}{2}", "Q (\\log{(\\frac{y}{Q})} + 1)"], "srepr_premise_expression": "log(Add(Symbol('Q', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True))))", "srepr_variable": "Symbol('Q', commutative=True)", "srepr_positive": "Add(Mul(Symbol('Q', commutative=True), log(Add(Symbol('Q', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True))))), Mul(Integer(-1), Symbol('Q', commutative=True)), Mul(Integer(-1), Symbol('y', commutative=True), log(Add(Symbol('Q', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True))))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('Q', commutative=True), log(Add(Mul(Integer(-1), Symbol('Q', commutative=True)), Symbol('y', commutative=True)))), Mul(Symbol('y', commutative=True), log(Add(Symbol('Q', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True))))), Mul(Integer(-1), Symbol('y', commutative=True)))", "Mul(Symbol('Q', commutative=True), Add(Mul(Integer(-1), Symbol('y', commutative=True)), log(Symbol('Q', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Mul(Integer(-1), Symbol('Q', commutative=True)), Mul(Integer(2), log(Symbol('y', commutative=True)))))", "Mul(Symbol('Q', commutative=True), Add(log(Mul(Pow(Symbol('Q', commutative=True), Integer(-1)), Symbol('y', commutative=True))), Integer(1)))"]}, {"premise_expression": "Y u", "variable": "u", "positive": "\\frac{Y u^{2}}{2}", "negatives": ["\\frac{Y^{2} u}{2}", "\\frac{u^{2}}{2 Y}", "\\frac{u (2 Y + u)}{2}", "\\frac{u^{2} \\cos{(Y)}}{2}"], "srepr_premise_expression": "Mul(Symbol('Y', commutative=True), Symbol('u', commutative=True))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('Y', commutative=True), Pow(Symbol('u', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('Y', commutative=True), Integer(2)), Symbol('u', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('Y', commutative=True), Integer(-1)), Pow(Symbol('u', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(2), Symbol('Y', commutative=True)), Symbol('u', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('u', commutative=True), Integer(2)), cos(Symbol('Y', commutative=True)))"]}, {"premise_expression": "e^{\\frac{h}{E}}", "variable": "E", "positive": "E e^{\\frac{h}{E}} - h \\operatorname{Ei}{(\\frac{h}{E})}", "negatives": ["E \\cos{(\\frac{h}{E})} + h \\operatorname{Si}{(\\frac{h}{E})}", "E e^{\\frac{h}{E}}", "E h + \\sin{(E)}", "E (\\log{(\\frac{E}{h})} - 1)"], "srepr_premise_expression": "exp(Mul(Pow(Symbol('E', commutative=True), Integer(-1)), Symbol('h', commutative=True)))", "srepr_variable": "Symbol('E', commutative=True)", "srepr_positive": "Add(Mul(Symbol('E', commutative=True), exp(Mul(Pow(Symbol('E', commutative=True), Integer(-1)), Symbol('h', commutative=True)))), Mul(Integer(-1), Symbol('h', commutative=True), Ei(Mul(Pow(Symbol('E', commutative=True), Integer(-1)), Symbol('h', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('E', commutative=True), cos(Mul(Pow(Symbol('E', commutative=True), Integer(-1)), Symbol('h', commutative=True)))), Mul(Symbol('h', commutative=True), Si(Mul(Pow(Symbol('E', commutative=True), Integer(-1)), Symbol('h', commutative=True)))))", "Mul(Symbol('E', commutative=True), exp(Mul(Pow(Symbol('E', commutative=True), Integer(-1)), Symbol('h', commutative=True))))", "Add(Mul(Symbol('E', commutative=True), Symbol('h', commutative=True)), sin(Symbol('E', commutative=True)))", "Mul(Symbol('E', commutative=True), Add(log(Mul(Symbol('E', commutative=True), Pow(Symbol('h', commutative=True), Integer(-1)))), Integer(-1)))"]}, {"premise_expression": "\\frac{g - n}{t}", "variable": "g", "positive": "\\frac{g (g - 2 n)}{2 t}", "negatives": ["\\frac{n (2 g - n)}{2 t}", "\\frac{g (- g - 2 n + 2 t)}{2}", "(g - n) \\log{(t)}", "\\frac{g (g + 2 n + 2 t)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('t', commutative=True), Integer(-1)), Add(Symbol('g', commutative=True), Mul(Integer(-1), Symbol('n', commutative=True))))", "srepr_variable": "Symbol('g', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('g', commutative=True), Pow(Symbol('t', commutative=True), Integer(-1)), Add(Symbol('g', commutative=True), Mul(Integer(-1), Integer(2), Symbol('n', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('n', commutative=True), Pow(Symbol('t', commutative=True), Integer(-1)), Add(Mul(Integer(2), Symbol('g', commutative=True)), Mul(Integer(-1), Symbol('n', commutative=True))))", "Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Mul(Integer(-1), Symbol('g', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('n', commutative=True)), Mul(Integer(2), Symbol('t', commutative=True))))", "Mul(Add(Symbol('g', commutative=True), Mul(Integer(-1), Symbol('n', commutative=True))), log(Symbol('t', commutative=True)))", "Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Symbol('g', commutative=True), Mul(Integer(2), Symbol('n', commutative=True)), Mul(Integer(2), Symbol('t', commutative=True))))"]}, {"premise_expression": "- S + V", "variable": "S", "positive": "\\frac{S (- S + 2 V)}{2}", "negatives": ["\\frac{V (- 2 S + V)}{2}", "- e^{- S + V}", "\\frac{S (\\log{(S)} - 1)}{V}", "S (\\log{(S V)} - 1)"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('S', commutative=True)), Symbol('V', commutative=True))", "srepr_variable": "Symbol('S', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Mul(Integer(-1), Symbol('S', commutative=True)), Mul(Integer(2), Symbol('V', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('V', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('S', commutative=True)), Symbol('V', commutative=True)))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('S', commutative=True)), Symbol('V', commutative=True))))", "Mul(Symbol('S', commutative=True), Pow(Symbol('V', commutative=True), Integer(-1)), Add(log(Symbol('S', commutative=True)), Integer(-1)))", "Mul(Symbol('S', commutative=True), Add(log(Mul(Symbol('S', commutative=True), Symbol('V', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\frac{f}{W}", "variable": "f", "positive": "\\frac{f^{2}}{2 W}", "negatives": ["f \\log{(W)}", "f^{2}", "\\frac{f (2 W - f)}{2}", "f (\\log{(\\frac{f}{W})} - 1)"], "srepr_premise_expression": "Mul(Pow(Symbol('W', commutative=True), Integer(-1)), Symbol('f', commutative=True))", "srepr_variable": "Symbol('f', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('W', commutative=True), Integer(-1)), Pow(Symbol('f', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('f', commutative=True), log(Symbol('W', commutative=True)))", "Pow(Symbol('f', commutative=True), Integer(2))", "Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Mul(Integer(2), Symbol('W', commutative=True)), Mul(Integer(-1), Symbol('f', commutative=True))))", "Mul(Symbol('f', commutative=True), Add(log(Mul(Pow(Symbol('W', commutative=True), Integer(-1)), Symbol('f', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\sin{(I + s)}", "variable": "s", "positive": "- \\cos{(I + s)}", "negatives": ["\\frac{s (2 I - s)}{2}", "I \\log{(s)}", "I s + \\sin{(s)}", "\\frac{s \\log{(I)}}{I}"], "srepr_premise_expression": "sin(Add(Symbol('I', commutative=True), Symbol('s', commutative=True)))", "srepr_variable": "Symbol('s', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('I', commutative=True), Symbol('s', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('s', commutative=True), Add(Mul(Integer(2), Symbol('I', commutative=True)), Mul(Integer(-1), Symbol('s', commutative=True))))", "Mul(Symbol('I', commutative=True), log(Symbol('s', commutative=True)))", "Add(Mul(Symbol('I', commutative=True), Symbol('s', commutative=True)), sin(Symbol('s', commutative=True)))", "Mul(Pow(Symbol('I', commutative=True), Integer(-1)), Symbol('s', commutative=True), log(Symbol('I', commutative=True)))"]}, {"premise_expression": "E - r", "variable": "E", "positive": "\\frac{E (E - 2 r)}{2}", "negatives": ["\\frac{r (2 E - r)}{2}", "\\frac{E (- E + 2 \\cos{(r)})}{2}", "\\frac{E (\\log{(E)} - 1)}{r}", "e^{r} \\log{(E)}"], "srepr_premise_expression": "Add(Symbol('E', commutative=True), Mul(Integer(-1), Symbol('r', commutative=True)))", "srepr_variable": "Symbol('E', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('E', commutative=True), Add(Symbol('E', commutative=True), Mul(Integer(-1), Integer(2), Symbol('r', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(2), Symbol('E', commutative=True)), Mul(Integer(-1), Symbol('r', commutative=True))))", "Mul(Rational(1, 2), Symbol('E', commutative=True), Add(Mul(Integer(-1), Symbol('E', commutative=True)), Mul(Integer(2), cos(Symbol('r', commutative=True)))))", "Mul(Symbol('E', commutative=True), Pow(Symbol('r', commutative=True), Integer(-1)), Add(log(Symbol('E', commutative=True)), Integer(-1)))", "Mul(exp(Symbol('r', commutative=True)), log(Symbol('E', commutative=True)))"]}, {"premise_expression": "\\frac{C}{B}", "variable": "C", "positive": "\\frac{C^{2}}{2 B}", "negatives": ["C \\log{(B)}", "B e^{C}", "- \\sin{(B - C)}", "C (\\log{(\\frac{C}{B})} - 1)"], "srepr_premise_expression": "Mul(Pow(Symbol('B', commutative=True), Integer(-1)), Symbol('C', commutative=True))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('B', commutative=True), Integer(-1)), Pow(Symbol('C', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('C', commutative=True), log(Symbol('B', commutative=True)))", "Mul(Symbol('B', commutative=True), exp(Symbol('C', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('B', commutative=True), Mul(Integer(-1), Symbol('C', commutative=True)))))", "Mul(Symbol('C', commutative=True), Add(log(Mul(Pow(Symbol('B', commutative=True), Integer(-1)), Symbol('C', commutative=True))), Integer(-1)))"]}, {"premise_expression": "Q - R", "variable": "Q", "positive": "\\frac{Q (Q - 2 R)}{2}", "negatives": ["\\frac{R (2 Q - R)}{2}", "\\sin{(Q - R)}", "Q R + e^{Q}", "- R \\cos{(Q)}"], "srepr_premise_expression": "Add(Symbol('Q', commutative=True), Mul(Integer(-1), Symbol('R', commutative=True)))", "srepr_variable": "Symbol('Q', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Symbol('Q', commutative=True), Mul(Integer(-1), Integer(2), Symbol('R', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('R', commutative=True), Add(Mul(Integer(2), Symbol('Q', commutative=True)), Mul(Integer(-1), Symbol('R', commutative=True))))", "sin(Add(Symbol('Q', commutative=True), Mul(Integer(-1), Symbol('R', commutative=True))))", "Add(Mul(Symbol('Q', commutative=True), Symbol('R', commutative=True)), exp(Symbol('Q', commutative=True)))", "Mul(Integer(-1), Symbol('R', commutative=True), cos(Symbol('Q', commutative=True)))"]}, {"premise_expression": "\\frac{\\log{(A)}}{a}", "variable": "a", "positive": "\\log{(A)} \\log{(a)}", "negatives": ["- \\cos{(A + a)}", "A (- a + \\log{(a)})", "- A a - \\cos{(a)}", "\\frac{A (\\log{(A)} - 1)}{a}"], "srepr_premise_expression": "Mul(Pow(Symbol('a', commutative=True), Integer(-1)), log(Symbol('A', commutative=True)))", "srepr_variable": "Symbol('a', commutative=True)", "srepr_positive": "Mul(log(Symbol('A', commutative=True)), log(Symbol('a', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('A', commutative=True), Symbol('a', commutative=True))))", "Mul(Symbol('A', commutative=True), Add(Mul(Integer(-1), Symbol('a', commutative=True)), log(Symbol('a', commutative=True))))", "Add(Mul(Integer(-1), Symbol('A', commutative=True), Symbol('a', commutative=True)), Mul(Integer(-1), cos(Symbol('a', commutative=True))))", "Mul(Symbol('A', commutative=True), Pow(Symbol('a', commutative=True), Integer(-1)), Add(log(Symbol('A', commutative=True)), Integer(-1)))"]}, {"premise_expression": "A - T", "variable": "A", "positive": "\\frac{A (A - 2 T)}{2}", "negatives": ["\\frac{A (- A + 2 T)}{2}", "\\frac{T (2 A - T)}{2}", "\\frac{A^{2} \\log{(T)}}{2}", "e^{A - T}"], "srepr_premise_expression": "Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('T', commutative=True)))", "srepr_variable": "Symbol('A', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Symbol('A', commutative=True), Mul(Integer(-1), Integer(2), Symbol('T', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Mul(Integer(-1), Symbol('A', commutative=True)), Mul(Integer(2), Symbol('T', commutative=True))))", "Mul(Rational(1, 2), Symbol('T', commutative=True), Add(Mul(Integer(2), Symbol('A', commutative=True)), Mul(Integer(-1), Symbol('T', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2)), log(Symbol('T', commutative=True)))", "exp(Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('T', commutative=True))))"]}, {"premise_expression": "- G + X", "variable": "X", "positive": "\\frac{X (- 2 G + X)}{2}", "negatives": ["\\frac{X (2 G - X)}{2}", "\\frac{G (- G + 2 X)}{2}", "\\frac{X^{2} \\log{(G)}}{2}", "- \\cos{(G - X)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('G', commutative=True)), Symbol('X', commutative=True))", "srepr_variable": "Symbol('X', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('X', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('G', commutative=True)), Symbol('X', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('X', commutative=True), Add(Mul(Integer(2), Symbol('G', commutative=True)), Mul(Integer(-1), Symbol('X', commutative=True))))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Mul(Integer(-1), Symbol('G', commutative=True)), Mul(Integer(2), Symbol('X', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('X', commutative=True), Integer(2)), log(Symbol('G', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('X', commutative=True)))))"]}, {"premise_expression": "- H + e^{x}", "variable": "x", "positive": "- H x + e^{x}", "negatives": ["- H x + \\sin{(x)}", "H \\sin{(x)}", "\\frac{H (- H + 2 e^{x})}{2}", "- e^{H - x}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('H', commutative=True)), exp(Symbol('x', commutative=True)))", "srepr_variable": "Symbol('x', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('H', commutative=True), Symbol('x', commutative=True)), exp(Symbol('x', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('H', commutative=True), Symbol('x', commutative=True)), sin(Symbol('x', commutative=True)))", "Mul(Symbol('H', commutative=True), sin(Symbol('x', commutative=True)))", "Mul(Rational(1, 2), Symbol('H', commutative=True), Add(Mul(Integer(-1), Symbol('H', commutative=True)), Mul(Integer(2), exp(Symbol('x', commutative=True)))))", "Mul(Integer(-1), exp(Add(Symbol('H', commutative=True), Mul(Integer(-1), Symbol('x', commutative=True)))))"]}, {"premise_expression": "- F + J", "variable": "F", "positive": "\\frac{F (- F + 2 J)}{2}", "negatives": ["\\frac{J (- 2 F + J)}{2}", "\\frac{F (- F + 2 e^{J})}{2}", "\\frac{F (F + 2 \\sin{(J)})}{2}", "\\sin{(F + J)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('F', commutative=True)), Symbol('J', commutative=True))", "srepr_variable": "Symbol('F', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Mul(Integer(-1), Symbol('F', commutative=True)), Mul(Integer(2), Symbol('J', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('J', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('F', commutative=True)), Symbol('J', commutative=True)))", "Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Mul(Integer(-1), Symbol('F', commutative=True)), Mul(Integer(2), exp(Symbol('J', commutative=True)))))", "Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Symbol('F', commutative=True), Mul(Integer(2), sin(Symbol('J', commutative=True)))))", "sin(Add(Symbol('F', commutative=True), Symbol('J', commutative=True)))"]}, {"premise_expression": "\\frac{k}{z}", "variable": "k", "positive": "\\frac{k^{2}}{2 z}", "negatives": ["k \\log{(z)}", "\\frac{k^{2} z}{2}", "\\frac{k^{2} (z + 1)}{2 z}", "- \\frac{\\cos{(k)}}{z}"], "srepr_premise_expression": "Mul(Symbol('k', commutative=True), Pow(Symbol('z', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('k', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('k', commutative=True), Integer(2)), Pow(Symbol('z', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('k', commutative=True), log(Symbol('z', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('k', commutative=True), Integer(2)), Symbol('z', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('k', commutative=True), Integer(2)), Pow(Symbol('z', commutative=True), Integer(-1)), Add(Symbol('z', commutative=True), Integer(1)))", "Mul(Integer(-1), Pow(Symbol('z', commutative=True), Integer(-1)), cos(Symbol('k', commutative=True)))"]}, {"premise_expression": "g - m", "variable": "g", "positive": "\\frac{g (g - 2 m)}{2}", "negatives": ["\\frac{m (2 g - m)}{2}", "\\frac{g^{2} m}{2}", "\\frac{g (g + 2 \\sin{(m)})}{2}", "\\sin{(g - m)}"], "srepr_premise_expression": "Add(Symbol('g', commutative=True), Mul(Integer(-1), Symbol('m', commutative=True)))", "srepr_variable": "Symbol('g', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Symbol('g', commutative=True), Mul(Integer(-1), Integer(2), Symbol('m', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Mul(Integer(2), Symbol('g', commutative=True)), Mul(Integer(-1), Symbol('m', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('g', commutative=True), Integer(2)), Symbol('m', commutative=True))", "Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Symbol('g', commutative=True), Mul(Integer(2), sin(Symbol('m', commutative=True)))))", "sin(Add(Symbol('g', commutative=True), Mul(Integer(-1), Symbol('m', commutative=True))))"]}, {"premise_expression": "\\cos{(\\frac{H}{Q})}", "variable": "Q", "positive": "H \\operatorname{Si}{(\\frac{H}{Q})} + Q \\cos{(\\frac{H}{Q})}", "negatives": ["\\frac{Q (- Q + 2 \\cos{(H)})}{2}", "- H Q - \\cos{(Q)}", "H Q + e^{Q}", "\\frac{Q (- Q + 2 e^{H})}{2}"], "srepr_premise_expression": "cos(Mul(Symbol('H', commutative=True), Pow(Symbol('Q', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('Q', commutative=True)", "srepr_positive": "Add(Mul(Symbol('H', commutative=True), Si(Mul(Symbol('H', commutative=True), Pow(Symbol('Q', commutative=True), Integer(-1))))), Mul(Symbol('Q', commutative=True), cos(Mul(Symbol('H', commutative=True), Pow(Symbol('Q', commutative=True), Integer(-1))))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Mul(Integer(-1), Symbol('Q', commutative=True)), Mul(Integer(2), cos(Symbol('H', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('H', commutative=True), Symbol('Q', commutative=True)), Mul(Integer(-1), cos(Symbol('Q', commutative=True))))", "Add(Mul(Symbol('H', commutative=True), Symbol('Q', commutative=True)), exp(Symbol('Q', commutative=True)))", "Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Mul(Integer(-1), Symbol('Q', commutative=True)), Mul(Integer(2), exp(Symbol('H', commutative=True)))))"]}, {"premise_expression": "\\log{(m^{E})}", "variable": "E", "positive": "\\frac{E^{2} \\log{(m)}}{2}", "negatives": ["m \\log{(E)}", "\\frac{E (- E + 2 \\log{(m)})}{2}", "E m (\\log{(E)} - 1)", "e^{m} \\log{(E)}"], "srepr_premise_expression": "log(Pow(Symbol('m', commutative=True), Symbol('E', commutative=True)))", "srepr_variable": "Symbol('E', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('E', commutative=True), Integer(2)), log(Symbol('m', commutative=True)))", "srepr_negatives": ["Mul(Symbol('m', commutative=True), log(Symbol('E', commutative=True)))", "Mul(Rational(1, 2), Symbol('E', commutative=True), Add(Mul(Integer(-1), Symbol('E', commutative=True)), Mul(Integer(2), log(Symbol('m', commutative=True)))))", "Mul(Symbol('E', commutative=True), Symbol('m', commutative=True), Add(log(Symbol('E', commutative=True)), Integer(-1)))", "Mul(exp(Symbol('m', commutative=True)), log(Symbol('E', commutative=True)))"]}, {"premise_expression": "\\cos{(R - h)}", "variable": "h", "positive": "- \\sin{(R - h)}", "negatives": ["\\sin{(R - h)}", "- \\frac{\\cos{(h)}}{R}", "R h (\\log{(h)} - 1)", "\\log{(h)} \\sin{(R)}"], "srepr_premise_expression": "cos(Add(Symbol('R', commutative=True), Mul(Integer(-1), Symbol('h', commutative=True))))", "srepr_variable": "Symbol('h', commutative=True)", "srepr_positive": "Mul(Integer(-1), sin(Add(Symbol('R', commutative=True), Mul(Integer(-1), Symbol('h', commutative=True)))))", "srepr_negatives": ["sin(Add(Symbol('R', commutative=True), Mul(Integer(-1), Symbol('h', commutative=True))))", "Mul(Integer(-1), Pow(Symbol('R', commutative=True), Integer(-1)), cos(Symbol('h', commutative=True)))", "Mul(Symbol('R', commutative=True), Symbol('h', commutative=True), Add(log(Symbol('h', commutative=True)), Integer(-1)))", "Mul(log(Symbol('h', commutative=True)), sin(Symbol('R', commutative=True)))"]}, {"premise_expression": "\\frac{M}{G}", "variable": "M", "positive": "\\frac{M^{2}}{2 G}", "negatives": ["M \\log{(G)}", "\\frac{G M^{2}}{2}", "- \\sin{(G - M)}", "- \\cos{(G - M)}"], "srepr_premise_expression": "Mul(Pow(Symbol('G', commutative=True), Integer(-1)), Symbol('M', commutative=True))", "srepr_variable": "Symbol('M', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(-1)), Pow(Symbol('M', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('M', commutative=True), log(Symbol('G', commutative=True)))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Pow(Symbol('M', commutative=True), Integer(2)))", "Mul(Integer(-1), sin(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('M', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('M', commutative=True)))))"]}, {"premise_expression": "- b + \\log{(z)}", "variable": "z", "positive": "z (- b + \\log{(z)} - 1)", "negatives": ["\\frac{b (- b + 2 \\log{(z)})}{2}", "\\log{(b)} \\log{(z)}", "\\frac{z (- z + 2 e^{b})}{2}", "\\sin{(b + z)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('b', commutative=True)), log(Symbol('z', commutative=True)))", "srepr_variable": "Symbol('z', commutative=True)", "srepr_positive": "Mul(Symbol('z', commutative=True), Add(Mul(Integer(-1), Symbol('b', commutative=True)), log(Symbol('z', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('b', commutative=True), Add(Mul(Integer(-1), Symbol('b', commutative=True)), Mul(Integer(2), log(Symbol('z', commutative=True)))))", "Mul(log(Symbol('b', commutative=True)), log(Symbol('z', commutative=True)))", "Mul(Rational(1, 2), Symbol('z', commutative=True), Add(Mul(Integer(-1), Symbol('z', commutative=True)), Mul(Integer(2), exp(Symbol('b', commutative=True)))))", "sin(Add(Symbol('b', commutative=True), Symbol('z', commutative=True)))"]}, {"premise_expression": "\\cos{(h - z)}", "variable": "h", "positive": "\\sin{(h - z)}", "negatives": ["- \\sin{(h - z)}", "\\cos{(h - z)}", "z \\sin{(h)}", "- e^{- h + z}"], "srepr_premise_expression": "cos(Add(Symbol('h', commutative=True), Mul(Integer(-1), Symbol('z', commutative=True))))", "srepr_variable": "Symbol('h', commutative=True)", "srepr_positive": "sin(Add(Symbol('h', commutative=True), Mul(Integer(-1), Symbol('z', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('h', commutative=True), Mul(Integer(-1), Symbol('z', commutative=True)))))", "cos(Add(Symbol('h', commutative=True), Mul(Integer(-1), Symbol('z', commutative=True))))", "Mul(Symbol('z', commutative=True), sin(Symbol('h', commutative=True)))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('h', commutative=True)), Symbol('z', commutative=True))))"]}, {"premise_expression": "e^{- U + z}", "variable": "z", "positive": "e^{- U + z}", "negatives": ["- e^{- U + z}", "\\sin{(U + z)}", "- \\cos{(U + z)}", "U e^{z}"], "srepr_premise_expression": "exp(Add(Mul(Integer(-1), Symbol('U', commutative=True)), Symbol('z', commutative=True)))", "srepr_variable": "Symbol('z', commutative=True)", "srepr_positive": "exp(Add(Mul(Integer(-1), Symbol('U', commutative=True)), Symbol('z', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('U', commutative=True)), Symbol('z', commutative=True))))", "sin(Add(Symbol('U', commutative=True), Symbol('z', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('U', commutative=True), Symbol('z', commutative=True))))", "Mul(Symbol('U', commutative=True), exp(Symbol('z', commutative=True)))"]}, {"premise_expression": "\\frac{N R}{c}", "variable": "c", "positive": "N R \\log{(c)}", "negatives": ["R^{N} \\log{(c)}", "\\frac{N \\log{(c)}}{R}", "\\frac{N R^{2}}{2 c}", "(- N + R) \\log{(c)}"], "srepr_premise_expression": "Mul(Symbol('N', commutative=True), Symbol('R', commutative=True), Pow(Symbol('c', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('c', commutative=True)", "srepr_positive": "Mul(Symbol('N', commutative=True), Symbol('R', commutative=True), log(Symbol('c', commutative=True)))", "srepr_negatives": ["Mul(Pow(Symbol('R', commutative=True), Symbol('N', commutative=True)), log(Symbol('c', commutative=True)))", "Mul(Symbol('N', commutative=True), Pow(Symbol('R', commutative=True), Integer(-1)), log(Symbol('c', commutative=True)))", "Mul(Rational(1, 2), Symbol('N', commutative=True), Pow(Symbol('R', commutative=True), Integer(2)), Pow(Symbol('c', commutative=True), Integer(-1)))", "Mul(Add(Mul(Integer(-1), Symbol('N', commutative=True)), Symbol('R', commutative=True)), log(Symbol('c', commutative=True)))"]}, {"premise_expression": "Q q + u", "variable": "Q", "positive": "\\frac{Q (Q q + 2 u)}{2}", "negatives": ["\\frac{q (Q q + 2 u)}{2}", "\\frac{Q (Q u - 2 q)}{2}", "\\frac{u (2 Q q + u)}{2}", "\\frac{Q^{2} (q + u)}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('Q', commutative=True), Symbol('q', commutative=True)), Symbol('u', commutative=True))", "srepr_variable": "Symbol('Q', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Mul(Symbol('Q', commutative=True), Symbol('q', commutative=True)), Mul(Integer(2), Symbol('u', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('q', commutative=True), Add(Mul(Symbol('Q', commutative=True), Symbol('q', commutative=True)), Mul(Integer(2), Symbol('u', commutative=True))))", "Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Mul(Symbol('Q', commutative=True), Symbol('u', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('q', commutative=True))))", "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(2), Symbol('Q', commutative=True), Symbol('q', commutative=True)), Symbol('u', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(2)), Add(Symbol('q', commutative=True), Symbol('u', commutative=True)))"]}, {"premise_expression": "G + h", "variable": "G", "positive": "\\frac{G (G + 2 h)}{2}", "negatives": ["\\frac{h (2 G + h)}{2}", "\\frac{G^{2} h}{2}", "\\frac{G^{2} \\cos{(h)}}{2}", "G h + e^{G}"], "srepr_premise_expression": "Add(Symbol('G', commutative=True), Symbol('h', commutative=True))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Symbol('G', commutative=True), Mul(Integer(2), Symbol('h', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('h', commutative=True), Add(Mul(Integer(2), Symbol('G', commutative=True)), Symbol('h', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(2)), Symbol('h', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(2)), cos(Symbol('h', commutative=True)))", "Add(Mul(Symbol('G', commutative=True), Symbol('h', commutative=True)), exp(Symbol('G', commutative=True)))"]}, {"premise_expression": "\\cos{(G - t)}", "variable": "G", "positive": "\\sin{(G - t)}", "negatives": ["- \\sin{(G - t)}", "\\frac{G (G + 2 t)}{2}", "t \\log{(G)}", "\\frac{G^{2} t}{2}"], "srepr_premise_expression": "cos(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('t', commutative=True))))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "sin(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('t', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('t', commutative=True)))))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Symbol('G', commutative=True), Mul(Integer(2), Symbol('t', commutative=True))))", "Mul(Symbol('t', commutative=True), log(Symbol('G', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(2)), Symbol('t', commutative=True))"]}, {"premise_expression": "G - M + b", "variable": "G", "positive": "G (\\frac{G}{2} - M + b)", "negatives": ["\\frac{M (2 G - M + 2 b)}{2}", "\\frac{b (2 G - 2 M + b)}{2}", "\\frac{G (G b - 2 M)}{2}", "\\frac{G (G M + 2 b)}{2}"], "srepr_premise_expression": "Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('M', commutative=True)), Symbol('b', commutative=True))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Mul(Symbol('G', commutative=True), Add(Mul(Rational(1, 2), Symbol('G', commutative=True)), Mul(Integer(-1), Symbol('M', commutative=True)), Symbol('b', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('M', commutative=True), Add(Mul(Integer(2), Symbol('G', commutative=True)), Mul(Integer(-1), Symbol('M', commutative=True)), Mul(Integer(2), Symbol('b', commutative=True))))", "Mul(Rational(1, 2), Symbol('b', commutative=True), Add(Mul(Integer(2), Symbol('G', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('M', commutative=True)), Symbol('b', commutative=True)))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Mul(Symbol('G', commutative=True), Symbol('b', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('M', commutative=True))))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Mul(Symbol('G', commutative=True), Symbol('M', commutative=True)), Mul(Integer(2), Symbol('b', commutative=True))))"]}, {"premise_expression": "K + a", "variable": "a", "positive": "\\frac{a (2 K + a)}{2}", "negatives": ["\\frac{K (K + 2 a)}{2}", "K \\sin{(a)}", "\\frac{a (a + 2 e^{K})}{2}", "\\log{(K)} \\log{(a)}"], "srepr_premise_expression": "Add(Symbol('K', commutative=True), Symbol('a', commutative=True))", "srepr_variable": "Symbol('a', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('a', commutative=True), Add(Mul(Integer(2), Symbol('K', commutative=True)), Symbol('a', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Symbol('K', commutative=True), Mul(Integer(2), Symbol('a', commutative=True))))", "Mul(Symbol('K', commutative=True), sin(Symbol('a', commutative=True)))", "Mul(Rational(1, 2), Symbol('a', commutative=True), Add(Symbol('a', commutative=True), Mul(Integer(2), exp(Symbol('K', commutative=True)))))", "Mul(log(Symbol('K', commutative=True)), log(Symbol('a', commutative=True)))"]}, {"premise_expression": "J z", "variable": "J", "positive": "\\frac{J^{2} z}{2}", "negatives": ["\\frac{J z^{2}}{2}", "\\frac{J^{2}}{2 z}", "J z + e^{J}", "e^{J - z}"], "srepr_premise_expression": "Mul(Symbol('J', commutative=True), Symbol('z', commutative=True))", "srepr_variable": "Symbol('J', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('J', commutative=True), Integer(2)), Symbol('z', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('J', commutative=True), Pow(Symbol('z', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('J', commutative=True), Integer(2)), Pow(Symbol('z', commutative=True), Integer(-1)))", "Add(Mul(Symbol('J', commutative=True), Symbol('z', commutative=True)), exp(Symbol('J', commutative=True)))", "exp(Add(Symbol('J', commutative=True), Mul(Integer(-1), Symbol('z', commutative=True))))"]}, {"premise_expression": "\\frac{\\log{(f)}}{J}", "variable": "f", "positive": "\\frac{f (\\log{(f)} - 1)}{J}", "negatives": ["f (\\log{(J f)} - 1)", "\\frac{f (2 J - f)}{2}", "\\frac{f (- 2 J + f)}{2}", "\\log{(J)} \\log{(f)}"], "srepr_premise_expression": "Mul(Pow(Symbol('J', commutative=True), Integer(-1)), log(Symbol('f', commutative=True)))", "srepr_variable": "Symbol('f', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('J', commutative=True), Integer(-1)), Symbol('f', commutative=True), Add(log(Symbol('f', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('f', commutative=True), Add(log(Mul(Symbol('J', commutative=True), Symbol('f', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Mul(Integer(2), Symbol('J', commutative=True)), Mul(Integer(-1), Symbol('f', commutative=True))))", "Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('J', commutative=True)), Symbol('f', commutative=True)))", "Mul(log(Symbol('J', commutative=True)), log(Symbol('f', commutative=True)))"]}, {"premise_expression": "x + \\sin{(V)}", "variable": "x", "positive": "\\frac{x (x + 2 \\sin{(V)})}{2}", "negatives": ["\\frac{x^{2} \\log{(V)}}{2}", "V x - \\cos{(V)}", "\\frac{x (2 V - x)}{2}", "x (V + \\log{(x)} - 1)"], "srepr_premise_expression": "Add(Symbol('x', commutative=True), sin(Symbol('V', commutative=True)))", "srepr_variable": "Symbol('x', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('x', commutative=True), Add(Symbol('x', commutative=True), Mul(Integer(2), sin(Symbol('V', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('x', commutative=True), Integer(2)), log(Symbol('V', commutative=True)))", "Add(Mul(Symbol('V', commutative=True), Symbol('x', commutative=True)), Mul(Integer(-1), cos(Symbol('V', commutative=True))))", "Mul(Rational(1, 2), Symbol('x', commutative=True), Add(Mul(Integer(2), Symbol('V', commutative=True)), Mul(Integer(-1), Symbol('x', commutative=True))))", "Mul(Symbol('x', commutative=True), Add(Symbol('V', commutative=True), log(Symbol('x', commutative=True)), Integer(-1)))"]}, {"premise_expression": "- A + E^{T}", "variable": "A", "positive": "\\frac{A (- A + 2 E^{T})}{2}", "negatives": ["\\frac{A E (- A + 2 T)}{2}", "\\frac{A (A + 2 E - 2 T)}{2}", "\\frac{A^{2} (E + T)}{2}", "\\frac{A (A + 2 E + 2 T)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('A', commutative=True)), Pow(Symbol('E', commutative=True), Symbol('T', commutative=True)))", "srepr_variable": "Symbol('A', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Mul(Integer(-1), Symbol('A', commutative=True)), Mul(Integer(2), Pow(Symbol('E', commutative=True), Symbol('T', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('A', commutative=True), Symbol('E', commutative=True), Add(Mul(Integer(-1), Symbol('A', commutative=True)), Mul(Integer(2), Symbol('T', commutative=True))))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Symbol('A', commutative=True), Mul(Integer(2), Symbol('E', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('T', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2)), Add(Symbol('E', commutative=True), Symbol('T', commutative=True)))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Symbol('A', commutative=True), Mul(Integer(2), Symbol('E', commutative=True)), Mul(Integer(2), Symbol('T', commutative=True))))"]}, {"premise_expression": "U + k + u", "variable": "k", "positive": "k (U + \\frac{k}{2} + u)", "negatives": ["\\frac{U (U + 2 k + 2 u)}{2}", "\\frac{u (2 U + 2 k + u)}{2}", "\\frac{k (- 2 U + k u)}{2}", "\\frac{U k^{2}}{2 u}"], "srepr_premise_expression": "Add(Symbol('U', commutative=True), Symbol('k', commutative=True), Symbol('u', commutative=True))", "srepr_variable": "Symbol('k', commutative=True)", "srepr_positive": "Mul(Symbol('k', commutative=True), Add(Symbol('U', commutative=True), Mul(Rational(1, 2), Symbol('k', commutative=True)), Symbol('u', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('U', commutative=True), Add(Symbol('U', commutative=True), Mul(Integer(2), Symbol('k', commutative=True)), Mul(Integer(2), Symbol('u', commutative=True))))", "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(2), Symbol('U', commutative=True)), Mul(Integer(2), Symbol('k', commutative=True)), Symbol('u', commutative=True)))", "Mul(Rational(1, 2), Symbol('k', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('U', commutative=True)), Mul(Symbol('k', commutative=True), Symbol('u', commutative=True))))", "Mul(Rational(1, 2), Symbol('U', commutative=True), Pow(Symbol('k', commutative=True), Integer(2)), Pow(Symbol('u', commutative=True), Integer(-1)))"]}, {"premise_expression": "\\sin^{S}{(A)}", "variable": "A", "positive": "\\int \\sin^{S}{(A)} dA", "negatives": ["\\int (A^{S})^{A} dA", "\\sin{(A - S)}", "- A S + \\sin{(A)}", "A S + \\sin{(A)}"], "srepr_premise_expression": "Pow(sin(Symbol('A', commutative=True)), Symbol('S', commutative=True))", "srepr_variable": "Symbol('A', commutative=True)", "srepr_positive": "Integral(Pow(sin(Symbol('A', commutative=True)), Symbol('S', commutative=True)), Tuple(Symbol('A', commutative=True)))", "srepr_negatives": ["NonElementaryIntegral(Pow(Pow(Symbol('A', commutative=True), Symbol('S', commutative=True)), Symbol('A', commutative=True)), Tuple(Symbol('A', commutative=True)))", "sin(Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('S', commutative=True))))", "Add(Mul(Integer(-1), Symbol('A', commutative=True), Symbol('S', commutative=True)), sin(Symbol('A', commutative=True)))", "Add(Mul(Symbol('A', commutative=True), Symbol('S', commutative=True)), sin(Symbol('A', commutative=True)))"]}, {"premise_expression": "v + x", "variable": "x", "positive": "\\frac{x (2 v + x)}{2}", "negatives": ["\\frac{v (v + 2 x)}{2}", "\\frac{x^{2} e^{v}}{2}", "\\frac{x^{2} \\log{(v)}}{2}", "\\frac{v x^{2}}{2}"], "srepr_premise_expression": "Add(Symbol('v', commutative=True), Symbol('x', commutative=True))", "srepr_variable": "Symbol('x', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('x', commutative=True), Add(Mul(Integer(2), Symbol('v', commutative=True)), Symbol('x', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('v', commutative=True), Add(Symbol('v', commutative=True), Mul(Integer(2), Symbol('x', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('x', commutative=True), Integer(2)), exp(Symbol('v', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('x', commutative=True), Integer(2)), log(Symbol('v', commutative=True)))", "Mul(Rational(1, 2), Symbol('v', commutative=True), Pow(Symbol('x', commutative=True), Integer(2)))"]}, {"premise_expression": "\\frac{c}{K}", "variable": "K", "positive": "c \\log{(K)}", "negatives": ["\\frac{c^{2}}{2 K}", "- K c - \\cos{(K)}", "\\log{(K)} \\sin{(c)}", "\\frac{K c (K - 2)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('K', commutative=True), Integer(-1)), Symbol('c', commutative=True))", "srepr_variable": "Symbol('K', commutative=True)", "srepr_positive": "Mul(Symbol('c', commutative=True), log(Symbol('K', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('K', commutative=True), Integer(-1)), Pow(Symbol('c', commutative=True), Integer(2)))", "Add(Mul(Integer(-1), Symbol('K', commutative=True), Symbol('c', commutative=True)), Mul(Integer(-1), cos(Symbol('K', commutative=True))))", "Mul(log(Symbol('K', commutative=True)), sin(Symbol('c', commutative=True)))", "Mul(Rational(1, 2), Symbol('K', commutative=True), Symbol('c', commutative=True), Add(Symbol('K', commutative=True), Integer(-2)))"]}, {"premise_expression": "- J + q + x", "variable": "q", "positive": "q (- J + \\frac{q}{2} + x)", "negatives": ["\\frac{q (2 J + q + 2 x)}{2}", "\\frac{q (2 J - q - 2 x)}{2}", "\\frac{x (- 2 J + 2 q + x)}{2}", "\\frac{J (- J + 2 q + 2 x)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('J', commutative=True)), Symbol('q', commutative=True), Symbol('x', commutative=True))", "srepr_variable": "Symbol('q', commutative=True)", "srepr_positive": "Mul(Symbol('q', commutative=True), Add(Mul(Integer(-1), Symbol('J', commutative=True)), Mul(Rational(1, 2), Symbol('q', commutative=True)), Symbol('x', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('q', commutative=True), Add(Mul(Integer(2), Symbol('J', commutative=True)), Symbol('q', commutative=True), Mul(Integer(2), Symbol('x', commutative=True))))", "Mul(Rational(1, 2), Symbol('q', commutative=True), Add(Mul(Integer(2), Symbol('J', commutative=True)), Mul(Integer(-1), Symbol('q', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('x', commutative=True))))", "Mul(Rational(1, 2), Symbol('x', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('J', commutative=True)), Mul(Integer(2), Symbol('q', commutative=True)), Symbol('x', commutative=True)))", "Mul(Rational(1, 2), Symbol('J', commutative=True), Add(Mul(Integer(-1), Symbol('J', commutative=True)), Mul(Integer(2), Symbol('q', commutative=True)), Mul(Integer(2), Symbol('x', commutative=True))))"]}, {"premise_expression": "- y + \\log{(q)}", "variable": "q", "positive": "q (- y + \\log{(q)} - 1)", "negatives": ["q (\\log{(q y)} - 1)", "\\frac{y (- y + 2 \\log{(q)})}{2}", "q (y + \\sin{(y)})", "\\frac{q (q + 2 y)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('y', commutative=True)), log(Symbol('q', commutative=True)))", "srepr_variable": "Symbol('q', commutative=True)", "srepr_positive": "Mul(Symbol('q', commutative=True), Add(Mul(Integer(-1), Symbol('y', commutative=True)), log(Symbol('q', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('q', commutative=True), Add(log(Mul(Symbol('q', commutative=True), Symbol('y', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('y', commutative=True), Add(Mul(Integer(-1), Symbol('y', commutative=True)), Mul(Integer(2), log(Symbol('q', commutative=True)))))", "Mul(Symbol('q', commutative=True), Add(Symbol('y', commutative=True), sin(Symbol('y', commutative=True))))", "Mul(Rational(1, 2), Symbol('q', commutative=True), Add(Symbol('q', commutative=True), Mul(Integer(2), Symbol('y', commutative=True))))"]}, {"premise_expression": "\\log{(h^{J})}", "variable": "J", "positive": "\\frac{J^{2} \\log{(h)}}{2}", "negatives": ["\\frac{J (J - 2 h)}{2}", "\\frac{J (- J + 2 \\cos{(h)})}{2}", "J (- h + \\log{(J^{h})})", "h (- J + \\log{(h^{J})})"], "srepr_premise_expression": "log(Pow(Symbol('h', commutative=True), Symbol('J', commutative=True)))", "srepr_variable": "Symbol('J', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('J', commutative=True), Integer(2)), log(Symbol('h', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('J', commutative=True), Add(Symbol('J', commutative=True), Mul(Integer(-1), Integer(2), Symbol('h', commutative=True))))", "Mul(Rational(1, 2), Symbol('J', commutative=True), Add(Mul(Integer(-1), Symbol('J', commutative=True)), Mul(Integer(2), cos(Symbol('h', commutative=True)))))", "Mul(Symbol('J', commutative=True), Add(Mul(Integer(-1), Symbol('h', commutative=True)), log(Pow(Symbol('J', commutative=True), Symbol('h', commutative=True)))))", "Mul(Symbol('h', commutative=True), Add(Mul(Integer(-1), Symbol('J', commutative=True)), log(Pow(Symbol('h', commutative=True), Symbol('J', commutative=True)))))"]}, {"premise_expression": "C + U + V", "variable": "U", "positive": "U (C + \\frac{U}{2} + V)", "negatives": ["\\frac{U (2 C + U - 2 V)}{2}", "\\frac{U (- 2 C + U + 2 V)}{2}", "\\frac{V (2 C + 2 U + V)}{2}", "\\frac{C (C + 2 U + 2 V)}{2}"], "srepr_premise_expression": "Add(Symbol('C', commutative=True), Symbol('U', commutative=True), Symbol('V', commutative=True))", "srepr_variable": "Symbol('U', commutative=True)", "srepr_positive": "Mul(Symbol('U', commutative=True), Add(Symbol('C', commutative=True), Mul(Rational(1, 2), Symbol('U', commutative=True)), Symbol('V', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('U', commutative=True), Add(Mul(Integer(2), Symbol('C', commutative=True)), Symbol('U', commutative=True), Mul(Integer(-1), Integer(2), Symbol('V', commutative=True))))", "Mul(Rational(1, 2), Symbol('U', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('C', commutative=True)), Symbol('U', commutative=True), Mul(Integer(2), Symbol('V', commutative=True))))", "Mul(Rational(1, 2), Symbol('V', commutative=True), Add(Mul(Integer(2), Symbol('C', commutative=True)), Mul(Integer(2), Symbol('U', commutative=True)), Symbol('V', commutative=True)))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Symbol('C', commutative=True), Mul(Integer(2), Symbol('U', commutative=True)), Mul(Integer(2), Symbol('V', commutative=True))))"]}, {"premise_expression": "\\log{(- j + t)}", "variable": "t", "positive": "- j \\log{(- j + t)} + t \\log{(- j + t)} - t", "negatives": ["j \\log{(- j + t)} - j - t \\log{(j - t)}", "j \\operatorname{Si}{(\\frac{j}{t})} + t \\cos{(\\frac{j}{t})}", "t (- j + \\log{(t^{j})})", "t (\\log{(j t)} - 1)"], "srepr_premise_expression": "log(Add(Mul(Integer(-1), Symbol('j', commutative=True)), Symbol('t', commutative=True)))", "srepr_variable": "Symbol('t', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('j', commutative=True), log(Add(Mul(Integer(-1), Symbol('j', commutative=True)), Symbol('t', commutative=True)))), Mul(Symbol('t', commutative=True), log(Add(Mul(Integer(-1), Symbol('j', commutative=True)), Symbol('t', commutative=True)))), Mul(Integer(-1), Symbol('t', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('j', commutative=True), log(Add(Mul(Integer(-1), Symbol('j', commutative=True)), Symbol('t', commutative=True)))), Mul(Integer(-1), Symbol('j', commutative=True)), Mul(Integer(-1), Symbol('t', commutative=True), log(Add(Symbol('j', commutative=True), Mul(Integer(-1), Symbol('t', commutative=True))))))", "Add(Mul(Symbol('j', commutative=True), Si(Mul(Symbol('j', commutative=True), Pow(Symbol('t', commutative=True), Integer(-1))))), Mul(Symbol('t', commutative=True), cos(Mul(Symbol('j', commutative=True), Pow(Symbol('t', commutative=True), Integer(-1))))))", "Mul(Symbol('t', commutative=True), Add(Mul(Integer(-1), Symbol('j', commutative=True)), log(Pow(Symbol('t', commutative=True), Symbol('j', commutative=True)))))", "Mul(Symbol('t', commutative=True), Add(log(Mul(Symbol('j', commutative=True), Symbol('t', commutative=True))), Integer(-1)))"]}, {"premise_expression": "e^{\\frac{B}{C}}", "variable": "C", "positive": "- B \\operatorname{Ei}{(\\frac{B}{C})} + C e^{\\frac{B}{C}}", "negatives": ["\\frac{C (- C + 2 e^{B})}{2}", "C e^{\\frac{B}{C}}", "- B C - \\cos{(C)}", "\\frac{C (C + 2 \\log{(B)})}{2}"], "srepr_premise_expression": "exp(Mul(Symbol('B', commutative=True), Pow(Symbol('C', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('B', commutative=True), Ei(Mul(Symbol('B', commutative=True), Pow(Symbol('C', commutative=True), Integer(-1))))), Mul(Symbol('C', commutative=True), exp(Mul(Symbol('B', commutative=True), Pow(Symbol('C', commutative=True), Integer(-1))))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Mul(Integer(-1), Symbol('C', commutative=True)), Mul(Integer(2), exp(Symbol('B', commutative=True)))))", "Mul(Symbol('C', commutative=True), exp(Mul(Symbol('B', commutative=True), Pow(Symbol('C', commutative=True), Integer(-1)))))", "Add(Mul(Integer(-1), Symbol('B', commutative=True), Symbol('C', commutative=True)), Mul(Integer(-1), cos(Symbol('C', commutative=True))))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Symbol('C', commutative=True), Mul(Integer(2), log(Symbol('B', commutative=True)))))"]}, {"premise_expression": "\\frac{k + m}{b}", "variable": "k", "positive": "\\frac{k (k + 2 m)}{2 b}", "negatives": ["\\frac{m (2 k + m)}{2 b}", "\\frac{k (k + 2 m^{b})}{2}", "\\frac{k m (k + 2)}{2}", "(k + m) \\log{(b)}"], "srepr_premise_expression": "Mul(Pow(Symbol('b', commutative=True), Integer(-1)), Add(Symbol('k', commutative=True), Symbol('m', commutative=True)))", "srepr_variable": "Symbol('k', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('b', commutative=True), Integer(-1)), Symbol('k', commutative=True), Add(Symbol('k', commutative=True), Mul(Integer(2), Symbol('m', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('b', commutative=True), Integer(-1)), Symbol('m', commutative=True), Add(Mul(Integer(2), Symbol('k', commutative=True)), Symbol('m', commutative=True)))", "Mul(Rational(1, 2), Symbol('k', commutative=True), Add(Symbol('k', commutative=True), Mul(Integer(2), Pow(Symbol('m', commutative=True), Symbol('b', commutative=True)))))", "Mul(Rational(1, 2), Symbol('k', commutative=True), Symbol('m', commutative=True), Add(Symbol('k', commutative=True), Integer(2)))", "Mul(Add(Symbol('k', commutative=True), Symbol('m', commutative=True)), log(Symbol('b', commutative=True)))"]}, {"premise_expression": "- F + t + w", "variable": "F", "positive": "F (- \\frac{F}{2} + t + w)", "negatives": ["\\frac{F (F + 2 t - 2 w)}{2}", "\\frac{t (- 2 F + t + 2 w)}{2}", "\\frac{w (- 2 F + 2 t + w)}{2}", "F (\\frac{F^{2}}{3} - t)"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('F', commutative=True)), Symbol('t', commutative=True), Symbol('w', commutative=True))", "srepr_variable": "Symbol('F', commutative=True)", "srepr_positive": "Mul(Symbol('F', commutative=True), Add(Mul(Integer(-1), Rational(1, 2), Symbol('F', commutative=True)), Symbol('t', commutative=True), Symbol('w', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Symbol('F', commutative=True), Mul(Integer(2), Symbol('t', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('w', commutative=True))))", "Mul(Rational(1, 2), Symbol('t', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('F', commutative=True)), Symbol('t', commutative=True), Mul(Integer(2), Symbol('w', commutative=True))))", "Mul(Rational(1, 2), Symbol('w', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('F', commutative=True)), Mul(Integer(2), Symbol('t', commutative=True)), Symbol('w', commutative=True)))", "Mul(Symbol('F', commutative=True), Add(Mul(Rational(1, 3), Pow(Symbol('F', commutative=True), Integer(2))), Mul(Integer(-1), Symbol('t', commutative=True))))"]}, {"premise_expression": "L (U + w)", "variable": "U", "positive": "\\frac{L U (U + 2 w)}{2}", "negatives": ["\\frac{L U (U + 2)}{2}", "\\frac{L^{2} (U + w)}{2}", "\\frac{L w (2 U + w)}{2}", "\\frac{U (2 L + U w)}{2}"], "srepr_premise_expression": "Mul(Symbol('L', commutative=True), Add(Symbol('U', commutative=True), Symbol('w', commutative=True)))", "srepr_variable": "Symbol('U', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('L', commutative=True), Symbol('U', commutative=True), Add(Symbol('U', commutative=True), Mul(Integer(2), Symbol('w', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('L', commutative=True), Symbol('U', commutative=True), Add(Symbol('U', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(2)), Add(Symbol('U', commutative=True), Symbol('w', commutative=True)))", "Mul(Rational(1, 2), Symbol('L', commutative=True), Symbol('w', commutative=True), Add(Mul(Integer(2), Symbol('U', commutative=True)), Symbol('w', commutative=True)))", "Mul(Rational(1, 2), Symbol('U', commutative=True), Add(Mul(Integer(2), Symbol('L', commutative=True)), Mul(Symbol('U', commutative=True), Symbol('w', commutative=True))))"]}, {"premise_expression": "L + \\frac{Z}{W}", "variable": "Z", "positive": "L Z + \\frac{Z^{2}}{2 W}", "negatives": ["L W + Z \\log{(W)}", "- \\frac{Z (2 L - Z)}{2 W}", "\\frac{L^{2}}{2} + \\frac{L Z}{W}", "\\frac{L \\log{(Z)}}{W}"], "srepr_premise_expression": "Add(Symbol('L', commutative=True), Mul(Pow(Symbol('W', commutative=True), Integer(-1)), Symbol('Z', commutative=True)))", "srepr_variable": "Symbol('Z', commutative=True)", "srepr_positive": "Add(Mul(Symbol('L', commutative=True), Symbol('Z', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('W', commutative=True), Integer(-1)), Pow(Symbol('Z', commutative=True), Integer(2))))", "srepr_negatives": ["Add(Mul(Symbol('L', commutative=True), Symbol('W', commutative=True)), Mul(Symbol('Z', commutative=True), log(Symbol('W', commutative=True))))", "Mul(Integer(-1), Rational(1, 2), Pow(Symbol('W', commutative=True), Integer(-1)), Symbol('Z', commutative=True), Add(Mul(Integer(2), Symbol('L', commutative=True)), Mul(Integer(-1), Symbol('Z', commutative=True))))", "Add(Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(2))), Mul(Symbol('L', commutative=True), Pow(Symbol('W', commutative=True), Integer(-1)), Symbol('Z', commutative=True)))", "Mul(Symbol('L', commutative=True), Pow(Symbol('W', commutative=True), Integer(-1)), log(Symbol('Z', commutative=True)))"]}, {"premise_expression": "b + c", "variable": "c", "positive": "\\frac{c (2 b + c)}{2}", "negatives": ["\\frac{b (b + 2 c)}{2}", "- \\cos{(b - c)}", "c (\\log{(\\frac{b}{c})} + 1)", "\\frac{c (c + 2 e^{b})}{2}"], "srepr_premise_expression": "Add(Symbol('b', commutative=True), Symbol('c', commutative=True))", "srepr_variable": "Symbol('c', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('c', commutative=True), Add(Mul(Integer(2), Symbol('b', commutative=True)), Symbol('c', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('b', commutative=True), Add(Symbol('b', commutative=True), Mul(Integer(2), Symbol('c', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('b', commutative=True), Mul(Integer(-1), Symbol('c', commutative=True)))))", "Mul(Symbol('c', commutative=True), Add(log(Mul(Symbol('b', commutative=True), Pow(Symbol('c', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Rational(1, 2), Symbol('c', commutative=True), Add(Symbol('c', commutative=True), Mul(Integer(2), exp(Symbol('b', commutative=True)))))"]}, {"premise_expression": "- \\sin{(S - r)}", "variable": "S", "positive": "\\cos{(S - r)}", "negatives": ["- \\cos{(S - r)}", "- \\cos{(S + r)}", "e^{S + r}", "\\frac{S (S + 2 r)}{2}"], "srepr_premise_expression": "Mul(Integer(-1), sin(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('r', commutative=True)))))", "srepr_variable": "Symbol('S', commutative=True)", "srepr_positive": "cos(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('r', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('r', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('S', commutative=True), Symbol('r', commutative=True))))", "exp(Add(Symbol('S', commutative=True), Symbol('r', commutative=True)))", "Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Symbol('S', commutative=True), Mul(Integer(2), Symbol('r', commutative=True))))"]}, {"premise_expression": "- \\sin{(y - z)}", "variable": "z", "positive": "- \\cos{(y - z)}", "negatives": ["\\cos{(y - z)}", "- \\cos{(y + z)}", "z (\\log{(\\frac{z}{y})} - 1)", "\\frac{z (- 2 y + z)}{2}"], "srepr_premise_expression": "Mul(Integer(-1), sin(Add(Symbol('y', commutative=True), Mul(Integer(-1), Symbol('z', commutative=True)))))", "srepr_variable": "Symbol('z', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('y', commutative=True), Mul(Integer(-1), Symbol('z', commutative=True)))))", "srepr_negatives": ["cos(Add(Symbol('y', commutative=True), Mul(Integer(-1), Symbol('z', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('y', commutative=True), Symbol('z', commutative=True))))", "Mul(Symbol('z', commutative=True), Add(log(Mul(Pow(Symbol('y', commutative=True), Integer(-1)), Symbol('z', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('z', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('y', commutative=True)), Symbol('z', commutative=True)))"]}, {"premise_expression": "e^{\\frac{Q}{m}}", "variable": "Q", "positive": "m e^{\\frac{Q}{m}}", "negatives": ["- Q m + e^{Q}", "\\frac{Q (Q + 2 m)}{2}", "\\frac{Q^{2} \\sin{(m)}}{2}", "\\frac{Q (- Q + 2 m)}{2}"], "srepr_premise_expression": "exp(Mul(Symbol('Q', commutative=True), Pow(Symbol('m', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('Q', commutative=True)", "srepr_positive": "Mul(Symbol('m', commutative=True), exp(Mul(Symbol('Q', commutative=True), Pow(Symbol('m', commutative=True), Integer(-1)))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('Q', commutative=True), Symbol('m', commutative=True)), exp(Symbol('Q', commutative=True)))", "Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Symbol('Q', commutative=True), Mul(Integer(2), Symbol('m', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(2)), sin(Symbol('m', commutative=True)))", "Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Mul(Integer(-1), Symbol('Q', commutative=True)), Mul(Integer(2), Symbol('m', commutative=True))))"]}, {"premise_expression": "\\frac{Q}{k}", "variable": "Q", "positive": "\\frac{Q^{2}}{2 k}", "negatives": ["Q \\log{(k)}", "\\frac{Q (Q + 2 k)}{2}", "\\frac{Q^{2} \\log{(k)}}{2}", "\\sin{(Q + k)}"], "srepr_premise_expression": "Mul(Symbol('Q', commutative=True), Pow(Symbol('k', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('Q', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(2)), Pow(Symbol('k', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('Q', commutative=True), log(Symbol('k', commutative=True)))", "Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Symbol('Q', commutative=True), Mul(Integer(2), Symbol('k', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(2)), log(Symbol('k', commutative=True)))", "sin(Add(Symbol('Q', commutative=True), Symbol('k', commutative=True)))"]}, {"premise_expression": "N - m + n", "variable": "m", "positive": "m (N - \\frac{m}{2} + n)", "negatives": ["\\frac{m (2 N - m - 2 n)}{2}", "\\frac{m (2 N + m - 2 n)}{2}", "\\frac{N (N - 2 m + 2 n)}{2}", "\\frac{n (2 N - 2 m + n)}{2}"], "srepr_premise_expression": "Add(Symbol('N', commutative=True), Mul(Integer(-1), Symbol('m', commutative=True)), Symbol('n', commutative=True))", "srepr_variable": "Symbol('m', commutative=True)", "srepr_positive": "Mul(Symbol('m', commutative=True), Add(Symbol('N', commutative=True), Mul(Integer(-1), Rational(1, 2), Symbol('m', commutative=True)), Symbol('n', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Mul(Integer(2), Symbol('N', commutative=True)), Mul(Integer(-1), Symbol('m', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('n', commutative=True))))", "Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Mul(Integer(2), Symbol('N', commutative=True)), Symbol('m', commutative=True), Mul(Integer(-1), Integer(2), Symbol('n', commutative=True))))", "Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Symbol('N', commutative=True), Mul(Integer(-1), Integer(2), Symbol('m', commutative=True)), Mul(Integer(2), Symbol('n', commutative=True))))", "Mul(Rational(1, 2), Symbol('n', commutative=True), Add(Mul(Integer(2), Symbol('N', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('m', commutative=True)), Symbol('n', commutative=True)))"]}, {"premise_expression": "\\sin{(g + l)}", "variable": "l", "positive": "- \\cos{(g + l)}", "negatives": ["- e^{g - l}", "l (- g + l)", "\\frac{g l (l - 2)}{2}", "g l - \\cos{(l)}"], "srepr_premise_expression": "sin(Add(Symbol('g', commutative=True), Symbol('l', commutative=True)))", "srepr_variable": "Symbol('l', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('g', commutative=True), Symbol('l', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Symbol('g', commutative=True), Mul(Integer(-1), Symbol('l', commutative=True)))))", "Mul(Symbol('l', commutative=True), Add(Mul(Integer(-1), Symbol('g', commutative=True)), Symbol('l', commutative=True)))", "Mul(Rational(1, 2), Symbol('g', commutative=True), Symbol('l', commutative=True), Add(Symbol('l', commutative=True), Integer(-2)))", "Add(Mul(Symbol('g', commutative=True), Symbol('l', commutative=True)), Mul(Integer(-1), cos(Symbol('l', commutative=True))))"]}, {"premise_expression": "\\frac{Y}{j}", "variable": "j", "positive": "Y \\log{(j)}", "negatives": ["\\frac{Y^{2}}{2 j}", "Y j - \\cos{(j)}", "\\frac{Y j^{2}}{2}", "\\frac{\\sin{(j)}}{Y}"], "srepr_premise_expression": "Mul(Symbol('Y', commutative=True), Pow(Symbol('j', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('j', commutative=True)", "srepr_positive": "Mul(Symbol('Y', commutative=True), log(Symbol('j', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('Y', commutative=True), Integer(2)), Pow(Symbol('j', commutative=True), Integer(-1)))", "Add(Mul(Symbol('Y', commutative=True), Symbol('j', commutative=True)), Mul(Integer(-1), cos(Symbol('j', commutative=True))))", "Mul(Rational(1, 2), Symbol('Y', commutative=True), Pow(Symbol('j', commutative=True), Integer(2)))", "Mul(Pow(Symbol('Y', commutative=True), Integer(-1)), sin(Symbol('j', commutative=True)))"]}, {"premise_expression": "\\frac{u}{m}", "variable": "u", "positive": "\\frac{u^{2}}{2 m}", "negatives": ["u \\log{(m)}", "m e^{\\frac{u}{m}}", "\\frac{u^{2} \\log{(m)}}{2}", "\\frac{u^{2} (m - 1)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('m', commutative=True), Integer(-1)), Symbol('u', commutative=True))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('m', commutative=True), Integer(-1)), Pow(Symbol('u', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('u', commutative=True), log(Symbol('m', commutative=True)))", "Mul(Symbol('m', commutative=True), exp(Mul(Pow(Symbol('m', commutative=True), Integer(-1)), Symbol('u', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('u', commutative=True), Integer(2)), log(Symbol('m', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('u', commutative=True), Integer(2)), Add(Symbol('m', commutative=True), Integer(-1)))"]}, {"premise_expression": "\\log{(S - b)}", "variable": "S", "positive": "S \\log{(S - b)} - S - b \\log{(S - b)}", "negatives": ["- S \\log{(- S + b)} + b \\log{(S - b)} - b", "\\frac{S (- S + 2 \\cos{(b)})}{2}", "- b \\cos{(S)}", "S \\sin{(b^{b})}"], "srepr_premise_expression": "log(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('b', commutative=True))))", "srepr_variable": "Symbol('S', commutative=True)", "srepr_positive": "Add(Mul(Symbol('S', commutative=True), log(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('b', commutative=True))))), Mul(Integer(-1), Symbol('S', commutative=True)), Mul(Integer(-1), Symbol('b', commutative=True), log(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('b', commutative=True))))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('S', commutative=True), log(Add(Mul(Integer(-1), Symbol('S', commutative=True)), Symbol('b', commutative=True)))), Mul(Symbol('b', commutative=True), log(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('b', commutative=True))))), Mul(Integer(-1), Symbol('b', commutative=True)))", "Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Mul(Integer(-1), Symbol('S', commutative=True)), Mul(Integer(2), cos(Symbol('b', commutative=True)))))", "Mul(Integer(-1), Symbol('b', commutative=True), cos(Symbol('S', commutative=True)))", "Mul(Symbol('S', commutative=True), sin(Pow(Symbol('b', commutative=True), Symbol('b', commutative=True))))"]}, {"premise_expression": "\\frac{t}{Q}", "variable": "t", "positive": "\\frac{t^{2}}{2 Q}", "negatives": ["t \\log{(Q)}", "\\frac{t (2 Q - t)}{2}", "- Q t + e^{t}", "- Q \\operatorname{Ei}{(\\frac{Q}{t})} + t e^{\\frac{Q}{t}}"], "srepr_premise_expression": "Mul(Pow(Symbol('Q', commutative=True), Integer(-1)), Symbol('t', commutative=True))", "srepr_variable": "Symbol('t', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(-1)), Pow(Symbol('t', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('t', commutative=True), log(Symbol('Q', commutative=True)))", "Mul(Rational(1, 2), Symbol('t', commutative=True), Add(Mul(Integer(2), Symbol('Q', commutative=True)), Mul(Integer(-1), Symbol('t', commutative=True))))", "Add(Mul(Integer(-1), Symbol('Q', commutative=True), Symbol('t', commutative=True)), exp(Symbol('t', commutative=True)))", "Add(Mul(Integer(-1), Symbol('Q', commutative=True), Ei(Mul(Symbol('Q', commutative=True), Pow(Symbol('t', commutative=True), Integer(-1))))), Mul(Symbol('t', commutative=True), exp(Mul(Symbol('Q', commutative=True), Pow(Symbol('t', commutative=True), Integer(-1))))))"]}, {"premise_expression": "g (B + h)", "variable": "g", "positive": "\\frac{g^{2} (B + h)}{2}", "negatives": ["\\frac{g^{2} (B - h)}{2}", "\\frac{g h (2 B + h)}{2}", "\\frac{B g (B + 2 h)}{2}", "\\frac{g^{2}}{2 B h}"], "srepr_premise_expression": "Mul(Symbol('g', commutative=True), Add(Symbol('B', commutative=True), Symbol('h', commutative=True)))", "srepr_variable": "Symbol('g', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('g', commutative=True), Integer(2)), Add(Symbol('B', commutative=True), Symbol('h', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('g', commutative=True), Integer(2)), Add(Symbol('B', commutative=True), Mul(Integer(-1), Symbol('h', commutative=True))))", "Mul(Rational(1, 2), Symbol('g', commutative=True), Symbol('h', commutative=True), Add(Mul(Integer(2), Symbol('B', commutative=True)), Symbol('h', commutative=True)))", "Mul(Rational(1, 2), Symbol('B', commutative=True), Symbol('g', commutative=True), Add(Symbol('B', commutative=True), Mul(Integer(2), Symbol('h', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('B', commutative=True), Integer(-1)), Pow(Symbol('g', commutative=True), Integer(2)), Pow(Symbol('h', commutative=True), Integer(-1)))"]}, {"premise_expression": "\\frac{\\sin{(x)}}{r}", "variable": "r", "positive": "\\log{(r)} \\sin{(x)}", "negatives": ["\\log{(r)} \\cos{(x)}", "e^{x} \\log{(r)}", "\\sin{(r - x)}", "- \\cos{(r + x)}"], "srepr_premise_expression": "Mul(Pow(Symbol('r', commutative=True), Integer(-1)), sin(Symbol('x', commutative=True)))", "srepr_variable": "Symbol('r', commutative=True)", "srepr_positive": "Mul(log(Symbol('r', commutative=True)), sin(Symbol('x', commutative=True)))", "srepr_negatives": ["Mul(log(Symbol('r', commutative=True)), cos(Symbol('x', commutative=True)))", "Mul(exp(Symbol('x', commutative=True)), log(Symbol('r', commutative=True)))", "sin(Add(Symbol('r', commutative=True), Mul(Integer(-1), Symbol('x', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('r', commutative=True), Symbol('x', commutative=True))))"]}, {"premise_expression": "Z + \\log{(u)}", "variable": "u", "positive": "u (Z + \\log{(u)} - 1)", "negatives": ["u (- Z + \\log{(u)} - 1)", "\\frac{Z (Z + 2 \\log{(u)})}{2}", "\\frac{u^{2} \\log{(Z)}}{2}", "\\frac{u (u + 2 \\cos{(Z)})}{2}"], "srepr_premise_expression": "Add(Symbol('Z', commutative=True), log(Symbol('u', commutative=True)))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "Mul(Symbol('u', commutative=True), Add(Symbol('Z', commutative=True), log(Symbol('u', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('u', commutative=True), Add(Mul(Integer(-1), Symbol('Z', commutative=True)), log(Symbol('u', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Symbol('Z', commutative=True), Mul(Integer(2), log(Symbol('u', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('u', commutative=True), Integer(2)), log(Symbol('Z', commutative=True)))", "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Symbol('u', commutative=True), Mul(Integer(2), cos(Symbol('Z', commutative=True)))))"]}, {"premise_expression": "B L", "variable": "L", "positive": "\\frac{B L^{2}}{2}", "negatives": ["\\frac{B^{2} L}{2}", "\\frac{L^{2} \\cos{(B)}}{2}", "\\frac{L (- 2 B + L)}{2}", "\\log{(L)} \\cos{(B)}"], "srepr_premise_expression": "Mul(Symbol('B', commutative=True), Symbol('L', commutative=True))", "srepr_variable": "Symbol('L', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('B', commutative=True), Pow(Symbol('L', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('B', commutative=True), Integer(2)), Symbol('L', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(2)), cos(Symbol('B', commutative=True)))", "Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('B', commutative=True)), Symbol('L', commutative=True)))", "Mul(log(Symbol('L', commutative=True)), cos(Symbol('B', commutative=True)))"]}, {"premise_expression": "- W + \\sin{(E)}", "variable": "E", "positive": "- E W - \\cos{(E)}", "negatives": ["E W - \\cos{(E)}", "\\frac{E^{2} \\sin{(W)}}{2}", "\\frac{W (- W + 2 \\sin{(E)})}{2}", "\\frac{\\sin{(E)}}{W}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('W', commutative=True)), sin(Symbol('E', commutative=True)))", "srepr_variable": "Symbol('E', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('E', commutative=True), Symbol('W', commutative=True)), Mul(Integer(-1), cos(Symbol('E', commutative=True))))", "srepr_negatives": ["Add(Mul(Symbol('E', commutative=True), Symbol('W', commutative=True)), Mul(Integer(-1), cos(Symbol('E', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('E', commutative=True), Integer(2)), sin(Symbol('W', commutative=True)))", "Mul(Rational(1, 2), Symbol('W', commutative=True), Add(Mul(Integer(-1), Symbol('W', commutative=True)), Mul(Integer(2), sin(Symbol('E', commutative=True)))))", "Mul(Pow(Symbol('W', commutative=True), Integer(-1)), sin(Symbol('E', commutative=True)))"]}, {"premise_expression": "\\log{(o + s)}", "variable": "s", "positive": "o \\log{(o + s)} + s \\log{(o + s)} - s", "negatives": ["o \\log{(o + s)} - o + s \\log{(o + s)}", "s (o + \\log{(s)} - 1)", "\\log{(s)} \\cos{(o)}", "\\frac{s (s + 2 e^{o})}{2}"], "srepr_premise_expression": "log(Add(Symbol('o', commutative=True), Symbol('s', commutative=True)))", "srepr_variable": "Symbol('s', commutative=True)", "srepr_positive": "Add(Mul(Symbol('o', commutative=True), log(Add(Symbol('o', commutative=True), Symbol('s', commutative=True)))), Mul(Symbol('s', commutative=True), log(Add(Symbol('o', commutative=True), Symbol('s', commutative=True)))), Mul(Integer(-1), Symbol('s', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('o', commutative=True), log(Add(Symbol('o', commutative=True), Symbol('s', commutative=True)))), Mul(Integer(-1), Symbol('o', commutative=True)), Mul(Symbol('s', commutative=True), log(Add(Symbol('o', commutative=True), Symbol('s', commutative=True)))))", "Mul(Symbol('s', commutative=True), Add(Symbol('o', commutative=True), log(Symbol('s', commutative=True)), Integer(-1)))", "Mul(log(Symbol('s', commutative=True)), cos(Symbol('o', commutative=True)))", "Mul(Rational(1, 2), Symbol('s', commutative=True), Add(Symbol('s', commutative=True), Mul(Integer(2), exp(Symbol('o', commutative=True)))))"]}, {"premise_expression": "V + n", "variable": "V", "positive": "\\frac{V (V + 2 n)}{2}", "negatives": ["\\frac{n (2 V + n)}{2}", "\\frac{V^{2} e^{n}}{2}", "V n - \\cos{(V)}", "\\frac{V (\\log{(V)} - 1)}{n}"], "srepr_premise_expression": "Add(Symbol('V', commutative=True), Symbol('n', commutative=True))", "srepr_variable": "Symbol('V', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('V', commutative=True), Add(Symbol('V', commutative=True), Mul(Integer(2), Symbol('n', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('n', commutative=True), Add(Mul(Integer(2), Symbol('V', commutative=True)), Symbol('n', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('V', commutative=True), Integer(2)), exp(Symbol('n', commutative=True)))", "Add(Mul(Symbol('V', commutative=True), Symbol('n', commutative=True)), Mul(Integer(-1), cos(Symbol('V', commutative=True))))", "Mul(Symbol('V', commutative=True), Pow(Symbol('n', commutative=True), Integer(-1)), Add(log(Symbol('V', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\log{(K + Y)}", "variable": "Y", "positive": "K \\log{(K + Y)} + Y \\log{(K + Y)} - Y", "negatives": ["K \\log{(K + Y)} - K + Y \\log{(K + Y)}", "Y (\\log{(K Y)} - 1)", "\\frac{Y (- Y + 2 e^{K})}{2}", "- \\cos{(K + Y)}"], "srepr_premise_expression": "log(Add(Symbol('K', commutative=True), Symbol('Y', commutative=True)))", "srepr_variable": "Symbol('Y', commutative=True)", "srepr_positive": "Add(Mul(Symbol('K', commutative=True), log(Add(Symbol('K', commutative=True), Symbol('Y', commutative=True)))), Mul(Symbol('Y', commutative=True), log(Add(Symbol('K', commutative=True), Symbol('Y', commutative=True)))), Mul(Integer(-1), Symbol('Y', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('K', commutative=True), log(Add(Symbol('K', commutative=True), Symbol('Y', commutative=True)))), Mul(Integer(-1), Symbol('K', commutative=True)), Mul(Symbol('Y', commutative=True), log(Add(Symbol('K', commutative=True), Symbol('Y', commutative=True)))))", "Mul(Symbol('Y', commutative=True), Add(log(Mul(Symbol('K', commutative=True), Symbol('Y', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('Y', commutative=True), Add(Mul(Integer(-1), Symbol('Y', commutative=True)), Mul(Integer(2), exp(Symbol('K', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('K', commutative=True), Symbol('Y', commutative=True))))"]}, {"premise_expression": "V - z", "variable": "V", "positive": "\\frac{V (V - 2 z)}{2}", "negatives": ["\\frac{V (V + 2 z)}{2}", "\\frac{z (2 V - z)}{2}", "\\sin{(V - z)}", "\\frac{V^{2} \\log{(z)}}{2}"], "srepr_premise_expression": "Add(Symbol('V', commutative=True), Mul(Integer(-1), Symbol('z', commutative=True)))", "srepr_variable": "Symbol('V', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('V', commutative=True), Add(Symbol('V', commutative=True), Mul(Integer(-1), Integer(2), Symbol('z', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('V', commutative=True), Add(Symbol('V', commutative=True), Mul(Integer(2), Symbol('z', commutative=True))))", "Mul(Rational(1, 2), Symbol('z', commutative=True), Add(Mul(Integer(2), Symbol('V', commutative=True)), Mul(Integer(-1), Symbol('z', commutative=True))))", "sin(Add(Symbol('V', commutative=True), Mul(Integer(-1), Symbol('z', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('V', commutative=True), Integer(2)), log(Symbol('z', commutative=True)))"]}, {"premise_expression": "\\sin{(I - W)}", "variable": "W", "positive": "\\cos{(I - W)}", "negatives": ["- \\cos{(I - W)}", "- \\frac{\\cos{(W)}}{I}", "\\frac{W (2 I + W)}{2}", "- I W - \\cos{(W)}"], "srepr_premise_expression": "sin(Add(Symbol('I', commutative=True), Mul(Integer(-1), Symbol('W', commutative=True))))", "srepr_variable": "Symbol('W', commutative=True)", "srepr_positive": "cos(Add(Symbol('I', commutative=True), Mul(Integer(-1), Symbol('W', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('I', commutative=True), Mul(Integer(-1), Symbol('W', commutative=True)))))", "Mul(Integer(-1), Pow(Symbol('I', commutative=True), Integer(-1)), cos(Symbol('W', commutative=True)))", "Mul(Rational(1, 2), Symbol('W', commutative=True), Add(Mul(Integer(2), Symbol('I', commutative=True)), Symbol('W', commutative=True)))", "Add(Mul(Integer(-1), Symbol('I', commutative=True), Symbol('W', commutative=True)), Mul(Integer(-1), cos(Symbol('W', commutative=True))))"]}, {"premise_expression": "F + M", "variable": "M", "positive": "\\frac{M (2 F + M)}{2}", "negatives": ["\\frac{F (F + 2 M)}{2}", "\\frac{M^{2} \\log{(F)}}{2}", "\\sin{(F + M)}", "- \\cos{(F + M)}"], "srepr_premise_expression": "Add(Symbol('F', commutative=True), Symbol('M', commutative=True))", "srepr_variable": "Symbol('M', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('M', commutative=True), Add(Mul(Integer(2), Symbol('F', commutative=True)), Symbol('M', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Symbol('F', commutative=True), Mul(Integer(2), Symbol('M', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('M', commutative=True), Integer(2)), log(Symbol('F', commutative=True)))", "sin(Add(Symbol('F', commutative=True), Symbol('M', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('F', commutative=True), Symbol('M', commutative=True))))"]}, {"premise_expression": "a + j", "variable": "j", "positive": "\\frac{j (2 a + j)}{2}", "negatives": ["\\frac{j (2 a - j)}{2}", "\\frac{a (a + 2 j)}{2}", "a j + \\sin{(j)}", "- a j + \\sin{(j)}"], "srepr_premise_expression": "Add(Symbol('a', commutative=True), Symbol('j', commutative=True))", "srepr_variable": "Symbol('j', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('j', commutative=True), Add(Mul(Integer(2), Symbol('a', commutative=True)), Symbol('j', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('j', commutative=True), Add(Mul(Integer(2), Symbol('a', commutative=True)), Mul(Integer(-1), Symbol('j', commutative=True))))", "Mul(Rational(1, 2), Symbol('a', commutative=True), Add(Symbol('a', commutative=True), Mul(Integer(2), Symbol('j', commutative=True))))", "Add(Mul(Symbol('a', commutative=True), Symbol('j', commutative=True)), sin(Symbol('j', commutative=True)))", "Add(Mul(Integer(-1), Symbol('a', commutative=True), Symbol('j', commutative=True)), sin(Symbol('j', commutative=True)))"]}, {"premise_expression": "- q + \\sin{(B)}", "variable": "q", "positive": "\\frac{q (- q + 2 \\sin{(B)})}{2}", "negatives": ["\\frac{q (- 2 B + q)}{2}", "\\frac{q^{2} \\log{(B)}}{2}", "- B q - \\cos{(B)}", "B \\operatorname{Si}{(\\frac{B}{q})} + q \\cos{(\\frac{B}{q})}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('q', commutative=True)), sin(Symbol('B', commutative=True)))", "srepr_variable": "Symbol('q', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('q', commutative=True), Add(Mul(Integer(-1), Symbol('q', commutative=True)), Mul(Integer(2), sin(Symbol('B', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('q', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('B', commutative=True)), Symbol('q', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('q', commutative=True), Integer(2)), log(Symbol('B', commutative=True)))", "Add(Mul(Integer(-1), Symbol('B', commutative=True), Symbol('q', commutative=True)), Mul(Integer(-1), cos(Symbol('B', commutative=True))))", "Add(Mul(Symbol('B', commutative=True), Si(Mul(Symbol('B', commutative=True), Pow(Symbol('q', commutative=True), Integer(-1))))), Mul(Symbol('q', commutative=True), cos(Mul(Symbol('B', commutative=True), Pow(Symbol('q', commutative=True), Integer(-1))))))"]}, {"premise_expression": "U \\log{(S)}", "variable": "U", "positive": "\\frac{U^{2} \\log{(S)}}{2}", "negatives": ["\\frac{U^{2} e^{S}}{2}", "S \\log{(U)}", "\\frac{U (- 2 S + U)}{2}", "S U (\\log{(S)} - 1)"], "srepr_premise_expression": "Mul(Symbol('U', commutative=True), log(Symbol('S', commutative=True)))", "srepr_variable": "Symbol('U', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('U', commutative=True), Integer(2)), log(Symbol('S', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('U', commutative=True), Integer(2)), exp(Symbol('S', commutative=True)))", "Mul(Symbol('S', commutative=True), log(Symbol('U', commutative=True)))", "Mul(Rational(1, 2), Symbol('U', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('S', commutative=True)), Symbol('U', commutative=True)))", "Mul(Symbol('S', commutative=True), Symbol('U', commutative=True), Add(log(Symbol('S', commutative=True)), Integer(-1)))"]}, {"premise_expression": "J c", "variable": "J", "positive": "\\frac{J^{2} c}{2}", "negatives": ["\\frac{J c^{2}}{2}", "\\frac{J^{2}}{2 c^{2}}", "e^{J - c}", "\\frac{J (J + 2 e^{c})}{2}"], "srepr_premise_expression": "Mul(Symbol('J', commutative=True), Symbol('c', commutative=True))", "srepr_variable": "Symbol('J', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('J', commutative=True), Integer(2)), Symbol('c', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('J', commutative=True), Pow(Symbol('c', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('J', commutative=True), Integer(2)), Pow(Symbol('c', commutative=True), Integer(-2)))", "exp(Add(Symbol('J', commutative=True), Mul(Integer(-1), Symbol('c', commutative=True))))", "Mul(Rational(1, 2), Symbol('J', commutative=True), Add(Symbol('J', commutative=True), Mul(Integer(2), exp(Symbol('c', commutative=True)))))"]}, {"premise_expression": "\\frac{\\sin{(V)}}{L}", "variable": "V", "positive": "- \\frac{\\cos{(V)}}{L}", "negatives": ["- L \\cos{(V)}", "- L V - \\cos{(V)}", "\\frac{V (- 2 L + V)}{2}", "e^{L + V}"], "srepr_premise_expression": "Mul(Pow(Symbol('L', commutative=True), Integer(-1)), sin(Symbol('V', commutative=True)))", "srepr_variable": "Symbol('V', commutative=True)", "srepr_positive": "Mul(Integer(-1), Pow(Symbol('L', commutative=True), Integer(-1)), cos(Symbol('V', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Symbol('L', commutative=True), cos(Symbol('V', commutative=True)))", "Add(Mul(Integer(-1), Symbol('L', commutative=True), Symbol('V', commutative=True)), Mul(Integer(-1), cos(Symbol('V', commutative=True))))", "Mul(Rational(1, 2), Symbol('V', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('L', commutative=True)), Symbol('V', commutative=True)))", "exp(Add(Symbol('L', commutative=True), Symbol('V', commutative=True)))"]}, {"premise_expression": "\\frac{\\log{(L)}}{C}", "variable": "L", "positive": "\\frac{L (\\log{(L)} - 1)}{C}", "negatives": ["L (- C + \\log{(L)} - 1)", "\\frac{L (- 2 C + L)}{2}", "\\log{(L)} \\cos{(C)}", "\\log{(C)} \\log{(L)}"], "srepr_premise_expression": "Mul(Pow(Symbol('C', commutative=True), Integer(-1)), log(Symbol('L', commutative=True)))", "srepr_variable": "Symbol('L', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('C', commutative=True), Integer(-1)), Symbol('L', commutative=True), Add(log(Symbol('L', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('L', commutative=True), Add(Mul(Integer(-1), Symbol('C', commutative=True)), log(Symbol('L', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('C', commutative=True)), Symbol('L', commutative=True)))", "Mul(log(Symbol('L', commutative=True)), cos(Symbol('C', commutative=True)))", "Mul(log(Symbol('C', commutative=True)), log(Symbol('L', commutative=True)))"]}, {"premise_expression": "\\log{(G^{x})}", "variable": "G", "positive": "G (- x + \\log{(G^{x})})", "negatives": ["G x + e^{G}", "x \\log{(G)}", "\\frac{x^{2} \\log{(G)}}{2}", "- \\cos{(G + x)}"], "srepr_premise_expression": "log(Pow(Symbol('G', commutative=True), Symbol('x', commutative=True)))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Mul(Symbol('G', commutative=True), Add(Mul(Integer(-1), Symbol('x', commutative=True)), log(Pow(Symbol('G', commutative=True), Symbol('x', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('G', commutative=True), Symbol('x', commutative=True)), exp(Symbol('G', commutative=True)))", "Mul(Symbol('x', commutative=True), log(Symbol('G', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('x', commutative=True), Integer(2)), log(Symbol('G', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('G', commutative=True), Symbol('x', commutative=True))))"]}, {"premise_expression": "L + w", "variable": "L", "positive": "\\frac{L (L + 2 w)}{2}", "negatives": ["\\frac{L (L - 2 w)}{2}", "\\frac{w (2 L + w)}{2}", "\\sin{(L + w)}", "\\frac{L^{2}}{2 w}"], "srepr_premise_expression": "Add(Symbol('L', commutative=True), Symbol('w', commutative=True))", "srepr_variable": "Symbol('L', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Symbol('L', commutative=True), Mul(Integer(2), Symbol('w', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Symbol('L', commutative=True), Mul(Integer(-1), Integer(2), Symbol('w', commutative=True))))", "Mul(Rational(1, 2), Symbol('w', commutative=True), Add(Mul(Integer(2), Symbol('L', commutative=True)), Symbol('w', commutative=True)))", "sin(Add(Symbol('L', commutative=True), Symbol('w', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(2)), Pow(Symbol('w', commutative=True), Integer(-1)))"]}, {"premise_expression": "e^{m + t}", "variable": "t", "positive": "e^{m + t}", "negatives": ["- \\cos{(m + t)}", "m e^{\\frac{t}{m}}", "m t + e^{t}", "\\log{(t)} \\cos{(m)}"], "srepr_premise_expression": "exp(Add(Symbol('m', commutative=True), Symbol('t', commutative=True)))", "srepr_variable": "Symbol('t', commutative=True)", "srepr_positive": "exp(Add(Symbol('m', commutative=True), Symbol('t', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('m', commutative=True), Symbol('t', commutative=True))))", "Mul(Symbol('m', commutative=True), exp(Mul(Pow(Symbol('m', commutative=True), Integer(-1)), Symbol('t', commutative=True))))", "Add(Mul(Symbol('m', commutative=True), Symbol('t', commutative=True)), exp(Symbol('t', commutative=True)))", "Mul(log(Symbol('t', commutative=True)), cos(Symbol('m', commutative=True)))"]}, {"premise_expression": "D + \\sin{(I)}", "variable": "D", "positive": "\\frac{D (D + 2 \\sin{(I)})}{2}", "negatives": ["\\frac{D^{2} \\log{(I)}}{2}", "D I - \\cos{(I)}", "\\cos{(D - I)}", "D (\\log{(\\frac{D}{I})} - 1)"], "srepr_premise_expression": "Add(Symbol('D', commutative=True), sin(Symbol('I', commutative=True)))", "srepr_variable": "Symbol('D', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('D', commutative=True), Add(Symbol('D', commutative=True), Mul(Integer(2), sin(Symbol('I', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(2)), log(Symbol('I', commutative=True)))", "Add(Mul(Symbol('D', commutative=True), Symbol('I', commutative=True)), Mul(Integer(-1), cos(Symbol('I', commutative=True))))", "cos(Add(Symbol('D', commutative=True), Mul(Integer(-1), Symbol('I', commutative=True))))", "Mul(Symbol('D', commutative=True), Add(log(Mul(Symbol('D', commutative=True), Pow(Symbol('I', commutative=True), Integer(-1)))), Integer(-1)))"]}, {"premise_expression": "- B + M + m", "variable": "M", "positive": "M (- B + \\frac{M}{2} + m)", "negatives": ["\\frac{B (- B + 2 M + 2 m)}{2}", "\\frac{m (- 2 B + 2 M + m)}{2}", "(B + m) \\log{(M)}", "\\frac{M^{2}}{2 B m}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('B', commutative=True)), Symbol('M', commutative=True), Symbol('m', commutative=True))", "srepr_variable": "Symbol('M', commutative=True)", "srepr_positive": "Mul(Symbol('M', commutative=True), Add(Mul(Integer(-1), Symbol('B', commutative=True)), Mul(Rational(1, 2), Symbol('M', commutative=True)), Symbol('m', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('B', commutative=True), Add(Mul(Integer(-1), Symbol('B', commutative=True)), Mul(Integer(2), Symbol('M', commutative=True)), Mul(Integer(2), Symbol('m', commutative=True))))", "Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('B', commutative=True)), Mul(Integer(2), Symbol('M', commutative=True)), Symbol('m', commutative=True)))", "Mul(Add(Symbol('B', commutative=True), Symbol('m', commutative=True)), log(Symbol('M', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('B', commutative=True), Integer(-1)), Pow(Symbol('M', commutative=True), Integer(2)), Pow(Symbol('m', commutative=True), Integer(-1)))"]}, {"premise_expression": "r + \\log{(J)}", "variable": "r", "positive": "\\frac{r (r + 2 \\log{(J)})}{2}", "negatives": ["\\frac{r (- r + 2 \\sin{(J)})}{2}", "\\frac{r^{2} \\log{(J)}}{2}", "J (r + \\log{(J)} - 1)", "- J r - \\cos{(r)}"], "srepr_premise_expression": "Add(Symbol('r', commutative=True), log(Symbol('J', commutative=True)))", "srepr_variable": "Symbol('r', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Symbol('r', commutative=True), Mul(Integer(2), log(Symbol('J', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(-1), Symbol('r', commutative=True)), Mul(Integer(2), sin(Symbol('J', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('r', commutative=True), Integer(2)), log(Symbol('J', commutative=True)))", "Mul(Symbol('J', commutative=True), Add(Symbol('r', commutative=True), log(Symbol('J', commutative=True)), Integer(-1)))", "Add(Mul(Integer(-1), Symbol('J', commutative=True), Symbol('r', commutative=True)), Mul(Integer(-1), cos(Symbol('r', commutative=True))))"]}, {"premise_expression": "\\frac{K v}{q}", "variable": "K", "positive": "\\frac{K^{2} v}{2 q}", "negatives": ["\\frac{K v^{2}}{2 q}", "\\frac{K^{2} q v}{2}", "K v \\log{(q)}", "q^{v} \\log{(K)}"], "srepr_premise_expression": "Mul(Symbol('K', commutative=True), Pow(Symbol('q', commutative=True), Integer(-1)), Symbol('v', commutative=True))", "srepr_variable": "Symbol('K', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('K', commutative=True), Integer(2)), Pow(Symbol('q', commutative=True), Integer(-1)), Symbol('v', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('K', commutative=True), Pow(Symbol('q', commutative=True), Integer(-1)), Pow(Symbol('v', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('K', commutative=True), Integer(2)), Symbol('q', commutative=True), Symbol('v', commutative=True))", "Mul(Symbol('K', commutative=True), Symbol('v', commutative=True), log(Symbol('q', commutative=True)))", "Mul(Pow(Symbol('q', commutative=True), Symbol('v', commutative=True)), log(Symbol('K', commutative=True)))"]}, {"premise_expression": "P + p - r", "variable": "r", "positive": "r (P + p - \\frac{r}{2})", "negatives": ["\\frac{P (P + 2 p - 2 r)}{2}", "\\frac{p (2 P + p - 2 r)}{2}", "\\frac{r (2 P p + r)}{2}", "\\frac{r (2 P + p r)}{2}"], "srepr_premise_expression": "Add(Symbol('P', commutative=True), Symbol('p', commutative=True), Mul(Integer(-1), Symbol('r', commutative=True)))", "srepr_variable": "Symbol('r', commutative=True)", "srepr_positive": "Mul(Symbol('r', commutative=True), Add(Symbol('P', commutative=True), Symbol('p', commutative=True), Mul(Integer(-1), Rational(1, 2), Symbol('r', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Symbol('P', commutative=True), Mul(Integer(2), Symbol('p', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('r', commutative=True))))", "Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Mul(Integer(2), Symbol('P', commutative=True)), Symbol('p', commutative=True), Mul(Integer(-1), Integer(2), Symbol('r', commutative=True))))", "Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(2), Symbol('P', commutative=True), Symbol('p', commutative=True)), Symbol('r', commutative=True)))", "Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(2), Symbol('P', commutative=True)), Mul(Symbol('p', commutative=True), Symbol('r', commutative=True))))"]}, {"premise_expression": "- P + e^{Z}", "variable": "Z", "positive": "- P Z + e^{Z}", "negatives": ["P e^{Z}", "P \\log{(Z)}", "\\frac{P (- P + 2 e^{Z})}{2}", "e^{P + Z}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('P', commutative=True)), exp(Symbol('Z', commutative=True)))", "srepr_variable": "Symbol('Z', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('P', commutative=True), Symbol('Z', commutative=True)), exp(Symbol('Z', commutative=True)))", "srepr_negatives": ["Mul(Symbol('P', commutative=True), exp(Symbol('Z', commutative=True)))", "Mul(Symbol('P', commutative=True), log(Symbol('Z', commutative=True)))", "Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Mul(Integer(-1), Symbol('P', commutative=True)), Mul(Integer(2), exp(Symbol('Z', commutative=True)))))", "exp(Add(Symbol('P', commutative=True), Symbol('Z', commutative=True)))"]}, {"premise_expression": "D q", "variable": "q", "positive": "\\frac{D q^{2}}{2}", "negatives": ["\\frac{D^{2} q}{2}", "\\frac{q^{2}}{2 D}", "D \\log{(q)}", "\\sin{(D + q)}"], "srepr_premise_expression": "Mul(Symbol('D', commutative=True), Symbol('q', commutative=True))", "srepr_variable": "Symbol('q', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('D', commutative=True), Pow(Symbol('q', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(2)), Symbol('q', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(-1)), Pow(Symbol('q', commutative=True), Integer(2)))", "Mul(Symbol('D', commutative=True), log(Symbol('q', commutative=True)))", "sin(Add(Symbol('D', commutative=True), Symbol('q', commutative=True)))"]}, {"premise_expression": "\\frac{M}{Z} - l", "variable": "Z", "positive": "M \\log{(Z)} - Z l", "negatives": ["M \\log{(Z)} + Z l", "\\frac{M^{2}}{2 Z} - M l", "\\frac{M l}{Z} - \\frac{l^{2}}{2}", "\\frac{Z (2 M l - Z)}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('M', commutative=True), Pow(Symbol('Z', commutative=True), Integer(-1))), Mul(Integer(-1), Symbol('l', commutative=True)))", "srepr_variable": "Symbol('Z', commutative=True)", "srepr_positive": "Add(Mul(Symbol('M', commutative=True), log(Symbol('Z', commutative=True))), Mul(Integer(-1), Symbol('Z', commutative=True), Symbol('l', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('M', commutative=True), log(Symbol('Z', commutative=True))), Mul(Symbol('Z', commutative=True), Symbol('l', commutative=True)))", "Add(Mul(Rational(1, 2), Pow(Symbol('M', commutative=True), Integer(2)), Pow(Symbol('Z', commutative=True), Integer(-1))), Mul(Integer(-1), Symbol('M', commutative=True), Symbol('l', commutative=True)))", "Add(Mul(Symbol('M', commutative=True), Pow(Symbol('Z', commutative=True), Integer(-1)), Symbol('l', commutative=True)), Mul(Integer(-1), Rational(1, 2), Pow(Symbol('l', commutative=True), Integer(2))))", "Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Mul(Integer(2), Symbol('M', commutative=True), Symbol('l', commutative=True)), Mul(Integer(-1), Symbol('Z', commutative=True))))"]}, {"premise_expression": "\\log{(K + f)}", "variable": "K", "positive": "K \\log{(K + f)} - K + f \\log{(K + f)}", "negatives": ["K \\log{(K + f)} + f \\log{(K + f)} - f", "- f \\cos{(K)}", "\\sin{(K - f)}", "e^{K + f}"], "srepr_premise_expression": "log(Add(Symbol('K', commutative=True), Symbol('f', commutative=True)))", "srepr_variable": "Symbol('K', commutative=True)", "srepr_positive": "Add(Mul(Symbol('K', commutative=True), log(Add(Symbol('K', commutative=True), Symbol('f', commutative=True)))), Mul(Integer(-1), Symbol('K', commutative=True)), Mul(Symbol('f', commutative=True), log(Add(Symbol('K', commutative=True), Symbol('f', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('K', commutative=True), log(Add(Symbol('K', commutative=True), Symbol('f', commutative=True)))), Mul(Symbol('f', commutative=True), log(Add(Symbol('K', commutative=True), Symbol('f', commutative=True)))), Mul(Integer(-1), Symbol('f', commutative=True)))", "Mul(Integer(-1), Symbol('f', commutative=True), cos(Symbol('K', commutative=True)))", "sin(Add(Symbol('K', commutative=True), Mul(Integer(-1), Symbol('f', commutative=True))))", "exp(Add(Symbol('K', commutative=True), Symbol('f', commutative=True)))"]}, {"premise_expression": "F + Z", "variable": "F", "positive": "\\frac{F (F + 2 Z)}{2}", "negatives": ["\\frac{Z (2 F + Z)}{2}", "\\frac{F (F + 2 \\sin{(Z)})}{2}", "\\frac{F^{2} Z}{2}", "e^{F + Z}"], "srepr_premise_expression": "Add(Symbol('F', commutative=True), Symbol('Z', commutative=True))", "srepr_variable": "Symbol('F', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Symbol('F', commutative=True), Mul(Integer(2), Symbol('Z', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Mul(Integer(2), Symbol('F', commutative=True)), Symbol('Z', commutative=True)))", "Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Symbol('F', commutative=True), Mul(Integer(2), sin(Symbol('Z', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('F', commutative=True), Integer(2)), Symbol('Z', commutative=True))", "exp(Add(Symbol('F', commutative=True), Symbol('Z', commutative=True)))"]}, {"premise_expression": "G Q", "variable": "G", "positive": "\\frac{G^{2} Q}{2}", "negatives": ["\\frac{G Q^{2}}{2}", "\\frac{G^{2} e^{Q}}{2}", "\\frac{G (G + 2 \\log{(Q)})}{2}", "G (- Q + \\log{(Q)})"], "srepr_premise_expression": "Mul(Symbol('G', commutative=True), Symbol('Q', commutative=True))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(2)), Symbol('Q', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('G', commutative=True), Pow(Symbol('Q', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(2)), exp(Symbol('Q', commutative=True)))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Symbol('G', commutative=True), Mul(Integer(2), log(Symbol('Q', commutative=True)))))", "Mul(Symbol('G', commutative=True), Add(Mul(Integer(-1), Symbol('Q', commutative=True)), log(Symbol('Q', commutative=True))))"]}, {"premise_expression": "e^{\\frac{Q}{p}}", "variable": "Q", "positive": "p e^{\\frac{Q}{p}}", "negatives": ["p \\log{(Q)}", "\\cos{(Q - p)}", "e^{p} \\log{(Q)}", "Q (\\log{(\\frac{Q}{p})} - 1)"], "srepr_premise_expression": "exp(Mul(Symbol('Q', commutative=True), Pow(Symbol('p', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('Q', commutative=True)", "srepr_positive": "Mul(Symbol('p', commutative=True), exp(Mul(Symbol('Q', commutative=True), Pow(Symbol('p', commutative=True), Integer(-1)))))", "srepr_negatives": ["Mul(Symbol('p', commutative=True), log(Symbol('Q', commutative=True)))", "cos(Add(Symbol('Q', commutative=True), Mul(Integer(-1), Symbol('p', commutative=True))))", "Mul(exp(Symbol('p', commutative=True)), log(Symbol('Q', commutative=True)))", "Mul(Symbol('Q', commutative=True), Add(log(Mul(Symbol('Q', commutative=True), Pow(Symbol('p', commutative=True), Integer(-1)))), Integer(-1)))"]}, {"premise_expression": "W z", "variable": "z", "positive": "\\frac{W z^{2}}{2}", "negatives": ["\\frac{W^{2} z}{2}", "- \\frac{\\cos{(z)}}{W}", "\\frac{z^{2} \\sin{(W)}}{2}", "- \\cos{(W - z)}"], "srepr_premise_expression": "Mul(Symbol('W', commutative=True), Symbol('z', commutative=True))", "srepr_variable": "Symbol('z', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('W', commutative=True), Pow(Symbol('z', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('W', commutative=True), Integer(2)), Symbol('z', commutative=True))", "Mul(Integer(-1), Pow(Symbol('W', commutative=True), Integer(-1)), cos(Symbol('z', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('z', commutative=True), Integer(2)), sin(Symbol('W', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('W', commutative=True), Mul(Integer(-1), Symbol('z', commutative=True)))))"]}, {"premise_expression": "J m", "variable": "m", "positive": "\\frac{J m^{2}}{2}", "negatives": ["\\frac{J^{2} m}{2}", "- J m + e^{m}", "\\frac{m (m + 2 \\log{(J)})}{2}", "\\frac{m (- m + 2 e^{J})}{2}"], "srepr_premise_expression": "Mul(Symbol('J', commutative=True), Symbol('m', commutative=True))", "srepr_variable": "Symbol('m', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('J', commutative=True), Pow(Symbol('m', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('J', commutative=True), Integer(2)), Symbol('m', commutative=True))", "Add(Mul(Integer(-1), Symbol('J', commutative=True), Symbol('m', commutative=True)), exp(Symbol('m', commutative=True)))", "Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Symbol('m', commutative=True), Mul(Integer(2), log(Symbol('J', commutative=True)))))", "Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Mul(Integer(-1), Symbol('m', commutative=True)), Mul(Integer(2), exp(Symbol('J', commutative=True)))))"]}, {"premise_expression": "L + W", "variable": "W", "positive": "\\frac{W (2 L + W)}{2}", "negatives": ["\\frac{L (L + 2 W)}{2}", "\\frac{W (\\log{(W)} - 1)}{L}", "- \\frac{\\cos{(W)}}{L}", "W (L + \\log{(W)} - 1)"], "srepr_premise_expression": "Add(Symbol('L', commutative=True), Symbol('W', commutative=True))", "srepr_variable": "Symbol('W', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('W', commutative=True), Add(Mul(Integer(2), Symbol('L', commutative=True)), Symbol('W', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Symbol('L', commutative=True), Mul(Integer(2), Symbol('W', commutative=True))))", "Mul(Pow(Symbol('L', commutative=True), Integer(-1)), Symbol('W', commutative=True), Add(log(Symbol('W', commutative=True)), Integer(-1)))", "Mul(Integer(-1), Pow(Symbol('L', commutative=True), Integer(-1)), cos(Symbol('W', commutative=True)))", "Mul(Symbol('W', commutative=True), Add(Symbol('L', commutative=True), log(Symbol('W', commutative=True)), Integer(-1)))"]}, {"premise_expression": "q + e^{P}", "variable": "q", "positive": "\\frac{q (q + 2 e^{P})}{2}", "negatives": ["\\frac{q (- q + 2 e^{P})}{2}", "P q + e^{P}", "\\frac{q (2 P + q)}{2}", "P q - \\cos{(q)}"], "srepr_premise_expression": "Add(Symbol('q', commutative=True), exp(Symbol('P', commutative=True)))", "srepr_variable": "Symbol('q', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('q', commutative=True), Add(Symbol('q', commutative=True), Mul(Integer(2), exp(Symbol('P', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('q', commutative=True), Add(Mul(Integer(-1), Symbol('q', commutative=True)), Mul(Integer(2), exp(Symbol('P', commutative=True)))))", "Add(Mul(Symbol('P', commutative=True), Symbol('q', commutative=True)), exp(Symbol('P', commutative=True)))", "Mul(Rational(1, 2), Symbol('q', commutative=True), Add(Mul(Integer(2), Symbol('P', commutative=True)), Symbol('q', commutative=True)))", "Add(Mul(Symbol('P', commutative=True), Symbol('q', commutative=True)), Mul(Integer(-1), cos(Symbol('q', commutative=True))))"]}, {"premise_expression": "\\frac{e^{o}}{h}", "variable": "h", "positive": "e^{o} \\log{(h)}", "negatives": ["- e^{- h + o}", "h (\\log{(h o)} - 1)", "h (\\log{(\\frac{o}{h})} + 1)", "\\frac{h (\\log{(h)} - 1)}{o}"], "srepr_premise_expression": "Mul(Pow(Symbol('h', commutative=True), Integer(-1)), exp(Symbol('o', commutative=True)))", "srepr_variable": "Symbol('h', commutative=True)", "srepr_positive": "Mul(exp(Symbol('o', commutative=True)), log(Symbol('h', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('h', commutative=True)), Symbol('o', commutative=True))))", "Mul(Symbol('h', commutative=True), Add(log(Mul(Symbol('h', commutative=True), Symbol('o', commutative=True))), Integer(-1)))", "Mul(Symbol('h', commutative=True), Add(log(Mul(Pow(Symbol('h', commutative=True), Integer(-1)), Symbol('o', commutative=True))), Integer(1)))", "Mul(Symbol('h', commutative=True), Pow(Symbol('o', commutative=True), Integer(-1)), Add(log(Symbol('h', commutative=True)), Integer(-1)))"]}, {"premise_expression": "B f", "variable": "B", "positive": "\\frac{B^{2} f}{2}", "negatives": ["\\frac{B f^{2}}{2}", "\\frac{B^{2} \\log{(f)}}{2}", "\\frac{B (B + 2 f)}{2}", "\\frac{B (- B + 2 f)}{2}"], "srepr_premise_expression": "Mul(Symbol('B', commutative=True), Symbol('f', commutative=True))", "srepr_variable": "Symbol('B', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('B', commutative=True), Integer(2)), Symbol('f', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('B', commutative=True), Pow(Symbol('f', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('B', commutative=True), Integer(2)), log(Symbol('f', commutative=True)))", "Mul(Rational(1, 2), Symbol('B', commutative=True), Add(Symbol('B', commutative=True), Mul(Integer(2), Symbol('f', commutative=True))))", "Mul(Rational(1, 2), Symbol('B', commutative=True), Add(Mul(Integer(-1), Symbol('B', commutative=True)), Mul(Integer(2), Symbol('f', commutative=True))))"]}, {"premise_expression": "- R + \\log{(C)}", "variable": "R", "positive": "\\frac{R (- R + 2 \\log{(C)})}{2}", "negatives": ["C (- R + \\log{(C)} - 1)", "R (- C + e^{C})", "\\frac{R^{2} \\cos{(C)}}{2}", "\\frac{R (2 C + R)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('R', commutative=True)), log(Symbol('C', commutative=True)))", "srepr_variable": "Symbol('R', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('R', commutative=True), Add(Mul(Integer(-1), Symbol('R', commutative=True)), Mul(Integer(2), log(Symbol('C', commutative=True)))))", "srepr_negatives": ["Mul(Symbol('C', commutative=True), Add(Mul(Integer(-1), Symbol('R', commutative=True)), log(Symbol('C', commutative=True)), Integer(-1)))", "Mul(Symbol('R', commutative=True), Add(Mul(Integer(-1), Symbol('C', commutative=True)), exp(Symbol('C', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('R', commutative=True), Integer(2)), cos(Symbol('C', commutative=True)))", "Mul(Rational(1, 2), Symbol('R', commutative=True), Add(Mul(Integer(2), Symbol('C', commutative=True)), Symbol('R', commutative=True)))"]}, {"premise_expression": "\\cos{(S - V)}", "variable": "V", "positive": "- \\sin{(S - V)}", "negatives": ["\\sin{(S - V)}", "e^{S + V}", "S \\sin{(V)}", "\\log{(S)} \\log{(V)}"], "srepr_premise_expression": "cos(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('V', commutative=True))))", "srepr_variable": "Symbol('V', commutative=True)", "srepr_positive": "Mul(Integer(-1), sin(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('V', commutative=True)))))", "srepr_negatives": ["sin(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('V', commutative=True))))", "exp(Add(Symbol('S', commutative=True), Symbol('V', commutative=True)))", "Mul(Symbol('S', commutative=True), sin(Symbol('V', commutative=True)))", "Mul(log(Symbol('S', commutative=True)), log(Symbol('V', commutative=True)))"]}, {"premise_expression": "\\frac{S}{L}", "variable": "L", "positive": "S \\log{(L)}", "negatives": ["S \\sin{(L)}", "\\frac{S^{2}}{2 L}", "- \\cos{(L - S)}", "L (\\log{(\\frac{S}{L})} + 1)"], "srepr_premise_expression": "Mul(Pow(Symbol('L', commutative=True), Integer(-1)), Symbol('S', commutative=True))", "srepr_variable": "Symbol('L', commutative=True)", "srepr_positive": "Mul(Symbol('S', commutative=True), log(Symbol('L', commutative=True)))", "srepr_negatives": ["Mul(Symbol('S', commutative=True), sin(Symbol('L', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(-1)), Pow(Symbol('S', commutative=True), Integer(2)))", "Mul(Integer(-1), cos(Add(Symbol('L', commutative=True), Mul(Integer(-1), Symbol('S', commutative=True)))))", "Mul(Symbol('L', commutative=True), Add(log(Mul(Pow(Symbol('L', commutative=True), Integer(-1)), Symbol('S', commutative=True))), Integer(1)))"]}, {"premise_expression": "\\frac{p}{Z}", "variable": "p", "positive": "\\frac{p^{2}}{2 Z}", "negatives": ["p \\log{(Z)}", "Z \\sin{(p)}", "e^{Z + p}", "p (\\log{(\\frac{Z}{p})} + 1)"], "srepr_premise_expression": "Mul(Pow(Symbol('Z', commutative=True), Integer(-1)), Symbol('p', commutative=True))", "srepr_variable": "Symbol('p', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('Z', commutative=True), Integer(-1)), Pow(Symbol('p', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('p', commutative=True), log(Symbol('Z', commutative=True)))", "Mul(Symbol('Z', commutative=True), sin(Symbol('p', commutative=True)))", "exp(Add(Symbol('Z', commutative=True), Symbol('p', commutative=True)))", "Mul(Symbol('p', commutative=True), Add(log(Mul(Symbol('Z', commutative=True), Pow(Symbol('p', commutative=True), Integer(-1)))), Integer(1)))"]}, {"premise_expression": "\\cos{(J - U)}", "variable": "J", "positive": "\\sin{(J - U)}", "negatives": ["- \\sin{(J - U)}", "\\frac{J (J - 2 U)}{2}", "U e^{J}", "\\frac{J (- J + 2 U)}{2}"], "srepr_premise_expression": "cos(Add(Symbol('J', commutative=True), Mul(Integer(-1), Symbol('U', commutative=True))))", "srepr_variable": "Symbol('J', commutative=True)", "srepr_positive": "sin(Add(Symbol('J', commutative=True), Mul(Integer(-1), Symbol('U', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('J', commutative=True), Mul(Integer(-1), Symbol('U', commutative=True)))))", "Mul(Rational(1, 2), Symbol('J', commutative=True), Add(Symbol('J', commutative=True), Mul(Integer(-1), Integer(2), Symbol('U', commutative=True))))", "Mul(Symbol('U', commutative=True), exp(Symbol('J', commutative=True)))", "Mul(Rational(1, 2), Symbol('J', commutative=True), Add(Mul(Integer(-1), Symbol('J', commutative=True)), Mul(Integer(2), Symbol('U', commutative=True))))"]}, {"premise_expression": "e^{L - S}", "variable": "S", "positive": "- e^{L - S}", "negatives": ["e^{L - S}", "L \\sin{(S)}", "L S + e^{S}", "\\log{(L)} \\log{(S)}"], "srepr_premise_expression": "exp(Add(Symbol('L', commutative=True), Mul(Integer(-1), Symbol('S', commutative=True))))", "srepr_variable": "Symbol('S', commutative=True)", "srepr_positive": "Mul(Integer(-1), exp(Add(Symbol('L', commutative=True), Mul(Integer(-1), Symbol('S', commutative=True)))))", "srepr_negatives": ["exp(Add(Symbol('L', commutative=True), Mul(Integer(-1), Symbol('S', commutative=True))))", "Mul(Symbol('L', commutative=True), sin(Symbol('S', commutative=True)))", "Add(Mul(Symbol('L', commutative=True), Symbol('S', commutative=True)), exp(Symbol('S', commutative=True)))", "Mul(log(Symbol('L', commutative=True)), log(Symbol('S', commutative=True)))"]}, {"premise_expression": "- L + q", "variable": "L", "positive": "\\frac{L (- L + 2 q)}{2}", "negatives": ["\\frac{q (- 2 L + q)}{2}", "\\frac{L (- L + 2 \\cos{(q)})}{2}", "\\frac{L^{2} \\log{(q)}}{2}", "- L q + e^{L}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('L', commutative=True)), Symbol('q', commutative=True))", "srepr_variable": "Symbol('L', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Mul(Integer(-1), Symbol('L', commutative=True)), Mul(Integer(2), Symbol('q', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('q', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('L', commutative=True)), Symbol('q', commutative=True)))", "Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Mul(Integer(-1), Symbol('L', commutative=True)), Mul(Integer(2), cos(Symbol('q', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(2)), log(Symbol('q', commutative=True)))", "Add(Mul(Integer(-1), Symbol('L', commutative=True), Symbol('q', commutative=True)), exp(Symbol('L', commutative=True)))"]}, {"premise_expression": "- U + \\cos{(W)}", "variable": "W", "positive": "- U W + \\sin{(W)}", "negatives": ["- U W + e^{W}", "U \\sin{(W)}", "U e^{W}", "\\frac{\\sin{(W)}}{U}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('U', commutative=True)), cos(Symbol('W', commutative=True)))", "srepr_variable": "Symbol('W', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('U', commutative=True), Symbol('W', commutative=True)), sin(Symbol('W', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('U', commutative=True), Symbol('W', commutative=True)), exp(Symbol('W', commutative=True)))", "Mul(Symbol('U', commutative=True), sin(Symbol('W', commutative=True)))", "Mul(Symbol('U', commutative=True), exp(Symbol('W', commutative=True)))", "Mul(Pow(Symbol('U', commutative=True), Integer(-1)), sin(Symbol('W', commutative=True)))"]}, {"premise_expression": "j - o", "variable": "j", "positive": "\\frac{j (j - 2 o)}{2}", "negatives": ["\\frac{o (2 j - o)}{2}", "\\frac{j (- j + 2 \\cos{(o)})}{2}", "- \\cos{(j + o)}", "- j o + e^{j}"], "srepr_premise_expression": "Add(Symbol('j', commutative=True), Mul(Integer(-1), Symbol('o', commutative=True)))", "srepr_variable": "Symbol('j', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('j', commutative=True), Add(Symbol('j', commutative=True), Mul(Integer(-1), Integer(2), Symbol('o', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Mul(Integer(2), Symbol('j', commutative=True)), Mul(Integer(-1), Symbol('o', commutative=True))))", "Mul(Rational(1, 2), Symbol('j', commutative=True), Add(Mul(Integer(-1), Symbol('j', commutative=True)), Mul(Integer(2), cos(Symbol('o', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('j', commutative=True), Symbol('o', commutative=True))))", "Add(Mul(Integer(-1), Symbol('j', commutative=True), Symbol('o', commutative=True)), exp(Symbol('j', commutative=True)))"]}, {"premise_expression": "- \\sin{(E - v)}", "variable": "v", "positive": "- \\cos{(E - v)}", "negatives": ["\\cos{(E - v)}", "e^{- E + v}", "\\frac{v (2 E - v)}{2}", "E v - \\cos{(v)}"], "srepr_premise_expression": "Mul(Integer(-1), sin(Add(Symbol('E', commutative=True), Mul(Integer(-1), Symbol('v', commutative=True)))))", "srepr_variable": "Symbol('v', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('E', commutative=True), Mul(Integer(-1), Symbol('v', commutative=True)))))", "srepr_negatives": ["cos(Add(Symbol('E', commutative=True), Mul(Integer(-1), Symbol('v', commutative=True))))", "exp(Add(Mul(Integer(-1), Symbol('E', commutative=True)), Symbol('v', commutative=True)))", "Mul(Rational(1, 2), Symbol('v', commutative=True), Add(Mul(Integer(2), Symbol('E', commutative=True)), Mul(Integer(-1), Symbol('v', commutative=True))))", "Add(Mul(Symbol('E', commutative=True), Symbol('v', commutative=True)), Mul(Integer(-1), cos(Symbol('v', commutative=True))))"]}, {"premise_expression": "b + \\log{(C)}", "variable": "b", "positive": "\\frac{b (b + 2 \\log{(C)})}{2}", "negatives": ["\\frac{b (- b + 2 \\log{(C)})}{2}", "\\frac{b (- b + 2 \\sin{(C)})}{2}", "C (b + \\log{(C)} - 1)", "\\frac{b^{2} \\sin{(C)}}{2}"], "srepr_premise_expression": "Add(Symbol('b', commutative=True), log(Symbol('C', commutative=True)))", "srepr_variable": "Symbol('b', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('b', commutative=True), Add(Symbol('b', commutative=True), Mul(Integer(2), log(Symbol('C', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('b', commutative=True), Add(Mul(Integer(-1), Symbol('b', commutative=True)), Mul(Integer(2), log(Symbol('C', commutative=True)))))", "Mul(Rational(1, 2), Symbol('b', commutative=True), Add(Mul(Integer(-1), Symbol('b', commutative=True)), Mul(Integer(2), sin(Symbol('C', commutative=True)))))", "Mul(Symbol('C', commutative=True), Add(Symbol('b', commutative=True), log(Symbol('C', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('b', commutative=True), Integer(2)), sin(Symbol('C', commutative=True)))"]}, {"premise_expression": "e^{- j + n}", "variable": "n", "positive": "e^{- j + n}", "negatives": ["- e^{- j + n}", "\\sin{(j + n)}", "- \\cos{(j - n)}", "\\frac{n (2 j + n)}{2}"], "srepr_premise_expression": "exp(Add(Mul(Integer(-1), Symbol('j', commutative=True)), Symbol('n', commutative=True)))", "srepr_variable": "Symbol('n', commutative=True)", "srepr_positive": "exp(Add(Mul(Integer(-1), Symbol('j', commutative=True)), Symbol('n', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('j', commutative=True)), Symbol('n', commutative=True))))", "sin(Add(Symbol('j', commutative=True), Symbol('n', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('j', commutative=True), Mul(Integer(-1), Symbol('n', commutative=True)))))", "Mul(Rational(1, 2), Symbol('n', commutative=True), Add(Mul(Integer(2), Symbol('j', commutative=True)), Symbol('n', commutative=True)))"]}, {"premise_expression": "\\log{(F^{M})}", "variable": "M", "positive": "\\frac{M^{2} \\log{(F)}}{2}", "negatives": ["F \\log{(M)}", "- F \\cos{(M)}", "\\frac{M (M + 2 \\sin{(F)})}{2}", "F (- M + \\log{(F^{M})})"], "srepr_premise_expression": "log(Pow(Symbol('F', commutative=True), Symbol('M', commutative=True)))", "srepr_variable": "Symbol('M', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('M', commutative=True), Integer(2)), log(Symbol('F', commutative=True)))", "srepr_negatives": ["Mul(Symbol('F', commutative=True), log(Symbol('M', commutative=True)))", "Mul(Integer(-1), Symbol('F', commutative=True), cos(Symbol('M', commutative=True)))", "Mul(Rational(1, 2), Symbol('M', commutative=True), Add(Symbol('M', commutative=True), Mul(Integer(2), sin(Symbol('F', commutative=True)))))", "Mul(Symbol('F', commutative=True), Add(Mul(Integer(-1), Symbol('M', commutative=True)), log(Pow(Symbol('F', commutative=True), Symbol('M', commutative=True)))))"]}, {"premise_expression": "- C + D", "variable": "C", "positive": "\\frac{C (- C + 2 D)}{2}", "negatives": ["\\frac{C (C - 2 D)}{2}", "\\frac{D (- 2 C + D)}{2}", "\\sin{(C + D)}", "C D + \\sin{(C)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('C', commutative=True)), Symbol('D', commutative=True))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Mul(Integer(-1), Symbol('C', commutative=True)), Mul(Integer(2), Symbol('D', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Symbol('C', commutative=True), Mul(Integer(-1), Integer(2), Symbol('D', commutative=True))))", "Mul(Rational(1, 2), Symbol('D', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('C', commutative=True)), Symbol('D', commutative=True)))", "sin(Add(Symbol('C', commutative=True), Symbol('D', commutative=True)))", "Add(Mul(Symbol('C', commutative=True), Symbol('D', commutative=True)), sin(Symbol('C', commutative=True)))"]}, {"premise_expression": "\\log{(S W)}", "variable": "W", "positive": "W (\\log{(S W)} - 1)", "negatives": ["S (\\log{(S W)} - 1)", "\\frac{W^{2} \\log{(S)}}{2}", "\\frac{W (2 S - W)}{2}", "e^{- S + W}"], "srepr_premise_expression": "log(Mul(Symbol('S', commutative=True), Symbol('W', commutative=True)))", "srepr_variable": "Symbol('W', commutative=True)", "srepr_positive": "Mul(Symbol('W', commutative=True), Add(log(Mul(Symbol('S', commutative=True), Symbol('W', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('S', commutative=True), Add(log(Mul(Symbol('S', commutative=True), Symbol('W', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('W', commutative=True), Integer(2)), log(Symbol('S', commutative=True)))", "Mul(Rational(1, 2), Symbol('W', commutative=True), Add(Mul(Integer(2), Symbol('S', commutative=True)), Mul(Integer(-1), Symbol('W', commutative=True))))", "exp(Add(Mul(Integer(-1), Symbol('S', commutative=True)), Symbol('W', commutative=True)))"]}, {"premise_expression": "G + T", "variable": "T", "positive": "\\frac{T (2 G + T)}{2}", "negatives": ["\\frac{G (G + 2 T)}{2}", "\\frac{T^{2} \\sin{(G)}}{2}", "\\frac{T^{2} \\log{(G)}}{2}", "\\frac{\\sin{(T)}}{G}"], "srepr_premise_expression": "Add(Symbol('G', commutative=True), Symbol('T', commutative=True))", "srepr_variable": "Symbol('T', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('T', commutative=True), Add(Mul(Integer(2), Symbol('G', commutative=True)), Symbol('T', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Symbol('G', commutative=True), Mul(Integer(2), Symbol('T', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('T', commutative=True), Integer(2)), sin(Symbol('G', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('T', commutative=True), Integer(2)), log(Symbol('G', commutative=True)))", "Mul(Pow(Symbol('G', commutative=True), Integer(-1)), sin(Symbol('T', commutative=True)))"]}, {"premise_expression": "\\cos{(A - g)}", "variable": "A", "positive": "\\sin{(A - g)}", "negatives": ["- \\sin{(A - g)}", "\\frac{A (A + 2 g)}{2}", "\\frac{A^{2} g}{2}", "\\frac{A^{2} \\log{(g)}}{2}"], "srepr_premise_expression": "cos(Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('g', commutative=True))))", "srepr_variable": "Symbol('A', commutative=True)", "srepr_positive": "sin(Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('g', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('g', commutative=True)))))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Symbol('A', commutative=True), Mul(Integer(2), Symbol('g', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2)), Symbol('g', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2)), log(Symbol('g', commutative=True)))"]}, {"premise_expression": "\\frac{f}{t}", "variable": "t", "positive": "f \\log{(t)}", "negatives": ["\\frac{f^{2}}{2 t}", "\\frac{f t^{2}}{2}", "- \\cos{(f - t)}", "- \\cos{(f + t)}"], "srepr_premise_expression": "Mul(Symbol('f', commutative=True), Pow(Symbol('t', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('t', commutative=True)", "srepr_positive": "Mul(Symbol('f', commutative=True), log(Symbol('t', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('f', commutative=True), Integer(2)), Pow(Symbol('t', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Symbol('f', commutative=True), Pow(Symbol('t', commutative=True), Integer(2)))", "Mul(Integer(-1), cos(Add(Symbol('f', commutative=True), Mul(Integer(-1), Symbol('t', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('f', commutative=True), Symbol('t', commutative=True))))"]}, {"premise_expression": "E z", "variable": "E", "positive": "\\frac{E^{2} z}{2}", "negatives": ["\\frac{E z^{2}}{2}", "\\frac{E (E - 2 z)}{2}", "\\frac{E (E + 2 z)}{2}", "z \\log{(E)}"], "srepr_premise_expression": "Mul(Symbol('E', commutative=True), Symbol('z', commutative=True))", "srepr_variable": "Symbol('E', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('E', commutative=True), Integer(2)), Symbol('z', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('E', commutative=True), Pow(Symbol('z', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('E', commutative=True), Add(Symbol('E', commutative=True), Mul(Integer(-1), Integer(2), Symbol('z', commutative=True))))", "Mul(Rational(1, 2), Symbol('E', commutative=True), Add(Symbol('E', commutative=True), Mul(Integer(2), Symbol('z', commutative=True))))", "Mul(Symbol('z', commutative=True), log(Symbol('E', commutative=True)))"]}, {"premise_expression": "\\frac{S}{W}", "variable": "S", "positive": "\\frac{S^{2}}{2 W}", "negatives": ["S \\log{(W)}", "\\frac{S^{2} \\cos{(W)}}{2}", "- \\cos{(S + W)}", "- \\cos{(S - W)}"], "srepr_premise_expression": "Mul(Symbol('S', commutative=True), Pow(Symbol('W', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('S', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('S', commutative=True), Integer(2)), Pow(Symbol('W', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('S', commutative=True), log(Symbol('W', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('S', commutative=True), Integer(2)), cos(Symbol('W', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('S', commutative=True), Symbol('W', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('W', commutative=True)))))"]}, {"premise_expression": "B G + F", "variable": "B", "positive": "\\frac{B (B G + 2 F)}{2}", "negatives": ["\\frac{G (B G + 2 F)}{2}", "\\frac{F (2 B G + F)}{2}", "\\frac{B (- B + 2 F + 2 G)}{2}", "B F G^{2}"], "srepr_premise_expression": "Add(Mul(Symbol('B', commutative=True), Symbol('G', commutative=True)), Symbol('F', commutative=True))", "srepr_variable": "Symbol('B', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('B', commutative=True), Add(Mul(Symbol('B', commutative=True), Symbol('G', commutative=True)), Mul(Integer(2), Symbol('F', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Mul(Symbol('B', commutative=True), Symbol('G', commutative=True)), Mul(Integer(2), Symbol('F', commutative=True))))", "Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Mul(Integer(2), Symbol('B', commutative=True), Symbol('G', commutative=True)), Symbol('F', commutative=True)))", "Mul(Rational(1, 2), Symbol('B', commutative=True), Add(Mul(Integer(-1), Symbol('B', commutative=True)), Mul(Integer(2), Symbol('F', commutative=True)), Mul(Integer(2), Symbol('G', commutative=True))))", "Mul(Symbol('B', commutative=True), Symbol('F', commutative=True), Pow(Symbol('G', commutative=True), Integer(2)))"]}, {"premise_expression": "\\log{(- Q + k)}", "variable": "k", "positive": "- Q \\log{(- Q + k)} + k \\log{(- Q + k)} - k", "negatives": ["Q \\log{(- Q + k)} - Q - k \\log{(Q - k)}", "Q \\operatorname{Si}{(\\frac{Q}{k})} + k \\cos{(\\frac{Q}{k})}", "k (- Q + \\log{(k)} - 1)", "\\frac{k (- k + 2 \\log{(Q)})}{2}"], "srepr_premise_expression": "log(Add(Mul(Integer(-1), Symbol('Q', commutative=True)), Symbol('k', commutative=True)))", "srepr_variable": "Symbol('k', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('Q', commutative=True), log(Add(Mul(Integer(-1), Symbol('Q', commutative=True)), Symbol('k', commutative=True)))), Mul(Symbol('k', commutative=True), log(Add(Mul(Integer(-1), Symbol('Q', commutative=True)), Symbol('k', commutative=True)))), Mul(Integer(-1), Symbol('k', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('Q', commutative=True), log(Add(Mul(Integer(-1), Symbol('Q', commutative=True)), Symbol('k', commutative=True)))), Mul(Integer(-1), Symbol('Q', commutative=True)), Mul(Integer(-1), Symbol('k', commutative=True), log(Add(Symbol('Q', commutative=True), Mul(Integer(-1), Symbol('k', commutative=True))))))", "Add(Mul(Symbol('Q', commutative=True), Si(Mul(Symbol('Q', commutative=True), Pow(Symbol('k', commutative=True), Integer(-1))))), Mul(Symbol('k', commutative=True), cos(Mul(Symbol('Q', commutative=True), Pow(Symbol('k', commutative=True), Integer(-1))))))", "Mul(Symbol('k', commutative=True), Add(Mul(Integer(-1), Symbol('Q', commutative=True)), log(Symbol('k', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('k', commutative=True), Add(Mul(Integer(-1), Symbol('k', commutative=True)), Mul(Integer(2), log(Symbol('Q', commutative=True)))))"]}, {"premise_expression": "\\log{(- o + r)}", "variable": "r", "positive": "- o \\log{(- o + r)} + r \\log{(- o + r)} - r", "negatives": ["o \\log{(- o + r)} - o - r \\log{(o - r)}", "o \\operatorname{Si}{(\\frac{o}{r})} + r \\cos{(\\frac{o}{r})}", "\\frac{r (- r + 2 \\log{(o)})}{2}", "r (\\log{(\\frac{r}{o})} - 1)"], "srepr_premise_expression": "log(Add(Mul(Integer(-1), Symbol('o', commutative=True)), Symbol('r', commutative=True)))", "srepr_variable": "Symbol('r', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('o', commutative=True), log(Add(Mul(Integer(-1), Symbol('o', commutative=True)), Symbol('r', commutative=True)))), Mul(Symbol('r', commutative=True), log(Add(Mul(Integer(-1), Symbol('o', commutative=True)), Symbol('r', commutative=True)))), Mul(Integer(-1), Symbol('r', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('o', commutative=True), log(Add(Mul(Integer(-1), Symbol('o', commutative=True)), Symbol('r', commutative=True)))), Mul(Integer(-1), Symbol('o', commutative=True)), Mul(Integer(-1), Symbol('r', commutative=True), log(Add(Symbol('o', commutative=True), Mul(Integer(-1), Symbol('r', commutative=True))))))", "Add(Mul(Symbol('o', commutative=True), Si(Mul(Symbol('o', commutative=True), Pow(Symbol('r', commutative=True), Integer(-1))))), Mul(Symbol('r', commutative=True), cos(Mul(Symbol('o', commutative=True), Pow(Symbol('r', commutative=True), Integer(-1))))))", "Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(-1), Symbol('r', commutative=True)), Mul(Integer(2), log(Symbol('o', commutative=True)))))", "Mul(Symbol('r', commutative=True), Add(log(Mul(Pow(Symbol('o', commutative=True), Integer(-1)), Symbol('r', commutative=True))), Integer(-1)))"]}, {"premise_expression": "o + \\cos{(g)}", "variable": "o", "positive": "\\frac{o (o + 2 \\cos{(g)})}{2}", "negatives": ["\\frac{o (o + 2 \\log{(g)})}{2}", "g o + \\sin{(g)}", "\\frac{o (2 g + o)}{2}", "- g \\cos{(o)}"], "srepr_premise_expression": "Add(Symbol('o', commutative=True), cos(Symbol('g', commutative=True)))", "srepr_variable": "Symbol('o', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Symbol('o', commutative=True), Mul(Integer(2), cos(Symbol('g', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Symbol('o', commutative=True), Mul(Integer(2), log(Symbol('g', commutative=True)))))", "Add(Mul(Symbol('g', commutative=True), Symbol('o', commutative=True)), sin(Symbol('g', commutative=True)))", "Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Mul(Integer(2), Symbol('g', commutative=True)), Symbol('o', commutative=True)))", "Mul(Integer(-1), Symbol('g', commutative=True), cos(Symbol('o', commutative=True)))"]}, {"premise_expression": "x (Q - z)", "variable": "Q", "positive": "\\frac{Q x (Q - 2 z)}{2}", "negatives": ["\\frac{Q x (Q + 2 z)}{2}", "\\frac{Q x (Q + 2 x)}{2}", "\\frac{x^{2} (Q - z)}{2}", "\\frac{x z (2 Q - z)}{2}"], "srepr_premise_expression": "Mul(Symbol('x', commutative=True), Add(Symbol('Q', commutative=True), Mul(Integer(-1), Symbol('z', commutative=True))))", "srepr_variable": "Symbol('Q', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('Q', commutative=True), Symbol('x', commutative=True), Add(Symbol('Q', commutative=True), Mul(Integer(-1), Integer(2), Symbol('z', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('Q', commutative=True), Symbol('x', commutative=True), Add(Symbol('Q', commutative=True), Mul(Integer(2), Symbol('z', commutative=True))))", "Mul(Rational(1, 2), Symbol('Q', commutative=True), Symbol('x', commutative=True), Add(Symbol('Q', commutative=True), Mul(Integer(2), Symbol('x', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('x', commutative=True), Integer(2)), Add(Symbol('Q', commutative=True), Mul(Integer(-1), Symbol('z', commutative=True))))", "Mul(Rational(1, 2), Symbol('x', commutative=True), Symbol('z', commutative=True), Add(Mul(Integer(2), Symbol('Q', commutative=True)), Mul(Integer(-1), Symbol('z', commutative=True))))"]}, {"premise_expression": "J j", "variable": "j", "positive": "\\frac{J j^{2}}{2}", "negatives": ["\\frac{J^{2} j}{2}", "\\frac{j^{2}}{2 J}", "J e^{j}", "\\frac{j (2 J - j)}{2}"], "srepr_premise_expression": "Mul(Symbol('J', commutative=True), Symbol('j', commutative=True))", "srepr_variable": "Symbol('j', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('J', commutative=True), Pow(Symbol('j', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('J', commutative=True), Integer(2)), Symbol('j', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('J', commutative=True), Integer(-1)), Pow(Symbol('j', commutative=True), Integer(2)))", "Mul(Symbol('J', commutative=True), exp(Symbol('j', commutative=True)))", "Mul(Rational(1, 2), Symbol('j', commutative=True), Add(Mul(Integer(2), Symbol('J', commutative=True)), Mul(Integer(-1), Symbol('j', commutative=True))))"]}, {"premise_expression": "C J", "variable": "C", "positive": "\\frac{C^{2} J}{2}", "negatives": ["\\frac{C J^{2}}{2}", "J \\log{(C)}", "- \\frac{\\cos{(C)}}{J}", "C J - \\cos{(C)}"], "srepr_premise_expression": "Mul(Symbol('C', commutative=True), Symbol('J', commutative=True))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2)), Symbol('J', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('C', commutative=True), Pow(Symbol('J', commutative=True), Integer(2)))", "Mul(Symbol('J', commutative=True), log(Symbol('C', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('J', commutative=True), Integer(-1)), cos(Symbol('C', commutative=True)))", "Add(Mul(Symbol('C', commutative=True), Symbol('J', commutative=True)), Mul(Integer(-1), cos(Symbol('C', commutative=True))))"]}, {"premise_expression": "\\sin{(\\frac{V}{A})}", "variable": "A", "positive": "A \\sin{(\\frac{V}{A})} - \\frac{V \\log{(\\frac{V^{2}}{A^{2}})}}{2} + V \\log{(\\frac{V}{A})} - V \\operatorname{Ci}{(\\frac{V}{A})}", "negatives": ["A \\log{(- A + V)} - A - V \\log{(A - V)}", "\\frac{A (- A + 2 \\log{(V)})}{2}", "\\frac{A (- A + 2 \\cos{(V)})}{2}", "\\frac{A (A + 2 \\sin{(V)})}{2}"], "srepr_premise_expression": "sin(Mul(Pow(Symbol('A', commutative=True), Integer(-1)), Symbol('V', commutative=True)))", "srepr_variable": "Symbol('A', commutative=True)", "srepr_positive": "Add(Mul(Symbol('A', commutative=True), sin(Mul(Pow(Symbol('A', commutative=True), Integer(-1)), Symbol('V', commutative=True)))), Mul(Integer(-1), Rational(1, 2), Symbol('V', commutative=True), log(Mul(Pow(Symbol('A', commutative=True), Integer(-2)), Pow(Symbol('V', commutative=True), Integer(2))))), Mul(Symbol('V', commutative=True), log(Mul(Pow(Symbol('A', commutative=True), Integer(-1)), Symbol('V', commutative=True)))), Mul(Integer(-1), Symbol('V', commutative=True), Ci(Mul(Pow(Symbol('A', commutative=True), Integer(-1)), Symbol('V', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('A', commutative=True), log(Add(Mul(Integer(-1), Symbol('A', commutative=True)), Symbol('V', commutative=True)))), Mul(Integer(-1), Symbol('A', commutative=True)), Mul(Integer(-1), Symbol('V', commutative=True), log(Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('V', commutative=True))))))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Mul(Integer(-1), Symbol('A', commutative=True)), Mul(Integer(2), log(Symbol('V', commutative=True)))))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Mul(Integer(-1), Symbol('A', commutative=True)), Mul(Integer(2), cos(Symbol('V', commutative=True)))))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Symbol('A', commutative=True), Mul(Integer(2), sin(Symbol('V', commutative=True)))))"]}, {"premise_expression": "\\frac{e^{N}}{Y}", "variable": "Y", "positive": "e^{N} \\log{(Y)}", "negatives": ["N Y + e^{Y}", "- N Y + e^{Y}", "- \\cos{(N + Y)}", "Y (N + \\log{(Y)} - 1)"], "srepr_premise_expression": "Mul(Pow(Symbol('Y', commutative=True), Integer(-1)), exp(Symbol('N', commutative=True)))", "srepr_variable": "Symbol('Y', commutative=True)", "srepr_positive": "Mul(exp(Symbol('N', commutative=True)), log(Symbol('Y', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('N', commutative=True), Symbol('Y', commutative=True)), exp(Symbol('Y', commutative=True)))", "Add(Mul(Integer(-1), Symbol('N', commutative=True), Symbol('Y', commutative=True)), exp(Symbol('Y', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('N', commutative=True), Symbol('Y', commutative=True))))", "Mul(Symbol('Y', commutative=True), Add(Symbol('N', commutative=True), log(Symbol('Y', commutative=True)), Integer(-1)))"]}, {"premise_expression": "N + X + Z", "variable": "X", "positive": "X (N + \\frac{X}{2} + Z)", "negatives": ["\\frac{X (2 N - X + 2 Z)}{2}", "\\frac{Z (2 N + 2 X + Z)}{2}", "\\frac{N (N + 2 X + 2 Z)}{2}", "\\frac{X^{2} (N + Z)}{2}"], "srepr_premise_expression": "Add(Symbol('N', commutative=True), Symbol('X', commutative=True), Symbol('Z', commutative=True))", "srepr_variable": "Symbol('X', commutative=True)", "srepr_positive": "Mul(Symbol('X', commutative=True), Add(Symbol('N', commutative=True), Mul(Rational(1, 2), Symbol('X', commutative=True)), Symbol('Z', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('X', commutative=True), Add(Mul(Integer(2), Symbol('N', commutative=True)), Mul(Integer(-1), Symbol('X', commutative=True)), Mul(Integer(2), Symbol('Z', commutative=True))))", "Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Mul(Integer(2), Symbol('N', commutative=True)), Mul(Integer(2), Symbol('X', commutative=True)), Symbol('Z', commutative=True)))", "Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Symbol('N', commutative=True), Mul(Integer(2), Symbol('X', commutative=True)), Mul(Integer(2), Symbol('Z', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('X', commutative=True), Integer(2)), Add(Symbol('N', commutative=True), Symbol('Z', commutative=True)))"]}, {"premise_expression": "P Z z", "variable": "P", "positive": "\\frac{P^{2} Z z}{2}", "negatives": ["\\frac{P Z^{2} z}{2}", "\\frac{P Z z^{2}}{2}", "\\frac{P^{2}}{2 Z z}", "\\frac{P^{2} (- Z + z)}{2}"], "srepr_premise_expression": "Mul(Symbol('P', commutative=True), Symbol('Z', commutative=True), Symbol('z', commutative=True))", "srepr_variable": "Symbol('P', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2)), Symbol('Z', commutative=True), Symbol('z', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('P', commutative=True), Pow(Symbol('Z', commutative=True), Integer(2)), Symbol('z', commutative=True))", "Mul(Rational(1, 2), Symbol('P', commutative=True), Symbol('Z', commutative=True), Pow(Symbol('z', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2)), Pow(Symbol('Z', commutative=True), Integer(-1)), Pow(Symbol('z', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2)), Add(Mul(Integer(-1), Symbol('Z', commutative=True)), Symbol('z', commutative=True)))"]}, {"premise_expression": "\\frac{w}{Q}", "variable": "w", "positive": "\\frac{w^{2}}{2 Q}", "negatives": ["w \\log{(Q)}", "Q e^{\\frac{w}{Q}}", "\\frac{w^{2} \\log{(Q)}}{2}", "\\frac{w^{2} \\sin{(Q)}}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('Q', commutative=True), Integer(-1)), Symbol('w', commutative=True))", "srepr_variable": "Symbol('w', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(-1)), Pow(Symbol('w', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('w', commutative=True), log(Symbol('Q', commutative=True)))", "Mul(Symbol('Q', commutative=True), exp(Mul(Pow(Symbol('Q', commutative=True), Integer(-1)), Symbol('w', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('w', commutative=True), Integer(2)), log(Symbol('Q', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('w', commutative=True), Integer(2)), sin(Symbol('Q', commutative=True)))"]}, {"premise_expression": "B + y", "variable": "y", "positive": "\\frac{y (2 B + y)}{2}", "negatives": ["\\frac{y (2 B - y)}{2}", "\\frac{B (B + 2 y)}{2}", "- \\cos{(B + y)}", "- \\cos{(B - y)}"], "srepr_premise_expression": "Add(Symbol('B', commutative=True), Symbol('y', commutative=True))", "srepr_variable": "Symbol('y', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('y', commutative=True), Add(Mul(Integer(2), Symbol('B', commutative=True)), Symbol('y', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('y', commutative=True), Add(Mul(Integer(2), Symbol('B', commutative=True)), Mul(Integer(-1), Symbol('y', commutative=True))))", "Mul(Rational(1, 2), Symbol('B', commutative=True), Add(Symbol('B', commutative=True), Mul(Integer(2), Symbol('y', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('B', commutative=True), Symbol('y', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('B', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True)))))"]}, {"premise_expression": "\\log{(m^{V})}", "variable": "V", "positive": "\\frac{V^{2} \\log{(m)}}{2}", "negatives": ["\\frac{V^{2} \\sin{(m)}}{2}", "\\frac{V (V + 2 \\log{(m)})}{2}", "V (- V + m)", "\\cos{(V - m)}"], "srepr_premise_expression": "log(Pow(Symbol('m', commutative=True), Symbol('V', commutative=True)))", "srepr_variable": "Symbol('V', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('V', commutative=True), Integer(2)), log(Symbol('m', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('V', commutative=True), Integer(2)), sin(Symbol('m', commutative=True)))", "Mul(Rational(1, 2), Symbol('V', commutative=True), Add(Symbol('V', commutative=True), Mul(Integer(2), log(Symbol('m', commutative=True)))))", "Mul(Symbol('V', commutative=True), Add(Mul(Integer(-1), Symbol('V', commutative=True)), Symbol('m', commutative=True)))", "cos(Add(Symbol('V', commutative=True), Mul(Integer(-1), Symbol('m', commutative=True))))"]}, {"premise_expression": "\\frac{Q}{X f}", "variable": "f", "positive": "\\frac{Q \\log{(f)}}{X}", "negatives": ["\\frac{Q \\log{(X)}}{f}", "Q f + X \\log{(f)}", "\\frac{Q^{X} f^{2}}{2}", "\\frac{Q^{2}}{2 X f}"], "srepr_premise_expression": "Mul(Symbol('Q', commutative=True), Pow(Symbol('X', commutative=True), Integer(-1)), Pow(Symbol('f', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('f', commutative=True)", "srepr_positive": "Mul(Symbol('Q', commutative=True), Pow(Symbol('X', commutative=True), Integer(-1)), log(Symbol('f', commutative=True)))", "srepr_negatives": ["Mul(Symbol('Q', commutative=True), Pow(Symbol('f', commutative=True), Integer(-1)), log(Symbol('X', commutative=True)))", "Add(Mul(Symbol('Q', commutative=True), Symbol('f', commutative=True)), Mul(Symbol('X', commutative=True), log(Symbol('f', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Symbol('X', commutative=True)), Pow(Symbol('f', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(2)), Pow(Symbol('X', commutative=True), Integer(-1)), Pow(Symbol('f', commutative=True), Integer(-1)))"]}, {"premise_expression": "- G + \\cos{(B)}", "variable": "B", "positive": "- B G + \\sin{(B)}", "negatives": ["B G + \\sin{(B)}", "- B G + e^{B}", "B G - \\cos{(B)}", "\\frac{B^{2}}{2 G}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('G', commutative=True)), cos(Symbol('B', commutative=True)))", "srepr_variable": "Symbol('B', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('B', commutative=True), Symbol('G', commutative=True)), sin(Symbol('B', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('B', commutative=True), Symbol('G', commutative=True)), sin(Symbol('B', commutative=True)))", "Add(Mul(Integer(-1), Symbol('B', commutative=True), Symbol('G', commutative=True)), exp(Symbol('B', commutative=True)))", "Add(Mul(Symbol('B', commutative=True), Symbol('G', commutative=True)), Mul(Integer(-1), cos(Symbol('B', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('B', commutative=True), Integer(2)), Pow(Symbol('G', commutative=True), Integer(-1)))"]}, {"premise_expression": "\\log{(n^{v})}", "variable": "v", "positive": "\\frac{v^{2} \\log{(n)}}{2}", "negatives": ["\\frac{v (2 n + v)}{2}", "\\frac{v (v + 2 \\log{(n)})}{2}", "\\frac{v (v + 2 \\sin{(n)})}{2}", "n e^{\\frac{v}{n}}"], "srepr_premise_expression": "log(Pow(Symbol('n', commutative=True), Symbol('v', commutative=True)))", "srepr_variable": "Symbol('v', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('v', commutative=True), Integer(2)), log(Symbol('n', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('v', commutative=True), Add(Mul(Integer(2), Symbol('n', commutative=True)), Symbol('v', commutative=True)))", "Mul(Rational(1, 2), Symbol('v', commutative=True), Add(Symbol('v', commutative=True), Mul(Integer(2), log(Symbol('n', commutative=True)))))", "Mul(Rational(1, 2), Symbol('v', commutative=True), Add(Symbol('v', commutative=True), Mul(Integer(2), sin(Symbol('n', commutative=True)))))", "Mul(Symbol('n', commutative=True), exp(Mul(Pow(Symbol('n', commutative=True), Integer(-1)), Symbol('v', commutative=True))))"]}, {"premise_expression": "\\frac{\\log{(m)}}{T}", "variable": "m", "positive": "\\frac{m (\\log{(m)} - 1)}{T}", "negatives": ["m (T + \\log{(m)} - 1)", "\\log{(T)} \\log{(m)}", "\\sin{(T + m)}", "\\frac{m^{2} \\cos{(T)}}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('T', commutative=True), Integer(-1)), log(Symbol('m', commutative=True)))", "srepr_variable": "Symbol('m', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('T', commutative=True), Integer(-1)), Symbol('m', commutative=True), Add(log(Symbol('m', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('m', commutative=True), Add(Symbol('T', commutative=True), log(Symbol('m', commutative=True)), Integer(-1)))", "Mul(log(Symbol('T', commutative=True)), log(Symbol('m', commutative=True)))", "sin(Add(Symbol('T', commutative=True), Symbol('m', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('m', commutative=True), Integer(2)), cos(Symbol('T', commutative=True)))"]}, {"premise_expression": "B - Y", "variable": "B", "positive": "\\frac{B (B - 2 Y)}{2}", "negatives": ["\\frac{Y (2 B - Y)}{2}", "\\frac{B (B + 2 e^{Y})}{2}", "- \\cos{(B - Y)}", "- \\cos{(B + Y)}"], "srepr_premise_expression": "Add(Symbol('B', commutative=True), Mul(Integer(-1), Symbol('Y', commutative=True)))", "srepr_variable": "Symbol('B', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('B', commutative=True), Add(Symbol('B', commutative=True), Mul(Integer(-1), Integer(2), Symbol('Y', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('Y', commutative=True), Add(Mul(Integer(2), Symbol('B', commutative=True)), Mul(Integer(-1), Symbol('Y', commutative=True))))", "Mul(Rational(1, 2), Symbol('B', commutative=True), Add(Symbol('B', commutative=True), Mul(Integer(2), exp(Symbol('Y', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('B', commutative=True), Mul(Integer(-1), Symbol('Y', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('B', commutative=True), Symbol('Y', commutative=True))))"]}, {"premise_expression": "B + S - l", "variable": "S", "positive": "S (B + \\frac{S}{2} - l)", "negatives": ["\\frac{S (2 B - S + 2 l)}{2}", "\\frac{B (B + 2 S - 2 l)}{2}", "\\frac{l (2 B + 2 S - l)}{2}", "\\frac{B S (S - 2 l)}{2}"], "srepr_premise_expression": "Add(Symbol('B', commutative=True), Symbol('S', commutative=True), Mul(Integer(-1), Symbol('l', commutative=True)))", "srepr_variable": "Symbol('S', commutative=True)", "srepr_positive": "Mul(Symbol('S', commutative=True), Add(Symbol('B', commutative=True), Mul(Rational(1, 2), Symbol('S', commutative=True)), Mul(Integer(-1), Symbol('l', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Mul(Integer(2), Symbol('B', commutative=True)), Mul(Integer(-1), Symbol('S', commutative=True)), Mul(Integer(2), Symbol('l', commutative=True))))", "Mul(Rational(1, 2), Symbol('B', commutative=True), Add(Symbol('B', commutative=True), Mul(Integer(2), Symbol('S', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('l', commutative=True))))", "Mul(Rational(1, 2), Symbol('l', commutative=True), Add(Mul(Integer(2), Symbol('B', commutative=True)), Mul(Integer(2), Symbol('S', commutative=True)), Mul(Integer(-1), Symbol('l', commutative=True))))", "Mul(Rational(1, 2), Symbol('B', commutative=True), Symbol('S', commutative=True), Add(Symbol('S', commutative=True), Mul(Integer(-1), Integer(2), Symbol('l', commutative=True))))"]}, {"premise_expression": "\\frac{\\log{(t)}}{c}", "variable": "t", "positive": "\\frac{t (\\log{(t)} - 1)}{c}", "negatives": ["\\log{(c)} \\log{(t)}", "\\frac{\\sin{(t)}}{c}", "c \\sin{(t)}", "\\sin{(c + t)}"], "srepr_premise_expression": "Mul(Pow(Symbol('c', commutative=True), Integer(-1)), log(Symbol('t', commutative=True)))", "srepr_variable": "Symbol('t', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('c', commutative=True), Integer(-1)), Symbol('t', commutative=True), Add(log(Symbol('t', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(log(Symbol('c', commutative=True)), log(Symbol('t', commutative=True)))", "Mul(Pow(Symbol('c', commutative=True), Integer(-1)), sin(Symbol('t', commutative=True)))", "Mul(Symbol('c', commutative=True), sin(Symbol('t', commutative=True)))", "sin(Add(Symbol('c', commutative=True), Symbol('t', commutative=True)))"]}, {"premise_expression": "- \\sin{(G - M)}", "variable": "M", "positive": "- \\cos{(G - M)}", "negatives": ["\\cos{(G - M)}", "\\sin{(G + M)}", "e^{G + M}", "- G M + \\sin{(M)}"], "srepr_premise_expression": "Mul(Integer(-1), sin(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('M', commutative=True)))))", "srepr_variable": "Symbol('M', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('M', commutative=True)))))", "srepr_negatives": ["cos(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('M', commutative=True))))", "sin(Add(Symbol('G', commutative=True), Symbol('M', commutative=True)))", "exp(Add(Symbol('G', commutative=True), Symbol('M', commutative=True)))", "Add(Mul(Integer(-1), Symbol('G', commutative=True), Symbol('M', commutative=True)), sin(Symbol('M', commutative=True)))"]}, {"premise_expression": "\\log{(V p)}", "variable": "V", "positive": "V (\\log{(V p)} - 1)", "negatives": ["p (\\log{(V p)} - 1)", "V (\\log{(\\frac{V}{p})} - 1)", "\\frac{V (V + 2 p)}{2}", "\\frac{V (V - 2 p)}{2}"], "srepr_premise_expression": "log(Mul(Symbol('V', commutative=True), Symbol('p', commutative=True)))", "srepr_variable": "Symbol('V', commutative=True)", "srepr_positive": "Mul(Symbol('V', commutative=True), Add(log(Mul(Symbol('V', commutative=True), Symbol('p', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('p', commutative=True), Add(log(Mul(Symbol('V', commutative=True), Symbol('p', commutative=True))), Integer(-1)))", "Mul(Symbol('V', commutative=True), Add(log(Mul(Symbol('V', commutative=True), Pow(Symbol('p', commutative=True), Integer(-1)))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('V', commutative=True), Add(Symbol('V', commutative=True), Mul(Integer(2), Symbol('p', commutative=True))))", "Mul(Rational(1, 2), Symbol('V', commutative=True), Add(Symbol('V', commutative=True), Mul(Integer(-1), Integer(2), Symbol('p', commutative=True))))"]}, {"premise_expression": "e^{f + t}", "variable": "t", "positive": "e^{f + t}", "negatives": ["\\log{(f)} \\log{(t)}", "t (f + \\log{(t)} - 1)", "\\frac{t (- t + 2 \\log{(f)})}{2}", "f \\log{(f + t)} + t \\log{(f + t)} - t"], "srepr_premise_expression": "exp(Add(Symbol('f', commutative=True), Symbol('t', commutative=True)))", "srepr_variable": "Symbol('t', commutative=True)", "srepr_positive": "exp(Add(Symbol('f', commutative=True), Symbol('t', commutative=True)))", "srepr_negatives": ["Mul(log(Symbol('f', commutative=True)), log(Symbol('t', commutative=True)))", "Mul(Symbol('t', commutative=True), Add(Symbol('f', commutative=True), log(Symbol('t', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('t', commutative=True), Add(Mul(Integer(-1), Symbol('t', commutative=True)), Mul(Integer(2), log(Symbol('f', commutative=True)))))", "Add(Mul(Symbol('f', commutative=True), log(Add(Symbol('f', commutative=True), Symbol('t', commutative=True)))), Mul(Symbol('t', commutative=True), log(Add(Symbol('f', commutative=True), Symbol('t', commutative=True)))), Mul(Integer(-1), Symbol('t', commutative=True)))"]}, {"premise_expression": "J q v", "variable": "J", "positive": "\\frac{J^{2} q v}{2}", "negatives": ["\\frac{J^{2} q^{v}}{2}", "\\frac{J q^{2} v}{2}", "\\frac{J q v^{2}}{2}", "0^{q} J"], "srepr_premise_expression": "Mul(Symbol('J', commutative=True), Symbol('q', commutative=True), Symbol('v', commutative=True))", "srepr_variable": "Symbol('J', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('J', commutative=True), Integer(2)), Symbol('q', commutative=True), Symbol('v', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('J', commutative=True), Integer(2)), Pow(Symbol('q', commutative=True), Symbol('v', commutative=True)))", "Mul(Rational(1, 2), Symbol('J', commutative=True), Pow(Symbol('q', commutative=True), Integer(2)), Symbol('v', commutative=True))", "Mul(Rational(1, 2), Symbol('J', commutative=True), Symbol('q', commutative=True), Pow(Symbol('v', commutative=True), Integer(2)))", "Mul(Pow(Integer(0), Symbol('q', commutative=True)), Symbol('J', commutative=True))"]}, {"premise_expression": "\\cos{(L - t)}", "variable": "t", "positive": "- \\sin{(L - t)}", "negatives": ["\\sin{(L - t)}", "\\frac{t^{2} (L - 1)}{2}", "e^{L} \\log{(t)}", "t"], "srepr_premise_expression": "cos(Add(Symbol('L', commutative=True), Mul(Integer(-1), Symbol('t', commutative=True))))", "srepr_variable": "Symbol('t', commutative=True)", "srepr_positive": "Mul(Integer(-1), sin(Add(Symbol('L', commutative=True), Mul(Integer(-1), Symbol('t', commutative=True)))))", "srepr_negatives": ["sin(Add(Symbol('L', commutative=True), Mul(Integer(-1), Symbol('t', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('t', commutative=True), Integer(2)), Add(Symbol('L', commutative=True), Integer(-1)))", "Mul(exp(Symbol('L', commutative=True)), log(Symbol('t', commutative=True)))", "Symbol('t', commutative=True)"]}, {"premise_expression": "\\frac{\\sin{(l)}}{U}", "variable": "U", "positive": "\\log{(U)} \\sin{(l)}", "negatives": ["\\log{(U)} \\log{(l)}", "\\cos{(U - l)}", "\\sin{(U - l)}", "l \\log{(U)}"], "srepr_premise_expression": "Mul(Pow(Symbol('U', commutative=True), Integer(-1)), sin(Symbol('l', commutative=True)))", "srepr_variable": "Symbol('U', commutative=True)", "srepr_positive": "Mul(log(Symbol('U', commutative=True)), sin(Symbol('l', commutative=True)))", "srepr_negatives": ["Mul(log(Symbol('U', commutative=True)), log(Symbol('l', commutative=True)))", "cos(Add(Symbol('U', commutative=True), Mul(Integer(-1), Symbol('l', commutative=True))))", "sin(Add(Symbol('U', commutative=True), Mul(Integer(-1), Symbol('l', commutative=True))))", "Mul(Symbol('l', commutative=True), log(Symbol('U', commutative=True)))"]}, {"premise_expression": "\\sin^{J}{(u)}", "variable": "u", "positive": "\\int \\sin^{J}{(u)} du", "negatives": ["u (\\log{(u^{2})} - 2)", "- \\cos{(J + u)}", "- \\cos{(J - u)}", "u (- J + \\log{(u)} - 1)"], "srepr_premise_expression": "Pow(sin(Symbol('u', commutative=True)), Symbol('J', commutative=True))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "Integral(Pow(sin(Symbol('u', commutative=True)), Symbol('J', commutative=True)), Tuple(Symbol('u', commutative=True)))", "srepr_negatives": ["Mul(Symbol('u', commutative=True), Add(log(Pow(Symbol('u', commutative=True), Integer(2))), Integer(-2)))", "Mul(Integer(-1), cos(Add(Symbol('J', commutative=True), Symbol('u', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('J', commutative=True), Mul(Integer(-1), Symbol('u', commutative=True)))))", "Mul(Symbol('u', commutative=True), Add(Mul(Integer(-1), Symbol('J', commutative=True)), log(Symbol('u', commutative=True)), Integer(-1)))"]}, {"premise_expression": "2 P - p", "variable": "p", "positive": "\\frac{p (4 P - p)}{2}", "negatives": ["P (P - p)", "- P \\cos{(p)}", "\\frac{p^{2}}{2 P}", "P e^{\\frac{p}{P}}"], "srepr_premise_expression": "Add(Mul(Integer(2), Symbol('P', commutative=True)), Mul(Integer(-1), Symbol('p', commutative=True)))", "srepr_variable": "Symbol('p', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Mul(Integer(4), Symbol('P', commutative=True)), Mul(Integer(-1), Symbol('p', commutative=True))))", "srepr_negatives": ["Mul(Symbol('P', commutative=True), Add(Symbol('P', commutative=True), Mul(Integer(-1), Symbol('p', commutative=True))))", "Mul(Integer(-1), Symbol('P', commutative=True), cos(Symbol('p', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(-1)), Pow(Symbol('p', commutative=True), Integer(2)))", "Mul(Symbol('P', commutative=True), exp(Mul(Pow(Symbol('P', commutative=True), Integer(-1)), Symbol('p', commutative=True))))"]}, {"premise_expression": "\\frac{L}{g t}", "variable": "g", "positive": "\\frac{L \\log{(g)}}{t}", "negatives": ["\\frac{L \\log{(t)}}{g}", "\\frac{L^{2}}{2 g t}", "(L + t) \\log{(g)}", "\\frac{g^{2} t}{2 L}"], "srepr_premise_expression": "Mul(Symbol('L', commutative=True), Pow(Symbol('g', commutative=True), Integer(-1)), Pow(Symbol('t', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('g', commutative=True)", "srepr_positive": "Mul(Symbol('L', commutative=True), Pow(Symbol('t', commutative=True), Integer(-1)), log(Symbol('g', commutative=True)))", "srepr_negatives": ["Mul(Symbol('L', commutative=True), Pow(Symbol('g', commutative=True), Integer(-1)), log(Symbol('t', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(2)), Pow(Symbol('g', commutative=True), Integer(-1)), Pow(Symbol('t', commutative=True), Integer(-1)))", "Mul(Add(Symbol('L', commutative=True), Symbol('t', commutative=True)), log(Symbol('g', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(-1)), Pow(Symbol('g', commutative=True), Integer(2)), Symbol('t', commutative=True))"]}, {"premise_expression": "\\frac{C}{u}", "variable": "C", "positive": "\\frac{C^{2}}{2 u}", "negatives": ["C \\log{(u)}", "u \\sin{(C)}", "\\frac{C (C - 2 u)}{2}", "\\sin{(C - u)}"], "srepr_premise_expression": "Mul(Symbol('C', commutative=True), Pow(Symbol('u', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2)), Pow(Symbol('u', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('C', commutative=True), log(Symbol('u', commutative=True)))", "Mul(Symbol('u', commutative=True), sin(Symbol('C', commutative=True)))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Symbol('C', commutative=True), Mul(Integer(-1), Integer(2), Symbol('u', commutative=True))))", "sin(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('u', commutative=True))))"]}, {"premise_expression": "t + \\sin{(b)}", "variable": "b", "positive": "b t - \\cos{(b)}", "negatives": ["b t + e^{b}", "\\frac{b (b + 2 t)}{2}", "\\frac{t (t + 2 \\sin{(b)})}{2}", "\\frac{b^{2} t}{2}"], "srepr_premise_expression": "Add(Symbol('t', commutative=True), sin(Symbol('b', commutative=True)))", "srepr_variable": "Symbol('b', commutative=True)", "srepr_positive": "Add(Mul(Symbol('b', commutative=True), Symbol('t', commutative=True)), Mul(Integer(-1), cos(Symbol('b', commutative=True))))", "srepr_negatives": ["Add(Mul(Symbol('b', commutative=True), Symbol('t', commutative=True)), exp(Symbol('b', commutative=True)))", "Mul(Rational(1, 2), Symbol('b', commutative=True), Add(Symbol('b', commutative=True), Mul(Integer(2), Symbol('t', commutative=True))))", "Mul(Rational(1, 2), Symbol('t', commutative=True), Add(Symbol('t', commutative=True), Mul(Integer(2), sin(Symbol('b', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('b', commutative=True), Integer(2)), Symbol('t', commutative=True))"]}, {"premise_expression": "\\sin{(Q - Z)}", "variable": "Z", "positive": "\\cos{(Q - Z)}", "negatives": ["- \\cos{(Q - Z)}", "- e^{Q - Z}", "\\frac{Z (2 Q + Z)}{2}", "\\log{(Q)} \\log{(Z)}"], "srepr_premise_expression": "sin(Add(Symbol('Q', commutative=True), Mul(Integer(-1), Symbol('Z', commutative=True))))", "srepr_variable": "Symbol('Z', commutative=True)", "srepr_positive": "cos(Add(Symbol('Q', commutative=True), Mul(Integer(-1), Symbol('Z', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('Q', commutative=True), Mul(Integer(-1), Symbol('Z', commutative=True)))))", "Mul(Integer(-1), exp(Add(Symbol('Q', commutative=True), Mul(Integer(-1), Symbol('Z', commutative=True)))))", "Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Mul(Integer(2), Symbol('Q', commutative=True)), Symbol('Z', commutative=True)))", "Mul(log(Symbol('Q', commutative=True)), log(Symbol('Z', commutative=True)))"]}, {"premise_expression": "\\cos{(S - Y)}", "variable": "Y", "positive": "- \\sin{(S - Y)}", "negatives": ["\\sin{(S - Y)}", "\\frac{\\sin{(Y)}}{S}", "- S Y + \\sin{(Y)}", "\\frac{S Y^{2}}{2}"], "srepr_premise_expression": "cos(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('Y', commutative=True))))", "srepr_variable": "Symbol('Y', commutative=True)", "srepr_positive": "Mul(Integer(-1), sin(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('Y', commutative=True)))))", "srepr_negatives": ["sin(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('Y', commutative=True))))", "Mul(Pow(Symbol('S', commutative=True), Integer(-1)), sin(Symbol('Y', commutative=True)))", "Add(Mul(Integer(-1), Symbol('S', commutative=True), Symbol('Y', commutative=True)), sin(Symbol('Y', commutative=True)))", "Mul(Rational(1, 2), Symbol('S', commutative=True), Pow(Symbol('Y', commutative=True), Integer(2)))"]}, {"premise_expression": "\\frac{H}{p}", "variable": "p", "positive": "H \\log{(p)}", "negatives": ["\\frac{H^{2}}{2 p}", "H p + \\sin{(p)}", "\\frac{p^{2} \\log{(H)}}{2}", "- \\cos{(H + p)}"], "srepr_premise_expression": "Mul(Symbol('H', commutative=True), Pow(Symbol('p', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('p', commutative=True)", "srepr_positive": "Mul(Symbol('H', commutative=True), log(Symbol('p', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('H', commutative=True), Integer(2)), Pow(Symbol('p', commutative=True), Integer(-1)))", "Add(Mul(Symbol('H', commutative=True), Symbol('p', commutative=True)), sin(Symbol('p', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('p', commutative=True), Integer(2)), log(Symbol('H', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('H', commutative=True), Symbol('p', commutative=True))))"]}, {"premise_expression": "\\log{(- R + a)}", "variable": "a", "positive": "- R \\log{(- R + a)} + a \\log{(- R + a)} - a", "negatives": ["R \\log{(- R + a)} - R - a \\log{(R - a)}", "- R \\operatorname{Ei}{(\\frac{R}{a})} + a e^{\\frac{R}{a}}", "e^{- R + a}", "\\int \\sin^{R}{(a)} da"], "srepr_premise_expression": "log(Add(Mul(Integer(-1), Symbol('R', commutative=True)), Symbol('a', commutative=True)))", "srepr_variable": "Symbol('a', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('R', commutative=True), log(Add(Mul(Integer(-1), Symbol('R', commutative=True)), Symbol('a', commutative=True)))), Mul(Symbol('a', commutative=True), log(Add(Mul(Integer(-1), Symbol('R', commutative=True)), Symbol('a', commutative=True)))), Mul(Integer(-1), Symbol('a', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('R', commutative=True), log(Add(Mul(Integer(-1), Symbol('R', commutative=True)), Symbol('a', commutative=True)))), Mul(Integer(-1), Symbol('R', commutative=True)), Mul(Integer(-1), Symbol('a', commutative=True), log(Add(Symbol('R', commutative=True), Mul(Integer(-1), Symbol('a', commutative=True))))))", "Add(Mul(Integer(-1), Symbol('R', commutative=True), Ei(Mul(Symbol('R', commutative=True), Pow(Symbol('a', commutative=True), Integer(-1))))), Mul(Symbol('a', commutative=True), exp(Mul(Symbol('R', commutative=True), Pow(Symbol('a', commutative=True), Integer(-1))))))", "exp(Add(Mul(Integer(-1), Symbol('R', commutative=True)), Symbol('a', commutative=True)))", "Integral(Pow(sin(Symbol('a', commutative=True)), Symbol('R', commutative=True)), Tuple(Symbol('a', commutative=True)))"]}, {"premise_expression": "e^{- S + Z}", "variable": "S", "positive": "- e^{- S + Z}", "negatives": ["e^{- S + Z}", "e^{Z} \\log{(S)}", "\\frac{S (S - 2 Z)}{2}", "Z \\log{(S)}"], "srepr_premise_expression": "exp(Add(Mul(Integer(-1), Symbol('S', commutative=True)), Symbol('Z', commutative=True)))", "srepr_variable": "Symbol('S', commutative=True)", "srepr_positive": "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('S', commutative=True)), Symbol('Z', commutative=True))))", "srepr_negatives": ["exp(Add(Mul(Integer(-1), Symbol('S', commutative=True)), Symbol('Z', commutative=True)))", "Mul(exp(Symbol('Z', commutative=True)), log(Symbol('S', commutative=True)))", "Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Symbol('S', commutative=True), Mul(Integer(-1), Integer(2), Symbol('Z', commutative=True))))", "Mul(Symbol('Z', commutative=True), log(Symbol('S', commutative=True)))"]}, {"premise_expression": "t + \\cos{(M)}", "variable": "M", "positive": "M t + \\sin{(M)}", "negatives": ["\\log{(M)} \\sin{(t)}", "M (t + \\log{(M)} - 1)", "\\frac{M (- M + 2 t)}{2}", "\\frac{M (- M + 2 \\sin{(t)})}{2}"], "srepr_premise_expression": "Add(Symbol('t', commutative=True), cos(Symbol('M', commutative=True)))", "srepr_variable": "Symbol('M', commutative=True)", "srepr_positive": "Add(Mul(Symbol('M', commutative=True), Symbol('t', commutative=True)), sin(Symbol('M', commutative=True)))", "srepr_negatives": ["Mul(log(Symbol('M', commutative=True)), sin(Symbol('t', commutative=True)))", "Mul(Symbol('M', commutative=True), Add(Symbol('t', commutative=True), log(Symbol('M', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('M', commutative=True), Add(Mul(Integer(-1), Symbol('M', commutative=True)), Mul(Integer(2), Symbol('t', commutative=True))))", "Mul(Rational(1, 2), Symbol('M', commutative=True), Add(Mul(Integer(-1), Symbol('M', commutative=True)), Mul(Integer(2), sin(Symbol('t', commutative=True)))))"]}, {"premise_expression": "I - t", "variable": "I", "positive": "\\frac{I (I - 2 t)}{2}", "negatives": ["\\frac{I (I + 2 t)}{2}", "\\frac{t (2 I - t)}{2}", "\\frac{I^{2} t}{2}", "\\frac{I^{2}}{2 t}"], "srepr_premise_expression": "Add(Symbol('I', commutative=True), Mul(Integer(-1), Symbol('t', commutative=True)))", "srepr_variable": "Symbol('I', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('I', commutative=True), Add(Symbol('I', commutative=True), Mul(Integer(-1), Integer(2), Symbol('t', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('I', commutative=True), Add(Symbol('I', commutative=True), Mul(Integer(2), Symbol('t', commutative=True))))", "Mul(Rational(1, 2), Symbol('t', commutative=True), Add(Mul(Integer(2), Symbol('I', commutative=True)), Mul(Integer(-1), Symbol('t', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(2)), Symbol('t', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(2)), Pow(Symbol('t', commutative=True), Integer(-1)))"]}, {"premise_expression": "b v", "variable": "v", "positive": "\\frac{b v^{2}}{2}", "negatives": ["\\frac{b^{2} v}{2}", "b v \\log{(b)}", "v e^{b^{b}}", "\\frac{v^{2} \\log{(b)}}{2}"], "srepr_premise_expression": "Mul(Symbol('b', commutative=True), Symbol('v', commutative=True))", "srepr_variable": "Symbol('v', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('b', commutative=True), Pow(Symbol('v', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('b', commutative=True), Integer(2)), Symbol('v', commutative=True))", "Mul(Symbol('b', commutative=True), Symbol('v', commutative=True), log(Symbol('b', commutative=True)))", "Mul(Symbol('v', commutative=True), exp(Pow(Symbol('b', commutative=True), Symbol('b', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('v', commutative=True), Integer(2)), log(Symbol('b', commutative=True)))"]}, {"premise_expression": "E + L", "variable": "E", "positive": "\\frac{E (E + 2 L)}{2}", "negatives": ["\\frac{L (2 E + L)}{2}", "\\frac{E^{2} \\sin{(L)}}{2}", "- E L + e^{E}", "L e^{\\frac{E}{L}}"], "srepr_premise_expression": "Add(Symbol('E', commutative=True), Symbol('L', commutative=True))", "srepr_variable": "Symbol('E', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('E', commutative=True), Add(Symbol('E', commutative=True), Mul(Integer(2), Symbol('L', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Mul(Integer(2), Symbol('E', commutative=True)), Symbol('L', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('E', commutative=True), Integer(2)), sin(Symbol('L', commutative=True)))", "Add(Mul(Integer(-1), Symbol('E', commutative=True), Symbol('L', commutative=True)), exp(Symbol('E', commutative=True)))", "Mul(Symbol('L', commutative=True), exp(Mul(Symbol('E', commutative=True), Pow(Symbol('L', commutative=True), Integer(-1)))))"]}, {"premise_expression": "g \\cos{(f)}", "variable": "g", "positive": "\\frac{g^{2} \\cos{(f)}}{2}", "negatives": ["\\frac{g^{2} \\log{(f)}}{2}", "\\frac{g (2 f - g)}{2}", "- f \\cos{(g)}", "g \\sin{(f)}"], "srepr_premise_expression": "Mul(Symbol('g', commutative=True), cos(Symbol('f', commutative=True)))", "srepr_variable": "Symbol('g', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('g', commutative=True), Integer(2)), cos(Symbol('f', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('g', commutative=True), Integer(2)), log(Symbol('f', commutative=True)))", "Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Mul(Integer(2), Symbol('f', commutative=True)), Mul(Integer(-1), Symbol('g', commutative=True))))", "Mul(Integer(-1), Symbol('f', commutative=True), cos(Symbol('g', commutative=True)))", "Mul(Symbol('g', commutative=True), sin(Symbol('f', commutative=True)))"]}, {"premise_expression": "v e^{V}", "variable": "V", "positive": "v e^{V}", "negatives": ["\\frac{v^{2} e^{V}}{2}", "V e^{v^{v}}", "V v + \\sin{(V)}", "V v - \\cos{(V)}"], "srepr_premise_expression": "Mul(Symbol('v', commutative=True), exp(Symbol('V', commutative=True)))", "srepr_variable": "Symbol('V', commutative=True)", "srepr_positive": "Mul(Symbol('v', commutative=True), exp(Symbol('V', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('v', commutative=True), Integer(2)), exp(Symbol('V', commutative=True)))", "Mul(Symbol('V', commutative=True), exp(Pow(Symbol('v', commutative=True), Symbol('v', commutative=True))))", "Add(Mul(Symbol('V', commutative=True), Symbol('v', commutative=True)), sin(Symbol('V', commutative=True)))", "Add(Mul(Symbol('V', commutative=True), Symbol('v', commutative=True)), Mul(Integer(-1), cos(Symbol('V', commutative=True))))"]}, {"premise_expression": "P + \\log{(o)}", "variable": "o", "positive": "o (P + \\log{(o)} - 1)", "negatives": ["\\frac{P (P + 2 \\log{(o)})}{2}", "\\frac{o^{2} \\log{(P)}}{2}", "e^{P} \\log{(o)}", "\\frac{o (2 P - o)}{2}"], "srepr_premise_expression": "Add(Symbol('P', commutative=True), log(Symbol('o', commutative=True)))", "srepr_variable": "Symbol('o', commutative=True)", "srepr_positive": "Mul(Symbol('o', commutative=True), Add(Symbol('P', commutative=True), log(Symbol('o', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Symbol('P', commutative=True), Mul(Integer(2), log(Symbol('o', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('o', commutative=True), Integer(2)), log(Symbol('P', commutative=True)))", "Mul(exp(Symbol('P', commutative=True)), log(Symbol('o', commutative=True)))", "Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Mul(Integer(2), Symbol('P', commutative=True)), Mul(Integer(-1), Symbol('o', commutative=True))))"]}, {"premise_expression": "P t", "variable": "t", "positive": "\\frac{P t^{2}}{2}", "negatives": ["\\frac{P^{2} t}{2}", "- \\frac{\\cos{(t)}}{P}", "\\frac{t^{2} e^{P}}{2}", "e^{P + t}"], "srepr_premise_expression": "Mul(Symbol('P', commutative=True), Symbol('t', commutative=True))", "srepr_variable": "Symbol('t', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('P', commutative=True), Pow(Symbol('t', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2)), Symbol('t', commutative=True))", "Mul(Integer(-1), Pow(Symbol('P', commutative=True), Integer(-1)), cos(Symbol('t', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('t', commutative=True), Integer(2)), exp(Symbol('P', commutative=True)))", "exp(Add(Symbol('P', commutative=True), Symbol('t', commutative=True)))"]}, {"premise_expression": "j e^{T}", "variable": "T", "positive": "j e^{T}", "negatives": ["\\frac{j^{2} e^{T}}{2}", "- \\frac{\\cos{(T)}}{j}", "- T j + \\sin{(T)}", "\\frac{T^{2} \\log{(j)}}{2}"], "srepr_premise_expression": "Mul(Symbol('j', commutative=True), exp(Symbol('T', commutative=True)))", "srepr_variable": "Symbol('T', commutative=True)", "srepr_positive": "Mul(Symbol('j', commutative=True), exp(Symbol('T', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('j', commutative=True), Integer(2)), exp(Symbol('T', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('j', commutative=True), Integer(-1)), cos(Symbol('T', commutative=True)))", "Add(Mul(Integer(-1), Symbol('T', commutative=True), Symbol('j', commutative=True)), sin(Symbol('T', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('T', commutative=True), Integer(2)), log(Symbol('j', commutative=True)))"]}, {"premise_expression": "D - y", "variable": "y", "positive": "\\frac{y (2 D - y)}{2}", "negatives": ["\\frac{D (D - 2 y)}{2}", "\\frac{y^{2} \\log{(D)}}{2}", "- \\cos{(D + y)}", "D \\sin{(y)}"], "srepr_premise_expression": "Add(Symbol('D', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True)))", "srepr_variable": "Symbol('y', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('y', commutative=True), Add(Mul(Integer(2), Symbol('D', commutative=True)), Mul(Integer(-1), Symbol('y', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('D', commutative=True), Add(Symbol('D', commutative=True), Mul(Integer(-1), Integer(2), Symbol('y', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('y', commutative=True), Integer(2)), log(Symbol('D', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('D', commutative=True), Symbol('y', commutative=True))))", "Mul(Symbol('D', commutative=True), sin(Symbol('y', commutative=True)))"]}, {"premise_expression": "\\log{(I + X)}", "variable": "X", "positive": "I \\log{(I + X)} + X \\log{(I + X)} - X", "negatives": ["- I \\log{(- I + X)} + X \\log{(- I + X)} - X", "I \\log{(I + X)} - I + X \\log{(I + X)}", "- I \\operatorname{Ei}{(\\frac{I}{X})} + X e^{\\frac{I}{X}}", "X (- I + \\log{(X)} - 1)"], "srepr_premise_expression": "log(Add(Symbol('I', commutative=True), Symbol('X', commutative=True)))", "srepr_variable": "Symbol('X', commutative=True)", "srepr_positive": "Add(Mul(Symbol('I', commutative=True), log(Add(Symbol('I', commutative=True), Symbol('X', commutative=True)))), Mul(Symbol('X', commutative=True), log(Add(Symbol('I', commutative=True), Symbol('X', commutative=True)))), Mul(Integer(-1), Symbol('X', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('I', commutative=True), log(Add(Mul(Integer(-1), Symbol('I', commutative=True)), Symbol('X', commutative=True)))), Mul(Symbol('X', commutative=True), log(Add(Mul(Integer(-1), Symbol('I', commutative=True)), Symbol('X', commutative=True)))), Mul(Integer(-1), Symbol('X', commutative=True)))", "Add(Mul(Symbol('I', commutative=True), log(Add(Symbol('I', commutative=True), Symbol('X', commutative=True)))), Mul(Integer(-1), Symbol('I', commutative=True)), Mul(Symbol('X', commutative=True), log(Add(Symbol('I', commutative=True), Symbol('X', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('I', commutative=True), Ei(Mul(Symbol('I', commutative=True), Pow(Symbol('X', commutative=True), Integer(-1))))), Mul(Symbol('X', commutative=True), exp(Mul(Symbol('I', commutative=True), Pow(Symbol('X', commutative=True), Integer(-1))))))", "Mul(Symbol('X', commutative=True), Add(Mul(Integer(-1), Symbol('I', commutative=True)), log(Symbol('X', commutative=True)), Integer(-1)))"]}, {"premise_expression": "l + e^{F}", "variable": "F", "positive": "F l + e^{F}", "negatives": ["\\frac{l (l + 2 e^{F})}{2}", "F \\cos{(l^{l})}", "e^{l} \\log{(F)}", "\\sin{(F - l)}"], "srepr_premise_expression": "Add(Symbol('l', commutative=True), exp(Symbol('F', commutative=True)))", "srepr_variable": "Symbol('F', commutative=True)", "srepr_positive": "Add(Mul(Symbol('F', commutative=True), Symbol('l', commutative=True)), exp(Symbol('F', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('l', commutative=True), Add(Symbol('l', commutative=True), Mul(Integer(2), exp(Symbol('F', commutative=True)))))", "Mul(Symbol('F', commutative=True), cos(Pow(Symbol('l', commutative=True), Symbol('l', commutative=True))))", "Mul(exp(Symbol('l', commutative=True)), log(Symbol('F', commutative=True)))", "sin(Add(Symbol('F', commutative=True), Mul(Integer(-1), Symbol('l', commutative=True))))"]}, {"premise_expression": "\\frac{\\cos{(g)}}{n}", "variable": "g", "positive": "\\frac{\\sin{(g)}}{n}", "negatives": ["e^{g + n}", "\\log{(g)} \\log{(n)}", "\\log{(n)} \\cos{(g)}", "\\frac{g (\\log{(g)} - 1)}{n}"], "srepr_premise_expression": "Mul(Pow(Symbol('n', commutative=True), Integer(-1)), cos(Symbol('g', commutative=True)))", "srepr_variable": "Symbol('g', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('n', commutative=True), Integer(-1)), sin(Symbol('g', commutative=True)))", "srepr_negatives": ["exp(Add(Symbol('g', commutative=True), Symbol('n', commutative=True)))", "Mul(log(Symbol('g', commutative=True)), log(Symbol('n', commutative=True)))", "Mul(log(Symbol('n', commutative=True)), cos(Symbol('g', commutative=True)))", "Mul(Symbol('g', commutative=True), Pow(Symbol('n', commutative=True), Integer(-1)), Add(log(Symbol('g', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\sin{(P - l)}", "variable": "P", "positive": "- \\cos{(P - l)}", "negatives": ["\\cos{(P - l)}", "- e^{- P + l}", "P (\\log{(P l)} - 1)", "\\frac{P (\\log{(P)} - 1)}{l}"], "srepr_premise_expression": "sin(Add(Symbol('P', commutative=True), Mul(Integer(-1), Symbol('l', commutative=True))))", "srepr_variable": "Symbol('P', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('P', commutative=True), Mul(Integer(-1), Symbol('l', commutative=True)))))", "srepr_negatives": ["cos(Add(Symbol('P', commutative=True), Mul(Integer(-1), Symbol('l', commutative=True))))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('P', commutative=True)), Symbol('l', commutative=True))))", "Mul(Symbol('P', commutative=True), Add(log(Mul(Symbol('P', commutative=True), Symbol('l', commutative=True))), Integer(-1)))", "Mul(Symbol('P', commutative=True), Pow(Symbol('l', commutative=True), Integer(-1)), Add(log(Symbol('P', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\frac{e^{h}}{l}", "variable": "l", "positive": "e^{h} \\log{(l)}", "negatives": ["- \\cos{(h - l)}", "\\frac{l (- 2 h + l)}{2}", "\\frac{l (2 h + l)}{2}", "\\frac{l^{2}}{2 h}"], "srepr_premise_expression": "Mul(Pow(Symbol('l', commutative=True), Integer(-1)), exp(Symbol('h', commutative=True)))", "srepr_variable": "Symbol('l', commutative=True)", "srepr_positive": "Mul(exp(Symbol('h', commutative=True)), log(Symbol('l', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('h', commutative=True), Mul(Integer(-1), Symbol('l', commutative=True)))))", "Mul(Rational(1, 2), Symbol('l', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('h', commutative=True)), Symbol('l', commutative=True)))", "Mul(Rational(1, 2), Symbol('l', commutative=True), Add(Mul(Integer(2), Symbol('h', commutative=True)), Symbol('l', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('h', commutative=True), Integer(-1)), Pow(Symbol('l', commutative=True), Integer(2)))"]}, {"premise_expression": "\\log{(B + f)}", "variable": "f", "positive": "B \\log{(B + f)} + f \\log{(B + f)} - f", "negatives": ["B \\log{(B + f)} - B + f \\log{(B + f)}", "f (\\log{(B f)} - 1)", "\\frac{f (f + 2 \\sin{(B)})}{2}", "B f + e^{f}"], "srepr_premise_expression": "log(Add(Symbol('B', commutative=True), Symbol('f', commutative=True)))", "srepr_variable": "Symbol('f', commutative=True)", "srepr_positive": "Add(Mul(Symbol('B', commutative=True), log(Add(Symbol('B', commutative=True), Symbol('f', commutative=True)))), Mul(Symbol('f', commutative=True), log(Add(Symbol('B', commutative=True), Symbol('f', commutative=True)))), Mul(Integer(-1), Symbol('f', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('B', commutative=True), log(Add(Symbol('B', commutative=True), Symbol('f', commutative=True)))), Mul(Integer(-1), Symbol('B', commutative=True)), Mul(Symbol('f', commutative=True), log(Add(Symbol('B', commutative=True), Symbol('f', commutative=True)))))", "Mul(Symbol('f', commutative=True), Add(log(Mul(Symbol('B', commutative=True), Symbol('f', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Symbol('f', commutative=True), Mul(Integer(2), sin(Symbol('B', commutative=True)))))", "Add(Mul(Symbol('B', commutative=True), Symbol('f', commutative=True)), exp(Symbol('f', commutative=True)))"]}, {"premise_expression": "Z e^{u}", "variable": "u", "positive": "Z e^{u}", "negatives": ["Z e^{\\frac{u}{Z}}", "\\frac{Z^{2} e^{u}}{2}", "\\frac{u^{2} \\log{(Z)}}{2}", "\\log{(u)} \\sin{(Z)}"], "srepr_premise_expression": "Mul(Symbol('Z', commutative=True), exp(Symbol('u', commutative=True)))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "Mul(Symbol('Z', commutative=True), exp(Symbol('u', commutative=True)))", "srepr_negatives": ["Mul(Symbol('Z', commutative=True), exp(Mul(Pow(Symbol('Z', commutative=True), Integer(-1)), Symbol('u', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('Z', commutative=True), Integer(2)), exp(Symbol('u', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('u', commutative=True), Integer(2)), log(Symbol('Z', commutative=True)))", "Mul(log(Symbol('u', commutative=True)), sin(Symbol('Z', commutative=True)))"]}, {"premise_expression": "h + l", "variable": "l", "positive": "\\frac{l (2 h + l)}{2}", "negatives": ["\\frac{h (h + 2 l)}{2}", "- \\cos{(h + l)}", "\\sin{(h + l)}", "e^{- h + l}"], "srepr_premise_expression": "Add(Symbol('h', commutative=True), Symbol('l', commutative=True))", "srepr_variable": "Symbol('l', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('l', commutative=True), Add(Mul(Integer(2), Symbol('h', commutative=True)), Symbol('l', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('h', commutative=True), Add(Symbol('h', commutative=True), Mul(Integer(2), Symbol('l', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('h', commutative=True), Symbol('l', commutative=True))))", "sin(Add(Symbol('h', commutative=True), Symbol('l', commutative=True)))", "exp(Add(Mul(Integer(-1), Symbol('h', commutative=True)), Symbol('l', commutative=True)))"]}, {"premise_expression": "\\cos{(I + T)}", "variable": "I", "positive": "\\sin{(I + T)}", "negatives": ["e^{I + T}", "\\frac{I (- I + 2 T)}{2}", "\\frac{I (I - 2 T)}{2}", "I e^{\\frac{T}{I}} - T \\operatorname{Ei}{(\\frac{T}{I})}"], "srepr_premise_expression": "cos(Add(Symbol('I', commutative=True), Symbol('T', commutative=True)))", "srepr_variable": "Symbol('I', commutative=True)", "srepr_positive": "sin(Add(Symbol('I', commutative=True), Symbol('T', commutative=True)))", "srepr_negatives": ["exp(Add(Symbol('I', commutative=True), Symbol('T', commutative=True)))", "Mul(Rational(1, 2), Symbol('I', commutative=True), Add(Mul(Integer(-1), Symbol('I', commutative=True)), Mul(Integer(2), Symbol('T', commutative=True))))", "Mul(Rational(1, 2), Symbol('I', commutative=True), Add(Symbol('I', commutative=True), Mul(Integer(-1), Integer(2), Symbol('T', commutative=True))))", "Add(Mul(Symbol('I', commutative=True), exp(Mul(Pow(Symbol('I', commutative=True), Integer(-1)), Symbol('T', commutative=True)))), Mul(Integer(-1), Symbol('T', commutative=True), Ei(Mul(Pow(Symbol('I', commutative=True), Integer(-1)), Symbol('T', commutative=True)))))"]}, {"premise_expression": "e^{P^{Y}}", "variable": "P", "positive": "\\frac{e^{- \\frac{i \\pi}{Y}} \\gamma(\\frac{1}{Y}, P^{Y} e^{i \\pi})}{Y}", "negatives": ["P \\log{(P - Y)} - P - Y \\log{(P - Y)}", "P (\\log{(P Y)} - 1)", "\\log{(P)} \\sin{(Y)}", "\\frac{P^{2} \\cos{(Y)}}{2}"], "srepr_premise_expression": "exp(Pow(Symbol('P', commutative=True), Symbol('Y', commutative=True)))", "srepr_variable": "Symbol('P', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('Y', commutative=True), Integer(-1)), exp(Mul(Integer(-1), I, pi, Pow(Symbol('Y', commutative=True), Integer(-1)))), lowergamma(Pow(Symbol('Y', commutative=True), Integer(-1)), Mul(Pow(Symbol('P', commutative=True), Symbol('Y', commutative=True)), exp_polar(Mul(I, pi)))))", "srepr_negatives": ["Add(Mul(Symbol('P', commutative=True), log(Add(Symbol('P', commutative=True), Mul(Integer(-1), Symbol('Y', commutative=True))))), Mul(Integer(-1), Symbol('P', commutative=True)), Mul(Integer(-1), Symbol('Y', commutative=True), log(Add(Symbol('P', commutative=True), Mul(Integer(-1), Symbol('Y', commutative=True))))))", "Mul(Symbol('P', commutative=True), Add(log(Mul(Symbol('P', commutative=True), Symbol('Y', commutative=True))), Integer(-1)))", "Mul(log(Symbol('P', commutative=True)), sin(Symbol('Y', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2)), cos(Symbol('Y', commutative=True)))"]}, {"premise_expression": "- Q + V r", "variable": "V", "positive": "\\frac{V (- 2 Q + V r)}{2}", "negatives": ["\\frac{r (- 2 Q + V r)}{2}", "\\frac{Q (- Q + 2 V r)}{2}", "\\frac{V r (2 Q + V)}{2}", "\\frac{Q V (- V + 2 r)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('Q', commutative=True)), Mul(Symbol('V', commutative=True), Symbol('r', commutative=True)))", "srepr_variable": "Symbol('V', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('V', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('Q', commutative=True)), Mul(Symbol('V', commutative=True), Symbol('r', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('Q', commutative=True)), Mul(Symbol('V', commutative=True), Symbol('r', commutative=True))))", "Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Mul(Integer(-1), Symbol('Q', commutative=True)), Mul(Integer(2), Symbol('V', commutative=True), Symbol('r', commutative=True))))", "Mul(Rational(1, 2), Symbol('V', commutative=True), Symbol('r', commutative=True), Add(Mul(Integer(2), Symbol('Q', commutative=True)), Symbol('V', commutative=True)))", "Mul(Rational(1, 2), Symbol('Q', commutative=True), Symbol('V', commutative=True), Add(Mul(Integer(-1), Symbol('V', commutative=True)), Mul(Integer(2), Symbol('r', commutative=True))))"]}, {"premise_expression": "K + e^{E}", "variable": "E", "positive": "E K + e^{E}", "negatives": ["\\frac{K (K + 2 e^{E})}{2}", "\\sin{(E - K)}", "\\log{(E)} \\sin{(K)}", "\\frac{E (\\log{(E)} - 1)}{K}"], "srepr_premise_expression": "Add(Symbol('K', commutative=True), exp(Symbol('E', commutative=True)))", "srepr_variable": "Symbol('E', commutative=True)", "srepr_positive": "Add(Mul(Symbol('E', commutative=True), Symbol('K', commutative=True)), exp(Symbol('E', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Symbol('K', commutative=True), Mul(Integer(2), exp(Symbol('E', commutative=True)))))", "sin(Add(Symbol('E', commutative=True), Mul(Integer(-1), Symbol('K', commutative=True))))", "Mul(log(Symbol('E', commutative=True)), sin(Symbol('K', commutative=True)))", "Mul(Symbol('E', commutative=True), Pow(Symbol('K', commutative=True), Integer(-1)), Add(log(Symbol('E', commutative=True)), Integer(-1)))"]}, {"premise_expression": "C + p", "variable": "p", "positive": "\\frac{p (2 C + p)}{2}", "negatives": ["\\frac{C (C + 2 p)}{2}", "- \\cos{(C + p)}", "e^{- C + p}", "\\frac{p^{2}}{2 C}"], "srepr_premise_expression": "Add(Symbol('C', commutative=True), Symbol('p', commutative=True))", "srepr_variable": "Symbol('p', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Mul(Integer(2), Symbol('C', commutative=True)), Symbol('p', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Symbol('C', commutative=True), Mul(Integer(2), Symbol('p', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('C', commutative=True), Symbol('p', commutative=True))))", "exp(Add(Mul(Integer(-1), Symbol('C', commutative=True)), Symbol('p', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(-1)), Pow(Symbol('p', commutative=True), Integer(2)))"]}, {"premise_expression": "e^{G - y}", "variable": "G", "positive": "e^{G - y}", "negatives": ["- e^{G - y}", "\\sin{(G - y)}", "e^{y} \\log{(G)}", "\\frac{G^{2}}{2 y}"], "srepr_premise_expression": "exp(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True))))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "exp(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True)))))", "sin(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True))))", "Mul(exp(Symbol('y', commutative=True)), log(Symbol('G', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(2)), Pow(Symbol('y', commutative=True), Integer(-1)))"]}, {"premise_expression": "- J + X", "variable": "X", "positive": "\\frac{X (- 2 J + X)}{2}", "negatives": ["\\frac{X (2 J - X)}{2}", "\\frac{J (- J + 2 X)}{2}", "e^{- J + X}", "e^{J + X}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('J', commutative=True)), Symbol('X', commutative=True))", "srepr_variable": "Symbol('X', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('X', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('J', commutative=True)), Symbol('X', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('X', commutative=True), Add(Mul(Integer(2), Symbol('J', commutative=True)), Mul(Integer(-1), Symbol('X', commutative=True))))", "Mul(Rational(1, 2), Symbol('J', commutative=True), Add(Mul(Integer(-1), Symbol('J', commutative=True)), Mul(Integer(2), Symbol('X', commutative=True))))", "exp(Add(Mul(Integer(-1), Symbol('J', commutative=True)), Symbol('X', commutative=True)))", "exp(Add(Symbol('J', commutative=True), Symbol('X', commutative=True)))"]}, {"premise_expression": "\\frac{N}{y}", "variable": "y", "positive": "N \\log{(y)}", "negatives": ["\\frac{N^{2}}{2 y}", "\\frac{y^{2}}{2 N}", "- N y + e^{y}", "y (\\log{(\\frac{y}{N})} - 1)"], "srepr_premise_expression": "Mul(Symbol('N', commutative=True), Pow(Symbol('y', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('y', commutative=True)", "srepr_positive": "Mul(Symbol('N', commutative=True), log(Symbol('y', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('N', commutative=True), Integer(2)), Pow(Symbol('y', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('N', commutative=True), Integer(-1)), Pow(Symbol('y', commutative=True), Integer(2)))", "Add(Mul(Integer(-1), Symbol('N', commutative=True), Symbol('y', commutative=True)), exp(Symbol('y', commutative=True)))", "Mul(Symbol('y', commutative=True), Add(log(Mul(Pow(Symbol('N', commutative=True), Integer(-1)), Symbol('y', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\frac{H x}{b}", "variable": "x", "positive": "\\frac{H x^{2}}{2 b}", "negatives": ["\\frac{H^{2} x}{2 b}", "H x \\log{(b)}", "\\frac{H b x^{2}}{2}", "H b \\log{(x)}"], "srepr_premise_expression": "Mul(Symbol('H', commutative=True), Pow(Symbol('b', commutative=True), Integer(-1)), Symbol('x', commutative=True))", "srepr_variable": "Symbol('x', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('H', commutative=True), Pow(Symbol('b', commutative=True), Integer(-1)), Pow(Symbol('x', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('H', commutative=True), Integer(2)), Pow(Symbol('b', commutative=True), Integer(-1)), Symbol('x', commutative=True))", "Mul(Symbol('H', commutative=True), Symbol('x', commutative=True), log(Symbol('b', commutative=True)))", "Mul(Rational(1, 2), Symbol('H', commutative=True), Symbol('b', commutative=True), Pow(Symbol('x', commutative=True), Integer(2)))", "Mul(Symbol('H', commutative=True), Symbol('b', commutative=True), log(Symbol('x', commutative=True)))"]}, {"premise_expression": "J + \\cos{(T)}", "variable": "J", "positive": "\\frac{J (J + 2 \\cos{(T)})}{2}", "negatives": ["J T + \\sin{(T)}", "J (- T + \\log{(J^{T})})", "\\log{(J)} \\sin{(T)}", "J (\\log{(\\frac{T}{J})} + 1)"], "srepr_premise_expression": "Add(Symbol('J', commutative=True), cos(Symbol('T', commutative=True)))", "srepr_variable": "Symbol('J', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('J', commutative=True), Add(Symbol('J', commutative=True), Mul(Integer(2), cos(Symbol('T', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('J', commutative=True), Symbol('T', commutative=True)), sin(Symbol('T', commutative=True)))", "Mul(Symbol('J', commutative=True), Add(Mul(Integer(-1), Symbol('T', commutative=True)), log(Pow(Symbol('J', commutative=True), Symbol('T', commutative=True)))))", "Mul(log(Symbol('J', commutative=True)), sin(Symbol('T', commutative=True)))", "Mul(Symbol('J', commutative=True), Add(log(Mul(Pow(Symbol('J', commutative=True), Integer(-1)), Symbol('T', commutative=True))), Integer(1)))"]}, {"premise_expression": "K - g", "variable": "g", "positive": "\\frac{g (2 K - g)}{2}", "negatives": ["\\frac{g (- 2 K + g)}{2}", "\\frac{K (K - 2 g)}{2}", "\\frac{g^{2} \\log{(K)}}{2}", "\\frac{g^{2} \\cos{(K)}}{2}"], "srepr_premise_expression": "Add(Symbol('K', commutative=True), Mul(Integer(-1), Symbol('g', commutative=True)))", "srepr_variable": "Symbol('g', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Mul(Integer(2), Symbol('K', commutative=True)), Mul(Integer(-1), Symbol('g', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('K', commutative=True)), Symbol('g', commutative=True)))", "Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Symbol('K', commutative=True), Mul(Integer(-1), Integer(2), Symbol('g', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('g', commutative=True), Integer(2)), log(Symbol('K', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('g', commutative=True), Integer(2)), cos(Symbol('K', commutative=True)))"]}, {"premise_expression": "- z + e^{k}", "variable": "k", "positive": "- k z + e^{k}", "negatives": ["- k z + \\sin{(k)}", "k z + \\sin{(k)}", "\\frac{z (- z + 2 e^{k})}{2}", "\\frac{k (k + 2 e^{z})}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('z', commutative=True)), exp(Symbol('k', commutative=True)))", "srepr_variable": "Symbol('k', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('k', commutative=True), Symbol('z', commutative=True)), exp(Symbol('k', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('k', commutative=True), Symbol('z', commutative=True)), sin(Symbol('k', commutative=True)))", "Add(Mul(Symbol('k', commutative=True), Symbol('z', commutative=True)), sin(Symbol('k', commutative=True)))", "Mul(Rational(1, 2), Symbol('z', commutative=True), Add(Mul(Integer(-1), Symbol('z', commutative=True)), Mul(Integer(2), exp(Symbol('k', commutative=True)))))", "Mul(Rational(1, 2), Symbol('k', commutative=True), Add(Symbol('k', commutative=True), Mul(Integer(2), exp(Symbol('z', commutative=True)))))"]}, {"premise_expression": "\\cos{(A + j)}", "variable": "j", "positive": "\\sin{(A + j)}", "negatives": ["\\cos{(A - j)}", "\\frac{j (2 A + j)}{2}", "\\frac{j (j + 2 \\sin{(A)})}{2}", "\\frac{j (j + 2 \\log{(A)})}{2}"], "srepr_premise_expression": "cos(Add(Symbol('A', commutative=True), Symbol('j', commutative=True)))", "srepr_variable": "Symbol('j', commutative=True)", "srepr_positive": "sin(Add(Symbol('A', commutative=True), Symbol('j', commutative=True)))", "srepr_negatives": ["cos(Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('j', commutative=True))))", "Mul(Rational(1, 2), Symbol('j', commutative=True), Add(Mul(Integer(2), Symbol('A', commutative=True)), Symbol('j', commutative=True)))", "Mul(Rational(1, 2), Symbol('j', commutative=True), Add(Symbol('j', commutative=True), Mul(Integer(2), sin(Symbol('A', commutative=True)))))", "Mul(Rational(1, 2), Symbol('j', commutative=True), Add(Symbol('j', commutative=True), Mul(Integer(2), log(Symbol('A', commutative=True)))))"]}, {"premise_expression": "R + u", "variable": "R", "positive": "\\frac{R (R + 2 u)}{2}", "negatives": ["\\frac{u (2 R + u)}{2}", "\\frac{R (R + 2 \\sin{(u)})}{2}", "\\frac{R (- R + 2 \\sin{(u)})}{2}", "\\frac{R^{2} \\cos{(u)}}{2}"], "srepr_premise_expression": "Add(Symbol('R', commutative=True), Symbol('u', commutative=True))", "srepr_variable": "Symbol('R', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('R', commutative=True), Add(Symbol('R', commutative=True), Mul(Integer(2), Symbol('u', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(2), Symbol('R', commutative=True)), Symbol('u', commutative=True)))", "Mul(Rational(1, 2), Symbol('R', commutative=True), Add(Symbol('R', commutative=True), Mul(Integer(2), sin(Symbol('u', commutative=True)))))", "Mul(Rational(1, 2), Symbol('R', commutative=True), Add(Mul(Integer(-1), Symbol('R', commutative=True)), Mul(Integer(2), sin(Symbol('u', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('R', commutative=True), Integer(2)), cos(Symbol('u', commutative=True)))"]}, {"premise_expression": "C + X", "variable": "C", "positive": "\\frac{C (C + 2 X)}{2}", "negatives": ["\\frac{X (2 C + X)}{2}", "\\frac{C (- C + 2 \\sin{(X)})}{2}", "\\sin{(C + X)}", "e^{C + X}"], "srepr_premise_expression": "Add(Symbol('C', commutative=True), Symbol('X', commutative=True))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Symbol('C', commutative=True), Mul(Integer(2), Symbol('X', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('X', commutative=True), Add(Mul(Integer(2), Symbol('C', commutative=True)), Symbol('X', commutative=True)))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Mul(Integer(-1), Symbol('C', commutative=True)), Mul(Integer(2), sin(Symbol('X', commutative=True)))))", "sin(Add(Symbol('C', commutative=True), Symbol('X', commutative=True)))", "exp(Add(Symbol('C', commutative=True), Symbol('X', commutative=True)))"]}, {"premise_expression": "- N + S", "variable": "N", "positive": "\\frac{N (- N + 2 S)}{2}", "negatives": ["\\frac{S (- 2 N + S)}{2}", "\\frac{N^{2} e^{S}}{2}", "- N S + e^{N}", "- N S - \\cos{(N)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('N', commutative=True)), Symbol('S', commutative=True))", "srepr_variable": "Symbol('N', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Mul(Integer(-1), Symbol('N', commutative=True)), Mul(Integer(2), Symbol('S', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('N', commutative=True)), Symbol('S', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('N', commutative=True), Integer(2)), exp(Symbol('S', commutative=True)))", "Add(Mul(Integer(-1), Symbol('N', commutative=True), Symbol('S', commutative=True)), exp(Symbol('N', commutative=True)))", "Add(Mul(Integer(-1), Symbol('N', commutative=True), Symbol('S', commutative=True)), Mul(Integer(-1), cos(Symbol('N', commutative=True))))"]}, {"premise_expression": "\\log{(\\frac{q}{C})}", "variable": "q", "positive": "q (\\log{(\\frac{q}{C})} - 1)", "negatives": ["C (\\log{(\\frac{q}{C})} + 1)", "q (\\log{(C q)} - 1)", "C q (\\log{(q)} - 1)", "C \\log{(q)}"], "srepr_premise_expression": "log(Mul(Pow(Symbol('C', commutative=True), Integer(-1)), Symbol('q', commutative=True)))", "srepr_variable": "Symbol('q', commutative=True)", "srepr_positive": "Mul(Symbol('q', commutative=True), Add(log(Mul(Pow(Symbol('C', commutative=True), Integer(-1)), Symbol('q', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('C', commutative=True), Add(log(Mul(Pow(Symbol('C', commutative=True), Integer(-1)), Symbol('q', commutative=True))), Integer(1)))", "Mul(Symbol('q', commutative=True), Add(log(Mul(Symbol('C', commutative=True), Symbol('q', commutative=True))), Integer(-1)))", "Mul(Symbol('C', commutative=True), Symbol('q', commutative=True), Add(log(Symbol('q', commutative=True)), Integer(-1)))", "Mul(Symbol('C', commutative=True), log(Symbol('q', commutative=True)))"]}, {"premise_expression": "\\frac{H - k}{A}", "variable": "k", "positive": "\\frac{k (2 H - k)}{2 A}", "negatives": ["\\frac{k (2 H + k)}{2 A}", "\\frac{k (2 A + k)}{2 H}", "\\frac{H (H - 2 k)}{2 A}", "\\frac{k (2 A - 2 H - k)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('A', commutative=True), Integer(-1)), Add(Symbol('H', commutative=True), Mul(Integer(-1), Symbol('k', commutative=True))))", "srepr_variable": "Symbol('k', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(-1)), Symbol('k', commutative=True), Add(Mul(Integer(2), Symbol('H', commutative=True)), Mul(Integer(-1), Symbol('k', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(-1)), Symbol('k', commutative=True), Add(Mul(Integer(2), Symbol('H', commutative=True)), Symbol('k', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('H', commutative=True), Integer(-1)), Symbol('k', commutative=True), Add(Mul(Integer(2), Symbol('A', commutative=True)), Symbol('k', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(-1)), Symbol('H', commutative=True), Add(Symbol('H', commutative=True), Mul(Integer(-1), Integer(2), Symbol('k', commutative=True))))", "Mul(Rational(1, 2), Symbol('k', commutative=True), Add(Mul(Integer(2), Symbol('A', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('H', commutative=True)), Mul(Integer(-1), Symbol('k', commutative=True))))"]}, {"premise_expression": "Z + e^{b}", "variable": "Z", "positive": "\\frac{Z (Z + 2 e^{b})}{2}", "negatives": ["\\frac{Z (Z - 2 b)}{2}", "Z b + e^{b}", "\\sin{(Z + b)}", "\\sin{(Z - b)}"], "srepr_premise_expression": "Add(Symbol('Z', commutative=True), exp(Symbol('b', commutative=True)))", "srepr_variable": "Symbol('Z', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Symbol('Z', commutative=True), Mul(Integer(2), exp(Symbol('b', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Symbol('Z', commutative=True), Mul(Integer(-1), Integer(2), Symbol('b', commutative=True))))", "Add(Mul(Symbol('Z', commutative=True), Symbol('b', commutative=True)), exp(Symbol('b', commutative=True)))", "sin(Add(Symbol('Z', commutative=True), Symbol('b', commutative=True)))", "sin(Add(Symbol('Z', commutative=True), Mul(Integer(-1), Symbol('b', commutative=True))))"]}, {"premise_expression": "\\cos{(\\frac{u}{j})}", "variable": "j", "positive": "j \\cos{(\\frac{u}{j})} + u \\operatorname{Si}{(\\frac{u}{j})}", "negatives": ["j e^{\\frac{u}{j}} - u \\operatorname{Ei}{(\\frac{u}{j})}", "\\frac{j (\\log{(j)} - 1)}{u}", "\\sin{(j + u)}", "- e^{- j + u}"], "srepr_premise_expression": "cos(Mul(Pow(Symbol('j', commutative=True), Integer(-1)), Symbol('u', commutative=True)))", "srepr_variable": "Symbol('j', commutative=True)", "srepr_positive": "Add(Mul(Symbol('j', commutative=True), cos(Mul(Pow(Symbol('j', commutative=True), Integer(-1)), Symbol('u', commutative=True)))), Mul(Symbol('u', commutative=True), Si(Mul(Pow(Symbol('j', commutative=True), Integer(-1)), Symbol('u', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('j', commutative=True), exp(Mul(Pow(Symbol('j', commutative=True), Integer(-1)), Symbol('u', commutative=True)))), Mul(Integer(-1), Symbol('u', commutative=True), Ei(Mul(Pow(Symbol('j', commutative=True), Integer(-1)), Symbol('u', commutative=True)))))", "Mul(Symbol('j', commutative=True), Pow(Symbol('u', commutative=True), Integer(-1)), Add(log(Symbol('j', commutative=True)), Integer(-1)))", "sin(Add(Symbol('j', commutative=True), Symbol('u', commutative=True)))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('j', commutative=True)), Symbol('u', commutative=True))))"]}, {"premise_expression": "P Z", "variable": "P", "positive": "\\frac{P^{2} Z}{2}", "negatives": ["\\frac{P Z^{2}}{2}", "\\frac{P Z (P + 2)}{2}", "P Z - \\cos{(P)}", "e^{P - Z}"], "srepr_premise_expression": "Mul(Symbol('P', commutative=True), Symbol('Z', commutative=True))", "srepr_variable": "Symbol('P', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2)), Symbol('Z', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('P', commutative=True), Pow(Symbol('Z', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('P', commutative=True), Symbol('Z', commutative=True), Add(Symbol('P', commutative=True), Integer(2)))", "Add(Mul(Symbol('P', commutative=True), Symbol('Z', commutative=True)), Mul(Integer(-1), cos(Symbol('P', commutative=True))))", "exp(Add(Symbol('P', commutative=True), Mul(Integer(-1), Symbol('Z', commutative=True))))"]}, {"premise_expression": "n^{W} + u", "variable": "u", "positive": "\\frac{u (2 n^{W} + u)}{2}", "negatives": ["\\frac{u^{2} (W + n)}{2}", "\\frac{u (2 W + 2 n + u)}{2}", "\\frac{u (2 W + 2 n - u)}{2}", "\\frac{u (2 W - 2 n - u)}{2}"], "srepr_premise_expression": "Add(Pow(Symbol('n', commutative=True), Symbol('W', commutative=True)), Symbol('u', commutative=True))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(2), Pow(Symbol('n', commutative=True), Symbol('W', commutative=True))), Symbol('u', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('u', commutative=True), Integer(2)), Add(Symbol('W', commutative=True), Symbol('n', commutative=True)))", "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(2), Symbol('W', commutative=True)), Mul(Integer(2), Symbol('n', commutative=True)), Symbol('u', commutative=True)))", "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(2), Symbol('W', commutative=True)), Mul(Integer(2), Symbol('n', commutative=True)), Mul(Integer(-1), Symbol('u', commutative=True))))", "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(2), Symbol('W', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('n', commutative=True)), Mul(Integer(-1), Symbol('u', commutative=True))))"]}, {"premise_expression": "e^{S - y}", "variable": "S", "positive": "e^{S - y}", "negatives": ["- e^{S - y}", "\\frac{S (S - 2 y)}{2}", "\\frac{S (S + 2 y)}{2}", "- y \\cos{(S)}"], "srepr_premise_expression": "exp(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True))))", "srepr_variable": "Symbol('S', commutative=True)", "srepr_positive": "exp(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True)))))", "Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Symbol('S', commutative=True), Mul(Integer(-1), Integer(2), Symbol('y', commutative=True))))", "Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Symbol('S', commutative=True), Mul(Integer(2), Symbol('y', commutative=True))))", "Mul(Integer(-1), Symbol('y', commutative=True), cos(Symbol('S', commutative=True)))"]}, {"premise_expression": "- A + Q - m", "variable": "m", "positive": "\\frac{m (- 2 A + 2 Q - m)}{2}", "negatives": ["\\frac{Q (- 2 A + Q - 2 m)}{2}", "\\frac{A (- A + 2 Q - 2 m)}{2}", "\\frac{m (4 Q - m)}{2}", "\\frac{A m (- 2 Q + m)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('A', commutative=True)), Symbol('Q', commutative=True), Mul(Integer(-1), Symbol('m', commutative=True)))", "srepr_variable": "Symbol('m', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('A', commutative=True)), Mul(Integer(2), Symbol('Q', commutative=True)), Mul(Integer(-1), Symbol('m', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('A', commutative=True)), Symbol('Q', commutative=True), Mul(Integer(-1), Integer(2), Symbol('m', commutative=True))))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Mul(Integer(-1), Symbol('A', commutative=True)), Mul(Integer(2), Symbol('Q', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('m', commutative=True))))", "Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Mul(Integer(4), Symbol('Q', commutative=True)), Mul(Integer(-1), Symbol('m', commutative=True))))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Symbol('m', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('Q', commutative=True)), Symbol('m', commutative=True)))"]}, {"premise_expression": "p \\log{(S)}", "variable": "S", "positive": "S p (\\log{(S)} - 1)", "negatives": ["S (\\log{(\\frac{p}{S})} + 1)", "\\frac{p^{2} \\log{(S)}}{2}", "e^{p} \\log{(S)}", "e^{S + p}"], "srepr_premise_expression": "Mul(Symbol('p', commutative=True), log(Symbol('S', commutative=True)))", "srepr_variable": "Symbol('S', commutative=True)", "srepr_positive": "Mul(Symbol('S', commutative=True), Symbol('p', commutative=True), Add(log(Symbol('S', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('S', commutative=True), Add(log(Mul(Pow(Symbol('S', commutative=True), Integer(-1)), Symbol('p', commutative=True))), Integer(1)))", "Mul(Rational(1, 2), Pow(Symbol('p', commutative=True), Integer(2)), log(Symbol('S', commutative=True)))", "Mul(exp(Symbol('p', commutative=True)), log(Symbol('S', commutative=True)))", "exp(Add(Symbol('S', commutative=True), Symbol('p', commutative=True)))"]}, {"premise_expression": "D - j - w", "variable": "D", "positive": "D (\\frac{D}{2} - j - w)", "negatives": ["\\frac{D (D - 2 j + 2 w)}{2}", "\\frac{w (2 D - 2 j - w)}{2}", "\\frac{j (2 D - j - 2 w)}{2}", "\\frac{D^{2}}{2} + \\frac{D j}{w}"], "srepr_premise_expression": "Add(Symbol('D', commutative=True), Mul(Integer(-1), Symbol('j', commutative=True)), Mul(Integer(-1), Symbol('w', commutative=True)))", "srepr_variable": "Symbol('D', commutative=True)", "srepr_positive": "Mul(Symbol('D', commutative=True), Add(Mul(Rational(1, 2), Symbol('D', commutative=True)), Mul(Integer(-1), Symbol('j', commutative=True)), Mul(Integer(-1), Symbol('w', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('D', commutative=True), Add(Symbol('D', commutative=True), Mul(Integer(-1), Integer(2), Symbol('j', commutative=True)), Mul(Integer(2), Symbol('w', commutative=True))))", "Mul(Rational(1, 2), Symbol('w', commutative=True), Add(Mul(Integer(2), Symbol('D', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('j', commutative=True)), Mul(Integer(-1), Symbol('w', commutative=True))))", "Mul(Rational(1, 2), Symbol('j', commutative=True), Add(Mul(Integer(2), Symbol('D', commutative=True)), Mul(Integer(-1), Symbol('j', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('w', commutative=True))))", "Add(Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(2))), Mul(Symbol('D', commutative=True), Symbol('j', commutative=True), Pow(Symbol('w', commutative=True), Integer(-1))))"]}, {"premise_expression": "\\sin{(Y + c)}", "variable": "c", "positive": "- \\cos{(Y + c)}", "negatives": ["- Y \\cos{(c)}", "Y \\log{(c)}", "Y e^{\\frac{c}{Y}}", "c (\\log{(\\frac{c}{Y})} - 1)"], "srepr_premise_expression": "sin(Add(Symbol('Y', commutative=True), Symbol('c', commutative=True)))", "srepr_variable": "Symbol('c', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('Y', commutative=True), Symbol('c', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), Symbol('Y', commutative=True), cos(Symbol('c', commutative=True)))", "Mul(Symbol('Y', commutative=True), log(Symbol('c', commutative=True)))", "Mul(Symbol('Y', commutative=True), exp(Mul(Pow(Symbol('Y', commutative=True), Integer(-1)), Symbol('c', commutative=True))))", "Mul(Symbol('c', commutative=True), Add(log(Mul(Pow(Symbol('Y', commutative=True), Integer(-1)), Symbol('c', commutative=True))), Integer(-1)))"]}, {"premise_expression": "- Z + \\sin{(I)}", "variable": "I", "positive": "- I Z - \\cos{(I)}", "negatives": ["Z \\log{(I)}", "\\frac{I^{2} \\log{(Z)}}{2}", "I (Z + \\log{(I)} - 1)", "\\sin{(I + Z)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('Z', commutative=True)), sin(Symbol('I', commutative=True)))", "srepr_variable": "Symbol('I', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('I', commutative=True), Symbol('Z', commutative=True)), Mul(Integer(-1), cos(Symbol('I', commutative=True))))", "srepr_negatives": ["Mul(Symbol('Z', commutative=True), log(Symbol('I', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(2)), log(Symbol('Z', commutative=True)))", "Mul(Symbol('I', commutative=True), Add(Symbol('Z', commutative=True), log(Symbol('I', commutative=True)), Integer(-1)))", "sin(Add(Symbol('I', commutative=True), Symbol('Z', commutative=True)))"]}, {"premise_expression": "k e^{R}", "variable": "R", "positive": "k e^{R}", "negatives": ["k e^{\\frac{R}{k}}", "\\frac{k^{2} e^{R}}{2}", "- \\frac{k}{R}", "\\frac{R^{2} e^{k}}{2}"], "srepr_premise_expression": "Mul(Symbol('k', commutative=True), exp(Symbol('R', commutative=True)))", "srepr_variable": "Symbol('R', commutative=True)", "srepr_positive": "Mul(Symbol('k', commutative=True), exp(Symbol('R', commutative=True)))", "srepr_negatives": ["Mul(Symbol('k', commutative=True), exp(Mul(Symbol('R', commutative=True), Pow(Symbol('k', commutative=True), Integer(-1)))))", "Mul(Rational(1, 2), Pow(Symbol('k', commutative=True), Integer(2)), exp(Symbol('R', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('R', commutative=True), Integer(-1)), Symbol('k', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('R', commutative=True), Integer(2)), exp(Symbol('k', commutative=True)))"]}, {"premise_expression": "- K + \\cos{(h)}", "variable": "K", "positive": "\\frac{K (- K + 2 \\cos{(h)})}{2}", "negatives": ["\\frac{K^{2} \\sin{(h)}}{2}", "- K h + \\sin{(h)}", "\\frac{K^{2}}{2 h}", "- K h + \\sin{(K)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('K', commutative=True)), cos(Symbol('h', commutative=True)))", "srepr_variable": "Symbol('K', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Mul(Integer(-1), Symbol('K', commutative=True)), Mul(Integer(2), cos(Symbol('h', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('K', commutative=True), Integer(2)), sin(Symbol('h', commutative=True)))", "Add(Mul(Integer(-1), Symbol('K', commutative=True), Symbol('h', commutative=True)), sin(Symbol('h', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('K', commutative=True), Integer(2)), Pow(Symbol('h', commutative=True), Integer(-1)))", "Add(Mul(Integer(-1), Symbol('K', commutative=True), Symbol('h', commutative=True)), sin(Symbol('K', commutative=True)))"]}, {"premise_expression": "V \\cos{(j)}", "variable": "j", "positive": "V \\sin{(j)}", "negatives": ["\\frac{V^{2} \\cos{(j)}}{2}", "e^{V} \\log{(j)}", "\\frac{j^{2} \\log{(V)}}{2}", "j (- V + \\log{(j)} - 1)"], "srepr_premise_expression": "Mul(Symbol('V', commutative=True), cos(Symbol('j', commutative=True)))", "srepr_variable": "Symbol('j', commutative=True)", "srepr_positive": "Mul(Symbol('V', commutative=True), sin(Symbol('j', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('V', commutative=True), Integer(2)), cos(Symbol('j', commutative=True)))", "Mul(exp(Symbol('V', commutative=True)), log(Symbol('j', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('j', commutative=True), Integer(2)), log(Symbol('V', commutative=True)))", "Mul(Symbol('j', commutative=True), Add(Mul(Integer(-1), Symbol('V', commutative=True)), log(Symbol('j', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\cos^{E}{(L)}", "variable": "L", "positive": "\\int \\cos^{E}{(L)} dL", "negatives": ["\\cos{(E - L)}", "- \\cos{(E + L)}", "E L - \\cos{(L)}", "- E L - \\cos{(L)}"], "srepr_premise_expression": "Pow(cos(Symbol('L', commutative=True)), Symbol('E', commutative=True))", "srepr_variable": "Symbol('L', commutative=True)", "srepr_positive": "Integral(Pow(cos(Symbol('L', commutative=True)), Symbol('E', commutative=True)), Tuple(Symbol('L', commutative=True)))", "srepr_negatives": ["cos(Add(Symbol('E', commutative=True), Mul(Integer(-1), Symbol('L', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('E', commutative=True), Symbol('L', commutative=True))))", "Add(Mul(Symbol('E', commutative=True), Symbol('L', commutative=True)), Mul(Integer(-1), cos(Symbol('L', commutative=True))))", "Add(Mul(Integer(-1), Symbol('E', commutative=True), Symbol('L', commutative=True)), Mul(Integer(-1), cos(Symbol('L', commutative=True))))"]}, {"premise_expression": "T \\sin{(k)}", "variable": "T", "positive": "\\frac{T^{2} \\sin{(k)}}{2}", "negatives": ["\\frac{T (T + 2 \\sin{(k)})}{2}", "\\frac{T (T - 2 k)}{2}", "- T \\cos{(k)}", "- \\frac{\\cos{(T)}}{k}"], "srepr_premise_expression": "Mul(Symbol('T', commutative=True), sin(Symbol('k', commutative=True)))", "srepr_variable": "Symbol('T', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('T', commutative=True), Integer(2)), sin(Symbol('k', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('T', commutative=True), Add(Symbol('T', commutative=True), Mul(Integer(2), sin(Symbol('k', commutative=True)))))", "Mul(Rational(1, 2), Symbol('T', commutative=True), Add(Symbol('T', commutative=True), Mul(Integer(-1), Integer(2), Symbol('k', commutative=True))))", "Mul(Integer(-1), Symbol('T', commutative=True), cos(Symbol('k', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('k', commutative=True), Integer(-1)), cos(Symbol('T', commutative=True)))"]}, {"premise_expression": "e^{- F + U}", "variable": "F", "positive": "- e^{- F + U}", "negatives": ["e^{- F + U}", "\\frac{F (- F + 2 U)}{2}", "\\frac{F (F + 2 U)}{2}", "F (\\log{(\\frac{U}{F})} + 1)"], "srepr_premise_expression": "exp(Add(Mul(Integer(-1), Symbol('F', commutative=True)), Symbol('U', commutative=True)))", "srepr_variable": "Symbol('F', commutative=True)", "srepr_positive": "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('F', commutative=True)), Symbol('U', commutative=True))))", "srepr_negatives": ["exp(Add(Mul(Integer(-1), Symbol('F', commutative=True)), Symbol('U', commutative=True)))", "Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Mul(Integer(-1), Symbol('F', commutative=True)), Mul(Integer(2), Symbol('U', commutative=True))))", "Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Symbol('F', commutative=True), Mul(Integer(2), Symbol('U', commutative=True))))", "Mul(Symbol('F', commutative=True), Add(log(Mul(Pow(Symbol('F', commutative=True), Integer(-1)), Symbol('U', commutative=True))), Integer(1)))"]}, {"premise_expression": "J + \\sin{(c)}", "variable": "c", "positive": "J c - \\cos{(c)}", "negatives": ["- J c + \\sin{(c)}", "\\frac{c^{2} \\cos{(J)}}{2}", "\\cos{(J - c)}", "\\frac{J (J + 2 \\sin{(c)})}{2}"], "srepr_premise_expression": "Add(Symbol('J', commutative=True), sin(Symbol('c', commutative=True)))", "srepr_variable": "Symbol('c', commutative=True)", "srepr_positive": "Add(Mul(Symbol('J', commutative=True), Symbol('c', commutative=True)), Mul(Integer(-1), cos(Symbol('c', commutative=True))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('J', commutative=True), Symbol('c', commutative=True)), sin(Symbol('c', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('c', commutative=True), Integer(2)), cos(Symbol('J', commutative=True)))", "cos(Add(Symbol('J', commutative=True), Mul(Integer(-1), Symbol('c', commutative=True))))", "Mul(Rational(1, 2), Symbol('J', commutative=True), Add(Symbol('J', commutative=True), Mul(Integer(2), sin(Symbol('c', commutative=True)))))"]}, {"premise_expression": "\\log{(f + n)}", "variable": "f", "positive": "f \\log{(f + n)} - f + n \\log{(f + n)}", "negatives": ["f \\log{(f + n)} + n \\log{(f + n)} - n", "f (- n + \\log{(f^{n})})", "\\frac{f (f + 2 \\cos{(n)})}{2}", "- \\cos{(f + n)}"], "srepr_premise_expression": "log(Add(Symbol('f', commutative=True), Symbol('n', commutative=True)))", "srepr_variable": "Symbol('f', commutative=True)", "srepr_positive": "Add(Mul(Symbol('f', commutative=True), log(Add(Symbol('f', commutative=True), Symbol('n', commutative=True)))), Mul(Integer(-1), Symbol('f', commutative=True)), Mul(Symbol('n', commutative=True), log(Add(Symbol('f', commutative=True), Symbol('n', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('f', commutative=True), log(Add(Symbol('f', commutative=True), Symbol('n', commutative=True)))), Mul(Symbol('n', commutative=True), log(Add(Symbol('f', commutative=True), Symbol('n', commutative=True)))), Mul(Integer(-1), Symbol('n', commutative=True)))", "Mul(Symbol('f', commutative=True), Add(Mul(Integer(-1), Symbol('n', commutative=True)), log(Pow(Symbol('f', commutative=True), Symbol('n', commutative=True)))))", "Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Symbol('f', commutative=True), Mul(Integer(2), cos(Symbol('n', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('f', commutative=True), Symbol('n', commutative=True))))"]}, {"premise_expression": "e^{- T + b}", "variable": "b", "positive": "e^{- T + b}", "negatives": ["- e^{- T + b}", "- \\cos{(T + b)}", "T \\log{(b)}", "\\frac{b (\\log{(b)} - 1)}{T}"], "srepr_premise_expression": "exp(Add(Mul(Integer(-1), Symbol('T', commutative=True)), Symbol('b', commutative=True)))", "srepr_variable": "Symbol('b', commutative=True)", "srepr_positive": "exp(Add(Mul(Integer(-1), Symbol('T', commutative=True)), Symbol('b', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('T', commutative=True)), Symbol('b', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('T', commutative=True), Symbol('b', commutative=True))))", "Mul(Symbol('T', commutative=True), log(Symbol('b', commutative=True)))", "Mul(Pow(Symbol('T', commutative=True), Integer(-1)), Symbol('b', commutative=True), Add(log(Symbol('b', commutative=True)), Integer(-1)))"]}, {"premise_expression": "C^{B} - N", "variable": "N", "positive": "\\frac{N (2 C^{B} - N)}{2}", "negatives": ["N (B^{B} + C)", "\\frac{N (- 2 B + C N)}{2}", "\\frac{N (- 2 B + 2 C + N)}{2}", "\\frac{N (- 2 B - 2 C + N)}{2}"], "srepr_premise_expression": "Add(Pow(Symbol('C', commutative=True), Symbol('B', commutative=True)), Mul(Integer(-1), Symbol('N', commutative=True)))", "srepr_variable": "Symbol('N', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Mul(Integer(2), Pow(Symbol('C', commutative=True), Symbol('B', commutative=True))), Mul(Integer(-1), Symbol('N', commutative=True))))", "srepr_negatives": ["Mul(Symbol('N', commutative=True), Add(Pow(Symbol('B', commutative=True), Symbol('B', commutative=True)), Symbol('C', commutative=True)))", "Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('B', commutative=True)), Mul(Symbol('C', commutative=True), Symbol('N', commutative=True))))", "Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('B', commutative=True)), Mul(Integer(2), Symbol('C', commutative=True)), Symbol('N', commutative=True)))", "Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('B', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('C', commutative=True)), Symbol('N', commutative=True)))"]}, {"premise_expression": "e^{\\frac{n}{y}}", "variable": "n", "positive": "y e^{\\frac{n}{y}}", "negatives": ["y \\sin{(n)}", "\\frac{n^{2}}{2 y}", "\\sin{(n - y)}", "- \\cos{(n + y)}"], "srepr_premise_expression": "exp(Mul(Symbol('n', commutative=True), Pow(Symbol('y', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('n', commutative=True)", "srepr_positive": "Mul(Symbol('y', commutative=True), exp(Mul(Symbol('n', commutative=True), Pow(Symbol('y', commutative=True), Integer(-1)))))", "srepr_negatives": ["Mul(Symbol('y', commutative=True), sin(Symbol('n', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('n', commutative=True), Integer(2)), Pow(Symbol('y', commutative=True), Integer(-1)))", "sin(Add(Symbol('n', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('n', commutative=True), Symbol('y', commutative=True))))"]}, {"premise_expression": "\\frac{e^{b}}{l}", "variable": "l", "positive": "e^{b} \\log{(l)}", "negatives": ["- \\sin{(b - l)}", "\\frac{b l^{2}}{2}", "- \\cos{(b + l)}", "\\frac{l (- 2 b + l)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('l', commutative=True), Integer(-1)), exp(Symbol('b', commutative=True)))", "srepr_variable": "Symbol('l', commutative=True)", "srepr_positive": "Mul(exp(Symbol('b', commutative=True)), log(Symbol('l', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('b', commutative=True), Mul(Integer(-1), Symbol('l', commutative=True)))))", "Mul(Rational(1, 2), Symbol('b', commutative=True), Pow(Symbol('l', commutative=True), Integer(2)))", "Mul(Integer(-1), cos(Add(Symbol('b', commutative=True), Symbol('l', commutative=True))))", "Mul(Rational(1, 2), Symbol('l', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('b', commutative=True)), Symbol('l', commutative=True)))"]}, {"premise_expression": "- N + n", "variable": "N", "positive": "\\frac{N (- N + 2 n)}{2}", "negatives": ["\\frac{n (- 2 N + n)}{2}", "\\frac{N (N + 2 \\cos{(n)})}{2}", "\\frac{N^{2} \\log{(n)}}{2}", "\\cos{(N - n)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('N', commutative=True)), Symbol('n', commutative=True))", "srepr_variable": "Symbol('N', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Mul(Integer(-1), Symbol('N', commutative=True)), Mul(Integer(2), Symbol('n', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('n', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('N', commutative=True)), Symbol('n', commutative=True)))", "Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Symbol('N', commutative=True), Mul(Integer(2), cos(Symbol('n', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('N', commutative=True), Integer(2)), log(Symbol('n', commutative=True)))", "cos(Add(Symbol('N', commutative=True), Mul(Integer(-1), Symbol('n', commutative=True))))"]}, {"premise_expression": "e^{C - J}", "variable": "J", "positive": "- e^{C - J}", "negatives": ["e^{C - J}", "- \\cos{(C - J)}", "C \\log{(J)}", "\\log{(C)} \\log{(J)}"], "srepr_premise_expression": "exp(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('J', commutative=True))))", "srepr_variable": "Symbol('J', commutative=True)", "srepr_positive": "Mul(Integer(-1), exp(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('J', commutative=True)))))", "srepr_negatives": ["exp(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('J', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('J', commutative=True)))))", "Mul(Symbol('C', commutative=True), log(Symbol('J', commutative=True)))", "Mul(log(Symbol('C', commutative=True)), log(Symbol('J', commutative=True)))"]}, {"premise_expression": "D v^{T}", "variable": "D", "positive": "\\frac{D^{2} v^{T}}{2}", "negatives": ["\\frac{D^{2} T v}{2}", "\\frac{D^{2} v}{2 T}", "\\frac{D^{2} (T - v)}{2}", "\\frac{T \\log{(D)}}{v}"], "srepr_premise_expression": "Mul(Symbol('D', commutative=True), Pow(Symbol('v', commutative=True), Symbol('T', commutative=True)))", "srepr_variable": "Symbol('D', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(2)), Pow(Symbol('v', commutative=True), Symbol('T', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(2)), Symbol('T', commutative=True), Symbol('v', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(2)), Pow(Symbol('T', commutative=True), Integer(-1)), Symbol('v', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(2)), Add(Symbol('T', commutative=True), Mul(Integer(-1), Symbol('v', commutative=True))))", "Mul(Symbol('T', commutative=True), Pow(Symbol('v', commutative=True), Integer(-1)), log(Symbol('D', commutative=True)))"]}, {"premise_expression": "\\sin^{L}{(D)}", "variable": "D", "positive": "\\int \\sin^{L}{(D)} dD", "negatives": ["\\int \\cos^{L}{(D)} dD", "\\log{(D)} \\sin{(L)}", "L \\log{(D)}", "\\frac{D (D + 2 e^{L})}{2}"], "srepr_premise_expression": "Pow(sin(Symbol('D', commutative=True)), Symbol('L', commutative=True))", "srepr_variable": "Symbol('D', commutative=True)", "srepr_positive": "Integral(Pow(sin(Symbol('D', commutative=True)), Symbol('L', commutative=True)), Tuple(Symbol('D', commutative=True)))", "srepr_negatives": ["Integral(Pow(cos(Symbol('D', commutative=True)), Symbol('L', commutative=True)), Tuple(Symbol('D', commutative=True)))", "Mul(log(Symbol('D', commutative=True)), sin(Symbol('L', commutative=True)))", "Mul(Symbol('L', commutative=True), log(Symbol('D', commutative=True)))", "Mul(Rational(1, 2), Symbol('D', commutative=True), Add(Symbol('D', commutative=True), Mul(Integer(2), exp(Symbol('L', commutative=True)))))"]}, {"premise_expression": "l - s", "variable": "s", "positive": "\\frac{s (2 l - s)}{2}", "negatives": ["\\frac{l (l - 2 s)}{2}", "- e^{l - s}", "- \\cos{(l - s)}", "\\frac{l s^{2}}{2}"], "srepr_premise_expression": "Add(Symbol('l', commutative=True), Mul(Integer(-1), Symbol('s', commutative=True)))", "srepr_variable": "Symbol('s', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('s', commutative=True), Add(Mul(Integer(2), Symbol('l', commutative=True)), Mul(Integer(-1), Symbol('s', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('l', commutative=True), Add(Symbol('l', commutative=True), Mul(Integer(-1), Integer(2), Symbol('s', commutative=True))))", "Mul(Integer(-1), exp(Add(Symbol('l', commutative=True), Mul(Integer(-1), Symbol('s', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('l', commutative=True), Mul(Integer(-1), Symbol('s', commutative=True)))))", "Mul(Rational(1, 2), Symbol('l', commutative=True), Pow(Symbol('s', commutative=True), Integer(2)))"]}, {"premise_expression": "- C + H", "variable": "C", "positive": "\\frac{C (- C + 2 H)}{2}", "negatives": ["\\frac{H (- 2 C + H)}{2}", "\\frac{C (- C + 2 \\cos{(H)})}{2}", "\\frac{C^{2} \\log{(H)}}{2}", "e^{C - H}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('C', commutative=True)), Symbol('H', commutative=True))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Mul(Integer(-1), Symbol('C', commutative=True)), Mul(Integer(2), Symbol('H', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('H', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('C', commutative=True)), Symbol('H', commutative=True)))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Mul(Integer(-1), Symbol('C', commutative=True)), Mul(Integer(2), cos(Symbol('H', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2)), log(Symbol('H', commutative=True)))", "exp(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('H', commutative=True))))"]}, {"premise_expression": "- F + \\cos{(h)}", "variable": "h", "positive": "- F h + \\sin{(h)}", "negatives": ["- F h - \\cos{(h)}", "F e^{h}", "F \\log{(h)}", "F e^{\\frac{h}{F}}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('F', commutative=True)), cos(Symbol('h', commutative=True)))", "srepr_variable": "Symbol('h', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('F', commutative=True), Symbol('h', commutative=True)), sin(Symbol('h', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('F', commutative=True), Symbol('h', commutative=True)), Mul(Integer(-1), cos(Symbol('h', commutative=True))))", "Mul(Symbol('F', commutative=True), exp(Symbol('h', commutative=True)))", "Mul(Symbol('F', commutative=True), log(Symbol('h', commutative=True)))", "Mul(Symbol('F', commutative=True), exp(Mul(Pow(Symbol('F', commutative=True), Integer(-1)), Symbol('h', commutative=True))))"]}, {"premise_expression": "\\frac{N x}{F}", "variable": "F", "positive": "N x \\log{(F)}", "negatives": ["\\log{(F)}", "\\frac{N x^{2}}{2 F}", "\\frac{N^{2} x}{2 F}", "\\frac{F^{2} N x}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('F', commutative=True), Integer(-1)), Symbol('N', commutative=True), Symbol('x', commutative=True))", "srepr_variable": "Symbol('F', commutative=True)", "srepr_positive": "Mul(Symbol('N', commutative=True), Symbol('x', commutative=True), log(Symbol('F', commutative=True)))", "srepr_negatives": ["log(Symbol('F', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('F', commutative=True), Integer(-1)), Symbol('N', commutative=True), Pow(Symbol('x', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('F', commutative=True), Integer(-1)), Pow(Symbol('N', commutative=True), Integer(2)), Symbol('x', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('F', commutative=True), Integer(2)), Symbol('N', commutative=True), Symbol('x', commutative=True))"]}, {"premise_expression": "\\cos{(p - u)}", "variable": "p", "positive": "\\sin{(p - u)}", "negatives": ["- \\sin{(p - u)}", "\\operatorname{Ei}{(p)}", "u e^{\\frac{p}{u}}", "0"], "srepr_premise_expression": "cos(Add(Symbol('p', commutative=True), Mul(Integer(-1), Symbol('u', commutative=True))))", "srepr_variable": "Symbol('p', commutative=True)", "srepr_positive": "sin(Add(Symbol('p', commutative=True), Mul(Integer(-1), Symbol('u', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('p', commutative=True), Mul(Integer(-1), Symbol('u', commutative=True)))))", "Ei(Symbol('p', commutative=True))", "Mul(Symbol('u', commutative=True), exp(Mul(Symbol('p', commutative=True), Pow(Symbol('u', commutative=True), Integer(-1)))))", "Integer(0)"]}, {"premise_expression": "- t + \\frac{w}{a}", "variable": "a", "positive": "- a t + w \\log{(a)}", "negatives": ["w^{t} \\log{(a)}", "- t w + \\frac{w^{2}}{2 a}", "- \\frac{t^{2}}{2} + \\frac{t w}{a}", "\\frac{a^{2}}{2 t w}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('t', commutative=True)), Mul(Pow(Symbol('a', commutative=True), Integer(-1)), Symbol('w', commutative=True)))", "srepr_variable": "Symbol('a', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('a', commutative=True), Symbol('t', commutative=True)), Mul(Symbol('w', commutative=True), log(Symbol('a', commutative=True))))", "srepr_negatives": ["Mul(Pow(Symbol('w', commutative=True), Symbol('t', commutative=True)), log(Symbol('a', commutative=True)))", "Add(Mul(Integer(-1), Symbol('t', commutative=True), Symbol('w', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('a', commutative=True), Integer(-1)), Pow(Symbol('w', commutative=True), Integer(2))))", "Add(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('t', commutative=True), Integer(2))), Mul(Pow(Symbol('a', commutative=True), Integer(-1)), Symbol('t', commutative=True), Symbol('w', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('a', commutative=True), Integer(2)), Pow(Symbol('t', commutative=True), Integer(-1)), Pow(Symbol('w', commutative=True), Integer(-1)))"]}, {"premise_expression": "\\frac{a}{Y}", "variable": "a", "positive": "\\frac{a^{2}}{2 Y}", "negatives": ["a \\log{(Y)}", "Y \\log{(a)}", "\\frac{a^{2} (Y - 1)}{2}", "\\cos{(Y - a)}"], "srepr_premise_expression": "Mul(Pow(Symbol('Y', commutative=True), Integer(-1)), Symbol('a', commutative=True))", "srepr_variable": "Symbol('a', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('Y', commutative=True), Integer(-1)), Pow(Symbol('a', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('a', commutative=True), log(Symbol('Y', commutative=True)))", "Mul(Symbol('Y', commutative=True), log(Symbol('a', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('a', commutative=True), Integer(2)), Add(Symbol('Y', commutative=True), Integer(-1)))", "cos(Add(Symbol('Y', commutative=True), Mul(Integer(-1), Symbol('a', commutative=True))))"]}, {"premise_expression": "- Y + k - l", "variable": "k", "positive": "k (- Y + \\frac{k}{2} - l)", "negatives": ["\\frac{k (2 Y + k - 2 l)}{2}", "\\frac{k (2 Y - k + 2 l)}{2}", "\\frac{Y (- Y + 2 k - 2 l)}{2}", "\\frac{l (- 2 Y + 2 k - l)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('Y', commutative=True)), Symbol('k', commutative=True), Mul(Integer(-1), Symbol('l', commutative=True)))", "srepr_variable": "Symbol('k', commutative=True)", "srepr_positive": "Mul(Symbol('k', commutative=True), Add(Mul(Integer(-1), Symbol('Y', commutative=True)), Mul(Rational(1, 2), Symbol('k', commutative=True)), Mul(Integer(-1), Symbol('l', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('k', commutative=True), Add(Mul(Integer(2), Symbol('Y', commutative=True)), Symbol('k', commutative=True), Mul(Integer(-1), Integer(2), Symbol('l', commutative=True))))", "Mul(Rational(1, 2), Symbol('k', commutative=True), Add(Mul(Integer(2), Symbol('Y', commutative=True)), Mul(Integer(-1), Symbol('k', commutative=True)), Mul(Integer(2), Symbol('l', commutative=True))))", "Mul(Rational(1, 2), Symbol('Y', commutative=True), Add(Mul(Integer(-1), Symbol('Y', commutative=True)), Mul(Integer(2), Symbol('k', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('l', commutative=True))))", "Mul(Rational(1, 2), Symbol('l', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('Y', commutative=True)), Mul(Integer(2), Symbol('k', commutative=True)), Mul(Integer(-1), Symbol('l', commutative=True))))"]}, {"premise_expression": "\\frac{T}{J}", "variable": "J", "positive": "T \\log{(J)}", "negatives": ["\\frac{T^{2}}{2 J}", "\\frac{J^{2} \\log{(T)}}{2}", "J (\\log{(\\frac{T}{J})} + 1)", "- e^{- J + T}"], "srepr_premise_expression": "Mul(Pow(Symbol('J', commutative=True), Integer(-1)), Symbol('T', commutative=True))", "srepr_variable": "Symbol('J', commutative=True)", "srepr_positive": "Mul(Symbol('T', commutative=True), log(Symbol('J', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('J', commutative=True), Integer(-1)), Pow(Symbol('T', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('J', commutative=True), Integer(2)), log(Symbol('T', commutative=True)))", "Mul(Symbol('J', commutative=True), Add(log(Mul(Pow(Symbol('J', commutative=True), Integer(-1)), Symbol('T', commutative=True))), Integer(1)))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('J', commutative=True)), Symbol('T', commutative=True))))"]}, {"premise_expression": "\\frac{f}{M}", "variable": "f", "positive": "\\frac{f^{2}}{2 M}", "negatives": ["f \\log{(M)}", "M e^{\\frac{f}{M}}", "\\frac{M f^{2}}{2}", "\\frac{f^{2} \\sin{(M)}}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('M', commutative=True), Integer(-1)), Symbol('f', commutative=True))", "srepr_variable": "Symbol('f', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('M', commutative=True), Integer(-1)), Pow(Symbol('f', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('f', commutative=True), log(Symbol('M', commutative=True)))", "Mul(Symbol('M', commutative=True), exp(Mul(Pow(Symbol('M', commutative=True), Integer(-1)), Symbol('f', commutative=True))))", "Mul(Rational(1, 2), Symbol('M', commutative=True), Pow(Symbol('f', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('f', commutative=True), Integer(2)), sin(Symbol('M', commutative=True)))"]}, {"premise_expression": "U + o s", "variable": "s", "positive": "\\frac{s (2 U + o s)}{2}", "negatives": ["\\frac{o (2 U + o s)}{2}", "\\frac{s (U s + 2 o)}{2}", "\\frac{s (2 U o - s)}{2}", "\\frac{U (U + 2 o s)}{2}"], "srepr_premise_expression": "Add(Symbol('U', commutative=True), Mul(Symbol('o', commutative=True), Symbol('s', commutative=True)))", "srepr_variable": "Symbol('s', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('s', commutative=True), Add(Mul(Integer(2), Symbol('U', commutative=True)), Mul(Symbol('o', commutative=True), Symbol('s', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Mul(Integer(2), Symbol('U', commutative=True)), Mul(Symbol('o', commutative=True), Symbol('s', commutative=True))))", "Mul(Rational(1, 2), Symbol('s', commutative=True), Add(Mul(Symbol('U', commutative=True), Symbol('s', commutative=True)), Mul(Integer(2), Symbol('o', commutative=True))))", "Mul(Rational(1, 2), Symbol('s', commutative=True), Add(Mul(Integer(2), Symbol('U', commutative=True), Symbol('o', commutative=True)), Mul(Integer(-1), Symbol('s', commutative=True))))", "Mul(Rational(1, 2), Symbol('U', commutative=True), Add(Symbol('U', commutative=True), Mul(Integer(2), Symbol('o', commutative=True), Symbol('s', commutative=True))))"]}, {"premise_expression": "H + K - n", "variable": "K", "positive": "K (H + \\frac{K}{2} - n)", "negatives": ["\\frac{K (- 2 H + K - 2 n)}{2}", "\\frac{n (2 H + 2 K - n)}{2}", "\\frac{H (H + 2 K - 2 n)}{2}", "\\frac{K (H K + 2 n)}{2}"], "srepr_premise_expression": "Add(Symbol('H', commutative=True), Symbol('K', commutative=True), Mul(Integer(-1), Symbol('n', commutative=True)))", "srepr_variable": "Symbol('K', commutative=True)", "srepr_positive": "Mul(Symbol('K', commutative=True), Add(Symbol('H', commutative=True), Mul(Rational(1, 2), Symbol('K', commutative=True)), Mul(Integer(-1), Symbol('n', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('H', commutative=True)), Symbol('K', commutative=True), Mul(Integer(-1), Integer(2), Symbol('n', commutative=True))))", "Mul(Rational(1, 2), Symbol('n', commutative=True), Add(Mul(Integer(2), Symbol('H', commutative=True)), Mul(Integer(2), Symbol('K', commutative=True)), Mul(Integer(-1), Symbol('n', commutative=True))))", "Mul(Rational(1, 2), Symbol('H', commutative=True), Add(Symbol('H', commutative=True), Mul(Integer(2), Symbol('K', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('n', commutative=True))))", "Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Mul(Symbol('H', commutative=True), Symbol('K', commutative=True)), Mul(Integer(2), Symbol('n', commutative=True))))"]}, {"premise_expression": "A f + m", "variable": "m", "positive": "\\frac{m (2 A f + m)}{2}", "negatives": ["\\frac{m (2 A + f m)}{2}", "\\frac{f (A f + 2 m)}{2}", "\\frac{A (A f + 2 m)}{2}", "\\frac{A m (- 2 f + m)}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('A', commutative=True), Symbol('f', commutative=True)), Symbol('m', commutative=True))", "srepr_variable": "Symbol('m', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Mul(Integer(2), Symbol('A', commutative=True), Symbol('f', commutative=True)), Symbol('m', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Mul(Integer(2), Symbol('A', commutative=True)), Mul(Symbol('f', commutative=True), Symbol('m', commutative=True))))", "Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Mul(Symbol('A', commutative=True), Symbol('f', commutative=True)), Mul(Integer(2), Symbol('m', commutative=True))))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Mul(Symbol('A', commutative=True), Symbol('f', commutative=True)), Mul(Integer(2), Symbol('m', commutative=True))))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Symbol('m', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('f', commutative=True)), Symbol('m', commutative=True)))"]}, {"premise_expression": "A + \\frac{M}{N}", "variable": "A", "positive": "\\frac{A^{2}}{2} + \\frac{A M}{N}", "negatives": ["\\frac{A^{2}}{2 N} + A M", "\\frac{A (A - 2 M + 2 N)}{2}", "\\frac{A^{2} M N}{2}", "\\frac{A^{2} N}{2 M}"], "srepr_premise_expression": "Add(Symbol('A', commutative=True), Mul(Symbol('M', commutative=True), Pow(Symbol('N', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('A', commutative=True)", "srepr_positive": "Add(Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2))), Mul(Symbol('A', commutative=True), Symbol('M', commutative=True), Pow(Symbol('N', commutative=True), Integer(-1))))", "srepr_negatives": ["Add(Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2)), Pow(Symbol('N', commutative=True), Integer(-1))), Mul(Symbol('A', commutative=True), Symbol('M', commutative=True)))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Symbol('A', commutative=True), Mul(Integer(-1), Integer(2), Symbol('M', commutative=True)), Mul(Integer(2), Symbol('N', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2)), Symbol('M', commutative=True), Symbol('N', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2)), Pow(Symbol('M', commutative=True), Integer(-1)), Symbol('N', commutative=True))"]}, {"premise_expression": "\\log{(U v)}", "variable": "v", "positive": "v (\\log{(U v)} - 1)", "negatives": ["U (\\log{(U v)} - 1)", "- \\sin{(U - v)}", "\\frac{v (- 2 U + v)}{2}", "\\sin{(U + v)}"], "srepr_premise_expression": "log(Mul(Symbol('U', commutative=True), Symbol('v', commutative=True)))", "srepr_variable": "Symbol('v', commutative=True)", "srepr_positive": "Mul(Symbol('v', commutative=True), Add(log(Mul(Symbol('U', commutative=True), Symbol('v', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('U', commutative=True), Add(log(Mul(Symbol('U', commutative=True), Symbol('v', commutative=True))), Integer(-1)))", "Mul(Integer(-1), sin(Add(Symbol('U', commutative=True), Mul(Integer(-1), Symbol('v', commutative=True)))))", "Mul(Rational(1, 2), Symbol('v', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('U', commutative=True)), Symbol('v', commutative=True)))", "sin(Add(Symbol('U', commutative=True), Symbol('v', commutative=True)))"]}, {"premise_expression": "I l + z", "variable": "I", "positive": "\\frac{I (I l + 2 z)}{2}", "negatives": ["\\frac{l (I l + 2 z)}{2}", "\\frac{z (2 I l + z)}{2}", "\\frac{I^{2} (- l + z)}{2}", "\\frac{I (- I + 2 z^{l})}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('I', commutative=True), Symbol('l', commutative=True)), Symbol('z', commutative=True))", "srepr_variable": "Symbol('I', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('I', commutative=True), Add(Mul(Symbol('I', commutative=True), Symbol('l', commutative=True)), Mul(Integer(2), Symbol('z', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('l', commutative=True), Add(Mul(Symbol('I', commutative=True), Symbol('l', commutative=True)), Mul(Integer(2), Symbol('z', commutative=True))))", "Mul(Rational(1, 2), Symbol('z', commutative=True), Add(Mul(Integer(2), Symbol('I', commutative=True), Symbol('l', commutative=True)), Symbol('z', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(2)), Add(Mul(Integer(-1), Symbol('l', commutative=True)), Symbol('z', commutative=True)))", "Mul(Rational(1, 2), Symbol('I', commutative=True), Add(Mul(Integer(-1), Symbol('I', commutative=True)), Mul(Integer(2), Pow(Symbol('z', commutative=True), Symbol('l', commutative=True)))))"]}, {"premise_expression": "\\sin{(J - f)}", "variable": "J", "positive": "- \\cos{(J - f)}", "negatives": ["\\cos{(J - f)}", "f \\sin{(J)}", "\\log{(J)} \\sin{(f)}", "\\frac{J^{2} \\log{(f)}}{2}"], "srepr_premise_expression": "sin(Add(Symbol('J', commutative=True), Mul(Integer(-1), Symbol('f', commutative=True))))", "srepr_variable": "Symbol('J', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('J', commutative=True), Mul(Integer(-1), Symbol('f', commutative=True)))))", "srepr_negatives": ["cos(Add(Symbol('J', commutative=True), Mul(Integer(-1), Symbol('f', commutative=True))))", "Mul(Symbol('f', commutative=True), sin(Symbol('J', commutative=True)))", "Mul(log(Symbol('J', commutative=True)), sin(Symbol('f', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('J', commutative=True), Integer(2)), log(Symbol('f', commutative=True)))"]}, {"premise_expression": "\\sin{(S + Y)}", "variable": "S", "positive": "- \\cos{(S + Y)}", "negatives": ["Y e^{\\frac{S}{Y}}", "Y e^{S}", "\\frac{S (\\log{(S)} - 1)}{Y}", "\\frac{S^{2} \\log{(Y)}}{2}"], "srepr_premise_expression": "sin(Add(Symbol('S', commutative=True), Symbol('Y', commutative=True)))", "srepr_variable": "Symbol('S', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('S', commutative=True), Symbol('Y', commutative=True))))", "srepr_negatives": ["Mul(Symbol('Y', commutative=True), exp(Mul(Symbol('S', commutative=True), Pow(Symbol('Y', commutative=True), Integer(-1)))))", "Mul(Symbol('Y', commutative=True), exp(Symbol('S', commutative=True)))", "Mul(Symbol('S', commutative=True), Pow(Symbol('Y', commutative=True), Integer(-1)), Add(log(Symbol('S', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('S', commutative=True), Integer(2)), log(Symbol('Y', commutative=True)))"]}, {"premise_expression": "C D o", "variable": "D", "positive": "\\frac{C D^{2} o}{2}", "negatives": ["\\frac{C D o^{2}}{2}", "\\frac{C^{2} D o}{2}", "\\frac{D^{2} o}{2 C}", "\\frac{C \\log{(D)}}{o}"], "srepr_premise_expression": "Mul(Symbol('C', commutative=True), Symbol('D', commutative=True), Symbol('o', commutative=True))", "srepr_variable": "Symbol('D', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('C', commutative=True), Pow(Symbol('D', commutative=True), Integer(2)), Symbol('o', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('C', commutative=True), Symbol('D', commutative=True), Pow(Symbol('o', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2)), Symbol('D', commutative=True), Symbol('o', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(-1)), Pow(Symbol('D', commutative=True), Integer(2)), Symbol('o', commutative=True))", "Mul(Symbol('C', commutative=True), Pow(Symbol('o', commutative=True), Integer(-1)), log(Symbol('D', commutative=True)))"]}, {"premise_expression": "\\frac{I}{R}", "variable": "R", "positive": "I \\log{(R)}", "negatives": ["I \\log{(R)} + R", "\\frac{I^{2}}{2 R}", "\\log{(I)} \\log{(R)}", "e^{I} \\log{(R)}"], "srepr_premise_expression": "Mul(Symbol('I', commutative=True), Pow(Symbol('R', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('R', commutative=True)", "srepr_positive": "Mul(Symbol('I', commutative=True), log(Symbol('R', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('I', commutative=True), log(Symbol('R', commutative=True))), Symbol('R', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(2)), Pow(Symbol('R', commutative=True), Integer(-1)))", "Mul(log(Symbol('I', commutative=True)), log(Symbol('R', commutative=True)))", "Mul(exp(Symbol('I', commutative=True)), log(Symbol('R', commutative=True)))"]}, {"premise_expression": "\\sin{(B - w)}", "variable": "w", "positive": "\\cos{(B - w)}", "negatives": ["- \\cos{(B - w)}", "B \\sin{(w)}", "B w + e^{w}", "\\frac{\\sin{(w)}}{B}"], "srepr_premise_expression": "sin(Add(Symbol('B', commutative=True), Mul(Integer(-1), Symbol('w', commutative=True))))", "srepr_variable": "Symbol('w', commutative=True)", "srepr_positive": "cos(Add(Symbol('B', commutative=True), Mul(Integer(-1), Symbol('w', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('B', commutative=True), Mul(Integer(-1), Symbol('w', commutative=True)))))", "Mul(Symbol('B', commutative=True), sin(Symbol('w', commutative=True)))", "Add(Mul(Symbol('B', commutative=True), Symbol('w', commutative=True)), exp(Symbol('w', commutative=True)))", "Mul(Pow(Symbol('B', commutative=True), Integer(-1)), sin(Symbol('w', commutative=True)))"]}, {"premise_expression": "D Q", "variable": "Q", "positive": "\\frac{D Q^{2}}{2}", "negatives": ["\\frac{D^{2} Q}{2}", "\\frac{D^{2} Q^{2}}{2}", "\\frac{Q \\sin{(D)}}{D}", "\\frac{Q^{2} \\cos{(D)}}{2}"], "srepr_premise_expression": "Mul(Symbol('D', commutative=True), Symbol('Q', commutative=True))", "srepr_variable": "Symbol('Q', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('D', commutative=True), Pow(Symbol('Q', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(2)), Symbol('Q', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(2)), Pow(Symbol('Q', commutative=True), Integer(2)))", "Mul(Pow(Symbol('D', commutative=True), Integer(-1)), Symbol('Q', commutative=True), sin(Symbol('D', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(2)), cos(Symbol('D', commutative=True)))"]}, {"premise_expression": "\\cos{(R - m)}", "variable": "m", "positive": "- \\sin{(R - m)}", "negatives": ["\\sin{(R - m)}", "\\cos{(R - m)}", "- R m - \\cos{(m)}", "\\frac{m^{2}}{2 R}"], "srepr_premise_expression": "cos(Add(Symbol('R', commutative=True), Mul(Integer(-1), Symbol('m', commutative=True))))", "srepr_variable": "Symbol('m', commutative=True)", "srepr_positive": "Mul(Integer(-1), sin(Add(Symbol('R', commutative=True), Mul(Integer(-1), Symbol('m', commutative=True)))))", "srepr_negatives": ["sin(Add(Symbol('R', commutative=True), Mul(Integer(-1), Symbol('m', commutative=True))))", "cos(Add(Symbol('R', commutative=True), Mul(Integer(-1), Symbol('m', commutative=True))))", "Add(Mul(Integer(-1), Symbol('R', commutative=True), Symbol('m', commutative=True)), Mul(Integer(-1), cos(Symbol('m', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('R', commutative=True), Integer(-1)), Pow(Symbol('m', commutative=True), Integer(2)))"]}, {"premise_expression": "- R + \\cos{(L)}", "variable": "L", "positive": "- L R + \\sin{(L)}", "negatives": ["L R - \\cos{(L)}", "e^{L + R}", "\\frac{L^{2} \\log{(R)}}{2}", "\\frac{R (- R + 2 \\cos{(L)})}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('R', commutative=True)), cos(Symbol('L', commutative=True)))", "srepr_variable": "Symbol('L', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('L', commutative=True), Symbol('R', commutative=True)), sin(Symbol('L', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('L', commutative=True), Symbol('R', commutative=True)), Mul(Integer(-1), cos(Symbol('L', commutative=True))))", "exp(Add(Symbol('L', commutative=True), Symbol('R', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(2)), log(Symbol('R', commutative=True)))", "Mul(Rational(1, 2), Symbol('R', commutative=True), Add(Mul(Integer(-1), Symbol('R', commutative=True)), Mul(Integer(2), cos(Symbol('L', commutative=True)))))"]}, {"premise_expression": "A W", "variable": "A", "positive": "\\frac{A^{2} W}{2}", "negatives": ["\\frac{A W^{2}}{2}", "W \\sin{(A)}", "\\sin{(A - W)}", "e^{A + W}"], "srepr_premise_expression": "Mul(Symbol('A', commutative=True), Symbol('W', commutative=True))", "srepr_variable": "Symbol('A', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2)), Symbol('W', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('A', commutative=True), Pow(Symbol('W', commutative=True), Integer(2)))", "Mul(Symbol('W', commutative=True), sin(Symbol('A', commutative=True)))", "sin(Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('W', commutative=True))))", "exp(Add(Symbol('A', commutative=True), Symbol('W', commutative=True)))"]}, {"premise_expression": "t + \\cos{(N)}", "variable": "N", "positive": "N t + \\sin{(N)}", "negatives": ["N t + e^{N}", "\\frac{\\sin{(N)}}{t}", "\\frac{N t (N + 2 t)}{2}", "\\frac{t (t + 2 \\cos{(N)})}{2}"], "srepr_premise_expression": "Add(Symbol('t', commutative=True), cos(Symbol('N', commutative=True)))", "srepr_variable": "Symbol('N', commutative=True)", "srepr_positive": "Add(Mul(Symbol('N', commutative=True), Symbol('t', commutative=True)), sin(Symbol('N', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('N', commutative=True), Symbol('t', commutative=True)), exp(Symbol('N', commutative=True)))", "Mul(Pow(Symbol('t', commutative=True), Integer(-1)), sin(Symbol('N', commutative=True)))", "Mul(Rational(1, 2), Symbol('N', commutative=True), Symbol('t', commutative=True), Add(Symbol('N', commutative=True), Mul(Integer(2), Symbol('t', commutative=True))))", "Mul(Rational(1, 2), Symbol('t', commutative=True), Add(Symbol('t', commutative=True), Mul(Integer(2), cos(Symbol('N', commutative=True)))))"]}, {"premise_expression": "\\frac{l}{Z}", "variable": "Z", "positive": "l \\log{(Z)}", "negatives": ["- l \\cos{(Z)}", "\\frac{l^{2}}{2 Z}", "\\frac{Z^{2} \\log{(l)}}{2}", "Z l + \\sin{(Z)}"], "srepr_premise_expression": "Mul(Pow(Symbol('Z', commutative=True), Integer(-1)), Symbol('l', commutative=True))", "srepr_variable": "Symbol('Z', commutative=True)", "srepr_positive": "Mul(Symbol('l', commutative=True), log(Symbol('Z', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Symbol('l', commutative=True), cos(Symbol('Z', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('Z', commutative=True), Integer(-1)), Pow(Symbol('l', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('Z', commutative=True), Integer(2)), log(Symbol('l', commutative=True)))", "Add(Mul(Symbol('Z', commutative=True), Symbol('l', commutative=True)), sin(Symbol('Z', commutative=True)))"]}, {"premise_expression": "\\log{(D - T)}", "variable": "T", "positive": "- D \\log{(- D + T)} + T \\log{(D - T)} - T", "negatives": ["D \\log{(D - T)} - D - T \\log{(D - T)}", "- D \\operatorname{Ei}{(\\frac{D}{T})} + T e^{\\frac{D}{T}}", "- D T - \\cos{(T)}", "- \\cos{(D - T)}"], "srepr_premise_expression": "log(Add(Symbol('D', commutative=True), Mul(Integer(-1), Symbol('T', commutative=True))))", "srepr_variable": "Symbol('T', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('D', commutative=True), log(Add(Mul(Integer(-1), Symbol('D', commutative=True)), Symbol('T', commutative=True)))), Mul(Symbol('T', commutative=True), log(Add(Symbol('D', commutative=True), Mul(Integer(-1), Symbol('T', commutative=True))))), Mul(Integer(-1), Symbol('T', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('D', commutative=True), log(Add(Symbol('D', commutative=True), Mul(Integer(-1), Symbol('T', commutative=True))))), Mul(Integer(-1), Symbol('D', commutative=True)), Mul(Integer(-1), Symbol('T', commutative=True), log(Add(Symbol('D', commutative=True), Mul(Integer(-1), Symbol('T', commutative=True))))))", "Add(Mul(Integer(-1), Symbol('D', commutative=True), Ei(Mul(Symbol('D', commutative=True), Pow(Symbol('T', commutative=True), Integer(-1))))), Mul(Symbol('T', commutative=True), exp(Mul(Symbol('D', commutative=True), Pow(Symbol('T', commutative=True), Integer(-1))))))", "Add(Mul(Integer(-1), Symbol('D', commutative=True), Symbol('T', commutative=True)), Mul(Integer(-1), cos(Symbol('T', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('D', commutative=True), Mul(Integer(-1), Symbol('T', commutative=True)))))"]}, {"premise_expression": "- X + n w", "variable": "X", "positive": "\\frac{X (- X + 2 n w)}{2}", "negatives": ["\\frac{X (- X + 2 n^{w})}{2}", "\\frac{n (- 2 X + n w)}{2}", "\\frac{w (- 2 X + n w)}{2}", "\\frac{X n (X + 2 w)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('X', commutative=True)), Mul(Symbol('n', commutative=True), Symbol('w', commutative=True)))", "srepr_variable": "Symbol('X', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('X', commutative=True), Add(Mul(Integer(-1), Symbol('X', commutative=True)), Mul(Integer(2), Symbol('n', commutative=True), Symbol('w', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('X', commutative=True), Add(Mul(Integer(-1), Symbol('X', commutative=True)), Mul(Integer(2), Pow(Symbol('n', commutative=True), Symbol('w', commutative=True)))))", "Mul(Rational(1, 2), Symbol('n', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('X', commutative=True)), Mul(Symbol('n', commutative=True), Symbol('w', commutative=True))))", "Mul(Rational(1, 2), Symbol('w', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('X', commutative=True)), Mul(Symbol('n', commutative=True), Symbol('w', commutative=True))))", "Mul(Rational(1, 2), Symbol('X', commutative=True), Symbol('n', commutative=True), Add(Symbol('X', commutative=True), Mul(Integer(2), Symbol('w', commutative=True))))"]}, {"premise_expression": "c - y", "variable": "y", "positive": "\\frac{y (2 c - y)}{2}", "negatives": ["\\frac{y (2 c + y)}{2}", "\\frac{c (c - 2 y)}{2}", "c y - \\cos{(y)}", "\\log{(y)} \\cos{(c)}"], "srepr_premise_expression": "Add(Symbol('c', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True)))", "srepr_variable": "Symbol('y', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('y', commutative=True), Add(Mul(Integer(2), Symbol('c', commutative=True)), Mul(Integer(-1), Symbol('y', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('y', commutative=True), Add(Mul(Integer(2), Symbol('c', commutative=True)), Symbol('y', commutative=True)))", "Mul(Rational(1, 2), Symbol('c', commutative=True), Add(Symbol('c', commutative=True), Mul(Integer(-1), Integer(2), Symbol('y', commutative=True))))", "Add(Mul(Symbol('c', commutative=True), Symbol('y', commutative=True)), Mul(Integer(-1), cos(Symbol('y', commutative=True))))", "Mul(log(Symbol('y', commutative=True)), cos(Symbol('c', commutative=True)))"]}, {"premise_expression": "- M + e^{T}", "variable": "T", "positive": "- M T + e^{T}", "negatives": ["- M T + \\sin{(T)}", "M \\log{(T)}", "\\frac{M (- M + 2 e^{T})}{2}", "e^{- M + T}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('M', commutative=True)), exp(Symbol('T', commutative=True)))", "srepr_variable": "Symbol('T', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('M', commutative=True), Symbol('T', commutative=True)), exp(Symbol('T', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('M', commutative=True), Symbol('T', commutative=True)), sin(Symbol('T', commutative=True)))", "Mul(Symbol('M', commutative=True), log(Symbol('T', commutative=True)))", "Mul(Rational(1, 2), Symbol('M', commutative=True), Add(Mul(Integer(-1), Symbol('M', commutative=True)), Mul(Integer(2), exp(Symbol('T', commutative=True)))))", "exp(Add(Mul(Integer(-1), Symbol('M', commutative=True)), Symbol('T', commutative=True)))"]}, {"premise_expression": "\\cos{(N - l)}", "variable": "N", "positive": "\\sin{(N - l)}", "negatives": ["- \\sin{(N - l)}", "\\frac{\\sin{(N)}}{l}", "N l - \\cos{(N)}", "N (\\log{(\\frac{N}{l})} - 1)"], "srepr_premise_expression": "cos(Add(Symbol('N', commutative=True), Mul(Integer(-1), Symbol('l', commutative=True))))", "srepr_variable": "Symbol('N', commutative=True)", "srepr_positive": "sin(Add(Symbol('N', commutative=True), Mul(Integer(-1), Symbol('l', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('N', commutative=True), Mul(Integer(-1), Symbol('l', commutative=True)))))", "Mul(Pow(Symbol('l', commutative=True), Integer(-1)), sin(Symbol('N', commutative=True)))", "Add(Mul(Symbol('N', commutative=True), Symbol('l', commutative=True)), Mul(Integer(-1), cos(Symbol('N', commutative=True))))", "Mul(Symbol('N', commutative=True), Add(log(Mul(Symbol('N', commutative=True), Pow(Symbol('l', commutative=True), Integer(-1)))), Integer(-1)))"]}, {"premise_expression": "\\frac{B}{N T}", "variable": "T", "positive": "\\frac{B \\log{(T)}}{N}", "negatives": ["\\frac{B \\log{(N)}}{T}", "B T", "\\frac{T^{2}}{2}", "\\frac{B^{2}}{2 N T}"], "srepr_premise_expression": "Mul(Symbol('B', commutative=True), Pow(Symbol('N', commutative=True), Integer(-1)), Pow(Symbol('T', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('T', commutative=True)", "srepr_positive": "Mul(Symbol('B', commutative=True), Pow(Symbol('N', commutative=True), Integer(-1)), log(Symbol('T', commutative=True)))", "srepr_negatives": ["Mul(Symbol('B', commutative=True), Pow(Symbol('T', commutative=True), Integer(-1)), log(Symbol('N', commutative=True)))", "Mul(Symbol('B', commutative=True), Symbol('T', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('T', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('B', commutative=True), Integer(2)), Pow(Symbol('N', commutative=True), Integer(-1)), Pow(Symbol('T', commutative=True), Integer(-1)))"]}, {"premise_expression": "\\log{(\\frac{c}{I})}", "variable": "c", "positive": "c (\\log{(\\frac{c}{I})} - 1)", "negatives": ["I (\\log{(\\frac{c}{I})} + 1)", "c (\\log{(\\frac{I}{c})} + 1)", "c (- I + \\log{(c)} - 1)", "- \\sin{(I - c)}"], "srepr_premise_expression": "log(Mul(Pow(Symbol('I', commutative=True), Integer(-1)), Symbol('c', commutative=True)))", "srepr_variable": "Symbol('c', commutative=True)", "srepr_positive": "Mul(Symbol('c', commutative=True), Add(log(Mul(Pow(Symbol('I', commutative=True), Integer(-1)), Symbol('c', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('I', commutative=True), Add(log(Mul(Pow(Symbol('I', commutative=True), Integer(-1)), Symbol('c', commutative=True))), Integer(1)))", "Mul(Symbol('c', commutative=True), Add(log(Mul(Symbol('I', commutative=True), Pow(Symbol('c', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Symbol('c', commutative=True), Add(Mul(Integer(-1), Symbol('I', commutative=True)), log(Symbol('c', commutative=True)), Integer(-1)))", "Mul(Integer(-1), sin(Add(Symbol('I', commutative=True), Mul(Integer(-1), Symbol('c', commutative=True)))))"]}, {"premise_expression": "F + \\log{(z)}", "variable": "F", "positive": "\\frac{F (F + 2 \\log{(z)})}{2}", "negatives": ["\\frac{F (- F + 2 \\log{(z)})}{2}", "\\frac{F (F - 2 z)}{2}", "z (F + \\log{(z)} - 1)", "\\frac{F^{2} e^{z}}{2}"], "srepr_premise_expression": "Add(Symbol('F', commutative=True), log(Symbol('z', commutative=True)))", "srepr_variable": "Symbol('F', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Symbol('F', commutative=True), Mul(Integer(2), log(Symbol('z', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Mul(Integer(-1), Symbol('F', commutative=True)), Mul(Integer(2), log(Symbol('z', commutative=True)))))", "Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Symbol('F', commutative=True), Mul(Integer(-1), Integer(2), Symbol('z', commutative=True))))", "Mul(Symbol('z', commutative=True), Add(Symbol('F', commutative=True), log(Symbol('z', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('F', commutative=True), Integer(2)), exp(Symbol('z', commutative=True)))"]}, {"premise_expression": "D R", "variable": "R", "positive": "\\frac{D R^{2}}{2}", "negatives": ["\\frac{D^{2} R}{2}", "\\frac{R^{2}}{2 D}", "- \\frac{\\cos{(R)}}{D}", "- D R - \\cos{(R)}"], "srepr_premise_expression": "Mul(Symbol('D', commutative=True), Symbol('R', commutative=True))", "srepr_variable": "Symbol('R', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('D', commutative=True), Pow(Symbol('R', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(2)), Symbol('R', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(-1)), Pow(Symbol('R', commutative=True), Integer(2)))", "Mul(Integer(-1), Pow(Symbol('D', commutative=True), Integer(-1)), cos(Symbol('R', commutative=True)))", "Add(Mul(Integer(-1), Symbol('D', commutative=True), Symbol('R', commutative=True)), Mul(Integer(-1), cos(Symbol('R', commutative=True))))"]}, {"premise_expression": "e^{\\frac{a}{b}}", "variable": "b", "positive": "- a \\operatorname{Ei}{(\\frac{a}{b})} + b e^{\\frac{a}{b}}", "negatives": ["a b + e^{b}", "\\frac{b (- b + 2 e^{a})}{2}", "b e^{\\frac{a}{b}}", "\\frac{b (2 a + b)}{2}"], "srepr_premise_expression": "exp(Mul(Symbol('a', commutative=True), Pow(Symbol('b', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('b', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('a', commutative=True), Ei(Mul(Symbol('a', commutative=True), Pow(Symbol('b', commutative=True), Integer(-1))))), Mul(Symbol('b', commutative=True), exp(Mul(Symbol('a', commutative=True), Pow(Symbol('b', commutative=True), Integer(-1))))))", "srepr_negatives": ["Add(Mul(Symbol('a', commutative=True), Symbol('b', commutative=True)), exp(Symbol('b', commutative=True)))", "Mul(Rational(1, 2), Symbol('b', commutative=True), Add(Mul(Integer(-1), Symbol('b', commutative=True)), Mul(Integer(2), exp(Symbol('a', commutative=True)))))", "Mul(Symbol('b', commutative=True), exp(Mul(Symbol('a', commutative=True), Pow(Symbol('b', commutative=True), Integer(-1)))))", "Mul(Rational(1, 2), Symbol('b', commutative=True), Add(Mul(Integer(2), Symbol('a', commutative=True)), Symbol('b', commutative=True)))"]}, {"premise_expression": "\\log{(p^{f})}", "variable": "f", "positive": "\\frac{f^{2} \\log{(p)}}{2}", "negatives": ["\\frac{f^{2} e^{p}}{2}", "\\frac{f (f + 2 \\sin{(p)})}{2}", "\\sin{(f + p)}", "f (- p + \\log{(f^{p})})"], "srepr_premise_expression": "log(Pow(Symbol('p', commutative=True), Symbol('f', commutative=True)))", "srepr_variable": "Symbol('f', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('f', commutative=True), Integer(2)), log(Symbol('p', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('f', commutative=True), Integer(2)), exp(Symbol('p', commutative=True)))", "Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Symbol('f', commutative=True), Mul(Integer(2), sin(Symbol('p', commutative=True)))))", "sin(Add(Symbol('f', commutative=True), Symbol('p', commutative=True)))", "Mul(Symbol('f', commutative=True), Add(Mul(Integer(-1), Symbol('p', commutative=True)), log(Pow(Symbol('f', commutative=True), Symbol('p', commutative=True)))))"]}, {"premise_expression": "\\frac{D}{b}", "variable": "D", "positive": "\\frac{D^{2}}{2 b}", "negatives": ["D \\log{(b)}", "\\frac{D^{2} \\log{(b)}}{2}", "\\frac{D^{2} (1 - b)}{2 b}", "- \\cos{(D + b)}"], "srepr_premise_expression": "Mul(Symbol('D', commutative=True), Pow(Symbol('b', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('D', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(2)), Pow(Symbol('b', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('D', commutative=True), log(Symbol('b', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(2)), log(Symbol('b', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(2)), Pow(Symbol('b', commutative=True), Integer(-1)), Add(Integer(1), Mul(Integer(-1), Symbol('b', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('D', commutative=True), Symbol('b', commutative=True))))"]}, {"premise_expression": "\\log{(M + T)}", "variable": "M", "positive": "M \\log{(M + T)} - M + T \\log{(M + T)}", "negatives": ["M \\log{(M + T)} + T \\log{(M + T)} - T", "M (T + \\log{(M)} - 1)", "M (\\log{(M T)} - 1)", "\\frac{M (- M + 2 \\sin{(T)})}{2}"], "srepr_premise_expression": "log(Add(Symbol('M', commutative=True), Symbol('T', commutative=True)))", "srepr_variable": "Symbol('M', commutative=True)", "srepr_positive": "Add(Mul(Symbol('M', commutative=True), log(Add(Symbol('M', commutative=True), Symbol('T', commutative=True)))), Mul(Integer(-1), Symbol('M', commutative=True)), Mul(Symbol('T', commutative=True), log(Add(Symbol('M', commutative=True), Symbol('T', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('M', commutative=True), log(Add(Symbol('M', commutative=True), Symbol('T', commutative=True)))), Mul(Symbol('T', commutative=True), log(Add(Symbol('M', commutative=True), Symbol('T', commutative=True)))), Mul(Integer(-1), Symbol('T', commutative=True)))", "Mul(Symbol('M', commutative=True), Add(Symbol('T', commutative=True), log(Symbol('M', commutative=True)), Integer(-1)))", "Mul(Symbol('M', commutative=True), Add(log(Mul(Symbol('M', commutative=True), Symbol('T', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('M', commutative=True), Add(Mul(Integer(-1), Symbol('M', commutative=True)), Mul(Integer(2), sin(Symbol('T', commutative=True)))))"]}, {"premise_expression": "\\frac{j}{G}", "variable": "G", "positive": "j \\log{(G)}", "negatives": ["\\frac{j^{2}}{2 G}", "- \\cos{(G + j)}", "- G j + e^{G}", "G (\\log{(G j)} - 1)"], "srepr_premise_expression": "Mul(Pow(Symbol('G', commutative=True), Integer(-1)), Symbol('j', commutative=True))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Mul(Symbol('j', commutative=True), log(Symbol('G', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(-1)), Pow(Symbol('j', commutative=True), Integer(2)))", "Mul(Integer(-1), cos(Add(Symbol('G', commutative=True), Symbol('j', commutative=True))))", "Add(Mul(Integer(-1), Symbol('G', commutative=True), Symbol('j', commutative=True)), exp(Symbol('G', commutative=True)))", "Mul(Symbol('G', commutative=True), Add(log(Mul(Symbol('G', commutative=True), Symbol('j', commutative=True))), Integer(-1)))"]}, {"premise_expression": "e^{\\frac{K}{L}}", "variable": "K", "positive": "L e^{\\frac{K}{L}}", "negatives": ["- \\cos{(K - L)}", "- \\cos{(K + L)}", "\\frac{K (K - 2 L)}{2}", "K L (\\log{(K)} - 1)"], "srepr_premise_expression": "exp(Mul(Symbol('K', commutative=True), Pow(Symbol('L', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('K', commutative=True)", "srepr_positive": "Mul(Symbol('L', commutative=True), exp(Mul(Symbol('K', commutative=True), Pow(Symbol('L', commutative=True), Integer(-1)))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('K', commutative=True), Mul(Integer(-1), Symbol('L', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('K', commutative=True), Symbol('L', commutative=True))))", "Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Symbol('K', commutative=True), Mul(Integer(-1), Integer(2), Symbol('L', commutative=True))))", "Mul(Symbol('K', commutative=True), Symbol('L', commutative=True), Add(log(Symbol('K', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\frac{n}{p}", "variable": "p", "positive": "n \\log{(p)}", "negatives": ["n e^{p}", "\\frac{n^{2}}{2 p}", "\\frac{p^{2}}{2 n}", "n p (\\log{(p)} - 1)"], "srepr_premise_expression": "Mul(Symbol('n', commutative=True), Pow(Symbol('p', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('p', commutative=True)", "srepr_positive": "Mul(Symbol('n', commutative=True), log(Symbol('p', commutative=True)))", "srepr_negatives": ["Mul(Symbol('n', commutative=True), exp(Symbol('p', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('n', commutative=True), Integer(2)), Pow(Symbol('p', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('n', commutative=True), Integer(-1)), Pow(Symbol('p', commutative=True), Integer(2)))", "Mul(Symbol('n', commutative=True), Symbol('p', commutative=True), Add(log(Symbol('p', commutative=True)), Integer(-1)))"]}, {"premise_expression": "N + S", "variable": "N", "positive": "\\frac{N (N + 2 S)}{2}", "negatives": ["\\frac{S (2 N + S)}{2}", "\\frac{N (- N + 2 \\log{(S)})}{2}", "\\frac{N^{2} \\log{(S)}}{2}", "e^{N - S}"], "srepr_premise_expression": "Add(Symbol('N', commutative=True), Symbol('S', commutative=True))", "srepr_variable": "Symbol('N', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Symbol('N', commutative=True), Mul(Integer(2), Symbol('S', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Mul(Integer(2), Symbol('N', commutative=True)), Symbol('S', commutative=True)))", "Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Mul(Integer(-1), Symbol('N', commutative=True)), Mul(Integer(2), log(Symbol('S', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('N', commutative=True), Integer(2)), log(Symbol('S', commutative=True)))", "exp(Add(Symbol('N', commutative=True), Mul(Integer(-1), Symbol('S', commutative=True))))"]}, {"premise_expression": "b + f", "variable": "f", "positive": "\\frac{f (2 b + f)}{2}", "negatives": ["\\frac{b (b + 2 f)}{2}", "b \\sin{(f)}", "\\frac{\\sin{(f)}}{b}", "- \\frac{\\cos{(f)}}{b}"], "srepr_premise_expression": "Add(Symbol('b', commutative=True), Symbol('f', commutative=True))", "srepr_variable": "Symbol('f', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Mul(Integer(2), Symbol('b', commutative=True)), Symbol('f', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('b', commutative=True), Add(Symbol('b', commutative=True), Mul(Integer(2), Symbol('f', commutative=True))))", "Mul(Symbol('b', commutative=True), sin(Symbol('f', commutative=True)))", "Mul(Pow(Symbol('b', commutative=True), Integer(-1)), sin(Symbol('f', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('b', commutative=True), Integer(-1)), cos(Symbol('f', commutative=True)))"]}, {"premise_expression": "Y + j", "variable": "j", "positive": "\\frac{j (2 Y + j)}{2}", "negatives": ["\\frac{Y (Y + 2 j)}{2}", "\\frac{j^{2} \\cos{(Y)}}{2}", "\\frac{j^{2} \\log{(Y)}}{2}", "e^{Y + j}"], "srepr_premise_expression": "Add(Symbol('Y', commutative=True), Symbol('j', commutative=True))", "srepr_variable": "Symbol('j', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('j', commutative=True), Add(Mul(Integer(2), Symbol('Y', commutative=True)), Symbol('j', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('Y', commutative=True), Add(Symbol('Y', commutative=True), Mul(Integer(2), Symbol('j', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('j', commutative=True), Integer(2)), cos(Symbol('Y', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('j', commutative=True), Integer(2)), log(Symbol('Y', commutative=True)))", "exp(Add(Symbol('Y', commutative=True), Symbol('j', commutative=True)))"]}, {"premise_expression": "G y", "variable": "G", "positive": "\\frac{G^{2} y}{2}", "negatives": ["\\frac{G y^{2}}{2}", "\\frac{G (G - 2 y)}{2}", "G y - \\cos{(G)}", "- G y - \\cos{(G)}"], "srepr_premise_expression": "Mul(Symbol('G', commutative=True), Symbol('y', commutative=True))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(2)), Symbol('y', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('G', commutative=True), Pow(Symbol('y', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Symbol('G', commutative=True), Mul(Integer(-1), Integer(2), Symbol('y', commutative=True))))", "Add(Mul(Symbol('G', commutative=True), Symbol('y', commutative=True)), Mul(Integer(-1), cos(Symbol('G', commutative=True))))", "Add(Mul(Integer(-1), Symbol('G', commutative=True), Symbol('y', commutative=True)), Mul(Integer(-1), cos(Symbol('G', commutative=True))))"]}, {"premise_expression": "T + c + s", "variable": "s", "positive": "s (T + c + \\frac{s}{2})", "negatives": ["\\frac{c (2 T + c + 2 s)}{2}", "\\frac{T (T + 2 c + 2 s)}{2}", "\\frac{s (2 T + s)}{2 c}", "(T + c) \\log{(s)}"], "srepr_premise_expression": "Add(Symbol('T', commutative=True), Symbol('c', commutative=True), Symbol('s', commutative=True))", "srepr_variable": "Symbol('s', commutative=True)", "srepr_positive": "Mul(Symbol('s', commutative=True), Add(Symbol('T', commutative=True), Symbol('c', commutative=True), Mul(Rational(1, 2), Symbol('s', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('c', commutative=True), Add(Mul(Integer(2), Symbol('T', commutative=True)), Symbol('c', commutative=True), Mul(Integer(2), Symbol('s', commutative=True))))", "Mul(Rational(1, 2), Symbol('T', commutative=True), Add(Symbol('T', commutative=True), Mul(Integer(2), Symbol('c', commutative=True)), Mul(Integer(2), Symbol('s', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('c', commutative=True), Integer(-1)), Symbol('s', commutative=True), Add(Mul(Integer(2), Symbol('T', commutative=True)), Symbol('s', commutative=True)))", "Mul(Add(Symbol('T', commutative=True), Symbol('c', commutative=True)), log(Symbol('s', commutative=True)))"]}, {"premise_expression": "- Y + \\sin{(o)}", "variable": "Y", "positive": "\\frac{Y (- Y + 2 \\sin{(o)})}{2}", "negatives": ["\\frac{Y^{2} \\sin{(o)}}{2}", "\\log{(Y)} \\sin{(o)}", "- Y o - \\cos{(o)}", "\\sin{(Y + o)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('Y', commutative=True)), sin(Symbol('o', commutative=True)))", "srepr_variable": "Symbol('Y', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('Y', commutative=True), Add(Mul(Integer(-1), Symbol('Y', commutative=True)), Mul(Integer(2), sin(Symbol('o', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('Y', commutative=True), Integer(2)), sin(Symbol('o', commutative=True)))", "Mul(log(Symbol('Y', commutative=True)), sin(Symbol('o', commutative=True)))", "Add(Mul(Integer(-1), Symbol('Y', commutative=True), Symbol('o', commutative=True)), Mul(Integer(-1), cos(Symbol('o', commutative=True))))", "sin(Add(Symbol('Y', commutative=True), Symbol('o', commutative=True)))"]}, {"premise_expression": "- \\sin{(b - y)}", "variable": "b", "positive": "\\cos{(b - y)}", "negatives": ["- \\cos{(b - y)}", "e^{b + y}", "\\frac{b (b - 2 y)}{2}", "b (y + \\log{(b)} - 1)"], "srepr_premise_expression": "Mul(Integer(-1), sin(Add(Symbol('b', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True)))))", "srepr_variable": "Symbol('b', commutative=True)", "srepr_positive": "cos(Add(Symbol('b', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('b', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True)))))", "exp(Add(Symbol('b', commutative=True), Symbol('y', commutative=True)))", "Mul(Rational(1, 2), Symbol('b', commutative=True), Add(Symbol('b', commutative=True), Mul(Integer(-1), Integer(2), Symbol('y', commutative=True))))", "Mul(Symbol('b', commutative=True), Add(Symbol('y', commutative=True), log(Symbol('b', commutative=True)), Integer(-1)))"]}, {"premise_expression": "r \\sin{(u)}", "variable": "r", "positive": "\\frac{r^{2} \\sin{(u)}}{2}", "negatives": ["- r \\cos{(u)}", "\\frac{r (- r + 2 u)}{2}", "\\frac{r (- r + 2 e^{u})}{2}", "e^{r + u}"], "srepr_premise_expression": "Mul(Symbol('r', commutative=True), sin(Symbol('u', commutative=True)))", "srepr_variable": "Symbol('r', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('r', commutative=True), Integer(2)), sin(Symbol('u', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Symbol('r', commutative=True), cos(Symbol('u', commutative=True)))", "Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(-1), Symbol('r', commutative=True)), Mul(Integer(2), Symbol('u', commutative=True))))", "Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(-1), Symbol('r', commutative=True)), Mul(Integer(2), exp(Symbol('u', commutative=True)))))", "exp(Add(Symbol('r', commutative=True), Symbol('u', commutative=True)))"]}, {"premise_expression": "\\log{(I - P)}", "variable": "I", "positive": "I \\log{(I - P)} - I - P \\log{(I - P)}", "negatives": ["- I \\log{(- I + P)} + P \\log{(I - P)} - P", "I (\\log{(I P)} - 1)", "\\log{(I)} \\cos{(P)}", "\\log{(I)} \\sin{(P)}"], "srepr_premise_expression": "log(Add(Symbol('I', commutative=True), Mul(Integer(-1), Symbol('P', commutative=True))))", "srepr_variable": "Symbol('I', commutative=True)", "srepr_positive": "Add(Mul(Symbol('I', commutative=True), log(Add(Symbol('I', commutative=True), Mul(Integer(-1), Symbol('P', commutative=True))))), Mul(Integer(-1), Symbol('I', commutative=True)), Mul(Integer(-1), Symbol('P', commutative=True), log(Add(Symbol('I', commutative=True), Mul(Integer(-1), Symbol('P', commutative=True))))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('I', commutative=True), log(Add(Mul(Integer(-1), Symbol('I', commutative=True)), Symbol('P', commutative=True)))), Mul(Symbol('P', commutative=True), log(Add(Symbol('I', commutative=True), Mul(Integer(-1), Symbol('P', commutative=True))))), Mul(Integer(-1), Symbol('P', commutative=True)))", "Mul(Symbol('I', commutative=True), Add(log(Mul(Symbol('I', commutative=True), Symbol('P', commutative=True))), Integer(-1)))", "Mul(log(Symbol('I', commutative=True)), cos(Symbol('P', commutative=True)))", "Mul(log(Symbol('I', commutative=True)), sin(Symbol('P', commutative=True)))"]}, {"premise_expression": "\\cos^{T}{(H)}", "variable": "H", "positive": "\\int \\cos^{T}{(H)} dH", "negatives": ["H (T + \\log{(H)} - 1)", "\\frac{H (\\log{(H)} - 1)}{T}", "\\frac{H (- H + 2 \\cos{(T)})}{2}", "\\frac{H^{2} \\log{(T)}}{2}"], "srepr_premise_expression": "Pow(cos(Symbol('H', commutative=True)), Symbol('T', commutative=True))", "srepr_variable": "Symbol('H', commutative=True)", "srepr_positive": "Integral(Pow(cos(Symbol('H', commutative=True)), Symbol('T', commutative=True)), Tuple(Symbol('H', commutative=True)))", "srepr_negatives": ["Mul(Symbol('H', commutative=True), Add(Symbol('T', commutative=True), log(Symbol('H', commutative=True)), Integer(-1)))", "Mul(Symbol('H', commutative=True), Pow(Symbol('T', commutative=True), Integer(-1)), Add(log(Symbol('H', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('H', commutative=True), Add(Mul(Integer(-1), Symbol('H', commutative=True)), Mul(Integer(2), cos(Symbol('T', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('H', commutative=True), Integer(2)), log(Symbol('T', commutative=True)))"]}, {"premise_expression": "s + e^{L}", "variable": "s", "positive": "\\frac{s (s + 2 e^{L})}{2}", "negatives": ["\\frac{s (- s + 2 \\log{(L)})}{2}", "L s + e^{L}", "\\frac{s (- 2 L + s)}{2}", "- L s + \\sin{(s)}"], "srepr_premise_expression": "Add(Symbol('s', commutative=True), exp(Symbol('L', commutative=True)))", "srepr_variable": "Symbol('s', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('s', commutative=True), Add(Symbol('s', commutative=True), Mul(Integer(2), exp(Symbol('L', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('s', commutative=True), Add(Mul(Integer(-1), Symbol('s', commutative=True)), Mul(Integer(2), log(Symbol('L', commutative=True)))))", "Add(Mul(Symbol('L', commutative=True), Symbol('s', commutative=True)), exp(Symbol('L', commutative=True)))", "Mul(Rational(1, 2), Symbol('s', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('L', commutative=True)), Symbol('s', commutative=True)))", "Add(Mul(Integer(-1), Symbol('L', commutative=True), Symbol('s', commutative=True)), sin(Symbol('s', commutative=True)))"]}, {"premise_expression": "F + k", "variable": "F", "positive": "\\frac{F (F + 2 k)}{2}", "negatives": ["\\frac{F (F - 2 k)}{2}", "\\frac{F (- F + 2 k)}{2}", "\\frac{k (2 F + k)}{2}", "\\frac{F (- F + 2 \\cos{(k)})}{2}"], "srepr_premise_expression": "Add(Symbol('F', commutative=True), Symbol('k', commutative=True))", "srepr_variable": "Symbol('F', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Symbol('F', commutative=True), Mul(Integer(2), Symbol('k', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Symbol('F', commutative=True), Mul(Integer(-1), Integer(2), Symbol('k', commutative=True))))", "Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Mul(Integer(-1), Symbol('F', commutative=True)), Mul(Integer(2), Symbol('k', commutative=True))))", "Mul(Rational(1, 2), Symbol('k', commutative=True), Add(Mul(Integer(2), Symbol('F', commutative=True)), Symbol('k', commutative=True)))", "Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Mul(Integer(-1), Symbol('F', commutative=True)), Mul(Integer(2), cos(Symbol('k', commutative=True)))))"]}, {"premise_expression": "E - u", "variable": "E", "positive": "\\frac{E (E - 2 u)}{2}", "negatives": ["\\frac{E (- E + 2 u)}{2}", "\\frac{u (2 E - u)}{2}", "\\frac{E^{2} u}{2}", "\\sin{(E - u)}"], "srepr_premise_expression": "Add(Symbol('E', commutative=True), Mul(Integer(-1), Symbol('u', commutative=True)))", "srepr_variable": "Symbol('E', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('E', commutative=True), Add(Symbol('E', commutative=True), Mul(Integer(-1), Integer(2), Symbol('u', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('E', commutative=True), Add(Mul(Integer(-1), Symbol('E', commutative=True)), Mul(Integer(2), Symbol('u', commutative=True))))", "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(2), Symbol('E', commutative=True)), Mul(Integer(-1), Symbol('u', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('E', commutative=True), Integer(2)), Symbol('u', commutative=True))", "sin(Add(Symbol('E', commutative=True), Mul(Integer(-1), Symbol('u', commutative=True))))"]}, {"premise_expression": "e^{\\frac{G}{Z}}", "variable": "Z", "positive": "- G \\operatorname{Ei}{(\\frac{G}{Z})} + Z e^{\\frac{G}{Z}}", "negatives": ["G Z + e^{Z}", "\\frac{Z (- Z + 2 e^{G})}{2}", "\\frac{Z (Z + 2 e^{G})}{2}", "Z e^{\\frac{G}{Z}}"], "srepr_premise_expression": "exp(Mul(Symbol('G', commutative=True), Pow(Symbol('Z', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('Z', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('G', commutative=True), Ei(Mul(Symbol('G', commutative=True), Pow(Symbol('Z', commutative=True), Integer(-1))))), Mul(Symbol('Z', commutative=True), exp(Mul(Symbol('G', commutative=True), Pow(Symbol('Z', commutative=True), Integer(-1))))))", "srepr_negatives": ["Add(Mul(Symbol('G', commutative=True), Symbol('Z', commutative=True)), exp(Symbol('Z', commutative=True)))", "Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Mul(Integer(-1), Symbol('Z', commutative=True)), Mul(Integer(2), exp(Symbol('G', commutative=True)))))", "Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Symbol('Z', commutative=True), Mul(Integer(2), exp(Symbol('G', commutative=True)))))", "Mul(Symbol('Z', commutative=True), exp(Mul(Symbol('G', commutative=True), Pow(Symbol('Z', commutative=True), Integer(-1)))))"]}, {"premise_expression": "p - x", "variable": "p", "positive": "\\frac{p (p - 2 x)}{2}", "negatives": ["\\frac{x (2 p - x)}{2}", "p \\sin{(x^{x})}", "- e^{- p + x}", "\\frac{\\sin{(p)}}{x}"], "srepr_premise_expression": "Add(Symbol('p', commutative=True), Mul(Integer(-1), Symbol('x', commutative=True)))", "srepr_variable": "Symbol('p', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Symbol('p', commutative=True), Mul(Integer(-1), Integer(2), Symbol('x', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('x', commutative=True), Add(Mul(Integer(2), Symbol('p', commutative=True)), Mul(Integer(-1), Symbol('x', commutative=True))))", "Mul(Symbol('p', commutative=True), sin(Pow(Symbol('x', commutative=True), Symbol('x', commutative=True))))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('p', commutative=True)), Symbol('x', commutative=True))))", "Mul(Pow(Symbol('x', commutative=True), Integer(-1)), sin(Symbol('p', commutative=True)))"]}, {"premise_expression": "c m", "variable": "m", "positive": "\\frac{c m^{2}}{2}", "negatives": ["\\frac{c^{2} m}{2}", "\\frac{m^{2} e^{c}}{2}", "\\frac{m (- 2 c + m)}{2}", "- c m - \\cos{(m)}"], "srepr_premise_expression": "Mul(Symbol('c', commutative=True), Symbol('m', commutative=True))", "srepr_variable": "Symbol('m', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('c', commutative=True), Pow(Symbol('m', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('c', commutative=True), Integer(2)), Symbol('m', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('m', commutative=True), Integer(2)), exp(Symbol('c', commutative=True)))", "Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('c', commutative=True)), Symbol('m', commutative=True)))", "Add(Mul(Integer(-1), Symbol('c', commutative=True), Symbol('m', commutative=True)), Mul(Integer(-1), cos(Symbol('m', commutative=True))))"]}, {"premise_expression": "A m", "variable": "A", "positive": "\\frac{A^{2} m}{2}", "negatives": ["\\frac{A m^{2}}{2}", "m \\log{(A)}", "e^{A - m}", "\\frac{A (- A + 2 \\log{(m)})}{2}"], "srepr_premise_expression": "Mul(Symbol('A', commutative=True), Symbol('m', commutative=True))", "srepr_variable": "Symbol('A', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2)), Symbol('m', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('A', commutative=True), Pow(Symbol('m', commutative=True), Integer(2)))", "Mul(Symbol('m', commutative=True), log(Symbol('A', commutative=True)))", "exp(Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('m', commutative=True))))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Mul(Integer(-1), Symbol('A', commutative=True)), Mul(Integer(2), log(Symbol('m', commutative=True)))))"]}, {"premise_expression": "\\frac{U}{z}", "variable": "z", "positive": "U \\log{(z)}", "negatives": ["\\frac{U^{2}}{2 z}", "\\frac{U z^{3}}{3}", "U z (\\log{(z)} - 1)", "- \\cos{(U + z)}"], "srepr_premise_expression": "Mul(Symbol('U', commutative=True), Pow(Symbol('z', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('z', commutative=True)", "srepr_positive": "Mul(Symbol('U', commutative=True), log(Symbol('z', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('U', commutative=True), Integer(2)), Pow(Symbol('z', commutative=True), Integer(-1)))", "Mul(Rational(1, 3), Symbol('U', commutative=True), Pow(Symbol('z', commutative=True), Integer(3)))", "Mul(Symbol('U', commutative=True), Symbol('z', commutative=True), Add(log(Symbol('z', commutative=True)), Integer(-1)))", "Mul(Integer(-1), cos(Add(Symbol('U', commutative=True), Symbol('z', commutative=True))))"]}, {"premise_expression": "\\log{(P + Q)}", "variable": "Q", "positive": "P \\log{(P + Q)} + Q \\log{(P + Q)} - Q", "negatives": ["P \\log{(P + Q)} - P + Q \\log{(P + Q)}", "P Q (\\log{(Q)} - 1)", "\\frac{Q (- Q + 2 e^{P})}{2}", "Q (- P + \\log{(Q^{P})})"], "srepr_premise_expression": "log(Add(Symbol('P', commutative=True), Symbol('Q', commutative=True)))", "srepr_variable": "Symbol('Q', commutative=True)", "srepr_positive": "Add(Mul(Symbol('P', commutative=True), log(Add(Symbol('P', commutative=True), Symbol('Q', commutative=True)))), Mul(Symbol('Q', commutative=True), log(Add(Symbol('P', commutative=True), Symbol('Q', commutative=True)))), Mul(Integer(-1), Symbol('Q', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('P', commutative=True), log(Add(Symbol('P', commutative=True), Symbol('Q', commutative=True)))), Mul(Integer(-1), Symbol('P', commutative=True)), Mul(Symbol('Q', commutative=True), log(Add(Symbol('P', commutative=True), Symbol('Q', commutative=True)))))", "Mul(Symbol('P', commutative=True), Symbol('Q', commutative=True), Add(log(Symbol('Q', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Mul(Integer(-1), Symbol('Q', commutative=True)), Mul(Integer(2), exp(Symbol('P', commutative=True)))))", "Mul(Symbol('Q', commutative=True), Add(Mul(Integer(-1), Symbol('P', commutative=True)), log(Pow(Symbol('Q', commutative=True), Symbol('P', commutative=True)))))"]}, {"premise_expression": "\\frac{F}{s}", "variable": "s", "positive": "F \\log{(s)}", "negatives": ["F \\sin{(s)}", "\\frac{F^{2}}{2 s}", "\\frac{F s^{2}}{2}", "\\frac{s^{2} \\log{(F)}}{2}"], "srepr_premise_expression": "Mul(Symbol('F', commutative=True), Pow(Symbol('s', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('s', commutative=True)", "srepr_positive": "Mul(Symbol('F', commutative=True), log(Symbol('s', commutative=True)))", "srepr_negatives": ["Mul(Symbol('F', commutative=True), sin(Symbol('s', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('F', commutative=True), Integer(2)), Pow(Symbol('s', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Symbol('F', commutative=True), Pow(Symbol('s', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('s', commutative=True), Integer(2)), log(Symbol('F', commutative=True)))"]}, {"premise_expression": "\\cos{(f + y)}", "variable": "f", "positive": "\\sin{(f + y)}", "negatives": ["\\frac{f (f - 2 y)}{2}", "\\log{(f)} \\sin{(y)}", "- y \\cos{(f)}", "\\frac{f^{2} \\log{(y)}}{2}"], "srepr_premise_expression": "cos(Add(Symbol('f', commutative=True), Symbol('y', commutative=True)))", "srepr_variable": "Symbol('f', commutative=True)", "srepr_positive": "sin(Add(Symbol('f', commutative=True), Symbol('y', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Symbol('f', commutative=True), Mul(Integer(-1), Integer(2), Symbol('y', commutative=True))))", "Mul(log(Symbol('f', commutative=True)), sin(Symbol('y', commutative=True)))", "Mul(Integer(-1), Symbol('y', commutative=True), cos(Symbol('f', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('f', commutative=True), Integer(2)), log(Symbol('y', commutative=True)))"]}, {"premise_expression": "\\frac{L}{X}", "variable": "X", "positive": "L \\log{(X)}", "negatives": ["\\frac{L^{2}}{2 X}", "e^{L} \\log{(X)}", "e X", "\\frac{X^{2}}{2 L}"], "srepr_premise_expression": "Mul(Symbol('L', commutative=True), Pow(Symbol('X', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('X', commutative=True)", "srepr_positive": "Mul(Symbol('L', commutative=True), log(Symbol('X', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(2)), Pow(Symbol('X', commutative=True), Integer(-1)))", "Mul(exp(Symbol('L', commutative=True)), log(Symbol('X', commutative=True)))", "Mul(E, Symbol('X', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(-1)), Pow(Symbol('X', commutative=True), Integer(2)))"]}, {"premise_expression": "S v", "variable": "S", "positive": "\\frac{S^{2} v}{2}", "negatives": ["\\frac{S v^{2}}{2}", "\\frac{S (S - 2 v)}{2}", "\\frac{S (- S + 2 v)}{2}", "v e^{\\frac{S}{v}}"], "srepr_premise_expression": "Mul(Symbol('S', commutative=True), Symbol('v', commutative=True))", "srepr_variable": "Symbol('S', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('S', commutative=True), Integer(2)), Symbol('v', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('S', commutative=True), Pow(Symbol('v', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Symbol('S', commutative=True), Mul(Integer(-1), Integer(2), Symbol('v', commutative=True))))", "Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Mul(Integer(-1), Symbol('S', commutative=True)), Mul(Integer(2), Symbol('v', commutative=True))))", "Mul(Symbol('v', commutative=True), exp(Mul(Symbol('S', commutative=True), Pow(Symbol('v', commutative=True), Integer(-1)))))"]}, {"premise_expression": "H - r", "variable": "r", "positive": "\\frac{r (2 H - r)}{2}", "negatives": ["\\frac{H (H - 2 r)}{2}", "\\frac{r^{2} \\cos{(H)}}{2}", "- \\sin{(H - r)}", "- \\cos{(H + r)}"], "srepr_premise_expression": "Add(Symbol('H', commutative=True), Mul(Integer(-1), Symbol('r', commutative=True)))", "srepr_variable": "Symbol('r', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(2), Symbol('H', commutative=True)), Mul(Integer(-1), Symbol('r', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('H', commutative=True), Add(Symbol('H', commutative=True), Mul(Integer(-1), Integer(2), Symbol('r', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('r', commutative=True), Integer(2)), cos(Symbol('H', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('H', commutative=True), Mul(Integer(-1), Symbol('r', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('H', commutative=True), Symbol('r', commutative=True))))"]}, {"premise_expression": "\\sin{(l + s)}", "variable": "s", "positive": "- \\cos{(l + s)}", "negatives": ["- \\sin{(l - s)}", "e^{- l + s}", "l s - \\cos{(s)}", "s (\\log{(l s)} - 1)"], "srepr_premise_expression": "sin(Add(Symbol('l', commutative=True), Symbol('s', commutative=True)))", "srepr_variable": "Symbol('s', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('l', commutative=True), Symbol('s', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('l', commutative=True), Mul(Integer(-1), Symbol('s', commutative=True)))))", "exp(Add(Mul(Integer(-1), Symbol('l', commutative=True)), Symbol('s', commutative=True)))", "Add(Mul(Symbol('l', commutative=True), Symbol('s', commutative=True)), Mul(Integer(-1), cos(Symbol('s', commutative=True))))", "Mul(Symbol('s', commutative=True), Add(log(Mul(Symbol('l', commutative=True), Symbol('s', commutative=True))), Integer(-1)))"]}, {"premise_expression": "C \\log{(l)}", "variable": "C", "positive": "\\frac{C^{2} \\log{(l)}}{2}", "negatives": ["l \\log{(C)}", "\\frac{C^{2}}{2 l}", "\\frac{C (C + 2 l)}{2}", "C l (\\log{(l)} - 1)"], "srepr_premise_expression": "Mul(Symbol('C', commutative=True), log(Symbol('l', commutative=True)))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2)), log(Symbol('l', commutative=True)))", "srepr_negatives": ["Mul(Symbol('l', commutative=True), log(Symbol('C', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2)), Pow(Symbol('l', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Symbol('C', commutative=True), Mul(Integer(2), Symbol('l', commutative=True))))", "Mul(Symbol('C', commutative=True), Symbol('l', commutative=True), Add(log(Symbol('l', commutative=True)), Integer(-1)))"]}, {"premise_expression": "Z \\cos{(E)}", "variable": "E", "positive": "Z \\sin{(E)}", "negatives": ["Z \\log{(E)}", "\\frac{\\sin{(E)}}{Z}", "\\log{(E)} \\sin{(Z)}", "\\frac{Z^{2} \\cos{(E)}}{2}"], "srepr_premise_expression": "Mul(Symbol('Z', commutative=True), cos(Symbol('E', commutative=True)))", "srepr_variable": "Symbol('E', commutative=True)", "srepr_positive": "Mul(Symbol('Z', commutative=True), sin(Symbol('E', commutative=True)))", "srepr_negatives": ["Mul(Symbol('Z', commutative=True), log(Symbol('E', commutative=True)))", "Mul(Pow(Symbol('Z', commutative=True), Integer(-1)), sin(Symbol('E', commutative=True)))", "Mul(log(Symbol('E', commutative=True)), sin(Symbol('Z', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('Z', commutative=True), Integer(2)), cos(Symbol('E', commutative=True)))"]}, {"premise_expression": "- \\sin{(R - x)}", "variable": "x", "positive": "- \\cos{(R - x)}", "negatives": ["\\cos{(R - x)}", "- e^{R - x}", "e^{- R + x}", "R \\sin{(x)}"], "srepr_premise_expression": "Mul(Integer(-1), sin(Add(Symbol('R', commutative=True), Mul(Integer(-1), Symbol('x', commutative=True)))))", "srepr_variable": "Symbol('x', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('R', commutative=True), Mul(Integer(-1), Symbol('x', commutative=True)))))", "srepr_negatives": ["cos(Add(Symbol('R', commutative=True), Mul(Integer(-1), Symbol('x', commutative=True))))", "Mul(Integer(-1), exp(Add(Symbol('R', commutative=True), Mul(Integer(-1), Symbol('x', commutative=True)))))", "exp(Add(Mul(Integer(-1), Symbol('R', commutative=True)), Symbol('x', commutative=True)))", "Mul(Symbol('R', commutative=True), sin(Symbol('x', commutative=True)))"]}, {"premise_expression": "V - f", "variable": "f", "positive": "\\frac{f (2 V - f)}{2}", "negatives": ["\\frac{V (V - 2 f)}{2}", "\\frac{f^{2} \\log{(V)}}{2}", "\\frac{V f^{2}}{2}", "\\frac{f (f + 2 \\cos{(V)})}{2}"], "srepr_premise_expression": "Add(Symbol('V', commutative=True), Mul(Integer(-1), Symbol('f', commutative=True)))", "srepr_variable": "Symbol('f', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Mul(Integer(2), Symbol('V', commutative=True)), Mul(Integer(-1), Symbol('f', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('V', commutative=True), Add(Symbol('V', commutative=True), Mul(Integer(-1), Integer(2), Symbol('f', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('f', commutative=True), Integer(2)), log(Symbol('V', commutative=True)))", "Mul(Rational(1, 2), Symbol('V', commutative=True), Pow(Symbol('f', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Symbol('f', commutative=True), Mul(Integer(2), cos(Symbol('V', commutative=True)))))"]}, {"premise_expression": "\\frac{X}{k u}", "variable": "X", "positive": "\\frac{X^{2}}{2 k u}", "negatives": ["\\frac{X^{2} k}{2 u}", "\\frac{X^{3} k}{3}", "\\frac{X \\log{(k)}}{u}", "\\frac{X \\log{(u)}}{k}"], "srepr_premise_expression": "Mul(Symbol('X', commutative=True), Pow(Symbol('k', commutative=True), Integer(-1)), Pow(Symbol('u', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('X', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('X', commutative=True), Integer(2)), Pow(Symbol('k', commutative=True), Integer(-1)), Pow(Symbol('u', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('X', commutative=True), Integer(2)), Symbol('k', commutative=True), Pow(Symbol('u', commutative=True), Integer(-1)))", "Mul(Rational(1, 3), Pow(Symbol('X', commutative=True), Integer(3)), Symbol('k', commutative=True))", "Mul(Symbol('X', commutative=True), Pow(Symbol('u', commutative=True), Integer(-1)), log(Symbol('k', commutative=True)))", "Mul(Symbol('X', commutative=True), Pow(Symbol('k', commutative=True), Integer(-1)), log(Symbol('u', commutative=True)))"]}, {"premise_expression": "G + M - f", "variable": "G", "positive": "G (\\frac{G}{2} + M - f)", "negatives": ["\\frac{G (G - 2 M - 2 f)}{2}", "\\frac{f (2 G + 2 M - f)}{2}", "\\frac{M (2 G + M - 2 f)}{2}", "- \\frac{G^{2}}{2} + \\frac{G f}{M}"], "srepr_premise_expression": "Add(Symbol('G', commutative=True), Symbol('M', commutative=True), Mul(Integer(-1), Symbol('f', commutative=True)))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Mul(Symbol('G', commutative=True), Add(Mul(Rational(1, 2), Symbol('G', commutative=True)), Symbol('M', commutative=True), Mul(Integer(-1), Symbol('f', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Symbol('G', commutative=True), Mul(Integer(-1), Integer(2), Symbol('M', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('f', commutative=True))))", "Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Mul(Integer(2), Symbol('G', commutative=True)), Mul(Integer(2), Symbol('M', commutative=True)), Mul(Integer(-1), Symbol('f', commutative=True))))", "Mul(Rational(1, 2), Symbol('M', commutative=True), Add(Mul(Integer(2), Symbol('G', commutative=True)), Symbol('M', commutative=True), Mul(Integer(-1), Integer(2), Symbol('f', commutative=True))))", "Add(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(2))), Mul(Symbol('G', commutative=True), Pow(Symbol('M', commutative=True), Integer(-1)), Symbol('f', commutative=True)))"]}, {"premise_expression": "B + \\cos{(G)}", "variable": "B", "positive": "\\frac{B (B + 2 \\cos{(G)})}{2}", "negatives": ["B G - \\cos{(B)}", "B G + \\sin{(G)}", "\\frac{B^{2} G}{2}", "\\frac{B^{2}}{2 G}"], "srepr_premise_expression": "Add(Symbol('B', commutative=True), cos(Symbol('G', commutative=True)))", "srepr_variable": "Symbol('B', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('B', commutative=True), Add(Symbol('B', commutative=True), Mul(Integer(2), cos(Symbol('G', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('B', commutative=True), Symbol('G', commutative=True)), Mul(Integer(-1), cos(Symbol('B', commutative=True))))", "Add(Mul(Symbol('B', commutative=True), Symbol('G', commutative=True)), sin(Symbol('G', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('B', commutative=True), Integer(2)), Symbol('G', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('B', commutative=True), Integer(2)), Pow(Symbol('G', commutative=True), Integer(-1)))"]}, {"premise_expression": "- o + \\frac{q}{b}", "variable": "b", "positive": "- b o + q \\log{(b)}", "negatives": ["o q \\log{(b)}", "- o q + \\frac{q^{2}}{2 b}", "\\frac{b (b + 2 q)}{2 o}", "\\frac{b^{2} q^{o}}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('o', commutative=True)), Mul(Pow(Symbol('b', commutative=True), Integer(-1)), Symbol('q', commutative=True)))", "srepr_variable": "Symbol('b', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('b', commutative=True), Symbol('o', commutative=True)), Mul(Symbol('q', commutative=True), log(Symbol('b', commutative=True))))", "srepr_negatives": ["Mul(Symbol('o', commutative=True), Symbol('q', commutative=True), log(Symbol('b', commutative=True)))", "Add(Mul(Integer(-1), Symbol('o', commutative=True), Symbol('q', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('b', commutative=True), Integer(-1)), Pow(Symbol('q', commutative=True), Integer(2))))", "Mul(Rational(1, 2), Symbol('b', commutative=True), Pow(Symbol('o', commutative=True), Integer(-1)), Add(Symbol('b', commutative=True), Mul(Integer(2), Symbol('q', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('b', commutative=True), Integer(2)), Pow(Symbol('q', commutative=True), Symbol('o', commutative=True)))"]}, {"premise_expression": "\\log{(s^{p})}", "variable": "p", "positive": "\\frac{p^{2} \\log{(s)}}{2}", "negatives": ["\\frac{p (p - 2 s)}{2}", "\\frac{p (p + 2 s)}{2}", "s \\sin{(p)}", "p s + e^{p}"], "srepr_premise_expression": "log(Pow(Symbol('s', commutative=True), Symbol('p', commutative=True)))", "srepr_variable": "Symbol('p', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('p', commutative=True), Integer(2)), log(Symbol('s', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Symbol('p', commutative=True), Mul(Integer(-1), Integer(2), Symbol('s', commutative=True))))", "Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Symbol('p', commutative=True), Mul(Integer(2), Symbol('s', commutative=True))))", "Mul(Symbol('s', commutative=True), sin(Symbol('p', commutative=True)))", "Add(Mul(Symbol('p', commutative=True), Symbol('s', commutative=True)), exp(Symbol('p', commutative=True)))"]}, {"premise_expression": "\\cos{(G - b)}", "variable": "G", "positive": "\\sin{(G - b)}", "negatives": ["- \\sin{(G - b)}", "b \\sin{(G)}", "- b \\cos{(G)}", "\\frac{G (\\log{(G)} - 1)}{b}"], "srepr_premise_expression": "cos(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('b', commutative=True))))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "sin(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('b', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('b', commutative=True)))))", "Mul(Symbol('b', commutative=True), sin(Symbol('G', commutative=True)))", "Mul(Integer(-1), Symbol('b', commutative=True), cos(Symbol('G', commutative=True)))", "Mul(Symbol('G', commutative=True), Pow(Symbol('b', commutative=True), Integer(-1)), Add(log(Symbol('G', commutative=True)), Integer(-1)))"]}, {"premise_expression": "S n", "variable": "S", "positive": "\\frac{S^{2} n}{2}", "negatives": ["\\frac{S n^{2}}{2}", "\\frac{S^{2}}{2 n}", "n \\log{(S)}", "- \\frac{\\cos{(S)}}{n}"], "srepr_premise_expression": "Mul(Symbol('S', commutative=True), Symbol('n', commutative=True))", "srepr_variable": "Symbol('S', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('S', commutative=True), Integer(2)), Symbol('n', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('S', commutative=True), Pow(Symbol('n', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('S', commutative=True), Integer(2)), Pow(Symbol('n', commutative=True), Integer(-1)))", "Mul(Symbol('n', commutative=True), log(Symbol('S', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('n', commutative=True), Integer(-1)), cos(Symbol('S', commutative=True)))"]}, {"premise_expression": "\\cos{(T - n)}", "variable": "T", "positive": "\\sin{(T - n)}", "negatives": ["- \\sin{(T - n)}", "\\frac{\\sin{(T)}}{n}", "- \\cos{(T - n)}", "- \\frac{\\cos{(T)}}{n}"], "srepr_premise_expression": "cos(Add(Symbol('T', commutative=True), Mul(Integer(-1), Symbol('n', commutative=True))))", "srepr_variable": "Symbol('T', commutative=True)", "srepr_positive": "sin(Add(Symbol('T', commutative=True), Mul(Integer(-1), Symbol('n', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('T', commutative=True), Mul(Integer(-1), Symbol('n', commutative=True)))))", "Mul(Pow(Symbol('n', commutative=True), Integer(-1)), sin(Symbol('T', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('T', commutative=True), Mul(Integer(-1), Symbol('n', commutative=True)))))", "Mul(Integer(-1), Pow(Symbol('n', commutative=True), Integer(-1)), cos(Symbol('T', commutative=True)))"]}, {"premise_expression": "o + \\sin{(a)}", "variable": "a", "positive": "a o - \\cos{(a)}", "negatives": ["a o + e^{a}", "- a o + \\sin{(a)}", "o \\log{(a)}", "\\frac{o (o + 2 \\sin{(a)})}{2}"], "srepr_premise_expression": "Add(Symbol('o', commutative=True), sin(Symbol('a', commutative=True)))", "srepr_variable": "Symbol('a', commutative=True)", "srepr_positive": "Add(Mul(Symbol('a', commutative=True), Symbol('o', commutative=True)), Mul(Integer(-1), cos(Symbol('a', commutative=True))))", "srepr_negatives": ["Add(Mul(Symbol('a', commutative=True), Symbol('o', commutative=True)), exp(Symbol('a', commutative=True)))", "Add(Mul(Integer(-1), Symbol('a', commutative=True), Symbol('o', commutative=True)), sin(Symbol('a', commutative=True)))", "Mul(Symbol('o', commutative=True), log(Symbol('a', commutative=True)))", "Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Symbol('o', commutative=True), Mul(Integer(2), sin(Symbol('a', commutative=True)))))"]}, {"premise_expression": "w + \\cos{(D)}", "variable": "w", "positive": "\\frac{w (w + 2 \\cos{(D)})}{2}", "negatives": ["D w - \\cos{(w)}", "\\frac{w^{2} e^{D}}{2}", "D w + \\sin{(D)}", "- D w + \\sin{(w)}"], "srepr_premise_expression": "Add(Symbol('w', commutative=True), cos(Symbol('D', commutative=True)))", "srepr_variable": "Symbol('w', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('w', commutative=True), Add(Symbol('w', commutative=True), Mul(Integer(2), cos(Symbol('D', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('D', commutative=True), Symbol('w', commutative=True)), Mul(Integer(-1), cos(Symbol('w', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('w', commutative=True), Integer(2)), exp(Symbol('D', commutative=True)))", "Add(Mul(Symbol('D', commutative=True), Symbol('w', commutative=True)), sin(Symbol('D', commutative=True)))", "Add(Mul(Integer(-1), Symbol('D', commutative=True), Symbol('w', commutative=True)), sin(Symbol('w', commutative=True)))"]}, {"premise_expression": "\\frac{\\cos{(I)}}{K}", "variable": "I", "positive": "\\frac{\\sin{(I)}}{K}", "negatives": ["\\sin{(I + K)}", "\\log{(I)} \\log{(K)}", "\\log{(I)} \\sin{(K)}", "\\frac{I^{2} e^{K}}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('K', commutative=True), Integer(-1)), cos(Symbol('I', commutative=True)))", "srepr_variable": "Symbol('I', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('K', commutative=True), Integer(-1)), sin(Symbol('I', commutative=True)))", "srepr_negatives": ["sin(Add(Symbol('I', commutative=True), Symbol('K', commutative=True)))", "Mul(log(Symbol('I', commutative=True)), log(Symbol('K', commutative=True)))", "Mul(log(Symbol('I', commutative=True)), sin(Symbol('K', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(2)), exp(Symbol('K', commutative=True)))"]}, {"premise_expression": "\\frac{v}{a}", "variable": "v", "positive": "\\frac{v^{2}}{2 a}", "negatives": ["v \\log{(a)}", "v \\cos{(a^{2})}", "a e^{v}", "\\frac{\\sin{(v)}}{a}"], "srepr_premise_expression": "Mul(Pow(Symbol('a', commutative=True), Integer(-1)), Symbol('v', commutative=True))", "srepr_variable": "Symbol('v', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('a', commutative=True), Integer(-1)), Pow(Symbol('v', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('v', commutative=True), log(Symbol('a', commutative=True)))", "Mul(Symbol('v', commutative=True), cos(Pow(Symbol('a', commutative=True), Integer(2))))", "Mul(Symbol('a', commutative=True), exp(Symbol('v', commutative=True)))", "Mul(Pow(Symbol('a', commutative=True), Integer(-1)), sin(Symbol('v', commutative=True)))"]}, {"premise_expression": "\\log{(Z j)}", "variable": "j", "positive": "j (\\log{(Z j)} - 1)", "negatives": ["Z (\\log{(Z j)} - 1)", "e^{Z + j}", "Z \\sin{(j)}", "\\frac{Z j^{2}}{2}"], "srepr_premise_expression": "log(Mul(Symbol('Z', commutative=True), Symbol('j', commutative=True)))", "srepr_variable": "Symbol('j', commutative=True)", "srepr_positive": "Mul(Symbol('j', commutative=True), Add(log(Mul(Symbol('Z', commutative=True), Symbol('j', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('Z', commutative=True), Add(log(Mul(Symbol('Z', commutative=True), Symbol('j', commutative=True))), Integer(-1)))", "exp(Add(Symbol('Z', commutative=True), Symbol('j', commutative=True)))", "Mul(Symbol('Z', commutative=True), sin(Symbol('j', commutative=True)))", "Mul(Rational(1, 2), Symbol('Z', commutative=True), Pow(Symbol('j', commutative=True), Integer(2)))"]}, {"premise_expression": "\\frac{l^{m}}{N}", "variable": "N", "positive": "l^{m} \\log{(N)}", "negatives": ["l m \\log{(N)}", "\\frac{m \\log{(N)}}{l}", "(l + m) \\log{(N)}", "\\frac{N^{2} l}{2 m}"], "srepr_premise_expression": "Mul(Pow(Symbol('N', commutative=True), Integer(-1)), Pow(Symbol('l', commutative=True), Symbol('m', commutative=True)))", "srepr_variable": "Symbol('N', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('l', commutative=True), Symbol('m', commutative=True)), log(Symbol('N', commutative=True)))", "srepr_negatives": ["Mul(Symbol('l', commutative=True), Symbol('m', commutative=True), log(Symbol('N', commutative=True)))", "Mul(Pow(Symbol('l', commutative=True), Integer(-1)), Symbol('m', commutative=True), log(Symbol('N', commutative=True)))", "Mul(Add(Symbol('l', commutative=True), Symbol('m', commutative=True)), log(Symbol('N', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('N', commutative=True), Integer(2)), Symbol('l', commutative=True), Pow(Symbol('m', commutative=True), Integer(-1)))"]}, {"premise_expression": "D - z", "variable": "z", "positive": "\\frac{z (2 D - z)}{2}", "negatives": ["\\frac{D (D - 2 z)}{2}", "\\frac{z^{2} \\log{(D)}}{2}", "\\frac{z^{2} \\sin{(D)}}{2}", "- \\sin{(D - z)}"], "srepr_premise_expression": "Add(Symbol('D', commutative=True), Mul(Integer(-1), Symbol('z', commutative=True)))", "srepr_variable": "Symbol('z', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('z', commutative=True), Add(Mul(Integer(2), Symbol('D', commutative=True)), Mul(Integer(-1), Symbol('z', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('D', commutative=True), Add(Symbol('D', commutative=True), Mul(Integer(-1), Integer(2), Symbol('z', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('z', commutative=True), Integer(2)), log(Symbol('D', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('z', commutative=True), Integer(2)), sin(Symbol('D', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('D', commutative=True), Mul(Integer(-1), Symbol('z', commutative=True)))))"]}, {"premise_expression": "k + w", "variable": "k", "positive": "\\frac{k (k + 2 w)}{2}", "negatives": ["\\frac{w (2 k + w)}{2}", "- k w + \\sin{(k)}", "k (\\log{(k w)} - 1)", "- \\frac{\\cos{(k)}}{w}"], "srepr_premise_expression": "Add(Symbol('k', commutative=True), Symbol('w', commutative=True))", "srepr_variable": "Symbol('k', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('k', commutative=True), Add(Symbol('k', commutative=True), Mul(Integer(2), Symbol('w', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('w', commutative=True), Add(Mul(Integer(2), Symbol('k', commutative=True)), Symbol('w', commutative=True)))", "Add(Mul(Integer(-1), Symbol('k', commutative=True), Symbol('w', commutative=True)), sin(Symbol('k', commutative=True)))", "Mul(Symbol('k', commutative=True), Add(log(Mul(Symbol('k', commutative=True), Symbol('w', commutative=True))), Integer(-1)))", "Mul(Integer(-1), Pow(Symbol('w', commutative=True), Integer(-1)), cos(Symbol('k', commutative=True)))"]}, {"premise_expression": "\\sin{(V - b)}", "variable": "V", "positive": "- \\cos{(V - b)}", "negatives": ["\\cos{(V - b)}", "- b \\cos{(V)}", "\\log{(V)} \\cos{(b)}", "\\log{(V)} \\log{(b)}"], "srepr_premise_expression": "sin(Add(Symbol('V', commutative=True), Mul(Integer(-1), Symbol('b', commutative=True))))", "srepr_variable": "Symbol('V', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('V', commutative=True), Mul(Integer(-1), Symbol('b', commutative=True)))))", "srepr_negatives": ["cos(Add(Symbol('V', commutative=True), Mul(Integer(-1), Symbol('b', commutative=True))))", "Mul(Integer(-1), Symbol('b', commutative=True), cos(Symbol('V', commutative=True)))", "Mul(log(Symbol('V', commutative=True)), cos(Symbol('b', commutative=True)))", "Mul(log(Symbol('V', commutative=True)), log(Symbol('b', commutative=True)))"]}, {"premise_expression": "- Q + \\frac{S}{L}", "variable": "L", "positive": "- L Q + S \\log{(L)}", "negatives": ["- Q S + \\frac{S^{2}}{2 L}", "\\frac{L (L + 2 Q S)}{2}", "- \\frac{Q^{2}}{2} + \\frac{Q S}{L}", "- \\frac{L (L - 2 S)}{2 Q}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('Q', commutative=True)), Mul(Pow(Symbol('L', commutative=True), Integer(-1)), Symbol('S', commutative=True)))", "srepr_variable": "Symbol('L', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('L', commutative=True), Symbol('Q', commutative=True)), Mul(Symbol('S', commutative=True), log(Symbol('L', commutative=True))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('Q', commutative=True), Symbol('S', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(-1)), Pow(Symbol('S', commutative=True), Integer(2))))", "Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Symbol('L', commutative=True), Mul(Integer(2), Symbol('Q', commutative=True), Symbol('S', commutative=True))))", "Add(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(2))), Mul(Pow(Symbol('L', commutative=True), Integer(-1)), Symbol('Q', commutative=True), Symbol('S', commutative=True)))", "Mul(Integer(-1), Rational(1, 2), Symbol('L', commutative=True), Pow(Symbol('Q', commutative=True), Integer(-1)), Add(Symbol('L', commutative=True), Mul(Integer(-1), Integer(2), Symbol('S', commutative=True))))"]}, {"premise_expression": "V \\sin{(u)}", "variable": "V", "positive": "\\frac{V^{2} \\sin{(u)}}{2}", "negatives": ["- V \\cos{(u)}", "- V u + \\sin{(V)}", "\\frac{V (V + 2 \\log{(u)})}{2}", "- \\frac{\\cos{(V)}}{u}"], "srepr_premise_expression": "Mul(Symbol('V', commutative=True), sin(Symbol('u', commutative=True)))", "srepr_variable": "Symbol('V', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('V', commutative=True), Integer(2)), sin(Symbol('u', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Symbol('V', commutative=True), cos(Symbol('u', commutative=True)))", "Add(Mul(Integer(-1), Symbol('V', commutative=True), Symbol('u', commutative=True)), sin(Symbol('V', commutative=True)))", "Mul(Rational(1, 2), Symbol('V', commutative=True), Add(Symbol('V', commutative=True), Mul(Integer(2), log(Symbol('u', commutative=True)))))", "Mul(Integer(-1), Pow(Symbol('u', commutative=True), Integer(-1)), cos(Symbol('V', commutative=True)))"]}, {"premise_expression": "\\frac{I}{T}", "variable": "T", "positive": "I \\log{(T)}", "negatives": ["\\frac{I^{2}}{2 T}", "\\frac{T (T + 2 \\log{(I)})}{2}", "\\frac{T (- T + 2 \\log{(I)})}{2}", "I \\operatorname{Si}{(\\frac{I}{T})} + T \\cos{(\\frac{I}{T})}"], "srepr_premise_expression": "Mul(Symbol('I', commutative=True), Pow(Symbol('T', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('T', commutative=True)", "srepr_positive": "Mul(Symbol('I', commutative=True), log(Symbol('T', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(2)), Pow(Symbol('T', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Symbol('T', commutative=True), Add(Symbol('T', commutative=True), Mul(Integer(2), log(Symbol('I', commutative=True)))))", "Mul(Rational(1, 2), Symbol('T', commutative=True), Add(Mul(Integer(-1), Symbol('T', commutative=True)), Mul(Integer(2), log(Symbol('I', commutative=True)))))", "Add(Mul(Symbol('I', commutative=True), Si(Mul(Symbol('I', commutative=True), Pow(Symbol('T', commutative=True), Integer(-1))))), Mul(Symbol('T', commutative=True), cos(Mul(Symbol('I', commutative=True), Pow(Symbol('T', commutative=True), Integer(-1))))))"]}, {"premise_expression": "- l + \\sin{(x)}", "variable": "x", "positive": "- l x - \\cos{(x)}", "negatives": ["l x + e^{x}", "\\log{(x)} \\cos{(l)}", "- e^{l - x}", "e^{l + x}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('l', commutative=True)), sin(Symbol('x', commutative=True)))", "srepr_variable": "Symbol('x', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('l', commutative=True), Symbol('x', commutative=True)), Mul(Integer(-1), cos(Symbol('x', commutative=True))))", "srepr_negatives": ["Add(Mul(Symbol('l', commutative=True), Symbol('x', commutative=True)), exp(Symbol('x', commutative=True)))", "Mul(log(Symbol('x', commutative=True)), cos(Symbol('l', commutative=True)))", "Mul(Integer(-1), exp(Add(Symbol('l', commutative=True), Mul(Integer(-1), Symbol('x', commutative=True)))))", "exp(Add(Symbol('l', commutative=True), Symbol('x', commutative=True)))"]}, {"premise_expression": "\\sin{(M + r)}", "variable": "M", "positive": "- \\cos{(M + r)}", "negatives": ["- \\frac{\\cos{(M)}}{r}", "M r - \\cos{(M)}", "r e^{M}", "\\frac{M^{2} \\log{(r)}}{2}"], "srepr_premise_expression": "sin(Add(Symbol('M', commutative=True), Symbol('r', commutative=True)))", "srepr_variable": "Symbol('M', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('M', commutative=True), Symbol('r', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), Pow(Symbol('r', commutative=True), Integer(-1)), cos(Symbol('M', commutative=True)))", "Add(Mul(Symbol('M', commutative=True), Symbol('r', commutative=True)), Mul(Integer(-1), cos(Symbol('M', commutative=True))))", "Mul(Symbol('r', commutative=True), exp(Symbol('M', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('M', commutative=True), Integer(2)), log(Symbol('r', commutative=True)))"]}, {"premise_expression": "\\log{(L + f)}", "variable": "f", "positive": "L \\log{(L + f)} + f \\log{(L + f)} - f", "negatives": ["L \\log{(L + f)} - L + f \\log{(L + f)}", "\\frac{f (- f + 2 \\cos{(L)})}{2}", "\\frac{L f (f + 2)}{2}", "\\frac{f^{2} \\log{(L)}}{2}"], "srepr_premise_expression": "log(Add(Symbol('L', commutative=True), Symbol('f', commutative=True)))", "srepr_variable": "Symbol('f', commutative=True)", "srepr_positive": "Add(Mul(Symbol('L', commutative=True), log(Add(Symbol('L', commutative=True), Symbol('f', commutative=True)))), Mul(Symbol('f', commutative=True), log(Add(Symbol('L', commutative=True), Symbol('f', commutative=True)))), Mul(Integer(-1), Symbol('f', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('L', commutative=True), log(Add(Symbol('L', commutative=True), Symbol('f', commutative=True)))), Mul(Integer(-1), Symbol('L', commutative=True)), Mul(Symbol('f', commutative=True), log(Add(Symbol('L', commutative=True), Symbol('f', commutative=True)))))", "Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Mul(Integer(-1), Symbol('f', commutative=True)), Mul(Integer(2), cos(Symbol('L', commutative=True)))))", "Mul(Rational(1, 2), Symbol('L', commutative=True), Symbol('f', commutative=True), Add(Symbol('f', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('f', commutative=True), Integer(2)), log(Symbol('L', commutative=True)))"]}, {"premise_expression": "b c", "variable": "b", "positive": "\\frac{b^{2} c}{2}", "negatives": ["\\frac{b c^{2}}{2}", "\\frac{b^{2} e^{c}}{2}", "- \\cos{(b + c)}", "\\log{(b)} \\log{(c)}"], "srepr_premise_expression": "Mul(Symbol('b', commutative=True), Symbol('c', commutative=True))", "srepr_variable": "Symbol('b', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('b', commutative=True), Integer(2)), Symbol('c', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('b', commutative=True), Pow(Symbol('c', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('b', commutative=True), Integer(2)), exp(Symbol('c', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('b', commutative=True), Symbol('c', commutative=True))))", "Mul(log(Symbol('b', commutative=True)), log(Symbol('c', commutative=True)))"]}, {"premise_expression": "\\log{(P c)}", "variable": "c", "positive": "c (\\log{(P c)} - 1)", "negatives": ["P (\\log{(P c)} - 1)", "\\log{(P)} \\log{(c)}", "\\frac{c (2 P + c)}{2}", "e^{P + c}"], "srepr_premise_expression": "log(Mul(Symbol('P', commutative=True), Symbol('c', commutative=True)))", "srepr_variable": "Symbol('c', commutative=True)", "srepr_positive": "Mul(Symbol('c', commutative=True), Add(log(Mul(Symbol('P', commutative=True), Symbol('c', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('P', commutative=True), Add(log(Mul(Symbol('P', commutative=True), Symbol('c', commutative=True))), Integer(-1)))", "Mul(log(Symbol('P', commutative=True)), log(Symbol('c', commutative=True)))", "Mul(Rational(1, 2), Symbol('c', commutative=True), Add(Mul(Integer(2), Symbol('P', commutative=True)), Symbol('c', commutative=True)))", "exp(Add(Symbol('P', commutative=True), Symbol('c', commutative=True)))"]}, {"premise_expression": "\\frac{J}{R}", "variable": "R", "positive": "J \\log{(R)}", "negatives": ["J e^{R}", "\\frac{J^{2}}{2 R}", "- J R - \\cos{(R)}", "- \\cos{(J + R)}"], "srepr_premise_expression": "Mul(Symbol('J', commutative=True), Pow(Symbol('R', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('R', commutative=True)", "srepr_positive": "Mul(Symbol('J', commutative=True), log(Symbol('R', commutative=True)))", "srepr_negatives": ["Mul(Symbol('J', commutative=True), exp(Symbol('R', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('J', commutative=True), Integer(2)), Pow(Symbol('R', commutative=True), Integer(-1)))", "Add(Mul(Integer(-1), Symbol('J', commutative=True), Symbol('R', commutative=True)), Mul(Integer(-1), cos(Symbol('R', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('J', commutative=True), Symbol('R', commutative=True))))"]}, {"premise_expression": "e^{\\frac{D}{W}}", "variable": "D", "positive": "W e^{\\frac{D}{W}}", "negatives": ["W e^{D}", "- W \\cos{(D)}", "\\frac{D^{2} \\cos{(W)}}{2}", "- D \\operatorname{Ei}{(\\frac{D}{W})} + W e^{\\frac{D}{W}}"], "srepr_premise_expression": "exp(Mul(Symbol('D', commutative=True), Pow(Symbol('W', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('D', commutative=True)", "srepr_positive": "Mul(Symbol('W', commutative=True), exp(Mul(Symbol('D', commutative=True), Pow(Symbol('W', commutative=True), Integer(-1)))))", "srepr_negatives": ["Mul(Symbol('W', commutative=True), exp(Symbol('D', commutative=True)))", "Mul(Integer(-1), Symbol('W', commutative=True), cos(Symbol('D', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(2)), cos(Symbol('W', commutative=True)))", "Add(Mul(Integer(-1), Symbol('D', commutative=True), Ei(Mul(Symbol('D', commutative=True), Pow(Symbol('W', commutative=True), Integer(-1))))), Mul(Symbol('W', commutative=True), exp(Mul(Symbol('D', commutative=True), Pow(Symbol('W', commutative=True), Integer(-1))))))"]}, {"premise_expression": "N + Z", "variable": "N", "positive": "\\frac{N (N + 2 Z)}{2}", "negatives": ["\\frac{Z (2 N + Z)}{2}", "\\frac{N^{2}}{2 Z}", "\\frac{N^{2} \\cos{(Z)}}{2}", "\\frac{\\sin{(N)}}{Z}"], "srepr_premise_expression": "Add(Symbol('N', commutative=True), Symbol('Z', commutative=True))", "srepr_variable": "Symbol('N', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Symbol('N', commutative=True), Mul(Integer(2), Symbol('Z', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Mul(Integer(2), Symbol('N', commutative=True)), Symbol('Z', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('N', commutative=True), Integer(2)), Pow(Symbol('Z', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('N', commutative=True), Integer(2)), cos(Symbol('Z', commutative=True)))", "Mul(Pow(Symbol('Z', commutative=True), Integer(-1)), sin(Symbol('N', commutative=True)))"]}, {"premise_expression": "\\frac{\\sin{(r)}}{L}", "variable": "r", "positive": "- \\frac{\\cos{(r)}}{L}", "negatives": ["L r - \\cos{(r)}", "L^{2} r", "\\frac{r^{2}}{2 L}", "- e^{L - r}"], "srepr_premise_expression": "Mul(Pow(Symbol('L', commutative=True), Integer(-1)), sin(Symbol('r', commutative=True)))", "srepr_variable": "Symbol('r', commutative=True)", "srepr_positive": "Mul(Integer(-1), Pow(Symbol('L', commutative=True), Integer(-1)), cos(Symbol('r', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('L', commutative=True), Symbol('r', commutative=True)), Mul(Integer(-1), cos(Symbol('r', commutative=True))))", "Mul(Pow(Symbol('L', commutative=True), Integer(2)), Symbol('r', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(-1)), Pow(Symbol('r', commutative=True), Integer(2)))", "Mul(Integer(-1), exp(Add(Symbol('L', commutative=True), Mul(Integer(-1), Symbol('r', commutative=True)))))"]}, {"premise_expression": "G w", "variable": "G", "positive": "\\frac{G^{2} w}{2}", "negatives": ["\\frac{G w^{2}}{2}", "w \\sin{(G)}", "- \\frac{\\cos{(G)}}{w}", "G \\cos^{w}{(w)}"], "srepr_premise_expression": "Mul(Symbol('G', commutative=True), Symbol('w', commutative=True))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(2)), Symbol('w', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('G', commutative=True), Pow(Symbol('w', commutative=True), Integer(2)))", "Mul(Symbol('w', commutative=True), sin(Symbol('G', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('w', commutative=True), Integer(-1)), cos(Symbol('G', commutative=True)))", "Mul(Symbol('G', commutative=True), Pow(cos(Symbol('w', commutative=True)), Symbol('w', commutative=True)))"]}, {"premise_expression": "- Q + \\frac{J}{A}", "variable": "J", "positive": "- J Q + \\frac{J^{2}}{2 A}", "negatives": ["- A Q + J \\log{(A)}", "- \\frac{J^{2}}{2} + \\frac{J Q}{A}", "- \\frac{Q^{2}}{2} + \\frac{J Q}{A}", "\\frac{J (- 2 A + J - 2 Q)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('Q', commutative=True)), Mul(Pow(Symbol('A', commutative=True), Integer(-1)), Symbol('J', commutative=True)))", "srepr_variable": "Symbol('J', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('J', commutative=True), Symbol('Q', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(-1)), Pow(Symbol('J', commutative=True), Integer(2))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('A', commutative=True), Symbol('Q', commutative=True)), Mul(Symbol('J', commutative=True), log(Symbol('A', commutative=True))))", "Add(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('J', commutative=True), Integer(2))), Mul(Pow(Symbol('A', commutative=True), Integer(-1)), Symbol('J', commutative=True), Symbol('Q', commutative=True)))", "Add(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(2))), Mul(Pow(Symbol('A', commutative=True), Integer(-1)), Symbol('J', commutative=True), Symbol('Q', commutative=True)))", "Mul(Rational(1, 2), Symbol('J', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('A', commutative=True)), Symbol('J', commutative=True), Mul(Integer(-1), Integer(2), Symbol('Q', commutative=True))))"]}, {"premise_expression": "n - z", "variable": "n", "positive": "\\frac{n (n - 2 z)}{2}", "negatives": ["\\frac{n (n + 2 z)}{2}", "\\frac{z (2 n - z)}{2}", "\\frac{n (n + 2 e^{z})}{2}", "\\sin{(n - z)}"], "srepr_premise_expression": "Add(Symbol('n', commutative=True), Mul(Integer(-1), Symbol('z', commutative=True)))", "srepr_variable": "Symbol('n', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('n', commutative=True), Add(Symbol('n', commutative=True), Mul(Integer(-1), Integer(2), Symbol('z', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('n', commutative=True), Add(Symbol('n', commutative=True), Mul(Integer(2), Symbol('z', commutative=True))))", "Mul(Rational(1, 2), Symbol('z', commutative=True), Add(Mul(Integer(2), Symbol('n', commutative=True)), Mul(Integer(-1), Symbol('z', commutative=True))))", "Mul(Rational(1, 2), Symbol('n', commutative=True), Add(Symbol('n', commutative=True), Mul(Integer(2), exp(Symbol('z', commutative=True)))))", "sin(Add(Symbol('n', commutative=True), Mul(Integer(-1), Symbol('z', commutative=True))))"]}, {"premise_expression": "\\frac{K}{w}", "variable": "w", "positive": "K \\log{(w)}", "negatives": ["- K \\cos{(w)}", "\\frac{K^{2}}{2 w}", "- K w + \\sin{(w)}", "\\log{(w)} \\cos{(K)}"], "srepr_premise_expression": "Mul(Symbol('K', commutative=True), Pow(Symbol('w', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('w', commutative=True)", "srepr_positive": "Mul(Symbol('K', commutative=True), log(Symbol('w', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Symbol('K', commutative=True), cos(Symbol('w', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('K', commutative=True), Integer(2)), Pow(Symbol('w', commutative=True), Integer(-1)))", "Add(Mul(Integer(-1), Symbol('K', commutative=True), Symbol('w', commutative=True)), sin(Symbol('w', commutative=True)))", "Mul(log(Symbol('w', commutative=True)), cos(Symbol('K', commutative=True)))"]}, {"premise_expression": "\\cos{(\\frac{R}{J})}", "variable": "J", "positive": "J \\cos{(\\frac{R}{J})} + R \\operatorname{Si}{(\\frac{R}{J})}", "negatives": ["J e^{\\frac{R}{J}} - R \\operatorname{Ei}{(\\frac{R}{J})}", "- \\cos{(J - R)}", "\\frac{J (J + 2 R)}{2}", "\\frac{J (J - 2 R)}{2}"], "srepr_premise_expression": "cos(Mul(Pow(Symbol('J', commutative=True), Integer(-1)), Symbol('R', commutative=True)))", "srepr_variable": "Symbol('J', commutative=True)", "srepr_positive": "Add(Mul(Symbol('J', commutative=True), cos(Mul(Pow(Symbol('J', commutative=True), Integer(-1)), Symbol('R', commutative=True)))), Mul(Symbol('R', commutative=True), Si(Mul(Pow(Symbol('J', commutative=True), Integer(-1)), Symbol('R', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('J', commutative=True), exp(Mul(Pow(Symbol('J', commutative=True), Integer(-1)), Symbol('R', commutative=True)))), Mul(Integer(-1), Symbol('R', commutative=True), Ei(Mul(Pow(Symbol('J', commutative=True), Integer(-1)), Symbol('R', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('J', commutative=True), Mul(Integer(-1), Symbol('R', commutative=True)))))", "Mul(Rational(1, 2), Symbol('J', commutative=True), Add(Symbol('J', commutative=True), Mul(Integer(2), Symbol('R', commutative=True))))", "Mul(Rational(1, 2), Symbol('J', commutative=True), Add(Symbol('J', commutative=True), Mul(Integer(-1), Integer(2), Symbol('R', commutative=True))))"]}, {"premise_expression": "m + n", "variable": "m", "positive": "\\frac{m (m + 2 n)}{2}", "negatives": ["\\frac{m (- m + 2 n)}{2}", "\\frac{n (2 m + n)}{2}", "\\frac{m (- m + 2 \\sin{(n)})}{2}", "e^{m + n}"], "srepr_premise_expression": "Add(Symbol('m', commutative=True), Symbol('n', commutative=True))", "srepr_variable": "Symbol('m', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Symbol('m', commutative=True), Mul(Integer(2), Symbol('n', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Mul(Integer(-1), Symbol('m', commutative=True)), Mul(Integer(2), Symbol('n', commutative=True))))", "Mul(Rational(1, 2), Symbol('n', commutative=True), Add(Mul(Integer(2), Symbol('m', commutative=True)), Symbol('n', commutative=True)))", "Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Mul(Integer(-1), Symbol('m', commutative=True)), Mul(Integer(2), sin(Symbol('n', commutative=True)))))", "exp(Add(Symbol('m', commutative=True), Symbol('n', commutative=True)))"]}, {"premise_expression": "a q", "variable": "q", "positive": "\\frac{a q^{2}}{2}", "negatives": ["\\frac{a^{2} q}{2}", "a \\log{(q)}", "a e^{q}", "\\frac{q^{2} \\log{(a)}}{2}"], "srepr_premise_expression": "Mul(Symbol('a', commutative=True), Symbol('q', commutative=True))", "srepr_variable": "Symbol('q', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('a', commutative=True), Pow(Symbol('q', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('a', commutative=True), Integer(2)), Symbol('q', commutative=True))", "Mul(Symbol('a', commutative=True), log(Symbol('q', commutative=True)))", "Mul(Symbol('a', commutative=True), exp(Symbol('q', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('q', commutative=True), Integer(2)), log(Symbol('a', commutative=True)))"]}, {"premise_expression": "- F + \\cos{(z)}", "variable": "F", "positive": "\\frac{F (- F + 2 \\cos{(z)})}{2}", "negatives": ["\\frac{F (- F + 2 e^{z})}{2}", "\\frac{F (F + 2 z)}{2}", "F (F + z)", "\\frac{F^{2} e^{z}}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('F', commutative=True)), cos(Symbol('z', commutative=True)))", "srepr_variable": "Symbol('F', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Mul(Integer(-1), Symbol('F', commutative=True)), Mul(Integer(2), cos(Symbol('z', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Mul(Integer(-1), Symbol('F', commutative=True)), Mul(Integer(2), exp(Symbol('z', commutative=True)))))", "Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Symbol('F', commutative=True), Mul(Integer(2), Symbol('z', commutative=True))))", "Mul(Symbol('F', commutative=True), Add(Symbol('F', commutative=True), Symbol('z', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('F', commutative=True), Integer(2)), exp(Symbol('z', commutative=True)))"]}, {"premise_expression": "\\frac{C}{w}", "variable": "w", "positive": "C \\log{(w)}", "negatives": ["C e^{w}", "w \\cos{(1)}", "\\frac{C^{2}}{2 w}", "\\cos{(C - w)}"], "srepr_premise_expression": "Mul(Symbol('C', commutative=True), Pow(Symbol('w', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('w', commutative=True)", "srepr_positive": "Mul(Symbol('C', commutative=True), log(Symbol('w', commutative=True)))", "srepr_negatives": ["Mul(Symbol('C', commutative=True), exp(Symbol('w', commutative=True)))", "Mul(Symbol('w', commutative=True), cos(Integer(1)))", "Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2)), Pow(Symbol('w', commutative=True), Integer(-1)))", "cos(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('w', commutative=True))))"]}, {"premise_expression": "- z + \\log{(k)}", "variable": "k", "positive": "k (- z + \\log{(k)} - 1)", "negatives": ["\\frac{z (- z + 2 \\log{(k)})}{2}", "\\sin{(k - z)}", "\\log{(k)} \\log{(z)}", "\\frac{k^{2} z}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('z', commutative=True)), log(Symbol('k', commutative=True)))", "srepr_variable": "Symbol('k', commutative=True)", "srepr_positive": "Mul(Symbol('k', commutative=True), Add(Mul(Integer(-1), Symbol('z', commutative=True)), log(Symbol('k', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('z', commutative=True), Add(Mul(Integer(-1), Symbol('z', commutative=True)), Mul(Integer(2), log(Symbol('k', commutative=True)))))", "sin(Add(Symbol('k', commutative=True), Mul(Integer(-1), Symbol('z', commutative=True))))", "Mul(log(Symbol('k', commutative=True)), log(Symbol('z', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('k', commutative=True), Integer(2)), Symbol('z', commutative=True))"]}, {"premise_expression": "o + \\sin{(q)}", "variable": "q", "positive": "o q - \\cos{(q)}", "negatives": ["q \\cos{(1)}", "\\frac{o q^{3}}{3}", "\\frac{o q^{2}}{2}", "\\frac{o (o + 2 \\sin{(q)})}{2}"], "srepr_premise_expression": "Add(Symbol('o', commutative=True), sin(Symbol('q', commutative=True)))", "srepr_variable": "Symbol('q', commutative=True)", "srepr_positive": "Add(Mul(Symbol('o', commutative=True), Symbol('q', commutative=True)), Mul(Integer(-1), cos(Symbol('q', commutative=True))))", "srepr_negatives": ["Mul(Symbol('q', commutative=True), cos(Integer(1)))", "Mul(Rational(1, 3), Symbol('o', commutative=True), Pow(Symbol('q', commutative=True), Integer(3)))", "Mul(Rational(1, 2), Symbol('o', commutative=True), Pow(Symbol('q', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Symbol('o', commutative=True), Mul(Integer(2), sin(Symbol('q', commutative=True)))))"]}, {"premise_expression": "N + f", "variable": "N", "positive": "\\frac{N (N + 2 f)}{2}", "negatives": ["\\frac{N (N - 2 f)}{2}", "\\frac{f (2 N + f)}{2}", "\\sin{(N - f)}", "N (- f + \\log{(N^{f})})"], "srepr_premise_expression": "Add(Symbol('N', commutative=True), Symbol('f', commutative=True))", "srepr_variable": "Symbol('N', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Symbol('N', commutative=True), Mul(Integer(2), Symbol('f', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Symbol('N', commutative=True), Mul(Integer(-1), Integer(2), Symbol('f', commutative=True))))", "Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Mul(Integer(2), Symbol('N', commutative=True)), Symbol('f', commutative=True)))", "sin(Add(Symbol('N', commutative=True), Mul(Integer(-1), Symbol('f', commutative=True))))", "Mul(Symbol('N', commutative=True), Add(Mul(Integer(-1), Symbol('f', commutative=True)), log(Pow(Symbol('N', commutative=True), Symbol('f', commutative=True)))))"]}, {"premise_expression": "\\log{(g r)}", "variable": "r", "positive": "r (\\log{(g r)} - 1)", "negatives": ["g (\\log{(g r)} - 1)", "r (\\log{(\\frac{r}{g})} - 1)", "\\log{(g)} \\log{(r)}", "\\frac{r^{2}}{2 g}"], "srepr_premise_expression": "log(Mul(Symbol('g', commutative=True), Symbol('r', commutative=True)))", "srepr_variable": "Symbol('r', commutative=True)", "srepr_positive": "Mul(Symbol('r', commutative=True), Add(log(Mul(Symbol('g', commutative=True), Symbol('r', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('g', commutative=True), Add(log(Mul(Symbol('g', commutative=True), Symbol('r', commutative=True))), Integer(-1)))", "Mul(Symbol('r', commutative=True), Add(log(Mul(Pow(Symbol('g', commutative=True), Integer(-1)), Symbol('r', commutative=True))), Integer(-1)))", "Mul(log(Symbol('g', commutative=True)), log(Symbol('r', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('g', commutative=True), Integer(-1)), Pow(Symbol('r', commutative=True), Integer(2)))"]}, {"premise_expression": "- B + e^{l}", "variable": "l", "positive": "- B l + e^{l}", "negatives": ["\\frac{B (- B + 2 e^{l})}{2}", "e^{B + l}", "\\log{(B)} \\log{(l)}", "\\frac{l (- 2 B + l)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('B', commutative=True)), exp(Symbol('l', commutative=True)))", "srepr_variable": "Symbol('l', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('B', commutative=True), Symbol('l', commutative=True)), exp(Symbol('l', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('B', commutative=True), Add(Mul(Integer(-1), Symbol('B', commutative=True)), Mul(Integer(2), exp(Symbol('l', commutative=True)))))", "exp(Add(Symbol('B', commutative=True), Symbol('l', commutative=True)))", "Mul(log(Symbol('B', commutative=True)), log(Symbol('l', commutative=True)))", "Mul(Rational(1, 2), Symbol('l', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('B', commutative=True)), Symbol('l', commutative=True)))"]}, {"premise_expression": "T Y", "variable": "Y", "positive": "\\frac{T Y^{2}}{2}", "negatives": ["\\frac{T^{2} Y}{2}", "T e^{Y}", "e^{T + Y}", "e^{T} \\log{(Y)}"], "srepr_premise_expression": "Mul(Symbol('T', commutative=True), Symbol('Y', commutative=True))", "srepr_variable": "Symbol('Y', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('T', commutative=True), Pow(Symbol('Y', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('T', commutative=True), Integer(2)), Symbol('Y', commutative=True))", "Mul(Symbol('T', commutative=True), exp(Symbol('Y', commutative=True)))", "exp(Add(Symbol('T', commutative=True), Symbol('Y', commutative=True)))", "Mul(exp(Symbol('T', commutative=True)), log(Symbol('Y', commutative=True)))"]}, {"premise_expression": "\\frac{q}{Q}", "variable": "q", "positive": "\\frac{q^{2}}{2 Q}", "negatives": ["q \\log{(Q)}", "\\frac{q^{2} \\log{(Q)}}{2}", "\\sin{(Q + q)}", "\\frac{q (2 Q + q)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('Q', commutative=True), Integer(-1)), Symbol('q', commutative=True))", "srepr_variable": "Symbol('q', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(-1)), Pow(Symbol('q', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('q', commutative=True), log(Symbol('Q', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('q', commutative=True), Integer(2)), log(Symbol('Q', commutative=True)))", "sin(Add(Symbol('Q', commutative=True), Symbol('q', commutative=True)))", "Mul(Rational(1, 2), Symbol('q', commutative=True), Add(Mul(Integer(2), Symbol('Q', commutative=True)), Symbol('q', commutative=True)))"]}, {"premise_expression": "\\log{(X - n)}", "variable": "n", "positive": "- X \\log{(- X + n)} + n \\log{(X - n)} - n", "negatives": ["- X \\log{(- X + n)} + n \\log{(- X + n)} - n", "X \\log{(X - n)} - X - n \\log{(X - n)}", "- X \\operatorname{Ei}{(\\frac{X}{n})} + n e^{\\frac{X}{n}}", "n (- X + \\log{(n)} - 1)"], "srepr_premise_expression": "log(Add(Symbol('X', commutative=True), Mul(Integer(-1), Symbol('n', commutative=True))))", "srepr_variable": "Symbol('n', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('X', commutative=True), log(Add(Mul(Integer(-1), Symbol('X', commutative=True)), Symbol('n', commutative=True)))), Mul(Symbol('n', commutative=True), log(Add(Symbol('X', commutative=True), Mul(Integer(-1), Symbol('n', commutative=True))))), Mul(Integer(-1), Symbol('n', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('X', commutative=True), log(Add(Mul(Integer(-1), Symbol('X', commutative=True)), Symbol('n', commutative=True)))), Mul(Symbol('n', commutative=True), log(Add(Mul(Integer(-1), Symbol('X', commutative=True)), Symbol('n', commutative=True)))), Mul(Integer(-1), Symbol('n', commutative=True)))", "Add(Mul(Symbol('X', commutative=True), log(Add(Symbol('X', commutative=True), Mul(Integer(-1), Symbol('n', commutative=True))))), Mul(Integer(-1), Symbol('X', commutative=True)), Mul(Integer(-1), Symbol('n', commutative=True), log(Add(Symbol('X', commutative=True), Mul(Integer(-1), Symbol('n', commutative=True))))))", "Add(Mul(Integer(-1), Symbol('X', commutative=True), Ei(Mul(Symbol('X', commutative=True), Pow(Symbol('n', commutative=True), Integer(-1))))), Mul(Symbol('n', commutative=True), exp(Mul(Symbol('X', commutative=True), Pow(Symbol('n', commutative=True), Integer(-1))))))", "Mul(Symbol('n', commutative=True), Add(Mul(Integer(-1), Symbol('X', commutative=True)), log(Symbol('n', commutative=True)), Integer(-1)))"]}, {"premise_expression": "F + g", "variable": "F", "positive": "\\frac{F (F + 2 g)}{2}", "negatives": ["\\frac{F (- F + 2 g)}{2}", "\\frac{g (2 F + g)}{2}", "\\frac{F (- F + 2 e^{g})}{2}", "e^{F + g}"], "srepr_premise_expression": "Add(Symbol('F', commutative=True), Symbol('g', commutative=True))", "srepr_variable": "Symbol('F', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Symbol('F', commutative=True), Mul(Integer(2), Symbol('g', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Mul(Integer(-1), Symbol('F', commutative=True)), Mul(Integer(2), Symbol('g', commutative=True))))", "Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Mul(Integer(2), Symbol('F', commutative=True)), Symbol('g', commutative=True)))", "Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Mul(Integer(-1), Symbol('F', commutative=True)), Mul(Integer(2), exp(Symbol('g', commutative=True)))))", "exp(Add(Symbol('F', commutative=True), Symbol('g', commutative=True)))"]}, {"premise_expression": "\\frac{A}{y} - D", "variable": "A", "positive": "\\frac{A^{2}}{2 y} - A D", "negatives": ["A \\log{(y)} - D y", "\\frac{A^{2} D}{2 y}", "\\frac{A^{2}}{2 D y}", "\\frac{A^{2} D y}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('A', commutative=True), Pow(Symbol('y', commutative=True), Integer(-1))), Mul(Integer(-1), Symbol('D', commutative=True)))", "srepr_variable": "Symbol('A', commutative=True)", "srepr_positive": "Add(Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2)), Pow(Symbol('y', commutative=True), Integer(-1))), Mul(Integer(-1), Symbol('A', commutative=True), Symbol('D', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('A', commutative=True), log(Symbol('y', commutative=True))), Mul(Integer(-1), Symbol('D', commutative=True), Symbol('y', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2)), Symbol('D', commutative=True), Pow(Symbol('y', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2)), Pow(Symbol('D', commutative=True), Integer(-1)), Pow(Symbol('y', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2)), Symbol('D', commutative=True), Symbol('y', commutative=True))"]}, {"premise_expression": "I \\cos{(V)}", "variable": "I", "positive": "\\frac{I^{2} \\cos{(V)}}{2}", "negatives": ["\\frac{I^{2} \\sin{(V)}}{2}", "I \\sin{(V)}", "V \\log{(I)}", "\\int \\sin^{V}{(I)} dI"], "srepr_premise_expression": "Mul(Symbol('I', commutative=True), cos(Symbol('V', commutative=True)))", "srepr_variable": "Symbol('I', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(2)), cos(Symbol('V', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(2)), sin(Symbol('V', commutative=True)))", "Mul(Symbol('I', commutative=True), sin(Symbol('V', commutative=True)))", "Mul(Symbol('V', commutative=True), log(Symbol('I', commutative=True)))", "Integral(Pow(sin(Symbol('I', commutative=True)), Symbol('V', commutative=True)), Tuple(Symbol('I', commutative=True)))"]}, {"premise_expression": "- T + j", "variable": "T", "positive": "\\frac{T (- T + 2 j)}{2}", "negatives": ["\\frac{j (- 2 T + j)}{2}", "\\frac{T^{2} \\cos{(j)}}{2}", "T (- j + \\log{(T^{j})})", "T (\\log{(\\frac{T}{j})} - 1)"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('T', commutative=True)), Symbol('j', commutative=True))", "srepr_variable": "Symbol('T', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('T', commutative=True), Add(Mul(Integer(-1), Symbol('T', commutative=True)), Mul(Integer(2), Symbol('j', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('j', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('T', commutative=True)), Symbol('j', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('T', commutative=True), Integer(2)), cos(Symbol('j', commutative=True)))", "Mul(Symbol('T', commutative=True), Add(Mul(Integer(-1), Symbol('j', commutative=True)), log(Pow(Symbol('T', commutative=True), Symbol('j', commutative=True)))))", "Mul(Symbol('T', commutative=True), Add(log(Mul(Symbol('T', commutative=True), Pow(Symbol('j', commutative=True), Integer(-1)))), Integer(-1)))"]}, {"premise_expression": "o + \\cos{(m)}", "variable": "m", "positive": "m o + \\sin{(m)}", "negatives": ["- m o + e^{m}", "\\frac{m^{2}}{2} + e^{m}", "\\frac{o (o + 2 \\cos{(m)})}{2}", "e^{m - o}"], "srepr_premise_expression": "Add(Symbol('o', commutative=True), cos(Symbol('m', commutative=True)))", "srepr_variable": "Symbol('m', commutative=True)", "srepr_positive": "Add(Mul(Symbol('m', commutative=True), Symbol('o', commutative=True)), sin(Symbol('m', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('m', commutative=True), Symbol('o', commutative=True)), exp(Symbol('m', commutative=True)))", "Add(Mul(Rational(1, 2), Pow(Symbol('m', commutative=True), Integer(2))), exp(Symbol('m', commutative=True)))", "Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Symbol('o', commutative=True), Mul(Integer(2), cos(Symbol('m', commutative=True)))))", "exp(Add(Symbol('m', commutative=True), Mul(Integer(-1), Symbol('o', commutative=True))))"]}, {"premise_expression": "H X", "variable": "H", "positive": "\\frac{H^{2} X}{2}", "negatives": ["\\frac{H X^{2}}{2}", "\\frac{H (H + 2 X)}{2}", "X e^{H}", "X \\sin{(H)}"], "srepr_premise_expression": "Mul(Symbol('H', commutative=True), Symbol('X', commutative=True))", "srepr_variable": "Symbol('H', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('H', commutative=True), Integer(2)), Symbol('X', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('H', commutative=True), Pow(Symbol('X', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('H', commutative=True), Add(Symbol('H', commutative=True), Mul(Integer(2), Symbol('X', commutative=True))))", "Mul(Symbol('X', commutative=True), exp(Symbol('H', commutative=True)))", "Mul(Symbol('X', commutative=True), sin(Symbol('H', commutative=True)))"]}, {"premise_expression": "f + y", "variable": "y", "positive": "\\frac{y (2 f + y)}{2}", "negatives": ["\\frac{f (f + 2 y)}{2}", "- \\cos{(f + y)}", "\\frac{y^{2}}{2 f}", "\\operatorname{Ei}{(y)}"], "srepr_premise_expression": "Add(Symbol('f', commutative=True), Symbol('y', commutative=True))", "srepr_variable": "Symbol('y', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('y', commutative=True), Add(Mul(Integer(2), Symbol('f', commutative=True)), Symbol('y', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Symbol('f', commutative=True), Mul(Integer(2), Symbol('y', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('f', commutative=True), Symbol('y', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('f', commutative=True), Integer(-1)), Pow(Symbol('y', commutative=True), Integer(2)))", "Ei(Symbol('y', commutative=True))"]}, {"premise_expression": "G g", "variable": "G", "positive": "\\frac{G^{2} g}{2}", "negatives": ["\\frac{G g^{2}}{2}", "- g \\cos{(G)}", "\\cos{(G - g)}", "- \\cos{(G - g)}"], "srepr_premise_expression": "Mul(Symbol('G', commutative=True), Symbol('g', commutative=True))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(2)), Symbol('g', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('G', commutative=True), Pow(Symbol('g', commutative=True), Integer(2)))", "Mul(Integer(-1), Symbol('g', commutative=True), cos(Symbol('G', commutative=True)))", "cos(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('g', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('g', commutative=True)))))"]}, {"premise_expression": "J (N + U)", "variable": "U", "positive": "\\frac{J U (2 N + U)}{2}", "negatives": ["\\frac{J^{2} (N + U)}{2}", "\\frac{J N (N + 2 U)}{2}", "\\frac{U^{2} (J + N)}{2}", "\\frac{U (2 J^{N} - U)}{2}"], "srepr_premise_expression": "Mul(Symbol('J', commutative=True), Add(Symbol('N', commutative=True), Symbol('U', commutative=True)))", "srepr_variable": "Symbol('U', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('J', commutative=True), Symbol('U', commutative=True), Add(Mul(Integer(2), Symbol('N', commutative=True)), Symbol('U', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('J', commutative=True), Integer(2)), Add(Symbol('N', commutative=True), Symbol('U', commutative=True)))", "Mul(Rational(1, 2), Symbol('J', commutative=True), Symbol('N', commutative=True), Add(Symbol('N', commutative=True), Mul(Integer(2), Symbol('U', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('U', commutative=True), Integer(2)), Add(Symbol('J', commutative=True), Symbol('N', commutative=True)))", "Mul(Rational(1, 2), Symbol('U', commutative=True), Add(Mul(Integer(2), Pow(Symbol('J', commutative=True), Symbol('N', commutative=True))), Mul(Integer(-1), Symbol('U', commutative=True))))"]}, {"premise_expression": "\\frac{\\sin{(b)}}{X}", "variable": "b", "positive": "- \\frac{\\cos{(b)}}{X}", "negatives": ["\\frac{\\sin{(b)}}{X}", "- \\cos{(X + b)}", "X e^{b}", "X e^{\\frac{b}{X}}"], "srepr_premise_expression": "Mul(Pow(Symbol('X', commutative=True), Integer(-1)), sin(Symbol('b', commutative=True)))", "srepr_variable": "Symbol('b', commutative=True)", "srepr_positive": "Mul(Integer(-1), Pow(Symbol('X', commutative=True), Integer(-1)), cos(Symbol('b', commutative=True)))", "srepr_negatives": ["Mul(Pow(Symbol('X', commutative=True), Integer(-1)), sin(Symbol('b', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('X', commutative=True), Symbol('b', commutative=True))))", "Mul(Symbol('X', commutative=True), exp(Symbol('b', commutative=True)))", "Mul(Symbol('X', commutative=True), exp(Mul(Pow(Symbol('X', commutative=True), Integer(-1)), Symbol('b', commutative=True))))"]}, {"premise_expression": "M + \\cos{(q)}", "variable": "M", "positive": "\\frac{M (M + 2 \\cos{(q)})}{2}", "negatives": ["\\frac{M^{2} \\log{(q)}}{2}", "\\frac{M^{2} e^{q}}{2}", "M q + \\sin{(q)}", "M (\\log{(2 M)} - 1)"], "srepr_premise_expression": "Add(Symbol('M', commutative=True), cos(Symbol('q', commutative=True)))", "srepr_variable": "Symbol('M', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('M', commutative=True), Add(Symbol('M', commutative=True), Mul(Integer(2), cos(Symbol('q', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('M', commutative=True), Integer(2)), log(Symbol('q', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('M', commutative=True), Integer(2)), exp(Symbol('q', commutative=True)))", "Add(Mul(Symbol('M', commutative=True), Symbol('q', commutative=True)), sin(Symbol('q', commutative=True)))", "Mul(Symbol('M', commutative=True), Add(log(Mul(Integer(2), Symbol('M', commutative=True))), Integer(-1)))"]}, {"premise_expression": "E - z", "variable": "z", "positive": "\\frac{z (2 E - z)}{2}", "negatives": ["\\frac{E (E - 2 z)}{2}", "\\frac{z (\\log{(z)} - 1)}{E}", "\\frac{z^{2}}{2 E}", "E e^{z}"], "srepr_premise_expression": "Add(Symbol('E', commutative=True), Mul(Integer(-1), Symbol('z', commutative=True)))", "srepr_variable": "Symbol('z', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('z', commutative=True), Add(Mul(Integer(2), Symbol('E', commutative=True)), Mul(Integer(-1), Symbol('z', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('E', commutative=True), Add(Symbol('E', commutative=True), Mul(Integer(-1), Integer(2), Symbol('z', commutative=True))))", "Mul(Pow(Symbol('E', commutative=True), Integer(-1)), Symbol('z', commutative=True), Add(log(Symbol('z', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('E', commutative=True), Integer(-1)), Pow(Symbol('z', commutative=True), Integer(2)))", "Mul(Symbol('E', commutative=True), exp(Symbol('z', commutative=True)))"]}, {"premise_expression": "H - s + t", "variable": "H", "positive": "H (\\frac{H}{2} - s + t)", "negatives": ["\\frac{H (- H + 2 s - 2 t)}{2}", "\\frac{s (2 H - s + 2 t)}{2}", "\\frac{t (2 H - 2 s + t)}{2}", "\\frac{H (H t - 2 s)}{2}"], "srepr_premise_expression": "Add(Symbol('H', commutative=True), Mul(Integer(-1), Symbol('s', commutative=True)), Symbol('t', commutative=True))", "srepr_variable": "Symbol('H', commutative=True)", "srepr_positive": "Mul(Symbol('H', commutative=True), Add(Mul(Rational(1, 2), Symbol('H', commutative=True)), Mul(Integer(-1), Symbol('s', commutative=True)), Symbol('t', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('H', commutative=True), Add(Mul(Integer(-1), Symbol('H', commutative=True)), Mul(Integer(2), Symbol('s', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('t', commutative=True))))", "Mul(Rational(1, 2), Symbol('s', commutative=True), Add(Mul(Integer(2), Symbol('H', commutative=True)), Mul(Integer(-1), Symbol('s', commutative=True)), Mul(Integer(2), Symbol('t', commutative=True))))", "Mul(Rational(1, 2), Symbol('t', commutative=True), Add(Mul(Integer(2), Symbol('H', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('s', commutative=True)), Symbol('t', commutative=True)))", "Mul(Rational(1, 2), Symbol('H', commutative=True), Add(Mul(Symbol('H', commutative=True), Symbol('t', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('s', commutative=True))))"]}, {"premise_expression": "E L", "variable": "L", "positive": "\\frac{E L^{2}}{2}", "negatives": ["\\frac{E^{2} L}{2}", "E \\log{(L)}", "- \\frac{\\cos{(L)}}{E}", "\\frac{L (2 E - L)}{2}"], "srepr_premise_expression": "Mul(Symbol('E', commutative=True), Symbol('L', commutative=True))", "srepr_variable": "Symbol('L', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('E', commutative=True), Pow(Symbol('L', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('E', commutative=True), Integer(2)), Symbol('L', commutative=True))", "Mul(Symbol('E', commutative=True), log(Symbol('L', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('E', commutative=True), Integer(-1)), cos(Symbol('L', commutative=True)))", "Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Mul(Integer(2), Symbol('E', commutative=True)), Mul(Integer(-1), Symbol('L', commutative=True))))"]}, {"premise_expression": "J - c - h", "variable": "c", "positive": "c (J - \\frac{c}{2} - h)", "negatives": ["\\frac{h (2 J - 2 c - h)}{2}", "\\frac{J (J - 2 c - 2 h)}{2}", "c (- 2 J + h)", "\\frac{c (J c + 2 h)}{2}"], "srepr_premise_expression": "Add(Symbol('J', commutative=True), Mul(Integer(-1), Symbol('c', commutative=True)), Mul(Integer(-1), Symbol('h', commutative=True)))", "srepr_variable": "Symbol('c', commutative=True)", "srepr_positive": "Mul(Symbol('c', commutative=True), Add(Symbol('J', commutative=True), Mul(Integer(-1), Rational(1, 2), Symbol('c', commutative=True)), Mul(Integer(-1), Symbol('h', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('h', commutative=True), Add(Mul(Integer(2), Symbol('J', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('c', commutative=True)), Mul(Integer(-1), Symbol('h', commutative=True))))", "Mul(Rational(1, 2), Symbol('J', commutative=True), Add(Symbol('J', commutative=True), Mul(Integer(-1), Integer(2), Symbol('c', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('h', commutative=True))))", "Mul(Symbol('c', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('J', commutative=True)), Symbol('h', commutative=True)))", "Mul(Rational(1, 2), Symbol('c', commutative=True), Add(Mul(Symbol('J', commutative=True), Symbol('c', commutative=True)), Mul(Integer(2), Symbol('h', commutative=True))))"]}, {"premise_expression": "H \\log{(y)}", "variable": "y", "positive": "H y (\\log{(y)} - 1)", "negatives": ["y (\\log{(H y)} - 1)", "y (\\log{(\\frac{H}{y})} + 1)", "\\frac{H^{2} \\log{(y)}}{2}", "\\frac{y^{2} \\log{(H)}}{2}"], "srepr_premise_expression": "Mul(Symbol('H', commutative=True), log(Symbol('y', commutative=True)))", "srepr_variable": "Symbol('y', commutative=True)", "srepr_positive": "Mul(Symbol('H', commutative=True), Symbol('y', commutative=True), Add(log(Symbol('y', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('y', commutative=True), Add(log(Mul(Symbol('H', commutative=True), Symbol('y', commutative=True))), Integer(-1)))", "Mul(Symbol('y', commutative=True), Add(log(Mul(Symbol('H', commutative=True), Pow(Symbol('y', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Rational(1, 2), Pow(Symbol('H', commutative=True), Integer(2)), log(Symbol('y', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('y', commutative=True), Integer(2)), log(Symbol('H', commutative=True)))"]}, {"premise_expression": "T + r", "variable": "r", "positive": "\\frac{r (2 T + r)}{2}", "negatives": ["\\frac{T (T + 2 r)}{2}", "\\frac{r (\\log{(r)} - 1)}{T}", "- T \\cos{(r)}", "\\log{(T)} \\log{(r)}"], "srepr_premise_expression": "Add(Symbol('T', commutative=True), Symbol('r', commutative=True))", "srepr_variable": "Symbol('r', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(2), Symbol('T', commutative=True)), Symbol('r', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('T', commutative=True), Add(Symbol('T', commutative=True), Mul(Integer(2), Symbol('r', commutative=True))))", "Mul(Pow(Symbol('T', commutative=True), Integer(-1)), Symbol('r', commutative=True), Add(log(Symbol('r', commutative=True)), Integer(-1)))", "Mul(Integer(-1), Symbol('T', commutative=True), cos(Symbol('r', commutative=True)))", "Mul(log(Symbol('T', commutative=True)), log(Symbol('r', commutative=True)))"]}, {"premise_expression": "S (Y - u)", "variable": "Y", "positive": "\\frac{S Y (Y - 2 u)}{2}", "negatives": ["\\frac{S^{2} (Y - u)}{2}", "\\frac{Y (S Y - 2 u)}{2}", "\\frac{S u (2 Y - u)}{2}", "\\frac{Y (S Y + 2 u)}{2}"], "srepr_premise_expression": "Mul(Symbol('S', commutative=True), Add(Symbol('Y', commutative=True), Mul(Integer(-1), Symbol('u', commutative=True))))", "srepr_variable": "Symbol('Y', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('S', commutative=True), Symbol('Y', commutative=True), Add(Symbol('Y', commutative=True), Mul(Integer(-1), Integer(2), Symbol('u', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('S', commutative=True), Integer(2)), Add(Symbol('Y', commutative=True), Mul(Integer(-1), Symbol('u', commutative=True))))", "Mul(Rational(1, 2), Symbol('Y', commutative=True), Add(Mul(Symbol('S', commutative=True), Symbol('Y', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('u', commutative=True))))", "Mul(Rational(1, 2), Symbol('S', commutative=True), Symbol('u', commutative=True), Add(Mul(Integer(2), Symbol('Y', commutative=True)), Mul(Integer(-1), Symbol('u', commutative=True))))", "Mul(Rational(1, 2), Symbol('Y', commutative=True), Add(Mul(Symbol('S', commutative=True), Symbol('Y', commutative=True)), Mul(Integer(2), Symbol('u', commutative=True))))"]}, {"premise_expression": "- l + \\sin{(K)}", "variable": "K", "positive": "- K l - \\cos{(K)}", "negatives": ["\\frac{K^{2} \\cos{(l)}}{2}", "- \\frac{\\cos{(K)}}{l}", "\\frac{K (K - 2 l)}{2}", "e^{K - l}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('l', commutative=True)), sin(Symbol('K', commutative=True)))", "srepr_variable": "Symbol('K', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('K', commutative=True), Symbol('l', commutative=True)), Mul(Integer(-1), cos(Symbol('K', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('K', commutative=True), Integer(2)), cos(Symbol('l', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('l', commutative=True), Integer(-1)), cos(Symbol('K', commutative=True)))", "Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Symbol('K', commutative=True), Mul(Integer(-1), Integer(2), Symbol('l', commutative=True))))", "exp(Add(Symbol('K', commutative=True), Mul(Integer(-1), Symbol('l', commutative=True))))"]}, {"premise_expression": "- N + o", "variable": "N", "positive": "\\frac{N (- N + 2 o)}{2}", "negatives": ["\\frac{o (- 2 N + o)}{2}", "\\frac{N^{2} e^{o}}{2}", "\\cos{(N - o)}", "o \\log{(N)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('N', commutative=True)), Symbol('o', commutative=True))", "srepr_variable": "Symbol('N', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Mul(Integer(-1), Symbol('N', commutative=True)), Mul(Integer(2), Symbol('o', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('N', commutative=True)), Symbol('o', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('N', commutative=True), Integer(2)), exp(Symbol('o', commutative=True)))", "cos(Add(Symbol('N', commutative=True), Mul(Integer(-1), Symbol('o', commutative=True))))", "Mul(Symbol('o', commutative=True), log(Symbol('N', commutative=True)))"]}, {"premise_expression": "- s + \\log{(R)}", "variable": "R", "positive": "R (- s + \\log{(R)} - 1)", "negatives": ["\\frac{s (- s + 2 \\log{(R)})}{2}", "\\frac{R (- R + 2 s)}{2}", "\\cos{(R - s)}", "\\sin{(R + s)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('s', commutative=True)), log(Symbol('R', commutative=True)))", "srepr_variable": "Symbol('R', commutative=True)", "srepr_positive": "Mul(Symbol('R', commutative=True), Add(Mul(Integer(-1), Symbol('s', commutative=True)), log(Symbol('R', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('s', commutative=True), Add(Mul(Integer(-1), Symbol('s', commutative=True)), Mul(Integer(2), log(Symbol('R', commutative=True)))))", "Mul(Rational(1, 2), Symbol('R', commutative=True), Add(Mul(Integer(-1), Symbol('R', commutative=True)), Mul(Integer(2), Symbol('s', commutative=True))))", "cos(Add(Symbol('R', commutative=True), Mul(Integer(-1), Symbol('s', commutative=True))))", "sin(Add(Symbol('R', commutative=True), Symbol('s', commutative=True)))"]}, {"premise_expression": "\\log{(B^{h})}", "variable": "B", "positive": "B (- h + \\log{(B^{h})})", "negatives": ["\\frac{B (- B + 2 \\cos{(h)})}{2}", "- B h + e^{B}", "B (\\log{(\\frac{B}{h})} - 1)", "\\frac{h^{2} \\log{(B)}}{2}"], "srepr_premise_expression": "log(Pow(Symbol('B', commutative=True), Symbol('h', commutative=True)))", "srepr_variable": "Symbol('B', commutative=True)", "srepr_positive": "Mul(Symbol('B', commutative=True), Add(Mul(Integer(-1), Symbol('h', commutative=True)), log(Pow(Symbol('B', commutative=True), Symbol('h', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('B', commutative=True), Add(Mul(Integer(-1), Symbol('B', commutative=True)), Mul(Integer(2), cos(Symbol('h', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('B', commutative=True), Symbol('h', commutative=True)), exp(Symbol('B', commutative=True)))", "Mul(Symbol('B', commutative=True), Add(log(Mul(Symbol('B', commutative=True), Pow(Symbol('h', commutative=True), Integer(-1)))), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('h', commutative=True), Integer(2)), log(Symbol('B', commutative=True)))"]}, {"premise_expression": "- C + K", "variable": "K", "positive": "\\frac{K (- 2 C + K)}{2}", "negatives": ["\\frac{C (- C + 2 K)}{2}", "\\frac{K^{2} \\cos{(C)}}{2}", "- \\sin{(C - K)}", "\\frac{K (- K + 2 \\cos{(C)})}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('C', commutative=True)), Symbol('K', commutative=True))", "srepr_variable": "Symbol('K', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('C', commutative=True)), Symbol('K', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Mul(Integer(-1), Symbol('C', commutative=True)), Mul(Integer(2), Symbol('K', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('K', commutative=True), Integer(2)), cos(Symbol('C', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('K', commutative=True)))))", "Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Mul(Integer(-1), Symbol('K', commutative=True)), Mul(Integer(2), cos(Symbol('C', commutative=True)))))"]}, {"premise_expression": "W + l + w", "variable": "w", "positive": "w (W + l + \\frac{w}{2})", "negatives": ["\\frac{w (- 2 W + 2 l + w)}{2}", "\\frac{l (2 W + l + 2 w)}{2}", "\\frac{W (W + 2 l + 2 w)}{2}", "\\frac{w^{2} (- W + l)}{2}"], "srepr_premise_expression": "Add(Symbol('W', commutative=True), Symbol('l', commutative=True), Symbol('w', commutative=True))", "srepr_variable": "Symbol('w', commutative=True)", "srepr_positive": "Mul(Symbol('w', commutative=True), Add(Symbol('W', commutative=True), Symbol('l', commutative=True), Mul(Rational(1, 2), Symbol('w', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('w', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('W', commutative=True)), Mul(Integer(2), Symbol('l', commutative=True)), Symbol('w', commutative=True)))", "Mul(Rational(1, 2), Symbol('l', commutative=True), Add(Mul(Integer(2), Symbol('W', commutative=True)), Symbol('l', commutative=True), Mul(Integer(2), Symbol('w', commutative=True))))", "Mul(Rational(1, 2), Symbol('W', commutative=True), Add(Symbol('W', commutative=True), Mul(Integer(2), Symbol('l', commutative=True)), Mul(Integer(2), Symbol('w', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('w', commutative=True), Integer(2)), Add(Mul(Integer(-1), Symbol('W', commutative=True)), Symbol('l', commutative=True)))"]}, {"premise_expression": "\\frac{Y}{g}", "variable": "g", "positive": "Y \\log{(g)}", "negatives": ["Y \\sin{(g)}", "\\frac{Y^{2}}{2 g}", "\\frac{Y g^{2}}{2}", "\\frac{g^{2}}{2 Y}"], "srepr_premise_expression": "Mul(Symbol('Y', commutative=True), Pow(Symbol('g', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('g', commutative=True)", "srepr_positive": "Mul(Symbol('Y', commutative=True), log(Symbol('g', commutative=True)))", "srepr_negatives": ["Mul(Symbol('Y', commutative=True), sin(Symbol('g', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('Y', commutative=True), Integer(2)), Pow(Symbol('g', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Symbol('Y', commutative=True), Pow(Symbol('g', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('Y', commutative=True), Integer(-1)), Pow(Symbol('g', commutative=True), Integer(2)))"]}, {"premise_expression": "b - f", "variable": "f", "positive": "\\frac{f (2 b - f)}{2}", "negatives": ["\\frac{b (b - 2 f)}{2}", "- \\cos{(b - f)}", "b \\log{(f)}", "\\frac{f (f + 2 \\sin{(b)})}{2}"], "srepr_premise_expression": "Add(Symbol('b', commutative=True), Mul(Integer(-1), Symbol('f', commutative=True)))", "srepr_variable": "Symbol('f', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Mul(Integer(2), Symbol('b', commutative=True)), Mul(Integer(-1), Symbol('f', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('b', commutative=True), Add(Symbol('b', commutative=True), Mul(Integer(-1), Integer(2), Symbol('f', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('b', commutative=True), Mul(Integer(-1), Symbol('f', commutative=True)))))", "Mul(Symbol('b', commutative=True), log(Symbol('f', commutative=True)))", "Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Symbol('f', commutative=True), Mul(Integer(2), sin(Symbol('b', commutative=True)))))"]}, {"premise_expression": "- J + t", "variable": "t", "positive": "\\frac{t (- 2 J + t)}{2}", "negatives": ["\\frac{J (- J + 2 t)}{2}", "\\frac{t^{2} \\cos{(J)}}{2}", "\\sin{(J + t)}", "e^{J + t}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('J', commutative=True)), Symbol('t', commutative=True))", "srepr_variable": "Symbol('t', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('t', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('J', commutative=True)), Symbol('t', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('J', commutative=True), Add(Mul(Integer(-1), Symbol('J', commutative=True)), Mul(Integer(2), Symbol('t', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('t', commutative=True), Integer(2)), cos(Symbol('J', commutative=True)))", "sin(Add(Symbol('J', commutative=True), Symbol('t', commutative=True)))", "exp(Add(Symbol('J', commutative=True), Symbol('t', commutative=True)))"]}, {"premise_expression": "H M", "variable": "H", "positive": "\\frac{H^{2} M}{2}", "negatives": ["\\frac{H M^{2}}{2}", "\\frac{H^{2}}{2 M}", "H", "\\sin{(H - M)}"], "srepr_premise_expression": "Mul(Symbol('H', commutative=True), Symbol('M', commutative=True))", "srepr_variable": "Symbol('H', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('H', commutative=True), Integer(2)), Symbol('M', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('H', commutative=True), Pow(Symbol('M', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('H', commutative=True), Integer(2)), Pow(Symbol('M', commutative=True), Integer(-1)))", "Symbol('H', commutative=True)", "sin(Add(Symbol('H', commutative=True), Mul(Integer(-1), Symbol('M', commutative=True))))"]}, {"premise_expression": "\\frac{Q}{v}", "variable": "Q", "positive": "\\frac{Q^{2}}{2 v}", "negatives": ["Q \\log{(v)}", "\\frac{Q^{2} \\log{(v)}}{2}", "\\frac{Q (- Q + 2 v)}{2}", "\\log{(Q)} \\log{(v)}"], "srepr_premise_expression": "Mul(Symbol('Q', commutative=True), Pow(Symbol('v', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('Q', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(2)), Pow(Symbol('v', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('Q', commutative=True), log(Symbol('v', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(2)), log(Symbol('v', commutative=True)))", "Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Mul(Integer(-1), Symbol('Q', commutative=True)), Mul(Integer(2), Symbol('v', commutative=True))))", "Mul(log(Symbol('Q', commutative=True)), log(Symbol('v', commutative=True)))"]}, {"premise_expression": "q \\log{(I)}", "variable": "I", "positive": "I q (\\log{(I)} - 1)", "negatives": ["I (- q + \\log{(I)} - 1)", "\\frac{q^{2} \\log{(I)}}{2}", "\\cos{(I - q)}", "\\frac{I^{2} \\log{(q)}}{2}"], "srepr_premise_expression": "Mul(Symbol('q', commutative=True), log(Symbol('I', commutative=True)))", "srepr_variable": "Symbol('I', commutative=True)", "srepr_positive": "Mul(Symbol('I', commutative=True), Symbol('q', commutative=True), Add(log(Symbol('I', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('I', commutative=True), Add(Mul(Integer(-1), Symbol('q', commutative=True)), log(Symbol('I', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('q', commutative=True), Integer(2)), log(Symbol('I', commutative=True)))", "cos(Add(Symbol('I', commutative=True), Mul(Integer(-1), Symbol('q', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(2)), log(Symbol('q', commutative=True)))"]}, {"premise_expression": "R - v - z", "variable": "v", "positive": "v (R - \\frac{v}{2} - z)", "negatives": ["\\frac{z (2 R - 2 v - z)}{2}", "\\frac{R (R - 2 v - 2 z)}{2}", "\\frac{v (R v - 2 z)}{2}", "\\frac{v (2 R^{z} - v)}{2}"], "srepr_premise_expression": "Add(Symbol('R', commutative=True), Mul(Integer(-1), Symbol('v', commutative=True)), Mul(Integer(-1), Symbol('z', commutative=True)))", "srepr_variable": "Symbol('v', commutative=True)", "srepr_positive": "Mul(Symbol('v', commutative=True), Add(Symbol('R', commutative=True), Mul(Integer(-1), Rational(1, 2), Symbol('v', commutative=True)), Mul(Integer(-1), Symbol('z', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('z', commutative=True), Add(Mul(Integer(2), Symbol('R', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('v', commutative=True)), Mul(Integer(-1), Symbol('z', commutative=True))))", "Mul(Rational(1, 2), Symbol('R', commutative=True), Add(Symbol('R', commutative=True), Mul(Integer(-1), Integer(2), Symbol('v', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('z', commutative=True))))", "Mul(Rational(1, 2), Symbol('v', commutative=True), Add(Mul(Symbol('R', commutative=True), Symbol('v', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('z', commutative=True))))", "Mul(Rational(1, 2), Symbol('v', commutative=True), Add(Mul(Integer(2), Pow(Symbol('R', commutative=True), Symbol('z', commutative=True))), Mul(Integer(-1), Symbol('v', commutative=True))))"]}, {"premise_expression": "e^{b - r}", "variable": "b", "positive": "e^{b - r}", "negatives": ["- e^{b - r}", "b (\\log{(\\frac{b}{r})} - 1)", "- b r - \\cos{(b)}", "b r + \\sin{(b)}"], "srepr_premise_expression": "exp(Add(Symbol('b', commutative=True), Mul(Integer(-1), Symbol('r', commutative=True))))", "srepr_variable": "Symbol('b', commutative=True)", "srepr_positive": "exp(Add(Symbol('b', commutative=True), Mul(Integer(-1), Symbol('r', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Symbol('b', commutative=True), Mul(Integer(-1), Symbol('r', commutative=True)))))", "Mul(Symbol('b', commutative=True), Add(log(Mul(Symbol('b', commutative=True), Pow(Symbol('r', commutative=True), Integer(-1)))), Integer(-1)))", "Add(Mul(Integer(-1), Symbol('b', commutative=True), Symbol('r', commutative=True)), Mul(Integer(-1), cos(Symbol('b', commutative=True))))", "Add(Mul(Symbol('b', commutative=True), Symbol('r', commutative=True)), sin(Symbol('b', commutative=True)))"]}, {"premise_expression": "c + \\sin{(a)}", "variable": "a", "positive": "a c - \\cos{(a)}", "negatives": ["c \\log{(a)}", "\\frac{a^{2}}{2 c}", "\\frac{a^{2} \\log{(c)}}{2}", "a e^{2 c}"], "srepr_premise_expression": "Add(Symbol('c', commutative=True), sin(Symbol('a', commutative=True)))", "srepr_variable": "Symbol('a', commutative=True)", "srepr_positive": "Add(Mul(Symbol('a', commutative=True), Symbol('c', commutative=True)), Mul(Integer(-1), cos(Symbol('a', commutative=True))))", "srepr_negatives": ["Mul(Symbol('c', commutative=True), log(Symbol('a', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('a', commutative=True), Integer(2)), Pow(Symbol('c', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('a', commutative=True), Integer(2)), log(Symbol('c', commutative=True)))", "Mul(Symbol('a', commutative=True), exp(Mul(Integer(2), Symbol('c', commutative=True))))"]}, {"premise_expression": "f \\cos{(Q)}", "variable": "f", "positive": "\\frac{f^{2} \\cos{(Q)}}{2}", "negatives": ["f \\sin{(Q)}", "\\frac{\\sin{(f)}}{Q}", "- \\cos{(Q + f)}", "e^{Q + f}"], "srepr_premise_expression": "Mul(Symbol('f', commutative=True), cos(Symbol('Q', commutative=True)))", "srepr_variable": "Symbol('f', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('f', commutative=True), Integer(2)), cos(Symbol('Q', commutative=True)))", "srepr_negatives": ["Mul(Symbol('f', commutative=True), sin(Symbol('Q', commutative=True)))", "Mul(Pow(Symbol('Q', commutative=True), Integer(-1)), sin(Symbol('f', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('Q', commutative=True), Symbol('f', commutative=True))))", "exp(Add(Symbol('Q', commutative=True), Symbol('f', commutative=True)))"]}, {"premise_expression": "N + \\sin{(y)}", "variable": "y", "positive": "N y - \\cos{(y)}", "negatives": ["- \\frac{\\cos{(y)}}{N}", "\\frac{N (N + 2 \\sin{(y)})}{2}", "\\frac{y^{2} \\log{(N)}}{2}", "y (- N + \\log{(y^{N})})"], "srepr_premise_expression": "Add(Symbol('N', commutative=True), sin(Symbol('y', commutative=True)))", "srepr_variable": "Symbol('y', commutative=True)", "srepr_positive": "Add(Mul(Symbol('N', commutative=True), Symbol('y', commutative=True)), Mul(Integer(-1), cos(Symbol('y', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), Pow(Symbol('N', commutative=True), Integer(-1)), cos(Symbol('y', commutative=True)))", "Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Symbol('N', commutative=True), Mul(Integer(2), sin(Symbol('y', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('y', commutative=True), Integer(2)), log(Symbol('N', commutative=True)))", "Mul(Symbol('y', commutative=True), Add(Mul(Integer(-1), Symbol('N', commutative=True)), log(Pow(Symbol('y', commutative=True), Symbol('N', commutative=True)))))"]}, {"premise_expression": "R + n", "variable": "n", "positive": "\\frac{n (2 R + n)}{2}", "negatives": ["\\frac{R (R + 2 n)}{2}", "\\frac{n^{2} \\cos{(R)}}{2}", "\\frac{n^{2} \\log{(R)}}{2}", "\\frac{R n (n - 2)}{2}"], "srepr_premise_expression": "Add(Symbol('R', commutative=True), Symbol('n', commutative=True))", "srepr_variable": "Symbol('n', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('n', commutative=True), Add(Mul(Integer(2), Symbol('R', commutative=True)), Symbol('n', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('R', commutative=True), Add(Symbol('R', commutative=True), Mul(Integer(2), Symbol('n', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('n', commutative=True), Integer(2)), cos(Symbol('R', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('n', commutative=True), Integer(2)), log(Symbol('R', commutative=True)))", "Mul(Rational(1, 2), Symbol('R', commutative=True), Symbol('n', commutative=True), Add(Symbol('n', commutative=True), Integer(-2)))"]}, {"premise_expression": "- \\sin{(r - v)}", "variable": "r", "positive": "\\cos{(r - v)}", "negatives": ["- \\cos{(r - v)}", "- \\cos{(r + v)}", "r v - \\cos{(r)}", "- r v - \\cos{(r)}"], "srepr_premise_expression": "Mul(Integer(-1), sin(Add(Symbol('r', commutative=True), Mul(Integer(-1), Symbol('v', commutative=True)))))", "srepr_variable": "Symbol('r', commutative=True)", "srepr_positive": "cos(Add(Symbol('r', commutative=True), Mul(Integer(-1), Symbol('v', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('r', commutative=True), Mul(Integer(-1), Symbol('v', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('r', commutative=True), Symbol('v', commutative=True))))", "Add(Mul(Symbol('r', commutative=True), Symbol('v', commutative=True)), Mul(Integer(-1), cos(Symbol('r', commutative=True))))", "Add(Mul(Integer(-1), Symbol('r', commutative=True), Symbol('v', commutative=True)), Mul(Integer(-1), cos(Symbol('r', commutative=True))))"]}, {"premise_expression": "X \\log{(D)}", "variable": "D", "positive": "D X (\\log{(D)} - 1)", "negatives": ["\\frac{X^{2} \\log{(D)}}{2}", "D X - \\cos{(D)}", "- e^{- D + X}", "\\log{(D)} \\cos{(X)}"], "srepr_premise_expression": "Mul(Symbol('X', commutative=True), log(Symbol('D', commutative=True)))", "srepr_variable": "Symbol('D', commutative=True)", "srepr_positive": "Mul(Symbol('D', commutative=True), Symbol('X', commutative=True), Add(log(Symbol('D', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('X', commutative=True), Integer(2)), log(Symbol('D', commutative=True)))", "Add(Mul(Symbol('D', commutative=True), Symbol('X', commutative=True)), Mul(Integer(-1), cos(Symbol('D', commutative=True))))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('D', commutative=True)), Symbol('X', commutative=True))))", "Mul(log(Symbol('D', commutative=True)), cos(Symbol('X', commutative=True)))"]}, {"premise_expression": "E J", "variable": "E", "positive": "\\frac{E^{2} J}{2}", "negatives": ["\\frac{E J^{2}}{2}", "\\frac{E^{2} \\sin{(J)}}{2}", "E", "e^{E + J}"], "srepr_premise_expression": "Mul(Symbol('E', commutative=True), Symbol('J', commutative=True))", "srepr_variable": "Symbol('E', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('E', commutative=True), Integer(2)), Symbol('J', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('E', commutative=True), Pow(Symbol('J', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('E', commutative=True), Integer(2)), sin(Symbol('J', commutative=True)))", "Symbol('E', commutative=True)", "exp(Add(Symbol('E', commutative=True), Symbol('J', commutative=True)))"]}, {"premise_expression": "U - n", "variable": "U", "positive": "\\frac{U (U - 2 n)}{2}", "negatives": ["\\frac{n (2 U - n)}{2}", "\\frac{U^{2} n}{2}", "\\sin{(U - n)}", "\\frac{U (- U + 2 e^{n})}{2}"], "srepr_premise_expression": "Add(Symbol('U', commutative=True), Mul(Integer(-1), Symbol('n', commutative=True)))", "srepr_variable": "Symbol('U', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('U', commutative=True), Add(Symbol('U', commutative=True), Mul(Integer(-1), Integer(2), Symbol('n', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('n', commutative=True), Add(Mul(Integer(2), Symbol('U', commutative=True)), Mul(Integer(-1), Symbol('n', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('U', commutative=True), Integer(2)), Symbol('n', commutative=True))", "sin(Add(Symbol('U', commutative=True), Mul(Integer(-1), Symbol('n', commutative=True))))", "Mul(Rational(1, 2), Symbol('U', commutative=True), Add(Mul(Integer(-1), Symbol('U', commutative=True)), Mul(Integer(2), exp(Symbol('n', commutative=True)))))"]}, {"premise_expression": "N + \\frac{Y}{S}", "variable": "S", "positive": "N S + Y \\log{(S)}", "negatives": ["N Y + \\frac{Y^{2}}{2 S}", "\\frac{N \\log{(S)}}{Y}", "\\frac{N^{2}}{2} + \\frac{N Y}{S}", "\\frac{N^{Y} S^{2}}{2}"], "srepr_premise_expression": "Add(Symbol('N', commutative=True), Mul(Pow(Symbol('S', commutative=True), Integer(-1)), Symbol('Y', commutative=True)))", "srepr_variable": "Symbol('S', commutative=True)", "srepr_positive": "Add(Mul(Symbol('N', commutative=True), Symbol('S', commutative=True)), Mul(Symbol('Y', commutative=True), log(Symbol('S', commutative=True))))", "srepr_negatives": ["Add(Mul(Symbol('N', commutative=True), Symbol('Y', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('S', commutative=True), Integer(-1)), Pow(Symbol('Y', commutative=True), Integer(2))))", "Mul(Symbol('N', commutative=True), Pow(Symbol('Y', commutative=True), Integer(-1)), log(Symbol('S', commutative=True)))", "Add(Mul(Rational(1, 2), Pow(Symbol('N', commutative=True), Integer(2))), Mul(Symbol('N', commutative=True), Pow(Symbol('S', commutative=True), Integer(-1)), Symbol('Y', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('N', commutative=True), Symbol('Y', commutative=True)), Pow(Symbol('S', commutative=True), Integer(2)))"]}, {"premise_expression": "\\cos{(S + y)}", "variable": "y", "positive": "\\sin{(S + y)}", "negatives": ["e^{- S + y}", "S e^{y}", "e^{S} \\log{(y)}", "- S y + \\sin{(y)}"], "srepr_premise_expression": "cos(Add(Symbol('S', commutative=True), Symbol('y', commutative=True)))", "srepr_variable": "Symbol('y', commutative=True)", "srepr_positive": "sin(Add(Symbol('S', commutative=True), Symbol('y', commutative=True)))", "srepr_negatives": ["exp(Add(Mul(Integer(-1), Symbol('S', commutative=True)), Symbol('y', commutative=True)))", "Mul(Symbol('S', commutative=True), exp(Symbol('y', commutative=True)))", "Mul(exp(Symbol('S', commutative=True)), log(Symbol('y', commutative=True)))", "Add(Mul(Integer(-1), Symbol('S', commutative=True), Symbol('y', commutative=True)), sin(Symbol('y', commutative=True)))"]}, {"premise_expression": "\\frac{J^{I}}{C}", "variable": "C", "positive": "J^{I} \\log{(C)}", "negatives": ["\\frac{C^{2} J}{2 I}", "\\frac{C^{2} I}{2 J}", "\\frac{C^{2} I J}{2}", "\\frac{C I (C - 2)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('C', commutative=True), Integer(-1)), Pow(Symbol('J', commutative=True), Symbol('I', commutative=True)))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('J', commutative=True), Symbol('I', commutative=True)), log(Symbol('C', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2)), Pow(Symbol('I', commutative=True), Integer(-1)), Symbol('J', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2)), Symbol('I', commutative=True), Pow(Symbol('J', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2)), Symbol('I', commutative=True), Symbol('J', commutative=True))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Symbol('I', commutative=True), Add(Symbol('C', commutative=True), Integer(-2)))"]}, {"premise_expression": "b + g + w", "variable": "w", "positive": "w (b + g + \\frac{w}{2})", "negatives": ["\\frac{w (2 b - 2 g - w)}{2}", "\\frac{b (b + 2 g + 2 w)}{2}", "\\frac{g (2 b + g + 2 w)}{2}", "\\frac{w (2 b g + w)}{2}"], "srepr_premise_expression": "Add(Symbol('b', commutative=True), Symbol('g', commutative=True), Symbol('w', commutative=True))", "srepr_variable": "Symbol('w', commutative=True)", "srepr_positive": "Mul(Symbol('w', commutative=True), Add(Symbol('b', commutative=True), Symbol('g', commutative=True), Mul(Rational(1, 2), Symbol('w', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('w', commutative=True), Add(Mul(Integer(2), Symbol('b', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('g', commutative=True)), Mul(Integer(-1), Symbol('w', commutative=True))))", "Mul(Rational(1, 2), Symbol('b', commutative=True), Add(Symbol('b', commutative=True), Mul(Integer(2), Symbol('g', commutative=True)), Mul(Integer(2), Symbol('w', commutative=True))))", "Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Mul(Integer(2), Symbol('b', commutative=True)), Symbol('g', commutative=True), Mul(Integer(2), Symbol('w', commutative=True))))", "Mul(Rational(1, 2), Symbol('w', commutative=True), Add(Mul(Integer(2), Symbol('b', commutative=True), Symbol('g', commutative=True)), Symbol('w', commutative=True)))"]}, {"premise_expression": "V (- I + w)", "variable": "I", "positive": "\\frac{I V (- I + 2 w)}{2}", "negatives": ["\\frac{V^{2} (- I + w)}{2}", "\\frac{V w (- 2 I + w)}{2}", "\\frac{I^{2} (V + w)}{2}", "\\frac{I^{2} (V - w)}{2}"], "srepr_premise_expression": "Mul(Symbol('V', commutative=True), Add(Mul(Integer(-1), Symbol('I', commutative=True)), Symbol('w', commutative=True)))", "srepr_variable": "Symbol('I', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('I', commutative=True), Symbol('V', commutative=True), Add(Mul(Integer(-1), Symbol('I', commutative=True)), Mul(Integer(2), Symbol('w', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('V', commutative=True), Integer(2)), Add(Mul(Integer(-1), Symbol('I', commutative=True)), Symbol('w', commutative=True)))", "Mul(Rational(1, 2), Symbol('V', commutative=True), Symbol('w', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('I', commutative=True)), Symbol('w', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(2)), Add(Symbol('V', commutative=True), Symbol('w', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(2)), Add(Symbol('V', commutative=True), Mul(Integer(-1), Symbol('w', commutative=True))))"]}, {"premise_expression": "\\log{(n^{v})}", "variable": "v", "positive": "\\frac{v^{2} \\log{(n)}}{2}", "negatives": ["\\frac{v^{2} e^{n}}{2}", "\\frac{v (\\log{(v)} - 1)}{n}", "\\log{(v)} \\sin{(n)}", "n (- v + \\log{(n^{v})})"], "srepr_premise_expression": "log(Pow(Symbol('n', commutative=True), Symbol('v', commutative=True)))", "srepr_variable": "Symbol('v', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('v', commutative=True), Integer(2)), log(Symbol('n', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('v', commutative=True), Integer(2)), exp(Symbol('n', commutative=True)))", "Mul(Pow(Symbol('n', commutative=True), Integer(-1)), Symbol('v', commutative=True), Add(log(Symbol('v', commutative=True)), Integer(-1)))", "Mul(log(Symbol('v', commutative=True)), sin(Symbol('n', commutative=True)))", "Mul(Symbol('n', commutative=True), Add(Mul(Integer(-1), Symbol('v', commutative=True)), log(Pow(Symbol('n', commutative=True), Symbol('v', commutative=True)))))"]}, {"premise_expression": "\\frac{B}{g}", "variable": "B", "positive": "\\frac{B^{2}}{2 g}", "negatives": ["B \\log{(g)}", "\\frac{B^{2} g}{2}", "g \\sin{(B)}", "e^{B - g}"], "srepr_premise_expression": "Mul(Symbol('B', commutative=True), Pow(Symbol('g', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('B', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('B', commutative=True), Integer(2)), Pow(Symbol('g', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('B', commutative=True), log(Symbol('g', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('B', commutative=True), Integer(2)), Symbol('g', commutative=True))", "Mul(Symbol('g', commutative=True), sin(Symbol('B', commutative=True)))", "exp(Add(Symbol('B', commutative=True), Mul(Integer(-1), Symbol('g', commutative=True))))"]}, {"premise_expression": "\\log{(k^{J})}", "variable": "J", "positive": "\\frac{J^{2} \\log{(k)}}{2}", "negatives": ["\\frac{J^{2} k}{2}", "k \\log{(J)}", "- k \\cos{(J)}", "k \\sin{(J)}"], "srepr_premise_expression": "log(Pow(Symbol('k', commutative=True), Symbol('J', commutative=True)))", "srepr_variable": "Symbol('J', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('J', commutative=True), Integer(2)), log(Symbol('k', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('J', commutative=True), Integer(2)), Symbol('k', commutative=True))", "Mul(Symbol('k', commutative=True), log(Symbol('J', commutative=True)))", "Mul(Integer(-1), Symbol('k', commutative=True), cos(Symbol('J', commutative=True)))", "Mul(Symbol('k', commutative=True), sin(Symbol('J', commutative=True)))"]}, {"premise_expression": "\\sin{(E - P)}", "variable": "E", "positive": "- \\cos{(E - P)}", "negatives": ["\\cos{(E - P)}", "\\sin{(E - P)}", "E P (\\log{(E)} - 1)", "- E P + e^{E}"], "srepr_premise_expression": "sin(Add(Symbol('E', commutative=True), Mul(Integer(-1), Symbol('P', commutative=True))))", "srepr_variable": "Symbol('E', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('E', commutative=True), Mul(Integer(-1), Symbol('P', commutative=True)))))", "srepr_negatives": ["cos(Add(Symbol('E', commutative=True), Mul(Integer(-1), Symbol('P', commutative=True))))", "sin(Add(Symbol('E', commutative=True), Mul(Integer(-1), Symbol('P', commutative=True))))", "Mul(Symbol('E', commutative=True), Symbol('P', commutative=True), Add(log(Symbol('E', commutative=True)), Integer(-1)))", "Add(Mul(Integer(-1), Symbol('E', commutative=True), Symbol('P', commutative=True)), exp(Symbol('E', commutative=True)))"]}, {"premise_expression": "k + x", "variable": "k", "positive": "\\frac{k (k + 2 x)}{2}", "negatives": ["\\frac{k (- k + 2 x)}{2}", "\\frac{x (2 k + x)}{2}", "\\frac{k (k + 2 \\log{(x)})}{2}", "\\frac{k (- k + 2 \\cos{(x)})}{2}"], "srepr_premise_expression": "Add(Symbol('k', commutative=True), Symbol('x', commutative=True))", "srepr_variable": "Symbol('k', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('k', commutative=True), Add(Symbol('k', commutative=True), Mul(Integer(2), Symbol('x', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('k', commutative=True), Add(Mul(Integer(-1), Symbol('k', commutative=True)), Mul(Integer(2), Symbol('x', commutative=True))))", "Mul(Rational(1, 2), Symbol('x', commutative=True), Add(Mul(Integer(2), Symbol('k', commutative=True)), Symbol('x', commutative=True)))", "Mul(Rational(1, 2), Symbol('k', commutative=True), Add(Symbol('k', commutative=True), Mul(Integer(2), log(Symbol('x', commutative=True)))))", "Mul(Rational(1, 2), Symbol('k', commutative=True), Add(Mul(Integer(-1), Symbol('k', commutative=True)), Mul(Integer(2), cos(Symbol('x', commutative=True)))))"]}, {"premise_expression": "- J + e^{t}", "variable": "J", "positive": "\\frac{J (- J + 2 e^{t})}{2}", "negatives": ["\\frac{J (- J + 2 t)}{2}", "- J t + e^{t}", "\\frac{J^{2} \\log{(t)}}{2}", "J t (\\log{(J)} - 1)"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('J', commutative=True)), exp(Symbol('t', commutative=True)))", "srepr_variable": "Symbol('J', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('J', commutative=True), Add(Mul(Integer(-1), Symbol('J', commutative=True)), Mul(Integer(2), exp(Symbol('t', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('J', commutative=True), Add(Mul(Integer(-1), Symbol('J', commutative=True)), Mul(Integer(2), Symbol('t', commutative=True))))", "Add(Mul(Integer(-1), Symbol('J', commutative=True), Symbol('t', commutative=True)), exp(Symbol('t', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('J', commutative=True), Integer(2)), log(Symbol('t', commutative=True)))", "Mul(Symbol('J', commutative=True), Symbol('t', commutative=True), Add(log(Symbol('J', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\frac{\\cos{(o)}}{c}", "variable": "c", "positive": "\\log{(c)} \\cos{(o)}", "negatives": ["\\cos{(c - o)}", "- \\cos{(c - o)}", "\\frac{\\sin{(o)}}{c}", "\\frac{c (c + 2 \\cos{(o)})}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('c', commutative=True), Integer(-1)), cos(Symbol('o', commutative=True)))", "srepr_variable": "Symbol('c', commutative=True)", "srepr_positive": "Mul(log(Symbol('c', commutative=True)), cos(Symbol('o', commutative=True)))", "srepr_negatives": ["cos(Add(Symbol('c', commutative=True), Mul(Integer(-1), Symbol('o', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('c', commutative=True), Mul(Integer(-1), Symbol('o', commutative=True)))))", "Mul(Pow(Symbol('c', commutative=True), Integer(-1)), sin(Symbol('o', commutative=True)))", "Mul(Rational(1, 2), Symbol('c', commutative=True), Add(Symbol('c', commutative=True), Mul(Integer(2), cos(Symbol('o', commutative=True)))))"]}, {"premise_expression": "q - u", "variable": "q", "positive": "\\frac{q (q - 2 u)}{2}", "negatives": ["\\frac{u (2 q - u)}{2}", "\\frac{q^{2} \\log{(u)}}{2}", "e^{q + u}", "q (\\log{(\\frac{u}{q})} + 1)"], "srepr_premise_expression": "Add(Symbol('q', commutative=True), Mul(Integer(-1), Symbol('u', commutative=True)))", "srepr_variable": "Symbol('q', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('q', commutative=True), Add(Symbol('q', commutative=True), Mul(Integer(-1), Integer(2), Symbol('u', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(2), Symbol('q', commutative=True)), Mul(Integer(-1), Symbol('u', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('q', commutative=True), Integer(2)), log(Symbol('u', commutative=True)))", "exp(Add(Symbol('q', commutative=True), Symbol('u', commutative=True)))", "Mul(Symbol('q', commutative=True), Add(log(Mul(Pow(Symbol('q', commutative=True), Integer(-1)), Symbol('u', commutative=True))), Integer(1)))"]}, {"premise_expression": "\\log{(- V + b)}", "variable": "V", "positive": "V \\log{(- V + b)} - V - b \\log{(V - b)}", "negatives": ["- V \\log{(- V + b)} + b \\log{(- V + b)} - b", "- \\cos{(V - b)}", "- e^{- V + b}", "e^{V + b}"], "srepr_premise_expression": "log(Add(Mul(Integer(-1), Symbol('V', commutative=True)), Symbol('b', commutative=True)))", "srepr_variable": "Symbol('V', commutative=True)", "srepr_positive": "Add(Mul(Symbol('V', commutative=True), log(Add(Mul(Integer(-1), Symbol('V', commutative=True)), Symbol('b', commutative=True)))), Mul(Integer(-1), Symbol('V', commutative=True)), Mul(Integer(-1), Symbol('b', commutative=True), log(Add(Symbol('V', commutative=True), Mul(Integer(-1), Symbol('b', commutative=True))))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('V', commutative=True), log(Add(Mul(Integer(-1), Symbol('V', commutative=True)), Symbol('b', commutative=True)))), Mul(Symbol('b', commutative=True), log(Add(Mul(Integer(-1), Symbol('V', commutative=True)), Symbol('b', commutative=True)))), Mul(Integer(-1), Symbol('b', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('V', commutative=True), Mul(Integer(-1), Symbol('b', commutative=True)))))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('V', commutative=True)), Symbol('b', commutative=True))))", "exp(Add(Symbol('V', commutative=True), Symbol('b', commutative=True)))"]}, {"premise_expression": "J h^{2}", "variable": "h", "positive": "\\frac{J h^{3}}{3}", "negatives": ["\\frac{J^{2} h^{2}}{2}", "h", "J h + \\sin{(h)}", "\\cos{(J - h)}"], "srepr_premise_expression": "Mul(Symbol('J', commutative=True), Pow(Symbol('h', commutative=True), Integer(2)))", "srepr_variable": "Symbol('h', commutative=True)", "srepr_positive": "Mul(Rational(1, 3), Symbol('J', commutative=True), Pow(Symbol('h', commutative=True), Integer(3)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('J', commutative=True), Integer(2)), Pow(Symbol('h', commutative=True), Integer(2)))", "Symbol('h', commutative=True)", "Add(Mul(Symbol('J', commutative=True), Symbol('h', commutative=True)), sin(Symbol('h', commutative=True)))", "cos(Add(Symbol('J', commutative=True), Mul(Integer(-1), Symbol('h', commutative=True))))"]}, {"premise_expression": "e^{P + h}", "variable": "h", "positive": "e^{P + h}", "negatives": ["e^{- P + h}", "P e^{\\frac{h}{P}}", "\\frac{h (2 P - h)}{2}", "P h + e^{h}"], "srepr_premise_expression": "exp(Add(Symbol('P', commutative=True), Symbol('h', commutative=True)))", "srepr_variable": "Symbol('h', commutative=True)", "srepr_positive": "exp(Add(Symbol('P', commutative=True), Symbol('h', commutative=True)))", "srepr_negatives": ["exp(Add(Mul(Integer(-1), Symbol('P', commutative=True)), Symbol('h', commutative=True)))", "Mul(Symbol('P', commutative=True), exp(Mul(Pow(Symbol('P', commutative=True), Integer(-1)), Symbol('h', commutative=True))))", "Mul(Rational(1, 2), Symbol('h', commutative=True), Add(Mul(Integer(2), Symbol('P', commutative=True)), Mul(Integer(-1), Symbol('h', commutative=True))))", "Add(Mul(Symbol('P', commutative=True), Symbol('h', commutative=True)), exp(Symbol('h', commutative=True)))"]}, {"premise_expression": "\\frac{e^{L}}{U}", "variable": "U", "positive": "e^{L} \\log{(U)}", "negatives": ["L U - \\cos{(U)}", "- \\cos{(L + U)}", "L U + \\sin{(U)}", "U (L + \\log{(U)} - 1)"], "srepr_premise_expression": "Mul(Pow(Symbol('U', commutative=True), Integer(-1)), exp(Symbol('L', commutative=True)))", "srepr_variable": "Symbol('U', commutative=True)", "srepr_positive": "Mul(exp(Symbol('L', commutative=True)), log(Symbol('U', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('L', commutative=True), Symbol('U', commutative=True)), Mul(Integer(-1), cos(Symbol('U', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('L', commutative=True), Symbol('U', commutative=True))))", "Add(Mul(Symbol('L', commutative=True), Symbol('U', commutative=True)), sin(Symbol('U', commutative=True)))", "Mul(Symbol('U', commutative=True), Add(Symbol('L', commutative=True), log(Symbol('U', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\sin^{c}{(V)}", "variable": "V", "positive": "\\int \\sin^{c}{(V)} dV", "negatives": ["\\log{(V)} \\sin{(c)}", "\\log{(V)} \\cos{(c)}", "e^{V + c}", "\\frac{V (\\log{(V)} - 1)}{c}"], "srepr_premise_expression": "Pow(sin(Symbol('V', commutative=True)), Symbol('c', commutative=True))", "srepr_variable": "Symbol('V', commutative=True)", "srepr_positive": "Integral(Pow(sin(Symbol('V', commutative=True)), Symbol('c', commutative=True)), Tuple(Symbol('V', commutative=True)))", "srepr_negatives": ["Mul(log(Symbol('V', commutative=True)), sin(Symbol('c', commutative=True)))", "Mul(log(Symbol('V', commutative=True)), cos(Symbol('c', commutative=True)))", "exp(Add(Symbol('V', commutative=True), Symbol('c', commutative=True)))", "Mul(Symbol('V', commutative=True), Pow(Symbol('c', commutative=True), Integer(-1)), Add(log(Symbol('V', commutative=True)), Integer(-1)))"]}, {"premise_expression": "A + Y", "variable": "Y", "positive": "\\frac{Y (2 A + Y)}{2}", "negatives": ["\\frac{Y (- 2 A + Y)}{2}", "\\frac{A (A + 2 Y)}{2}", "\\frac{Y^{2} \\log{(A)}}{2}", "\\sin{(A + Y)}"], "srepr_premise_expression": "Add(Symbol('A', commutative=True), Symbol('Y', commutative=True))", "srepr_variable": "Symbol('Y', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('Y', commutative=True), Add(Mul(Integer(2), Symbol('A', commutative=True)), Symbol('Y', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('Y', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('A', commutative=True)), Symbol('Y', commutative=True)))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Symbol('A', commutative=True), Mul(Integer(2), Symbol('Y', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('Y', commutative=True), Integer(2)), log(Symbol('A', commutative=True)))", "sin(Add(Symbol('A', commutative=True), Symbol('Y', commutative=True)))"]}, {"premise_expression": "\\frac{K}{y}", "variable": "y", "positive": "K \\log{(y)}", "negatives": ["\\frac{K^{2}}{2 y}", "\\frac{K y^{2}}{2}", "- K y + e^{y}", "- K y + \\sin{(y)}"], "srepr_premise_expression": "Mul(Symbol('K', commutative=True), Pow(Symbol('y', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('y', commutative=True)", "srepr_positive": "Mul(Symbol('K', commutative=True), log(Symbol('y', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('K', commutative=True), Integer(2)), Pow(Symbol('y', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Symbol('K', commutative=True), Pow(Symbol('y', commutative=True), Integer(2)))", "Add(Mul(Integer(-1), Symbol('K', commutative=True), Symbol('y', commutative=True)), exp(Symbol('y', commutative=True)))", "Add(Mul(Integer(-1), Symbol('K', commutative=True), Symbol('y', commutative=True)), sin(Symbol('y', commutative=True)))"]}, {"premise_expression": "m + \\log{(c)}", "variable": "c", "positive": "c (m + \\log{(c)} - 1)", "negatives": ["\\frac{m (m + 2 \\log{(c)})}{2}", "\\frac{c^{2} \\log{(m)}}{2}", "\\frac{c (c + 2 \\cos{(m)})}{2}", "\\frac{c (c + 2 \\sin{(m)})}{2}"], "srepr_premise_expression": "Add(Symbol('m', commutative=True), log(Symbol('c', commutative=True)))", "srepr_variable": "Symbol('c', commutative=True)", "srepr_positive": "Mul(Symbol('c', commutative=True), Add(Symbol('m', commutative=True), log(Symbol('c', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Symbol('m', commutative=True), Mul(Integer(2), log(Symbol('c', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('c', commutative=True), Integer(2)), log(Symbol('m', commutative=True)))", "Mul(Rational(1, 2), Symbol('c', commutative=True), Add(Symbol('c', commutative=True), Mul(Integer(2), cos(Symbol('m', commutative=True)))))", "Mul(Rational(1, 2), Symbol('c', commutative=True), Add(Symbol('c', commutative=True), Mul(Integer(2), sin(Symbol('m', commutative=True)))))"]}, {"premise_expression": "\\log{(K W)}", "variable": "K", "positive": "K (\\log{(K W)} - 1)", "negatives": ["W (\\log{(K W)} - 1)", "e^{K - W}", "\\sin{(K + W)}", "- K W - \\cos{(K)}"], "srepr_premise_expression": "log(Mul(Symbol('K', commutative=True), Symbol('W', commutative=True)))", "srepr_variable": "Symbol('K', commutative=True)", "srepr_positive": "Mul(Symbol('K', commutative=True), Add(log(Mul(Symbol('K', commutative=True), Symbol('W', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('W', commutative=True), Add(log(Mul(Symbol('K', commutative=True), Symbol('W', commutative=True))), Integer(-1)))", "exp(Add(Symbol('K', commutative=True), Mul(Integer(-1), Symbol('W', commutative=True))))", "sin(Add(Symbol('K', commutative=True), Symbol('W', commutative=True)))", "Add(Mul(Integer(-1), Symbol('K', commutative=True), Symbol('W', commutative=True)), Mul(Integer(-1), cos(Symbol('K', commutative=True))))"]}, {"premise_expression": "V - u", "variable": "u", "positive": "\\frac{u (2 V - u)}{2}", "negatives": ["\\frac{V (V - 2 u)}{2}", "\\frac{u^{2} \\cos{(V)}}{2}", "\\frac{u^{2} \\sin{(V)}}{2}", "V^{2} \\log{(u)}"], "srepr_premise_expression": "Add(Symbol('V', commutative=True), Mul(Integer(-1), Symbol('u', commutative=True)))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(2), Symbol('V', commutative=True)), Mul(Integer(-1), Symbol('u', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('V', commutative=True), Add(Symbol('V', commutative=True), Mul(Integer(-1), Integer(2), Symbol('u', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('u', commutative=True), Integer(2)), cos(Symbol('V', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('u', commutative=True), Integer(2)), sin(Symbol('V', commutative=True)))", "Mul(Pow(Symbol('V', commutative=True), Integer(2)), log(Symbol('u', commutative=True)))"]}, {"premise_expression": "F + w", "variable": "F", "positive": "\\frac{F (F + 2 w)}{2}", "negatives": ["\\frac{F (F - 2 w)}{2}", "\\frac{w (2 F + w)}{2}", "F \\cos{(2 w)}", "\\frac{F^{2} e^{w}}{2}"], "srepr_premise_expression": "Add(Symbol('F', commutative=True), Symbol('w', commutative=True))", "srepr_variable": "Symbol('F', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Symbol('F', commutative=True), Mul(Integer(2), Symbol('w', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Symbol('F', commutative=True), Mul(Integer(-1), Integer(2), Symbol('w', commutative=True))))", "Mul(Rational(1, 2), Symbol('w', commutative=True), Add(Mul(Integer(2), Symbol('F', commutative=True)), Symbol('w', commutative=True)))", "Mul(Symbol('F', commutative=True), cos(Mul(Integer(2), Symbol('w', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('F', commutative=True), Integer(2)), exp(Symbol('w', commutative=True)))"]}, {"premise_expression": "p v", "variable": "p", "positive": "\\frac{p^{2} v}{2}", "negatives": ["\\frac{p v^{2}}{2}", "\\frac{p^{2}}{2 v}", "e^{p + v}", "e^{p - v}"], "srepr_premise_expression": "Mul(Symbol('p', commutative=True), Symbol('v', commutative=True))", "srepr_variable": "Symbol('p', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('p', commutative=True), Integer(2)), Symbol('v', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('p', commutative=True), Pow(Symbol('v', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('p', commutative=True), Integer(2)), Pow(Symbol('v', commutative=True), Integer(-1)))", "exp(Add(Symbol('p', commutative=True), Symbol('v', commutative=True)))", "exp(Add(Symbol('p', commutative=True), Mul(Integer(-1), Symbol('v', commutative=True))))"]}, {"premise_expression": "\\log{(a^{o})}", "variable": "a", "positive": "a (- o + \\log{(a^{o})})", "negatives": ["a o + e^{a}", "\\frac{a (- a + 2 o)}{2}", "- a o - \\cos{(a)}", "\\frac{o^{2} \\log{(a)}}{2}"], "srepr_premise_expression": "log(Pow(Symbol('a', commutative=True), Symbol('o', commutative=True)))", "srepr_variable": "Symbol('a', commutative=True)", "srepr_positive": "Mul(Symbol('a', commutative=True), Add(Mul(Integer(-1), Symbol('o', commutative=True)), log(Pow(Symbol('a', commutative=True), Symbol('o', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('a', commutative=True), Symbol('o', commutative=True)), exp(Symbol('a', commutative=True)))", "Mul(Rational(1, 2), Symbol('a', commutative=True), Add(Mul(Integer(-1), Symbol('a', commutative=True)), Mul(Integer(2), Symbol('o', commutative=True))))", "Add(Mul(Integer(-1), Symbol('a', commutative=True), Symbol('o', commutative=True)), Mul(Integer(-1), cos(Symbol('a', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('o', commutative=True), Integer(2)), log(Symbol('a', commutative=True)))"]}, {"premise_expression": "J + x", "variable": "J", "positive": "\\frac{J (J + 2 x)}{2}", "negatives": ["\\frac{x (2 J + x)}{2}", "\\frac{J^{2} x}{2}", "\\frac{J^{2} \\log{(x)}}{2}", "\\frac{J (\\log{(J)} - 1)}{x}"], "srepr_premise_expression": "Add(Symbol('J', commutative=True), Symbol('x', commutative=True))", "srepr_variable": "Symbol('J', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('J', commutative=True), Add(Symbol('J', commutative=True), Mul(Integer(2), Symbol('x', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('x', commutative=True), Add(Mul(Integer(2), Symbol('J', commutative=True)), Symbol('x', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('J', commutative=True), Integer(2)), Symbol('x', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('J', commutative=True), Integer(2)), log(Symbol('x', commutative=True)))", "Mul(Symbol('J', commutative=True), Pow(Symbol('x', commutative=True), Integer(-1)), Add(log(Symbol('J', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\sin^{R}{(v)}", "variable": "v", "positive": "\\int \\sin^{R}{(v)} dv", "negatives": ["\\int \\cos^{R}{(v)} dv", "- R v + \\sin{(v)}", "e^{R + v}", "R v - \\cos{(v)}"], "srepr_premise_expression": "Pow(sin(Symbol('v', commutative=True)), Symbol('R', commutative=True))", "srepr_variable": "Symbol('v', commutative=True)", "srepr_positive": "Integral(Pow(sin(Symbol('v', commutative=True)), Symbol('R', commutative=True)), Tuple(Symbol('v', commutative=True)))", "srepr_negatives": ["Integral(Pow(cos(Symbol('v', commutative=True)), Symbol('R', commutative=True)), Tuple(Symbol('v', commutative=True)))", "Add(Mul(Integer(-1), Symbol('R', commutative=True), Symbol('v', commutative=True)), sin(Symbol('v', commutative=True)))", "exp(Add(Symbol('R', commutative=True), Symbol('v', commutative=True)))", "Add(Mul(Symbol('R', commutative=True), Symbol('v', commutative=True)), Mul(Integer(-1), cos(Symbol('v', commutative=True))))"]}, {"premise_expression": "c \\sin{(K)}", "variable": "c", "positive": "\\frac{c^{2} \\sin{(K)}}{2}", "negatives": ["- c \\cos{(K)}", "e^{K + c}", "c (\\log{(\\frac{c}{K})} - 1)", "\\frac{c (\\log{(c)} - 1)}{K}"], "srepr_premise_expression": "Mul(Symbol('c', commutative=True), sin(Symbol('K', commutative=True)))", "srepr_variable": "Symbol('c', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('c', commutative=True), Integer(2)), sin(Symbol('K', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Symbol('c', commutative=True), cos(Symbol('K', commutative=True)))", "exp(Add(Symbol('K', commutative=True), Symbol('c', commutative=True)))", "Mul(Symbol('c', commutative=True), Add(log(Mul(Pow(Symbol('K', commutative=True), Integer(-1)), Symbol('c', commutative=True))), Integer(-1)))", "Mul(Pow(Symbol('K', commutative=True), Integer(-1)), Symbol('c', commutative=True), Add(log(Symbol('c', commutative=True)), Integer(-1)))"]}, {"premise_expression": "N + e^{V}", "variable": "V", "positive": "N V + e^{V}", "negatives": ["- N V + e^{V}", "\\frac{N (N + 2 e^{V})}{2}", "e^{N + V}", "- e^{N - V}"], "srepr_premise_expression": "Add(Symbol('N', commutative=True), exp(Symbol('V', commutative=True)))", "srepr_variable": "Symbol('V', commutative=True)", "srepr_positive": "Add(Mul(Symbol('N', commutative=True), Symbol('V', commutative=True)), exp(Symbol('V', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('N', commutative=True), Symbol('V', commutative=True)), exp(Symbol('V', commutative=True)))", "Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Symbol('N', commutative=True), Mul(Integer(2), exp(Symbol('V', commutative=True)))))", "exp(Add(Symbol('N', commutative=True), Symbol('V', commutative=True)))", "Mul(Integer(-1), exp(Add(Symbol('N', commutative=True), Mul(Integer(-1), Symbol('V', commutative=True)))))"]}, {"premise_expression": "\\frac{h}{a}", "variable": "a", "positive": "h \\log{(a)}", "negatives": ["\\frac{h^{2}}{2 a}", "- \\cos{(a + h)}", "\\cos{(a - h)}", "\\frac{a^{2}}{2 h} + a"], "srepr_premise_expression": "Mul(Pow(Symbol('a', commutative=True), Integer(-1)), Symbol('h', commutative=True))", "srepr_variable": "Symbol('a', commutative=True)", "srepr_positive": "Mul(Symbol('h', commutative=True), log(Symbol('a', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('a', commutative=True), Integer(-1)), Pow(Symbol('h', commutative=True), Integer(2)))", "Mul(Integer(-1), cos(Add(Symbol('a', commutative=True), Symbol('h', commutative=True))))", "cos(Add(Symbol('a', commutative=True), Mul(Integer(-1), Symbol('h', commutative=True))))", "Add(Mul(Rational(1, 2), Pow(Symbol('a', commutative=True), Integer(2)), Pow(Symbol('h', commutative=True), Integer(-1))), Symbol('a', commutative=True))"]}, {"premise_expression": "\\frac{h}{K}", "variable": "h", "positive": "\\frac{h^{2}}{2 K}", "negatives": ["h \\log{(K)}", "- \\cos{(K + h)}", "K h + \\sin{(h)}", "h (\\log{(\\frac{h}{K})} - 1)"], "srepr_premise_expression": "Mul(Pow(Symbol('K', commutative=True), Integer(-1)), Symbol('h', commutative=True))", "srepr_variable": "Symbol('h', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('K', commutative=True), Integer(-1)), Pow(Symbol('h', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('h', commutative=True), log(Symbol('K', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('K', commutative=True), Symbol('h', commutative=True))))", "Add(Mul(Symbol('K', commutative=True), Symbol('h', commutative=True)), sin(Symbol('h', commutative=True)))", "Mul(Symbol('h', commutative=True), Add(log(Mul(Pow(Symbol('K', commutative=True), Integer(-1)), Symbol('h', commutative=True))), Integer(-1)))"]}, {"premise_expression": "Z m", "variable": "m", "positive": "\\frac{Z m^{2}}{2}", "negatives": ["\\frac{Z^{2} m}{2}", "\\frac{m (2 Z - m)}{2}", "\\sin{(Z + m)}", "\\frac{m (- 2 Z + m)}{2}"], "srepr_premise_expression": "Mul(Symbol('Z', commutative=True), Symbol('m', commutative=True))", "srepr_variable": "Symbol('m', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('Z', commutative=True), Pow(Symbol('m', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('Z', commutative=True), Integer(2)), Symbol('m', commutative=True))", "Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Mul(Integer(2), Symbol('Z', commutative=True)), Mul(Integer(-1), Symbol('m', commutative=True))))", "sin(Add(Symbol('Z', commutative=True), Symbol('m', commutative=True)))", "Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('Z', commutative=True)), Symbol('m', commutative=True)))"]}, {"premise_expression": "\\cos{(l - x)}", "variable": "l", "positive": "\\sin{(l - x)}", "negatives": ["- \\sin{(l - x)}", "\\cos{(l - x)}", "\\frac{\\sin{(l)}}{x}", "\\frac{l x (l - 2)}{2}"], "srepr_premise_expression": "cos(Add(Symbol('l', commutative=True), Mul(Integer(-1), Symbol('x', commutative=True))))", "srepr_variable": "Symbol('l', commutative=True)", "srepr_positive": "sin(Add(Symbol('l', commutative=True), Mul(Integer(-1), Symbol('x', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('l', commutative=True), Mul(Integer(-1), Symbol('x', commutative=True)))))", "cos(Add(Symbol('l', commutative=True), Mul(Integer(-1), Symbol('x', commutative=True))))", "Mul(Pow(Symbol('x', commutative=True), Integer(-1)), sin(Symbol('l', commutative=True)))", "Mul(Rational(1, 2), Symbol('l', commutative=True), Symbol('x', commutative=True), Add(Symbol('l', commutative=True), Integer(-2)))"]}, {"premise_expression": "k + \\cos{(W)}", "variable": "k", "positive": "\\frac{k (k + 2 \\cos{(W)})}{2}", "negatives": ["W k + \\sin{(W)}", "\\frac{k (2 W + k)}{2}", "\\frac{k (- 2 W + k)}{2}", "\\frac{W k^{2}}{2}"], "srepr_premise_expression": "Add(Symbol('k', commutative=True), cos(Symbol('W', commutative=True)))", "srepr_variable": "Symbol('k', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('k', commutative=True), Add(Symbol('k', commutative=True), Mul(Integer(2), cos(Symbol('W', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('W', commutative=True), Symbol('k', commutative=True)), sin(Symbol('W', commutative=True)))", "Mul(Rational(1, 2), Symbol('k', commutative=True), Add(Mul(Integer(2), Symbol('W', commutative=True)), Symbol('k', commutative=True)))", "Mul(Rational(1, 2), Symbol('k', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('W', commutative=True)), Symbol('k', commutative=True)))", "Mul(Rational(1, 2), Symbol('W', commutative=True), Pow(Symbol('k', commutative=True), Integer(2)))"]}, {"premise_expression": "- K + c + r", "variable": "c", "positive": "c (- K + \\frac{c}{2} + r)", "negatives": ["\\frac{c (2 K + c + 2 r)}{2}", "\\frac{c (2 K - c + 2 r)}{2}", "\\frac{r (- 2 K + 2 c + r)}{2}", "\\frac{K (- K + 2 c + 2 r)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('K', commutative=True)), Symbol('c', commutative=True), Symbol('r', commutative=True))", "srepr_variable": "Symbol('c', commutative=True)", "srepr_positive": "Mul(Symbol('c', commutative=True), Add(Mul(Integer(-1), Symbol('K', commutative=True)), Mul(Rational(1, 2), Symbol('c', commutative=True)), Symbol('r', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('c', commutative=True), Add(Mul(Integer(2), Symbol('K', commutative=True)), Symbol('c', commutative=True), Mul(Integer(2), Symbol('r', commutative=True))))", "Mul(Rational(1, 2), Symbol('c', commutative=True), Add(Mul(Integer(2), Symbol('K', commutative=True)), Mul(Integer(-1), Symbol('c', commutative=True)), Mul(Integer(2), Symbol('r', commutative=True))))", "Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('K', commutative=True)), Mul(Integer(2), Symbol('c', commutative=True)), Symbol('r', commutative=True)))", "Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Mul(Integer(-1), Symbol('K', commutative=True)), Mul(Integer(2), Symbol('c', commutative=True)), Mul(Integer(2), Symbol('r', commutative=True))))"]}, {"premise_expression": "H + h - v", "variable": "v", "positive": "v (H + h - \\frac{v}{2})", "negatives": ["\\frac{v (- 2 H + 2 h + v)}{2}", "\\frac{h (2 H + h - 2 v)}{2}", "\\frac{H (H + 2 h - 2 v)}{2}", "\\frac{v (2 H^{h} - v)}{2}"], "srepr_premise_expression": "Add(Symbol('H', commutative=True), Symbol('h', commutative=True), Mul(Integer(-1), Symbol('v', commutative=True)))", "srepr_variable": "Symbol('v', commutative=True)", "srepr_positive": "Mul(Symbol('v', commutative=True), Add(Symbol('H', commutative=True), Symbol('h', commutative=True), Mul(Integer(-1), Rational(1, 2), Symbol('v', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('v', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('H', commutative=True)), Mul(Integer(2), Symbol('h', commutative=True)), Symbol('v', commutative=True)))", "Mul(Rational(1, 2), Symbol('h', commutative=True), Add(Mul(Integer(2), Symbol('H', commutative=True)), Symbol('h', commutative=True), Mul(Integer(-1), Integer(2), Symbol('v', commutative=True))))", "Mul(Rational(1, 2), Symbol('H', commutative=True), Add(Symbol('H', commutative=True), Mul(Integer(2), Symbol('h', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('v', commutative=True))))", "Mul(Rational(1, 2), Symbol('v', commutative=True), Add(Mul(Integer(2), Pow(Symbol('H', commutative=True), Symbol('h', commutative=True))), Mul(Integer(-1), Symbol('v', commutative=True))))"]}, {"premise_expression": "R Z", "variable": "R", "positive": "\\frac{R^{2} Z}{2}", "negatives": ["\\frac{R Z^{2}}{2}", "\\frac{R^{2} \\sin{(Z)}}{2}", "\\frac{R (R + 2 Z)}{2}", "Z \\log{(R)}"], "srepr_premise_expression": "Mul(Symbol('R', commutative=True), Symbol('Z', commutative=True))", "srepr_variable": "Symbol('R', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('R', commutative=True), Integer(2)), Symbol('Z', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('R', commutative=True), Pow(Symbol('Z', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('R', commutative=True), Integer(2)), sin(Symbol('Z', commutative=True)))", "Mul(Rational(1, 2), Symbol('R', commutative=True), Add(Symbol('R', commutative=True), Mul(Integer(2), Symbol('Z', commutative=True))))", "Mul(Symbol('Z', commutative=True), log(Symbol('R', commutative=True)))"]}, {"premise_expression": "\\sin{(C + f)}", "variable": "C", "positive": "- \\cos{(C + f)}", "negatives": ["e^{C + f}", "- f \\cos{(C)}", "f \\log{(C)}", "C (\\log{(\\frac{C}{f})} - 1)"], "srepr_premise_expression": "sin(Add(Symbol('C', commutative=True), Symbol('f', commutative=True)))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('C', commutative=True), Symbol('f', commutative=True))))", "srepr_negatives": ["exp(Add(Symbol('C', commutative=True), Symbol('f', commutative=True)))", "Mul(Integer(-1), Symbol('f', commutative=True), cos(Symbol('C', commutative=True)))", "Mul(Symbol('f', commutative=True), log(Symbol('C', commutative=True)))", "Mul(Symbol('C', commutative=True), Add(log(Mul(Symbol('C', commutative=True), Pow(Symbol('f', commutative=True), Integer(-1)))), Integer(-1)))"]}, {"premise_expression": "\\frac{\\cos{(B)}}{L}", "variable": "L", "positive": "\\log{(L)} \\cos{(B)}", "negatives": ["B L - \\cos{(L)}", "\\frac{\\sin{(L)}}{B}", "\\frac{\\sin{(B)}}{L}", "e^{B + L}"], "srepr_premise_expression": "Mul(Pow(Symbol('L', commutative=True), Integer(-1)), cos(Symbol('B', commutative=True)))", "srepr_variable": "Symbol('L', commutative=True)", "srepr_positive": "Mul(log(Symbol('L', commutative=True)), cos(Symbol('B', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('B', commutative=True), Symbol('L', commutative=True)), Mul(Integer(-1), cos(Symbol('L', commutative=True))))", "Mul(Pow(Symbol('B', commutative=True), Integer(-1)), sin(Symbol('L', commutative=True)))", "Mul(Pow(Symbol('L', commutative=True), Integer(-1)), sin(Symbol('B', commutative=True)))", "exp(Add(Symbol('B', commutative=True), Symbol('L', commutative=True)))"]}, {"premise_expression": "\\log{(f^{o})}", "variable": "o", "positive": "\\frac{o^{2} \\log{(f)}}{2}", "negatives": ["\\frac{o (2 f + o)}{2}", "f \\log{(o)}", "\\frac{o (- o + 2 \\sin{(f)})}{2}", "o (f + \\log{(o)} - 1)"], "srepr_premise_expression": "log(Pow(Symbol('f', commutative=True), Symbol('o', commutative=True)))", "srepr_variable": "Symbol('o', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('o', commutative=True), Integer(2)), log(Symbol('f', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Mul(Integer(2), Symbol('f', commutative=True)), Symbol('o', commutative=True)))", "Mul(Symbol('f', commutative=True), log(Symbol('o', commutative=True)))", "Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Mul(Integer(-1), Symbol('o', commutative=True)), Mul(Integer(2), sin(Symbol('f', commutative=True)))))", "Mul(Symbol('o', commutative=True), Add(Symbol('f', commutative=True), log(Symbol('o', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\frac{V}{l}", "variable": "l", "positive": "V \\log{(l)}", "negatives": ["V \\log{(l)} + l", "\\frac{V^{2}}{2 l}", "- \\frac{\\cos{(l)}}{V}", "V l + e^{l}"], "srepr_premise_expression": "Mul(Symbol('V', commutative=True), Pow(Symbol('l', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('l', commutative=True)", "srepr_positive": "Mul(Symbol('V', commutative=True), log(Symbol('l', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('V', commutative=True), log(Symbol('l', commutative=True))), Symbol('l', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('V', commutative=True), Integer(2)), Pow(Symbol('l', commutative=True), Integer(-1)))", "Mul(Integer(-1), Pow(Symbol('V', commutative=True), Integer(-1)), cos(Symbol('l', commutative=True)))", "Add(Mul(Symbol('V', commutative=True), Symbol('l', commutative=True)), exp(Symbol('l', commutative=True)))"]}, {"premise_expression": "I + M", "variable": "I", "positive": "\\frac{I (I + 2 M)}{2}", "negatives": ["\\frac{M (2 I + M)}{2}", "e^{I - M}", "\\cos{(I - M)}", "I M - \\cos{(I)}"], "srepr_premise_expression": "Add(Symbol('I', commutative=True), Symbol('M', commutative=True))", "srepr_variable": "Symbol('I', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('I', commutative=True), Add(Symbol('I', commutative=True), Mul(Integer(2), Symbol('M', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('M', commutative=True), Add(Mul(Integer(2), Symbol('I', commutative=True)), Symbol('M', commutative=True)))", "exp(Add(Symbol('I', commutative=True), Mul(Integer(-1), Symbol('M', commutative=True))))", "cos(Add(Symbol('I', commutative=True), Mul(Integer(-1), Symbol('M', commutative=True))))", "Add(Mul(Symbol('I', commutative=True), Symbol('M', commutative=True)), Mul(Integer(-1), cos(Symbol('I', commutative=True))))"]}, {"premise_expression": "\\cos{(\\frac{b}{I})}", "variable": "I", "positive": "I \\cos{(\\frac{b}{I})} + b \\operatorname{Si}{(\\frac{b}{I})}", "negatives": ["I e^{\\frac{b}{I}} - b \\operatorname{Ei}{(\\frac{b}{I})}", "\\frac{I (I + 2 b)}{2}", "\\frac{I (- I + 2 e^{b})}{2}", "\\frac{I (I - 2 b)}{2}"], "srepr_premise_expression": "cos(Mul(Pow(Symbol('I', commutative=True), Integer(-1)), Symbol('b', commutative=True)))", "srepr_variable": "Symbol('I', commutative=True)", "srepr_positive": "Add(Mul(Symbol('I', commutative=True), cos(Mul(Pow(Symbol('I', commutative=True), Integer(-1)), Symbol('b', commutative=True)))), Mul(Symbol('b', commutative=True), Si(Mul(Pow(Symbol('I', commutative=True), Integer(-1)), Symbol('b', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('I', commutative=True), exp(Mul(Pow(Symbol('I', commutative=True), Integer(-1)), Symbol('b', commutative=True)))), Mul(Integer(-1), Symbol('b', commutative=True), Ei(Mul(Pow(Symbol('I', commutative=True), Integer(-1)), Symbol('b', commutative=True)))))", "Mul(Rational(1, 2), Symbol('I', commutative=True), Add(Symbol('I', commutative=True), Mul(Integer(2), Symbol('b', commutative=True))))", "Mul(Rational(1, 2), Symbol('I', commutative=True), Add(Mul(Integer(-1), Symbol('I', commutative=True)), Mul(Integer(2), exp(Symbol('b', commutative=True)))))", "Mul(Rational(1, 2), Symbol('I', commutative=True), Add(Symbol('I', commutative=True), Mul(Integer(-1), Integer(2), Symbol('b', commutative=True))))"]}, {"premise_expression": "- S + \\frac{h}{R}", "variable": "S", "positive": "- \\frac{S^{2}}{2} + \\frac{S h}{R}", "negatives": ["\\frac{R S (- S + 2 h)}{2}", "\\frac{S^{2} (R + h)}{2}", "- S h + \\frac{S^{2}}{2 R}", "- S h + \\frac{h^{2}}{2 R}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('S', commutative=True)), Mul(Pow(Symbol('R', commutative=True), Integer(-1)), Symbol('h', commutative=True)))", "srepr_variable": "Symbol('S', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('S', commutative=True), Integer(2))), Mul(Pow(Symbol('R', commutative=True), Integer(-1)), Symbol('S', commutative=True), Symbol('h', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('R', commutative=True), Symbol('S', commutative=True), Add(Mul(Integer(-1), Symbol('S', commutative=True)), Mul(Integer(2), Symbol('h', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('S', commutative=True), Integer(2)), Add(Symbol('R', commutative=True), Symbol('h', commutative=True)))", "Add(Mul(Integer(-1), Symbol('S', commutative=True), Symbol('h', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('R', commutative=True), Integer(-1)), Pow(Symbol('S', commutative=True), Integer(2))))", "Add(Mul(Integer(-1), Symbol('S', commutative=True), Symbol('h', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('R', commutative=True), Integer(-1)), Pow(Symbol('h', commutative=True), Integer(2))))"]}, {"premise_expression": "Q W - j", "variable": "Q", "positive": "\\frac{Q (Q W - 2 j)}{2}", "negatives": ["\\frac{W (Q W - 2 j)}{2}", "\\frac{Q (Q j + 2 W)}{2}", "\\frac{j (2 Q W - j)}{2}", "\\frac{Q^{2} (W + j)}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('Q', commutative=True), Symbol('W', commutative=True)), Mul(Integer(-1), Symbol('j', commutative=True)))", "srepr_variable": "Symbol('Q', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Mul(Symbol('Q', commutative=True), Symbol('W', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('j', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('W', commutative=True), Add(Mul(Symbol('Q', commutative=True), Symbol('W', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('j', commutative=True))))", "Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Mul(Symbol('Q', commutative=True), Symbol('j', commutative=True)), Mul(Integer(2), Symbol('W', commutative=True))))", "Mul(Rational(1, 2), Symbol('j', commutative=True), Add(Mul(Integer(2), Symbol('Q', commutative=True), Symbol('W', commutative=True)), Mul(Integer(-1), Symbol('j', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(2)), Add(Symbol('W', commutative=True), Symbol('j', commutative=True)))"]}, {"premise_expression": "j e^{T}", "variable": "T", "positive": "j e^{T}", "negatives": ["- j \\cos{(T)}", "\\frac{j^{2} e^{T}}{2}", "- T j - \\cos{(T)}", "\\frac{T (T - 2 j)}{2}"], "srepr_premise_expression": "Mul(Symbol('j', commutative=True), exp(Symbol('T', commutative=True)))", "srepr_variable": "Symbol('T', commutative=True)", "srepr_positive": "Mul(Symbol('j', commutative=True), exp(Symbol('T', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Symbol('j', commutative=True), cos(Symbol('T', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('j', commutative=True), Integer(2)), exp(Symbol('T', commutative=True)))", "Add(Mul(Integer(-1), Symbol('T', commutative=True), Symbol('j', commutative=True)), Mul(Integer(-1), cos(Symbol('T', commutative=True))))", "Mul(Rational(1, 2), Symbol('T', commutative=True), Add(Symbol('T', commutative=True), Mul(Integer(-1), Integer(2), Symbol('j', commutative=True))))"]}, {"premise_expression": "- P + \\frac{I}{G}", "variable": "I", "positive": "- I P + \\frac{I^{2}}{2 G}", "negatives": ["- G P + I \\log{(G)}", "\\frac{I^{2} P}{2 G}", "- G I + P \\log{(I)}", "- \\frac{P^{2}}{2} + \\frac{I P}{G}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('P', commutative=True)), Mul(Pow(Symbol('G', commutative=True), Integer(-1)), Symbol('I', commutative=True)))", "srepr_variable": "Symbol('I', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('I', commutative=True), Symbol('P', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(-1)), Pow(Symbol('I', commutative=True), Integer(2))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('G', commutative=True), Symbol('P', commutative=True)), Mul(Symbol('I', commutative=True), log(Symbol('G', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(-1)), Pow(Symbol('I', commutative=True), Integer(2)), Symbol('P', commutative=True))", "Add(Mul(Integer(-1), Symbol('G', commutative=True), Symbol('I', commutative=True)), Mul(Symbol('P', commutative=True), log(Symbol('I', commutative=True))))", "Add(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2))), Mul(Pow(Symbol('G', commutative=True), Integer(-1)), Symbol('I', commutative=True), Symbol('P', commutative=True)))"]}, {"premise_expression": "- M + c + m", "variable": "m", "positive": "m (- M + c + \\frac{m}{2})", "negatives": ["\\frac{m (2 M + 2 c + m)}{2}", "\\frac{M (- M + 2 c + 2 m)}{2}", "\\frac{c (- 2 M + c + 2 m)}{2}", "\\frac{m (- 2 M + c m)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('M', commutative=True)), Symbol('c', commutative=True), Symbol('m', commutative=True))", "srepr_variable": "Symbol('m', commutative=True)", "srepr_positive": "Mul(Symbol('m', commutative=True), Add(Mul(Integer(-1), Symbol('M', commutative=True)), Symbol('c', commutative=True), Mul(Rational(1, 2), Symbol('m', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Mul(Integer(2), Symbol('M', commutative=True)), Mul(Integer(2), Symbol('c', commutative=True)), Symbol('m', commutative=True)))", "Mul(Rational(1, 2), Symbol('M', commutative=True), Add(Mul(Integer(-1), Symbol('M', commutative=True)), Mul(Integer(2), Symbol('c', commutative=True)), Mul(Integer(2), Symbol('m', commutative=True))))", "Mul(Rational(1, 2), Symbol('c', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('M', commutative=True)), Symbol('c', commutative=True), Mul(Integer(2), Symbol('m', commutative=True))))", "Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('M', commutative=True)), Mul(Symbol('c', commutative=True), Symbol('m', commutative=True))))"]}, {"premise_expression": "\\frac{Q}{H}", "variable": "H", "positive": "Q \\log{(H)}", "negatives": ["\\frac{Q^{2}}{2 H}", "- \\frac{\\cos{(H)}}{Q}", "- \\cos{(H - Q)}", "H (\\log{(\\frac{H}{Q})} - 1)"], "srepr_premise_expression": "Mul(Pow(Symbol('H', commutative=True), Integer(-1)), Symbol('Q', commutative=True))", "srepr_variable": "Symbol('H', commutative=True)", "srepr_positive": "Mul(Symbol('Q', commutative=True), log(Symbol('H', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('H', commutative=True), Integer(-1)), Pow(Symbol('Q', commutative=True), Integer(2)))", "Mul(Integer(-1), Pow(Symbol('Q', commutative=True), Integer(-1)), cos(Symbol('H', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('H', commutative=True), Mul(Integer(-1), Symbol('Q', commutative=True)))))", "Mul(Symbol('H', commutative=True), Add(log(Mul(Symbol('H', commutative=True), Pow(Symbol('Q', commutative=True), Integer(-1)))), Integer(-1)))"]}, {"premise_expression": "S - Y", "variable": "Y", "positive": "\\frac{Y (2 S - Y)}{2}", "negatives": ["\\frac{Y (2 S + Y)}{2}", "\\frac{S (S - 2 Y)}{2}", "- \\cos{(S - Y)}", "\\frac{Y^{2}}{2 S}"], "srepr_premise_expression": "Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('Y', commutative=True)))", "srepr_variable": "Symbol('Y', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('Y', commutative=True), Add(Mul(Integer(2), Symbol('S', commutative=True)), Mul(Integer(-1), Symbol('Y', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('Y', commutative=True), Add(Mul(Integer(2), Symbol('S', commutative=True)), Symbol('Y', commutative=True)))", "Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Symbol('S', commutative=True), Mul(Integer(-1), Integer(2), Symbol('Y', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('Y', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('S', commutative=True), Integer(-1)), Pow(Symbol('Y', commutative=True), Integer(2)))"]}, {"premise_expression": "B - R", "variable": "R", "positive": "\\frac{R (2 B - R)}{2}", "negatives": ["\\frac{B (B - 2 R)}{2}", "\\frac{R^{2} e^{B}}{2}", "\\frac{R (R + 2 \\log{(B)})}{2}", "\\log{(B)} \\log{(R)}"], "srepr_premise_expression": "Add(Symbol('B', commutative=True), Mul(Integer(-1), Symbol('R', commutative=True)))", "srepr_variable": "Symbol('R', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('R', commutative=True), Add(Mul(Integer(2), Symbol('B', commutative=True)), Mul(Integer(-1), Symbol('R', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('B', commutative=True), Add(Symbol('B', commutative=True), Mul(Integer(-1), Integer(2), Symbol('R', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('R', commutative=True), Integer(2)), exp(Symbol('B', commutative=True)))", "Mul(Rational(1, 2), Symbol('R', commutative=True), Add(Symbol('R', commutative=True), Mul(Integer(2), log(Symbol('B', commutative=True)))))", "Mul(log(Symbol('B', commutative=True)), log(Symbol('R', commutative=True)))"]}, {"premise_expression": "\\frac{\\sin{(Y)}}{n}", "variable": "n", "positive": "\\log{(n)} \\sin{(Y)}", "negatives": ["- \\frac{\\cos{(Y)}}{n}", "- \\cos{(Y - n)}", "\\sin{(Y + n)}", "\\frac{n^{2} \\log{(Y)}}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('n', commutative=True), Integer(-1)), sin(Symbol('Y', commutative=True)))", "srepr_variable": "Symbol('n', commutative=True)", "srepr_positive": "Mul(log(Symbol('n', commutative=True)), sin(Symbol('Y', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Pow(Symbol('n', commutative=True), Integer(-1)), cos(Symbol('Y', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('Y', commutative=True), Mul(Integer(-1), Symbol('n', commutative=True)))))", "sin(Add(Symbol('Y', commutative=True), Symbol('n', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('n', commutative=True), Integer(2)), log(Symbol('Y', commutative=True)))"]}, {"premise_expression": "I + Z", "variable": "Z", "positive": "\\frac{Z (2 I + Z)}{2}", "negatives": ["\\frac{I (I + 2 Z)}{2}", "\\frac{Z^{2} e^{I}}{2}", "e^{I + Z}", "\\cos{(I - Z)}"], "srepr_premise_expression": "Add(Symbol('I', commutative=True), Symbol('Z', commutative=True))", "srepr_variable": "Symbol('Z', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Mul(Integer(2), Symbol('I', commutative=True)), Symbol('Z', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('I', commutative=True), Add(Symbol('I', commutative=True), Mul(Integer(2), Symbol('Z', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('Z', commutative=True), Integer(2)), exp(Symbol('I', commutative=True)))", "exp(Add(Symbol('I', commutative=True), Symbol('Z', commutative=True)))", "cos(Add(Symbol('I', commutative=True), Mul(Integer(-1), Symbol('Z', commutative=True))))"]}, {"premise_expression": "\\frac{w}{B}", "variable": "w", "positive": "\\frac{w^{2}}{2 B}", "negatives": ["w \\log{(B)}", "\\frac{w^{2} \\log{(B)}}{2}", "\\frac{w (- 2 B + w)}{2}", "w (\\log{(\\frac{w}{B})} - 1)"], "srepr_premise_expression": "Mul(Pow(Symbol('B', commutative=True), Integer(-1)), Symbol('w', commutative=True))", "srepr_variable": "Symbol('w', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('B', commutative=True), Integer(-1)), Pow(Symbol('w', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('w', commutative=True), log(Symbol('B', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('w', commutative=True), Integer(2)), log(Symbol('B', commutative=True)))", "Mul(Rational(1, 2), Symbol('w', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('B', commutative=True)), Symbol('w', commutative=True)))", "Mul(Symbol('w', commutative=True), Add(log(Mul(Pow(Symbol('B', commutative=True), Integer(-1)), Symbol('w', commutative=True))), Integer(-1)))"]}, {"premise_expression": "- B + b + z", "variable": "b", "positive": "b (- B + \\frac{b}{2} + z)", "negatives": ["\\frac{b (2 B - b - 2 z)}{2}", "\\frac{z (- 2 B + 2 b + z)}{2}", "\\frac{B (- B + 2 b + 2 z)}{2}", "\\frac{b (- 2 B - b + 2 z)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('B', commutative=True)), Symbol('b', commutative=True), Symbol('z', commutative=True))", "srepr_variable": "Symbol('b', commutative=True)", "srepr_positive": "Mul(Symbol('b', commutative=True), Add(Mul(Integer(-1), Symbol('B', commutative=True)), Mul(Rational(1, 2), Symbol('b', commutative=True)), Symbol('z', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('b', commutative=True), Add(Mul(Integer(2), Symbol('B', commutative=True)), Mul(Integer(-1), Symbol('b', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('z', commutative=True))))", "Mul(Rational(1, 2), Symbol('z', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('B', commutative=True)), Mul(Integer(2), Symbol('b', commutative=True)), Symbol('z', commutative=True)))", "Mul(Rational(1, 2), Symbol('B', commutative=True), Add(Mul(Integer(-1), Symbol('B', commutative=True)), Mul(Integer(2), Symbol('b', commutative=True)), Mul(Integer(2), Symbol('z', commutative=True))))", "Mul(Rational(1, 2), Symbol('b', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('B', commutative=True)), Mul(Integer(-1), Symbol('b', commutative=True)), Mul(Integer(2), Symbol('z', commutative=True))))"]}, {"premise_expression": "B + e^{w}", "variable": "w", "positive": "B w + e^{w}", "negatives": ["\\frac{B (B + 2 e^{w})}{2}", "\\frac{B w^{2}}{2}", "\\frac{w^{2}}{2 B}", "\\frac{w (- 2 B + w)}{2}"], "srepr_premise_expression": "Add(Symbol('B', commutative=True), exp(Symbol('w', commutative=True)))", "srepr_variable": "Symbol('w', commutative=True)", "srepr_positive": "Add(Mul(Symbol('B', commutative=True), Symbol('w', commutative=True)), exp(Symbol('w', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('B', commutative=True), Add(Symbol('B', commutative=True), Mul(Integer(2), exp(Symbol('w', commutative=True)))))", "Mul(Rational(1, 2), Symbol('B', commutative=True), Pow(Symbol('w', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('B', commutative=True), Integer(-1)), Pow(Symbol('w', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('w', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('B', commutative=True)), Symbol('w', commutative=True)))"]}, {"premise_expression": "c - p", "variable": "p", "positive": "\\frac{p (2 c - p)}{2}", "negatives": ["\\frac{c (c - 2 p)}{2}", "\\frac{p^{2} \\cos{(c)}}{2}", "- \\sin{(c - p)}", "e^{- c + p}"], "srepr_premise_expression": "Add(Symbol('c', commutative=True), Mul(Integer(-1), Symbol('p', commutative=True)))", "srepr_variable": "Symbol('p', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Mul(Integer(2), Symbol('c', commutative=True)), Mul(Integer(-1), Symbol('p', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('c', commutative=True), Add(Symbol('c', commutative=True), Mul(Integer(-1), Integer(2), Symbol('p', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('p', commutative=True), Integer(2)), cos(Symbol('c', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('c', commutative=True), Mul(Integer(-1), Symbol('p', commutative=True)))))", "exp(Add(Mul(Integer(-1), Symbol('c', commutative=True)), Symbol('p', commutative=True)))"]}, {"premise_expression": "- j + \\sin{(z)}", "variable": "z", "positive": "- j z - \\cos{(z)}", "negatives": ["j \\log{(z)}", "\\frac{z^{2} \\log{(j)}}{2}", "\\frac{j (- j + 2 \\sin{(z)})}{2}", "z (j + \\log{(z)} - 1)"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('j', commutative=True)), sin(Symbol('z', commutative=True)))", "srepr_variable": "Symbol('z', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('j', commutative=True), Symbol('z', commutative=True)), Mul(Integer(-1), cos(Symbol('z', commutative=True))))", "srepr_negatives": ["Mul(Symbol('j', commutative=True), log(Symbol('z', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('z', commutative=True), Integer(2)), log(Symbol('j', commutative=True)))", "Mul(Rational(1, 2), Symbol('j', commutative=True), Add(Mul(Integer(-1), Symbol('j', commutative=True)), Mul(Integer(2), sin(Symbol('z', commutative=True)))))", "Mul(Symbol('z', commutative=True), Add(Symbol('j', commutative=True), log(Symbol('z', commutative=True)), Integer(-1)))"]}, {"premise_expression": "P q", "variable": "q", "positive": "\\frac{P q^{2}}{2}", "negatives": ["\\frac{P^{2} q}{2}", "P^{P} q", "q e^{P^{P}}", "e^{- P + q}"], "srepr_premise_expression": "Mul(Symbol('P', commutative=True), Symbol('q', commutative=True))", "srepr_variable": "Symbol('q', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('P', commutative=True), Pow(Symbol('q', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2)), Symbol('q', commutative=True))", "Mul(Pow(Symbol('P', commutative=True), Symbol('P', commutative=True)), Symbol('q', commutative=True))", "Mul(Symbol('q', commutative=True), exp(Pow(Symbol('P', commutative=True), Symbol('P', commutative=True))))", "exp(Add(Mul(Integer(-1), Symbol('P', commutative=True)), Symbol('q', commutative=True)))"]}, {"premise_expression": "p + \\sin{(S)}", "variable": "S", "positive": "S p - \\cos{(S)}", "negatives": ["S p + e^{S}", "- S p + \\sin{(S)}", "\\frac{S^{2} \\cos{(p)}}{2}", "\\log{(S)} \\cos{(p)}"], "srepr_premise_expression": "Add(Symbol('p', commutative=True), sin(Symbol('S', commutative=True)))", "srepr_variable": "Symbol('S', commutative=True)", "srepr_positive": "Add(Mul(Symbol('S', commutative=True), Symbol('p', commutative=True)), Mul(Integer(-1), cos(Symbol('S', commutative=True))))", "srepr_negatives": ["Add(Mul(Symbol('S', commutative=True), Symbol('p', commutative=True)), exp(Symbol('S', commutative=True)))", "Add(Mul(Integer(-1), Symbol('S', commutative=True), Symbol('p', commutative=True)), sin(Symbol('S', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('S', commutative=True), Integer(2)), cos(Symbol('p', commutative=True)))", "Mul(log(Symbol('S', commutative=True)), cos(Symbol('p', commutative=True)))"]}, {"premise_expression": "X + e^{B}", "variable": "B", "positive": "B X + e^{B}", "negatives": ["\\frac{X (X + 2 e^{B})}{2}", "X \\log{(B)}", "\\cos{(B - X)}", "\\frac{B (B + 2 \\cos{(X)})}{2}"], "srepr_premise_expression": "Add(Symbol('X', commutative=True), exp(Symbol('B', commutative=True)))", "srepr_variable": "Symbol('B', commutative=True)", "srepr_positive": "Add(Mul(Symbol('B', commutative=True), Symbol('X', commutative=True)), exp(Symbol('B', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('X', commutative=True), Add(Symbol('X', commutative=True), Mul(Integer(2), exp(Symbol('B', commutative=True)))))", "Mul(Symbol('X', commutative=True), log(Symbol('B', commutative=True)))", "cos(Add(Symbol('B', commutative=True), Mul(Integer(-1), Symbol('X', commutative=True))))", "Mul(Rational(1, 2), Symbol('B', commutative=True), Add(Symbol('B', commutative=True), Mul(Integer(2), cos(Symbol('X', commutative=True)))))"]}, {"premise_expression": "\\frac{K}{q}", "variable": "q", "positive": "K \\log{(q)}", "negatives": ["\\frac{K^{2}}{2 q}", "\\frac{K q^{3}}{3}", "K q - \\cos{(q)}", "- K q - \\cos{(q)}"], "srepr_premise_expression": "Mul(Symbol('K', commutative=True), Pow(Symbol('q', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('q', commutative=True)", "srepr_positive": "Mul(Symbol('K', commutative=True), log(Symbol('q', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('K', commutative=True), Integer(2)), Pow(Symbol('q', commutative=True), Integer(-1)))", "Mul(Rational(1, 3), Symbol('K', commutative=True), Pow(Symbol('q', commutative=True), Integer(3)))", "Add(Mul(Symbol('K', commutative=True), Symbol('q', commutative=True)), Mul(Integer(-1), cos(Symbol('q', commutative=True))))", "Add(Mul(Integer(-1), Symbol('K', commutative=True), Symbol('q', commutative=True)), Mul(Integer(-1), cos(Symbol('q', commutative=True))))"]}, {"premise_expression": "\\frac{y}{r}", "variable": "y", "positive": "\\frac{y^{2}}{2 r}", "negatives": ["y \\log{(r)}", "r e^{\\frac{y}{r}}", "\\frac{y (2 r - y)}{2}", "\\log{(y)} \\sin{(r)}"], "srepr_premise_expression": "Mul(Pow(Symbol('r', commutative=True), Integer(-1)), Symbol('y', commutative=True))", "srepr_variable": "Symbol('y', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('r', commutative=True), Integer(-1)), Pow(Symbol('y', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('y', commutative=True), log(Symbol('r', commutative=True)))", "Mul(Symbol('r', commutative=True), exp(Mul(Pow(Symbol('r', commutative=True), Integer(-1)), Symbol('y', commutative=True))))", "Mul(Rational(1, 2), Symbol('y', commutative=True), Add(Mul(Integer(2), Symbol('r', commutative=True)), Mul(Integer(-1), Symbol('y', commutative=True))))", "Mul(log(Symbol('y', commutative=True)), sin(Symbol('r', commutative=True)))"]}, {"premise_expression": "e^{M + m}", "variable": "m", "positive": "e^{M + m}", "negatives": ["M e^{m}", "M m + \\sin{(m)}", "- M m + e^{m}", "\\log{(m)} \\cos{(M)}"], "srepr_premise_expression": "exp(Add(Symbol('M', commutative=True), Symbol('m', commutative=True)))", "srepr_variable": "Symbol('m', commutative=True)", "srepr_positive": "exp(Add(Symbol('M', commutative=True), Symbol('m', commutative=True)))", "srepr_negatives": ["Mul(Symbol('M', commutative=True), exp(Symbol('m', commutative=True)))", "Add(Mul(Symbol('M', commutative=True), Symbol('m', commutative=True)), sin(Symbol('m', commutative=True)))", "Add(Mul(Integer(-1), Symbol('M', commutative=True), Symbol('m', commutative=True)), exp(Symbol('m', commutative=True)))", "Mul(log(Symbol('m', commutative=True)), cos(Symbol('M', commutative=True)))"]}, {"premise_expression": "N \\log{(R)}", "variable": "N", "positive": "\\frac{N^{2} \\log{(R)}}{2}", "negatives": ["\\frac{N (N + 2 \\log{(R)})}{2}", "\\frac{N^{2}}{2 R}", "N R (\\log{(R)} - 1)", "\\frac{N (- N + 2 R)}{2}"], "srepr_premise_expression": "Mul(Symbol('N', commutative=True), log(Symbol('R', commutative=True)))", "srepr_variable": "Symbol('N', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('N', commutative=True), Integer(2)), log(Symbol('R', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Symbol('N', commutative=True), Mul(Integer(2), log(Symbol('R', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('N', commutative=True), Integer(2)), Pow(Symbol('R', commutative=True), Integer(-1)))", "Mul(Symbol('N', commutative=True), Symbol('R', commutative=True), Add(log(Symbol('R', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Mul(Integer(-1), Symbol('N', commutative=True)), Mul(Integer(2), Symbol('R', commutative=True))))"]}, {"premise_expression": "- C + \\frac{E}{w}", "variable": "w", "positive": "- C w + E \\log{(w)}", "negatives": ["C E \\log{(w)}", "- C E + \\frac{E^{2}}{2 w}", "\\frac{E \\log{(w)}}{C}", "- \\frac{C^{2}}{2} + \\frac{C E}{w}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('C', commutative=True)), Mul(Symbol('E', commutative=True), Pow(Symbol('w', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('w', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('C', commutative=True), Symbol('w', commutative=True)), Mul(Symbol('E', commutative=True), log(Symbol('w', commutative=True))))", "srepr_negatives": ["Mul(Symbol('C', commutative=True), Symbol('E', commutative=True), log(Symbol('w', commutative=True)))", "Add(Mul(Integer(-1), Symbol('C', commutative=True), Symbol('E', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('E', commutative=True), Integer(2)), Pow(Symbol('w', commutative=True), Integer(-1))))", "Mul(Pow(Symbol('C', commutative=True), Integer(-1)), Symbol('E', commutative=True), log(Symbol('w', commutative=True)))", "Add(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2))), Mul(Symbol('C', commutative=True), Symbol('E', commutative=True), Pow(Symbol('w', commutative=True), Integer(-1))))"]}, {"premise_expression": "\\frac{j}{s}", "variable": "j", "positive": "\\frac{j^{2}}{2 s}", "negatives": ["j \\log{(s)}", "s e^{j}", "\\frac{j (j - 2 s)}{2}", "\\log{(j)} \\sin{(s)}"], "srepr_premise_expression": "Mul(Symbol('j', commutative=True), Pow(Symbol('s', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('j', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('j', commutative=True), Integer(2)), Pow(Symbol('s', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('j', commutative=True), log(Symbol('s', commutative=True)))", "Mul(Symbol('s', commutative=True), exp(Symbol('j', commutative=True)))", "Mul(Rational(1, 2), Symbol('j', commutative=True), Add(Symbol('j', commutative=True), Mul(Integer(-1), Integer(2), Symbol('s', commutative=True))))", "Mul(log(Symbol('j', commutative=True)), sin(Symbol('s', commutative=True)))"]}, {"premise_expression": "\\frac{a}{L}", "variable": "a", "positive": "\\frac{a^{2}}{2 L}", "negatives": ["a \\log{(L)}", "\\frac{L a^{2}}{2}", "\\frac{a^{2} \\log{(L)}}{2}", "e^{- L + a}"], "srepr_premise_expression": "Mul(Pow(Symbol('L', commutative=True), Integer(-1)), Symbol('a', commutative=True))", "srepr_variable": "Symbol('a', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(-1)), Pow(Symbol('a', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('a', commutative=True), log(Symbol('L', commutative=True)))", "Mul(Rational(1, 2), Symbol('L', commutative=True), Pow(Symbol('a', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('a', commutative=True), Integer(2)), log(Symbol('L', commutative=True)))", "exp(Add(Mul(Integer(-1), Symbol('L', commutative=True)), Symbol('a', commutative=True)))"]}, {"premise_expression": "j + e^{m}", "variable": "m", "positive": "j m + e^{m}", "negatives": ["- j m + e^{m}", "j m + \\sin{(m)}", "j e^{\\frac{m}{j}}", "\\frac{j (j + 2 e^{m})}{2}"], "srepr_premise_expression": "Add(Symbol('j', commutative=True), exp(Symbol('m', commutative=True)))", "srepr_variable": "Symbol('m', commutative=True)", "srepr_positive": "Add(Mul(Symbol('j', commutative=True), Symbol('m', commutative=True)), exp(Symbol('m', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('j', commutative=True), Symbol('m', commutative=True)), exp(Symbol('m', commutative=True)))", "Add(Mul(Symbol('j', commutative=True), Symbol('m', commutative=True)), sin(Symbol('m', commutative=True)))", "Mul(Symbol('j', commutative=True), exp(Mul(Pow(Symbol('j', commutative=True), Integer(-1)), Symbol('m', commutative=True))))", "Mul(Rational(1, 2), Symbol('j', commutative=True), Add(Symbol('j', commutative=True), Mul(Integer(2), exp(Symbol('m', commutative=True)))))"]}, {"premise_expression": "- A + e^{T}", "variable": "A", "positive": "\\frac{A (- A + 2 e^{T})}{2}", "negatives": ["\\frac{A (- A + 2 \\sin{(T)})}{2}", "- A T + e^{T}", "A T + e^{A}", "\\frac{A e^{T}}{T}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('A', commutative=True)), exp(Symbol('T', commutative=True)))", "srepr_variable": "Symbol('A', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Mul(Integer(-1), Symbol('A', commutative=True)), Mul(Integer(2), exp(Symbol('T', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Mul(Integer(-1), Symbol('A', commutative=True)), Mul(Integer(2), sin(Symbol('T', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('A', commutative=True), Symbol('T', commutative=True)), exp(Symbol('T', commutative=True)))", "Add(Mul(Symbol('A', commutative=True), Symbol('T', commutative=True)), exp(Symbol('A', commutative=True)))", "Mul(Symbol('A', commutative=True), Pow(Symbol('T', commutative=True), Integer(-1)), exp(Symbol('T', commutative=True)))"]}, {"premise_expression": "x \\log{(s)}", "variable": "s", "positive": "s x (\\log{(s)} - 1)", "negatives": ["s (\\log{(\\frac{s}{x})} - 1)", "\\frac{x^{2} \\log{(s)}}{2}", "\\log{(s)} \\sin{(x)}", "- \\frac{\\cos{(s)}}{x}"], "srepr_premise_expression": "Mul(Symbol('x', commutative=True), log(Symbol('s', commutative=True)))", "srepr_variable": "Symbol('s', commutative=True)", "srepr_positive": "Mul(Symbol('s', commutative=True), Symbol('x', commutative=True), Add(log(Symbol('s', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('s', commutative=True), Add(log(Mul(Symbol('s', commutative=True), Pow(Symbol('x', commutative=True), Integer(-1)))), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('x', commutative=True), Integer(2)), log(Symbol('s', commutative=True)))", "Mul(log(Symbol('s', commutative=True)), sin(Symbol('x', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('x', commutative=True), Integer(-1)), cos(Symbol('s', commutative=True)))"]}, {"premise_expression": "\\log{(E L)}", "variable": "E", "positive": "E (\\log{(E L)} - 1)", "negatives": ["L (\\log{(E L)} - 1)", "\\log{(E)} \\log{(L)}", "\\log{(E)} \\cos{(L)}", "e^{E + L}"], "srepr_premise_expression": "log(Mul(Symbol('E', commutative=True), Symbol('L', commutative=True)))", "srepr_variable": "Symbol('E', commutative=True)", "srepr_positive": "Mul(Symbol('E', commutative=True), Add(log(Mul(Symbol('E', commutative=True), Symbol('L', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('L', commutative=True), Add(log(Mul(Symbol('E', commutative=True), Symbol('L', commutative=True))), Integer(-1)))", "Mul(log(Symbol('E', commutative=True)), log(Symbol('L', commutative=True)))", "Mul(log(Symbol('E', commutative=True)), cos(Symbol('L', commutative=True)))", "exp(Add(Symbol('E', commutative=True), Symbol('L', commutative=True)))"]}, {"premise_expression": "\\log{(u^{n})}", "variable": "u", "positive": "u (- n + \\log{(u^{n})})", "negatives": ["\\frac{u (- u + 2 \\sin{(n)})}{2}", "e^{- n + u}", "\\frac{n^{2} \\log{(u)}}{2}", "- n u - \\cos{(u)}"], "srepr_premise_expression": "log(Pow(Symbol('u', commutative=True), Symbol('n', commutative=True)))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "Mul(Symbol('u', commutative=True), Add(Mul(Integer(-1), Symbol('n', commutative=True)), log(Pow(Symbol('u', commutative=True), Symbol('n', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(-1), Symbol('u', commutative=True)), Mul(Integer(2), sin(Symbol('n', commutative=True)))))", "exp(Add(Mul(Integer(-1), Symbol('n', commutative=True)), Symbol('u', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('n', commutative=True), Integer(2)), log(Symbol('u', commutative=True)))", "Add(Mul(Integer(-1), Symbol('n', commutative=True), Symbol('u', commutative=True)), Mul(Integer(-1), cos(Symbol('u', commutative=True))))"]}, {"premise_expression": "\\log{(M z)}", "variable": "z", "positive": "z (\\log{(M z)} - 1)", "negatives": ["M (\\log{(M z)} - 1)", "- \\cos{(M - z)}", "- \\cos{(M + z)}", "\\frac{z (- 2 M + z)}{2}"], "srepr_premise_expression": "log(Mul(Symbol('M', commutative=True), Symbol('z', commutative=True)))", "srepr_variable": "Symbol('z', commutative=True)", "srepr_positive": "Mul(Symbol('z', commutative=True), Add(log(Mul(Symbol('M', commutative=True), Symbol('z', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('M', commutative=True), Add(log(Mul(Symbol('M', commutative=True), Symbol('z', commutative=True))), Integer(-1)))", "Mul(Integer(-1), cos(Add(Symbol('M', commutative=True), Mul(Integer(-1), Symbol('z', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('M', commutative=True), Symbol('z', commutative=True))))", "Mul(Rational(1, 2), Symbol('z', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('M', commutative=True)), Symbol('z', commutative=True)))"]}, {"premise_expression": "F - r - x", "variable": "r", "positive": "r (F - \\frac{r}{2} - x)", "negatives": ["\\frac{x (2 F - 2 r - x)}{2}", "\\frac{F (F - 2 r - 2 x)}{2}", "r (1 - F)", "\\frac{r (2 F x - r)}{2}"], "srepr_premise_expression": "Add(Symbol('F', commutative=True), Mul(Integer(-1), Symbol('r', commutative=True)), Mul(Integer(-1), Symbol('x', commutative=True)))", "srepr_variable": "Symbol('r', commutative=True)", "srepr_positive": "Mul(Symbol('r', commutative=True), Add(Symbol('F', commutative=True), Mul(Integer(-1), Rational(1, 2), Symbol('r', commutative=True)), Mul(Integer(-1), Symbol('x', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('x', commutative=True), Add(Mul(Integer(2), Symbol('F', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('r', commutative=True)), Mul(Integer(-1), Symbol('x', commutative=True))))", "Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Symbol('F', commutative=True), Mul(Integer(-1), Integer(2), Symbol('r', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('x', commutative=True))))", "Mul(Symbol('r', commutative=True), Add(Integer(1), Mul(Integer(-1), Symbol('F', commutative=True))))", "Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(2), Symbol('F', commutative=True), Symbol('x', commutative=True)), Mul(Integer(-1), Symbol('r', commutative=True))))"]}, {"premise_expression": "\\frac{P}{y}", "variable": "y", "positive": "P \\log{(y)}", "negatives": ["\\frac{P^{2}}{2 y}", "\\frac{P y^{2}}{2}", "\\frac{y^{2}}{2 P}", "- \\cos{(P + y)}"], "srepr_premise_expression": "Mul(Symbol('P', commutative=True), Pow(Symbol('y', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('y', commutative=True)", "srepr_positive": "Mul(Symbol('P', commutative=True), log(Symbol('y', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2)), Pow(Symbol('y', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Symbol('P', commutative=True), Pow(Symbol('y', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(-1)), Pow(Symbol('y', commutative=True), Integer(2)))", "Mul(Integer(-1), cos(Add(Symbol('P', commutative=True), Symbol('y', commutative=True))))"]}, {"premise_expression": "e^{A^{H}}", "variable": "A", "positive": "\\frac{e^{- \\frac{i \\pi}{H}} \\gamma(\\frac{1}{H}, A^{H} e^{i \\pi})}{H}", "negatives": ["A (\\log{(\\frac{A}{H})} - 1)", "\\frac{A (- A + 2 \\cos{(H)})}{2}", "\\frac{A (A - 4 H)}{2}", "e^{A - H}"], "srepr_premise_expression": "exp(Pow(Symbol('A', commutative=True), Symbol('H', commutative=True)))", "srepr_variable": "Symbol('A', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('H', commutative=True), Integer(-1)), exp(Mul(Integer(-1), I, pi, Pow(Symbol('H', commutative=True), Integer(-1)))), lowergamma(Pow(Symbol('H', commutative=True), Integer(-1)), Mul(Pow(Symbol('A', commutative=True), Symbol('H', commutative=True)), exp_polar(Mul(I, pi)))))", "srepr_negatives": ["Mul(Symbol('A', commutative=True), Add(log(Mul(Symbol('A', commutative=True), Pow(Symbol('H', commutative=True), Integer(-1)))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Mul(Integer(-1), Symbol('A', commutative=True)), Mul(Integer(2), cos(Symbol('H', commutative=True)))))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Symbol('A', commutative=True), Mul(Integer(-1), Integer(4), Symbol('H', commutative=True))))", "exp(Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('H', commutative=True))))"]}, {"premise_expression": "r + \\log{(j)}", "variable": "r", "positive": "\\frac{r (r + 2 \\log{(j)})}{2}", "negatives": ["\\frac{r (r + 2 e^{j})}{2}", "j (r + \\log{(j)} - 1)", "\\frac{r (- 2 j + r)}{2}", "\\frac{r (2 j - r)}{2}"], "srepr_premise_expression": "Add(Symbol('r', commutative=True), log(Symbol('j', commutative=True)))", "srepr_variable": "Symbol('r', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Symbol('r', commutative=True), Mul(Integer(2), log(Symbol('j', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Symbol('r', commutative=True), Mul(Integer(2), exp(Symbol('j', commutative=True)))))", "Mul(Symbol('j', commutative=True), Add(Symbol('r', commutative=True), log(Symbol('j', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('j', commutative=True)), Symbol('r', commutative=True)))", "Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(2), Symbol('j', commutative=True)), Mul(Integer(-1), Symbol('r', commutative=True))))"]}, {"premise_expression": "V + t", "variable": "t", "positive": "\\frac{t (2 V + t)}{2}", "negatives": ["\\frac{V (V + 2 t)}{2}", "e^{V + t}", "\\frac{V t^{2}}{2}", "\\frac{t (t + 2 \\sin{(V)})}{2}"], "srepr_premise_expression": "Add(Symbol('V', commutative=True), Symbol('t', commutative=True))", "srepr_variable": "Symbol('t', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('t', commutative=True), Add(Mul(Integer(2), Symbol('V', commutative=True)), Symbol('t', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('V', commutative=True), Add(Symbol('V', commutative=True), Mul(Integer(2), Symbol('t', commutative=True))))", "exp(Add(Symbol('V', commutative=True), Symbol('t', commutative=True)))", "Mul(Rational(1, 2), Symbol('V', commutative=True), Pow(Symbol('t', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('t', commutative=True), Add(Symbol('t', commutative=True), Mul(Integer(2), sin(Symbol('V', commutative=True)))))"]}, {"premise_expression": "\\frac{\\cos{(F)}}{R}", "variable": "R", "positive": "\\log{(R)} \\cos{(F)}", "negatives": ["\\frac{\\sin{(F)}}{R}", "e^{- F + R}", "- F R + e^{R}", "e^{F + R}"], "srepr_premise_expression": "Mul(Pow(Symbol('R', commutative=True), Integer(-1)), cos(Symbol('F', commutative=True)))", "srepr_variable": "Symbol('R', commutative=True)", "srepr_positive": "Mul(log(Symbol('R', commutative=True)), cos(Symbol('F', commutative=True)))", "srepr_negatives": ["Mul(Pow(Symbol('R', commutative=True), Integer(-1)), sin(Symbol('F', commutative=True)))", "exp(Add(Mul(Integer(-1), Symbol('F', commutative=True)), Symbol('R', commutative=True)))", "Add(Mul(Integer(-1), Symbol('F', commutative=True), Symbol('R', commutative=True)), exp(Symbol('R', commutative=True)))", "exp(Add(Symbol('F', commutative=True), Symbol('R', commutative=True)))"]}, {"premise_expression": "\\frac{A}{V}", "variable": "A", "positive": "\\frac{A^{2}}{2 V}", "negatives": ["A \\log{(V)}", "A (A + V)", "\\frac{A^{2} \\log{(V)}}{2}", "A (\\log{(\\frac{A}{V})} - 1)"], "srepr_premise_expression": "Mul(Symbol('A', commutative=True), Pow(Symbol('V', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('A', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2)), Pow(Symbol('V', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('A', commutative=True), log(Symbol('V', commutative=True)))", "Mul(Symbol('A', commutative=True), Add(Symbol('A', commutative=True), Symbol('V', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2)), log(Symbol('V', commutative=True)))", "Mul(Symbol('A', commutative=True), Add(log(Mul(Symbol('A', commutative=True), Pow(Symbol('V', commutative=True), Integer(-1)))), Integer(-1)))"]}, {"premise_expression": "- c + e^{M}", "variable": "c", "positive": "\\frac{c (- c + 2 e^{M})}{2}", "negatives": ["- M c + e^{M}", "\\frac{c^{2}}{2 M}", "c e^{2 M}", "M c - \\cos{(c)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('c', commutative=True)), exp(Symbol('M', commutative=True)))", "srepr_variable": "Symbol('c', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('c', commutative=True), Add(Mul(Integer(-1), Symbol('c', commutative=True)), Mul(Integer(2), exp(Symbol('M', commutative=True)))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('M', commutative=True), Symbol('c', commutative=True)), exp(Symbol('M', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('M', commutative=True), Integer(-1)), Pow(Symbol('c', commutative=True), Integer(2)))", "Mul(Symbol('c', commutative=True), exp(Mul(Integer(2), Symbol('M', commutative=True))))", "Add(Mul(Symbol('M', commutative=True), Symbol('c', commutative=True)), Mul(Integer(-1), cos(Symbol('c', commutative=True))))"]}, {"premise_expression": "- T + x", "variable": "T", "positive": "\\frac{T (- T + 2 x)}{2}", "negatives": ["\\frac{T (T + 2 x)}{2}", "\\frac{x (- 2 T + x)}{2}", "\\frac{T^{2} \\sin{(x)}}{2}", "- \\cos{(T + x)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('T', commutative=True)), Symbol('x', commutative=True))", "srepr_variable": "Symbol('T', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('T', commutative=True), Add(Mul(Integer(-1), Symbol('T', commutative=True)), Mul(Integer(2), Symbol('x', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('T', commutative=True), Add(Symbol('T', commutative=True), Mul(Integer(2), Symbol('x', commutative=True))))", "Mul(Rational(1, 2), Symbol('x', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('T', commutative=True)), Symbol('x', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('T', commutative=True), Integer(2)), sin(Symbol('x', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('T', commutative=True), Symbol('x', commutative=True))))"]}, {"premise_expression": "\\frac{\\log{(o)}}{k}", "variable": "k", "positive": "\\log{(k)} \\log{(o)}", "negatives": ["e^{k + o}", "\\frac{k (\\log{(k)} - 1)}{o}", "o e^{\\frac{k}{o}}", "\\frac{o (\\log{(o)} - 1)}{k}"], "srepr_premise_expression": "Mul(Pow(Symbol('k', commutative=True), Integer(-1)), log(Symbol('o', commutative=True)))", "srepr_variable": "Symbol('k', commutative=True)", "srepr_positive": "Mul(log(Symbol('k', commutative=True)), log(Symbol('o', commutative=True)))", "srepr_negatives": ["exp(Add(Symbol('k', commutative=True), Symbol('o', commutative=True)))", "Mul(Symbol('k', commutative=True), Pow(Symbol('o', commutative=True), Integer(-1)), Add(log(Symbol('k', commutative=True)), Integer(-1)))", "Mul(Symbol('o', commutative=True), exp(Mul(Symbol('k', commutative=True), Pow(Symbol('o', commutative=True), Integer(-1)))))", "Mul(Pow(Symbol('k', commutative=True), Integer(-1)), Symbol('o', commutative=True), Add(log(Symbol('o', commutative=True)), Integer(-1)))"]}, {"premise_expression": "q + \\frac{k}{A}", "variable": "A", "positive": "A q + k \\log{(A)}", "negatives": ["- A k + q \\log{(A)}", "k q + \\frac{k^{2}}{2 A}", "\\frac{A (A + 2 k)}{2 q}", "\\frac{q^{2}}{2} + \\frac{k q}{A}"], "srepr_premise_expression": "Add(Symbol('q', commutative=True), Mul(Pow(Symbol('A', commutative=True), Integer(-1)), Symbol('k', commutative=True)))", "srepr_variable": "Symbol('A', commutative=True)", "srepr_positive": "Add(Mul(Symbol('A', commutative=True), Symbol('q', commutative=True)), Mul(Symbol('k', commutative=True), log(Symbol('A', commutative=True))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('A', commutative=True), Symbol('k', commutative=True)), Mul(Symbol('q', commutative=True), log(Symbol('A', commutative=True))))", "Add(Mul(Symbol('k', commutative=True), Symbol('q', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(-1)), Pow(Symbol('k', commutative=True), Integer(2))))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Pow(Symbol('q', commutative=True), Integer(-1)), Add(Symbol('A', commutative=True), Mul(Integer(2), Symbol('k', commutative=True))))", "Add(Mul(Rational(1, 2), Pow(Symbol('q', commutative=True), Integer(2))), Mul(Pow(Symbol('A', commutative=True), Integer(-1)), Symbol('k', commutative=True), Symbol('q', commutative=True)))"]}, {"premise_expression": "\\log{(M^{S})}", "variable": "S", "positive": "\\frac{S^{2} \\log{(M)}}{2}", "negatives": ["\\frac{S (- S + 2 \\log{(M)})}{2}", "\\frac{\\sin{(2 S)}}{2}", "M e^{S}", "M (- S + \\log{(M^{S})})"], "srepr_premise_expression": "log(Pow(Symbol('M', commutative=True), Symbol('S', commutative=True)))", "srepr_variable": "Symbol('S', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('S', commutative=True), Integer(2)), log(Symbol('M', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Mul(Integer(-1), Symbol('S', commutative=True)), Mul(Integer(2), log(Symbol('M', commutative=True)))))", "Mul(Rational(1, 2), sin(Mul(Integer(2), Symbol('S', commutative=True))))", "Mul(Symbol('M', commutative=True), exp(Symbol('S', commutative=True)))", "Mul(Symbol('M', commutative=True), Add(Mul(Integer(-1), Symbol('S', commutative=True)), log(Pow(Symbol('M', commutative=True), Symbol('S', commutative=True)))))"]}, {"premise_expression": "\\frac{\\sin{(T)}}{o}", "variable": "o", "positive": "\\log{(o)} \\sin{(T)}", "negatives": ["- \\frac{\\cos{(T)}}{o}", "\\frac{o (2 T - o)}{2}", "- T o - \\cos{(o)}", "\\frac{o (- o + 2 \\log{(T)})}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('o', commutative=True), Integer(-1)), sin(Symbol('T', commutative=True)))", "srepr_variable": "Symbol('o', commutative=True)", "srepr_positive": "Mul(log(Symbol('o', commutative=True)), sin(Symbol('T', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Pow(Symbol('o', commutative=True), Integer(-1)), cos(Symbol('T', commutative=True)))", "Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Mul(Integer(2), Symbol('T', commutative=True)), Mul(Integer(-1), Symbol('o', commutative=True))))", "Add(Mul(Integer(-1), Symbol('T', commutative=True), Symbol('o', commutative=True)), Mul(Integer(-1), cos(Symbol('o', commutative=True))))", "Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Mul(Integer(-1), Symbol('o', commutative=True)), Mul(Integer(2), log(Symbol('T', commutative=True)))))"]}, {"premise_expression": "- g + z", "variable": "g", "positive": "\\frac{g (- g + 2 z)}{2}", "negatives": ["\\frac{g (g + 2 z)}{2}", "\\frac{z (- 2 g + z)}{2}", "- e^{- g + z}", "\\frac{g^{2} \\cos{(z)}}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('g', commutative=True)), Symbol('z', commutative=True))", "srepr_variable": "Symbol('g', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Mul(Integer(-1), Symbol('g', commutative=True)), Mul(Integer(2), Symbol('z', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Symbol('g', commutative=True), Mul(Integer(2), Symbol('z', commutative=True))))", "Mul(Rational(1, 2), Symbol('z', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('g', commutative=True)), Symbol('z', commutative=True)))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('g', commutative=True)), Symbol('z', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('g', commutative=True), Integer(2)), cos(Symbol('z', commutative=True)))"]}, {"premise_expression": "\\log{(C + z)}", "variable": "C", "positive": "C \\log{(C + z)} - C + z \\log{(C + z)}", "negatives": ["C \\log{(C + z)} + z \\log{(C + z)} - z", "C (- z + \\log{(C)} - 1)", "C (z + \\log{(C)} - 1)", "\\frac{C (- C + 2 z)}{2}"], "srepr_premise_expression": "log(Add(Symbol('C', commutative=True), Symbol('z', commutative=True)))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Add(Mul(Symbol('C', commutative=True), log(Add(Symbol('C', commutative=True), Symbol('z', commutative=True)))), Mul(Integer(-1), Symbol('C', commutative=True)), Mul(Symbol('z', commutative=True), log(Add(Symbol('C', commutative=True), Symbol('z', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('C', commutative=True), log(Add(Symbol('C', commutative=True), Symbol('z', commutative=True)))), Mul(Symbol('z', commutative=True), log(Add(Symbol('C', commutative=True), Symbol('z', commutative=True)))), Mul(Integer(-1), Symbol('z', commutative=True)))", "Mul(Symbol('C', commutative=True), Add(Mul(Integer(-1), Symbol('z', commutative=True)), log(Symbol('C', commutative=True)), Integer(-1)))", "Mul(Symbol('C', commutative=True), Add(Symbol('z', commutative=True), log(Symbol('C', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Mul(Integer(-1), Symbol('C', commutative=True)), Mul(Integer(2), Symbol('z', commutative=True))))"]}, {"premise_expression": "\\frac{W}{p}", "variable": "p", "positive": "W \\log{(p)}", "negatives": ["W e^{p}", "\\frac{W^{2}}{2 p}", "\\log{(W)} \\log{(p)}", "\\frac{W p^{2}}{2}"], "srepr_premise_expression": "Mul(Symbol('W', commutative=True), Pow(Symbol('p', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('p', commutative=True)", "srepr_positive": "Mul(Symbol('W', commutative=True), log(Symbol('p', commutative=True)))", "srepr_negatives": ["Mul(Symbol('W', commutative=True), exp(Symbol('p', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('W', commutative=True), Integer(2)), Pow(Symbol('p', commutative=True), Integer(-1)))", "Mul(log(Symbol('W', commutative=True)), log(Symbol('p', commutative=True)))", "Mul(Rational(1, 2), Symbol('W', commutative=True), Pow(Symbol('p', commutative=True), Integer(2)))"]}, {"premise_expression": "H + w", "variable": "H", "positive": "\\frac{H (H + 2 w)}{2}", "negatives": ["\\frac{w (2 H + w)}{2}", "\\frac{H^{2} \\cos{(w)}}{2}", "e^{H - w}", "H w - \\cos{(H)}"], "srepr_premise_expression": "Add(Symbol('H', commutative=True), Symbol('w', commutative=True))", "srepr_variable": "Symbol('H', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('H', commutative=True), Add(Symbol('H', commutative=True), Mul(Integer(2), Symbol('w', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('w', commutative=True), Add(Mul(Integer(2), Symbol('H', commutative=True)), Symbol('w', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('H', commutative=True), Integer(2)), cos(Symbol('w', commutative=True)))", "exp(Add(Symbol('H', commutative=True), Mul(Integer(-1), Symbol('w', commutative=True))))", "Add(Mul(Symbol('H', commutative=True), Symbol('w', commutative=True)), Mul(Integer(-1), cos(Symbol('H', commutative=True))))"]}, {"premise_expression": "A e^{g}", "variable": "g", "positive": "A e^{g}", "negatives": ["\\frac{A^{2} e^{g}}{2}", "\\frac{A g^{2}}{2}", "\\frac{\\sin{(g)}}{A}", "- \\cos{(A + g)}"], "srepr_premise_expression": "Mul(Symbol('A', commutative=True), exp(Symbol('g', commutative=True)))", "srepr_variable": "Symbol('g', commutative=True)", "srepr_positive": "Mul(Symbol('A', commutative=True), exp(Symbol('g', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2)), exp(Symbol('g', commutative=True)))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Pow(Symbol('g', commutative=True), Integer(2)))", "Mul(Pow(Symbol('A', commutative=True), Integer(-1)), sin(Symbol('g', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('A', commutative=True), Symbol('g', commutative=True))))"]}, {"premise_expression": "\\log{(\\frac{f}{K})}", "variable": "f", "positive": "f (\\log{(\\frac{f}{K})} - 1)", "negatives": ["K (\\log{(\\frac{f}{K})} + 1)", "\\frac{f (\\log{(f)} - 1)}{K}", "K \\log{(f)}", "\\cos{(K - f)}"], "srepr_premise_expression": "log(Mul(Pow(Symbol('K', commutative=True), Integer(-1)), Symbol('f', commutative=True)))", "srepr_variable": "Symbol('f', commutative=True)", "srepr_positive": "Mul(Symbol('f', commutative=True), Add(log(Mul(Pow(Symbol('K', commutative=True), Integer(-1)), Symbol('f', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('K', commutative=True), Add(log(Mul(Pow(Symbol('K', commutative=True), Integer(-1)), Symbol('f', commutative=True))), Integer(1)))", "Mul(Pow(Symbol('K', commutative=True), Integer(-1)), Symbol('f', commutative=True), Add(log(Symbol('f', commutative=True)), Integer(-1)))", "Mul(Symbol('K', commutative=True), log(Symbol('f', commutative=True)))", "cos(Add(Symbol('K', commutative=True), Mul(Integer(-1), Symbol('f', commutative=True))))"]}, {"premise_expression": "- r + e^{m}", "variable": "r", "positive": "\\frac{r (- r + 2 e^{m})}{2}", "negatives": ["\\frac{r (- r + 2 \\cos{(m)})}{2}", "- m r + e^{m}", "\\frac{r (- 2 m + r)}{2}", "- m r + e^{r}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('r', commutative=True)), exp(Symbol('m', commutative=True)))", "srepr_variable": "Symbol('r', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(-1), Symbol('r', commutative=True)), Mul(Integer(2), exp(Symbol('m', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(-1), Symbol('r', commutative=True)), Mul(Integer(2), cos(Symbol('m', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('m', commutative=True), Symbol('r', commutative=True)), exp(Symbol('m', commutative=True)))", "Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('m', commutative=True)), Symbol('r', commutative=True)))", "Add(Mul(Integer(-1), Symbol('m', commutative=True), Symbol('r', commutative=True)), exp(Symbol('r', commutative=True)))"]}, {"premise_expression": "\\frac{C}{N}", "variable": "C", "positive": "\\frac{C^{2}}{2 N}", "negatives": ["C \\log{(N)}", "\\frac{C (- C + 2 N)}{2}", "C N - \\cos{(C)}", "0"], "srepr_premise_expression": "Mul(Symbol('C', commutative=True), Pow(Symbol('N', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2)), Pow(Symbol('N', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('C', commutative=True), log(Symbol('N', commutative=True)))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Mul(Integer(-1), Symbol('C', commutative=True)), Mul(Integer(2), Symbol('N', commutative=True))))", "Add(Mul(Symbol('C', commutative=True), Symbol('N', commutative=True)), Mul(Integer(-1), cos(Symbol('C', commutative=True))))", "Integer(0)"]}, {"premise_expression": "\\frac{\\cos{(c)}}{S}", "variable": "c", "positive": "\\frac{\\sin{(c)}}{S}", "negatives": ["\\log{(S)} \\cos{(c)}", "\\frac{c (c + 2 \\sin{(S)})}{2}", "c (\\log{(\\frac{S}{c})} + 1)", "\\frac{c (- c + 2 \\sin{(S)})}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('S', commutative=True), Integer(-1)), cos(Symbol('c', commutative=True)))", "srepr_variable": "Symbol('c', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('S', commutative=True), Integer(-1)), sin(Symbol('c', commutative=True)))", "srepr_negatives": ["Mul(log(Symbol('S', commutative=True)), cos(Symbol('c', commutative=True)))", "Mul(Rational(1, 2), Symbol('c', commutative=True), Add(Symbol('c', commutative=True), Mul(Integer(2), sin(Symbol('S', commutative=True)))))", "Mul(Symbol('c', commutative=True), Add(log(Mul(Symbol('S', commutative=True), Pow(Symbol('c', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Rational(1, 2), Symbol('c', commutative=True), Add(Mul(Integer(-1), Symbol('c', commutative=True)), Mul(Integer(2), sin(Symbol('S', commutative=True)))))"]}, {"premise_expression": "- v + \\sin{(h)}", "variable": "h", "positive": "- h v - \\cos{(h)}", "negatives": ["h v - \\cos{(h)}", "e^{v} \\log{(h)}", "\\cos{(h - v)}", "- \\cos{(h + v)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('v', commutative=True)), sin(Symbol('h', commutative=True)))", "srepr_variable": "Symbol('h', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('h', commutative=True), Symbol('v', commutative=True)), Mul(Integer(-1), cos(Symbol('h', commutative=True))))", "srepr_negatives": ["Add(Mul(Symbol('h', commutative=True), Symbol('v', commutative=True)), Mul(Integer(-1), cos(Symbol('h', commutative=True))))", "Mul(exp(Symbol('v', commutative=True)), log(Symbol('h', commutative=True)))", "cos(Add(Symbol('h', commutative=True), Mul(Integer(-1), Symbol('v', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('h', commutative=True), Symbol('v', commutative=True))))"]}, {"premise_expression": "p e^{h}", "variable": "p", "positive": "\\frac{p^{2} e^{h}}{2}", "negatives": ["\\frac{p^{2} \\log{(h)}}{2}", "p e^{h}", "h e^{\\frac{p}{h}}", "\\frac{h p^{2}}{2}"], "srepr_premise_expression": "Mul(Symbol('p', commutative=True), exp(Symbol('h', commutative=True)))", "srepr_variable": "Symbol('p', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('p', commutative=True), Integer(2)), exp(Symbol('h', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('p', commutative=True), Integer(2)), log(Symbol('h', commutative=True)))", "Mul(Symbol('p', commutative=True), exp(Symbol('h', commutative=True)))", "Mul(Symbol('h', commutative=True), exp(Mul(Pow(Symbol('h', commutative=True), Integer(-1)), Symbol('p', commutative=True))))", "Mul(Rational(1, 2), Symbol('h', commutative=True), Pow(Symbol('p', commutative=True), Integer(2)))"]}, {"premise_expression": "c + y", "variable": "y", "positive": "\\frac{y (2 c + y)}{2}", "negatives": ["\\frac{y (2 c - y)}{2}", "\\frac{c (c + 2 y)}{2}", "- e^{c - y}", "\\frac{y^{2}}{2} + \\sin{(y)}"], "srepr_premise_expression": "Add(Symbol('c', commutative=True), Symbol('y', commutative=True))", "srepr_variable": "Symbol('y', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('y', commutative=True), Add(Mul(Integer(2), Symbol('c', commutative=True)), Symbol('y', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('y', commutative=True), Add(Mul(Integer(2), Symbol('c', commutative=True)), Mul(Integer(-1), Symbol('y', commutative=True))))", "Mul(Rational(1, 2), Symbol('c', commutative=True), Add(Symbol('c', commutative=True), Mul(Integer(2), Symbol('y', commutative=True))))", "Mul(Integer(-1), exp(Add(Symbol('c', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True)))))", "Add(Mul(Rational(1, 2), Pow(Symbol('y', commutative=True), Integer(2))), sin(Symbol('y', commutative=True)))"]}, {"premise_expression": "D + p", "variable": "D", "positive": "\\frac{D (D + 2 p)}{2}", "negatives": ["\\frac{D (- D + 2 p)}{2}", "\\frac{p (2 D + p)}{2}", "\\frac{D^{2} \\cos{(p)}}{2}", "\\sin{(D - p)}"], "srepr_premise_expression": "Add(Symbol('D', commutative=True), Symbol('p', commutative=True))", "srepr_variable": "Symbol('D', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('D', commutative=True), Add(Symbol('D', commutative=True), Mul(Integer(2), Symbol('p', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('D', commutative=True), Add(Mul(Integer(-1), Symbol('D', commutative=True)), Mul(Integer(2), Symbol('p', commutative=True))))", "Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Mul(Integer(2), Symbol('D', commutative=True)), Symbol('p', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(2)), cos(Symbol('p', commutative=True)))", "sin(Add(Symbol('D', commutative=True), Mul(Integer(-1), Symbol('p', commutative=True))))"]}, {"premise_expression": "\\log{(M k)}", "variable": "k", "positive": "k (\\log{(M k)} - 1)", "negatives": ["M (\\log{(M k)} - 1)", "k (\\log{(\\frac{M}{k})} + 1)", "k (\\log{(\\frac{k}{M})} - 1)", "k (M + \\log{(k)} - 1)"], "srepr_premise_expression": "log(Mul(Symbol('M', commutative=True), Symbol('k', commutative=True)))", "srepr_variable": "Symbol('k', commutative=True)", "srepr_positive": "Mul(Symbol('k', commutative=True), Add(log(Mul(Symbol('M', commutative=True), Symbol('k', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('M', commutative=True), Add(log(Mul(Symbol('M', commutative=True), Symbol('k', commutative=True))), Integer(-1)))", "Mul(Symbol('k', commutative=True), Add(log(Mul(Symbol('M', commutative=True), Pow(Symbol('k', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Symbol('k', commutative=True), Add(log(Mul(Pow(Symbol('M', commutative=True), Integer(-1)), Symbol('k', commutative=True))), Integer(-1)))", "Mul(Symbol('k', commutative=True), Add(Symbol('M', commutative=True), log(Symbol('k', commutative=True)), Integer(-1)))"]}, {"premise_expression": "U - x", "variable": "x", "positive": "\\frac{x (2 U - x)}{2}", "negatives": ["\\frac{U (U - 2 x)}{2}", "e^{U + x}", "e^{U} \\log{(x)}", "\\frac{x (x + 2 e^{U})}{2}"], "srepr_premise_expression": "Add(Symbol('U', commutative=True), Mul(Integer(-1), Symbol('x', commutative=True)))", "srepr_variable": "Symbol('x', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('x', commutative=True), Add(Mul(Integer(2), Symbol('U', commutative=True)), Mul(Integer(-1), Symbol('x', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('U', commutative=True), Add(Symbol('U', commutative=True), Mul(Integer(-1), Integer(2), Symbol('x', commutative=True))))", "exp(Add(Symbol('U', commutative=True), Symbol('x', commutative=True)))", "Mul(exp(Symbol('U', commutative=True)), log(Symbol('x', commutative=True)))", "Mul(Rational(1, 2), Symbol('x', commutative=True), Add(Symbol('x', commutative=True), Mul(Integer(2), exp(Symbol('U', commutative=True)))))"]}, {"premise_expression": "U \\log{(R)}", "variable": "U", "positive": "\\frac{U^{2} \\log{(R)}}{2}", "negatives": ["\\frac{U^{2} \\cos{(R)}}{2}", "\\frac{U^{2} \\sin{(R)}}{2}", "\\frac{U (2 R - U)}{2}", "\\frac{U (2 R + U)}{2}"], "srepr_premise_expression": "Mul(Symbol('U', commutative=True), log(Symbol('R', commutative=True)))", "srepr_variable": "Symbol('U', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('U', commutative=True), Integer(2)), log(Symbol('R', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('U', commutative=True), Integer(2)), cos(Symbol('R', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('U', commutative=True), Integer(2)), sin(Symbol('R', commutative=True)))", "Mul(Rational(1, 2), Symbol('U', commutative=True), Add(Mul(Integer(2), Symbol('R', commutative=True)), Mul(Integer(-1), Symbol('U', commutative=True))))", "Mul(Rational(1, 2), Symbol('U', commutative=True), Add(Mul(Integer(2), Symbol('R', commutative=True)), Symbol('U', commutative=True)))"]}, {"premise_expression": "D e^{F}", "variable": "F", "positive": "D e^{F}", "negatives": ["\\frac{D^{2} e^{F}}{2}", "\\log{(D)} \\log{(F)}", "- \\cos{(D + F)}", "\\frac{F^{2} \\sin{(D)}}{2}"], "srepr_premise_expression": "Mul(Symbol('D', commutative=True), exp(Symbol('F', commutative=True)))", "srepr_variable": "Symbol('F', commutative=True)", "srepr_positive": "Mul(Symbol('D', commutative=True), exp(Symbol('F', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(2)), exp(Symbol('F', commutative=True)))", "Mul(log(Symbol('D', commutative=True)), log(Symbol('F', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('D', commutative=True), Symbol('F', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('F', commutative=True), Integer(2)), sin(Symbol('D', commutative=True)))"]}, {"premise_expression": "a + e^{z}", "variable": "z", "positive": "a z + e^{z}", "negatives": ["a z - \\cos{(z)}", "\\frac{a (a + 2 e^{z})}{2}", "\\cos{(a - z)}", "\\frac{a z^{2}}{2}"], "srepr_premise_expression": "Add(Symbol('a', commutative=True), exp(Symbol('z', commutative=True)))", "srepr_variable": "Symbol('z', commutative=True)", "srepr_positive": "Add(Mul(Symbol('a', commutative=True), Symbol('z', commutative=True)), exp(Symbol('z', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('a', commutative=True), Symbol('z', commutative=True)), Mul(Integer(-1), cos(Symbol('z', commutative=True))))", "Mul(Rational(1, 2), Symbol('a', commutative=True), Add(Symbol('a', commutative=True), Mul(Integer(2), exp(Symbol('z', commutative=True)))))", "cos(Add(Symbol('a', commutative=True), Mul(Integer(-1), Symbol('z', commutative=True))))", "Mul(Rational(1, 2), Symbol('a', commutative=True), Pow(Symbol('z', commutative=True), Integer(2)))"]}, {"premise_expression": "\\cos{(\\frac{y}{b})}", "variable": "b", "positive": "b \\cos{(\\frac{y}{b})} + y \\operatorname{Si}{(\\frac{y}{b})}", "negatives": ["b e^{\\frac{y}{b}} - y \\operatorname{Ei}{(\\frac{y}{b})}", "b (\\log{(\\frac{y}{b})} + 1)", "\\frac{b (- b + 2 y)}{2}", "b y - \\cos{(b)}"], "srepr_premise_expression": "cos(Mul(Pow(Symbol('b', commutative=True), Integer(-1)), Symbol('y', commutative=True)))", "srepr_variable": "Symbol('b', commutative=True)", "srepr_positive": "Add(Mul(Symbol('b', commutative=True), cos(Mul(Pow(Symbol('b', commutative=True), Integer(-1)), Symbol('y', commutative=True)))), Mul(Symbol('y', commutative=True), Si(Mul(Pow(Symbol('b', commutative=True), Integer(-1)), Symbol('y', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('b', commutative=True), exp(Mul(Pow(Symbol('b', commutative=True), Integer(-1)), Symbol('y', commutative=True)))), Mul(Integer(-1), Symbol('y', commutative=True), Ei(Mul(Pow(Symbol('b', commutative=True), Integer(-1)), Symbol('y', commutative=True)))))", "Mul(Symbol('b', commutative=True), Add(log(Mul(Pow(Symbol('b', commutative=True), Integer(-1)), Symbol('y', commutative=True))), Integer(1)))", "Mul(Rational(1, 2), Symbol('b', commutative=True), Add(Mul(Integer(-1), Symbol('b', commutative=True)), Mul(Integer(2), Symbol('y', commutative=True))))", "Add(Mul(Symbol('b', commutative=True), Symbol('y', commutative=True)), Mul(Integer(-1), cos(Symbol('b', commutative=True))))"]}, {"premise_expression": "D L T", "variable": "L", "positive": "\\frac{D L^{2} T}{2}", "negatives": ["\\frac{D^{2} L T}{2}", "\\frac{D L T^{2}}{2}", "\\frac{D L^{2}}{2 T}", "\\frac{D \\log{(L)}}{T}"], "srepr_premise_expression": "Mul(Symbol('D', commutative=True), Symbol('L', commutative=True), Symbol('T', commutative=True))", "srepr_variable": "Symbol('L', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('D', commutative=True), Pow(Symbol('L', commutative=True), Integer(2)), Symbol('T', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(2)), Symbol('L', commutative=True), Symbol('T', commutative=True))", "Mul(Rational(1, 2), Symbol('D', commutative=True), Symbol('L', commutative=True), Pow(Symbol('T', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('D', commutative=True), Pow(Symbol('L', commutative=True), Integer(2)), Pow(Symbol('T', commutative=True), Integer(-1)))", "Mul(Symbol('D', commutative=True), Pow(Symbol('T', commutative=True), Integer(-1)), log(Symbol('L', commutative=True)))"]}, {"premise_expression": "\\frac{W}{a}", "variable": "a", "positive": "W \\log{(a)}", "negatives": ["\\frac{W^{2}}{2 a}", "W (a + \\log{(a)})", "W a - \\cos{(a)}", "- \\cos{(W - a)}"], "srepr_premise_expression": "Mul(Symbol('W', commutative=True), Pow(Symbol('a', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('a', commutative=True)", "srepr_positive": "Mul(Symbol('W', commutative=True), log(Symbol('a', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('W', commutative=True), Integer(2)), Pow(Symbol('a', commutative=True), Integer(-1)))", "Mul(Symbol('W', commutative=True), Add(Symbol('a', commutative=True), log(Symbol('a', commutative=True))))", "Add(Mul(Symbol('W', commutative=True), Symbol('a', commutative=True)), Mul(Integer(-1), cos(Symbol('a', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('W', commutative=True), Mul(Integer(-1), Symbol('a', commutative=True)))))"]}, {"premise_expression": "- x + \\sin{(J)}", "variable": "x", "positive": "\\frac{x (- x + 2 \\sin{(J)})}{2}", "negatives": ["\\frac{x^{2} \\sin{(J)}}{2}", "\\frac{x^{2} \\cos{(J)}}{2}", "- J x - \\cos{(J)}", "\\frac{x^{2}}{2 J}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('x', commutative=True)), sin(Symbol('J', commutative=True)))", "srepr_variable": "Symbol('x', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('x', commutative=True), Add(Mul(Integer(-1), Symbol('x', commutative=True)), Mul(Integer(2), sin(Symbol('J', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('x', commutative=True), Integer(2)), sin(Symbol('J', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('x', commutative=True), Integer(2)), cos(Symbol('J', commutative=True)))", "Add(Mul(Integer(-1), Symbol('J', commutative=True), Symbol('x', commutative=True)), Mul(Integer(-1), cos(Symbol('J', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('J', commutative=True), Integer(-1)), Pow(Symbol('x', commutative=True), Integer(2)))"]}, {"premise_expression": "\\frac{o^{M}}{H}", "variable": "H", "positive": "o^{M} \\log{(H)}", "negatives": ["M o \\log{(H)}", "\\frac{H^{2} o}{2 M}", "\\frac{H^{2} M o}{2}", "\\frac{H^{2} o^{M}}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('H', commutative=True), Integer(-1)), Pow(Symbol('o', commutative=True), Symbol('M', commutative=True)))", "srepr_variable": "Symbol('H', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('o', commutative=True), Symbol('M', commutative=True)), log(Symbol('H', commutative=True)))", "srepr_negatives": ["Mul(Symbol('M', commutative=True), Symbol('o', commutative=True), log(Symbol('H', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('H', commutative=True), Integer(2)), Pow(Symbol('M', commutative=True), Integer(-1)), Symbol('o', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('H', commutative=True), Integer(2)), Symbol('M', commutative=True), Symbol('o', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('H', commutative=True), Integer(2)), Pow(Symbol('o', commutative=True), Symbol('M', commutative=True)))"]}, {"premise_expression": "T - p", "variable": "T", "positive": "\\frac{T (T - 2 p)}{2}", "negatives": ["\\frac{T (- T + 2 p)}{2}", "\\frac{p (2 T - p)}{2}", "\\frac{T (T + 2 \\sin{(p)})}{2}", "\\frac{T (T + 2 e^{p})}{2}"], "srepr_premise_expression": "Add(Symbol('T', commutative=True), Mul(Integer(-1), Symbol('p', commutative=True)))", "srepr_variable": "Symbol('T', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('T', commutative=True), Add(Symbol('T', commutative=True), Mul(Integer(-1), Integer(2), Symbol('p', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('T', commutative=True), Add(Mul(Integer(-1), Symbol('T', commutative=True)), Mul(Integer(2), Symbol('p', commutative=True))))", "Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Mul(Integer(2), Symbol('T', commutative=True)), Mul(Integer(-1), Symbol('p', commutative=True))))", "Mul(Rational(1, 2), Symbol('T', commutative=True), Add(Symbol('T', commutative=True), Mul(Integer(2), sin(Symbol('p', commutative=True)))))", "Mul(Rational(1, 2), Symbol('T', commutative=True), Add(Symbol('T', commutative=True), Mul(Integer(2), exp(Symbol('p', commutative=True)))))"]}, {"premise_expression": "\\log{(D - P)}", "variable": "P", "positive": "- D \\log{(- D + P)} + P \\log{(D - P)} - P", "negatives": ["- D \\log{(- D + P)} + P \\log{(- D + P)} - P", "D \\log{(D - P)} - D - P \\log{(D - P)}", "P (- D + \\log{(P)} - 1)", "\\log{(P)} \\cos{(D)}"], "srepr_premise_expression": "log(Add(Symbol('D', commutative=True), Mul(Integer(-1), Symbol('P', commutative=True))))", "srepr_variable": "Symbol('P', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('D', commutative=True), log(Add(Mul(Integer(-1), Symbol('D', commutative=True)), Symbol('P', commutative=True)))), Mul(Symbol('P', commutative=True), log(Add(Symbol('D', commutative=True), Mul(Integer(-1), Symbol('P', commutative=True))))), Mul(Integer(-1), Symbol('P', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('D', commutative=True), log(Add(Mul(Integer(-1), Symbol('D', commutative=True)), Symbol('P', commutative=True)))), Mul(Symbol('P', commutative=True), log(Add(Mul(Integer(-1), Symbol('D', commutative=True)), Symbol('P', commutative=True)))), Mul(Integer(-1), Symbol('P', commutative=True)))", "Add(Mul(Symbol('D', commutative=True), log(Add(Symbol('D', commutative=True), Mul(Integer(-1), Symbol('P', commutative=True))))), Mul(Integer(-1), Symbol('D', commutative=True)), Mul(Integer(-1), Symbol('P', commutative=True), log(Add(Symbol('D', commutative=True), Mul(Integer(-1), Symbol('P', commutative=True))))))", "Mul(Symbol('P', commutative=True), Add(Mul(Integer(-1), Symbol('D', commutative=True)), log(Symbol('P', commutative=True)), Integer(-1)))", "Mul(log(Symbol('P', commutative=True)), cos(Symbol('D', commutative=True)))"]}, {"premise_expression": "M - t", "variable": "t", "positive": "\\frac{t (2 M - t)}{2}", "negatives": ["\\frac{M (M - 2 t)}{2}", "- e^{M - t}", "\\cos{(M - t)}", "e^{M + t}"], "srepr_premise_expression": "Add(Symbol('M', commutative=True), Mul(Integer(-1), Symbol('t', commutative=True)))", "srepr_variable": "Symbol('t', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('t', commutative=True), Add(Mul(Integer(2), Symbol('M', commutative=True)), Mul(Integer(-1), Symbol('t', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('M', commutative=True), Add(Symbol('M', commutative=True), Mul(Integer(-1), Integer(2), Symbol('t', commutative=True))))", "Mul(Integer(-1), exp(Add(Symbol('M', commutative=True), Mul(Integer(-1), Symbol('t', commutative=True)))))", "cos(Add(Symbol('M', commutative=True), Mul(Integer(-1), Symbol('t', commutative=True))))", "exp(Add(Symbol('M', commutative=True), Symbol('t', commutative=True)))"]}, {"premise_expression": "\\log{(\\frac{H}{R})}", "variable": "R", "positive": "R (\\log{(\\frac{H}{R})} + 1)", "negatives": ["H (\\log{(\\frac{H}{R})} - 1)", "\\frac{R^{2} \\log{(H)}}{2}", "\\sin{(H + R)}", "\\frac{R (2 H + R)}{2}"], "srepr_premise_expression": "log(Mul(Symbol('H', commutative=True), Pow(Symbol('R', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('R', commutative=True)", "srepr_positive": "Mul(Symbol('R', commutative=True), Add(log(Mul(Symbol('H', commutative=True), Pow(Symbol('R', commutative=True), Integer(-1)))), Integer(1)))", "srepr_negatives": ["Mul(Symbol('H', commutative=True), Add(log(Mul(Symbol('H', commutative=True), Pow(Symbol('R', commutative=True), Integer(-1)))), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('R', commutative=True), Integer(2)), log(Symbol('H', commutative=True)))", "sin(Add(Symbol('H', commutative=True), Symbol('R', commutative=True)))", "Mul(Rational(1, 2), Symbol('R', commutative=True), Add(Mul(Integer(2), Symbol('H', commutative=True)), Symbol('R', commutative=True)))"]}, {"premise_expression": "- p + \\sin{(f)}", "variable": "p", "positive": "\\frac{p (- p + 2 \\sin{(f)})}{2}", "negatives": ["\\frac{p (p + 2 \\sin{(f)})}{2}", "\\frac{p (2 f - p)}{2}", "- f p - \\cos{(f)}", "\\sin{(f + p)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('p', commutative=True)), sin(Symbol('f', commutative=True)))", "srepr_variable": "Symbol('p', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Mul(Integer(-1), Symbol('p', commutative=True)), Mul(Integer(2), sin(Symbol('f', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Symbol('p', commutative=True), Mul(Integer(2), sin(Symbol('f', commutative=True)))))", "Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Mul(Integer(2), Symbol('f', commutative=True)), Mul(Integer(-1), Symbol('p', commutative=True))))", "Add(Mul(Integer(-1), Symbol('f', commutative=True), Symbol('p', commutative=True)), Mul(Integer(-1), cos(Symbol('f', commutative=True))))", "sin(Add(Symbol('f', commutative=True), Symbol('p', commutative=True)))"]}, {"premise_expression": "e^{\\frac{B}{N}}", "variable": "B", "positive": "N e^{\\frac{B}{N}}", "negatives": ["- N \\cos{(B)}", "\\frac{B^{2} \\log{(N)}}{2}", "B N - \\cos{(B)}", "B (\\log{(B N)} - 1)"], "srepr_premise_expression": "exp(Mul(Symbol('B', commutative=True), Pow(Symbol('N', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('B', commutative=True)", "srepr_positive": "Mul(Symbol('N', commutative=True), exp(Mul(Symbol('B', commutative=True), Pow(Symbol('N', commutative=True), Integer(-1)))))", "srepr_negatives": ["Mul(Integer(-1), Symbol('N', commutative=True), cos(Symbol('B', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('B', commutative=True), Integer(2)), log(Symbol('N', commutative=True)))", "Add(Mul(Symbol('B', commutative=True), Symbol('N', commutative=True)), Mul(Integer(-1), cos(Symbol('B', commutative=True))))", "Mul(Symbol('B', commutative=True), Add(log(Mul(Symbol('B', commutative=True), Symbol('N', commutative=True))), Integer(-1)))"]}, {"premise_expression": "C + X + f", "variable": "f", "positive": "f (C + X + \\frac{f}{2})", "negatives": ["\\frac{f (- 2 C + 2 X + f)}{2}", "\\frac{f (2 C - 2 X + f)}{2}", "\\frac{C (C + 2 X + 2 f)}{2}", "\\frac{X (2 C + X + 2 f)}{2}"], "srepr_premise_expression": "Add(Symbol('C', commutative=True), Symbol('X', commutative=True), Symbol('f', commutative=True))", "srepr_variable": "Symbol('f', commutative=True)", "srepr_positive": "Mul(Symbol('f', commutative=True), Add(Symbol('C', commutative=True), Symbol('X', commutative=True), Mul(Rational(1, 2), Symbol('f', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('C', commutative=True)), Mul(Integer(2), Symbol('X', commutative=True)), Symbol('f', commutative=True)))", "Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Mul(Integer(2), Symbol('C', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('X', commutative=True)), Symbol('f', commutative=True)))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Symbol('C', commutative=True), Mul(Integer(2), Symbol('X', commutative=True)), Mul(Integer(2), Symbol('f', commutative=True))))", "Mul(Rational(1, 2), Symbol('X', commutative=True), Add(Mul(Integer(2), Symbol('C', commutative=True)), Symbol('X', commutative=True), Mul(Integer(2), Symbol('f', commutative=True))))"]}, {"premise_expression": "\\frac{\\cos{(j)}}{S}", "variable": "S", "positive": "\\log{(S)} \\cos{(j)}", "negatives": ["S j - \\cos{(S)}", "- \\cos{(S + j)}", "\\frac{S^{2} \\log{(j)}}{2}", "\\frac{\\sin{(j)}}{S}"], "srepr_premise_expression": "Mul(Pow(Symbol('S', commutative=True), Integer(-1)), cos(Symbol('j', commutative=True)))", "srepr_variable": "Symbol('S', commutative=True)", "srepr_positive": "Mul(log(Symbol('S', commutative=True)), cos(Symbol('j', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('S', commutative=True), Symbol('j', commutative=True)), Mul(Integer(-1), cos(Symbol('S', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('S', commutative=True), Symbol('j', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('S', commutative=True), Integer(2)), log(Symbol('j', commutative=True)))", "Mul(Pow(Symbol('S', commutative=True), Integer(-1)), sin(Symbol('j', commutative=True)))"]}, {"premise_expression": "\\log{(B h)}", "variable": "B", "positive": "B (\\log{(B h)} - 1)", "negatives": ["h (\\log{(B h)} - 1)", "\\frac{B (B + 2 h)}{2}", "- e^{- B + h}", "B h - \\cos{(B)}"], "srepr_premise_expression": "log(Mul(Symbol('B', commutative=True), Symbol('h', commutative=True)))", "srepr_variable": "Symbol('B', commutative=True)", "srepr_positive": "Mul(Symbol('B', commutative=True), Add(log(Mul(Symbol('B', commutative=True), Symbol('h', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('h', commutative=True), Add(log(Mul(Symbol('B', commutative=True), Symbol('h', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('B', commutative=True), Add(Symbol('B', commutative=True), Mul(Integer(2), Symbol('h', commutative=True))))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('B', commutative=True)), Symbol('h', commutative=True))))", "Add(Mul(Symbol('B', commutative=True), Symbol('h', commutative=True)), Mul(Integer(-1), cos(Symbol('B', commutative=True))))"]}, {"premise_expression": "I j", "variable": "j", "positive": "\\frac{I j^{2}}{2}", "negatives": ["\\frac{I^{2} j}{2}", "\\cos{(I - j)}", "\\sin{(I + j)}", "\\log{(j)} \\sin{(I)}"], "srepr_premise_expression": "Mul(Symbol('I', commutative=True), Symbol('j', commutative=True))", "srepr_variable": "Symbol('j', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('I', commutative=True), Pow(Symbol('j', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(2)), Symbol('j', commutative=True))", "cos(Add(Symbol('I', commutative=True), Mul(Integer(-1), Symbol('j', commutative=True))))", "sin(Add(Symbol('I', commutative=True), Symbol('j', commutative=True)))", "Mul(log(Symbol('j', commutative=True)), sin(Symbol('I', commutative=True)))"]}, {"premise_expression": "\\frac{e^{W}}{D}", "variable": "D", "positive": "e^{W} \\log{(D)}", "negatives": ["W^{2} \\log{(D)}", "D (W + \\log{(W)})", "- e^{- D + W}", "- D W + e^{D}"], "srepr_premise_expression": "Mul(Pow(Symbol('D', commutative=True), Integer(-1)), exp(Symbol('W', commutative=True)))", "srepr_variable": "Symbol('D', commutative=True)", "srepr_positive": "Mul(exp(Symbol('W', commutative=True)), log(Symbol('D', commutative=True)))", "srepr_negatives": ["Mul(Pow(Symbol('W', commutative=True), Integer(2)), log(Symbol('D', commutative=True)))", "Mul(Symbol('D', commutative=True), Add(Symbol('W', commutative=True), log(Symbol('W', commutative=True))))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('D', commutative=True)), Symbol('W', commutative=True))))", "Add(Mul(Integer(-1), Symbol('D', commutative=True), Symbol('W', commutative=True)), exp(Symbol('D', commutative=True)))"]}, {"premise_expression": "\\frac{j}{F}", "variable": "j", "positive": "\\frac{j^{2}}{2 F}", "negatives": ["j \\log{(F)}", "j^{2} (\\frac{F}{2} + \\frac{j}{3})", "\\sin{(F + j)}", "- \\sin{(F - j)}"], "srepr_premise_expression": "Mul(Pow(Symbol('F', commutative=True), Integer(-1)), Symbol('j', commutative=True))", "srepr_variable": "Symbol('j', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('F', commutative=True), Integer(-1)), Pow(Symbol('j', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('j', commutative=True), log(Symbol('F', commutative=True)))", "Mul(Pow(Symbol('j', commutative=True), Integer(2)), Add(Mul(Rational(1, 2), Symbol('F', commutative=True)), Mul(Rational(1, 3), Symbol('j', commutative=True))))", "sin(Add(Symbol('F', commutative=True), Symbol('j', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('F', commutative=True), Mul(Integer(-1), Symbol('j', commutative=True)))))"]}, {"premise_expression": "\\frac{\\sin{(c)}}{l}", "variable": "l", "positive": "\\log{(l)} \\sin{(c)}", "negatives": ["\\frac{l^{2} e^{c}}{2}", "- \\frac{\\cos{(c)}}{l}", "\\sin{(c + l)}", "- \\cos{(c + l)}"], "srepr_premise_expression": "Mul(Pow(Symbol('l', commutative=True), Integer(-1)), sin(Symbol('c', commutative=True)))", "srepr_variable": "Symbol('l', commutative=True)", "srepr_positive": "Mul(log(Symbol('l', commutative=True)), sin(Symbol('c', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('l', commutative=True), Integer(2)), exp(Symbol('c', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('l', commutative=True), Integer(-1)), cos(Symbol('c', commutative=True)))", "sin(Add(Symbol('c', commutative=True), Symbol('l', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('c', commutative=True), Symbol('l', commutative=True))))"]}, {"premise_expression": "c - s", "variable": "s", "positive": "\\frac{s (2 c - s)}{2}", "negatives": ["\\frac{s (2 c + s)}{2}", "\\frac{c (c - 2 s)}{2}", "\\frac{s^{2} \\log{(c)}}{2}", "\\frac{s^{2} e^{c}}{2}"], "srepr_premise_expression": "Add(Symbol('c', commutative=True), Mul(Integer(-1), Symbol('s', commutative=True)))", "srepr_variable": "Symbol('s', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('s', commutative=True), Add(Mul(Integer(2), Symbol('c', commutative=True)), Mul(Integer(-1), Symbol('s', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('s', commutative=True), Add(Mul(Integer(2), Symbol('c', commutative=True)), Symbol('s', commutative=True)))", "Mul(Rational(1, 2), Symbol('c', commutative=True), Add(Symbol('c', commutative=True), Mul(Integer(-1), Integer(2), Symbol('s', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('s', commutative=True), Integer(2)), log(Symbol('c', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('s', commutative=True), Integer(2)), exp(Symbol('c', commutative=True)))"]}, {"premise_expression": "\\frac{R - k}{R}", "variable": "R", "positive": "R - k \\log{(R)}", "negatives": ["k - \\frac{k^{2}}{2 R}", "k e^{\\frac{R}{k}}", "R (- k + \\log{(R)} - 1)", "- e^{- R + k}"], "srepr_premise_expression": "Mul(Pow(Symbol('R', commutative=True), Integer(-1)), Add(Symbol('R', commutative=True), Mul(Integer(-1), Symbol('k', commutative=True))))", "srepr_variable": "Symbol('R', commutative=True)", "srepr_positive": "Add(Symbol('R', commutative=True), Mul(Integer(-1), Symbol('k', commutative=True), log(Symbol('R', commutative=True))))", "srepr_negatives": ["Add(Symbol('k', commutative=True), Mul(Integer(-1), Rational(1, 2), Pow(Symbol('R', commutative=True), Integer(-1)), Pow(Symbol('k', commutative=True), Integer(2))))", "Mul(Symbol('k', commutative=True), exp(Mul(Symbol('R', commutative=True), Pow(Symbol('k', commutative=True), Integer(-1)))))", "Mul(Symbol('R', commutative=True), Add(Mul(Integer(-1), Symbol('k', commutative=True)), log(Symbol('R', commutative=True)), Integer(-1)))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('R', commutative=True)), Symbol('k', commutative=True))))"]}, {"premise_expression": "Y j", "variable": "Y", "positive": "\\frac{Y^{2} j}{2}", "negatives": ["\\frac{Y j^{2}}{2}", "\\frac{Y (- Y + 2 j)}{2}", "\\cos{(Y - j)}", "- Y j + e^{Y}"], "srepr_premise_expression": "Mul(Symbol('Y', commutative=True), Symbol('j', commutative=True))", "srepr_variable": "Symbol('Y', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('Y', commutative=True), Integer(2)), Symbol('j', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('Y', commutative=True), Pow(Symbol('j', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('Y', commutative=True), Add(Mul(Integer(-1), Symbol('Y', commutative=True)), Mul(Integer(2), Symbol('j', commutative=True))))", "cos(Add(Symbol('Y', commutative=True), Mul(Integer(-1), Symbol('j', commutative=True))))", "Add(Mul(Integer(-1), Symbol('Y', commutative=True), Symbol('j', commutative=True)), exp(Symbol('Y', commutative=True)))"]}, {"premise_expression": "\\sin{(u - v)}", "variable": "u", "positive": "- \\cos{(u - v)}", "negatives": ["\\cos{(u - v)}", "- \\frac{\\cos{(u)}}{v}", "\\frac{\\sin{(u)}}{v}", "\\frac{u (u + 2 v)}{2}"], "srepr_premise_expression": "sin(Add(Symbol('u', commutative=True), Mul(Integer(-1), Symbol('v', commutative=True))))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('u', commutative=True), Mul(Integer(-1), Symbol('v', commutative=True)))))", "srepr_negatives": ["cos(Add(Symbol('u', commutative=True), Mul(Integer(-1), Symbol('v', commutative=True))))", "Mul(Integer(-1), Pow(Symbol('v', commutative=True), Integer(-1)), cos(Symbol('u', commutative=True)))", "Mul(Pow(Symbol('v', commutative=True), Integer(-1)), sin(Symbol('u', commutative=True)))", "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Symbol('u', commutative=True), Mul(Integer(2), Symbol('v', commutative=True))))"]}, {"premise_expression": "- \\sin{(E - h)}", "variable": "E", "positive": "\\cos{(E - h)}", "negatives": ["- \\cos{(E - h)}", "E", "\\frac{E^{2} h}{2}", "e^{h} \\log{(E)}"], "srepr_premise_expression": "Mul(Integer(-1), sin(Add(Symbol('E', commutative=True), Mul(Integer(-1), Symbol('h', commutative=True)))))", "srepr_variable": "Symbol('E', commutative=True)", "srepr_positive": "cos(Add(Symbol('E', commutative=True), Mul(Integer(-1), Symbol('h', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('E', commutative=True), Mul(Integer(-1), Symbol('h', commutative=True)))))", "Symbol('E', commutative=True)", "Mul(Rational(1, 2), Pow(Symbol('E', commutative=True), Integer(2)), Symbol('h', commutative=True))", "Mul(exp(Symbol('h', commutative=True)), log(Symbol('E', commutative=True)))"]}, {"premise_expression": "- t + e^{N}", "variable": "t", "positive": "\\frac{t (- t + 2 e^{N})}{2}", "negatives": ["\\frac{t (t + 2 \\log{(N)})}{2}", "- N t + e^{N}", "\\frac{t (- 2 N + t)}{2}", "\\frac{t^{2}}{2 N}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('t', commutative=True)), exp(Symbol('N', commutative=True)))", "srepr_variable": "Symbol('t', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('t', commutative=True), Add(Mul(Integer(-1), Symbol('t', commutative=True)), Mul(Integer(2), exp(Symbol('N', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('t', commutative=True), Add(Symbol('t', commutative=True), Mul(Integer(2), log(Symbol('N', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('N', commutative=True), Symbol('t', commutative=True)), exp(Symbol('N', commutative=True)))", "Mul(Rational(1, 2), Symbol('t', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('N', commutative=True)), Symbol('t', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('N', commutative=True), Integer(-1)), Pow(Symbol('t', commutative=True), Integer(2)))"]}, {"premise_expression": "\\frac{\\sin{(w)}}{C}", "variable": "C", "positive": "\\log{(C)} \\sin{(w)}", "negatives": ["C (C - w)", "\\frac{C^{2}}{2 w}", "- \\frac{\\cos{(w)}}{C}", "\\frac{C (C + 2 w)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('C', commutative=True), Integer(-1)), sin(Symbol('w', commutative=True)))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Mul(log(Symbol('C', commutative=True)), sin(Symbol('w', commutative=True)))", "srepr_negatives": ["Mul(Symbol('C', commutative=True), Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('w', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2)), Pow(Symbol('w', commutative=True), Integer(-1)))", "Mul(Integer(-1), Pow(Symbol('C', commutative=True), Integer(-1)), cos(Symbol('w', commutative=True)))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Symbol('C', commutative=True), Mul(Integer(2), Symbol('w', commutative=True))))"]}, {"premise_expression": "I + V - x", "variable": "V", "positive": "V (I + \\frac{V}{2} - x)", "negatives": ["\\frac{V (2 I + V + 2 x)}{2}", "\\frac{I (I + 2 V - 2 x)}{2}", "\\frac{x (2 I + 2 V - x)}{2}", "\\frac{V (2 I - V)}{2 x}"], "srepr_premise_expression": "Add(Symbol('I', commutative=True), Symbol('V', commutative=True), Mul(Integer(-1), Symbol('x', commutative=True)))", "srepr_variable": "Symbol('V', commutative=True)", "srepr_positive": "Mul(Symbol('V', commutative=True), Add(Symbol('I', commutative=True), Mul(Rational(1, 2), Symbol('V', commutative=True)), Mul(Integer(-1), Symbol('x', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('V', commutative=True), Add(Mul(Integer(2), Symbol('I', commutative=True)), Symbol('V', commutative=True), Mul(Integer(2), Symbol('x', commutative=True))))", "Mul(Rational(1, 2), Symbol('I', commutative=True), Add(Symbol('I', commutative=True), Mul(Integer(2), Symbol('V', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('x', commutative=True))))", "Mul(Rational(1, 2), Symbol('x', commutative=True), Add(Mul(Integer(2), Symbol('I', commutative=True)), Mul(Integer(2), Symbol('V', commutative=True)), Mul(Integer(-1), Symbol('x', commutative=True))))", "Mul(Rational(1, 2), Symbol('V', commutative=True), Pow(Symbol('x', commutative=True), Integer(-1)), Add(Mul(Integer(2), Symbol('I', commutative=True)), Mul(Integer(-1), Symbol('V', commutative=True))))"]}, {"premise_expression": "\\log{(D + I)}", "variable": "D", "positive": "D \\log{(D + I)} - D + I \\log{(D + I)}", "negatives": ["D \\log{(- D + I)} - D - I \\log{(D - I)}", "D \\log{(D - I)} - D - I \\log{(D - I)}", "D \\log{(D + I)} + I \\log{(D + I)} - I", "D (- I + \\log{(D)} - 1)"], "srepr_premise_expression": "log(Add(Symbol('D', commutative=True), Symbol('I', commutative=True)))", "srepr_variable": "Symbol('D', commutative=True)", "srepr_positive": "Add(Mul(Symbol('D', commutative=True), log(Add(Symbol('D', commutative=True), Symbol('I', commutative=True)))), Mul(Integer(-1), Symbol('D', commutative=True)), Mul(Symbol('I', commutative=True), log(Add(Symbol('D', commutative=True), Symbol('I', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('D', commutative=True), log(Add(Mul(Integer(-1), Symbol('D', commutative=True)), Symbol('I', commutative=True)))), Mul(Integer(-1), Symbol('D', commutative=True)), Mul(Integer(-1), Symbol('I', commutative=True), log(Add(Symbol('D', commutative=True), Mul(Integer(-1), Symbol('I', commutative=True))))))", "Add(Mul(Symbol('D', commutative=True), log(Add(Symbol('D', commutative=True), Mul(Integer(-1), Symbol('I', commutative=True))))), Mul(Integer(-1), Symbol('D', commutative=True)), Mul(Integer(-1), Symbol('I', commutative=True), log(Add(Symbol('D', commutative=True), Mul(Integer(-1), Symbol('I', commutative=True))))))", "Add(Mul(Symbol('D', commutative=True), log(Add(Symbol('D', commutative=True), Symbol('I', commutative=True)))), Mul(Symbol('I', commutative=True), log(Add(Symbol('D', commutative=True), Symbol('I', commutative=True)))), Mul(Integer(-1), Symbol('I', commutative=True)))", "Mul(Symbol('D', commutative=True), Add(Mul(Integer(-1), Symbol('I', commutative=True)), log(Symbol('D', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\frac{N X}{Z}", "variable": "X", "positive": "\\frac{N X^{2}}{2 Z}", "negatives": ["\\frac{N^{2} X}{2 Z}", "N X \\log{(Z)}", "2 N X Z", "X Z (N + Z)"], "srepr_premise_expression": "Mul(Symbol('N', commutative=True), Symbol('X', commutative=True), Pow(Symbol('Z', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('X', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('N', commutative=True), Pow(Symbol('X', commutative=True), Integer(2)), Pow(Symbol('Z', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('N', commutative=True), Integer(2)), Symbol('X', commutative=True), Pow(Symbol('Z', commutative=True), Integer(-1)))", "Mul(Symbol('N', commutative=True), Symbol('X', commutative=True), log(Symbol('Z', commutative=True)))", "Mul(Integer(2), Symbol('N', commutative=True), Symbol('X', commutative=True), Symbol('Z', commutative=True))", "Mul(Symbol('X', commutative=True), Symbol('Z', commutative=True), Add(Symbol('N', commutative=True), Symbol('Z', commutative=True)))"]}, {"premise_expression": "\\frac{\\log{(k)}}{S}", "variable": "S", "positive": "\\log{(S)} \\log{(k)}", "negatives": ["- k \\cos{(S)}", "- \\cos{(S + k)}", "- S k - \\cos{(S)}", "\\frac{k (\\log{(k)} - 1)}{S}"], "srepr_premise_expression": "Mul(Pow(Symbol('S', commutative=True), Integer(-1)), log(Symbol('k', commutative=True)))", "srepr_variable": "Symbol('S', commutative=True)", "srepr_positive": "Mul(log(Symbol('S', commutative=True)), log(Symbol('k', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Symbol('k', commutative=True), cos(Symbol('S', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('S', commutative=True), Symbol('k', commutative=True))))", "Add(Mul(Integer(-1), Symbol('S', commutative=True), Symbol('k', commutative=True)), Mul(Integer(-1), cos(Symbol('S', commutative=True))))", "Mul(Pow(Symbol('S', commutative=True), Integer(-1)), Symbol('k', commutative=True), Add(log(Symbol('k', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\frac{j}{r}", "variable": "r", "positive": "j \\log{(r)}", "negatives": ["\\frac{j^{2}}{2 r}", "j e^{\\frac{r}{j}}", "\\frac{r^{2} \\log{(j)}}{2}", "\\sin{(j + r)}"], "srepr_premise_expression": "Mul(Symbol('j', commutative=True), Pow(Symbol('r', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('r', commutative=True)", "srepr_positive": "Mul(Symbol('j', commutative=True), log(Symbol('r', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('j', commutative=True), Integer(2)), Pow(Symbol('r', commutative=True), Integer(-1)))", "Mul(Symbol('j', commutative=True), exp(Mul(Pow(Symbol('j', commutative=True), Integer(-1)), Symbol('r', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('r', commutative=True), Integer(2)), log(Symbol('j', commutative=True)))", "sin(Add(Symbol('j', commutative=True), Symbol('r', commutative=True)))"]}, {"premise_expression": "\\cos{(L + N)}", "variable": "L", "positive": "\\sin{(L + N)}", "negatives": ["e^{L - N}", "\\frac{L (L + 2 N)}{2}", "\\frac{L^{2} N}{2}", "\\frac{L^{3} N}{3}"], "srepr_premise_expression": "cos(Add(Symbol('L', commutative=True), Symbol('N', commutative=True)))", "srepr_variable": "Symbol('L', commutative=True)", "srepr_positive": "sin(Add(Symbol('L', commutative=True), Symbol('N', commutative=True)))", "srepr_negatives": ["exp(Add(Symbol('L', commutative=True), Mul(Integer(-1), Symbol('N', commutative=True))))", "Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Symbol('L', commutative=True), Mul(Integer(2), Symbol('N', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(2)), Symbol('N', commutative=True))", "Mul(Rational(1, 3), Pow(Symbol('L', commutative=True), Integer(3)), Symbol('N', commutative=True))"]}, {"premise_expression": "\\cos{(\\frac{Q}{a})}", "variable": "a", "positive": "Q \\operatorname{Si}{(\\frac{Q}{a})} + a \\cos{(\\frac{Q}{a})}", "negatives": ["- Q \\operatorname{Ei}{(\\frac{Q}{a})} + a e^{\\frac{Q}{a}}", "\\frac{a (a + 2 \\log{(Q)})}{2}", "- Q a + \\frac{a^{2}}{2 Q}", "\\log{(Q)} \\log{(a)}"], "srepr_premise_expression": "cos(Mul(Symbol('Q', commutative=True), Pow(Symbol('a', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('a', commutative=True)", "srepr_positive": "Add(Mul(Symbol('Q', commutative=True), Si(Mul(Symbol('Q', commutative=True), Pow(Symbol('a', commutative=True), Integer(-1))))), Mul(Symbol('a', commutative=True), cos(Mul(Symbol('Q', commutative=True), Pow(Symbol('a', commutative=True), Integer(-1))))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('Q', commutative=True), Ei(Mul(Symbol('Q', commutative=True), Pow(Symbol('a', commutative=True), Integer(-1))))), Mul(Symbol('a', commutative=True), exp(Mul(Symbol('Q', commutative=True), Pow(Symbol('a', commutative=True), Integer(-1))))))", "Mul(Rational(1, 2), Symbol('a', commutative=True), Add(Symbol('a', commutative=True), Mul(Integer(2), log(Symbol('Q', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('Q', commutative=True), Symbol('a', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(-1)), Pow(Symbol('a', commutative=True), Integer(2))))", "Mul(log(Symbol('Q', commutative=True)), log(Symbol('a', commutative=True)))"]}, {"premise_expression": "Q + o", "variable": "o", "positive": "\\frac{o (2 Q + o)}{2}", "negatives": ["\\frac{o (2 Q - o)}{2}", "\\frac{Q (Q + 2 o)}{2}", "\\frac{o^{2} \\log{(Q)}}{2}", "- \\sin{(Q - o)}"], "srepr_premise_expression": "Add(Symbol('Q', commutative=True), Symbol('o', commutative=True))", "srepr_variable": "Symbol('o', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Mul(Integer(2), Symbol('Q', commutative=True)), Symbol('o', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Mul(Integer(2), Symbol('Q', commutative=True)), Mul(Integer(-1), Symbol('o', commutative=True))))", "Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Symbol('Q', commutative=True), Mul(Integer(2), Symbol('o', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('o', commutative=True), Integer(2)), log(Symbol('Q', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('Q', commutative=True), Mul(Integer(-1), Symbol('o', commutative=True)))))"]}, {"premise_expression": "A y", "variable": "y", "positive": "\\frac{A y^{2}}{2}", "negatives": ["\\frac{A^{2} y}{2}", "A \\log{(y)}", "\\frac{y (2 A + y)}{2}", "- A y + \\sin{(y)}"], "srepr_premise_expression": "Mul(Symbol('A', commutative=True), Symbol('y', commutative=True))", "srepr_variable": "Symbol('y', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('A', commutative=True), Pow(Symbol('y', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2)), Symbol('y', commutative=True))", "Mul(Symbol('A', commutative=True), log(Symbol('y', commutative=True)))", "Mul(Rational(1, 2), Symbol('y', commutative=True), Add(Mul(Integer(2), Symbol('A', commutative=True)), Symbol('y', commutative=True)))", "Add(Mul(Integer(-1), Symbol('A', commutative=True), Symbol('y', commutative=True)), sin(Symbol('y', commutative=True)))"]}, {"premise_expression": "- w + \\sin{(P)}", "variable": "w", "positive": "\\frac{w (- w + 2 \\sin{(P)})}{2}", "negatives": ["\\frac{w (w + 2 \\sin{(P)})}{2}", "P w + \\sin{(w)}", "\\frac{w^{2} e^{P}}{2}", "- P w - \\cos{(P)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('w', commutative=True)), sin(Symbol('P', commutative=True)))", "srepr_variable": "Symbol('w', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('w', commutative=True), Add(Mul(Integer(-1), Symbol('w', commutative=True)), Mul(Integer(2), sin(Symbol('P', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('w', commutative=True), Add(Symbol('w', commutative=True), Mul(Integer(2), sin(Symbol('P', commutative=True)))))", "Add(Mul(Symbol('P', commutative=True), Symbol('w', commutative=True)), sin(Symbol('w', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('w', commutative=True), Integer(2)), exp(Symbol('P', commutative=True)))", "Add(Mul(Integer(-1), Symbol('P', commutative=True), Symbol('w', commutative=True)), Mul(Integer(-1), cos(Symbol('P', commutative=True))))"]}, {"premise_expression": "\\cos{(\\frac{f}{Y})}", "variable": "Y", "positive": "Y \\cos{(\\frac{f}{Y})} + f \\operatorname{Si}{(\\frac{f}{Y})}", "negatives": ["\\log{(Y)} \\sin{(f)}", "Y (\\log{(Y f)} - 1)", "\\log{(Y)} \\cos{(f)}", "e^{Y + f}"], "srepr_premise_expression": "cos(Mul(Pow(Symbol('Y', commutative=True), Integer(-1)), Symbol('f', commutative=True)))", "srepr_variable": "Symbol('Y', commutative=True)", "srepr_positive": "Add(Mul(Symbol('Y', commutative=True), cos(Mul(Pow(Symbol('Y', commutative=True), Integer(-1)), Symbol('f', commutative=True)))), Mul(Symbol('f', commutative=True), Si(Mul(Pow(Symbol('Y', commutative=True), Integer(-1)), Symbol('f', commutative=True)))))", "srepr_negatives": ["Mul(log(Symbol('Y', commutative=True)), sin(Symbol('f', commutative=True)))", "Mul(Symbol('Y', commutative=True), Add(log(Mul(Symbol('Y', commutative=True), Symbol('f', commutative=True))), Integer(-1)))", "Mul(log(Symbol('Y', commutative=True)), cos(Symbol('f', commutative=True)))", "exp(Add(Symbol('Y', commutative=True), Symbol('f', commutative=True)))"]}, {"premise_expression": "F S", "variable": "F", "positive": "\\frac{F^{2} S}{2}", "negatives": ["\\frac{F S^{2}}{2}", "\\frac{F^{2} \\sin{(S)}}{2}", "F (2 S)^{S}", "\\frac{F (F + 2 S)}{2}"], "srepr_premise_expression": "Mul(Symbol('F', commutative=True), Symbol('S', commutative=True))", "srepr_variable": "Symbol('F', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('F', commutative=True), Integer(2)), Symbol('S', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('F', commutative=True), Pow(Symbol('S', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('F', commutative=True), Integer(2)), sin(Symbol('S', commutative=True)))", "Mul(Symbol('F', commutative=True), Pow(Mul(Integer(2), Symbol('S', commutative=True)), Symbol('S', commutative=True)))", "Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Symbol('F', commutative=True), Mul(Integer(2), Symbol('S', commutative=True))))"]}, {"premise_expression": "- f + n", "variable": "f", "positive": "\\frac{f (- f + 2 n)}{2}", "negatives": ["\\frac{n (- 2 f + n)}{2}", "- e^{- f + n}", "f (- n + \\log{(f)} - 1)", "n \\log{(f)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('f', commutative=True)), Symbol('n', commutative=True))", "srepr_variable": "Symbol('f', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Mul(Integer(-1), Symbol('f', commutative=True)), Mul(Integer(2), Symbol('n', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('n', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('f', commutative=True)), Symbol('n', commutative=True)))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('f', commutative=True)), Symbol('n', commutative=True))))", "Mul(Symbol('f', commutative=True), Add(Mul(Integer(-1), Symbol('n', commutative=True)), log(Symbol('f', commutative=True)), Integer(-1)))", "Mul(Symbol('n', commutative=True), log(Symbol('f', commutative=True)))"]}, {"premise_expression": "l + e^{K}", "variable": "l", "positive": "\\frac{l (l + 2 e^{K})}{2}", "negatives": ["\\frac{l (l + 2 \\log{(K)})}{2}", "\\frac{l (- l + 2 \\cos{(K)})}{2}", "K l + e^{K}", "\\frac{l (2 K + l)}{2}"], "srepr_premise_expression": "Add(Symbol('l', commutative=True), exp(Symbol('K', commutative=True)))", "srepr_variable": "Symbol('l', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('l', commutative=True), Add(Symbol('l', commutative=True), Mul(Integer(2), exp(Symbol('K', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('l', commutative=True), Add(Symbol('l', commutative=True), Mul(Integer(2), log(Symbol('K', commutative=True)))))", "Mul(Rational(1, 2), Symbol('l', commutative=True), Add(Mul(Integer(-1), Symbol('l', commutative=True)), Mul(Integer(2), cos(Symbol('K', commutative=True)))))", "Add(Mul(Symbol('K', commutative=True), Symbol('l', commutative=True)), exp(Symbol('K', commutative=True)))", "Mul(Rational(1, 2), Symbol('l', commutative=True), Add(Mul(Integer(2), Symbol('K', commutative=True)), Symbol('l', commutative=True)))"]}, {"premise_expression": "\\cos{(W + x)}", "variable": "W", "positive": "\\sin{(W + x)}", "negatives": ["- \\cos{(W + x)}", "\\frac{W (W + 2 x)}{2}", "x e^{\\frac{W}{x}}", "x \\log{(W)}"], "srepr_premise_expression": "cos(Add(Symbol('W', commutative=True), Symbol('x', commutative=True)))", "srepr_variable": "Symbol('W', commutative=True)", "srepr_positive": "sin(Add(Symbol('W', commutative=True), Symbol('x', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('W', commutative=True), Symbol('x', commutative=True))))", "Mul(Rational(1, 2), Symbol('W', commutative=True), Add(Symbol('W', commutative=True), Mul(Integer(2), Symbol('x', commutative=True))))", "Mul(Symbol('x', commutative=True), exp(Mul(Symbol('W', commutative=True), Pow(Symbol('x', commutative=True), Integer(-1)))))", "Mul(Symbol('x', commutative=True), log(Symbol('W', commutative=True)))"]}, {"premise_expression": "b p", "variable": "b", "positive": "\\frac{b^{2} p}{2}", "negatives": ["\\frac{b p^{2}}{2}", "\\frac{b^{2} e^{p}}{2}", "\\frac{b^{2}}{2 p}", "\\cos{(b - p)}"], "srepr_premise_expression": "Mul(Symbol('b', commutative=True), Symbol('p', commutative=True))", "srepr_variable": "Symbol('b', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('b', commutative=True), Integer(2)), Symbol('p', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('b', commutative=True), Pow(Symbol('p', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('b', commutative=True), Integer(2)), exp(Symbol('p', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('b', commutative=True), Integer(2)), Pow(Symbol('p', commutative=True), Integer(-1)))", "cos(Add(Symbol('b', commutative=True), Mul(Integer(-1), Symbol('p', commutative=True))))"]}, {"premise_expression": "h w y", "variable": "h", "positive": "\\frac{h^{2} w y}{2}", "negatives": ["\\frac{h w^{2} y}{2}", "\\frac{h^{2} y^{w}}{2}", "\\frac{h w y^{2}}{2}", "\\frac{h^{2} (- w + y)}{2}"], "srepr_premise_expression": "Mul(Symbol('h', commutative=True), Symbol('w', commutative=True), Symbol('y', commutative=True))", "srepr_variable": "Symbol('h', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('h', commutative=True), Integer(2)), Symbol('w', commutative=True), Symbol('y', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('h', commutative=True), Pow(Symbol('w', commutative=True), Integer(2)), Symbol('y', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('h', commutative=True), Integer(2)), Pow(Symbol('y', commutative=True), Symbol('w', commutative=True)))", "Mul(Rational(1, 2), Symbol('h', commutative=True), Symbol('w', commutative=True), Pow(Symbol('y', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('h', commutative=True), Integer(2)), Add(Mul(Integer(-1), Symbol('w', commutative=True)), Symbol('y', commutative=True)))"]}, {"premise_expression": "\\log{(c^{g})}", "variable": "g", "positive": "\\frac{g^{2} \\log{(c)}}{2}", "negatives": ["\\frac{g^{2} \\sin{(c)}}{2}", "\\frac{g (g + 2 \\log{(c)})}{2}", "\\frac{g (2 c - g)}{2}", "\\frac{g \\sin{(c)}}{c}"], "srepr_premise_expression": "log(Pow(Symbol('c', commutative=True), Symbol('g', commutative=True)))", "srepr_variable": "Symbol('g', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('g', commutative=True), Integer(2)), log(Symbol('c', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('g', commutative=True), Integer(2)), sin(Symbol('c', commutative=True)))", "Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Symbol('g', commutative=True), Mul(Integer(2), log(Symbol('c', commutative=True)))))", "Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Mul(Integer(2), Symbol('c', commutative=True)), Mul(Integer(-1), Symbol('g', commutative=True))))", "Mul(Pow(Symbol('c', commutative=True), Integer(-1)), Symbol('g', commutative=True), sin(Symbol('c', commutative=True)))"]}, {"premise_expression": "- D + g", "variable": "g", "positive": "\\frac{g (- 2 D + g)}{2}", "negatives": ["\\frac{D (- D + 2 g)}{2}", "\\frac{g^{2} e^{D}}{2}", "- \\frac{\\cos{(g)}}{D}", "- D g + e^{g}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('D', commutative=True)), Symbol('g', commutative=True))", "srepr_variable": "Symbol('g', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('D', commutative=True)), Symbol('g', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('D', commutative=True), Add(Mul(Integer(-1), Symbol('D', commutative=True)), Mul(Integer(2), Symbol('g', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('g', commutative=True), Integer(2)), exp(Symbol('D', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('D', commutative=True), Integer(-1)), cos(Symbol('g', commutative=True)))", "Add(Mul(Integer(-1), Symbol('D', commutative=True), Symbol('g', commutative=True)), exp(Symbol('g', commutative=True)))"]}, {"premise_expression": "\\log{(A - U)}", "variable": "U", "positive": "- A \\log{(- A + U)} + U \\log{(A - U)} - U", "negatives": ["A \\log{(A - U)} - A - U \\log{(A - U)}", "\\frac{U (- U + 2 e^{A})}{2}", "- A U + \\sin{(U)}", "\\frac{U (U + 2 e^{A})}{2}"], "srepr_premise_expression": "log(Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('U', commutative=True))))", "srepr_variable": "Symbol('U', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('A', commutative=True), log(Add(Mul(Integer(-1), Symbol('A', commutative=True)), Symbol('U', commutative=True)))), Mul(Symbol('U', commutative=True), log(Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('U', commutative=True))))), Mul(Integer(-1), Symbol('U', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('A', commutative=True), log(Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('U', commutative=True))))), Mul(Integer(-1), Symbol('A', commutative=True)), Mul(Integer(-1), Symbol('U', commutative=True), log(Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('U', commutative=True))))))", "Mul(Rational(1, 2), Symbol('U', commutative=True), Add(Mul(Integer(-1), Symbol('U', commutative=True)), Mul(Integer(2), exp(Symbol('A', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('A', commutative=True), Symbol('U', commutative=True)), sin(Symbol('U', commutative=True)))", "Mul(Rational(1, 2), Symbol('U', commutative=True), Add(Symbol('U', commutative=True), Mul(Integer(2), exp(Symbol('A', commutative=True)))))"]}, {"premise_expression": "b - p", "variable": "p", "positive": "\\frac{p (2 b - p)}{2}", "negatives": ["\\frac{b (b - 2 p)}{2}", "\\frac{p (p + 2 e^{b})}{2}", "\\frac{p (p + 2 \\log{(b)})}{2}", "- \\frac{\\cos{(p)}}{b}"], "srepr_premise_expression": "Add(Symbol('b', commutative=True), Mul(Integer(-1), Symbol('p', commutative=True)))", "srepr_variable": "Symbol('p', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Mul(Integer(2), Symbol('b', commutative=True)), Mul(Integer(-1), Symbol('p', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('b', commutative=True), Add(Symbol('b', commutative=True), Mul(Integer(-1), Integer(2), Symbol('p', commutative=True))))", "Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Symbol('p', commutative=True), Mul(Integer(2), exp(Symbol('b', commutative=True)))))", "Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Symbol('p', commutative=True), Mul(Integer(2), log(Symbol('b', commutative=True)))))", "Mul(Integer(-1), Pow(Symbol('b', commutative=True), Integer(-1)), cos(Symbol('p', commutative=True)))"]}, {"premise_expression": "\\frac{g}{r}", "variable": "g", "positive": "\\frac{g^{2}}{2 r}", "negatives": ["g \\log{(r)}", "\\frac{g (g - 2 r)}{2}", "\\frac{g^{2} e^{r}}{2}", "\\frac{\\sin{(g)}}{r}"], "srepr_premise_expression": "Mul(Symbol('g', commutative=True), Pow(Symbol('r', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('g', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('g', commutative=True), Integer(2)), Pow(Symbol('r', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('g', commutative=True), log(Symbol('r', commutative=True)))", "Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Symbol('g', commutative=True), Mul(Integer(-1), Integer(2), Symbol('r', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('g', commutative=True), Integer(2)), exp(Symbol('r', commutative=True)))", "Mul(Pow(Symbol('r', commutative=True), Integer(-1)), sin(Symbol('g', commutative=True)))"]}, {"premise_expression": "Z \\cos{(n)}", "variable": "n", "positive": "Z \\sin{(n)}", "negatives": ["- Z n + \\sin{(n)}", "Z n + e^{n}", "\\frac{Z^{2} \\cos{(n)}}{2}", "- \\cos{(Z - n)}"], "srepr_premise_expression": "Mul(Symbol('Z', commutative=True), cos(Symbol('n', commutative=True)))", "srepr_variable": "Symbol('n', commutative=True)", "srepr_positive": "Mul(Symbol('Z', commutative=True), sin(Symbol('n', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('Z', commutative=True), Symbol('n', commutative=True)), sin(Symbol('n', commutative=True)))", "Add(Mul(Symbol('Z', commutative=True), Symbol('n', commutative=True)), exp(Symbol('n', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('Z', commutative=True), Integer(2)), cos(Symbol('n', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('Z', commutative=True), Mul(Integer(-1), Symbol('n', commutative=True)))))"]}, {"premise_expression": "\\frac{k}{H Y}", "variable": "k", "positive": "\\frac{k^{2}}{2 H Y}", "negatives": ["\\frac{Y k^{2}}{2 H}", "\\frac{k \\log{(H)}}{Y}", "\\frac{k \\log{(Y)}}{H}", "- H k + \\frac{k^{2}}{2 Y}"], "srepr_premise_expression": "Mul(Pow(Symbol('H', commutative=True), Integer(-1)), Pow(Symbol('Y', commutative=True), Integer(-1)), Symbol('k', commutative=True))", "srepr_variable": "Symbol('k', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('H', commutative=True), Integer(-1)), Pow(Symbol('Y', commutative=True), Integer(-1)), Pow(Symbol('k', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('H', commutative=True), Integer(-1)), Symbol('Y', commutative=True), Pow(Symbol('k', commutative=True), Integer(2)))", "Mul(Pow(Symbol('Y', commutative=True), Integer(-1)), Symbol('k', commutative=True), log(Symbol('H', commutative=True)))", "Mul(Pow(Symbol('H', commutative=True), Integer(-1)), Symbol('k', commutative=True), log(Symbol('Y', commutative=True)))", "Add(Mul(Integer(-1), Symbol('H', commutative=True), Symbol('k', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('Y', commutative=True), Integer(-1)), Pow(Symbol('k', commutative=True), Integer(2))))"]}, {"premise_expression": "z \\log{(n)}", "variable": "n", "positive": "n z (\\log{(n)} - 1)", "negatives": ["\\frac{z^{2} \\log{(n)}}{2}", "\\frac{n^{2} \\log{(z)}}{2}", "n z + \\sin{(n)}", "e^{z} \\log{(n)}"], "srepr_premise_expression": "Mul(Symbol('z', commutative=True), log(Symbol('n', commutative=True)))", "srepr_variable": "Symbol('n', commutative=True)", "srepr_positive": "Mul(Symbol('n', commutative=True), Symbol('z', commutative=True), Add(log(Symbol('n', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('z', commutative=True), Integer(2)), log(Symbol('n', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('n', commutative=True), Integer(2)), log(Symbol('z', commutative=True)))", "Add(Mul(Symbol('n', commutative=True), Symbol('z', commutative=True)), sin(Symbol('n', commutative=True)))", "Mul(exp(Symbol('z', commutative=True)), log(Symbol('n', commutative=True)))"]}, {"premise_expression": "u (R + U)", "variable": "R", "positive": "\\frac{R u (R + 2 U)}{2}", "negatives": ["\\frac{u^{2} (R + U)}{2}", "\\frac{U u (2 R + U)}{2}", "\\frac{R (- R + 2 u^{U})}{2}", "\\frac{R (R + 2 u)}{2 U}"], "srepr_premise_expression": "Mul(Symbol('u', commutative=True), Add(Symbol('R', commutative=True), Symbol('U', commutative=True)))", "srepr_variable": "Symbol('R', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('R', commutative=True), Symbol('u', commutative=True), Add(Symbol('R', commutative=True), Mul(Integer(2), Symbol('U', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('u', commutative=True), Integer(2)), Add(Symbol('R', commutative=True), Symbol('U', commutative=True)))", "Mul(Rational(1, 2), Symbol('U', commutative=True), Symbol('u', commutative=True), Add(Mul(Integer(2), Symbol('R', commutative=True)), Symbol('U', commutative=True)))", "Mul(Rational(1, 2), Symbol('R', commutative=True), Add(Mul(Integer(-1), Symbol('R', commutative=True)), Mul(Integer(2), Pow(Symbol('u', commutative=True), Symbol('U', commutative=True)))))", "Mul(Rational(1, 2), Symbol('R', commutative=True), Pow(Symbol('U', commutative=True), Integer(-1)), Add(Symbol('R', commutative=True), Mul(Integer(2), Symbol('u', commutative=True))))"]}, {"premise_expression": "\\log{(K Z)}", "variable": "Z", "positive": "Z (\\log{(K Z)} - 1)", "negatives": ["K (\\log{(K Z)} - 1)", "- e^{K - Z}", "K e^{\\frac{Z}{K}}", "\\frac{Z (Z + 2 \\cos{(K)})}{2}"], "srepr_premise_expression": "log(Mul(Symbol('K', commutative=True), Symbol('Z', commutative=True)))", "srepr_variable": "Symbol('Z', commutative=True)", "srepr_positive": "Mul(Symbol('Z', commutative=True), Add(log(Mul(Symbol('K', commutative=True), Symbol('Z', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('K', commutative=True), Add(log(Mul(Symbol('K', commutative=True), Symbol('Z', commutative=True))), Integer(-1)))", "Mul(Integer(-1), exp(Add(Symbol('K', commutative=True), Mul(Integer(-1), Symbol('Z', commutative=True)))))", "Mul(Symbol('K', commutative=True), exp(Mul(Pow(Symbol('K', commutative=True), Integer(-1)), Symbol('Z', commutative=True))))", "Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Symbol('Z', commutative=True), Mul(Integer(2), cos(Symbol('K', commutative=True)))))"]}, {"premise_expression": "\\cos{(G + N)}", "variable": "G", "positive": "\\sin{(G + N)}", "negatives": ["\\frac{G (G - 2 N)}{2}", "G (\\log{(\\frac{G}{N})} - 1)", "\\frac{G^{2} \\log{(N)}}{2}", "\\frac{G^{2} \\sin{(N)}}{2}"], "srepr_premise_expression": "cos(Add(Symbol('G', commutative=True), Symbol('N', commutative=True)))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "sin(Add(Symbol('G', commutative=True), Symbol('N', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Symbol('G', commutative=True), Mul(Integer(-1), Integer(2), Symbol('N', commutative=True))))", "Mul(Symbol('G', commutative=True), Add(log(Mul(Symbol('G', commutative=True), Pow(Symbol('N', commutative=True), Integer(-1)))), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(2)), log(Symbol('N', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(2)), sin(Symbol('N', commutative=True)))"]}, {"premise_expression": "- I + N", "variable": "N", "positive": "\\frac{N (- 2 I + N)}{2}", "negatives": ["\\frac{N (2 I + N)}{2}", "\\frac{N (2 I - N)}{2}", "\\frac{I (- I + 2 N)}{2}", "\\sin{(I + N)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('I', commutative=True)), Symbol('N', commutative=True))", "srepr_variable": "Symbol('N', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('I', commutative=True)), Symbol('N', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Mul(Integer(2), Symbol('I', commutative=True)), Symbol('N', commutative=True)))", "Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Mul(Integer(2), Symbol('I', commutative=True)), Mul(Integer(-1), Symbol('N', commutative=True))))", "Mul(Rational(1, 2), Symbol('I', commutative=True), Add(Mul(Integer(-1), Symbol('I', commutative=True)), Mul(Integer(2), Symbol('N', commutative=True))))", "sin(Add(Symbol('I', commutative=True), Symbol('N', commutative=True)))"]}, {"premise_expression": "I + K + a", "variable": "K", "positive": "K (I + \\frac{K}{2} + a)", "negatives": ["\\frac{K (2 I - K + 2 a)}{2}", "\\frac{I (I + 2 K + 2 a)}{2}", "\\frac{a (2 I + 2 K + a)}{2}", "\\frac{K (2 I + K)}{2 a}"], "srepr_premise_expression": "Add(Symbol('I', commutative=True), Symbol('K', commutative=True), Symbol('a', commutative=True))", "srepr_variable": "Symbol('K', commutative=True)", "srepr_positive": "Mul(Symbol('K', commutative=True), Add(Symbol('I', commutative=True), Mul(Rational(1, 2), Symbol('K', commutative=True)), Symbol('a', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Mul(Integer(2), Symbol('I', commutative=True)), Mul(Integer(-1), Symbol('K', commutative=True)), Mul(Integer(2), Symbol('a', commutative=True))))", "Mul(Rational(1, 2), Symbol('I', commutative=True), Add(Symbol('I', commutative=True), Mul(Integer(2), Symbol('K', commutative=True)), Mul(Integer(2), Symbol('a', commutative=True))))", "Mul(Rational(1, 2), Symbol('a', commutative=True), Add(Mul(Integer(2), Symbol('I', commutative=True)), Mul(Integer(2), Symbol('K', commutative=True)), Symbol('a', commutative=True)))", "Mul(Rational(1, 2), Symbol('K', commutative=True), Pow(Symbol('a', commutative=True), Integer(-1)), Add(Mul(Integer(2), Symbol('I', commutative=True)), Symbol('K', commutative=True)))"]}, {"premise_expression": "\\cos{(W - c)}", "variable": "c", "positive": "- \\sin{(W - c)}", "negatives": ["\\sin{(W - c)}", "\\cos{(W - c)}", "c \\sin{(2 W)}", "W \\log{(c)}"], "srepr_premise_expression": "cos(Add(Symbol('W', commutative=True), Mul(Integer(-1), Symbol('c', commutative=True))))", "srepr_variable": "Symbol('c', commutative=True)", "srepr_positive": "Mul(Integer(-1), sin(Add(Symbol('W', commutative=True), Mul(Integer(-1), Symbol('c', commutative=True)))))", "srepr_negatives": ["sin(Add(Symbol('W', commutative=True), Mul(Integer(-1), Symbol('c', commutative=True))))", "cos(Add(Symbol('W', commutative=True), Mul(Integer(-1), Symbol('c', commutative=True))))", "Mul(Symbol('c', commutative=True), sin(Mul(Integer(2), Symbol('W', commutative=True))))", "Mul(Symbol('W', commutative=True), log(Symbol('c', commutative=True)))"]}, {"premise_expression": "\\log{(K + l)}", "variable": "K", "positive": "K \\log{(K + l)} - K + l \\log{(K + l)}", "negatives": ["K \\log{(K + l)} + l \\log{(K + l)} - l", "\\frac{K (- K + 2 l)}{2}", "\\frac{K (- K + 2 e^{l})}{2}", "\\frac{K (K + 2 \\sin{(l)})}{2}"], "srepr_premise_expression": "log(Add(Symbol('K', commutative=True), Symbol('l', commutative=True)))", "srepr_variable": "Symbol('K', commutative=True)", "srepr_positive": "Add(Mul(Symbol('K', commutative=True), log(Add(Symbol('K', commutative=True), Symbol('l', commutative=True)))), Mul(Integer(-1), Symbol('K', commutative=True)), Mul(Symbol('l', commutative=True), log(Add(Symbol('K', commutative=True), Symbol('l', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('K', commutative=True), log(Add(Symbol('K', commutative=True), Symbol('l', commutative=True)))), Mul(Symbol('l', commutative=True), log(Add(Symbol('K', commutative=True), Symbol('l', commutative=True)))), Mul(Integer(-1), Symbol('l', commutative=True)))", "Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Mul(Integer(-1), Symbol('K', commutative=True)), Mul(Integer(2), Symbol('l', commutative=True))))", "Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Mul(Integer(-1), Symbol('K', commutative=True)), Mul(Integer(2), exp(Symbol('l', commutative=True)))))", "Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Symbol('K', commutative=True), Mul(Integer(2), sin(Symbol('l', commutative=True)))))"]}, {"premise_expression": "- D + \\cos{(y)}", "variable": "D", "positive": "\\frac{D (- D + 2 \\cos{(y)})}{2}", "negatives": ["\\frac{D (- D + 2 \\log{(y)})}{2}", "\\frac{D (- D + 2 e^{y})}{2}", "\\frac{D (D + 2 e^{y})}{2}", "\\frac{D (D - 2 y)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('D', commutative=True)), cos(Symbol('y', commutative=True)))", "srepr_variable": "Symbol('D', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('D', commutative=True), Add(Mul(Integer(-1), Symbol('D', commutative=True)), Mul(Integer(2), cos(Symbol('y', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('D', commutative=True), Add(Mul(Integer(-1), Symbol('D', commutative=True)), Mul(Integer(2), log(Symbol('y', commutative=True)))))", "Mul(Rational(1, 2), Symbol('D', commutative=True), Add(Mul(Integer(-1), Symbol('D', commutative=True)), Mul(Integer(2), exp(Symbol('y', commutative=True)))))", "Mul(Rational(1, 2), Symbol('D', commutative=True), Add(Symbol('D', commutative=True), Mul(Integer(2), exp(Symbol('y', commutative=True)))))", "Mul(Rational(1, 2), Symbol('D', commutative=True), Add(Symbol('D', commutative=True), Mul(Integer(-1), Integer(2), Symbol('y', commutative=True))))"]}, {"premise_expression": "\\frac{l}{m}", "variable": "m", "positive": "l \\log{(m)}", "negatives": ["l e^{m}", "\\frac{l^{2}}{2 m}", "l m - \\cos{(m)}", "\\log{(m)} \\sin{(l)}"], "srepr_premise_expression": "Mul(Symbol('l', commutative=True), Pow(Symbol('m', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('m', commutative=True)", "srepr_positive": "Mul(Symbol('l', commutative=True), log(Symbol('m', commutative=True)))", "srepr_negatives": ["Mul(Symbol('l', commutative=True), exp(Symbol('m', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('l', commutative=True), Integer(2)), Pow(Symbol('m', commutative=True), Integer(-1)))", "Add(Mul(Symbol('l', commutative=True), Symbol('m', commutative=True)), Mul(Integer(-1), cos(Symbol('m', commutative=True))))", "Mul(log(Symbol('m', commutative=True)), sin(Symbol('l', commutative=True)))"]}, {"premise_expression": "T + X + n", "variable": "T", "positive": "T (\\frac{T}{2} + X + n)", "negatives": ["\\frac{T (T - 2 X + 2 n)}{2}", "\\frac{n (2 T + 2 X + n)}{2}", "\\frac{X (2 T + X + 2 n)}{2}", "\\frac{T^{2} (- X + n)}{2}"], "srepr_premise_expression": "Add(Symbol('T', commutative=True), Symbol('X', commutative=True), Symbol('n', commutative=True))", "srepr_variable": "Symbol('T', commutative=True)", "srepr_positive": "Mul(Symbol('T', commutative=True), Add(Mul(Rational(1, 2), Symbol('T', commutative=True)), Symbol('X', commutative=True), Symbol('n', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('T', commutative=True), Add(Symbol('T', commutative=True), Mul(Integer(-1), Integer(2), Symbol('X', commutative=True)), Mul(Integer(2), Symbol('n', commutative=True))))", "Mul(Rational(1, 2), Symbol('n', commutative=True), Add(Mul(Integer(2), Symbol('T', commutative=True)), Mul(Integer(2), Symbol('X', commutative=True)), Symbol('n', commutative=True)))", "Mul(Rational(1, 2), Symbol('X', commutative=True), Add(Mul(Integer(2), Symbol('T', commutative=True)), Symbol('X', commutative=True), Mul(Integer(2), Symbol('n', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('T', commutative=True), Integer(2)), Add(Mul(Integer(-1), Symbol('X', commutative=True)), Symbol('n', commutative=True)))"]}, {"premise_expression": "\\cos{(A + R)}", "variable": "A", "positive": "\\sin{(A + R)}", "negatives": ["A R - \\cos{(A)}", "A (\\log{(\\frac{A}{R})} - 1)", "A (- R + \\log{(A)} - 1)", "\\int \\cos^{R}{(A)} dA"], "srepr_premise_expression": "cos(Add(Symbol('A', commutative=True), Symbol('R', commutative=True)))", "srepr_variable": "Symbol('A', commutative=True)", "srepr_positive": "sin(Add(Symbol('A', commutative=True), Symbol('R', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('A', commutative=True), Symbol('R', commutative=True)), Mul(Integer(-1), cos(Symbol('A', commutative=True))))", "Mul(Symbol('A', commutative=True), Add(log(Mul(Symbol('A', commutative=True), Pow(Symbol('R', commutative=True), Integer(-1)))), Integer(-1)))", "Mul(Symbol('A', commutative=True), Add(Mul(Integer(-1), Symbol('R', commutative=True)), log(Symbol('A', commutative=True)), Integer(-1)))", "Integral(Pow(cos(Symbol('A', commutative=True)), Symbol('R', commutative=True)), Tuple(Symbol('A', commutative=True)))"]}, {"premise_expression": "\\cos{(P - w)}", "variable": "w", "positive": "- \\sin{(P - w)}", "negatives": ["\\sin{(P - w)}", "\\sin{(P + w)}", "\\frac{P w (w - 2)}{2}", "w (\\log{(P w)} - 1)"], "srepr_premise_expression": "cos(Add(Symbol('P', commutative=True), Mul(Integer(-1), Symbol('w', commutative=True))))", "srepr_variable": "Symbol('w', commutative=True)", "srepr_positive": "Mul(Integer(-1), sin(Add(Symbol('P', commutative=True), Mul(Integer(-1), Symbol('w', commutative=True)))))", "srepr_negatives": ["sin(Add(Symbol('P', commutative=True), Mul(Integer(-1), Symbol('w', commutative=True))))", "sin(Add(Symbol('P', commutative=True), Symbol('w', commutative=True)))", "Mul(Rational(1, 2), Symbol('P', commutative=True), Symbol('w', commutative=True), Add(Symbol('w', commutative=True), Integer(-2)))", "Mul(Symbol('w', commutative=True), Add(log(Mul(Symbol('P', commutative=True), Symbol('w', commutative=True))), Integer(-1)))"]}, {"premise_expression": "- X + \\log{(G)}", "variable": "X", "positive": "\\frac{X (- X + 2 \\log{(G)})}{2}", "negatives": ["\\frac{X (- X + 2 \\cos{(G)})}{2}", "\\frac{X^{2} \\log{(G)}}{2}", "G (- X + \\log{(G)} - 1)", "G X + \\sin{(X)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('X', commutative=True)), log(Symbol('G', commutative=True)))", "srepr_variable": "Symbol('X', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('X', commutative=True), Add(Mul(Integer(-1), Symbol('X', commutative=True)), Mul(Integer(2), log(Symbol('G', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('X', commutative=True), Add(Mul(Integer(-1), Symbol('X', commutative=True)), Mul(Integer(2), cos(Symbol('G', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('X', commutative=True), Integer(2)), log(Symbol('G', commutative=True)))", "Mul(Symbol('G', commutative=True), Add(Mul(Integer(-1), Symbol('X', commutative=True)), log(Symbol('G', commutative=True)), Integer(-1)))", "Add(Mul(Symbol('G', commutative=True), Symbol('X', commutative=True)), sin(Symbol('X', commutative=True)))"]}, {"premise_expression": "P o", "variable": "P", "positive": "\\frac{P^{2} o}{2}", "negatives": ["\\frac{P o^{2}}{2}", "o \\log{(P)}", "o e^{P}", "P (e^{o})^{o}"], "srepr_premise_expression": "Mul(Symbol('P', commutative=True), Symbol('o', commutative=True))", "srepr_variable": "Symbol('P', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2)), Symbol('o', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('P', commutative=True), Pow(Symbol('o', commutative=True), Integer(2)))", "Mul(Symbol('o', commutative=True), log(Symbol('P', commutative=True)))", "Mul(Symbol('o', commutative=True), exp(Symbol('P', commutative=True)))", "Mul(Symbol('P', commutative=True), Pow(exp(Symbol('o', commutative=True)), Symbol('o', commutative=True)))"]}, {"premise_expression": "\\log{(I - z)}", "variable": "z", "positive": "- I \\log{(- I + z)} + z \\log{(I - z)} - z", "negatives": ["- I \\log{(- I + z)} + z \\log{(- I + z)} - z", "I \\log{(I - z)} - I - z \\log{(I - z)}", "z (- I + \\log{(z^{I})})", "\\frac{z (z + 2 \\cos{(I)})}{2}"], "srepr_premise_expression": "log(Add(Symbol('I', commutative=True), Mul(Integer(-1), Symbol('z', commutative=True))))", "srepr_variable": "Symbol('z', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('I', commutative=True), log(Add(Mul(Integer(-1), Symbol('I', commutative=True)), Symbol('z', commutative=True)))), Mul(Symbol('z', commutative=True), log(Add(Symbol('I', commutative=True), Mul(Integer(-1), Symbol('z', commutative=True))))), Mul(Integer(-1), Symbol('z', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('I', commutative=True), log(Add(Mul(Integer(-1), Symbol('I', commutative=True)), Symbol('z', commutative=True)))), Mul(Symbol('z', commutative=True), log(Add(Mul(Integer(-1), Symbol('I', commutative=True)), Symbol('z', commutative=True)))), Mul(Integer(-1), Symbol('z', commutative=True)))", "Add(Mul(Symbol('I', commutative=True), log(Add(Symbol('I', commutative=True), Mul(Integer(-1), Symbol('z', commutative=True))))), Mul(Integer(-1), Symbol('I', commutative=True)), Mul(Integer(-1), Symbol('z', commutative=True), log(Add(Symbol('I', commutative=True), Mul(Integer(-1), Symbol('z', commutative=True))))))", "Mul(Symbol('z', commutative=True), Add(Mul(Integer(-1), Symbol('I', commutative=True)), log(Pow(Symbol('z', commutative=True), Symbol('I', commutative=True)))))", "Mul(Rational(1, 2), Symbol('z', commutative=True), Add(Symbol('z', commutative=True), Mul(Integer(2), cos(Symbol('I', commutative=True)))))"]}, {"premise_expression": "\\sin^{F}{(z)}", "variable": "z", "positive": "\\int \\sin^{F}{(z)} dz", "negatives": ["F \\sin{(z)}", "\\frac{z (z + 2 \\sin{(F)})}{2}", "z (\\log{(\\frac{F}{z})} + 1)", "z (- F + \\log{(z)} - 1)"], "srepr_premise_expression": "Pow(sin(Symbol('z', commutative=True)), Symbol('F', commutative=True))", "srepr_variable": "Symbol('z', commutative=True)", "srepr_positive": "Integral(Pow(sin(Symbol('z', commutative=True)), Symbol('F', commutative=True)), Tuple(Symbol('z', commutative=True)))", "srepr_negatives": ["Mul(Symbol('F', commutative=True), sin(Symbol('z', commutative=True)))", "Mul(Rational(1, 2), Symbol('z', commutative=True), Add(Symbol('z', commutative=True), Mul(Integer(2), sin(Symbol('F', commutative=True)))))", "Mul(Symbol('z', commutative=True), Add(log(Mul(Symbol('F', commutative=True), Pow(Symbol('z', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Symbol('z', commutative=True), Add(Mul(Integer(-1), Symbol('F', commutative=True)), log(Symbol('z', commutative=True)), Integer(-1)))"]}, {"premise_expression": "n y", "variable": "y", "positive": "\\frac{n y^{2}}{2}", "negatives": ["\\frac{n^{2} y}{2}", "n e^{y}", "y \\cos{(1)}", "\\frac{y^{2} \\cos{(n)}}{2}"], "srepr_premise_expression": "Mul(Symbol('n', commutative=True), Symbol('y', commutative=True))", "srepr_variable": "Symbol('y', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('n', commutative=True), Pow(Symbol('y', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('n', commutative=True), Integer(2)), Symbol('y', commutative=True))", "Mul(Symbol('n', commutative=True), exp(Symbol('y', commutative=True)))", "Mul(Symbol('y', commutative=True), cos(Integer(1)))", "Mul(Rational(1, 2), Pow(Symbol('y', commutative=True), Integer(2)), cos(Symbol('n', commutative=True)))"]}, {"premise_expression": "r + \\log{(p)}", "variable": "p", "positive": "p (r + \\log{(p)} - 1)", "negatives": ["p (- r + \\log{(p^{r})})", "p (\\log{(p r)} - 1)", "\\frac{r (r + 2 \\log{(p)})}{2}", "\\frac{p r (p - 2)}{2}"], "srepr_premise_expression": "Add(Symbol('r', commutative=True), log(Symbol('p', commutative=True)))", "srepr_variable": "Symbol('p', commutative=True)", "srepr_positive": "Mul(Symbol('p', commutative=True), Add(Symbol('r', commutative=True), log(Symbol('p', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('p', commutative=True), Add(Mul(Integer(-1), Symbol('r', commutative=True)), log(Pow(Symbol('p', commutative=True), Symbol('r', commutative=True)))))", "Mul(Symbol('p', commutative=True), Add(log(Mul(Symbol('p', commutative=True), Symbol('r', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Symbol('r', commutative=True), Mul(Integer(2), log(Symbol('p', commutative=True)))))", "Mul(Rational(1, 2), Symbol('p', commutative=True), Symbol('r', commutative=True), Add(Symbol('p', commutative=True), Integer(-2)))"]}, {"premise_expression": "- \\sin{(D - o)}", "variable": "o", "positive": "- \\cos{(D - o)}", "negatives": ["\\cos{(D - o)}", "- \\sin{(D - o)}", "\\frac{o^{2}}{2 D}", "\\frac{o^{2} \\log{(D)}}{2}"], "srepr_premise_expression": "Mul(Integer(-1), sin(Add(Symbol('D', commutative=True), Mul(Integer(-1), Symbol('o', commutative=True)))))", "srepr_variable": "Symbol('o', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('D', commutative=True), Mul(Integer(-1), Symbol('o', commutative=True)))))", "srepr_negatives": ["cos(Add(Symbol('D', commutative=True), Mul(Integer(-1), Symbol('o', commutative=True))))", "Mul(Integer(-1), sin(Add(Symbol('D', commutative=True), Mul(Integer(-1), Symbol('o', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(-1)), Pow(Symbol('o', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('o', commutative=True), Integer(2)), log(Symbol('D', commutative=True)))"]}, {"premise_expression": "Q + n", "variable": "n", "positive": "\\frac{n (2 Q + n)}{2}", "negatives": ["\\frac{Q (Q + 2 n)}{2}", "e^{- Q + n}", "\\cos{(Q - n)}", "\\frac{n (n + 2 \\cos{(Q)})}{2}"], "srepr_premise_expression": "Add(Symbol('Q', commutative=True), Symbol('n', commutative=True))", "srepr_variable": "Symbol('n', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('n', commutative=True), Add(Mul(Integer(2), Symbol('Q', commutative=True)), Symbol('n', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Symbol('Q', commutative=True), Mul(Integer(2), Symbol('n', commutative=True))))", "exp(Add(Mul(Integer(-1), Symbol('Q', commutative=True)), Symbol('n', commutative=True)))", "cos(Add(Symbol('Q', commutative=True), Mul(Integer(-1), Symbol('n', commutative=True))))", "Mul(Rational(1, 2), Symbol('n', commutative=True), Add(Symbol('n', commutative=True), Mul(Integer(2), cos(Symbol('Q', commutative=True)))))"]}, {"premise_expression": "- F + I x", "variable": "F", "positive": "\\frac{F (- F + 2 I x)}{2}", "negatives": ["\\frac{x (- 2 F + I x)}{2}", "\\frac{I (- 2 F + I x)}{2}", "\\frac{F (F I + 2 x)}{2}", "\\frac{F (I - x)}{I}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('F', commutative=True)), Mul(Symbol('I', commutative=True), Symbol('x', commutative=True)))", "srepr_variable": "Symbol('F', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Mul(Integer(-1), Symbol('F', commutative=True)), Mul(Integer(2), Symbol('I', commutative=True), Symbol('x', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('x', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('F', commutative=True)), Mul(Symbol('I', commutative=True), Symbol('x', commutative=True))))", "Mul(Rational(1, 2), Symbol('I', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('F', commutative=True)), Mul(Symbol('I', commutative=True), Symbol('x', commutative=True))))", "Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Mul(Symbol('F', commutative=True), Symbol('I', commutative=True)), Mul(Integer(2), Symbol('x', commutative=True))))", "Mul(Symbol('F', commutative=True), Pow(Symbol('I', commutative=True), Integer(-1)), Add(Symbol('I', commutative=True), Mul(Integer(-1), Symbol('x', commutative=True))))"]}, {"premise_expression": "C t", "variable": "C", "positive": "\\frac{C^{2} t}{2}", "negatives": ["\\frac{C t^{2}}{2}", "\\frac{C^{2} \\cos{(t)}}{2}", "\\frac{C (- C + 2 t)}{2}", "t e^{\\frac{C}{t}}"], "srepr_premise_expression": "Mul(Symbol('C', commutative=True), Symbol('t', commutative=True))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2)), Symbol('t', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('C', commutative=True), Pow(Symbol('t', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2)), cos(Symbol('t', commutative=True)))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Mul(Integer(-1), Symbol('C', commutative=True)), Mul(Integer(2), Symbol('t', commutative=True))))", "Mul(Symbol('t', commutative=True), exp(Mul(Symbol('C', commutative=True), Pow(Symbol('t', commutative=True), Integer(-1)))))"]}, {"premise_expression": "\\cos^{H}{(U)}", "variable": "U", "positive": "\\int \\cos^{H}{(U)} dU", "negatives": ["- H U - \\cos{(U)}", "- H \\cos{(U)}", "e^{H + U}", "U (\\log{(\\frac{H}{U})} + 1)"], "srepr_premise_expression": "Pow(cos(Symbol('U', commutative=True)), Symbol('H', commutative=True))", "srepr_variable": "Symbol('U', commutative=True)", "srepr_positive": "Integral(Pow(cos(Symbol('U', commutative=True)), Symbol('H', commutative=True)), Tuple(Symbol('U', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('H', commutative=True), Symbol('U', commutative=True)), Mul(Integer(-1), cos(Symbol('U', commutative=True))))", "Mul(Integer(-1), Symbol('H', commutative=True), cos(Symbol('U', commutative=True)))", "exp(Add(Symbol('H', commutative=True), Symbol('U', commutative=True)))", "Mul(Symbol('U', commutative=True), Add(log(Mul(Symbol('H', commutative=True), Pow(Symbol('U', commutative=True), Integer(-1)))), Integer(1)))"]}, {"premise_expression": "\\log{(s t)}", "variable": "t", "positive": "t (\\log{(s t)} - 1)", "negatives": ["s (\\log{(s t)} - 1)", "t (\\log{(\\frac{s}{t})} + 1)", "t (- s + \\log{(t)} - 1)", "- \\sin{(s - t)}"], "srepr_premise_expression": "log(Mul(Symbol('s', commutative=True), Symbol('t', commutative=True)))", "srepr_variable": "Symbol('t', commutative=True)", "srepr_positive": "Mul(Symbol('t', commutative=True), Add(log(Mul(Symbol('s', commutative=True), Symbol('t', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('s', commutative=True), Add(log(Mul(Symbol('s', commutative=True), Symbol('t', commutative=True))), Integer(-1)))", "Mul(Symbol('t', commutative=True), Add(log(Mul(Symbol('s', commutative=True), Pow(Symbol('t', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Symbol('t', commutative=True), Add(Mul(Integer(-1), Symbol('s', commutative=True)), log(Symbol('t', commutative=True)), Integer(-1)))", "Mul(Integer(-1), sin(Add(Symbol('s', commutative=True), Mul(Integer(-1), Symbol('t', commutative=True)))))"]}, {"premise_expression": "\\log{(D u)}", "variable": "D", "positive": "D (\\log{(D u)} - 1)", "negatives": ["u (\\log{(D u)} - 1)", "D u (\\log{(D)} - 1)", "D (- u + \\log{(D)} - 1)", "\\frac{D^{2} \\log{(u)}}{2}"], "srepr_premise_expression": "log(Mul(Symbol('D', commutative=True), Symbol('u', commutative=True)))", "srepr_variable": "Symbol('D', commutative=True)", "srepr_positive": "Mul(Symbol('D', commutative=True), Add(log(Mul(Symbol('D', commutative=True), Symbol('u', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('u', commutative=True), Add(log(Mul(Symbol('D', commutative=True), Symbol('u', commutative=True))), Integer(-1)))", "Mul(Symbol('D', commutative=True), Symbol('u', commutative=True), Add(log(Symbol('D', commutative=True)), Integer(-1)))", "Mul(Symbol('D', commutative=True), Add(Mul(Integer(-1), Symbol('u', commutative=True)), log(Symbol('D', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(2)), log(Symbol('u', commutative=True)))"]}, {"premise_expression": "g o", "variable": "g", "positive": "\\frac{g^{2} o}{2}", "negatives": ["\\frac{g o^{2}}{2}", "\\frac{g^{2} e^{o}}{2}", "\\frac{g (g + 2 o)}{2}", "\\sin{(g - o)}"], "srepr_premise_expression": "Mul(Symbol('g', commutative=True), Symbol('o', commutative=True))", "srepr_variable": "Symbol('g', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('g', commutative=True), Integer(2)), Symbol('o', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('g', commutative=True), Pow(Symbol('o', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('g', commutative=True), Integer(2)), exp(Symbol('o', commutative=True)))", "Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Symbol('g', commutative=True), Mul(Integer(2), Symbol('o', commutative=True))))", "sin(Add(Symbol('g', commutative=True), Mul(Integer(-1), Symbol('o', commutative=True))))"]}, {"premise_expression": "\\frac{N}{F}", "variable": "F", "positive": "N \\log{(F)}", "negatives": ["N \\sin{(F)}", "\\frac{N^{2}}{2 F}", "F \\sin{(1)}", "- \\cos{(F - N)}"], "srepr_premise_expression": "Mul(Pow(Symbol('F', commutative=True), Integer(-1)), Symbol('N', commutative=True))", "srepr_variable": "Symbol('F', commutative=True)", "srepr_positive": "Mul(Symbol('N', commutative=True), log(Symbol('F', commutative=True)))", "srepr_negatives": ["Mul(Symbol('N', commutative=True), sin(Symbol('F', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('F', commutative=True), Integer(-1)), Pow(Symbol('N', commutative=True), Integer(2)))", "Mul(Symbol('F', commutative=True), sin(Integer(1)))", "Mul(Integer(-1), cos(Add(Symbol('F', commutative=True), Mul(Integer(-1), Symbol('N', commutative=True)))))"]}, {"premise_expression": "\\cos{(K - l)}", "variable": "K", "positive": "\\sin{(K - l)}", "negatives": ["- \\sin{(K - l)}", "K \\log{(2 l)}", "\\frac{K^{2}}{2 l}", "- l \\cos{(K)}"], "srepr_premise_expression": "cos(Add(Symbol('K', commutative=True), Mul(Integer(-1), Symbol('l', commutative=True))))", "srepr_variable": "Symbol('K', commutative=True)", "srepr_positive": "sin(Add(Symbol('K', commutative=True), Mul(Integer(-1), Symbol('l', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('K', commutative=True), Mul(Integer(-1), Symbol('l', commutative=True)))))", "Mul(Symbol('K', commutative=True), log(Mul(Integer(2), Symbol('l', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('K', commutative=True), Integer(2)), Pow(Symbol('l', commutative=True), Integer(-1)))", "Mul(Integer(-1), Symbol('l', commutative=True), cos(Symbol('K', commutative=True)))"]}, {"premise_expression": "\\frac{A}{h} + J", "variable": "A", "positive": "\\frac{A^{2}}{2 h} + A J", "negatives": ["A \\log{(h)} + J h", "\\frac{A^{2} (J + h)}{2}", "\\frac{A (A h - 2 J)}{2}", "\\frac{A^{2} J h}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('A', commutative=True), Pow(Symbol('h', commutative=True), Integer(-1))), Symbol('J', commutative=True))", "srepr_variable": "Symbol('A', commutative=True)", "srepr_positive": "Add(Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2)), Pow(Symbol('h', commutative=True), Integer(-1))), Mul(Symbol('A', commutative=True), Symbol('J', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('A', commutative=True), log(Symbol('h', commutative=True))), Mul(Symbol('J', commutative=True), Symbol('h', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2)), Add(Symbol('J', commutative=True), Symbol('h', commutative=True)))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Mul(Symbol('A', commutative=True), Symbol('h', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('J', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2)), Symbol('J', commutative=True), Symbol('h', commutative=True))"]}, {"premise_expression": "- P + Q + p", "variable": "p", "positive": "p (- P + Q + \\frac{p}{2})", "negatives": ["\\frac{p (2 P + 2 Q + p)}{2}", "\\frac{Q (- 2 P + Q + 2 p)}{2}", "\\frac{P (- P + 2 Q + 2 p)}{2}", "\\frac{p (P + Q)}{Q}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('P', commutative=True)), Symbol('Q', commutative=True), Symbol('p', commutative=True))", "srepr_variable": "Symbol('p', commutative=True)", "srepr_positive": "Mul(Symbol('p', commutative=True), Add(Mul(Integer(-1), Symbol('P', commutative=True)), Symbol('Q', commutative=True), Mul(Rational(1, 2), Symbol('p', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Mul(Integer(2), Symbol('P', commutative=True)), Mul(Integer(2), Symbol('Q', commutative=True)), Symbol('p', commutative=True)))", "Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('P', commutative=True)), Symbol('Q', commutative=True), Mul(Integer(2), Symbol('p', commutative=True))))", "Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Mul(Integer(-1), Symbol('P', commutative=True)), Mul(Integer(2), Symbol('Q', commutative=True)), Mul(Integer(2), Symbol('p', commutative=True))))", "Mul(Pow(Symbol('Q', commutative=True), Integer(-1)), Symbol('p', commutative=True), Add(Symbol('P', commutative=True), Symbol('Q', commutative=True)))"]}, {"premise_expression": "\\log{(X^{T})}", "variable": "T", "positive": "\\frac{T^{2} \\log{(X)}}{2}", "negatives": ["\\frac{T^{2} \\sin{(X)}}{2}", "\\frac{T (T + 2 X)}{2}", "- T + X \\log{(T)}", "T (\\log{(T X)} - 1)"], "srepr_premise_expression": "log(Pow(Symbol('X', commutative=True), Symbol('T', commutative=True)))", "srepr_variable": "Symbol('T', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('T', commutative=True), Integer(2)), log(Symbol('X', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('T', commutative=True), Integer(2)), sin(Symbol('X', commutative=True)))", "Mul(Rational(1, 2), Symbol('T', commutative=True), Add(Symbol('T', commutative=True), Mul(Integer(2), Symbol('X', commutative=True))))", "Add(Mul(Integer(-1), Symbol('T', commutative=True)), Mul(Symbol('X', commutative=True), log(Symbol('T', commutative=True))))", "Mul(Symbol('T', commutative=True), Add(log(Mul(Symbol('T', commutative=True), Symbol('X', commutative=True))), Integer(-1)))"]}, {"premise_expression": "e^{G - y}", "variable": "G", "positive": "e^{G - y}", "negatives": ["- e^{G - y}", "- \\cos{(G - y)}", "\\frac{G (G - 2 y)}{2}", "- \\frac{\\cos{(G)}}{y}"], "srepr_premise_expression": "exp(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True))))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "exp(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True)))))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Symbol('G', commutative=True), Mul(Integer(-1), Integer(2), Symbol('y', commutative=True))))", "Mul(Integer(-1), Pow(Symbol('y', commutative=True), Integer(-1)), cos(Symbol('G', commutative=True)))"]}, {"premise_expression": "\\cos{(\\frac{a}{j})}", "variable": "j", "positive": "a \\operatorname{Si}{(\\frac{a}{j})} + j \\cos{(\\frac{a}{j})}", "negatives": ["a j - \\cos{(j)}", "\\frac{j (- j + 2 \\cos{(a)})}{2}", "- a j - \\cos{(j)}", "\\frac{j (j + 2 e^{a})}{2}"], "srepr_premise_expression": "cos(Mul(Symbol('a', commutative=True), Pow(Symbol('j', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('j', commutative=True)", "srepr_positive": "Add(Mul(Symbol('a', commutative=True), Si(Mul(Symbol('a', commutative=True), Pow(Symbol('j', commutative=True), Integer(-1))))), Mul(Symbol('j', commutative=True), cos(Mul(Symbol('a', commutative=True), Pow(Symbol('j', commutative=True), Integer(-1))))))", "srepr_negatives": ["Add(Mul(Symbol('a', commutative=True), Symbol('j', commutative=True)), Mul(Integer(-1), cos(Symbol('j', commutative=True))))", "Mul(Rational(1, 2), Symbol('j', commutative=True), Add(Mul(Integer(-1), Symbol('j', commutative=True)), Mul(Integer(2), cos(Symbol('a', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('a', commutative=True), Symbol('j', commutative=True)), Mul(Integer(-1), cos(Symbol('j', commutative=True))))", "Mul(Rational(1, 2), Symbol('j', commutative=True), Add(Symbol('j', commutative=True), Mul(Integer(2), exp(Symbol('a', commutative=True)))))"]}, {"premise_expression": "G u", "variable": "G", "positive": "\\frac{G^{2} u}{2}", "negatives": ["\\frac{G u^{2}}{2}", "\\frac{G^{2} (u - 1)}{2}", "\\frac{G (G + 2 u)}{2}", "G (G + u)"], "srepr_premise_expression": "Mul(Symbol('G', commutative=True), Symbol('u', commutative=True))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(2)), Symbol('u', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('G', commutative=True), Pow(Symbol('u', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(2)), Add(Symbol('u', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Symbol('G', commutative=True), Mul(Integer(2), Symbol('u', commutative=True))))", "Mul(Symbol('G', commutative=True), Add(Symbol('G', commutative=True), Symbol('u', commutative=True)))"]}, {"premise_expression": "D + H M", "variable": "H", "positive": "\\frac{H (2 D + H M)}{2}", "negatives": ["\\frac{M (2 D + H M)}{2}", "\\frac{D (D + 2 H M)}{2}", "\\frac{H^{2} (D - M)}{2}", "H (- D + 2 M)"], "srepr_premise_expression": "Add(Symbol('D', commutative=True), Mul(Symbol('H', commutative=True), Symbol('M', commutative=True)))", "srepr_variable": "Symbol('H', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('H', commutative=True), Add(Mul(Integer(2), Symbol('D', commutative=True)), Mul(Symbol('H', commutative=True), Symbol('M', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('M', commutative=True), Add(Mul(Integer(2), Symbol('D', commutative=True)), Mul(Symbol('H', commutative=True), Symbol('M', commutative=True))))", "Mul(Rational(1, 2), Symbol('D', commutative=True), Add(Symbol('D', commutative=True), Mul(Integer(2), Symbol('H', commutative=True), Symbol('M', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('H', commutative=True), Integer(2)), Add(Symbol('D', commutative=True), Mul(Integer(-1), Symbol('M', commutative=True))))", "Mul(Symbol('H', commutative=True), Add(Mul(Integer(-1), Symbol('D', commutative=True)), Mul(Integer(2), Symbol('M', commutative=True))))"]}, {"premise_expression": "\\cos{(\\frac{I}{C})}", "variable": "C", "positive": "C \\cos{(\\frac{I}{C})} + I \\operatorname{Si}{(\\frac{I}{C})}", "negatives": ["- \\cos{(C + I)}", "\\frac{C (- C + 2 \\sin{(I)})}{2}", "- \\cos{(C - I)}", "\\frac{C (- C + 2 \\cos{(I)})}{2}"], "srepr_premise_expression": "cos(Mul(Pow(Symbol('C', commutative=True), Integer(-1)), Symbol('I', commutative=True)))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Add(Mul(Symbol('C', commutative=True), cos(Mul(Pow(Symbol('C', commutative=True), Integer(-1)), Symbol('I', commutative=True)))), Mul(Symbol('I', commutative=True), Si(Mul(Pow(Symbol('C', commutative=True), Integer(-1)), Symbol('I', commutative=True)))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('C', commutative=True), Symbol('I', commutative=True))))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Mul(Integer(-1), Symbol('C', commutative=True)), Mul(Integer(2), sin(Symbol('I', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('I', commutative=True)))))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Mul(Integer(-1), Symbol('C', commutative=True)), Mul(Integer(2), cos(Symbol('I', commutative=True)))))"]}, {"premise_expression": "f + l", "variable": "l", "positive": "\\frac{l (2 f + l)}{2}", "negatives": ["\\frac{l (- 2 f + l)}{2}", "\\frac{f (f + 2 l)}{2}", "\\frac{f l^{2}}{2}", "f \\log{(l)}"], "srepr_premise_expression": "Add(Symbol('f', commutative=True), Symbol('l', commutative=True))", "srepr_variable": "Symbol('l', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('l', commutative=True), Add(Mul(Integer(2), Symbol('f', commutative=True)), Symbol('l', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('l', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('f', commutative=True)), Symbol('l', commutative=True)))", "Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Symbol('f', commutative=True), Mul(Integer(2), Symbol('l', commutative=True))))", "Mul(Rational(1, 2), Symbol('f', commutative=True), Pow(Symbol('l', commutative=True), Integer(2)))", "Mul(Symbol('f', commutative=True), log(Symbol('l', commutative=True)))"]}, {"premise_expression": "\\log{(- a + z)}", "variable": "z", "positive": "- a \\log{(- a + z)} + z \\log{(- a + z)} - z", "negatives": ["a \\log{(- a + z)} - a - z \\log{(a - z)}", "e^{a} \\log{(z)}", "z (\\log{(\\frac{z}{a})} - 1)", "a z + e^{z}"], "srepr_premise_expression": "log(Add(Mul(Integer(-1), Symbol('a', commutative=True)), Symbol('z', commutative=True)))", "srepr_variable": "Symbol('z', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('a', commutative=True), log(Add(Mul(Integer(-1), Symbol('a', commutative=True)), Symbol('z', commutative=True)))), Mul(Symbol('z', commutative=True), log(Add(Mul(Integer(-1), Symbol('a', commutative=True)), Symbol('z', commutative=True)))), Mul(Integer(-1), Symbol('z', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('a', commutative=True), log(Add(Mul(Integer(-1), Symbol('a', commutative=True)), Symbol('z', commutative=True)))), Mul(Integer(-1), Symbol('a', commutative=True)), Mul(Integer(-1), Symbol('z', commutative=True), log(Add(Symbol('a', commutative=True), Mul(Integer(-1), Symbol('z', commutative=True))))))", "Mul(exp(Symbol('a', commutative=True)), log(Symbol('z', commutative=True)))", "Mul(Symbol('z', commutative=True), Add(log(Mul(Pow(Symbol('a', commutative=True), Integer(-1)), Symbol('z', commutative=True))), Integer(-1)))", "Add(Mul(Symbol('a', commutative=True), Symbol('z', commutative=True)), exp(Symbol('z', commutative=True)))"]}, {"premise_expression": "- v + e^{P}", "variable": "P", "positive": "- P v + e^{P}", "negatives": ["P v + e^{P}", "v e^{P}", "\\frac{v (- v + 2 e^{P})}{2}", "- \\cos{(P + v)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('v', commutative=True)), exp(Symbol('P', commutative=True)))", "srepr_variable": "Symbol('P', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('P', commutative=True), Symbol('v', commutative=True)), exp(Symbol('P', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('P', commutative=True), Symbol('v', commutative=True)), exp(Symbol('P', commutative=True)))", "Mul(Symbol('v', commutative=True), exp(Symbol('P', commutative=True)))", "Mul(Rational(1, 2), Symbol('v', commutative=True), Add(Mul(Integer(-1), Symbol('v', commutative=True)), Mul(Integer(2), exp(Symbol('P', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('P', commutative=True), Symbol('v', commutative=True))))"]}, {"premise_expression": "- q + e^{j}", "variable": "j", "positive": "- j q + e^{j}", "negatives": ["j q - \\cos{(j)}", "\\frac{q (- q + 2 e^{j})}{2}", "\\frac{j (j + 2 e^{q})}{2}", "e^{j + q}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('q', commutative=True)), exp(Symbol('j', commutative=True)))", "srepr_variable": "Symbol('j', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('j', commutative=True), Symbol('q', commutative=True)), exp(Symbol('j', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('j', commutative=True), Symbol('q', commutative=True)), Mul(Integer(-1), cos(Symbol('j', commutative=True))))", "Mul(Rational(1, 2), Symbol('q', commutative=True), Add(Mul(Integer(-1), Symbol('q', commutative=True)), Mul(Integer(2), exp(Symbol('j', commutative=True)))))", "Mul(Rational(1, 2), Symbol('j', commutative=True), Add(Symbol('j', commutative=True), Mul(Integer(2), exp(Symbol('q', commutative=True)))))", "exp(Add(Symbol('j', commutative=True), Symbol('q', commutative=True)))"]}, {"premise_expression": "\\log{(\\frac{S}{F})}", "variable": "S", "positive": "S (\\log{(\\frac{S}{F})} - 1)", "negatives": ["F (\\log{(\\frac{S}{F})} + 1)", "\\sin{(F + S)}", "\\frac{S (S + 2 \\sin{(F)})}{2}", "F S + e^{S}"], "srepr_premise_expression": "log(Mul(Pow(Symbol('F', commutative=True), Integer(-1)), Symbol('S', commutative=True)))", "srepr_variable": "Symbol('S', commutative=True)", "srepr_positive": "Mul(Symbol('S', commutative=True), Add(log(Mul(Pow(Symbol('F', commutative=True), Integer(-1)), Symbol('S', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('F', commutative=True), Add(log(Mul(Pow(Symbol('F', commutative=True), Integer(-1)), Symbol('S', commutative=True))), Integer(1)))", "sin(Add(Symbol('F', commutative=True), Symbol('S', commutative=True)))", "Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Symbol('S', commutative=True), Mul(Integer(2), sin(Symbol('F', commutative=True)))))", "Add(Mul(Symbol('F', commutative=True), Symbol('S', commutative=True)), exp(Symbol('S', commutative=True)))"]}, {"premise_expression": "V X", "variable": "X", "positive": "\\frac{V X^{2}}{2}", "negatives": ["\\frac{V^{2} X}{2}", "\\log{(V)} \\log{(X)}", "- \\cos{(V + X)}", "\\frac{X (X + 2 \\cos{(V)})}{2}"], "srepr_premise_expression": "Mul(Symbol('V', commutative=True), Symbol('X', commutative=True))", "srepr_variable": "Symbol('X', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('V', commutative=True), Pow(Symbol('X', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('V', commutative=True), Integer(2)), Symbol('X', commutative=True))", "Mul(log(Symbol('V', commutative=True)), log(Symbol('X', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('V', commutative=True), Symbol('X', commutative=True))))", "Mul(Rational(1, 2), Symbol('X', commutative=True), Add(Symbol('X', commutative=True), Mul(Integer(2), cos(Symbol('V', commutative=True)))))"]}, {"premise_expression": "\\frac{\\sin{(g)}}{Q}", "variable": "g", "positive": "- \\frac{\\cos{(g)}}{Q}", "negatives": ["\\cos{(Q - g)}", "Q e^{g}", "\\frac{g^{2} \\log{(Q)}}{2}", "\\log{(g)} \\sin{(Q)}"], "srepr_premise_expression": "Mul(Pow(Symbol('Q', commutative=True), Integer(-1)), sin(Symbol('g', commutative=True)))", "srepr_variable": "Symbol('g', commutative=True)", "srepr_positive": "Mul(Integer(-1), Pow(Symbol('Q', commutative=True), Integer(-1)), cos(Symbol('g', commutative=True)))", "srepr_negatives": ["cos(Add(Symbol('Q', commutative=True), Mul(Integer(-1), Symbol('g', commutative=True))))", "Mul(Symbol('Q', commutative=True), exp(Symbol('g', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('g', commutative=True), Integer(2)), log(Symbol('Q', commutative=True)))", "Mul(log(Symbol('g', commutative=True)), sin(Symbol('Q', commutative=True)))"]}, {"premise_expression": "A - j", "variable": "j", "positive": "\\frac{j (2 A - j)}{2}", "negatives": ["\\frac{A (A - 2 j)}{2}", "\\frac{j^{2} e^{A}}{2}", "- \\cos{(A + j)}", "- \\frac{\\cos{(j)}}{A}"], "srepr_premise_expression": "Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('j', commutative=True)))", "srepr_variable": "Symbol('j', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('j', commutative=True), Add(Mul(Integer(2), Symbol('A', commutative=True)), Mul(Integer(-1), Symbol('j', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Symbol('A', commutative=True), Mul(Integer(-1), Integer(2), Symbol('j', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('j', commutative=True), Integer(2)), exp(Symbol('A', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('A', commutative=True), Symbol('j', commutative=True))))", "Mul(Integer(-1), Pow(Symbol('A', commutative=True), Integer(-1)), cos(Symbol('j', commutative=True)))"]}, {"premise_expression": "\\log{(\\frac{D}{p})}", "variable": "D", "positive": "D (\\log{(\\frac{D}{p})} - 1)", "negatives": ["p (\\log{(\\frac{D}{p})} + 1)", "\\cos{(D - p)}", "\\sin{(D + p)}", "\\frac{D (D + 2 p)}{2}"], "srepr_premise_expression": "log(Mul(Symbol('D', commutative=True), Pow(Symbol('p', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('D', commutative=True)", "srepr_positive": "Mul(Symbol('D', commutative=True), Add(log(Mul(Symbol('D', commutative=True), Pow(Symbol('p', commutative=True), Integer(-1)))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('p', commutative=True), Add(log(Mul(Symbol('D', commutative=True), Pow(Symbol('p', commutative=True), Integer(-1)))), Integer(1)))", "cos(Add(Symbol('D', commutative=True), Mul(Integer(-1), Symbol('p', commutative=True))))", "sin(Add(Symbol('D', commutative=True), Symbol('p', commutative=True)))", "Mul(Rational(1, 2), Symbol('D', commutative=True), Add(Symbol('D', commutative=True), Mul(Integer(2), Symbol('p', commutative=True))))"]}, {"premise_expression": "- Z + e^{Q}", "variable": "Q", "positive": "- Q Z + e^{Q}", "negatives": ["- Q Z + \\sin{(Q)}", "\\frac{Z (- Z + 2 e^{Q})}{2}", "Z \\log{(Q)}", "\\frac{Q^{2}}{2 Z}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('Z', commutative=True)), exp(Symbol('Q', commutative=True)))", "srepr_variable": "Symbol('Q', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('Q', commutative=True), Symbol('Z', commutative=True)), exp(Symbol('Q', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('Q', commutative=True), Symbol('Z', commutative=True)), sin(Symbol('Q', commutative=True)))", "Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Mul(Integer(-1), Symbol('Z', commutative=True)), Mul(Integer(2), exp(Symbol('Q', commutative=True)))))", "Mul(Symbol('Z', commutative=True), log(Symbol('Q', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(2)), Pow(Symbol('Z', commutative=True), Integer(-1)))"]}, {"premise_expression": "Y - z", "variable": "Y", "positive": "\\frac{Y (Y - 2 z)}{2}", "negatives": ["\\frac{z (2 Y - z)}{2}", "\\frac{Y (Y + 2 \\sin{(z)})}{2}", "\\frac{Y^{2} \\log{(z)}}{2}", "\\frac{Y^{2} \\sin{(z)}}{2}"], "srepr_premise_expression": "Add(Symbol('Y', commutative=True), Mul(Integer(-1), Symbol('z', commutative=True)))", "srepr_variable": "Symbol('Y', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('Y', commutative=True), Add(Symbol('Y', commutative=True), Mul(Integer(-1), Integer(2), Symbol('z', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('z', commutative=True), Add(Mul(Integer(2), Symbol('Y', commutative=True)), Mul(Integer(-1), Symbol('z', commutative=True))))", "Mul(Rational(1, 2), Symbol('Y', commutative=True), Add(Symbol('Y', commutative=True), Mul(Integer(2), sin(Symbol('z', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('Y', commutative=True), Integer(2)), log(Symbol('z', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('Y', commutative=True), Integer(2)), sin(Symbol('z', commutative=True)))"]}, {"premise_expression": "W u", "variable": "W", "positive": "\\frac{W^{2} u}{2}", "negatives": ["\\frac{W u^{2}}{2}", "\\frac{W (- W + 2 u)}{2}", "u e^{W}", "- u \\cos{(W)}"], "srepr_premise_expression": "Mul(Symbol('W', commutative=True), Symbol('u', commutative=True))", "srepr_variable": "Symbol('W', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('W', commutative=True), Integer(2)), Symbol('u', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('W', commutative=True), Pow(Symbol('u', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('W', commutative=True), Add(Mul(Integer(-1), Symbol('W', commutative=True)), Mul(Integer(2), Symbol('u', commutative=True))))", "Mul(Symbol('u', commutative=True), exp(Symbol('W', commutative=True)))", "Mul(Integer(-1), Symbol('u', commutative=True), cos(Symbol('W', commutative=True)))"]}, {"premise_expression": "\\cos{(E + G)}", "variable": "G", "positive": "\\sin{(E + G)}", "negatives": ["\\cos{(E - G)}", "- \\cos{(E - G)}", "E e^{G}", "E \\log{(G)}"], "srepr_premise_expression": "cos(Add(Symbol('E', commutative=True), Symbol('G', commutative=True)))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "sin(Add(Symbol('E', commutative=True), Symbol('G', commutative=True)))", "srepr_negatives": ["cos(Add(Symbol('E', commutative=True), Mul(Integer(-1), Symbol('G', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('E', commutative=True), Mul(Integer(-1), Symbol('G', commutative=True)))))", "Mul(Symbol('E', commutative=True), exp(Symbol('G', commutative=True)))", "Mul(Symbol('E', commutative=True), log(Symbol('G', commutative=True)))"]}, {"premise_expression": "- D + b", "variable": "D", "positive": "\\frac{D (- D + 2 b)}{2}", "negatives": ["\\frac{b (- 2 D + b)}{2}", "\\frac{D (D + 2 \\cos{(b)})}{2}", "\\frac{D^{2} b}{2}", "\\frac{D^{2} \\cos{(b)}}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('D', commutative=True)), Symbol('b', commutative=True))", "srepr_variable": "Symbol('D', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('D', commutative=True), Add(Mul(Integer(-1), Symbol('D', commutative=True)), Mul(Integer(2), Symbol('b', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('b', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('D', commutative=True)), Symbol('b', commutative=True)))", "Mul(Rational(1, 2), Symbol('D', commutative=True), Add(Symbol('D', commutative=True), Mul(Integer(2), cos(Symbol('b', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(2)), Symbol('b', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(2)), cos(Symbol('b', commutative=True)))"]}, {"premise_expression": "- q + s^{h}", "variable": "q", "positive": "\\frac{q (- q + 2 s^{h})}{2}", "negatives": ["- \\frac{q (q - 2 s)}{2 h}", "\\frac{q (q - 2 s)}{2 h}", "\\frac{q (- 2 h + q - 2 s)}{2}", "\\frac{q s (2 h + q)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('q', commutative=True)), Pow(Symbol('s', commutative=True), Symbol('h', commutative=True)))", "srepr_variable": "Symbol('q', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('q', commutative=True), Add(Mul(Integer(-1), Symbol('q', commutative=True)), Mul(Integer(2), Pow(Symbol('s', commutative=True), Symbol('h', commutative=True)))))", "srepr_negatives": ["Mul(Integer(-1), Rational(1, 2), Pow(Symbol('h', commutative=True), Integer(-1)), Symbol('q', commutative=True), Add(Symbol('q', commutative=True), Mul(Integer(-1), Integer(2), Symbol('s', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('h', commutative=True), Integer(-1)), Symbol('q', commutative=True), Add(Symbol('q', commutative=True), Mul(Integer(-1), Integer(2), Symbol('s', commutative=True))))", "Mul(Rational(1, 2), Symbol('q', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('h', commutative=True)), Symbol('q', commutative=True), Mul(Integer(-1), Integer(2), Symbol('s', commutative=True))))", "Mul(Rational(1, 2), Symbol('q', commutative=True), Symbol('s', commutative=True), Add(Mul(Integer(2), Symbol('h', commutative=True)), Symbol('q', commutative=True)))"]}, {"premise_expression": "V + \\frac{E}{D}", "variable": "E", "positive": "E V + \\frac{E^{2}}{2 D}", "negatives": ["D V + E \\log{(D)}", "D E + V \\log{(E)}", "\\frac{E (2 D + E V)}{2}", "\\frac{V^{2}}{2} + \\frac{E V}{D}"], "srepr_premise_expression": "Add(Symbol('V', commutative=True), Mul(Pow(Symbol('D', commutative=True), Integer(-1)), Symbol('E', commutative=True)))", "srepr_variable": "Symbol('E', commutative=True)", "srepr_positive": "Add(Mul(Symbol('E', commutative=True), Symbol('V', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(-1)), Pow(Symbol('E', commutative=True), Integer(2))))", "srepr_negatives": ["Add(Mul(Symbol('D', commutative=True), Symbol('V', commutative=True)), Mul(Symbol('E', commutative=True), log(Symbol('D', commutative=True))))", "Add(Mul(Symbol('D', commutative=True), Symbol('E', commutative=True)), Mul(Symbol('V', commutative=True), log(Symbol('E', commutative=True))))", "Mul(Rational(1, 2), Symbol('E', commutative=True), Add(Mul(Integer(2), Symbol('D', commutative=True)), Mul(Symbol('E', commutative=True), Symbol('V', commutative=True))))", "Add(Mul(Rational(1, 2), Pow(Symbol('V', commutative=True), Integer(2))), Mul(Pow(Symbol('D', commutative=True), Integer(-1)), Symbol('E', commutative=True), Symbol('V', commutative=True)))"]}, {"premise_expression": "e^{X + z}", "variable": "z", "positive": "e^{X + z}", "negatives": ["X e^{z}", "- X \\cos{(z)}", "- \\frac{\\cos{(z)}}{X}", "z (\\log{(\\frac{z}{X})} - 1)"], "srepr_premise_expression": "exp(Add(Symbol('X', commutative=True), Symbol('z', commutative=True)))", "srepr_variable": "Symbol('z', commutative=True)", "srepr_positive": "exp(Add(Symbol('X', commutative=True), Symbol('z', commutative=True)))", "srepr_negatives": ["Mul(Symbol('X', commutative=True), exp(Symbol('z', commutative=True)))", "Mul(Integer(-1), Symbol('X', commutative=True), cos(Symbol('z', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('X', commutative=True), Integer(-1)), cos(Symbol('z', commutative=True)))", "Mul(Symbol('z', commutative=True), Add(log(Mul(Pow(Symbol('X', commutative=True), Integer(-1)), Symbol('z', commutative=True))), Integer(-1)))"]}, {"premise_expression": "- V + \\cos{(w)}", "variable": "w", "positive": "- V w + \\sin{(w)}", "negatives": ["- V w - \\cos{(w)}", "V w - \\cos{(w)}", "\\frac{w^{2} \\sin{(V)}}{2}", "\\frac{\\sin{(w)}}{V}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('V', commutative=True)), cos(Symbol('w', commutative=True)))", "srepr_variable": "Symbol('w', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('V', commutative=True), Symbol('w', commutative=True)), sin(Symbol('w', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('V', commutative=True), Symbol('w', commutative=True)), Mul(Integer(-1), cos(Symbol('w', commutative=True))))", "Add(Mul(Symbol('V', commutative=True), Symbol('w', commutative=True)), Mul(Integer(-1), cos(Symbol('w', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('w', commutative=True), Integer(2)), sin(Symbol('V', commutative=True)))", "Mul(Pow(Symbol('V', commutative=True), Integer(-1)), sin(Symbol('w', commutative=True)))"]}, {"premise_expression": "\\sin{(Z + s)}", "variable": "s", "positive": "- \\cos{(Z + s)}", "negatives": ["- Z s + \\sin{(s)}", "Z e^{s}", "\\frac{s^{2}}{2 Z}", "s (\\log{(\\frac{s}{Z})} - 1)"], "srepr_premise_expression": "sin(Add(Symbol('Z', commutative=True), Symbol('s', commutative=True)))", "srepr_variable": "Symbol('s', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('Z', commutative=True), Symbol('s', commutative=True))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('Z', commutative=True), Symbol('s', commutative=True)), sin(Symbol('s', commutative=True)))", "Mul(Symbol('Z', commutative=True), exp(Symbol('s', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('Z', commutative=True), Integer(-1)), Pow(Symbol('s', commutative=True), Integer(2)))", "Mul(Symbol('s', commutative=True), Add(log(Mul(Pow(Symbol('Z', commutative=True), Integer(-1)), Symbol('s', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\frac{P}{W}", "variable": "P", "positive": "\\frac{P^{2}}{2 W}", "negatives": ["P \\log{(W)}", "\\frac{P^{2} W}{2}", "\\frac{P (P + 2 W)}{2}", "\\sin{(P + W)}"], "srepr_premise_expression": "Mul(Symbol('P', commutative=True), Pow(Symbol('W', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('P', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2)), Pow(Symbol('W', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('P', commutative=True), log(Symbol('W', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2)), Symbol('W', commutative=True))", "Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Symbol('P', commutative=True), Mul(Integer(2), Symbol('W', commutative=True))))", "sin(Add(Symbol('P', commutative=True), Symbol('W', commutative=True)))"]}, {"premise_expression": "G + L", "variable": "L", "positive": "\\frac{L (2 G + L)}{2}", "negatives": ["\\frac{L (2 G - L)}{2}", "\\frac{G (G + 2 L)}{2}", "\\frac{L^{2}}{2 G}", "\\frac{G L^{2}}{2}"], "srepr_premise_expression": "Add(Symbol('G', commutative=True), Symbol('L', commutative=True))", "srepr_variable": "Symbol('L', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Mul(Integer(2), Symbol('G', commutative=True)), Symbol('L', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Mul(Integer(2), Symbol('G', commutative=True)), Mul(Integer(-1), Symbol('L', commutative=True))))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Symbol('G', commutative=True), Mul(Integer(2), Symbol('L', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(-1)), Pow(Symbol('L', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Pow(Symbol('L', commutative=True), Integer(2)))"]}, {"premise_expression": "\\cos^{B}{(S)}", "variable": "S", "positive": "\\int \\cos^{B}{(S)} dS", "negatives": ["e^{B} \\log{(S)}", "- e^{B - S}", "- \\sin{(B - S)}", "\\frac{S (2 B - S)}{2}"], "srepr_premise_expression": "Pow(cos(Symbol('S', commutative=True)), Symbol('B', commutative=True))", "srepr_variable": "Symbol('S', commutative=True)", "srepr_positive": "Integral(Pow(cos(Symbol('S', commutative=True)), Symbol('B', commutative=True)), Tuple(Symbol('S', commutative=True)))", "srepr_negatives": ["Mul(exp(Symbol('B', commutative=True)), log(Symbol('S', commutative=True)))", "Mul(Integer(-1), exp(Add(Symbol('B', commutative=True), Mul(Integer(-1), Symbol('S', commutative=True)))))", "Mul(Integer(-1), sin(Add(Symbol('B', commutative=True), Mul(Integer(-1), Symbol('S', commutative=True)))))", "Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Mul(Integer(2), Symbol('B', commutative=True)), Mul(Integer(-1), Symbol('S', commutative=True))))"]}, {"premise_expression": "\\frac{\\log{(c)}}{z}", "variable": "z", "positive": "\\log{(c)} \\log{(z)}", "negatives": ["e^{c + z}", "\\frac{c (\\log{(c)} - 1)}{z}", "c e^{\\frac{z}{c}}", "- \\frac{\\cos{(z)}}{c}"], "srepr_premise_expression": "Mul(Pow(Symbol('z', commutative=True), Integer(-1)), log(Symbol('c', commutative=True)))", "srepr_variable": "Symbol('z', commutative=True)", "srepr_positive": "Mul(log(Symbol('c', commutative=True)), log(Symbol('z', commutative=True)))", "srepr_negatives": ["exp(Add(Symbol('c', commutative=True), Symbol('z', commutative=True)))", "Mul(Symbol('c', commutative=True), Pow(Symbol('z', commutative=True), Integer(-1)), Add(log(Symbol('c', commutative=True)), Integer(-1)))", "Mul(Symbol('c', commutative=True), exp(Mul(Pow(Symbol('c', commutative=True), Integer(-1)), Symbol('z', commutative=True))))", "Mul(Integer(-1), Pow(Symbol('c', commutative=True), Integer(-1)), cos(Symbol('z', commutative=True)))"]}, {"premise_expression": "\\sin{(C - g)}", "variable": "C", "positive": "- \\cos{(C - g)}", "negatives": ["\\cos{(C - g)}", "- g \\cos{(C)}", "2 C g", "\\frac{C (- C + 2 g)}{2}"], "srepr_premise_expression": "sin(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('g', commutative=True))))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('g', commutative=True)))))", "srepr_negatives": ["cos(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('g', commutative=True))))", "Mul(Integer(-1), Symbol('g', commutative=True), cos(Symbol('C', commutative=True)))", "Mul(Integer(2), Symbol('C', commutative=True), Symbol('g', commutative=True))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Mul(Integer(-1), Symbol('C', commutative=True)), Mul(Integer(2), Symbol('g', commutative=True))))"]}, {"premise_expression": "\\frac{U - v}{j}", "variable": "v", "positive": "\\frac{v (2 U - v)}{2 j}", "negatives": ["\\frac{v (2 U + v)}{2 j}", "\\frac{U (U - 2 v)}{2 j}", "\\frac{v (2 j^{U} - v)}{2}", "\\frac{j v (- 2 U + v)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('j', commutative=True), Integer(-1)), Add(Symbol('U', commutative=True), Mul(Integer(-1), Symbol('v', commutative=True))))", "srepr_variable": "Symbol('v', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('j', commutative=True), Integer(-1)), Symbol('v', commutative=True), Add(Mul(Integer(2), Symbol('U', commutative=True)), Mul(Integer(-1), Symbol('v', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('j', commutative=True), Integer(-1)), Symbol('v', commutative=True), Add(Mul(Integer(2), Symbol('U', commutative=True)), Symbol('v', commutative=True)))", "Mul(Rational(1, 2), Symbol('U', commutative=True), Pow(Symbol('j', commutative=True), Integer(-1)), Add(Symbol('U', commutative=True), Mul(Integer(-1), Integer(2), Symbol('v', commutative=True))))", "Mul(Rational(1, 2), Symbol('v', commutative=True), Add(Mul(Integer(2), Pow(Symbol('j', commutative=True), Symbol('U', commutative=True))), Mul(Integer(-1), Symbol('v', commutative=True))))", "Mul(Rational(1, 2), Symbol('j', commutative=True), Symbol('v', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('U', commutative=True)), Symbol('v', commutative=True)))"]}, {"premise_expression": "H s", "variable": "H", "positive": "\\frac{H^{2} s}{2}", "negatives": ["\\frac{H s^{2}}{2}", "\\frac{H^{2}}{2 s}", "\\frac{H (H - 2 s)}{2}", "s e^{H}"], "srepr_premise_expression": "Mul(Symbol('H', commutative=True), Symbol('s', commutative=True))", "srepr_variable": "Symbol('H', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('H', commutative=True), Integer(2)), Symbol('s', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('H', commutative=True), Pow(Symbol('s', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('H', commutative=True), Integer(2)), Pow(Symbol('s', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Symbol('H', commutative=True), Add(Symbol('H', commutative=True), Mul(Integer(-1), Integer(2), Symbol('s', commutative=True))))", "Mul(Symbol('s', commutative=True), exp(Symbol('H', commutative=True)))"]}, {"premise_expression": "K + N", "variable": "K", "positive": "\\frac{K (K + 2 N)}{2}", "negatives": ["\\frac{N (2 K + N)}{2}", "\\frac{K^{2} e^{N}}{2}", "\\cos{(K - N)}", "\\frac{K^{2} (N - 1)}{2}"], "srepr_premise_expression": "Add(Symbol('K', commutative=True), Symbol('N', commutative=True))", "srepr_variable": "Symbol('K', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Symbol('K', commutative=True), Mul(Integer(2), Symbol('N', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Mul(Integer(2), Symbol('K', commutative=True)), Symbol('N', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('K', commutative=True), Integer(2)), exp(Symbol('N', commutative=True)))", "cos(Add(Symbol('K', commutative=True), Mul(Integer(-1), Symbol('N', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('K', commutative=True), Integer(2)), Add(Symbol('N', commutative=True), Integer(-1)))"]}, {"premise_expression": "a + b", "variable": "a", "positive": "\\frac{a (a + 2 b)}{2}", "negatives": ["\\frac{b (2 a + b)}{2}", "\\frac{a^{2} \\log{(b)}}{2}", "- \\cos{(a + b)}", "\\sin{(a - b)}"], "srepr_premise_expression": "Add(Symbol('a', commutative=True), Symbol('b', commutative=True))", "srepr_variable": "Symbol('a', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('a', commutative=True), Add(Symbol('a', commutative=True), Mul(Integer(2), Symbol('b', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('b', commutative=True), Add(Mul(Integer(2), Symbol('a', commutative=True)), Symbol('b', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('a', commutative=True), Integer(2)), log(Symbol('b', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('a', commutative=True), Symbol('b', commutative=True))))", "sin(Add(Symbol('a', commutative=True), Mul(Integer(-1), Symbol('b', commutative=True))))"]}, {"premise_expression": "\\frac{\\cos{(l)}}{Y}", "variable": "l", "positive": "\\frac{\\sin{(l)}}{Y}", "negatives": ["Y \\sin{(l)}", "Y e^{l}", "- Y \\cos{(l)}", "Y l + \\sin{(l)}"], "srepr_premise_expression": "Mul(Pow(Symbol('Y', commutative=True), Integer(-1)), cos(Symbol('l', commutative=True)))", "srepr_variable": "Symbol('l', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('Y', commutative=True), Integer(-1)), sin(Symbol('l', commutative=True)))", "srepr_negatives": ["Mul(Symbol('Y', commutative=True), sin(Symbol('l', commutative=True)))", "Mul(Symbol('Y', commutative=True), exp(Symbol('l', commutative=True)))", "Mul(Integer(-1), Symbol('Y', commutative=True), cos(Symbol('l', commutative=True)))", "Add(Mul(Symbol('Y', commutative=True), Symbol('l', commutative=True)), sin(Symbol('l', commutative=True)))"]}, {"premise_expression": "\\sin{(M - o)}", "variable": "o", "positive": "\\cos{(M - o)}", "negatives": ["- \\cos{(M - o)}", "\\sin{(M + o)}", "- \\sin{(M - o)}", "e^{M + o}"], "srepr_premise_expression": "sin(Add(Symbol('M', commutative=True), Mul(Integer(-1), Symbol('o', commutative=True))))", "srepr_variable": "Symbol('o', commutative=True)", "srepr_positive": "cos(Add(Symbol('M', commutative=True), Mul(Integer(-1), Symbol('o', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('M', commutative=True), Mul(Integer(-1), Symbol('o', commutative=True)))))", "sin(Add(Symbol('M', commutative=True), Symbol('o', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('M', commutative=True), Mul(Integer(-1), Symbol('o', commutative=True)))))", "exp(Add(Symbol('M', commutative=True), Symbol('o', commutative=True)))"]}, {"premise_expression": "\\log{(P u)}", "variable": "P", "positive": "P (\\log{(P u)} - 1)", "negatives": ["u (\\log{(P u)} - 1)", "P (\\log{(\\frac{u}{P})} + 1)", "\\frac{P^{2} (u - 1)}{2}", "P (- u + \\log{(P^{u})})"], "srepr_premise_expression": "log(Mul(Symbol('P', commutative=True), Symbol('u', commutative=True)))", "srepr_variable": "Symbol('P', commutative=True)", "srepr_positive": "Mul(Symbol('P', commutative=True), Add(log(Mul(Symbol('P', commutative=True), Symbol('u', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('u', commutative=True), Add(log(Mul(Symbol('P', commutative=True), Symbol('u', commutative=True))), Integer(-1)))", "Mul(Symbol('P', commutative=True), Add(log(Mul(Pow(Symbol('P', commutative=True), Integer(-1)), Symbol('u', commutative=True))), Integer(1)))", "Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2)), Add(Symbol('u', commutative=True), Integer(-1)))", "Mul(Symbol('P', commutative=True), Add(Mul(Integer(-1), Symbol('u', commutative=True)), log(Pow(Symbol('P', commutative=True), Symbol('u', commutative=True)))))"]}, {"premise_expression": "G a", "variable": "G", "positive": "\\frac{G^{2} a}{2}", "negatives": ["\\frac{G a^{2}}{2}", "\\frac{G^{2}}{2 a}", "\\frac{G (G + 2 a)}{2}", "- \\frac{\\cos{(G)}}{a}"], "srepr_premise_expression": "Mul(Symbol('G', commutative=True), Symbol('a', commutative=True))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(2)), Symbol('a', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('G', commutative=True), Pow(Symbol('a', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(2)), Pow(Symbol('a', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Symbol('G', commutative=True), Mul(Integer(2), Symbol('a', commutative=True))))", "Mul(Integer(-1), Pow(Symbol('a', commutative=True), Integer(-1)), cos(Symbol('G', commutative=True)))"]}, {"premise_expression": "L w", "variable": "L", "positive": "\\frac{L^{2} w}{2}", "negatives": ["\\frac{L w^{2}}{2}", "\\frac{L^{2} \\log{(w)}}{2}", "\\sin{(L - w)}", "L w + e^{L}"], "srepr_premise_expression": "Mul(Symbol('L', commutative=True), Symbol('w', commutative=True))", "srepr_variable": "Symbol('L', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(2)), Symbol('w', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('L', commutative=True), Pow(Symbol('w', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(2)), log(Symbol('w', commutative=True)))", "sin(Add(Symbol('L', commutative=True), Mul(Integer(-1), Symbol('w', commutative=True))))", "Add(Mul(Symbol('L', commutative=True), Symbol('w', commutative=True)), exp(Symbol('L', commutative=True)))"]}, {"premise_expression": "\\log{(Z + q)}", "variable": "q", "positive": "Z \\log{(Z + q)} + q \\log{(Z + q)} - q", "negatives": ["Z \\log{(Z + q)} - Z + q \\log{(Z + q)}", "q (- Z + \\log{(q^{Z})})", "\\frac{q (- 2 Z + q)}{2}", "Z \\log{(q)}"], "srepr_premise_expression": "log(Add(Symbol('Z', commutative=True), Symbol('q', commutative=True)))", "srepr_variable": "Symbol('q', commutative=True)", "srepr_positive": "Add(Mul(Symbol('Z', commutative=True), log(Add(Symbol('Z', commutative=True), Symbol('q', commutative=True)))), Mul(Symbol('q', commutative=True), log(Add(Symbol('Z', commutative=True), Symbol('q', commutative=True)))), Mul(Integer(-1), Symbol('q', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('Z', commutative=True), log(Add(Symbol('Z', commutative=True), Symbol('q', commutative=True)))), Mul(Integer(-1), Symbol('Z', commutative=True)), Mul(Symbol('q', commutative=True), log(Add(Symbol('Z', commutative=True), Symbol('q', commutative=True)))))", "Mul(Symbol('q', commutative=True), Add(Mul(Integer(-1), Symbol('Z', commutative=True)), log(Pow(Symbol('q', commutative=True), Symbol('Z', commutative=True)))))", "Mul(Rational(1, 2), Symbol('q', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('Z', commutative=True)), Symbol('q', commutative=True)))", "Mul(Symbol('Z', commutative=True), log(Symbol('q', commutative=True)))"]}, {"premise_expression": "p + e^{A}", "variable": "p", "positive": "\\frac{p (p + 2 e^{A})}{2}", "negatives": ["\\frac{p (p + 2 \\cos{(A)})}{2}", "\\frac{p (- p + 2 \\sin{(A)})}{2}", "A p + e^{A}", "\\frac{p (2 A - p)}{2}"], "srepr_premise_expression": "Add(Symbol('p', commutative=True), exp(Symbol('A', commutative=True)))", "srepr_variable": "Symbol('p', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Symbol('p', commutative=True), Mul(Integer(2), exp(Symbol('A', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Symbol('p', commutative=True), Mul(Integer(2), cos(Symbol('A', commutative=True)))))", "Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Mul(Integer(-1), Symbol('p', commutative=True)), Mul(Integer(2), sin(Symbol('A', commutative=True)))))", "Add(Mul(Symbol('A', commutative=True), Symbol('p', commutative=True)), exp(Symbol('A', commutative=True)))", "Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Mul(Integer(2), Symbol('A', commutative=True)), Mul(Integer(-1), Symbol('p', commutative=True))))"]}, {"premise_expression": "\\log{(L p)}", "variable": "L", "positive": "L (\\log{(L p)} - 1)", "negatives": ["p (\\log{(L p)} - 1)", "\\frac{L (L + 2 \\cos{(p)})}{2}", "\\frac{L (L + 2 \\sin{(p)})}{2}", "\\frac{L (- L + 2 \\sin{(p)})}{2}"], "srepr_premise_expression": "log(Mul(Symbol('L', commutative=True), Symbol('p', commutative=True)))", "srepr_variable": "Symbol('L', commutative=True)", "srepr_positive": "Mul(Symbol('L', commutative=True), Add(log(Mul(Symbol('L', commutative=True), Symbol('p', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('p', commutative=True), Add(log(Mul(Symbol('L', commutative=True), Symbol('p', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Symbol('L', commutative=True), Mul(Integer(2), cos(Symbol('p', commutative=True)))))", "Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Symbol('L', commutative=True), Mul(Integer(2), sin(Symbol('p', commutative=True)))))", "Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Mul(Integer(-1), Symbol('L', commutative=True)), Mul(Integer(2), sin(Symbol('p', commutative=True)))))"]}, {"premise_expression": "E - f", "variable": "f", "positive": "\\frac{f (2 E - f)}{2}", "negatives": ["\\frac{E (E - 2 f)}{2}", "- \\sin{(E - f)}", "\\frac{E f^{2}}{2}", "\\frac{f^{2}}{2 E}"], "srepr_premise_expression": "Add(Symbol('E', commutative=True), Mul(Integer(-1), Symbol('f', commutative=True)))", "srepr_variable": "Symbol('f', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Mul(Integer(2), Symbol('E', commutative=True)), Mul(Integer(-1), Symbol('f', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('E', commutative=True), Add(Symbol('E', commutative=True), Mul(Integer(-1), Integer(2), Symbol('f', commutative=True))))", "Mul(Integer(-1), sin(Add(Symbol('E', commutative=True), Mul(Integer(-1), Symbol('f', commutative=True)))))", "Mul(Rational(1, 2), Symbol('E', commutative=True), Pow(Symbol('f', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('E', commutative=True), Integer(-1)), Pow(Symbol('f', commutative=True), Integer(2)))"]}, {"premise_expression": "\\log{(P - t)}", "variable": "P", "positive": "P \\log{(P - t)} - P - t \\log{(P - t)}", "negatives": ["- P \\log{(- P + t)} + t \\log{(P - t)} - t", "\\frac{P (- P + 2 \\log{(t)})}{2}", "- P t - \\cos{(P)}", "\\frac{P (P + 2 e^{t})}{2}"], "srepr_premise_expression": "log(Add(Symbol('P', commutative=True), Mul(Integer(-1), Symbol('t', commutative=True))))", "srepr_variable": "Symbol('P', commutative=True)", "srepr_positive": "Add(Mul(Symbol('P', commutative=True), log(Add(Symbol('P', commutative=True), Mul(Integer(-1), Symbol('t', commutative=True))))), Mul(Integer(-1), Symbol('P', commutative=True)), Mul(Integer(-1), Symbol('t', commutative=True), log(Add(Symbol('P', commutative=True), Mul(Integer(-1), Symbol('t', commutative=True))))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('P', commutative=True), log(Add(Mul(Integer(-1), Symbol('P', commutative=True)), Symbol('t', commutative=True)))), Mul(Symbol('t', commutative=True), log(Add(Symbol('P', commutative=True), Mul(Integer(-1), Symbol('t', commutative=True))))), Mul(Integer(-1), Symbol('t', commutative=True)))", "Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Mul(Integer(-1), Symbol('P', commutative=True)), Mul(Integer(2), log(Symbol('t', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('P', commutative=True), Symbol('t', commutative=True)), Mul(Integer(-1), cos(Symbol('P', commutative=True))))", "Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Symbol('P', commutative=True), Mul(Integer(2), exp(Symbol('t', commutative=True)))))"]}, {"premise_expression": "Y + r", "variable": "r", "positive": "\\frac{r (2 Y + r)}{2}", "negatives": ["\\frac{Y (Y + 2 r)}{2}", "\\frac{r^{2} \\sin{(Y)}}{2}", "\\frac{r^{2} (1 - Y)}{2 Y}", "\\frac{Y r^{2}}{2}"], "srepr_premise_expression": "Add(Symbol('Y', commutative=True), Symbol('r', commutative=True))", "srepr_variable": "Symbol('r', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(2), Symbol('Y', commutative=True)), Symbol('r', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('Y', commutative=True), Add(Symbol('Y', commutative=True), Mul(Integer(2), Symbol('r', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('r', commutative=True), Integer(2)), sin(Symbol('Y', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('Y', commutative=True), Integer(-1)), Pow(Symbol('r', commutative=True), Integer(2)), Add(Integer(1), Mul(Integer(-1), Symbol('Y', commutative=True))))", "Mul(Rational(1, 2), Symbol('Y', commutative=True), Pow(Symbol('r', commutative=True), Integer(2)))"]}, {"premise_expression": "- v + \\sin{(R)}", "variable": "v", "positive": "\\frac{v (- v + 2 \\sin{(R)})}{2}", "negatives": ["\\frac{v (- v + 2 \\log{(R)})}{2}", "\\frac{v^{2} e^{R}}{2}", "\\log{(v)} \\sin{(R)}", "- R v - \\cos{(R)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('v', commutative=True)), sin(Symbol('R', commutative=True)))", "srepr_variable": "Symbol('v', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('v', commutative=True), Add(Mul(Integer(-1), Symbol('v', commutative=True)), Mul(Integer(2), sin(Symbol('R', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('v', commutative=True), Add(Mul(Integer(-1), Symbol('v', commutative=True)), Mul(Integer(2), log(Symbol('R', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('v', commutative=True), Integer(2)), exp(Symbol('R', commutative=True)))", "Mul(log(Symbol('v', commutative=True)), sin(Symbol('R', commutative=True)))", "Add(Mul(Integer(-1), Symbol('R', commutative=True), Symbol('v', commutative=True)), Mul(Integer(-1), cos(Symbol('R', commutative=True))))"]}, {"premise_expression": "Y + f + x", "variable": "x", "positive": "x (Y + f + \\frac{x}{2})", "negatives": ["\\frac{x (- 2 Y + 2 f + x)}{2}", "\\frac{f (2 Y + f + 2 x)}{2}", "\\frac{Y (Y + 2 f + 2 x)}{2}", "x (Y + x)"], "srepr_premise_expression": "Add(Symbol('Y', commutative=True), Symbol('f', commutative=True), Symbol('x', commutative=True))", "srepr_variable": "Symbol('x', commutative=True)", "srepr_positive": "Mul(Symbol('x', commutative=True), Add(Symbol('Y', commutative=True), Symbol('f', commutative=True), Mul(Rational(1, 2), Symbol('x', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('x', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('Y', commutative=True)), Mul(Integer(2), Symbol('f', commutative=True)), Symbol('x', commutative=True)))", "Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Mul(Integer(2), Symbol('Y', commutative=True)), Symbol('f', commutative=True), Mul(Integer(2), Symbol('x', commutative=True))))", "Mul(Rational(1, 2), Symbol('Y', commutative=True), Add(Symbol('Y', commutative=True), Mul(Integer(2), Symbol('f', commutative=True)), Mul(Integer(2), Symbol('x', commutative=True))))", "Mul(Symbol('x', commutative=True), Add(Symbol('Y', commutative=True), Symbol('x', commutative=True)))"]}, {"premise_expression": "\\cos{(M + v)}", "variable": "v", "positive": "\\sin{(M + v)}", "negatives": ["- \\sin{(M - v)}", "M v - \\cos{(v)}", "e^{M} \\log{(v)}", "M v + e^{v}"], "srepr_premise_expression": "cos(Add(Symbol('M', commutative=True), Symbol('v', commutative=True)))", "srepr_variable": "Symbol('v', commutative=True)", "srepr_positive": "sin(Add(Symbol('M', commutative=True), Symbol('v', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('M', commutative=True), Mul(Integer(-1), Symbol('v', commutative=True)))))", "Add(Mul(Symbol('M', commutative=True), Symbol('v', commutative=True)), Mul(Integer(-1), cos(Symbol('v', commutative=True))))", "Mul(exp(Symbol('M', commutative=True)), log(Symbol('v', commutative=True)))", "Add(Mul(Symbol('M', commutative=True), Symbol('v', commutative=True)), exp(Symbol('v', commutative=True)))"]}, {"premise_expression": "\\frac{G j}{v}", "variable": "v", "positive": "G j \\log{(v)}", "negatives": ["\\frac{G j^{2}}{2 v}", "(- G + j) \\log{(v)}", "\\frac{G^{2} j}{2 v}", "\\frac{G v^{2}}{2 j}"], "srepr_premise_expression": "Mul(Symbol('G', commutative=True), Symbol('j', commutative=True), Pow(Symbol('v', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('v', commutative=True)", "srepr_positive": "Mul(Symbol('G', commutative=True), Symbol('j', commutative=True), log(Symbol('v', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('G', commutative=True), Pow(Symbol('j', commutative=True), Integer(2)), Pow(Symbol('v', commutative=True), Integer(-1)))", "Mul(Add(Mul(Integer(-1), Symbol('G', commutative=True)), Symbol('j', commutative=True)), log(Symbol('v', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(2)), Symbol('j', commutative=True), Pow(Symbol('v', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Pow(Symbol('j', commutative=True), Integer(-1)), Pow(Symbol('v', commutative=True), Integer(2)))"]}, {"premise_expression": "\\log{(G - b)}", "variable": "G", "positive": "G \\log{(G - b)} - G - b \\log{(G - b)}", "negatives": ["- G \\log{(- G + b)} + b \\log{(G - b)} - b", "G (- b + \\log{(G)} - 1)", "G b (\\log{(G)} - 1)", "G e^{\\frac{b}{G}} - b \\operatorname{Ei}{(\\frac{b}{G})}"], "srepr_premise_expression": "log(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('b', commutative=True))))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Add(Mul(Symbol('G', commutative=True), log(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('b', commutative=True))))), Mul(Integer(-1), Symbol('G', commutative=True)), Mul(Integer(-1), Symbol('b', commutative=True), log(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('b', commutative=True))))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('G', commutative=True), log(Add(Mul(Integer(-1), Symbol('G', commutative=True)), Symbol('b', commutative=True)))), Mul(Symbol('b', commutative=True), log(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('b', commutative=True))))), Mul(Integer(-1), Symbol('b', commutative=True)))", "Mul(Symbol('G', commutative=True), Add(Mul(Integer(-1), Symbol('b', commutative=True)), log(Symbol('G', commutative=True)), Integer(-1)))", "Mul(Symbol('G', commutative=True), Symbol('b', commutative=True), Add(log(Symbol('G', commutative=True)), Integer(-1)))", "Add(Mul(Symbol('G', commutative=True), exp(Mul(Pow(Symbol('G', commutative=True), Integer(-1)), Symbol('b', commutative=True)))), Mul(Integer(-1), Symbol('b', commutative=True), Ei(Mul(Pow(Symbol('G', commutative=True), Integer(-1)), Symbol('b', commutative=True)))))"]}, {"premise_expression": "\\log{(E - c)}", "variable": "c", "positive": "- E \\log{(- E + c)} + c \\log{(E - c)} - c", "negatives": ["E \\log{(E - c)} - E - c \\log{(E - c)}", "c (- E + \\log{(c^{E})})", "\\log{(c)} \\cos{(E)}", "\\frac{c (- c + 2 \\sin{(E)})}{2}"], "srepr_premise_expression": "log(Add(Symbol('E', commutative=True), Mul(Integer(-1), Symbol('c', commutative=True))))", "srepr_variable": "Symbol('c', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('E', commutative=True), log(Add(Mul(Integer(-1), Symbol('E', commutative=True)), Symbol('c', commutative=True)))), Mul(Symbol('c', commutative=True), log(Add(Symbol('E', commutative=True), Mul(Integer(-1), Symbol('c', commutative=True))))), Mul(Integer(-1), Symbol('c', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('E', commutative=True), log(Add(Symbol('E', commutative=True), Mul(Integer(-1), Symbol('c', commutative=True))))), Mul(Integer(-1), Symbol('E', commutative=True)), Mul(Integer(-1), Symbol('c', commutative=True), log(Add(Symbol('E', commutative=True), Mul(Integer(-1), Symbol('c', commutative=True))))))", "Mul(Symbol('c', commutative=True), Add(Mul(Integer(-1), Symbol('E', commutative=True)), log(Pow(Symbol('c', commutative=True), Symbol('E', commutative=True)))))", "Mul(log(Symbol('c', commutative=True)), cos(Symbol('E', commutative=True)))", "Mul(Rational(1, 2), Symbol('c', commutative=True), Add(Mul(Integer(-1), Symbol('c', commutative=True)), Mul(Integer(2), sin(Symbol('E', commutative=True)))))"]}, {"premise_expression": "- I + e^{x}", "variable": "I", "positive": "\\frac{I (- I + 2 e^{x})}{2}", "negatives": ["- I x + e^{x}", "I x + e^{I}", "\\frac{I^{2} \\cos{(x)}}{2}", "\\cos{(I - x)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('I', commutative=True)), exp(Symbol('x', commutative=True)))", "srepr_variable": "Symbol('I', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('I', commutative=True), Add(Mul(Integer(-1), Symbol('I', commutative=True)), Mul(Integer(2), exp(Symbol('x', commutative=True)))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('I', commutative=True), Symbol('x', commutative=True)), exp(Symbol('x', commutative=True)))", "Add(Mul(Symbol('I', commutative=True), Symbol('x', commutative=True)), exp(Symbol('I', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(2)), cos(Symbol('x', commutative=True)))", "cos(Add(Symbol('I', commutative=True), Mul(Integer(-1), Symbol('x', commutative=True))))"]}, {"premise_expression": "- N + a", "variable": "a", "positive": "\\frac{a (- 2 N + a)}{2}", "negatives": ["\\frac{N (- N + 2 a)}{2}", "\\frac{a^{2} \\log{(N)}}{2}", "- \\sin{(N - a)}", "- \\cos{(N - a)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('N', commutative=True)), Symbol('a', commutative=True))", "srepr_variable": "Symbol('a', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('a', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('N', commutative=True)), Symbol('a', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Mul(Integer(-1), Symbol('N', commutative=True)), Mul(Integer(2), Symbol('a', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('a', commutative=True), Integer(2)), log(Symbol('N', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('N', commutative=True), Mul(Integer(-1), Symbol('a', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('N', commutative=True), Mul(Integer(-1), Symbol('a', commutative=True)))))"]}, {"premise_expression": "D + L", "variable": "L", "positive": "\\frac{L (2 D + L)}{2}", "negatives": ["\\frac{D (D + 2 L)}{2}", "\\frac{L^{2} \\sin{(D)}}{2}", "\\frac{L^{2}}{2 D}", "\\frac{\\sin{(L)}}{D}"], "srepr_premise_expression": "Add(Symbol('D', commutative=True), Symbol('L', commutative=True))", "srepr_variable": "Symbol('L', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Mul(Integer(2), Symbol('D', commutative=True)), Symbol('L', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('D', commutative=True), Add(Symbol('D', commutative=True), Mul(Integer(2), Symbol('L', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(2)), sin(Symbol('D', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(-1)), Pow(Symbol('L', commutative=True), Integer(2)))", "Mul(Pow(Symbol('D', commutative=True), Integer(-1)), sin(Symbol('L', commutative=True)))"]}, {"premise_expression": "\\frac{\\cos{(N)}}{l}", "variable": "N", "positive": "\\frac{\\sin{(N)}}{l}", "negatives": ["l e^{\\frac{N}{l}}", "- \\cos{(N + l)}", "\\log{(N)} \\sin{(l)}", "\\log{(l)} \\cos{(N)}"], "srepr_premise_expression": "Mul(Pow(Symbol('l', commutative=True), Integer(-1)), cos(Symbol('N', commutative=True)))", "srepr_variable": "Symbol('N', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('l', commutative=True), Integer(-1)), sin(Symbol('N', commutative=True)))", "srepr_negatives": ["Mul(Symbol('l', commutative=True), exp(Mul(Symbol('N', commutative=True), Pow(Symbol('l', commutative=True), Integer(-1)))))", "Mul(Integer(-1), cos(Add(Symbol('N', commutative=True), Symbol('l', commutative=True))))", "Mul(log(Symbol('N', commutative=True)), sin(Symbol('l', commutative=True)))", "Mul(log(Symbol('l', commutative=True)), cos(Symbol('N', commutative=True)))"]}, {"premise_expression": "G + V", "variable": "G", "positive": "\\frac{G (G + 2 V)}{2}", "negatives": ["\\frac{V (2 G + V)}{2}", "\\frac{G (- G + 2 e^{V})}{2}", "- \\cos{(G + V)}", "- G V + e^{G}"], "srepr_premise_expression": "Add(Symbol('G', commutative=True), Symbol('V', commutative=True))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Symbol('G', commutative=True), Mul(Integer(2), Symbol('V', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('V', commutative=True), Add(Mul(Integer(2), Symbol('G', commutative=True)), Symbol('V', commutative=True)))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Mul(Integer(-1), Symbol('G', commutative=True)), Mul(Integer(2), exp(Symbol('V', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('G', commutative=True), Symbol('V', commutative=True))))", "Add(Mul(Integer(-1), Symbol('G', commutative=True), Symbol('V', commutative=True)), exp(Symbol('G', commutative=True)))"]}, {"premise_expression": "\\frac{M}{Y}", "variable": "M", "positive": "\\frac{M^{2}}{2 Y}", "negatives": ["M \\log{(Y)}", "Y e^{\\frac{M}{Y}}", "Y e^{M}", "\\frac{M \\cos{(Y)}}{Y}"], "srepr_premise_expression": "Mul(Symbol('M', commutative=True), Pow(Symbol('Y', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('M', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('M', commutative=True), Integer(2)), Pow(Symbol('Y', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('M', commutative=True), log(Symbol('Y', commutative=True)))", "Mul(Symbol('Y', commutative=True), exp(Mul(Symbol('M', commutative=True), Pow(Symbol('Y', commutative=True), Integer(-1)))))", "Mul(Symbol('Y', commutative=True), exp(Symbol('M', commutative=True)))", "Mul(Symbol('M', commutative=True), Pow(Symbol('Y', commutative=True), Integer(-1)), cos(Symbol('Y', commutative=True)))"]}, {"premise_expression": "t + \\cos{(y)}", "variable": "y", "positive": "t y + \\sin{(y)}", "negatives": ["- t \\cos{(y)}", "t \\log{(y)}", "\\sin{(t + y)}", "\\frac{t (t + 2 \\cos{(y)})}{2}"], "srepr_premise_expression": "Add(Symbol('t', commutative=True), cos(Symbol('y', commutative=True)))", "srepr_variable": "Symbol('y', commutative=True)", "srepr_positive": "Add(Mul(Symbol('t', commutative=True), Symbol('y', commutative=True)), sin(Symbol('y', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Symbol('t', commutative=True), cos(Symbol('y', commutative=True)))", "Mul(Symbol('t', commutative=True), log(Symbol('y', commutative=True)))", "sin(Add(Symbol('t', commutative=True), Symbol('y', commutative=True)))", "Mul(Rational(1, 2), Symbol('t', commutative=True), Add(Symbol('t', commutative=True), Mul(Integer(2), cos(Symbol('y', commutative=True)))))"]}, {"premise_expression": "N + j", "variable": "j", "positive": "\\frac{j (2 N + j)}{2}", "negatives": ["\\frac{N (N + 2 j)}{2}", "- \\sin{(N - j)}", "\\cos{(N - j)}", "N \\sin{(j)}"], "srepr_premise_expression": "Add(Symbol('N', commutative=True), Symbol('j', commutative=True))", "srepr_variable": "Symbol('j', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('j', commutative=True), Add(Mul(Integer(2), Symbol('N', commutative=True)), Symbol('j', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Symbol('N', commutative=True), Mul(Integer(2), Symbol('j', commutative=True))))", "Mul(Integer(-1), sin(Add(Symbol('N', commutative=True), Mul(Integer(-1), Symbol('j', commutative=True)))))", "cos(Add(Symbol('N', commutative=True), Mul(Integer(-1), Symbol('j', commutative=True))))", "Mul(Symbol('N', commutative=True), sin(Symbol('j', commutative=True)))"]}, {"premise_expression": "T a", "variable": "a", "positive": "\\frac{T a^{2}}{2}", "negatives": ["\\frac{T^{2} a}{2}", "T \\log{(a)}", "- \\sin{(T - a)}", "e^{- T + a}"], "srepr_premise_expression": "Mul(Symbol('T', commutative=True), Symbol('a', commutative=True))", "srepr_variable": "Symbol('a', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('T', commutative=True), Pow(Symbol('a', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('T', commutative=True), Integer(2)), Symbol('a', commutative=True))", "Mul(Symbol('T', commutative=True), log(Symbol('a', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('T', commutative=True), Mul(Integer(-1), Symbol('a', commutative=True)))))", "exp(Add(Mul(Integer(-1), Symbol('T', commutative=True)), Symbol('a', commutative=True)))"]}, {"premise_expression": "- S + \\sin{(r)}", "variable": "S", "positive": "\\frac{S (- S + 2 \\sin{(r)})}{2}", "negatives": ["\\frac{S (- S + 2 \\cos{(r)})}{2}", "\\frac{S (S - 2 r)}{2}", "- S r - \\cos{(r)}", "\\frac{S^{2} r}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('S', commutative=True)), sin(Symbol('r', commutative=True)))", "srepr_variable": "Symbol('S', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Mul(Integer(-1), Symbol('S', commutative=True)), Mul(Integer(2), sin(Symbol('r', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Mul(Integer(-1), Symbol('S', commutative=True)), Mul(Integer(2), cos(Symbol('r', commutative=True)))))", "Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Symbol('S', commutative=True), Mul(Integer(-1), Integer(2), Symbol('r', commutative=True))))", "Add(Mul(Integer(-1), Symbol('S', commutative=True), Symbol('r', commutative=True)), Mul(Integer(-1), cos(Symbol('r', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('S', commutative=True), Integer(2)), Symbol('r', commutative=True))"]}, {"premise_expression": "B + \\sin{(E)}", "variable": "E", "positive": "B E - \\cos{(E)}", "negatives": ["\\sin{(B + E)}", "\\cos{(B - E)}", "\\frac{B (B + 2 \\sin{(E)})}{2}", "\\frac{E^{2} \\sin{(B)}}{2}"], "srepr_premise_expression": "Add(Symbol('B', commutative=True), sin(Symbol('E', commutative=True)))", "srepr_variable": "Symbol('E', commutative=True)", "srepr_positive": "Add(Mul(Symbol('B', commutative=True), Symbol('E', commutative=True)), Mul(Integer(-1), cos(Symbol('E', commutative=True))))", "srepr_negatives": ["sin(Add(Symbol('B', commutative=True), Symbol('E', commutative=True)))", "cos(Add(Symbol('B', commutative=True), Mul(Integer(-1), Symbol('E', commutative=True))))", "Mul(Rational(1, 2), Symbol('B', commutative=True), Add(Symbol('B', commutative=True), Mul(Integer(2), sin(Symbol('E', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('E', commutative=True), Integer(2)), sin(Symbol('B', commutative=True)))"]}, {"premise_expression": "\\frac{F Y}{o}", "variable": "Y", "positive": "\\frac{F Y^{2}}{2 o}", "negatives": ["\\frac{F^{2} Y}{2 o}", "\\frac{Y^{2}}{2 F o}", "F Y \\log{(o)}", "F o \\log{(Y)}"], "srepr_premise_expression": "Mul(Symbol('F', commutative=True), Symbol('Y', commutative=True), Pow(Symbol('o', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('Y', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('F', commutative=True), Pow(Symbol('Y', commutative=True), Integer(2)), Pow(Symbol('o', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('F', commutative=True), Integer(2)), Symbol('Y', commutative=True), Pow(Symbol('o', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('F', commutative=True), Integer(-1)), Pow(Symbol('Y', commutative=True), Integer(2)), Pow(Symbol('o', commutative=True), Integer(-1)))", "Mul(Symbol('F', commutative=True), Symbol('Y', commutative=True), log(Symbol('o', commutative=True)))", "Mul(Symbol('F', commutative=True), Symbol('o', commutative=True), log(Symbol('Y', commutative=True)))"]}, {"premise_expression": "x + \\sin{(N)}", "variable": "x", "positive": "\\frac{x (x + 2 \\sin{(N)})}{2}", "negatives": ["\\frac{x^{2} \\log{(N)}}{2}", "N x - \\cos{(N)}", "\\frac{x (2 N - x)}{2}", "x (N + \\log{(x)} - 1)"], "srepr_premise_expression": "Add(Symbol('x', commutative=True), sin(Symbol('N', commutative=True)))", "srepr_variable": "Symbol('x', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('x', commutative=True), Add(Symbol('x', commutative=True), Mul(Integer(2), sin(Symbol('N', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('x', commutative=True), Integer(2)), log(Symbol('N', commutative=True)))", "Add(Mul(Symbol('N', commutative=True), Symbol('x', commutative=True)), Mul(Integer(-1), cos(Symbol('N', commutative=True))))", "Mul(Rational(1, 2), Symbol('x', commutative=True), Add(Mul(Integer(2), Symbol('N', commutative=True)), Mul(Integer(-1), Symbol('x', commutative=True))))", "Mul(Symbol('x', commutative=True), Add(Symbol('N', commutative=True), log(Symbol('x', commutative=True)), Integer(-1)))"]}, {"premise_expression": "E Q", "variable": "E", "positive": "\\frac{E^{2} Q}{2}", "negatives": ["\\frac{E Q^{2}}{2}", "\\frac{E^{2} e^{Q}}{2}", "\\frac{\\sin{(E)}}{Q}", "- \\frac{\\cos{(E)}}{Q}"], "srepr_premise_expression": "Mul(Symbol('E', commutative=True), Symbol('Q', commutative=True))", "srepr_variable": "Symbol('E', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('E', commutative=True), Integer(2)), Symbol('Q', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('E', commutative=True), Pow(Symbol('Q', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('E', commutative=True), Integer(2)), exp(Symbol('Q', commutative=True)))", "Mul(Pow(Symbol('Q', commutative=True), Integer(-1)), sin(Symbol('E', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('Q', commutative=True), Integer(-1)), cos(Symbol('E', commutative=True)))"]}, {"premise_expression": "\\log{(\\frac{y}{P})}", "variable": "y", "positive": "y (\\log{(\\frac{y}{P})} - 1)", "negatives": ["P (\\log{(\\frac{y}{P})} + 1)", "P y (\\log{(y)} - 1)", "y (- P + \\log{(y)} - 1)", "\\frac{y^{2} \\log{(P)}}{2}"], "srepr_premise_expression": "log(Mul(Pow(Symbol('P', commutative=True), Integer(-1)), Symbol('y', commutative=True)))", "srepr_variable": "Symbol('y', commutative=True)", "srepr_positive": "Mul(Symbol('y', commutative=True), Add(log(Mul(Pow(Symbol('P', commutative=True), Integer(-1)), Symbol('y', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('P', commutative=True), Add(log(Mul(Pow(Symbol('P', commutative=True), Integer(-1)), Symbol('y', commutative=True))), Integer(1)))", "Mul(Symbol('P', commutative=True), Symbol('y', commutative=True), Add(log(Symbol('y', commutative=True)), Integer(-1)))", "Mul(Symbol('y', commutative=True), Add(Mul(Integer(-1), Symbol('P', commutative=True)), log(Symbol('y', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('y', commutative=True), Integer(2)), log(Symbol('P', commutative=True)))"]}, {"premise_expression": "\\frac{A}{P}", "variable": "P", "positive": "A \\log{(P)}", "negatives": ["\\frac{A^{2}}{2 P}", "A P + e^{P}", "- \\cos{(A - P)}", "\\cos{(A - P)}"], "srepr_premise_expression": "Mul(Symbol('A', commutative=True), Pow(Symbol('P', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('P', commutative=True)", "srepr_positive": "Mul(Symbol('A', commutative=True), log(Symbol('P', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2)), Pow(Symbol('P', commutative=True), Integer(-1)))", "Add(Mul(Symbol('A', commutative=True), Symbol('P', commutative=True)), exp(Symbol('P', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('P', commutative=True)))))", "cos(Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('P', commutative=True))))"]}, {"premise_expression": "e^{t + w}", "variable": "w", "positive": "e^{t + w}", "negatives": ["- \\cos{(t + w)}", "t w + e^{w}", "- t w + \\sin{(w)}", "\\frac{\\sin{(w)}}{t}"], "srepr_premise_expression": "exp(Add(Symbol('t', commutative=True), Symbol('w', commutative=True)))", "srepr_variable": "Symbol('w', commutative=True)", "srepr_positive": "exp(Add(Symbol('t', commutative=True), Symbol('w', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('t', commutative=True), Symbol('w', commutative=True))))", "Add(Mul(Symbol('t', commutative=True), Symbol('w', commutative=True)), exp(Symbol('w', commutative=True)))", "Add(Mul(Integer(-1), Symbol('t', commutative=True), Symbol('w', commutative=True)), sin(Symbol('w', commutative=True)))", "Mul(Pow(Symbol('t', commutative=True), Integer(-1)), sin(Symbol('w', commutative=True)))"]}, {"premise_expression": "- \\sin{(F - G)}", "variable": "F", "positive": "\\cos{(F - G)}", "negatives": ["- \\cos{(F - G)}", "e^{F - G}", "- \\frac{\\cos{(F)}}{G}", "\\frac{F (\\log{(F)} - 1)}{G}"], "srepr_premise_expression": "Mul(Integer(-1), sin(Add(Symbol('F', commutative=True), Mul(Integer(-1), Symbol('G', commutative=True)))))", "srepr_variable": "Symbol('F', commutative=True)", "srepr_positive": "cos(Add(Symbol('F', commutative=True), Mul(Integer(-1), Symbol('G', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('F', commutative=True), Mul(Integer(-1), Symbol('G', commutative=True)))))", "exp(Add(Symbol('F', commutative=True), Mul(Integer(-1), Symbol('G', commutative=True))))", "Mul(Integer(-1), Pow(Symbol('G', commutative=True), Integer(-1)), cos(Symbol('F', commutative=True)))", "Mul(Symbol('F', commutative=True), Pow(Symbol('G', commutative=True), Integer(-1)), Add(log(Symbol('F', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\frac{- Q + W}{Z}", "variable": "Q", "positive": "\\frac{Q (- Q + 2 W)}{2 Z}", "negatives": ["\\frac{Q (Q + 2 W)}{2 Z}", "- \\frac{W (2 Q - W)}{2 Z}", "\\frac{Q (- Q + 2 W^{Z})}{2}", "\\frac{Q (- Q + 2 W Z)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('Z', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('Q', commutative=True)), Symbol('W', commutative=True)))", "srepr_variable": "Symbol('Q', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('Q', commutative=True), Pow(Symbol('Z', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('Q', commutative=True)), Mul(Integer(2), Symbol('W', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('Q', commutative=True), Pow(Symbol('Z', commutative=True), Integer(-1)), Add(Symbol('Q', commutative=True), Mul(Integer(2), Symbol('W', commutative=True))))", "Mul(Integer(-1), Rational(1, 2), Symbol('W', commutative=True), Pow(Symbol('Z', commutative=True), Integer(-1)), Add(Mul(Integer(2), Symbol('Q', commutative=True)), Mul(Integer(-1), Symbol('W', commutative=True))))", "Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Mul(Integer(-1), Symbol('Q', commutative=True)), Mul(Integer(2), Pow(Symbol('W', commutative=True), Symbol('Z', commutative=True)))))", "Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Mul(Integer(-1), Symbol('Q', commutative=True)), Mul(Integer(2), Symbol('W', commutative=True), Symbol('Z', commutative=True))))"]}, {"premise_expression": "\\sin^{f}{(D)}", "variable": "D", "positive": "\\int \\sin^{f}{(D)} dD", "negatives": ["D f (\\log{(D)} - 1)", "\\log{(D)} \\cos{(f)}", "f \\log{(D)}", "\\frac{D (- D + 2 f)}{2}"], "srepr_premise_expression": "Pow(sin(Symbol('D', commutative=True)), Symbol('f', commutative=True))", "srepr_variable": "Symbol('D', commutative=True)", "srepr_positive": "Integral(Pow(sin(Symbol('D', commutative=True)), Symbol('f', commutative=True)), Tuple(Symbol('D', commutative=True)))", "srepr_negatives": ["Mul(Symbol('D', commutative=True), Symbol('f', commutative=True), Add(log(Symbol('D', commutative=True)), Integer(-1)))", "Mul(log(Symbol('D', commutative=True)), cos(Symbol('f', commutative=True)))", "Mul(Symbol('f', commutative=True), log(Symbol('D', commutative=True)))", "Mul(Rational(1, 2), Symbol('D', commutative=True), Add(Mul(Integer(-1), Symbol('D', commutative=True)), Mul(Integer(2), Symbol('f', commutative=True))))"]}, {"premise_expression": "\\cos{(\\frac{b}{P})}", "variable": "P", "positive": "P \\cos{(\\frac{b}{P})} + b \\operatorname{Si}{(\\frac{b}{P})}", "negatives": ["\\frac{P (- P + 2 \\sin{(b)})}{2}", "- P b - \\cos{(P)}", "e^{b} \\log{(P)}", "e^{P - b}"], "srepr_premise_expression": "cos(Mul(Pow(Symbol('P', commutative=True), Integer(-1)), Symbol('b', commutative=True)))", "srepr_variable": "Symbol('P', commutative=True)", "srepr_positive": "Add(Mul(Symbol('P', commutative=True), cos(Mul(Pow(Symbol('P', commutative=True), Integer(-1)), Symbol('b', commutative=True)))), Mul(Symbol('b', commutative=True), Si(Mul(Pow(Symbol('P', commutative=True), Integer(-1)), Symbol('b', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Mul(Integer(-1), Symbol('P', commutative=True)), Mul(Integer(2), sin(Symbol('b', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('P', commutative=True), Symbol('b', commutative=True)), Mul(Integer(-1), cos(Symbol('P', commutative=True))))", "Mul(exp(Symbol('b', commutative=True)), log(Symbol('P', commutative=True)))", "exp(Add(Symbol('P', commutative=True), Mul(Integer(-1), Symbol('b', commutative=True))))"]}, {"premise_expression": "v + \\sin{(D)}", "variable": "D", "positive": "D v - \\cos{(D)}", "negatives": ["\\frac{D^{2} \\cos{(v)}}{2}", "v \\sin{(D)}", "\\frac{D (D + 2 \\cos{(v)})}{2}", "\\frac{v (v + 2 \\sin{(D)})}{2}"], "srepr_premise_expression": "Add(Symbol('v', commutative=True), sin(Symbol('D', commutative=True)))", "srepr_variable": "Symbol('D', commutative=True)", "srepr_positive": "Add(Mul(Symbol('D', commutative=True), Symbol('v', commutative=True)), Mul(Integer(-1), cos(Symbol('D', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(2)), cos(Symbol('v', commutative=True)))", "Mul(Symbol('v', commutative=True), sin(Symbol('D', commutative=True)))", "Mul(Rational(1, 2), Symbol('D', commutative=True), Add(Symbol('D', commutative=True), Mul(Integer(2), cos(Symbol('v', commutative=True)))))", "Mul(Rational(1, 2), Symbol('v', commutative=True), Add(Symbol('v', commutative=True), Mul(Integer(2), sin(Symbol('D', commutative=True)))))"]}, {"premise_expression": "M + p", "variable": "p", "positive": "\\frac{p (2 M + p)}{2}", "negatives": ["\\frac{M (M + 2 p)}{2}", "\\frac{p^{2} \\log{(M)}}{2}", "e^{- M + p}", "- \\cos{(M - p)}"], "srepr_premise_expression": "Add(Symbol('M', commutative=True), Symbol('p', commutative=True))", "srepr_variable": "Symbol('p', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Mul(Integer(2), Symbol('M', commutative=True)), Symbol('p', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('M', commutative=True), Add(Symbol('M', commutative=True), Mul(Integer(2), Symbol('p', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('p', commutative=True), Integer(2)), log(Symbol('M', commutative=True)))", "exp(Add(Mul(Integer(-1), Symbol('M', commutative=True)), Symbol('p', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('M', commutative=True), Mul(Integer(-1), Symbol('p', commutative=True)))))"]}, {"premise_expression": "\\frac{T}{D}", "variable": "T", "positive": "\\frac{T^{2}}{2 D}", "negatives": ["T \\log{(D)}", "\\frac{T^{2} \\sin{(D)}}{2}", "- \\frac{\\cos{(T)}}{D}", "- e^{D - T}"], "srepr_premise_expression": "Mul(Pow(Symbol('D', commutative=True), Integer(-1)), Symbol('T', commutative=True))", "srepr_variable": "Symbol('T', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(-1)), Pow(Symbol('T', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('T', commutative=True), log(Symbol('D', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('T', commutative=True), Integer(2)), sin(Symbol('D', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('D', commutative=True), Integer(-1)), cos(Symbol('T', commutative=True)))", "Mul(Integer(-1), exp(Add(Symbol('D', commutative=True), Mul(Integer(-1), Symbol('T', commutative=True)))))"]}, {"premise_expression": "N + y", "variable": "y", "positive": "\\frac{y (2 N + y)}{2}", "negatives": ["\\frac{N (N + 2 y)}{2}", "- \\cos{(N + y)}", "\\frac{y^{2}}{2 N}", "y (\\log{(\\frac{N}{y})} + 1)"], "srepr_premise_expression": "Add(Symbol('N', commutative=True), Symbol('y', commutative=True))", "srepr_variable": "Symbol('y', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('y', commutative=True), Add(Mul(Integer(2), Symbol('N', commutative=True)), Symbol('y', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Symbol('N', commutative=True), Mul(Integer(2), Symbol('y', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('N', commutative=True), Symbol('y', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('N', commutative=True), Integer(-1)), Pow(Symbol('y', commutative=True), Integer(2)))", "Mul(Symbol('y', commutative=True), Add(log(Mul(Symbol('N', commutative=True), Pow(Symbol('y', commutative=True), Integer(-1)))), Integer(1)))"]}, {"premise_expression": "l + \\log{(o)}", "variable": "l", "positive": "\\frac{l (l + 2 \\log{(o)})}{2}", "negatives": ["\\frac{l (- l + 2 e^{o})}{2}", "\\frac{l^{2} \\log{(o)}}{2}", "o (l + \\log{(o)} - 1)", "l (- o + \\log{(l^{o})})"], "srepr_premise_expression": "Add(Symbol('l', commutative=True), log(Symbol('o', commutative=True)))", "srepr_variable": "Symbol('l', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('l', commutative=True), Add(Symbol('l', commutative=True), Mul(Integer(2), log(Symbol('o', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('l', commutative=True), Add(Mul(Integer(-1), Symbol('l', commutative=True)), Mul(Integer(2), exp(Symbol('o', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('l', commutative=True), Integer(2)), log(Symbol('o', commutative=True)))", "Mul(Symbol('o', commutative=True), Add(Symbol('l', commutative=True), log(Symbol('o', commutative=True)), Integer(-1)))", "Mul(Symbol('l', commutative=True), Add(Mul(Integer(-1), Symbol('o', commutative=True)), log(Pow(Symbol('l', commutative=True), Symbol('o', commutative=True)))))"]}, {"premise_expression": "Z - m", "variable": "Z", "positive": "\\frac{Z (Z - 2 m)}{2}", "negatives": ["\\frac{m (2 Z - m)}{2}", "\\frac{Z^{2} m}{2}", "\\frac{Z (- Z + 2 e^{m})}{2}", "\\frac{Z^{2} \\log{(m)}}{2}"], "srepr_premise_expression": "Add(Symbol('Z', commutative=True), Mul(Integer(-1), Symbol('m', commutative=True)))", "srepr_variable": "Symbol('Z', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Symbol('Z', commutative=True), Mul(Integer(-1), Integer(2), Symbol('m', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Mul(Integer(2), Symbol('Z', commutative=True)), Mul(Integer(-1), Symbol('m', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('Z', commutative=True), Integer(2)), Symbol('m', commutative=True))", "Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Mul(Integer(-1), Symbol('Z', commutative=True)), Mul(Integer(2), exp(Symbol('m', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('Z', commutative=True), Integer(2)), log(Symbol('m', commutative=True)))"]}, {"premise_expression": "\\frac{E^{r}}{G}", "variable": "G", "positive": "E^{r} \\log{(G)}", "negatives": ["(E - r) \\log{(G)}", "\\frac{E G (2 E + G)}{2}", "\\frac{G (E G + 2 r)}{2}", "\\frac{G (2 E - G + 2 r)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('E', commutative=True), Symbol('r', commutative=True)), Pow(Symbol('G', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('E', commutative=True), Symbol('r', commutative=True)), log(Symbol('G', commutative=True)))", "srepr_negatives": ["Mul(Add(Symbol('E', commutative=True), Mul(Integer(-1), Symbol('r', commutative=True))), log(Symbol('G', commutative=True)))", "Mul(Rational(1, 2), Symbol('E', commutative=True), Symbol('G', commutative=True), Add(Mul(Integer(2), Symbol('E', commutative=True)), Symbol('G', commutative=True)))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Mul(Symbol('E', commutative=True), Symbol('G', commutative=True)), Mul(Integer(2), Symbol('r', commutative=True))))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Mul(Integer(2), Symbol('E', commutative=True)), Mul(Integer(-1), Symbol('G', commutative=True)), Mul(Integer(2), Symbol('r', commutative=True))))"]}, {"premise_expression": "\\frac{H K}{k}", "variable": "H", "positive": "\\frac{H^{2} K}{2 k}", "negatives": ["\\frac{H K^{2}}{2 k}", "H K \\log{(k)}", "\\frac{H (H K + 2 k)}{2}", "H (K + 1)"], "srepr_premise_expression": "Mul(Symbol('H', commutative=True), Symbol('K', commutative=True), Pow(Symbol('k', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('H', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('H', commutative=True), Integer(2)), Symbol('K', commutative=True), Pow(Symbol('k', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('H', commutative=True), Pow(Symbol('K', commutative=True), Integer(2)), Pow(Symbol('k', commutative=True), Integer(-1)))", "Mul(Symbol('H', commutative=True), Symbol('K', commutative=True), log(Symbol('k', commutative=True)))", "Mul(Rational(1, 2), Symbol('H', commutative=True), Add(Mul(Symbol('H', commutative=True), Symbol('K', commutative=True)), Mul(Integer(2), Symbol('k', commutative=True))))", "Mul(Symbol('H', commutative=True), Add(Symbol('K', commutative=True), Integer(1)))"]}, {"premise_expression": "\\log{(\\frac{W}{K})}", "variable": "W", "positive": "W (\\log{(\\frac{W}{K})} - 1)", "negatives": ["K (\\log{(\\frac{W}{K})} + 1)", "W (\\log{(\\frac{K}{W})} + 1)", "- \\sin{(K - W)}", "e^{K + W}"], "srepr_premise_expression": "log(Mul(Pow(Symbol('K', commutative=True), Integer(-1)), Symbol('W', commutative=True)))", "srepr_variable": "Symbol('W', commutative=True)", "srepr_positive": "Mul(Symbol('W', commutative=True), Add(log(Mul(Pow(Symbol('K', commutative=True), Integer(-1)), Symbol('W', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('K', commutative=True), Add(log(Mul(Pow(Symbol('K', commutative=True), Integer(-1)), Symbol('W', commutative=True))), Integer(1)))", "Mul(Symbol('W', commutative=True), Add(log(Mul(Symbol('K', commutative=True), Pow(Symbol('W', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Integer(-1), sin(Add(Symbol('K', commutative=True), Mul(Integer(-1), Symbol('W', commutative=True)))))", "exp(Add(Symbol('K', commutative=True), Symbol('W', commutative=True)))"]}, {"premise_expression": "\\sin^{c}{(b)}", "variable": "b", "positive": "\\int \\sin^{c}{(b)} db", "negatives": ["\\int \\cos^{c}{(b)} db", "- \\cos{(b + c)}", "\\frac{b (b + 2 \\sin{(c)})}{2}", "\\frac{b^{2} c}{2}"], "srepr_premise_expression": "Pow(sin(Symbol('b', commutative=True)), Symbol('c', commutative=True))", "srepr_variable": "Symbol('b', commutative=True)", "srepr_positive": "Integral(Pow(sin(Symbol('b', commutative=True)), Symbol('c', commutative=True)), Tuple(Symbol('b', commutative=True)))", "srepr_negatives": ["Integral(Pow(cos(Symbol('b', commutative=True)), Symbol('c', commutative=True)), Tuple(Symbol('b', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('b', commutative=True), Symbol('c', commutative=True))))", "Mul(Rational(1, 2), Symbol('b', commutative=True), Add(Symbol('b', commutative=True), Mul(Integer(2), sin(Symbol('c', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('b', commutative=True), Integer(2)), Symbol('c', commutative=True))"]}, {"premise_expression": "G - u", "variable": "u", "positive": "\\frac{u (2 G - u)}{2}", "negatives": ["\\frac{u (- 2 G + u)}{2}", "\\frac{G (G - 2 u)}{2}", "\\frac{u^{2} \\log{(G)}}{2}", "\\frac{u^{2} \\cos{(G)}}{2}"], "srepr_premise_expression": "Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('u', commutative=True)))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(2), Symbol('G', commutative=True)), Mul(Integer(-1), Symbol('u', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('G', commutative=True)), Symbol('u', commutative=True)))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Symbol('G', commutative=True), Mul(Integer(-1), Integer(2), Symbol('u', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('u', commutative=True), Integer(2)), log(Symbol('G', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('u', commutative=True), Integer(2)), cos(Symbol('G', commutative=True)))"]}, {"premise_expression": "U + l", "variable": "U", "positive": "\\frac{U (U + 2 l)}{2}", "negatives": ["\\frac{l (2 U + l)}{2}", "- U l + \\sin{(U)}", "- \\cos{(U - l)}", "- \\frac{\\cos{(U)}}{l}"], "srepr_premise_expression": "Add(Symbol('U', commutative=True), Symbol('l', commutative=True))", "srepr_variable": "Symbol('U', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('U', commutative=True), Add(Symbol('U', commutative=True), Mul(Integer(2), Symbol('l', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('l', commutative=True), Add(Mul(Integer(2), Symbol('U', commutative=True)), Symbol('l', commutative=True)))", "Add(Mul(Integer(-1), Symbol('U', commutative=True), Symbol('l', commutative=True)), sin(Symbol('U', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('U', commutative=True), Mul(Integer(-1), Symbol('l', commutative=True)))))", "Mul(Integer(-1), Pow(Symbol('l', commutative=True), Integer(-1)), cos(Symbol('U', commutative=True)))"]}, {"premise_expression": "B + \\sin{(w)}", "variable": "B", "positive": "\\frac{B (B + 2 \\sin{(w)})}{2}", "negatives": ["\\frac{B (B + 2 \\cos{(w)})}{2}", "\\frac{B (B - 2 w)}{2}", "B w - \\cos{(w)}", "\\sin{(B + w)}"], "srepr_premise_expression": "Add(Symbol('B', commutative=True), sin(Symbol('w', commutative=True)))", "srepr_variable": "Symbol('B', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('B', commutative=True), Add(Symbol('B', commutative=True), Mul(Integer(2), sin(Symbol('w', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('B', commutative=True), Add(Symbol('B', commutative=True), Mul(Integer(2), cos(Symbol('w', commutative=True)))))", "Mul(Rational(1, 2), Symbol('B', commutative=True), Add(Symbol('B', commutative=True), Mul(Integer(-1), Integer(2), Symbol('w', commutative=True))))", "Add(Mul(Symbol('B', commutative=True), Symbol('w', commutative=True)), Mul(Integer(-1), cos(Symbol('w', commutative=True))))", "sin(Add(Symbol('B', commutative=True), Symbol('w', commutative=True)))"]}, {"premise_expression": "e^{c + h}", "variable": "h", "positive": "e^{c + h}", "negatives": ["\\frac{h (2 c + h)}{2}", "c \\log{(h)}", "\\log{(c)} \\log{(h)}", "\\frac{c h^{2}}{2}"], "srepr_premise_expression": "exp(Add(Symbol('c', commutative=True), Symbol('h', commutative=True)))", "srepr_variable": "Symbol('h', commutative=True)", "srepr_positive": "exp(Add(Symbol('c', commutative=True), Symbol('h', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('h', commutative=True), Add(Mul(Integer(2), Symbol('c', commutative=True)), Symbol('h', commutative=True)))", "Mul(Symbol('c', commutative=True), log(Symbol('h', commutative=True)))", "Mul(log(Symbol('c', commutative=True)), log(Symbol('h', commutative=True)))", "Mul(Rational(1, 2), Symbol('c', commutative=True), Pow(Symbol('h', commutative=True), Integer(2)))"]}, {"premise_expression": "w + \\cos{(D)}", "variable": "D", "positive": "D w + \\sin{(D)}", "negatives": ["- D w + e^{D}", "D w - \\cos{(D)}", "\\frac{D^{2}}{2 w}", "D (- w + \\log{(D^{w})})"], "srepr_premise_expression": "Add(Symbol('w', commutative=True), cos(Symbol('D', commutative=True)))", "srepr_variable": "Symbol('D', commutative=True)", "srepr_positive": "Add(Mul(Symbol('D', commutative=True), Symbol('w', commutative=True)), sin(Symbol('D', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('D', commutative=True), Symbol('w', commutative=True)), exp(Symbol('D', commutative=True)))", "Add(Mul(Symbol('D', commutative=True), Symbol('w', commutative=True)), Mul(Integer(-1), cos(Symbol('D', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(2)), Pow(Symbol('w', commutative=True), Integer(-1)))", "Mul(Symbol('D', commutative=True), Add(Mul(Integer(-1), Symbol('w', commutative=True)), log(Pow(Symbol('D', commutative=True), Symbol('w', commutative=True)))))"]}, {"premise_expression": "e^{\\frac{r}{C}}", "variable": "C", "positive": "C e^{\\frac{r}{C}} - r \\operatorname{Ei}{(\\frac{r}{C})}", "negatives": ["C e^{\\frac{r}{C}}", "- C r + e^{C}", "\\frac{C (C + 2 e^{r})}{2}", "\\sin{(C - r)}"], "srepr_premise_expression": "exp(Mul(Pow(Symbol('C', commutative=True), Integer(-1)), Symbol('r', commutative=True)))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Add(Mul(Symbol('C', commutative=True), exp(Mul(Pow(Symbol('C', commutative=True), Integer(-1)), Symbol('r', commutative=True)))), Mul(Integer(-1), Symbol('r', commutative=True), Ei(Mul(Pow(Symbol('C', commutative=True), Integer(-1)), Symbol('r', commutative=True)))))", "srepr_negatives": ["Mul(Symbol('C', commutative=True), exp(Mul(Pow(Symbol('C', commutative=True), Integer(-1)), Symbol('r', commutative=True))))", "Add(Mul(Integer(-1), Symbol('C', commutative=True), Symbol('r', commutative=True)), exp(Symbol('C', commutative=True)))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Symbol('C', commutative=True), Mul(Integer(2), exp(Symbol('r', commutative=True)))))", "sin(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('r', commutative=True))))"]}, {"premise_expression": "I p + c", "variable": "c", "positive": "\\frac{c (2 I p + c)}{2}", "negatives": ["\\frac{I (I p + 2 c)}{2}", "\\frac{p (I p + 2 c)}{2}", "\\frac{c^{2}}{2 I p}", "\\frac{c (c + 2 p^{I})}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('I', commutative=True), Symbol('p', commutative=True)), Symbol('c', commutative=True))", "srepr_variable": "Symbol('c', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('c', commutative=True), Add(Mul(Integer(2), Symbol('I', commutative=True), Symbol('p', commutative=True)), Symbol('c', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('I', commutative=True), Add(Mul(Symbol('I', commutative=True), Symbol('p', commutative=True)), Mul(Integer(2), Symbol('c', commutative=True))))", "Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Mul(Symbol('I', commutative=True), Symbol('p', commutative=True)), Mul(Integer(2), Symbol('c', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(-1)), Pow(Symbol('c', commutative=True), Integer(2)), Pow(Symbol('p', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Symbol('c', commutative=True), Add(Symbol('c', commutative=True), Mul(Integer(2), Pow(Symbol('p', commutative=True), Symbol('I', commutative=True)))))"]}, {"premise_expression": "u \\sin{(t)}", "variable": "u", "positive": "\\frac{u^{2} \\sin{(t)}}{2}", "negatives": ["\\frac{u^{2} \\log{(t)}}{2}", "\\frac{u (2 t + u)}{2}", "\\frac{u^{2}}{2 t}", "- u \\cos{(t)}"], "srepr_premise_expression": "Mul(Symbol('u', commutative=True), sin(Symbol('t', commutative=True)))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('u', commutative=True), Integer(2)), sin(Symbol('t', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('u', commutative=True), Integer(2)), log(Symbol('t', commutative=True)))", "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(2), Symbol('t', commutative=True)), Symbol('u', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('t', commutative=True), Integer(-1)), Pow(Symbol('u', commutative=True), Integer(2)))", "Mul(Integer(-1), Symbol('u', commutative=True), cos(Symbol('t', commutative=True)))"]}, {"premise_expression": "- Y + e^{Z}", "variable": "Z", "positive": "- Y Z + e^{Z}", "negatives": ["- Y Z + \\sin{(Z)}", "\\frac{Y (- Y + 2 e^{Z})}{2}", "\\frac{Z^{2} e^{Y}}{2}", "- Y \\log{(Z)} + Z"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('Y', commutative=True)), exp(Symbol('Z', commutative=True)))", "srepr_variable": "Symbol('Z', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('Y', commutative=True), Symbol('Z', commutative=True)), exp(Symbol('Z', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('Y', commutative=True), Symbol('Z', commutative=True)), sin(Symbol('Z', commutative=True)))", "Mul(Rational(1, 2), Symbol('Y', commutative=True), Add(Mul(Integer(-1), Symbol('Y', commutative=True)), Mul(Integer(2), exp(Symbol('Z', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('Z', commutative=True), Integer(2)), exp(Symbol('Y', commutative=True)))", "Add(Mul(Integer(-1), Symbol('Y', commutative=True), log(Symbol('Z', commutative=True))), Symbol('Z', commutative=True))"]}, {"premise_expression": "- n + z", "variable": "z", "positive": "\\frac{z (- 2 n + z)}{2}", "negatives": ["\\frac{n (- n + 2 z)}{2}", "e^{- n + z}", "\\frac{z^{2} \\log{(n)}}{2}", "\\frac{z^{2} \\cos{(n)}}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('n', commutative=True)), Symbol('z', commutative=True))", "srepr_variable": "Symbol('z', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('z', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('n', commutative=True)), Symbol('z', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('n', commutative=True), Add(Mul(Integer(-1), Symbol('n', commutative=True)), Mul(Integer(2), Symbol('z', commutative=True))))", "exp(Add(Mul(Integer(-1), Symbol('n', commutative=True)), Symbol('z', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('z', commutative=True), Integer(2)), log(Symbol('n', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('z', commutative=True), Integer(2)), cos(Symbol('n', commutative=True)))"]}, {"premise_expression": "e^{G^{c}}", "variable": "G", "positive": "\\frac{e^{- \\frac{i \\pi}{c}} \\gamma(\\frac{1}{c}, G^{c} e^{i \\pi})}{c}", "negatives": ["\\frac{G (- G + 2 e^{c})}{2}", "\\frac{G^{2} \\log{(c)}}{2}", "G c (\\log{(G)} - 1)", "\\frac{G (G + 2 c)}{2}"], "srepr_premise_expression": "exp(Pow(Symbol('G', commutative=True), Symbol('c', commutative=True)))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('c', commutative=True), Integer(-1)), exp(Mul(Integer(-1), I, pi, Pow(Symbol('c', commutative=True), Integer(-1)))), lowergamma(Pow(Symbol('c', commutative=True), Integer(-1)), Mul(Pow(Symbol('G', commutative=True), Symbol('c', commutative=True)), exp_polar(Mul(I, pi)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Mul(Integer(-1), Symbol('G', commutative=True)), Mul(Integer(2), exp(Symbol('c', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(2)), log(Symbol('c', commutative=True)))", "Mul(Symbol('G', commutative=True), Symbol('c', commutative=True), Add(log(Symbol('G', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Symbol('G', commutative=True), Mul(Integer(2), Symbol('c', commutative=True))))"]}, {"premise_expression": "\\cos{(\\frac{z}{M})}", "variable": "M", "positive": "M \\cos{(\\frac{z}{M})} + z \\operatorname{Si}{(\\frac{z}{M})}", "negatives": ["\\frac{M (M + 2 z)}{2}", "- \\cos{(M - z)}", "\\frac{M (- M + 2 \\sin{(z)})}{2}", "e^{M + z}"], "srepr_premise_expression": "cos(Mul(Pow(Symbol('M', commutative=True), Integer(-1)), Symbol('z', commutative=True)))", "srepr_variable": "Symbol('M', commutative=True)", "srepr_positive": "Add(Mul(Symbol('M', commutative=True), cos(Mul(Pow(Symbol('M', commutative=True), Integer(-1)), Symbol('z', commutative=True)))), Mul(Symbol('z', commutative=True), Si(Mul(Pow(Symbol('M', commutative=True), Integer(-1)), Symbol('z', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('M', commutative=True), Add(Symbol('M', commutative=True), Mul(Integer(2), Symbol('z', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('M', commutative=True), Mul(Integer(-1), Symbol('z', commutative=True)))))", "Mul(Rational(1, 2), Symbol('M', commutative=True), Add(Mul(Integer(-1), Symbol('M', commutative=True)), Mul(Integer(2), sin(Symbol('z', commutative=True)))))", "exp(Add(Symbol('M', commutative=True), Symbol('z', commutative=True)))"]}, {"premise_expression": "\\frac{Z}{E}", "variable": "Z", "positive": "\\frac{Z^{2}}{2 E}", "negatives": ["Z \\log{(E)}", "\\frac{Z^{2} \\log{(E)}}{2}", "\\frac{Z^{2} \\cos{(E)}}{2}", "\\frac{Z (Z + 2 e^{E})}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('E', commutative=True), Integer(-1)), Symbol('Z', commutative=True))", "srepr_variable": "Symbol('Z', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('E', commutative=True), Integer(-1)), Pow(Symbol('Z', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('Z', commutative=True), log(Symbol('E', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('Z', commutative=True), Integer(2)), log(Symbol('E', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('Z', commutative=True), Integer(2)), cos(Symbol('E', commutative=True)))", "Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Symbol('Z', commutative=True), Mul(Integer(2), exp(Symbol('E', commutative=True)))))"]}, {"premise_expression": "\\frac{F + R}{p}", "variable": "F", "positive": "\\frac{F (F + 2 R)}{2 p}", "negatives": ["\\frac{R (2 F + R)}{2 p}", "\\frac{F (- F - 2 R + 2 p)}{2}", "\\frac{F^{2} p}{2 R}", "(F + R) \\log{(p)}"], "srepr_premise_expression": "Mul(Pow(Symbol('p', commutative=True), Integer(-1)), Add(Symbol('F', commutative=True), Symbol('R', commutative=True)))", "srepr_variable": "Symbol('F', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('F', commutative=True), Pow(Symbol('p', commutative=True), Integer(-1)), Add(Symbol('F', commutative=True), Mul(Integer(2), Symbol('R', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('R', commutative=True), Pow(Symbol('p', commutative=True), Integer(-1)), Add(Mul(Integer(2), Symbol('F', commutative=True)), Symbol('R', commutative=True)))", "Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Mul(Integer(-1), Symbol('F', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('R', commutative=True)), Mul(Integer(2), Symbol('p', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('F', commutative=True), Integer(2)), Pow(Symbol('R', commutative=True), Integer(-1)), Symbol('p', commutative=True))", "Mul(Add(Symbol('F', commutative=True), Symbol('R', commutative=True)), log(Symbol('p', commutative=True)))"]}, {"premise_expression": "K + m", "variable": "K", "positive": "\\frac{K (K + 2 m)}{2}", "negatives": ["\\frac{m (2 K + m)}{2}", "\\frac{K (K + 2 \\log{(m)})}{2}", "\\sin{(K + m)}", "- \\frac{\\cos{(K)}}{m}"], "srepr_premise_expression": "Add(Symbol('K', commutative=True), Symbol('m', commutative=True))", "srepr_variable": "Symbol('K', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Symbol('K', commutative=True), Mul(Integer(2), Symbol('m', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Mul(Integer(2), Symbol('K', commutative=True)), Symbol('m', commutative=True)))", "Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Symbol('K', commutative=True), Mul(Integer(2), log(Symbol('m', commutative=True)))))", "sin(Add(Symbol('K', commutative=True), Symbol('m', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('m', commutative=True), Integer(-1)), cos(Symbol('K', commutative=True)))"]}, {"premise_expression": "\\frac{s}{I}", "variable": "s", "positive": "\\frac{s^{2}}{2 I}", "negatives": ["s \\log{(I)}", "\\frac{\\sin{(s)}}{I}", "- \\sin{(I - s)}", "\\log{(s)} \\sin{(I)}"], "srepr_premise_expression": "Mul(Pow(Symbol('I', commutative=True), Integer(-1)), Symbol('s', commutative=True))", "srepr_variable": "Symbol('s', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(-1)), Pow(Symbol('s', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('s', commutative=True), log(Symbol('I', commutative=True)))", "Mul(Pow(Symbol('I', commutative=True), Integer(-1)), sin(Symbol('s', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('I', commutative=True), Mul(Integer(-1), Symbol('s', commutative=True)))))", "Mul(log(Symbol('s', commutative=True)), sin(Symbol('I', commutative=True)))"]}, {"premise_expression": "e^{E + j}", "variable": "E", "positive": "e^{E + j}", "negatives": ["\\cos{(E - j)}", "\\frac{E (E + 2 j)}{2}", "\\frac{E^{2}}{2 j}", "\\log{(E)} \\sin{(j)}"], "srepr_premise_expression": "exp(Add(Symbol('E', commutative=True), Symbol('j', commutative=True)))", "srepr_variable": "Symbol('E', commutative=True)", "srepr_positive": "exp(Add(Symbol('E', commutative=True), Symbol('j', commutative=True)))", "srepr_negatives": ["cos(Add(Symbol('E', commutative=True), Mul(Integer(-1), Symbol('j', commutative=True))))", "Mul(Rational(1, 2), Symbol('E', commutative=True), Add(Symbol('E', commutative=True), Mul(Integer(2), Symbol('j', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('E', commutative=True), Integer(2)), Pow(Symbol('j', commutative=True), Integer(-1)))", "Mul(log(Symbol('E', commutative=True)), sin(Symbol('j', commutative=True)))"]}, {"premise_expression": "\\frac{\\log{(b)}}{P}", "variable": "b", "positive": "\\frac{b (\\log{(b)} - 1)}{P}", "negatives": ["P \\log{(b)} + b", "b (- P + \\log{(b)} - 1)", "P \\log{(b)}", "\\log{(P)} \\log{(b)}"], "srepr_premise_expression": "Mul(Pow(Symbol('P', commutative=True), Integer(-1)), log(Symbol('b', commutative=True)))", "srepr_variable": "Symbol('b', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('P', commutative=True), Integer(-1)), Symbol('b', commutative=True), Add(log(Symbol('b', commutative=True)), Integer(-1)))", "srepr_negatives": ["Add(Mul(Symbol('P', commutative=True), log(Symbol('b', commutative=True))), Symbol('b', commutative=True))", "Mul(Symbol('b', commutative=True), Add(Mul(Integer(-1), Symbol('P', commutative=True)), log(Symbol('b', commutative=True)), Integer(-1)))", "Mul(Symbol('P', commutative=True), log(Symbol('b', commutative=True)))", "Mul(log(Symbol('P', commutative=True)), log(Symbol('b', commutative=True)))"]}, {"premise_expression": "e^{a - k}", "variable": "a", "positive": "e^{a - k}", "negatives": ["- e^{a - k}", "- e^{- a + k}", "\\sin{(a + k)}", "\\frac{a (a + 2 k)}{2}"], "srepr_premise_expression": "exp(Add(Symbol('a', commutative=True), Mul(Integer(-1), Symbol('k', commutative=True))))", "srepr_variable": "Symbol('a', commutative=True)", "srepr_positive": "exp(Add(Symbol('a', commutative=True), Mul(Integer(-1), Symbol('k', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Symbol('a', commutative=True), Mul(Integer(-1), Symbol('k', commutative=True)))))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('a', commutative=True)), Symbol('k', commutative=True))))", "sin(Add(Symbol('a', commutative=True), Symbol('k', commutative=True)))", "Mul(Rational(1, 2), Symbol('a', commutative=True), Add(Symbol('a', commutative=True), Mul(Integer(2), Symbol('k', commutative=True))))"]}, {"premise_expression": "\\frac{\\log{(B)}}{C}", "variable": "C", "positive": "\\log{(B)} \\log{(C)}", "negatives": ["\\cos{(B - C)}", "- \\cos{(B + C)}", "\\frac{B (\\log{(B)} - 1)}{C}", "B C + \\sin{(C)}"], "srepr_premise_expression": "Mul(Pow(Symbol('C', commutative=True), Integer(-1)), log(Symbol('B', commutative=True)))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Mul(log(Symbol('B', commutative=True)), log(Symbol('C', commutative=True)))", "srepr_negatives": ["cos(Add(Symbol('B', commutative=True), Mul(Integer(-1), Symbol('C', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('B', commutative=True), Symbol('C', commutative=True))))", "Mul(Symbol('B', commutative=True), Pow(Symbol('C', commutative=True), Integer(-1)), Add(log(Symbol('B', commutative=True)), Integer(-1)))", "Add(Mul(Symbol('B', commutative=True), Symbol('C', commutative=True)), sin(Symbol('C', commutative=True)))"]}, {"premise_expression": "\\frac{D}{s}", "variable": "s", "positive": "D \\log{(s)}", "negatives": ["\\frac{D^{2}}{2 s}", "\\frac{D s^{2}}{2}", "- D s - \\cos{(s)}", "e^{- D + s}"], "srepr_premise_expression": "Mul(Symbol('D', commutative=True), Pow(Symbol('s', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('s', commutative=True)", "srepr_positive": "Mul(Symbol('D', commutative=True), log(Symbol('s', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(2)), Pow(Symbol('s', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Symbol('D', commutative=True), Pow(Symbol('s', commutative=True), Integer(2)))", "Add(Mul(Integer(-1), Symbol('D', commutative=True), Symbol('s', commutative=True)), Mul(Integer(-1), cos(Symbol('s', commutative=True))))", "exp(Add(Mul(Integer(-1), Symbol('D', commutative=True)), Symbol('s', commutative=True)))"]}, {"premise_expression": "z \\sin{(I)}", "variable": "z", "positive": "\\frac{z^{2} \\sin{(I)}}{2}", "negatives": ["\\frac{z (- z + 2 \\sin{(I)})}{2}", "- z \\cos{(I)}", "- \\cos{(I + z)}", "z (\\log{(\\frac{z}{I})} - 1)"], "srepr_premise_expression": "Mul(Symbol('z', commutative=True), sin(Symbol('I', commutative=True)))", "srepr_variable": "Symbol('z', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('z', commutative=True), Integer(2)), sin(Symbol('I', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('z', commutative=True), Add(Mul(Integer(-1), Symbol('z', commutative=True)), Mul(Integer(2), sin(Symbol('I', commutative=True)))))", "Mul(Integer(-1), Symbol('z', commutative=True), cos(Symbol('I', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('I', commutative=True), Symbol('z', commutative=True))))", "Mul(Symbol('z', commutative=True), Add(log(Mul(Pow(Symbol('I', commutative=True), Integer(-1)), Symbol('z', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\log{(\\frac{j}{b})}", "variable": "b", "positive": "b (\\log{(\\frac{j}{b})} + 1)", "negatives": ["j (\\log{(\\frac{j}{b})} - 1)", "b j (\\log{(b)} - 1)", "- \\cos{(b + j)}", "\\sin{(b + j)}"], "srepr_premise_expression": "log(Mul(Pow(Symbol('b', commutative=True), Integer(-1)), Symbol('j', commutative=True)))", "srepr_variable": "Symbol('b', commutative=True)", "srepr_positive": "Mul(Symbol('b', commutative=True), Add(log(Mul(Pow(Symbol('b', commutative=True), Integer(-1)), Symbol('j', commutative=True))), Integer(1)))", "srepr_negatives": ["Mul(Symbol('j', commutative=True), Add(log(Mul(Pow(Symbol('b', commutative=True), Integer(-1)), Symbol('j', commutative=True))), Integer(-1)))", "Mul(Symbol('b', commutative=True), Symbol('j', commutative=True), Add(log(Symbol('b', commutative=True)), Integer(-1)))", "Mul(Integer(-1), cos(Add(Symbol('b', commutative=True), Symbol('j', commutative=True))))", "sin(Add(Symbol('b', commutative=True), Symbol('j', commutative=True)))"]}, {"premise_expression": "G - s", "variable": "G", "positive": "\\frac{G (G - 2 s)}{2}", "negatives": ["\\frac{s (2 G - s)}{2}", "\\frac{G^{2} \\log{(s)}}{2}", "\\frac{G^{2}}{2 s}", "\\frac{G^{2} \\cos{(s)}}{2}"], "srepr_premise_expression": "Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('s', commutative=True)))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Symbol('G', commutative=True), Mul(Integer(-1), Integer(2), Symbol('s', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('s', commutative=True), Add(Mul(Integer(2), Symbol('G', commutative=True)), Mul(Integer(-1), Symbol('s', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(2)), log(Symbol('s', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(2)), Pow(Symbol('s', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(2)), cos(Symbol('s', commutative=True)))"]}, {"premise_expression": "\\cos{(\\frac{p}{M})}", "variable": "M", "positive": "M \\cos{(\\frac{p}{M})} + p \\operatorname{Si}{(\\frac{p}{M})}", "negatives": ["\\frac{M (M + 2 p)}{2}", "- M p + \\sin{(M)}", "\\frac{M (M - 2 p)}{2}", "\\sin{(M - p)}"], "srepr_premise_expression": "cos(Mul(Pow(Symbol('M', commutative=True), Integer(-1)), Symbol('p', commutative=True)))", "srepr_variable": "Symbol('M', commutative=True)", "srepr_positive": "Add(Mul(Symbol('M', commutative=True), cos(Mul(Pow(Symbol('M', commutative=True), Integer(-1)), Symbol('p', commutative=True)))), Mul(Symbol('p', commutative=True), Si(Mul(Pow(Symbol('M', commutative=True), Integer(-1)), Symbol('p', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('M', commutative=True), Add(Symbol('M', commutative=True), Mul(Integer(2), Symbol('p', commutative=True))))", "Add(Mul(Integer(-1), Symbol('M', commutative=True), Symbol('p', commutative=True)), sin(Symbol('M', commutative=True)))", "Mul(Rational(1, 2), Symbol('M', commutative=True), Add(Symbol('M', commutative=True), Mul(Integer(-1), Integer(2), Symbol('p', commutative=True))))", "sin(Add(Symbol('M', commutative=True), Mul(Integer(-1), Symbol('p', commutative=True))))"]}, {"premise_expression": "\\sin{(\\frac{p}{U})}", "variable": "U", "positive": "U \\sin{(\\frac{p}{U})} - \\frac{p \\log{(\\frac{p^{2}}{U^{2}})}}{2} + p \\log{(\\frac{p}{U})} - p \\operatorname{Ci}{(\\frac{p}{U})}", "negatives": ["U \\log{(U + p)} - U + p \\log{(U + p)}", "U (- p + \\log{(U^{p})})", "\\frac{U (- U + 2 \\log{(p)})}{2}", "\\frac{U (- U + 2 e^{p})}{2}"], "srepr_premise_expression": "sin(Mul(Pow(Symbol('U', commutative=True), Integer(-1)), Symbol('p', commutative=True)))", "srepr_variable": "Symbol('U', commutative=True)", "srepr_positive": "Add(Mul(Symbol('U', commutative=True), sin(Mul(Pow(Symbol('U', commutative=True), Integer(-1)), Symbol('p', commutative=True)))), Mul(Integer(-1), Rational(1, 2), Symbol('p', commutative=True), log(Mul(Pow(Symbol('U', commutative=True), Integer(-2)), Pow(Symbol('p', commutative=True), Integer(2))))), Mul(Symbol('p', commutative=True), log(Mul(Pow(Symbol('U', commutative=True), Integer(-1)), Symbol('p', commutative=True)))), Mul(Integer(-1), Symbol('p', commutative=True), Ci(Mul(Pow(Symbol('U', commutative=True), Integer(-1)), Symbol('p', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('U', commutative=True), log(Add(Symbol('U', commutative=True), Symbol('p', commutative=True)))), Mul(Integer(-1), Symbol('U', commutative=True)), Mul(Symbol('p', commutative=True), log(Add(Symbol('U', commutative=True), Symbol('p', commutative=True)))))", "Mul(Symbol('U', commutative=True), Add(Mul(Integer(-1), Symbol('p', commutative=True)), log(Pow(Symbol('U', commutative=True), Symbol('p', commutative=True)))))", "Mul(Rational(1, 2), Symbol('U', commutative=True), Add(Mul(Integer(-1), Symbol('U', commutative=True)), Mul(Integer(2), log(Symbol('p', commutative=True)))))", "Mul(Rational(1, 2), Symbol('U', commutative=True), Add(Mul(Integer(-1), Symbol('U', commutative=True)), Mul(Integer(2), exp(Symbol('p', commutative=True)))))"]}, {"premise_expression": "- U + Y", "variable": "Y", "positive": "\\frac{Y (- 2 U + Y)}{2}", "negatives": ["\\frac{U (- U + 2 Y)}{2}", "\\frac{Y^{2} \\cos{(U)}}{2}", "\\cos{(U - Y)}", "- \\sin{(U - Y)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('U', commutative=True)), Symbol('Y', commutative=True))", "srepr_variable": "Symbol('Y', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('Y', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('U', commutative=True)), Symbol('Y', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('U', commutative=True), Add(Mul(Integer(-1), Symbol('U', commutative=True)), Mul(Integer(2), Symbol('Y', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('Y', commutative=True), Integer(2)), cos(Symbol('U', commutative=True)))", "cos(Add(Symbol('U', commutative=True), Mul(Integer(-1), Symbol('Y', commutative=True))))", "Mul(Integer(-1), sin(Add(Symbol('U', commutative=True), Mul(Integer(-1), Symbol('Y', commutative=True)))))"]}, {"premise_expression": "w \\sin{(V)}", "variable": "V", "positive": "- w \\cos{(V)}", "negatives": ["V w \\log{(w)}", "- V w + \\sin{(V)}", "\\log{(V)} \\cos{(w)}", "\\frac{w^{2} \\sin{(V)}}{2}"], "srepr_premise_expression": "Mul(Symbol('w', commutative=True), sin(Symbol('V', commutative=True)))", "srepr_variable": "Symbol('V', commutative=True)", "srepr_positive": "Mul(Integer(-1), Symbol('w', commutative=True), cos(Symbol('V', commutative=True)))", "srepr_negatives": ["Mul(Symbol('V', commutative=True), Symbol('w', commutative=True), log(Symbol('w', commutative=True)))", "Add(Mul(Integer(-1), Symbol('V', commutative=True), Symbol('w', commutative=True)), sin(Symbol('V', commutative=True)))", "Mul(log(Symbol('V', commutative=True)), cos(Symbol('w', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('w', commutative=True), Integer(2)), sin(Symbol('V', commutative=True)))"]}, {"premise_expression": "D + P", "variable": "P", "positive": "\\frac{P (2 D + P)}{2}", "negatives": ["\\frac{D (D + 2 P)}{2}", "\\frac{P^{2} \\log{(D)}}{2}", "- \\cos{(D + P)}", "\\frac{D P^{2}}{2}"], "srepr_premise_expression": "Add(Symbol('D', commutative=True), Symbol('P', commutative=True))", "srepr_variable": "Symbol('P', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Mul(Integer(2), Symbol('D', commutative=True)), Symbol('P', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('D', commutative=True), Add(Symbol('D', commutative=True), Mul(Integer(2), Symbol('P', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2)), log(Symbol('D', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('D', commutative=True), Symbol('P', commutative=True))))", "Mul(Rational(1, 2), Symbol('D', commutative=True), Pow(Symbol('P', commutative=True), Integer(2)))"]}, {"premise_expression": "\\cos{(N - P)}", "variable": "N", "positive": "\\sin{(N - P)}", "negatives": ["- \\sin{(N - P)}", "\\frac{\\sin{(N)}}{P}", "- \\cos{(N + P)}", "P \\sin{(N)}"], "srepr_premise_expression": "cos(Add(Symbol('N', commutative=True), Mul(Integer(-1), Symbol('P', commutative=True))))", "srepr_variable": "Symbol('N', commutative=True)", "srepr_positive": "sin(Add(Symbol('N', commutative=True), Mul(Integer(-1), Symbol('P', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('N', commutative=True), Mul(Integer(-1), Symbol('P', commutative=True)))))", "Mul(Pow(Symbol('P', commutative=True), Integer(-1)), sin(Symbol('N', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('N', commutative=True), Symbol('P', commutative=True))))", "Mul(Symbol('P', commutative=True), sin(Symbol('N', commutative=True)))"]}, {"premise_expression": "\\frac{P}{G}", "variable": "P", "positive": "\\frac{P^{2}}{2 G}", "negatives": ["P \\log{(G)}", "G e^{\\frac{P}{G}}", "- G \\cos{(P)}", "P"], "srepr_premise_expression": "Mul(Pow(Symbol('G', commutative=True), Integer(-1)), Symbol('P', commutative=True))", "srepr_variable": "Symbol('P', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(-1)), Pow(Symbol('P', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('P', commutative=True), log(Symbol('G', commutative=True)))", "Mul(Symbol('G', commutative=True), exp(Mul(Pow(Symbol('G', commutative=True), Integer(-1)), Symbol('P', commutative=True))))", "Mul(Integer(-1), Symbol('G', commutative=True), cos(Symbol('P', commutative=True)))", "Symbol('P', commutative=True)"]}, {"premise_expression": "D e^{y}", "variable": "y", "positive": "D e^{y}", "negatives": ["\\frac{D^{2} e^{y}}{2}", "\\frac{y^{2} \\sin{(D)}}{2}", "y (D + \\log{(y)} - 1)", "\\frac{y (y + 2 \\sin{(D)})}{2}"], "srepr_premise_expression": "Mul(Symbol('D', commutative=True), exp(Symbol('y', commutative=True)))", "srepr_variable": "Symbol('y', commutative=True)", "srepr_positive": "Mul(Symbol('D', commutative=True), exp(Symbol('y', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(2)), exp(Symbol('y', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('y', commutative=True), Integer(2)), sin(Symbol('D', commutative=True)))", "Mul(Symbol('y', commutative=True), Add(Symbol('D', commutative=True), log(Symbol('y', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('y', commutative=True), Add(Symbol('y', commutative=True), Mul(Integer(2), sin(Symbol('D', commutative=True)))))"]}, {"premise_expression": "\\frac{S}{a}", "variable": "a", "positive": "S \\log{(a)}", "negatives": ["\\frac{S^{2}}{2 a}", "S a + \\sin{(a)}", "- \\cos{(S - a)}", "- S a + \\sin{(a)}"], "srepr_premise_expression": "Mul(Symbol('S', commutative=True), Pow(Symbol('a', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('a', commutative=True)", "srepr_positive": "Mul(Symbol('S', commutative=True), log(Symbol('a', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('S', commutative=True), Integer(2)), Pow(Symbol('a', commutative=True), Integer(-1)))", "Add(Mul(Symbol('S', commutative=True), Symbol('a', commutative=True)), sin(Symbol('a', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('a', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('S', commutative=True), Symbol('a', commutative=True)), sin(Symbol('a', commutative=True)))"]}, {"premise_expression": "l x", "variable": "x", "positive": "\\frac{l x^{2}}{2}", "negatives": ["\\frac{l^{2} x}{2}", "l e^{\\frac{x}{l}}", "l \\log{(x)}", "e^{l + x}"], "srepr_premise_expression": "Mul(Symbol('l', commutative=True), Symbol('x', commutative=True))", "srepr_variable": "Symbol('x', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('l', commutative=True), Pow(Symbol('x', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('l', commutative=True), Integer(2)), Symbol('x', commutative=True))", "Mul(Symbol('l', commutative=True), exp(Mul(Pow(Symbol('l', commutative=True), Integer(-1)), Symbol('x', commutative=True))))", "Mul(Symbol('l', commutative=True), log(Symbol('x', commutative=True)))", "exp(Add(Symbol('l', commutative=True), Symbol('x', commutative=True)))"]}, {"premise_expression": "\\frac{q}{D k}", "variable": "k", "positive": "\\frac{q \\log{(k)}}{D}", "negatives": ["\\frac{q \\log{(D)}}{k}", "\\frac{D \\log{(k)}}{q}", "D q \\log{(k)}", "\\frac{D k^{2} q}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('D', commutative=True), Integer(-1)), Pow(Symbol('k', commutative=True), Integer(-1)), Symbol('q', commutative=True))", "srepr_variable": "Symbol('k', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('D', commutative=True), Integer(-1)), Symbol('q', commutative=True), log(Symbol('k', commutative=True)))", "srepr_negatives": ["Mul(Pow(Symbol('k', commutative=True), Integer(-1)), Symbol('q', commutative=True), log(Symbol('D', commutative=True)))", "Mul(Symbol('D', commutative=True), Pow(Symbol('q', commutative=True), Integer(-1)), log(Symbol('k', commutative=True)))", "Mul(Symbol('D', commutative=True), Symbol('q', commutative=True), log(Symbol('k', commutative=True)))", "Mul(Rational(1, 2), Symbol('D', commutative=True), Pow(Symbol('k', commutative=True), Integer(2)), Symbol('q', commutative=True))"]}, {"premise_expression": "\\log{(o^{V})}", "variable": "o", "positive": "o (- V + \\log{(o^{V})})", "negatives": ["\\frac{o (- 2 V + o)}{2}", "\\frac{V^{2} \\log{(o)}}{2}", "\\frac{o^{2}}{2 V}", "o (\\log{(\\frac{V}{o})} + 1)"], "srepr_premise_expression": "log(Pow(Symbol('o', commutative=True), Symbol('V', commutative=True)))", "srepr_variable": "Symbol('o', commutative=True)", "srepr_positive": "Mul(Symbol('o', commutative=True), Add(Mul(Integer(-1), Symbol('V', commutative=True)), log(Pow(Symbol('o', commutative=True), Symbol('V', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('V', commutative=True)), Symbol('o', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('V', commutative=True), Integer(2)), log(Symbol('o', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('V', commutative=True), Integer(-1)), Pow(Symbol('o', commutative=True), Integer(2)))", "Mul(Symbol('o', commutative=True), Add(log(Mul(Symbol('V', commutative=True), Pow(Symbol('o', commutative=True), Integer(-1)))), Integer(1)))"]}, {"premise_expression": "\\frac{p}{u}", "variable": "u", "positive": "p \\log{(u)}", "negatives": ["\\frac{p^{2}}{2 u}", "p u + e^{u}", "- \\cos{(p + u)}", "\\frac{u (2 p - u)}{2}"], "srepr_premise_expression": "Mul(Symbol('p', commutative=True), Pow(Symbol('u', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "Mul(Symbol('p', commutative=True), log(Symbol('u', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('p', commutative=True), Integer(2)), Pow(Symbol('u', commutative=True), Integer(-1)))", "Add(Mul(Symbol('p', commutative=True), Symbol('u', commutative=True)), exp(Symbol('u', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('p', commutative=True), Symbol('u', commutative=True))))", "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(2), Symbol('p', commutative=True)), Mul(Integer(-1), Symbol('u', commutative=True))))"]}, {"premise_expression": "Y h", "variable": "h", "positive": "\\frac{Y h^{2}}{2}", "negatives": ["\\frac{Y^{2} h}{2}", "\\frac{\\sin{(h)}}{Y}", "Y h + e^{h}", "\\frac{h (2 Y - h)}{2}"], "srepr_premise_expression": "Mul(Symbol('Y', commutative=True), Symbol('h', commutative=True))", "srepr_variable": "Symbol('h', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('Y', commutative=True), Pow(Symbol('h', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('Y', commutative=True), Integer(2)), Symbol('h', commutative=True))", "Mul(Pow(Symbol('Y', commutative=True), Integer(-1)), sin(Symbol('h', commutative=True)))", "Add(Mul(Symbol('Y', commutative=True), Symbol('h', commutative=True)), exp(Symbol('h', commutative=True)))", "Mul(Rational(1, 2), Symbol('h', commutative=True), Add(Mul(Integer(2), Symbol('Y', commutative=True)), Mul(Integer(-1), Symbol('h', commutative=True))))"]}, {"premise_expression": "e^{\\frac{S}{M}}", "variable": "S", "positive": "M e^{\\frac{S}{M}}", "negatives": ["\\frac{M S^{2}}{2}", "e^{- M + S}", "\\log{(S)} \\sin{(M)}", "M e^{\\frac{S}{M}} - S \\operatorname{Ei}{(\\frac{S}{M})}"], "srepr_premise_expression": "exp(Mul(Pow(Symbol('M', commutative=True), Integer(-1)), Symbol('S', commutative=True)))", "srepr_variable": "Symbol('S', commutative=True)", "srepr_positive": "Mul(Symbol('M', commutative=True), exp(Mul(Pow(Symbol('M', commutative=True), Integer(-1)), Symbol('S', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('M', commutative=True), Pow(Symbol('S', commutative=True), Integer(2)))", "exp(Add(Mul(Integer(-1), Symbol('M', commutative=True)), Symbol('S', commutative=True)))", "Mul(log(Symbol('S', commutative=True)), sin(Symbol('M', commutative=True)))", "Add(Mul(Symbol('M', commutative=True), exp(Mul(Pow(Symbol('M', commutative=True), Integer(-1)), Symbol('S', commutative=True)))), Mul(Integer(-1), Symbol('S', commutative=True), Ei(Mul(Pow(Symbol('M', commutative=True), Integer(-1)), Symbol('S', commutative=True)))))"]}, {"premise_expression": "\\frac{e^{F}}{Z}", "variable": "Z", "positive": "e^{F} \\log{(Z)}", "negatives": ["e^{- F + Z}", "- F Z + e^{Z}", "F Z (\\log{(Z)} - 1)", "\\frac{Z (- 2 F + Z)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('Z', commutative=True), Integer(-1)), exp(Symbol('F', commutative=True)))", "srepr_variable": "Symbol('Z', commutative=True)", "srepr_positive": "Mul(exp(Symbol('F', commutative=True)), log(Symbol('Z', commutative=True)))", "srepr_negatives": ["exp(Add(Mul(Integer(-1), Symbol('F', commutative=True)), Symbol('Z', commutative=True)))", "Add(Mul(Integer(-1), Symbol('F', commutative=True), Symbol('Z', commutative=True)), exp(Symbol('Z', commutative=True)))", "Mul(Symbol('F', commutative=True), Symbol('Z', commutative=True), Add(log(Symbol('Z', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('F', commutative=True)), Symbol('Z', commutative=True)))"]}, {"premise_expression": "\\frac{- F + N}{C}", "variable": "F", "positive": "\\frac{F (- F + 2 N)}{2 C}", "negatives": ["- \\frac{N (2 F - N)}{2 C}", "\\frac{F (C F - 2 N)}{2}", "- \\frac{F (2 C - F)}{2 N}", "F (- F + N)"], "srepr_premise_expression": "Mul(Pow(Symbol('C', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('F', commutative=True)), Symbol('N', commutative=True)))", "srepr_variable": "Symbol('F', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(-1)), Symbol('F', commutative=True), Add(Mul(Integer(-1), Symbol('F', commutative=True)), Mul(Integer(2), Symbol('N', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(-1)), Symbol('N', commutative=True), Add(Mul(Integer(2), Symbol('F', commutative=True)), Mul(Integer(-1), Symbol('N', commutative=True))))", "Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Mul(Symbol('C', commutative=True), Symbol('F', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('N', commutative=True))))", "Mul(Integer(-1), Rational(1, 2), Symbol('F', commutative=True), Pow(Symbol('N', commutative=True), Integer(-1)), Add(Mul(Integer(2), Symbol('C', commutative=True)), Mul(Integer(-1), Symbol('F', commutative=True))))", "Mul(Symbol('F', commutative=True), Add(Mul(Integer(-1), Symbol('F', commutative=True)), Symbol('N', commutative=True)))"]}, {"premise_expression": "- \\sin{(H - U)}", "variable": "U", "positive": "- \\cos{(H - U)}", "negatives": ["\\cos{(H - U)}", "- H \\cos{(U)}", "- H U + e^{U}", "\\frac{U (\\log{(U)} - 1)}{H}"], "srepr_premise_expression": "Mul(Integer(-1), sin(Add(Symbol('H', commutative=True), Mul(Integer(-1), Symbol('U', commutative=True)))))", "srepr_variable": "Symbol('U', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('H', commutative=True), Mul(Integer(-1), Symbol('U', commutative=True)))))", "srepr_negatives": ["cos(Add(Symbol('H', commutative=True), Mul(Integer(-1), Symbol('U', commutative=True))))", "Mul(Integer(-1), Symbol('H', commutative=True), cos(Symbol('U', commutative=True)))", "Add(Mul(Integer(-1), Symbol('H', commutative=True), Symbol('U', commutative=True)), exp(Symbol('U', commutative=True)))", "Mul(Pow(Symbol('H', commutative=True), Integer(-1)), Symbol('U', commutative=True), Add(log(Symbol('U', commutative=True)), Integer(-1)))"]}, {"premise_expression": "t \\log{(k)}", "variable": "k", "positive": "k t (\\log{(k)} - 1)", "negatives": ["k (t + \\log{(k)} - 1)", "t \\log{(k)}", "\\frac{t^{2} \\log{(k)}}{2}", "\\frac{k^{2}}{2 t}"], "srepr_premise_expression": "Mul(Symbol('t', commutative=True), log(Symbol('k', commutative=True)))", "srepr_variable": "Symbol('k', commutative=True)", "srepr_positive": "Mul(Symbol('k', commutative=True), Symbol('t', commutative=True), Add(log(Symbol('k', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('k', commutative=True), Add(Symbol('t', commutative=True), log(Symbol('k', commutative=True)), Integer(-1)))", "Mul(Symbol('t', commutative=True), log(Symbol('k', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('t', commutative=True), Integer(2)), log(Symbol('k', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('k', commutative=True), Integer(2)), Pow(Symbol('t', commutative=True), Integer(-1)))"]}, {"premise_expression": "\\frac{B}{q}", "variable": "q", "positive": "B \\log{(q)}", "negatives": ["\\frac{B^{2}}{2 q}", "e^{B} \\log{(q)}", "B e^{\\frac{q}{B}}", "\\sin{(B + q)}"], "srepr_premise_expression": "Mul(Symbol('B', commutative=True), Pow(Symbol('q', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('q', commutative=True)", "srepr_positive": "Mul(Symbol('B', commutative=True), log(Symbol('q', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('B', commutative=True), Integer(2)), Pow(Symbol('q', commutative=True), Integer(-1)))", "Mul(exp(Symbol('B', commutative=True)), log(Symbol('q', commutative=True)))", "Mul(Symbol('B', commutative=True), exp(Mul(Pow(Symbol('B', commutative=True), Integer(-1)), Symbol('q', commutative=True))))", "sin(Add(Symbol('B', commutative=True), Symbol('q', commutative=True)))"]}, {"premise_expression": "Q t", "variable": "t", "positive": "\\frac{Q t^{2}}{2}", "negatives": ["\\frac{Q^{2} t}{2}", "e t", "\\frac{Q t (2 Q + t)}{2}", "Q t - \\cos{(t)}"], "srepr_premise_expression": "Mul(Symbol('Q', commutative=True), Symbol('t', commutative=True))", "srepr_variable": "Symbol('t', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('Q', commutative=True), Pow(Symbol('t', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(2)), Symbol('t', commutative=True))", "Mul(E, Symbol('t', commutative=True))", "Mul(Rational(1, 2), Symbol('Q', commutative=True), Symbol('t', commutative=True), Add(Mul(Integer(2), Symbol('Q', commutative=True)), Symbol('t', commutative=True)))", "Add(Mul(Symbol('Q', commutative=True), Symbol('t', commutative=True)), Mul(Integer(-1), cos(Symbol('t', commutative=True))))"]}, {"premise_expression": "u + y", "variable": "u", "positive": "\\frac{u (u + 2 y)}{2}", "negatives": ["\\frac{y (2 u + y)}{2}", "\\frac{u (- u + 2 \\cos{(y)})}{2}", "\\frac{u^{2} \\sin{(y)}}{2}", "u (\\log{(u y)} - 1)"], "srepr_premise_expression": "Add(Symbol('u', commutative=True), Symbol('y', commutative=True))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Symbol('u', commutative=True), Mul(Integer(2), Symbol('y', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('y', commutative=True), Add(Mul(Integer(2), Symbol('u', commutative=True)), Symbol('y', commutative=True)))", "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(-1), Symbol('u', commutative=True)), Mul(Integer(2), cos(Symbol('y', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('u', commutative=True), Integer(2)), sin(Symbol('y', commutative=True)))", "Mul(Symbol('u', commutative=True), Add(log(Mul(Symbol('u', commutative=True), Symbol('y', commutative=True))), Integer(-1)))"]}, {"premise_expression": "C - z", "variable": "z", "positive": "\\frac{z (2 C - z)}{2}", "negatives": ["\\frac{C (C - 2 z)}{2}", "e^{- C + z}", "\\frac{z (\\log{(z)} - 1)}{C}", "\\frac{z (z + 2 \\cos{(C)})}{2}"], "srepr_premise_expression": "Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('z', commutative=True)))", "srepr_variable": "Symbol('z', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('z', commutative=True), Add(Mul(Integer(2), Symbol('C', commutative=True)), Mul(Integer(-1), Symbol('z', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Symbol('C', commutative=True), Mul(Integer(-1), Integer(2), Symbol('z', commutative=True))))", "exp(Add(Mul(Integer(-1), Symbol('C', commutative=True)), Symbol('z', commutative=True)))", "Mul(Pow(Symbol('C', commutative=True), Integer(-1)), Symbol('z', commutative=True), Add(log(Symbol('z', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('z', commutative=True), Add(Symbol('z', commutative=True), Mul(Integer(2), cos(Symbol('C', commutative=True)))))"]}, {"premise_expression": "Y + x", "variable": "x", "positive": "\\frac{x (2 Y + x)}{2}", "negatives": ["\\frac{Y (Y + 2 x)}{2}", "- \\cos{(Y + x)}", "Y \\log{(x)}", "Y \\sin{(x)}"], "srepr_premise_expression": "Add(Symbol('Y', commutative=True), Symbol('x', commutative=True))", "srepr_variable": "Symbol('x', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('x', commutative=True), Add(Mul(Integer(2), Symbol('Y', commutative=True)), Symbol('x', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('Y', commutative=True), Add(Symbol('Y', commutative=True), Mul(Integer(2), Symbol('x', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('Y', commutative=True), Symbol('x', commutative=True))))", "Mul(Symbol('Y', commutative=True), log(Symbol('x', commutative=True)))", "Mul(Symbol('Y', commutative=True), sin(Symbol('x', commutative=True)))"]}, {"premise_expression": "M \\cos{(u)}", "variable": "M", "positive": "\\frac{M^{2} \\cos{(u)}}{2}", "negatives": ["\\frac{M (M + 2 u)}{2}", "\\frac{M^{2}}{2 u}", "M \\sin{(u)}", "\\frac{M (- M + 2 \\log{(u)})}{2}"], "srepr_premise_expression": "Mul(Symbol('M', commutative=True), cos(Symbol('u', commutative=True)))", "srepr_variable": "Symbol('M', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('M', commutative=True), Integer(2)), cos(Symbol('u', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('M', commutative=True), Add(Symbol('M', commutative=True), Mul(Integer(2), Symbol('u', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('M', commutative=True), Integer(2)), Pow(Symbol('u', commutative=True), Integer(-1)))", "Mul(Symbol('M', commutative=True), sin(Symbol('u', commutative=True)))", "Mul(Rational(1, 2), Symbol('M', commutative=True), Add(Mul(Integer(-1), Symbol('M', commutative=True)), Mul(Integer(2), log(Symbol('u', commutative=True)))))"]}, {"premise_expression": "\\sin{(A + F)}", "variable": "F", "positive": "- \\cos{(A + F)}", "negatives": ["A \\log{(F)}", "\\frac{A F^{2}}{2}", "F (A + \\log{(F)} - 1)", "\\frac{F (- F + 2 \\log{(A)})}{2}"], "srepr_premise_expression": "sin(Add(Symbol('A', commutative=True), Symbol('F', commutative=True)))", "srepr_variable": "Symbol('F', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('A', commutative=True), Symbol('F', commutative=True))))", "srepr_negatives": ["Mul(Symbol('A', commutative=True), log(Symbol('F', commutative=True)))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Pow(Symbol('F', commutative=True), Integer(2)))", "Mul(Symbol('F', commutative=True), Add(Symbol('A', commutative=True), log(Symbol('F', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Mul(Integer(-1), Symbol('F', commutative=True)), Mul(Integer(2), log(Symbol('A', commutative=True)))))"]}, {"premise_expression": "- T + o v", "variable": "v", "positive": "\\frac{v (- 2 T + o v)}{2}", "negatives": ["\\frac{o (- 2 T + o v)}{2}", "\\frac{T (- T + 2 o v)}{2}", "\\frac{v (2 o^{T} + v)}{2}", "- \\frac{v^{2}}{2} + \\frac{o v}{T}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('T', commutative=True)), Mul(Symbol('o', commutative=True), Symbol('v', commutative=True)))", "srepr_variable": "Symbol('v', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('v', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('T', commutative=True)), Mul(Symbol('o', commutative=True), Symbol('v', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('T', commutative=True)), Mul(Symbol('o', commutative=True), Symbol('v', commutative=True))))", "Mul(Rational(1, 2), Symbol('T', commutative=True), Add(Mul(Integer(-1), Symbol('T', commutative=True)), Mul(Integer(2), Symbol('o', commutative=True), Symbol('v', commutative=True))))", "Mul(Rational(1, 2), Symbol('v', commutative=True), Add(Mul(Integer(2), Pow(Symbol('o', commutative=True), Symbol('T', commutative=True))), Symbol('v', commutative=True)))", "Add(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('v', commutative=True), Integer(2))), Mul(Pow(Symbol('T', commutative=True), Integer(-1)), Symbol('o', commutative=True), Symbol('v', commutative=True)))"]}, {"premise_expression": "\\cos{(Q + c)}", "variable": "Q", "positive": "\\sin{(Q + c)}", "negatives": ["e^{Q - c}", "- \\frac{\\cos{(Q)}}{c}", "Q c e^{c}", "- Q c - \\cos{(Q)}"], "srepr_premise_expression": "cos(Add(Symbol('Q', commutative=True), Symbol('c', commutative=True)))", "srepr_variable": "Symbol('Q', commutative=True)", "srepr_positive": "sin(Add(Symbol('Q', commutative=True), Symbol('c', commutative=True)))", "srepr_negatives": ["exp(Add(Symbol('Q', commutative=True), Mul(Integer(-1), Symbol('c', commutative=True))))", "Mul(Integer(-1), Pow(Symbol('c', commutative=True), Integer(-1)), cos(Symbol('Q', commutative=True)))", "Mul(Symbol('Q', commutative=True), Symbol('c', commutative=True), exp(Symbol('c', commutative=True)))", "Add(Mul(Integer(-1), Symbol('Q', commutative=True), Symbol('c', commutative=True)), Mul(Integer(-1), cos(Symbol('Q', commutative=True))))"]}, {"premise_expression": "\\frac{\\cos{(M)}}{q}", "variable": "q", "positive": "\\log{(q)} \\cos{(M)}", "negatives": ["\\frac{q^{2} \\log{(M)}}{2}", "\\frac{\\sin{(M)}}{q}", "q (\\log{(\\frac{M}{q})} + 1)", "\\frac{q (2 M - q)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('q', commutative=True), Integer(-1)), cos(Symbol('M', commutative=True)))", "srepr_variable": "Symbol('q', commutative=True)", "srepr_positive": "Mul(log(Symbol('q', commutative=True)), cos(Symbol('M', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('q', commutative=True), Integer(2)), log(Symbol('M', commutative=True)))", "Mul(Pow(Symbol('q', commutative=True), Integer(-1)), sin(Symbol('M', commutative=True)))", "Mul(Symbol('q', commutative=True), Add(log(Mul(Symbol('M', commutative=True), Pow(Symbol('q', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Rational(1, 2), Symbol('q', commutative=True), Add(Mul(Integer(2), Symbol('M', commutative=True)), Mul(Integer(-1), Symbol('q', commutative=True))))"]}, {"premise_expression": "\\frac{I q}{b}", "variable": "I", "positive": "\\frac{I^{2} q}{2 b}", "negatives": ["\\frac{I q^{2}}{2 b}", "I q \\log{(b)}", "\\frac{I (I q - 2 b)}{2}", "\\frac{I (I q + 2 b)}{2}"], "srepr_premise_expression": "Mul(Symbol('I', commutative=True), Pow(Symbol('b', commutative=True), Integer(-1)), Symbol('q', commutative=True))", "srepr_variable": "Symbol('I', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(2)), Pow(Symbol('b', commutative=True), Integer(-1)), Symbol('q', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('I', commutative=True), Pow(Symbol('b', commutative=True), Integer(-1)), Pow(Symbol('q', commutative=True), Integer(2)))", "Mul(Symbol('I', commutative=True), Symbol('q', commutative=True), log(Symbol('b', commutative=True)))", "Mul(Rational(1, 2), Symbol('I', commutative=True), Add(Mul(Symbol('I', commutative=True), Symbol('q', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('b', commutative=True))))", "Mul(Rational(1, 2), Symbol('I', commutative=True), Add(Mul(Symbol('I', commutative=True), Symbol('q', commutative=True)), Mul(Integer(2), Symbol('b', commutative=True))))"]}, {"premise_expression": "\\sin{(L + a)}", "variable": "L", "positive": "- \\cos{(L + a)}", "negatives": ["a \\sin{(L)}", "L (a + \\log{(L)} - 1)", "L e^{\\frac{a}{L}} - a \\operatorname{Ei}{(\\frac{a}{L})}", "\\int \\sin^{a}{(L)} dL"], "srepr_premise_expression": "sin(Add(Symbol('L', commutative=True), Symbol('a', commutative=True)))", "srepr_variable": "Symbol('L', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('L', commutative=True), Symbol('a', commutative=True))))", "srepr_negatives": ["Mul(Symbol('a', commutative=True), sin(Symbol('L', commutative=True)))", "Mul(Symbol('L', commutative=True), Add(Symbol('a', commutative=True), log(Symbol('L', commutative=True)), Integer(-1)))", "Add(Mul(Symbol('L', commutative=True), exp(Mul(Pow(Symbol('L', commutative=True), Integer(-1)), Symbol('a', commutative=True)))), Mul(Integer(-1), Symbol('a', commutative=True), Ei(Mul(Pow(Symbol('L', commutative=True), Integer(-1)), Symbol('a', commutative=True)))))", "Integral(Pow(sin(Symbol('L', commutative=True)), Symbol('a', commutative=True)), Tuple(Symbol('L', commutative=True)))"]}, {"premise_expression": "\\cos{(X - l)}", "variable": "l", "positive": "- \\sin{(X - l)}", "negatives": ["\\sin{(X - l)}", "\\frac{l (- 2 X + l)}{2}", "l \\cos{(X^{X})}", "l^{2} (\\frac{X}{2} - \\frac{l}{3})"], "srepr_premise_expression": "cos(Add(Symbol('X', commutative=True), Mul(Integer(-1), Symbol('l', commutative=True))))", "srepr_variable": "Symbol('l', commutative=True)", "srepr_positive": "Mul(Integer(-1), sin(Add(Symbol('X', commutative=True), Mul(Integer(-1), Symbol('l', commutative=True)))))", "srepr_negatives": ["sin(Add(Symbol('X', commutative=True), Mul(Integer(-1), Symbol('l', commutative=True))))", "Mul(Rational(1, 2), Symbol('l', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('X', commutative=True)), Symbol('l', commutative=True)))", "Mul(Symbol('l', commutative=True), cos(Pow(Symbol('X', commutative=True), Symbol('X', commutative=True))))", "Mul(Pow(Symbol('l', commutative=True), Integer(2)), Add(Mul(Rational(1, 2), Symbol('X', commutative=True)), Mul(Integer(-1), Rational(1, 3), Symbol('l', commutative=True))))"]}, {"premise_expression": "- J + \\sin{(x)}", "variable": "J", "positive": "\\frac{J (- J + 2 \\sin{(x)})}{2}", "negatives": ["\\frac{J (J + 2 \\cos{(x)})}{2}", "- J x - \\cos{(x)}", "J x + e^{J}", "J x - \\cos{(J)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('J', commutative=True)), sin(Symbol('x', commutative=True)))", "srepr_variable": "Symbol('J', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('J', commutative=True), Add(Mul(Integer(-1), Symbol('J', commutative=True)), Mul(Integer(2), sin(Symbol('x', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('J', commutative=True), Add(Symbol('J', commutative=True), Mul(Integer(2), cos(Symbol('x', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('J', commutative=True), Symbol('x', commutative=True)), Mul(Integer(-1), cos(Symbol('x', commutative=True))))", "Add(Mul(Symbol('J', commutative=True), Symbol('x', commutative=True)), exp(Symbol('J', commutative=True)))", "Add(Mul(Symbol('J', commutative=True), Symbol('x', commutative=True)), Mul(Integer(-1), cos(Symbol('J', commutative=True))))"]}, {"premise_expression": "\\frac{u}{v}", "variable": "u", "positive": "\\frac{u^{2}}{2 v}", "negatives": ["u \\log{(v)}", "- \\frac{u^{2}}{2 v} + u", "\\frac{u (- u + 2 v)}{2}", "e^{u - v}"], "srepr_premise_expression": "Mul(Symbol('u', commutative=True), Pow(Symbol('v', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('u', commutative=True), Integer(2)), Pow(Symbol('v', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('u', commutative=True), log(Symbol('v', commutative=True)))", "Add(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('u', commutative=True), Integer(2)), Pow(Symbol('v', commutative=True), Integer(-1))), Symbol('u', commutative=True))", "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(-1), Symbol('u', commutative=True)), Mul(Integer(2), Symbol('v', commutative=True))))", "exp(Add(Symbol('u', commutative=True), Mul(Integer(-1), Symbol('v', commutative=True))))"]}, {"premise_expression": "Y \\sin{(t)}", "variable": "Y", "positive": "\\frac{Y^{2} \\sin{(t)}}{2}", "negatives": ["\\frac{Y^{2} \\log{(t)}}{2}", "\\frac{Y^{2} t}{2}", "\\frac{Y (- Y + 2 \\sin{(t)})}{2}", "- Y \\cos{(t)}"], "srepr_premise_expression": "Mul(Symbol('Y', commutative=True), sin(Symbol('t', commutative=True)))", "srepr_variable": "Symbol('Y', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('Y', commutative=True), Integer(2)), sin(Symbol('t', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('Y', commutative=True), Integer(2)), log(Symbol('t', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('Y', commutative=True), Integer(2)), Symbol('t', commutative=True))", "Mul(Rational(1, 2), Symbol('Y', commutative=True), Add(Mul(Integer(-1), Symbol('Y', commutative=True)), Mul(Integer(2), sin(Symbol('t', commutative=True)))))", "Mul(Integer(-1), Symbol('Y', commutative=True), cos(Symbol('t', commutative=True)))"]}, {"premise_expression": "\\frac{\\cos{(H)}}{f}", "variable": "f", "positive": "\\log{(f)} \\cos{(H)}", "negatives": ["f \\cos{(2 H)}", "- \\frac{\\cos{(f)}}{H}", "\\frac{\\sin{(H)}}{f}", "- \\cos{(H + f)}"], "srepr_premise_expression": "Mul(Pow(Symbol('f', commutative=True), Integer(-1)), cos(Symbol('H', commutative=True)))", "srepr_variable": "Symbol('f', commutative=True)", "srepr_positive": "Mul(log(Symbol('f', commutative=True)), cos(Symbol('H', commutative=True)))", "srepr_negatives": ["Mul(Symbol('f', commutative=True), cos(Mul(Integer(2), Symbol('H', commutative=True))))", "Mul(Integer(-1), Pow(Symbol('H', commutative=True), Integer(-1)), cos(Symbol('f', commutative=True)))", "Mul(Pow(Symbol('f', commutative=True), Integer(-1)), sin(Symbol('H', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('H', commutative=True), Symbol('f', commutative=True))))"]}, {"premise_expression": "D \\log{(y)}", "variable": "D", "positive": "\\frac{D^{2} \\log{(y)}}{2}", "negatives": ["\\frac{D^{2} y^{2}}{2}", "y \\log{(D)}", "D y (\\log{(y)} - 1)", "\\frac{D (- D + 2 y)}{2}"], "srepr_premise_expression": "Mul(Symbol('D', commutative=True), log(Symbol('y', commutative=True)))", "srepr_variable": "Symbol('D', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(2)), log(Symbol('y', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(2)), Pow(Symbol('y', commutative=True), Integer(2)))", "Mul(Symbol('y', commutative=True), log(Symbol('D', commutative=True)))", "Mul(Symbol('D', commutative=True), Symbol('y', commutative=True), Add(log(Symbol('y', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('D', commutative=True), Add(Mul(Integer(-1), Symbol('D', commutative=True)), Mul(Integer(2), Symbol('y', commutative=True))))"]}, {"premise_expression": "\\log{(C y)}", "variable": "y", "positive": "y (\\log{(C y)} - 1)", "negatives": ["C (\\log{(C y)} - 1)", "y (- C + \\log{(y)} - 1)", "\\cos{(C - y)}", "\\frac{y (- 2 C + y)}{2}"], "srepr_premise_expression": "log(Mul(Symbol('C', commutative=True), Symbol('y', commutative=True)))", "srepr_variable": "Symbol('y', commutative=True)", "srepr_positive": "Mul(Symbol('y', commutative=True), Add(log(Mul(Symbol('C', commutative=True), Symbol('y', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('C', commutative=True), Add(log(Mul(Symbol('C', commutative=True), Symbol('y', commutative=True))), Integer(-1)))", "Mul(Symbol('y', commutative=True), Add(Mul(Integer(-1), Symbol('C', commutative=True)), log(Symbol('y', commutative=True)), Integer(-1)))", "cos(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True))))", "Mul(Rational(1, 2), Symbol('y', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('C', commutative=True)), Symbol('y', commutative=True)))"]}, {"premise_expression": "\\frac{R}{N}", "variable": "N", "positive": "R \\log{(N)}", "negatives": ["R e^{N}", "\\frac{R^{2}}{2 N}", "R e^{\\frac{N}{R}}", "N"], "srepr_premise_expression": "Mul(Pow(Symbol('N', commutative=True), Integer(-1)), Symbol('R', commutative=True))", "srepr_variable": "Symbol('N', commutative=True)", "srepr_positive": "Mul(Symbol('R', commutative=True), log(Symbol('N', commutative=True)))", "srepr_negatives": ["Mul(Symbol('R', commutative=True), exp(Symbol('N', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('N', commutative=True), Integer(-1)), Pow(Symbol('R', commutative=True), Integer(2)))", "Mul(Symbol('R', commutative=True), exp(Mul(Symbol('N', commutative=True), Pow(Symbol('R', commutative=True), Integer(-1)))))", "Symbol('N', commutative=True)"]}, {"premise_expression": "y (- S + Z)", "variable": "Z", "positive": "\\frac{Z y (- 2 S + Z)}{2}", "negatives": ["\\frac{Z (- 2 S + Z y)}{2}", "\\frac{S y (- S + 2 Z)}{2}", "\\frac{y^{2} (- S + Z)}{2}", "\\frac{Z^{2} y^{S}}{2}"], "srepr_premise_expression": "Mul(Symbol('y', commutative=True), Add(Mul(Integer(-1), Symbol('S', commutative=True)), Symbol('Z', commutative=True)))", "srepr_variable": "Symbol('Z', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('Z', commutative=True), Symbol('y', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('S', commutative=True)), Symbol('Z', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('S', commutative=True)), Mul(Symbol('Z', commutative=True), Symbol('y', commutative=True))))", "Mul(Rational(1, 2), Symbol('S', commutative=True), Symbol('y', commutative=True), Add(Mul(Integer(-1), Symbol('S', commutative=True)), Mul(Integer(2), Symbol('Z', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('y', commutative=True), Integer(2)), Add(Mul(Integer(-1), Symbol('S', commutative=True)), Symbol('Z', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('Z', commutative=True), Integer(2)), Pow(Symbol('y', commutative=True), Symbol('S', commutative=True)))"]}, {"premise_expression": "- k + \\sin{(A)}", "variable": "A", "positive": "- A k - \\cos{(A)}", "negatives": ["- A k + \\sin{(A)}", "\\frac{A^{2} \\cos{(k)}}{2}", "e^{k} \\log{(A)}", "\\frac{A (A - 2 k)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('k', commutative=True)), sin(Symbol('A', commutative=True)))", "srepr_variable": "Symbol('A', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('A', commutative=True), Symbol('k', commutative=True)), Mul(Integer(-1), cos(Symbol('A', commutative=True))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('A', commutative=True), Symbol('k', commutative=True)), sin(Symbol('A', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2)), cos(Symbol('k', commutative=True)))", "Mul(exp(Symbol('k', commutative=True)), log(Symbol('A', commutative=True)))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Symbol('A', commutative=True), Mul(Integer(-1), Integer(2), Symbol('k', commutative=True))))"]}, {"premise_expression": "\\cos{(E + F)}", "variable": "E", "positive": "\\sin{(E + F)}", "negatives": ["\\sin{(E - F)}", "- e^{- E + F}", "F \\sin{(E)}", "\\frac{E (- E + 2 F)}{2}"], "srepr_premise_expression": "cos(Add(Symbol('E', commutative=True), Symbol('F', commutative=True)))", "srepr_variable": "Symbol('E', commutative=True)", "srepr_positive": "sin(Add(Symbol('E', commutative=True), Symbol('F', commutative=True)))", "srepr_negatives": ["sin(Add(Symbol('E', commutative=True), Mul(Integer(-1), Symbol('F', commutative=True))))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('E', commutative=True)), Symbol('F', commutative=True))))", "Mul(Symbol('F', commutative=True), sin(Symbol('E', commutative=True)))", "Mul(Rational(1, 2), Symbol('E', commutative=True), Add(Mul(Integer(-1), Symbol('E', commutative=True)), Mul(Integer(2), Symbol('F', commutative=True))))"]}, {"premise_expression": "\\frac{h}{a u}", "variable": "u", "positive": "\\frac{h \\log{(u)}}{a}", "negatives": ["\\frac{h \\log{(a)}}{u}", "\\frac{a \\log{(u)}}{h}", "a^{h} \\log{(u)}", "\\frac{u^{2}}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('a', commutative=True), Integer(-1)), Symbol('h', commutative=True), Pow(Symbol('u', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('a', commutative=True), Integer(-1)), Symbol('h', commutative=True), log(Symbol('u', commutative=True)))", "srepr_negatives": ["Mul(Symbol('h', commutative=True), Pow(Symbol('u', commutative=True), Integer(-1)), log(Symbol('a', commutative=True)))", "Mul(Symbol('a', commutative=True), Pow(Symbol('h', commutative=True), Integer(-1)), log(Symbol('u', commutative=True)))", "Mul(Pow(Symbol('a', commutative=True), Symbol('h', commutative=True)), log(Symbol('u', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('u', commutative=True), Integer(2)))"]}, {"premise_expression": "Y e^{j}", "variable": "j", "positive": "Y e^{j}", "negatives": ["\\frac{Y^{2} e^{j}}{2}", "\\frac{Y j^{2}}{2}", "e^{- Y + j}", "\\log{(j)} \\sin{(Y)}"], "srepr_premise_expression": "Mul(Symbol('Y', commutative=True), exp(Symbol('j', commutative=True)))", "srepr_variable": "Symbol('j', commutative=True)", "srepr_positive": "Mul(Symbol('Y', commutative=True), exp(Symbol('j', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('Y', commutative=True), Integer(2)), exp(Symbol('j', commutative=True)))", "Mul(Rational(1, 2), Symbol('Y', commutative=True), Pow(Symbol('j', commutative=True), Integer(2)))", "exp(Add(Mul(Integer(-1), Symbol('Y', commutative=True)), Symbol('j', commutative=True)))", "Mul(log(Symbol('j', commutative=True)), sin(Symbol('Y', commutative=True)))"]}, {"premise_expression": "e^{\\frac{o}{N}}", "variable": "N", "positive": "N e^{\\frac{o}{N}} - o \\operatorname{Ei}{(\\frac{o}{N})}", "negatives": ["N e^{\\frac{o}{N}}", "e^{N + o}", "\\frac{N o (- N + 2 o)}{2}", "\\frac{N (N + 2 o)}{2}"], "srepr_premise_expression": "exp(Mul(Pow(Symbol('N', commutative=True), Integer(-1)), Symbol('o', commutative=True)))", "srepr_variable": "Symbol('N', commutative=True)", "srepr_positive": "Add(Mul(Symbol('N', commutative=True), exp(Mul(Pow(Symbol('N', commutative=True), Integer(-1)), Symbol('o', commutative=True)))), Mul(Integer(-1), Symbol('o', commutative=True), Ei(Mul(Pow(Symbol('N', commutative=True), Integer(-1)), Symbol('o', commutative=True)))))", "srepr_negatives": ["Mul(Symbol('N', commutative=True), exp(Mul(Pow(Symbol('N', commutative=True), Integer(-1)), Symbol('o', commutative=True))))", "exp(Add(Symbol('N', commutative=True), Symbol('o', commutative=True)))", "Mul(Rational(1, 2), Symbol('N', commutative=True), Symbol('o', commutative=True), Add(Mul(Integer(-1), Symbol('N', commutative=True)), Mul(Integer(2), Symbol('o', commutative=True))))", "Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Symbol('N', commutative=True), Mul(Integer(2), Symbol('o', commutative=True))))"]}, {"premise_expression": "J - M + p", "variable": "J", "positive": "J (\\frac{J}{2} - M + p)", "negatives": ["\\frac{M (2 J - M + 2 p)}{2}", "\\frac{p (2 J - 2 M + p)}{2}", "\\frac{J (J p - 2 M)}{2}", "\\frac{J (J + 2 M^{p})}{2}"], "srepr_premise_expression": "Add(Symbol('J', commutative=True), Mul(Integer(-1), Symbol('M', commutative=True)), Symbol('p', commutative=True))", "srepr_variable": "Symbol('J', commutative=True)", "srepr_positive": "Mul(Symbol('J', commutative=True), Add(Mul(Rational(1, 2), Symbol('J', commutative=True)), Mul(Integer(-1), Symbol('M', commutative=True)), Symbol('p', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('M', commutative=True), Add(Mul(Integer(2), Symbol('J', commutative=True)), Mul(Integer(-1), Symbol('M', commutative=True)), Mul(Integer(2), Symbol('p', commutative=True))))", "Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Mul(Integer(2), Symbol('J', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('M', commutative=True)), Symbol('p', commutative=True)))", "Mul(Rational(1, 2), Symbol('J', commutative=True), Add(Mul(Symbol('J', commutative=True), Symbol('p', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('M', commutative=True))))", "Mul(Rational(1, 2), Symbol('J', commutative=True), Add(Symbol('J', commutative=True), Mul(Integer(2), Pow(Symbol('M', commutative=True), Symbol('p', commutative=True)))))"]}, {"premise_expression": "Y + a", "variable": "a", "positive": "\\frac{a (2 Y + a)}{2}", "negatives": ["\\frac{a (- 2 Y + a)}{2}", "\\frac{Y (Y + 2 a)}{2}", "\\cos{(Y - a)}", "- \\sin{(Y - a)}"], "srepr_premise_expression": "Add(Symbol('Y', commutative=True), Symbol('a', commutative=True))", "srepr_variable": "Symbol('a', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('a', commutative=True), Add(Mul(Integer(2), Symbol('Y', commutative=True)), Symbol('a', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('a', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('Y', commutative=True)), Symbol('a', commutative=True)))", "Mul(Rational(1, 2), Symbol('Y', commutative=True), Add(Symbol('Y', commutative=True), Mul(Integer(2), Symbol('a', commutative=True))))", "cos(Add(Symbol('Y', commutative=True), Mul(Integer(-1), Symbol('a', commutative=True))))", "Mul(Integer(-1), sin(Add(Symbol('Y', commutative=True), Mul(Integer(-1), Symbol('a', commutative=True)))))"]}, {"premise_expression": "H U + u", "variable": "H", "positive": "\\frac{H (H U + 2 u)}{2}", "negatives": ["\\frac{U (H U + 2 u)}{2}", "\\frac{H (H U - 2 u)}{2}", "\\frac{u (2 H U + u)}{2}", "\\frac{H^{2} (U + u)}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('H', commutative=True), Symbol('U', commutative=True)), Symbol('u', commutative=True))", "srepr_variable": "Symbol('H', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('H', commutative=True), Add(Mul(Symbol('H', commutative=True), Symbol('U', commutative=True)), Mul(Integer(2), Symbol('u', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('U', commutative=True), Add(Mul(Symbol('H', commutative=True), Symbol('U', commutative=True)), Mul(Integer(2), Symbol('u', commutative=True))))", "Mul(Rational(1, 2), Symbol('H', commutative=True), Add(Mul(Symbol('H', commutative=True), Symbol('U', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('u', commutative=True))))", "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(2), Symbol('H', commutative=True), Symbol('U', commutative=True)), Symbol('u', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('H', commutative=True), Integer(2)), Add(Symbol('U', commutative=True), Symbol('u', commutative=True)))"]}, {"premise_expression": "L - R", "variable": "L", "positive": "\\frac{L (L - 2 R)}{2}", "negatives": ["\\frac{R (2 L - R)}{2}", "\\frac{L (L + 2 \\sin{(R)})}{2}", "\\frac{L^{2} \\sin{(R)}}{2}", "\\frac{L^{2} e^{R}}{2}"], "srepr_premise_expression": "Add(Symbol('L', commutative=True), Mul(Integer(-1), Symbol('R', commutative=True)))", "srepr_variable": "Symbol('L', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Symbol('L', commutative=True), Mul(Integer(-1), Integer(2), Symbol('R', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('R', commutative=True), Add(Mul(Integer(2), Symbol('L', commutative=True)), Mul(Integer(-1), Symbol('R', commutative=True))))", "Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Symbol('L', commutative=True), Mul(Integer(2), sin(Symbol('R', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(2)), sin(Symbol('R', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(2)), exp(Symbol('R', commutative=True)))"]}, {"premise_expression": "X \\sin{(o)}", "variable": "o", "positive": "- X \\cos{(o)}", "negatives": ["X \\log{(o)}", "\\frac{X o^{2}}{2}", "\\frac{X^{2} \\sin{(o)}}{2}", "e^{X + o}"], "srepr_premise_expression": "Mul(Symbol('X', commutative=True), sin(Symbol('o', commutative=True)))", "srepr_variable": "Symbol('o', commutative=True)", "srepr_positive": "Mul(Integer(-1), Symbol('X', commutative=True), cos(Symbol('o', commutative=True)))", "srepr_negatives": ["Mul(Symbol('X', commutative=True), log(Symbol('o', commutative=True)))", "Mul(Rational(1, 2), Symbol('X', commutative=True), Pow(Symbol('o', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('X', commutative=True), Integer(2)), sin(Symbol('o', commutative=True)))", "exp(Add(Symbol('X', commutative=True), Symbol('o', commutative=True)))"]}, {"premise_expression": "- p + \\cos{(K)}", "variable": "K", "positive": "- K p + \\sin{(K)}", "negatives": ["\\frac{K^{2} \\sin{(p)}}{2}", "\\frac{K^{2}}{2 p}", "\\sin{(K - p)}", "\\log{(K)} \\log{(p)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('p', commutative=True)), cos(Symbol('K', commutative=True)))", "srepr_variable": "Symbol('K', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('K', commutative=True), Symbol('p', commutative=True)), sin(Symbol('K', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('K', commutative=True), Integer(2)), sin(Symbol('p', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('K', commutative=True), Integer(2)), Pow(Symbol('p', commutative=True), Integer(-1)))", "sin(Add(Symbol('K', commutative=True), Mul(Integer(-1), Symbol('p', commutative=True))))", "Mul(log(Symbol('K', commutative=True)), log(Symbol('p', commutative=True)))"]}, {"premise_expression": "\\frac{V}{b}", "variable": "V", "positive": "\\frac{V^{2}}{2 b}", "negatives": ["V \\log{(b)}", "\\frac{V (- V + 2 \\sin{(b)})}{2}", "V \\cos{(\\frac{b}{V})} + b \\operatorname{Si}{(\\frac{b}{V})}", "\\int \\cos^{b}{(V)} dV"], "srepr_premise_expression": "Mul(Symbol('V', commutative=True), Pow(Symbol('b', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('V', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('V', commutative=True), Integer(2)), Pow(Symbol('b', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('V', commutative=True), log(Symbol('b', commutative=True)))", "Mul(Rational(1, 2), Symbol('V', commutative=True), Add(Mul(Integer(-1), Symbol('V', commutative=True)), Mul(Integer(2), sin(Symbol('b', commutative=True)))))", "Add(Mul(Symbol('V', commutative=True), cos(Mul(Pow(Symbol('V', commutative=True), Integer(-1)), Symbol('b', commutative=True)))), Mul(Symbol('b', commutative=True), Si(Mul(Pow(Symbol('V', commutative=True), Integer(-1)), Symbol('b', commutative=True)))))", "Integral(Pow(cos(Symbol('V', commutative=True)), Symbol('b', commutative=True)), Tuple(Symbol('V', commutative=True)))"]}, {"premise_expression": "V j", "variable": "j", "positive": "\\frac{V j^{2}}{2}", "negatives": ["\\frac{V^{2} j}{2}", "\\frac{j^{2}}{2 V}", "\\frac{j^{2} e^{V}}{2}", "\\sin{(V + j)}"], "srepr_premise_expression": "Mul(Symbol('V', commutative=True), Symbol('j', commutative=True))", "srepr_variable": "Symbol('j', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('V', commutative=True), Pow(Symbol('j', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('V', commutative=True), Integer(2)), Symbol('j', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('V', commutative=True), Integer(-1)), Pow(Symbol('j', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('j', commutative=True), Integer(2)), exp(Symbol('V', commutative=True)))", "sin(Add(Symbol('V', commutative=True), Symbol('j', commutative=True)))"]}, {"premise_expression": "\\frac{V W}{L}", "variable": "V", "positive": "\\frac{V^{2} W}{2 L}", "negatives": ["\\frac{V W^{2}}{2 L}", "\\frac{L V^{2} W}{2}", "V W \\log{(L)}", "\\frac{V (2 L - V - 2 W)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('L', commutative=True), Integer(-1)), Symbol('V', commutative=True), Symbol('W', commutative=True))", "srepr_variable": "Symbol('V', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(-1)), Pow(Symbol('V', commutative=True), Integer(2)), Symbol('W', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(-1)), Symbol('V', commutative=True), Pow(Symbol('W', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('L', commutative=True), Pow(Symbol('V', commutative=True), Integer(2)), Symbol('W', commutative=True))", "Mul(Symbol('V', commutative=True), Symbol('W', commutative=True), log(Symbol('L', commutative=True)))", "Mul(Rational(1, 2), Symbol('V', commutative=True), Add(Mul(Integer(2), Symbol('L', commutative=True)), Mul(Integer(-1), Symbol('V', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('W', commutative=True))))"]}, {"premise_expression": "\\frac{z}{P}", "variable": "P", "positive": "z \\log{(P)}", "negatives": ["P \\cos{(1)}", "\\frac{z^{2}}{2 P}", "\\frac{P^{2} z}{2}", "P z (\\log{(P)} - 1)"], "srepr_premise_expression": "Mul(Pow(Symbol('P', commutative=True), Integer(-1)), Symbol('z', commutative=True))", "srepr_variable": "Symbol('P', commutative=True)", "srepr_positive": "Mul(Symbol('z', commutative=True), log(Symbol('P', commutative=True)))", "srepr_negatives": ["Mul(Symbol('P', commutative=True), cos(Integer(1)))", "Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(-1)), Pow(Symbol('z', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2)), Symbol('z', commutative=True))", "Mul(Symbol('P', commutative=True), Symbol('z', commutative=True), Add(log(Symbol('P', commutative=True)), Integer(-1)))"]}, {"premise_expression": "e^{\\frac{M}{R}}", "variable": "R", "positive": "- M \\operatorname{Ei}{(\\frac{M}{R})} + R e^{\\frac{M}{R}}", "negatives": ["- M R + e^{R}", "\\frac{R (- R + 2 e^{M})}{2}", "R e^{\\frac{M}{R}}", "M R + \\sin{(R)}"], "srepr_premise_expression": "exp(Mul(Symbol('M', commutative=True), Pow(Symbol('R', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('R', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('M', commutative=True), Ei(Mul(Symbol('M', commutative=True), Pow(Symbol('R', commutative=True), Integer(-1))))), Mul(Symbol('R', commutative=True), exp(Mul(Symbol('M', commutative=True), Pow(Symbol('R', commutative=True), Integer(-1))))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('M', commutative=True), Symbol('R', commutative=True)), exp(Symbol('R', commutative=True)))", "Mul(Rational(1, 2), Symbol('R', commutative=True), Add(Mul(Integer(-1), Symbol('R', commutative=True)), Mul(Integer(2), exp(Symbol('M', commutative=True)))))", "Mul(Symbol('R', commutative=True), exp(Mul(Symbol('M', commutative=True), Pow(Symbol('R', commutative=True), Integer(-1)))))", "Add(Mul(Symbol('M', commutative=True), Symbol('R', commutative=True)), sin(Symbol('R', commutative=True)))"]}, {"premise_expression": "P y", "variable": "P", "positive": "\\frac{P^{2} y}{2}", "negatives": ["\\frac{P y^{2}}{2}", "\\frac{P (P + 2 y)}{2}", "\\frac{P (- P + 2 y)}{2}", "\\frac{P^{2} (y + 1)}{2 y}"], "srepr_premise_expression": "Mul(Symbol('P', commutative=True), Symbol('y', commutative=True))", "srepr_variable": "Symbol('P', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2)), Symbol('y', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('P', commutative=True), Pow(Symbol('y', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Symbol('P', commutative=True), Mul(Integer(2), Symbol('y', commutative=True))))", "Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Mul(Integer(-1), Symbol('P', commutative=True)), Mul(Integer(2), Symbol('y', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2)), Pow(Symbol('y', commutative=True), Integer(-1)), Add(Symbol('y', commutative=True), Integer(1)))"]}, {"premise_expression": "e^{\\frac{G}{C}}", "variable": "G", "positive": "C e^{\\frac{G}{C}}", "negatives": ["\\cos{(C - G)}", "- C G - \\cos{(G)}", "\\frac{G^{2} \\sin{(C)}}{2}", "C e^{\\frac{G}{C}} - G \\operatorname{Ei}{(\\frac{G}{C})}"], "srepr_premise_expression": "exp(Mul(Pow(Symbol('C', commutative=True), Integer(-1)), Symbol('G', commutative=True)))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Mul(Symbol('C', commutative=True), exp(Mul(Pow(Symbol('C', commutative=True), Integer(-1)), Symbol('G', commutative=True))))", "srepr_negatives": ["cos(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('G', commutative=True))))", "Add(Mul(Integer(-1), Symbol('C', commutative=True), Symbol('G', commutative=True)), Mul(Integer(-1), cos(Symbol('G', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(2)), sin(Symbol('C', commutative=True)))", "Add(Mul(Symbol('C', commutative=True), exp(Mul(Pow(Symbol('C', commutative=True), Integer(-1)), Symbol('G', commutative=True)))), Mul(Integer(-1), Symbol('G', commutative=True), Ei(Mul(Pow(Symbol('C', commutative=True), Integer(-1)), Symbol('G', commutative=True)))))"]}, {"premise_expression": "\\frac{o}{p}", "variable": "p", "positive": "o \\log{(p)}", "negatives": ["\\frac{o^{2}}{2 p}", "\\frac{o p^{2}}{2}", "- \\cos{(o + p)}", "\\frac{p^{2} \\log{(o)}}{2}"], "srepr_premise_expression": "Mul(Symbol('o', commutative=True), Pow(Symbol('p', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('p', commutative=True)", "srepr_positive": "Mul(Symbol('o', commutative=True), log(Symbol('p', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('o', commutative=True), Integer(2)), Pow(Symbol('p', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Symbol('o', commutative=True), Pow(Symbol('p', commutative=True), Integer(2)))", "Mul(Integer(-1), cos(Add(Symbol('o', commutative=True), Symbol('p', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('p', commutative=True), Integer(2)), log(Symbol('o', commutative=True)))"]}, {"premise_expression": "\\cos^{J}{(H)}", "variable": "H", "positive": "\\int \\cos^{J}{(H)} dH", "negatives": ["J \\log{(H)}", "\\frac{H^{2}}{2 J}", "J e^{H}", "\\frac{H (H + 2 J)}{2}"], "srepr_premise_expression": "Pow(cos(Symbol('H', commutative=True)), Symbol('J', commutative=True))", "srepr_variable": "Symbol('H', commutative=True)", "srepr_positive": "Integral(Pow(cos(Symbol('H', commutative=True)), Symbol('J', commutative=True)), Tuple(Symbol('H', commutative=True)))", "srepr_negatives": ["Mul(Symbol('J', commutative=True), log(Symbol('H', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('H', commutative=True), Integer(2)), Pow(Symbol('J', commutative=True), Integer(-1)))", "Mul(Symbol('J', commutative=True), exp(Symbol('H', commutative=True)))", "Mul(Rational(1, 2), Symbol('H', commutative=True), Add(Symbol('H', commutative=True), Mul(Integer(2), Symbol('J', commutative=True))))"]}, {"premise_expression": "n e^{U}", "variable": "U", "positive": "n e^{U}", "negatives": ["n \\sin{(U)}", "\\frac{n^{2} e^{U}}{2}", "- \\frac{\\cos{(U)}}{n}", "\\sin{(U + n)}"], "srepr_premise_expression": "Mul(Symbol('n', commutative=True), exp(Symbol('U', commutative=True)))", "srepr_variable": "Symbol('U', commutative=True)", "srepr_positive": "Mul(Symbol('n', commutative=True), exp(Symbol('U', commutative=True)))", "srepr_negatives": ["Mul(Symbol('n', commutative=True), sin(Symbol('U', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('n', commutative=True), Integer(2)), exp(Symbol('U', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('n', commutative=True), Integer(-1)), cos(Symbol('U', commutative=True)))", "sin(Add(Symbol('U', commutative=True), Symbol('n', commutative=True)))"]}, {"premise_expression": "\\frac{G}{P}", "variable": "G", "positive": "\\frac{G^{2}}{2 P}", "negatives": ["G \\log{(P)}", "\\frac{G^{2} P}{2}", "\\frac{G (G - 2 P)}{2}", "e^{G + P}"], "srepr_premise_expression": "Mul(Symbol('G', commutative=True), Pow(Symbol('P', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(2)), Pow(Symbol('P', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('G', commutative=True), log(Symbol('P', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(2)), Symbol('P', commutative=True))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Symbol('G', commutative=True), Mul(Integer(-1), Integer(2), Symbol('P', commutative=True))))", "exp(Add(Symbol('G', commutative=True), Symbol('P', commutative=True)))"]}, {"premise_expression": "\\log{(S c)}", "variable": "c", "positive": "c (\\log{(S c)} - 1)", "negatives": ["S (\\log{(S c)} - 1)", "\\frac{c (\\log{(c)} - 1)}{S}", "- \\cos{(S - c)}", "S \\log{(c)}"], "srepr_premise_expression": "log(Mul(Symbol('S', commutative=True), Symbol('c', commutative=True)))", "srepr_variable": "Symbol('c', commutative=True)", "srepr_positive": "Mul(Symbol('c', commutative=True), Add(log(Mul(Symbol('S', commutative=True), Symbol('c', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('S', commutative=True), Add(log(Mul(Symbol('S', commutative=True), Symbol('c', commutative=True))), Integer(-1)))", "Mul(Pow(Symbol('S', commutative=True), Integer(-1)), Symbol('c', commutative=True), Add(log(Symbol('c', commutative=True)), Integer(-1)))", "Mul(Integer(-1), cos(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('c', commutative=True)))))", "Mul(Symbol('S', commutative=True), log(Symbol('c', commutative=True)))"]}, {"premise_expression": "- \\sin{(Z - m)}", "variable": "m", "positive": "- \\cos{(Z - m)}", "negatives": ["\\cos{(Z - m)}", "e^{- Z + m}", "\\frac{m (2 Z - m)}{2}", "m (\\log{(Z m)} - 1)"], "srepr_premise_expression": "Mul(Integer(-1), sin(Add(Symbol('Z', commutative=True), Mul(Integer(-1), Symbol('m', commutative=True)))))", "srepr_variable": "Symbol('m', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('Z', commutative=True), Mul(Integer(-1), Symbol('m', commutative=True)))))", "srepr_negatives": ["cos(Add(Symbol('Z', commutative=True), Mul(Integer(-1), Symbol('m', commutative=True))))", "exp(Add(Mul(Integer(-1), Symbol('Z', commutative=True)), Symbol('m', commutative=True)))", "Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Mul(Integer(2), Symbol('Z', commutative=True)), Mul(Integer(-1), Symbol('m', commutative=True))))", "Mul(Symbol('m', commutative=True), Add(log(Mul(Symbol('Z', commutative=True), Symbol('m', commutative=True))), Integer(-1)))"]}, {"premise_expression": "I - b", "variable": "b", "positive": "\\frac{b (2 I - b)}{2}", "negatives": ["\\frac{I (I - 2 b)}{2}", "\\frac{I b^{2}}{2}", "b (\\log{(I b)} - 1)", "\\frac{b (b + 2 \\sin{(I)})}{2}"], "srepr_premise_expression": "Add(Symbol('I', commutative=True), Mul(Integer(-1), Symbol('b', commutative=True)))", "srepr_variable": "Symbol('b', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('b', commutative=True), Add(Mul(Integer(2), Symbol('I', commutative=True)), Mul(Integer(-1), Symbol('b', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('I', commutative=True), Add(Symbol('I', commutative=True), Mul(Integer(-1), Integer(2), Symbol('b', commutative=True))))", "Mul(Rational(1, 2), Symbol('I', commutative=True), Pow(Symbol('b', commutative=True), Integer(2)))", "Mul(Symbol('b', commutative=True), Add(log(Mul(Symbol('I', commutative=True), Symbol('b', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('b', commutative=True), Add(Symbol('b', commutative=True), Mul(Integer(2), sin(Symbol('I', commutative=True)))))"]}, {"premise_expression": "- D + a", "variable": "D", "positive": "\\frac{D (- D + 2 a)}{2}", "negatives": ["\\frac{a (- 2 D + a)}{2}", "\\frac{D (D + 2 e^{a})}{2}", "\\frac{D^{2} \\log{(a)}}{2}", "- e^{- D + a}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('D', commutative=True)), Symbol('a', commutative=True))", "srepr_variable": "Symbol('D', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('D', commutative=True), Add(Mul(Integer(-1), Symbol('D', commutative=True)), Mul(Integer(2), Symbol('a', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('a', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('D', commutative=True)), Symbol('a', commutative=True)))", "Mul(Rational(1, 2), Symbol('D', commutative=True), Add(Symbol('D', commutative=True), Mul(Integer(2), exp(Symbol('a', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(2)), log(Symbol('a', commutative=True)))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('D', commutative=True)), Symbol('a', commutative=True))))"]}, {"premise_expression": "\\frac{\\log{(U)}}{t}", "variable": "U", "positive": "\\frac{U (\\log{(U)} - 1)}{t}", "negatives": ["- \\cos{(U - t)}", "\\log{(U)} \\log{(t)}", "\\log{(U)} \\sin{(t)}", "- \\cos{(U + t)}"], "srepr_premise_expression": "Mul(Pow(Symbol('t', commutative=True), Integer(-1)), log(Symbol('U', commutative=True)))", "srepr_variable": "Symbol('U', commutative=True)", "srepr_positive": "Mul(Symbol('U', commutative=True), Pow(Symbol('t', commutative=True), Integer(-1)), Add(log(Symbol('U', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('U', commutative=True), Mul(Integer(-1), Symbol('t', commutative=True)))))", "Mul(log(Symbol('U', commutative=True)), log(Symbol('t', commutative=True)))", "Mul(log(Symbol('U', commutative=True)), sin(Symbol('t', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('U', commutative=True), Symbol('t', commutative=True))))"]}, {"premise_expression": "e^{\\frac{s}{l}}", "variable": "s", "positive": "l e^{\\frac{s}{l}}", "negatives": ["\\frac{l s^{2}}{2}", "\\frac{\\sin{(s)}}{l}", "- l s - \\cos{(s)}", "\\sin{(l + s)}"], "srepr_premise_expression": "exp(Mul(Pow(Symbol('l', commutative=True), Integer(-1)), Symbol('s', commutative=True)))", "srepr_variable": "Symbol('s', commutative=True)", "srepr_positive": "Mul(Symbol('l', commutative=True), exp(Mul(Pow(Symbol('l', commutative=True), Integer(-1)), Symbol('s', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('l', commutative=True), Pow(Symbol('s', commutative=True), Integer(2)))", "Mul(Pow(Symbol('l', commutative=True), Integer(-1)), sin(Symbol('s', commutative=True)))", "Add(Mul(Integer(-1), Symbol('l', commutative=True), Symbol('s', commutative=True)), Mul(Integer(-1), cos(Symbol('s', commutative=True))))", "sin(Add(Symbol('l', commutative=True), Symbol('s', commutative=True)))"]}, {"premise_expression": "- \\sin{(C - P)}", "variable": "C", "positive": "\\cos{(C - P)}", "negatives": ["- \\cos{(C - P)}", "\\frac{C (C + 2 P)}{2}", "\\frac{C^{2}}{2 P}", "C (\\log{(C P)} - 1)"], "srepr_premise_expression": "Mul(Integer(-1), sin(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('P', commutative=True)))))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "cos(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('P', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('P', commutative=True)))))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Symbol('C', commutative=True), Mul(Integer(2), Symbol('P', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2)), Pow(Symbol('P', commutative=True), Integer(-1)))", "Mul(Symbol('C', commutative=True), Add(log(Mul(Symbol('C', commutative=True), Symbol('P', commutative=True))), Integer(-1)))"]}, {"premise_expression": "- K + e^{a}", "variable": "a", "positive": "- K a + e^{a}", "negatives": ["\\frac{K (- K + 2 e^{a})}{2}", "\\sin{(K + a)}", "\\frac{a^{2}}{2 K}", "\\frac{a^{2} \\log{(K)}}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('K', commutative=True)), exp(Symbol('a', commutative=True)))", "srepr_variable": "Symbol('a', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('K', commutative=True), Symbol('a', commutative=True)), exp(Symbol('a', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Mul(Integer(-1), Symbol('K', commutative=True)), Mul(Integer(2), exp(Symbol('a', commutative=True)))))", "sin(Add(Symbol('K', commutative=True), Symbol('a', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('K', commutative=True), Integer(-1)), Pow(Symbol('a', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('a', commutative=True), Integer(2)), log(Symbol('K', commutative=True)))"]}, {"premise_expression": "\\log{(f)}^{m}", "variable": "f", "positive": "(- \\log{(f)})^{- m} \\log{(f)}^{m} \\Gamma(m + 1, - \\log{(f)})", "negatives": ["f \\log{(f - m)} - f - m \\log{(f - m)}", "f (\\log{(f m)} - 1)", "f (m + \\log{(f)} - 1)", "\\frac{f (\\log{(f)} - 1)}{m}"], "srepr_premise_expression": "Pow(log(Symbol('f', commutative=True)), Symbol('m', commutative=True))", "srepr_variable": "Symbol('f', commutative=True)", "srepr_positive": "Mul(Pow(Mul(Integer(-1), log(Symbol('f', commutative=True))), Mul(Integer(-1), Symbol('m', commutative=True))), Pow(log(Symbol('f', commutative=True)), Symbol('m', commutative=True)), uppergamma(Add(Symbol('m', commutative=True), Integer(1)), Mul(Integer(-1), log(Symbol('f', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('f', commutative=True), log(Add(Symbol('f', commutative=True), Mul(Integer(-1), Symbol('m', commutative=True))))), Mul(Integer(-1), Symbol('f', commutative=True)), Mul(Integer(-1), Symbol('m', commutative=True), log(Add(Symbol('f', commutative=True), Mul(Integer(-1), Symbol('m', commutative=True))))))", "Mul(Symbol('f', commutative=True), Add(log(Mul(Symbol('f', commutative=True), Symbol('m', commutative=True))), Integer(-1)))", "Mul(Symbol('f', commutative=True), Add(Symbol('m', commutative=True), log(Symbol('f', commutative=True)), Integer(-1)))", "Mul(Symbol('f', commutative=True), Pow(Symbol('m', commutative=True), Integer(-1)), Add(log(Symbol('f', commutative=True)), Integer(-1)))"]}, {"premise_expression": "- l + \\frac{w}{v}", "variable": "w", "positive": "- l w + \\frac{w^{2}}{2 v}", "negatives": ["- l v + w \\log{(v)}", "\\frac{w (2 l + w)}{2 v}", "\\frac{l v w^{2}}{2}", "- \\frac{l^{2}}{2} + \\frac{l w}{v}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('l', commutative=True)), Mul(Pow(Symbol('v', commutative=True), Integer(-1)), Symbol('w', commutative=True)))", "srepr_variable": "Symbol('w', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('l', commutative=True), Symbol('w', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('v', commutative=True), Integer(-1)), Pow(Symbol('w', commutative=True), Integer(2))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('l', commutative=True), Symbol('v', commutative=True)), Mul(Symbol('w', commutative=True), log(Symbol('v', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('v', commutative=True), Integer(-1)), Symbol('w', commutative=True), Add(Mul(Integer(2), Symbol('l', commutative=True)), Symbol('w', commutative=True)))", "Mul(Rational(1, 2), Symbol('l', commutative=True), Symbol('v', commutative=True), Pow(Symbol('w', commutative=True), Integer(2)))", "Add(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('l', commutative=True), Integer(2))), Mul(Symbol('l', commutative=True), Pow(Symbol('v', commutative=True), Integer(-1)), Symbol('w', commutative=True)))"]}, {"premise_expression": "Z (T + y)", "variable": "Z", "positive": "\\frac{Z^{2} (T + y)}{2}", "negatives": ["\\frac{Z^{2} (T - y)}{2}", "\\frac{Z y (2 T + y)}{2}", "\\frac{Z (2 T + Z y)}{2}", "\\frac{T Z (T + 2 y)}{2}"], "srepr_premise_expression": "Mul(Symbol('Z', commutative=True), Add(Symbol('T', commutative=True), Symbol('y', commutative=True)))", "srepr_variable": "Symbol('Z', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('Z', commutative=True), Integer(2)), Add(Symbol('T', commutative=True), Symbol('y', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('Z', commutative=True), Integer(2)), Add(Symbol('T', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True))))", "Mul(Rational(1, 2), Symbol('Z', commutative=True), Symbol('y', commutative=True), Add(Mul(Integer(2), Symbol('T', commutative=True)), Symbol('y', commutative=True)))", "Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Mul(Integer(2), Symbol('T', commutative=True)), Mul(Symbol('Z', commutative=True), Symbol('y', commutative=True))))", "Mul(Rational(1, 2), Symbol('T', commutative=True), Symbol('Z', commutative=True), Add(Symbol('T', commutative=True), Mul(Integer(2), Symbol('y', commutative=True))))"]}, {"premise_expression": "\\frac{k}{E}", "variable": "E", "positive": "k \\log{(E)}", "negatives": ["\\frac{k^{2}}{2 E}", "\\log{(E)} \\log{(k)}", "\\frac{E^{2} \\log{(k)}}{2}", "\\cos{(E - k)}"], "srepr_premise_expression": "Mul(Pow(Symbol('E', commutative=True), Integer(-1)), Symbol('k', commutative=True))", "srepr_variable": "Symbol('E', commutative=True)", "srepr_positive": "Mul(Symbol('k', commutative=True), log(Symbol('E', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('E', commutative=True), Integer(-1)), Pow(Symbol('k', commutative=True), Integer(2)))", "Mul(log(Symbol('E', commutative=True)), log(Symbol('k', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('E', commutative=True), Integer(2)), log(Symbol('k', commutative=True)))", "cos(Add(Symbol('E', commutative=True), Mul(Integer(-1), Symbol('k', commutative=True))))"]}, {"premise_expression": "e^{- K + c}", "variable": "K", "positive": "- e^{- K + c}", "negatives": ["e^{- K + c}", "\\frac{K (- K + 2 c)}{2}", "\\log{(K)} \\sin{(c)}", "\\frac{K^{2} \\sin{(c)}}{2}"], "srepr_premise_expression": "exp(Add(Mul(Integer(-1), Symbol('K', commutative=True)), Symbol('c', commutative=True)))", "srepr_variable": "Symbol('K', commutative=True)", "srepr_positive": "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('K', commutative=True)), Symbol('c', commutative=True))))", "srepr_negatives": ["exp(Add(Mul(Integer(-1), Symbol('K', commutative=True)), Symbol('c', commutative=True)))", "Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Mul(Integer(-1), Symbol('K', commutative=True)), Mul(Integer(2), Symbol('c', commutative=True))))", "Mul(log(Symbol('K', commutative=True)), sin(Symbol('c', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('K', commutative=True), Integer(2)), sin(Symbol('c', commutative=True)))"]}, {"premise_expression": "\\frac{g}{B}", "variable": "g", "positive": "\\frac{g^{2}}{2 B}", "negatives": ["g \\log{(B)}", "B \\sin{(g)}", "- \\frac{\\cos{(g)}}{B}", "- \\cos{(B - g)}"], "srepr_premise_expression": "Mul(Pow(Symbol('B', commutative=True), Integer(-1)), Symbol('g', commutative=True))", "srepr_variable": "Symbol('g', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('B', commutative=True), Integer(-1)), Pow(Symbol('g', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('g', commutative=True), log(Symbol('B', commutative=True)))", "Mul(Symbol('B', commutative=True), sin(Symbol('g', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('B', commutative=True), Integer(-1)), cos(Symbol('g', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('B', commutative=True), Mul(Integer(-1), Symbol('g', commutative=True)))))"]}, {"premise_expression": "\\frac{v}{o}", "variable": "o", "positive": "v \\log{(o)}", "negatives": ["\\frac{v^{2}}{2 o}", "\\frac{o^{2} v}{2}", "\\sin{(o - v)}", "\\frac{o^{2} e^{v}}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('o', commutative=True), Integer(-1)), Symbol('v', commutative=True))", "srepr_variable": "Symbol('o', commutative=True)", "srepr_positive": "Mul(Symbol('v', commutative=True), log(Symbol('o', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('o', commutative=True), Integer(-1)), Pow(Symbol('v', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('o', commutative=True), Integer(2)), Symbol('v', commutative=True))", "sin(Add(Symbol('o', commutative=True), Mul(Integer(-1), Symbol('v', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('o', commutative=True), Integer(2)), exp(Symbol('v', commutative=True)))"]}, {"premise_expression": "M + V", "variable": "M", "positive": "\\frac{M (M + 2 V)}{2}", "negatives": ["\\frac{V (2 M + V)}{2}", "M (V + \\cos{(V)})", "\\frac{M^{2}}{2 V}", "M V + e^{M}"], "srepr_premise_expression": "Add(Symbol('M', commutative=True), Symbol('V', commutative=True))", "srepr_variable": "Symbol('M', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('M', commutative=True), Add(Symbol('M', commutative=True), Mul(Integer(2), Symbol('V', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('V', commutative=True), Add(Mul(Integer(2), Symbol('M', commutative=True)), Symbol('V', commutative=True)))", "Mul(Symbol('M', commutative=True), Add(Symbol('V', commutative=True), cos(Symbol('V', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('M', commutative=True), Integer(2)), Pow(Symbol('V', commutative=True), Integer(-1)))", "Add(Mul(Symbol('M', commutative=True), Symbol('V', commutative=True)), exp(Symbol('M', commutative=True)))"]}, {"premise_expression": "\\frac{P}{G}", "variable": "P", "positive": "\\frac{P^{2}}{2 G}", "negatives": ["P \\log{(G)}", "\\frac{G P^{2}}{2}", "G \\sin{(P)}", "\\sin{(G + P)}"], "srepr_premise_expression": "Mul(Pow(Symbol('G', commutative=True), Integer(-1)), Symbol('P', commutative=True))", "srepr_variable": "Symbol('P', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(-1)), Pow(Symbol('P', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('P', commutative=True), log(Symbol('G', commutative=True)))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Pow(Symbol('P', commutative=True), Integer(2)))", "Mul(Symbol('G', commutative=True), sin(Symbol('P', commutative=True)))", "sin(Add(Symbol('G', commutative=True), Symbol('P', commutative=True)))"]}, {"premise_expression": "\\frac{\\log{(M)}}{p}", "variable": "M", "positive": "\\frac{M (\\log{(M)} - 1)}{p}", "negatives": ["\\log{(M)} \\log{(p)}", "\\frac{M (M + 2 p)}{2}", "\\frac{M (- M + 2 p)}{2}", "\\frac{\\sin{(M)}}{p}"], "srepr_premise_expression": "Mul(Pow(Symbol('p', commutative=True), Integer(-1)), log(Symbol('M', commutative=True)))", "srepr_variable": "Symbol('M', commutative=True)", "srepr_positive": "Mul(Symbol('M', commutative=True), Pow(Symbol('p', commutative=True), Integer(-1)), Add(log(Symbol('M', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(log(Symbol('M', commutative=True)), log(Symbol('p', commutative=True)))", "Mul(Rational(1, 2), Symbol('M', commutative=True), Add(Symbol('M', commutative=True), Mul(Integer(2), Symbol('p', commutative=True))))", "Mul(Rational(1, 2), Symbol('M', commutative=True), Add(Mul(Integer(-1), Symbol('M', commutative=True)), Mul(Integer(2), Symbol('p', commutative=True))))", "Mul(Pow(Symbol('p', commutative=True), Integer(-1)), sin(Symbol('M', commutative=True)))"]}, {"premise_expression": "\\log{(K - j)}", "variable": "j", "positive": "- K \\log{(- K + j)} + j \\log{(K - j)} - j", "negatives": ["- K \\log{(- K + j)} + j \\log{(- K + j)} - j", "K \\log{(K - j)} - K - j \\log{(K - j)}", "- K \\operatorname{Ei}{(\\frac{K}{j})} + j e^{\\frac{K}{j}}", "j (K + \\log{(j)} - 1)"], "srepr_premise_expression": "log(Add(Symbol('K', commutative=True), Mul(Integer(-1), Symbol('j', commutative=True))))", "srepr_variable": "Symbol('j', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('K', commutative=True), log(Add(Mul(Integer(-1), Symbol('K', commutative=True)), Symbol('j', commutative=True)))), Mul(Symbol('j', commutative=True), log(Add(Symbol('K', commutative=True), Mul(Integer(-1), Symbol('j', commutative=True))))), Mul(Integer(-1), Symbol('j', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('K', commutative=True), log(Add(Mul(Integer(-1), Symbol('K', commutative=True)), Symbol('j', commutative=True)))), Mul(Symbol('j', commutative=True), log(Add(Mul(Integer(-1), Symbol('K', commutative=True)), Symbol('j', commutative=True)))), Mul(Integer(-1), Symbol('j', commutative=True)))", "Add(Mul(Symbol('K', commutative=True), log(Add(Symbol('K', commutative=True), Mul(Integer(-1), Symbol('j', commutative=True))))), Mul(Integer(-1), Symbol('K', commutative=True)), Mul(Integer(-1), Symbol('j', commutative=True), log(Add(Symbol('K', commutative=True), Mul(Integer(-1), Symbol('j', commutative=True))))))", "Add(Mul(Integer(-1), Symbol('K', commutative=True), Ei(Mul(Symbol('K', commutative=True), Pow(Symbol('j', commutative=True), Integer(-1))))), Mul(Symbol('j', commutative=True), exp(Mul(Symbol('K', commutative=True), Pow(Symbol('j', commutative=True), Integer(-1))))))", "Mul(Symbol('j', commutative=True), Add(Symbol('K', commutative=True), log(Symbol('j', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\frac{L}{M}", "variable": "M", "positive": "L \\log{(M)}", "negatives": ["\\frac{L^{2}}{2 M}", "\\cos{(L - M)}", "0", "\\frac{M^{2} \\sin{(L)}}{2}"], "srepr_premise_expression": "Mul(Symbol('L', commutative=True), Pow(Symbol('M', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('M', commutative=True)", "srepr_positive": "Mul(Symbol('L', commutative=True), log(Symbol('M', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(2)), Pow(Symbol('M', commutative=True), Integer(-1)))", "cos(Add(Symbol('L', commutative=True), Mul(Integer(-1), Symbol('M', commutative=True))))", "Integer(0)", "Mul(Rational(1, 2), Pow(Symbol('M', commutative=True), Integer(2)), sin(Symbol('L', commutative=True)))"]}, {"premise_expression": "\\log{(\\frac{r}{f})}", "variable": "r", "positive": "r (\\log{(\\frac{r}{f})} - 1)", "negatives": ["f (\\log{(\\frac{r}{f})} + 1)", "\\frac{r^{2} \\log{(f)}}{2}", "- \\sin{(f - r)}", "- \\cos{(f + r)}"], "srepr_premise_expression": "log(Mul(Pow(Symbol('f', commutative=True), Integer(-1)), Symbol('r', commutative=True)))", "srepr_variable": "Symbol('r', commutative=True)", "srepr_positive": "Mul(Symbol('r', commutative=True), Add(log(Mul(Pow(Symbol('f', commutative=True), Integer(-1)), Symbol('r', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('f', commutative=True), Add(log(Mul(Pow(Symbol('f', commutative=True), Integer(-1)), Symbol('r', commutative=True))), Integer(1)))", "Mul(Rational(1, 2), Pow(Symbol('r', commutative=True), Integer(2)), log(Symbol('f', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('f', commutative=True), Mul(Integer(-1), Symbol('r', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('f', commutative=True), Symbol('r', commutative=True))))"]}, {"premise_expression": "\\frac{B}{p}", "variable": "p", "positive": "B \\log{(p)}", "negatives": ["- B \\cos{(p)}", "\\frac{B^{2}}{2 p}", "e^{B} \\log{(p)}", "B e^{\\frac{p}{B}}"], "srepr_premise_expression": "Mul(Symbol('B', commutative=True), Pow(Symbol('p', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('p', commutative=True)", "srepr_positive": "Mul(Symbol('B', commutative=True), log(Symbol('p', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Symbol('B', commutative=True), cos(Symbol('p', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('B', commutative=True), Integer(2)), Pow(Symbol('p', commutative=True), Integer(-1)))", "Mul(exp(Symbol('B', commutative=True)), log(Symbol('p', commutative=True)))", "Mul(Symbol('B', commutative=True), exp(Mul(Pow(Symbol('B', commutative=True), Integer(-1)), Symbol('p', commutative=True))))"]}, {"premise_expression": "C + \\cos{(L)}", "variable": "L", "positive": "C L + \\sin{(L)}", "negatives": ["C \\log{(L)}", "\\log{(L)} \\sin{(C)}", "\\frac{C (C + 2 \\cos{(L)})}{2}", "\\log{(C)} \\log{(L)}"], "srepr_premise_expression": "Add(Symbol('C', commutative=True), cos(Symbol('L', commutative=True)))", "srepr_variable": "Symbol('L', commutative=True)", "srepr_positive": "Add(Mul(Symbol('C', commutative=True), Symbol('L', commutative=True)), sin(Symbol('L', commutative=True)))", "srepr_negatives": ["Mul(Symbol('C', commutative=True), log(Symbol('L', commutative=True)))", "Mul(log(Symbol('L', commutative=True)), sin(Symbol('C', commutative=True)))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Symbol('C', commutative=True), Mul(Integer(2), cos(Symbol('L', commutative=True)))))", "Mul(log(Symbol('C', commutative=True)), log(Symbol('L', commutative=True)))"]}, {"premise_expression": "Q (- j + q)", "variable": "j", "positive": "\\frac{Q j (- j + 2 q)}{2}", "negatives": ["\\frac{Q^{2} (- j + q)}{2}", "\\frac{Q q (- 2 j + q)}{2}", "\\frac{j (- 2 Q + j + 2 q)}{2}", "\\frac{j^{2} q}{2 Q}"], "srepr_premise_expression": "Mul(Symbol('Q', commutative=True), Add(Mul(Integer(-1), Symbol('j', commutative=True)), Symbol('q', commutative=True)))", "srepr_variable": "Symbol('j', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('Q', commutative=True), Symbol('j', commutative=True), Add(Mul(Integer(-1), Symbol('j', commutative=True)), Mul(Integer(2), Symbol('q', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(2)), Add(Mul(Integer(-1), Symbol('j', commutative=True)), Symbol('q', commutative=True)))", "Mul(Rational(1, 2), Symbol('Q', commutative=True), Symbol('q', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('j', commutative=True)), Symbol('q', commutative=True)))", "Mul(Rational(1, 2), Symbol('j', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('Q', commutative=True)), Symbol('j', commutative=True), Mul(Integer(2), Symbol('q', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(-1)), Pow(Symbol('j', commutative=True), Integer(2)), Symbol('q', commutative=True))"]}, {"premise_expression": "\\frac{L}{t} + h", "variable": "t", "positive": "L \\log{(t)} + h t", "negatives": ["\\frac{L^{2}}{2 t} + L h", "\\frac{L h}{t} + \\frac{h^{2}}{2}", "\\frac{t (2 L + h t)}{2}", "\\frac{t (- 2 L + h t)}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('L', commutative=True), Pow(Symbol('t', commutative=True), Integer(-1))), Symbol('h', commutative=True))", "srepr_variable": "Symbol('t', commutative=True)", "srepr_positive": "Add(Mul(Symbol('L', commutative=True), log(Symbol('t', commutative=True))), Mul(Symbol('h', commutative=True), Symbol('t', commutative=True)))", "srepr_negatives": ["Add(Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(2)), Pow(Symbol('t', commutative=True), Integer(-1))), Mul(Symbol('L', commutative=True), Symbol('h', commutative=True)))", "Add(Mul(Symbol('L', commutative=True), Symbol('h', commutative=True), Pow(Symbol('t', commutative=True), Integer(-1))), Mul(Rational(1, 2), Pow(Symbol('h', commutative=True), Integer(2))))", "Mul(Rational(1, 2), Symbol('t', commutative=True), Add(Mul(Integer(2), Symbol('L', commutative=True)), Mul(Symbol('h', commutative=True), Symbol('t', commutative=True))))", "Mul(Rational(1, 2), Symbol('t', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('L', commutative=True)), Mul(Symbol('h', commutative=True), Symbol('t', commutative=True))))"]}, {"premise_expression": "\\frac{Z}{R}", "variable": "Z", "positive": "\\frac{Z^{2}}{2 R}", "negatives": ["Z \\log{(R)}", "\\frac{Z^{2} e^{R}}{2}", "R e^{Z}", "e^{R + Z}"], "srepr_premise_expression": "Mul(Pow(Symbol('R', commutative=True), Integer(-1)), Symbol('Z', commutative=True))", "srepr_variable": "Symbol('Z', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('R', commutative=True), Integer(-1)), Pow(Symbol('Z', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('Z', commutative=True), log(Symbol('R', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('Z', commutative=True), Integer(2)), exp(Symbol('R', commutative=True)))", "Mul(Symbol('R', commutative=True), exp(Symbol('Z', commutative=True)))", "exp(Add(Symbol('R', commutative=True), Symbol('Z', commutative=True)))"]}, {"premise_expression": "\\frac{h - r}{h}", "variable": "r", "positive": "r - \\frac{r^{2}}{2 h}", "negatives": ["h - r \\log{(h)}", "\\frac{h r^{2}}{2}", "- h \\cos{(r)}", "h \\log{(r)}"], "srepr_premise_expression": "Mul(Pow(Symbol('h', commutative=True), Integer(-1)), Add(Symbol('h', commutative=True), Mul(Integer(-1), Symbol('r', commutative=True))))", "srepr_variable": "Symbol('r', commutative=True)", "srepr_positive": "Add(Symbol('r', commutative=True), Mul(Integer(-1), Rational(1, 2), Pow(Symbol('h', commutative=True), Integer(-1)), Pow(Symbol('r', commutative=True), Integer(2))))", "srepr_negatives": ["Add(Symbol('h', commutative=True), Mul(Integer(-1), Symbol('r', commutative=True), log(Symbol('h', commutative=True))))", "Mul(Rational(1, 2), Symbol('h', commutative=True), Pow(Symbol('r', commutative=True), Integer(2)))", "Mul(Integer(-1), Symbol('h', commutative=True), cos(Symbol('r', commutative=True)))", "Mul(Symbol('h', commutative=True), log(Symbol('r', commutative=True)))"]}, {"premise_expression": "\\frac{M}{o}", "variable": "M", "positive": "\\frac{M^{2}}{2 o}", "negatives": ["M \\log{(o)}", "\\frac{M^{2} e^{o}}{2}", "e^{M - o}", "M o + \\sin{(M)}"], "srepr_premise_expression": "Mul(Symbol('M', commutative=True), Pow(Symbol('o', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('M', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('M', commutative=True), Integer(2)), Pow(Symbol('o', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('M', commutative=True), log(Symbol('o', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('M', commutative=True), Integer(2)), exp(Symbol('o', commutative=True)))", "exp(Add(Symbol('M', commutative=True), Mul(Integer(-1), Symbol('o', commutative=True))))", "Add(Mul(Symbol('M', commutative=True), Symbol('o', commutative=True)), sin(Symbol('M', commutative=True)))"]}, {"premise_expression": "J - j + u", "variable": "j", "positive": "j (J - \\frac{j}{2} + u)", "negatives": ["\\frac{j (2 J - j - 2 u)}{2}", "\\frac{u (2 J - 2 j + u)}{2}", "\\frac{J (J - 2 j + 2 u)}{2}", "\\frac{j (J j + 2 u)}{2}"], "srepr_premise_expression": "Add(Symbol('J', commutative=True), Mul(Integer(-1), Symbol('j', commutative=True)), Symbol('u', commutative=True))", "srepr_variable": "Symbol('j', commutative=True)", "srepr_positive": "Mul(Symbol('j', commutative=True), Add(Symbol('J', commutative=True), Mul(Integer(-1), Rational(1, 2), Symbol('j', commutative=True)), Symbol('u', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('j', commutative=True), Add(Mul(Integer(2), Symbol('J', commutative=True)), Mul(Integer(-1), Symbol('j', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('u', commutative=True))))", "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(2), Symbol('J', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('j', commutative=True)), Symbol('u', commutative=True)))", "Mul(Rational(1, 2), Symbol('J', commutative=True), Add(Symbol('J', commutative=True), Mul(Integer(-1), Integer(2), Symbol('j', commutative=True)), Mul(Integer(2), Symbol('u', commutative=True))))", "Mul(Rational(1, 2), Symbol('j', commutative=True), Add(Mul(Symbol('J', commutative=True), Symbol('j', commutative=True)), Mul(Integer(2), Symbol('u', commutative=True))))"]}, {"premise_expression": "Y h", "variable": "h", "positive": "\\frac{Y h^{2}}{2}", "negatives": ["\\frac{Y^{2} h}{2}", "Y \\log{(h)}", "\\frac{h^{2} \\sin{(Y)}}{2}", "Y h - \\cos{(h)}"], "srepr_premise_expression": "Mul(Symbol('Y', commutative=True), Symbol('h', commutative=True))", "srepr_variable": "Symbol('h', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('Y', commutative=True), Pow(Symbol('h', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('Y', commutative=True), Integer(2)), Symbol('h', commutative=True))", "Mul(Symbol('Y', commutative=True), log(Symbol('h', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('h', commutative=True), Integer(2)), sin(Symbol('Y', commutative=True)))", "Add(Mul(Symbol('Y', commutative=True), Symbol('h', commutative=True)), Mul(Integer(-1), cos(Symbol('h', commutative=True))))"]}, {"premise_expression": "e^{E + x}", "variable": "x", "positive": "e^{E + x}", "negatives": ["- e^{E - x}", "\\sin{(E + x)}", "\\log{(x)} \\cos{(E)}", "\\frac{x^{2} \\log{(E)}}{2}"], "srepr_premise_expression": "exp(Add(Symbol('E', commutative=True), Symbol('x', commutative=True)))", "srepr_variable": "Symbol('x', commutative=True)", "srepr_positive": "exp(Add(Symbol('E', commutative=True), Symbol('x', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Symbol('E', commutative=True), Mul(Integer(-1), Symbol('x', commutative=True)))))", "sin(Add(Symbol('E', commutative=True), Symbol('x', commutative=True)))", "Mul(log(Symbol('x', commutative=True)), cos(Symbol('E', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('x', commutative=True), Integer(2)), log(Symbol('E', commutative=True)))"]}, {"premise_expression": "\\cos{(R - W)}", "variable": "W", "positive": "- \\sin{(R - W)}", "negatives": ["\\sin{(R - W)}", "R \\sin{(W)}", "- R \\cos{(W)}", "R \\log{(W)}"], "srepr_premise_expression": "cos(Add(Symbol('R', commutative=True), Mul(Integer(-1), Symbol('W', commutative=True))))", "srepr_variable": "Symbol('W', commutative=True)", "srepr_positive": "Mul(Integer(-1), sin(Add(Symbol('R', commutative=True), Mul(Integer(-1), Symbol('W', commutative=True)))))", "srepr_negatives": ["sin(Add(Symbol('R', commutative=True), Mul(Integer(-1), Symbol('W', commutative=True))))", "Mul(Symbol('R', commutative=True), sin(Symbol('W', commutative=True)))", "Mul(Integer(-1), Symbol('R', commutative=True), cos(Symbol('W', commutative=True)))", "Mul(Symbol('R', commutative=True), log(Symbol('W', commutative=True)))"]}, {"premise_expression": "\\frac{\\sin{(H)}}{p}", "variable": "p", "positive": "\\log{(p)} \\sin{(H)}", "negatives": ["H \\log{(p)}", "- \\frac{\\cos{(H)}}{p}", "p (\\log{(H p)} - 1)", "e^{H + p}"], "srepr_premise_expression": "Mul(Pow(Symbol('p', commutative=True), Integer(-1)), sin(Symbol('H', commutative=True)))", "srepr_variable": "Symbol('p', commutative=True)", "srepr_positive": "Mul(log(Symbol('p', commutative=True)), sin(Symbol('H', commutative=True)))", "srepr_negatives": ["Mul(Symbol('H', commutative=True), log(Symbol('p', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('p', commutative=True), Integer(-1)), cos(Symbol('H', commutative=True)))", "Mul(Symbol('p', commutative=True), Add(log(Mul(Symbol('H', commutative=True), Symbol('p', commutative=True))), Integer(-1)))", "exp(Add(Symbol('H', commutative=True), Symbol('p', commutative=True)))"]}, {"premise_expression": "\\cos{(\\frac{H}{U})}", "variable": "U", "positive": "H \\operatorname{Si}{(\\frac{H}{U})} + U \\cos{(\\frac{H}{U})}", "negatives": ["\\frac{U (- U + 2 \\log{(H)})}{2}", "U (H - U)", "- \\sin{(H - U)}", "\\frac{U (2 H - U)}{2}"], "srepr_premise_expression": "cos(Mul(Symbol('H', commutative=True), Pow(Symbol('U', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('U', commutative=True)", "srepr_positive": "Add(Mul(Symbol('H', commutative=True), Si(Mul(Symbol('H', commutative=True), Pow(Symbol('U', commutative=True), Integer(-1))))), Mul(Symbol('U', commutative=True), cos(Mul(Symbol('H', commutative=True), Pow(Symbol('U', commutative=True), Integer(-1))))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('U', commutative=True), Add(Mul(Integer(-1), Symbol('U', commutative=True)), Mul(Integer(2), log(Symbol('H', commutative=True)))))", "Mul(Symbol('U', commutative=True), Add(Symbol('H', commutative=True), Mul(Integer(-1), Symbol('U', commutative=True))))", "Mul(Integer(-1), sin(Add(Symbol('H', commutative=True), Mul(Integer(-1), Symbol('U', commutative=True)))))", "Mul(Rational(1, 2), Symbol('U', commutative=True), Add(Mul(Integer(2), Symbol('H', commutative=True)), Mul(Integer(-1), Symbol('U', commutative=True))))"]}, {"premise_expression": "\\frac{g}{H}", "variable": "g", "positive": "\\frac{g^{2}}{2 H}", "negatives": ["g \\log{(H)}", "\\frac{g^{2} \\log{(H)}}{2}", "\\frac{g^{2} \\sin{(H)}}{2}", "H g - \\cos{(g)}"], "srepr_premise_expression": "Mul(Pow(Symbol('H', commutative=True), Integer(-1)), Symbol('g', commutative=True))", "srepr_variable": "Symbol('g', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('H', commutative=True), Integer(-1)), Pow(Symbol('g', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('g', commutative=True), log(Symbol('H', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('g', commutative=True), Integer(2)), log(Symbol('H', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('g', commutative=True), Integer(2)), sin(Symbol('H', commutative=True)))", "Add(Mul(Symbol('H', commutative=True), Symbol('g', commutative=True)), Mul(Integer(-1), cos(Symbol('g', commutative=True))))"]}, {"premise_expression": "\\frac{J}{k}", "variable": "k", "positive": "J \\log{(k)}", "negatives": ["\\frac{J^{2}}{2 k}", "\\cos{(J - k)}", "k (\\log{(\\frac{J}{k})} + 1)", "J \\log{(k)} + \\frac{k^{2}}{2}"], "srepr_premise_expression": "Mul(Symbol('J', commutative=True), Pow(Symbol('k', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('k', commutative=True)", "srepr_positive": "Mul(Symbol('J', commutative=True), log(Symbol('k', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('J', commutative=True), Integer(2)), Pow(Symbol('k', commutative=True), Integer(-1)))", "cos(Add(Symbol('J', commutative=True), Mul(Integer(-1), Symbol('k', commutative=True))))", "Mul(Symbol('k', commutative=True), Add(log(Mul(Symbol('J', commutative=True), Pow(Symbol('k', commutative=True), Integer(-1)))), Integer(1)))", "Add(Mul(Symbol('J', commutative=True), log(Symbol('k', commutative=True))), Mul(Rational(1, 2), Pow(Symbol('k', commutative=True), Integer(2))))"]}, {"premise_expression": "\\frac{\\cos{(L)}}{l}", "variable": "l", "positive": "\\log{(l)} \\cos{(L)}", "negatives": ["L e^{l}", "l (\\log{(\\frac{l}{L})} - 1)", "\\frac{\\sin{(L)}}{l}", "L e^{\\frac{l}{L}}"], "srepr_premise_expression": "Mul(Pow(Symbol('l', commutative=True), Integer(-1)), cos(Symbol('L', commutative=True)))", "srepr_variable": "Symbol('l', commutative=True)", "srepr_positive": "Mul(log(Symbol('l', commutative=True)), cos(Symbol('L', commutative=True)))", "srepr_negatives": ["Mul(Symbol('L', commutative=True), exp(Symbol('l', commutative=True)))", "Mul(Symbol('l', commutative=True), Add(log(Mul(Pow(Symbol('L', commutative=True), Integer(-1)), Symbol('l', commutative=True))), Integer(-1)))", "Mul(Pow(Symbol('l', commutative=True), Integer(-1)), sin(Symbol('L', commutative=True)))", "Mul(Symbol('L', commutative=True), exp(Mul(Pow(Symbol('L', commutative=True), Integer(-1)), Symbol('l', commutative=True))))"]}, {"premise_expression": "\\log{(K + t)}", "variable": "K", "positive": "K \\log{(K + t)} - K + t \\log{(K + t)}", "negatives": ["K \\log{(K - t)} - K - t \\log{(K - t)}", "K \\log{(K + t)} + t \\log{(K + t)} - t", "\\frac{K (- K + 2 \\cos{(t)})}{2}", "e^{t} \\log{(K)}"], "srepr_premise_expression": "log(Add(Symbol('K', commutative=True), Symbol('t', commutative=True)))", "srepr_variable": "Symbol('K', commutative=True)", "srepr_positive": "Add(Mul(Symbol('K', commutative=True), log(Add(Symbol('K', commutative=True), Symbol('t', commutative=True)))), Mul(Integer(-1), Symbol('K', commutative=True)), Mul(Symbol('t', commutative=True), log(Add(Symbol('K', commutative=True), Symbol('t', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('K', commutative=True), log(Add(Symbol('K', commutative=True), Mul(Integer(-1), Symbol('t', commutative=True))))), Mul(Integer(-1), Symbol('K', commutative=True)), Mul(Integer(-1), Symbol('t', commutative=True), log(Add(Symbol('K', commutative=True), Mul(Integer(-1), Symbol('t', commutative=True))))))", "Add(Mul(Symbol('K', commutative=True), log(Add(Symbol('K', commutative=True), Symbol('t', commutative=True)))), Mul(Symbol('t', commutative=True), log(Add(Symbol('K', commutative=True), Symbol('t', commutative=True)))), Mul(Integer(-1), Symbol('t', commutative=True)))", "Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Mul(Integer(-1), Symbol('K', commutative=True)), Mul(Integer(2), cos(Symbol('t', commutative=True)))))", "Mul(exp(Symbol('t', commutative=True)), log(Symbol('K', commutative=True)))"]}, {"premise_expression": "I x", "variable": "x", "positive": "\\frac{I x^{2}}{2}", "negatives": ["\\frac{I^{2} x}{2}", "\\frac{x (2 I + x)}{2}", "\\cos{(I - x)}", "- I x + \\sin{(x)}"], "srepr_premise_expression": "Mul(Symbol('I', commutative=True), Symbol('x', commutative=True))", "srepr_variable": "Symbol('x', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('I', commutative=True), Pow(Symbol('x', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(2)), Symbol('x', commutative=True))", "Mul(Rational(1, 2), Symbol('x', commutative=True), Add(Mul(Integer(2), Symbol('I', commutative=True)), Symbol('x', commutative=True)))", "cos(Add(Symbol('I', commutative=True), Mul(Integer(-1), Symbol('x', commutative=True))))", "Add(Mul(Integer(-1), Symbol('I', commutative=True), Symbol('x', commutative=True)), sin(Symbol('x', commutative=True)))"]}, {"premise_expression": "\\frac{G}{t}", "variable": "G", "positive": "\\frac{G^{2}}{2 t}", "negatives": ["G \\log{(t)}", "t \\sin{(G)}", "G (- t + \\log{(G^{t})})", "\\frac{G (G + 2 e^{t})}{2}"], "srepr_premise_expression": "Mul(Symbol('G', commutative=True), Pow(Symbol('t', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(2)), Pow(Symbol('t', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('G', commutative=True), log(Symbol('t', commutative=True)))", "Mul(Symbol('t', commutative=True), sin(Symbol('G', commutative=True)))", "Mul(Symbol('G', commutative=True), Add(Mul(Integer(-1), Symbol('t', commutative=True)), log(Pow(Symbol('G', commutative=True), Symbol('t', commutative=True)))))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Symbol('G', commutative=True), Mul(Integer(2), exp(Symbol('t', commutative=True)))))"]}, {"premise_expression": "\\frac{X}{Z}", "variable": "X", "positive": "\\frac{X^{2}}{2 Z}", "negatives": ["X \\log{(Z)}", "Z e^{\\frac{X}{Z}}", "Z \\log{(X)}", "\\frac{X (X - 2 Z)}{2}"], "srepr_premise_expression": "Mul(Symbol('X', commutative=True), Pow(Symbol('Z', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('X', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('X', commutative=True), Integer(2)), Pow(Symbol('Z', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('X', commutative=True), log(Symbol('Z', commutative=True)))", "Mul(Symbol('Z', commutative=True), exp(Mul(Symbol('X', commutative=True), Pow(Symbol('Z', commutative=True), Integer(-1)))))", "Mul(Symbol('Z', commutative=True), log(Symbol('X', commutative=True)))", "Mul(Rational(1, 2), Symbol('X', commutative=True), Add(Symbol('X', commutative=True), Mul(Integer(-1), Integer(2), Symbol('Z', commutative=True))))"]}, {"premise_expression": "\\log{(G + R)}", "variable": "G", "positive": "G \\log{(G + R)} - G + R \\log{(G + R)}", "negatives": ["G \\log{(G + R)} + R \\log{(G + R)} - R", "\\frac{G (G + 2 \\log{(R)})}{2}", "G (\\log{(G R)} - 1)", "G \\cos{(\\frac{R}{G})} + R \\operatorname{Si}{(\\frac{R}{G})}"], "srepr_premise_expression": "log(Add(Symbol('G', commutative=True), Symbol('R', commutative=True)))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Add(Mul(Symbol('G', commutative=True), log(Add(Symbol('G', commutative=True), Symbol('R', commutative=True)))), Mul(Integer(-1), Symbol('G', commutative=True)), Mul(Symbol('R', commutative=True), log(Add(Symbol('G', commutative=True), Symbol('R', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('G', commutative=True), log(Add(Symbol('G', commutative=True), Symbol('R', commutative=True)))), Mul(Symbol('R', commutative=True), log(Add(Symbol('G', commutative=True), Symbol('R', commutative=True)))), Mul(Integer(-1), Symbol('R', commutative=True)))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Symbol('G', commutative=True), Mul(Integer(2), log(Symbol('R', commutative=True)))))", "Mul(Symbol('G', commutative=True), Add(log(Mul(Symbol('G', commutative=True), Symbol('R', commutative=True))), Integer(-1)))", "Add(Mul(Symbol('G', commutative=True), cos(Mul(Pow(Symbol('G', commutative=True), Integer(-1)), Symbol('R', commutative=True)))), Mul(Symbol('R', commutative=True), Si(Mul(Pow(Symbol('G', commutative=True), Integer(-1)), Symbol('R', commutative=True)))))"]}, {"premise_expression": "a + \\cos{(p)}", "variable": "p", "positive": "a p + \\sin{(p)}", "negatives": ["- a p - \\cos{(p)}", "a \\log{(p)}", "- e^{a - p}", "a e^{\\frac{p}{a}}"], "srepr_premise_expression": "Add(Symbol('a', commutative=True), cos(Symbol('p', commutative=True)))", "srepr_variable": "Symbol('p', commutative=True)", "srepr_positive": "Add(Mul(Symbol('a', commutative=True), Symbol('p', commutative=True)), sin(Symbol('p', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('a', commutative=True), Symbol('p', commutative=True)), Mul(Integer(-1), cos(Symbol('p', commutative=True))))", "Mul(Symbol('a', commutative=True), log(Symbol('p', commutative=True)))", "Mul(Integer(-1), exp(Add(Symbol('a', commutative=True), Mul(Integer(-1), Symbol('p', commutative=True)))))", "Mul(Symbol('a', commutative=True), exp(Mul(Pow(Symbol('a', commutative=True), Integer(-1)), Symbol('p', commutative=True))))"]}, {"premise_expression": "A + e^{r}", "variable": "A", "positive": "\\frac{A (A + 2 e^{r})}{2}", "negatives": ["\\frac{A (A + 2 r)}{2}", "\\frac{A (A - 2 r)}{2}", "A r + e^{r}", "- A r + e^{A}"], "srepr_premise_expression": "Add(Symbol('A', commutative=True), exp(Symbol('r', commutative=True)))", "srepr_variable": "Symbol('A', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Symbol('A', commutative=True), Mul(Integer(2), exp(Symbol('r', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Symbol('A', commutative=True), Mul(Integer(2), Symbol('r', commutative=True))))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Symbol('A', commutative=True), Mul(Integer(-1), Integer(2), Symbol('r', commutative=True))))", "Add(Mul(Symbol('A', commutative=True), Symbol('r', commutative=True)), exp(Symbol('r', commutative=True)))", "Add(Mul(Integer(-1), Symbol('A', commutative=True), Symbol('r', commutative=True)), exp(Symbol('A', commutative=True)))"]}, {"premise_expression": "- P + \\sin{(S)}", "variable": "P", "positive": "\\frac{P (- P + 2 \\sin{(S)})}{2}", "negatives": ["- P S - \\cos{(S)}", "P (- S + \\log{(P)} - 1)", "\\frac{\\sin{(P)}}{S}", "P e^{\\frac{S}{P}} - S \\operatorname{Ei}{(\\frac{S}{P})}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('P', commutative=True)), sin(Symbol('S', commutative=True)))", "srepr_variable": "Symbol('P', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Mul(Integer(-1), Symbol('P', commutative=True)), Mul(Integer(2), sin(Symbol('S', commutative=True)))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('P', commutative=True), Symbol('S', commutative=True)), Mul(Integer(-1), cos(Symbol('S', commutative=True))))", "Mul(Symbol('P', commutative=True), Add(Mul(Integer(-1), Symbol('S', commutative=True)), log(Symbol('P', commutative=True)), Integer(-1)))", "Mul(Pow(Symbol('S', commutative=True), Integer(-1)), sin(Symbol('P', commutative=True)))", "Add(Mul(Symbol('P', commutative=True), exp(Mul(Pow(Symbol('P', commutative=True), Integer(-1)), Symbol('S', commutative=True)))), Mul(Integer(-1), Symbol('S', commutative=True), Ei(Mul(Pow(Symbol('P', commutative=True), Integer(-1)), Symbol('S', commutative=True)))))"]}, {"premise_expression": "\\sin^{f}{(w)}", "variable": "w", "positive": "\\int \\sin^{f}{(w)} dw", "negatives": ["w (f + \\log{(w)} - 1)", "w (- f + \\log{(w^{f})})", "w (\\log{(f w)} - 1)", "\\cos{(f - w)}"], "srepr_premise_expression": "Pow(sin(Symbol('w', commutative=True)), Symbol('f', commutative=True))", "srepr_variable": "Symbol('w', commutative=True)", "srepr_positive": "Integral(Pow(sin(Symbol('w', commutative=True)), Symbol('f', commutative=True)), Tuple(Symbol('w', commutative=True)))", "srepr_negatives": ["Mul(Symbol('w', commutative=True), Add(Symbol('f', commutative=True), log(Symbol('w', commutative=True)), Integer(-1)))", "Mul(Symbol('w', commutative=True), Add(Mul(Integer(-1), Symbol('f', commutative=True)), log(Pow(Symbol('w', commutative=True), Symbol('f', commutative=True)))))", "Mul(Symbol('w', commutative=True), Add(log(Mul(Symbol('f', commutative=True), Symbol('w', commutative=True))), Integer(-1)))", "cos(Add(Symbol('f', commutative=True), Mul(Integer(-1), Symbol('w', commutative=True))))"]}, {"premise_expression": "- M + \\cos{(a)}", "variable": "a", "positive": "- M a + \\sin{(a)}", "negatives": ["\\frac{a (- a + 2 \\sin{(M)})}{2}", "\\frac{a (2 M + a)}{2}", "\\frac{M (- M + 2 \\cos{(a)})}{2}", "\\frac{a^{2} e^{M}}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('M', commutative=True)), cos(Symbol('a', commutative=True)))", "srepr_variable": "Symbol('a', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('M', commutative=True), Symbol('a', commutative=True)), sin(Symbol('a', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('a', commutative=True), Add(Mul(Integer(-1), Symbol('a', commutative=True)), Mul(Integer(2), sin(Symbol('M', commutative=True)))))", "Mul(Rational(1, 2), Symbol('a', commutative=True), Add(Mul(Integer(2), Symbol('M', commutative=True)), Symbol('a', commutative=True)))", "Mul(Rational(1, 2), Symbol('M', commutative=True), Add(Mul(Integer(-1), Symbol('M', commutative=True)), Mul(Integer(2), cos(Symbol('a', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('a', commutative=True), Integer(2)), exp(Symbol('M', commutative=True)))"]}, {"premise_expression": "\\log{(\\frac{b}{J})}", "variable": "b", "positive": "b (\\log{(\\frac{b}{J})} - 1)", "negatives": ["J (\\log{(\\frac{b}{J})} + 1)", "\\cos{(J - b)}", "\\frac{b (2 J - b)}{2}", "\\sin{(J + b)}"], "srepr_premise_expression": "log(Mul(Pow(Symbol('J', commutative=True), Integer(-1)), Symbol('b', commutative=True)))", "srepr_variable": "Symbol('b', commutative=True)", "srepr_positive": "Mul(Symbol('b', commutative=True), Add(log(Mul(Pow(Symbol('J', commutative=True), Integer(-1)), Symbol('b', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('J', commutative=True), Add(log(Mul(Pow(Symbol('J', commutative=True), Integer(-1)), Symbol('b', commutative=True))), Integer(1)))", "cos(Add(Symbol('J', commutative=True), Mul(Integer(-1), Symbol('b', commutative=True))))", "Mul(Rational(1, 2), Symbol('b', commutative=True), Add(Mul(Integer(2), Symbol('J', commutative=True)), Mul(Integer(-1), Symbol('b', commutative=True))))", "sin(Add(Symbol('J', commutative=True), Symbol('b', commutative=True)))"]}, {"premise_expression": "\\frac{A}{Q}", "variable": "A", "positive": "\\frac{A^{2}}{2 Q}", "negatives": ["A \\log{(Q)}", "\\frac{A^{2} e^{Q}}{2}", "\\frac{A (- A + 2 Q)}{2}", "e^{A + Q}"], "srepr_premise_expression": "Mul(Symbol('A', commutative=True), Pow(Symbol('Q', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('A', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2)), Pow(Symbol('Q', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('A', commutative=True), log(Symbol('Q', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2)), exp(Symbol('Q', commutative=True)))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Mul(Integer(-1), Symbol('A', commutative=True)), Mul(Integer(2), Symbol('Q', commutative=True))))", "exp(Add(Symbol('A', commutative=True), Symbol('Q', commutative=True)))"]}, {"premise_expression": "\\frac{H}{I}", "variable": "I", "positive": "H \\log{(I)}", "negatives": ["\\frac{H^{2}}{2 I}", "\\operatorname{Si}{(I)}", "\\frac{I^{2}}{2 H}", "- H I - \\cos{(I)}"], "srepr_premise_expression": "Mul(Symbol('H', commutative=True), Pow(Symbol('I', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('I', commutative=True)", "srepr_positive": "Mul(Symbol('H', commutative=True), log(Symbol('I', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('H', commutative=True), Integer(2)), Pow(Symbol('I', commutative=True), Integer(-1)))", "Si(Symbol('I', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('H', commutative=True), Integer(-1)), Pow(Symbol('I', commutative=True), Integer(2)))", "Add(Mul(Integer(-1), Symbol('H', commutative=True), Symbol('I', commutative=True)), Mul(Integer(-1), cos(Symbol('I', commutative=True))))"]}, {"premise_expression": "- G + n", "variable": "G", "positive": "\\frac{G (- G + 2 n)}{2}", "negatives": ["\\frac{n (- 2 G + n)}{2}", "\\frac{G (- G + 2 \\log{(n)})}{2}", "\\frac{G^{2} \\log{(n)}}{2}", "\\frac{G^{2} \\sin{(n)}}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('G', commutative=True)), Symbol('n', commutative=True))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Mul(Integer(-1), Symbol('G', commutative=True)), Mul(Integer(2), Symbol('n', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('n', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('G', commutative=True)), Symbol('n', commutative=True)))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Mul(Integer(-1), Symbol('G', commutative=True)), Mul(Integer(2), log(Symbol('n', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(2)), log(Symbol('n', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(2)), sin(Symbol('n', commutative=True)))"]}, {"premise_expression": "\\frac{e^{K}}{m}", "variable": "m", "positive": "e^{K} \\log{(m)}", "negatives": ["K m - \\cos{(m)}", "- \\cos{(K - m)}", "- K m + e^{m}", "- \\frac{\\cos{(m)}}{K}"], "srepr_premise_expression": "Mul(Pow(Symbol('m', commutative=True), Integer(-1)), exp(Symbol('K', commutative=True)))", "srepr_variable": "Symbol('m', commutative=True)", "srepr_positive": "Mul(exp(Symbol('K', commutative=True)), log(Symbol('m', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('K', commutative=True), Symbol('m', commutative=True)), Mul(Integer(-1), cos(Symbol('m', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('K', commutative=True), Mul(Integer(-1), Symbol('m', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('K', commutative=True), Symbol('m', commutative=True)), exp(Symbol('m', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('K', commutative=True), Integer(-1)), cos(Symbol('m', commutative=True)))"]}, {"premise_expression": "V e^{D}", "variable": "D", "positive": "V e^{D}", "negatives": ["\\frac{V^{2} e^{D}}{2}", "- D V + e^{D}", "e^{D + V}", "\\frac{D^{2}}{2 V}"], "srepr_premise_expression": "Mul(Symbol('V', commutative=True), exp(Symbol('D', commutative=True)))", "srepr_variable": "Symbol('D', commutative=True)", "srepr_positive": "Mul(Symbol('V', commutative=True), exp(Symbol('D', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('V', commutative=True), Integer(2)), exp(Symbol('D', commutative=True)))", "Add(Mul(Integer(-1), Symbol('D', commutative=True), Symbol('V', commutative=True)), exp(Symbol('D', commutative=True)))", "exp(Add(Symbol('D', commutative=True), Symbol('V', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(2)), Pow(Symbol('V', commutative=True), Integer(-1)))"]}, {"premise_expression": "\\frac{s}{P}", "variable": "P", "positive": "s \\log{(P)}", "negatives": ["\\frac{s^{2}}{2 P}", "\\frac{P^{2} s}{2}", "0", "P (\\log{(P s)} - 1)"], "srepr_premise_expression": "Mul(Pow(Symbol('P', commutative=True), Integer(-1)), Symbol('s', commutative=True))", "srepr_variable": "Symbol('P', commutative=True)", "srepr_positive": "Mul(Symbol('s', commutative=True), log(Symbol('P', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(-1)), Pow(Symbol('s', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2)), Symbol('s', commutative=True))", "Integer(0)", "Mul(Symbol('P', commutative=True), Add(log(Mul(Symbol('P', commutative=True), Symbol('s', commutative=True))), Integer(-1)))"]}, {"premise_expression": "- P + b - t", "variable": "t", "positive": "\\frac{t (- 2 P + 2 b - t)}{2}", "negatives": ["\\frac{t (2 P + 2 b - t)}{2}", "\\frac{b (- 2 P + b - 2 t)}{2}", "\\frac{P (- P + 2 b - 2 t)}{2}", "\\frac{t (2 b^{2} + t)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('P', commutative=True)), Symbol('b', commutative=True), Mul(Integer(-1), Symbol('t', commutative=True)))", "srepr_variable": "Symbol('t', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('t', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('P', commutative=True)), Mul(Integer(2), Symbol('b', commutative=True)), Mul(Integer(-1), Symbol('t', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('t', commutative=True), Add(Mul(Integer(2), Symbol('P', commutative=True)), Mul(Integer(2), Symbol('b', commutative=True)), Mul(Integer(-1), Symbol('t', commutative=True))))", "Mul(Rational(1, 2), Symbol('b', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('P', commutative=True)), Symbol('b', commutative=True), Mul(Integer(-1), Integer(2), Symbol('t', commutative=True))))", "Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Mul(Integer(-1), Symbol('P', commutative=True)), Mul(Integer(2), Symbol('b', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('t', commutative=True))))", "Mul(Rational(1, 2), Symbol('t', commutative=True), Add(Mul(Integer(2), Pow(Symbol('b', commutative=True), Integer(2))), Symbol('t', commutative=True)))"]}, {"premise_expression": "Q \\log{(v)}", "variable": "Q", "positive": "\\frac{Q^{2} \\log{(v)}}{2}", "negatives": ["\\frac{Q (Q - 2 v)}{2}", "\\frac{Q^{2}}{2 v}", "Q v (\\log{(v)} - 1)", "v \\sin{(Q)}"], "srepr_premise_expression": "Mul(Symbol('Q', commutative=True), log(Symbol('v', commutative=True)))", "srepr_variable": "Symbol('Q', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(2)), log(Symbol('v', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Symbol('Q', commutative=True), Mul(Integer(-1), Integer(2), Symbol('v', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(2)), Pow(Symbol('v', commutative=True), Integer(-1)))", "Mul(Symbol('Q', commutative=True), Symbol('v', commutative=True), Add(log(Symbol('v', commutative=True)), Integer(-1)))", "Mul(Symbol('v', commutative=True), sin(Symbol('Q', commutative=True)))"]}, {"premise_expression": "\\frac{e^{c}}{n}", "variable": "n", "positive": "e^{c} \\log{(n)}", "negatives": ["\\log{(c)} \\log{(n)}", "n (c + \\log{(n)} - 1)", "n (\\log{(\\frac{n}{c})} - 1)", "0"], "srepr_premise_expression": "Mul(Pow(Symbol('n', commutative=True), Integer(-1)), exp(Symbol('c', commutative=True)))", "srepr_variable": "Symbol('n', commutative=True)", "srepr_positive": "Mul(exp(Symbol('c', commutative=True)), log(Symbol('n', commutative=True)))", "srepr_negatives": ["Mul(log(Symbol('c', commutative=True)), log(Symbol('n', commutative=True)))", "Mul(Symbol('n', commutative=True), Add(Symbol('c', commutative=True), log(Symbol('n', commutative=True)), Integer(-1)))", "Mul(Symbol('n', commutative=True), Add(log(Mul(Pow(Symbol('c', commutative=True), Integer(-1)), Symbol('n', commutative=True))), Integer(-1)))", "Integer(0)"]}, {"premise_expression": "\\log{(x^{A})}", "variable": "A", "positive": "\\frac{A^{2} \\log{(x)}}{2}", "negatives": ["x \\log{(A)}", "- \\frac{A^{2}}{2} + x \\log{(A)}", "A (\\log{(\\frac{x}{A})} + 1)", "- A x + \\sin{(A)}"], "srepr_premise_expression": "log(Pow(Symbol('x', commutative=True), Symbol('A', commutative=True)))", "srepr_variable": "Symbol('A', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2)), log(Symbol('x', commutative=True)))", "srepr_negatives": ["Mul(Symbol('x', commutative=True), log(Symbol('A', commutative=True)))", "Add(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2))), Mul(Symbol('x', commutative=True), log(Symbol('A', commutative=True))))", "Mul(Symbol('A', commutative=True), Add(log(Mul(Pow(Symbol('A', commutative=True), Integer(-1)), Symbol('x', commutative=True))), Integer(1)))", "Add(Mul(Integer(-1), Symbol('A', commutative=True), Symbol('x', commutative=True)), sin(Symbol('A', commutative=True)))"]}, {"premise_expression": "\\frac{W}{r}", "variable": "W", "positive": "\\frac{W^{2}}{2 r}", "negatives": ["W \\log{(r)}", "\\frac{W^{2} r}{2}", "\\frac{W (W - 2 r)}{2}", "\\cos{(W - r)}"], "srepr_premise_expression": "Mul(Symbol('W', commutative=True), Pow(Symbol('r', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('W', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('W', commutative=True), Integer(2)), Pow(Symbol('r', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('W', commutative=True), log(Symbol('r', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('W', commutative=True), Integer(2)), Symbol('r', commutative=True))", "Mul(Rational(1, 2), Symbol('W', commutative=True), Add(Symbol('W', commutative=True), Mul(Integer(-1), Integer(2), Symbol('r', commutative=True))))", "cos(Add(Symbol('W', commutative=True), Mul(Integer(-1), Symbol('r', commutative=True))))"]}, {"premise_expression": "- f + e^{U}", "variable": "U", "positive": "- U f + e^{U}", "negatives": ["\\frac{U^{2} e^{f}}{2}", "\\frac{f (- f + 2 e^{U})}{2}", "\\frac{U (U + 2 f)}{2}", "\\frac{U (U + 2 e^{f})}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('f', commutative=True)), exp(Symbol('U', commutative=True)))", "srepr_variable": "Symbol('U', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('U', commutative=True), Symbol('f', commutative=True)), exp(Symbol('U', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('U', commutative=True), Integer(2)), exp(Symbol('f', commutative=True)))", "Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Mul(Integer(-1), Symbol('f', commutative=True)), Mul(Integer(2), exp(Symbol('U', commutative=True)))))", "Mul(Rational(1, 2), Symbol('U', commutative=True), Add(Symbol('U', commutative=True), Mul(Integer(2), Symbol('f', commutative=True))))", "Mul(Rational(1, 2), Symbol('U', commutative=True), Add(Symbol('U', commutative=True), Mul(Integer(2), exp(Symbol('f', commutative=True)))))"]}, {"premise_expression": "\\log{(F + l)}", "variable": "l", "positive": "F \\log{(F + l)} + l \\log{(F + l)} - l", "negatives": ["F \\log{(F + l)} - F + l \\log{(F + l)}", "\\log{(F)} \\log{(l)}", "l (- F + \\log{(l)} - 1)", "\\frac{l^{2} \\log{(F)}}{2}"], "srepr_premise_expression": "log(Add(Symbol('F', commutative=True), Symbol('l', commutative=True)))", "srepr_variable": "Symbol('l', commutative=True)", "srepr_positive": "Add(Mul(Symbol('F', commutative=True), log(Add(Symbol('F', commutative=True), Symbol('l', commutative=True)))), Mul(Symbol('l', commutative=True), log(Add(Symbol('F', commutative=True), Symbol('l', commutative=True)))), Mul(Integer(-1), Symbol('l', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('F', commutative=True), log(Add(Symbol('F', commutative=True), Symbol('l', commutative=True)))), Mul(Integer(-1), Symbol('F', commutative=True)), Mul(Symbol('l', commutative=True), log(Add(Symbol('F', commutative=True), Symbol('l', commutative=True)))))", "Mul(log(Symbol('F', commutative=True)), log(Symbol('l', commutative=True)))", "Mul(Symbol('l', commutative=True), Add(Mul(Integer(-1), Symbol('F', commutative=True)), log(Symbol('l', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('l', commutative=True), Integer(2)), log(Symbol('F', commutative=True)))"]}, {"premise_expression": "P - Q + R", "variable": "P", "positive": "P (\\frac{P}{2} - Q + R)", "negatives": ["\\frac{P (P + 2 Q + 2 R)}{2}", "\\frac{P (- P + 2 Q - 2 R)}{2}", "\\frac{Q (2 P - Q + 2 R)}{2}", "\\frac{R (2 P - 2 Q + R)}{2}"], "srepr_premise_expression": "Add(Symbol('P', commutative=True), Mul(Integer(-1), Symbol('Q', commutative=True)), Symbol('R', commutative=True))", "srepr_variable": "Symbol('P', commutative=True)", "srepr_positive": "Mul(Symbol('P', commutative=True), Add(Mul(Rational(1, 2), Symbol('P', commutative=True)), Mul(Integer(-1), Symbol('Q', commutative=True)), Symbol('R', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Symbol('P', commutative=True), Mul(Integer(2), Symbol('Q', commutative=True)), Mul(Integer(2), Symbol('R', commutative=True))))", "Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Mul(Integer(-1), Symbol('P', commutative=True)), Mul(Integer(2), Symbol('Q', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('R', commutative=True))))", "Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Mul(Integer(2), Symbol('P', commutative=True)), Mul(Integer(-1), Symbol('Q', commutative=True)), Mul(Integer(2), Symbol('R', commutative=True))))", "Mul(Rational(1, 2), Symbol('R', commutative=True), Add(Mul(Integer(2), Symbol('P', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('Q', commutative=True)), Symbol('R', commutative=True)))"]}, {"premise_expression": "\\frac{G}{t}", "variable": "t", "positive": "G \\log{(t)}", "negatives": ["\\frac{G^{2}}{2 t}", "e^{G + t}", "\\log{(t)} \\sin{(G)}", "t (\\log{(G t)} - 1)"], "srepr_premise_expression": "Mul(Symbol('G', commutative=True), Pow(Symbol('t', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('t', commutative=True)", "srepr_positive": "Mul(Symbol('G', commutative=True), log(Symbol('t', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(2)), Pow(Symbol('t', commutative=True), Integer(-1)))", "exp(Add(Symbol('G', commutative=True), Symbol('t', commutative=True)))", "Mul(log(Symbol('t', commutative=True)), sin(Symbol('G', commutative=True)))", "Mul(Symbol('t', commutative=True), Add(log(Mul(Symbol('G', commutative=True), Symbol('t', commutative=True))), Integer(-1)))"]}, {"premise_expression": "e^{- T + p}", "variable": "p", "positive": "e^{- T + p}", "negatives": ["- e^{- T + p}", "- e^{T - p}", "- \\cos{(T - p)}", "- T p + e^{p}"], "srepr_premise_expression": "exp(Add(Mul(Integer(-1), Symbol('T', commutative=True)), Symbol('p', commutative=True)))", "srepr_variable": "Symbol('p', commutative=True)", "srepr_positive": "exp(Add(Mul(Integer(-1), Symbol('T', commutative=True)), Symbol('p', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('T', commutative=True)), Symbol('p', commutative=True))))", "Mul(Integer(-1), exp(Add(Symbol('T', commutative=True), Mul(Integer(-1), Symbol('p', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('T', commutative=True), Mul(Integer(-1), Symbol('p', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('T', commutative=True), Symbol('p', commutative=True)), exp(Symbol('p', commutative=True)))"]}, {"premise_expression": "A K", "variable": "K", "positive": "\\frac{A K^{2}}{2}", "negatives": ["\\frac{A^{2} K}{2}", "K^{2}", "- A \\cos{(K)}", "e^{- A + K}"], "srepr_premise_expression": "Mul(Symbol('A', commutative=True), Symbol('K', commutative=True))", "srepr_variable": "Symbol('K', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('A', commutative=True), Pow(Symbol('K', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2)), Symbol('K', commutative=True))", "Pow(Symbol('K', commutative=True), Integer(2))", "Mul(Integer(-1), Symbol('A', commutative=True), cos(Symbol('K', commutative=True)))", "exp(Add(Mul(Integer(-1), Symbol('A', commutative=True)), Symbol('K', commutative=True)))"]}, {"premise_expression": "- T + q", "variable": "q", "positive": "\\frac{q (- 2 T + q)}{2}", "negatives": ["\\frac{T (- T + 2 q)}{2}", "\\frac{q^{2} \\cos{(T)}}{2}", "\\frac{q^{2} \\log{(T)}}{2}", "\\cos{(T - q)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('T', commutative=True)), Symbol('q', commutative=True))", "srepr_variable": "Symbol('q', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('q', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('T', commutative=True)), Symbol('q', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('T', commutative=True), Add(Mul(Integer(-1), Symbol('T', commutative=True)), Mul(Integer(2), Symbol('q', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('q', commutative=True), Integer(2)), cos(Symbol('T', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('q', commutative=True), Integer(2)), log(Symbol('T', commutative=True)))", "cos(Add(Symbol('T', commutative=True), Mul(Integer(-1), Symbol('q', commutative=True))))"]}, {"premise_expression": "l q - z", "variable": "z", "positive": "\\frac{z (2 l q - z)}{2}", "negatives": ["\\frac{z (2 l + q z)}{2}", "\\frac{q (l q - 2 z)}{2}", "\\frac{l (l q - 2 z)}{2}", "\\frac{q z (- 2 l + z)}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('l', commutative=True), Symbol('q', commutative=True)), Mul(Integer(-1), Symbol('z', commutative=True)))", "srepr_variable": "Symbol('z', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('z', commutative=True), Add(Mul(Integer(2), Symbol('l', commutative=True), Symbol('q', commutative=True)), Mul(Integer(-1), Symbol('z', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('z', commutative=True), Add(Mul(Integer(2), Symbol('l', commutative=True)), Mul(Symbol('q', commutative=True), Symbol('z', commutative=True))))", "Mul(Rational(1, 2), Symbol('q', commutative=True), Add(Mul(Symbol('l', commutative=True), Symbol('q', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('z', commutative=True))))", "Mul(Rational(1, 2), Symbol('l', commutative=True), Add(Mul(Symbol('l', commutative=True), Symbol('q', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('z', commutative=True))))", "Mul(Rational(1, 2), Symbol('q', commutative=True), Symbol('z', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('l', commutative=True)), Symbol('z', commutative=True)))"]}, {"premise_expression": "C + T", "variable": "C", "positive": "\\frac{C (C + 2 T)}{2}", "negatives": ["\\frac{T (2 C + T)}{2}", "e^{C - T}", "\\cos{(C - T)}", "T e^{\\frac{C}{T}}"], "srepr_premise_expression": "Add(Symbol('C', commutative=True), Symbol('T', commutative=True))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Symbol('C', commutative=True), Mul(Integer(2), Symbol('T', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('T', commutative=True), Add(Mul(Integer(2), Symbol('C', commutative=True)), Symbol('T', commutative=True)))", "exp(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('T', commutative=True))))", "cos(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('T', commutative=True))))", "Mul(Symbol('T', commutative=True), exp(Mul(Symbol('C', commutative=True), Pow(Symbol('T', commutative=True), Integer(-1)))))"]}, {"premise_expression": "\\frac{Z}{j v}", "variable": "Z", "positive": "\\frac{Z^{2}}{2 j v}", "negatives": ["\\frac{Z^{2} v}{2 j}", "\\frac{Z^{2} j}{2 v}", "\\frac{Z \\log{(j)}}{v}", "\\frac{Z \\log{(v)}}{j}"], "srepr_premise_expression": "Mul(Symbol('Z', commutative=True), Pow(Symbol('j', commutative=True), Integer(-1)), Pow(Symbol('v', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('Z', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('Z', commutative=True), Integer(2)), Pow(Symbol('j', commutative=True), Integer(-1)), Pow(Symbol('v', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('Z', commutative=True), Integer(2)), Pow(Symbol('j', commutative=True), Integer(-1)), Symbol('v', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('Z', commutative=True), Integer(2)), Symbol('j', commutative=True), Pow(Symbol('v', commutative=True), Integer(-1)))", "Mul(Symbol('Z', commutative=True), Pow(Symbol('v', commutative=True), Integer(-1)), log(Symbol('j', commutative=True)))", "Mul(Symbol('Z', commutative=True), Pow(Symbol('j', commutative=True), Integer(-1)), log(Symbol('v', commutative=True)))"]}, {"premise_expression": "\\frac{k + m}{s}", "variable": "s", "positive": "(k + m) \\log{(s)}", "negatives": ["k m \\log{(s)}", "\\frac{m (2 k + m)}{2 s}", "\\frac{k (k + 2 m)}{2 s}", "\\frac{s (2 k + 2 m - s)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('s', commutative=True), Integer(-1)), Add(Symbol('k', commutative=True), Symbol('m', commutative=True)))", "srepr_variable": "Symbol('s', commutative=True)", "srepr_positive": "Mul(Add(Symbol('k', commutative=True), Symbol('m', commutative=True)), log(Symbol('s', commutative=True)))", "srepr_negatives": ["Mul(Symbol('k', commutative=True), Symbol('m', commutative=True), log(Symbol('s', commutative=True)))", "Mul(Rational(1, 2), Symbol('m', commutative=True), Pow(Symbol('s', commutative=True), Integer(-1)), Add(Mul(Integer(2), Symbol('k', commutative=True)), Symbol('m', commutative=True)))", "Mul(Rational(1, 2), Symbol('k', commutative=True), Pow(Symbol('s', commutative=True), Integer(-1)), Add(Symbol('k', commutative=True), Mul(Integer(2), Symbol('m', commutative=True))))", "Mul(Rational(1, 2), Symbol('s', commutative=True), Add(Mul(Integer(2), Symbol('k', commutative=True)), Mul(Integer(2), Symbol('m', commutative=True)), Mul(Integer(-1), Symbol('s', commutative=True))))"]}, {"premise_expression": "\\frac{e^{T}}{W}", "variable": "W", "positive": "e^{T} \\log{(W)}", "negatives": ["T e^{\\frac{W}{T}}", "- \\sin{(T - W)}", "W (T + \\log{(W)} - 1)", "\\frac{W (2 T + W)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('W', commutative=True), Integer(-1)), exp(Symbol('T', commutative=True)))", "srepr_variable": "Symbol('W', commutative=True)", "srepr_positive": "Mul(exp(Symbol('T', commutative=True)), log(Symbol('W', commutative=True)))", "srepr_negatives": ["Mul(Symbol('T', commutative=True), exp(Mul(Pow(Symbol('T', commutative=True), Integer(-1)), Symbol('W', commutative=True))))", "Mul(Integer(-1), sin(Add(Symbol('T', commutative=True), Mul(Integer(-1), Symbol('W', commutative=True)))))", "Mul(Symbol('W', commutative=True), Add(Symbol('T', commutative=True), log(Symbol('W', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('W', commutative=True), Add(Mul(Integer(2), Symbol('T', commutative=True)), Symbol('W', commutative=True)))"]}, {"premise_expression": "\\frac{q}{X p}", "variable": "p", "positive": "\\frac{q \\log{(p)}}{X}", "negatives": ["\\frac{q \\log{(X)}}{p}", "\\frac{X p^{2} q}{2}", "\\frac{q^{2}}{2 X p}", "\\frac{p^{2} q}{2 X}"], "srepr_premise_expression": "Mul(Pow(Symbol('X', commutative=True), Integer(-1)), Pow(Symbol('p', commutative=True), Integer(-1)), Symbol('q', commutative=True))", "srepr_variable": "Symbol('p', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('X', commutative=True), Integer(-1)), Symbol('q', commutative=True), log(Symbol('p', commutative=True)))", "srepr_negatives": ["Mul(Pow(Symbol('p', commutative=True), Integer(-1)), Symbol('q', commutative=True), log(Symbol('X', commutative=True)))", "Mul(Rational(1, 2), Symbol('X', commutative=True), Pow(Symbol('p', commutative=True), Integer(2)), Symbol('q', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('X', commutative=True), Integer(-1)), Pow(Symbol('p', commutative=True), Integer(-1)), Pow(Symbol('q', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('X', commutative=True), Integer(-1)), Pow(Symbol('p', commutative=True), Integer(2)), Symbol('q', commutative=True))"]}, {"premise_expression": "J - x", "variable": "J", "positive": "\\frac{J (J - 2 x)}{2}", "negatives": ["\\frac{x (2 J - x)}{2}", "\\frac{J (- J + 2 \\sin{(x)})}{2}", "\\frac{J (- J + 2 \\log{(x)})}{2}", "J (\\log{(J x)} - 1)"], "srepr_premise_expression": "Add(Symbol('J', commutative=True), Mul(Integer(-1), Symbol('x', commutative=True)))", "srepr_variable": "Symbol('J', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('J', commutative=True), Add(Symbol('J', commutative=True), Mul(Integer(-1), Integer(2), Symbol('x', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('x', commutative=True), Add(Mul(Integer(2), Symbol('J', commutative=True)), Mul(Integer(-1), Symbol('x', commutative=True))))", "Mul(Rational(1, 2), Symbol('J', commutative=True), Add(Mul(Integer(-1), Symbol('J', commutative=True)), Mul(Integer(2), sin(Symbol('x', commutative=True)))))", "Mul(Rational(1, 2), Symbol('J', commutative=True), Add(Mul(Integer(-1), Symbol('J', commutative=True)), Mul(Integer(2), log(Symbol('x', commutative=True)))))", "Mul(Symbol('J', commutative=True), Add(log(Mul(Symbol('J', commutative=True), Symbol('x', commutative=True))), Integer(-1)))"]}, {"premise_expression": "- N + \\log{(T)}", "variable": "N", "positive": "\\frac{N (- N + 2 \\log{(T)})}{2}", "negatives": ["\\frac{N (N + 2 \\sin{(T)})}{2}", "\\frac{N (- N + 2 T)}{2}", "\\frac{N (N + 2 T)}{2}", "\\frac{N^{2} \\log{(T)}}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('N', commutative=True)), log(Symbol('T', commutative=True)))", "srepr_variable": "Symbol('N', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Mul(Integer(-1), Symbol('N', commutative=True)), Mul(Integer(2), log(Symbol('T', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Symbol('N', commutative=True), Mul(Integer(2), sin(Symbol('T', commutative=True)))))", "Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Mul(Integer(-1), Symbol('N', commutative=True)), Mul(Integer(2), Symbol('T', commutative=True))))", "Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Symbol('N', commutative=True), Mul(Integer(2), Symbol('T', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('N', commutative=True), Integer(2)), log(Symbol('T', commutative=True)))"]}, {"premise_expression": "e^{\\frac{u}{A}}", "variable": "u", "positive": "A e^{\\frac{u}{A}}", "negatives": ["e^{- A + u}", "\\tilde{\\infty} u", "A e^{\\frac{u}{A}} - u \\operatorname{Ei}{(\\frac{u}{A})}", "\\frac{u (u + 2 e^{A})}{2}"], "srepr_premise_expression": "exp(Mul(Pow(Symbol('A', commutative=True), Integer(-1)), Symbol('u', commutative=True)))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "Mul(Symbol('A', commutative=True), exp(Mul(Pow(Symbol('A', commutative=True), Integer(-1)), Symbol('u', commutative=True))))", "srepr_negatives": ["exp(Add(Mul(Integer(-1), Symbol('A', commutative=True)), Symbol('u', commutative=True)))", "Mul(zoo, Symbol('u', commutative=True))", "Add(Mul(Symbol('A', commutative=True), exp(Mul(Pow(Symbol('A', commutative=True), Integer(-1)), Symbol('u', commutative=True)))), Mul(Integer(-1), Symbol('u', commutative=True), Ei(Mul(Pow(Symbol('A', commutative=True), Integer(-1)), Symbol('u', commutative=True)))))", "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Symbol('u', commutative=True), Mul(Integer(2), exp(Symbol('A', commutative=True)))))"]}, {"premise_expression": "- m + e^{I}", "variable": "I", "positive": "- I m + e^{I}", "negatives": ["- I m + \\sin{(I)}", "- m \\cos{(I)}", "\\frac{m (- m + 2 e^{I})}{2}", "\\frac{I (I + 2 e^{m})}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('m', commutative=True)), exp(Symbol('I', commutative=True)))", "srepr_variable": "Symbol('I', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('I', commutative=True), Symbol('m', commutative=True)), exp(Symbol('I', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('I', commutative=True), Symbol('m', commutative=True)), sin(Symbol('I', commutative=True)))", "Mul(Integer(-1), Symbol('m', commutative=True), cos(Symbol('I', commutative=True)))", "Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Mul(Integer(-1), Symbol('m', commutative=True)), Mul(Integer(2), exp(Symbol('I', commutative=True)))))", "Mul(Rational(1, 2), Symbol('I', commutative=True), Add(Symbol('I', commutative=True), Mul(Integer(2), exp(Symbol('m', commutative=True)))))"]}, {"premise_expression": "\\frac{\\log{(p)}}{G}", "variable": "p", "positive": "\\frac{p (\\log{(p)} - 1)}{G}", "negatives": ["\\log{(G)} \\log{(p)}", "\\frac{\\sin{(p)}}{G}", "p (- G + \\log{(p^{G})})", "\\frac{p (p + 2 \\sin{(G)})}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('G', commutative=True), Integer(-1)), log(Symbol('p', commutative=True)))", "srepr_variable": "Symbol('p', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('G', commutative=True), Integer(-1)), Symbol('p', commutative=True), Add(log(Symbol('p', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(log(Symbol('G', commutative=True)), log(Symbol('p', commutative=True)))", "Mul(Pow(Symbol('G', commutative=True), Integer(-1)), sin(Symbol('p', commutative=True)))", "Mul(Symbol('p', commutative=True), Add(Mul(Integer(-1), Symbol('G', commutative=True)), log(Pow(Symbol('p', commutative=True), Symbol('G', commutative=True)))))", "Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Symbol('p', commutative=True), Mul(Integer(2), sin(Symbol('G', commutative=True)))))"]}, {"premise_expression": "e^{c - u}", "variable": "u", "positive": "- e^{c - u}", "negatives": ["e^{c - u}", "- \\cos{(c + u)}", "\\frac{u (2 c - u)}{2}", "- c u + e^{u}"], "srepr_premise_expression": "exp(Add(Symbol('c', commutative=True), Mul(Integer(-1), Symbol('u', commutative=True))))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "Mul(Integer(-1), exp(Add(Symbol('c', commutative=True), Mul(Integer(-1), Symbol('u', commutative=True)))))", "srepr_negatives": ["exp(Add(Symbol('c', commutative=True), Mul(Integer(-1), Symbol('u', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('c', commutative=True), Symbol('u', commutative=True))))", "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(2), Symbol('c', commutative=True)), Mul(Integer(-1), Symbol('u', commutative=True))))", "Add(Mul(Integer(-1), Symbol('c', commutative=True), Symbol('u', commutative=True)), exp(Symbol('u', commutative=True)))"]}, {"premise_expression": "\\log{(a + f)}", "variable": "f", "positive": "a \\log{(a + f)} + f \\log{(a + f)} - f", "negatives": ["a \\log{(a + f)} - a + f \\log{(a + f)}", "f (a + \\log{(f)} - 1)", "\\frac{f (- f + 2 \\cos{(a)})}{2}", "f (\\log{(a f)} - 1)"], "srepr_premise_expression": "log(Add(Symbol('a', commutative=True), Symbol('f', commutative=True)))", "srepr_variable": "Symbol('f', commutative=True)", "srepr_positive": "Add(Mul(Symbol('a', commutative=True), log(Add(Symbol('a', commutative=True), Symbol('f', commutative=True)))), Mul(Symbol('f', commutative=True), log(Add(Symbol('a', commutative=True), Symbol('f', commutative=True)))), Mul(Integer(-1), Symbol('f', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('a', commutative=True), log(Add(Symbol('a', commutative=True), Symbol('f', commutative=True)))), Mul(Integer(-1), Symbol('a', commutative=True)), Mul(Symbol('f', commutative=True), log(Add(Symbol('a', commutative=True), Symbol('f', commutative=True)))))", "Mul(Symbol('f', commutative=True), Add(Symbol('a', commutative=True), log(Symbol('f', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Mul(Integer(-1), Symbol('f', commutative=True)), Mul(Integer(2), cos(Symbol('a', commutative=True)))))", "Mul(Symbol('f', commutative=True), Add(log(Mul(Symbol('a', commutative=True), Symbol('f', commutative=True))), Integer(-1)))"]}, {"premise_expression": "o + e^{j}", "variable": "j", "positive": "j o + e^{j}", "negatives": ["- j o + e^{j}", "\\frac{o (o + 2 e^{j})}{2}", "\\frac{j (j + 2 o)}{2}", "o \\log{(j)}"], "srepr_premise_expression": "Add(Symbol('o', commutative=True), exp(Symbol('j', commutative=True)))", "srepr_variable": "Symbol('j', commutative=True)", "srepr_positive": "Add(Mul(Symbol('j', commutative=True), Symbol('o', commutative=True)), exp(Symbol('j', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('j', commutative=True), Symbol('o', commutative=True)), exp(Symbol('j', commutative=True)))", "Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Symbol('o', commutative=True), Mul(Integer(2), exp(Symbol('j', commutative=True)))))", "Mul(Rational(1, 2), Symbol('j', commutative=True), Add(Symbol('j', commutative=True), Mul(Integer(2), Symbol('o', commutative=True))))", "Mul(Symbol('o', commutative=True), log(Symbol('j', commutative=True)))"]}, {"premise_expression": "\\frac{j}{Y k}", "variable": "Y", "positive": "\\frac{j \\log{(Y)}}{k}", "negatives": ["\\frac{j \\log{(k)}}{Y}", "\\frac{j^{2}}{2 Y k}", "Y j k^{k}", "(- j + k) \\log{(Y)}"], "srepr_premise_expression": "Mul(Pow(Symbol('Y', commutative=True), Integer(-1)), Symbol('j', commutative=True), Pow(Symbol('k', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('Y', commutative=True)", "srepr_positive": "Mul(Symbol('j', commutative=True), Pow(Symbol('k', commutative=True), Integer(-1)), log(Symbol('Y', commutative=True)))", "srepr_negatives": ["Mul(Pow(Symbol('Y', commutative=True), Integer(-1)), Symbol('j', commutative=True), log(Symbol('k', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('Y', commutative=True), Integer(-1)), Pow(Symbol('j', commutative=True), Integer(2)), Pow(Symbol('k', commutative=True), Integer(-1)))", "Mul(Symbol('Y', commutative=True), Symbol('j', commutative=True), Pow(Symbol('k', commutative=True), Symbol('k', commutative=True)))", "Mul(Add(Mul(Integer(-1), Symbol('j', commutative=True)), Symbol('k', commutative=True)), log(Symbol('Y', commutative=True)))"]}, {"premise_expression": "k \\log{(f)}", "variable": "f", "positive": "f k (\\log{(f)} - 1)", "negatives": ["\\frac{k^{2} \\log{(f)}}{2}", "\\frac{f^{2} \\log{(k)}}{2}", "\\cos{(f - k)}", "\\frac{f^{2}}{2 k}"], "srepr_premise_expression": "Mul(Symbol('k', commutative=True), log(Symbol('f', commutative=True)))", "srepr_variable": "Symbol('f', commutative=True)", "srepr_positive": "Mul(Symbol('f', commutative=True), Symbol('k', commutative=True), Add(log(Symbol('f', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('k', commutative=True), Integer(2)), log(Symbol('f', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('f', commutative=True), Integer(2)), log(Symbol('k', commutative=True)))", "cos(Add(Symbol('f', commutative=True), Mul(Integer(-1), Symbol('k', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('f', commutative=True), Integer(2)), Pow(Symbol('k', commutative=True), Integer(-1)))"]}, {"premise_expression": "- A + Q m", "variable": "Q", "positive": "\\frac{Q (- 2 A + Q m)}{2}", "negatives": ["\\frac{m (- 2 A + Q m)}{2}", "\\frac{Q m (- 2 A + Q)}{2}", "\\frac{A (- A + 2 Q m)}{2}", "\\frac{Q^{2} (A + m)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('A', commutative=True)), Mul(Symbol('Q', commutative=True), Symbol('m', commutative=True)))", "srepr_variable": "Symbol('Q', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('A', commutative=True)), Mul(Symbol('Q', commutative=True), Symbol('m', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('A', commutative=True)), Mul(Symbol('Q', commutative=True), Symbol('m', commutative=True))))", "Mul(Rational(1, 2), Symbol('Q', commutative=True), Symbol('m', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('A', commutative=True)), Symbol('Q', commutative=True)))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Mul(Integer(-1), Symbol('A', commutative=True)), Mul(Integer(2), Symbol('Q', commutative=True), Symbol('m', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(2)), Add(Symbol('A', commutative=True), Symbol('m', commutative=True)))"]}, {"premise_expression": "\\frac{I}{k t}", "variable": "k", "positive": "\\frac{I \\log{(k)}}{t}", "negatives": ["\\frac{I \\log{(t)}}{k}", "\\frac{I k^{2} t}{2}", "\\frac{I^{2}}{2 k t}", "\\frac{I k^{2}}{2 t}"], "srepr_premise_expression": "Mul(Symbol('I', commutative=True), Pow(Symbol('k', commutative=True), Integer(-1)), Pow(Symbol('t', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('k', commutative=True)", "srepr_positive": "Mul(Symbol('I', commutative=True), Pow(Symbol('t', commutative=True), Integer(-1)), log(Symbol('k', commutative=True)))", "srepr_negatives": ["Mul(Symbol('I', commutative=True), Pow(Symbol('k', commutative=True), Integer(-1)), log(Symbol('t', commutative=True)))", "Mul(Rational(1, 2), Symbol('I', commutative=True), Pow(Symbol('k', commutative=True), Integer(2)), Symbol('t', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(2)), Pow(Symbol('k', commutative=True), Integer(-1)), Pow(Symbol('t', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Symbol('I', commutative=True), Pow(Symbol('k', commutative=True), Integer(2)), Pow(Symbol('t', commutative=True), Integer(-1)))"]}, {"premise_expression": "F + e^{n}", "variable": "n", "positive": "F n + e^{n}", "negatives": ["F e^{\\frac{n}{F}}", "\\frac{F (F + 2 e^{n})}{2}", "\\frac{n^{2} e^{F}}{2}", "\\frac{n^{2}}{2 F}"], "srepr_premise_expression": "Add(Symbol('F', commutative=True), exp(Symbol('n', commutative=True)))", "srepr_variable": "Symbol('n', commutative=True)", "srepr_positive": "Add(Mul(Symbol('F', commutative=True), Symbol('n', commutative=True)), exp(Symbol('n', commutative=True)))", "srepr_negatives": ["Mul(Symbol('F', commutative=True), exp(Mul(Pow(Symbol('F', commutative=True), Integer(-1)), Symbol('n', commutative=True))))", "Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Symbol('F', commutative=True), Mul(Integer(2), exp(Symbol('n', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('n', commutative=True), Integer(2)), exp(Symbol('F', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('F', commutative=True), Integer(-1)), Pow(Symbol('n', commutative=True), Integer(2)))"]}, {"premise_expression": "\\frac{\\sin{(n)}}{Z}", "variable": "n", "positive": "- \\frac{\\cos{(n)}}{Z}", "negatives": ["\\cos{(Z - n)}", "\\frac{n^{2}}{2 Z}", "\\frac{n (\\log{(n)} - 1)}{Z}", "\\log{(Z)} \\sin{(n)}"], "srepr_premise_expression": "Mul(Pow(Symbol('Z', commutative=True), Integer(-1)), sin(Symbol('n', commutative=True)))", "srepr_variable": "Symbol('n', commutative=True)", "srepr_positive": "Mul(Integer(-1), Pow(Symbol('Z', commutative=True), Integer(-1)), cos(Symbol('n', commutative=True)))", "srepr_negatives": ["cos(Add(Symbol('Z', commutative=True), Mul(Integer(-1), Symbol('n', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('Z', commutative=True), Integer(-1)), Pow(Symbol('n', commutative=True), Integer(2)))", "Mul(Pow(Symbol('Z', commutative=True), Integer(-1)), Symbol('n', commutative=True), Add(log(Symbol('n', commutative=True)), Integer(-1)))", "Mul(log(Symbol('Z', commutative=True)), sin(Symbol('n', commutative=True)))"]}, {"premise_expression": "T \\sin{(D)}", "variable": "T", "positive": "\\frac{T^{2} \\sin{(D)}}{2}", "negatives": ["\\frac{T^{2} \\cos{(D)}}{2}", "\\frac{T^{2} (D - 1)}{2}", "\\frac{T (T + 2 \\sin{(D)})}{2}", "- T \\cos{(D)}"], "srepr_premise_expression": "Mul(Symbol('T', commutative=True), sin(Symbol('D', commutative=True)))", "srepr_variable": "Symbol('T', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('T', commutative=True), Integer(2)), sin(Symbol('D', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('T', commutative=True), Integer(2)), cos(Symbol('D', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('T', commutative=True), Integer(2)), Add(Symbol('D', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Symbol('T', commutative=True), Add(Symbol('T', commutative=True), Mul(Integer(2), sin(Symbol('D', commutative=True)))))", "Mul(Integer(-1), Symbol('T', commutative=True), cos(Symbol('D', commutative=True)))"]}, {"premise_expression": "S - Z", "variable": "S", "positive": "\\frac{S (S - 2 Z)}{2}", "negatives": ["\\frac{S (S + 2 Z)}{2}", "\\frac{Z (2 S - Z)}{2}", "\\frac{S (S + 2 \\log{(Z)})}{2}", "S \\sin{(Z^{Z})}"], "srepr_premise_expression": "Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('Z', commutative=True)))", "srepr_variable": "Symbol('S', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Symbol('S', commutative=True), Mul(Integer(-1), Integer(2), Symbol('Z', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Symbol('S', commutative=True), Mul(Integer(2), Symbol('Z', commutative=True))))", "Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Mul(Integer(2), Symbol('S', commutative=True)), Mul(Integer(-1), Symbol('Z', commutative=True))))", "Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Symbol('S', commutative=True), Mul(Integer(2), log(Symbol('Z', commutative=True)))))", "Mul(Symbol('S', commutative=True), sin(Pow(Symbol('Z', commutative=True), Symbol('Z', commutative=True))))"]}, {"premise_expression": "q + \\log{(f)}", "variable": "q", "positive": "\\frac{q (q + 2 \\log{(f)})}{2}", "negatives": ["\\frac{q (- q + 2 \\sin{(f)})}{2}", "f (q + \\log{(f)} - 1)", "f q - \\cos{(q)}", "f \\log{(q)}"], "srepr_premise_expression": "Add(Symbol('q', commutative=True), log(Symbol('f', commutative=True)))", "srepr_variable": "Symbol('q', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('q', commutative=True), Add(Symbol('q', commutative=True), Mul(Integer(2), log(Symbol('f', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('q', commutative=True), Add(Mul(Integer(-1), Symbol('q', commutative=True)), Mul(Integer(2), sin(Symbol('f', commutative=True)))))", "Mul(Symbol('f', commutative=True), Add(Symbol('q', commutative=True), log(Symbol('f', commutative=True)), Integer(-1)))", "Add(Mul(Symbol('f', commutative=True), Symbol('q', commutative=True)), Mul(Integer(-1), cos(Symbol('q', commutative=True))))", "Mul(Symbol('f', commutative=True), log(Symbol('q', commutative=True)))"]}, {"premise_expression": "Q - b", "variable": "Q", "positive": "\\frac{Q (Q - 2 b)}{2}", "negatives": ["\\frac{b (2 Q - b)}{2}", "\\frac{Q^{2} b}{2}", "\\frac{Q (- Q + 2 \\cos{(b)})}{2}", "\\frac{Q^{2} \\cos{(b)}}{2}"], "srepr_premise_expression": "Add(Symbol('Q', commutative=True), Mul(Integer(-1), Symbol('b', commutative=True)))", "srepr_variable": "Symbol('Q', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Symbol('Q', commutative=True), Mul(Integer(-1), Integer(2), Symbol('b', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('b', commutative=True), Add(Mul(Integer(2), Symbol('Q', commutative=True)), Mul(Integer(-1), Symbol('b', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(2)), Symbol('b', commutative=True))", "Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Mul(Integer(-1), Symbol('Q', commutative=True)), Mul(Integer(2), cos(Symbol('b', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(2)), cos(Symbol('b', commutative=True)))"]}, {"premise_expression": "x y", "variable": "y", "positive": "\\frac{x y^{2}}{2}", "negatives": ["\\frac{x^{2} y}{2}", "\\frac{y^{2}}{2 x}", "x \\log{(y)}", "\\frac{y^{2} \\sin{(x)}}{2}"], "srepr_premise_expression": "Mul(Symbol('x', commutative=True), Symbol('y', commutative=True))", "srepr_variable": "Symbol('y', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('x', commutative=True), Pow(Symbol('y', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('x', commutative=True), Integer(2)), Symbol('y', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('x', commutative=True), Integer(-1)), Pow(Symbol('y', commutative=True), Integer(2)))", "Mul(Symbol('x', commutative=True), log(Symbol('y', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('y', commutative=True), Integer(2)), sin(Symbol('x', commutative=True)))"]}, {"premise_expression": "A - H + z", "variable": "A", "positive": "A (\\frac{A}{2} - H + z)", "negatives": ["\\frac{z (2 A - 2 H + z)}{2}", "\\frac{H (2 A - H + 2 z)}{2}", "\\frac{A^{2} (H + z)}{2}", "\\frac{A (A - 2 H)}{2 z}"], "srepr_premise_expression": "Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('H', commutative=True)), Symbol('z', commutative=True))", "srepr_variable": "Symbol('A', commutative=True)", "srepr_positive": "Mul(Symbol('A', commutative=True), Add(Mul(Rational(1, 2), Symbol('A', commutative=True)), Mul(Integer(-1), Symbol('H', commutative=True)), Symbol('z', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('z', commutative=True), Add(Mul(Integer(2), Symbol('A', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('H', commutative=True)), Symbol('z', commutative=True)))", "Mul(Rational(1, 2), Symbol('H', commutative=True), Add(Mul(Integer(2), Symbol('A', commutative=True)), Mul(Integer(-1), Symbol('H', commutative=True)), Mul(Integer(2), Symbol('z', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2)), Add(Symbol('H', commutative=True), Symbol('z', commutative=True)))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Pow(Symbol('z', commutative=True), Integer(-1)), Add(Symbol('A', commutative=True), Mul(Integer(-1), Integer(2), Symbol('H', commutative=True))))"]}, {"premise_expression": "\\frac{\\sin{(K)}}{r}", "variable": "K", "positive": "- \\frac{\\cos{(K)}}{r}", "negatives": ["r \\log{(K)}", "r e^{\\frac{K}{r}}", "K r - \\cos{(K)}", "\\sin{(K - r)}"], "srepr_premise_expression": "Mul(Pow(Symbol('r', commutative=True), Integer(-1)), sin(Symbol('K', commutative=True)))", "srepr_variable": "Symbol('K', commutative=True)", "srepr_positive": "Mul(Integer(-1), Pow(Symbol('r', commutative=True), Integer(-1)), cos(Symbol('K', commutative=True)))", "srepr_negatives": ["Mul(Symbol('r', commutative=True), log(Symbol('K', commutative=True)))", "Mul(Symbol('r', commutative=True), exp(Mul(Symbol('K', commutative=True), Pow(Symbol('r', commutative=True), Integer(-1)))))", "Add(Mul(Symbol('K', commutative=True), Symbol('r', commutative=True)), Mul(Integer(-1), cos(Symbol('K', commutative=True))))", "sin(Add(Symbol('K', commutative=True), Mul(Integer(-1), Symbol('r', commutative=True))))"]}, {"premise_expression": "- \\sin{(A - y)}", "variable": "A", "positive": "\\cos{(A - y)}", "negatives": ["- \\cos{(A - y)}", "\\sin{(A + y)}", "y \\log{(A)}", "A"], "srepr_premise_expression": "Mul(Integer(-1), sin(Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True)))))", "srepr_variable": "Symbol('A', commutative=True)", "srepr_positive": "cos(Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True)))))", "sin(Add(Symbol('A', commutative=True), Symbol('y', commutative=True)))", "Mul(Symbol('y', commutative=True), log(Symbol('A', commutative=True)))", "Symbol('A', commutative=True)"]}, {"premise_expression": "G + e^{c}", "variable": "G", "positive": "\\frac{G (G + 2 e^{c})}{2}", "negatives": ["\\frac{G (G + 2 \\sin{(c)})}{2}", "G c + e^{c}", "G (- c + \\log{(G^{c})})", "e^{G - c}"], "srepr_premise_expression": "Add(Symbol('G', commutative=True), exp(Symbol('c', commutative=True)))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Symbol('G', commutative=True), Mul(Integer(2), exp(Symbol('c', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Symbol('G', commutative=True), Mul(Integer(2), sin(Symbol('c', commutative=True)))))", "Add(Mul(Symbol('G', commutative=True), Symbol('c', commutative=True)), exp(Symbol('c', commutative=True)))", "Mul(Symbol('G', commutative=True), Add(Mul(Integer(-1), Symbol('c', commutative=True)), log(Pow(Symbol('G', commutative=True), Symbol('c', commutative=True)))))", "exp(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('c', commutative=True))))"]}, {"premise_expression": "C - G", "variable": "C", "positive": "\\frac{C (C - 2 G)}{2}", "negatives": ["\\frac{G (2 C - G)}{2}", "\\frac{C (- C + 2 \\log{(G)})}{2}", "\\sin{(C - G)}", "\\sin{(C + G)}"], "srepr_premise_expression": "Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('G', commutative=True)))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Symbol('C', commutative=True), Mul(Integer(-1), Integer(2), Symbol('G', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Mul(Integer(2), Symbol('C', commutative=True)), Mul(Integer(-1), Symbol('G', commutative=True))))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Mul(Integer(-1), Symbol('C', commutative=True)), Mul(Integer(2), log(Symbol('G', commutative=True)))))", "sin(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('G', commutative=True))))", "sin(Add(Symbol('C', commutative=True), Symbol('G', commutative=True)))"]}, {"premise_expression": "\\frac{l - y}{B}", "variable": "y", "positive": "\\frac{y (2 l - y)}{2 B}", "negatives": ["\\frac{l (l - 2 y)}{2 B}", "\\frac{y (2 B l - y)}{2}", "\\frac{y (2 B + l y)}{2}", "(l - y) \\log{(B)}"], "srepr_premise_expression": "Mul(Pow(Symbol('B', commutative=True), Integer(-1)), Add(Symbol('l', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True))))", "srepr_variable": "Symbol('y', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('B', commutative=True), Integer(-1)), Symbol('y', commutative=True), Add(Mul(Integer(2), Symbol('l', commutative=True)), Mul(Integer(-1), Symbol('y', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('B', commutative=True), Integer(-1)), Symbol('l', commutative=True), Add(Symbol('l', commutative=True), Mul(Integer(-1), Integer(2), Symbol('y', commutative=True))))", "Mul(Rational(1, 2), Symbol('y', commutative=True), Add(Mul(Integer(2), Symbol('B', commutative=True), Symbol('l', commutative=True)), Mul(Integer(-1), Symbol('y', commutative=True))))", "Mul(Rational(1, 2), Symbol('y', commutative=True), Add(Mul(Integer(2), Symbol('B', commutative=True)), Mul(Symbol('l', commutative=True), Symbol('y', commutative=True))))", "Mul(Add(Symbol('l', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True))), log(Symbol('B', commutative=True)))"]}, {"premise_expression": "\\frac{S}{z}", "variable": "S", "positive": "\\frac{S^{2}}{2 z}", "negatives": ["S \\log{(z)}", "\\frac{S (S + 2 z)}{2}", "e^{S - z}", "\\sin{(S + z)}"], "srepr_premise_expression": "Mul(Symbol('S', commutative=True), Pow(Symbol('z', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('S', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('S', commutative=True), Integer(2)), Pow(Symbol('z', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('S', commutative=True), log(Symbol('z', commutative=True)))", "Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Symbol('S', commutative=True), Mul(Integer(2), Symbol('z', commutative=True))))", "exp(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('z', commutative=True))))", "sin(Add(Symbol('S', commutative=True), Symbol('z', commutative=True)))"]}, {"premise_expression": "T \\sin{(N)}", "variable": "T", "positive": "\\frac{T^{2} \\sin{(N)}}{2}", "negatives": ["\\frac{\\sin{(T)}}{N}", "- T \\cos{(N)}", "\\frac{N T^{2}}{2}", "\\log{(T)} \\cos{(N)}"], "srepr_premise_expression": "Mul(Symbol('T', commutative=True), sin(Symbol('N', commutative=True)))", "srepr_variable": "Symbol('T', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('T', commutative=True), Integer(2)), sin(Symbol('N', commutative=True)))", "srepr_negatives": ["Mul(Pow(Symbol('N', commutative=True), Integer(-1)), sin(Symbol('T', commutative=True)))", "Mul(Integer(-1), Symbol('T', commutative=True), cos(Symbol('N', commutative=True)))", "Mul(Rational(1, 2), Symbol('N', commutative=True), Pow(Symbol('T', commutative=True), Integer(2)))", "Mul(log(Symbol('T', commutative=True)), cos(Symbol('N', commutative=True)))"]}, {"premise_expression": "\\frac{B}{s} + I", "variable": "B", "positive": "\\frac{B^{2}}{2 s} + B I", "negatives": ["B \\log{(s)} + I s", "\\frac{B^{2}}{2 I s}", "\\frac{B^{2} (- I + s)}{2}", "B^{2} (\\frac{B}{3} - \\frac{s}{2})"], "srepr_premise_expression": "Add(Mul(Symbol('B', commutative=True), Pow(Symbol('s', commutative=True), Integer(-1))), Symbol('I', commutative=True))", "srepr_variable": "Symbol('B', commutative=True)", "srepr_positive": "Add(Mul(Rational(1, 2), Pow(Symbol('B', commutative=True), Integer(2)), Pow(Symbol('s', commutative=True), Integer(-1))), Mul(Symbol('B', commutative=True), Symbol('I', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('B', commutative=True), log(Symbol('s', commutative=True))), Mul(Symbol('I', commutative=True), Symbol('s', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('B', commutative=True), Integer(2)), Pow(Symbol('I', commutative=True), Integer(-1)), Pow(Symbol('s', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('B', commutative=True), Integer(2)), Add(Mul(Integer(-1), Symbol('I', commutative=True)), Symbol('s', commutative=True)))", "Mul(Pow(Symbol('B', commutative=True), Integer(2)), Add(Mul(Rational(1, 3), Symbol('B', commutative=True)), Mul(Integer(-1), Rational(1, 2), Symbol('s', commutative=True))))"]}, {"premise_expression": "\\frac{P}{F}", "variable": "P", "positive": "\\frac{P^{2}}{2 F}", "negatives": ["P \\log{(F)}", "\\frac{P^{2} \\cos{(F)}}{2}", "- \\frac{\\cos{(P)}}{F}", "F P + e^{P}"], "srepr_premise_expression": "Mul(Pow(Symbol('F', commutative=True), Integer(-1)), Symbol('P', commutative=True))", "srepr_variable": "Symbol('P', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('F', commutative=True), Integer(-1)), Pow(Symbol('P', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('P', commutative=True), log(Symbol('F', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2)), cos(Symbol('F', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('F', commutative=True), Integer(-1)), cos(Symbol('P', commutative=True)))", "Add(Mul(Symbol('F', commutative=True), Symbol('P', commutative=True)), exp(Symbol('P', commutative=True)))"]}, {"premise_expression": "\\frac{J + r}{b}", "variable": "b", "positive": "(J + r) \\log{(b)}", "negatives": ["b - r \\log{(b)}", "- J b + r \\log{(b)}", "\\frac{r (2 J + r)}{2 b}", "\\frac{J (J + 2 r)}{2 b}"], "srepr_premise_expression": "Mul(Pow(Symbol('b', commutative=True), Integer(-1)), Add(Symbol('J', commutative=True), Symbol('r', commutative=True)))", "srepr_variable": "Symbol('b', commutative=True)", "srepr_positive": "Mul(Add(Symbol('J', commutative=True), Symbol('r', commutative=True)), log(Symbol('b', commutative=True)))", "srepr_negatives": ["Add(Symbol('b', commutative=True), Mul(Integer(-1), Symbol('r', commutative=True), log(Symbol('b', commutative=True))))", "Add(Mul(Integer(-1), Symbol('J', commutative=True), Symbol('b', commutative=True)), Mul(Symbol('r', commutative=True), log(Symbol('b', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('b', commutative=True), Integer(-1)), Symbol('r', commutative=True), Add(Mul(Integer(2), Symbol('J', commutative=True)), Symbol('r', commutative=True)))", "Mul(Rational(1, 2), Symbol('J', commutative=True), Pow(Symbol('b', commutative=True), Integer(-1)), Add(Symbol('J', commutative=True), Mul(Integer(2), Symbol('r', commutative=True))))"]}, {"premise_expression": "\\log{(D^{T})}", "variable": "T", "positive": "\\frac{T^{2} \\log{(D)}}{2}", "negatives": ["\\frac{T (- T + 2 \\log{(D)})}{2}", "\\frac{T^{2}}{2 D}", "T (\\log{(\\frac{T}{D})} - 1)", "D (- T + \\log{(D^{T})})"], "srepr_premise_expression": "log(Pow(Symbol('D', commutative=True), Symbol('T', commutative=True)))", "srepr_variable": "Symbol('T', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('T', commutative=True), Integer(2)), log(Symbol('D', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('T', commutative=True), Add(Mul(Integer(-1), Symbol('T', commutative=True)), Mul(Integer(2), log(Symbol('D', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(-1)), Pow(Symbol('T', commutative=True), Integer(2)))", "Mul(Symbol('T', commutative=True), Add(log(Mul(Pow(Symbol('D', commutative=True), Integer(-1)), Symbol('T', commutative=True))), Integer(-1)))", "Mul(Symbol('D', commutative=True), Add(Mul(Integer(-1), Symbol('T', commutative=True)), log(Pow(Symbol('D', commutative=True), Symbol('T', commutative=True)))))"]}, {"premise_expression": "q - s", "variable": "q", "positive": "\\frac{q (q - 2 s)}{2}", "negatives": ["\\frac{s (2 q - s)}{2}", "\\frac{q^{2} s}{2}", "\\frac{q (q + 2 \\cos{(s)})}{2}", "\\sin{(q - s)}"], "srepr_premise_expression": "Add(Symbol('q', commutative=True), Mul(Integer(-1), Symbol('s', commutative=True)))", "srepr_variable": "Symbol('q', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('q', commutative=True), Add(Symbol('q', commutative=True), Mul(Integer(-1), Integer(2), Symbol('s', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('s', commutative=True), Add(Mul(Integer(2), Symbol('q', commutative=True)), Mul(Integer(-1), Symbol('s', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('q', commutative=True), Integer(2)), Symbol('s', commutative=True))", "Mul(Rational(1, 2), Symbol('q', commutative=True), Add(Symbol('q', commutative=True), Mul(Integer(2), cos(Symbol('s', commutative=True)))))", "sin(Add(Symbol('q', commutative=True), Mul(Integer(-1), Symbol('s', commutative=True))))"]}, {"premise_expression": "\\log{(\\frac{z}{n})}", "variable": "n", "positive": "n (\\log{(\\frac{z}{n})} + 1)", "negatives": ["z (\\log{(\\frac{z}{n})} - 1)", "z \\log{(n)}", "\\frac{n^{2}}{2 z}", "z e^{n}"], "srepr_premise_expression": "log(Mul(Pow(Symbol('n', commutative=True), Integer(-1)), Symbol('z', commutative=True)))", "srepr_variable": "Symbol('n', commutative=True)", "srepr_positive": "Mul(Symbol('n', commutative=True), Add(log(Mul(Pow(Symbol('n', commutative=True), Integer(-1)), Symbol('z', commutative=True))), Integer(1)))", "srepr_negatives": ["Mul(Symbol('z', commutative=True), Add(log(Mul(Pow(Symbol('n', commutative=True), Integer(-1)), Symbol('z', commutative=True))), Integer(-1)))", "Mul(Symbol('z', commutative=True), log(Symbol('n', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('n', commutative=True), Integer(2)), Pow(Symbol('z', commutative=True), Integer(-1)))", "Mul(Symbol('z', commutative=True), exp(Symbol('n', commutative=True)))"]}, {"premise_expression": "\\frac{I}{a}", "variable": "I", "positive": "\\frac{I^{2}}{2 a}", "negatives": ["I \\log{(a)}", "\\frac{I (I + 2 a)}{2}", "\\frac{I^{2} \\sin{(a)}}{2}", "e^{I + a}"], "srepr_premise_expression": "Mul(Symbol('I', commutative=True), Pow(Symbol('a', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('I', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(2)), Pow(Symbol('a', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('I', commutative=True), log(Symbol('a', commutative=True)))", "Mul(Rational(1, 2), Symbol('I', commutative=True), Add(Symbol('I', commutative=True), Mul(Integer(2), Symbol('a', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(2)), sin(Symbol('a', commutative=True)))", "exp(Add(Symbol('I', commutative=True), Symbol('a', commutative=True)))"]}, {"premise_expression": "\\log{(- l + s)}", "variable": "l", "positive": "l \\log{(- l + s)} - l - s \\log{(l - s)}", "negatives": ["- l \\log{(- l + s)} + s \\log{(- l + s)} - s", "l (- s + \\log{(l^{s})})", "\\frac{l (- l + 2 \\log{(s)})}{2}", "l (\\log{(\\frac{s}{l})} + 1)"], "srepr_premise_expression": "log(Add(Mul(Integer(-1), Symbol('l', commutative=True)), Symbol('s', commutative=True)))", "srepr_variable": "Symbol('l', commutative=True)", "srepr_positive": "Add(Mul(Symbol('l', commutative=True), log(Add(Mul(Integer(-1), Symbol('l', commutative=True)), Symbol('s', commutative=True)))), Mul(Integer(-1), Symbol('l', commutative=True)), Mul(Integer(-1), Symbol('s', commutative=True), log(Add(Symbol('l', commutative=True), Mul(Integer(-1), Symbol('s', commutative=True))))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('l', commutative=True), log(Add(Mul(Integer(-1), Symbol('l', commutative=True)), Symbol('s', commutative=True)))), Mul(Symbol('s', commutative=True), log(Add(Mul(Integer(-1), Symbol('l', commutative=True)), Symbol('s', commutative=True)))), Mul(Integer(-1), Symbol('s', commutative=True)))", "Mul(Symbol('l', commutative=True), Add(Mul(Integer(-1), Symbol('s', commutative=True)), log(Pow(Symbol('l', commutative=True), Symbol('s', commutative=True)))))", "Mul(Rational(1, 2), Symbol('l', commutative=True), Add(Mul(Integer(-1), Symbol('l', commutative=True)), Mul(Integer(2), log(Symbol('s', commutative=True)))))", "Mul(Symbol('l', commutative=True), Add(log(Mul(Pow(Symbol('l', commutative=True), Integer(-1)), Symbol('s', commutative=True))), Integer(1)))"]}, {"premise_expression": "- A + s + t", "variable": "s", "positive": "s (- A + \\frac{s}{2} + t)", "negatives": ["\\frac{s (2 A + s + 2 t)}{2}", "\\frac{t (- 2 A + 2 s + t)}{2}", "\\frac{A (- A + 2 s + 2 t)}{2}", "s t + \\frac{s^{2}}{2 A}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('A', commutative=True)), Symbol('s', commutative=True), Symbol('t', commutative=True))", "srepr_variable": "Symbol('s', commutative=True)", "srepr_positive": "Mul(Symbol('s', commutative=True), Add(Mul(Integer(-1), Symbol('A', commutative=True)), Mul(Rational(1, 2), Symbol('s', commutative=True)), Symbol('t', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('s', commutative=True), Add(Mul(Integer(2), Symbol('A', commutative=True)), Symbol('s', commutative=True), Mul(Integer(2), Symbol('t', commutative=True))))", "Mul(Rational(1, 2), Symbol('t', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('A', commutative=True)), Mul(Integer(2), Symbol('s', commutative=True)), Symbol('t', commutative=True)))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Mul(Integer(-1), Symbol('A', commutative=True)), Mul(Integer(2), Symbol('s', commutative=True)), Mul(Integer(2), Symbol('t', commutative=True))))", "Add(Mul(Symbol('s', commutative=True), Symbol('t', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(-1)), Pow(Symbol('s', commutative=True), Integer(2))))"]}, {"premise_expression": "\\frac{m}{T}", "variable": "T", "positive": "m \\log{(T)}", "negatives": ["- m \\cos{(T)}", "\\frac{m^{2}}{2 T}", "\\log{(T)} \\log{(m)}", "- T m + e^{T}"], "srepr_premise_expression": "Mul(Pow(Symbol('T', commutative=True), Integer(-1)), Symbol('m', commutative=True))", "srepr_variable": "Symbol('T', commutative=True)", "srepr_positive": "Mul(Symbol('m', commutative=True), log(Symbol('T', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Symbol('m', commutative=True), cos(Symbol('T', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('T', commutative=True), Integer(-1)), Pow(Symbol('m', commutative=True), Integer(2)))", "Mul(log(Symbol('T', commutative=True)), log(Symbol('m', commutative=True)))", "Add(Mul(Integer(-1), Symbol('T', commutative=True), Symbol('m', commutative=True)), exp(Symbol('T', commutative=True)))"]}, {"premise_expression": "- Y + p q", "variable": "q", "positive": "\\frac{q (- 2 Y + p q)}{2}", "negatives": ["\\frac{p (- 2 Y + p q)}{2}", "\\frac{Y (- Y + 2 p q)}{2}", "\\frac{Y q (- 2 p + q)}{2}", "Y \\log{(q)} + p q"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('Y', commutative=True)), Mul(Symbol('p', commutative=True), Symbol('q', commutative=True)))", "srepr_variable": "Symbol('q', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('q', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('Y', commutative=True)), Mul(Symbol('p', commutative=True), Symbol('q', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('Y', commutative=True)), Mul(Symbol('p', commutative=True), Symbol('q', commutative=True))))", "Mul(Rational(1, 2), Symbol('Y', commutative=True), Add(Mul(Integer(-1), Symbol('Y', commutative=True)), Mul(Integer(2), Symbol('p', commutative=True), Symbol('q', commutative=True))))", "Mul(Rational(1, 2), Symbol('Y', commutative=True), Symbol('q', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('p', commutative=True)), Symbol('q', commutative=True)))", "Add(Mul(Symbol('Y', commutative=True), log(Symbol('q', commutative=True))), Mul(Symbol('p', commutative=True), Symbol('q', commutative=True)))"]}, {"premise_expression": "- Q + \\sin{(a)}", "variable": "Q", "positive": "\\frac{Q (- Q + 2 \\sin{(a)})}{2}", "negatives": ["\\frac{Q (- Q + 2 \\log{(Q)} - 2)}{2}", "- Q a - \\cos{(a)}", "\\sin{(Q + a)}", "e^{Q + a}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('Q', commutative=True)), sin(Symbol('a', commutative=True)))", "srepr_variable": "Symbol('Q', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Mul(Integer(-1), Symbol('Q', commutative=True)), Mul(Integer(2), sin(Symbol('a', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Mul(Integer(-1), Symbol('Q', commutative=True)), Mul(Integer(2), log(Symbol('Q', commutative=True))), Integer(-2)))", "Add(Mul(Integer(-1), Symbol('Q', commutative=True), Symbol('a', commutative=True)), Mul(Integer(-1), cos(Symbol('a', commutative=True))))", "sin(Add(Symbol('Q', commutative=True), Symbol('a', commutative=True)))", "exp(Add(Symbol('Q', commutative=True), Symbol('a', commutative=True)))"]}, {"premise_expression": "e^{N + X}", "variable": "N", "positive": "e^{N + X}", "negatives": ["\\sin{(N + X)}", "\\frac{N (- N + 2 X)}{2}", "\\log{(N)} \\cos{(X)}", "- X \\cos{(N)}"], "srepr_premise_expression": "exp(Add(Symbol('N', commutative=True), Symbol('X', commutative=True)))", "srepr_variable": "Symbol('N', commutative=True)", "srepr_positive": "exp(Add(Symbol('N', commutative=True), Symbol('X', commutative=True)))", "srepr_negatives": ["sin(Add(Symbol('N', commutative=True), Symbol('X', commutative=True)))", "Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Mul(Integer(-1), Symbol('N', commutative=True)), Mul(Integer(2), Symbol('X', commutative=True))))", "Mul(log(Symbol('N', commutative=True)), cos(Symbol('X', commutative=True)))", "Mul(Integer(-1), Symbol('X', commutative=True), cos(Symbol('N', commutative=True)))"]}, {"premise_expression": "C + w", "variable": "C", "positive": "\\frac{C (C + 2 w)}{2}", "negatives": ["\\frac{C (C - 2 w)}{2}", "\\frac{w (2 C + w)}{2}", "\\frac{C^{2} \\log{(w)}}{2}", "C \\cos{(w^{2})}"], "srepr_premise_expression": "Add(Symbol('C', commutative=True), Symbol('w', commutative=True))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Symbol('C', commutative=True), Mul(Integer(2), Symbol('w', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Symbol('C', commutative=True), Mul(Integer(-1), Integer(2), Symbol('w', commutative=True))))", "Mul(Rational(1, 2), Symbol('w', commutative=True), Add(Mul(Integer(2), Symbol('C', commutative=True)), Symbol('w', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2)), log(Symbol('w', commutative=True)))", "Mul(Symbol('C', commutative=True), cos(Pow(Symbol('w', commutative=True), Integer(2))))"]}, {"premise_expression": "P x", "variable": "x", "positive": "\\frac{P x^{2}}{2}", "negatives": ["\\frac{P^{2} x}{2}", "P x + \\sin{(x)}", "- P x + \\sin{(x)}", "\\frac{x (- 2 P + x)}{2}"], "srepr_premise_expression": "Mul(Symbol('P', commutative=True), Symbol('x', commutative=True))", "srepr_variable": "Symbol('x', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('P', commutative=True), Pow(Symbol('x', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2)), Symbol('x', commutative=True))", "Add(Mul(Symbol('P', commutative=True), Symbol('x', commutative=True)), sin(Symbol('x', commutative=True)))", "Add(Mul(Integer(-1), Symbol('P', commutative=True), Symbol('x', commutative=True)), sin(Symbol('x', commutative=True)))", "Mul(Rational(1, 2), Symbol('x', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('P', commutative=True)), Symbol('x', commutative=True)))"]}, {"premise_expression": "W e^{q}", "variable": "q", "positive": "W e^{q}", "negatives": ["W q + e^{q}", "\\frac{W^{2} e^{q}}{2}", "- W q + e^{q}", "\\frac{q^{2} e^{W}}{2}"], "srepr_premise_expression": "Mul(Symbol('W', commutative=True), exp(Symbol('q', commutative=True)))", "srepr_variable": "Symbol('q', commutative=True)", "srepr_positive": "Mul(Symbol('W', commutative=True), exp(Symbol('q', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('W', commutative=True), Symbol('q', commutative=True)), exp(Symbol('q', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('W', commutative=True), Integer(2)), exp(Symbol('q', commutative=True)))", "Add(Mul(Integer(-1), Symbol('W', commutative=True), Symbol('q', commutative=True)), exp(Symbol('q', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('q', commutative=True), Integer(2)), exp(Symbol('W', commutative=True)))"]}, {"premise_expression": "G X", "variable": "X", "positive": "\\frac{G X^{2}}{2}", "negatives": ["\\frac{G^{2} X}{2}", "X \\cos{(G^{G})}", "\\frac{X (X + 2 \\sin{(G)})}{2}", "\\frac{X (X + 2 e^{G})}{2}"], "srepr_premise_expression": "Mul(Symbol('G', commutative=True), Symbol('X', commutative=True))", "srepr_variable": "Symbol('X', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('G', commutative=True), Pow(Symbol('X', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(2)), Symbol('X', commutative=True))", "Mul(Symbol('X', commutative=True), cos(Pow(Symbol('G', commutative=True), Symbol('G', commutative=True))))", "Mul(Rational(1, 2), Symbol('X', commutative=True), Add(Symbol('X', commutative=True), Mul(Integer(2), sin(Symbol('G', commutative=True)))))", "Mul(Rational(1, 2), Symbol('X', commutative=True), Add(Symbol('X', commutative=True), Mul(Integer(2), exp(Symbol('G', commutative=True)))))"]}, {"premise_expression": "- V + \\cos{(w)}", "variable": "w", "positive": "- V w + \\sin{(w)}", "negatives": ["V w - \\cos{(w)}", "- \\sin{(V - w)}", "\\frac{w^{2} \\cos{(V)}}{2}", "\\frac{V (- V + 2 \\cos{(w)})}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('V', commutative=True)), cos(Symbol('w', commutative=True)))", "srepr_variable": "Symbol('w', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('V', commutative=True), Symbol('w', commutative=True)), sin(Symbol('w', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('V', commutative=True), Symbol('w', commutative=True)), Mul(Integer(-1), cos(Symbol('w', commutative=True))))", "Mul(Integer(-1), sin(Add(Symbol('V', commutative=True), Mul(Integer(-1), Symbol('w', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('w', commutative=True), Integer(2)), cos(Symbol('V', commutative=True)))", "Mul(Rational(1, 2), Symbol('V', commutative=True), Add(Mul(Integer(-1), Symbol('V', commutative=True)), Mul(Integer(2), cos(Symbol('w', commutative=True)))))"]}, {"premise_expression": "\\frac{b}{y}", "variable": "b", "positive": "\\frac{b^{2}}{2 y}", "negatives": ["b \\log{(y)}", "\\sin{(b - y)}", "\\cos{(b - y)}", "\\frac{b (b + 2 \\log{(y)})}{2}"], "srepr_premise_expression": "Mul(Symbol('b', commutative=True), Pow(Symbol('y', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('b', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('b', commutative=True), Integer(2)), Pow(Symbol('y', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('b', commutative=True), log(Symbol('y', commutative=True)))", "sin(Add(Symbol('b', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True))))", "cos(Add(Symbol('b', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True))))", "Mul(Rational(1, 2), Symbol('b', commutative=True), Add(Symbol('b', commutative=True), Mul(Integer(2), log(Symbol('y', commutative=True)))))"]}, {"premise_expression": "A - V", "variable": "V", "positive": "\\frac{V (2 A - V)}{2}", "negatives": ["\\frac{V (2 A + V)}{2}", "\\frac{A (A - 2 V)}{2}", "- \\sin{(A - V)}", "\\frac{A V^{2}}{2}"], "srepr_premise_expression": "Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('V', commutative=True)))", "srepr_variable": "Symbol('V', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('V', commutative=True), Add(Mul(Integer(2), Symbol('A', commutative=True)), Mul(Integer(-1), Symbol('V', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('V', commutative=True), Add(Mul(Integer(2), Symbol('A', commutative=True)), Symbol('V', commutative=True)))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Symbol('A', commutative=True), Mul(Integer(-1), Integer(2), Symbol('V', commutative=True))))", "Mul(Integer(-1), sin(Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('V', commutative=True)))))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Pow(Symbol('V', commutative=True), Integer(2)))"]}, {"premise_expression": "X (C + W)", "variable": "C", "positive": "\\frac{C X (C + 2 W)}{2}", "negatives": ["\\frac{C W (C + 2 X)}{2}", "\\frac{C W (- C + 2 X)}{2}", "\\frac{W X (2 C + W)}{2}", "\\frac{X^{2} (C + W)}{2}"], "srepr_premise_expression": "Mul(Symbol('X', commutative=True), Add(Symbol('C', commutative=True), Symbol('W', commutative=True)))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('C', commutative=True), Symbol('X', commutative=True), Add(Symbol('C', commutative=True), Mul(Integer(2), Symbol('W', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('C', commutative=True), Symbol('W', commutative=True), Add(Symbol('C', commutative=True), Mul(Integer(2), Symbol('X', commutative=True))))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Symbol('W', commutative=True), Add(Mul(Integer(-1), Symbol('C', commutative=True)), Mul(Integer(2), Symbol('X', commutative=True))))", "Mul(Rational(1, 2), Symbol('W', commutative=True), Symbol('X', commutative=True), Add(Mul(Integer(2), Symbol('C', commutative=True)), Symbol('W', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('X', commutative=True), Integer(2)), Add(Symbol('C', commutative=True), Symbol('W', commutative=True)))"]}, {"premise_expression": "A - P", "variable": "A", "positive": "\\frac{A (A - 2 P)}{2}", "negatives": ["\\frac{A (A + 2 P)}{2}", "\\frac{A P (A + 2 P)}{2}", "\\frac{P (2 A - P)}{2}", "A P + \\sin{(A)}"], "srepr_premise_expression": "Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('P', commutative=True)))", "srepr_variable": "Symbol('A', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Symbol('A', commutative=True), Mul(Integer(-1), Integer(2), Symbol('P', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Symbol('A', commutative=True), Mul(Integer(2), Symbol('P', commutative=True))))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Symbol('P', commutative=True), Add(Symbol('A', commutative=True), Mul(Integer(2), Symbol('P', commutative=True))))", "Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Mul(Integer(2), Symbol('A', commutative=True)), Mul(Integer(-1), Symbol('P', commutative=True))))", "Add(Mul(Symbol('A', commutative=True), Symbol('P', commutative=True)), sin(Symbol('A', commutative=True)))"]}, {"premise_expression": "\\frac{N r}{Y}", "variable": "r", "positive": "\\frac{N r^{2}}{2 Y}", "negatives": ["\\frac{N^{2} r}{2 Y}", "\\frac{r^{2}}{2 N Y}", "N r \\log{(Y)}", "Y r + \\frac{r^{2}}{2 N}"], "srepr_premise_expression": "Mul(Symbol('N', commutative=True), Pow(Symbol('Y', commutative=True), Integer(-1)), Symbol('r', commutative=True))", "srepr_variable": "Symbol('r', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('N', commutative=True), Pow(Symbol('Y', commutative=True), Integer(-1)), Pow(Symbol('r', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('N', commutative=True), Integer(2)), Pow(Symbol('Y', commutative=True), Integer(-1)), Symbol('r', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('N', commutative=True), Integer(-1)), Pow(Symbol('Y', commutative=True), Integer(-1)), Pow(Symbol('r', commutative=True), Integer(2)))", "Mul(Symbol('N', commutative=True), Symbol('r', commutative=True), log(Symbol('Y', commutative=True)))", "Add(Mul(Symbol('Y', commutative=True), Symbol('r', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('N', commutative=True), Integer(-1)), Pow(Symbol('r', commutative=True), Integer(2))))"]}, {"premise_expression": "- h + \\sin{(J)}", "variable": "h", "positive": "\\frac{h (- h + 2 \\sin{(J)})}{2}", "negatives": ["\\frac{h^{2} \\cos{(J)}}{2}", "- J h - \\cos{(J)}", "h (- J + \\log{(h)} - 1)", "- J h - \\cos{(h)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('h', commutative=True)), sin(Symbol('J', commutative=True)))", "srepr_variable": "Symbol('h', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('h', commutative=True), Add(Mul(Integer(-1), Symbol('h', commutative=True)), Mul(Integer(2), sin(Symbol('J', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('h', commutative=True), Integer(2)), cos(Symbol('J', commutative=True)))", "Add(Mul(Integer(-1), Symbol('J', commutative=True), Symbol('h', commutative=True)), Mul(Integer(-1), cos(Symbol('J', commutative=True))))", "Mul(Symbol('h', commutative=True), Add(Mul(Integer(-1), Symbol('J', commutative=True)), log(Symbol('h', commutative=True)), Integer(-1)))", "Add(Mul(Integer(-1), Symbol('J', commutative=True), Symbol('h', commutative=True)), Mul(Integer(-1), cos(Symbol('h', commutative=True))))"]}, {"premise_expression": "\\frac{- V + n}{I}", "variable": "V", "positive": "\\frac{V (- V + 2 n)}{2 I}", "negatives": ["\\frac{n (- 2 V + n)}{2 I}", "(- V + n) \\log{(I)}", "\\frac{I V^{2}}{2 n}", "- I V + n \\log{(V)}"], "srepr_premise_expression": "Mul(Pow(Symbol('I', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('V', commutative=True)), Symbol('n', commutative=True)))", "srepr_variable": "Symbol('V', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(-1)), Symbol('V', commutative=True), Add(Mul(Integer(-1), Symbol('V', commutative=True)), Mul(Integer(2), Symbol('n', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(-1)), Symbol('n', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('V', commutative=True)), Symbol('n', commutative=True)))", "Mul(Add(Mul(Integer(-1), Symbol('V', commutative=True)), Symbol('n', commutative=True)), log(Symbol('I', commutative=True)))", "Mul(Rational(1, 2), Symbol('I', commutative=True), Pow(Symbol('V', commutative=True), Integer(2)), Pow(Symbol('n', commutative=True), Integer(-1)))", "Add(Mul(Integer(-1), Symbol('I', commutative=True), Symbol('V', commutative=True)), Mul(Symbol('n', commutative=True), log(Symbol('V', commutative=True))))"]}, {"premise_expression": "\\frac{B^{m}}{o}", "variable": "o", "positive": "B^{m} \\log{(o)}", "negatives": ["\\frac{B m o^{2}}{2}", "B \\log{(o)} + m o", "\\frac{o^{2} (B - m)}{2}", "\\frac{o (2 m^{B} - o)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('B', commutative=True), Symbol('m', commutative=True)), Pow(Symbol('o', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('o', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('B', commutative=True), Symbol('m', commutative=True)), log(Symbol('o', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('B', commutative=True), Symbol('m', commutative=True), Pow(Symbol('o', commutative=True), Integer(2)))", "Add(Mul(Symbol('B', commutative=True), log(Symbol('o', commutative=True))), Mul(Symbol('m', commutative=True), Symbol('o', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('o', commutative=True), Integer(2)), Add(Symbol('B', commutative=True), Mul(Integer(-1), Symbol('m', commutative=True))))", "Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Mul(Integer(2), Pow(Symbol('m', commutative=True), Symbol('B', commutative=True))), Mul(Integer(-1), Symbol('o', commutative=True))))"]}, {"premise_expression": "\\frac{D v}{p}", "variable": "D", "positive": "\\frac{D^{2} v}{2 p}", "negatives": ["\\frac{D v^{2}}{2 p}", "D v \\log{(p)}", "\\frac{D v (- D + 2 p)}{2}", "\\frac{D (D p - 2 v)}{2}"], "srepr_premise_expression": "Mul(Symbol('D', commutative=True), Pow(Symbol('p', commutative=True), Integer(-1)), Symbol('v', commutative=True))", "srepr_variable": "Symbol('D', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(2)), Pow(Symbol('p', commutative=True), Integer(-1)), Symbol('v', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('D', commutative=True), Pow(Symbol('p', commutative=True), Integer(-1)), Pow(Symbol('v', commutative=True), Integer(2)))", "Mul(Symbol('D', commutative=True), Symbol('v', commutative=True), log(Symbol('p', commutative=True)))", "Mul(Rational(1, 2), Symbol('D', commutative=True), Symbol('v', commutative=True), Add(Mul(Integer(-1), Symbol('D', commutative=True)), Mul(Integer(2), Symbol('p', commutative=True))))", "Mul(Rational(1, 2), Symbol('D', commutative=True), Add(Mul(Symbol('D', commutative=True), Symbol('p', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('v', commutative=True))))"]}, {"premise_expression": "\\frac{u}{p}", "variable": "p", "positive": "u \\log{(p)}", "negatives": ["u \\sin{(p)}", "\\frac{u^{2}}{2 p}", "\\frac{p^{2} \\log{(u)}}{2}", "\\frac{p^{2} u}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('p', commutative=True), Integer(-1)), Symbol('u', commutative=True))", "srepr_variable": "Symbol('p', commutative=True)", "srepr_positive": "Mul(Symbol('u', commutative=True), log(Symbol('p', commutative=True)))", "srepr_negatives": ["Mul(Symbol('u', commutative=True), sin(Symbol('p', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('p', commutative=True), Integer(-1)), Pow(Symbol('u', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('p', commutative=True), Integer(2)), log(Symbol('u', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('p', commutative=True), Integer(2)), Symbol('u', commutative=True))"]}, {"premise_expression": "\\frac{H T}{G}", "variable": "T", "positive": "\\frac{H T^{2}}{2 G}", "negatives": ["\\frac{H^{2} T}{2 G}", "H T \\log{(G)}", "G T + \\frac{T^{2}}{2 H}", "\\frac{G^{H} T^{2}}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('G', commutative=True), Integer(-1)), Symbol('H', commutative=True), Symbol('T', commutative=True))", "srepr_variable": "Symbol('T', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(-1)), Symbol('H', commutative=True), Pow(Symbol('T', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(-1)), Pow(Symbol('H', commutative=True), Integer(2)), Symbol('T', commutative=True))", "Mul(Symbol('H', commutative=True), Symbol('T', commutative=True), log(Symbol('G', commutative=True)))", "Add(Mul(Symbol('G', commutative=True), Symbol('T', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('H', commutative=True), Integer(-1)), Pow(Symbol('T', commutative=True), Integer(2))))", "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Symbol('H', commutative=True)), Pow(Symbol('T', commutative=True), Integer(2)))"]}, {"premise_expression": "\\log{(S + X)}", "variable": "X", "positive": "S \\log{(S + X)} + X \\log{(S + X)} - X", "negatives": ["S \\log{(S + X)} - S + X \\log{(S + X)}", "- S \\operatorname{Ei}{(\\frac{S}{X})} + X e^{\\frac{S}{X}}", "X (\\log{(S X)} - 1)", "X (\\log{(\\frac{S}{X})} + 1)"], "srepr_premise_expression": "log(Add(Symbol('S', commutative=True), Symbol('X', commutative=True)))", "srepr_variable": "Symbol('X', commutative=True)", "srepr_positive": "Add(Mul(Symbol('S', commutative=True), log(Add(Symbol('S', commutative=True), Symbol('X', commutative=True)))), Mul(Symbol('X', commutative=True), log(Add(Symbol('S', commutative=True), Symbol('X', commutative=True)))), Mul(Integer(-1), Symbol('X', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('S', commutative=True), log(Add(Symbol('S', commutative=True), Symbol('X', commutative=True)))), Mul(Integer(-1), Symbol('S', commutative=True)), Mul(Symbol('X', commutative=True), log(Add(Symbol('S', commutative=True), Symbol('X', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('S', commutative=True), Ei(Mul(Symbol('S', commutative=True), Pow(Symbol('X', commutative=True), Integer(-1))))), Mul(Symbol('X', commutative=True), exp(Mul(Symbol('S', commutative=True), Pow(Symbol('X', commutative=True), Integer(-1))))))", "Mul(Symbol('X', commutative=True), Add(log(Mul(Symbol('S', commutative=True), Symbol('X', commutative=True))), Integer(-1)))", "Mul(Symbol('X', commutative=True), Add(log(Mul(Symbol('S', commutative=True), Pow(Symbol('X', commutative=True), Integer(-1)))), Integer(1)))"]}, {"premise_expression": "\\frac{U n}{f}", "variable": "U", "positive": "\\frac{U^{2} n}{2 f}", "negatives": ["\\frac{U n^{2}}{2 f}", "\\frac{U^{2} f n}{2}", "U n \\log{(f)}", "\\frac{U (U n - 2 f)}{2}"], "srepr_premise_expression": "Mul(Symbol('U', commutative=True), Pow(Symbol('f', commutative=True), Integer(-1)), Symbol('n', commutative=True))", "srepr_variable": "Symbol('U', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('U', commutative=True), Integer(2)), Pow(Symbol('f', commutative=True), Integer(-1)), Symbol('n', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('U', commutative=True), Pow(Symbol('f', commutative=True), Integer(-1)), Pow(Symbol('n', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('U', commutative=True), Integer(2)), Symbol('f', commutative=True), Symbol('n', commutative=True))", "Mul(Symbol('U', commutative=True), Symbol('n', commutative=True), log(Symbol('f', commutative=True)))", "Mul(Rational(1, 2), Symbol('U', commutative=True), Add(Mul(Symbol('U', commutative=True), Symbol('n', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('f', commutative=True))))"]}, {"premise_expression": "K - r", "variable": "r", "positive": "\\frac{r (2 K - r)}{2}", "negatives": ["\\frac{K (K - 2 r)}{2}", "K \\log{(r)}", "\\frac{r (r + 2 \\log{(K)})}{2}", "K r + \\sin{(r)}"], "srepr_premise_expression": "Add(Symbol('K', commutative=True), Mul(Integer(-1), Symbol('r', commutative=True)))", "srepr_variable": "Symbol('r', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(2), Symbol('K', commutative=True)), Mul(Integer(-1), Symbol('r', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Symbol('K', commutative=True), Mul(Integer(-1), Integer(2), Symbol('r', commutative=True))))", "Mul(Symbol('K', commutative=True), log(Symbol('r', commutative=True)))", "Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Symbol('r', commutative=True), Mul(Integer(2), log(Symbol('K', commutative=True)))))", "Add(Mul(Symbol('K', commutative=True), Symbol('r', commutative=True)), sin(Symbol('r', commutative=True)))"]}, {"premise_expression": "- g + m", "variable": "g", "positive": "\\frac{g (- g + 2 m)}{2}", "negatives": ["\\frac{m (- 2 g + m)}{2}", "\\frac{g^{2} e^{m}}{2}", "\\frac{g^{2} \\log{(m)}}{2}", "\\frac{g (\\log{(g)} - 1)}{m}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('g', commutative=True)), Symbol('m', commutative=True))", "srepr_variable": "Symbol('g', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Mul(Integer(-1), Symbol('g', commutative=True)), Mul(Integer(2), Symbol('m', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('g', commutative=True)), Symbol('m', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('g', commutative=True), Integer(2)), exp(Symbol('m', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('g', commutative=True), Integer(2)), log(Symbol('m', commutative=True)))", "Mul(Symbol('g', commutative=True), Pow(Symbol('m', commutative=True), Integer(-1)), Add(log(Symbol('g', commutative=True)), Integer(-1)))"]}, {"premise_expression": "U n", "variable": "U", "positive": "\\frac{U^{2} n}{2}", "negatives": ["\\frac{U n^{2}}{2}", "\\frac{U \\cos{(n)}}{n}", "U e^{n^{2}}", "n e^{U}"], "srepr_premise_expression": "Mul(Symbol('U', commutative=True), Symbol('n', commutative=True))", "srepr_variable": "Symbol('U', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('U', commutative=True), Integer(2)), Symbol('n', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('U', commutative=True), Pow(Symbol('n', commutative=True), Integer(2)))", "Mul(Symbol('U', commutative=True), Pow(Symbol('n', commutative=True), Integer(-1)), cos(Symbol('n', commutative=True)))", "Mul(Symbol('U', commutative=True), exp(Pow(Symbol('n', commutative=True), Integer(2))))", "Mul(Symbol('n', commutative=True), exp(Symbol('U', commutative=True)))"]}, {"premise_expression": "u \\log{(Y)}", "variable": "Y", "positive": "Y u (\\log{(Y)} - 1)", "negatives": ["\\frac{u^{2} \\log{(Y)}}{2}", "Y u - \\cos{(Y)}", "u e^{Y}", "e^{u} \\log{(Y)}"], "srepr_premise_expression": "Mul(Symbol('u', commutative=True), log(Symbol('Y', commutative=True)))", "srepr_variable": "Symbol('Y', commutative=True)", "srepr_positive": "Mul(Symbol('Y', commutative=True), Symbol('u', commutative=True), Add(log(Symbol('Y', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('u', commutative=True), Integer(2)), log(Symbol('Y', commutative=True)))", "Add(Mul(Symbol('Y', commutative=True), Symbol('u', commutative=True)), Mul(Integer(-1), cos(Symbol('Y', commutative=True))))", "Mul(Symbol('u', commutative=True), exp(Symbol('Y', commutative=True)))", "Mul(exp(Symbol('u', commutative=True)), log(Symbol('Y', commutative=True)))"]}, {"premise_expression": "2 G - s", "variable": "s", "positive": "\\frac{s (4 G - s)}{2}", "negatives": ["G (G - s)", "\\frac{s^{2} \\log{(G)}}{2}", "e^{G + s}", "\\frac{s (\\log{(s)} - 1)}{G}"], "srepr_premise_expression": "Add(Mul(Integer(2), Symbol('G', commutative=True)), Mul(Integer(-1), Symbol('s', commutative=True)))", "srepr_variable": "Symbol('s', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('s', commutative=True), Add(Mul(Integer(4), Symbol('G', commutative=True)), Mul(Integer(-1), Symbol('s', commutative=True))))", "srepr_negatives": ["Mul(Symbol('G', commutative=True), Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('s', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('s', commutative=True), Integer(2)), log(Symbol('G', commutative=True)))", "exp(Add(Symbol('G', commutative=True), Symbol('s', commutative=True)))", "Mul(Pow(Symbol('G', commutative=True), Integer(-1)), Symbol('s', commutative=True), Add(log(Symbol('s', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\frac{- F + K}{m}", "variable": "m", "positive": "(- F + K) \\log{(m)}", "negatives": ["- \\frac{K (2 F - K)}{2 m}", "- \\frac{F (F - 2 K)}{2 m}", "\\frac{m (2 F + 2 K + m)}{2}", "\\frac{m (- 2 F - 2 K + m)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('m', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('F', commutative=True)), Symbol('K', commutative=True)))", "srepr_variable": "Symbol('m', commutative=True)", "srepr_positive": "Mul(Add(Mul(Integer(-1), Symbol('F', commutative=True)), Symbol('K', commutative=True)), log(Symbol('m', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Rational(1, 2), Symbol('K', commutative=True), Pow(Symbol('m', commutative=True), Integer(-1)), Add(Mul(Integer(2), Symbol('F', commutative=True)), Mul(Integer(-1), Symbol('K', commutative=True))))", "Mul(Integer(-1), Rational(1, 2), Symbol('F', commutative=True), Pow(Symbol('m', commutative=True), Integer(-1)), Add(Symbol('F', commutative=True), Mul(Integer(-1), Integer(2), Symbol('K', commutative=True))))", "Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Mul(Integer(2), Symbol('F', commutative=True)), Mul(Integer(2), Symbol('K', commutative=True)), Symbol('m', commutative=True)))", "Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('F', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('K', commutative=True)), Symbol('m', commutative=True)))"]}, {"premise_expression": "\\frac{e^{M}}{C}", "variable": "C", "positive": "e^{M} \\log{(C)}", "negatives": ["M \\log{(C)}", "e^{C + M}", "- e^{- C + M}", "C \\log{(M^{M})}"], "srepr_premise_expression": "Mul(Pow(Symbol('C', commutative=True), Integer(-1)), exp(Symbol('M', commutative=True)))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Mul(exp(Symbol('M', commutative=True)), log(Symbol('C', commutative=True)))", "srepr_negatives": ["Mul(Symbol('M', commutative=True), log(Symbol('C', commutative=True)))", "exp(Add(Symbol('C', commutative=True), Symbol('M', commutative=True)))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('C', commutative=True)), Symbol('M', commutative=True))))", "Mul(Symbol('C', commutative=True), log(Pow(Symbol('M', commutative=True), Symbol('M', commutative=True))))"]}, {"premise_expression": "- U + V", "variable": "V", "positive": "\\frac{V (- 2 U + V)}{2}", "negatives": ["\\frac{U (- U + 2 V)}{2}", "- \\cos{(U + V)}", "\\sin{(U + V)}", "- \\sin{(U - V)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('U', commutative=True)), Symbol('V', commutative=True))", "srepr_variable": "Symbol('V', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('V', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('U', commutative=True)), Symbol('V', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('U', commutative=True), Add(Mul(Integer(-1), Symbol('U', commutative=True)), Mul(Integer(2), Symbol('V', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('U', commutative=True), Symbol('V', commutative=True))))", "sin(Add(Symbol('U', commutative=True), Symbol('V', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('U', commutative=True), Mul(Integer(-1), Symbol('V', commutative=True)))))"]}, {"premise_expression": "\\sin{(X + Z)}", "variable": "Z", "positive": "- \\cos{(X + Z)}", "negatives": ["- X \\cos{(Z)}", "X \\log{(Z)}", "\\frac{Z (2 X - Z)}{2}", "X Z - \\cos{(Z)}"], "srepr_premise_expression": "sin(Add(Symbol('X', commutative=True), Symbol('Z', commutative=True)))", "srepr_variable": "Symbol('Z', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('X', commutative=True), Symbol('Z', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), Symbol('X', commutative=True), cos(Symbol('Z', commutative=True)))", "Mul(Symbol('X', commutative=True), log(Symbol('Z', commutative=True)))", "Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Mul(Integer(2), Symbol('X', commutative=True)), Mul(Integer(-1), Symbol('Z', commutative=True))))", "Add(Mul(Symbol('X', commutative=True), Symbol('Z', commutative=True)), Mul(Integer(-1), cos(Symbol('Z', commutative=True))))"]}, {"premise_expression": "\\frac{p}{j}", "variable": "j", "positive": "p \\log{(j)}", "negatives": ["p e^{j}", "\\frac{p^{2}}{2 j}", "- \\cos{(j + p)}", "\\sin{(j + p)}"], "srepr_premise_expression": "Mul(Pow(Symbol('j', commutative=True), Integer(-1)), Symbol('p', commutative=True))", "srepr_variable": "Symbol('j', commutative=True)", "srepr_positive": "Mul(Symbol('p', commutative=True), log(Symbol('j', commutative=True)))", "srepr_negatives": ["Mul(Symbol('p', commutative=True), exp(Symbol('j', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('j', commutative=True), Integer(-1)), Pow(Symbol('p', commutative=True), Integer(2)))", "Mul(Integer(-1), cos(Add(Symbol('j', commutative=True), Symbol('p', commutative=True))))", "sin(Add(Symbol('j', commutative=True), Symbol('p', commutative=True)))"]}, {"premise_expression": "e^{m + z}", "variable": "m", "positive": "e^{m + z}", "negatives": ["z e^{\\frac{m}{z}}", "e^{z} \\log{(m)}", "\\frac{m (m + 2 \\sin{(z)})}{2}", "\\frac{m (- m + 2 \\sin{(z)})}{2}"], "srepr_premise_expression": "exp(Add(Symbol('m', commutative=True), Symbol('z', commutative=True)))", "srepr_variable": "Symbol('m', commutative=True)", "srepr_positive": "exp(Add(Symbol('m', commutative=True), Symbol('z', commutative=True)))", "srepr_negatives": ["Mul(Symbol('z', commutative=True), exp(Mul(Symbol('m', commutative=True), Pow(Symbol('z', commutative=True), Integer(-1)))))", "Mul(exp(Symbol('z', commutative=True)), log(Symbol('m', commutative=True)))", "Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Symbol('m', commutative=True), Mul(Integer(2), sin(Symbol('z', commutative=True)))))", "Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Mul(Integer(-1), Symbol('m', commutative=True)), Mul(Integer(2), sin(Symbol('z', commutative=True)))))"]}, {"premise_expression": "e^{p + x}", "variable": "x", "positive": "e^{p + x}", "negatives": ["\\frac{x (- 2 p + x)}{2}", "- p x + \\sin{(x)}", "\\frac{x^{2} \\log{(p)}}{2}", "p \\operatorname{Si}{(\\frac{p}{x})} + x \\cos{(\\frac{p}{x})}"], "srepr_premise_expression": "exp(Add(Symbol('p', commutative=True), Symbol('x', commutative=True)))", "srepr_variable": "Symbol('x', commutative=True)", "srepr_positive": "exp(Add(Symbol('p', commutative=True), Symbol('x', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('x', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('p', commutative=True)), Symbol('x', commutative=True)))", "Add(Mul(Integer(-1), Symbol('p', commutative=True), Symbol('x', commutative=True)), sin(Symbol('x', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('x', commutative=True), Integer(2)), log(Symbol('p', commutative=True)))", "Add(Mul(Symbol('p', commutative=True), Si(Mul(Symbol('p', commutative=True), Pow(Symbol('x', commutative=True), Integer(-1))))), Mul(Symbol('x', commutative=True), cos(Mul(Symbol('p', commutative=True), Pow(Symbol('x', commutative=True), Integer(-1))))))"]}, {"premise_expression": "- f - r + w", "variable": "r", "positive": "\\frac{r (- 2 f - r + 2 w)}{2}", "negatives": ["\\frac{f (- f - 2 r + 2 w)}{2}", "\\frac{r (- 2 f + r w)}{2}", "\\frac{w (- 2 f - 2 r + w)}{2}", "\\frac{r^{2} (f + w)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('f', commutative=True)), Mul(Integer(-1), Symbol('r', commutative=True)), Symbol('w', commutative=True))", "srepr_variable": "Symbol('r', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('f', commutative=True)), Mul(Integer(-1), Symbol('r', commutative=True)), Mul(Integer(2), Symbol('w', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Mul(Integer(-1), Symbol('f', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('r', commutative=True)), Mul(Integer(2), Symbol('w', commutative=True))))", "Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('f', commutative=True)), Mul(Symbol('r', commutative=True), Symbol('w', commutative=True))))", "Mul(Rational(1, 2), Symbol('w', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('f', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('r', commutative=True)), Symbol('w', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('r', commutative=True), Integer(2)), Add(Symbol('f', commutative=True), Symbol('w', commutative=True)))"]}, {"premise_expression": "\\frac{z}{q}", "variable": "z", "positive": "\\frac{z^{2}}{2 q}", "negatives": ["z \\log{(q)}", "\\frac{q z^{2}}{2}", "\\frac{z^{2} (q - 1)}{2}", "\\frac{z (2 q + z)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('q', commutative=True), Integer(-1)), Symbol('z', commutative=True))", "srepr_variable": "Symbol('z', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('q', commutative=True), Integer(-1)), Pow(Symbol('z', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('z', commutative=True), log(Symbol('q', commutative=True)))", "Mul(Rational(1, 2), Symbol('q', commutative=True), Pow(Symbol('z', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('z', commutative=True), Integer(2)), Add(Symbol('q', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Symbol('z', commutative=True), Add(Mul(Integer(2), Symbol('q', commutative=True)), Symbol('z', commutative=True)))"]}, {"premise_expression": "F \\log{(r)}", "variable": "F", "positive": "\\frac{F^{2} \\log{(r)}}{2}", "negatives": ["\\frac{F^{2} e^{r}}{2}", "F r (\\log{(r)} - 1)", "e^{r} \\log{(F)}", "- F r - \\cos{(F)}"], "srepr_premise_expression": "Mul(Symbol('F', commutative=True), log(Symbol('r', commutative=True)))", "srepr_variable": "Symbol('F', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('F', commutative=True), Integer(2)), log(Symbol('r', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('F', commutative=True), Integer(2)), exp(Symbol('r', commutative=True)))", "Mul(Symbol('F', commutative=True), Symbol('r', commutative=True), Add(log(Symbol('r', commutative=True)), Integer(-1)))", "Mul(exp(Symbol('r', commutative=True)), log(Symbol('F', commutative=True)))", "Add(Mul(Integer(-1), Symbol('F', commutative=True), Symbol('r', commutative=True)), Mul(Integer(-1), cos(Symbol('F', commutative=True))))"]}, {"premise_expression": "G v + S", "variable": "S", "positive": "\\frac{S (2 G v + S)}{2}", "negatives": ["\\frac{G (G v + 2 S)}{2}", "\\frac{v (G v + 2 S)}{2}", "S (- G + S)", "\\frac{G^{v} S^{2}}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('G', commutative=True), Symbol('v', commutative=True)), Symbol('S', commutative=True))", "srepr_variable": "Symbol('S', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Mul(Integer(2), Symbol('G', commutative=True), Symbol('v', commutative=True)), Symbol('S', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Mul(Symbol('G', commutative=True), Symbol('v', commutative=True)), Mul(Integer(2), Symbol('S', commutative=True))))", "Mul(Rational(1, 2), Symbol('v', commutative=True), Add(Mul(Symbol('G', commutative=True), Symbol('v', commutative=True)), Mul(Integer(2), Symbol('S', commutative=True))))", "Mul(Symbol('S', commutative=True), Add(Mul(Integer(-1), Symbol('G', commutative=True)), Symbol('S', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Symbol('v', commutative=True)), Pow(Symbol('S', commutative=True), Integer(2)))"]}, {"premise_expression": "- S + c", "variable": "S", "positive": "\\frac{S (- S + 2 c)}{2}", "negatives": ["\\frac{c (- 2 S + c)}{2}", "\\frac{S (S + 2 e^{c})}{2}", "e^{S + c}", "- \\cos{(S + c)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('S', commutative=True)), Symbol('c', commutative=True))", "srepr_variable": "Symbol('S', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Mul(Integer(-1), Symbol('S', commutative=True)), Mul(Integer(2), Symbol('c', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('c', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('S', commutative=True)), Symbol('c', commutative=True)))", "Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Symbol('S', commutative=True), Mul(Integer(2), exp(Symbol('c', commutative=True)))))", "exp(Add(Symbol('S', commutative=True), Symbol('c', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('S', commutative=True), Symbol('c', commutative=True))))"]}, {"premise_expression": "\\log{(G)}^{U}", "variable": "G", "positive": "(- \\log{(G)})^{- U} \\log{(G)}^{U} \\Gamma(U + 1, - \\log{(G)})", "negatives": ["G \\log{(G - U)} - G - U \\log{(G - U)}", "\\log{(G)} \\cos{(U)}", "G U + \\sin{(G)}", "\\frac{e^{- \\frac{i \\pi}{U}} \\gamma(\\frac{1}{U}, G^{U} e^{i \\pi})}{U}"], "srepr_premise_expression": "Pow(log(Symbol('G', commutative=True)), Symbol('U', commutative=True))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Mul(Pow(Mul(Integer(-1), log(Symbol('G', commutative=True))), Mul(Integer(-1), Symbol('U', commutative=True))), Pow(log(Symbol('G', commutative=True)), Symbol('U', commutative=True)), uppergamma(Add(Symbol('U', commutative=True), Integer(1)), Mul(Integer(-1), log(Symbol('G', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('G', commutative=True), log(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('U', commutative=True))))), Mul(Integer(-1), Symbol('G', commutative=True)), Mul(Integer(-1), Symbol('U', commutative=True), log(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('U', commutative=True))))))", "Mul(log(Symbol('G', commutative=True)), cos(Symbol('U', commutative=True)))", "Add(Mul(Symbol('G', commutative=True), Symbol('U', commutative=True)), sin(Symbol('G', commutative=True)))", "Mul(Pow(Symbol('U', commutative=True), Integer(-1)), exp(Mul(Integer(-1), I, pi, Pow(Symbol('U', commutative=True), Integer(-1)))), lowergamma(Pow(Symbol('U', commutative=True), Integer(-1)), Mul(Pow(Symbol('G', commutative=True), Symbol('U', commutative=True)), exp_polar(Mul(I, pi)))))"]}, {"premise_expression": "e^{- h + v}", "variable": "v", "positive": "e^{- h + v}", "negatives": ["- e^{- h + v}", "- \\sin{(h - v)}", "h \\sin{(v)}", "h v + e^{v}"], "srepr_premise_expression": "exp(Add(Mul(Integer(-1), Symbol('h', commutative=True)), Symbol('v', commutative=True)))", "srepr_variable": "Symbol('v', commutative=True)", "srepr_positive": "exp(Add(Mul(Integer(-1), Symbol('h', commutative=True)), Symbol('v', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('h', commutative=True)), Symbol('v', commutative=True))))", "Mul(Integer(-1), sin(Add(Symbol('h', commutative=True), Mul(Integer(-1), Symbol('v', commutative=True)))))", "Mul(Symbol('h', commutative=True), sin(Symbol('v', commutative=True)))", "Add(Mul(Symbol('h', commutative=True), Symbol('v', commutative=True)), exp(Symbol('v', commutative=True)))"]}, {"premise_expression": "\\sin^{J}{(G)}", "variable": "G", "positive": "\\int \\sin^{J}{(G)} dG", "negatives": ["- G J + \\sin{(G)}", "e^{G - J}", "e^{G + J}", "\\frac{G (- G + 2 e^{J})}{2}"], "srepr_premise_expression": "Pow(sin(Symbol('G', commutative=True)), Symbol('J', commutative=True))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Integral(Pow(sin(Symbol('G', commutative=True)), Symbol('J', commutative=True)), Tuple(Symbol('G', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('G', commutative=True), Symbol('J', commutative=True)), sin(Symbol('G', commutative=True)))", "exp(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('J', commutative=True))))", "exp(Add(Symbol('G', commutative=True), Symbol('J', commutative=True)))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Mul(Integer(-1), Symbol('G', commutative=True)), Mul(Integer(2), exp(Symbol('J', commutative=True)))))"]}, {"premise_expression": "\\frac{P}{c}", "variable": "P", "positive": "\\frac{P^{2}}{2 c}", "negatives": ["P \\log{(c)}", "\\frac{P^{2} c}{2}", "e^{P + c}", "\\frac{P (- P + 2 \\sin{(c)})}{2}"], "srepr_premise_expression": "Mul(Symbol('P', commutative=True), Pow(Symbol('c', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('P', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2)), Pow(Symbol('c', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('P', commutative=True), log(Symbol('c', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2)), Symbol('c', commutative=True))", "exp(Add(Symbol('P', commutative=True), Symbol('c', commutative=True)))", "Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Mul(Integer(-1), Symbol('P', commutative=True)), Mul(Integer(2), sin(Symbol('c', commutative=True)))))"]}, {"premise_expression": "V + \\sin{(E)}", "variable": "E", "positive": "E V - \\cos{(E)}", "negatives": ["\\frac{E^{2} \\log{(V)}}{2}", "\\frac{E (E + 2 V)}{2}", "E \\sin{(2 V)}", "\\frac{E^{2}}{2 V}"], "srepr_premise_expression": "Add(Symbol('V', commutative=True), sin(Symbol('E', commutative=True)))", "srepr_variable": "Symbol('E', commutative=True)", "srepr_positive": "Add(Mul(Symbol('E', commutative=True), Symbol('V', commutative=True)), Mul(Integer(-1), cos(Symbol('E', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('E', commutative=True), Integer(2)), log(Symbol('V', commutative=True)))", "Mul(Rational(1, 2), Symbol('E', commutative=True), Add(Symbol('E', commutative=True), Mul(Integer(2), Symbol('V', commutative=True))))", "Mul(Symbol('E', commutative=True), sin(Mul(Integer(2), Symbol('V', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('E', commutative=True), Integer(2)), Pow(Symbol('V', commutative=True), Integer(-1)))"]}, {"premise_expression": "Z + t", "variable": "t", "positive": "\\frac{t (2 Z + t)}{2}", "negatives": ["\\frac{Z (Z + 2 t)}{2}", "e^{- Z + t}", "\\frac{\\sin{(t)}}{Z}", "\\frac{t (- t + 2 \\sin{(Z)})}{2}"], "srepr_premise_expression": "Add(Symbol('Z', commutative=True), Symbol('t', commutative=True))", "srepr_variable": "Symbol('t', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('t', commutative=True), Add(Mul(Integer(2), Symbol('Z', commutative=True)), Symbol('t', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Symbol('Z', commutative=True), Mul(Integer(2), Symbol('t', commutative=True))))", "exp(Add(Mul(Integer(-1), Symbol('Z', commutative=True)), Symbol('t', commutative=True)))", "Mul(Pow(Symbol('Z', commutative=True), Integer(-1)), sin(Symbol('t', commutative=True)))", "Mul(Rational(1, 2), Symbol('t', commutative=True), Add(Mul(Integer(-1), Symbol('t', commutative=True)), Mul(Integer(2), sin(Symbol('Z', commutative=True)))))"]}, {"premise_expression": "l z + p", "variable": "z", "positive": "\\frac{z (l z + 2 p)}{2}", "negatives": ["\\frac{l (l z + 2 p)}{2}", "\\frac{z (l z - 2 p)}{2}", "\\frac{p (2 l z + p)}{2}", "\\frac{p z (2 l + z)}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('l', commutative=True), Symbol('z', commutative=True)), Symbol('p', commutative=True))", "srepr_variable": "Symbol('z', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('z', commutative=True), Add(Mul(Symbol('l', commutative=True), Symbol('z', commutative=True)), Mul(Integer(2), Symbol('p', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('l', commutative=True), Add(Mul(Symbol('l', commutative=True), Symbol('z', commutative=True)), Mul(Integer(2), Symbol('p', commutative=True))))", "Mul(Rational(1, 2), Symbol('z', commutative=True), Add(Mul(Symbol('l', commutative=True), Symbol('z', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('p', commutative=True))))", "Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Mul(Integer(2), Symbol('l', commutative=True), Symbol('z', commutative=True)), Symbol('p', commutative=True)))", "Mul(Rational(1, 2), Symbol('p', commutative=True), Symbol('z', commutative=True), Add(Mul(Integer(2), Symbol('l', commutative=True)), Symbol('z', commutative=True)))"]}, {"premise_expression": "- h + \\log{(B)}", "variable": "B", "positive": "B (- h + \\log{(B)} - 1)", "negatives": ["B h (\\log{(B)} - 1)", "\\frac{h (- h + 2 \\log{(B)})}{2}", "B h - \\cos{(B)}", "\\frac{B (- B + 2 h)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('h', commutative=True)), log(Symbol('B', commutative=True)))", "srepr_variable": "Symbol('B', commutative=True)", "srepr_positive": "Mul(Symbol('B', commutative=True), Add(Mul(Integer(-1), Symbol('h', commutative=True)), log(Symbol('B', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('B', commutative=True), Symbol('h', commutative=True), Add(log(Symbol('B', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('h', commutative=True), Add(Mul(Integer(-1), Symbol('h', commutative=True)), Mul(Integer(2), log(Symbol('B', commutative=True)))))", "Add(Mul(Symbol('B', commutative=True), Symbol('h', commutative=True)), Mul(Integer(-1), cos(Symbol('B', commutative=True))))", "Mul(Rational(1, 2), Symbol('B', commutative=True), Add(Mul(Integer(-1), Symbol('B', commutative=True)), Mul(Integer(2), Symbol('h', commutative=True))))"]}, {"premise_expression": "R + g - h", "variable": "R", "positive": "R (\\frac{R}{2} + g - h)", "negatives": ["\\frac{R (- R + 2 g + 2 h)}{2}", "\\frac{h (2 R + 2 g - h)}{2}", "\\frac{g (2 R + g - 2 h)}{2}", "\\frac{R^{2}}{2 h} - R g"], "srepr_premise_expression": "Add(Symbol('R', commutative=True), Symbol('g', commutative=True), Mul(Integer(-1), Symbol('h', commutative=True)))", "srepr_variable": "Symbol('R', commutative=True)", "srepr_positive": "Mul(Symbol('R', commutative=True), Add(Mul(Rational(1, 2), Symbol('R', commutative=True)), Symbol('g', commutative=True), Mul(Integer(-1), Symbol('h', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('R', commutative=True), Add(Mul(Integer(-1), Symbol('R', commutative=True)), Mul(Integer(2), Symbol('g', commutative=True)), Mul(Integer(2), Symbol('h', commutative=True))))", "Mul(Rational(1, 2), Symbol('h', commutative=True), Add(Mul(Integer(2), Symbol('R', commutative=True)), Mul(Integer(2), Symbol('g', commutative=True)), Mul(Integer(-1), Symbol('h', commutative=True))))", "Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Mul(Integer(2), Symbol('R', commutative=True)), Symbol('g', commutative=True), Mul(Integer(-1), Integer(2), Symbol('h', commutative=True))))", "Add(Mul(Rational(1, 2), Pow(Symbol('R', commutative=True), Integer(2)), Pow(Symbol('h', commutative=True), Integer(-1))), Mul(Integer(-1), Symbol('R', commutative=True), Symbol('g', commutative=True)))"]}, {"premise_expression": "\\cos^{p}{(I)}", "variable": "I", "positive": "\\int \\cos^{p}{(I)} dI", "negatives": ["- \\cos{(I + p)}", "e^{I - p}", "\\frac{I (I - 2 p)}{2}", "\\frac{I^{2}}{2} + p \\log{(I)}"], "srepr_premise_expression": "Pow(cos(Symbol('I', commutative=True)), Symbol('p', commutative=True))", "srepr_variable": "Symbol('I', commutative=True)", "srepr_positive": "Integral(Pow(cos(Symbol('I', commutative=True)), Symbol('p', commutative=True)), Tuple(Symbol('I', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('I', commutative=True), Symbol('p', commutative=True))))", "exp(Add(Symbol('I', commutative=True), Mul(Integer(-1), Symbol('p', commutative=True))))", "Mul(Rational(1, 2), Symbol('I', commutative=True), Add(Symbol('I', commutative=True), Mul(Integer(-1), Integer(2), Symbol('p', commutative=True))))", "Add(Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(2))), Mul(Symbol('p', commutative=True), log(Symbol('I', commutative=True))))"]}, {"premise_expression": "- m + \\cos{(v)}", "variable": "m", "positive": "\\frac{m (- m + 2 \\cos{(v)})}{2}", "negatives": ["- m v + \\sin{(v)}", "m v + e^{m}", "m (v + \\log{(m)} - 1)", "- v \\cos{(m)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('m', commutative=True)), cos(Symbol('v', commutative=True)))", "srepr_variable": "Symbol('m', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Mul(Integer(-1), Symbol('m', commutative=True)), Mul(Integer(2), cos(Symbol('v', commutative=True)))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('m', commutative=True), Symbol('v', commutative=True)), sin(Symbol('v', commutative=True)))", "Add(Mul(Symbol('m', commutative=True), Symbol('v', commutative=True)), exp(Symbol('m', commutative=True)))", "Mul(Symbol('m', commutative=True), Add(Symbol('v', commutative=True), log(Symbol('m', commutative=True)), Integer(-1)))", "Mul(Integer(-1), Symbol('v', commutative=True), cos(Symbol('m', commutative=True)))"]}, {"premise_expression": "o + p^{a}", "variable": "o", "positive": "\\frac{o (o + 2 p^{a})}{2}", "negatives": ["\\frac{a o (o + 2 p)}{2}", "\\frac{o (o + 2 p)}{2 a}", "\\frac{a o^{2} p}{2}", "\\frac{o^{2} (a + p)}{2}"], "srepr_premise_expression": "Add(Symbol('o', commutative=True), Pow(Symbol('p', commutative=True), Symbol('a', commutative=True)))", "srepr_variable": "Symbol('o', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Symbol('o', commutative=True), Mul(Integer(2), Pow(Symbol('p', commutative=True), Symbol('a', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('a', commutative=True), Symbol('o', commutative=True), Add(Symbol('o', commutative=True), Mul(Integer(2), Symbol('p', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('a', commutative=True), Integer(-1)), Symbol('o', commutative=True), Add(Symbol('o', commutative=True), Mul(Integer(2), Symbol('p', commutative=True))))", "Mul(Rational(1, 2), Symbol('a', commutative=True), Pow(Symbol('o', commutative=True), Integer(2)), Symbol('p', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('o', commutative=True), Integer(2)), Add(Symbol('a', commutative=True), Symbol('p', commutative=True)))"]}, {"premise_expression": "\\log{(- k + l)}", "variable": "k", "positive": "k \\log{(- k + l)} - k - l \\log{(k - l)}", "negatives": ["k \\log{(k - l)} - k - l \\log{(k - l)}", "- k \\log{(- k + l)} + l \\log{(- k + l)} - l", "k (l + \\log{(k)} - 1)", "- k l - \\cos{(k)}"], "srepr_premise_expression": "log(Add(Mul(Integer(-1), Symbol('k', commutative=True)), Symbol('l', commutative=True)))", "srepr_variable": "Symbol('k', commutative=True)", "srepr_positive": "Add(Mul(Symbol('k', commutative=True), log(Add(Mul(Integer(-1), Symbol('k', commutative=True)), Symbol('l', commutative=True)))), Mul(Integer(-1), Symbol('k', commutative=True)), Mul(Integer(-1), Symbol('l', commutative=True), log(Add(Symbol('k', commutative=True), Mul(Integer(-1), Symbol('l', commutative=True))))))", "srepr_negatives": ["Add(Mul(Symbol('k', commutative=True), log(Add(Symbol('k', commutative=True), Mul(Integer(-1), Symbol('l', commutative=True))))), Mul(Integer(-1), Symbol('k', commutative=True)), Mul(Integer(-1), Symbol('l', commutative=True), log(Add(Symbol('k', commutative=True), Mul(Integer(-1), Symbol('l', commutative=True))))))", "Add(Mul(Integer(-1), Symbol('k', commutative=True), log(Add(Mul(Integer(-1), Symbol('k', commutative=True)), Symbol('l', commutative=True)))), Mul(Symbol('l', commutative=True), log(Add(Mul(Integer(-1), Symbol('k', commutative=True)), Symbol('l', commutative=True)))), Mul(Integer(-1), Symbol('l', commutative=True)))", "Mul(Symbol('k', commutative=True), Add(Symbol('l', commutative=True), log(Symbol('k', commutative=True)), Integer(-1)))", "Add(Mul(Integer(-1), Symbol('k', commutative=True), Symbol('l', commutative=True)), Mul(Integer(-1), cos(Symbol('k', commutative=True))))"]}, {"premise_expression": "K n", "variable": "n", "positive": "\\frac{K n^{2}}{2}", "negatives": ["\\frac{K^{2} n}{2}", "- K n + \\sin{(n)}", "\\log{(n)} \\cos{(K)}", "- \\cos{(K + n)}"], "srepr_premise_expression": "Mul(Symbol('K', commutative=True), Symbol('n', commutative=True))", "srepr_variable": "Symbol('n', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('K', commutative=True), Pow(Symbol('n', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('K', commutative=True), Integer(2)), Symbol('n', commutative=True))", "Add(Mul(Integer(-1), Symbol('K', commutative=True), Symbol('n', commutative=True)), sin(Symbol('n', commutative=True)))", "Mul(log(Symbol('n', commutative=True)), cos(Symbol('K', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('K', commutative=True), Symbol('n', commutative=True))))"]}, {"premise_expression": "K e^{F}", "variable": "F", "positive": "K e^{F}", "negatives": ["- K \\cos{(F)}", "\\frac{K^{2} e^{F}}{2}", "- F K + e^{F}", "\\frac{F^{2}}{2 K}"], "srepr_premise_expression": "Mul(Symbol('K', commutative=True), exp(Symbol('F', commutative=True)))", "srepr_variable": "Symbol('F', commutative=True)", "srepr_positive": "Mul(Symbol('K', commutative=True), exp(Symbol('F', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Symbol('K', commutative=True), cos(Symbol('F', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('K', commutative=True), Integer(2)), exp(Symbol('F', commutative=True)))", "Add(Mul(Integer(-1), Symbol('F', commutative=True), Symbol('K', commutative=True)), exp(Symbol('F', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('F', commutative=True), Integer(2)), Pow(Symbol('K', commutative=True), Integer(-1)))"]}, {"premise_expression": "\\sin^{D}{(o)}", "variable": "o", "positive": "\\int \\sin^{D}{(o)} do", "negatives": ["- \\sin{(D - o)}", "o \\sin{(2 D)}", "\\log{(o)} \\cos{(D)}", "o (- D + \\log{(o^{D})})"], "srepr_premise_expression": "Pow(sin(Symbol('o', commutative=True)), Symbol('D', commutative=True))", "srepr_variable": "Symbol('o', commutative=True)", "srepr_positive": "Integral(Pow(sin(Symbol('o', commutative=True)), Symbol('D', commutative=True)), Tuple(Symbol('o', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('D', commutative=True), Mul(Integer(-1), Symbol('o', commutative=True)))))", "Mul(Symbol('o', commutative=True), sin(Mul(Integer(2), Symbol('D', commutative=True))))", "Mul(log(Symbol('o', commutative=True)), cos(Symbol('D', commutative=True)))", "Mul(Symbol('o', commutative=True), Add(Mul(Integer(-1), Symbol('D', commutative=True)), log(Pow(Symbol('o', commutative=True), Symbol('D', commutative=True)))))"]}, {"premise_expression": "Y \\sin{(F)}", "variable": "Y", "positive": "\\frac{Y^{2} \\sin{(F)}}{2}", "negatives": ["\\frac{Y^{2} \\cos{(F)}}{2}", "\\frac{Y^{2} \\log{(F)}}{2}", "\\frac{Y^{2} e^{F}}{2}", "- Y \\cos{(F)}"], "srepr_premise_expression": "Mul(Symbol('Y', commutative=True), sin(Symbol('F', commutative=True)))", "srepr_variable": "Symbol('Y', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('Y', commutative=True), Integer(2)), sin(Symbol('F', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('Y', commutative=True), Integer(2)), cos(Symbol('F', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('Y', commutative=True), Integer(2)), log(Symbol('F', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('Y', commutative=True), Integer(2)), exp(Symbol('F', commutative=True)))", "Mul(Integer(-1), Symbol('Y', commutative=True), cos(Symbol('F', commutative=True)))"]}, {"premise_expression": "e^{a - k}", "variable": "a", "positive": "e^{a - k}", "negatives": ["- e^{a - k}", "- \\cos{(a - k)}", "\\frac{a (a - 2 k)}{2}", "\\log{(a)} \\sin{(k)}"], "srepr_premise_expression": "exp(Add(Symbol('a', commutative=True), Mul(Integer(-1), Symbol('k', commutative=True))))", "srepr_variable": "Symbol('a', commutative=True)", "srepr_positive": "exp(Add(Symbol('a', commutative=True), Mul(Integer(-1), Symbol('k', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Symbol('a', commutative=True), Mul(Integer(-1), Symbol('k', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('a', commutative=True), Mul(Integer(-1), Symbol('k', commutative=True)))))", "Mul(Rational(1, 2), Symbol('a', commutative=True), Add(Symbol('a', commutative=True), Mul(Integer(-1), Integer(2), Symbol('k', commutative=True))))", "Mul(log(Symbol('a', commutative=True)), sin(Symbol('k', commutative=True)))"]}, {"premise_expression": "o t", "variable": "o", "positive": "\\frac{o^{2} t}{2}", "negatives": ["\\frac{o t^{2}}{2}", "\\frac{o^{2}}{2 t}", "\\frac{o^{2}}{2 t} + o", "\\cos{(o - t)}"], "srepr_premise_expression": "Mul(Symbol('o', commutative=True), Symbol('t', commutative=True))", "srepr_variable": "Symbol('o', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('o', commutative=True), Integer(2)), Symbol('t', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('o', commutative=True), Pow(Symbol('t', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('o', commutative=True), Integer(2)), Pow(Symbol('t', commutative=True), Integer(-1)))", "Add(Mul(Rational(1, 2), Pow(Symbol('o', commutative=True), Integer(2)), Pow(Symbol('t', commutative=True), Integer(-1))), Symbol('o', commutative=True))", "cos(Add(Symbol('o', commutative=True), Mul(Integer(-1), Symbol('t', commutative=True))))"]}, {"premise_expression": "H e^{Q}", "variable": "H", "positive": "\\frac{H^{2} e^{Q}}{2}", "negatives": ["\\frac{H^{2} \\sin{(Q)}}{2}", "H e^{Q}", "H Q + e^{H}", "\\frac{\\sin{(H)}}{Q}"], "srepr_premise_expression": "Mul(Symbol('H', commutative=True), exp(Symbol('Q', commutative=True)))", "srepr_variable": "Symbol('H', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('H', commutative=True), Integer(2)), exp(Symbol('Q', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('H', commutative=True), Integer(2)), sin(Symbol('Q', commutative=True)))", "Mul(Symbol('H', commutative=True), exp(Symbol('Q', commutative=True)))", "Add(Mul(Symbol('H', commutative=True), Symbol('Q', commutative=True)), exp(Symbol('H', commutative=True)))", "Mul(Pow(Symbol('Q', commutative=True), Integer(-1)), sin(Symbol('H', commutative=True)))"]}, {"premise_expression": "e^{\\frac{s}{X}}", "variable": "X", "positive": "X e^{\\frac{s}{X}} - s \\operatorname{Ei}{(\\frac{s}{X})}", "negatives": ["X e^{\\frac{s}{X}}", "X \\sin{(X)} + \\cos{(X)}", "X s - \\cos{(X)}", "\\frac{X (X - 2 s)}{2}"], "srepr_premise_expression": "exp(Mul(Pow(Symbol('X', commutative=True), Integer(-1)), Symbol('s', commutative=True)))", "srepr_variable": "Symbol('X', commutative=True)", "srepr_positive": "Add(Mul(Symbol('X', commutative=True), exp(Mul(Pow(Symbol('X', commutative=True), Integer(-1)), Symbol('s', commutative=True)))), Mul(Integer(-1), Symbol('s', commutative=True), Ei(Mul(Pow(Symbol('X', commutative=True), Integer(-1)), Symbol('s', commutative=True)))))", "srepr_negatives": ["Mul(Symbol('X', commutative=True), exp(Mul(Pow(Symbol('X', commutative=True), Integer(-1)), Symbol('s', commutative=True))))", "Add(Mul(Symbol('X', commutative=True), sin(Symbol('X', commutative=True))), cos(Symbol('X', commutative=True)))", "Add(Mul(Symbol('X', commutative=True), Symbol('s', commutative=True)), Mul(Integer(-1), cos(Symbol('X', commutative=True))))", "Mul(Rational(1, 2), Symbol('X', commutative=True), Add(Symbol('X', commutative=True), Mul(Integer(-1), Integer(2), Symbol('s', commutative=True))))"]}, {"premise_expression": "C - l", "variable": "C", "positive": "\\frac{C (C - 2 l)}{2}", "negatives": ["\\frac{l (2 C - l)}{2}", "\\frac{C (C + 2 \\log{(l)})}{2}", "\\frac{C^{2} \\cos{(l)}}{2}", "\\frac{C (- C + 2 \\log{(l)})}{2}"], "srepr_premise_expression": "Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('l', commutative=True)))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Symbol('C', commutative=True), Mul(Integer(-1), Integer(2), Symbol('l', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('l', commutative=True), Add(Mul(Integer(2), Symbol('C', commutative=True)), Mul(Integer(-1), Symbol('l', commutative=True))))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Symbol('C', commutative=True), Mul(Integer(2), log(Symbol('l', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2)), cos(Symbol('l', commutative=True)))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Mul(Integer(-1), Symbol('C', commutative=True)), Mul(Integer(2), log(Symbol('l', commutative=True)))))"]}, {"premise_expression": "\\frac{A g}{L}", "variable": "A", "positive": "\\frac{A^{2} g}{2 L}", "negatives": ["\\frac{A g^{2}}{2 L}", "A g \\log{(L)}", "\\frac{A (A + 2 g)}{2 L}", "L g \\log{(A)}"], "srepr_premise_expression": "Mul(Symbol('A', commutative=True), Pow(Symbol('L', commutative=True), Integer(-1)), Symbol('g', commutative=True))", "srepr_variable": "Symbol('A', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2)), Pow(Symbol('L', commutative=True), Integer(-1)), Symbol('g', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('A', commutative=True), Pow(Symbol('L', commutative=True), Integer(-1)), Pow(Symbol('g', commutative=True), Integer(2)))", "Mul(Symbol('A', commutative=True), Symbol('g', commutative=True), log(Symbol('L', commutative=True)))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Pow(Symbol('L', commutative=True), Integer(-1)), Add(Symbol('A', commutative=True), Mul(Integer(2), Symbol('g', commutative=True))))", "Mul(Symbol('L', commutative=True), Symbol('g', commutative=True), log(Symbol('A', commutative=True)))"]}, {"premise_expression": "H p", "variable": "p", "positive": "\\frac{H p^{2}}{2}", "negatives": ["\\frac{H^{2} p}{2}", "\\frac{p (2 H + p)}{2}", "\\frac{p^{2} e^{H}}{2}", "\\frac{p (- 2 H + p)}{2}"], "srepr_premise_expression": "Mul(Symbol('H', commutative=True), Symbol('p', commutative=True))", "srepr_variable": "Symbol('p', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('H', commutative=True), Pow(Symbol('p', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('H', commutative=True), Integer(2)), Symbol('p', commutative=True))", "Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Mul(Integer(2), Symbol('H', commutative=True)), Symbol('p', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('p', commutative=True), Integer(2)), exp(Symbol('H', commutative=True)))", "Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('H', commutative=True)), Symbol('p', commutative=True)))"]}, {"premise_expression": "J + R z", "variable": "z", "positive": "\\frac{z (2 J + R z)}{2}", "negatives": ["\\frac{R (2 J + R z)}{2}", "\\frac{z^{2} (J + R)}{2}", "\\frac{R z (2 J + z)}{2}", "\\frac{J (J + 2 R z)}{2}"], "srepr_premise_expression": "Add(Symbol('J', commutative=True), Mul(Symbol('R', commutative=True), Symbol('z', commutative=True)))", "srepr_variable": "Symbol('z', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('z', commutative=True), Add(Mul(Integer(2), Symbol('J', commutative=True)), Mul(Symbol('R', commutative=True), Symbol('z', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('R', commutative=True), Add(Mul(Integer(2), Symbol('J', commutative=True)), Mul(Symbol('R', commutative=True), Symbol('z', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('z', commutative=True), Integer(2)), Add(Symbol('J', commutative=True), Symbol('R', commutative=True)))", "Mul(Rational(1, 2), Symbol('R', commutative=True), Symbol('z', commutative=True), Add(Mul(Integer(2), Symbol('J', commutative=True)), Symbol('z', commutative=True)))", "Mul(Rational(1, 2), Symbol('J', commutative=True), Add(Symbol('J', commutative=True), Mul(Integer(2), Symbol('R', commutative=True), Symbol('z', commutative=True))))"]}, {"premise_expression": "- j + \\frac{t}{D}", "variable": "D", "positive": "- D j + t \\log{(D)}", "negatives": ["D t + j \\log{(D)}", "(- j + t) \\log{(D)}", "j t \\log{(D)}", "- j t + \\frac{t^{2}}{2 D}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('j', commutative=True)), Mul(Pow(Symbol('D', commutative=True), Integer(-1)), Symbol('t', commutative=True)))", "srepr_variable": "Symbol('D', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('D', commutative=True), Symbol('j', commutative=True)), Mul(Symbol('t', commutative=True), log(Symbol('D', commutative=True))))", "srepr_negatives": ["Add(Mul(Symbol('D', commutative=True), Symbol('t', commutative=True)), Mul(Symbol('j', commutative=True), log(Symbol('D', commutative=True))))", "Mul(Add(Mul(Integer(-1), Symbol('j', commutative=True)), Symbol('t', commutative=True)), log(Symbol('D', commutative=True)))", "Mul(Symbol('j', commutative=True), Symbol('t', commutative=True), log(Symbol('D', commutative=True)))", "Add(Mul(Integer(-1), Symbol('j', commutative=True), Symbol('t', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(-1)), Pow(Symbol('t', commutative=True), Integer(2))))"]}, {"premise_expression": "- \\sin{(J - z)}", "variable": "z", "positive": "- \\cos{(J - z)}", "negatives": ["\\cos{(J - z)}", "- \\sin{(J - z)}", "- \\frac{\\cos{(z)}}{J}", "e^{- J + z}"], "srepr_premise_expression": "Mul(Integer(-1), sin(Add(Symbol('J', commutative=True), Mul(Integer(-1), Symbol('z', commutative=True)))))", "srepr_variable": "Symbol('z', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('J', commutative=True), Mul(Integer(-1), Symbol('z', commutative=True)))))", "srepr_negatives": ["cos(Add(Symbol('J', commutative=True), Mul(Integer(-1), Symbol('z', commutative=True))))", "Mul(Integer(-1), sin(Add(Symbol('J', commutative=True), Mul(Integer(-1), Symbol('z', commutative=True)))))", "Mul(Integer(-1), Pow(Symbol('J', commutative=True), Integer(-1)), cos(Symbol('z', commutative=True)))", "exp(Add(Mul(Integer(-1), Symbol('J', commutative=True)), Symbol('z', commutative=True)))"]}, {"premise_expression": "A e^{f}", "variable": "A", "positive": "\\frac{A^{2} e^{f}}{2}", "negatives": ["\\frac{A^{2} \\log{(f)}}{2}", "A e^{f}", "f e^{\\frac{A}{f}}", "A \\sin^{f}{(f)}"], "srepr_premise_expression": "Mul(Symbol('A', commutative=True), exp(Symbol('f', commutative=True)))", "srepr_variable": "Symbol('A', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2)), exp(Symbol('f', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2)), log(Symbol('f', commutative=True)))", "Mul(Symbol('A', commutative=True), exp(Symbol('f', commutative=True)))", "Mul(Symbol('f', commutative=True), exp(Mul(Symbol('A', commutative=True), Pow(Symbol('f', commutative=True), Integer(-1)))))", "Mul(Symbol('A', commutative=True), Pow(sin(Symbol('f', commutative=True)), Symbol('f', commutative=True)))"]}, {"premise_expression": "\\sin{(T - o)}", "variable": "T", "positive": "- \\cos{(T - o)}", "negatives": ["\\cos{(T - o)}", "- \\cos{(T + o)}", "\\sin{(T + o)}", "\\frac{\\sin{(T)}}{o}"], "srepr_premise_expression": "sin(Add(Symbol('T', commutative=True), Mul(Integer(-1), Symbol('o', commutative=True))))", "srepr_variable": "Symbol('T', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('T', commutative=True), Mul(Integer(-1), Symbol('o', commutative=True)))))", "srepr_negatives": ["cos(Add(Symbol('T', commutative=True), Mul(Integer(-1), Symbol('o', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('T', commutative=True), Symbol('o', commutative=True))))", "sin(Add(Symbol('T', commutative=True), Symbol('o', commutative=True)))", "Mul(Pow(Symbol('o', commutative=True), Integer(-1)), sin(Symbol('T', commutative=True)))"]}, {"premise_expression": "- n + y", "variable": "y", "positive": "\\frac{y (- 2 n + y)}{2}", "negatives": ["\\frac{n (- n + 2 y)}{2}", "n \\sin{(y)}", "\\frac{n y^{2}}{2}", "n y + \\sin{(y)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('n', commutative=True)), Symbol('y', commutative=True))", "srepr_variable": "Symbol('y', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('y', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('n', commutative=True)), Symbol('y', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('n', commutative=True), Add(Mul(Integer(-1), Symbol('n', commutative=True)), Mul(Integer(2), Symbol('y', commutative=True))))", "Mul(Symbol('n', commutative=True), sin(Symbol('y', commutative=True)))", "Mul(Rational(1, 2), Symbol('n', commutative=True), Pow(Symbol('y', commutative=True), Integer(2)))", "Add(Mul(Symbol('n', commutative=True), Symbol('y', commutative=True)), sin(Symbol('y', commutative=True)))"]}, {"premise_expression": "- W + e^{a}", "variable": "W", "positive": "\\frac{W (- W + 2 e^{a})}{2}", "negatives": ["\\frac{W (- W + 2 \\cos{(a)})}{2}", "\\frac{W (W + 2 a)}{2}", "- W a + e^{a}", "\\sin{(W + a)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('W', commutative=True)), exp(Symbol('a', commutative=True)))", "srepr_variable": "Symbol('W', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('W', commutative=True), Add(Mul(Integer(-1), Symbol('W', commutative=True)), Mul(Integer(2), exp(Symbol('a', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('W', commutative=True), Add(Mul(Integer(-1), Symbol('W', commutative=True)), Mul(Integer(2), cos(Symbol('a', commutative=True)))))", "Mul(Rational(1, 2), Symbol('W', commutative=True), Add(Symbol('W', commutative=True), Mul(Integer(2), Symbol('a', commutative=True))))", "Add(Mul(Integer(-1), Symbol('W', commutative=True), Symbol('a', commutative=True)), exp(Symbol('a', commutative=True)))", "sin(Add(Symbol('W', commutative=True), Symbol('a', commutative=True)))"]}, {"premise_expression": "\\log{(R^{j})}", "variable": "j", "positive": "\\frac{j^{2} \\log{(R)}}{2}", "negatives": ["\\frac{j \\sin{(R)}}{R}", "\\frac{j (- j + 2 e^{R})}{2}", "j (- R + \\log{(j^{R})})", "R (- j + \\log{(R^{j})})"], "srepr_premise_expression": "log(Pow(Symbol('R', commutative=True), Symbol('j', commutative=True)))", "srepr_variable": "Symbol('j', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('j', commutative=True), Integer(2)), log(Symbol('R', commutative=True)))", "srepr_negatives": ["Mul(Pow(Symbol('R', commutative=True), Integer(-1)), Symbol('j', commutative=True), sin(Symbol('R', commutative=True)))", "Mul(Rational(1, 2), Symbol('j', commutative=True), Add(Mul(Integer(-1), Symbol('j', commutative=True)), Mul(Integer(2), exp(Symbol('R', commutative=True)))))", "Mul(Symbol('j', commutative=True), Add(Mul(Integer(-1), Symbol('R', commutative=True)), log(Pow(Symbol('j', commutative=True), Symbol('R', commutative=True)))))", "Mul(Symbol('R', commutative=True), Add(Mul(Integer(-1), Symbol('j', commutative=True)), log(Pow(Symbol('R', commutative=True), Symbol('j', commutative=True)))))"]}, {"premise_expression": "\\frac{l}{A P}", "variable": "l", "positive": "\\frac{l^{2}}{2 A P}", "negatives": ["\\frac{l \\log{(A)}}{P}", "\\frac{l^{2}}{2} + \\frac{P l}{A}", "\\frac{l \\log{(P)}}{A}", "\\frac{P l (2 A + l)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('A', commutative=True), Integer(-1)), Pow(Symbol('P', commutative=True), Integer(-1)), Symbol('l', commutative=True))", "srepr_variable": "Symbol('l', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(-1)), Pow(Symbol('P', commutative=True), Integer(-1)), Pow(Symbol('l', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Pow(Symbol('P', commutative=True), Integer(-1)), Symbol('l', commutative=True), log(Symbol('A', commutative=True)))", "Add(Mul(Rational(1, 2), Pow(Symbol('l', commutative=True), Integer(2))), Mul(Pow(Symbol('A', commutative=True), Integer(-1)), Symbol('P', commutative=True), Symbol('l', commutative=True)))", "Mul(Pow(Symbol('A', commutative=True), Integer(-1)), Symbol('l', commutative=True), log(Symbol('P', commutative=True)))", "Mul(Rational(1, 2), Symbol('P', commutative=True), Symbol('l', commutative=True), Add(Mul(Integer(2), Symbol('A', commutative=True)), Symbol('l', commutative=True)))"]}, {"premise_expression": "c w", "variable": "c", "positive": "\\frac{c^{2} w}{2}", "negatives": ["\\frac{c w^{2}}{2}", "\\frac{c^{2}}{2 w}", "\\frac{c (c - 2 w)}{2}", "c w + e^{c}"], "srepr_premise_expression": "Mul(Symbol('c', commutative=True), Symbol('w', commutative=True))", "srepr_variable": "Symbol('c', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('c', commutative=True), Integer(2)), Symbol('w', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('c', commutative=True), Pow(Symbol('w', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('c', commutative=True), Integer(2)), Pow(Symbol('w', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Symbol('c', commutative=True), Add(Symbol('c', commutative=True), Mul(Integer(-1), Integer(2), Symbol('w', commutative=True))))", "Add(Mul(Symbol('c', commutative=True), Symbol('w', commutative=True)), exp(Symbol('c', commutative=True)))"]}, {"premise_expression": "\\frac{v}{k}", "variable": "k", "positive": "v \\log{(k)}", "negatives": ["\\frac{v^{2}}{2 k}", "\\frac{k^{2} \\cos{(v)}}{2}", "e^{k - v}", "k (\\log{(k v)} - 1)"], "srepr_premise_expression": "Mul(Pow(Symbol('k', commutative=True), Integer(-1)), Symbol('v', commutative=True))", "srepr_variable": "Symbol('k', commutative=True)", "srepr_positive": "Mul(Symbol('v', commutative=True), log(Symbol('k', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('k', commutative=True), Integer(-1)), Pow(Symbol('v', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('k', commutative=True), Integer(2)), cos(Symbol('v', commutative=True)))", "exp(Add(Symbol('k', commutative=True), Mul(Integer(-1), Symbol('v', commutative=True))))", "Mul(Symbol('k', commutative=True), Add(log(Mul(Symbol('k', commutative=True), Symbol('v', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\frac{z}{k}", "variable": "z", "positive": "\\frac{z^{2}}{2 k}", "negatives": ["z \\log{(k)}", "k \\sin{(z)}", "\\frac{z (2 k - z)}{2}", "\\sin{(k + z)}"], "srepr_premise_expression": "Mul(Pow(Symbol('k', commutative=True), Integer(-1)), Symbol('z', commutative=True))", "srepr_variable": "Symbol('z', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('k', commutative=True), Integer(-1)), Pow(Symbol('z', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('z', commutative=True), log(Symbol('k', commutative=True)))", "Mul(Symbol('k', commutative=True), sin(Symbol('z', commutative=True)))", "Mul(Rational(1, 2), Symbol('z', commutative=True), Add(Mul(Integer(2), Symbol('k', commutative=True)), Mul(Integer(-1), Symbol('z', commutative=True))))", "sin(Add(Symbol('k', commutative=True), Symbol('z', commutative=True)))"]}, {"premise_expression": "\\frac{\\cos{(J)}}{l}", "variable": "l", "positive": "\\log{(l)} \\cos{(J)}", "negatives": ["e^{J} \\log{(l)}", "\\frac{l^{2} \\cos{(J)}}{2}", "\\frac{\\sin{(l)}}{J}", "l (J + l)"], "srepr_premise_expression": "Mul(Pow(Symbol('l', commutative=True), Integer(-1)), cos(Symbol('J', commutative=True)))", "srepr_variable": "Symbol('l', commutative=True)", "srepr_positive": "Mul(log(Symbol('l', commutative=True)), cos(Symbol('J', commutative=True)))", "srepr_negatives": ["Mul(exp(Symbol('J', commutative=True)), log(Symbol('l', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('l', commutative=True), Integer(2)), cos(Symbol('J', commutative=True)))", "Mul(Pow(Symbol('J', commutative=True), Integer(-1)), sin(Symbol('l', commutative=True)))", "Mul(Symbol('l', commutative=True), Add(Symbol('J', commutative=True), Symbol('l', commutative=True)))"]}, {"premise_expression": "K + L", "variable": "K", "positive": "\\frac{K (K + 2 L)}{2}", "negatives": ["\\frac{L (2 K + L)}{2}", "\\frac{K (K + 2 e^{L})}{2}", "\\frac{K (- K + 2 \\sin{(L)})}{2}", "\\sin{(K - L)}"], "srepr_premise_expression": "Add(Symbol('K', commutative=True), Symbol('L', commutative=True))", "srepr_variable": "Symbol('K', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Symbol('K', commutative=True), Mul(Integer(2), Symbol('L', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Mul(Integer(2), Symbol('K', commutative=True)), Symbol('L', commutative=True)))", "Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Symbol('K', commutative=True), Mul(Integer(2), exp(Symbol('L', commutative=True)))))", "Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Mul(Integer(-1), Symbol('K', commutative=True)), Mul(Integer(2), sin(Symbol('L', commutative=True)))))", "sin(Add(Symbol('K', commutative=True), Mul(Integer(-1), Symbol('L', commutative=True))))"]}, {"premise_expression": "\\cos{(M + v)}", "variable": "v", "positive": "\\sin{(M + v)}", "negatives": ["e^{- M + v}", "M \\sin{(v)}", "\\frac{v (2 M + v)}{2}", "\\frac{v (2 M - v)}{2}"], "srepr_premise_expression": "cos(Add(Symbol('M', commutative=True), Symbol('v', commutative=True)))", "srepr_variable": "Symbol('v', commutative=True)", "srepr_positive": "sin(Add(Symbol('M', commutative=True), Symbol('v', commutative=True)))", "srepr_negatives": ["exp(Add(Mul(Integer(-1), Symbol('M', commutative=True)), Symbol('v', commutative=True)))", "Mul(Symbol('M', commutative=True), sin(Symbol('v', commutative=True)))", "Mul(Rational(1, 2), Symbol('v', commutative=True), Add(Mul(Integer(2), Symbol('M', commutative=True)), Symbol('v', commutative=True)))", "Mul(Rational(1, 2), Symbol('v', commutative=True), Add(Mul(Integer(2), Symbol('M', commutative=True)), Mul(Integer(-1), Symbol('v', commutative=True))))"]}, {"premise_expression": "\\frac{B}{u} - r", "variable": "u", "positive": "B \\log{(u)} - r u", "negatives": ["B \\log{(u)} + u", "\\frac{B^{2}}{2 u} - B r", "\\frac{B r}{u} - \\frac{r^{2}}{2}", "\\frac{B r u^{2}}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('B', commutative=True), Pow(Symbol('u', commutative=True), Integer(-1))), Mul(Integer(-1), Symbol('r', commutative=True)))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "Add(Mul(Symbol('B', commutative=True), log(Symbol('u', commutative=True))), Mul(Integer(-1), Symbol('r', commutative=True), Symbol('u', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('B', commutative=True), log(Symbol('u', commutative=True))), Symbol('u', commutative=True))", "Add(Mul(Rational(1, 2), Pow(Symbol('B', commutative=True), Integer(2)), Pow(Symbol('u', commutative=True), Integer(-1))), Mul(Integer(-1), Symbol('B', commutative=True), Symbol('r', commutative=True)))", "Add(Mul(Symbol('B', commutative=True), Symbol('r', commutative=True), Pow(Symbol('u', commutative=True), Integer(-1))), Mul(Integer(-1), Rational(1, 2), Pow(Symbol('r', commutative=True), Integer(2))))", "Mul(Rational(1, 2), Symbol('B', commutative=True), Symbol('r', commutative=True), Pow(Symbol('u', commutative=True), Integer(2)))"]}, {"premise_expression": "\\frac{\\log{(n)}}{g}", "variable": "g", "positive": "\\log{(g)} \\log{(n)}", "negatives": ["\\log{(g)} \\cos{(n)}", "g \\log{(n^{n})}", "- \\frac{\\cos{(g)}}{n}", "\\frac{g^{2} e^{n}}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('g', commutative=True), Integer(-1)), log(Symbol('n', commutative=True)))", "srepr_variable": "Symbol('g', commutative=True)", "srepr_positive": "Mul(log(Symbol('g', commutative=True)), log(Symbol('n', commutative=True)))", "srepr_negatives": ["Mul(log(Symbol('g', commutative=True)), cos(Symbol('n', commutative=True)))", "Mul(Symbol('g', commutative=True), log(Pow(Symbol('n', commutative=True), Symbol('n', commutative=True))))", "Mul(Integer(-1), Pow(Symbol('n', commutative=True), Integer(-1)), cos(Symbol('g', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('g', commutative=True), Integer(2)), exp(Symbol('n', commutative=True)))"]}, {"premise_expression": "N R", "variable": "N", "positive": "\\frac{N^{2} R}{2}", "negatives": ["\\frac{N R^{2}}{2}", "2 N R", "\\frac{N^{2} \\cos{(R)}}{2}", "\\frac{N (N - 2 R)}{2}"], "srepr_premise_expression": "Mul(Symbol('N', commutative=True), Symbol('R', commutative=True))", "srepr_variable": "Symbol('N', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('N', commutative=True), Integer(2)), Symbol('R', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('N', commutative=True), Pow(Symbol('R', commutative=True), Integer(2)))", "Mul(Integer(2), Symbol('N', commutative=True), Symbol('R', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('N', commutative=True), Integer(2)), cos(Symbol('R', commutative=True)))", "Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Symbol('N', commutative=True), Mul(Integer(-1), Integer(2), Symbol('R', commutative=True))))"]}, {"premise_expression": "B - z", "variable": "B", "positive": "\\frac{B (B - 2 z)}{2}", "negatives": ["\\frac{B (- B + 2 z)}{2}", "\\frac{z (2 B - z)}{2}", "\\sin{(B - z)}", "B z - \\cos{(B)}"], "srepr_premise_expression": "Add(Symbol('B', commutative=True), Mul(Integer(-1), Symbol('z', commutative=True)))", "srepr_variable": "Symbol('B', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('B', commutative=True), Add(Symbol('B', commutative=True), Mul(Integer(-1), Integer(2), Symbol('z', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('B', commutative=True), Add(Mul(Integer(-1), Symbol('B', commutative=True)), Mul(Integer(2), Symbol('z', commutative=True))))", "Mul(Rational(1, 2), Symbol('z', commutative=True), Add(Mul(Integer(2), Symbol('B', commutative=True)), Mul(Integer(-1), Symbol('z', commutative=True))))", "sin(Add(Symbol('B', commutative=True), Mul(Integer(-1), Symbol('z', commutative=True))))", "Add(Mul(Symbol('B', commutative=True), Symbol('z', commutative=True)), Mul(Integer(-1), cos(Symbol('B', commutative=True))))"]}, {"premise_expression": "- r + e^{H}", "variable": "r", "positive": "\\frac{r (- r + 2 e^{H})}{2}", "negatives": ["- H r + e^{H}", "- H r + e^{r}", "\\frac{r^{2} \\sin{(H)}}{2}", "- H \\operatorname{Ei}{(\\frac{H}{r})} + r e^{\\frac{H}{r}}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('r', commutative=True)), exp(Symbol('H', commutative=True)))", "srepr_variable": "Symbol('r', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(-1), Symbol('r', commutative=True)), Mul(Integer(2), exp(Symbol('H', commutative=True)))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('H', commutative=True), Symbol('r', commutative=True)), exp(Symbol('H', commutative=True)))", "Add(Mul(Integer(-1), Symbol('H', commutative=True), Symbol('r', commutative=True)), exp(Symbol('r', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('r', commutative=True), Integer(2)), sin(Symbol('H', commutative=True)))", "Add(Mul(Integer(-1), Symbol('H', commutative=True), Ei(Mul(Symbol('H', commutative=True), Pow(Symbol('r', commutative=True), Integer(-1))))), Mul(Symbol('r', commutative=True), exp(Mul(Symbol('H', commutative=True), Pow(Symbol('r', commutative=True), Integer(-1))))))"]}, {"premise_expression": "\\frac{P}{L}", "variable": "P", "positive": "\\frac{P^{2}}{2 L}", "negatives": ["P \\log{(L)}", "\\frac{P (2 L - P)}{2}", "\\frac{P (2 L + P)}{2}", "- \\cos{(L + P)}"], "srepr_premise_expression": "Mul(Pow(Symbol('L', commutative=True), Integer(-1)), Symbol('P', commutative=True))", "srepr_variable": "Symbol('P', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(-1)), Pow(Symbol('P', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('P', commutative=True), log(Symbol('L', commutative=True)))", "Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Mul(Integer(2), Symbol('L', commutative=True)), Mul(Integer(-1), Symbol('P', commutative=True))))", "Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Mul(Integer(2), Symbol('L', commutative=True)), Symbol('P', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('L', commutative=True), Symbol('P', commutative=True))))"]}, {"premise_expression": "o e^{j}", "variable": "o", "positive": "\\frac{o^{2} e^{j}}{2}", "negatives": ["o e^{j}", "\\frac{o (- 2 j + o)}{2}", "\\frac{j o^{2}}{2}", "- e^{j - o}"], "srepr_premise_expression": "Mul(Symbol('o', commutative=True), exp(Symbol('j', commutative=True)))", "srepr_variable": "Symbol('o', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('o', commutative=True), Integer(2)), exp(Symbol('j', commutative=True)))", "srepr_negatives": ["Mul(Symbol('o', commutative=True), exp(Symbol('j', commutative=True)))", "Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('j', commutative=True)), Symbol('o', commutative=True)))", "Mul(Rational(1, 2), Symbol('j', commutative=True), Pow(Symbol('o', commutative=True), Integer(2)))", "Mul(Integer(-1), exp(Add(Symbol('j', commutative=True), Mul(Integer(-1), Symbol('o', commutative=True)))))"]}, {"premise_expression": "c \\log{(n)}", "variable": "c", "positive": "\\frac{c^{2} \\log{(n)}}{2}", "negatives": ["c n (\\log{(n)} - 1)", "\\frac{c (- c + 2 n)}{2}", "\\frac{c (c + 2 \\sin{(n)})}{2}", "- \\frac{\\cos{(c)}}{n}"], "srepr_premise_expression": "Mul(Symbol('c', commutative=True), log(Symbol('n', commutative=True)))", "srepr_variable": "Symbol('c', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('c', commutative=True), Integer(2)), log(Symbol('n', commutative=True)))", "srepr_negatives": ["Mul(Symbol('c', commutative=True), Symbol('n', commutative=True), Add(log(Symbol('n', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('c', commutative=True), Add(Mul(Integer(-1), Symbol('c', commutative=True)), Mul(Integer(2), Symbol('n', commutative=True))))", "Mul(Rational(1, 2), Symbol('c', commutative=True), Add(Symbol('c', commutative=True), Mul(Integer(2), sin(Symbol('n', commutative=True)))))", "Mul(Integer(-1), Pow(Symbol('n', commutative=True), Integer(-1)), cos(Symbol('c', commutative=True)))"]}, {"premise_expression": "- o + \\frac{q}{b}", "variable": "o", "positive": "- \\frac{o^{2}}{2} + \\frac{o q}{b}", "negatives": ["\\frac{b o (o + 2 q)}{2}", "\\frac{o q (- 2 b + o)}{2}", "\\frac{b o^{2}}{2 q}", "\\frac{o (2 b^{q} + o)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('o', commutative=True)), Mul(Pow(Symbol('b', commutative=True), Integer(-1)), Symbol('q', commutative=True)))", "srepr_variable": "Symbol('o', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('o', commutative=True), Integer(2))), Mul(Pow(Symbol('b', commutative=True), Integer(-1)), Symbol('o', commutative=True), Symbol('q', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('b', commutative=True), Symbol('o', commutative=True), Add(Symbol('o', commutative=True), Mul(Integer(2), Symbol('q', commutative=True))))", "Mul(Rational(1, 2), Symbol('o', commutative=True), Symbol('q', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('b', commutative=True)), Symbol('o', commutative=True)))", "Mul(Rational(1, 2), Symbol('b', commutative=True), Pow(Symbol('o', commutative=True), Integer(2)), Pow(Symbol('q', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Mul(Integer(2), Pow(Symbol('b', commutative=True), Symbol('q', commutative=True))), Symbol('o', commutative=True)))"]}, {"premise_expression": "\\frac{f}{B}", "variable": "B", "positive": "f \\log{(B)}", "negatives": ["\\frac{f^{2}}{2 B}", "- \\frac{\\cos{(B)}}{f}", "- \\cos{(B + f)}", "- B f + \\sin{(B)}"], "srepr_premise_expression": "Mul(Pow(Symbol('B', commutative=True), Integer(-1)), Symbol('f', commutative=True))", "srepr_variable": "Symbol('B', commutative=True)", "srepr_positive": "Mul(Symbol('f', commutative=True), log(Symbol('B', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('B', commutative=True), Integer(-1)), Pow(Symbol('f', commutative=True), Integer(2)))", "Mul(Integer(-1), Pow(Symbol('f', commutative=True), Integer(-1)), cos(Symbol('B', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('B', commutative=True), Symbol('f', commutative=True))))", "Add(Mul(Integer(-1), Symbol('B', commutative=True), Symbol('f', commutative=True)), sin(Symbol('B', commutative=True)))"]}, {"premise_expression": "s u", "variable": "s", "positive": "\\frac{s^{2} u}{2}", "negatives": ["\\frac{s u^{2}}{2}", "\\frac{s (- s + 2 u)}{2}", "- u \\cos{(s)}", "- s u + e^{s}"], "srepr_premise_expression": "Mul(Symbol('s', commutative=True), Symbol('u', commutative=True))", "srepr_variable": "Symbol('s', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('s', commutative=True), Integer(2)), Symbol('u', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('s', commutative=True), Pow(Symbol('u', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('s', commutative=True), Add(Mul(Integer(-1), Symbol('s', commutative=True)), Mul(Integer(2), Symbol('u', commutative=True))))", "Mul(Integer(-1), Symbol('u', commutative=True), cos(Symbol('s', commutative=True)))", "Add(Mul(Integer(-1), Symbol('s', commutative=True), Symbol('u', commutative=True)), exp(Symbol('s', commutative=True)))"]}, {"premise_expression": "- b + \\cos{(q)}", "variable": "q", "positive": "- b q + \\sin{(q)}", "negatives": ["b q + \\sin{(q)}", "\\cos{(b - q)}", "b e^{\\frac{q}{b}}", "\\frac{b (- b + 2 \\cos{(q)})}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('b', commutative=True)), cos(Symbol('q', commutative=True)))", "srepr_variable": "Symbol('q', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('b', commutative=True), Symbol('q', commutative=True)), sin(Symbol('q', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('b', commutative=True), Symbol('q', commutative=True)), sin(Symbol('q', commutative=True)))", "cos(Add(Symbol('b', commutative=True), Mul(Integer(-1), Symbol('q', commutative=True))))", "Mul(Symbol('b', commutative=True), exp(Mul(Pow(Symbol('b', commutative=True), Integer(-1)), Symbol('q', commutative=True))))", "Mul(Rational(1, 2), Symbol('b', commutative=True), Add(Mul(Integer(-1), Symbol('b', commutative=True)), Mul(Integer(2), cos(Symbol('q', commutative=True)))))"]}, {"premise_expression": "G + e^{u}", "variable": "G", "positive": "\\frac{G (G + 2 e^{u})}{2}", "negatives": ["\\frac{G (G + 2 \\cos{(u)})}{2}", "G u + e^{u}", "\\sin{(G + u)}", "G (- u + \\log{(G)} - 1)"], "srepr_premise_expression": "Add(Symbol('G', commutative=True), exp(Symbol('u', commutative=True)))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Symbol('G', commutative=True), Mul(Integer(2), exp(Symbol('u', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Symbol('G', commutative=True), Mul(Integer(2), cos(Symbol('u', commutative=True)))))", "Add(Mul(Symbol('G', commutative=True), Symbol('u', commutative=True)), exp(Symbol('u', commutative=True)))", "sin(Add(Symbol('G', commutative=True), Symbol('u', commutative=True)))", "Mul(Symbol('G', commutative=True), Add(Mul(Integer(-1), Symbol('u', commutative=True)), log(Symbol('G', commutative=True)), Integer(-1)))"]}, {"premise_expression": "o (C + f)", "variable": "C", "positive": "\\frac{C o (C + 2 f)}{2}", "negatives": ["\\frac{o^{2} (C + f)}{2}", "\\frac{f o (2 C + f)}{2}", "\\frac{C (- C + 2 o^{f})}{2}", "\\frac{C (- C + 2 f^{o})}{2}"], "srepr_premise_expression": "Mul(Symbol('o', commutative=True), Add(Symbol('C', commutative=True), Symbol('f', commutative=True)))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('C', commutative=True), Symbol('o', commutative=True), Add(Symbol('C', commutative=True), Mul(Integer(2), Symbol('f', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('o', commutative=True), Integer(2)), Add(Symbol('C', commutative=True), Symbol('f', commutative=True)))", "Mul(Rational(1, 2), Symbol('f', commutative=True), Symbol('o', commutative=True), Add(Mul(Integer(2), Symbol('C', commutative=True)), Symbol('f', commutative=True)))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Mul(Integer(-1), Symbol('C', commutative=True)), Mul(Integer(2), Pow(Symbol('o', commutative=True), Symbol('f', commutative=True)))))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Mul(Integer(-1), Symbol('C', commutative=True)), Mul(Integer(2), Pow(Symbol('f', commutative=True), Symbol('o', commutative=True)))))"]}, {"premise_expression": "A + P + Q", "variable": "A", "positive": "A (\\frac{A}{2} + P + Q)", "negatives": ["\\frac{Q (2 A + 2 P + Q)}{2}", "\\frac{P (2 A + P + 2 Q)}{2}", "- \\frac{A^{2}}{2} + \\frac{A P}{Q}", "A (1 - P)"], "srepr_premise_expression": "Add(Symbol('A', commutative=True), Symbol('P', commutative=True), Symbol('Q', commutative=True))", "srepr_variable": "Symbol('A', commutative=True)", "srepr_positive": "Mul(Symbol('A', commutative=True), Add(Mul(Rational(1, 2), Symbol('A', commutative=True)), Symbol('P', commutative=True), Symbol('Q', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Mul(Integer(2), Symbol('A', commutative=True)), Mul(Integer(2), Symbol('P', commutative=True)), Symbol('Q', commutative=True)))", "Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Mul(Integer(2), Symbol('A', commutative=True)), Symbol('P', commutative=True), Mul(Integer(2), Symbol('Q', commutative=True))))", "Add(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2))), Mul(Symbol('A', commutative=True), Symbol('P', commutative=True), Pow(Symbol('Q', commutative=True), Integer(-1))))", "Mul(Symbol('A', commutative=True), Add(Integer(1), Mul(Integer(-1), Symbol('P', commutative=True))))"]}, {"premise_expression": "- W + X", "variable": "X", "positive": "\\frac{X (- 2 W + X)}{2}", "negatives": ["\\frac{W (- W + 2 X)}{2}", "e^{W + X}", "\\sin{(W + X)}", "W e^{X}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('W', commutative=True)), Symbol('X', commutative=True))", "srepr_variable": "Symbol('X', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('X', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('W', commutative=True)), Symbol('X', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('W', commutative=True), Add(Mul(Integer(-1), Symbol('W', commutative=True)), Mul(Integer(2), Symbol('X', commutative=True))))", "exp(Add(Symbol('W', commutative=True), Symbol('X', commutative=True)))", "sin(Add(Symbol('W', commutative=True), Symbol('X', commutative=True)))", "Mul(Symbol('W', commutative=True), exp(Symbol('X', commutative=True)))"]}, {"premise_expression": "\\sin{(Y + q)}", "variable": "Y", "positive": "- \\cos{(Y + q)}", "negatives": ["- Y q + \\sin{(Y)}", "Y (\\log{(Y q)} - 1)", "Y q + e^{Y}", "Y q + \\sin{(Y)}"], "srepr_premise_expression": "sin(Add(Symbol('Y', commutative=True), Symbol('q', commutative=True)))", "srepr_variable": "Symbol('Y', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('Y', commutative=True), Symbol('q', commutative=True))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('Y', commutative=True), Symbol('q', commutative=True)), sin(Symbol('Y', commutative=True)))", "Mul(Symbol('Y', commutative=True), Add(log(Mul(Symbol('Y', commutative=True), Symbol('q', commutative=True))), Integer(-1)))", "Add(Mul(Symbol('Y', commutative=True), Symbol('q', commutative=True)), exp(Symbol('Y', commutative=True)))", "Add(Mul(Symbol('Y', commutative=True), Symbol('q', commutative=True)), sin(Symbol('Y', commutative=True)))"]}, {"premise_expression": "e^{\\frac{E}{l}}", "variable": "l", "positive": "- E \\operatorname{Ei}{(\\frac{E}{l})} + l e^{\\frac{E}{l}}", "negatives": ["\\frac{l (l + 2 e^{E})}{2}", "l e^{\\frac{E}{l}}", "\\frac{l (l + 2 \\log{(E)})}{2}", "\\frac{l (l + 2 \\sin{(E)})}{2}"], "srepr_premise_expression": "exp(Mul(Symbol('E', commutative=True), Pow(Symbol('l', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('l', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('E', commutative=True), Ei(Mul(Symbol('E', commutative=True), Pow(Symbol('l', commutative=True), Integer(-1))))), Mul(Symbol('l', commutative=True), exp(Mul(Symbol('E', commutative=True), Pow(Symbol('l', commutative=True), Integer(-1))))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('l', commutative=True), Add(Symbol('l', commutative=True), Mul(Integer(2), exp(Symbol('E', commutative=True)))))", "Mul(Symbol('l', commutative=True), exp(Mul(Symbol('E', commutative=True), Pow(Symbol('l', commutative=True), Integer(-1)))))", "Mul(Rational(1, 2), Symbol('l', commutative=True), Add(Symbol('l', commutative=True), Mul(Integer(2), log(Symbol('E', commutative=True)))))", "Mul(Rational(1, 2), Symbol('l', commutative=True), Add(Symbol('l', commutative=True), Mul(Integer(2), sin(Symbol('E', commutative=True)))))"]}, {"premise_expression": "\\cos{(a + y)}", "variable": "y", "positive": "\\sin{(a + y)}", "negatives": ["- \\cos{(a + y)}", "\\frac{y (- 2 a + y)}{2}", "y (\\log{(\\frac{a}{y})} + 1)", "\\frac{y (- y + 2 \\log{(a)})}{2}"], "srepr_premise_expression": "cos(Add(Symbol('a', commutative=True), Symbol('y', commutative=True)))", "srepr_variable": "Symbol('y', commutative=True)", "srepr_positive": "sin(Add(Symbol('a', commutative=True), Symbol('y', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('a', commutative=True), Symbol('y', commutative=True))))", "Mul(Rational(1, 2), Symbol('y', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('a', commutative=True)), Symbol('y', commutative=True)))", "Mul(Symbol('y', commutative=True), Add(log(Mul(Symbol('a', commutative=True), Pow(Symbol('y', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Rational(1, 2), Symbol('y', commutative=True), Add(Mul(Integer(-1), Symbol('y', commutative=True)), Mul(Integer(2), log(Symbol('a', commutative=True)))))"]}, {"premise_expression": "K + z", "variable": "z", "positive": "\\frac{z (2 K + z)}{2}", "negatives": ["\\frac{z (- 2 K + z)}{2}", "\\frac{K (K + 2 z)}{2}", "e^{- K + z}", "\\sin{(K + z)}"], "srepr_premise_expression": "Add(Symbol('K', commutative=True), Symbol('z', commutative=True))", "srepr_variable": "Symbol('z', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('z', commutative=True), Add(Mul(Integer(2), Symbol('K', commutative=True)), Symbol('z', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('z', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('K', commutative=True)), Symbol('z', commutative=True)))", "Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Symbol('K', commutative=True), Mul(Integer(2), Symbol('z', commutative=True))))", "exp(Add(Mul(Integer(-1), Symbol('K', commutative=True)), Symbol('z', commutative=True)))", "sin(Add(Symbol('K', commutative=True), Symbol('z', commutative=True)))"]}, {"premise_expression": "\\sin{(J - P)}", "variable": "J", "positive": "- \\cos{(J - P)}", "negatives": ["\\cos{(J - P)}", "\\frac{J (J - 2 P)}{2}", "\\frac{J (J + 2 P)}{2}", "\\log{(J)} \\cos{(P)}"], "srepr_premise_expression": "sin(Add(Symbol('J', commutative=True), Mul(Integer(-1), Symbol('P', commutative=True))))", "srepr_variable": "Symbol('J', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('J', commutative=True), Mul(Integer(-1), Symbol('P', commutative=True)))))", "srepr_negatives": ["cos(Add(Symbol('J', commutative=True), Mul(Integer(-1), Symbol('P', commutative=True))))", "Mul(Rational(1, 2), Symbol('J', commutative=True), Add(Symbol('J', commutative=True), Mul(Integer(-1), Integer(2), Symbol('P', commutative=True))))", "Mul(Rational(1, 2), Symbol('J', commutative=True), Add(Symbol('J', commutative=True), Mul(Integer(2), Symbol('P', commutative=True))))", "Mul(log(Symbol('J', commutative=True)), cos(Symbol('P', commutative=True)))"]}, {"premise_expression": "\\frac{F^{p}}{D}", "variable": "D", "positive": "F^{p} \\log{(D)}", "negatives": ["\\frac{D^{2} F}{2 p}", "D p", "\\frac{D^{2} (F + p)}{2}", "\\frac{D^{2}}{2} + \\frac{D F}{p}"], "srepr_premise_expression": "Mul(Pow(Symbol('D', commutative=True), Integer(-1)), Pow(Symbol('F', commutative=True), Symbol('p', commutative=True)))", "srepr_variable": "Symbol('D', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('F', commutative=True), Symbol('p', commutative=True)), log(Symbol('D', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(2)), Symbol('F', commutative=True), Pow(Symbol('p', commutative=True), Integer(-1)))", "Mul(Symbol('D', commutative=True), Symbol('p', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(2)), Add(Symbol('F', commutative=True), Symbol('p', commutative=True)))", "Add(Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(2))), Mul(Symbol('D', commutative=True), Symbol('F', commutative=True), Pow(Symbol('p', commutative=True), Integer(-1))))"]}, {"premise_expression": "\\sin{(\\frac{E}{o})}", "variable": "o", "positive": "E \\log{(\\frac{E}{o})} - \\frac{E \\log{(\\frac{E^{2}}{o^{2}})}}{2} - E \\operatorname{Ci}{(\\frac{E}{o})} + o \\sin{(\\frac{E}{o})}", "negatives": ["E \\log{(E + o)} + o \\log{(E + o)} - o", "- E \\log{(- E + o)} + o \\log{(E - o)} - o", "- E \\log{(- E + o)} + o \\log{(- E + o)} - o", "\\log{(o)} \\sin{(E)}"], "srepr_premise_expression": "sin(Mul(Symbol('E', commutative=True), Pow(Symbol('o', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('o', commutative=True)", "srepr_positive": "Add(Mul(Symbol('E', commutative=True), log(Mul(Symbol('E', commutative=True), Pow(Symbol('o', commutative=True), Integer(-1))))), Mul(Integer(-1), Rational(1, 2), Symbol('E', commutative=True), log(Mul(Pow(Symbol('E', commutative=True), Integer(2)), Pow(Symbol('o', commutative=True), Integer(-2))))), Mul(Integer(-1), Symbol('E', commutative=True), Ci(Mul(Symbol('E', commutative=True), Pow(Symbol('o', commutative=True), Integer(-1))))), Mul(Symbol('o', commutative=True), sin(Mul(Symbol('E', commutative=True), Pow(Symbol('o', commutative=True), Integer(-1))))))", "srepr_negatives": ["Add(Mul(Symbol('E', commutative=True), log(Add(Symbol('E', commutative=True), Symbol('o', commutative=True)))), Mul(Symbol('o', commutative=True), log(Add(Symbol('E', commutative=True), Symbol('o', commutative=True)))), Mul(Integer(-1), Symbol('o', commutative=True)))", "Add(Mul(Integer(-1), Symbol('E', commutative=True), log(Add(Mul(Integer(-1), Symbol('E', commutative=True)), Symbol('o', commutative=True)))), Mul(Symbol('o', commutative=True), log(Add(Symbol('E', commutative=True), Mul(Integer(-1), Symbol('o', commutative=True))))), Mul(Integer(-1), Symbol('o', commutative=True)))", "Add(Mul(Integer(-1), Symbol('E', commutative=True), log(Add(Mul(Integer(-1), Symbol('E', commutative=True)), Symbol('o', commutative=True)))), Mul(Symbol('o', commutative=True), log(Add(Mul(Integer(-1), Symbol('E', commutative=True)), Symbol('o', commutative=True)))), Mul(Integer(-1), Symbol('o', commutative=True)))", "Mul(log(Symbol('o', commutative=True)), sin(Symbol('E', commutative=True)))"]}, {"premise_expression": "G + \\cos{(V)}", "variable": "G", "positive": "\\frac{G (G + 2 \\cos{(V)})}{2}", "negatives": ["\\frac{G (G + 2 \\log{(V)})}{2}", "\\frac{G (- G + 2 e^{V})}{2}", "G V + \\sin{(V)}", "G (- V + \\log{(G^{V})})"], "srepr_premise_expression": "Add(Symbol('G', commutative=True), cos(Symbol('V', commutative=True)))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Symbol('G', commutative=True), Mul(Integer(2), cos(Symbol('V', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Symbol('G', commutative=True), Mul(Integer(2), log(Symbol('V', commutative=True)))))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Mul(Integer(-1), Symbol('G', commutative=True)), Mul(Integer(2), exp(Symbol('V', commutative=True)))))", "Add(Mul(Symbol('G', commutative=True), Symbol('V', commutative=True)), sin(Symbol('V', commutative=True)))", "Mul(Symbol('G', commutative=True), Add(Mul(Integer(-1), Symbol('V', commutative=True)), log(Pow(Symbol('G', commutative=True), Symbol('V', commutative=True)))))"]}, {"premise_expression": "\\sin{(D - H)}", "variable": "D", "positive": "- \\cos{(D - H)}", "negatives": ["\\cos{(D - H)}", "e^{D + H}", "- e^{- D + H}", "D \\sin{(H^{2})}"], "srepr_premise_expression": "sin(Add(Symbol('D', commutative=True), Mul(Integer(-1), Symbol('H', commutative=True))))", "srepr_variable": "Symbol('D', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('D', commutative=True), Mul(Integer(-1), Symbol('H', commutative=True)))))", "srepr_negatives": ["cos(Add(Symbol('D', commutative=True), Mul(Integer(-1), Symbol('H', commutative=True))))", "exp(Add(Symbol('D', commutative=True), Symbol('H', commutative=True)))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('D', commutative=True)), Symbol('H', commutative=True))))", "Mul(Symbol('D', commutative=True), sin(Pow(Symbol('H', commutative=True), Integer(2))))"]}, {"premise_expression": "\\frac{D Z}{w}", "variable": "Z", "positive": "\\frac{D Z^{2}}{2 w}", "negatives": ["\\frac{D^{2} Z}{2 w}", "D Z \\log{(w)}", "\\frac{Z (D Z + 2 w)}{2}", "\\frac{Z (D Z - 2 w)}{2}"], "srepr_premise_expression": "Mul(Symbol('D', commutative=True), Symbol('Z', commutative=True), Pow(Symbol('w', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('Z', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('D', commutative=True), Pow(Symbol('Z', commutative=True), Integer(2)), Pow(Symbol('w', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(2)), Symbol('Z', commutative=True), Pow(Symbol('w', commutative=True), Integer(-1)))", "Mul(Symbol('D', commutative=True), Symbol('Z', commutative=True), log(Symbol('w', commutative=True)))", "Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Mul(Symbol('D', commutative=True), Symbol('Z', commutative=True)), Mul(Integer(2), Symbol('w', commutative=True))))", "Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Mul(Symbol('D', commutative=True), Symbol('Z', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('w', commutative=True))))"]}, {"premise_expression": "- A + E^{Q}", "variable": "A", "positive": "\\frac{A (- A + 2 E^{Q})}{2}", "negatives": ["\\frac{A (- A + 2 E Q)}{2}", "\\frac{A (- A - 2 E + 2 Q)}{2}", "\\frac{A E (A - 2 Q)}{2}", "\\frac{A (A + 2 Q)}{2 E}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('A', commutative=True)), Pow(Symbol('E', commutative=True), Symbol('Q', commutative=True)))", "srepr_variable": "Symbol('A', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Mul(Integer(-1), Symbol('A', commutative=True)), Mul(Integer(2), Pow(Symbol('E', commutative=True), Symbol('Q', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Mul(Integer(-1), Symbol('A', commutative=True)), Mul(Integer(2), Symbol('E', commutative=True), Symbol('Q', commutative=True))))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Mul(Integer(-1), Symbol('A', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('E', commutative=True)), Mul(Integer(2), Symbol('Q', commutative=True))))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Symbol('E', commutative=True), Add(Symbol('A', commutative=True), Mul(Integer(-1), Integer(2), Symbol('Q', commutative=True))))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Pow(Symbol('E', commutative=True), Integer(-1)), Add(Symbol('A', commutative=True), Mul(Integer(2), Symbol('Q', commutative=True))))"]}, {"premise_expression": "\\frac{Z + x}{R}", "variable": "x", "positive": "\\frac{x (2 Z + x)}{2 R}", "negatives": ["\\frac{Z (Z + 2 x)}{2 R}", "\\frac{x (2 R + Z x)}{2}", "\\frac{x (2 R Z - x)}{2}", "(Z + x) \\log{(R)}"], "srepr_premise_expression": "Mul(Pow(Symbol('R', commutative=True), Integer(-1)), Add(Symbol('Z', commutative=True), Symbol('x', commutative=True)))", "srepr_variable": "Symbol('x', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('R', commutative=True), Integer(-1)), Symbol('x', commutative=True), Add(Mul(Integer(2), Symbol('Z', commutative=True)), Symbol('x', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('R', commutative=True), Integer(-1)), Symbol('Z', commutative=True), Add(Symbol('Z', commutative=True), Mul(Integer(2), Symbol('x', commutative=True))))", "Mul(Rational(1, 2), Symbol('x', commutative=True), Add(Mul(Integer(2), Symbol('R', commutative=True)), Mul(Symbol('Z', commutative=True), Symbol('x', commutative=True))))", "Mul(Rational(1, 2), Symbol('x', commutative=True), Add(Mul(Integer(2), Symbol('R', commutative=True), Symbol('Z', commutative=True)), Mul(Integer(-1), Symbol('x', commutative=True))))", "Mul(Add(Symbol('Z', commutative=True), Symbol('x', commutative=True)), log(Symbol('R', commutative=True)))"]}, {"premise_expression": "j + o", "variable": "j", "positive": "\\frac{j (j + 2 o)}{2}", "negatives": ["\\frac{j (j - 2 o)}{2}", "\\frac{o (2 j + o)}{2}", "\\frac{j^{2} \\log{(o)}}{2}", "\\sin{(j - o)}"], "srepr_premise_expression": "Add(Symbol('j', commutative=True), Symbol('o', commutative=True))", "srepr_variable": "Symbol('j', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('j', commutative=True), Add(Symbol('j', commutative=True), Mul(Integer(2), Symbol('o', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('j', commutative=True), Add(Symbol('j', commutative=True), Mul(Integer(-1), Integer(2), Symbol('o', commutative=True))))", "Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Mul(Integer(2), Symbol('j', commutative=True)), Symbol('o', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('j', commutative=True), Integer(2)), log(Symbol('o', commutative=True)))", "sin(Add(Symbol('j', commutative=True), Mul(Integer(-1), Symbol('o', commutative=True))))"]}, {"premise_expression": "a b", "variable": "a", "positive": "\\frac{a^{2} b}{2}", "negatives": ["\\frac{a b^{2}}{2}", "\\frac{a^{2}}{2 b}", "a \\log{(2 b)}", "b \\sin{(a)}"], "srepr_premise_expression": "Mul(Symbol('a', commutative=True), Symbol('b', commutative=True))", "srepr_variable": "Symbol('a', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('a', commutative=True), Integer(2)), Symbol('b', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('a', commutative=True), Pow(Symbol('b', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('a', commutative=True), Integer(2)), Pow(Symbol('b', commutative=True), Integer(-1)))", "Mul(Symbol('a', commutative=True), log(Mul(Integer(2), Symbol('b', commutative=True))))", "Mul(Symbol('b', commutative=True), sin(Symbol('a', commutative=True)))"]}, {"premise_expression": "\\frac{\\log{(T)}}{g}", "variable": "g", "positive": "\\log{(T)} \\log{(g)}", "negatives": ["\\frac{g^{2} \\log{(T)}}{2}", "\\frac{T (\\log{(T)} - 1)}{g}", "\\frac{\\sin{(g)}}{T}", "\\frac{g (- 2 T + g)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('g', commutative=True), Integer(-1)), log(Symbol('T', commutative=True)))", "srepr_variable": "Symbol('g', commutative=True)", "srepr_positive": "Mul(log(Symbol('T', commutative=True)), log(Symbol('g', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('g', commutative=True), Integer(2)), log(Symbol('T', commutative=True)))", "Mul(Symbol('T', commutative=True), Pow(Symbol('g', commutative=True), Integer(-1)), Add(log(Symbol('T', commutative=True)), Integer(-1)))", "Mul(Pow(Symbol('T', commutative=True), Integer(-1)), sin(Symbol('g', commutative=True)))", "Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('T', commutative=True)), Symbol('g', commutative=True)))"]}, {"premise_expression": "\\frac{\\cos{(H)}}{J}", "variable": "H", "positive": "\\frac{\\sin{(H)}}{J}", "negatives": ["J e^{\\frac{H}{J}}", "\\log{(H)} \\cos{(J)}", "\\frac{H (H + 2 J)}{2}", "\\log{(J)} \\cos{(H)}"], "srepr_premise_expression": "Mul(Pow(Symbol('J', commutative=True), Integer(-1)), cos(Symbol('H', commutative=True)))", "srepr_variable": "Symbol('H', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('J', commutative=True), Integer(-1)), sin(Symbol('H', commutative=True)))", "srepr_negatives": ["Mul(Symbol('J', commutative=True), exp(Mul(Symbol('H', commutative=True), Pow(Symbol('J', commutative=True), Integer(-1)))))", "Mul(log(Symbol('H', commutative=True)), cos(Symbol('J', commutative=True)))", "Mul(Rational(1, 2), Symbol('H', commutative=True), Add(Symbol('H', commutative=True), Mul(Integer(2), Symbol('J', commutative=True))))", "Mul(log(Symbol('J', commutative=True)), cos(Symbol('H', commutative=True)))"]}, {"premise_expression": "- B + U", "variable": "B", "positive": "\\frac{B (- B + 2 U)}{2}", "negatives": ["\\frac{B (B + 2 U)}{2}", "\\frac{U (- 2 B + U)}{2}", "\\frac{B^{2} U}{2}", "\\frac{B^{2} \\log{(U)}}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('B', commutative=True)), Symbol('U', commutative=True))", "srepr_variable": "Symbol('B', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('B', commutative=True), Add(Mul(Integer(-1), Symbol('B', commutative=True)), Mul(Integer(2), Symbol('U', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('B', commutative=True), Add(Symbol('B', commutative=True), Mul(Integer(2), Symbol('U', commutative=True))))", "Mul(Rational(1, 2), Symbol('U', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('B', commutative=True)), Symbol('U', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('B', commutative=True), Integer(2)), Symbol('U', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('B', commutative=True), Integer(2)), log(Symbol('U', commutative=True)))"]}, {"premise_expression": "G - g", "variable": "g", "positive": "\\frac{g (2 G - g)}{2}", "negatives": ["\\frac{G (G - 2 g)}{2}", "\\frac{g^{2} \\sin{(G)}}{2}", "- \\cos{(G - g)}", "e^{G + g}"], "srepr_premise_expression": "Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('g', commutative=True)))", "srepr_variable": "Symbol('g', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Mul(Integer(2), Symbol('G', commutative=True)), Mul(Integer(-1), Symbol('g', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Symbol('G', commutative=True), Mul(Integer(-1), Integer(2), Symbol('g', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('g', commutative=True), Integer(2)), sin(Symbol('G', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('g', commutative=True)))))", "exp(Add(Symbol('G', commutative=True), Symbol('g', commutative=True)))"]}, {"premise_expression": "t + \\sin{(F)}", "variable": "t", "positive": "\\frac{t (t + 2 \\sin{(F)})}{2}", "negatives": ["F t - \\cos{(F)}", "\\frac{t (2 F + t)}{2}", "\\frac{t (2 F - t)}{2}", "F t - \\cos{(t)}"], "srepr_premise_expression": "Add(Symbol('t', commutative=True), sin(Symbol('F', commutative=True)))", "srepr_variable": "Symbol('t', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('t', commutative=True), Add(Symbol('t', commutative=True), Mul(Integer(2), sin(Symbol('F', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('F', commutative=True), Symbol('t', commutative=True)), Mul(Integer(-1), cos(Symbol('F', commutative=True))))", "Mul(Rational(1, 2), Symbol('t', commutative=True), Add(Mul(Integer(2), Symbol('F', commutative=True)), Symbol('t', commutative=True)))", "Mul(Rational(1, 2), Symbol('t', commutative=True), Add(Mul(Integer(2), Symbol('F', commutative=True)), Mul(Integer(-1), Symbol('t', commutative=True))))", "Add(Mul(Symbol('F', commutative=True), Symbol('t', commutative=True)), Mul(Integer(-1), cos(Symbol('t', commutative=True))))"]}, {"premise_expression": "\\frac{R}{H}", "variable": "H", "positive": "R \\log{(H)}", "negatives": ["R e^{H}", "\\frac{R^{2}}{2 H}", "- \\frac{\\cos{(H)}}{R}", "\\frac{H \\cos{(R)}}{R}"], "srepr_premise_expression": "Mul(Pow(Symbol('H', commutative=True), Integer(-1)), Symbol('R', commutative=True))", "srepr_variable": "Symbol('H', commutative=True)", "srepr_positive": "Mul(Symbol('R', commutative=True), log(Symbol('H', commutative=True)))", "srepr_negatives": ["Mul(Symbol('R', commutative=True), exp(Symbol('H', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('H', commutative=True), Integer(-1)), Pow(Symbol('R', commutative=True), Integer(2)))", "Mul(Integer(-1), Pow(Symbol('R', commutative=True), Integer(-1)), cos(Symbol('H', commutative=True)))", "Mul(Symbol('H', commutative=True), Pow(Symbol('R', commutative=True), Integer(-1)), cos(Symbol('R', commutative=True)))"]}, {"premise_expression": "\\frac{t}{b}", "variable": "t", "positive": "\\frac{t^{2}}{2 b}", "negatives": ["t \\log{(b)}", "\\frac{t^{2} \\cos{(b)}}{2}", "\\frac{t^{2} \\log{(b)}}{2}", "- \\sin{(b - t)}"], "srepr_premise_expression": "Mul(Pow(Symbol('b', commutative=True), Integer(-1)), Symbol('t', commutative=True))", "srepr_variable": "Symbol('t', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('b', commutative=True), Integer(-1)), Pow(Symbol('t', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('t', commutative=True), log(Symbol('b', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('t', commutative=True), Integer(2)), cos(Symbol('b', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('t', commutative=True), Integer(2)), log(Symbol('b', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('b', commutative=True), Mul(Integer(-1), Symbol('t', commutative=True)))))"]}, {"premise_expression": "\\log{(o^{c})}", "variable": "c", "positive": "\\frac{c^{2} \\log{(o)}}{2}", "negatives": ["o \\sin{(c)}", "c (\\log{(\\frac{c}{o})} - 1)", "- \\cos{(c + o)}", "o (- c + \\log{(o^{c})})"], "srepr_premise_expression": "log(Pow(Symbol('o', commutative=True), Symbol('c', commutative=True)))", "srepr_variable": "Symbol('c', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('c', commutative=True), Integer(2)), log(Symbol('o', commutative=True)))", "srepr_negatives": ["Mul(Symbol('o', commutative=True), sin(Symbol('c', commutative=True)))", "Mul(Symbol('c', commutative=True), Add(log(Mul(Symbol('c', commutative=True), Pow(Symbol('o', commutative=True), Integer(-1)))), Integer(-1)))", "Mul(Integer(-1), cos(Add(Symbol('c', commutative=True), Symbol('o', commutative=True))))", "Mul(Symbol('o', commutative=True), Add(Mul(Integer(-1), Symbol('c', commutative=True)), log(Pow(Symbol('o', commutative=True), Symbol('c', commutative=True)))))"]}, {"premise_expression": "A p", "variable": "A", "positive": "\\frac{A^{2} p}{2}", "negatives": ["\\frac{A p^{2}}{2}", "A^{2}", "\\frac{A (A - 2 p)}{2}", "A p + e^{A}"], "srepr_premise_expression": "Mul(Symbol('A', commutative=True), Symbol('p', commutative=True))", "srepr_variable": "Symbol('A', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2)), Symbol('p', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('A', commutative=True), Pow(Symbol('p', commutative=True), Integer(2)))", "Pow(Symbol('A', commutative=True), Integer(2))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Symbol('A', commutative=True), Mul(Integer(-1), Integer(2), Symbol('p', commutative=True))))", "Add(Mul(Symbol('A', commutative=True), Symbol('p', commutative=True)), exp(Symbol('A', commutative=True)))"]}, {"premise_expression": "- b + \\log{(x)}", "variable": "x", "positive": "x (- b + \\log{(x)} - 1)", "negatives": ["\\frac{b (- b + 2 \\log{(x)})}{2}", "x (\\log{(\\frac{b}{x})} + 1)", "\\frac{x (2 b + x)}{2}", "- \\sin{(b - x)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('b', commutative=True)), log(Symbol('x', commutative=True)))", "srepr_variable": "Symbol('x', commutative=True)", "srepr_positive": "Mul(Symbol('x', commutative=True), Add(Mul(Integer(-1), Symbol('b', commutative=True)), log(Symbol('x', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('b', commutative=True), Add(Mul(Integer(-1), Symbol('b', commutative=True)), Mul(Integer(2), log(Symbol('x', commutative=True)))))", "Mul(Symbol('x', commutative=True), Add(log(Mul(Symbol('b', commutative=True), Pow(Symbol('x', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Rational(1, 2), Symbol('x', commutative=True), Add(Mul(Integer(2), Symbol('b', commutative=True)), Symbol('x', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('b', commutative=True), Mul(Integer(-1), Symbol('x', commutative=True)))))"]}, {"premise_expression": "A + \\log{(k)}", "variable": "A", "positive": "\\frac{A (A + 2 \\log{(k)})}{2}", "negatives": ["\\frac{A (A + 2 \\cos{(k)})}{2}", "\\frac{A (A + 2 k)}{2}", "k (A + \\log{(k)} - 1)", "A k + e^{A}"], "srepr_premise_expression": "Add(Symbol('A', commutative=True), log(Symbol('k', commutative=True)))", "srepr_variable": "Symbol('A', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Symbol('A', commutative=True), Mul(Integer(2), log(Symbol('k', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Symbol('A', commutative=True), Mul(Integer(2), cos(Symbol('k', commutative=True)))))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Symbol('A', commutative=True), Mul(Integer(2), Symbol('k', commutative=True))))", "Mul(Symbol('k', commutative=True), Add(Symbol('A', commutative=True), log(Symbol('k', commutative=True)), Integer(-1)))", "Add(Mul(Symbol('A', commutative=True), Symbol('k', commutative=True)), exp(Symbol('A', commutative=True)))"]}, {"premise_expression": "- M + e^{N}", "variable": "M", "positive": "\\frac{M (- M + 2 e^{N})}{2}", "negatives": ["- M N + e^{N}", "\\frac{M^{2} \\cos{(N)}}{2}", "e^{M + N}", "- \\cos{(M - N)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('M', commutative=True)), exp(Symbol('N', commutative=True)))", "srepr_variable": "Symbol('M', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('M', commutative=True), Add(Mul(Integer(-1), Symbol('M', commutative=True)), Mul(Integer(2), exp(Symbol('N', commutative=True)))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('M', commutative=True), Symbol('N', commutative=True)), exp(Symbol('N', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('M', commutative=True), Integer(2)), cos(Symbol('N', commutative=True)))", "exp(Add(Symbol('M', commutative=True), Symbol('N', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('M', commutative=True), Mul(Integer(-1), Symbol('N', commutative=True)))))"]}, {"premise_expression": "E \\log{(G)}", "variable": "E", "positive": "\\frac{E^{2} \\log{(G)}}{2}", "negatives": ["\\frac{E^{2} e^{G}}{2}", "E G (\\log{(G)} - 1)", "\\frac{E (E + 2 \\cos{(G)})}{2}", "G \\sin{(E)}"], "srepr_premise_expression": "Mul(Symbol('E', commutative=True), log(Symbol('G', commutative=True)))", "srepr_variable": "Symbol('E', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('E', commutative=True), Integer(2)), log(Symbol('G', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('E', commutative=True), Integer(2)), exp(Symbol('G', commutative=True)))", "Mul(Symbol('E', commutative=True), Symbol('G', commutative=True), Add(log(Symbol('G', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('E', commutative=True), Add(Symbol('E', commutative=True), Mul(Integer(2), cos(Symbol('G', commutative=True)))))", "Mul(Symbol('G', commutative=True), sin(Symbol('E', commutative=True)))"]}, {"premise_expression": "\\frac{\\cos{(J)}}{f}", "variable": "f", "positive": "\\log{(f)} \\cos{(J)}", "negatives": ["\\frac{f (f + 2 \\cos{(J)})}{2}", "\\frac{\\sin{(J)}}{f}", "e^{J + f}", "e^{- J + f}"], "srepr_premise_expression": "Mul(Pow(Symbol('f', commutative=True), Integer(-1)), cos(Symbol('J', commutative=True)))", "srepr_variable": "Symbol('f', commutative=True)", "srepr_positive": "Mul(log(Symbol('f', commutative=True)), cos(Symbol('J', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Symbol('f', commutative=True), Mul(Integer(2), cos(Symbol('J', commutative=True)))))", "Mul(Pow(Symbol('f', commutative=True), Integer(-1)), sin(Symbol('J', commutative=True)))", "exp(Add(Symbol('J', commutative=True), Symbol('f', commutative=True)))", "exp(Add(Mul(Integer(-1), Symbol('J', commutative=True)), Symbol('f', commutative=True)))"]}, {"premise_expression": "\\frac{f}{P}", "variable": "P", "positive": "f \\log{(P)}", "negatives": ["f e^{P}", "\\frac{f^{2}}{2 P}", "\\frac{P^{2} f}{2}", "\\frac{P^{2} \\cos{(f)}}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('P', commutative=True), Integer(-1)), Symbol('f', commutative=True))", "srepr_variable": "Symbol('P', commutative=True)", "srepr_positive": "Mul(Symbol('f', commutative=True), log(Symbol('P', commutative=True)))", "srepr_negatives": ["Mul(Symbol('f', commutative=True), exp(Symbol('P', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(-1)), Pow(Symbol('f', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2)), Symbol('f', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2)), cos(Symbol('f', commutative=True)))"]}, {"premise_expression": "\\log{(I)}^{G}", "variable": "I", "positive": "(- \\log{(I)})^{- G} \\log{(I)}^{G} \\Gamma(G + 1, - \\log{(I)})", "negatives": ["\\frac{I (- I + 2 \\log{(G)})}{2}", "- G I + \\sin{(I)}", "- \\cos{(G + I)}", "e^{G + I}"], "srepr_premise_expression": "Pow(log(Symbol('I', commutative=True)), Symbol('G', commutative=True))", "srepr_variable": "Symbol('I', commutative=True)", "srepr_positive": "Mul(Pow(Mul(Integer(-1), log(Symbol('I', commutative=True))), Mul(Integer(-1), Symbol('G', commutative=True))), Pow(log(Symbol('I', commutative=True)), Symbol('G', commutative=True)), uppergamma(Add(Symbol('G', commutative=True), Integer(1)), Mul(Integer(-1), log(Symbol('I', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('I', commutative=True), Add(Mul(Integer(-1), Symbol('I', commutative=True)), Mul(Integer(2), log(Symbol('G', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('G', commutative=True), Symbol('I', commutative=True)), sin(Symbol('I', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('G', commutative=True), Symbol('I', commutative=True))))", "exp(Add(Symbol('G', commutative=True), Symbol('I', commutative=True)))"]}, {"premise_expression": "e^{h + u}", "variable": "h", "positive": "e^{h + u}", "negatives": ["u e^{\\frac{h}{u}}", "u e^{h}", "\\frac{h (h + 2 u)}{2}", "h u - \\cos{(h)}"], "srepr_premise_expression": "exp(Add(Symbol('h', commutative=True), Symbol('u', commutative=True)))", "srepr_variable": "Symbol('h', commutative=True)", "srepr_positive": "exp(Add(Symbol('h', commutative=True), Symbol('u', commutative=True)))", "srepr_negatives": ["Mul(Symbol('u', commutative=True), exp(Mul(Symbol('h', commutative=True), Pow(Symbol('u', commutative=True), Integer(-1)))))", "Mul(Symbol('u', commutative=True), exp(Symbol('h', commutative=True)))", "Mul(Rational(1, 2), Symbol('h', commutative=True), Add(Symbol('h', commutative=True), Mul(Integer(2), Symbol('u', commutative=True))))", "Add(Mul(Symbol('h', commutative=True), Symbol('u', commutative=True)), Mul(Integer(-1), cos(Symbol('h', commutative=True))))"]}, {"premise_expression": "\\frac{o}{t}", "variable": "t", "positive": "o \\log{(t)}", "negatives": ["\\frac{o^{2}}{2 t}", "o e^{\\frac{t}{o}}", "- \\frac{\\cos{(t)}}{o}", "\\frac{t^{2} \\log{(o)}}{2}"], "srepr_premise_expression": "Mul(Symbol('o', commutative=True), Pow(Symbol('t', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('t', commutative=True)", "srepr_positive": "Mul(Symbol('o', commutative=True), log(Symbol('t', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('o', commutative=True), Integer(2)), Pow(Symbol('t', commutative=True), Integer(-1)))", "Mul(Symbol('o', commutative=True), exp(Mul(Pow(Symbol('o', commutative=True), Integer(-1)), Symbol('t', commutative=True))))", "Mul(Integer(-1), Pow(Symbol('o', commutative=True), Integer(-1)), cos(Symbol('t', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('t', commutative=True), Integer(2)), log(Symbol('o', commutative=True)))"]}, {"premise_expression": "\\frac{\\sin{(k)}}{N}", "variable": "N", "positive": "\\log{(N)} \\sin{(k)}", "negatives": ["e^{k} \\log{(N)}", "\\sin{(N - k)}", "\\frac{N (\\log{(N)} - 1)}{k}", "- \\frac{\\cos{(k)}}{N}"], "srepr_premise_expression": "Mul(Pow(Symbol('N', commutative=True), Integer(-1)), sin(Symbol('k', commutative=True)))", "srepr_variable": "Symbol('N', commutative=True)", "srepr_positive": "Mul(log(Symbol('N', commutative=True)), sin(Symbol('k', commutative=True)))", "srepr_negatives": ["Mul(exp(Symbol('k', commutative=True)), log(Symbol('N', commutative=True)))", "sin(Add(Symbol('N', commutative=True), Mul(Integer(-1), Symbol('k', commutative=True))))", "Mul(Symbol('N', commutative=True), Pow(Symbol('k', commutative=True), Integer(-1)), Add(log(Symbol('N', commutative=True)), Integer(-1)))", "Mul(Integer(-1), Pow(Symbol('N', commutative=True), Integer(-1)), cos(Symbol('k', commutative=True)))"]}, {"premise_expression": "U e^{p}", "variable": "U", "positive": "\\frac{U^{2} e^{p}}{2}", "negatives": ["\\frac{U^{2} \\log{(p)}}{2}", "\\frac{U^{2} \\sin{(p)}}{2}", "U e^{p}", "\\frac{U^{2} p}{2}"], "srepr_premise_expression": "Mul(Symbol('U', commutative=True), exp(Symbol('p', commutative=True)))", "srepr_variable": "Symbol('U', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('U', commutative=True), Integer(2)), exp(Symbol('p', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('U', commutative=True), Integer(2)), log(Symbol('p', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('U', commutative=True), Integer(2)), sin(Symbol('p', commutative=True)))", "Mul(Symbol('U', commutative=True), exp(Symbol('p', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('U', commutative=True), Integer(2)), Symbol('p', commutative=True))"]}, {"premise_expression": "C b", "variable": "C", "positive": "\\frac{C^{2} b}{2}", "negatives": ["\\frac{C b^{2}}{2}", "\\frac{C (C + 2 b)}{2}", "\\sin{(C + b)}", "\\cos{(C - b)}"], "srepr_premise_expression": "Mul(Symbol('C', commutative=True), Symbol('b', commutative=True))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2)), Symbol('b', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('C', commutative=True), Pow(Symbol('b', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Symbol('C', commutative=True), Mul(Integer(2), Symbol('b', commutative=True))))", "sin(Add(Symbol('C', commutative=True), Symbol('b', commutative=True)))", "cos(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('b', commutative=True))))"]}, {"premise_expression": "\\frac{G - m}{w}", "variable": "G", "positive": "\\frac{G (G - 2 m)}{2 w}", "negatives": ["\\frac{m (2 G - m)}{2 w}", "\\frac{G (G + 2 m w)}{2}", "(G - m) \\log{(w)}", "\\frac{G (G - 2 m - 2 w)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('w', commutative=True), Integer(-1)), Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('m', commutative=True))))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('G', commutative=True), Pow(Symbol('w', commutative=True), Integer(-1)), Add(Symbol('G', commutative=True), Mul(Integer(-1), Integer(2), Symbol('m', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('m', commutative=True), Pow(Symbol('w', commutative=True), Integer(-1)), Add(Mul(Integer(2), Symbol('G', commutative=True)), Mul(Integer(-1), Symbol('m', commutative=True))))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Symbol('G', commutative=True), Mul(Integer(2), Symbol('m', commutative=True), Symbol('w', commutative=True))))", "Mul(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('m', commutative=True))), log(Symbol('w', commutative=True)))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Symbol('G', commutative=True), Mul(Integer(-1), Integer(2), Symbol('m', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('w', commutative=True))))"]}, {"premise_expression": "\\frac{K - X}{G}", "variable": "X", "positive": "\\frac{X (2 K - X)}{2 G}", "negatives": ["\\frac{K (K - 2 X)}{2 G}", "\\frac{G X (- 2 K + X)}{2}", "(K - X) \\log{(G)}", "- K X + \\frac{X^{2}}{2 G}"], "srepr_premise_expression": "Mul(Pow(Symbol('G', commutative=True), Integer(-1)), Add(Symbol('K', commutative=True), Mul(Integer(-1), Symbol('X', commutative=True))))", "srepr_variable": "Symbol('X', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(-1)), Symbol('X', commutative=True), Add(Mul(Integer(2), Symbol('K', commutative=True)), Mul(Integer(-1), Symbol('X', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(-1)), Symbol('K', commutative=True), Add(Symbol('K', commutative=True), Mul(Integer(-1), Integer(2), Symbol('X', commutative=True))))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Symbol('X', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('K', commutative=True)), Symbol('X', commutative=True)))", "Mul(Add(Symbol('K', commutative=True), Mul(Integer(-1), Symbol('X', commutative=True))), log(Symbol('G', commutative=True)))", "Add(Mul(Integer(-1), Symbol('K', commutative=True), Symbol('X', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(-1)), Pow(Symbol('X', commutative=True), Integer(2))))"]}, {"premise_expression": "(S - Z)^{S}", "variable": "S", "positive": "\\int (S - Z)^{S} dS", "negatives": ["\\sin{(S - Z)}", "- \\cos{(S + Z)}", "S (\\log{(\\frac{S}{Z})} - 1)", "S Z - \\cos{(S)}"], "srepr_premise_expression": "Pow(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('Z', commutative=True))), Symbol('S', commutative=True))", "srepr_variable": "Symbol('S', commutative=True)", "srepr_positive": "NonElementaryIntegral(Pow(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('Z', commutative=True))), Symbol('S', commutative=True)), Tuple(Symbol('S', commutative=True)))", "srepr_negatives": ["sin(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('Z', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('S', commutative=True), Symbol('Z', commutative=True))))", "Mul(Symbol('S', commutative=True), Add(log(Mul(Symbol('S', commutative=True), Pow(Symbol('Z', commutative=True), Integer(-1)))), Integer(-1)))", "Add(Mul(Symbol('S', commutative=True), Symbol('Z', commutative=True)), Mul(Integer(-1), cos(Symbol('S', commutative=True))))"]}, {"premise_expression": "- K + \\frac{T}{p}", "variable": "p", "positive": "- K p + T \\log{(p)}", "negatives": ["- K T + \\frac{T^{2}}{2 p}", "T^{T} \\log{(p)}", "\\frac{T \\log{(p)}}{K}", "- \\frac{K^{2}}{2} + \\frac{K T}{p}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('K', commutative=True)), Mul(Symbol('T', commutative=True), Pow(Symbol('p', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('p', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('K', commutative=True), Symbol('p', commutative=True)), Mul(Symbol('T', commutative=True), log(Symbol('p', commutative=True))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('K', commutative=True), Symbol('T', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('T', commutative=True), Integer(2)), Pow(Symbol('p', commutative=True), Integer(-1))))", "Mul(Pow(Symbol('T', commutative=True), Symbol('T', commutative=True)), log(Symbol('p', commutative=True)))", "Mul(Pow(Symbol('K', commutative=True), Integer(-1)), Symbol('T', commutative=True), log(Symbol('p', commutative=True)))", "Add(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('K', commutative=True), Integer(2))), Mul(Symbol('K', commutative=True), Symbol('T', commutative=True), Pow(Symbol('p', commutative=True), Integer(-1))))"]}, {"premise_expression": "\\frac{K - a}{z}", "variable": "K", "positive": "\\frac{K (K - 2 a)}{2 z}", "negatives": ["\\frac{K (K + 2 a)}{2 z}", "\\frac{a (2 K - a)}{2 z}", "\\frac{K (- K + 2 a z)}{2}", "\\frac{K (K a + 2 z)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('z', commutative=True), Integer(-1)), Add(Symbol('K', commutative=True), Mul(Integer(-1), Symbol('a', commutative=True))))", "srepr_variable": "Symbol('K', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('K', commutative=True), Pow(Symbol('z', commutative=True), Integer(-1)), Add(Symbol('K', commutative=True), Mul(Integer(-1), Integer(2), Symbol('a', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('K', commutative=True), Pow(Symbol('z', commutative=True), Integer(-1)), Add(Symbol('K', commutative=True), Mul(Integer(2), Symbol('a', commutative=True))))", "Mul(Rational(1, 2), Symbol('a', commutative=True), Pow(Symbol('z', commutative=True), Integer(-1)), Add(Mul(Integer(2), Symbol('K', commutative=True)), Mul(Integer(-1), Symbol('a', commutative=True))))", "Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Mul(Integer(-1), Symbol('K', commutative=True)), Mul(Integer(2), Symbol('a', commutative=True), Symbol('z', commutative=True))))", "Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Mul(Symbol('K', commutative=True), Symbol('a', commutative=True)), Mul(Integer(2), Symbol('z', commutative=True))))"]}, {"premise_expression": "e^{- C + u}", "variable": "u", "positive": "e^{- C + u}", "negatives": ["- e^{- C + u}", "- \\sin{(C - u)}", "C \\sin{(u)}", "C u + e^{u}"], "srepr_premise_expression": "exp(Add(Mul(Integer(-1), Symbol('C', commutative=True)), Symbol('u', commutative=True)))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "exp(Add(Mul(Integer(-1), Symbol('C', commutative=True)), Symbol('u', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('C', commutative=True)), Symbol('u', commutative=True))))", "Mul(Integer(-1), sin(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('u', commutative=True)))))", "Mul(Symbol('C', commutative=True), sin(Symbol('u', commutative=True)))", "Add(Mul(Symbol('C', commutative=True), Symbol('u', commutative=True)), exp(Symbol('u', commutative=True)))"]}, {"premise_expression": "\\frac{V}{Y}", "variable": "Y", "positive": "V \\log{(Y)}", "negatives": ["\\frac{V^{2}}{2 Y}", "\\sin{(V + Y)}", "- \\cos{(V + Y)}", "- V Y + e^{Y}"], "srepr_premise_expression": "Mul(Symbol('V', commutative=True), Pow(Symbol('Y', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('Y', commutative=True)", "srepr_positive": "Mul(Symbol('V', commutative=True), log(Symbol('Y', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('V', commutative=True), Integer(2)), Pow(Symbol('Y', commutative=True), Integer(-1)))", "sin(Add(Symbol('V', commutative=True), Symbol('Y', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('V', commutative=True), Symbol('Y', commutative=True))))", "Add(Mul(Integer(-1), Symbol('V', commutative=True), Symbol('Y', commutative=True)), exp(Symbol('Y', commutative=True)))"]}, {"premise_expression": "- P + z", "variable": "z", "positive": "\\frac{z (- 2 P + z)}{2}", "negatives": ["\\frac{P (- P + 2 z)}{2}", "\\frac{z^{2} \\sin{(P)}}{2}", "- \\cos{(P + z)}", "\\frac{z (- z + 2 \\cos{(P)})}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('P', commutative=True)), Symbol('z', commutative=True))", "srepr_variable": "Symbol('z', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('z', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('P', commutative=True)), Symbol('z', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Mul(Integer(-1), Symbol('P', commutative=True)), Mul(Integer(2), Symbol('z', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('z', commutative=True), Integer(2)), sin(Symbol('P', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('P', commutative=True), Symbol('z', commutative=True))))", "Mul(Rational(1, 2), Symbol('z', commutative=True), Add(Mul(Integer(-1), Symbol('z', commutative=True)), Mul(Integer(2), cos(Symbol('P', commutative=True)))))"]}, {"premise_expression": "- C + \\frac{R}{C}", "variable": "C", "positive": "- \\frac{C^{2}}{2} + R \\log{(C)}", "negatives": ["- C R + \\frac{R^{2}}{2 C}", "\\frac{C^{2} R}{2}", "\\frac{C (- C + 2 e^{R})}{2}", "C R (\\log{(C)} - 1)"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('C', commutative=True)), Mul(Pow(Symbol('C', commutative=True), Integer(-1)), Symbol('R', commutative=True)))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2))), Mul(Symbol('R', commutative=True), log(Symbol('C', commutative=True))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('C', commutative=True), Symbol('R', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(-1)), Pow(Symbol('R', commutative=True), Integer(2))))", "Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2)), Symbol('R', commutative=True))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Mul(Integer(-1), Symbol('C', commutative=True)), Mul(Integer(2), exp(Symbol('R', commutative=True)))))", "Mul(Symbol('C', commutative=True), Symbol('R', commutative=True), Add(log(Symbol('C', commutative=True)), Integer(-1)))"]}, {"premise_expression": "e^{B + J}", "variable": "B", "positive": "e^{B + J}", "negatives": ["\\sin{(B - J)}", "B J - \\cos{(B)}", "B (\\log{(\\frac{B}{J})} - 1)", "B (\\log{(B J)} - 1)"], "srepr_premise_expression": "exp(Add(Symbol('B', commutative=True), Symbol('J', commutative=True)))", "srepr_variable": "Symbol('B', commutative=True)", "srepr_positive": "exp(Add(Symbol('B', commutative=True), Symbol('J', commutative=True)))", "srepr_negatives": ["sin(Add(Symbol('B', commutative=True), Mul(Integer(-1), Symbol('J', commutative=True))))", "Add(Mul(Symbol('B', commutative=True), Symbol('J', commutative=True)), Mul(Integer(-1), cos(Symbol('B', commutative=True))))", "Mul(Symbol('B', commutative=True), Add(log(Mul(Symbol('B', commutative=True), Pow(Symbol('J', commutative=True), Integer(-1)))), Integer(-1)))", "Mul(Symbol('B', commutative=True), Add(log(Mul(Symbol('B', commutative=True), Symbol('J', commutative=True))), Integer(-1)))"]}, {"premise_expression": "(h - u)^{u}", "variable": "u", "positive": "\\int (h - u)^{u} du", "negatives": ["- e^{h - u}", "e^{h + u}", "\\log{(u)} \\sin{(h)}", "\\frac{u (2 h + u)}{2}"], "srepr_premise_expression": "Pow(Add(Symbol('h', commutative=True), Mul(Integer(-1), Symbol('u', commutative=True))), Symbol('u', commutative=True))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "NonElementaryIntegral(Pow(Add(Symbol('h', commutative=True), Mul(Integer(-1), Symbol('u', commutative=True))), Symbol('u', commutative=True)), Tuple(Symbol('u', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Symbol('h', commutative=True), Mul(Integer(-1), Symbol('u', commutative=True)))))", "exp(Add(Symbol('h', commutative=True), Symbol('u', commutative=True)))", "Mul(log(Symbol('u', commutative=True)), sin(Symbol('h', commutative=True)))", "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(2), Symbol('h', commutative=True)), Symbol('u', commutative=True)))"]}, {"premise_expression": "g + e^{c}", "variable": "c", "positive": "c g + e^{c}", "negatives": ["g e^{c}", "- c g - \\cos{(c)}", "c (g + \\sin{(g)})", "\\frac{g (g + 2 e^{c})}{2}"], "srepr_premise_expression": "Add(Symbol('g', commutative=True), exp(Symbol('c', commutative=True)))", "srepr_variable": "Symbol('c', commutative=True)", "srepr_positive": "Add(Mul(Symbol('c', commutative=True), Symbol('g', commutative=True)), exp(Symbol('c', commutative=True)))", "srepr_negatives": ["Mul(Symbol('g', commutative=True), exp(Symbol('c', commutative=True)))", "Add(Mul(Integer(-1), Symbol('c', commutative=True), Symbol('g', commutative=True)), Mul(Integer(-1), cos(Symbol('c', commutative=True))))", "Mul(Symbol('c', commutative=True), Add(Symbol('g', commutative=True), sin(Symbol('g', commutative=True))))", "Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Symbol('g', commutative=True), Mul(Integer(2), exp(Symbol('c', commutative=True)))))"]}, {"premise_expression": "\\log{(o - q)}", "variable": "q", "positive": "- o \\log{(- o + q)} + q \\log{(o - q)} - q", "negatives": ["- o \\log{(- o + q)} + q \\log{(- o + q)} - q", "o \\log{(o - q)} - o - q \\log{(o - q)}", "q (- o + \\log{(q^{o})})", "q (\\log{(o q)} - 1)"], "srepr_premise_expression": "log(Add(Symbol('o', commutative=True), Mul(Integer(-1), Symbol('q', commutative=True))))", "srepr_variable": "Symbol('q', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('o', commutative=True), log(Add(Mul(Integer(-1), Symbol('o', commutative=True)), Symbol('q', commutative=True)))), Mul(Symbol('q', commutative=True), log(Add(Symbol('o', commutative=True), Mul(Integer(-1), Symbol('q', commutative=True))))), Mul(Integer(-1), Symbol('q', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('o', commutative=True), log(Add(Mul(Integer(-1), Symbol('o', commutative=True)), Symbol('q', commutative=True)))), Mul(Symbol('q', commutative=True), log(Add(Mul(Integer(-1), Symbol('o', commutative=True)), Symbol('q', commutative=True)))), Mul(Integer(-1), Symbol('q', commutative=True)))", "Add(Mul(Symbol('o', commutative=True), log(Add(Symbol('o', commutative=True), Mul(Integer(-1), Symbol('q', commutative=True))))), Mul(Integer(-1), Symbol('o', commutative=True)), Mul(Integer(-1), Symbol('q', commutative=True), log(Add(Symbol('o', commutative=True), Mul(Integer(-1), Symbol('q', commutative=True))))))", "Mul(Symbol('q', commutative=True), Add(Mul(Integer(-1), Symbol('o', commutative=True)), log(Pow(Symbol('q', commutative=True), Symbol('o', commutative=True)))))", "Mul(Symbol('q', commutative=True), Add(log(Mul(Symbol('o', commutative=True), Symbol('q', commutative=True))), Integer(-1)))"]}, {"premise_expression": "m + \\sin{(r)}", "variable": "r", "positive": "m r - \\cos{(r)}", "negatives": ["m \\log{(r)}", "m e^{r}", "e^{- m + r}", "\\frac{m (m + 2 \\sin{(r)})}{2}"], "srepr_premise_expression": "Add(Symbol('m', commutative=True), sin(Symbol('r', commutative=True)))", "srepr_variable": "Symbol('r', commutative=True)", "srepr_positive": "Add(Mul(Symbol('m', commutative=True), Symbol('r', commutative=True)), Mul(Integer(-1), cos(Symbol('r', commutative=True))))", "srepr_negatives": ["Mul(Symbol('m', commutative=True), log(Symbol('r', commutative=True)))", "Mul(Symbol('m', commutative=True), exp(Symbol('r', commutative=True)))", "exp(Add(Mul(Integer(-1), Symbol('m', commutative=True)), Symbol('r', commutative=True)))", "Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Symbol('m', commutative=True), Mul(Integer(2), sin(Symbol('r', commutative=True)))))"]}, {"premise_expression": "\\frac{C}{J} + M", "variable": "C", "positive": "\\frac{C^{2}}{2 J} + C M", "negatives": ["\\frac{C^{2}}{2 M} + C J", "C \\log{(J)} + J M", "\\frac{C^{2}}{2} + \\frac{C J}{M}", "\\frac{C^{2} M}{2 J}"], "srepr_premise_expression": "Add(Mul(Symbol('C', commutative=True), Pow(Symbol('J', commutative=True), Integer(-1))), Symbol('M', commutative=True))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Add(Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2)), Pow(Symbol('J', commutative=True), Integer(-1))), Mul(Symbol('C', commutative=True), Symbol('M', commutative=True)))", "srepr_negatives": ["Add(Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2)), Pow(Symbol('M', commutative=True), Integer(-1))), Mul(Symbol('C', commutative=True), Symbol('J', commutative=True)))", "Add(Mul(Symbol('C', commutative=True), log(Symbol('J', commutative=True))), Mul(Symbol('J', commutative=True), Symbol('M', commutative=True)))", "Add(Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2))), Mul(Symbol('C', commutative=True), Symbol('J', commutative=True), Pow(Symbol('M', commutative=True), Integer(-1))))", "Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2)), Pow(Symbol('J', commutative=True), Integer(-1)), Symbol('M', commutative=True))"]}, {"premise_expression": "\\log{(M + b)}", "variable": "M", "positive": "M \\log{(M + b)} - M + b \\log{(M + b)}", "negatives": ["M \\log{(M - b)} - M - b \\log{(M - b)}", "M \\log{(M + b)} + b \\log{(M + b)} - b", "M (b + \\log{(M)} - 1)", "M (\\log{(M b)} - 1)"], "srepr_premise_expression": "log(Add(Symbol('M', commutative=True), Symbol('b', commutative=True)))", "srepr_variable": "Symbol('M', commutative=True)", "srepr_positive": "Add(Mul(Symbol('M', commutative=True), log(Add(Symbol('M', commutative=True), Symbol('b', commutative=True)))), Mul(Integer(-1), Symbol('M', commutative=True)), Mul(Symbol('b', commutative=True), log(Add(Symbol('M', commutative=True), Symbol('b', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('M', commutative=True), log(Add(Symbol('M', commutative=True), Mul(Integer(-1), Symbol('b', commutative=True))))), Mul(Integer(-1), Symbol('M', commutative=True)), Mul(Integer(-1), Symbol('b', commutative=True), log(Add(Symbol('M', commutative=True), Mul(Integer(-1), Symbol('b', commutative=True))))))", "Add(Mul(Symbol('M', commutative=True), log(Add(Symbol('M', commutative=True), Symbol('b', commutative=True)))), Mul(Symbol('b', commutative=True), log(Add(Symbol('M', commutative=True), Symbol('b', commutative=True)))), Mul(Integer(-1), Symbol('b', commutative=True)))", "Mul(Symbol('M', commutative=True), Add(Symbol('b', commutative=True), log(Symbol('M', commutative=True)), Integer(-1)))", "Mul(Symbol('M', commutative=True), Add(log(Mul(Symbol('M', commutative=True), Symbol('b', commutative=True))), Integer(-1)))"]}, {"premise_expression": "- H + W", "variable": "W", "positive": "\\frac{W (- 2 H + W)}{2}", "negatives": ["\\frac{H (- H + 2 W)}{2}", "\\frac{W^{2} \\log{(H)}}{2}", "e^{H + W}", "\\frac{W (- W + 2 e^{H})}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('H', commutative=True)), Symbol('W', commutative=True))", "srepr_variable": "Symbol('W', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('W', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('H', commutative=True)), Symbol('W', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('H', commutative=True), Add(Mul(Integer(-1), Symbol('H', commutative=True)), Mul(Integer(2), Symbol('W', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('W', commutative=True), Integer(2)), log(Symbol('H', commutative=True)))", "exp(Add(Symbol('H', commutative=True), Symbol('W', commutative=True)))", "Mul(Rational(1, 2), Symbol('W', commutative=True), Add(Mul(Integer(-1), Symbol('W', commutative=True)), Mul(Integer(2), exp(Symbol('H', commutative=True)))))"]}, {"premise_expression": "\\frac{u}{f}", "variable": "u", "positive": "\\frac{u^{2}}{2 f}", "negatives": ["u \\log{(f)}", "f \\sin{(u)}", "u", "\\log{(u)} \\cos{(f)}"], "srepr_premise_expression": "Mul(Pow(Symbol('f', commutative=True), Integer(-1)), Symbol('u', commutative=True))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('f', commutative=True), Integer(-1)), Pow(Symbol('u', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('u', commutative=True), log(Symbol('f', commutative=True)))", "Mul(Symbol('f', commutative=True), sin(Symbol('u', commutative=True)))", "Symbol('u', commutative=True)", "Mul(log(Symbol('u', commutative=True)), cos(Symbol('f', commutative=True)))"]}, {"premise_expression": "\\frac{- P + s}{q}", "variable": "s", "positive": "\\frac{s (- 2 P + s)}{2 q}", "negatives": ["\\frac{s (2 P - s)}{2 q}", "\\frac{s (2 q + s)}{2 P}", "\\frac{P (- P + 2 s)}{2 q}", "\\frac{s^{2} (P + q)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('q', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('P', commutative=True)), Symbol('s', commutative=True)))", "srepr_variable": "Symbol('s', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('q', commutative=True), Integer(-1)), Symbol('s', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('P', commutative=True)), Symbol('s', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('q', commutative=True), Integer(-1)), Symbol('s', commutative=True), Add(Mul(Integer(2), Symbol('P', commutative=True)), Mul(Integer(-1), Symbol('s', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(-1)), Symbol('s', commutative=True), Add(Mul(Integer(2), Symbol('q', commutative=True)), Symbol('s', commutative=True)))", "Mul(Rational(1, 2), Symbol('P', commutative=True), Pow(Symbol('q', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('P', commutative=True)), Mul(Integer(2), Symbol('s', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('s', commutative=True), Integer(2)), Add(Symbol('P', commutative=True), Symbol('q', commutative=True)))"]}, {"premise_expression": "\\sin{(D + F)}", "variable": "F", "positive": "- \\cos{(D + F)}", "negatives": ["- D \\cos{(F)}", "F (\\log{(\\frac{D}{F})} + 1)", "\\frac{F^{2} \\log{(D)}}{2}", "F (- D + \\log{(F^{D})})"], "srepr_premise_expression": "sin(Add(Symbol('D', commutative=True), Symbol('F', commutative=True)))", "srepr_variable": "Symbol('F', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('D', commutative=True), Symbol('F', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), Symbol('D', commutative=True), cos(Symbol('F', commutative=True)))", "Mul(Symbol('F', commutative=True), Add(log(Mul(Symbol('D', commutative=True), Pow(Symbol('F', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Rational(1, 2), Pow(Symbol('F', commutative=True), Integer(2)), log(Symbol('D', commutative=True)))", "Mul(Symbol('F', commutative=True), Add(Mul(Integer(-1), Symbol('D', commutative=True)), log(Pow(Symbol('F', commutative=True), Symbol('D', commutative=True)))))"]}, {"premise_expression": "b + j y", "variable": "y", "positive": "\\frac{y (2 b + j y)}{2}", "negatives": ["\\frac{j (2 b + j y)}{2}", "\\frac{y (b y + 2 j)}{2}", "\\frac{b (b + 2 j y)}{2}", "\\frac{b y (2 j + y)}{2}"], "srepr_premise_expression": "Add(Symbol('b', commutative=True), Mul(Symbol('j', commutative=True), Symbol('y', commutative=True)))", "srepr_variable": "Symbol('y', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('y', commutative=True), Add(Mul(Integer(2), Symbol('b', commutative=True)), Mul(Symbol('j', commutative=True), Symbol('y', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('j', commutative=True), Add(Mul(Integer(2), Symbol('b', commutative=True)), Mul(Symbol('j', commutative=True), Symbol('y', commutative=True))))", "Mul(Rational(1, 2), Symbol('y', commutative=True), Add(Mul(Symbol('b', commutative=True), Symbol('y', commutative=True)), Mul(Integer(2), Symbol('j', commutative=True))))", "Mul(Rational(1, 2), Symbol('b', commutative=True), Add(Symbol('b', commutative=True), Mul(Integer(2), Symbol('j', commutative=True), Symbol('y', commutative=True))))", "Mul(Rational(1, 2), Symbol('b', commutative=True), Symbol('y', commutative=True), Add(Mul(Integer(2), Symbol('j', commutative=True)), Symbol('y', commutative=True)))"]}, {"premise_expression": "\\frac{w}{m}", "variable": "m", "positive": "w \\log{(m)}", "negatives": ["\\frac{w^{2}}{2 m}", "e^{w} \\log{(m)}", "\\log{(m)} \\log{(w)}", "\\frac{m^{2}}{2 w}"], "srepr_premise_expression": "Mul(Pow(Symbol('m', commutative=True), Integer(-1)), Symbol('w', commutative=True))", "srepr_variable": "Symbol('m', commutative=True)", "srepr_positive": "Mul(Symbol('w', commutative=True), log(Symbol('m', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('m', commutative=True), Integer(-1)), Pow(Symbol('w', commutative=True), Integer(2)))", "Mul(exp(Symbol('w', commutative=True)), log(Symbol('m', commutative=True)))", "Mul(log(Symbol('m', commutative=True)), log(Symbol('w', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('m', commutative=True), Integer(2)), Pow(Symbol('w', commutative=True), Integer(-1)))"]}, {"premise_expression": "\\log{(\\frac{C}{P})}", "variable": "P", "positive": "P (\\log{(\\frac{C}{P})} + 1)", "negatives": ["C (\\log{(\\frac{C}{P})} - 1)", "P (\\log{(\\frac{P}{C})} - 1)", "\\frac{P (\\log{(P)} - 1)}{C}", "\\log{(P)} \\sin{(C)}"], "srepr_premise_expression": "log(Mul(Symbol('C', commutative=True), Pow(Symbol('P', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('P', commutative=True)", "srepr_positive": "Mul(Symbol('P', commutative=True), Add(log(Mul(Symbol('C', commutative=True), Pow(Symbol('P', commutative=True), Integer(-1)))), Integer(1)))", "srepr_negatives": ["Mul(Symbol('C', commutative=True), Add(log(Mul(Symbol('C', commutative=True), Pow(Symbol('P', commutative=True), Integer(-1)))), Integer(-1)))", "Mul(Symbol('P', commutative=True), Add(log(Mul(Pow(Symbol('C', commutative=True), Integer(-1)), Symbol('P', commutative=True))), Integer(-1)))", "Mul(Pow(Symbol('C', commutative=True), Integer(-1)), Symbol('P', commutative=True), Add(log(Symbol('P', commutative=True)), Integer(-1)))", "Mul(log(Symbol('P', commutative=True)), sin(Symbol('C', commutative=True)))"]}, {"premise_expression": "\\frac{q}{J}", "variable": "J", "positive": "q \\log{(J)}", "negatives": ["\\frac{q^{2}}{2 J}", "- \\frac{\\cos{(J)}}{q}", "\\frac{J^{2} q}{2}", "J (\\log{(\\frac{q}{J})} + 1)"], "srepr_premise_expression": "Mul(Pow(Symbol('J', commutative=True), Integer(-1)), Symbol('q', commutative=True))", "srepr_variable": "Symbol('J', commutative=True)", "srepr_positive": "Mul(Symbol('q', commutative=True), log(Symbol('J', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('J', commutative=True), Integer(-1)), Pow(Symbol('q', commutative=True), Integer(2)))", "Mul(Integer(-1), Pow(Symbol('q', commutative=True), Integer(-1)), cos(Symbol('J', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('J', commutative=True), Integer(2)), Symbol('q', commutative=True))", "Mul(Symbol('J', commutative=True), Add(log(Mul(Pow(Symbol('J', commutative=True), Integer(-1)), Symbol('q', commutative=True))), Integer(1)))"]}, {"premise_expression": "L - o", "variable": "L", "positive": "\\frac{L (L - 2 o)}{2}", "negatives": ["\\frac{o (2 L - o)}{2}", "\\frac{L (L + 2 \\cos{(o)})}{2}", "\\frac{L (- L + 2 \\log{(o)})}{2}", "- \\frac{L^{2}}{2} + \\sin{(L)}"], "srepr_premise_expression": "Add(Symbol('L', commutative=True), Mul(Integer(-1), Symbol('o', commutative=True)))", "srepr_variable": "Symbol('L', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Symbol('L', commutative=True), Mul(Integer(-1), Integer(2), Symbol('o', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Mul(Integer(2), Symbol('L', commutative=True)), Mul(Integer(-1), Symbol('o', commutative=True))))", "Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Symbol('L', commutative=True), Mul(Integer(2), cos(Symbol('o', commutative=True)))))", "Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Mul(Integer(-1), Symbol('L', commutative=True)), Mul(Integer(2), log(Symbol('o', commutative=True)))))", "Add(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(2))), sin(Symbol('L', commutative=True)))"]}, {"premise_expression": "\\frac{u}{G}", "variable": "u", "positive": "\\frac{u^{2}}{2 G}", "negatives": ["u \\log{(G)}", "- G u + \\frac{u^{2}}{2 G}", "\\frac{u^{2} \\log{(G)}}{2}", "\\frac{u^{2} \\cos{(G)}}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('G', commutative=True), Integer(-1)), Symbol('u', commutative=True))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(-1)), Pow(Symbol('u', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('u', commutative=True), log(Symbol('G', commutative=True)))", "Add(Mul(Integer(-1), Symbol('G', commutative=True), Symbol('u', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(-1)), Pow(Symbol('u', commutative=True), Integer(2))))", "Mul(Rational(1, 2), Pow(Symbol('u', commutative=True), Integer(2)), log(Symbol('G', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('u', commutative=True), Integer(2)), cos(Symbol('G', commutative=True)))"]}, {"premise_expression": "u \\cos{(U)}", "variable": "u", "positive": "\\frac{u^{2} \\cos{(U)}}{2}", "negatives": ["\\frac{u^{2} e^{U}}{2}", "\\frac{u (2 U - u)}{2}", "u \\sin{(U)}", "\\frac{u (- u + 2 \\log{(U)})}{2}"], "srepr_premise_expression": "Mul(Symbol('u', commutative=True), cos(Symbol('U', commutative=True)))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('u', commutative=True), Integer(2)), cos(Symbol('U', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('u', commutative=True), Integer(2)), exp(Symbol('U', commutative=True)))", "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(2), Symbol('U', commutative=True)), Mul(Integer(-1), Symbol('u', commutative=True))))", "Mul(Symbol('u', commutative=True), sin(Symbol('U', commutative=True)))", "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(-1), Symbol('u', commutative=True)), Mul(Integer(2), log(Symbol('U', commutative=True)))))"]}, {"premise_expression": "K + \\frac{S}{a}", "variable": "S", "positive": "K S + \\frac{S^{2}}{2 a}", "negatives": ["K a + S \\log{(a)}", "\\frac{S^{2} a}{2 K}", "S (S + a)", "\\frac{K^{2}}{2} + \\frac{K S}{a}"], "srepr_premise_expression": "Add(Symbol('K', commutative=True), Mul(Symbol('S', commutative=True), Pow(Symbol('a', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('S', commutative=True)", "srepr_positive": "Add(Mul(Symbol('K', commutative=True), Symbol('S', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('S', commutative=True), Integer(2)), Pow(Symbol('a', commutative=True), Integer(-1))))", "srepr_negatives": ["Add(Mul(Symbol('K', commutative=True), Symbol('a', commutative=True)), Mul(Symbol('S', commutative=True), log(Symbol('a', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('K', commutative=True), Integer(-1)), Pow(Symbol('S', commutative=True), Integer(2)), Symbol('a', commutative=True))", "Mul(Symbol('S', commutative=True), Add(Symbol('S', commutative=True), Symbol('a', commutative=True)))", "Add(Mul(Rational(1, 2), Pow(Symbol('K', commutative=True), Integer(2))), Mul(Symbol('K', commutative=True), Symbol('S', commutative=True), Pow(Symbol('a', commutative=True), Integer(-1))))"]}, {"premise_expression": "\\frac{h}{y}", "variable": "y", "positive": "h \\log{(y)}", "negatives": ["\\frac{h^{2}}{2 y}", "\\frac{h y^{2}}{2}", "- \\cos{(h + y)}", "- \\cos{(h - y)}"], "srepr_premise_expression": "Mul(Symbol('h', commutative=True), Pow(Symbol('y', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('y', commutative=True)", "srepr_positive": "Mul(Symbol('h', commutative=True), log(Symbol('y', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('h', commutative=True), Integer(2)), Pow(Symbol('y', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Symbol('h', commutative=True), Pow(Symbol('y', commutative=True), Integer(2)))", "Mul(Integer(-1), cos(Add(Symbol('h', commutative=True), Symbol('y', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('h', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True)))))"]}, {"premise_expression": "G Z", "variable": "Z", "positive": "\\frac{G Z^{2}}{2}", "negatives": ["\\frac{G^{2} Z}{2}", "G \\log{(Z)}", "G \\sin{(Z)}", "\\frac{Z^{2} \\log{(G)}}{2}"], "srepr_premise_expression": "Mul(Symbol('G', commutative=True), Symbol('Z', commutative=True))", "srepr_variable": "Symbol('Z', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('G', commutative=True), Pow(Symbol('Z', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(2)), Symbol('Z', commutative=True))", "Mul(Symbol('G', commutative=True), log(Symbol('Z', commutative=True)))", "Mul(Symbol('G', commutative=True), sin(Symbol('Z', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('Z', commutative=True), Integer(2)), log(Symbol('G', commutative=True)))"]}, {"premise_expression": "- H + W o", "variable": "o", "positive": "\\frac{o (- 2 H + W o)}{2}", "negatives": ["\\frac{W (- 2 H + W o)}{2}", "\\frac{o (2 H + W o)}{2}", "\\frac{H (- H + 2 W o)}{2}", "\\frac{W o (2 H - o)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('H', commutative=True)), Mul(Symbol('W', commutative=True), Symbol('o', commutative=True)))", "srepr_variable": "Symbol('o', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('H', commutative=True)), Mul(Symbol('W', commutative=True), Symbol('o', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('W', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('H', commutative=True)), Mul(Symbol('W', commutative=True), Symbol('o', commutative=True))))", "Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Mul(Integer(2), Symbol('H', commutative=True)), Mul(Symbol('W', commutative=True), Symbol('o', commutative=True))))", "Mul(Rational(1, 2), Symbol('H', commutative=True), Add(Mul(Integer(-1), Symbol('H', commutative=True)), Mul(Integer(2), Symbol('W', commutative=True), Symbol('o', commutative=True))))", "Mul(Rational(1, 2), Symbol('W', commutative=True), Symbol('o', commutative=True), Add(Mul(Integer(2), Symbol('H', commutative=True)), Mul(Integer(-1), Symbol('o', commutative=True))))"]}, {"premise_expression": "K - U - X", "variable": "U", "positive": "U (K - \\frac{U}{2} - X)", "negatives": ["\\frac{U (2 K + U - 2 X)}{2}", "\\frac{K (K - 2 U - 2 X)}{2}", "\\frac{X (2 K - 2 U - X)}{2}", "\\frac{U^{2}}{2 K X}"], "srepr_premise_expression": "Add(Symbol('K', commutative=True), Mul(Integer(-1), Symbol('U', commutative=True)), Mul(Integer(-1), Symbol('X', commutative=True)))", "srepr_variable": "Symbol('U', commutative=True)", "srepr_positive": "Mul(Symbol('U', commutative=True), Add(Symbol('K', commutative=True), Mul(Integer(-1), Rational(1, 2), Symbol('U', commutative=True)), Mul(Integer(-1), Symbol('X', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('U', commutative=True), Add(Mul(Integer(2), Symbol('K', commutative=True)), Symbol('U', commutative=True), Mul(Integer(-1), Integer(2), Symbol('X', commutative=True))))", "Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Symbol('K', commutative=True), Mul(Integer(-1), Integer(2), Symbol('U', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('X', commutative=True))))", "Mul(Rational(1, 2), Symbol('X', commutative=True), Add(Mul(Integer(2), Symbol('K', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('U', commutative=True)), Mul(Integer(-1), Symbol('X', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('K', commutative=True), Integer(-1)), Pow(Symbol('U', commutative=True), Integer(2)), Pow(Symbol('X', commutative=True), Integer(-1)))"]}, {"premise_expression": "o \\log{(v)}", "variable": "v", "positive": "o v (\\log{(v)} - 1)", "negatives": ["v (\\log{(o v)} - 1)", "\\frac{o^{2} \\log{(v)}}{2}", "\\log{(v)} \\cos{(o)}", "\\log{(v)} \\sin{(o)}"], "srepr_premise_expression": "Mul(Symbol('o', commutative=True), log(Symbol('v', commutative=True)))", "srepr_variable": "Symbol('v', commutative=True)", "srepr_positive": "Mul(Symbol('o', commutative=True), Symbol('v', commutative=True), Add(log(Symbol('v', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('v', commutative=True), Add(log(Mul(Symbol('o', commutative=True), Symbol('v', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('o', commutative=True), Integer(2)), log(Symbol('v', commutative=True)))", "Mul(log(Symbol('v', commutative=True)), cos(Symbol('o', commutative=True)))", "Mul(log(Symbol('v', commutative=True)), sin(Symbol('o', commutative=True)))"]}, {"premise_expression": "\\log{(\\frac{F}{w})}", "variable": "F", "positive": "F (\\log{(\\frac{F}{w})} - 1)", "negatives": ["w (\\log{(\\frac{F}{w})} + 1)", "F (- w + \\log{(F)} - 1)", "F (- w + \\log{(F^{w})})", "F e^{2 w}"], "srepr_premise_expression": "log(Mul(Symbol('F', commutative=True), Pow(Symbol('w', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('F', commutative=True)", "srepr_positive": "Mul(Symbol('F', commutative=True), Add(log(Mul(Symbol('F', commutative=True), Pow(Symbol('w', commutative=True), Integer(-1)))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('w', commutative=True), Add(log(Mul(Symbol('F', commutative=True), Pow(Symbol('w', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Symbol('F', commutative=True), Add(Mul(Integer(-1), Symbol('w', commutative=True)), log(Symbol('F', commutative=True)), Integer(-1)))", "Mul(Symbol('F', commutative=True), Add(Mul(Integer(-1), Symbol('w', commutative=True)), log(Pow(Symbol('F', commutative=True), Symbol('w', commutative=True)))))", "Mul(Symbol('F', commutative=True), exp(Mul(Integer(2), Symbol('w', commutative=True))))"]}, {"premise_expression": "C + F y", "variable": "C", "positive": "\\frac{C (C + 2 F y)}{2}", "negatives": ["\\frac{y (2 C + F y)}{2}", "\\frac{F (2 C + F y)}{2}", "\\frac{C^{2} F y}{2}", "\\frac{C (C - 2 y)}{2 F}"], "srepr_premise_expression": "Add(Symbol('C', commutative=True), Mul(Symbol('F', commutative=True), Symbol('y', commutative=True)))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Symbol('C', commutative=True), Mul(Integer(2), Symbol('F', commutative=True), Symbol('y', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('y', commutative=True), Add(Mul(Integer(2), Symbol('C', commutative=True)), Mul(Symbol('F', commutative=True), Symbol('y', commutative=True))))", "Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Mul(Integer(2), Symbol('C', commutative=True)), Mul(Symbol('F', commutative=True), Symbol('y', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2)), Symbol('F', commutative=True), Symbol('y', commutative=True))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Pow(Symbol('F', commutative=True), Integer(-1)), Add(Symbol('C', commutative=True), Mul(Integer(-1), Integer(2), Symbol('y', commutative=True))))"]}, {"premise_expression": "C - s", "variable": "s", "positive": "\\frac{s (2 C - s)}{2}", "negatives": ["\\frac{C (C - 2 s)}{2}", "\\frac{s^{2} \\log{(C)}}{2}", "- e^{C - s}", "C \\sin{(s)}"], "srepr_premise_expression": "Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('s', commutative=True)))", "srepr_variable": "Symbol('s', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('s', commutative=True), Add(Mul(Integer(2), Symbol('C', commutative=True)), Mul(Integer(-1), Symbol('s', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Symbol('C', commutative=True), Mul(Integer(-1), Integer(2), Symbol('s', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('s', commutative=True), Integer(2)), log(Symbol('C', commutative=True)))", "Mul(Integer(-1), exp(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('s', commutative=True)))))", "Mul(Symbol('C', commutative=True), sin(Symbol('s', commutative=True)))"]}, {"premise_expression": "\\log{(Z + u)}", "variable": "u", "positive": "Z \\log{(Z + u)} + u \\log{(Z + u)} - u", "negatives": ["Z \\log{(Z + u)} - Z + u \\log{(Z + u)}", "\\frac{u (u + 2 \\log{(Z)})}{2}", "u (\\log{(Z u)} - 1)", "- Z u + \\sin{(u)}"], "srepr_premise_expression": "log(Add(Symbol('Z', commutative=True), Symbol('u', commutative=True)))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "Add(Mul(Symbol('Z', commutative=True), log(Add(Symbol('Z', commutative=True), Symbol('u', commutative=True)))), Mul(Symbol('u', commutative=True), log(Add(Symbol('Z', commutative=True), Symbol('u', commutative=True)))), Mul(Integer(-1), Symbol('u', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('Z', commutative=True), log(Add(Symbol('Z', commutative=True), Symbol('u', commutative=True)))), Mul(Integer(-1), Symbol('Z', commutative=True)), Mul(Symbol('u', commutative=True), log(Add(Symbol('Z', commutative=True), Symbol('u', commutative=True)))))", "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Symbol('u', commutative=True), Mul(Integer(2), log(Symbol('Z', commutative=True)))))", "Mul(Symbol('u', commutative=True), Add(log(Mul(Symbol('Z', commutative=True), Symbol('u', commutative=True))), Integer(-1)))", "Add(Mul(Integer(-1), Symbol('Z', commutative=True), Symbol('u', commutative=True)), sin(Symbol('u', commutative=True)))"]}, {"premise_expression": "\\cos^{S}{(u)}", "variable": "u", "positive": "\\int \\cos^{S}{(u)} du", "negatives": ["e^{S} \\log{(u)}", "\\frac{u (- 2 S + u)}{2}", "\\frac{S u^{2}}{2}", "\\frac{u (- u + 2 \\log{(S)})}{2}"], "srepr_premise_expression": "Pow(cos(Symbol('u', commutative=True)), Symbol('S', commutative=True))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "Integral(Pow(cos(Symbol('u', commutative=True)), Symbol('S', commutative=True)), Tuple(Symbol('u', commutative=True)))", "srepr_negatives": ["Mul(exp(Symbol('S', commutative=True)), log(Symbol('u', commutative=True)))", "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('S', commutative=True)), Symbol('u', commutative=True)))", "Mul(Rational(1, 2), Symbol('S', commutative=True), Pow(Symbol('u', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(-1), Symbol('u', commutative=True)), Mul(Integer(2), log(Symbol('S', commutative=True)))))"]}, {"premise_expression": "k u", "variable": "k", "positive": "\\frac{k^{2} u}{2}", "negatives": ["\\frac{k u^{2}}{2}", "\\frac{k^{2} \\log{(u)}}{2}", "\\frac{k (k + 2 u)}{2}", "u e^{\\frac{k}{u}}"], "srepr_premise_expression": "Mul(Symbol('k', commutative=True), Symbol('u', commutative=True))", "srepr_variable": "Symbol('k', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('k', commutative=True), Integer(2)), Symbol('u', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('k', commutative=True), Pow(Symbol('u', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('k', commutative=True), Integer(2)), log(Symbol('u', commutative=True)))", "Mul(Rational(1, 2), Symbol('k', commutative=True), Add(Symbol('k', commutative=True), Mul(Integer(2), Symbol('u', commutative=True))))", "Mul(Symbol('u', commutative=True), exp(Mul(Symbol('k', commutative=True), Pow(Symbol('u', commutative=True), Integer(-1)))))"]}, {"premise_expression": "A + I", "variable": "I", "positive": "\\frac{I (2 A + I)}{2}", "negatives": ["\\frac{A (A + 2 I)}{2}", "\\frac{I^{2} \\log{(A)}}{2}", "e^{- A + I}", "\\sin{(A + I)}"], "srepr_premise_expression": "Add(Symbol('A', commutative=True), Symbol('I', commutative=True))", "srepr_variable": "Symbol('I', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('I', commutative=True), Add(Mul(Integer(2), Symbol('A', commutative=True)), Symbol('I', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Symbol('A', commutative=True), Mul(Integer(2), Symbol('I', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(2)), log(Symbol('A', commutative=True)))", "exp(Add(Mul(Integer(-1), Symbol('A', commutative=True)), Symbol('I', commutative=True)))", "sin(Add(Symbol('A', commutative=True), Symbol('I', commutative=True)))"]}, {"premise_expression": "\\cos{(\\frac{k}{a})}", "variable": "a", "positive": "a \\cos{(\\frac{k}{a})} + k \\operatorname{Si}{(\\frac{k}{a})}", "negatives": ["a (\\log{(\\frac{k}{a})} + 1)", "\\frac{a k (a - 2 k)}{2}", "\\frac{a (a + 2 \\cos{(k)})}{2}", "- a k + \\sin{(a)}"], "srepr_premise_expression": "cos(Mul(Pow(Symbol('a', commutative=True), Integer(-1)), Symbol('k', commutative=True)))", "srepr_variable": "Symbol('a', commutative=True)", "srepr_positive": "Add(Mul(Symbol('a', commutative=True), cos(Mul(Pow(Symbol('a', commutative=True), Integer(-1)), Symbol('k', commutative=True)))), Mul(Symbol('k', commutative=True), Si(Mul(Pow(Symbol('a', commutative=True), Integer(-1)), Symbol('k', commutative=True)))))", "srepr_negatives": ["Mul(Symbol('a', commutative=True), Add(log(Mul(Pow(Symbol('a', commutative=True), Integer(-1)), Symbol('k', commutative=True))), Integer(1)))", "Mul(Rational(1, 2), Symbol('a', commutative=True), Symbol('k', commutative=True), Add(Symbol('a', commutative=True), Mul(Integer(-1), Integer(2), Symbol('k', commutative=True))))", "Mul(Rational(1, 2), Symbol('a', commutative=True), Add(Symbol('a', commutative=True), Mul(Integer(2), cos(Symbol('k', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('a', commutative=True), Symbol('k', commutative=True)), sin(Symbol('a', commutative=True)))"]}, {"premise_expression": "e^{\\frac{A}{m}}", "variable": "m", "positive": "- A \\operatorname{Ei}{(\\frac{A}{m})} + m e^{\\frac{A}{m}}", "negatives": ["A m + e^{m}", "m e^{\\frac{A}{m}}", "- A m - \\cos{(m)}", "A m + \\sin{(m)}"], "srepr_premise_expression": "exp(Mul(Symbol('A', commutative=True), Pow(Symbol('m', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('m', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('A', commutative=True), Ei(Mul(Symbol('A', commutative=True), Pow(Symbol('m', commutative=True), Integer(-1))))), Mul(Symbol('m', commutative=True), exp(Mul(Symbol('A', commutative=True), Pow(Symbol('m', commutative=True), Integer(-1))))))", "srepr_negatives": ["Add(Mul(Symbol('A', commutative=True), Symbol('m', commutative=True)), exp(Symbol('m', commutative=True)))", "Mul(Symbol('m', commutative=True), exp(Mul(Symbol('A', commutative=True), Pow(Symbol('m', commutative=True), Integer(-1)))))", "Add(Mul(Integer(-1), Symbol('A', commutative=True), Symbol('m', commutative=True)), Mul(Integer(-1), cos(Symbol('m', commutative=True))))", "Add(Mul(Symbol('A', commutative=True), Symbol('m', commutative=True)), sin(Symbol('m', commutative=True)))"]}, {"premise_expression": "\\frac{I W}{x}", "variable": "x", "positive": "I W \\log{(x)}", "negatives": ["\\frac{I W^{2}}{2 x}", "\\frac{I W x^{2}}{2}", "\\frac{I^{2} W}{2 x}", "\\frac{I^{2} x}{W}"], "srepr_premise_expression": "Mul(Symbol('I', commutative=True), Symbol('W', commutative=True), Pow(Symbol('x', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('x', commutative=True)", "srepr_positive": "Mul(Symbol('I', commutative=True), Symbol('W', commutative=True), log(Symbol('x', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('I', commutative=True), Pow(Symbol('W', commutative=True), Integer(2)), Pow(Symbol('x', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Symbol('I', commutative=True), Symbol('W', commutative=True), Pow(Symbol('x', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(2)), Symbol('W', commutative=True), Pow(Symbol('x', commutative=True), Integer(-1)))", "Mul(Pow(Symbol('I', commutative=True), Integer(2)), Pow(Symbol('W', commutative=True), Integer(-1)), Symbol('x', commutative=True))"]}, {"premise_expression": "- s + \\cos{(o)}", "variable": "s", "positive": "\\frac{s (- s + 2 \\cos{(o)})}{2}", "negatives": ["\\frac{s (- s + 2 e^{o})}{2}", "\\frac{s^{2} \\cos{(o)}}{2}", "s (- o + \\log{(s^{o})})", "- o s + \\sin{(o)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('s', commutative=True)), cos(Symbol('o', commutative=True)))", "srepr_variable": "Symbol('s', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('s', commutative=True), Add(Mul(Integer(-1), Symbol('s', commutative=True)), Mul(Integer(2), cos(Symbol('o', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('s', commutative=True), Add(Mul(Integer(-1), Symbol('s', commutative=True)), Mul(Integer(2), exp(Symbol('o', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('s', commutative=True), Integer(2)), cos(Symbol('o', commutative=True)))", "Mul(Symbol('s', commutative=True), Add(Mul(Integer(-1), Symbol('o', commutative=True)), log(Pow(Symbol('s', commutative=True), Symbol('o', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('o', commutative=True), Symbol('s', commutative=True)), sin(Symbol('o', commutative=True)))"]}, {"premise_expression": "\\sin{(G - r)}", "variable": "r", "positive": "\\cos{(G - r)}", "negatives": ["- \\cos{(G - r)}", "- G r - \\cos{(r)}", "e^{G} \\log{(r)}", "G r + \\sin{(r)}"], "srepr_premise_expression": "sin(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('r', commutative=True))))", "srepr_variable": "Symbol('r', commutative=True)", "srepr_positive": "cos(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('r', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('r', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('G', commutative=True), Symbol('r', commutative=True)), Mul(Integer(-1), cos(Symbol('r', commutative=True))))", "Mul(exp(Symbol('G', commutative=True)), log(Symbol('r', commutative=True)))", "Add(Mul(Symbol('G', commutative=True), Symbol('r', commutative=True)), sin(Symbol('r', commutative=True)))"]}, {"premise_expression": "I + s", "variable": "I", "positive": "\\frac{I (I + 2 s)}{2}", "negatives": ["\\frac{s (2 I + s)}{2}", "\\frac{I (I + 2 \\log{(s)})}{2}", "\\cos{(I - s)}", "I (- s + \\log{(I)} - 1)"], "srepr_premise_expression": "Add(Symbol('I', commutative=True), Symbol('s', commutative=True))", "srepr_variable": "Symbol('I', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('I', commutative=True), Add(Symbol('I', commutative=True), Mul(Integer(2), Symbol('s', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('s', commutative=True), Add(Mul(Integer(2), Symbol('I', commutative=True)), Symbol('s', commutative=True)))", "Mul(Rational(1, 2), Symbol('I', commutative=True), Add(Symbol('I', commutative=True), Mul(Integer(2), log(Symbol('s', commutative=True)))))", "cos(Add(Symbol('I', commutative=True), Mul(Integer(-1), Symbol('s', commutative=True))))", "Mul(Symbol('I', commutative=True), Add(Mul(Integer(-1), Symbol('s', commutative=True)), log(Symbol('I', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\log{(P^{F})}", "variable": "P", "positive": "P (- F + \\log{(P^{F})})", "negatives": ["\\frac{F^{2} \\log{(P)}}{2}", "- F P + \\sin{(P)}", "P (\\log{(F P)} - 1)", "- \\frac{\\cos{(P)}}{F}"], "srepr_premise_expression": "log(Pow(Symbol('P', commutative=True), Symbol('F', commutative=True)))", "srepr_variable": "Symbol('P', commutative=True)", "srepr_positive": "Mul(Symbol('P', commutative=True), Add(Mul(Integer(-1), Symbol('F', commutative=True)), log(Pow(Symbol('P', commutative=True), Symbol('F', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('F', commutative=True), Integer(2)), log(Symbol('P', commutative=True)))", "Add(Mul(Integer(-1), Symbol('F', commutative=True), Symbol('P', commutative=True)), sin(Symbol('P', commutative=True)))", "Mul(Symbol('P', commutative=True), Add(log(Mul(Symbol('F', commutative=True), Symbol('P', commutative=True))), Integer(-1)))", "Mul(Integer(-1), Pow(Symbol('F', commutative=True), Integer(-1)), cos(Symbol('P', commutative=True)))"]}, {"premise_expression": "X r", "variable": "r", "positive": "\\frac{X r^{2}}{2}", "negatives": ["\\frac{X^{2} r}{2}", "\\frac{r^{2}}{2 X}", "- \\frac{\\cos{(r)}}{X}", "\\frac{r^{2} (X - 1)}{2}"], "srepr_premise_expression": "Mul(Symbol('X', commutative=True), Symbol('r', commutative=True))", "srepr_variable": "Symbol('r', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('X', commutative=True), Pow(Symbol('r', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('X', commutative=True), Integer(2)), Symbol('r', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('X', commutative=True), Integer(-1)), Pow(Symbol('r', commutative=True), Integer(2)))", "Mul(Integer(-1), Pow(Symbol('X', commutative=True), Integer(-1)), cos(Symbol('r', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('r', commutative=True), Integer(2)), Add(Symbol('X', commutative=True), Integer(-1)))"]}, {"premise_expression": "q u", "variable": "q", "positive": "\\frac{q^{2} u}{2}", "negatives": ["\\frac{q u^{2}}{2}", "\\frac{q^{2}}{2 u}", "q (\\log{(q u)} - 1)", "\\frac{q (- q + 2 e^{u})}{2}"], "srepr_premise_expression": "Mul(Symbol('q', commutative=True), Symbol('u', commutative=True))", "srepr_variable": "Symbol('q', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('q', commutative=True), Integer(2)), Symbol('u', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('q', commutative=True), Pow(Symbol('u', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('q', commutative=True), Integer(2)), Pow(Symbol('u', commutative=True), Integer(-1)))", "Mul(Symbol('q', commutative=True), Add(log(Mul(Symbol('q', commutative=True), Symbol('u', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('q', commutative=True), Add(Mul(Integer(-1), Symbol('q', commutative=True)), Mul(Integer(2), exp(Symbol('u', commutative=True)))))"]}, {"premise_expression": "y (K - P)", "variable": "K", "positive": "\\frac{K y (K - 2 P)}{2}", "negatives": ["\\frac{K P (K + 2 y)}{2}", "\\frac{K (K y - 2 P)}{2}", "\\frac{P y (2 K - P)}{2}", "\\frac{y^{2} (K - P)}{2}"], "srepr_premise_expression": "Mul(Symbol('y', commutative=True), Add(Symbol('K', commutative=True), Mul(Integer(-1), Symbol('P', commutative=True))))", "srepr_variable": "Symbol('K', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('K', commutative=True), Symbol('y', commutative=True), Add(Symbol('K', commutative=True), Mul(Integer(-1), Integer(2), Symbol('P', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('K', commutative=True), Symbol('P', commutative=True), Add(Symbol('K', commutative=True), Mul(Integer(2), Symbol('y', commutative=True))))", "Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Mul(Symbol('K', commutative=True), Symbol('y', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('P', commutative=True))))", "Mul(Rational(1, 2), Symbol('P', commutative=True), Symbol('y', commutative=True), Add(Mul(Integer(2), Symbol('K', commutative=True)), Mul(Integer(-1), Symbol('P', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('y', commutative=True), Integer(2)), Add(Symbol('K', commutative=True), Mul(Integer(-1), Symbol('P', commutative=True))))"]}, {"premise_expression": "Z + \\cos{(E)}", "variable": "Z", "positive": "\\frac{Z (Z + 2 \\cos{(E)})}{2}", "negatives": ["\\frac{Z (- Z + 2 \\cos{(E)})}{2}", "E Z + \\sin{(E)}", "- E Z - \\cos{(Z)}", "E Z + \\sin{(Z)}"], "srepr_premise_expression": "Add(Symbol('Z', commutative=True), cos(Symbol('E', commutative=True)))", "srepr_variable": "Symbol('Z', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Symbol('Z', commutative=True), Mul(Integer(2), cos(Symbol('E', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Mul(Integer(-1), Symbol('Z', commutative=True)), Mul(Integer(2), cos(Symbol('E', commutative=True)))))", "Add(Mul(Symbol('E', commutative=True), Symbol('Z', commutative=True)), sin(Symbol('E', commutative=True)))", "Add(Mul(Integer(-1), Symbol('E', commutative=True), Symbol('Z', commutative=True)), Mul(Integer(-1), cos(Symbol('Z', commutative=True))))", "Add(Mul(Symbol('E', commutative=True), Symbol('Z', commutative=True)), sin(Symbol('Z', commutative=True)))"]}, {"premise_expression": "I s", "variable": "s", "positive": "\\frac{I s^{2}}{2}", "negatives": ["\\frac{I^{2} s}{2}", "\\frac{s^{2} \\log{(I)}}{2}", "\\frac{s (2 I + s)}{2}", "I \\log{(I + s)} + s \\log{(I + s)} - s"], "srepr_premise_expression": "Mul(Symbol('I', commutative=True), Symbol('s', commutative=True))", "srepr_variable": "Symbol('s', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('I', commutative=True), Pow(Symbol('s', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(2)), Symbol('s', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('s', commutative=True), Integer(2)), log(Symbol('I', commutative=True)))", "Mul(Rational(1, 2), Symbol('s', commutative=True), Add(Mul(Integer(2), Symbol('I', commutative=True)), Symbol('s', commutative=True)))", "Add(Mul(Symbol('I', commutative=True), log(Add(Symbol('I', commutative=True), Symbol('s', commutative=True)))), Mul(Symbol('s', commutative=True), log(Add(Symbol('I', commutative=True), Symbol('s', commutative=True)))), Mul(Integer(-1), Symbol('s', commutative=True)))"]}, {"premise_expression": "F \\cos{(Q)}", "variable": "F", "positive": "\\frac{F^{2} \\cos{(Q)}}{2}", "negatives": ["\\frac{F^{2} \\sin{(Q)}}{2}", "F \\sin{(Q)}", "\\frac{F (F + 2 e^{Q})}{2}", "\\sin{(F - Q)}"], "srepr_premise_expression": "Mul(Symbol('F', commutative=True), cos(Symbol('Q', commutative=True)))", "srepr_variable": "Symbol('F', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('F', commutative=True), Integer(2)), cos(Symbol('Q', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('F', commutative=True), Integer(2)), sin(Symbol('Q', commutative=True)))", "Mul(Symbol('F', commutative=True), sin(Symbol('Q', commutative=True)))", "Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Symbol('F', commutative=True), Mul(Integer(2), exp(Symbol('Q', commutative=True)))))", "sin(Add(Symbol('F', commutative=True), Mul(Integer(-1), Symbol('Q', commutative=True))))"]}, {"premise_expression": "\\sin{(H - Z)}", "variable": "Z", "positive": "\\cos{(H - Z)}", "negatives": ["- \\cos{(H - Z)}", "H e^{\\frac{Z}{H}}", "Z (\\log{(\\frac{Z}{H})} - 1)", "\\log{(Z)} \\cos{(H)}"], "srepr_premise_expression": "sin(Add(Symbol('H', commutative=True), Mul(Integer(-1), Symbol('Z', commutative=True))))", "srepr_variable": "Symbol('Z', commutative=True)", "srepr_positive": "cos(Add(Symbol('H', commutative=True), Mul(Integer(-1), Symbol('Z', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('H', commutative=True), Mul(Integer(-1), Symbol('Z', commutative=True)))))", "Mul(Symbol('H', commutative=True), exp(Mul(Pow(Symbol('H', commutative=True), Integer(-1)), Symbol('Z', commutative=True))))", "Mul(Symbol('Z', commutative=True), Add(log(Mul(Pow(Symbol('H', commutative=True), Integer(-1)), Symbol('Z', commutative=True))), Integer(-1)))", "Mul(log(Symbol('Z', commutative=True)), cos(Symbol('H', commutative=True)))"]}, {"premise_expression": "\\cos^{T}{(V)}", "variable": "V", "positive": "\\int \\cos^{T}{(V)} dV", "negatives": ["e^{- T + V}", "- T V + \\sin{(V)}", "\\frac{V (V + 2 e^{T})}{2}", "\\frac{V (- V + 2 \\sin{(T)})}{2}"], "srepr_premise_expression": "Pow(cos(Symbol('V', commutative=True)), Symbol('T', commutative=True))", "srepr_variable": "Symbol('V', commutative=True)", "srepr_positive": "Integral(Pow(cos(Symbol('V', commutative=True)), Symbol('T', commutative=True)), Tuple(Symbol('V', commutative=True)))", "srepr_negatives": ["exp(Add(Mul(Integer(-1), Symbol('T', commutative=True)), Symbol('V', commutative=True)))", "Add(Mul(Integer(-1), Symbol('T', commutative=True), Symbol('V', commutative=True)), sin(Symbol('V', commutative=True)))", "Mul(Rational(1, 2), Symbol('V', commutative=True), Add(Symbol('V', commutative=True), Mul(Integer(2), exp(Symbol('T', commutative=True)))))", "Mul(Rational(1, 2), Symbol('V', commutative=True), Add(Mul(Integer(-1), Symbol('V', commutative=True)), Mul(Integer(2), sin(Symbol('T', commutative=True)))))"]}, {"premise_expression": "\\log{(\\frac{Q}{b})}", "variable": "Q", "positive": "Q (\\log{(\\frac{Q}{b})} - 1)", "negatives": ["b (\\log{(\\frac{Q}{b})} + 1)", "b e^{Q}", "\\frac{Q (Q + 2 \\log{(b)})}{2}", "\\frac{Q (Q + 2 \\sin{(b)})}{2}"], "srepr_premise_expression": "log(Mul(Symbol('Q', commutative=True), Pow(Symbol('b', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('Q', commutative=True)", "srepr_positive": "Mul(Symbol('Q', commutative=True), Add(log(Mul(Symbol('Q', commutative=True), Pow(Symbol('b', commutative=True), Integer(-1)))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('b', commutative=True), Add(log(Mul(Symbol('Q', commutative=True), Pow(Symbol('b', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Symbol('b', commutative=True), exp(Symbol('Q', commutative=True)))", "Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Symbol('Q', commutative=True), Mul(Integer(2), log(Symbol('b', commutative=True)))))", "Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Symbol('Q', commutative=True), Mul(Integer(2), sin(Symbol('b', commutative=True)))))"]}, {"premise_expression": "\\cos{(V - a)}", "variable": "V", "positive": "\\sin{(V - a)}", "negatives": ["- \\sin{(V - a)}", "e^{V - a}", "\\frac{V (V + 2 a)}{2}", "- a \\cos{(V)}"], "srepr_premise_expression": "cos(Add(Symbol('V', commutative=True), Mul(Integer(-1), Symbol('a', commutative=True))))", "srepr_variable": "Symbol('V', commutative=True)", "srepr_positive": "sin(Add(Symbol('V', commutative=True), Mul(Integer(-1), Symbol('a', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('V', commutative=True), Mul(Integer(-1), Symbol('a', commutative=True)))))", "exp(Add(Symbol('V', commutative=True), Mul(Integer(-1), Symbol('a', commutative=True))))", "Mul(Rational(1, 2), Symbol('V', commutative=True), Add(Symbol('V', commutative=True), Mul(Integer(2), Symbol('a', commutative=True))))", "Mul(Integer(-1), Symbol('a', commutative=True), cos(Symbol('V', commutative=True)))"]}, {"premise_expression": "- w + \\log{(p)}", "variable": "p", "positive": "p (- w + \\log{(p)} - 1)", "negatives": ["p (\\log{(p w)} - 1)", "\\frac{w (- w + 2 \\log{(p)})}{2}", "p (\\log{(\\frac{w}{p})} + 1)", "p w - \\cos{(p)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('w', commutative=True)), log(Symbol('p', commutative=True)))", "srepr_variable": "Symbol('p', commutative=True)", "srepr_positive": "Mul(Symbol('p', commutative=True), Add(Mul(Integer(-1), Symbol('w', commutative=True)), log(Symbol('p', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('p', commutative=True), Add(log(Mul(Symbol('p', commutative=True), Symbol('w', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('w', commutative=True), Add(Mul(Integer(-1), Symbol('w', commutative=True)), Mul(Integer(2), log(Symbol('p', commutative=True)))))", "Mul(Symbol('p', commutative=True), Add(log(Mul(Pow(Symbol('p', commutative=True), Integer(-1)), Symbol('w', commutative=True))), Integer(1)))", "Add(Mul(Symbol('p', commutative=True), Symbol('w', commutative=True)), Mul(Integer(-1), cos(Symbol('p', commutative=True))))"]}, {"premise_expression": "H + V", "variable": "V", "positive": "\\frac{V (2 H + V)}{2}", "negatives": ["\\frac{H (H + 2 V)}{2}", "\\frac{V^{2} \\cos{(H)}}{2}", "\\sin{(H + V)}", "\\frac{\\sin{(V)}}{H}"], "srepr_premise_expression": "Add(Symbol('H', commutative=True), Symbol('V', commutative=True))", "srepr_variable": "Symbol('V', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('V', commutative=True), Add(Mul(Integer(2), Symbol('H', commutative=True)), Symbol('V', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('H', commutative=True), Add(Symbol('H', commutative=True), Mul(Integer(2), Symbol('V', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('V', commutative=True), Integer(2)), cos(Symbol('H', commutative=True)))", "sin(Add(Symbol('H', commutative=True), Symbol('V', commutative=True)))", "Mul(Pow(Symbol('H', commutative=True), Integer(-1)), sin(Symbol('V', commutative=True)))"]}, {"premise_expression": "\\frac{- M + b}{N}", "variable": "b", "positive": "\\frac{b (- 2 M + b)}{2 N}", "negatives": ["\\frac{M (- M + 2 b)}{2 N}", "\\frac{b^{2} (M + N)}{2}", "(- M + b) \\log{(N)}", "\\frac{b (2 M - 2 N + b)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('N', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('M', commutative=True)), Symbol('b', commutative=True)))", "srepr_variable": "Symbol('b', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('N', commutative=True), Integer(-1)), Symbol('b', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('M', commutative=True)), Symbol('b', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('M', commutative=True), Pow(Symbol('N', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('M', commutative=True)), Mul(Integer(2), Symbol('b', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('b', commutative=True), Integer(2)), Add(Symbol('M', commutative=True), Symbol('N', commutative=True)))", "Mul(Add(Mul(Integer(-1), Symbol('M', commutative=True)), Symbol('b', commutative=True)), log(Symbol('N', commutative=True)))", "Mul(Rational(1, 2), Symbol('b', commutative=True), Add(Mul(Integer(2), Symbol('M', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('N', commutative=True)), Symbol('b', commutative=True)))"]}, {"premise_expression": "M + T", "variable": "T", "positive": "\\frac{T (2 M + T)}{2}", "negatives": ["\\frac{T (2 M - T)}{2}", "\\frac{M (M + 2 T)}{2}", "\\frac{T^{2} \\sin{(M)}}{2}", "\\frac{T (\\log{(T)} - 1)}{M}"], "srepr_premise_expression": "Add(Symbol('M', commutative=True), Symbol('T', commutative=True))", "srepr_variable": "Symbol('T', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('T', commutative=True), Add(Mul(Integer(2), Symbol('M', commutative=True)), Symbol('T', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('T', commutative=True), Add(Mul(Integer(2), Symbol('M', commutative=True)), Mul(Integer(-1), Symbol('T', commutative=True))))", "Mul(Rational(1, 2), Symbol('M', commutative=True), Add(Symbol('M', commutative=True), Mul(Integer(2), Symbol('T', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('T', commutative=True), Integer(2)), sin(Symbol('M', commutative=True)))", "Mul(Pow(Symbol('M', commutative=True), Integer(-1)), Symbol('T', commutative=True), Add(log(Symbol('T', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\log{(b v)}", "variable": "v", "positive": "v (\\log{(b v)} - 1)", "negatives": ["b (\\log{(b v)} - 1)", "b \\log{(v)}", "- e^{b - v}", "v (- b + \\log{(v^{b})})"], "srepr_premise_expression": "log(Mul(Symbol('b', commutative=True), Symbol('v', commutative=True)))", "srepr_variable": "Symbol('v', commutative=True)", "srepr_positive": "Mul(Symbol('v', commutative=True), Add(log(Mul(Symbol('b', commutative=True), Symbol('v', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('b', commutative=True), Add(log(Mul(Symbol('b', commutative=True), Symbol('v', commutative=True))), Integer(-1)))", "Mul(Symbol('b', commutative=True), log(Symbol('v', commutative=True)))", "Mul(Integer(-1), exp(Add(Symbol('b', commutative=True), Mul(Integer(-1), Symbol('v', commutative=True)))))", "Mul(Symbol('v', commutative=True), Add(Mul(Integer(-1), Symbol('b', commutative=True)), log(Pow(Symbol('v', commutative=True), Symbol('b', commutative=True)))))"]}, {"premise_expression": "n + r", "variable": "n", "positive": "\\frac{n (n + 2 r)}{2}", "negatives": ["\\frac{n (- n + 2 r)}{2}", "\\frac{r (2 n + r)}{2}", "\\frac{n (n + 2 \\cos{(r)})}{2}", "- n r + e^{n}"], "srepr_premise_expression": "Add(Symbol('n', commutative=True), Symbol('r', commutative=True))", "srepr_variable": "Symbol('n', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('n', commutative=True), Add(Symbol('n', commutative=True), Mul(Integer(2), Symbol('r', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('n', commutative=True), Add(Mul(Integer(-1), Symbol('n', commutative=True)), Mul(Integer(2), Symbol('r', commutative=True))))", "Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(2), Symbol('n', commutative=True)), Symbol('r', commutative=True)))", "Mul(Rational(1, 2), Symbol('n', commutative=True), Add(Symbol('n', commutative=True), Mul(Integer(2), cos(Symbol('r', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('n', commutative=True), Symbol('r', commutative=True)), exp(Symbol('n', commutative=True)))"]}, {"premise_expression": "\\log{(C + V)}", "variable": "C", "positive": "C \\log{(C + V)} - C + V \\log{(C + V)}", "negatives": ["C \\log{(C + V)} + V \\log{(C + V)} - V", "C (- V + \\log{(C^{V})})", "\\frac{C (- C + 2 e^{V})}{2}", "\\frac{C (- C + 2 V)}{2}"], "srepr_premise_expression": "log(Add(Symbol('C', commutative=True), Symbol('V', commutative=True)))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Add(Mul(Symbol('C', commutative=True), log(Add(Symbol('C', commutative=True), Symbol('V', commutative=True)))), Mul(Integer(-1), Symbol('C', commutative=True)), Mul(Symbol('V', commutative=True), log(Add(Symbol('C', commutative=True), Symbol('V', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('C', commutative=True), log(Add(Symbol('C', commutative=True), Symbol('V', commutative=True)))), Mul(Symbol('V', commutative=True), log(Add(Symbol('C', commutative=True), Symbol('V', commutative=True)))), Mul(Integer(-1), Symbol('V', commutative=True)))", "Mul(Symbol('C', commutative=True), Add(Mul(Integer(-1), Symbol('V', commutative=True)), log(Pow(Symbol('C', commutative=True), Symbol('V', commutative=True)))))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Mul(Integer(-1), Symbol('C', commutative=True)), Mul(Integer(2), exp(Symbol('V', commutative=True)))))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Mul(Integer(-1), Symbol('C', commutative=True)), Mul(Integer(2), Symbol('V', commutative=True))))"]}, {"premise_expression": "\\log{(P^{U})}", "variable": "P", "positive": "P (- U + \\log{(P^{U})})", "negatives": ["\\frac{P (P + 2 U)}{2}", "\\frac{P (P + 2 \\sin{(U)})}{2}", "\\frac{U^{2} \\log{(P)}}{2}", "- \\cos{(P + U)}"], "srepr_premise_expression": "log(Pow(Symbol('P', commutative=True), Symbol('U', commutative=True)))", "srepr_variable": "Symbol('P', commutative=True)", "srepr_positive": "Mul(Symbol('P', commutative=True), Add(Mul(Integer(-1), Symbol('U', commutative=True)), log(Pow(Symbol('P', commutative=True), Symbol('U', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Symbol('P', commutative=True), Mul(Integer(2), Symbol('U', commutative=True))))", "Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Symbol('P', commutative=True), Mul(Integer(2), sin(Symbol('U', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('U', commutative=True), Integer(2)), log(Symbol('P', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('P', commutative=True), Symbol('U', commutative=True))))"]}, {"premise_expression": "- N + \\sin{(s)}", "variable": "N", "positive": "\\frac{N (- N + 2 \\sin{(s)})}{2}", "negatives": ["\\frac{N (N + 2 e^{s})}{2}", "- N s - \\cos{(s)}", "\\frac{N^{2}}{2 s}", "\\cos{(N - s)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('N', commutative=True)), sin(Symbol('s', commutative=True)))", "srepr_variable": "Symbol('N', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Mul(Integer(-1), Symbol('N', commutative=True)), Mul(Integer(2), sin(Symbol('s', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Symbol('N', commutative=True), Mul(Integer(2), exp(Symbol('s', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('N', commutative=True), Symbol('s', commutative=True)), Mul(Integer(-1), cos(Symbol('s', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('N', commutative=True), Integer(2)), Pow(Symbol('s', commutative=True), Integer(-1)))", "cos(Add(Symbol('N', commutative=True), Mul(Integer(-1), Symbol('s', commutative=True))))"]}, {"premise_expression": "\\cos{(V - j)}", "variable": "j", "positive": "- \\sin{(V - j)}", "negatives": ["\\sin{(V - j)}", "V \\sin{(j)}", "\\frac{\\sin{(j)}}{V}", "- \\frac{\\cos{(j)}}{V}"], "srepr_premise_expression": "cos(Add(Symbol('V', commutative=True), Mul(Integer(-1), Symbol('j', commutative=True))))", "srepr_variable": "Symbol('j', commutative=True)", "srepr_positive": "Mul(Integer(-1), sin(Add(Symbol('V', commutative=True), Mul(Integer(-1), Symbol('j', commutative=True)))))", "srepr_negatives": ["sin(Add(Symbol('V', commutative=True), Mul(Integer(-1), Symbol('j', commutative=True))))", "Mul(Symbol('V', commutative=True), sin(Symbol('j', commutative=True)))", "Mul(Pow(Symbol('V', commutative=True), Integer(-1)), sin(Symbol('j', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('V', commutative=True), Integer(-1)), cos(Symbol('j', commutative=True)))"]}, {"premise_expression": "\\sin{(\\frac{U}{C})}", "variable": "C", "positive": "C \\sin{(\\frac{U}{C})} - \\frac{U \\log{(\\frac{U^{2}}{C^{2}})}}{2} + U \\log{(\\frac{U}{C})} - U \\operatorname{Ci}{(\\frac{U}{C})}", "negatives": ["C \\log{(C - U)} - C - U \\log{(C - U)}", "C \\log{(C + U)} - C + U \\log{(C + U)}", "C (\\log{(C U)} - 1)", "\\frac{C (C + 2 e^{U})}{2}"], "srepr_premise_expression": "sin(Mul(Pow(Symbol('C', commutative=True), Integer(-1)), Symbol('U', commutative=True)))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Add(Mul(Symbol('C', commutative=True), sin(Mul(Pow(Symbol('C', commutative=True), Integer(-1)), Symbol('U', commutative=True)))), Mul(Integer(-1), Rational(1, 2), Symbol('U', commutative=True), log(Mul(Pow(Symbol('C', commutative=True), Integer(-2)), Pow(Symbol('U', commutative=True), Integer(2))))), Mul(Symbol('U', commutative=True), log(Mul(Pow(Symbol('C', commutative=True), Integer(-1)), Symbol('U', commutative=True)))), Mul(Integer(-1), Symbol('U', commutative=True), Ci(Mul(Pow(Symbol('C', commutative=True), Integer(-1)), Symbol('U', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('C', commutative=True), log(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('U', commutative=True))))), Mul(Integer(-1), Symbol('C', commutative=True)), Mul(Integer(-1), Symbol('U', commutative=True), log(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('U', commutative=True))))))", "Add(Mul(Symbol('C', commutative=True), log(Add(Symbol('C', commutative=True), Symbol('U', commutative=True)))), Mul(Integer(-1), Symbol('C', commutative=True)), Mul(Symbol('U', commutative=True), log(Add(Symbol('C', commutative=True), Symbol('U', commutative=True)))))", "Mul(Symbol('C', commutative=True), Add(log(Mul(Symbol('C', commutative=True), Symbol('U', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Symbol('C', commutative=True), Mul(Integer(2), exp(Symbol('U', commutative=True)))))"]}, {"premise_expression": "\\frac{g}{p}", "variable": "p", "positive": "g \\log{(p)}", "negatives": ["\\frac{g^{2}}{2 p}", "g e^{\\frac{p}{g}}", "g p - \\cos{(p)}", "\\cos{(g - p)}"], "srepr_premise_expression": "Mul(Symbol('g', commutative=True), Pow(Symbol('p', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('p', commutative=True)", "srepr_positive": "Mul(Symbol('g', commutative=True), log(Symbol('p', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('g', commutative=True), Integer(2)), Pow(Symbol('p', commutative=True), Integer(-1)))", "Mul(Symbol('g', commutative=True), exp(Mul(Pow(Symbol('g', commutative=True), Integer(-1)), Symbol('p', commutative=True))))", "Add(Mul(Symbol('g', commutative=True), Symbol('p', commutative=True)), Mul(Integer(-1), cos(Symbol('p', commutative=True))))", "cos(Add(Symbol('g', commutative=True), Mul(Integer(-1), Symbol('p', commutative=True))))"]}, {"premise_expression": "- Q + g", "variable": "Q", "positive": "\\frac{Q (- Q + 2 g)}{2}", "negatives": ["\\frac{Q (Q - 2 g)}{2}", "\\frac{g (- 2 Q + g)}{2}", "\\frac{Q (- Q + 2 \\log{(g)})}{2}", "\\frac{Q (- Q + 2 \\cos{(g)})}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('Q', commutative=True)), Symbol('g', commutative=True))", "srepr_variable": "Symbol('Q', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Mul(Integer(-1), Symbol('Q', commutative=True)), Mul(Integer(2), Symbol('g', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Symbol('Q', commutative=True), Mul(Integer(-1), Integer(2), Symbol('g', commutative=True))))", "Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('Q', commutative=True)), Symbol('g', commutative=True)))", "Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Mul(Integer(-1), Symbol('Q', commutative=True)), Mul(Integer(2), log(Symbol('g', commutative=True)))))", "Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Mul(Integer(-1), Symbol('Q', commutative=True)), Mul(Integer(2), cos(Symbol('g', commutative=True)))))"]}, {"premise_expression": "\\log{(F + a)}", "variable": "F", "positive": "F \\log{(F + a)} - F + a \\log{(F + a)}", "negatives": ["F \\log{(F - a)} - F - a \\log{(F - a)}", "F \\log{(F + a)} + a \\log{(F + a)} - a", "\\frac{F (- F + 2 \\log{(a)})}{2}", "F e^{\\frac{a}{F}} - a \\operatorname{Ei}{(\\frac{a}{F})}"], "srepr_premise_expression": "log(Add(Symbol('F', commutative=True), Symbol('a', commutative=True)))", "srepr_variable": "Symbol('F', commutative=True)", "srepr_positive": "Add(Mul(Symbol('F', commutative=True), log(Add(Symbol('F', commutative=True), Symbol('a', commutative=True)))), Mul(Integer(-1), Symbol('F', commutative=True)), Mul(Symbol('a', commutative=True), log(Add(Symbol('F', commutative=True), Symbol('a', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('F', commutative=True), log(Add(Symbol('F', commutative=True), Mul(Integer(-1), Symbol('a', commutative=True))))), Mul(Integer(-1), Symbol('F', commutative=True)), Mul(Integer(-1), Symbol('a', commutative=True), log(Add(Symbol('F', commutative=True), Mul(Integer(-1), Symbol('a', commutative=True))))))", "Add(Mul(Symbol('F', commutative=True), log(Add(Symbol('F', commutative=True), Symbol('a', commutative=True)))), Mul(Symbol('a', commutative=True), log(Add(Symbol('F', commutative=True), Symbol('a', commutative=True)))), Mul(Integer(-1), Symbol('a', commutative=True)))", "Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Mul(Integer(-1), Symbol('F', commutative=True)), Mul(Integer(2), log(Symbol('a', commutative=True)))))", "Add(Mul(Symbol('F', commutative=True), exp(Mul(Pow(Symbol('F', commutative=True), Integer(-1)), Symbol('a', commutative=True)))), Mul(Integer(-1), Symbol('a', commutative=True), Ei(Mul(Pow(Symbol('F', commutative=True), Integer(-1)), Symbol('a', commutative=True)))))"]}, {"premise_expression": "\\frac{W^{w}}{M}", "variable": "M", "positive": "W^{w} \\log{(M)}", "negatives": ["W^{2} \\log{(M)}", "(- W + w) \\log{(M)}", "\\frac{M^{2} W w}{2}", "M^{2} (\\frac{M}{3} - \\frac{W}{2})"], "srepr_premise_expression": "Mul(Pow(Symbol('M', commutative=True), Integer(-1)), Pow(Symbol('W', commutative=True), Symbol('w', commutative=True)))", "srepr_variable": "Symbol('M', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('W', commutative=True), Symbol('w', commutative=True)), log(Symbol('M', commutative=True)))", "srepr_negatives": ["Mul(Pow(Symbol('W', commutative=True), Integer(2)), log(Symbol('M', commutative=True)))", "Mul(Add(Mul(Integer(-1), Symbol('W', commutative=True)), Symbol('w', commutative=True)), log(Symbol('M', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('M', commutative=True), Integer(2)), Symbol('W', commutative=True), Symbol('w', commutative=True))", "Mul(Pow(Symbol('M', commutative=True), Integer(2)), Add(Mul(Rational(1, 3), Symbol('M', commutative=True)), Mul(Integer(-1), Rational(1, 2), Symbol('W', commutative=True))))"]}, {"premise_expression": "Z + \\sin{(p)}", "variable": "Z", "positive": "\\frac{Z (Z + 2 \\sin{(p)})}{2}", "negatives": ["\\frac{Z (Z + 2 \\cos{(p)})}{2}", "Z p - \\cos{(p)}", "- Z p - \\cos{(Z)}", "- \\cos{(Z - p)}"], "srepr_premise_expression": "Add(Symbol('Z', commutative=True), sin(Symbol('p', commutative=True)))", "srepr_variable": "Symbol('Z', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Symbol('Z', commutative=True), Mul(Integer(2), sin(Symbol('p', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Symbol('Z', commutative=True), Mul(Integer(2), cos(Symbol('p', commutative=True)))))", "Add(Mul(Symbol('Z', commutative=True), Symbol('p', commutative=True)), Mul(Integer(-1), cos(Symbol('p', commutative=True))))", "Add(Mul(Integer(-1), Symbol('Z', commutative=True), Symbol('p', commutative=True)), Mul(Integer(-1), cos(Symbol('Z', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('Z', commutative=True), Mul(Integer(-1), Symbol('p', commutative=True)))))"]}, {"premise_expression": "\\frac{T}{j}", "variable": "T", "positive": "\\frac{T^{2}}{2 j}", "negatives": ["T \\log{(j)}", "\\frac{T^{2} j}{2}", "\\sin{(T + j)}", "\\frac{T (- T + 2 j)}{2}"], "srepr_premise_expression": "Mul(Symbol('T', commutative=True), Pow(Symbol('j', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('T', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('T', commutative=True), Integer(2)), Pow(Symbol('j', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('T', commutative=True), log(Symbol('j', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('T', commutative=True), Integer(2)), Symbol('j', commutative=True))", "sin(Add(Symbol('T', commutative=True), Symbol('j', commutative=True)))", "Mul(Rational(1, 2), Symbol('T', commutative=True), Add(Mul(Integer(-1), Symbol('T', commutative=True)), Mul(Integer(2), Symbol('j', commutative=True))))"]}, {"premise_expression": "\\sin^{r}{(D)}", "variable": "D", "positive": "\\int \\sin^{r}{(D)} dD", "negatives": ["D (e^{r})^{r}", "D (r + \\log{(D)} - 1)", "e^{D + r}", "- D r + e^{D}"], "srepr_premise_expression": "Pow(sin(Symbol('D', commutative=True)), Symbol('r', commutative=True))", "srepr_variable": "Symbol('D', commutative=True)", "srepr_positive": "Integral(Pow(sin(Symbol('D', commutative=True)), Symbol('r', commutative=True)), Tuple(Symbol('D', commutative=True)))", "srepr_negatives": ["Mul(Symbol('D', commutative=True), Pow(exp(Symbol('r', commutative=True)), Symbol('r', commutative=True)))", "Mul(Symbol('D', commutative=True), Add(Symbol('r', commutative=True), log(Symbol('D', commutative=True)), Integer(-1)))", "exp(Add(Symbol('D', commutative=True), Symbol('r', commutative=True)))", "Add(Mul(Integer(-1), Symbol('D', commutative=True), Symbol('r', commutative=True)), exp(Symbol('D', commutative=True)))"]}, {"premise_expression": "T + h + u", "variable": "h", "positive": "h (T + \\frac{h}{2} + u)", "negatives": ["\\frac{h (2 T - h + 2 u)}{2}", "\\frac{h (- 2 T + h - 2 u)}{2}", "\\frac{u (2 T + 2 h + u)}{2}", "\\frac{T (T + 2 h + 2 u)}{2}"], "srepr_premise_expression": "Add(Symbol('T', commutative=True), Symbol('h', commutative=True), Symbol('u', commutative=True))", "srepr_variable": "Symbol('h', commutative=True)", "srepr_positive": "Mul(Symbol('h', commutative=True), Add(Symbol('T', commutative=True), Mul(Rational(1, 2), Symbol('h', commutative=True)), Symbol('u', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('h', commutative=True), Add(Mul(Integer(2), Symbol('T', commutative=True)), Mul(Integer(-1), Symbol('h', commutative=True)), Mul(Integer(2), Symbol('u', commutative=True))))", "Mul(Rational(1, 2), Symbol('h', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('T', commutative=True)), Symbol('h', commutative=True), Mul(Integer(-1), Integer(2), Symbol('u', commutative=True))))", "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(2), Symbol('T', commutative=True)), Mul(Integer(2), Symbol('h', commutative=True)), Symbol('u', commutative=True)))", "Mul(Rational(1, 2), Symbol('T', commutative=True), Add(Symbol('T', commutative=True), Mul(Integer(2), Symbol('h', commutative=True)), Mul(Integer(2), Symbol('u', commutative=True))))"]}, {"premise_expression": "\\frac{y}{u}", "variable": "u", "positive": "y \\log{(u)}", "negatives": ["\\frac{y^{2}}{2 u}", "\\frac{u^{2} y}{2}", "u", "\\log{(u)} \\log{(y)}"], "srepr_premise_expression": "Mul(Pow(Symbol('u', commutative=True), Integer(-1)), Symbol('y', commutative=True))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "Mul(Symbol('y', commutative=True), log(Symbol('u', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('u', commutative=True), Integer(-1)), Pow(Symbol('y', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('u', commutative=True), Integer(2)), Symbol('y', commutative=True))", "Symbol('u', commutative=True)", "Mul(log(Symbol('u', commutative=True)), log(Symbol('y', commutative=True)))"]}, {"premise_expression": "e^{V - y}", "variable": "V", "positive": "e^{V - y}", "negatives": ["- e^{V - y}", "\\sin{(V - y)}", "- e^{- V + y}", "V \\log{(y^{2})}"], "srepr_premise_expression": "exp(Add(Symbol('V', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True))))", "srepr_variable": "Symbol('V', commutative=True)", "srepr_positive": "exp(Add(Symbol('V', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Symbol('V', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True)))))", "sin(Add(Symbol('V', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True))))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('V', commutative=True)), Symbol('y', commutative=True))))", "Mul(Symbol('V', commutative=True), log(Pow(Symbol('y', commutative=True), Integer(2))))"]}, {"premise_expression": "e^{\\frac{R}{z}}", "variable": "z", "positive": "- R \\operatorname{Ei}{(\\frac{R}{z})} + z e^{\\frac{R}{z}}", "negatives": ["z e^{\\frac{R}{z}}", "R e^{\\frac{z}{R}}", "e^{R + z}", "z (\\log{(R z)} - 1)"], "srepr_premise_expression": "exp(Mul(Symbol('R', commutative=True), Pow(Symbol('z', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('z', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('R', commutative=True), Ei(Mul(Symbol('R', commutative=True), Pow(Symbol('z', commutative=True), Integer(-1))))), Mul(Symbol('z', commutative=True), exp(Mul(Symbol('R', commutative=True), Pow(Symbol('z', commutative=True), Integer(-1))))))", "srepr_negatives": ["Mul(Symbol('z', commutative=True), exp(Mul(Symbol('R', commutative=True), Pow(Symbol('z', commutative=True), Integer(-1)))))", "Mul(Symbol('R', commutative=True), exp(Mul(Pow(Symbol('R', commutative=True), Integer(-1)), Symbol('z', commutative=True))))", "exp(Add(Symbol('R', commutative=True), Symbol('z', commutative=True)))", "Mul(Symbol('z', commutative=True), Add(log(Mul(Symbol('R', commutative=True), Symbol('z', commutative=True))), Integer(-1)))"]}, {"premise_expression": "L + o", "variable": "L", "positive": "\\frac{L (L + 2 o)}{2}", "negatives": ["\\frac{o (2 L + o)}{2}", "\\frac{L (L + 2 e^{o})}{2}", "\\frac{L^{2}}{2 o}", "\\cos{(L - o)}"], "srepr_premise_expression": "Add(Symbol('L', commutative=True), Symbol('o', commutative=True))", "srepr_variable": "Symbol('L', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Symbol('L', commutative=True), Mul(Integer(2), Symbol('o', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Mul(Integer(2), Symbol('L', commutative=True)), Symbol('o', commutative=True)))", "Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Symbol('L', commutative=True), Mul(Integer(2), exp(Symbol('o', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(2)), Pow(Symbol('o', commutative=True), Integer(-1)))", "cos(Add(Symbol('L', commutative=True), Mul(Integer(-1), Symbol('o', commutative=True))))"]}, {"premise_expression": "\\sin^{V}{(c)}", "variable": "c", "positive": "\\int \\sin^{V}{(c)} dc", "negatives": ["e^{- V + c}", "e^{V + c}", "\\frac{c^{2}}{2 V}", "\\frac{c^{2} \\log{(V)}}{2}"], "srepr_premise_expression": "Pow(sin(Symbol('c', commutative=True)), Symbol('V', commutative=True))", "srepr_variable": "Symbol('c', commutative=True)", "srepr_positive": "Integral(Pow(sin(Symbol('c', commutative=True)), Symbol('V', commutative=True)), Tuple(Symbol('c', commutative=True)))", "srepr_negatives": ["exp(Add(Mul(Integer(-1), Symbol('V', commutative=True)), Symbol('c', commutative=True)))", "exp(Add(Symbol('V', commutative=True), Symbol('c', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('V', commutative=True), Integer(-1)), Pow(Symbol('c', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('c', commutative=True), Integer(2)), log(Symbol('V', commutative=True)))"]}, {"premise_expression": "\\sin{(M - y)}", "variable": "y", "positive": "\\cos{(M - y)}", "negatives": ["- \\cos{(M - y)}", "\\frac{y (2 M + y)}{2}", "\\frac{e^{2 y}}{2}", "y (\\log{(\\frac{M}{y})} + 1)"], "srepr_premise_expression": "sin(Add(Symbol('M', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True))))", "srepr_variable": "Symbol('y', commutative=True)", "srepr_positive": "cos(Add(Symbol('M', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('M', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True)))))", "Mul(Rational(1, 2), Symbol('y', commutative=True), Add(Mul(Integer(2), Symbol('M', commutative=True)), Symbol('y', commutative=True)))", "Mul(Rational(1, 2), exp(Mul(Integer(2), Symbol('y', commutative=True))))", "Mul(Symbol('y', commutative=True), Add(log(Mul(Symbol('M', commutative=True), Pow(Symbol('y', commutative=True), Integer(-1)))), Integer(1)))"]}, {"premise_expression": "S + c", "variable": "c", "positive": "\\frac{c (2 S + c)}{2}", "negatives": ["\\frac{S (S + 2 c)}{2}", "\\cos{(S - c)}", "- \\sin{(S - c)}", "\\frac{c (c + 2 e^{S})}{2}"], "srepr_premise_expression": "Add(Symbol('S', commutative=True), Symbol('c', commutative=True))", "srepr_variable": "Symbol('c', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('c', commutative=True), Add(Mul(Integer(2), Symbol('S', commutative=True)), Symbol('c', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Symbol('S', commutative=True), Mul(Integer(2), Symbol('c', commutative=True))))", "cos(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('c', commutative=True))))", "Mul(Integer(-1), sin(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('c', commutative=True)))))", "Mul(Rational(1, 2), Symbol('c', commutative=True), Add(Symbol('c', commutative=True), Mul(Integer(2), exp(Symbol('S', commutative=True)))))"]}, {"premise_expression": "\\sin{(H + R)}", "variable": "H", "positive": "- \\cos{(H + R)}", "negatives": ["R e^{\\frac{H}{R}}", "\\log{(H)} \\cos{(R)}", "\\frac{H^{2} \\sin{(R)}}{2}", "\\frac{H^{2} e^{R}}{2}"], "srepr_premise_expression": "sin(Add(Symbol('H', commutative=True), Symbol('R', commutative=True)))", "srepr_variable": "Symbol('H', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('H', commutative=True), Symbol('R', commutative=True))))", "srepr_negatives": ["Mul(Symbol('R', commutative=True), exp(Mul(Symbol('H', commutative=True), Pow(Symbol('R', commutative=True), Integer(-1)))))", "Mul(log(Symbol('H', commutative=True)), cos(Symbol('R', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('H', commutative=True), Integer(2)), sin(Symbol('R', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('H', commutative=True), Integer(2)), exp(Symbol('R', commutative=True)))"]}, {"premise_expression": "\\frac{m}{c}", "variable": "c", "positive": "m \\log{(c)}", "negatives": ["\\frac{m^{2}}{2 c}", "\\frac{\\sin{(c)}}{m}", "c m (\\log{(c)} - 1)", "\\frac{c (- c + 2 m)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('c', commutative=True), Integer(-1)), Symbol('m', commutative=True))", "srepr_variable": "Symbol('c', commutative=True)", "srepr_positive": "Mul(Symbol('m', commutative=True), log(Symbol('c', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('c', commutative=True), Integer(-1)), Pow(Symbol('m', commutative=True), Integer(2)))", "Mul(Pow(Symbol('m', commutative=True), Integer(-1)), sin(Symbol('c', commutative=True)))", "Mul(Symbol('c', commutative=True), Symbol('m', commutative=True), Add(log(Symbol('c', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('c', commutative=True), Add(Mul(Integer(-1), Symbol('c', commutative=True)), Mul(Integer(2), Symbol('m', commutative=True))))"]}, {"premise_expression": "n^{W} + u", "variable": "u", "positive": "\\frac{u (2 n^{W} + u)}{2}", "negatives": ["\\frac{u (2 W n + u)}{2}", "\\frac{u (2 W + u)}{2 n}", "\\frac{u (- 2 W + 2 n - u)}{2}", "\\frac{u (W u - 2 n)}{2}"], "srepr_premise_expression": "Add(Pow(Symbol('n', commutative=True), Symbol('W', commutative=True)), Symbol('u', commutative=True))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(2), Pow(Symbol('n', commutative=True), Symbol('W', commutative=True))), Symbol('u', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(2), Symbol('W', commutative=True), Symbol('n', commutative=True)), Symbol('u', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('n', commutative=True), Integer(-1)), Symbol('u', commutative=True), Add(Mul(Integer(2), Symbol('W', commutative=True)), Symbol('u', commutative=True)))", "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('W', commutative=True)), Mul(Integer(2), Symbol('n', commutative=True)), Mul(Integer(-1), Symbol('u', commutative=True))))", "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Symbol('W', commutative=True), Symbol('u', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('n', commutative=True))))"]}, {"premise_expression": "- c + \\sin{(g)}", "variable": "g", "positive": "- c g - \\cos{(g)}", "negatives": ["- c g + \\sin{(g)}", "c g + \\sin{(g)}", "c (g + \\log{(g)})", "- \\frac{\\cos{(g)}}{c}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('c', commutative=True)), sin(Symbol('g', commutative=True)))", "srepr_variable": "Symbol('g', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('c', commutative=True), Symbol('g', commutative=True)), Mul(Integer(-1), cos(Symbol('g', commutative=True))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('c', commutative=True), Symbol('g', commutative=True)), sin(Symbol('g', commutative=True)))", "Add(Mul(Symbol('c', commutative=True), Symbol('g', commutative=True)), sin(Symbol('g', commutative=True)))", "Mul(Symbol('c', commutative=True), Add(Symbol('g', commutative=True), log(Symbol('g', commutative=True))))", "Mul(Integer(-1), Pow(Symbol('c', commutative=True), Integer(-1)), cos(Symbol('g', commutative=True)))"]}, {"premise_expression": "V - k", "variable": "k", "positive": "\\frac{k (2 V - k)}{2}", "negatives": ["\\frac{k (2 V + k)}{2}", "k (V - k)", "\\frac{V (V - 2 k)}{2}", "- e^{V - k}"], "srepr_premise_expression": "Add(Symbol('V', commutative=True), Mul(Integer(-1), Symbol('k', commutative=True)))", "srepr_variable": "Symbol('k', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('k', commutative=True), Add(Mul(Integer(2), Symbol('V', commutative=True)), Mul(Integer(-1), Symbol('k', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('k', commutative=True), Add(Mul(Integer(2), Symbol('V', commutative=True)), Symbol('k', commutative=True)))", "Mul(Symbol('k', commutative=True), Add(Symbol('V', commutative=True), Mul(Integer(-1), Symbol('k', commutative=True))))", "Mul(Rational(1, 2), Symbol('V', commutative=True), Add(Symbol('V', commutative=True), Mul(Integer(-1), Integer(2), Symbol('k', commutative=True))))", "Mul(Integer(-1), exp(Add(Symbol('V', commutative=True), Mul(Integer(-1), Symbol('k', commutative=True)))))"]}, {"premise_expression": "\\frac{B}{Z}", "variable": "B", "positive": "\\frac{B^{2}}{2 Z}", "negatives": ["B \\log{(Z)}", "\\frac{B^{2} Z}{2}", "\\frac{\\sin{(B)}}{Z}", "- \\cos{(B - Z)}"], "srepr_premise_expression": "Mul(Symbol('B', commutative=True), Pow(Symbol('Z', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('B', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('B', commutative=True), Integer(2)), Pow(Symbol('Z', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('B', commutative=True), log(Symbol('Z', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('B', commutative=True), Integer(2)), Symbol('Z', commutative=True))", "Mul(Pow(Symbol('Z', commutative=True), Integer(-1)), sin(Symbol('B', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('B', commutative=True), Mul(Integer(-1), Symbol('Z', commutative=True)))))"]}, {"premise_expression": "- C + v", "variable": "C", "positive": "\\frac{C (- C + 2 v)}{2}", "negatives": ["\\frac{v (- 2 C + v)}{2}", "\\sin{(C + v)}", "C v + \\sin{(C)}", "\\sin{(C - v)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('C', commutative=True)), Symbol('v', commutative=True))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Mul(Integer(-1), Symbol('C', commutative=True)), Mul(Integer(2), Symbol('v', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('v', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('C', commutative=True)), Symbol('v', commutative=True)))", "sin(Add(Symbol('C', commutative=True), Symbol('v', commutative=True)))", "Add(Mul(Symbol('C', commutative=True), Symbol('v', commutative=True)), sin(Symbol('C', commutative=True)))", "sin(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('v', commutative=True))))"]}, {"premise_expression": "\\log{(Y^{T})}", "variable": "Y", "positive": "Y (- T + \\log{(Y^{T})})", "negatives": ["\\frac{T^{2} \\log{(Y)}}{2}", "\\sin{(T + Y)}", "- \\frac{\\cos{(Y)}}{T}", "\\int \\sin^{T}{(Y)} dY"], "srepr_premise_expression": "log(Pow(Symbol('Y', commutative=True), Symbol('T', commutative=True)))", "srepr_variable": "Symbol('Y', commutative=True)", "srepr_positive": "Mul(Symbol('Y', commutative=True), Add(Mul(Integer(-1), Symbol('T', commutative=True)), log(Pow(Symbol('Y', commutative=True), Symbol('T', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('T', commutative=True), Integer(2)), log(Symbol('Y', commutative=True)))", "sin(Add(Symbol('T', commutative=True), Symbol('Y', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('T', commutative=True), Integer(-1)), cos(Symbol('Y', commutative=True)))", "Integral(Pow(sin(Symbol('Y', commutative=True)), Symbol('T', commutative=True)), Tuple(Symbol('Y', commutative=True)))"]}, {"premise_expression": "\\cos^{W}{(j)}", "variable": "j", "positive": "\\int \\cos^{W}{(j)} dj", "negatives": ["\\log{(j)} \\sin{(W)}", "- W \\cos{(j)}", "W e^{\\frac{j}{W}}", "\\frac{j^{2} \\cos{(W)}}{2}"], "srepr_premise_expression": "Pow(cos(Symbol('j', commutative=True)), Symbol('W', commutative=True))", "srepr_variable": "Symbol('j', commutative=True)", "srepr_positive": "Integral(Pow(cos(Symbol('j', commutative=True)), Symbol('W', commutative=True)), Tuple(Symbol('j', commutative=True)))", "srepr_negatives": ["Mul(log(Symbol('j', commutative=True)), sin(Symbol('W', commutative=True)))", "Mul(Integer(-1), Symbol('W', commutative=True), cos(Symbol('j', commutative=True)))", "Mul(Symbol('W', commutative=True), exp(Mul(Pow(Symbol('W', commutative=True), Integer(-1)), Symbol('j', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('j', commutative=True), Integer(2)), cos(Symbol('W', commutative=True)))"]}, {"premise_expression": "G + e^{S}", "variable": "S", "positive": "G S + e^{S}", "negatives": ["G e^{S}", "\\frac{G (G + 2 e^{S})}{2}", "G \\log{(S)}", "\\sin{(G + S)}"], "srepr_premise_expression": "Add(Symbol('G', commutative=True), exp(Symbol('S', commutative=True)))", "srepr_variable": "Symbol('S', commutative=True)", "srepr_positive": "Add(Mul(Symbol('G', commutative=True), Symbol('S', commutative=True)), exp(Symbol('S', commutative=True)))", "srepr_negatives": ["Mul(Symbol('G', commutative=True), exp(Symbol('S', commutative=True)))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Symbol('G', commutative=True), Mul(Integer(2), exp(Symbol('S', commutative=True)))))", "Mul(Symbol('G', commutative=True), log(Symbol('S', commutative=True)))", "sin(Add(Symbol('G', commutative=True), Symbol('S', commutative=True)))"]}, {"premise_expression": "\\frac{C}{r}", "variable": "C", "positive": "\\frac{C^{2}}{2 r}", "negatives": ["C \\log{(r)}", "\\frac{C (C + 2 r)}{2}", "e^{C - r}", "\\frac{C^{2} (1 - r)}{2 r}"], "srepr_premise_expression": "Mul(Symbol('C', commutative=True), Pow(Symbol('r', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2)), Pow(Symbol('r', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('C', commutative=True), log(Symbol('r', commutative=True)))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Symbol('C', commutative=True), Mul(Integer(2), Symbol('r', commutative=True))))", "exp(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('r', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2)), Pow(Symbol('r', commutative=True), Integer(-1)), Add(Integer(1), Mul(Integer(-1), Symbol('r', commutative=True))))"]}, {"premise_expression": "T - r", "variable": "r", "positive": "\\frac{r (2 T - r)}{2}", "negatives": ["\\frac{T (T - 2 r)}{2}", "\\sin{(T + r)}", "\\frac{T r^{2}}{2}", "r (\\log{(\\frac{T}{r})} + 1)"], "srepr_premise_expression": "Add(Symbol('T', commutative=True), Mul(Integer(-1), Symbol('r', commutative=True)))", "srepr_variable": "Symbol('r', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(2), Symbol('T', commutative=True)), Mul(Integer(-1), Symbol('r', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('T', commutative=True), Add(Symbol('T', commutative=True), Mul(Integer(-1), Integer(2), Symbol('r', commutative=True))))", "sin(Add(Symbol('T', commutative=True), Symbol('r', commutative=True)))", "Mul(Rational(1, 2), Symbol('T', commutative=True), Pow(Symbol('r', commutative=True), Integer(2)))", "Mul(Symbol('r', commutative=True), Add(log(Mul(Symbol('T', commutative=True), Pow(Symbol('r', commutative=True), Integer(-1)))), Integer(1)))"]}, {"premise_expression": "K + g + q", "variable": "q", "positive": "q (K + g + \\frac{q}{2})", "negatives": ["\\frac{K (K + 2 g + 2 q)}{2}", "\\frac{g (2 K + g + 2 q)}{2}", "\\frac{q (K q - 2 g)}{2}", "\\frac{q (2 K + q)}{2 g}"], "srepr_premise_expression": "Add(Symbol('K', commutative=True), Symbol('g', commutative=True), Symbol('q', commutative=True))", "srepr_variable": "Symbol('q', commutative=True)", "srepr_positive": "Mul(Symbol('q', commutative=True), Add(Symbol('K', commutative=True), Symbol('g', commutative=True), Mul(Rational(1, 2), Symbol('q', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Symbol('K', commutative=True), Mul(Integer(2), Symbol('g', commutative=True)), Mul(Integer(2), Symbol('q', commutative=True))))", "Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Mul(Integer(2), Symbol('K', commutative=True)), Symbol('g', commutative=True), Mul(Integer(2), Symbol('q', commutative=True))))", "Mul(Rational(1, 2), Symbol('q', commutative=True), Add(Mul(Symbol('K', commutative=True), Symbol('q', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('g', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('g', commutative=True), Integer(-1)), Symbol('q', commutative=True), Add(Mul(Integer(2), Symbol('K', commutative=True)), Symbol('q', commutative=True)))"]}, {"premise_expression": "\\frac{\\log{(G)}}{r}", "variable": "G", "positive": "\\frac{G (\\log{(G)} - 1)}{r}", "negatives": ["\\log{(G)} \\log{(r)}", "G^{2} (\\frac{G}{3} - \\frac{r}{2})", "\\frac{G (G + 2 r)}{2}", "e^{G - r}"], "srepr_premise_expression": "Mul(Pow(Symbol('r', commutative=True), Integer(-1)), log(Symbol('G', commutative=True)))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Mul(Symbol('G', commutative=True), Pow(Symbol('r', commutative=True), Integer(-1)), Add(log(Symbol('G', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(log(Symbol('G', commutative=True)), log(Symbol('r', commutative=True)))", "Mul(Pow(Symbol('G', commutative=True), Integer(2)), Add(Mul(Rational(1, 3), Symbol('G', commutative=True)), Mul(Integer(-1), Rational(1, 2), Symbol('r', commutative=True))))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Symbol('G', commutative=True), Mul(Integer(2), Symbol('r', commutative=True))))", "exp(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('r', commutative=True))))"]}, {"premise_expression": "k (F - I)", "variable": "I", "positive": "\\frac{I k (2 F - I)}{2}", "negatives": ["\\frac{k^{2} (F - I)}{2}", "\\frac{F k (F - 2 I)}{2}", "\\frac{I (2 F k + I)}{2}", "I (I + k)"], "srepr_premise_expression": "Mul(Symbol('k', commutative=True), Add(Symbol('F', commutative=True), Mul(Integer(-1), Symbol('I', commutative=True))))", "srepr_variable": "Symbol('I', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('I', commutative=True), Symbol('k', commutative=True), Add(Mul(Integer(2), Symbol('F', commutative=True)), Mul(Integer(-1), Symbol('I', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('k', commutative=True), Integer(2)), Add(Symbol('F', commutative=True), Mul(Integer(-1), Symbol('I', commutative=True))))", "Mul(Rational(1, 2), Symbol('F', commutative=True), Symbol('k', commutative=True), Add(Symbol('F', commutative=True), Mul(Integer(-1), Integer(2), Symbol('I', commutative=True))))", "Mul(Rational(1, 2), Symbol('I', commutative=True), Add(Mul(Integer(2), Symbol('F', commutative=True), Symbol('k', commutative=True)), Symbol('I', commutative=True)))", "Mul(Symbol('I', commutative=True), Add(Symbol('I', commutative=True), Symbol('k', commutative=True)))"]}, {"premise_expression": "- G + \\sin{(N)}", "variable": "G", "positive": "\\frac{G (- G + 2 \\sin{(N)})}{2}", "negatives": ["\\frac{G (- G + 2 e^{N})}{2}", "\\frac{G (G + 2 N)}{2}", "\\frac{G^{2} e^{N}}{2}", "- G N - \\cos{(N)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('G', commutative=True)), sin(Symbol('N', commutative=True)))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Mul(Integer(-1), Symbol('G', commutative=True)), Mul(Integer(2), sin(Symbol('N', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Mul(Integer(-1), Symbol('G', commutative=True)), Mul(Integer(2), exp(Symbol('N', commutative=True)))))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Symbol('G', commutative=True), Mul(Integer(2), Symbol('N', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(2)), exp(Symbol('N', commutative=True)))", "Add(Mul(Integer(-1), Symbol('G', commutative=True), Symbol('N', commutative=True)), Mul(Integer(-1), cos(Symbol('N', commutative=True))))"]}, {"premise_expression": "\\frac{r + t}{H}", "variable": "t", "positive": "\\frac{t (2 r + t)}{2 H}", "negatives": ["\\frac{t (- 2 H + t)}{2 r}", "\\frac{r (r + 2 t)}{2 H}", "\\frac{t (2 H r + t)}{2}", "\\frac{r t (2 H + t)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('H', commutative=True), Integer(-1)), Add(Symbol('r', commutative=True), Symbol('t', commutative=True)))", "srepr_variable": "Symbol('t', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('H', commutative=True), Integer(-1)), Symbol('t', commutative=True), Add(Mul(Integer(2), Symbol('r', commutative=True)), Symbol('t', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('r', commutative=True), Integer(-1)), Symbol('t', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('H', commutative=True)), Symbol('t', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('H', commutative=True), Integer(-1)), Symbol('r', commutative=True), Add(Symbol('r', commutative=True), Mul(Integer(2), Symbol('t', commutative=True))))", "Mul(Rational(1, 2), Symbol('t', commutative=True), Add(Mul(Integer(2), Symbol('H', commutative=True), Symbol('r', commutative=True)), Symbol('t', commutative=True)))", "Mul(Rational(1, 2), Symbol('r', commutative=True), Symbol('t', commutative=True), Add(Mul(Integer(2), Symbol('H', commutative=True)), Symbol('t', commutative=True)))"]}, {"premise_expression": "A + o + q", "variable": "o", "positive": "o (A + \\frac{o}{2} + q)", "negatives": ["\\frac{o (2 A - o - 2 q)}{2}", "\\frac{q (2 A + 2 o + q)}{2}", "\\frac{A (A + 2 o + 2 q)}{2}", "\\frac{o (A o - 2 q)}{2}"], "srepr_premise_expression": "Add(Symbol('A', commutative=True), Symbol('o', commutative=True), Symbol('q', commutative=True))", "srepr_variable": "Symbol('o', commutative=True)", "srepr_positive": "Mul(Symbol('o', commutative=True), Add(Symbol('A', commutative=True), Mul(Rational(1, 2), Symbol('o', commutative=True)), Symbol('q', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Mul(Integer(2), Symbol('A', commutative=True)), Mul(Integer(-1), Symbol('o', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('q', commutative=True))))", "Mul(Rational(1, 2), Symbol('q', commutative=True), Add(Mul(Integer(2), Symbol('A', commutative=True)), Mul(Integer(2), Symbol('o', commutative=True)), Symbol('q', commutative=True)))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Symbol('A', commutative=True), Mul(Integer(2), Symbol('o', commutative=True)), Mul(Integer(2), Symbol('q', commutative=True))))", "Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Mul(Symbol('A', commutative=True), Symbol('o', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('q', commutative=True))))"]}, {"premise_expression": "\\frac{\\sin{(S)}}{b}", "variable": "S", "positive": "- \\frac{\\cos{(S)}}{b}", "negatives": ["b \\sin{(S)}", "\\frac{S^{2} \\cos{(b)}}{2}", "b^{2} \\log{(S)}", "S b + \\sin{(S)}"], "srepr_premise_expression": "Mul(Pow(Symbol('b', commutative=True), Integer(-1)), sin(Symbol('S', commutative=True)))", "srepr_variable": "Symbol('S', commutative=True)", "srepr_positive": "Mul(Integer(-1), Pow(Symbol('b', commutative=True), Integer(-1)), cos(Symbol('S', commutative=True)))", "srepr_negatives": ["Mul(Symbol('b', commutative=True), sin(Symbol('S', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('S', commutative=True), Integer(2)), cos(Symbol('b', commutative=True)))", "Mul(Pow(Symbol('b', commutative=True), Integer(2)), log(Symbol('S', commutative=True)))", "Add(Mul(Symbol('S', commutative=True), Symbol('b', commutative=True)), sin(Symbol('S', commutative=True)))"]}, {"premise_expression": "e^{- A + u}", "variable": "u", "positive": "e^{- A + u}", "negatives": ["- e^{- A + u}", "e^{A + u}", "- e^{A - u}", "A e^{u}"], "srepr_premise_expression": "exp(Add(Mul(Integer(-1), Symbol('A', commutative=True)), Symbol('u', commutative=True)))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "exp(Add(Mul(Integer(-1), Symbol('A', commutative=True)), Symbol('u', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('A', commutative=True)), Symbol('u', commutative=True))))", "exp(Add(Symbol('A', commutative=True), Symbol('u', commutative=True)))", "Mul(Integer(-1), exp(Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('u', commutative=True)))))", "Mul(Symbol('A', commutative=True), exp(Symbol('u', commutative=True)))"]}, {"premise_expression": "a + u", "variable": "u", "positive": "\\frac{u (2 a + u)}{2}", "negatives": ["\\frac{a (a + 2 u)}{2}", "e^{- a + u}", "- \\sin{(a - u)}", "a e^{u}"], "srepr_premise_expression": "Add(Symbol('a', commutative=True), Symbol('u', commutative=True))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(2), Symbol('a', commutative=True)), Symbol('u', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('a', commutative=True), Add(Symbol('a', commutative=True), Mul(Integer(2), Symbol('u', commutative=True))))", "exp(Add(Mul(Integer(-1), Symbol('a', commutative=True)), Symbol('u', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('a', commutative=True), Mul(Integer(-1), Symbol('u', commutative=True)))))", "Mul(Symbol('a', commutative=True), exp(Symbol('u', commutative=True)))"]}, {"premise_expression": "\\frac{T}{N}", "variable": "T", "positive": "\\frac{T^{2}}{2 N}", "negatives": ["T \\log{(N)}", "N \\log{(T)}", "\\sin{(N + T)}", "- e^{N - T}"], "srepr_premise_expression": "Mul(Pow(Symbol('N', commutative=True), Integer(-1)), Symbol('T', commutative=True))", "srepr_variable": "Symbol('T', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('N', commutative=True), Integer(-1)), Pow(Symbol('T', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('T', commutative=True), log(Symbol('N', commutative=True)))", "Mul(Symbol('N', commutative=True), log(Symbol('T', commutative=True)))", "sin(Add(Symbol('N', commutative=True), Symbol('T', commutative=True)))", "Mul(Integer(-1), exp(Add(Symbol('N', commutative=True), Mul(Integer(-1), Symbol('T', commutative=True)))))"]}, {"premise_expression": "\\frac{n}{A k}", "variable": "k", "positive": "\\frac{n \\log{(k)}}{A}", "negatives": ["\\frac{n \\log{(A)}}{k}", "\\frac{A \\log{(k)}}{n}", "(A + n) \\log{(k)}", "\\frac{A k^{2} n}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('A', commutative=True), Integer(-1)), Pow(Symbol('k', commutative=True), Integer(-1)), Symbol('n', commutative=True))", "srepr_variable": "Symbol('k', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('A', commutative=True), Integer(-1)), Symbol('n', commutative=True), log(Symbol('k', commutative=True)))", "srepr_negatives": ["Mul(Pow(Symbol('k', commutative=True), Integer(-1)), Symbol('n', commutative=True), log(Symbol('A', commutative=True)))", "Mul(Symbol('A', commutative=True), Pow(Symbol('n', commutative=True), Integer(-1)), log(Symbol('k', commutative=True)))", "Mul(Add(Symbol('A', commutative=True), Symbol('n', commutative=True)), log(Symbol('k', commutative=True)))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Pow(Symbol('k', commutative=True), Integer(2)), Symbol('n', commutative=True))"]}, {"premise_expression": "\\frac{c}{v}", "variable": "v", "positive": "c \\log{(v)}", "negatives": ["\\frac{c^{2}}{2 v}", "e^{c} \\log{(v)}", "c v - \\cos{(v)}", "c v + \\sin{(v)}"], "srepr_premise_expression": "Mul(Symbol('c', commutative=True), Pow(Symbol('v', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('v', commutative=True)", "srepr_positive": "Mul(Symbol('c', commutative=True), log(Symbol('v', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('c', commutative=True), Integer(2)), Pow(Symbol('v', commutative=True), Integer(-1)))", "Mul(exp(Symbol('c', commutative=True)), log(Symbol('v', commutative=True)))", "Add(Mul(Symbol('c', commutative=True), Symbol('v', commutative=True)), Mul(Integer(-1), cos(Symbol('v', commutative=True))))", "Add(Mul(Symbol('c', commutative=True), Symbol('v', commutative=True)), sin(Symbol('v', commutative=True)))"]}, {"premise_expression": "- \\sin{(G - Y)}", "variable": "Y", "positive": "- \\cos{(G - Y)}", "negatives": ["\\cos{(G - Y)}", "- G Y - \\cos{(Y)}", "\\frac{Y (- 2 G + Y)}{2}", "G Y + e^{Y}"], "srepr_premise_expression": "Mul(Integer(-1), sin(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('Y', commutative=True)))))", "srepr_variable": "Symbol('Y', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('Y', commutative=True)))))", "srepr_negatives": ["cos(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('Y', commutative=True))))", "Add(Mul(Integer(-1), Symbol('G', commutative=True), Symbol('Y', commutative=True)), Mul(Integer(-1), cos(Symbol('Y', commutative=True))))", "Mul(Rational(1, 2), Symbol('Y', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('G', commutative=True)), Symbol('Y', commutative=True)))", "Add(Mul(Symbol('G', commutative=True), Symbol('Y', commutative=True)), exp(Symbol('Y', commutative=True)))"]}, {"premise_expression": "\\frac{Z}{r z}", "variable": "r", "positive": "\\frac{Z \\log{(r)}}{z}", "negatives": ["\\frac{Z \\log{(z)}}{r}", "Z z \\log{(r)}", "\\frac{Z^{2}}{2 r z}", "(Z + z) \\log{(r)}"], "srepr_premise_expression": "Mul(Symbol('Z', commutative=True), Pow(Symbol('r', commutative=True), Integer(-1)), Pow(Symbol('z', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('r', commutative=True)", "srepr_positive": "Mul(Symbol('Z', commutative=True), Pow(Symbol('z', commutative=True), Integer(-1)), log(Symbol('r', commutative=True)))", "srepr_negatives": ["Mul(Symbol('Z', commutative=True), Pow(Symbol('r', commutative=True), Integer(-1)), log(Symbol('z', commutative=True)))", "Mul(Symbol('Z', commutative=True), Symbol('z', commutative=True), log(Symbol('r', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('Z', commutative=True), Integer(2)), Pow(Symbol('r', commutative=True), Integer(-1)), Pow(Symbol('z', commutative=True), Integer(-1)))", "Mul(Add(Symbol('Z', commutative=True), Symbol('z', commutative=True)), log(Symbol('r', commutative=True)))"]}, {"premise_expression": "\\cos^{b}{(E)}", "variable": "E", "positive": "\\int \\cos^{b}{(E)} dE", "negatives": ["\\int \\sin^{b}{(E)} dE", "\\cos{(E - b)}", "E (\\log{(E b)} - 1)", "b e^{E}"], "srepr_premise_expression": "Pow(cos(Symbol('E', commutative=True)), Symbol('b', commutative=True))", "srepr_variable": "Symbol('E', commutative=True)", "srepr_positive": "Integral(Pow(cos(Symbol('E', commutative=True)), Symbol('b', commutative=True)), Tuple(Symbol('E', commutative=True)))", "srepr_negatives": ["Integral(Pow(sin(Symbol('E', commutative=True)), Symbol('b', commutative=True)), Tuple(Symbol('E', commutative=True)))", "cos(Add(Symbol('E', commutative=True), Mul(Integer(-1), Symbol('b', commutative=True))))", "Mul(Symbol('E', commutative=True), Add(log(Mul(Symbol('E', commutative=True), Symbol('b', commutative=True))), Integer(-1)))", "Mul(Symbol('b', commutative=True), exp(Symbol('E', commutative=True)))"]}, {"premise_expression": "D e^{A}", "variable": "A", "positive": "D e^{A}", "negatives": ["\\frac{D^{2} e^{A}}{2}", "A (\\log{(A D)} - 1)", "A (D + \\log{(A)} - 1)", "A (- D + \\log{(A)} - 1)"], "srepr_premise_expression": "Mul(Symbol('D', commutative=True), exp(Symbol('A', commutative=True)))", "srepr_variable": "Symbol('A', commutative=True)", "srepr_positive": "Mul(Symbol('D', commutative=True), exp(Symbol('A', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(2)), exp(Symbol('A', commutative=True)))", "Mul(Symbol('A', commutative=True), Add(log(Mul(Symbol('A', commutative=True), Symbol('D', commutative=True))), Integer(-1)))", "Mul(Symbol('A', commutative=True), Add(Symbol('D', commutative=True), log(Symbol('A', commutative=True)), Integer(-1)))", "Mul(Symbol('A', commutative=True), Add(Mul(Integer(-1), Symbol('D', commutative=True)), log(Symbol('A', commutative=True)), Integer(-1)))"]}, {"premise_expression": "C + o", "variable": "C", "positive": "\\frac{C (C + 2 o)}{2}", "negatives": ["\\frac{o (2 C + o)}{2}", "\\frac{C (C + 2 \\cos{(o)})}{2}", "\\frac{C (C + 2 \\log{(o)})}{2}", "C o + \\sin{(C)}"], "srepr_premise_expression": "Add(Symbol('C', commutative=True), Symbol('o', commutative=True))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Symbol('C', commutative=True), Mul(Integer(2), Symbol('o', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Mul(Integer(2), Symbol('C', commutative=True)), Symbol('o', commutative=True)))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Symbol('C', commutative=True), Mul(Integer(2), cos(Symbol('o', commutative=True)))))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Symbol('C', commutative=True), Mul(Integer(2), log(Symbol('o', commutative=True)))))", "Add(Mul(Symbol('C', commutative=True), Symbol('o', commutative=True)), sin(Symbol('C', commutative=True)))"]}, {"premise_expression": "\\frac{y}{E}", "variable": "E", "positive": "y \\log{(E)}", "negatives": ["- y \\cos{(E)}", "\\frac{y^{2}}{2 E}", "E y - \\cos{(E)}", "\\frac{E^{2}}{2 y}"], "srepr_premise_expression": "Mul(Pow(Symbol('E', commutative=True), Integer(-1)), Symbol('y', commutative=True))", "srepr_variable": "Symbol('E', commutative=True)", "srepr_positive": "Mul(Symbol('y', commutative=True), log(Symbol('E', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Symbol('y', commutative=True), cos(Symbol('E', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('E', commutative=True), Integer(-1)), Pow(Symbol('y', commutative=True), Integer(2)))", "Add(Mul(Symbol('E', commutative=True), Symbol('y', commutative=True)), Mul(Integer(-1), cos(Symbol('E', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('E', commutative=True), Integer(2)), Pow(Symbol('y', commutative=True), Integer(-1)))"]}, {"premise_expression": "\\log{(D k)}", "variable": "k", "positive": "k (\\log{(D k)} - 1)", "negatives": ["D (\\log{(D k)} - 1)", "k (\\log{(\\frac{k}{D})} - 1)", "D \\log{(k)}", "\\frac{k^{2} \\log{(D)}}{2}"], "srepr_premise_expression": "log(Mul(Symbol('D', commutative=True), Symbol('k', commutative=True)))", "srepr_variable": "Symbol('k', commutative=True)", "srepr_positive": "Mul(Symbol('k', commutative=True), Add(log(Mul(Symbol('D', commutative=True), Symbol('k', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('D', commutative=True), Add(log(Mul(Symbol('D', commutative=True), Symbol('k', commutative=True))), Integer(-1)))", "Mul(Symbol('k', commutative=True), Add(log(Mul(Pow(Symbol('D', commutative=True), Integer(-1)), Symbol('k', commutative=True))), Integer(-1)))", "Mul(Symbol('D', commutative=True), log(Symbol('k', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('k', commutative=True), Integer(2)), log(Symbol('D', commutative=True)))"]}, {"premise_expression": "\\frac{N}{n}", "variable": "n", "positive": "N \\log{(n)}", "negatives": ["\\frac{N^{2}}{2 n}", "N n + \\sin{(n)}", "\\frac{n^{2}}{2 N}", "n (\\log{(\\frac{n}{N})} - 1)"], "srepr_premise_expression": "Mul(Symbol('N', commutative=True), Pow(Symbol('n', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('n', commutative=True)", "srepr_positive": "Mul(Symbol('N', commutative=True), log(Symbol('n', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('N', commutative=True), Integer(2)), Pow(Symbol('n', commutative=True), Integer(-1)))", "Add(Mul(Symbol('N', commutative=True), Symbol('n', commutative=True)), sin(Symbol('n', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('N', commutative=True), Integer(-1)), Pow(Symbol('n', commutative=True), Integer(2)))", "Mul(Symbol('n', commutative=True), Add(log(Mul(Pow(Symbol('N', commutative=True), Integer(-1)), Symbol('n', commutative=True))), Integer(-1)))"]}, {"premise_expression": "R l", "variable": "l", "positive": "\\frac{R l^{2}}{2}", "negatives": ["\\frac{R^{2} l}{2}", "R \\sin{(l)}", "\\frac{\\sin{(l)}}{R}", "\\cos{(R - l)}"], "srepr_premise_expression": "Mul(Symbol('R', commutative=True), Symbol('l', commutative=True))", "srepr_variable": "Symbol('l', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('R', commutative=True), Pow(Symbol('l', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('R', commutative=True), Integer(2)), Symbol('l', commutative=True))", "Mul(Symbol('R', commutative=True), sin(Symbol('l', commutative=True)))", "Mul(Pow(Symbol('R', commutative=True), Integer(-1)), sin(Symbol('l', commutative=True)))", "cos(Add(Symbol('R', commutative=True), Mul(Integer(-1), Symbol('l', commutative=True))))"]}, {"premise_expression": "e^{N - S}", "variable": "N", "positive": "e^{N - S}", "negatives": ["- e^{N - S}", "e^{N + S}", "\\frac{\\sin{(N)}}{S}", "\\frac{N (N - 2 S)}{2}"], "srepr_premise_expression": "exp(Add(Symbol('N', commutative=True), Mul(Integer(-1), Symbol('S', commutative=True))))", "srepr_variable": "Symbol('N', commutative=True)", "srepr_positive": "exp(Add(Symbol('N', commutative=True), Mul(Integer(-1), Symbol('S', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Symbol('N', commutative=True), Mul(Integer(-1), Symbol('S', commutative=True)))))", "exp(Add(Symbol('N', commutative=True), Symbol('S', commutative=True)))", "Mul(Pow(Symbol('S', commutative=True), Integer(-1)), sin(Symbol('N', commutative=True)))", "Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Symbol('N', commutative=True), Mul(Integer(-1), Integer(2), Symbol('S', commutative=True))))"]}, {"premise_expression": "e^{- Z + r}", "variable": "r", "positive": "e^{- Z + r}", "negatives": ["- e^{- Z + r}", "- \\sin{(Z - r)}", "\\frac{r (2 Z - r)}{2}", "Z \\sin{(r)}"], "srepr_premise_expression": "exp(Add(Mul(Integer(-1), Symbol('Z', commutative=True)), Symbol('r', commutative=True)))", "srepr_variable": "Symbol('r', commutative=True)", "srepr_positive": "exp(Add(Mul(Integer(-1), Symbol('Z', commutative=True)), Symbol('r', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('Z', commutative=True)), Symbol('r', commutative=True))))", "Mul(Integer(-1), sin(Add(Symbol('Z', commutative=True), Mul(Integer(-1), Symbol('r', commutative=True)))))", "Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(2), Symbol('Z', commutative=True)), Mul(Integer(-1), Symbol('r', commutative=True))))", "Mul(Symbol('Z', commutative=True), sin(Symbol('r', commutative=True)))"]}, {"premise_expression": "- m + y", "variable": "y", "positive": "\\frac{y (- 2 m + y)}{2}", "negatives": ["\\frac{m (- m + 2 y)}{2}", "e^{- m + y}", "e^{m + y}", "y (- m + \\log{(m)})"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('m', commutative=True)), Symbol('y', commutative=True))", "srepr_variable": "Symbol('y', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('y', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('m', commutative=True)), Symbol('y', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Mul(Integer(-1), Symbol('m', commutative=True)), Mul(Integer(2), Symbol('y', commutative=True))))", "exp(Add(Mul(Integer(-1), Symbol('m', commutative=True)), Symbol('y', commutative=True)))", "exp(Add(Symbol('m', commutative=True), Symbol('y', commutative=True)))", "Mul(Symbol('y', commutative=True), Add(Mul(Integer(-1), Symbol('m', commutative=True)), log(Symbol('m', commutative=True))))"]}, {"premise_expression": "U + \\log{(K)}", "variable": "K", "positive": "K (U + \\log{(K)} - 1)", "negatives": ["\\frac{U (U + 2 \\log{(K)})}{2}", "K U + e^{K}", "\\frac{K (- K + 2 \\cos{(U)})}{2}", "\\frac{K (K - 2 U)}{2}"], "srepr_premise_expression": "Add(Symbol('U', commutative=True), log(Symbol('K', commutative=True)))", "srepr_variable": "Symbol('K', commutative=True)", "srepr_positive": "Mul(Symbol('K', commutative=True), Add(Symbol('U', commutative=True), log(Symbol('K', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('U', commutative=True), Add(Symbol('U', commutative=True), Mul(Integer(2), log(Symbol('K', commutative=True)))))", "Add(Mul(Symbol('K', commutative=True), Symbol('U', commutative=True)), exp(Symbol('K', commutative=True)))", "Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Mul(Integer(-1), Symbol('K', commutative=True)), Mul(Integer(2), cos(Symbol('U', commutative=True)))))", "Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Symbol('K', commutative=True), Mul(Integer(-1), Integer(2), Symbol('U', commutative=True))))"]}, {"premise_expression": "\\log{(q^{S})}", "variable": "S", "positive": "\\frac{S^{2} \\log{(q)}}{2}", "negatives": ["\\log{(S)} \\log{(q)}", "S q (\\log{(S)} - 1)", "S (q + \\log{(S)} - 1)", "- \\cos{(S - q)}"], "srepr_premise_expression": "log(Pow(Symbol('q', commutative=True), Symbol('S', commutative=True)))", "srepr_variable": "Symbol('S', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('S', commutative=True), Integer(2)), log(Symbol('q', commutative=True)))", "srepr_negatives": ["Mul(log(Symbol('S', commutative=True)), log(Symbol('q', commutative=True)))", "Mul(Symbol('S', commutative=True), Symbol('q', commutative=True), Add(log(Symbol('S', commutative=True)), Integer(-1)))", "Mul(Symbol('S', commutative=True), Add(Symbol('q', commutative=True), log(Symbol('S', commutative=True)), Integer(-1)))", "Mul(Integer(-1), cos(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('q', commutative=True)))))"]}, {"premise_expression": "\\cos{(Q + R)}", "variable": "Q", "positive": "\\sin{(Q + R)}", "negatives": ["\\frac{\\sin{(Q)}}{R}", "\\frac{Q (Q + 2 R)}{2}", "\\frac{Q^{2}}{2 R}", "R e^{Q}"], "srepr_premise_expression": "cos(Add(Symbol('Q', commutative=True), Symbol('R', commutative=True)))", "srepr_variable": "Symbol('Q', commutative=True)", "srepr_positive": "sin(Add(Symbol('Q', commutative=True), Symbol('R', commutative=True)))", "srepr_negatives": ["Mul(Pow(Symbol('R', commutative=True), Integer(-1)), sin(Symbol('Q', commutative=True)))", "Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Symbol('Q', commutative=True), Mul(Integer(2), Symbol('R', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(2)), Pow(Symbol('R', commutative=True), Integer(-1)))", "Mul(Symbol('R', commutative=True), exp(Symbol('Q', commutative=True)))"]}, {"premise_expression": "\\frac{- E + F}{n}", "variable": "E", "positive": "\\frac{E (- E + 2 F)}{2 n}", "negatives": ["\\frac{E (E + 2 F)}{2 n}", "- \\frac{F (2 E - F)}{2 n}", "(- E + F) \\log{(n)}", "\\frac{E^{2}}{2 F n}"], "srepr_premise_expression": "Mul(Pow(Symbol('n', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('E', commutative=True)), Symbol('F', commutative=True)))", "srepr_variable": "Symbol('E', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('E', commutative=True), Pow(Symbol('n', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('E', commutative=True)), Mul(Integer(2), Symbol('F', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('E', commutative=True), Pow(Symbol('n', commutative=True), Integer(-1)), Add(Symbol('E', commutative=True), Mul(Integer(2), Symbol('F', commutative=True))))", "Mul(Integer(-1), Rational(1, 2), Symbol('F', commutative=True), Pow(Symbol('n', commutative=True), Integer(-1)), Add(Mul(Integer(2), Symbol('E', commutative=True)), Mul(Integer(-1), Symbol('F', commutative=True))))", "Mul(Add(Mul(Integer(-1), Symbol('E', commutative=True)), Symbol('F', commutative=True)), log(Symbol('n', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('E', commutative=True), Integer(2)), Pow(Symbol('F', commutative=True), Integer(-1)), Pow(Symbol('n', commutative=True), Integer(-1)))"]}, {"premise_expression": "- K + s", "variable": "s", "positive": "\\frac{s (- 2 K + s)}{2}", "negatives": ["\\frac{K (- K + 2 s)}{2}", "- \\cos{(K + s)}", "e^{K + s}", "- \\frac{\\cos{(s)}}{K}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('K', commutative=True)), Symbol('s', commutative=True))", "srepr_variable": "Symbol('s', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('s', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('K', commutative=True)), Symbol('s', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Mul(Integer(-1), Symbol('K', commutative=True)), Mul(Integer(2), Symbol('s', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('K', commutative=True), Symbol('s', commutative=True))))", "exp(Add(Symbol('K', commutative=True), Symbol('s', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('K', commutative=True), Integer(-1)), cos(Symbol('s', commutative=True)))"]}, {"premise_expression": "\\log{(\\frac{o}{v})}", "variable": "o", "positive": "o (\\log{(\\frac{o}{v})} - 1)", "negatives": ["v (\\log{(\\frac{o}{v})} + 1)", "\\frac{o (o + 2 v)}{2}", "\\sin{(o + v)}", "v \\sin{(o)}"], "srepr_premise_expression": "log(Mul(Symbol('o', commutative=True), Pow(Symbol('v', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('o', commutative=True)", "srepr_positive": "Mul(Symbol('o', commutative=True), Add(log(Mul(Symbol('o', commutative=True), Pow(Symbol('v', commutative=True), Integer(-1)))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('v', commutative=True), Add(log(Mul(Symbol('o', commutative=True), Pow(Symbol('v', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Symbol('o', commutative=True), Mul(Integer(2), Symbol('v', commutative=True))))", "sin(Add(Symbol('o', commutative=True), Symbol('v', commutative=True)))", "Mul(Symbol('v', commutative=True), sin(Symbol('o', commutative=True)))"]}, {"premise_expression": "E j", "variable": "j", "positive": "\\frac{E j^{2}}{2}", "negatives": ["\\frac{E^{2} j}{2}", "E \\log{(j)}", "- \\frac{\\cos{(j)}}{E}", "\\frac{j (2 E - j)}{2}"], "srepr_premise_expression": "Mul(Symbol('E', commutative=True), Symbol('j', commutative=True))", "srepr_variable": "Symbol('j', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('E', commutative=True), Pow(Symbol('j', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('E', commutative=True), Integer(2)), Symbol('j', commutative=True))", "Mul(Symbol('E', commutative=True), log(Symbol('j', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('E', commutative=True), Integer(-1)), cos(Symbol('j', commutative=True)))", "Mul(Rational(1, 2), Symbol('j', commutative=True), Add(Mul(Integer(2), Symbol('E', commutative=True)), Mul(Integer(-1), Symbol('j', commutative=True))))"]}, {"premise_expression": "- X + j", "variable": "j", "positive": "\\frac{j (- 2 X + j)}{2}", "negatives": ["\\frac{j (2 X + j)}{2}", "\\frac{X (- X + 2 j)}{2}", "- \\cos{(X - j)}", "- \\frac{\\cos{(j)}}{X}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('X', commutative=True)), Symbol('j', commutative=True))", "srepr_variable": "Symbol('j', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('j', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('X', commutative=True)), Symbol('j', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('j', commutative=True), Add(Mul(Integer(2), Symbol('X', commutative=True)), Symbol('j', commutative=True)))", "Mul(Rational(1, 2), Symbol('X', commutative=True), Add(Mul(Integer(-1), Symbol('X', commutative=True)), Mul(Integer(2), Symbol('j', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('X', commutative=True), Mul(Integer(-1), Symbol('j', commutative=True)))))", "Mul(Integer(-1), Pow(Symbol('X', commutative=True), Integer(-1)), cos(Symbol('j', commutative=True)))"]}, {"premise_expression": "C + \\log{(g)}", "variable": "g", "positive": "g (C + \\log{(g)} - 1)", "negatives": ["\\frac{C (C + 2 \\log{(g)})}{2}", "\\frac{g (2 C + g)}{2}", "C \\log{(g)}", "\\frac{g (g + 2 \\cos{(C)})}{2}"], "srepr_premise_expression": "Add(Symbol('C', commutative=True), log(Symbol('g', commutative=True)))", "srepr_variable": "Symbol('g', commutative=True)", "srepr_positive": "Mul(Symbol('g', commutative=True), Add(Symbol('C', commutative=True), log(Symbol('g', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Symbol('C', commutative=True), Mul(Integer(2), log(Symbol('g', commutative=True)))))", "Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Mul(Integer(2), Symbol('C', commutative=True)), Symbol('g', commutative=True)))", "Mul(Symbol('C', commutative=True), log(Symbol('g', commutative=True)))", "Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Symbol('g', commutative=True), Mul(Integer(2), cos(Symbol('C', commutative=True)))))"]}, {"premise_expression": "\\frac{Z}{A}", "variable": "A", "positive": "Z \\log{(A)}", "negatives": ["\\frac{Z^{2}}{2 A}", "- \\cos{(A + Z)}", "A Z + \\sin{(A)}", "\\frac{A (A + 2 Z)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('A', commutative=True), Integer(-1)), Symbol('Z', commutative=True))", "srepr_variable": "Symbol('A', commutative=True)", "srepr_positive": "Mul(Symbol('Z', commutative=True), log(Symbol('A', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(-1)), Pow(Symbol('Z', commutative=True), Integer(2)))", "Mul(Integer(-1), cos(Add(Symbol('A', commutative=True), Symbol('Z', commutative=True))))", "Add(Mul(Symbol('A', commutative=True), Symbol('Z', commutative=True)), sin(Symbol('A', commutative=True)))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Symbol('A', commutative=True), Mul(Integer(2), Symbol('Z', commutative=True))))"]}, {"premise_expression": "- X + m + n", "variable": "m", "positive": "m (- X + \\frac{m}{2} + n)", "negatives": ["\\frac{m (2 X + m + 2 n)}{2}", "\\frac{m (2 X - m + 2 n)}{2}", "\\frac{X (- X + 2 m + 2 n)}{2}", "\\frac{n (- 2 X + 2 m + n)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('X', commutative=True)), Symbol('m', commutative=True), Symbol('n', commutative=True))", "srepr_variable": "Symbol('m', commutative=True)", "srepr_positive": "Mul(Symbol('m', commutative=True), Add(Mul(Integer(-1), Symbol('X', commutative=True)), Mul(Rational(1, 2), Symbol('m', commutative=True)), Symbol('n', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Mul(Integer(2), Symbol('X', commutative=True)), Symbol('m', commutative=True), Mul(Integer(2), Symbol('n', commutative=True))))", "Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Mul(Integer(2), Symbol('X', commutative=True)), Mul(Integer(-1), Symbol('m', commutative=True)), Mul(Integer(2), Symbol('n', commutative=True))))", "Mul(Rational(1, 2), Symbol('X', commutative=True), Add(Mul(Integer(-1), Symbol('X', commutative=True)), Mul(Integer(2), Symbol('m', commutative=True)), Mul(Integer(2), Symbol('n', commutative=True))))", "Mul(Rational(1, 2), Symbol('n', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('X', commutative=True)), Mul(Integer(2), Symbol('m', commutative=True)), Symbol('n', commutative=True)))"]}, {"premise_expression": "\\sin{(C + W)}", "variable": "W", "positive": "- \\cos{(C + W)}", "negatives": ["- e^{C - W}", "e^{C + W}", "W (\\log{(C W)} - 1)", "\\frac{W^{2}}{2 C}"], "srepr_premise_expression": "sin(Add(Symbol('C', commutative=True), Symbol('W', commutative=True)))", "srepr_variable": "Symbol('W', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('C', commutative=True), Symbol('W', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('W', commutative=True)))))", "exp(Add(Symbol('C', commutative=True), Symbol('W', commutative=True)))", "Mul(Symbol('W', commutative=True), Add(log(Mul(Symbol('C', commutative=True), Symbol('W', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(-1)), Pow(Symbol('W', commutative=True), Integer(2)))"]}, {"premise_expression": "\\frac{\\cos{(U)}}{g}", "variable": "g", "positive": "\\log{(g)} \\cos{(U)}", "negatives": ["U \\log{(g)}", "- \\frac{\\cos{(g)}}{U}", "\\frac{g (g + 2 \\cos{(U)})}{2}", "U e^{g}"], "srepr_premise_expression": "Mul(Pow(Symbol('g', commutative=True), Integer(-1)), cos(Symbol('U', commutative=True)))", "srepr_variable": "Symbol('g', commutative=True)", "srepr_positive": "Mul(log(Symbol('g', commutative=True)), cos(Symbol('U', commutative=True)))", "srepr_negatives": ["Mul(Symbol('U', commutative=True), log(Symbol('g', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('U', commutative=True), Integer(-1)), cos(Symbol('g', commutative=True)))", "Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Symbol('g', commutative=True), Mul(Integer(2), cos(Symbol('U', commutative=True)))))", "Mul(Symbol('U', commutative=True), exp(Symbol('g', commutative=True)))"]}, {"premise_expression": "\\frac{w}{o}", "variable": "w", "positive": "\\frac{w^{2}}{2 o}", "negatives": ["w \\log{(o)}", "o \\log{(w)}", "\\frac{w^{2} e^{o}}{2}", "\\frac{w^{2} \\log{(o)}}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('o', commutative=True), Integer(-1)), Symbol('w', commutative=True))", "srepr_variable": "Symbol('w', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('o', commutative=True), Integer(-1)), Pow(Symbol('w', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('w', commutative=True), log(Symbol('o', commutative=True)))", "Mul(Symbol('o', commutative=True), log(Symbol('w', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('w', commutative=True), Integer(2)), exp(Symbol('o', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('w', commutative=True), Integer(2)), log(Symbol('o', commutative=True)))"]}, {"premise_expression": "- V + \\cos{(t)}", "variable": "t", "positive": "- V t + \\sin{(t)}", "negatives": ["e^{V} \\log{(t)}", "\\frac{V t^{2}}{2}", "\\cos{(V - t)}", "\\frac{V (- V + 2 \\cos{(t)})}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('V', commutative=True)), cos(Symbol('t', commutative=True)))", "srepr_variable": "Symbol('t', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('V', commutative=True), Symbol('t', commutative=True)), sin(Symbol('t', commutative=True)))", "srepr_negatives": ["Mul(exp(Symbol('V', commutative=True)), log(Symbol('t', commutative=True)))", "Mul(Rational(1, 2), Symbol('V', commutative=True), Pow(Symbol('t', commutative=True), Integer(2)))", "cos(Add(Symbol('V', commutative=True), Mul(Integer(-1), Symbol('t', commutative=True))))", "Mul(Rational(1, 2), Symbol('V', commutative=True), Add(Mul(Integer(-1), Symbol('V', commutative=True)), Mul(Integer(2), cos(Symbol('t', commutative=True)))))"]}, {"premise_expression": "\\frac{K Q}{b}", "variable": "K", "positive": "\\frac{K^{2} Q}{2 b}", "negatives": ["\\frac{K Q^{2}}{2 b}", "\\frac{K^{2} Q b}{2}", "K Q \\log{(b)}", "\\frac{K (K Q - 2 b)}{2}"], "srepr_premise_expression": "Mul(Symbol('K', commutative=True), Symbol('Q', commutative=True), Pow(Symbol('b', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('K', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('K', commutative=True), Integer(2)), Symbol('Q', commutative=True), Pow(Symbol('b', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('K', commutative=True), Pow(Symbol('Q', commutative=True), Integer(2)), Pow(Symbol('b', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('K', commutative=True), Integer(2)), Symbol('Q', commutative=True), Symbol('b', commutative=True))", "Mul(Symbol('K', commutative=True), Symbol('Q', commutative=True), log(Symbol('b', commutative=True)))", "Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Mul(Symbol('K', commutative=True), Symbol('Q', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('b', commutative=True))))"]}, {"premise_expression": "m \\log{(V)}", "variable": "V", "positive": "V m (\\log{(V)} - 1)", "negatives": ["V (\\log{(\\frac{V}{m})} - 1)", "\\frac{m^{2} \\log{(V)}}{2}", "\\frac{V^{2}}{2 m}", "- V m - \\cos{(V)}"], "srepr_premise_expression": "Mul(Symbol('m', commutative=True), log(Symbol('V', commutative=True)))", "srepr_variable": "Symbol('V', commutative=True)", "srepr_positive": "Mul(Symbol('V', commutative=True), Symbol('m', commutative=True), Add(log(Symbol('V', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('V', commutative=True), Add(log(Mul(Symbol('V', commutative=True), Pow(Symbol('m', commutative=True), Integer(-1)))), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('m', commutative=True), Integer(2)), log(Symbol('V', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('V', commutative=True), Integer(2)), Pow(Symbol('m', commutative=True), Integer(-1)))", "Add(Mul(Integer(-1), Symbol('V', commutative=True), Symbol('m', commutative=True)), Mul(Integer(-1), cos(Symbol('V', commutative=True))))"]}, {"premise_expression": "w \\log{(F)}", "variable": "w", "positive": "\\frac{w^{2} \\log{(F)}}{2}", "negatives": ["\\frac{w (2 F + w)}{2}", "F \\log{(w)}", "F w (\\log{(F)} - 1)", "- \\sin{(F - w)}"], "srepr_premise_expression": "Mul(Symbol('w', commutative=True), log(Symbol('F', commutative=True)))", "srepr_variable": "Symbol('w', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('w', commutative=True), Integer(2)), log(Symbol('F', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('w', commutative=True), Add(Mul(Integer(2), Symbol('F', commutative=True)), Symbol('w', commutative=True)))", "Mul(Symbol('F', commutative=True), log(Symbol('w', commutative=True)))", "Mul(Symbol('F', commutative=True), Symbol('w', commutative=True), Add(log(Symbol('F', commutative=True)), Integer(-1)))", "Mul(Integer(-1), sin(Add(Symbol('F', commutative=True), Mul(Integer(-1), Symbol('w', commutative=True)))))"]}, {"premise_expression": "\\log{(p^{f})}", "variable": "f", "positive": "\\frac{f^{2} \\log{(p)}}{2}", "negatives": ["\\log{(f)} \\log{(p)}", "\\frac{f (f + 2 \\sin{(p)})}{2}", "f (\\log{(f p)} - 1)", "- f p + e^{f}"], "srepr_premise_expression": "log(Pow(Symbol('p', commutative=True), Symbol('f', commutative=True)))", "srepr_variable": "Symbol('f', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('f', commutative=True), Integer(2)), log(Symbol('p', commutative=True)))", "srepr_negatives": ["Mul(log(Symbol('f', commutative=True)), log(Symbol('p', commutative=True)))", "Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Symbol('f', commutative=True), Mul(Integer(2), sin(Symbol('p', commutative=True)))))", "Mul(Symbol('f', commutative=True), Add(log(Mul(Symbol('f', commutative=True), Symbol('p', commutative=True))), Integer(-1)))", "Add(Mul(Integer(-1), Symbol('f', commutative=True), Symbol('p', commutative=True)), exp(Symbol('f', commutative=True)))"]}, {"premise_expression": "\\log{(B + T)}", "variable": "B", "positive": "B \\log{(B + T)} - B + T \\log{(B + T)}", "negatives": ["B \\log{(B + T)} + T \\log{(B + T)} - T", "\\frac{B (\\log{(B)} - 1)}{T}", "B (\\log{(\\frac{T}{B})} + 1)", "\\frac{B (- B + 2 \\sin{(T)})}{2}"], "srepr_premise_expression": "log(Add(Symbol('B', commutative=True), Symbol('T', commutative=True)))", "srepr_variable": "Symbol('B', commutative=True)", "srepr_positive": "Add(Mul(Symbol('B', commutative=True), log(Add(Symbol('B', commutative=True), Symbol('T', commutative=True)))), Mul(Integer(-1), Symbol('B', commutative=True)), Mul(Symbol('T', commutative=True), log(Add(Symbol('B', commutative=True), Symbol('T', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('B', commutative=True), log(Add(Symbol('B', commutative=True), Symbol('T', commutative=True)))), Mul(Symbol('T', commutative=True), log(Add(Symbol('B', commutative=True), Symbol('T', commutative=True)))), Mul(Integer(-1), Symbol('T', commutative=True)))", "Mul(Symbol('B', commutative=True), Pow(Symbol('T', commutative=True), Integer(-1)), Add(log(Symbol('B', commutative=True)), Integer(-1)))", "Mul(Symbol('B', commutative=True), Add(log(Mul(Pow(Symbol('B', commutative=True), Integer(-1)), Symbol('T', commutative=True))), Integer(1)))", "Mul(Rational(1, 2), Symbol('B', commutative=True), Add(Mul(Integer(-1), Symbol('B', commutative=True)), Mul(Integer(2), sin(Symbol('T', commutative=True)))))"]}, {"premise_expression": "a + \\cos{(G)}", "variable": "G", "positive": "G a + \\sin{(G)}", "negatives": ["a \\log{(G)}", "\\frac{G (G - 2 a)}{2}", "\\frac{a (a + 2 \\cos{(G)})}{2}", "\\sin{(G + a)}"], "srepr_premise_expression": "Add(Symbol('a', commutative=True), cos(Symbol('G', commutative=True)))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Add(Mul(Symbol('G', commutative=True), Symbol('a', commutative=True)), sin(Symbol('G', commutative=True)))", "srepr_negatives": ["Mul(Symbol('a', commutative=True), log(Symbol('G', commutative=True)))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Symbol('G', commutative=True), Mul(Integer(-1), Integer(2), Symbol('a', commutative=True))))", "Mul(Rational(1, 2), Symbol('a', commutative=True), Add(Symbol('a', commutative=True), Mul(Integer(2), cos(Symbol('G', commutative=True)))))", "sin(Add(Symbol('G', commutative=True), Symbol('a', commutative=True)))"]}, {"premise_expression": "\\frac{K}{C}", "variable": "C", "positive": "K \\log{(C)}", "negatives": ["\\frac{K^{2}}{2 C}", "C K - \\cos{(C)}", "C K + e^{C}", "\\sin{(C + K)}"], "srepr_premise_expression": "Mul(Pow(Symbol('C', commutative=True), Integer(-1)), Symbol('K', commutative=True))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Mul(Symbol('K', commutative=True), log(Symbol('C', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(-1)), Pow(Symbol('K', commutative=True), Integer(2)))", "Add(Mul(Symbol('C', commutative=True), Symbol('K', commutative=True)), Mul(Integer(-1), cos(Symbol('C', commutative=True))))", "Add(Mul(Symbol('C', commutative=True), Symbol('K', commutative=True)), exp(Symbol('C', commutative=True)))", "sin(Add(Symbol('C', commutative=True), Symbol('K', commutative=True)))"]}, {"premise_expression": "E m", "variable": "m", "positive": "\\frac{E m^{2}}{2}", "negatives": ["\\frac{E^{2} m}{2}", "E e^{\\frac{m}{E}}", "\\frac{m (2 E - m)}{2}", "\\frac{m (2 E + m)}{2}"], "srepr_premise_expression": "Mul(Symbol('E', commutative=True), Symbol('m', commutative=True))", "srepr_variable": "Symbol('m', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('E', commutative=True), Pow(Symbol('m', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('E', commutative=True), Integer(2)), Symbol('m', commutative=True))", "Mul(Symbol('E', commutative=True), exp(Mul(Pow(Symbol('E', commutative=True), Integer(-1)), Symbol('m', commutative=True))))", "Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Mul(Integer(2), Symbol('E', commutative=True)), Mul(Integer(-1), Symbol('m', commutative=True))))", "Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Mul(Integer(2), Symbol('E', commutative=True)), Symbol('m', commutative=True)))"]}, {"premise_expression": "\\frac{f}{g}", "variable": "f", "positive": "\\frac{f^{2}}{2 g}", "negatives": ["f \\log{(g)}", "\\frac{f^{2} \\log{(g)}}{2}", "\\frac{f (f - 2 g)}{2}", "\\frac{f (f + 2 e^{g})}{2}"], "srepr_premise_expression": "Mul(Symbol('f', commutative=True), Pow(Symbol('g', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('f', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('f', commutative=True), Integer(2)), Pow(Symbol('g', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('f', commutative=True), log(Symbol('g', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('f', commutative=True), Integer(2)), log(Symbol('g', commutative=True)))", "Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Symbol('f', commutative=True), Mul(Integer(-1), Integer(2), Symbol('g', commutative=True))))", "Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Symbol('f', commutative=True), Mul(Integer(2), exp(Symbol('g', commutative=True)))))"]}, {"premise_expression": "X \\cos{(t)}", "variable": "X", "positive": "\\frac{X^{2} \\cos{(t)}}{2}", "negatives": ["\\frac{X (X + 2 t)}{2}", "\\frac{X (X - 2 t)}{2}", "X \\sin{(t)}", "\\frac{X (X + 2 \\log{(t)})}{2}"], "srepr_premise_expression": "Mul(Symbol('X', commutative=True), cos(Symbol('t', commutative=True)))", "srepr_variable": "Symbol('X', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('X', commutative=True), Integer(2)), cos(Symbol('t', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('X', commutative=True), Add(Symbol('X', commutative=True), Mul(Integer(2), Symbol('t', commutative=True))))", "Mul(Rational(1, 2), Symbol('X', commutative=True), Add(Symbol('X', commutative=True), Mul(Integer(-1), Integer(2), Symbol('t', commutative=True))))", "Mul(Symbol('X', commutative=True), sin(Symbol('t', commutative=True)))", "Mul(Rational(1, 2), Symbol('X', commutative=True), Add(Symbol('X', commutative=True), Mul(Integer(2), log(Symbol('t', commutative=True)))))"]}, {"premise_expression": "\\cos{(D - h)}", "variable": "D", "positive": "\\sin{(D - h)}", "negatives": ["- \\sin{(D - h)}", "e^{D - h}", "\\cos{(D - h)}", "e^{D + h}"], "srepr_premise_expression": "cos(Add(Symbol('D', commutative=True), Mul(Integer(-1), Symbol('h', commutative=True))))", "srepr_variable": "Symbol('D', commutative=True)", "srepr_positive": "sin(Add(Symbol('D', commutative=True), Mul(Integer(-1), Symbol('h', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('D', commutative=True), Mul(Integer(-1), Symbol('h', commutative=True)))))", "exp(Add(Symbol('D', commutative=True), Mul(Integer(-1), Symbol('h', commutative=True))))", "cos(Add(Symbol('D', commutative=True), Mul(Integer(-1), Symbol('h', commutative=True))))", "exp(Add(Symbol('D', commutative=True), Symbol('h', commutative=True)))"]}, {"premise_expression": "a e^{M}", "variable": "M", "positive": "a e^{M}", "negatives": ["\\frac{a^{2} e^{M}}{2}", "M a + e^{M}", "e^{M + a}", "\\frac{M^{2} a}{2}"], "srepr_premise_expression": "Mul(Symbol('a', commutative=True), exp(Symbol('M', commutative=True)))", "srepr_variable": "Symbol('M', commutative=True)", "srepr_positive": "Mul(Symbol('a', commutative=True), exp(Symbol('M', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('a', commutative=True), Integer(2)), exp(Symbol('M', commutative=True)))", "Add(Mul(Symbol('M', commutative=True), Symbol('a', commutative=True)), exp(Symbol('M', commutative=True)))", "exp(Add(Symbol('M', commutative=True), Symbol('a', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('M', commutative=True), Integer(2)), Symbol('a', commutative=True))"]}, {"premise_expression": "K - n", "variable": "K", "positive": "\\frac{K (K - 2 n)}{2}", "negatives": ["\\frac{K (- K + 2 n)}{2}", "\\frac{n (2 K - n)}{2}", "\\frac{K (- K + 2 \\cos{(n)})}{2}", "\\frac{K^{2} \\log{(n)}}{2}"], "srepr_premise_expression": "Add(Symbol('K', commutative=True), Mul(Integer(-1), Symbol('n', commutative=True)))", "srepr_variable": "Symbol('K', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Symbol('K', commutative=True), Mul(Integer(-1), Integer(2), Symbol('n', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Mul(Integer(-1), Symbol('K', commutative=True)), Mul(Integer(2), Symbol('n', commutative=True))))", "Mul(Rational(1, 2), Symbol('n', commutative=True), Add(Mul(Integer(2), Symbol('K', commutative=True)), Mul(Integer(-1), Symbol('n', commutative=True))))", "Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Mul(Integer(-1), Symbol('K', commutative=True)), Mul(Integer(2), cos(Symbol('n', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('K', commutative=True), Integer(2)), log(Symbol('n', commutative=True)))"]}, {"premise_expression": "\\frac{D}{C}", "variable": "C", "positive": "D \\log{(C)}", "negatives": ["\\frac{D^{2}}{2 C}", "\\cos{(C - D)}", "\\frac{C^{2} \\cos{(D)}}{2}", "\\frac{C (- C + 2 \\cos{(D)})}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('C', commutative=True), Integer(-1)), Symbol('D', commutative=True))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Mul(Symbol('D', commutative=True), log(Symbol('C', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(-1)), Pow(Symbol('D', commutative=True), Integer(2)))", "cos(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('D', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2)), cos(Symbol('D', commutative=True)))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Mul(Integer(-1), Symbol('C', commutative=True)), Mul(Integer(2), cos(Symbol('D', commutative=True)))))"]}, {"premise_expression": "R o", "variable": "R", "positive": "\\frac{R^{2} o}{2}", "negatives": ["\\frac{R o^{2}}{2}", "\\frac{R^{2} \\cos{(o)}}{2}", "o \\sin{(R)}", "e^{R - o}"], "srepr_premise_expression": "Mul(Symbol('R', commutative=True), Symbol('o', commutative=True))", "srepr_variable": "Symbol('R', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('R', commutative=True), Integer(2)), Symbol('o', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('R', commutative=True), Pow(Symbol('o', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('R', commutative=True), Integer(2)), cos(Symbol('o', commutative=True)))", "Mul(Symbol('o', commutative=True), sin(Symbol('R', commutative=True)))", "exp(Add(Symbol('R', commutative=True), Mul(Integer(-1), Symbol('o', commutative=True))))"]}, {"premise_expression": "F + P", "variable": "F", "positive": "\\frac{F (F + 2 P)}{2}", "negatives": ["\\frac{P (2 F + P)}{2}", "\\frac{F (F + 2 \\cos{(P)})}{2}", "\\frac{F^{2} P}{2}", "\\frac{F^{2} \\cos{(P)}}{2}"], "srepr_premise_expression": "Add(Symbol('F', commutative=True), Symbol('P', commutative=True))", "srepr_variable": "Symbol('F', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Symbol('F', commutative=True), Mul(Integer(2), Symbol('P', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Mul(Integer(2), Symbol('F', commutative=True)), Symbol('P', commutative=True)))", "Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Symbol('F', commutative=True), Mul(Integer(2), cos(Symbol('P', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('F', commutative=True), Integer(2)), Symbol('P', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('F', commutative=True), Integer(2)), cos(Symbol('P', commutative=True)))"]}, {"premise_expression": "V \\log{(I)}", "variable": "I", "positive": "I V (\\log{(I)} - 1)", "negatives": ["V \\log{(I)}", "\\frac{V^{2} \\log{(I)}}{2}", "- \\cos{(I - V)}", "e^{I - V}"], "srepr_premise_expression": "Mul(Symbol('V', commutative=True), log(Symbol('I', commutative=True)))", "srepr_variable": "Symbol('I', commutative=True)", "srepr_positive": "Mul(Symbol('I', commutative=True), Symbol('V', commutative=True), Add(log(Symbol('I', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('V', commutative=True), log(Symbol('I', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('V', commutative=True), Integer(2)), log(Symbol('I', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('I', commutative=True), Mul(Integer(-1), Symbol('V', commutative=True)))))", "exp(Add(Symbol('I', commutative=True), Mul(Integer(-1), Symbol('V', commutative=True))))"]}, {"premise_expression": "\\frac{P}{k}", "variable": "P", "positive": "\\frac{P^{2}}{2 k}", "negatives": ["P \\log{(k)}", "k e^{P}", "\\frac{P^{2} \\log{(k)}}{2}", "\\sin{(P + k)}"], "srepr_premise_expression": "Mul(Symbol('P', commutative=True), Pow(Symbol('k', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('P', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2)), Pow(Symbol('k', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('P', commutative=True), log(Symbol('k', commutative=True)))", "Mul(Symbol('k', commutative=True), exp(Symbol('P', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2)), log(Symbol('k', commutative=True)))", "sin(Add(Symbol('P', commutative=True), Symbol('k', commutative=True)))"]}, {"premise_expression": "\\cos{(\\frac{k}{q})}", "variable": "q", "positive": "k \\operatorname{Si}{(\\frac{k}{q})} + q \\cos{(\\frac{k}{q})}", "negatives": ["- k \\operatorname{Ei}{(\\frac{k}{q})} + q e^{\\frac{k}{q}}", "\\frac{q (- q + 2 \\sin{(k)})}{2}", "\\frac{q (2 k - q)}{2}", "- \\cos{(k - q)}"], "srepr_premise_expression": "cos(Mul(Symbol('k', commutative=True), Pow(Symbol('q', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('q', commutative=True)", "srepr_positive": "Add(Mul(Symbol('k', commutative=True), Si(Mul(Symbol('k', commutative=True), Pow(Symbol('q', commutative=True), Integer(-1))))), Mul(Symbol('q', commutative=True), cos(Mul(Symbol('k', commutative=True), Pow(Symbol('q', commutative=True), Integer(-1))))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('k', commutative=True), Ei(Mul(Symbol('k', commutative=True), Pow(Symbol('q', commutative=True), Integer(-1))))), Mul(Symbol('q', commutative=True), exp(Mul(Symbol('k', commutative=True), Pow(Symbol('q', commutative=True), Integer(-1))))))", "Mul(Rational(1, 2), Symbol('q', commutative=True), Add(Mul(Integer(-1), Symbol('q', commutative=True)), Mul(Integer(2), sin(Symbol('k', commutative=True)))))", "Mul(Rational(1, 2), Symbol('q', commutative=True), Add(Mul(Integer(2), Symbol('k', commutative=True)), Mul(Integer(-1), Symbol('q', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('k', commutative=True), Mul(Integer(-1), Symbol('q', commutative=True)))))"]}, {"premise_expression": "- K + M + k", "variable": "k", "positive": "k (- K + M + \\frac{k}{2})", "negatives": ["\\frac{K (- K + 2 M + 2 k)}{2}", "\\frac{M (- 2 K + M + 2 k)}{2}", "\\frac{k^{2}}{2} + \\frac{M k}{K}", "\\frac{K k}{M} + \\frac{k^{2}}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('K', commutative=True)), Symbol('M', commutative=True), Symbol('k', commutative=True))", "srepr_variable": "Symbol('k', commutative=True)", "srepr_positive": "Mul(Symbol('k', commutative=True), Add(Mul(Integer(-1), Symbol('K', commutative=True)), Symbol('M', commutative=True), Mul(Rational(1, 2), Symbol('k', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Mul(Integer(-1), Symbol('K', commutative=True)), Mul(Integer(2), Symbol('M', commutative=True)), Mul(Integer(2), Symbol('k', commutative=True))))", "Mul(Rational(1, 2), Symbol('M', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('K', commutative=True)), Symbol('M', commutative=True), Mul(Integer(2), Symbol('k', commutative=True))))", "Add(Mul(Rational(1, 2), Pow(Symbol('k', commutative=True), Integer(2))), Mul(Pow(Symbol('K', commutative=True), Integer(-1)), Symbol('M', commutative=True), Symbol('k', commutative=True)))", "Add(Mul(Symbol('K', commutative=True), Pow(Symbol('M', commutative=True), Integer(-1)), Symbol('k', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('k', commutative=True), Integer(2))))"]}, {"premise_expression": "\\cos{(k + v)}", "variable": "v", "positive": "\\sin{(k + v)}", "negatives": ["e^{k + v}", "\\cos{(k - v)}", "k \\sin{(v)}", "\\log{(k)} \\log{(v)}"], "srepr_premise_expression": "cos(Add(Symbol('k', commutative=True), Symbol('v', commutative=True)))", "srepr_variable": "Symbol('v', commutative=True)", "srepr_positive": "sin(Add(Symbol('k', commutative=True), Symbol('v', commutative=True)))", "srepr_negatives": ["exp(Add(Symbol('k', commutative=True), Symbol('v', commutative=True)))", "cos(Add(Symbol('k', commutative=True), Mul(Integer(-1), Symbol('v', commutative=True))))", "Mul(Symbol('k', commutative=True), sin(Symbol('v', commutative=True)))", "Mul(log(Symbol('k', commutative=True)), log(Symbol('v', commutative=True)))"]}, {"premise_expression": "e^{- T + t}", "variable": "T", "positive": "- e^{- T + t}", "negatives": ["e^{- T + t}", "\\sin{(T + t)}", "\\frac{T (T + 2 t)}{2}", "T (\\log{(\\frac{t}{T})} + 1)"], "srepr_premise_expression": "exp(Add(Mul(Integer(-1), Symbol('T', commutative=True)), Symbol('t', commutative=True)))", "srepr_variable": "Symbol('T', commutative=True)", "srepr_positive": "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('T', commutative=True)), Symbol('t', commutative=True))))", "srepr_negatives": ["exp(Add(Mul(Integer(-1), Symbol('T', commutative=True)), Symbol('t', commutative=True)))", "sin(Add(Symbol('T', commutative=True), Symbol('t', commutative=True)))", "Mul(Rational(1, 2), Symbol('T', commutative=True), Add(Symbol('T', commutative=True), Mul(Integer(2), Symbol('t', commutative=True))))", "Mul(Symbol('T', commutative=True), Add(log(Mul(Pow(Symbol('T', commutative=True), Integer(-1)), Symbol('t', commutative=True))), Integer(1)))"]}, {"premise_expression": "N - h", "variable": "h", "positive": "\\frac{h (2 N - h)}{2}", "negatives": ["\\frac{h (4 N - h)}{2}", "\\frac{N h (2 N - h)}{2}", "\\frac{N (N - 2 h)}{2}", "\\frac{h^{2} \\cos{(N)}}{2}"], "srepr_premise_expression": "Add(Symbol('N', commutative=True), Mul(Integer(-1), Symbol('h', commutative=True)))", "srepr_variable": "Symbol('h', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('h', commutative=True), Add(Mul(Integer(2), Symbol('N', commutative=True)), Mul(Integer(-1), Symbol('h', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('h', commutative=True), Add(Mul(Integer(4), Symbol('N', commutative=True)), Mul(Integer(-1), Symbol('h', commutative=True))))", "Mul(Rational(1, 2), Symbol('N', commutative=True), Symbol('h', commutative=True), Add(Mul(Integer(2), Symbol('N', commutative=True)), Mul(Integer(-1), Symbol('h', commutative=True))))", "Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Symbol('N', commutative=True), Mul(Integer(-1), Integer(2), Symbol('h', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('h', commutative=True), Integer(2)), cos(Symbol('N', commutative=True)))"]}, {"premise_expression": "\\cos{(R - l)}", "variable": "R", "positive": "\\sin{(R - l)}", "negatives": ["- \\sin{(R - l)}", "\\frac{R e^{l}}{l}", "\\frac{R^{2} \\log{(l)}}{2}", "e^{l} \\log{(R)}"], "srepr_premise_expression": "cos(Add(Symbol('R', commutative=True), Mul(Integer(-1), Symbol('l', commutative=True))))", "srepr_variable": "Symbol('R', commutative=True)", "srepr_positive": "sin(Add(Symbol('R', commutative=True), Mul(Integer(-1), Symbol('l', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('R', commutative=True), Mul(Integer(-1), Symbol('l', commutative=True)))))", "Mul(Symbol('R', commutative=True), Pow(Symbol('l', commutative=True), Integer(-1)), exp(Symbol('l', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('R', commutative=True), Integer(2)), log(Symbol('l', commutative=True)))", "Mul(exp(Symbol('l', commutative=True)), log(Symbol('R', commutative=True)))"]}, {"premise_expression": "K s", "variable": "K", "positive": "\\frac{K^{2} s}{2}", "negatives": ["\\frac{K s^{2}}{2}", "s \\log{(K)}", "K", "\\frac{K (K + 2 e^{s})}{2}"], "srepr_premise_expression": "Mul(Symbol('K', commutative=True), Symbol('s', commutative=True))", "srepr_variable": "Symbol('K', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('K', commutative=True), Integer(2)), Symbol('s', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('K', commutative=True), Pow(Symbol('s', commutative=True), Integer(2)))", "Mul(Symbol('s', commutative=True), log(Symbol('K', commutative=True)))", "Symbol('K', commutative=True)", "Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Symbol('K', commutative=True), Mul(Integer(2), exp(Symbol('s', commutative=True)))))"]}, {"premise_expression": "K + k", "variable": "k", "positive": "\\frac{k (2 K + k)}{2}", "negatives": ["\\frac{K (K + 2 k)}{2}", "\\frac{k^{2}}{2 K}", "\\frac{k (k + 2 \\sin{(K)})}{2}", "\\frac{k (- k + 2 e^{K})}{2}"], "srepr_premise_expression": "Add(Symbol('K', commutative=True), Symbol('k', commutative=True))", "srepr_variable": "Symbol('k', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('k', commutative=True), Add(Mul(Integer(2), Symbol('K', commutative=True)), Symbol('k', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Symbol('K', commutative=True), Mul(Integer(2), Symbol('k', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('K', commutative=True), Integer(-1)), Pow(Symbol('k', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('k', commutative=True), Add(Symbol('k', commutative=True), Mul(Integer(2), sin(Symbol('K', commutative=True)))))", "Mul(Rational(1, 2), Symbol('k', commutative=True), Add(Mul(Integer(-1), Symbol('k', commutative=True)), Mul(Integer(2), exp(Symbol('K', commutative=True)))))"]}, {"premise_expression": "J V", "variable": "J", "positive": "\\frac{J^{2} V}{2}", "negatives": ["\\frac{J V^{2}}{2}", "\\frac{J^{2}}{2 V}", "e^{J + V}", "- J V + e^{J}"], "srepr_premise_expression": "Mul(Symbol('J', commutative=True), Symbol('V', commutative=True))", "srepr_variable": "Symbol('J', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('J', commutative=True), Integer(2)), Symbol('V', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('J', commutative=True), Pow(Symbol('V', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('J', commutative=True), Integer(2)), Pow(Symbol('V', commutative=True), Integer(-1)))", "exp(Add(Symbol('J', commutative=True), Symbol('V', commutative=True)))", "Add(Mul(Integer(-1), Symbol('J', commutative=True), Symbol('V', commutative=True)), exp(Symbol('J', commutative=True)))"]}, {"premise_expression": "- \\sin{(o - p)}", "variable": "o", "positive": "\\cos{(o - p)}", "negatives": ["- \\cos{(o - p)}", "\\sin{(o - p)}", "e^{o + p}", "- e^{- o + p}"], "srepr_premise_expression": "Mul(Integer(-1), sin(Add(Symbol('o', commutative=True), Mul(Integer(-1), Symbol('p', commutative=True)))))", "srepr_variable": "Symbol('o', commutative=True)", "srepr_positive": "cos(Add(Symbol('o', commutative=True), Mul(Integer(-1), Symbol('p', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('o', commutative=True), Mul(Integer(-1), Symbol('p', commutative=True)))))", "sin(Add(Symbol('o', commutative=True), Mul(Integer(-1), Symbol('p', commutative=True))))", "exp(Add(Symbol('o', commutative=True), Symbol('p', commutative=True)))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('o', commutative=True)), Symbol('p', commutative=True))))"]}, {"premise_expression": "- S + u", "variable": "S", "positive": "\\frac{S (- S + 2 u)}{2}", "negatives": ["\\frac{S (S + 2 u)}{2}", "\\frac{S (S - 2 u)}{2}", "\\frac{u (- 2 S + u)}{2}", "\\frac{S u (S - 2)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('S', commutative=True)), Symbol('u', commutative=True))", "srepr_variable": "Symbol('S', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Mul(Integer(-1), Symbol('S', commutative=True)), Mul(Integer(2), Symbol('u', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Symbol('S', commutative=True), Mul(Integer(2), Symbol('u', commutative=True))))", "Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Symbol('S', commutative=True), Mul(Integer(-1), Integer(2), Symbol('u', commutative=True))))", "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('S', commutative=True)), Symbol('u', commutative=True)))", "Mul(Rational(1, 2), Symbol('S', commutative=True), Symbol('u', commutative=True), Add(Symbol('S', commutative=True), Integer(-2)))"]}, {"premise_expression": "C + k", "variable": "C", "positive": "\\frac{C (C + 2 k)}{2}", "negatives": ["\\frac{k (2 C + k)}{2}", "\\sin{(C - k)}", "\\frac{C (\\log{(C)} - 1)}{k}", "\\log{(C)} \\log{(k)}"], "srepr_premise_expression": "Add(Symbol('C', commutative=True), Symbol('k', commutative=True))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Symbol('C', commutative=True), Mul(Integer(2), Symbol('k', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('k', commutative=True), Add(Mul(Integer(2), Symbol('C', commutative=True)), Symbol('k', commutative=True)))", "sin(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('k', commutative=True))))", "Mul(Symbol('C', commutative=True), Pow(Symbol('k', commutative=True), Integer(-1)), Add(log(Symbol('C', commutative=True)), Integer(-1)))", "Mul(log(Symbol('C', commutative=True)), log(Symbol('k', commutative=True)))"]}, {"premise_expression": "\\frac{\\log{(h)}}{t}", "variable": "h", "positive": "\\frac{h (\\log{(h)} - 1)}{t}", "negatives": ["h (\\log{(\\frac{h}{t})} - 1)", "h (t + \\log{(h)} - 1)", "\\log{(h)} \\log{(t)}", "\\log{(h)} \\cos{(t)}"], "srepr_premise_expression": "Mul(Pow(Symbol('t', commutative=True), Integer(-1)), log(Symbol('h', commutative=True)))", "srepr_variable": "Symbol('h', commutative=True)", "srepr_positive": "Mul(Symbol('h', commutative=True), Pow(Symbol('t', commutative=True), Integer(-1)), Add(log(Symbol('h', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('h', commutative=True), Add(log(Mul(Symbol('h', commutative=True), Pow(Symbol('t', commutative=True), Integer(-1)))), Integer(-1)))", "Mul(Symbol('h', commutative=True), Add(Symbol('t', commutative=True), log(Symbol('h', commutative=True)), Integer(-1)))", "Mul(log(Symbol('h', commutative=True)), log(Symbol('t', commutative=True)))", "Mul(log(Symbol('h', commutative=True)), cos(Symbol('t', commutative=True)))"]}, {"premise_expression": "F - P", "variable": "F", "positive": "\\frac{F (F - 2 P)}{2}", "negatives": ["\\frac{P (2 F - P)}{2}", "\\frac{F (F + 2 \\log{(P)})}{2}", "\\frac{F (- F + 2 \\cos{(P)})}{2}", "- \\cos{(F + P)}"], "srepr_premise_expression": "Add(Symbol('F', commutative=True), Mul(Integer(-1), Symbol('P', commutative=True)))", "srepr_variable": "Symbol('F', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Symbol('F', commutative=True), Mul(Integer(-1), Integer(2), Symbol('P', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Mul(Integer(2), Symbol('F', commutative=True)), Mul(Integer(-1), Symbol('P', commutative=True))))", "Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Symbol('F', commutative=True), Mul(Integer(2), log(Symbol('P', commutative=True)))))", "Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Mul(Integer(-1), Symbol('F', commutative=True)), Mul(Integer(2), cos(Symbol('P', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('F', commutative=True), Symbol('P', commutative=True))))"]}, {"premise_expression": "\\log{(Q + Z)}", "variable": "Z", "positive": "Q \\log{(Q + Z)} + Z \\log{(Q + Z)} - Z", "negatives": ["Q \\log{(Q + Z)} - Q + Z \\log{(Q + Z)}", "Q \\operatorname{Si}{(\\frac{Q}{Z})} + Z \\cos{(\\frac{Q}{Z})}", "- Q \\operatorname{Ei}{(\\frac{Q}{Z})} + Z e^{\\frac{Q}{Z}}", "\\frac{Z (Z + 2 \\log{(Q)})}{2}"], "srepr_premise_expression": "log(Add(Symbol('Q', commutative=True), Symbol('Z', commutative=True)))", "srepr_variable": "Symbol('Z', commutative=True)", "srepr_positive": "Add(Mul(Symbol('Q', commutative=True), log(Add(Symbol('Q', commutative=True), Symbol('Z', commutative=True)))), Mul(Symbol('Z', commutative=True), log(Add(Symbol('Q', commutative=True), Symbol('Z', commutative=True)))), Mul(Integer(-1), Symbol('Z', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('Q', commutative=True), log(Add(Symbol('Q', commutative=True), Symbol('Z', commutative=True)))), Mul(Integer(-1), Symbol('Q', commutative=True)), Mul(Symbol('Z', commutative=True), log(Add(Symbol('Q', commutative=True), Symbol('Z', commutative=True)))))", "Add(Mul(Symbol('Q', commutative=True), Si(Mul(Symbol('Q', commutative=True), Pow(Symbol('Z', commutative=True), Integer(-1))))), Mul(Symbol('Z', commutative=True), cos(Mul(Symbol('Q', commutative=True), Pow(Symbol('Z', commutative=True), Integer(-1))))))", "Add(Mul(Integer(-1), Symbol('Q', commutative=True), Ei(Mul(Symbol('Q', commutative=True), Pow(Symbol('Z', commutative=True), Integer(-1))))), Mul(Symbol('Z', commutative=True), exp(Mul(Symbol('Q', commutative=True), Pow(Symbol('Z', commutative=True), Integer(-1))))))", "Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Symbol('Z', commutative=True), Mul(Integer(2), log(Symbol('Q', commutative=True)))))"]}, {"premise_expression": "e^{J - u}", "variable": "u", "positive": "- e^{J - u}", "negatives": ["e^{J - u}", "- \\cos{(J - u)}", "\\frac{u (2 J + u)}{2}", "\\frac{u^{2}}{2 J}"], "srepr_premise_expression": "exp(Add(Symbol('J', commutative=True), Mul(Integer(-1), Symbol('u', commutative=True))))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "Mul(Integer(-1), exp(Add(Symbol('J', commutative=True), Mul(Integer(-1), Symbol('u', commutative=True)))))", "srepr_negatives": ["exp(Add(Symbol('J', commutative=True), Mul(Integer(-1), Symbol('u', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('J', commutative=True), Mul(Integer(-1), Symbol('u', commutative=True)))))", "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(2), Symbol('J', commutative=True)), Symbol('u', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('J', commutative=True), Integer(-1)), Pow(Symbol('u', commutative=True), Integer(2)))"]}, {"premise_expression": "\\frac{l}{W}", "variable": "W", "positive": "l \\log{(W)}", "negatives": ["\\frac{l^{2}}{2 W}", "\\log{(W)} \\log{(l)}", "W l + e^{W}", "- e^{- W + l}"], "srepr_premise_expression": "Mul(Pow(Symbol('W', commutative=True), Integer(-1)), Symbol('l', commutative=True))", "srepr_variable": "Symbol('W', commutative=True)", "srepr_positive": "Mul(Symbol('l', commutative=True), log(Symbol('W', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('W', commutative=True), Integer(-1)), Pow(Symbol('l', commutative=True), Integer(2)))", "Mul(log(Symbol('W', commutative=True)), log(Symbol('l', commutative=True)))", "Add(Mul(Symbol('W', commutative=True), Symbol('l', commutative=True)), exp(Symbol('W', commutative=True)))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('W', commutative=True)), Symbol('l', commutative=True))))"]}, {"premise_expression": "m \\sin{(M)}", "variable": "m", "positive": "\\frac{m^{2} \\sin{(M)}}{2}", "negatives": ["- m \\cos{(M)}", "- \\cos{(M + m)}", "- e^{M - m}", "m (\\log{(M m)} - 1)"], "srepr_premise_expression": "Mul(Symbol('m', commutative=True), sin(Symbol('M', commutative=True)))", "srepr_variable": "Symbol('m', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('m', commutative=True), Integer(2)), sin(Symbol('M', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Symbol('m', commutative=True), cos(Symbol('M', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('M', commutative=True), Symbol('m', commutative=True))))", "Mul(Integer(-1), exp(Add(Symbol('M', commutative=True), Mul(Integer(-1), Symbol('m', commutative=True)))))", "Mul(Symbol('m', commutative=True), Add(log(Mul(Symbol('M', commutative=True), Symbol('m', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\sin{(\\frac{X}{E})}", "variable": "E", "positive": "E \\sin{(\\frac{X}{E})} - \\frac{X \\log{(\\frac{X^{2}}{E^{2}})}}{2} + X \\log{(\\frac{X}{E})} - X \\operatorname{Ci}{(\\frac{X}{E})}", "negatives": ["E (- X + \\log{(E^{X})})", "\\frac{E (- E + 2 \\cos{(X)})}{2}", "E {{}_{1}F_{2}(\\begin{matrix} \\frac{1}{2 X} \\ \\frac{1}{2}, 1 + \\frac{1}{2 X} \\end{matrix}\\middle| {- \\frac{E^{2 X}}{4}})}", "(- \\log{(E)})^{- X} \\log{(E)}^{X} \\Gamma(X + 1, - \\log{(E)})"], "srepr_premise_expression": "sin(Mul(Pow(Symbol('E', commutative=True), Integer(-1)), Symbol('X', commutative=True)))", "srepr_variable": "Symbol('E', commutative=True)", "srepr_positive": "Add(Mul(Symbol('E', commutative=True), sin(Mul(Pow(Symbol('E', commutative=True), Integer(-1)), Symbol('X', commutative=True)))), Mul(Integer(-1), Rational(1, 2), Symbol('X', commutative=True), log(Mul(Pow(Symbol('E', commutative=True), Integer(-2)), Pow(Symbol('X', commutative=True), Integer(2))))), Mul(Symbol('X', commutative=True), log(Mul(Pow(Symbol('E', commutative=True), Integer(-1)), Symbol('X', commutative=True)))), Mul(Integer(-1), Symbol('X', commutative=True), Ci(Mul(Pow(Symbol('E', commutative=True), Integer(-1)), Symbol('X', commutative=True)))))", "srepr_negatives": ["Mul(Symbol('E', commutative=True), Add(Mul(Integer(-1), Symbol('X', commutative=True)), log(Pow(Symbol('E', commutative=True), Symbol('X', commutative=True)))))", "Mul(Rational(1, 2), Symbol('E', commutative=True), Add(Mul(Integer(-1), Symbol('E', commutative=True)), Mul(Integer(2), cos(Symbol('X', commutative=True)))))", "Mul(Symbol('E', commutative=True), hyper(TupleArg(Mul(Rational(1, 2), Pow(Symbol('X', commutative=True), Integer(-1)))), TupleArg(Rational(1, 2), Add(Integer(1), Mul(Rational(1, 2), Pow(Symbol('X', commutative=True), Integer(-1))))), Mul(Integer(-1), Rational(1, 4), Pow(Symbol('E', commutative=True), Mul(Integer(2), Symbol('X', commutative=True))))))", "Mul(Pow(Mul(Integer(-1), log(Symbol('E', commutative=True))), Mul(Integer(-1), Symbol('X', commutative=True))), Pow(log(Symbol('E', commutative=True)), Symbol('X', commutative=True)), uppergamma(Add(Symbol('X', commutative=True), Integer(1)), Mul(Integer(-1), log(Symbol('E', commutative=True)))))"]}, {"premise_expression": "Z - f + m", "variable": "f", "positive": "f (Z - \\frac{f}{2} + m)", "negatives": ["\\frac{f (2 Z - f - 2 m)}{2}", "\\frac{Z (Z - 2 f + 2 m)}{2}", "\\frac{m (2 Z - 2 f + m)}{2}", "\\frac{f (Z f + 2 m)}{2}"], "srepr_premise_expression": "Add(Symbol('Z', commutative=True), Mul(Integer(-1), Symbol('f', commutative=True)), Symbol('m', commutative=True))", "srepr_variable": "Symbol('f', commutative=True)", "srepr_positive": "Mul(Symbol('f', commutative=True), Add(Symbol('Z', commutative=True), Mul(Integer(-1), Rational(1, 2), Symbol('f', commutative=True)), Symbol('m', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Mul(Integer(2), Symbol('Z', commutative=True)), Mul(Integer(-1), Symbol('f', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('m', commutative=True))))", "Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Symbol('Z', commutative=True), Mul(Integer(-1), Integer(2), Symbol('f', commutative=True)), Mul(Integer(2), Symbol('m', commutative=True))))", "Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Mul(Integer(2), Symbol('Z', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('f', commutative=True)), Symbol('m', commutative=True)))", "Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Mul(Symbol('Z', commutative=True), Symbol('f', commutative=True)), Mul(Integer(2), Symbol('m', commutative=True))))"]}, {"premise_expression": "h - m", "variable": "h", "positive": "\\frac{h (h - 2 m)}{2}", "negatives": ["\\frac{m (2 h - m)}{2}", "\\frac{h^{2} \\log{(m)}}{2}", "\\frac{h (- h + 2 \\cos{(m)})}{2}", "\\log{(h)} \\sin{(m)}"], "srepr_premise_expression": "Add(Symbol('h', commutative=True), Mul(Integer(-1), Symbol('m', commutative=True)))", "srepr_variable": "Symbol('h', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('h', commutative=True), Add(Symbol('h', commutative=True), Mul(Integer(-1), Integer(2), Symbol('m', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Mul(Integer(2), Symbol('h', commutative=True)), Mul(Integer(-1), Symbol('m', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('h', commutative=True), Integer(2)), log(Symbol('m', commutative=True)))", "Mul(Rational(1, 2), Symbol('h', commutative=True), Add(Mul(Integer(-1), Symbol('h', commutative=True)), Mul(Integer(2), cos(Symbol('m', commutative=True)))))", "Mul(log(Symbol('h', commutative=True)), sin(Symbol('m', commutative=True)))"]}, {"premise_expression": "\\frac{y}{f}", "variable": "f", "positive": "y \\log{(f)}", "negatives": ["y e^{f}", "\\frac{y^{2}}{2 f}", "\\frac{f^{2}}{2 y}", "\\frac{f^{2} y}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('f', commutative=True), Integer(-1)), Symbol('y', commutative=True))", "srepr_variable": "Symbol('f', commutative=True)", "srepr_positive": "Mul(Symbol('y', commutative=True), log(Symbol('f', commutative=True)))", "srepr_negatives": ["Mul(Symbol('y', commutative=True), exp(Symbol('f', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('f', commutative=True), Integer(-1)), Pow(Symbol('y', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('f', commutative=True), Integer(2)), Pow(Symbol('y', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('f', commutative=True), Integer(2)), Symbol('y', commutative=True))"]}, {"premise_expression": "G \\cos{(w)}", "variable": "w", "positive": "G \\sin{(w)}", "negatives": ["\\frac{G w^{2}}{2}", "- \\sin{(G - w)}", "\\frac{G^{2} \\cos{(w)}}{2}", "- G w + e^{w}"], "srepr_premise_expression": "Mul(Symbol('G', commutative=True), cos(Symbol('w', commutative=True)))", "srepr_variable": "Symbol('w', commutative=True)", "srepr_positive": "Mul(Symbol('G', commutative=True), sin(Symbol('w', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('G', commutative=True), Pow(Symbol('w', commutative=True), Integer(2)))", "Mul(Integer(-1), sin(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('w', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(2)), cos(Symbol('w', commutative=True)))", "Add(Mul(Integer(-1), Symbol('G', commutative=True), Symbol('w', commutative=True)), exp(Symbol('w', commutative=True)))"]}, {"premise_expression": "- c + \\sin{(w)}", "variable": "w", "positive": "- c w - \\cos{(w)}", "negatives": ["e^{c} \\log{(w)}", "e^{c + w}", "\\frac{w^{2} \\log{(c)}}{2}", "\\frac{w (- w + 2 \\cos{(c)})}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('c', commutative=True)), sin(Symbol('w', commutative=True)))", "srepr_variable": "Symbol('w', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('c', commutative=True), Symbol('w', commutative=True)), Mul(Integer(-1), cos(Symbol('w', commutative=True))))", "srepr_negatives": ["Mul(exp(Symbol('c', commutative=True)), log(Symbol('w', commutative=True)))", "exp(Add(Symbol('c', commutative=True), Symbol('w', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('w', commutative=True), Integer(2)), log(Symbol('c', commutative=True)))", "Mul(Rational(1, 2), Symbol('w', commutative=True), Add(Mul(Integer(-1), Symbol('w', commutative=True)), Mul(Integer(2), cos(Symbol('c', commutative=True)))))"]}, {"premise_expression": "\\frac{\\sin{(h)}}{E}", "variable": "E", "positive": "\\log{(E)} \\sin{(h)}", "negatives": ["- \\cos{(E + h)}", "h \\log{(E)}", "\\frac{E (E + 2 \\sin{(h)})}{2}", "- \\frac{\\cos{(h)}}{E}"], "srepr_premise_expression": "Mul(Pow(Symbol('E', commutative=True), Integer(-1)), sin(Symbol('h', commutative=True)))", "srepr_variable": "Symbol('E', commutative=True)", "srepr_positive": "Mul(log(Symbol('E', commutative=True)), sin(Symbol('h', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('E', commutative=True), Symbol('h', commutative=True))))", "Mul(Symbol('h', commutative=True), log(Symbol('E', commutative=True)))", "Mul(Rational(1, 2), Symbol('E', commutative=True), Add(Symbol('E', commutative=True), Mul(Integer(2), sin(Symbol('h', commutative=True)))))", "Mul(Integer(-1), Pow(Symbol('E', commutative=True), Integer(-1)), cos(Symbol('h', commutative=True)))"]}, {"premise_expression": "\\log{(- T + m)}", "variable": "m", "positive": "- T \\log{(- T + m)} + m \\log{(- T + m)} - m", "negatives": ["T \\log{(- T + m)} - T - m \\log{(T - m)}", "T \\operatorname{Si}{(\\frac{T}{m})} + m \\cos{(\\frac{T}{m})}", "\\log{(T)} \\log{(m)}", "- T m + \\sin{(m)}"], "srepr_premise_expression": "log(Add(Mul(Integer(-1), Symbol('T', commutative=True)), Symbol('m', commutative=True)))", "srepr_variable": "Symbol('m', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('T', commutative=True), log(Add(Mul(Integer(-1), Symbol('T', commutative=True)), Symbol('m', commutative=True)))), Mul(Symbol('m', commutative=True), log(Add(Mul(Integer(-1), Symbol('T', commutative=True)), Symbol('m', commutative=True)))), Mul(Integer(-1), Symbol('m', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('T', commutative=True), log(Add(Mul(Integer(-1), Symbol('T', commutative=True)), Symbol('m', commutative=True)))), Mul(Integer(-1), Symbol('T', commutative=True)), Mul(Integer(-1), Symbol('m', commutative=True), log(Add(Symbol('T', commutative=True), Mul(Integer(-1), Symbol('m', commutative=True))))))", "Add(Mul(Symbol('T', commutative=True), Si(Mul(Symbol('T', commutative=True), Pow(Symbol('m', commutative=True), Integer(-1))))), Mul(Symbol('m', commutative=True), cos(Mul(Symbol('T', commutative=True), Pow(Symbol('m', commutative=True), Integer(-1))))))", "Mul(log(Symbol('T', commutative=True)), log(Symbol('m', commutative=True)))", "Add(Mul(Integer(-1), Symbol('T', commutative=True), Symbol('m', commutative=True)), sin(Symbol('m', commutative=True)))"]}, {"premise_expression": "e^{\\frac{L}{E}}", "variable": "L", "positive": "E e^{\\frac{L}{E}}", "negatives": ["E L + e^{L}", "\\frac{L^{2}}{2 E}", "\\sin{(E + L)}", "\\frac{L^{2} \\cos{(E)}}{2}"], "srepr_premise_expression": "exp(Mul(Pow(Symbol('E', commutative=True), Integer(-1)), Symbol('L', commutative=True)))", "srepr_variable": "Symbol('L', commutative=True)", "srepr_positive": "Mul(Symbol('E', commutative=True), exp(Mul(Pow(Symbol('E', commutative=True), Integer(-1)), Symbol('L', commutative=True))))", "srepr_negatives": ["Add(Mul(Symbol('E', commutative=True), Symbol('L', commutative=True)), exp(Symbol('L', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('E', commutative=True), Integer(-1)), Pow(Symbol('L', commutative=True), Integer(2)))", "sin(Add(Symbol('E', commutative=True), Symbol('L', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(2)), cos(Symbol('E', commutative=True)))"]}, {"premise_expression": "\\log{(\\frac{K}{l})}", "variable": "l", "positive": "l (\\log{(\\frac{K}{l})} + 1)", "negatives": ["K (\\log{(\\frac{K}{l})} - 1)", "\\sin{(K + l)}", "- K \\cos{(l)}", "\\frac{l (l + 2 \\log{(K)})}{2}"], "srepr_premise_expression": "log(Mul(Symbol('K', commutative=True), Pow(Symbol('l', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('l', commutative=True)", "srepr_positive": "Mul(Symbol('l', commutative=True), Add(log(Mul(Symbol('K', commutative=True), Pow(Symbol('l', commutative=True), Integer(-1)))), Integer(1)))", "srepr_negatives": ["Mul(Symbol('K', commutative=True), Add(log(Mul(Symbol('K', commutative=True), Pow(Symbol('l', commutative=True), Integer(-1)))), Integer(-1)))", "sin(Add(Symbol('K', commutative=True), Symbol('l', commutative=True)))", "Mul(Integer(-1), Symbol('K', commutative=True), cos(Symbol('l', commutative=True)))", "Mul(Rational(1, 2), Symbol('l', commutative=True), Add(Symbol('l', commutative=True), Mul(Integer(2), log(Symbol('K', commutative=True)))))"]}, {"premise_expression": "- B + \\log{(x)}", "variable": "B", "positive": "\\frac{B (- B + 2 \\log{(x)})}{2}", "negatives": ["\\frac{B (- B + 2 x)}{2}", "x (- B + \\log{(x)} - 1)", "B x - \\cos{(B)}", "B (\\log{(B x)} - 1)"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('B', commutative=True)), log(Symbol('x', commutative=True)))", "srepr_variable": "Symbol('B', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('B', commutative=True), Add(Mul(Integer(-1), Symbol('B', commutative=True)), Mul(Integer(2), log(Symbol('x', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('B', commutative=True), Add(Mul(Integer(-1), Symbol('B', commutative=True)), Mul(Integer(2), Symbol('x', commutative=True))))", "Mul(Symbol('x', commutative=True), Add(Mul(Integer(-1), Symbol('B', commutative=True)), log(Symbol('x', commutative=True)), Integer(-1)))", "Add(Mul(Symbol('B', commutative=True), Symbol('x', commutative=True)), Mul(Integer(-1), cos(Symbol('B', commutative=True))))", "Mul(Symbol('B', commutative=True), Add(log(Mul(Symbol('B', commutative=True), Symbol('x', commutative=True))), Integer(-1)))"]}, {"premise_expression": "- G + f", "variable": "f", "positive": "\\frac{f (- 2 G + f)}{2}", "negatives": ["\\frac{f (2 G + f)}{2}", "\\frac{f (2 G - f)}{2}", "\\frac{G (- G + 2 f)}{2}", "- \\sin{(G - f)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('G', commutative=True)), Symbol('f', commutative=True))", "srepr_variable": "Symbol('f', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('G', commutative=True)), Symbol('f', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Mul(Integer(2), Symbol('G', commutative=True)), Symbol('f', commutative=True)))", "Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Mul(Integer(2), Symbol('G', commutative=True)), Mul(Integer(-1), Symbol('f', commutative=True))))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Mul(Integer(-1), Symbol('G', commutative=True)), Mul(Integer(2), Symbol('f', commutative=True))))", "Mul(Integer(-1), sin(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('f', commutative=True)))))"]}, {"premise_expression": "\\cos^{M}{(J)}", "variable": "J", "positive": "\\int \\cos^{M}{(J)} dJ", "negatives": ["J (- M + \\log{(J^{M})})", "- J M - \\cos{(J)}", "e^{J + M}", "\\frac{J^{2} \\log{(M)}}{2}"], "srepr_premise_expression": "Pow(cos(Symbol('J', commutative=True)), Symbol('M', commutative=True))", "srepr_variable": "Symbol('J', commutative=True)", "srepr_positive": "Integral(Pow(cos(Symbol('J', commutative=True)), Symbol('M', commutative=True)), Tuple(Symbol('J', commutative=True)))", "srepr_negatives": ["Mul(Symbol('J', commutative=True), Add(Mul(Integer(-1), Symbol('M', commutative=True)), log(Pow(Symbol('J', commutative=True), Symbol('M', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('J', commutative=True), Symbol('M', commutative=True)), Mul(Integer(-1), cos(Symbol('J', commutative=True))))", "exp(Add(Symbol('J', commutative=True), Symbol('M', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('J', commutative=True), Integer(2)), log(Symbol('M', commutative=True)))"]}, {"premise_expression": "e^{\\frac{q}{G}}", "variable": "q", "positive": "G e^{\\frac{q}{G}}", "negatives": ["G \\sin{(q)}", "e^{G + q}", "\\frac{q^{2} \\cos{(G)}}{2}", "q (\\log{(\\frac{q}{G})} - 1)"], "srepr_premise_expression": "exp(Mul(Pow(Symbol('G', commutative=True), Integer(-1)), Symbol('q', commutative=True)))", "srepr_variable": "Symbol('q', commutative=True)", "srepr_positive": "Mul(Symbol('G', commutative=True), exp(Mul(Pow(Symbol('G', commutative=True), Integer(-1)), Symbol('q', commutative=True))))", "srepr_negatives": ["Mul(Symbol('G', commutative=True), sin(Symbol('q', commutative=True)))", "exp(Add(Symbol('G', commutative=True), Symbol('q', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('q', commutative=True), Integer(2)), cos(Symbol('G', commutative=True)))", "Mul(Symbol('q', commutative=True), Add(log(Mul(Pow(Symbol('G', commutative=True), Integer(-1)), Symbol('q', commutative=True))), Integer(-1)))"]}, {"premise_expression": "e^{\\frac{s}{X}}", "variable": "s", "positive": "X e^{\\frac{s}{X}}", "negatives": ["\\frac{X s^{2}}{2}", "e^{X + s}", "\\frac{s^{2} \\log{(X)}}{2}", "- \\cos{(X - s)}"], "srepr_premise_expression": "exp(Mul(Pow(Symbol('X', commutative=True), Integer(-1)), Symbol('s', commutative=True)))", "srepr_variable": "Symbol('s', commutative=True)", "srepr_positive": "Mul(Symbol('X', commutative=True), exp(Mul(Pow(Symbol('X', commutative=True), Integer(-1)), Symbol('s', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('X', commutative=True), Pow(Symbol('s', commutative=True), Integer(2)))", "exp(Add(Symbol('X', commutative=True), Symbol('s', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('s', commutative=True), Integer(2)), log(Symbol('X', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('X', commutative=True), Mul(Integer(-1), Symbol('s', commutative=True)))))"]}, {"premise_expression": "k + \\cos{(v)}", "variable": "k", "positive": "\\frac{k (k + 2 \\cos{(v)})}{2}", "negatives": ["\\frac{k (k + 2 \\log{(v)})}{2}", "k v + \\sin{(v)}", "k v + e^{k}", "\\log{(k)} \\log{(v)}"], "srepr_premise_expression": "Add(Symbol('k', commutative=True), cos(Symbol('v', commutative=True)))", "srepr_variable": "Symbol('k', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('k', commutative=True), Add(Symbol('k', commutative=True), Mul(Integer(2), cos(Symbol('v', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('k', commutative=True), Add(Symbol('k', commutative=True), Mul(Integer(2), log(Symbol('v', commutative=True)))))", "Add(Mul(Symbol('k', commutative=True), Symbol('v', commutative=True)), sin(Symbol('v', commutative=True)))", "Add(Mul(Symbol('k', commutative=True), Symbol('v', commutative=True)), exp(Symbol('k', commutative=True)))", "Mul(log(Symbol('k', commutative=True)), log(Symbol('v', commutative=True)))"]}, {"premise_expression": "L + W", "variable": "W", "positive": "\\frac{W (2 L + W)}{2}", "negatives": ["\\frac{L (L + 2 W)}{2}", "- \\sin{(L - W)}", "- \\cos{(L - W)}", "\\frac{W (W + 2 \\sin{(L)})}{2}"], "srepr_premise_expression": "Add(Symbol('L', commutative=True), Symbol('W', commutative=True))", "srepr_variable": "Symbol('W', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('W', commutative=True), Add(Mul(Integer(2), Symbol('L', commutative=True)), Symbol('W', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Symbol('L', commutative=True), Mul(Integer(2), Symbol('W', commutative=True))))", "Mul(Integer(-1), sin(Add(Symbol('L', commutative=True), Mul(Integer(-1), Symbol('W', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('L', commutative=True), Mul(Integer(-1), Symbol('W', commutative=True)))))", "Mul(Rational(1, 2), Symbol('W', commutative=True), Add(Symbol('W', commutative=True), Mul(Integer(2), sin(Symbol('L', commutative=True)))))"]}, {"premise_expression": "\\frac{r}{w}", "variable": "w", "positive": "r \\log{(w)}", "negatives": ["\\frac{r^{2}}{2 w}", "r w - \\cos{(w)}", "- \\cos{(r + w)}", "\\cos{(r - w)}"], "srepr_premise_expression": "Mul(Symbol('r', commutative=True), Pow(Symbol('w', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('w', commutative=True)", "srepr_positive": "Mul(Symbol('r', commutative=True), log(Symbol('w', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('r', commutative=True), Integer(2)), Pow(Symbol('w', commutative=True), Integer(-1)))", "Add(Mul(Symbol('r', commutative=True), Symbol('w', commutative=True)), Mul(Integer(-1), cos(Symbol('w', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('r', commutative=True), Symbol('w', commutative=True))))", "cos(Add(Symbol('r', commutative=True), Mul(Integer(-1), Symbol('w', commutative=True))))"]}, {"premise_expression": "\\frac{k}{C}", "variable": "k", "positive": "\\frac{k^{2}}{2 C}", "negatives": ["k \\log{(C)}", "\\frac{k^{2} \\cos{(C)}}{2}", "\\frac{\\sin{(k)}}{C}", "C k - \\cos{(k)}"], "srepr_premise_expression": "Mul(Pow(Symbol('C', commutative=True), Integer(-1)), Symbol('k', commutative=True))", "srepr_variable": "Symbol('k', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(-1)), Pow(Symbol('k', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('k', commutative=True), log(Symbol('C', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('k', commutative=True), Integer(2)), cos(Symbol('C', commutative=True)))", "Mul(Pow(Symbol('C', commutative=True), Integer(-1)), sin(Symbol('k', commutative=True)))", "Add(Mul(Symbol('C', commutative=True), Symbol('k', commutative=True)), Mul(Integer(-1), cos(Symbol('k', commutative=True))))"]}, {"premise_expression": "\\log{(\\frac{a}{U})}", "variable": "U", "positive": "U (\\log{(\\frac{a}{U})} + 1)", "negatives": ["a (\\log{(\\frac{a}{U})} - 1)", "U a (\\log{(U)} - 1)", "\\frac{U (U + 2 a)}{2}", "\\frac{U (U + 2 \\cos{(a)})}{2}"], "srepr_premise_expression": "log(Mul(Pow(Symbol('U', commutative=True), Integer(-1)), Symbol('a', commutative=True)))", "srepr_variable": "Symbol('U', commutative=True)", "srepr_positive": "Mul(Symbol('U', commutative=True), Add(log(Mul(Pow(Symbol('U', commutative=True), Integer(-1)), Symbol('a', commutative=True))), Integer(1)))", "srepr_negatives": ["Mul(Symbol('a', commutative=True), Add(log(Mul(Pow(Symbol('U', commutative=True), Integer(-1)), Symbol('a', commutative=True))), Integer(-1)))", "Mul(Symbol('U', commutative=True), Symbol('a', commutative=True), Add(log(Symbol('U', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('U', commutative=True), Add(Symbol('U', commutative=True), Mul(Integer(2), Symbol('a', commutative=True))))", "Mul(Rational(1, 2), Symbol('U', commutative=True), Add(Symbol('U', commutative=True), Mul(Integer(2), cos(Symbol('a', commutative=True)))))"]}, {"premise_expression": "- Y + \\cos{(D)}", "variable": "Y", "positive": "\\frac{Y (- Y + 2 \\cos{(D)})}{2}", "negatives": ["\\frac{Y (Y + 2 \\log{(D)})}{2}", "\\frac{Y^{2} \\cos{(D)}}{2}", "\\log{(Y)} \\cos{(D)}", "- D Y + \\sin{(D)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('Y', commutative=True)), cos(Symbol('D', commutative=True)))", "srepr_variable": "Symbol('Y', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('Y', commutative=True), Add(Mul(Integer(-1), Symbol('Y', commutative=True)), Mul(Integer(2), cos(Symbol('D', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('Y', commutative=True), Add(Symbol('Y', commutative=True), Mul(Integer(2), log(Symbol('D', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('Y', commutative=True), Integer(2)), cos(Symbol('D', commutative=True)))", "Mul(log(Symbol('Y', commutative=True)), cos(Symbol('D', commutative=True)))", "Add(Mul(Integer(-1), Symbol('D', commutative=True), Symbol('Y', commutative=True)), sin(Symbol('D', commutative=True)))"]}, {"premise_expression": "\\frac{E}{k}", "variable": "k", "positive": "E \\log{(k)}", "negatives": ["E \\sin{(k)}", "\\frac{E^{2}}{2 k}", "\\frac{\\sin{(k)}}{E}", "\\frac{k (\\log{(k)} - 1)}{E}"], "srepr_premise_expression": "Mul(Symbol('E', commutative=True), Pow(Symbol('k', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('k', commutative=True)", "srepr_positive": "Mul(Symbol('E', commutative=True), log(Symbol('k', commutative=True)))", "srepr_negatives": ["Mul(Symbol('E', commutative=True), sin(Symbol('k', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('E', commutative=True), Integer(2)), Pow(Symbol('k', commutative=True), Integer(-1)))", "Mul(Pow(Symbol('E', commutative=True), Integer(-1)), sin(Symbol('k', commutative=True)))", "Mul(Pow(Symbol('E', commutative=True), Integer(-1)), Symbol('k', commutative=True), Add(log(Symbol('k', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\frac{E}{T}", "variable": "T", "positive": "E \\log{(T)}", "negatives": ["\\frac{E^{2}}{2 T}", "\\frac{E T^{2}}{2}", "\\frac{T^{2} \\log{(E)}}{2}", "- \\cos{(E + T)}"], "srepr_premise_expression": "Mul(Symbol('E', commutative=True), Pow(Symbol('T', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('T', commutative=True)", "srepr_positive": "Mul(Symbol('E', commutative=True), log(Symbol('T', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('E', commutative=True), Integer(2)), Pow(Symbol('T', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Symbol('E', commutative=True), Pow(Symbol('T', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('T', commutative=True), Integer(2)), log(Symbol('E', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('E', commutative=True), Symbol('T', commutative=True))))"]}, {"premise_expression": "\\frac{\\cos{(W)}}{J}", "variable": "J", "positive": "\\log{(J)} \\cos{(W)}", "negatives": ["e^{W} \\log{(J)}", "e^{J + W}", "\\frac{J (J + 2 \\cos{(W)})}{2}", "\\frac{\\sin{(W)}}{J}"], "srepr_premise_expression": "Mul(Pow(Symbol('J', commutative=True), Integer(-1)), cos(Symbol('W', commutative=True)))", "srepr_variable": "Symbol('J', commutative=True)", "srepr_positive": "Mul(log(Symbol('J', commutative=True)), cos(Symbol('W', commutative=True)))", "srepr_negatives": ["Mul(exp(Symbol('W', commutative=True)), log(Symbol('J', commutative=True)))", "exp(Add(Symbol('J', commutative=True), Symbol('W', commutative=True)))", "Mul(Rational(1, 2), Symbol('J', commutative=True), Add(Symbol('J', commutative=True), Mul(Integer(2), cos(Symbol('W', commutative=True)))))", "Mul(Pow(Symbol('J', commutative=True), Integer(-1)), sin(Symbol('W', commutative=True)))"]}, {"premise_expression": "l^{n} - o", "variable": "o", "positive": "\\frac{o (2 l^{n} - o)}{2}", "negatives": ["\\frac{o (2 l n + o)}{2}", "\\frac{n o (2 l - o)}{2}", "\\frac{o (- 2 l + n o)}{2}", "o (2 l + n)"], "srepr_premise_expression": "Add(Pow(Symbol('l', commutative=True), Symbol('n', commutative=True)), Mul(Integer(-1), Symbol('o', commutative=True)))", "srepr_variable": "Symbol('o', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Mul(Integer(2), Pow(Symbol('l', commutative=True), Symbol('n', commutative=True))), Mul(Integer(-1), Symbol('o', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Mul(Integer(2), Symbol('l', commutative=True), Symbol('n', commutative=True)), Symbol('o', commutative=True)))", "Mul(Rational(1, 2), Symbol('n', commutative=True), Symbol('o', commutative=True), Add(Mul(Integer(2), Symbol('l', commutative=True)), Mul(Integer(-1), Symbol('o', commutative=True))))", "Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('l', commutative=True)), Mul(Symbol('n', commutative=True), Symbol('o', commutative=True))))", "Mul(Symbol('o', commutative=True), Add(Mul(Integer(2), Symbol('l', commutative=True)), Symbol('n', commutative=True)))"]}, {"premise_expression": "\\sin{(M - W)}", "variable": "W", "positive": "\\cos{(M - W)}", "negatives": ["- \\cos{(M - W)}", "- M \\cos{(W)}", "\\frac{W (\\log{(W)} - 1)}{M}", "W (\\log{(W^{2})} - 2)"], "srepr_premise_expression": "sin(Add(Symbol('M', commutative=True), Mul(Integer(-1), Symbol('W', commutative=True))))", "srepr_variable": "Symbol('W', commutative=True)", "srepr_positive": "cos(Add(Symbol('M', commutative=True), Mul(Integer(-1), Symbol('W', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('M', commutative=True), Mul(Integer(-1), Symbol('W', commutative=True)))))", "Mul(Integer(-1), Symbol('M', commutative=True), cos(Symbol('W', commutative=True)))", "Mul(Pow(Symbol('M', commutative=True), Integer(-1)), Symbol('W', commutative=True), Add(log(Symbol('W', commutative=True)), Integer(-1)))", "Mul(Symbol('W', commutative=True), Add(log(Pow(Symbol('W', commutative=True), Integer(2))), Integer(-2)))"]}, {"premise_expression": "\\cos^{f}{(G)}", "variable": "G", "positive": "\\int \\cos^{f}{(G)} dG", "negatives": ["- \\frac{\\cos{(G)}}{f}", "f \\log{(G)}", "\\frac{G^{2} \\log{(f)}}{2}", "\\frac{G (G - 2 f)}{2}"], "srepr_premise_expression": "Pow(cos(Symbol('G', commutative=True)), Symbol('f', commutative=True))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Integral(Pow(cos(Symbol('G', commutative=True)), Symbol('f', commutative=True)), Tuple(Symbol('G', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Pow(Symbol('f', commutative=True), Integer(-1)), cos(Symbol('G', commutative=True)))", "Mul(Symbol('f', commutative=True), log(Symbol('G', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(2)), log(Symbol('f', commutative=True)))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Symbol('G', commutative=True), Mul(Integer(-1), Integer(2), Symbol('f', commutative=True))))"]}, {"premise_expression": "B + p + z", "variable": "z", "positive": "z (B + p + \\frac{z}{2})", "negatives": ["\\frac{z (- 2 B + 2 p + z)}{2}", "\\frac{B (B + 2 p + 2 z)}{2}", "\\frac{p (2 B + p + 2 z)}{2}", "\\frac{z (2 B - z)}{2 p}"], "srepr_premise_expression": "Add(Symbol('B', commutative=True), Symbol('p', commutative=True), Symbol('z', commutative=True))", "srepr_variable": "Symbol('z', commutative=True)", "srepr_positive": "Mul(Symbol('z', commutative=True), Add(Symbol('B', commutative=True), Symbol('p', commutative=True), Mul(Rational(1, 2), Symbol('z', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('z', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('B', commutative=True)), Mul(Integer(2), Symbol('p', commutative=True)), Symbol('z', commutative=True)))", "Mul(Rational(1, 2), Symbol('B', commutative=True), Add(Symbol('B', commutative=True), Mul(Integer(2), Symbol('p', commutative=True)), Mul(Integer(2), Symbol('z', commutative=True))))", "Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Mul(Integer(2), Symbol('B', commutative=True)), Symbol('p', commutative=True), Mul(Integer(2), Symbol('z', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('p', commutative=True), Integer(-1)), Symbol('z', commutative=True), Add(Mul(Integer(2), Symbol('B', commutative=True)), Mul(Integer(-1), Symbol('z', commutative=True))))"]}, {"premise_expression": "\\frac{\\log{(C)}}{K}", "variable": "C", "positive": "\\frac{C (\\log{(C)} - 1)}{K}", "negatives": ["K \\log{(C)}", "\\log{(C)} \\log{(K)}", "\\frac{C (- C + 2 K)}{2}", "e^{C + K}"], "srepr_premise_expression": "Mul(Pow(Symbol('K', commutative=True), Integer(-1)), log(Symbol('C', commutative=True)))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Mul(Symbol('C', commutative=True), Pow(Symbol('K', commutative=True), Integer(-1)), Add(log(Symbol('C', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('K', commutative=True), log(Symbol('C', commutative=True)))", "Mul(log(Symbol('C', commutative=True)), log(Symbol('K', commutative=True)))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Mul(Integer(-1), Symbol('C', commutative=True)), Mul(Integer(2), Symbol('K', commutative=True))))", "exp(Add(Symbol('C', commutative=True), Symbol('K', commutative=True)))"]}, {"premise_expression": "\\frac{W}{A t}", "variable": "t", "positive": "\\frac{W \\log{(t)}}{A}", "negatives": ["\\frac{W \\log{(A)}}{t}", "\\frac{W^{2}}{2 A t}", "\\frac{t (2 A W - t)}{2}", "\\frac{A t}{W} - \\frac{t^{2}}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('A', commutative=True), Integer(-1)), Symbol('W', commutative=True), Pow(Symbol('t', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('t', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('A', commutative=True), Integer(-1)), Symbol('W', commutative=True), log(Symbol('t', commutative=True)))", "srepr_negatives": ["Mul(Symbol('W', commutative=True), Pow(Symbol('t', commutative=True), Integer(-1)), log(Symbol('A', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(-1)), Pow(Symbol('W', commutative=True), Integer(2)), Pow(Symbol('t', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Symbol('t', commutative=True), Add(Mul(Integer(2), Symbol('A', commutative=True), Symbol('W', commutative=True)), Mul(Integer(-1), Symbol('t', commutative=True))))", "Add(Mul(Symbol('A', commutative=True), Pow(Symbol('W', commutative=True), Integer(-1)), Symbol('t', commutative=True)), Mul(Integer(-1), Rational(1, 2), Pow(Symbol('t', commutative=True), Integer(2))))"]}, {"premise_expression": "\\log{(X + b)}", "variable": "b", "positive": "X \\log{(X + b)} + b \\log{(X + b)} - b", "negatives": ["- X \\log{(- X + b)} + b \\log{(X - b)} - b", "X \\log{(X + b)} - X + b \\log{(X + b)}", "b (X + \\log{(b)} - 1)", "X b + e^{b}"], "srepr_premise_expression": "log(Add(Symbol('X', commutative=True), Symbol('b', commutative=True)))", "srepr_variable": "Symbol('b', commutative=True)", "srepr_positive": "Add(Mul(Symbol('X', commutative=True), log(Add(Symbol('X', commutative=True), Symbol('b', commutative=True)))), Mul(Symbol('b', commutative=True), log(Add(Symbol('X', commutative=True), Symbol('b', commutative=True)))), Mul(Integer(-1), Symbol('b', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('X', commutative=True), log(Add(Mul(Integer(-1), Symbol('X', commutative=True)), Symbol('b', commutative=True)))), Mul(Symbol('b', commutative=True), log(Add(Symbol('X', commutative=True), Mul(Integer(-1), Symbol('b', commutative=True))))), Mul(Integer(-1), Symbol('b', commutative=True)))", "Add(Mul(Symbol('X', commutative=True), log(Add(Symbol('X', commutative=True), Symbol('b', commutative=True)))), Mul(Integer(-1), Symbol('X', commutative=True)), Mul(Symbol('b', commutative=True), log(Add(Symbol('X', commutative=True), Symbol('b', commutative=True)))))", "Mul(Symbol('b', commutative=True), Add(Symbol('X', commutative=True), log(Symbol('b', commutative=True)), Integer(-1)))", "Add(Mul(Symbol('X', commutative=True), Symbol('b', commutative=True)), exp(Symbol('b', commutative=True)))"]}, {"premise_expression": "\\cos{(A + f)}", "variable": "f", "positive": "\\sin{(A + f)}", "negatives": ["- \\cos{(A + f)}", "\\frac{f (2 A + f)}{2}", "\\frac{f (2 A - f)}{2}", "A f + e^{f}"], "srepr_premise_expression": "cos(Add(Symbol('A', commutative=True), Symbol('f', commutative=True)))", "srepr_variable": "Symbol('f', commutative=True)", "srepr_positive": "sin(Add(Symbol('A', commutative=True), Symbol('f', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('A', commutative=True), Symbol('f', commutative=True))))", "Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Mul(Integer(2), Symbol('A', commutative=True)), Symbol('f', commutative=True)))", "Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Mul(Integer(2), Symbol('A', commutative=True)), Mul(Integer(-1), Symbol('f', commutative=True))))", "Add(Mul(Symbol('A', commutative=True), Symbol('f', commutative=True)), exp(Symbol('f', commutative=True)))"]}, {"premise_expression": "- b + \\frac{j}{U}", "variable": "b", "positive": "- \\frac{b^{2}}{2} + \\frac{b j}{U}", "negatives": ["\\frac{U b}{j} + \\frac{b^{2}}{2}", "\\frac{b^{2} (- U + j)}{2}", "\\frac{b j (- 2 U + b)}{2}", "\\frac{U b (b - 2 j)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('b', commutative=True)), Mul(Pow(Symbol('U', commutative=True), Integer(-1)), Symbol('j', commutative=True)))", "srepr_variable": "Symbol('b', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('b', commutative=True), Integer(2))), Mul(Pow(Symbol('U', commutative=True), Integer(-1)), Symbol('b', commutative=True), Symbol('j', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('U', commutative=True), Symbol('b', commutative=True), Pow(Symbol('j', commutative=True), Integer(-1))), Mul(Rational(1, 2), Pow(Symbol('b', commutative=True), Integer(2))))", "Mul(Rational(1, 2), Pow(Symbol('b', commutative=True), Integer(2)), Add(Mul(Integer(-1), Symbol('U', commutative=True)), Symbol('j', commutative=True)))", "Mul(Rational(1, 2), Symbol('b', commutative=True), Symbol('j', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('U', commutative=True)), Symbol('b', commutative=True)))", "Mul(Rational(1, 2), Symbol('U', commutative=True), Symbol('b', commutative=True), Add(Symbol('b', commutative=True), Mul(Integer(-1), Integer(2), Symbol('j', commutative=True))))"]}, {"premise_expression": "\\frac{g + x}{V}", "variable": "x", "positive": "\\frac{x (2 g + x)}{2 V}", "negatives": ["\\frac{g (g + 2 x)}{2 V}", "\\frac{x (2 V g + x)}{2}", "\\frac{g x (2 V + x)}{2}", "\\frac{x (2 V + g x)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('V', commutative=True), Integer(-1)), Add(Symbol('g', commutative=True), Symbol('x', commutative=True)))", "srepr_variable": "Symbol('x', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('V', commutative=True), Integer(-1)), Symbol('x', commutative=True), Add(Mul(Integer(2), Symbol('g', commutative=True)), Symbol('x', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('V', commutative=True), Integer(-1)), Symbol('g', commutative=True), Add(Symbol('g', commutative=True), Mul(Integer(2), Symbol('x', commutative=True))))", "Mul(Rational(1, 2), Symbol('x', commutative=True), Add(Mul(Integer(2), Symbol('V', commutative=True), Symbol('g', commutative=True)), Symbol('x', commutative=True)))", "Mul(Rational(1, 2), Symbol('g', commutative=True), Symbol('x', commutative=True), Add(Mul(Integer(2), Symbol('V', commutative=True)), Symbol('x', commutative=True)))", "Mul(Rational(1, 2), Symbol('x', commutative=True), Add(Mul(Integer(2), Symbol('V', commutative=True)), Mul(Symbol('g', commutative=True), Symbol('x', commutative=True))))"]}, {"premise_expression": "e^{\\frac{X}{G}}", "variable": "G", "positive": "G e^{\\frac{X}{G}} - X \\operatorname{Ei}{(\\frac{X}{G})}", "negatives": ["G e^{\\frac{X}{G}}", "e^{G - X}", "e^{G + X}", "\\frac{G (\\log{(G)} - 1)}{X}"], "srepr_premise_expression": "exp(Mul(Pow(Symbol('G', commutative=True), Integer(-1)), Symbol('X', commutative=True)))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Add(Mul(Symbol('G', commutative=True), exp(Mul(Pow(Symbol('G', commutative=True), Integer(-1)), Symbol('X', commutative=True)))), Mul(Integer(-1), Symbol('X', commutative=True), Ei(Mul(Pow(Symbol('G', commutative=True), Integer(-1)), Symbol('X', commutative=True)))))", "srepr_negatives": ["Mul(Symbol('G', commutative=True), exp(Mul(Pow(Symbol('G', commutative=True), Integer(-1)), Symbol('X', commutative=True))))", "exp(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('X', commutative=True))))", "exp(Add(Symbol('G', commutative=True), Symbol('X', commutative=True)))", "Mul(Symbol('G', commutative=True), Pow(Symbol('X', commutative=True), Integer(-1)), Add(log(Symbol('G', commutative=True)), Integer(-1)))"]}, {"premise_expression": "X - u", "variable": "X", "positive": "\\frac{X (X - 2 u)}{2}", "negatives": ["\\frac{u (2 X - u)}{2}", "\\frac{X^{2}}{2 u}", "e^{X - u}", "- \\cos{(X + u)}"], "srepr_premise_expression": "Add(Symbol('X', commutative=True), Mul(Integer(-1), Symbol('u', commutative=True)))", "srepr_variable": "Symbol('X', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('X', commutative=True), Add(Symbol('X', commutative=True), Mul(Integer(-1), Integer(2), Symbol('u', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(2), Symbol('X', commutative=True)), Mul(Integer(-1), Symbol('u', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('X', commutative=True), Integer(2)), Pow(Symbol('u', commutative=True), Integer(-1)))", "exp(Add(Symbol('X', commutative=True), Mul(Integer(-1), Symbol('u', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('X', commutative=True), Symbol('u', commutative=True))))"]}, {"premise_expression": "- V + \\frac{R}{N}", "variable": "N", "positive": "- N V + R \\log{(N)}", "negatives": ["- R V + \\frac{R^{2}}{2 N}", "V^{R} \\log{(N)}", "R V \\log{(N)}", "- \\frac{V^{2}}{2} + \\frac{R V}{N}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('V', commutative=True)), Mul(Pow(Symbol('N', commutative=True), Integer(-1)), Symbol('R', commutative=True)))", "srepr_variable": "Symbol('N', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('N', commutative=True), Symbol('V', commutative=True)), Mul(Symbol('R', commutative=True), log(Symbol('N', commutative=True))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('R', commutative=True), Symbol('V', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('N', commutative=True), Integer(-1)), Pow(Symbol('R', commutative=True), Integer(2))))", "Mul(Pow(Symbol('V', commutative=True), Symbol('R', commutative=True)), log(Symbol('N', commutative=True)))", "Mul(Symbol('R', commutative=True), Symbol('V', commutative=True), log(Symbol('N', commutative=True)))", "Add(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('V', commutative=True), Integer(2))), Mul(Pow(Symbol('N', commutative=True), Integer(-1)), Symbol('R', commutative=True), Symbol('V', commutative=True)))"]}, {"premise_expression": "\\log{(\\frac{D}{j})}", "variable": "D", "positive": "D (\\log{(\\frac{D}{j})} - 1)", "negatives": ["j (\\log{(\\frac{D}{j})} + 1)", "j e^{\\frac{D}{j}}", "\\log{(D)} \\sin{(j)}", "\\frac{D (D - 2 j)}{2}"], "srepr_premise_expression": "log(Mul(Symbol('D', commutative=True), Pow(Symbol('j', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('D', commutative=True)", "srepr_positive": "Mul(Symbol('D', commutative=True), Add(log(Mul(Symbol('D', commutative=True), Pow(Symbol('j', commutative=True), Integer(-1)))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('j', commutative=True), Add(log(Mul(Symbol('D', commutative=True), Pow(Symbol('j', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Symbol('j', commutative=True), exp(Mul(Symbol('D', commutative=True), Pow(Symbol('j', commutative=True), Integer(-1)))))", "Mul(log(Symbol('D', commutative=True)), sin(Symbol('j', commutative=True)))", "Mul(Rational(1, 2), Symbol('D', commutative=True), Add(Symbol('D', commutative=True), Mul(Integer(-1), Integer(2), Symbol('j', commutative=True))))"]}, {"premise_expression": "\\log{(o + q)}", "variable": "q", "positive": "o \\log{(o + q)} + q \\log{(o + q)} - q", "negatives": ["o \\log{(o + q)} - o + q \\log{(o + q)}", "o q + e^{q}", "o q \\cos{(o)}", "e^{o + q}"], "srepr_premise_expression": "log(Add(Symbol('o', commutative=True), Symbol('q', commutative=True)))", "srepr_variable": "Symbol('q', commutative=True)", "srepr_positive": "Add(Mul(Symbol('o', commutative=True), log(Add(Symbol('o', commutative=True), Symbol('q', commutative=True)))), Mul(Symbol('q', commutative=True), log(Add(Symbol('o', commutative=True), Symbol('q', commutative=True)))), Mul(Integer(-1), Symbol('q', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('o', commutative=True), log(Add(Symbol('o', commutative=True), Symbol('q', commutative=True)))), Mul(Integer(-1), Symbol('o', commutative=True)), Mul(Symbol('q', commutative=True), log(Add(Symbol('o', commutative=True), Symbol('q', commutative=True)))))", "Add(Mul(Symbol('o', commutative=True), Symbol('q', commutative=True)), exp(Symbol('q', commutative=True)))", "Mul(Symbol('o', commutative=True), Symbol('q', commutative=True), cos(Symbol('o', commutative=True)))", "exp(Add(Symbol('o', commutative=True), Symbol('q', commutative=True)))"]}, {"premise_expression": "E L", "variable": "E", "positive": "\\frac{E^{2} L}{2}", "negatives": ["\\frac{E L^{2}}{2}", "\\frac{E (E - 2 L)}{2}", "e^{E - L}", "e^{E + L}"], "srepr_premise_expression": "Mul(Symbol('E', commutative=True), Symbol('L', commutative=True))", "srepr_variable": "Symbol('E', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('E', commutative=True), Integer(2)), Symbol('L', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('E', commutative=True), Pow(Symbol('L', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('E', commutative=True), Add(Symbol('E', commutative=True), Mul(Integer(-1), Integer(2), Symbol('L', commutative=True))))", "exp(Add(Symbol('E', commutative=True), Mul(Integer(-1), Symbol('L', commutative=True))))", "exp(Add(Symbol('E', commutative=True), Symbol('L', commutative=True)))"]}, {"premise_expression": "\\frac{z}{t}", "variable": "z", "positive": "\\frac{z^{2}}{2 t}", "negatives": ["z \\log{(t)}", "\\frac{z^{2} \\cos{(t)}}{2}", "2 t z", "\\cos{(t - z)}"], "srepr_premise_expression": "Mul(Pow(Symbol('t', commutative=True), Integer(-1)), Symbol('z', commutative=True))", "srepr_variable": "Symbol('z', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('t', commutative=True), Integer(-1)), Pow(Symbol('z', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('z', commutative=True), log(Symbol('t', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('z', commutative=True), Integer(2)), cos(Symbol('t', commutative=True)))", "Mul(Integer(2), Symbol('t', commutative=True), Symbol('z', commutative=True))", "cos(Add(Symbol('t', commutative=True), Mul(Integer(-1), Symbol('z', commutative=True))))"]}, {"premise_expression": "Q + Z", "variable": "Z", "positive": "\\frac{Z (2 Q + Z)}{2}", "negatives": ["\\frac{Z (2 Q - Z)}{2}", "\\frac{Q (Q + 2 Z)}{2}", "\\frac{Q Z^{2}}{2}", "Q Z + e^{Z}"], "srepr_premise_expression": "Add(Symbol('Q', commutative=True), Symbol('Z', commutative=True))", "srepr_variable": "Symbol('Z', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Mul(Integer(2), Symbol('Q', commutative=True)), Symbol('Z', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Mul(Integer(2), Symbol('Q', commutative=True)), Mul(Integer(-1), Symbol('Z', commutative=True))))", "Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Symbol('Q', commutative=True), Mul(Integer(2), Symbol('Z', commutative=True))))", "Mul(Rational(1, 2), Symbol('Q', commutative=True), Pow(Symbol('Z', commutative=True), Integer(2)))", "Add(Mul(Symbol('Q', commutative=True), Symbol('Z', commutative=True)), exp(Symbol('Z', commutative=True)))"]}, {"premise_expression": "\\log{(\\frac{H}{D})}", "variable": "D", "positive": "D (\\log{(\\frac{H}{D})} + 1)", "negatives": ["H (\\log{(\\frac{H}{D})} - 1)", "\\frac{D (\\log{(D)} - 1)}{H}", "- \\cos{(D + H)}", "D e^{H^{H}}"], "srepr_premise_expression": "log(Mul(Pow(Symbol('D', commutative=True), Integer(-1)), Symbol('H', commutative=True)))", "srepr_variable": "Symbol('D', commutative=True)", "srepr_positive": "Mul(Symbol('D', commutative=True), Add(log(Mul(Pow(Symbol('D', commutative=True), Integer(-1)), Symbol('H', commutative=True))), Integer(1)))", "srepr_negatives": ["Mul(Symbol('H', commutative=True), Add(log(Mul(Pow(Symbol('D', commutative=True), Integer(-1)), Symbol('H', commutative=True))), Integer(-1)))", "Mul(Symbol('D', commutative=True), Pow(Symbol('H', commutative=True), Integer(-1)), Add(log(Symbol('D', commutative=True)), Integer(-1)))", "Mul(Integer(-1), cos(Add(Symbol('D', commutative=True), Symbol('H', commutative=True))))", "Mul(Symbol('D', commutative=True), exp(Pow(Symbol('H', commutative=True), Symbol('H', commutative=True))))"]}, {"premise_expression": "\\log{(L + m)}", "variable": "L", "positive": "L \\log{(L + m)} - L + m \\log{(L + m)}", "negatives": ["L \\log{(L - m)} - L - m \\log{(L - m)}", "L \\log{(L + m)} + m \\log{(L + m)} - m", "L (\\log{(\\frac{L}{m})} - 1)", "L (\\log{(\\frac{m}{L})} + 1)"], "srepr_premise_expression": "log(Add(Symbol('L', commutative=True), Symbol('m', commutative=True)))", "srepr_variable": "Symbol('L', commutative=True)", "srepr_positive": "Add(Mul(Symbol('L', commutative=True), log(Add(Symbol('L', commutative=True), Symbol('m', commutative=True)))), Mul(Integer(-1), Symbol('L', commutative=True)), Mul(Symbol('m', commutative=True), log(Add(Symbol('L', commutative=True), Symbol('m', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('L', commutative=True), log(Add(Symbol('L', commutative=True), Mul(Integer(-1), Symbol('m', commutative=True))))), Mul(Integer(-1), Symbol('L', commutative=True)), Mul(Integer(-1), Symbol('m', commutative=True), log(Add(Symbol('L', commutative=True), Mul(Integer(-1), Symbol('m', commutative=True))))))", "Add(Mul(Symbol('L', commutative=True), log(Add(Symbol('L', commutative=True), Symbol('m', commutative=True)))), Mul(Symbol('m', commutative=True), log(Add(Symbol('L', commutative=True), Symbol('m', commutative=True)))), Mul(Integer(-1), Symbol('m', commutative=True)))", "Mul(Symbol('L', commutative=True), Add(log(Mul(Symbol('L', commutative=True), Pow(Symbol('m', commutative=True), Integer(-1)))), Integer(-1)))", "Mul(Symbol('L', commutative=True), Add(log(Mul(Pow(Symbol('L', commutative=True), Integer(-1)), Symbol('m', commutative=True))), Integer(1)))"]}, {"premise_expression": "o s", "variable": "s", "positive": "\\frac{o s^{2}}{2}", "negatives": ["\\frac{o^{2} s}{2}", "o e^{\\frac{s}{o}}", "\\log{(s)} \\cos{(o)}", "\\log{(o)} \\log{(s)}"], "srepr_premise_expression": "Mul(Symbol('o', commutative=True), Symbol('s', commutative=True))", "srepr_variable": "Symbol('s', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('o', commutative=True), Pow(Symbol('s', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('o', commutative=True), Integer(2)), Symbol('s', commutative=True))", "Mul(Symbol('o', commutative=True), exp(Mul(Pow(Symbol('o', commutative=True), Integer(-1)), Symbol('s', commutative=True))))", "Mul(log(Symbol('s', commutative=True)), cos(Symbol('o', commutative=True)))", "Mul(log(Symbol('o', commutative=True)), log(Symbol('s', commutative=True)))"]}, {"premise_expression": "E - J", "variable": "J", "positive": "\\frac{J (2 E - J)}{2}", "negatives": ["\\frac{E (E - 2 J)}{2}", "\\frac{J^{2} \\log{(E)}}{2}", "e^{- E + J}", "- \\frac{\\cos{(J)}}{E}"], "srepr_premise_expression": "Add(Symbol('E', commutative=True), Mul(Integer(-1), Symbol('J', commutative=True)))", "srepr_variable": "Symbol('J', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('J', commutative=True), Add(Mul(Integer(2), Symbol('E', commutative=True)), Mul(Integer(-1), Symbol('J', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('E', commutative=True), Add(Symbol('E', commutative=True), Mul(Integer(-1), Integer(2), Symbol('J', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('J', commutative=True), Integer(2)), log(Symbol('E', commutative=True)))", "exp(Add(Mul(Integer(-1), Symbol('E', commutative=True)), Symbol('J', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('E', commutative=True), Integer(-1)), cos(Symbol('J', commutative=True)))"]}, {"premise_expression": "A - K", "variable": "K", "positive": "\\frac{K (2 A - K)}{2}", "negatives": ["\\frac{A (A - 2 K)}{2}", "\\cos{(A - K)}", "\\frac{K (\\log{(K)} - 1)}{A}", "- A \\cos{(K)}"], "srepr_premise_expression": "Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('K', commutative=True)))", "srepr_variable": "Symbol('K', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Mul(Integer(2), Symbol('A', commutative=True)), Mul(Integer(-1), Symbol('K', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Symbol('A', commutative=True), Mul(Integer(-1), Integer(2), Symbol('K', commutative=True))))", "cos(Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('K', commutative=True))))", "Mul(Pow(Symbol('A', commutative=True), Integer(-1)), Symbol('K', commutative=True), Add(log(Symbol('K', commutative=True)), Integer(-1)))", "Mul(Integer(-1), Symbol('A', commutative=True), cos(Symbol('K', commutative=True)))"]}, {"premise_expression": "C + G", "variable": "C", "positive": "\\frac{C (C + 2 G)}{2}", "negatives": ["\\frac{G (2 C + G)}{2}", "\\frac{C (C + 2 \\log{(G)})}{2}", "\\sin{(C - G)}", "\\frac{C^{2}}{2 G} + C"], "srepr_premise_expression": "Add(Symbol('C', commutative=True), Symbol('G', commutative=True))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Symbol('C', commutative=True), Mul(Integer(2), Symbol('G', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Mul(Integer(2), Symbol('C', commutative=True)), Symbol('G', commutative=True)))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Symbol('C', commutative=True), Mul(Integer(2), log(Symbol('G', commutative=True)))))", "sin(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('G', commutative=True))))", "Add(Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2)), Pow(Symbol('G', commutative=True), Integer(-1))), Symbol('C', commutative=True))"]}, {"premise_expression": "- p + v", "variable": "p", "positive": "\\frac{p (- p + 2 v)}{2}", "negatives": ["\\frac{v (- 2 p + v)}{2}", "\\frac{p^{2} v}{2}", "\\sin{(p + v)}", "- \\cos{(p + v)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('p', commutative=True)), Symbol('v', commutative=True))", "srepr_variable": "Symbol('p', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Mul(Integer(-1), Symbol('p', commutative=True)), Mul(Integer(2), Symbol('v', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('v', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('p', commutative=True)), Symbol('v', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('p', commutative=True), Integer(2)), Symbol('v', commutative=True))", "sin(Add(Symbol('p', commutative=True), Symbol('v', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('p', commutative=True), Symbol('v', commutative=True))))"]}, {"premise_expression": "\\log{(X l)}", "variable": "X", "positive": "X (\\log{(X l)} - 1)", "negatives": ["l (\\log{(X l)} - 1)", "X (- l + \\log{(X)} - 1)", "\\frac{X (X + 2 l)}{2}", "X l^{l}"], "srepr_premise_expression": "log(Mul(Symbol('X', commutative=True), Symbol('l', commutative=True)))", "srepr_variable": "Symbol('X', commutative=True)", "srepr_positive": "Mul(Symbol('X', commutative=True), Add(log(Mul(Symbol('X', commutative=True), Symbol('l', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('l', commutative=True), Add(log(Mul(Symbol('X', commutative=True), Symbol('l', commutative=True))), Integer(-1)))", "Mul(Symbol('X', commutative=True), Add(Mul(Integer(-1), Symbol('l', commutative=True)), log(Symbol('X', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('X', commutative=True), Add(Symbol('X', commutative=True), Mul(Integer(2), Symbol('l', commutative=True))))", "Mul(Symbol('X', commutative=True), Pow(Symbol('l', commutative=True), Symbol('l', commutative=True)))"]}, {"premise_expression": "n + e^{I}", "variable": "I", "positive": "I n + e^{I}", "negatives": ["I n + \\sin{(I)}", "I (- n + e^{n})", "\\frac{n (n + 2 e^{I})}{2}", "\\frac{I (I + 2 n)}{2}"], "srepr_premise_expression": "Add(Symbol('n', commutative=True), exp(Symbol('I', commutative=True)))", "srepr_variable": "Symbol('I', commutative=True)", "srepr_positive": "Add(Mul(Symbol('I', commutative=True), Symbol('n', commutative=True)), exp(Symbol('I', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('I', commutative=True), Symbol('n', commutative=True)), sin(Symbol('I', commutative=True)))", "Mul(Symbol('I', commutative=True), Add(Mul(Integer(-1), Symbol('n', commutative=True)), exp(Symbol('n', commutative=True))))", "Mul(Rational(1, 2), Symbol('n', commutative=True), Add(Symbol('n', commutative=True), Mul(Integer(2), exp(Symbol('I', commutative=True)))))", "Mul(Rational(1, 2), Symbol('I', commutative=True), Add(Symbol('I', commutative=True), Mul(Integer(2), Symbol('n', commutative=True))))"]}, {"premise_expression": "\\frac{b}{I}", "variable": "I", "positive": "b \\log{(I)}", "negatives": ["\\frac{b^{2}}{2 I}", "I \\log{(b^{b})}", "I b (\\log{(I)} - 1)", "- I b + e^{I}"], "srepr_premise_expression": "Mul(Pow(Symbol('I', commutative=True), Integer(-1)), Symbol('b', commutative=True))", "srepr_variable": "Symbol('I', commutative=True)", "srepr_positive": "Mul(Symbol('b', commutative=True), log(Symbol('I', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(-1)), Pow(Symbol('b', commutative=True), Integer(2)))", "Mul(Symbol('I', commutative=True), log(Pow(Symbol('b', commutative=True), Symbol('b', commutative=True))))", "Mul(Symbol('I', commutative=True), Symbol('b', commutative=True), Add(log(Symbol('I', commutative=True)), Integer(-1)))", "Add(Mul(Integer(-1), Symbol('I', commutative=True), Symbol('b', commutative=True)), exp(Symbol('I', commutative=True)))"]}, {"premise_expression": "- G + Y", "variable": "G", "positive": "\\frac{G (- G + 2 Y)}{2}", "negatives": ["\\frac{Y (- 2 G + Y)}{2}", "\\frac{G (- G + 2 \\sin{(Y)})}{2}", "\\frac{G^{2} e^{Y}}{2}", "e^{G + Y}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('G', commutative=True)), Symbol('Y', commutative=True))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Mul(Integer(-1), Symbol('G', commutative=True)), Mul(Integer(2), Symbol('Y', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('Y', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('G', commutative=True)), Symbol('Y', commutative=True)))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Mul(Integer(-1), Symbol('G', commutative=True)), Mul(Integer(2), sin(Symbol('Y', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(2)), exp(Symbol('Y', commutative=True)))", "exp(Add(Symbol('G', commutative=True), Symbol('Y', commutative=True)))"]}, {"premise_expression": "\\frac{f}{W}", "variable": "f", "positive": "\\frac{f^{2}}{2 W}", "negatives": ["f \\log{(W)}", "W \\sin{(f)}", "\\frac{f (2 W + f)}{2}", "- \\sin{(W - f)}"], "srepr_premise_expression": "Mul(Pow(Symbol('W', commutative=True), Integer(-1)), Symbol('f', commutative=True))", "srepr_variable": "Symbol('f', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('W', commutative=True), Integer(-1)), Pow(Symbol('f', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('f', commutative=True), log(Symbol('W', commutative=True)))", "Mul(Symbol('W', commutative=True), sin(Symbol('f', commutative=True)))", "Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Mul(Integer(2), Symbol('W', commutative=True)), Symbol('f', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('W', commutative=True), Mul(Integer(-1), Symbol('f', commutative=True)))))"]}, {"premise_expression": "\\sin^{C}{(S)}", "variable": "S", "positive": "\\int \\sin^{C}{(S)} dS", "negatives": ["\\sin{(C + S)}", "C e^{\\frac{S}{C}}", "\\cos{(C - S)}", "\\frac{S^{2}}{2 C}"], "srepr_premise_expression": "Pow(sin(Symbol('S', commutative=True)), Symbol('C', commutative=True))", "srepr_variable": "Symbol('S', commutative=True)", "srepr_positive": "Integral(Pow(sin(Symbol('S', commutative=True)), Symbol('C', commutative=True)), Tuple(Symbol('S', commutative=True)))", "srepr_negatives": ["sin(Add(Symbol('C', commutative=True), Symbol('S', commutative=True)))", "Mul(Symbol('C', commutative=True), exp(Mul(Pow(Symbol('C', commutative=True), Integer(-1)), Symbol('S', commutative=True))))", "cos(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('S', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(-1)), Pow(Symbol('S', commutative=True), Integer(2)))"]}, {"premise_expression": "\\frac{N}{b}", "variable": "b", "positive": "N \\log{(b)}", "negatives": ["\\frac{N^{2}}{2 b}", "e^{- N + b}", "\\frac{b (2 N - b)}{2}", "\\frac{b^{2} \\sin{(N)}}{2}"], "srepr_premise_expression": "Mul(Symbol('N', commutative=True), Pow(Symbol('b', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('b', commutative=True)", "srepr_positive": "Mul(Symbol('N', commutative=True), log(Symbol('b', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('N', commutative=True), Integer(2)), Pow(Symbol('b', commutative=True), Integer(-1)))", "exp(Add(Mul(Integer(-1), Symbol('N', commutative=True)), Symbol('b', commutative=True)))", "Mul(Rational(1, 2), Symbol('b', commutative=True), Add(Mul(Integer(2), Symbol('N', commutative=True)), Mul(Integer(-1), Symbol('b', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('b', commutative=True), Integer(2)), sin(Symbol('N', commutative=True)))"]}, {"premise_expression": "\\frac{M}{u} + q", "variable": "u", "positive": "M \\log{(u)} + q u", "negatives": ["\\frac{M^{2}}{2 u} + M q", "\\frac{M q}{u} + \\frac{q^{2}}{2}", "u (M + u)", "\\frac{M u^{2}}{2 q}"], "srepr_premise_expression": "Add(Mul(Symbol('M', commutative=True), Pow(Symbol('u', commutative=True), Integer(-1))), Symbol('q', commutative=True))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "Add(Mul(Symbol('M', commutative=True), log(Symbol('u', commutative=True))), Mul(Symbol('q', commutative=True), Symbol('u', commutative=True)))", "srepr_negatives": ["Add(Mul(Rational(1, 2), Pow(Symbol('M', commutative=True), Integer(2)), Pow(Symbol('u', commutative=True), Integer(-1))), Mul(Symbol('M', commutative=True), Symbol('q', commutative=True)))", "Add(Mul(Symbol('M', commutative=True), Symbol('q', commutative=True), Pow(Symbol('u', commutative=True), Integer(-1))), Mul(Rational(1, 2), Pow(Symbol('q', commutative=True), Integer(2))))", "Mul(Symbol('u', commutative=True), Add(Symbol('M', commutative=True), Symbol('u', commutative=True)))", "Mul(Rational(1, 2), Symbol('M', commutative=True), Pow(Symbol('q', commutative=True), Integer(-1)), Pow(Symbol('u', commutative=True), Integer(2)))"]}, {"premise_expression": "N + p", "variable": "N", "positive": "\\frac{N (N + 2 p)}{2}", "negatives": ["\\frac{p (2 N + p)}{2}", "\\frac{N^{2} e^{p}}{2}", "- \\cos{(N + p)}", "\\cos{(N - p)}"], "srepr_premise_expression": "Add(Symbol('N', commutative=True), Symbol('p', commutative=True))", "srepr_variable": "Symbol('N', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Symbol('N', commutative=True), Mul(Integer(2), Symbol('p', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Mul(Integer(2), Symbol('N', commutative=True)), Symbol('p', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('N', commutative=True), Integer(2)), exp(Symbol('p', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('N', commutative=True), Symbol('p', commutative=True))))", "cos(Add(Symbol('N', commutative=True), Mul(Integer(-1), Symbol('p', commutative=True))))"]}, {"premise_expression": "A + e^{G}", "variable": "A", "positive": "\\frac{A (A + 2 e^{G})}{2}", "negatives": ["\\frac{A (A + 2 \\sin{(G)})}{2}", "A G + e^{G}", "\\sin{(A - G)}", "\\log{(A)} \\sin{(G)}"], "srepr_premise_expression": "Add(Symbol('A', commutative=True), exp(Symbol('G', commutative=True)))", "srepr_variable": "Symbol('A', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Symbol('A', commutative=True), Mul(Integer(2), exp(Symbol('G', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Symbol('A', commutative=True), Mul(Integer(2), sin(Symbol('G', commutative=True)))))", "Add(Mul(Symbol('A', commutative=True), Symbol('G', commutative=True)), exp(Symbol('G', commutative=True)))", "sin(Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('G', commutative=True))))", "Mul(log(Symbol('A', commutative=True)), sin(Symbol('G', commutative=True)))"]}, {"premise_expression": "\\cos^{b}{(k)}", "variable": "k", "positive": "\\int \\cos^{b}{(k)} dk", "negatives": ["- \\frac{\\cos{(k)}}{b}", "- b k + \\sin{(k)}", "\\frac{k (2 b - k)}{2}", "\\frac{k^{2} (2 k + 3)}{6}"], "srepr_premise_expression": "Pow(cos(Symbol('k', commutative=True)), Symbol('b', commutative=True))", "srepr_variable": "Symbol('k', commutative=True)", "srepr_positive": "Integral(Pow(cos(Symbol('k', commutative=True)), Symbol('b', commutative=True)), Tuple(Symbol('k', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Pow(Symbol('b', commutative=True), Integer(-1)), cos(Symbol('k', commutative=True)))", "Add(Mul(Integer(-1), Symbol('b', commutative=True), Symbol('k', commutative=True)), sin(Symbol('k', commutative=True)))", "Mul(Rational(1, 2), Symbol('k', commutative=True), Add(Mul(Integer(2), Symbol('b', commutative=True)), Mul(Integer(-1), Symbol('k', commutative=True))))", "Mul(Rational(1, 6), Pow(Symbol('k', commutative=True), Integer(2)), Add(Mul(Integer(2), Symbol('k', commutative=True)), Integer(3)))"]}, {"premise_expression": "\\log{(\\frac{J}{M})}", "variable": "M", "positive": "M (\\log{(\\frac{J}{M})} + 1)", "negatives": ["J (\\log{(\\frac{J}{M})} - 1)", "\\log{(J)} \\log{(M)}", "\\frac{M^{2} \\log{(J)}}{2}", "\\log{(M)} \\sin{(J)}"], "srepr_premise_expression": "log(Mul(Symbol('J', commutative=True), Pow(Symbol('M', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('M', commutative=True)", "srepr_positive": "Mul(Symbol('M', commutative=True), Add(log(Mul(Symbol('J', commutative=True), Pow(Symbol('M', commutative=True), Integer(-1)))), Integer(1)))", "srepr_negatives": ["Mul(Symbol('J', commutative=True), Add(log(Mul(Symbol('J', commutative=True), Pow(Symbol('M', commutative=True), Integer(-1)))), Integer(-1)))", "Mul(log(Symbol('J', commutative=True)), log(Symbol('M', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('M', commutative=True), Integer(2)), log(Symbol('J', commutative=True)))", "Mul(log(Symbol('M', commutative=True)), sin(Symbol('J', commutative=True)))"]}, {"premise_expression": "x + e^{Y}", "variable": "x", "positive": "\\frac{x (x + 2 e^{Y})}{2}", "negatives": ["\\frac{x (x + 2 \\sin{(Y)})}{2}", "Y x + e^{Y}", "\\frac{x (2 Y - x)}{2}", "Y x + \\sin{(x)}"], "srepr_premise_expression": "Add(Symbol('x', commutative=True), exp(Symbol('Y', commutative=True)))", "srepr_variable": "Symbol('x', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('x', commutative=True), Add(Symbol('x', commutative=True), Mul(Integer(2), exp(Symbol('Y', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('x', commutative=True), Add(Symbol('x', commutative=True), Mul(Integer(2), sin(Symbol('Y', commutative=True)))))", "Add(Mul(Symbol('Y', commutative=True), Symbol('x', commutative=True)), exp(Symbol('Y', commutative=True)))", "Mul(Rational(1, 2), Symbol('x', commutative=True), Add(Mul(Integer(2), Symbol('Y', commutative=True)), Mul(Integer(-1), Symbol('x', commutative=True))))", "Add(Mul(Symbol('Y', commutative=True), Symbol('x', commutative=True)), sin(Symbol('x', commutative=True)))"]}, {"premise_expression": "V - X", "variable": "X", "positive": "\\frac{X (2 V - X)}{2}", "negatives": ["\\frac{V (V - 2 X)}{2}", "- \\cos{(V + X)}", "\\frac{V X^{2}}{2}", "\\frac{\\sin{(X)}}{V}"], "srepr_premise_expression": "Add(Symbol('V', commutative=True), Mul(Integer(-1), Symbol('X', commutative=True)))", "srepr_variable": "Symbol('X', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('X', commutative=True), Add(Mul(Integer(2), Symbol('V', commutative=True)), Mul(Integer(-1), Symbol('X', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('V', commutative=True), Add(Symbol('V', commutative=True), Mul(Integer(-1), Integer(2), Symbol('X', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('V', commutative=True), Symbol('X', commutative=True))))", "Mul(Rational(1, 2), Symbol('V', commutative=True), Pow(Symbol('X', commutative=True), Integer(2)))", "Mul(Pow(Symbol('V', commutative=True), Integer(-1)), sin(Symbol('X', commutative=True)))"]}, {"premise_expression": "- z + \\log{(p)}", "variable": "p", "positive": "p (- z + \\log{(p)} - 1)", "negatives": ["\\frac{z (- z + 2 \\log{(p)})}{2}", "p - z \\log{(p)}", "\\frac{p (- p + 2 \\cos{(z)})}{2}", "- p z - \\cos{(p)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('z', commutative=True)), log(Symbol('p', commutative=True)))", "srepr_variable": "Symbol('p', commutative=True)", "srepr_positive": "Mul(Symbol('p', commutative=True), Add(Mul(Integer(-1), Symbol('z', commutative=True)), log(Symbol('p', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('z', commutative=True), Add(Mul(Integer(-1), Symbol('z', commutative=True)), Mul(Integer(2), log(Symbol('p', commutative=True)))))", "Add(Symbol('p', commutative=True), Mul(Integer(-1), Symbol('z', commutative=True), log(Symbol('p', commutative=True))))", "Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Mul(Integer(-1), Symbol('p', commutative=True)), Mul(Integer(2), cos(Symbol('z', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('p', commutative=True), Symbol('z', commutative=True)), Mul(Integer(-1), cos(Symbol('p', commutative=True))))"]}, {"premise_expression": "\\cos{(N - Z)}", "variable": "N", "positive": "\\sin{(N - Z)}", "negatives": ["- \\sin{(N - Z)}", "\\frac{\\sin{(N)}}{Z}", "- e^{- N + Z}", "\\frac{N (N + 2 Z)}{2}"], "srepr_premise_expression": "cos(Add(Symbol('N', commutative=True), Mul(Integer(-1), Symbol('Z', commutative=True))))", "srepr_variable": "Symbol('N', commutative=True)", "srepr_positive": "sin(Add(Symbol('N', commutative=True), Mul(Integer(-1), Symbol('Z', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('N', commutative=True), Mul(Integer(-1), Symbol('Z', commutative=True)))))", "Mul(Pow(Symbol('Z', commutative=True), Integer(-1)), sin(Symbol('N', commutative=True)))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('N', commutative=True)), Symbol('Z', commutative=True))))", "Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Symbol('N', commutative=True), Mul(Integer(2), Symbol('Z', commutative=True))))"]}, {"premise_expression": "\\frac{- K + k}{N}", "variable": "k", "positive": "\\frac{k (- 2 K + k)}{2 N}", "negatives": ["\\frac{k (2 N - k)}{2 K}", "\\frac{K (- K + 2 k)}{2 N}", "(- K + k) \\log{(N)}", "\\frac{k (2 K + 2 N + k)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('N', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('K', commutative=True)), Symbol('k', commutative=True)))", "srepr_variable": "Symbol('k', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('N', commutative=True), Integer(-1)), Symbol('k', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('K', commutative=True)), Symbol('k', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('K', commutative=True), Integer(-1)), Symbol('k', commutative=True), Add(Mul(Integer(2), Symbol('N', commutative=True)), Mul(Integer(-1), Symbol('k', commutative=True))))", "Mul(Rational(1, 2), Symbol('K', commutative=True), Pow(Symbol('N', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('K', commutative=True)), Mul(Integer(2), Symbol('k', commutative=True))))", "Mul(Add(Mul(Integer(-1), Symbol('K', commutative=True)), Symbol('k', commutative=True)), log(Symbol('N', commutative=True)))", "Mul(Rational(1, 2), Symbol('k', commutative=True), Add(Mul(Integer(2), Symbol('K', commutative=True)), Mul(Integer(2), Symbol('N', commutative=True)), Symbol('k', commutative=True)))"]}, {"premise_expression": "R l - s", "variable": "R", "positive": "\\frac{R (R l - 2 s)}{2}", "negatives": ["\\frac{l (R l - 2 s)}{2}", "\\frac{R (R s - 2 l)}{2}", "\\frac{s (2 R l - s)}{2}", "\\frac{R s (R - 2 l)}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('R', commutative=True), Symbol('l', commutative=True)), Mul(Integer(-1), Symbol('s', commutative=True)))", "srepr_variable": "Symbol('R', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('R', commutative=True), Add(Mul(Symbol('R', commutative=True), Symbol('l', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('s', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('l', commutative=True), Add(Mul(Symbol('R', commutative=True), Symbol('l', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('s', commutative=True))))", "Mul(Rational(1, 2), Symbol('R', commutative=True), Add(Mul(Symbol('R', commutative=True), Symbol('s', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('l', commutative=True))))", "Mul(Rational(1, 2), Symbol('s', commutative=True), Add(Mul(Integer(2), Symbol('R', commutative=True), Symbol('l', commutative=True)), Mul(Integer(-1), Symbol('s', commutative=True))))", "Mul(Rational(1, 2), Symbol('R', commutative=True), Symbol('s', commutative=True), Add(Symbol('R', commutative=True), Mul(Integer(-1), Integer(2), Symbol('l', commutative=True))))"]}, {"premise_expression": "\\frac{s^{A}}{H}", "variable": "H", "positive": "s^{A} \\log{(H)}", "negatives": ["A s \\log{(H)}", "\\frac{H s (2 A + H)}{2}", "\\frac{H (2 A + H s)}{2}", "\\frac{H (2 A + H - 2 s)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('H', commutative=True), Integer(-1)), Pow(Symbol('s', commutative=True), Symbol('A', commutative=True)))", "srepr_variable": "Symbol('H', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('s', commutative=True), Symbol('A', commutative=True)), log(Symbol('H', commutative=True)))", "srepr_negatives": ["Mul(Symbol('A', commutative=True), Symbol('s', commutative=True), log(Symbol('H', commutative=True)))", "Mul(Rational(1, 2), Symbol('H', commutative=True), Symbol('s', commutative=True), Add(Mul(Integer(2), Symbol('A', commutative=True)), Symbol('H', commutative=True)))", "Mul(Rational(1, 2), Symbol('H', commutative=True), Add(Mul(Integer(2), Symbol('A', commutative=True)), Mul(Symbol('H', commutative=True), Symbol('s', commutative=True))))", "Mul(Rational(1, 2), Symbol('H', commutative=True), Add(Mul(Integer(2), Symbol('A', commutative=True)), Symbol('H', commutative=True), Mul(Integer(-1), Integer(2), Symbol('s', commutative=True))))"]}, {"premise_expression": "G a^{A}", "variable": "G", "positive": "\\frac{G^{2} a^{A}}{2}", "negatives": ["\\frac{A G^{2} a}{2}", "\\frac{A G^{2}}{2 a}", "A^{a} \\log{(G)}", "\\frac{G (- 2 A + G a)}{2}"], "srepr_premise_expression": "Mul(Symbol('G', commutative=True), Pow(Symbol('a', commutative=True), Symbol('A', commutative=True)))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(2)), Pow(Symbol('a', commutative=True), Symbol('A', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('A', commutative=True), Pow(Symbol('G', commutative=True), Integer(2)), Symbol('a', commutative=True))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Pow(Symbol('G', commutative=True), Integer(2)), Pow(Symbol('a', commutative=True), Integer(-1)))", "Mul(Pow(Symbol('A', commutative=True), Symbol('a', commutative=True)), log(Symbol('G', commutative=True)))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('A', commutative=True)), Mul(Symbol('G', commutative=True), Symbol('a', commutative=True))))"]}, {"premise_expression": "\\frac{u}{t}", "variable": "t", "positive": "u \\log{(t)}", "negatives": ["\\frac{u^{2}}{2 t}", "\\frac{t (\\log{(t)} - 1)}{u}", "\\sin{(t + u)}", "e^{t + u}"], "srepr_premise_expression": "Mul(Pow(Symbol('t', commutative=True), Integer(-1)), Symbol('u', commutative=True))", "srepr_variable": "Symbol('t', commutative=True)", "srepr_positive": "Mul(Symbol('u', commutative=True), log(Symbol('t', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('t', commutative=True), Integer(-1)), Pow(Symbol('u', commutative=True), Integer(2)))", "Mul(Symbol('t', commutative=True), Pow(Symbol('u', commutative=True), Integer(-1)), Add(log(Symbol('t', commutative=True)), Integer(-1)))", "sin(Add(Symbol('t', commutative=True), Symbol('u', commutative=True)))", "exp(Add(Symbol('t', commutative=True), Symbol('u', commutative=True)))"]}, {"premise_expression": "\\frac{w}{x}", "variable": "x", "positive": "w \\log{(x)}", "negatives": ["w \\sin{(x)}", "\\frac{w^{2}}{2 x}", "\\frac{x^{2} \\log{(w)}}{2}", "- \\cos{(w + x)}"], "srepr_premise_expression": "Mul(Symbol('w', commutative=True), Pow(Symbol('x', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('x', commutative=True)", "srepr_positive": "Mul(Symbol('w', commutative=True), log(Symbol('x', commutative=True)))", "srepr_negatives": ["Mul(Symbol('w', commutative=True), sin(Symbol('x', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('w', commutative=True), Integer(2)), Pow(Symbol('x', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('x', commutative=True), Integer(2)), log(Symbol('w', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('w', commutative=True), Symbol('x', commutative=True))))"]}, {"premise_expression": "G Y", "variable": "Y", "positive": "\\frac{G Y^{2}}{2}", "negatives": ["\\frac{G^{2} Y}{2}", "G^{G} Y", "G Y + \\sin{(Y)}", "- \\cos{(G - Y)}"], "srepr_premise_expression": "Mul(Symbol('G', commutative=True), Symbol('Y', commutative=True))", "srepr_variable": "Symbol('Y', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('G', commutative=True), Pow(Symbol('Y', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(2)), Symbol('Y', commutative=True))", "Mul(Pow(Symbol('G', commutative=True), Symbol('G', commutative=True)), Symbol('Y', commutative=True))", "Add(Mul(Symbol('G', commutative=True), Symbol('Y', commutative=True)), sin(Symbol('Y', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('Y', commutative=True)))))"]}, {"premise_expression": "- F + \\sin{(J)}", "variable": "F", "positive": "\\frac{F (- F + 2 \\sin{(J)})}{2}", "negatives": ["\\frac{F (- F + 2 e^{J})}{2}", "- F J - \\cos{(J)}", "- e^{- F + J}", "- \\cos{(F - J)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('F', commutative=True)), sin(Symbol('J', commutative=True)))", "srepr_variable": "Symbol('F', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Mul(Integer(-1), Symbol('F', commutative=True)), Mul(Integer(2), sin(Symbol('J', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Mul(Integer(-1), Symbol('F', commutative=True)), Mul(Integer(2), exp(Symbol('J', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('F', commutative=True), Symbol('J', commutative=True)), Mul(Integer(-1), cos(Symbol('J', commutative=True))))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('F', commutative=True)), Symbol('J', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('F', commutative=True), Mul(Integer(-1), Symbol('J', commutative=True)))))"]}, {"premise_expression": "t + u", "variable": "u", "positive": "\\frac{u (2 t + u)}{2}", "negatives": ["\\frac{t (t + 2 u)}{2}", "\\frac{u^{2} \\cos{(t)}}{2}", "\\frac{u^{2} e^{t}}{2}", "- \\cos{(t + u)}"], "srepr_premise_expression": "Add(Symbol('t', commutative=True), Symbol('u', commutative=True))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(2), Symbol('t', commutative=True)), Symbol('u', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('t', commutative=True), Add(Symbol('t', commutative=True), Mul(Integer(2), Symbol('u', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('u', commutative=True), Integer(2)), cos(Symbol('t', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('u', commutative=True), Integer(2)), exp(Symbol('t', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('t', commutative=True), Symbol('u', commutative=True))))"]}, {"premise_expression": "\\cos^{B}{(U)}", "variable": "U", "positive": "\\int \\cos^{B}{(U)} dU", "negatives": ["\\log{(U)} \\sin{(B)}", "- \\frac{\\cos{(U)}}{B}", "B U - \\cos{(U)}", "- B U - \\cos{(U)}"], "srepr_premise_expression": "Pow(cos(Symbol('U', commutative=True)), Symbol('B', commutative=True))", "srepr_variable": "Symbol('U', commutative=True)", "srepr_positive": "Integral(Pow(cos(Symbol('U', commutative=True)), Symbol('B', commutative=True)), Tuple(Symbol('U', commutative=True)))", "srepr_negatives": ["Mul(log(Symbol('U', commutative=True)), sin(Symbol('B', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('B', commutative=True), Integer(-1)), cos(Symbol('U', commutative=True)))", "Add(Mul(Symbol('B', commutative=True), Symbol('U', commutative=True)), Mul(Integer(-1), cos(Symbol('U', commutative=True))))", "Add(Mul(Integer(-1), Symbol('B', commutative=True), Symbol('U', commutative=True)), Mul(Integer(-1), cos(Symbol('U', commutative=True))))"]}, {"premise_expression": "\\frac{e^{T}}{b}", "variable": "b", "positive": "e^{T} \\log{(b)}", "negatives": ["e^{T + b}", "\\frac{b (2 T - b)}{2}", "\\frac{b^{2} e^{T}}{2}", "b (\\log{(T b)} - 1)"], "srepr_premise_expression": "Mul(Pow(Symbol('b', commutative=True), Integer(-1)), exp(Symbol('T', commutative=True)))", "srepr_variable": "Symbol('b', commutative=True)", "srepr_positive": "Mul(exp(Symbol('T', commutative=True)), log(Symbol('b', commutative=True)))", "srepr_negatives": ["exp(Add(Symbol('T', commutative=True), Symbol('b', commutative=True)))", "Mul(Rational(1, 2), Symbol('b', commutative=True), Add(Mul(Integer(2), Symbol('T', commutative=True)), Mul(Integer(-1), Symbol('b', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('b', commutative=True), Integer(2)), exp(Symbol('T', commutative=True)))", "Mul(Symbol('b', commutative=True), Add(log(Mul(Symbol('T', commutative=True), Symbol('b', commutative=True))), Integer(-1)))"]}, {"premise_expression": "B + x", "variable": "B", "positive": "\\frac{B (B + 2 x)}{2}", "negatives": ["\\frac{x (2 B + x)}{2}", "\\frac{B^{2} e^{x}}{2}", "\\cos{(B - x)}", "- \\cos{(B + x)}"], "srepr_premise_expression": "Add(Symbol('B', commutative=True), Symbol('x', commutative=True))", "srepr_variable": "Symbol('B', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('B', commutative=True), Add(Symbol('B', commutative=True), Mul(Integer(2), Symbol('x', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('x', commutative=True), Add(Mul(Integer(2), Symbol('B', commutative=True)), Symbol('x', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('B', commutative=True), Integer(2)), exp(Symbol('x', commutative=True)))", "cos(Add(Symbol('B', commutative=True), Mul(Integer(-1), Symbol('x', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('B', commutative=True), Symbol('x', commutative=True))))"]}, {"premise_expression": "E c", "variable": "c", "positive": "\\frac{E c^{2}}{2}", "negatives": ["\\frac{E^{2} c}{2}", "E c + e^{c}", "c^{2} (\\frac{E}{2} - \\frac{c}{3})", "E c (\\log{(c)} - 1)"], "srepr_premise_expression": "Mul(Symbol('E', commutative=True), Symbol('c', commutative=True))", "srepr_variable": "Symbol('c', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('E', commutative=True), Pow(Symbol('c', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('E', commutative=True), Integer(2)), Symbol('c', commutative=True))", "Add(Mul(Symbol('E', commutative=True), Symbol('c', commutative=True)), exp(Symbol('c', commutative=True)))", "Mul(Pow(Symbol('c', commutative=True), Integer(2)), Add(Mul(Rational(1, 2), Symbol('E', commutative=True)), Mul(Integer(-1), Rational(1, 3), Symbol('c', commutative=True))))", "Mul(Symbol('E', commutative=True), Symbol('c', commutative=True), Add(log(Symbol('c', commutative=True)), Integer(-1)))"]}, {"premise_expression": "R - z", "variable": "z", "positive": "\\frac{z (2 R - z)}{2}", "negatives": ["\\frac{R (R - 2 z)}{2}", "- \\cos{(R + z)}", "z (\\log{(R z)} - 1)", "\\frac{z (- z + 2 \\log{(R)})}{2}"], "srepr_premise_expression": "Add(Symbol('R', commutative=True), Mul(Integer(-1), Symbol('z', commutative=True)))", "srepr_variable": "Symbol('z', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('z', commutative=True), Add(Mul(Integer(2), Symbol('R', commutative=True)), Mul(Integer(-1), Symbol('z', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('R', commutative=True), Add(Symbol('R', commutative=True), Mul(Integer(-1), Integer(2), Symbol('z', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('R', commutative=True), Symbol('z', commutative=True))))", "Mul(Symbol('z', commutative=True), Add(log(Mul(Symbol('R', commutative=True), Symbol('z', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('z', commutative=True), Add(Mul(Integer(-1), Symbol('z', commutative=True)), Mul(Integer(2), log(Symbol('R', commutative=True)))))"]}, {"premise_expression": "D + u", "variable": "u", "positive": "\\frac{u (2 D + u)}{2}", "negatives": ["\\frac{D (D + 2 u)}{2}", "\\frac{u^{2} \\sin{(D)}}{2}", "\\frac{u^{2} e^{D}}{2}", "\\sin{(D + u)}"], "srepr_premise_expression": "Add(Symbol('D', commutative=True), Symbol('u', commutative=True))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(2), Symbol('D', commutative=True)), Symbol('u', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('D', commutative=True), Add(Symbol('D', commutative=True), Mul(Integer(2), Symbol('u', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('u', commutative=True), Integer(2)), sin(Symbol('D', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('u', commutative=True), Integer(2)), exp(Symbol('D', commutative=True)))", "sin(Add(Symbol('D', commutative=True), Symbol('u', commutative=True)))"]}, {"premise_expression": "\\frac{e^{F}}{L}", "variable": "L", "positive": "e^{F} \\log{(L)}", "negatives": ["\\frac{L (- 2 F + L)}{2}", "- \\frac{\\cos{(L)}}{F}", "\\frac{L^{2} \\sin{(F)}}{2}", "\\frac{L^{2} e^{F}}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('L', commutative=True), Integer(-1)), exp(Symbol('F', commutative=True)))", "srepr_variable": "Symbol('L', commutative=True)", "srepr_positive": "Mul(exp(Symbol('F', commutative=True)), log(Symbol('L', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('F', commutative=True)), Symbol('L', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('F', commutative=True), Integer(-1)), cos(Symbol('L', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(2)), sin(Symbol('F', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(2)), exp(Symbol('F', commutative=True)))"]}, {"premise_expression": "F r", "variable": "F", "positive": "\\frac{F^{2} r}{2}", "negatives": ["\\frac{F r^{2}}{2}", "\\frac{F (- F + 2 r)}{2}", "r \\sin{(F)}", "- \\frac{\\cos{(F)}}{r}"], "srepr_premise_expression": "Mul(Symbol('F', commutative=True), Symbol('r', commutative=True))", "srepr_variable": "Symbol('F', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('F', commutative=True), Integer(2)), Symbol('r', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('F', commutative=True), Pow(Symbol('r', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Mul(Integer(-1), Symbol('F', commutative=True)), Mul(Integer(2), Symbol('r', commutative=True))))", "Mul(Symbol('r', commutative=True), sin(Symbol('F', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('r', commutative=True), Integer(-1)), cos(Symbol('F', commutative=True)))"]}, {"premise_expression": "Q p", "variable": "p", "positive": "\\frac{Q p^{2}}{2}", "negatives": ["\\frac{Q^{2} p}{2}", "\\frac{p^{2}}{2 Q}", "- \\frac{\\cos{(p)}}{Q}", "- Q p + \\sin{(p)}"], "srepr_premise_expression": "Mul(Symbol('Q', commutative=True), Symbol('p', commutative=True))", "srepr_variable": "Symbol('p', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('Q', commutative=True), Pow(Symbol('p', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(2)), Symbol('p', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(-1)), Pow(Symbol('p', commutative=True), Integer(2)))", "Mul(Integer(-1), Pow(Symbol('Q', commutative=True), Integer(-1)), cos(Symbol('p', commutative=True)))", "Add(Mul(Integer(-1), Symbol('Q', commutative=True), Symbol('p', commutative=True)), sin(Symbol('p', commutative=True)))"]}, {"premise_expression": "\\sin{(S - v)}", "variable": "S", "positive": "- \\cos{(S - v)}", "negatives": ["\\cos{(S - v)}", "\\sin{(S + v)}", "S (\\log{(\\frac{S}{v})} - 1)", "\\frac{S (- S + 2 v)}{2}"], "srepr_premise_expression": "sin(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('v', commutative=True))))", "srepr_variable": "Symbol('S', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('v', commutative=True)))))", "srepr_negatives": ["cos(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('v', commutative=True))))", "sin(Add(Symbol('S', commutative=True), Symbol('v', commutative=True)))", "Mul(Symbol('S', commutative=True), Add(log(Mul(Symbol('S', commutative=True), Pow(Symbol('v', commutative=True), Integer(-1)))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Mul(Integer(-1), Symbol('S', commutative=True)), Mul(Integer(2), Symbol('v', commutative=True))))"]}, {"premise_expression": "- N + \\sin{(D)}", "variable": "N", "positive": "\\frac{N (- N + 2 \\sin{(D)})}{2}", "negatives": ["\\frac{N^{2} e^{D}}{2}", "- D N - \\cos{(D)}", "D N + e^{N}", "N (D + \\log{(N)} - 1)"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('N', commutative=True)), sin(Symbol('D', commutative=True)))", "srepr_variable": "Symbol('N', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Mul(Integer(-1), Symbol('N', commutative=True)), Mul(Integer(2), sin(Symbol('D', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('N', commutative=True), Integer(2)), exp(Symbol('D', commutative=True)))", "Add(Mul(Integer(-1), Symbol('D', commutative=True), Symbol('N', commutative=True)), Mul(Integer(-1), cos(Symbol('D', commutative=True))))", "Add(Mul(Symbol('D', commutative=True), Symbol('N', commutative=True)), exp(Symbol('N', commutative=True)))", "Mul(Symbol('N', commutative=True), Add(Symbol('D', commutative=True), log(Symbol('N', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\cos{(M + N)}", "variable": "N", "positive": "\\sin{(M + N)}", "negatives": ["e^{M + N}", "\\frac{N (- 2 M + N)}{2}", "M N (\\log{(N)} - 1)", "N (M + \\log{(N)} - 1)"], "srepr_premise_expression": "cos(Add(Symbol('M', commutative=True), Symbol('N', commutative=True)))", "srepr_variable": "Symbol('N', commutative=True)", "srepr_positive": "sin(Add(Symbol('M', commutative=True), Symbol('N', commutative=True)))", "srepr_negatives": ["exp(Add(Symbol('M', commutative=True), Symbol('N', commutative=True)))", "Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('M', commutative=True)), Symbol('N', commutative=True)))", "Mul(Symbol('M', commutative=True), Symbol('N', commutative=True), Add(log(Symbol('N', commutative=True)), Integer(-1)))", "Mul(Symbol('N', commutative=True), Add(Symbol('M', commutative=True), log(Symbol('N', commutative=True)), Integer(-1)))"]}, {"premise_expression": "D + G", "variable": "G", "positive": "\\frac{G (2 D + G)}{2}", "negatives": ["\\frac{G (2 D - G)}{2}", "\\frac{D (D + 2 G)}{2}", "\\frac{G^{2} \\log{(D)}}{2}", "- \\cos{(D + G)}"], "srepr_premise_expression": "Add(Symbol('D', commutative=True), Symbol('G', commutative=True))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Mul(Integer(2), Symbol('D', commutative=True)), Symbol('G', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Mul(Integer(2), Symbol('D', commutative=True)), Mul(Integer(-1), Symbol('G', commutative=True))))", "Mul(Rational(1, 2), Symbol('D', commutative=True), Add(Symbol('D', commutative=True), Mul(Integer(2), Symbol('G', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(2)), log(Symbol('D', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('D', commutative=True), Symbol('G', commutative=True))))"]}, {"premise_expression": "\\frac{z}{Q}", "variable": "Q", "positive": "z \\log{(Q)}", "negatives": ["\\frac{z^{2}}{2 Q}", "\\frac{Q^{2} \\log{(z)}}{2}", "e^{Q + z}", "\\frac{Q (Q - 2 z)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('Q', commutative=True), Integer(-1)), Symbol('z', commutative=True))", "srepr_variable": "Symbol('Q', commutative=True)", "srepr_positive": "Mul(Symbol('z', commutative=True), log(Symbol('Q', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(-1)), Pow(Symbol('z', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(2)), log(Symbol('z', commutative=True)))", "exp(Add(Symbol('Q', commutative=True), Symbol('z', commutative=True)))", "Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Symbol('Q', commutative=True), Mul(Integer(-1), Integer(2), Symbol('z', commutative=True))))"]}, {"premise_expression": "\\cos{(A - m)}", "variable": "A", "positive": "\\sin{(A - m)}", "negatives": ["- \\sin{(A - m)}", "- \\frac{\\cos{(A)}}{m}", "\\log{(A)} \\cos{(m)}", "A m - \\cos{(A)}"], "srepr_premise_expression": "cos(Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('m', commutative=True))))", "srepr_variable": "Symbol('A', commutative=True)", "srepr_positive": "sin(Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('m', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('m', commutative=True)))))", "Mul(Integer(-1), Pow(Symbol('m', commutative=True), Integer(-1)), cos(Symbol('A', commutative=True)))", "Mul(log(Symbol('A', commutative=True)), cos(Symbol('m', commutative=True)))", "Add(Mul(Symbol('A', commutative=True), Symbol('m', commutative=True)), Mul(Integer(-1), cos(Symbol('A', commutative=True))))"]}, {"premise_expression": "\\frac{Y}{C}", "variable": "Y", "positive": "\\frac{Y^{2}}{2 C}", "negatives": ["Y \\log{(C)}", "C e^{\\frac{Y}{C}}", "C \\log{(Y)}", "C \\sin{(Y)}"], "srepr_premise_expression": "Mul(Pow(Symbol('C', commutative=True), Integer(-1)), Symbol('Y', commutative=True))", "srepr_variable": "Symbol('Y', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(-1)), Pow(Symbol('Y', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('Y', commutative=True), log(Symbol('C', commutative=True)))", "Mul(Symbol('C', commutative=True), exp(Mul(Pow(Symbol('C', commutative=True), Integer(-1)), Symbol('Y', commutative=True))))", "Mul(Symbol('C', commutative=True), log(Symbol('Y', commutative=True)))", "Mul(Symbol('C', commutative=True), sin(Symbol('Y', commutative=True)))"]}, {"premise_expression": "V X - k", "variable": "X", "positive": "\\frac{X (V X - 2 k)}{2}", "negatives": ["\\frac{V (V X - 2 k)}{2}", "\\frac{X (2 V + X k)}{2}", "\\frac{k (2 V X - k)}{2}", "\\frac{V X (X + 2 k)}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('V', commutative=True), Symbol('X', commutative=True)), Mul(Integer(-1), Symbol('k', commutative=True)))", "srepr_variable": "Symbol('X', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('X', commutative=True), Add(Mul(Symbol('V', commutative=True), Symbol('X', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('k', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('V', commutative=True), Add(Mul(Symbol('V', commutative=True), Symbol('X', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('k', commutative=True))))", "Mul(Rational(1, 2), Symbol('X', commutative=True), Add(Mul(Integer(2), Symbol('V', commutative=True)), Mul(Symbol('X', commutative=True), Symbol('k', commutative=True))))", "Mul(Rational(1, 2), Symbol('k', commutative=True), Add(Mul(Integer(2), Symbol('V', commutative=True), Symbol('X', commutative=True)), Mul(Integer(-1), Symbol('k', commutative=True))))", "Mul(Rational(1, 2), Symbol('V', commutative=True), Symbol('X', commutative=True), Add(Symbol('X', commutative=True), Mul(Integer(2), Symbol('k', commutative=True))))"]}, {"premise_expression": "\\frac{w}{o}", "variable": "w", "positive": "\\frac{w^{2}}{2 o}", "negatives": ["w \\log{(o)}", "\\frac{w^{2} \\log{(o)}}{2}", "w (o + w)", "- o \\cos{(w)}"], "srepr_premise_expression": "Mul(Pow(Symbol('o', commutative=True), Integer(-1)), Symbol('w', commutative=True))", "srepr_variable": "Symbol('w', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('o', commutative=True), Integer(-1)), Pow(Symbol('w', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('w', commutative=True), log(Symbol('o', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('w', commutative=True), Integer(2)), log(Symbol('o', commutative=True)))", "Mul(Symbol('w', commutative=True), Add(Symbol('o', commutative=True), Symbol('w', commutative=True)))", "Mul(Integer(-1), Symbol('o', commutative=True), cos(Symbol('w', commutative=True)))"]}, {"premise_expression": "e^{E + b}", "variable": "E", "positive": "e^{E + b}", "negatives": ["- e^{- E + b}", "\\sin{(E - b)}", "\\log{(E)} \\sin{(b)}", "\\frac{E^{2} b}{2}"], "srepr_premise_expression": "exp(Add(Symbol('E', commutative=True), Symbol('b', commutative=True)))", "srepr_variable": "Symbol('E', commutative=True)", "srepr_positive": "exp(Add(Symbol('E', commutative=True), Symbol('b', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('E', commutative=True)), Symbol('b', commutative=True))))", "sin(Add(Symbol('E', commutative=True), Mul(Integer(-1), Symbol('b', commutative=True))))", "Mul(log(Symbol('E', commutative=True)), sin(Symbol('b', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('E', commutative=True), Integer(2)), Symbol('b', commutative=True))"]}, {"premise_expression": "\\frac{\\log{(s)}}{a}", "variable": "a", "positive": "\\log{(a)} \\log{(s)}", "negatives": ["e^{s} \\log{(a)}", "a \\log{(2 s)}", "\\frac{\\sin{(a)}}{s}", "e^{a - s}"], "srepr_premise_expression": "Mul(Pow(Symbol('a', commutative=True), Integer(-1)), log(Symbol('s', commutative=True)))", "srepr_variable": "Symbol('a', commutative=True)", "srepr_positive": "Mul(log(Symbol('a', commutative=True)), log(Symbol('s', commutative=True)))", "srepr_negatives": ["Mul(exp(Symbol('s', commutative=True)), log(Symbol('a', commutative=True)))", "Mul(Symbol('a', commutative=True), log(Mul(Integer(2), Symbol('s', commutative=True))))", "Mul(Pow(Symbol('s', commutative=True), Integer(-1)), sin(Symbol('a', commutative=True)))", "exp(Add(Symbol('a', commutative=True), Mul(Integer(-1), Symbol('s', commutative=True))))"]}, {"premise_expression": "I \\log{(b)}", "variable": "b", "positive": "I b (\\log{(b)} - 1)", "negatives": ["\\frac{I^{2} \\log{(b)}}{2}", "\\cos{(I - b)}", "I \\sin{(b)}", "\\log{(b)} \\sin{(I)}"], "srepr_premise_expression": "Mul(Symbol('I', commutative=True), log(Symbol('b', commutative=True)))", "srepr_variable": "Symbol('b', commutative=True)", "srepr_positive": "Mul(Symbol('I', commutative=True), Symbol('b', commutative=True), Add(log(Symbol('b', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(2)), log(Symbol('b', commutative=True)))", "cos(Add(Symbol('I', commutative=True), Mul(Integer(-1), Symbol('b', commutative=True))))", "Mul(Symbol('I', commutative=True), sin(Symbol('b', commutative=True)))", "Mul(log(Symbol('b', commutative=True)), sin(Symbol('I', commutative=True)))"]}, {"premise_expression": "\\log{(B - K)}", "variable": "B", "positive": "B \\log{(B - K)} - B - K \\log{(B - K)}", "negatives": ["- B \\log{(- B + K)} + K \\log{(B - K)} - K", "\\log{(B)} \\cos{(K)}", "B (\\log{(\\frac{K}{B})} + 1)", "\\frac{B (B + 2 \\sin{(K)})}{2}"], "srepr_premise_expression": "log(Add(Symbol('B', commutative=True), Mul(Integer(-1), Symbol('K', commutative=True))))", "srepr_variable": "Symbol('B', commutative=True)", "srepr_positive": "Add(Mul(Symbol('B', commutative=True), log(Add(Symbol('B', commutative=True), Mul(Integer(-1), Symbol('K', commutative=True))))), Mul(Integer(-1), Symbol('B', commutative=True)), Mul(Integer(-1), Symbol('K', commutative=True), log(Add(Symbol('B', commutative=True), Mul(Integer(-1), Symbol('K', commutative=True))))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('B', commutative=True), log(Add(Mul(Integer(-1), Symbol('B', commutative=True)), Symbol('K', commutative=True)))), Mul(Symbol('K', commutative=True), log(Add(Symbol('B', commutative=True), Mul(Integer(-1), Symbol('K', commutative=True))))), Mul(Integer(-1), Symbol('K', commutative=True)))", "Mul(log(Symbol('B', commutative=True)), cos(Symbol('K', commutative=True)))", "Mul(Symbol('B', commutative=True), Add(log(Mul(Pow(Symbol('B', commutative=True), Integer(-1)), Symbol('K', commutative=True))), Integer(1)))", "Mul(Rational(1, 2), Symbol('B', commutative=True), Add(Symbol('B', commutative=True), Mul(Integer(2), sin(Symbol('K', commutative=True)))))"]}, {"premise_expression": "P + k", "variable": "k", "positive": "\\frac{k (2 P + k)}{2}", "negatives": ["\\frac{P (P + 2 k)}{2}", "\\cos{(P - k)}", "P \\log{(k)}", "\\frac{k (- k + 2 e^{P})}{2}"], "srepr_premise_expression": "Add(Symbol('P', commutative=True), Symbol('k', commutative=True))", "srepr_variable": "Symbol('k', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('k', commutative=True), Add(Mul(Integer(2), Symbol('P', commutative=True)), Symbol('k', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Symbol('P', commutative=True), Mul(Integer(2), Symbol('k', commutative=True))))", "cos(Add(Symbol('P', commutative=True), Mul(Integer(-1), Symbol('k', commutative=True))))", "Mul(Symbol('P', commutative=True), log(Symbol('k', commutative=True)))", "Mul(Rational(1, 2), Symbol('k', commutative=True), Add(Mul(Integer(-1), Symbol('k', commutative=True)), Mul(Integer(2), exp(Symbol('P', commutative=True)))))"]}, {"premise_expression": "e^{\\frac{o}{m}}", "variable": "o", "positive": "m e^{\\frac{o}{m}}", "negatives": ["o e^{m^{2}}", "\\log{(o)} \\sin{(m)}", "\\frac{o (2 m + o)}{2}", "m e^{\\frac{o}{m}} - o \\operatorname{Ei}{(\\frac{o}{m})}"], "srepr_premise_expression": "exp(Mul(Pow(Symbol('m', commutative=True), Integer(-1)), Symbol('o', commutative=True)))", "srepr_variable": "Symbol('o', commutative=True)", "srepr_positive": "Mul(Symbol('m', commutative=True), exp(Mul(Pow(Symbol('m', commutative=True), Integer(-1)), Symbol('o', commutative=True))))", "srepr_negatives": ["Mul(Symbol('o', commutative=True), exp(Pow(Symbol('m', commutative=True), Integer(2))))", "Mul(log(Symbol('o', commutative=True)), sin(Symbol('m', commutative=True)))", "Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Mul(Integer(2), Symbol('m', commutative=True)), Symbol('o', commutative=True)))", "Add(Mul(Symbol('m', commutative=True), exp(Mul(Pow(Symbol('m', commutative=True), Integer(-1)), Symbol('o', commutative=True)))), Mul(Integer(-1), Symbol('o', commutative=True), Ei(Mul(Pow(Symbol('m', commutative=True), Integer(-1)), Symbol('o', commutative=True)))))"]}, {"premise_expression": "e^{T + Z}", "variable": "T", "positive": "e^{T + Z}", "negatives": ["- e^{- T + Z}", "\\sin{(T - Z)}", "Z e^{\\frac{T}{Z}}", "T^{2} (\\frac{T}{3} + \\frac{Z}{2})"], "srepr_premise_expression": "exp(Add(Symbol('T', commutative=True), Symbol('Z', commutative=True)))", "srepr_variable": "Symbol('T', commutative=True)", "srepr_positive": "exp(Add(Symbol('T', commutative=True), Symbol('Z', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('T', commutative=True)), Symbol('Z', commutative=True))))", "sin(Add(Symbol('T', commutative=True), Mul(Integer(-1), Symbol('Z', commutative=True))))", "Mul(Symbol('Z', commutative=True), exp(Mul(Symbol('T', commutative=True), Pow(Symbol('Z', commutative=True), Integer(-1)))))", "Mul(Pow(Symbol('T', commutative=True), Integer(2)), Add(Mul(Rational(1, 3), Symbol('T', commutative=True)), Mul(Rational(1, 2), Symbol('Z', commutative=True))))"]}, {"premise_expression": "A P", "variable": "A", "positive": "\\frac{A^{2} P}{2}", "negatives": ["\\frac{A P^{2}}{2}", "P e^{\\frac{A}{P}}", "- \\cos{(A + P)}", "\\frac{A (A + 2 \\cos{(P)})}{2}"], "srepr_premise_expression": "Mul(Symbol('A', commutative=True), Symbol('P', commutative=True))", "srepr_variable": "Symbol('A', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2)), Symbol('P', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('A', commutative=True), Pow(Symbol('P', commutative=True), Integer(2)))", "Mul(Symbol('P', commutative=True), exp(Mul(Symbol('A', commutative=True), Pow(Symbol('P', commutative=True), Integer(-1)))))", "Mul(Integer(-1), cos(Add(Symbol('A', commutative=True), Symbol('P', commutative=True))))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Symbol('A', commutative=True), Mul(Integer(2), cos(Symbol('P', commutative=True)))))"]}, {"premise_expression": "S + u", "variable": "u", "positive": "\\frac{u (2 S + u)}{2}", "negatives": ["\\frac{u (2 S - u)}{2}", "\\frac{S (S + 2 u)}{2}", "\\frac{u^{2} \\log{(S)}}{2}", "\\frac{u^{2} \\cos{(S)}}{2}"], "srepr_premise_expression": "Add(Symbol('S', commutative=True), Symbol('u', commutative=True))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(2), Symbol('S', commutative=True)), Symbol('u', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(2), Symbol('S', commutative=True)), Mul(Integer(-1), Symbol('u', commutative=True))))", "Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Symbol('S', commutative=True), Mul(Integer(2), Symbol('u', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('u', commutative=True), Integer(2)), log(Symbol('S', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('u', commutative=True), Integer(2)), cos(Symbol('S', commutative=True)))"]}, {"premise_expression": "\\log{(Q + l)}", "variable": "Q", "positive": "Q \\log{(Q + l)} - Q + l \\log{(Q + l)}", "negatives": ["Q \\log{(Q + l)} + l \\log{(Q + l)} - l", "\\frac{Q (- Q + 2 \\log{(l)})}{2}", "Q (\\log{(\\frac{l}{Q})} + 1)", "Q l + \\sin{(Q)}"], "srepr_premise_expression": "log(Add(Symbol('Q', commutative=True), Symbol('l', commutative=True)))", "srepr_variable": "Symbol('Q', commutative=True)", "srepr_positive": "Add(Mul(Symbol('Q', commutative=True), log(Add(Symbol('Q', commutative=True), Symbol('l', commutative=True)))), Mul(Integer(-1), Symbol('Q', commutative=True)), Mul(Symbol('l', commutative=True), log(Add(Symbol('Q', commutative=True), Symbol('l', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('Q', commutative=True), log(Add(Symbol('Q', commutative=True), Symbol('l', commutative=True)))), Mul(Symbol('l', commutative=True), log(Add(Symbol('Q', commutative=True), Symbol('l', commutative=True)))), Mul(Integer(-1), Symbol('l', commutative=True)))", "Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Mul(Integer(-1), Symbol('Q', commutative=True)), Mul(Integer(2), log(Symbol('l', commutative=True)))))", "Mul(Symbol('Q', commutative=True), Add(log(Mul(Pow(Symbol('Q', commutative=True), Integer(-1)), Symbol('l', commutative=True))), Integer(1)))", "Add(Mul(Symbol('Q', commutative=True), Symbol('l', commutative=True)), sin(Symbol('Q', commutative=True)))"]}, {"premise_expression": "I + \\frac{M}{k}", "variable": "k", "positive": "I k + M \\log{(k)}", "negatives": ["(- I + M) \\log{(k)}", "I M + \\frac{M^{2}}{2 k}", "- M k + \\frac{k^{2}}{2 I}", "\\frac{I^{2}}{2} + \\frac{I M}{k}"], "srepr_premise_expression": "Add(Symbol('I', commutative=True), Mul(Symbol('M', commutative=True), Pow(Symbol('k', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('k', commutative=True)", "srepr_positive": "Add(Mul(Symbol('I', commutative=True), Symbol('k', commutative=True)), Mul(Symbol('M', commutative=True), log(Symbol('k', commutative=True))))", "srepr_negatives": ["Mul(Add(Mul(Integer(-1), Symbol('I', commutative=True)), Symbol('M', commutative=True)), log(Symbol('k', commutative=True)))", "Add(Mul(Symbol('I', commutative=True), Symbol('M', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('M', commutative=True), Integer(2)), Pow(Symbol('k', commutative=True), Integer(-1))))", "Add(Mul(Integer(-1), Symbol('M', commutative=True), Symbol('k', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(-1)), Pow(Symbol('k', commutative=True), Integer(2))))", "Add(Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(2))), Mul(Symbol('I', commutative=True), Symbol('M', commutative=True), Pow(Symbol('k', commutative=True), Integer(-1))))"]}, {"premise_expression": "\\frac{Y}{C}", "variable": "C", "positive": "Y \\log{(C)}", "negatives": ["\\frac{Y^{2}}{2 C}", "- \\frac{\\cos{(C)}}{Y}", "\\frac{C^{2}}{2 Y}", "C Y (\\log{(C)} - 1)"], "srepr_premise_expression": "Mul(Pow(Symbol('C', commutative=True), Integer(-1)), Symbol('Y', commutative=True))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Mul(Symbol('Y', commutative=True), log(Symbol('C', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(-1)), Pow(Symbol('Y', commutative=True), Integer(2)))", "Mul(Integer(-1), Pow(Symbol('Y', commutative=True), Integer(-1)), cos(Symbol('C', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2)), Pow(Symbol('Y', commutative=True), Integer(-1)))", "Mul(Symbol('C', commutative=True), Symbol('Y', commutative=True), Add(log(Symbol('C', commutative=True)), Integer(-1)))"]}, {"premise_expression": "A + B", "variable": "B", "positive": "\\frac{B (2 A + B)}{2}", "negatives": ["\\frac{A (A + 2 B)}{2}", "e^{- A + B}", "\\sin{(A + B)}", "- \\sin{(A - B)}"], "srepr_premise_expression": "Add(Symbol('A', commutative=True), Symbol('B', commutative=True))", "srepr_variable": "Symbol('B', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('B', commutative=True), Add(Mul(Integer(2), Symbol('A', commutative=True)), Symbol('B', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Symbol('A', commutative=True), Mul(Integer(2), Symbol('B', commutative=True))))", "exp(Add(Mul(Integer(-1), Symbol('A', commutative=True)), Symbol('B', commutative=True)))", "sin(Add(Symbol('A', commutative=True), Symbol('B', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('B', commutative=True)))))"]}, {"premise_expression": "\\frac{I}{c}", "variable": "c", "positive": "I \\log{(c)}", "negatives": ["\\frac{I^{2}}{2 c}", "I e^{\\frac{c}{I}}", "I c + e^{c}", "\\frac{c^{2} \\log{(I)}}{2}"], "srepr_premise_expression": "Mul(Symbol('I', commutative=True), Pow(Symbol('c', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('c', commutative=True)", "srepr_positive": "Mul(Symbol('I', commutative=True), log(Symbol('c', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(2)), Pow(Symbol('c', commutative=True), Integer(-1)))", "Mul(Symbol('I', commutative=True), exp(Mul(Pow(Symbol('I', commutative=True), Integer(-1)), Symbol('c', commutative=True))))", "Add(Mul(Symbol('I', commutative=True), Symbol('c', commutative=True)), exp(Symbol('c', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('c', commutative=True), Integer(2)), log(Symbol('I', commutative=True)))"]}, {"premise_expression": "\\frac{\\cos{(b)}}{h}", "variable": "b", "positive": "\\frac{\\sin{(b)}}{h}", "negatives": ["h e^{\\frac{b}{h}}", "- \\cos{(b + h)}", "\\frac{b^{2} \\log{(h)}}{2}", "\\log{(h)} \\cos{(b)}"], "srepr_premise_expression": "Mul(Pow(Symbol('h', commutative=True), Integer(-1)), cos(Symbol('b', commutative=True)))", "srepr_variable": "Symbol('b', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('h', commutative=True), Integer(-1)), sin(Symbol('b', commutative=True)))", "srepr_negatives": ["Mul(Symbol('h', commutative=True), exp(Mul(Symbol('b', commutative=True), Pow(Symbol('h', commutative=True), Integer(-1)))))", "Mul(Integer(-1), cos(Add(Symbol('b', commutative=True), Symbol('h', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('b', commutative=True), Integer(2)), log(Symbol('h', commutative=True)))", "Mul(log(Symbol('h', commutative=True)), cos(Symbol('b', commutative=True)))"]}, {"premise_expression": "A - a + v", "variable": "v", "positive": "v (A - a + \\frac{v}{2})", "negatives": ["\\frac{A (A - 2 a + 2 v)}{2}", "\\frac{a (2 A - a + 2 v)}{2}", "\\frac{v (2 A a - v)}{2}", "\\frac{v (2 a^{A} - v)}{2}"], "srepr_premise_expression": "Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('a', commutative=True)), Symbol('v', commutative=True))", "srepr_variable": "Symbol('v', commutative=True)", "srepr_positive": "Mul(Symbol('v', commutative=True), Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('a', commutative=True)), Mul(Rational(1, 2), Symbol('v', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Symbol('A', commutative=True), Mul(Integer(-1), Integer(2), Symbol('a', commutative=True)), Mul(Integer(2), Symbol('v', commutative=True))))", "Mul(Rational(1, 2), Symbol('a', commutative=True), Add(Mul(Integer(2), Symbol('A', commutative=True)), Mul(Integer(-1), Symbol('a', commutative=True)), Mul(Integer(2), Symbol('v', commutative=True))))", "Mul(Rational(1, 2), Symbol('v', commutative=True), Add(Mul(Integer(2), Symbol('A', commutative=True), Symbol('a', commutative=True)), Mul(Integer(-1), Symbol('v', commutative=True))))", "Mul(Rational(1, 2), Symbol('v', commutative=True), Add(Mul(Integer(2), Pow(Symbol('a', commutative=True), Symbol('A', commutative=True))), Mul(Integer(-1), Symbol('v', commutative=True))))"]}, {"premise_expression": "e^{G^{M}}", "variable": "G", "positive": "\\frac{e^{- \\frac{i \\pi}{M}} \\gamma(\\frac{1}{M}, G^{M} e^{i \\pi})}{M}", "negatives": ["\\int (G + M)^{G} dG", "G (\\log{(G M)} - 1)", "\\frac{G (\\log{(G)} - 1)}{M}", "G (- M + \\log{(G)} - 1)"], "srepr_premise_expression": "exp(Pow(Symbol('G', commutative=True), Symbol('M', commutative=True)))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('M', commutative=True), Integer(-1)), exp(Mul(Integer(-1), I, pi, Pow(Symbol('M', commutative=True), Integer(-1)))), lowergamma(Pow(Symbol('M', commutative=True), Integer(-1)), Mul(Pow(Symbol('G', commutative=True), Symbol('M', commutative=True)), exp_polar(Mul(I, pi)))))", "srepr_negatives": ["NonElementaryIntegral(Pow(Add(Symbol('G', commutative=True), Symbol('M', commutative=True)), Symbol('G', commutative=True)), Tuple(Symbol('G', commutative=True)))", "Mul(Symbol('G', commutative=True), Add(log(Mul(Symbol('G', commutative=True), Symbol('M', commutative=True))), Integer(-1)))", "Mul(Symbol('G', commutative=True), Pow(Symbol('M', commutative=True), Integer(-1)), Add(log(Symbol('G', commutative=True)), Integer(-1)))", "Mul(Symbol('G', commutative=True), Add(Mul(Integer(-1), Symbol('M', commutative=True)), log(Symbol('G', commutative=True)), Integer(-1)))"]}, {"premise_expression": "- m + y", "variable": "m", "positive": "\\frac{m (- m + 2 y)}{2}", "negatives": ["\\frac{y (- 2 m + y)}{2}", "\\frac{m (m + 2 \\log{(y)})}{2}", "m y + \\sin{(m)}", "m y + e^{m}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('m', commutative=True)), Symbol('y', commutative=True))", "srepr_variable": "Symbol('m', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Mul(Integer(-1), Symbol('m', commutative=True)), Mul(Integer(2), Symbol('y', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('y', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('m', commutative=True)), Symbol('y', commutative=True)))", "Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Symbol('m', commutative=True), Mul(Integer(2), log(Symbol('y', commutative=True)))))", "Add(Mul(Symbol('m', commutative=True), Symbol('y', commutative=True)), sin(Symbol('m', commutative=True)))", "Add(Mul(Symbol('m', commutative=True), Symbol('y', commutative=True)), exp(Symbol('m', commutative=True)))"]}, {"premise_expression": "P u", "variable": "P", "positive": "\\frac{P^{2} u}{2}", "negatives": ["\\frac{P u^{2}}{2}", "\\frac{P^{2} e^{u}}{2}", "u \\sin{(P)}", "u e^{\\frac{P}{u}}"], "srepr_premise_expression": "Mul(Symbol('P', commutative=True), Symbol('u', commutative=True))", "srepr_variable": "Symbol('P', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2)), Symbol('u', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('P', commutative=True), Pow(Symbol('u', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2)), exp(Symbol('u', commutative=True)))", "Mul(Symbol('u', commutative=True), sin(Symbol('P', commutative=True)))", "Mul(Symbol('u', commutative=True), exp(Mul(Symbol('P', commutative=True), Pow(Symbol('u', commutative=True), Integer(-1)))))"]}, {"premise_expression": "\\frac{\\log{(I)}}{V}", "variable": "I", "positive": "\\frac{I (\\log{(I)} - 1)}{V}", "negatives": ["\\log{(I)} \\log{(V)}", "\\frac{I (I + 2 V)}{2}", "e^{I - V}", "I V + e^{I}"], "srepr_premise_expression": "Mul(Pow(Symbol('V', commutative=True), Integer(-1)), log(Symbol('I', commutative=True)))", "srepr_variable": "Symbol('I', commutative=True)", "srepr_positive": "Mul(Symbol('I', commutative=True), Pow(Symbol('V', commutative=True), Integer(-1)), Add(log(Symbol('I', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(log(Symbol('I', commutative=True)), log(Symbol('V', commutative=True)))", "Mul(Rational(1, 2), Symbol('I', commutative=True), Add(Symbol('I', commutative=True), Mul(Integer(2), Symbol('V', commutative=True))))", "exp(Add(Symbol('I', commutative=True), Mul(Integer(-1), Symbol('V', commutative=True))))", "Add(Mul(Symbol('I', commutative=True), Symbol('V', commutative=True)), exp(Symbol('I', commutative=True)))"]}, {"premise_expression": "h - q", "variable": "q", "positive": "\\frac{q (2 h - q)}{2}", "negatives": ["\\frac{h (h - 2 q)}{2}", "\\frac{q (\\log{(q)} - 1)}{h}", "\\frac{h q^{2}}{2}", "h e^{q}"], "srepr_premise_expression": "Add(Symbol('h', commutative=True), Mul(Integer(-1), Symbol('q', commutative=True)))", "srepr_variable": "Symbol('q', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('q', commutative=True), Add(Mul(Integer(2), Symbol('h', commutative=True)), Mul(Integer(-1), Symbol('q', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('h', commutative=True), Add(Symbol('h', commutative=True), Mul(Integer(-1), Integer(2), Symbol('q', commutative=True))))", "Mul(Pow(Symbol('h', commutative=True), Integer(-1)), Symbol('q', commutative=True), Add(log(Symbol('q', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('h', commutative=True), Pow(Symbol('q', commutative=True), Integer(2)))", "Mul(Symbol('h', commutative=True), exp(Symbol('q', commutative=True)))"]}, {"premise_expression": "- \\sin{(S - W)}", "variable": "W", "positive": "- \\cos{(S - W)}", "negatives": ["\\cos{(S - W)}", "e^{S + W}", "- \\frac{\\cos{(W)}}{S}", "- S W - \\cos{(W)}"], "srepr_premise_expression": "Mul(Integer(-1), sin(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('W', commutative=True)))))", "srepr_variable": "Symbol('W', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('W', commutative=True)))))", "srepr_negatives": ["cos(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('W', commutative=True))))", "exp(Add(Symbol('S', commutative=True), Symbol('W', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('S', commutative=True), Integer(-1)), cos(Symbol('W', commutative=True)))", "Add(Mul(Integer(-1), Symbol('S', commutative=True), Symbol('W', commutative=True)), Mul(Integer(-1), cos(Symbol('W', commutative=True))))"]}, {"premise_expression": "\\frac{c}{f}", "variable": "c", "positive": "\\frac{c^{2}}{2 f}", "negatives": ["c \\log{(f)}", "f \\sin{(c)}", "- \\cos{(c - f)}", "\\log{(c)} \\sin{(f)}"], "srepr_premise_expression": "Mul(Symbol('c', commutative=True), Pow(Symbol('f', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('c', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('c', commutative=True), Integer(2)), Pow(Symbol('f', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('c', commutative=True), log(Symbol('f', commutative=True)))", "Mul(Symbol('f', commutative=True), sin(Symbol('c', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('c', commutative=True), Mul(Integer(-1), Symbol('f', commutative=True)))))", "Mul(log(Symbol('c', commutative=True)), sin(Symbol('f', commutative=True)))"]}, {"premise_expression": "j (N + R)", "variable": "R", "positive": "\\frac{R j (2 N + R)}{2}", "negatives": ["\\frac{j^{2} (N + R)}{2}", "\\frac{N j (N + 2 R)}{2}", "\\frac{R (- 2 N + R j)}{2}", "\\frac{R (N R + 2 j)}{2}"], "srepr_premise_expression": "Mul(Symbol('j', commutative=True), Add(Symbol('N', commutative=True), Symbol('R', commutative=True)))", "srepr_variable": "Symbol('R', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('R', commutative=True), Symbol('j', commutative=True), Add(Mul(Integer(2), Symbol('N', commutative=True)), Symbol('R', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('j', commutative=True), Integer(2)), Add(Symbol('N', commutative=True), Symbol('R', commutative=True)))", "Mul(Rational(1, 2), Symbol('N', commutative=True), Symbol('j', commutative=True), Add(Symbol('N', commutative=True), Mul(Integer(2), Symbol('R', commutative=True))))", "Mul(Rational(1, 2), Symbol('R', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('N', commutative=True)), Mul(Symbol('R', commutative=True), Symbol('j', commutative=True))))", "Mul(Rational(1, 2), Symbol('R', commutative=True), Add(Mul(Symbol('N', commutative=True), Symbol('R', commutative=True)), Mul(Integer(2), Symbol('j', commutative=True))))"]}, {"premise_expression": "\\frac{A}{h} + J", "variable": "J", "positive": "\\frac{A J}{h} + \\frac{J^{2}}{2}", "negatives": ["\\frac{A J (J + 2 h)}{2}", "\\frac{A J^{2} h}{2}", "A \\log{(h)} + J h", "\\frac{A^{2}}{2 h} + A J"], "srepr_premise_expression": "Add(Mul(Symbol('A', commutative=True), Pow(Symbol('h', commutative=True), Integer(-1))), Symbol('J', commutative=True))", "srepr_variable": "Symbol('J', commutative=True)", "srepr_positive": "Add(Mul(Symbol('A', commutative=True), Symbol('J', commutative=True), Pow(Symbol('h', commutative=True), Integer(-1))), Mul(Rational(1, 2), Pow(Symbol('J', commutative=True), Integer(2))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('A', commutative=True), Symbol('J', commutative=True), Add(Symbol('J', commutative=True), Mul(Integer(2), Symbol('h', commutative=True))))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Pow(Symbol('J', commutative=True), Integer(2)), Symbol('h', commutative=True))", "Add(Mul(Symbol('A', commutative=True), log(Symbol('h', commutative=True))), Mul(Symbol('J', commutative=True), Symbol('h', commutative=True)))", "Add(Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2)), Pow(Symbol('h', commutative=True), Integer(-1))), Mul(Symbol('A', commutative=True), Symbol('J', commutative=True)))"]}, {"premise_expression": "- t + \\cos{(x)}", "variable": "x", "positive": "- t x + \\sin{(x)}", "negatives": ["- \\sin{(t - x)}", "- \\cos{(t - x)}", "e^{t + x}", "\\frac{t (- t + 2 \\cos{(x)})}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('t', commutative=True)), cos(Symbol('x', commutative=True)))", "srepr_variable": "Symbol('x', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('t', commutative=True), Symbol('x', commutative=True)), sin(Symbol('x', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('t', commutative=True), Mul(Integer(-1), Symbol('x', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('t', commutative=True), Mul(Integer(-1), Symbol('x', commutative=True)))))", "exp(Add(Symbol('t', commutative=True), Symbol('x', commutative=True)))", "Mul(Rational(1, 2), Symbol('t', commutative=True), Add(Mul(Integer(-1), Symbol('t', commutative=True)), Mul(Integer(2), cos(Symbol('x', commutative=True)))))"]}, {"premise_expression": "- a + p", "variable": "a", "positive": "\\frac{a (- a + 2 p)}{2}", "negatives": ["\\frac{a (a - 2 p)}{2}", "\\frac{p (- 2 a + p)}{2}", "\\frac{a (- a + 2 \\sin{(p)})}{2}", "a p + e^{a}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('a', commutative=True)), Symbol('p', commutative=True))", "srepr_variable": "Symbol('a', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('a', commutative=True), Add(Mul(Integer(-1), Symbol('a', commutative=True)), Mul(Integer(2), Symbol('p', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('a', commutative=True), Add(Symbol('a', commutative=True), Mul(Integer(-1), Integer(2), Symbol('p', commutative=True))))", "Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('a', commutative=True)), Symbol('p', commutative=True)))", "Mul(Rational(1, 2), Symbol('a', commutative=True), Add(Mul(Integer(-1), Symbol('a', commutative=True)), Mul(Integer(2), sin(Symbol('p', commutative=True)))))", "Add(Mul(Symbol('a', commutative=True), Symbol('p', commutative=True)), exp(Symbol('a', commutative=True)))"]}, {"premise_expression": "Q \\log{(B)}", "variable": "Q", "positive": "\\frac{Q^{2} \\log{(B)}}{2}", "negatives": ["\\frac{Q (Q + 2 \\log{(B)})}{2}", "\\frac{Q (2 B + Q)}{2}", "B Q (\\log{(B)} - 1)", "\\frac{Q (- Q + 2 \\cos{(B)})}{2}"], "srepr_premise_expression": "Mul(Symbol('Q', commutative=True), log(Symbol('B', commutative=True)))", "srepr_variable": "Symbol('Q', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(2)), log(Symbol('B', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Symbol('Q', commutative=True), Mul(Integer(2), log(Symbol('B', commutative=True)))))", "Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Mul(Integer(2), Symbol('B', commutative=True)), Symbol('Q', commutative=True)))", "Mul(Symbol('B', commutative=True), Symbol('Q', commutative=True), Add(log(Symbol('B', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Mul(Integer(-1), Symbol('Q', commutative=True)), Mul(Integer(2), cos(Symbol('B', commutative=True)))))"]}, {"premise_expression": "G + \\log{(H)}", "variable": "G", "positive": "\\frac{G (G + 2 \\log{(H)})}{2}", "negatives": ["\\frac{G (G - 2 H)}{2}", "H (G + \\log{(H)} - 1)", "G (- H + \\log{(G)} - 1)", "\\frac{G^{2} H}{2}"], "srepr_premise_expression": "Add(Symbol('G', commutative=True), log(Symbol('H', commutative=True)))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Symbol('G', commutative=True), Mul(Integer(2), log(Symbol('H', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Symbol('G', commutative=True), Mul(Integer(-1), Integer(2), Symbol('H', commutative=True))))", "Mul(Symbol('H', commutative=True), Add(Symbol('G', commutative=True), log(Symbol('H', commutative=True)), Integer(-1)))", "Mul(Symbol('G', commutative=True), Add(Mul(Integer(-1), Symbol('H', commutative=True)), log(Symbol('G', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(2)), Symbol('H', commutative=True))"]}, {"premise_expression": "\\cos^{w}{(Z)}", "variable": "Z", "positive": "\\int \\cos^{w}{(Z)} dZ", "negatives": ["\\frac{\\sin{(Z)}}{w}", "\\sin{(Z - w)}", "\\frac{Z (Z - 2 w)}{2}", "- Z w + e^{Z}"], "srepr_premise_expression": "Pow(cos(Symbol('Z', commutative=True)), Symbol('w', commutative=True))", "srepr_variable": "Symbol('Z', commutative=True)", "srepr_positive": "Integral(Pow(cos(Symbol('Z', commutative=True)), Symbol('w', commutative=True)), Tuple(Symbol('Z', commutative=True)))", "srepr_negatives": ["Mul(Pow(Symbol('w', commutative=True), Integer(-1)), sin(Symbol('Z', commutative=True)))", "sin(Add(Symbol('Z', commutative=True), Mul(Integer(-1), Symbol('w', commutative=True))))", "Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Symbol('Z', commutative=True), Mul(Integer(-1), Integer(2), Symbol('w', commutative=True))))", "Add(Mul(Integer(-1), Symbol('Z', commutative=True), Symbol('w', commutative=True)), exp(Symbol('Z', commutative=True)))"]}, {"premise_expression": "\\frac{M + u}{V}", "variable": "M", "positive": "\\frac{M (M + 2 u)}{2 V}", "negatives": ["\\frac{M (- M + 2 u)}{2 V}", "\\frac{u (2 M + u)}{2 V}", "\\frac{M (M u - 2 V)}{2}", "(M + u) \\log{(V)}"], "srepr_premise_expression": "Mul(Pow(Symbol('V', commutative=True), Integer(-1)), Add(Symbol('M', commutative=True), Symbol('u', commutative=True)))", "srepr_variable": "Symbol('M', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('M', commutative=True), Pow(Symbol('V', commutative=True), Integer(-1)), Add(Symbol('M', commutative=True), Mul(Integer(2), Symbol('u', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('M', commutative=True), Pow(Symbol('V', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('M', commutative=True)), Mul(Integer(2), Symbol('u', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('V', commutative=True), Integer(-1)), Symbol('u', commutative=True), Add(Mul(Integer(2), Symbol('M', commutative=True)), Symbol('u', commutative=True)))", "Mul(Rational(1, 2), Symbol('M', commutative=True), Add(Mul(Symbol('M', commutative=True), Symbol('u', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('V', commutative=True))))", "Mul(Add(Symbol('M', commutative=True), Symbol('u', commutative=True)), log(Symbol('V', commutative=True)))"]}, {"premise_expression": "\\frac{m}{G}", "variable": "G", "positive": "m \\log{(G)}", "negatives": ["\\frac{m^{2}}{2 G}", "- \\frac{\\cos{(G)}}{m}", "\\frac{G^{2} \\log{(m)}}{2}", "\\log{(G)} \\sin{(m)}"], "srepr_premise_expression": "Mul(Pow(Symbol('G', commutative=True), Integer(-1)), Symbol('m', commutative=True))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Mul(Symbol('m', commutative=True), log(Symbol('G', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(-1)), Pow(Symbol('m', commutative=True), Integer(2)))", "Mul(Integer(-1), Pow(Symbol('m', commutative=True), Integer(-1)), cos(Symbol('G', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(2)), log(Symbol('m', commutative=True)))", "Mul(log(Symbol('G', commutative=True)), sin(Symbol('m', commutative=True)))"]}, {"premise_expression": "x + e^{V}", "variable": "x", "positive": "\\frac{x (x + 2 e^{V})}{2}", "negatives": ["\\frac{x^{2} e^{V}}{2}", "V x + e^{V}", "\\frac{x^{2} \\cos{(V)}}{2}", "- V x + \\sin{(x)}"], "srepr_premise_expression": "Add(Symbol('x', commutative=True), exp(Symbol('V', commutative=True)))", "srepr_variable": "Symbol('x', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('x', commutative=True), Add(Symbol('x', commutative=True), Mul(Integer(2), exp(Symbol('V', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('x', commutative=True), Integer(2)), exp(Symbol('V', commutative=True)))", "Add(Mul(Symbol('V', commutative=True), Symbol('x', commutative=True)), exp(Symbol('V', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('x', commutative=True), Integer(2)), cos(Symbol('V', commutative=True)))", "Add(Mul(Integer(-1), Symbol('V', commutative=True), Symbol('x', commutative=True)), sin(Symbol('x', commutative=True)))"]}, {"premise_expression": "\\log{(\\frac{w}{t})}", "variable": "w", "positive": "w (\\log{(\\frac{w}{t})} - 1)", "negatives": ["t (\\log{(\\frac{w}{t})} + 1)", "\\frac{w^{2} \\log{(t)}}{2}", "- e^{t - w}", "\\frac{w (- 2 t + w)}{2}"], "srepr_premise_expression": "log(Mul(Pow(Symbol('t', commutative=True), Integer(-1)), Symbol('w', commutative=True)))", "srepr_variable": "Symbol('w', commutative=True)", "srepr_positive": "Mul(Symbol('w', commutative=True), Add(log(Mul(Pow(Symbol('t', commutative=True), Integer(-1)), Symbol('w', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('t', commutative=True), Add(log(Mul(Pow(Symbol('t', commutative=True), Integer(-1)), Symbol('w', commutative=True))), Integer(1)))", "Mul(Rational(1, 2), Pow(Symbol('w', commutative=True), Integer(2)), log(Symbol('t', commutative=True)))", "Mul(Integer(-1), exp(Add(Symbol('t', commutative=True), Mul(Integer(-1), Symbol('w', commutative=True)))))", "Mul(Rational(1, 2), Symbol('w', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('t', commutative=True)), Symbol('w', commutative=True)))"]}, {"premise_expression": "- g + r", "variable": "r", "positive": "\\frac{r (- 2 g + r)}{2}", "negatives": ["\\frac{g (- g + 2 r)}{2}", "- g r + e^{r}", "r (\\log{(\\frac{r}{g})} - 1)", "- g r + \\sin{(r)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('g', commutative=True)), Symbol('r', commutative=True))", "srepr_variable": "Symbol('r', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('g', commutative=True)), Symbol('r', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Mul(Integer(-1), Symbol('g', commutative=True)), Mul(Integer(2), Symbol('r', commutative=True))))", "Add(Mul(Integer(-1), Symbol('g', commutative=True), Symbol('r', commutative=True)), exp(Symbol('r', commutative=True)))", "Mul(Symbol('r', commutative=True), Add(log(Mul(Pow(Symbol('g', commutative=True), Integer(-1)), Symbol('r', commutative=True))), Integer(-1)))", "Add(Mul(Integer(-1), Symbol('g', commutative=True), Symbol('r', commutative=True)), sin(Symbol('r', commutative=True)))"]}, {"premise_expression": "M + \\frac{a}{p}", "variable": "a", "positive": "M a + \\frac{a^{2}}{2 p}", "negatives": ["M p + a \\log{(p)}", "\\frac{a (2 M + a - 2 p)}{2}", "\\frac{a^{2} p}{2 M}", "\\frac{M a^{2} p}{2}"], "srepr_premise_expression": "Add(Symbol('M', commutative=True), Mul(Symbol('a', commutative=True), Pow(Symbol('p', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('a', commutative=True)", "srepr_positive": "Add(Mul(Symbol('M', commutative=True), Symbol('a', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('a', commutative=True), Integer(2)), Pow(Symbol('p', commutative=True), Integer(-1))))", "srepr_negatives": ["Add(Mul(Symbol('M', commutative=True), Symbol('p', commutative=True)), Mul(Symbol('a', commutative=True), log(Symbol('p', commutative=True))))", "Mul(Rational(1, 2), Symbol('a', commutative=True), Add(Mul(Integer(2), Symbol('M', commutative=True)), Symbol('a', commutative=True), Mul(Integer(-1), Integer(2), Symbol('p', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('M', commutative=True), Integer(-1)), Pow(Symbol('a', commutative=True), Integer(2)), Symbol('p', commutative=True))", "Mul(Rational(1, 2), Symbol('M', commutative=True), Pow(Symbol('a', commutative=True), Integer(2)), Symbol('p', commutative=True))"]}, {"premise_expression": "\\frac{c}{h}", "variable": "h", "positive": "c \\log{(h)}", "negatives": ["\\frac{c^{2}}{2 h}", "- \\sin{(c - h)}", "h (\\log{(\\frac{h}{c})} - 1)", "\\frac{h (2 c - h)}{2}"], "srepr_premise_expression": "Mul(Symbol('c', commutative=True), Pow(Symbol('h', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('h', commutative=True)", "srepr_positive": "Mul(Symbol('c', commutative=True), log(Symbol('h', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('c', commutative=True), Integer(2)), Pow(Symbol('h', commutative=True), Integer(-1)))", "Mul(Integer(-1), sin(Add(Symbol('c', commutative=True), Mul(Integer(-1), Symbol('h', commutative=True)))))", "Mul(Symbol('h', commutative=True), Add(log(Mul(Pow(Symbol('c', commutative=True), Integer(-1)), Symbol('h', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('h', commutative=True), Add(Mul(Integer(2), Symbol('c', commutative=True)), Mul(Integer(-1), Symbol('h', commutative=True))))"]}, {"premise_expression": "\\cos{(w^{A})}", "variable": "w", "positive": "w {{}_{1}F_{2}(\\begin{matrix} \\frac{1}{2 A} \\ \\frac{1}{2}, 1 + \\frac{1}{2 A} \\end{matrix}\\middle| {- \\frac{w^{2 A}}{4}})}", "negatives": ["w (- A + \\log{(w^{A})})", "\\frac{w (w + 2 \\cos{(A)})}{2}", "\\frac{w (2 A - w)}{2}", "w (\\log{(A w)} - 1)"], "srepr_premise_expression": "cos(Pow(Symbol('w', commutative=True), Symbol('A', commutative=True)))", "srepr_variable": "Symbol('w', commutative=True)", "srepr_positive": "Mul(Symbol('w', commutative=True), hyper(TupleArg(Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(-1)))), TupleArg(Rational(1, 2), Add(Integer(1), Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(-1))))), Mul(Integer(-1), Rational(1, 4), Pow(Symbol('w', commutative=True), Mul(Integer(2), Symbol('A', commutative=True))))))", "srepr_negatives": ["Mul(Symbol('w', commutative=True), Add(Mul(Integer(-1), Symbol('A', commutative=True)), log(Pow(Symbol('w', commutative=True), Symbol('A', commutative=True)))))", "Mul(Rational(1, 2), Symbol('w', commutative=True), Add(Symbol('w', commutative=True), Mul(Integer(2), cos(Symbol('A', commutative=True)))))", "Mul(Rational(1, 2), Symbol('w', commutative=True), Add(Mul(Integer(2), Symbol('A', commutative=True)), Mul(Integer(-1), Symbol('w', commutative=True))))", "Mul(Symbol('w', commutative=True), Add(log(Mul(Symbol('A', commutative=True), Symbol('w', commutative=True))), Integer(-1)))"]}, {"premise_expression": "- E + n", "variable": "E", "positive": "\\frac{E (- E + 2 n)}{2}", "negatives": ["\\frac{E (E + 2 n)}{2}", "\\frac{n (- 2 E + n)}{2}", "\\frac{E (E + 2 \\cos{(n)})}{2}", "\\frac{E^{2}}{2 n}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('E', commutative=True)), Symbol('n', commutative=True))", "srepr_variable": "Symbol('E', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('E', commutative=True), Add(Mul(Integer(-1), Symbol('E', commutative=True)), Mul(Integer(2), Symbol('n', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('E', commutative=True), Add(Symbol('E', commutative=True), Mul(Integer(2), Symbol('n', commutative=True))))", "Mul(Rational(1, 2), Symbol('n', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('E', commutative=True)), Symbol('n', commutative=True)))", "Mul(Rational(1, 2), Symbol('E', commutative=True), Add(Symbol('E', commutative=True), Mul(Integer(2), cos(Symbol('n', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('E', commutative=True), Integer(2)), Pow(Symbol('n', commutative=True), Integer(-1)))"]}, {"premise_expression": "- F + e^{R}", "variable": "F", "positive": "\\frac{F (- F + 2 e^{R})}{2}", "negatives": ["\\frac{F (F + 2 e^{R})}{2}", "\\frac{F (F + 2 \\sin{(R)})}{2}", "- F R + e^{R}", "R e^{F}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('F', commutative=True)), exp(Symbol('R', commutative=True)))", "srepr_variable": "Symbol('F', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Mul(Integer(-1), Symbol('F', commutative=True)), Mul(Integer(2), exp(Symbol('R', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Symbol('F', commutative=True), Mul(Integer(2), exp(Symbol('R', commutative=True)))))", "Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Symbol('F', commutative=True), Mul(Integer(2), sin(Symbol('R', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('F', commutative=True), Symbol('R', commutative=True)), exp(Symbol('R', commutative=True)))", "Mul(Symbol('R', commutative=True), exp(Symbol('F', commutative=True)))"]}, {"premise_expression": "S + r", "variable": "S", "positive": "\\frac{S (S + 2 r)}{2}", "negatives": ["\\frac{S (- S + 2 r)}{2}", "\\frac{r (2 S + r)}{2}", "\\frac{S (S + 2 \\cos{(r)})}{2}", "\\frac{S^{2} \\cos{(r)}}{2}"], "srepr_premise_expression": "Add(Symbol('S', commutative=True), Symbol('r', commutative=True))", "srepr_variable": "Symbol('S', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Symbol('S', commutative=True), Mul(Integer(2), Symbol('r', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Mul(Integer(-1), Symbol('S', commutative=True)), Mul(Integer(2), Symbol('r', commutative=True))))", "Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(2), Symbol('S', commutative=True)), Symbol('r', commutative=True)))", "Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Symbol('S', commutative=True), Mul(Integer(2), cos(Symbol('r', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('S', commutative=True), Integer(2)), cos(Symbol('r', commutative=True)))"]}, {"premise_expression": "\\sin^{C}{(m)}", "variable": "m", "positive": "\\int \\sin^{C}{(m)} dm", "negatives": ["- \\sin{(C - m)}", "- C m + \\sin{(m)}", "m (- C + \\log{(m^{C})})", "m (\\log{(C m)} - 1)"], "srepr_premise_expression": "Pow(sin(Symbol('m', commutative=True)), Symbol('C', commutative=True))", "srepr_variable": "Symbol('m', commutative=True)", "srepr_positive": "Integral(Pow(sin(Symbol('m', commutative=True)), Symbol('C', commutative=True)), Tuple(Symbol('m', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('m', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('C', commutative=True), Symbol('m', commutative=True)), sin(Symbol('m', commutative=True)))", "Mul(Symbol('m', commutative=True), Add(Mul(Integer(-1), Symbol('C', commutative=True)), log(Pow(Symbol('m', commutative=True), Symbol('C', commutative=True)))))", "Mul(Symbol('m', commutative=True), Add(log(Mul(Symbol('C', commutative=True), Symbol('m', commutative=True))), Integer(-1)))"]}, {"premise_expression": "H + Y", "variable": "Y", "positive": "\\frac{Y (2 H + Y)}{2}", "negatives": ["\\frac{H (H + 2 Y)}{2}", "\\frac{Y^{2} \\log{(H)}}{2}", "- H \\cos{(Y)}", "\\frac{\\sin{(Y)}}{H}"], "srepr_premise_expression": "Add(Symbol('H', commutative=True), Symbol('Y', commutative=True))", "srepr_variable": "Symbol('Y', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('Y', commutative=True), Add(Mul(Integer(2), Symbol('H', commutative=True)), Symbol('Y', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('H', commutative=True), Add(Symbol('H', commutative=True), Mul(Integer(2), Symbol('Y', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('Y', commutative=True), Integer(2)), log(Symbol('H', commutative=True)))", "Mul(Integer(-1), Symbol('H', commutative=True), cos(Symbol('Y', commutative=True)))", "Mul(Pow(Symbol('H', commutative=True), Integer(-1)), sin(Symbol('Y', commutative=True)))"]}, {"premise_expression": "T Z + c", "variable": "c", "positive": "\\frac{c (2 T Z + c)}{2}", "negatives": ["\\frac{T (T Z + 2 c)}{2}", "\\frac{Z (T Z + 2 c)}{2}", "\\frac{c (2 Z + c)}{2 T}", "\\frac{c (2 T - 2 Z + c)}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('T', commutative=True), Symbol('Z', commutative=True)), Symbol('c', commutative=True))", "srepr_variable": "Symbol('c', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('c', commutative=True), Add(Mul(Integer(2), Symbol('T', commutative=True), Symbol('Z', commutative=True)), Symbol('c', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('T', commutative=True), Add(Mul(Symbol('T', commutative=True), Symbol('Z', commutative=True)), Mul(Integer(2), Symbol('c', commutative=True))))", "Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Mul(Symbol('T', commutative=True), Symbol('Z', commutative=True)), Mul(Integer(2), Symbol('c', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('T', commutative=True), Integer(-1)), Symbol('c', commutative=True), Add(Mul(Integer(2), Symbol('Z', commutative=True)), Symbol('c', commutative=True)))", "Mul(Rational(1, 2), Symbol('c', commutative=True), Add(Mul(Integer(2), Symbol('T', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('Z', commutative=True)), Symbol('c', commutative=True)))"]}, {"premise_expression": "- L + \\sin{(v)}", "variable": "v", "positive": "- L v - \\cos{(v)}", "negatives": ["- \\frac{\\cos{(v)}}{L}", "- \\sin{(L - v)}", "\\frac{L (- L + 2 \\sin{(v)})}{2}", "\\frac{v (- 2 L + v)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('L', commutative=True)), sin(Symbol('v', commutative=True)))", "srepr_variable": "Symbol('v', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('L', commutative=True), Symbol('v', commutative=True)), Mul(Integer(-1), cos(Symbol('v', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), Pow(Symbol('L', commutative=True), Integer(-1)), cos(Symbol('v', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('L', commutative=True), Mul(Integer(-1), Symbol('v', commutative=True)))))", "Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Mul(Integer(-1), Symbol('L', commutative=True)), Mul(Integer(2), sin(Symbol('v', commutative=True)))))", "Mul(Rational(1, 2), Symbol('v', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('L', commutative=True)), Symbol('v', commutative=True)))"]}, {"premise_expression": "U + n", "variable": "U", "positive": "\\frac{U (U + 2 n)}{2}", "negatives": ["\\frac{n (2 U + n)}{2}", "\\frac{U (U + 2 \\cos{(n)})}{2}", "- U n + \\sin{(U)}", "- \\frac{\\cos{(U)}}{n}"], "srepr_premise_expression": "Add(Symbol('U', commutative=True), Symbol('n', commutative=True))", "srepr_variable": "Symbol('U', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('U', commutative=True), Add(Symbol('U', commutative=True), Mul(Integer(2), Symbol('n', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('n', commutative=True), Add(Mul(Integer(2), Symbol('U', commutative=True)), Symbol('n', commutative=True)))", "Mul(Rational(1, 2), Symbol('U', commutative=True), Add(Symbol('U', commutative=True), Mul(Integer(2), cos(Symbol('n', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('U', commutative=True), Symbol('n', commutative=True)), sin(Symbol('U', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('n', commutative=True), Integer(-1)), cos(Symbol('U', commutative=True)))"]}, {"premise_expression": "- w + \\cos{(M)}", "variable": "w", "positive": "\\frac{w (- w + 2 \\cos{(M)})}{2}", "negatives": ["\\frac{w^{2} \\log{(M)}}{2}", "\\frac{w^{2} e^{M}}{2}", "- M w + \\sin{(M)}", "\\cos{(M - w)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('w', commutative=True)), cos(Symbol('M', commutative=True)))", "srepr_variable": "Symbol('w', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('w', commutative=True), Add(Mul(Integer(-1), Symbol('w', commutative=True)), Mul(Integer(2), cos(Symbol('M', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('w', commutative=True), Integer(2)), log(Symbol('M', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('w', commutative=True), Integer(2)), exp(Symbol('M', commutative=True)))", "Add(Mul(Integer(-1), Symbol('M', commutative=True), Symbol('w', commutative=True)), sin(Symbol('M', commutative=True)))", "cos(Add(Symbol('M', commutative=True), Mul(Integer(-1), Symbol('w', commutative=True))))"]}, {"premise_expression": "e^{- m + w}", "variable": "m", "positive": "- e^{- m + w}", "negatives": ["e^{- m + w}", "- \\cos{(m + w)}", "\\frac{m (m - 2 w)}{2}", "m w (\\log{(m)} - 1)"], "srepr_premise_expression": "exp(Add(Mul(Integer(-1), Symbol('m', commutative=True)), Symbol('w', commutative=True)))", "srepr_variable": "Symbol('m', commutative=True)", "srepr_positive": "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('m', commutative=True)), Symbol('w', commutative=True))))", "srepr_negatives": ["exp(Add(Mul(Integer(-1), Symbol('m', commutative=True)), Symbol('w', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('m', commutative=True), Symbol('w', commutative=True))))", "Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Symbol('m', commutative=True), Mul(Integer(-1), Integer(2), Symbol('w', commutative=True))))", "Mul(Symbol('m', commutative=True), Symbol('w', commutative=True), Add(log(Symbol('m', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\frac{G}{P} + t", "variable": "P", "positive": "G \\log{(P)} + P t", "negatives": ["\\frac{G^{2}}{2 P} + G t", "t^{G} \\log{(P)}", "\\frac{G t}{P} + \\frac{t^{2}}{2}", "\\frac{P (2 G + P t)}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('G', commutative=True), Pow(Symbol('P', commutative=True), Integer(-1))), Symbol('t', commutative=True))", "srepr_variable": "Symbol('P', commutative=True)", "srepr_positive": "Add(Mul(Symbol('G', commutative=True), log(Symbol('P', commutative=True))), Mul(Symbol('P', commutative=True), Symbol('t', commutative=True)))", "srepr_negatives": ["Add(Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(2)), Pow(Symbol('P', commutative=True), Integer(-1))), Mul(Symbol('G', commutative=True), Symbol('t', commutative=True)))", "Mul(Pow(Symbol('t', commutative=True), Symbol('G', commutative=True)), log(Symbol('P', commutative=True)))", "Add(Mul(Symbol('G', commutative=True), Pow(Symbol('P', commutative=True), Integer(-1)), Symbol('t', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('t', commutative=True), Integer(2))))", "Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Mul(Integer(2), Symbol('G', commutative=True)), Mul(Symbol('P', commutative=True), Symbol('t', commutative=True))))"]}, {"premise_expression": "e^{A + v}", "variable": "v", "positive": "e^{A + v}", "negatives": ["A v - \\cos{(v)}", "v (\\log{(\\frac{v}{A})} - 1)", "\\log{(v)} \\cos{(A)}", "\\frac{v^{2} \\sin{(A)}}{2}"], "srepr_premise_expression": "exp(Add(Symbol('A', commutative=True), Symbol('v', commutative=True)))", "srepr_variable": "Symbol('v', commutative=True)", "srepr_positive": "exp(Add(Symbol('A', commutative=True), Symbol('v', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('A', commutative=True), Symbol('v', commutative=True)), Mul(Integer(-1), cos(Symbol('v', commutative=True))))", "Mul(Symbol('v', commutative=True), Add(log(Mul(Pow(Symbol('A', commutative=True), Integer(-1)), Symbol('v', commutative=True))), Integer(-1)))", "Mul(log(Symbol('v', commutative=True)), cos(Symbol('A', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('v', commutative=True), Integer(2)), sin(Symbol('A', commutative=True)))"]}, {"premise_expression": "\\frac{C}{J}", "variable": "J", "positive": "C \\log{(J)}", "negatives": ["\\frac{C^{2}}{2 J}", "- \\cos{(C + J)}", "\\sin{(C + J)}", "J (\\log{(\\frac{J}{C})} - 1)"], "srepr_premise_expression": "Mul(Symbol('C', commutative=True), Pow(Symbol('J', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('J', commutative=True)", "srepr_positive": "Mul(Symbol('C', commutative=True), log(Symbol('J', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2)), Pow(Symbol('J', commutative=True), Integer(-1)))", "Mul(Integer(-1), cos(Add(Symbol('C', commutative=True), Symbol('J', commutative=True))))", "sin(Add(Symbol('C', commutative=True), Symbol('J', commutative=True)))", "Mul(Symbol('J', commutative=True), Add(log(Mul(Pow(Symbol('C', commutative=True), Integer(-1)), Symbol('J', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\cos{(Y - q)}", "variable": "Y", "positive": "\\sin{(Y - q)}", "negatives": ["- \\sin{(Y - q)}", "\\sin{(Y + q)}", "e^{Y - q}", "q \\log{(Y)}"], "srepr_premise_expression": "cos(Add(Symbol('Y', commutative=True), Mul(Integer(-1), Symbol('q', commutative=True))))", "srepr_variable": "Symbol('Y', commutative=True)", "srepr_positive": "sin(Add(Symbol('Y', commutative=True), Mul(Integer(-1), Symbol('q', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('Y', commutative=True), Mul(Integer(-1), Symbol('q', commutative=True)))))", "sin(Add(Symbol('Y', commutative=True), Symbol('q', commutative=True)))", "exp(Add(Symbol('Y', commutative=True), Mul(Integer(-1), Symbol('q', commutative=True))))", "Mul(Symbol('q', commutative=True), log(Symbol('Y', commutative=True)))"]}, {"premise_expression": "H \\sin{(V)}", "variable": "V", "positive": "- H \\cos{(V)}", "negatives": ["H \\log{(V)}", "H V - \\cos{(V)}", "- H V + \\sin{(V)}", "\\frac{H^{2} \\sin{(V)}}{2}"], "srepr_premise_expression": "Mul(Symbol('H', commutative=True), sin(Symbol('V', commutative=True)))", "srepr_variable": "Symbol('V', commutative=True)", "srepr_positive": "Mul(Integer(-1), Symbol('H', commutative=True), cos(Symbol('V', commutative=True)))", "srepr_negatives": ["Mul(Symbol('H', commutative=True), log(Symbol('V', commutative=True)))", "Add(Mul(Symbol('H', commutative=True), Symbol('V', commutative=True)), Mul(Integer(-1), cos(Symbol('V', commutative=True))))", "Add(Mul(Integer(-1), Symbol('H', commutative=True), Symbol('V', commutative=True)), sin(Symbol('V', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('H', commutative=True), Integer(2)), sin(Symbol('V', commutative=True)))"]}, {"premise_expression": "\\frac{N}{j s}", "variable": "N", "positive": "\\frac{N^{2}}{2 j s}", "negatives": ["\\frac{N^{2} s}{2 j}", "\\frac{N^{2} j}{2 s}", "\\frac{N (N + 2 j s)}{2}", "\\frac{N \\log{(j)}}{s}"], "srepr_premise_expression": "Mul(Symbol('N', commutative=True), Pow(Symbol('j', commutative=True), Integer(-1)), Pow(Symbol('s', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('N', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('N', commutative=True), Integer(2)), Pow(Symbol('j', commutative=True), Integer(-1)), Pow(Symbol('s', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('N', commutative=True), Integer(2)), Pow(Symbol('j', commutative=True), Integer(-1)), Symbol('s', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('N', commutative=True), Integer(2)), Symbol('j', commutative=True), Pow(Symbol('s', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Symbol('N', commutative=True), Mul(Integer(2), Symbol('j', commutative=True), Symbol('s', commutative=True))))", "Mul(Symbol('N', commutative=True), Pow(Symbol('s', commutative=True), Integer(-1)), log(Symbol('j', commutative=True)))"]}, {"premise_expression": "\\cos{(Q + x)}", "variable": "x", "positive": "\\sin{(Q + x)}", "negatives": ["- \\sin{(Q - x)}", "- e^{Q - x}", "Q \\sin{(x)}", "x \\sin{(x)} + \\cos{(x)}"], "srepr_premise_expression": "cos(Add(Symbol('Q', commutative=True), Symbol('x', commutative=True)))", "srepr_variable": "Symbol('x', commutative=True)", "srepr_positive": "sin(Add(Symbol('Q', commutative=True), Symbol('x', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('Q', commutative=True), Mul(Integer(-1), Symbol('x', commutative=True)))))", "Mul(Integer(-1), exp(Add(Symbol('Q', commutative=True), Mul(Integer(-1), Symbol('x', commutative=True)))))", "Mul(Symbol('Q', commutative=True), sin(Symbol('x', commutative=True)))", "Add(Mul(Symbol('x', commutative=True), sin(Symbol('x', commutative=True))), cos(Symbol('x', commutative=True)))"]}, {"premise_expression": "- H + N X", "variable": "X", "positive": "\\frac{X (- 2 H + N X)}{2}", "negatives": ["\\frac{N (- 2 H + N X)}{2}", "\\frac{H (- H + 2 N X)}{2}", "\\frac{X (- 2 H + 2 N - X)}{2}", "\\frac{X (2 H + 2 N + X)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('H', commutative=True)), Mul(Symbol('N', commutative=True), Symbol('X', commutative=True)))", "srepr_variable": "Symbol('X', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('X', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('H', commutative=True)), Mul(Symbol('N', commutative=True), Symbol('X', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('H', commutative=True)), Mul(Symbol('N', commutative=True), Symbol('X', commutative=True))))", "Mul(Rational(1, 2), Symbol('H', commutative=True), Add(Mul(Integer(-1), Symbol('H', commutative=True)), Mul(Integer(2), Symbol('N', commutative=True), Symbol('X', commutative=True))))", "Mul(Rational(1, 2), Symbol('X', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('H', commutative=True)), Mul(Integer(2), Symbol('N', commutative=True)), Mul(Integer(-1), Symbol('X', commutative=True))))", "Mul(Rational(1, 2), Symbol('X', commutative=True), Add(Mul(Integer(2), Symbol('H', commutative=True)), Mul(Integer(2), Symbol('N', commutative=True)), Symbol('X', commutative=True)))"]}, {"premise_expression": "\\frac{V Y}{v}", "variable": "V", "positive": "\\frac{V^{2} Y}{2 v}", "negatives": ["\\frac{V Y^{2}}{2 v}", "\\frac{V^{2} Y v}{2}", "V Y \\log{(v)}", "\\frac{V (V + 2 v)}{2 Y}"], "srepr_premise_expression": "Mul(Symbol('V', commutative=True), Symbol('Y', commutative=True), Pow(Symbol('v', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('V', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('V', commutative=True), Integer(2)), Symbol('Y', commutative=True), Pow(Symbol('v', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('V', commutative=True), Pow(Symbol('Y', commutative=True), Integer(2)), Pow(Symbol('v', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('V', commutative=True), Integer(2)), Symbol('Y', commutative=True), Symbol('v', commutative=True))", "Mul(Symbol('V', commutative=True), Symbol('Y', commutative=True), log(Symbol('v', commutative=True)))", "Mul(Rational(1, 2), Symbol('V', commutative=True), Pow(Symbol('Y', commutative=True), Integer(-1)), Add(Symbol('V', commutative=True), Mul(Integer(2), Symbol('v', commutative=True))))"]}, {"premise_expression": "A + b", "variable": "b", "positive": "\\frac{b (2 A + b)}{2}", "negatives": ["\\frac{A (A + 2 b)}{2}", "\\sin{(A + b)}", "A \\log{(b)}", "A e^{b}"], "srepr_premise_expression": "Add(Symbol('A', commutative=True), Symbol('b', commutative=True))", "srepr_variable": "Symbol('b', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('b', commutative=True), Add(Mul(Integer(2), Symbol('A', commutative=True)), Symbol('b', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Symbol('A', commutative=True), Mul(Integer(2), Symbol('b', commutative=True))))", "sin(Add(Symbol('A', commutative=True), Symbol('b', commutative=True)))", "Mul(Symbol('A', commutative=True), log(Symbol('b', commutative=True)))", "Mul(Symbol('A', commutative=True), exp(Symbol('b', commutative=True)))"]}, {"premise_expression": "\\sin{(U + u)}", "variable": "u", "positive": "- \\cos{(U + u)}", "negatives": ["- U \\cos{(u)}", "\\frac{u (2 U + u)}{2}", "U \\log{(u)}", "- U u - \\cos{(u)}"], "srepr_premise_expression": "sin(Add(Symbol('U', commutative=True), Symbol('u', commutative=True)))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('U', commutative=True), Symbol('u', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), Symbol('U', commutative=True), cos(Symbol('u', commutative=True)))", "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(2), Symbol('U', commutative=True)), Symbol('u', commutative=True)))", "Mul(Symbol('U', commutative=True), log(Symbol('u', commutative=True)))", "Add(Mul(Integer(-1), Symbol('U', commutative=True), Symbol('u', commutative=True)), Mul(Integer(-1), cos(Symbol('u', commutative=True))))"]}, {"premise_expression": "Z f", "variable": "Z", "positive": "\\frac{Z^{2} f}{2}", "negatives": ["\\frac{Z f^{2}}{2}", "\\frac{Z^{2} \\sin{(f)}}{2}", "\\cos{(Z - f)}", "\\frac{Z (- Z + 2 \\sin{(f)})}{2}"], "srepr_premise_expression": "Mul(Symbol('Z', commutative=True), Symbol('f', commutative=True))", "srepr_variable": "Symbol('Z', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('Z', commutative=True), Integer(2)), Symbol('f', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('Z', commutative=True), Pow(Symbol('f', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('Z', commutative=True), Integer(2)), sin(Symbol('f', commutative=True)))", "cos(Add(Symbol('Z', commutative=True), Mul(Integer(-1), Symbol('f', commutative=True))))", "Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Mul(Integer(-1), Symbol('Z', commutative=True)), Mul(Integer(2), sin(Symbol('f', commutative=True)))))"]}, {"premise_expression": "\\frac{I}{L f}", "variable": "I", "positive": "\\frac{I^{2}}{2 L f}", "negatives": ["\\frac{I^{2} L f}{2}", "\\frac{I^{2}}{2} + \\frac{I f}{L}", "\\frac{I \\log{(L)}}{f}", "\\frac{I \\log{(f)}}{L}"], "srepr_premise_expression": "Mul(Symbol('I', commutative=True), Pow(Symbol('L', commutative=True), Integer(-1)), Pow(Symbol('f', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('I', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(2)), Pow(Symbol('L', commutative=True), Integer(-1)), Pow(Symbol('f', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(2)), Symbol('L', commutative=True), Symbol('f', commutative=True))", "Add(Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(2))), Mul(Symbol('I', commutative=True), Pow(Symbol('L', commutative=True), Integer(-1)), Symbol('f', commutative=True)))", "Mul(Symbol('I', commutative=True), Pow(Symbol('f', commutative=True), Integer(-1)), log(Symbol('L', commutative=True)))", "Mul(Symbol('I', commutative=True), Pow(Symbol('L', commutative=True), Integer(-1)), log(Symbol('f', commutative=True)))"]}, {"premise_expression": "\\sin{(f + z)}", "variable": "f", "positive": "- \\cos{(f + z)}", "negatives": ["\\sin{(f + z)}", "\\frac{f e^{z}}{z}", "f z (\\log{(f)} - 1)", "f (\\log{(\\frac{f}{z})} - 1)"], "srepr_premise_expression": "sin(Add(Symbol('f', commutative=True), Symbol('z', commutative=True)))", "srepr_variable": "Symbol('f', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('f', commutative=True), Symbol('z', commutative=True))))", "srepr_negatives": ["sin(Add(Symbol('f', commutative=True), Symbol('z', commutative=True)))", "Mul(Symbol('f', commutative=True), Pow(Symbol('z', commutative=True), Integer(-1)), exp(Symbol('z', commutative=True)))", "Mul(Symbol('f', commutative=True), Symbol('z', commutative=True), Add(log(Symbol('f', commutative=True)), Integer(-1)))", "Mul(Symbol('f', commutative=True), Add(log(Mul(Symbol('f', commutative=True), Pow(Symbol('z', commutative=True), Integer(-1)))), Integer(-1)))"]}, {"premise_expression": "\\frac{G}{b}", "variable": "G", "positive": "\\frac{G^{2}}{2 b}", "negatives": ["G \\log{(b)}", "\\frac{G (G - 2 b)}{2}", "\\sin{(G + b)}", "\\frac{\\sin{(G)}}{b}"], "srepr_premise_expression": "Mul(Symbol('G', commutative=True), Pow(Symbol('b', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(2)), Pow(Symbol('b', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('G', commutative=True), log(Symbol('b', commutative=True)))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Symbol('G', commutative=True), Mul(Integer(-1), Integer(2), Symbol('b', commutative=True))))", "sin(Add(Symbol('G', commutative=True), Symbol('b', commutative=True)))", "Mul(Pow(Symbol('b', commutative=True), Integer(-1)), sin(Symbol('G', commutative=True)))"]}, {"premise_expression": "p + e^{C}", "variable": "C", "positive": "C p + e^{C}", "negatives": ["\\frac{p (p + 2 e^{C})}{2}", "\\frac{C^{2} e^{p}}{2}", "C \\log{(2 p)}", "\\frac{C^{2} \\sin{(p)}}{2}"], "srepr_premise_expression": "Add(Symbol('p', commutative=True), exp(Symbol('C', commutative=True)))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Add(Mul(Symbol('C', commutative=True), Symbol('p', commutative=True)), exp(Symbol('C', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Symbol('p', commutative=True), Mul(Integer(2), exp(Symbol('C', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2)), exp(Symbol('p', commutative=True)))", "Mul(Symbol('C', commutative=True), log(Mul(Integer(2), Symbol('p', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2)), sin(Symbol('p', commutative=True)))"]}, {"premise_expression": "T (n - q)", "variable": "n", "positive": "\\frac{T n (n - 2 q)}{2}", "negatives": ["\\frac{T^{2} (n - q)}{2}", "\\frac{T q (2 n - q)}{2}", "\\frac{T n^{2} q}{2}", "\\frac{n^{2} (T + q)}{2}"], "srepr_premise_expression": "Mul(Symbol('T', commutative=True), Add(Symbol('n', commutative=True), Mul(Integer(-1), Symbol('q', commutative=True))))", "srepr_variable": "Symbol('n', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('T', commutative=True), Symbol('n', commutative=True), Add(Symbol('n', commutative=True), Mul(Integer(-1), Integer(2), Symbol('q', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('T', commutative=True), Integer(2)), Add(Symbol('n', commutative=True), Mul(Integer(-1), Symbol('q', commutative=True))))", "Mul(Rational(1, 2), Symbol('T', commutative=True), Symbol('q', commutative=True), Add(Mul(Integer(2), Symbol('n', commutative=True)), Mul(Integer(-1), Symbol('q', commutative=True))))", "Mul(Rational(1, 2), Symbol('T', commutative=True), Pow(Symbol('n', commutative=True), Integer(2)), Symbol('q', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('n', commutative=True), Integer(2)), Add(Symbol('T', commutative=True), Symbol('q', commutative=True)))"]}, {"premise_expression": "G - R", "variable": "G", "positive": "\\frac{G (G - 2 R)}{2}", "negatives": ["\\frac{R (2 G - R)}{2}", "\\frac{G (G + 2 \\cos{(R)})}{2}", "\\frac{G^{2}}{2 R}", "G R + e^{G}"], "srepr_premise_expression": "Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('R', commutative=True)))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Symbol('G', commutative=True), Mul(Integer(-1), Integer(2), Symbol('R', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('R', commutative=True), Add(Mul(Integer(2), Symbol('G', commutative=True)), Mul(Integer(-1), Symbol('R', commutative=True))))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Symbol('G', commutative=True), Mul(Integer(2), cos(Symbol('R', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(2)), Pow(Symbol('R', commutative=True), Integer(-1)))", "Add(Mul(Symbol('G', commutative=True), Symbol('R', commutative=True)), exp(Symbol('G', commutative=True)))"]}, {"premise_expression": "\\log{(t^{C})}", "variable": "t", "positive": "t (- C + \\log{(t^{C})})", "negatives": ["t (- C + \\log{(t)} - 1)", "\\frac{t (- t + 2 \\log{(C)})}{2}", "C t - \\cos{(t)}", "\\frac{t (t + 2 \\cos{(C)})}{2}"], "srepr_premise_expression": "log(Pow(Symbol('t', commutative=True), Symbol('C', commutative=True)))", "srepr_variable": "Symbol('t', commutative=True)", "srepr_positive": "Mul(Symbol('t', commutative=True), Add(Mul(Integer(-1), Symbol('C', commutative=True)), log(Pow(Symbol('t', commutative=True), Symbol('C', commutative=True)))))", "srepr_negatives": ["Mul(Symbol('t', commutative=True), Add(Mul(Integer(-1), Symbol('C', commutative=True)), log(Symbol('t', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('t', commutative=True), Add(Mul(Integer(-1), Symbol('t', commutative=True)), Mul(Integer(2), log(Symbol('C', commutative=True)))))", "Add(Mul(Symbol('C', commutative=True), Symbol('t', commutative=True)), Mul(Integer(-1), cos(Symbol('t', commutative=True))))", "Mul(Rational(1, 2), Symbol('t', commutative=True), Add(Symbol('t', commutative=True), Mul(Integer(2), cos(Symbol('C', commutative=True)))))"]}, {"premise_expression": "U \\log{(y)}", "variable": "y", "positive": "U y (\\log{(y)} - 1)", "negatives": ["y (\\log{(U y)} - 1)", "\\frac{U^{2} \\log{(y)}}{2}", "- \\cos{(U - y)}", "U e^{\\frac{y}{U}}"], "srepr_premise_expression": "Mul(Symbol('U', commutative=True), log(Symbol('y', commutative=True)))", "srepr_variable": "Symbol('y', commutative=True)", "srepr_positive": "Mul(Symbol('U', commutative=True), Symbol('y', commutative=True), Add(log(Symbol('y', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('y', commutative=True), Add(log(Mul(Symbol('U', commutative=True), Symbol('y', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('U', commutative=True), Integer(2)), log(Symbol('y', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('U', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True)))))", "Mul(Symbol('U', commutative=True), exp(Mul(Pow(Symbol('U', commutative=True), Integer(-1)), Symbol('y', commutative=True))))"]}, {"premise_expression": "S s", "variable": "s", "positive": "\\frac{S s^{2}}{2}", "negatives": ["\\frac{S^{2} s}{2}", "S e^{\\frac{s}{S}}", "\\frac{s (- 2 S + s)}{2}", "- S s + e^{s}"], "srepr_premise_expression": "Mul(Symbol('S', commutative=True), Symbol('s', commutative=True))", "srepr_variable": "Symbol('s', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('S', commutative=True), Pow(Symbol('s', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('S', commutative=True), Integer(2)), Symbol('s', commutative=True))", "Mul(Symbol('S', commutative=True), exp(Mul(Pow(Symbol('S', commutative=True), Integer(-1)), Symbol('s', commutative=True))))", "Mul(Rational(1, 2), Symbol('s', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('S', commutative=True)), Symbol('s', commutative=True)))", "Add(Mul(Integer(-1), Symbol('S', commutative=True), Symbol('s', commutative=True)), exp(Symbol('s', commutative=True)))"]}, {"premise_expression": "R p", "variable": "R", "positive": "\\frac{R^{2} p}{2}", "negatives": ["\\frac{R p^{2}}{2}", "\\frac{R (- R + 2 p)}{2}", "p \\log{(R)}", "e^{R + p}"], "srepr_premise_expression": "Mul(Symbol('R', commutative=True), Symbol('p', commutative=True))", "srepr_variable": "Symbol('R', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('R', commutative=True), Integer(2)), Symbol('p', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('R', commutative=True), Pow(Symbol('p', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('R', commutative=True), Add(Mul(Integer(-1), Symbol('R', commutative=True)), Mul(Integer(2), Symbol('p', commutative=True))))", "Mul(Symbol('p', commutative=True), log(Symbol('R', commutative=True)))", "exp(Add(Symbol('R', commutative=True), Symbol('p', commutative=True)))"]}, {"premise_expression": "\\cos{(A - f)}", "variable": "A", "positive": "\\sin{(A - f)}", "negatives": ["- \\sin{(A - f)}", "- e^{- A + f}", "A f (\\log{(A)} - 1)", "A (\\log{(A f)} - 1)"], "srepr_premise_expression": "cos(Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('f', commutative=True))))", "srepr_variable": "Symbol('A', commutative=True)", "srepr_positive": "sin(Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('f', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('f', commutative=True)))))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('A', commutative=True)), Symbol('f', commutative=True))))", "Mul(Symbol('A', commutative=True), Symbol('f', commutative=True), Add(log(Symbol('A', commutative=True)), Integer(-1)))", "Mul(Symbol('A', commutative=True), Add(log(Mul(Symbol('A', commutative=True), Symbol('f', commutative=True))), Integer(-1)))"]}, {"premise_expression": "S + l", "variable": "S", "positive": "\\frac{S (S + 2 l)}{2}", "negatives": ["\\frac{S (S - 2 l)}{2}", "\\frac{l (2 S + l)}{2}", "\\frac{S (S + 2 \\cos{(l)})}{2}", "\\frac{S (- S + 2 \\log{(l)})}{2}"], "srepr_premise_expression": "Add(Symbol('S', commutative=True), Symbol('l', commutative=True))", "srepr_variable": "Symbol('S', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Symbol('S', commutative=True), Mul(Integer(2), Symbol('l', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Symbol('S', commutative=True), Mul(Integer(-1), Integer(2), Symbol('l', commutative=True))))", "Mul(Rational(1, 2), Symbol('l', commutative=True), Add(Mul(Integer(2), Symbol('S', commutative=True)), Symbol('l', commutative=True)))", "Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Symbol('S', commutative=True), Mul(Integer(2), cos(Symbol('l', commutative=True)))))", "Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Mul(Integer(-1), Symbol('S', commutative=True)), Mul(Integer(2), log(Symbol('l', commutative=True)))))"]}, {"premise_expression": "\\frac{a}{Q}", "variable": "Q", "positive": "a \\log{(Q)}", "negatives": ["- a \\cos{(Q)}", "\\frac{a^{2}}{2 Q}", "\\frac{Q^{2} a}{2}", "- Q a - \\cos{(Q)}"], "srepr_premise_expression": "Mul(Pow(Symbol('Q', commutative=True), Integer(-1)), Symbol('a', commutative=True))", "srepr_variable": "Symbol('Q', commutative=True)", "srepr_positive": "Mul(Symbol('a', commutative=True), log(Symbol('Q', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Symbol('a', commutative=True), cos(Symbol('Q', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(-1)), Pow(Symbol('a', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(2)), Symbol('a', commutative=True))", "Add(Mul(Integer(-1), Symbol('Q', commutative=True), Symbol('a', commutative=True)), Mul(Integer(-1), cos(Symbol('Q', commutative=True))))"]}, {"premise_expression": "\\frac{F g}{f}", "variable": "g", "positive": "\\frac{F g^{2}}{2 f}", "negatives": ["\\frac{F^{2} g}{2 f}", "F g \\log{(f)}", "\\frac{g (2 F - g)}{2 f}", "\\frac{g (F g + 2 f)}{2}"], "srepr_premise_expression": "Mul(Symbol('F', commutative=True), Pow(Symbol('f', commutative=True), Integer(-1)), Symbol('g', commutative=True))", "srepr_variable": "Symbol('g', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('F', commutative=True), Pow(Symbol('f', commutative=True), Integer(-1)), Pow(Symbol('g', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('F', commutative=True), Integer(2)), Pow(Symbol('f', commutative=True), Integer(-1)), Symbol('g', commutative=True))", "Mul(Symbol('F', commutative=True), Symbol('g', commutative=True), log(Symbol('f', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('f', commutative=True), Integer(-1)), Symbol('g', commutative=True), Add(Mul(Integer(2), Symbol('F', commutative=True)), Mul(Integer(-1), Symbol('g', commutative=True))))", "Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Mul(Symbol('F', commutative=True), Symbol('g', commutative=True)), Mul(Integer(2), Symbol('f', commutative=True))))"]}, {"premise_expression": "- K + e^{B}", "variable": "K", "positive": "\\frac{K (- K + 2 e^{B})}{2}", "negatives": ["\\frac{K (K + 2 e^{B})}{2}", "- B K + e^{B}", "\\frac{K^{2} \\sin{(B)}}{2}", "- B K + \\sin{(K)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('K', commutative=True)), exp(Symbol('B', commutative=True)))", "srepr_variable": "Symbol('K', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Mul(Integer(-1), Symbol('K', commutative=True)), Mul(Integer(2), exp(Symbol('B', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Symbol('K', commutative=True), Mul(Integer(2), exp(Symbol('B', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('B', commutative=True), Symbol('K', commutative=True)), exp(Symbol('B', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('K', commutative=True), Integer(2)), sin(Symbol('B', commutative=True)))", "Add(Mul(Integer(-1), Symbol('B', commutative=True), Symbol('K', commutative=True)), sin(Symbol('K', commutative=True)))"]}, {"premise_expression": "P - S + T", "variable": "P", "positive": "P (\\frac{P}{2} - S + T)", "negatives": ["\\frac{T (2 P - 2 S + T)}{2}", "\\frac{S (2 P - S + 2 T)}{2}", "\\frac{P (P T - 2 S)}{2}", "\\frac{P (P + 2 S)}{2 T}"], "srepr_premise_expression": "Add(Symbol('P', commutative=True), Mul(Integer(-1), Symbol('S', commutative=True)), Symbol('T', commutative=True))", "srepr_variable": "Symbol('P', commutative=True)", "srepr_positive": "Mul(Symbol('P', commutative=True), Add(Mul(Rational(1, 2), Symbol('P', commutative=True)), Mul(Integer(-1), Symbol('S', commutative=True)), Symbol('T', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('T', commutative=True), Add(Mul(Integer(2), Symbol('P', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('S', commutative=True)), Symbol('T', commutative=True)))", "Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Mul(Integer(2), Symbol('P', commutative=True)), Mul(Integer(-1), Symbol('S', commutative=True)), Mul(Integer(2), Symbol('T', commutative=True))))", "Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Mul(Symbol('P', commutative=True), Symbol('T', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('S', commutative=True))))", "Mul(Rational(1, 2), Symbol('P', commutative=True), Pow(Symbol('T', commutative=True), Integer(-1)), Add(Symbol('P', commutative=True), Mul(Integer(2), Symbol('S', commutative=True))))"]}, {"premise_expression": "(\\frac{F}{Z})^{F}", "variable": "F", "positive": "\\int (\\frac{F}{Z})^{F} dF", "negatives": ["F (\\log{(F Z)} - 1)", "\\sin{(F - Z)}", "- \\cos{(F - Z)}", "- F Z - \\cos{(F)}"], "srepr_premise_expression": "Pow(Mul(Symbol('F', commutative=True), Pow(Symbol('Z', commutative=True), Integer(-1))), Symbol('F', commutative=True))", "srepr_variable": "Symbol('F', commutative=True)", "srepr_positive": "NonElementaryIntegral(Pow(Mul(Symbol('F', commutative=True), Pow(Symbol('Z', commutative=True), Integer(-1))), Symbol('F', commutative=True)), Tuple(Symbol('F', commutative=True)))", "srepr_negatives": ["Mul(Symbol('F', commutative=True), Add(log(Mul(Symbol('F', commutative=True), Symbol('Z', commutative=True))), Integer(-1)))", "sin(Add(Symbol('F', commutative=True), Mul(Integer(-1), Symbol('Z', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('F', commutative=True), Mul(Integer(-1), Symbol('Z', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('F', commutative=True), Symbol('Z', commutative=True)), Mul(Integer(-1), cos(Symbol('F', commutative=True))))"]}, {"premise_expression": "D + h", "variable": "h", "positive": "\\frac{h (2 D + h)}{2}", "negatives": ["\\frac{D (D + 2 h)}{2}", "- e^{D - h}", "\\frac{h (\\log{(h)} - 1)}{D}", "\\frac{h^{2}}{2 D}"], "srepr_premise_expression": "Add(Symbol('D', commutative=True), Symbol('h', commutative=True))", "srepr_variable": "Symbol('h', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('h', commutative=True), Add(Mul(Integer(2), Symbol('D', commutative=True)), Symbol('h', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('D', commutative=True), Add(Symbol('D', commutative=True), Mul(Integer(2), Symbol('h', commutative=True))))", "Mul(Integer(-1), exp(Add(Symbol('D', commutative=True), Mul(Integer(-1), Symbol('h', commutative=True)))))", "Mul(Pow(Symbol('D', commutative=True), Integer(-1)), Symbol('h', commutative=True), Add(log(Symbol('h', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(-1)), Pow(Symbol('h', commutative=True), Integer(2)))"]}, {"premise_expression": "- H + \\frac{a}{s}", "variable": "H", "positive": "- \\frac{H^{2}}{2} + \\frac{H a}{s}", "negatives": ["\\frac{H (H + 2 a + 2 s)}{2}", "\\frac{H a (H + 2 s)}{2}", "- H s + a \\log{(s)}", "\\frac{H (- H + 2 a s)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('H', commutative=True)), Mul(Symbol('a', commutative=True), Pow(Symbol('s', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('H', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('H', commutative=True), Integer(2))), Mul(Symbol('H', commutative=True), Symbol('a', commutative=True), Pow(Symbol('s', commutative=True), Integer(-1))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('H', commutative=True), Add(Symbol('H', commutative=True), Mul(Integer(2), Symbol('a', commutative=True)), Mul(Integer(2), Symbol('s', commutative=True))))", "Mul(Rational(1, 2), Symbol('H', commutative=True), Symbol('a', commutative=True), Add(Symbol('H', commutative=True), Mul(Integer(2), Symbol('s', commutative=True))))", "Add(Mul(Integer(-1), Symbol('H', commutative=True), Symbol('s', commutative=True)), Mul(Symbol('a', commutative=True), log(Symbol('s', commutative=True))))", "Mul(Rational(1, 2), Symbol('H', commutative=True), Add(Mul(Integer(-1), Symbol('H', commutative=True)), Mul(Integer(2), Symbol('a', commutative=True), Symbol('s', commutative=True))))"]}, {"premise_expression": "C - V - t", "variable": "t", "positive": "t (C - V - \\frac{t}{2})", "negatives": ["\\frac{t (- 2 C + 2 V + t)}{2}", "\\frac{C (C - 2 V - 2 t)}{2}", "\\frac{V (2 C - V - 2 t)}{2}", "t (- C + V^{C})"], "srepr_premise_expression": "Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('V', commutative=True)), Mul(Integer(-1), Symbol('t', commutative=True)))", "srepr_variable": "Symbol('t', commutative=True)", "srepr_positive": "Mul(Symbol('t', commutative=True), Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('V', commutative=True)), Mul(Integer(-1), Rational(1, 2), Symbol('t', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('t', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('C', commutative=True)), Mul(Integer(2), Symbol('V', commutative=True)), Symbol('t', commutative=True)))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Symbol('C', commutative=True), Mul(Integer(-1), Integer(2), Symbol('V', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('t', commutative=True))))", "Mul(Rational(1, 2), Symbol('V', commutative=True), Add(Mul(Integer(2), Symbol('C', commutative=True)), Mul(Integer(-1), Symbol('V', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('t', commutative=True))))", "Mul(Symbol('t', commutative=True), Add(Mul(Integer(-1), Symbol('C', commutative=True)), Pow(Symbol('V', commutative=True), Symbol('C', commutative=True))))"]}, {"premise_expression": "h \\log{(B)}", "variable": "h", "positive": "\\frac{h^{2} \\log{(B)}}{2}", "negatives": ["\\frac{h^{2} e^{B}}{2}", "\\frac{h (2 B - h)}{2}", "B h (\\log{(B)} - 1)", "\\frac{B h (h - 2)}{2}"], "srepr_premise_expression": "Mul(Symbol('h', commutative=True), log(Symbol('B', commutative=True)))", "srepr_variable": "Symbol('h', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('h', commutative=True), Integer(2)), log(Symbol('B', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('h', commutative=True), Integer(2)), exp(Symbol('B', commutative=True)))", "Mul(Rational(1, 2), Symbol('h', commutative=True), Add(Mul(Integer(2), Symbol('B', commutative=True)), Mul(Integer(-1), Symbol('h', commutative=True))))", "Mul(Symbol('B', commutative=True), Symbol('h', commutative=True), Add(log(Symbol('B', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('B', commutative=True), Symbol('h', commutative=True), Add(Symbol('h', commutative=True), Integer(-2)))"]}, {"premise_expression": "\\cos{(\\frac{h}{s})}", "variable": "s", "positive": "h \\operatorname{Si}{(\\frac{h}{s})} + s \\cos{(\\frac{h}{s})}", "negatives": ["- h s + \\sin{(s)}", "s (h + \\log{(s)} - 1)", "\\frac{s (2 h - s)}{2}", "h \\log{(s)}"], "srepr_premise_expression": "cos(Mul(Symbol('h', commutative=True), Pow(Symbol('s', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('s', commutative=True)", "srepr_positive": "Add(Mul(Symbol('h', commutative=True), Si(Mul(Symbol('h', commutative=True), Pow(Symbol('s', commutative=True), Integer(-1))))), Mul(Symbol('s', commutative=True), cos(Mul(Symbol('h', commutative=True), Pow(Symbol('s', commutative=True), Integer(-1))))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('h', commutative=True), Symbol('s', commutative=True)), sin(Symbol('s', commutative=True)))", "Mul(Symbol('s', commutative=True), Add(Symbol('h', commutative=True), log(Symbol('s', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('s', commutative=True), Add(Mul(Integer(2), Symbol('h', commutative=True)), Mul(Integer(-1), Symbol('s', commutative=True))))", "Mul(Symbol('h', commutative=True), log(Symbol('s', commutative=True)))"]}, {"premise_expression": "V l", "variable": "l", "positive": "\\frac{V l^{2}}{2}", "negatives": ["\\frac{V^{2} l}{2}", "V e^{\\frac{l}{V}}", "\\frac{l (2 V + l)}{2}", "\\frac{l^{2} \\log{(V)}}{2}"], "srepr_premise_expression": "Mul(Symbol('V', commutative=True), Symbol('l', commutative=True))", "srepr_variable": "Symbol('l', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('V', commutative=True), Pow(Symbol('l', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('V', commutative=True), Integer(2)), Symbol('l', commutative=True))", "Mul(Symbol('V', commutative=True), exp(Mul(Pow(Symbol('V', commutative=True), Integer(-1)), Symbol('l', commutative=True))))", "Mul(Rational(1, 2), Symbol('l', commutative=True), Add(Mul(Integer(2), Symbol('V', commutative=True)), Symbol('l', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('l', commutative=True), Integer(2)), log(Symbol('V', commutative=True)))"]}, {"premise_expression": "\\frac{k}{y}", "variable": "y", "positive": "k \\log{(y)}", "negatives": ["\\frac{k^{2}}{2 y}", "\\frac{y (\\log{(y)} - 1)}{k}", "\\frac{y^{2} e^{k}}{2}", "\\frac{y (y + 2 \\log{(k)})}{2}"], "srepr_premise_expression": "Mul(Symbol('k', commutative=True), Pow(Symbol('y', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('y', commutative=True)", "srepr_positive": "Mul(Symbol('k', commutative=True), log(Symbol('y', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('k', commutative=True), Integer(2)), Pow(Symbol('y', commutative=True), Integer(-1)))", "Mul(Pow(Symbol('k', commutative=True), Integer(-1)), Symbol('y', commutative=True), Add(log(Symbol('y', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('y', commutative=True), Integer(2)), exp(Symbol('k', commutative=True)))", "Mul(Rational(1, 2), Symbol('y', commutative=True), Add(Symbol('y', commutative=True), Mul(Integer(2), log(Symbol('k', commutative=True)))))"]}, {"premise_expression": "\\cos^{y}{(u)}", "variable": "u", "positive": "\\int \\cos^{y}{(u)} du", "negatives": ["u (\\log{(\\frac{u}{y})} - 1)", "u y + e^{u}", "- u y + e^{u}", "u \\cos{(\\frac{y}{u})} + y \\operatorname{Si}{(\\frac{y}{u})}"], "srepr_premise_expression": "Pow(cos(Symbol('u', commutative=True)), Symbol('y', commutative=True))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "Integral(Pow(cos(Symbol('u', commutative=True)), Symbol('y', commutative=True)), Tuple(Symbol('u', commutative=True)))", "srepr_negatives": ["Mul(Symbol('u', commutative=True), Add(log(Mul(Symbol('u', commutative=True), Pow(Symbol('y', commutative=True), Integer(-1)))), Integer(-1)))", "Add(Mul(Symbol('u', commutative=True), Symbol('y', commutative=True)), exp(Symbol('u', commutative=True)))", "Add(Mul(Integer(-1), Symbol('u', commutative=True), Symbol('y', commutative=True)), exp(Symbol('u', commutative=True)))", "Add(Mul(Symbol('u', commutative=True), cos(Mul(Pow(Symbol('u', commutative=True), Integer(-1)), Symbol('y', commutative=True)))), Mul(Symbol('y', commutative=True), Si(Mul(Pow(Symbol('u', commutative=True), Integer(-1)), Symbol('y', commutative=True)))))"]}, {"premise_expression": "\\cos{(F + Z)}", "variable": "F", "positive": "\\sin{(F + Z)}", "negatives": ["\\frac{\\sin{(F)}}{Z}", "- \\frac{\\cos{(F)}}{Z}", "F (\\log{(\\frac{Z}{F})} + 1)", "- F Z + \\sin{(F)}"], "srepr_premise_expression": "cos(Add(Symbol('F', commutative=True), Symbol('Z', commutative=True)))", "srepr_variable": "Symbol('F', commutative=True)", "srepr_positive": "sin(Add(Symbol('F', commutative=True), Symbol('Z', commutative=True)))", "srepr_negatives": ["Mul(Pow(Symbol('Z', commutative=True), Integer(-1)), sin(Symbol('F', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('Z', commutative=True), Integer(-1)), cos(Symbol('F', commutative=True)))", "Mul(Symbol('F', commutative=True), Add(log(Mul(Pow(Symbol('F', commutative=True), Integer(-1)), Symbol('Z', commutative=True))), Integer(1)))", "Add(Mul(Integer(-1), Symbol('F', commutative=True), Symbol('Z', commutative=True)), sin(Symbol('F', commutative=True)))"]}, {"premise_expression": "P + c", "variable": "c", "positive": "\\frac{c (2 P + c)}{2}", "negatives": ["\\frac{P (P + 2 c)}{2}", "e^{P + c}", "c (\\log{(P c)} - 1)", "\\frac{c (- c + 2 \\sin{(P)})}{2}"], "srepr_premise_expression": "Add(Symbol('P', commutative=True), Symbol('c', commutative=True))", "srepr_variable": "Symbol('c', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('c', commutative=True), Add(Mul(Integer(2), Symbol('P', commutative=True)), Symbol('c', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Symbol('P', commutative=True), Mul(Integer(2), Symbol('c', commutative=True))))", "exp(Add(Symbol('P', commutative=True), Symbol('c', commutative=True)))", "Mul(Symbol('c', commutative=True), Add(log(Mul(Symbol('P', commutative=True), Symbol('c', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('c', commutative=True), Add(Mul(Integer(-1), Symbol('c', commutative=True)), Mul(Integer(2), sin(Symbol('P', commutative=True)))))"]}, {"premise_expression": "H b", "variable": "H", "positive": "\\frac{H^{2} b}{2}", "negatives": ["\\frac{H b^{2}}{2}", "\\frac{H (H + 2 b)}{2}", "\\sin{(H - b)}", "e^{H + b}"], "srepr_premise_expression": "Mul(Symbol('H', commutative=True), Symbol('b', commutative=True))", "srepr_variable": "Symbol('H', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('H', commutative=True), Integer(2)), Symbol('b', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('H', commutative=True), Pow(Symbol('b', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('H', commutative=True), Add(Symbol('H', commutative=True), Mul(Integer(2), Symbol('b', commutative=True))))", "sin(Add(Symbol('H', commutative=True), Mul(Integer(-1), Symbol('b', commutative=True))))", "exp(Add(Symbol('H', commutative=True), Symbol('b', commutative=True)))"]}, {"premise_expression": "- q + \\sin{(A)}", "variable": "q", "positive": "\\frac{q (- q + 2 \\sin{(A)})}{2}", "negatives": ["- A q - \\cos{(A)}", "\\frac{q^{2}}{2 A}", "\\frac{q (\\log{(q)} - 1)}{A}", "\\sin{(A + q)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('q', commutative=True)), sin(Symbol('A', commutative=True)))", "srepr_variable": "Symbol('q', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('q', commutative=True), Add(Mul(Integer(-1), Symbol('q', commutative=True)), Mul(Integer(2), sin(Symbol('A', commutative=True)))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('A', commutative=True), Symbol('q', commutative=True)), Mul(Integer(-1), cos(Symbol('A', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(-1)), Pow(Symbol('q', commutative=True), Integer(2)))", "Mul(Pow(Symbol('A', commutative=True), Integer(-1)), Symbol('q', commutative=True), Add(log(Symbol('q', commutative=True)), Integer(-1)))", "sin(Add(Symbol('A', commutative=True), Symbol('q', commutative=True)))"]}, {"premise_expression": "R b^{p}", "variable": "R", "positive": "\\frac{R^{2} b^{p}}{2}", "negatives": ["\\frac{R b (R - 2 p)}{2}", "\\frac{R (R p - 2 b)}{2}", "\\frac{R (R + 2 p)}{2 b}", "\\frac{R (R + 2 b)}{2 p}"], "srepr_premise_expression": "Mul(Symbol('R', commutative=True), Pow(Symbol('b', commutative=True), Symbol('p', commutative=True)))", "srepr_variable": "Symbol('R', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('R', commutative=True), Integer(2)), Pow(Symbol('b', commutative=True), Symbol('p', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('R', commutative=True), Symbol('b', commutative=True), Add(Symbol('R', commutative=True), Mul(Integer(-1), Integer(2), Symbol('p', commutative=True))))", "Mul(Rational(1, 2), Symbol('R', commutative=True), Add(Mul(Symbol('R', commutative=True), Symbol('p', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('b', commutative=True))))", "Mul(Rational(1, 2), Symbol('R', commutative=True), Pow(Symbol('b', commutative=True), Integer(-1)), Add(Symbol('R', commutative=True), Mul(Integer(2), Symbol('p', commutative=True))))", "Mul(Rational(1, 2), Symbol('R', commutative=True), Pow(Symbol('p', commutative=True), Integer(-1)), Add(Symbol('R', commutative=True), Mul(Integer(2), Symbol('b', commutative=True))))"]}, {"premise_expression": "m + e^{J}", "variable": "m", "positive": "\\frac{m (m + 2 e^{J})}{2}", "negatives": ["\\frac{m (m + 2 \\cos{(J)})}{2}", "J m + e^{J}", "m + \\frac{m^{2}}{2 J}", "- J m - \\cos{(m)}"], "srepr_premise_expression": "Add(Symbol('m', commutative=True), exp(Symbol('J', commutative=True)))", "srepr_variable": "Symbol('m', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Symbol('m', commutative=True), Mul(Integer(2), exp(Symbol('J', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Symbol('m', commutative=True), Mul(Integer(2), cos(Symbol('J', commutative=True)))))", "Add(Mul(Symbol('J', commutative=True), Symbol('m', commutative=True)), exp(Symbol('J', commutative=True)))", "Add(Symbol('m', commutative=True), Mul(Rational(1, 2), Pow(Symbol('J', commutative=True), Integer(-1)), Pow(Symbol('m', commutative=True), Integer(2))))", "Add(Mul(Integer(-1), Symbol('J', commutative=True), Symbol('m', commutative=True)), Mul(Integer(-1), cos(Symbol('m', commutative=True))))"]}, {"premise_expression": "- Z + l", "variable": "Z", "positive": "\\frac{Z (- Z + 2 l)}{2}", "negatives": ["\\frac{l (- 2 Z + l)}{2}", "\\frac{Z (- Z + 2 \\cos{(l)})}{2}", "\\sin{(Z + l)}", "\\frac{Z^{2} (2 Z + 3)}{6}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('Z', commutative=True)), Symbol('l', commutative=True))", "srepr_variable": "Symbol('Z', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Mul(Integer(-1), Symbol('Z', commutative=True)), Mul(Integer(2), Symbol('l', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('l', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('Z', commutative=True)), Symbol('l', commutative=True)))", "Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Mul(Integer(-1), Symbol('Z', commutative=True)), Mul(Integer(2), cos(Symbol('l', commutative=True)))))", "sin(Add(Symbol('Z', commutative=True), Symbol('l', commutative=True)))", "Mul(Rational(1, 6), Pow(Symbol('Z', commutative=True), Integer(2)), Add(Mul(Integer(2), Symbol('Z', commutative=True)), Integer(3)))"]}, {"premise_expression": "\\sin{(F + V)}", "variable": "V", "positive": "- \\cos{(F + V)}", "negatives": ["\\frac{V (2 F + V)}{2}", "F V - \\cos{(V)}", "\\frac{V^{2} \\log{(F)}}{2}", "\\frac{V (V + 2 e^{F})}{2}"], "srepr_premise_expression": "sin(Add(Symbol('F', commutative=True), Symbol('V', commutative=True)))", "srepr_variable": "Symbol('V', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('F', commutative=True), Symbol('V', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('V', commutative=True), Add(Mul(Integer(2), Symbol('F', commutative=True)), Symbol('V', commutative=True)))", "Add(Mul(Symbol('F', commutative=True), Symbol('V', commutative=True)), Mul(Integer(-1), cos(Symbol('V', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('V', commutative=True), Integer(2)), log(Symbol('F', commutative=True)))", "Mul(Rational(1, 2), Symbol('V', commutative=True), Add(Symbol('V', commutative=True), Mul(Integer(2), exp(Symbol('F', commutative=True)))))"]}, {"premise_expression": "\\frac{\\log{(T)}}{g}", "variable": "g", "positive": "\\log{(T)} \\log{(g)}", "negatives": ["\\frac{T (\\log{(T)} - 1)}{g}", "g (\\log{(T g)} - 1)", "T g (\\log{(g)} - 1)", "g (\\log{(\\frac{g}{T})} - 1)"], "srepr_premise_expression": "Mul(Pow(Symbol('g', commutative=True), Integer(-1)), log(Symbol('T', commutative=True)))", "srepr_variable": "Symbol('g', commutative=True)", "srepr_positive": "Mul(log(Symbol('T', commutative=True)), log(Symbol('g', commutative=True)))", "srepr_negatives": ["Mul(Symbol('T', commutative=True), Pow(Symbol('g', commutative=True), Integer(-1)), Add(log(Symbol('T', commutative=True)), Integer(-1)))", "Mul(Symbol('g', commutative=True), Add(log(Mul(Symbol('T', commutative=True), Symbol('g', commutative=True))), Integer(-1)))", "Mul(Symbol('T', commutative=True), Symbol('g', commutative=True), Add(log(Symbol('g', commutative=True)), Integer(-1)))", "Mul(Symbol('g', commutative=True), Add(log(Mul(Pow(Symbol('T', commutative=True), Integer(-1)), Symbol('g', commutative=True))), Integer(-1)))"]}, {"premise_expression": "q (- N + Y)", "variable": "q", "positive": "\\frac{q^{2} (- N + Y)}{2}", "negatives": ["\\frac{N q (- N + 2 Y)}{2}", "\\frac{Y q (- 2 N + Y)}{2}", "\\frac{q (- 2 N + 2 Y + q)}{2}", "\\frac{N Y q^{2}}{2}"], "srepr_premise_expression": "Mul(Symbol('q', commutative=True), Add(Mul(Integer(-1), Symbol('N', commutative=True)), Symbol('Y', commutative=True)))", "srepr_variable": "Symbol('q', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('q', commutative=True), Integer(2)), Add(Mul(Integer(-1), Symbol('N', commutative=True)), Symbol('Y', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('N', commutative=True), Symbol('q', commutative=True), Add(Mul(Integer(-1), Symbol('N', commutative=True)), Mul(Integer(2), Symbol('Y', commutative=True))))", "Mul(Rational(1, 2), Symbol('Y', commutative=True), Symbol('q', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('N', commutative=True)), Symbol('Y', commutative=True)))", "Mul(Rational(1, 2), Symbol('q', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('N', commutative=True)), Mul(Integer(2), Symbol('Y', commutative=True)), Symbol('q', commutative=True)))", "Mul(Rational(1, 2), Symbol('N', commutative=True), Symbol('Y', commutative=True), Pow(Symbol('q', commutative=True), Integer(2)))"]}, {"premise_expression": "W c", "variable": "c", "positive": "\\frac{W c^{2}}{2}", "negatives": ["\\frac{c^{2}}{2}", "\\frac{W^{2} c}{2}", "\\frac{c^{2}}{2 W}", "e^{W + c}"], "srepr_premise_expression": "Mul(Symbol('W', commutative=True), Symbol('c', commutative=True))", "srepr_variable": "Symbol('c', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('W', commutative=True), Pow(Symbol('c', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('c', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('W', commutative=True), Integer(2)), Symbol('c', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('W', commutative=True), Integer(-1)), Pow(Symbol('c', commutative=True), Integer(2)))", "exp(Add(Symbol('W', commutative=True), Symbol('c', commutative=True)))"]}, {"premise_expression": "\\sin{(C + g)}", "variable": "g", "positive": "- \\cos{(C + g)}", "negatives": ["g \\sin{(1)}", "\\frac{g^{3}}{3}", "\\frac{g (g + 2 \\log{(C)})}{2}", "\\frac{g (g + 2 e^{C})}{2}"], "srepr_premise_expression": "sin(Add(Symbol('C', commutative=True), Symbol('g', commutative=True)))", "srepr_variable": "Symbol('g', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('C', commutative=True), Symbol('g', commutative=True))))", "srepr_negatives": ["Mul(Symbol('g', commutative=True), sin(Integer(1)))", "Mul(Rational(1, 3), Pow(Symbol('g', commutative=True), Integer(3)))", "Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Symbol('g', commutative=True), Mul(Integer(2), log(Symbol('C', commutative=True)))))", "Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Symbol('g', commutative=True), Mul(Integer(2), exp(Symbol('C', commutative=True)))))"]}, {"premise_expression": "P + T", "variable": "T", "positive": "\\frac{T (2 P + T)}{2}", "negatives": ["\\frac{T (- 2 P + T)}{2}", "\\frac{P (P + 2 T)}{2}", "\\frac{T^{2} \\log{(P)}}{2}", "e^{P + T}"], "srepr_premise_expression": "Add(Symbol('P', commutative=True), Symbol('T', commutative=True))", "srepr_variable": "Symbol('T', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('T', commutative=True), Add(Mul(Integer(2), Symbol('P', commutative=True)), Symbol('T', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('T', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('P', commutative=True)), Symbol('T', commutative=True)))", "Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Symbol('P', commutative=True), Mul(Integer(2), Symbol('T', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('T', commutative=True), Integer(2)), log(Symbol('P', commutative=True)))", "exp(Add(Symbol('P', commutative=True), Symbol('T', commutative=True)))"]}, {"premise_expression": "- V + \\frac{X}{P}", "variable": "V", "positive": "- \\frac{V^{2}}{2} + \\frac{V X}{P}", "negatives": ["\\frac{P V^{2}}{2 X}", "\\frac{V^{2} X}{2 P}", "P \\log{(V)} + V X", "- V X + \\frac{X^{2}}{2 P}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('V', commutative=True)), Mul(Pow(Symbol('P', commutative=True), Integer(-1)), Symbol('X', commutative=True)))", "srepr_variable": "Symbol('V', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('V', commutative=True), Integer(2))), Mul(Pow(Symbol('P', commutative=True), Integer(-1)), Symbol('V', commutative=True), Symbol('X', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('P', commutative=True), Pow(Symbol('V', commutative=True), Integer(2)), Pow(Symbol('X', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(-1)), Pow(Symbol('V', commutative=True), Integer(2)), Symbol('X', commutative=True))", "Add(Mul(Symbol('P', commutative=True), log(Symbol('V', commutative=True))), Mul(Symbol('V', commutative=True), Symbol('X', commutative=True)))", "Add(Mul(Integer(-1), Symbol('V', commutative=True), Symbol('X', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(-1)), Pow(Symbol('X', commutative=True), Integer(2))))"]}, {"premise_expression": "s \\log{(I)}", "variable": "s", "positive": "\\frac{s^{2} \\log{(I)}}{2}", "negatives": ["\\frac{s (- 2 I + s)}{2}", "\\frac{s^{2}}{2 I}", "I s (\\log{(I)} - 1)", "s (\\log{(\\frac{s}{I})} - 1)"], "srepr_premise_expression": "Mul(Symbol('s', commutative=True), log(Symbol('I', commutative=True)))", "srepr_variable": "Symbol('s', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('s', commutative=True), Integer(2)), log(Symbol('I', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('s', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('I', commutative=True)), Symbol('s', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(-1)), Pow(Symbol('s', commutative=True), Integer(2)))", "Mul(Symbol('I', commutative=True), Symbol('s', commutative=True), Add(log(Symbol('I', commutative=True)), Integer(-1)))", "Mul(Symbol('s', commutative=True), Add(log(Mul(Pow(Symbol('I', commutative=True), Integer(-1)), Symbol('s', commutative=True))), Integer(-1)))"]}, {"premise_expression": "e^{f^{m}}", "variable": "f", "positive": "\\frac{e^{- \\frac{i \\pi}{m}} \\gamma(\\frac{1}{m}, f^{m} e^{i \\pi})}{m}", "negatives": ["\\frac{f (- f + 2 \\log{(m)})}{2}", "f \\log{(f + m)} - f + m \\log{(f + m)}", "\\log{(f)} \\cos{(m)}", "f \\log{(- f + m)} - f - m \\log{(f - m)}"], "srepr_premise_expression": "exp(Pow(Symbol('f', commutative=True), Symbol('m', commutative=True)))", "srepr_variable": "Symbol('f', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('m', commutative=True), Integer(-1)), exp(Mul(Integer(-1), I, pi, Pow(Symbol('m', commutative=True), Integer(-1)))), lowergamma(Pow(Symbol('m', commutative=True), Integer(-1)), Mul(Pow(Symbol('f', commutative=True), Symbol('m', commutative=True)), exp_polar(Mul(I, pi)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Mul(Integer(-1), Symbol('f', commutative=True)), Mul(Integer(2), log(Symbol('m', commutative=True)))))", "Add(Mul(Symbol('f', commutative=True), log(Add(Symbol('f', commutative=True), Symbol('m', commutative=True)))), Mul(Integer(-1), Symbol('f', commutative=True)), Mul(Symbol('m', commutative=True), log(Add(Symbol('f', commutative=True), Symbol('m', commutative=True)))))", "Mul(log(Symbol('f', commutative=True)), cos(Symbol('m', commutative=True)))", "Add(Mul(Symbol('f', commutative=True), log(Add(Mul(Integer(-1), Symbol('f', commutative=True)), Symbol('m', commutative=True)))), Mul(Integer(-1), Symbol('f', commutative=True)), Mul(Integer(-1), Symbol('m', commutative=True), log(Add(Symbol('f', commutative=True), Mul(Integer(-1), Symbol('m', commutative=True))))))"]}, {"premise_expression": "B e^{E}", "variable": "E", "positive": "B e^{E}", "negatives": ["\\frac{B^{2} e^{E}}{2}", "- e^{B - E}", "B E + \\sin{(E)}", "B E - \\cos{(E)}"], "srepr_premise_expression": "Mul(Symbol('B', commutative=True), exp(Symbol('E', commutative=True)))", "srepr_variable": "Symbol('E', commutative=True)", "srepr_positive": "Mul(Symbol('B', commutative=True), exp(Symbol('E', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('B', commutative=True), Integer(2)), exp(Symbol('E', commutative=True)))", "Mul(Integer(-1), exp(Add(Symbol('B', commutative=True), Mul(Integer(-1), Symbol('E', commutative=True)))))", "Add(Mul(Symbol('B', commutative=True), Symbol('E', commutative=True)), sin(Symbol('E', commutative=True)))", "Add(Mul(Symbol('B', commutative=True), Symbol('E', commutative=True)), Mul(Integer(-1), cos(Symbol('E', commutative=True))))"]}, {"premise_expression": "\\frac{\\cos{(E)}}{X}", "variable": "X", "positive": "\\log{(X)} \\cos{(E)}", "negatives": ["E \\log{(X)} - X", "E \\sin{(X)}", "\\frac{\\sin{(E)}}{X}", "e^{- E + X}"], "srepr_premise_expression": "Mul(Pow(Symbol('X', commutative=True), Integer(-1)), cos(Symbol('E', commutative=True)))", "srepr_variable": "Symbol('X', commutative=True)", "srepr_positive": "Mul(log(Symbol('X', commutative=True)), cos(Symbol('E', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('E', commutative=True), log(Symbol('X', commutative=True))), Mul(Integer(-1), Symbol('X', commutative=True)))", "Mul(Symbol('E', commutative=True), sin(Symbol('X', commutative=True)))", "Mul(Pow(Symbol('X', commutative=True), Integer(-1)), sin(Symbol('E', commutative=True)))", "exp(Add(Mul(Integer(-1), Symbol('E', commutative=True)), Symbol('X', commutative=True)))"]}, {"premise_expression": "\\frac{W}{M}", "variable": "W", "positive": "\\frac{W^{2}}{2 M}", "negatives": ["W \\log{(M)}", "\\frac{W^{2} e^{M}}{2}", "M \\log{(W)}", "\\cos{(M - W)}"], "srepr_premise_expression": "Mul(Pow(Symbol('M', commutative=True), Integer(-1)), Symbol('W', commutative=True))", "srepr_variable": "Symbol('W', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('M', commutative=True), Integer(-1)), Pow(Symbol('W', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('W', commutative=True), log(Symbol('M', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('W', commutative=True), Integer(2)), exp(Symbol('M', commutative=True)))", "Mul(Symbol('M', commutative=True), log(Symbol('W', commutative=True)))", "cos(Add(Symbol('M', commutative=True), Mul(Integer(-1), Symbol('W', commutative=True))))"]}, {"premise_expression": "\\frac{S}{L}", "variable": "L", "positive": "S \\log{(L)}", "negatives": ["\\frac{S^{2}}{2 L}", "\\frac{\\sin{(L)}}{S}", "\\frac{L^{2} S}{2}", "\\cos{(L - S)}"], "srepr_premise_expression": "Mul(Pow(Symbol('L', commutative=True), Integer(-1)), Symbol('S', commutative=True))", "srepr_variable": "Symbol('L', commutative=True)", "srepr_positive": "Mul(Symbol('S', commutative=True), log(Symbol('L', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(-1)), Pow(Symbol('S', commutative=True), Integer(2)))", "Mul(Pow(Symbol('S', commutative=True), Integer(-1)), sin(Symbol('L', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(2)), Symbol('S', commutative=True))", "cos(Add(Symbol('L', commutative=True), Mul(Integer(-1), Symbol('S', commutative=True))))"]}, {"premise_expression": "n e^{a}", "variable": "n", "positive": "\\frac{n^{2} e^{a}}{2}", "negatives": ["n e^{a}", "\\frac{n (2 a + n)}{2}", "\\frac{n (n + 2 e^{a})}{2}", "\\frac{n (n + 2 \\cos{(a)})}{2}"], "srepr_premise_expression": "Mul(Symbol('n', commutative=True), exp(Symbol('a', commutative=True)))", "srepr_variable": "Symbol('n', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('n', commutative=True), Integer(2)), exp(Symbol('a', commutative=True)))", "srepr_negatives": ["Mul(Symbol('n', commutative=True), exp(Symbol('a', commutative=True)))", "Mul(Rational(1, 2), Symbol('n', commutative=True), Add(Mul(Integer(2), Symbol('a', commutative=True)), Symbol('n', commutative=True)))", "Mul(Rational(1, 2), Symbol('n', commutative=True), Add(Symbol('n', commutative=True), Mul(Integer(2), exp(Symbol('a', commutative=True)))))", "Mul(Rational(1, 2), Symbol('n', commutative=True), Add(Symbol('n', commutative=True), Mul(Integer(2), cos(Symbol('a', commutative=True)))))"]}, {"premise_expression": "\\cos{(\\frac{A}{b})}", "variable": "b", "positive": "A \\operatorname{Si}{(\\frac{A}{b})} + b \\cos{(\\frac{A}{b})}", "negatives": ["A b - \\cos{(b)}", "\\log{(A)} \\log{(b)}", "\\frac{b (2 A + b)}{2}", "\\log{(b)} \\sin{(A)}"], "srepr_premise_expression": "cos(Mul(Symbol('A', commutative=True), Pow(Symbol('b', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('b', commutative=True)", "srepr_positive": "Add(Mul(Symbol('A', commutative=True), Si(Mul(Symbol('A', commutative=True), Pow(Symbol('b', commutative=True), Integer(-1))))), Mul(Symbol('b', commutative=True), cos(Mul(Symbol('A', commutative=True), Pow(Symbol('b', commutative=True), Integer(-1))))))", "srepr_negatives": ["Add(Mul(Symbol('A', commutative=True), Symbol('b', commutative=True)), Mul(Integer(-1), cos(Symbol('b', commutative=True))))", "Mul(log(Symbol('A', commutative=True)), log(Symbol('b', commutative=True)))", "Mul(Rational(1, 2), Symbol('b', commutative=True), Add(Mul(Integer(2), Symbol('A', commutative=True)), Symbol('b', commutative=True)))", "Mul(log(Symbol('b', commutative=True)), sin(Symbol('A', commutative=True)))"]}, {"premise_expression": "B V - G", "variable": "B", "positive": "\\frac{B (B V - 2 G)}{2}", "negatives": ["\\frac{V (B V - 2 G)}{2}", "\\frac{B (B G - 2 V)}{2}", "\\frac{G (2 B V - G)}{2}", "\\frac{B (B + 2 V^{G})}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('B', commutative=True), Symbol('V', commutative=True)), Mul(Integer(-1), Symbol('G', commutative=True)))", "srepr_variable": "Symbol('B', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('B', commutative=True), Add(Mul(Symbol('B', commutative=True), Symbol('V', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('G', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('V', commutative=True), Add(Mul(Symbol('B', commutative=True), Symbol('V', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('G', commutative=True))))", "Mul(Rational(1, 2), Symbol('B', commutative=True), Add(Mul(Symbol('B', commutative=True), Symbol('G', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('V', commutative=True))))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Mul(Integer(2), Symbol('B', commutative=True), Symbol('V', commutative=True)), Mul(Integer(-1), Symbol('G', commutative=True))))", "Mul(Rational(1, 2), Symbol('B', commutative=True), Add(Symbol('B', commutative=True), Mul(Integer(2), Pow(Symbol('V', commutative=True), Symbol('G', commutative=True)))))"]}, {"premise_expression": "- a + \\frac{t}{m}", "variable": "m", "positive": "- a m + t \\log{(m)}", "negatives": ["a t \\log{(m)}", "- a t + \\frac{t^{2}}{2 m}", "\\frac{a \\log{(m)}}{t}", "- \\frac{a^{2}}{2} + \\frac{a t}{m}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('a', commutative=True)), Mul(Pow(Symbol('m', commutative=True), Integer(-1)), Symbol('t', commutative=True)))", "srepr_variable": "Symbol('m', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('a', commutative=True), Symbol('m', commutative=True)), Mul(Symbol('t', commutative=True), log(Symbol('m', commutative=True))))", "srepr_negatives": ["Mul(Symbol('a', commutative=True), Symbol('t', commutative=True), log(Symbol('m', commutative=True)))", "Add(Mul(Integer(-1), Symbol('a', commutative=True), Symbol('t', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('m', commutative=True), Integer(-1)), Pow(Symbol('t', commutative=True), Integer(2))))", "Mul(Symbol('a', commutative=True), Pow(Symbol('t', commutative=True), Integer(-1)), log(Symbol('m', commutative=True)))", "Add(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('a', commutative=True), Integer(2))), Mul(Symbol('a', commutative=True), Pow(Symbol('m', commutative=True), Integer(-1)), Symbol('t', commutative=True)))"]}, {"premise_expression": "C e^{N}", "variable": "C", "positive": "\\frac{C^{2} e^{N}}{2}", "negatives": ["\\frac{C^{2} \\sin{(N)}}{2}", "\\frac{C^{2} \\log{(N)}}{2}", "C e^{N}", "\\frac{C^{2} N}{2}"], "srepr_premise_expression": "Mul(Symbol('C', commutative=True), exp(Symbol('N', commutative=True)))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2)), exp(Symbol('N', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2)), sin(Symbol('N', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2)), log(Symbol('N', commutative=True)))", "Mul(Symbol('C', commutative=True), exp(Symbol('N', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2)), Symbol('N', commutative=True))"]}, {"premise_expression": "A + W h", "variable": "h", "positive": "\\frac{h (2 A + W h)}{2}", "negatives": ["\\frac{W (2 A + W h)}{2}", "\\frac{A (A + 2 W h)}{2}", "\\frac{h (2 A + h)}{2 W}", "\\frac{h (2 A + 2 W + h)}{2}"], "srepr_premise_expression": "Add(Symbol('A', commutative=True), Mul(Symbol('W', commutative=True), Symbol('h', commutative=True)))", "srepr_variable": "Symbol('h', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('h', commutative=True), Add(Mul(Integer(2), Symbol('A', commutative=True)), Mul(Symbol('W', commutative=True), Symbol('h', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('W', commutative=True), Add(Mul(Integer(2), Symbol('A', commutative=True)), Mul(Symbol('W', commutative=True), Symbol('h', commutative=True))))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Symbol('A', commutative=True), Mul(Integer(2), Symbol('W', commutative=True), Symbol('h', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('W', commutative=True), Integer(-1)), Symbol('h', commutative=True), Add(Mul(Integer(2), Symbol('A', commutative=True)), Symbol('h', commutative=True)))", "Mul(Rational(1, 2), Symbol('h', commutative=True), Add(Mul(Integer(2), Symbol('A', commutative=True)), Mul(Integer(2), Symbol('W', commutative=True)), Symbol('h', commutative=True)))"]}, {"premise_expression": "\\log{(K + T)}", "variable": "K", "positive": "K \\log{(K + T)} - K + T \\log{(K + T)}", "negatives": ["K \\log{(K + T)} + T \\log{(K + T)} - T", "K \\cos{(\\frac{T}{K})} + T \\operatorname{Si}{(\\frac{T}{K})}", "\\log{(K)} \\sin{(T)}", "\\sin{(K - T)}"], "srepr_premise_expression": "log(Add(Symbol('K', commutative=True), Symbol('T', commutative=True)))", "srepr_variable": "Symbol('K', commutative=True)", "srepr_positive": "Add(Mul(Symbol('K', commutative=True), log(Add(Symbol('K', commutative=True), Symbol('T', commutative=True)))), Mul(Integer(-1), Symbol('K', commutative=True)), Mul(Symbol('T', commutative=True), log(Add(Symbol('K', commutative=True), Symbol('T', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('K', commutative=True), log(Add(Symbol('K', commutative=True), Symbol('T', commutative=True)))), Mul(Symbol('T', commutative=True), log(Add(Symbol('K', commutative=True), Symbol('T', commutative=True)))), Mul(Integer(-1), Symbol('T', commutative=True)))", "Add(Mul(Symbol('K', commutative=True), cos(Mul(Pow(Symbol('K', commutative=True), Integer(-1)), Symbol('T', commutative=True)))), Mul(Symbol('T', commutative=True), Si(Mul(Pow(Symbol('K', commutative=True), Integer(-1)), Symbol('T', commutative=True)))))", "Mul(log(Symbol('K', commutative=True)), sin(Symbol('T', commutative=True)))", "sin(Add(Symbol('K', commutative=True), Mul(Integer(-1), Symbol('T', commutative=True))))"]}, {"premise_expression": "\\frac{- L + l}{s}", "variable": "L", "positive": "\\frac{L (- L + 2 l)}{2 s}", "negatives": ["\\frac{l (- 2 L + l)}{2 s}", "\\frac{L (- L + 2 l^{s})}{2}", "\\frac{L (L + 2 l s)}{2}", "(- L + l) \\log{(s)}"], "srepr_premise_expression": "Mul(Pow(Symbol('s', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('L', commutative=True)), Symbol('l', commutative=True)))", "srepr_variable": "Symbol('L', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('L', commutative=True), Pow(Symbol('s', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('L', commutative=True)), Mul(Integer(2), Symbol('l', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('l', commutative=True), Pow(Symbol('s', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Integer(2), Symbol('L', commutative=True)), Symbol('l', commutative=True)))", "Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Mul(Integer(-1), Symbol('L', commutative=True)), Mul(Integer(2), Pow(Symbol('l', commutative=True), Symbol('s', commutative=True)))))", "Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Symbol('L', commutative=True), Mul(Integer(2), Symbol('l', commutative=True), Symbol('s', commutative=True))))", "Mul(Add(Mul(Integer(-1), Symbol('L', commutative=True)), Symbol('l', commutative=True)), log(Symbol('s', commutative=True)))"]}, {"premise_expression": "c - v", "variable": "v", "positive": "\\frac{v (2 c - v)}{2}", "negatives": ["\\frac{c (c - 2 v)}{2}", "\\sin{(c + v)}", "c v - \\cos{(v)}", "\\frac{v (v + 2 \\sin{(c)})}{2}"], "srepr_premise_expression": "Add(Symbol('c', commutative=True), Mul(Integer(-1), Symbol('v', commutative=True)))", "srepr_variable": "Symbol('v', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('v', commutative=True), Add(Mul(Integer(2), Symbol('c', commutative=True)), Mul(Integer(-1), Symbol('v', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('c', commutative=True), Add(Symbol('c', commutative=True), Mul(Integer(-1), Integer(2), Symbol('v', commutative=True))))", "sin(Add(Symbol('c', commutative=True), Symbol('v', commutative=True)))", "Add(Mul(Symbol('c', commutative=True), Symbol('v', commutative=True)), Mul(Integer(-1), cos(Symbol('v', commutative=True))))", "Mul(Rational(1, 2), Symbol('v', commutative=True), Add(Symbol('v', commutative=True), Mul(Integer(2), sin(Symbol('c', commutative=True)))))"]}, {"premise_expression": "\\frac{- C + w}{j}", "variable": "C", "positive": "\\frac{C (- C + 2 w)}{2 j}", "negatives": ["\\frac{w (- 2 C + w)}{2 j}", "\\frac{C (- C + 2 j w)}{2}", "\\frac{C j (C + 2 w)}{2}", "\\frac{C (C w + 2 j)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('j', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('C', commutative=True)), Symbol('w', commutative=True)))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('C', commutative=True), Pow(Symbol('j', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('C', commutative=True)), Mul(Integer(2), Symbol('w', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('j', commutative=True), Integer(-1)), Symbol('w', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('C', commutative=True)), Symbol('w', commutative=True)))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Mul(Integer(-1), Symbol('C', commutative=True)), Mul(Integer(2), Symbol('j', commutative=True), Symbol('w', commutative=True))))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Symbol('j', commutative=True), Add(Symbol('C', commutative=True), Mul(Integer(2), Symbol('w', commutative=True))))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Mul(Symbol('C', commutative=True), Symbol('w', commutative=True)), Mul(Integer(2), Symbol('j', commutative=True))))"]}, {"premise_expression": "\\frac{e^{j}}{o}", "variable": "o", "positive": "e^{j} \\log{(o)}", "negatives": ["e^{j + o}", "- \\cos{(j + o)}", "- j o + e^{o}", "- \\frac{\\cos{(o)}}{j}"], "srepr_premise_expression": "Mul(Pow(Symbol('o', commutative=True), Integer(-1)), exp(Symbol('j', commutative=True)))", "srepr_variable": "Symbol('o', commutative=True)", "srepr_positive": "Mul(exp(Symbol('j', commutative=True)), log(Symbol('o', commutative=True)))", "srepr_negatives": ["exp(Add(Symbol('j', commutative=True), Symbol('o', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('j', commutative=True), Symbol('o', commutative=True))))", "Add(Mul(Integer(-1), Symbol('j', commutative=True), Symbol('o', commutative=True)), exp(Symbol('o', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('j', commutative=True), Integer(-1)), cos(Symbol('o', commutative=True)))"]}, {"premise_expression": "\\frac{B}{C} + l", "variable": "C", "positive": "B \\log{(C)} + C l", "negatives": ["\\frac{B^{2}}{2 C} + B l", "\\frac{B l}{C} + \\frac{l^{2}}{2}", "\\frac{C^{2}}{2} + \\frac{C l}{B}", "\\frac{C (B C + 2 l)}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('B', commutative=True), Pow(Symbol('C', commutative=True), Integer(-1))), Symbol('l', commutative=True))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Add(Mul(Symbol('B', commutative=True), log(Symbol('C', commutative=True))), Mul(Symbol('C', commutative=True), Symbol('l', commutative=True)))", "srepr_negatives": ["Add(Mul(Rational(1, 2), Pow(Symbol('B', commutative=True), Integer(2)), Pow(Symbol('C', commutative=True), Integer(-1))), Mul(Symbol('B', commutative=True), Symbol('l', commutative=True)))", "Add(Mul(Symbol('B', commutative=True), Pow(Symbol('C', commutative=True), Integer(-1)), Symbol('l', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('l', commutative=True), Integer(2))))", "Add(Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2))), Mul(Pow(Symbol('B', commutative=True), Integer(-1)), Symbol('C', commutative=True), Symbol('l', commutative=True)))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Mul(Symbol('B', commutative=True), Symbol('C', commutative=True)), Mul(Integer(2), Symbol('l', commutative=True))))"]}, {"premise_expression": "D u", "variable": "u", "positive": "\\frac{D u^{2}}{2}", "negatives": ["\\frac{D^{2} u}{2}", "\\frac{u (2 D - u)}{2}", "D u - \\cos{(u)}", "- D u - \\cos{(u)}"], "srepr_premise_expression": "Mul(Symbol('D', commutative=True), Symbol('u', commutative=True))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('D', commutative=True), Pow(Symbol('u', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(2)), Symbol('u', commutative=True))", "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(2), Symbol('D', commutative=True)), Mul(Integer(-1), Symbol('u', commutative=True))))", "Add(Mul(Symbol('D', commutative=True), Symbol('u', commutative=True)), Mul(Integer(-1), cos(Symbol('u', commutative=True))))", "Add(Mul(Integer(-1), Symbol('D', commutative=True), Symbol('u', commutative=True)), Mul(Integer(-1), cos(Symbol('u', commutative=True))))"]}, {"premise_expression": "N l n", "variable": "l", "positive": "\\frac{N l^{2} n}{2}", "negatives": ["\\frac{N^{2} l n}{2}", "\\frac{N l n^{2}}{2}", "\\frac{N^{n} l^{2}}{2}", "N n \\log{(l)}"], "srepr_premise_expression": "Mul(Symbol('N', commutative=True), Symbol('l', commutative=True), Symbol('n', commutative=True))", "srepr_variable": "Symbol('l', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('N', commutative=True), Pow(Symbol('l', commutative=True), Integer(2)), Symbol('n', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('N', commutative=True), Integer(2)), Symbol('l', commutative=True), Symbol('n', commutative=True))", "Mul(Rational(1, 2), Symbol('N', commutative=True), Symbol('l', commutative=True), Pow(Symbol('n', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('N', commutative=True), Symbol('n', commutative=True)), Pow(Symbol('l', commutative=True), Integer(2)))", "Mul(Symbol('N', commutative=True), Symbol('n', commutative=True), log(Symbol('l', commutative=True)))"]}, {"premise_expression": "J (N + b)", "variable": "N", "positive": "\\frac{J N (N + 2 b)}{2}", "negatives": ["\\frac{J^{2} (N + b)}{2}", "\\frac{J b (2 N + b)}{2}", "\\frac{N (2 J + N b)}{2}", "\\frac{N^{2}}{2 b^{2}}"], "srepr_premise_expression": "Mul(Symbol('J', commutative=True), Add(Symbol('N', commutative=True), Symbol('b', commutative=True)))", "srepr_variable": "Symbol('N', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('J', commutative=True), Symbol('N', commutative=True), Add(Symbol('N', commutative=True), Mul(Integer(2), Symbol('b', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('J', commutative=True), Integer(2)), Add(Symbol('N', commutative=True), Symbol('b', commutative=True)))", "Mul(Rational(1, 2), Symbol('J', commutative=True), Symbol('b', commutative=True), Add(Mul(Integer(2), Symbol('N', commutative=True)), Symbol('b', commutative=True)))", "Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Mul(Integer(2), Symbol('J', commutative=True)), Mul(Symbol('N', commutative=True), Symbol('b', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('N', commutative=True), Integer(2)), Pow(Symbol('b', commutative=True), Integer(-2)))"]}, {"premise_expression": "\\log{(N - l)}", "variable": "N", "positive": "N \\log{(N - l)} - N - l \\log{(N - l)}", "negatives": ["- N \\log{(- N + l)} + l \\log{(N - l)} - l", "\\frac{N (- N + 2 \\cos{(l)})}{2}", "\\frac{N (N - 2 l)}{2}", "\\frac{N (N + 2 l)}{2}"], "srepr_premise_expression": "log(Add(Symbol('N', commutative=True), Mul(Integer(-1), Symbol('l', commutative=True))))", "srepr_variable": "Symbol('N', commutative=True)", "srepr_positive": "Add(Mul(Symbol('N', commutative=True), log(Add(Symbol('N', commutative=True), Mul(Integer(-1), Symbol('l', commutative=True))))), Mul(Integer(-1), Symbol('N', commutative=True)), Mul(Integer(-1), Symbol('l', commutative=True), log(Add(Symbol('N', commutative=True), Mul(Integer(-1), Symbol('l', commutative=True))))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('N', commutative=True), log(Add(Mul(Integer(-1), Symbol('N', commutative=True)), Symbol('l', commutative=True)))), Mul(Symbol('l', commutative=True), log(Add(Symbol('N', commutative=True), Mul(Integer(-1), Symbol('l', commutative=True))))), Mul(Integer(-1), Symbol('l', commutative=True)))", "Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Mul(Integer(-1), Symbol('N', commutative=True)), Mul(Integer(2), cos(Symbol('l', commutative=True)))))", "Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Symbol('N', commutative=True), Mul(Integer(-1), Integer(2), Symbol('l', commutative=True))))", "Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Symbol('N', commutative=True), Mul(Integer(2), Symbol('l', commutative=True))))"]}, {"premise_expression": "- W + y", "variable": "y", "positive": "\\frac{y (- 2 W + y)}{2}", "negatives": ["\\frac{y (2 W + y)}{2}", "\\frac{W (- W + 2 y)}{2}", "\\frac{y^{2} \\log{(W)}}{2}", "- \\sin{(W - y)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('W', commutative=True)), Symbol('y', commutative=True))", "srepr_variable": "Symbol('y', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('y', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('W', commutative=True)), Symbol('y', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('y', commutative=True), Add(Mul(Integer(2), Symbol('W', commutative=True)), Symbol('y', commutative=True)))", "Mul(Rational(1, 2), Symbol('W', commutative=True), Add(Mul(Integer(-1), Symbol('W', commutative=True)), Mul(Integer(2), Symbol('y', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('y', commutative=True), Integer(2)), log(Symbol('W', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('W', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True)))))"]}, {"premise_expression": "E + X + n", "variable": "n", "positive": "n (E + X + \\frac{n}{2})", "negatives": ["\\frac{n (- 2 E + 2 X + n)}{2}", "\\frac{X (2 E + X + 2 n)}{2}", "\\frac{E (E + 2 X + 2 n)}{2}", "\\frac{n (- 2 X + n)}{2 E}"], "srepr_premise_expression": "Add(Symbol('E', commutative=True), Symbol('X', commutative=True), Symbol('n', commutative=True))", "srepr_variable": "Symbol('n', commutative=True)", "srepr_positive": "Mul(Symbol('n', commutative=True), Add(Symbol('E', commutative=True), Symbol('X', commutative=True), Mul(Rational(1, 2), Symbol('n', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('n', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('E', commutative=True)), Mul(Integer(2), Symbol('X', commutative=True)), Symbol('n', commutative=True)))", "Mul(Rational(1, 2), Symbol('X', commutative=True), Add(Mul(Integer(2), Symbol('E', commutative=True)), Symbol('X', commutative=True), Mul(Integer(2), Symbol('n', commutative=True))))", "Mul(Rational(1, 2), Symbol('E', commutative=True), Add(Symbol('E', commutative=True), Mul(Integer(2), Symbol('X', commutative=True)), Mul(Integer(2), Symbol('n', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('E', commutative=True), Integer(-1)), Symbol('n', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('X', commutative=True)), Symbol('n', commutative=True)))"]}, {"premise_expression": "- L + y", "variable": "L", "positive": "\\frac{L (- L + 2 y)}{2}", "negatives": ["\\frac{y (- 2 L + y)}{2}", "\\frac{L^{2} y}{2}", "- e^{- L + y}", "y e^{L}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('L', commutative=True)), Symbol('y', commutative=True))", "srepr_variable": "Symbol('L', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Mul(Integer(-1), Symbol('L', commutative=True)), Mul(Integer(2), Symbol('y', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('y', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('L', commutative=True)), Symbol('y', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(2)), Symbol('y', commutative=True))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('L', commutative=True)), Symbol('y', commutative=True))))", "Mul(Symbol('y', commutative=True), exp(Symbol('L', commutative=True)))"]}, {"premise_expression": "e^{s + y}", "variable": "y", "positive": "e^{s + y}", "negatives": ["- \\cos{(s - y)}", "\\frac{s y (y + 2)}{2}", "- s y + \\sin{(y)}", "s y + \\sin{(y)}"], "srepr_premise_expression": "exp(Add(Symbol('s', commutative=True), Symbol('y', commutative=True)))", "srepr_variable": "Symbol('y', commutative=True)", "srepr_positive": "exp(Add(Symbol('s', commutative=True), Symbol('y', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('s', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True)))))", "Mul(Rational(1, 2), Symbol('s', commutative=True), Symbol('y', commutative=True), Add(Symbol('y', commutative=True), Integer(2)))", "Add(Mul(Integer(-1), Symbol('s', commutative=True), Symbol('y', commutative=True)), sin(Symbol('y', commutative=True)))", "Add(Mul(Symbol('s', commutative=True), Symbol('y', commutative=True)), sin(Symbol('y', commutative=True)))"]}, {"premise_expression": "\\sin{(\\frac{E}{j})}", "variable": "j", "positive": "E \\log{(\\frac{E}{j})} - \\frac{E \\log{(\\frac{E^{2}}{j^{2}})}}{2} - E \\operatorname{Ci}{(\\frac{E}{j})} + j \\sin{(\\frac{E}{j})}", "negatives": ["E \\log{(E + j)} + j \\log{(E + j)} - j", "E \\operatorname{Si}{(\\frac{E}{j})} + j \\cos{(\\frac{E}{j})}", "j (\\log{(\\frac{E}{j})} + 1)", "\\frac{j (- j + 2 \\log{(E)})}{2}"], "srepr_premise_expression": "sin(Mul(Symbol('E', commutative=True), Pow(Symbol('j', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('j', commutative=True)", "srepr_positive": "Add(Mul(Symbol('E', commutative=True), log(Mul(Symbol('E', commutative=True), Pow(Symbol('j', commutative=True), Integer(-1))))), Mul(Integer(-1), Rational(1, 2), Symbol('E', commutative=True), log(Mul(Pow(Symbol('E', commutative=True), Integer(2)), Pow(Symbol('j', commutative=True), Integer(-2))))), Mul(Integer(-1), Symbol('E', commutative=True), Ci(Mul(Symbol('E', commutative=True), Pow(Symbol('j', commutative=True), Integer(-1))))), Mul(Symbol('j', commutative=True), sin(Mul(Symbol('E', commutative=True), Pow(Symbol('j', commutative=True), Integer(-1))))))", "srepr_negatives": ["Add(Mul(Symbol('E', commutative=True), log(Add(Symbol('E', commutative=True), Symbol('j', commutative=True)))), Mul(Symbol('j', commutative=True), log(Add(Symbol('E', commutative=True), Symbol('j', commutative=True)))), Mul(Integer(-1), Symbol('j', commutative=True)))", "Add(Mul(Symbol('E', commutative=True), Si(Mul(Symbol('E', commutative=True), Pow(Symbol('j', commutative=True), Integer(-1))))), Mul(Symbol('j', commutative=True), cos(Mul(Symbol('E', commutative=True), Pow(Symbol('j', commutative=True), Integer(-1))))))", "Mul(Symbol('j', commutative=True), Add(log(Mul(Symbol('E', commutative=True), Pow(Symbol('j', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Rational(1, 2), Symbol('j', commutative=True), Add(Mul(Integer(-1), Symbol('j', commutative=True)), Mul(Integer(2), log(Symbol('E', commutative=True)))))"]}, {"premise_expression": "E n", "variable": "n", "positive": "\\frac{E n^{2}}{2}", "negatives": ["\\frac{E^{2} n}{2}", "\\frac{n^{2} \\log{(E)}}{2}", "n (E + \\sin{(E)})", "n (- E + \\log{(n)} - 1)"], "srepr_premise_expression": "Mul(Symbol('E', commutative=True), Symbol('n', commutative=True))", "srepr_variable": "Symbol('n', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('E', commutative=True), Pow(Symbol('n', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('E', commutative=True), Integer(2)), Symbol('n', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('n', commutative=True), Integer(2)), log(Symbol('E', commutative=True)))", "Mul(Symbol('n', commutative=True), Add(Symbol('E', commutative=True), sin(Symbol('E', commutative=True))))", "Mul(Symbol('n', commutative=True), Add(Mul(Integer(-1), Symbol('E', commutative=True)), log(Symbol('n', commutative=True)), Integer(-1)))"]}, {"premise_expression": "B E b", "variable": "E", "positive": "\\frac{B E^{2} b}{2}", "negatives": ["\\frac{B^{2} E b}{2}", "\\frac{B E b^{2}}{2}", "\\frac{E b (2 B - E)}{2}", "\\frac{E (- E + 2 b)}{2 B}"], "srepr_premise_expression": "Mul(Symbol('B', commutative=True), Symbol('E', commutative=True), Symbol('b', commutative=True))", "srepr_variable": "Symbol('E', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('B', commutative=True), Pow(Symbol('E', commutative=True), Integer(2)), Symbol('b', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('B', commutative=True), Integer(2)), Symbol('E', commutative=True), Symbol('b', commutative=True))", "Mul(Rational(1, 2), Symbol('B', commutative=True), Symbol('E', commutative=True), Pow(Symbol('b', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('E', commutative=True), Symbol('b', commutative=True), Add(Mul(Integer(2), Symbol('B', commutative=True)), Mul(Integer(-1), Symbol('E', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('B', commutative=True), Integer(-1)), Symbol('E', commutative=True), Add(Mul(Integer(-1), Symbol('E', commutative=True)), Mul(Integer(2), Symbol('b', commutative=True))))"]}, {"premise_expression": "Y e^{b}", "variable": "b", "positive": "Y e^{b}", "negatives": ["\\frac{Y^{2} e^{b}}{2}", "- e^{Y - b}", "\\frac{\\sin{(b)}}{Y}", "\\frac{b^{2} e^{Y}}{2}"], "srepr_premise_expression": "Mul(Symbol('Y', commutative=True), exp(Symbol('b', commutative=True)))", "srepr_variable": "Symbol('b', commutative=True)", "srepr_positive": "Mul(Symbol('Y', commutative=True), exp(Symbol('b', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('Y', commutative=True), Integer(2)), exp(Symbol('b', commutative=True)))", "Mul(Integer(-1), exp(Add(Symbol('Y', commutative=True), Mul(Integer(-1), Symbol('b', commutative=True)))))", "Mul(Pow(Symbol('Y', commutative=True), Integer(-1)), sin(Symbol('b', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('b', commutative=True), Integer(2)), exp(Symbol('Y', commutative=True)))"]}, {"premise_expression": "e^{\\frac{u}{A}}", "variable": "u", "positive": "A e^{\\frac{u}{A}}", "negatives": ["- A \\cos{(u)}", "e u", "(u - 1) e^{u}", "u - \\frac{u^{2}}{2 A}"], "srepr_premise_expression": "exp(Mul(Pow(Symbol('A', commutative=True), Integer(-1)), Symbol('u', commutative=True)))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "Mul(Symbol('A', commutative=True), exp(Mul(Pow(Symbol('A', commutative=True), Integer(-1)), Symbol('u', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), Symbol('A', commutative=True), cos(Symbol('u', commutative=True)))", "Mul(E, Symbol('u', commutative=True))", "Mul(Add(Symbol('u', commutative=True), Integer(-1)), exp(Symbol('u', commutative=True)))", "Add(Symbol('u', commutative=True), Mul(Integer(-1), Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(-1)), Pow(Symbol('u', commutative=True), Integer(2))))"]}, {"premise_expression": "\\frac{u}{C}", "variable": "u", "positive": "\\frac{u^{2}}{2 C}", "negatives": ["u \\log{(C)}", "\\frac{C u^{2}}{2}", "\\frac{u^{2} \\sin{(C)}}{2}", "\\sin{(C + u)}"], "srepr_premise_expression": "Mul(Pow(Symbol('C', commutative=True), Integer(-1)), Symbol('u', commutative=True))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(-1)), Pow(Symbol('u', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('u', commutative=True), log(Symbol('C', commutative=True)))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Pow(Symbol('u', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('u', commutative=True), Integer(2)), sin(Symbol('C', commutative=True)))", "sin(Add(Symbol('C', commutative=True), Symbol('u', commutative=True)))"]}, {"premise_expression": "e^{S - m}", "variable": "m", "positive": "- e^{S - m}", "negatives": ["e^{S - m}", "- S m + \\sin{(m)}", "S m + \\sin{(m)}", "\\log{(S)} \\log{(m)}"], "srepr_premise_expression": "exp(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('m', commutative=True))))", "srepr_variable": "Symbol('m', commutative=True)", "srepr_positive": "Mul(Integer(-1), exp(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('m', commutative=True)))))", "srepr_negatives": ["exp(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('m', commutative=True))))", "Add(Mul(Integer(-1), Symbol('S', commutative=True), Symbol('m', commutative=True)), sin(Symbol('m', commutative=True)))", "Add(Mul(Symbol('S', commutative=True), Symbol('m', commutative=True)), sin(Symbol('m', commutative=True)))", "Mul(log(Symbol('S', commutative=True)), log(Symbol('m', commutative=True)))"]}, {"premise_expression": "g - s", "variable": "s", "positive": "\\frac{s (2 g - s)}{2}", "negatives": ["\\frac{g (g - 2 s)}{2}", "- \\sin{(g - s)}", "e^{- g + s}", "\\frac{s (- s + 2 \\log{(g)})}{2}"], "srepr_premise_expression": "Add(Symbol('g', commutative=True), Mul(Integer(-1), Symbol('s', commutative=True)))", "srepr_variable": "Symbol('s', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('s', commutative=True), Add(Mul(Integer(2), Symbol('g', commutative=True)), Mul(Integer(-1), Symbol('s', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Symbol('g', commutative=True), Mul(Integer(-1), Integer(2), Symbol('s', commutative=True))))", "Mul(Integer(-1), sin(Add(Symbol('g', commutative=True), Mul(Integer(-1), Symbol('s', commutative=True)))))", "exp(Add(Mul(Integer(-1), Symbol('g', commutative=True)), Symbol('s', commutative=True)))", "Mul(Rational(1, 2), Symbol('s', commutative=True), Add(Mul(Integer(-1), Symbol('s', commutative=True)), Mul(Integer(2), log(Symbol('g', commutative=True)))))"]}, {"premise_expression": "\\frac{G q}{K}", "variable": "G", "positive": "\\frac{G^{2} q}{2 K}", "negatives": ["\\frac{G^{2} K}{2 q}", "\\frac{G q^{2}}{2 K}", "G q \\log{(K)}", "\\frac{G^{2} K^{q}}{2}"], "srepr_premise_expression": "Mul(Symbol('G', commutative=True), Pow(Symbol('K', commutative=True), Integer(-1)), Symbol('q', commutative=True))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(2)), Pow(Symbol('K', commutative=True), Integer(-1)), Symbol('q', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(2)), Symbol('K', commutative=True), Pow(Symbol('q', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Pow(Symbol('K', commutative=True), Integer(-1)), Pow(Symbol('q', commutative=True), Integer(2)))", "Mul(Symbol('G', commutative=True), Symbol('q', commutative=True), log(Symbol('K', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(2)), Pow(Symbol('K', commutative=True), Symbol('q', commutative=True)))"]}, {"premise_expression": "L + m", "variable": "L", "positive": "\\frac{L (L + 2 m)}{2}", "negatives": ["\\frac{m (2 L + m)}{2}", "L \\log{(2 m)}", "- L m + \\sin{(L)}", "\\log{(L)} \\cos{(m)}"], "srepr_premise_expression": "Add(Symbol('L', commutative=True), Symbol('m', commutative=True))", "srepr_variable": "Symbol('L', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Symbol('L', commutative=True), Mul(Integer(2), Symbol('m', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Mul(Integer(2), Symbol('L', commutative=True)), Symbol('m', commutative=True)))", "Mul(Symbol('L', commutative=True), log(Mul(Integer(2), Symbol('m', commutative=True))))", "Add(Mul(Integer(-1), Symbol('L', commutative=True), Symbol('m', commutative=True)), sin(Symbol('L', commutative=True)))", "Mul(log(Symbol('L', commutative=True)), cos(Symbol('m', commutative=True)))"]}, {"premise_expression": "D + \\cos{(y)}", "variable": "D", "positive": "\\frac{D (D + 2 \\cos{(y)})}{2}", "negatives": ["\\frac{D (- D + 2 y)}{2}", "\\frac{D^{2} e^{y}}{2}", "\\frac{D^{2} \\sin{(y)}}{2}", "D y + \\sin{(y)}"], "srepr_premise_expression": "Add(Symbol('D', commutative=True), cos(Symbol('y', commutative=True)))", "srepr_variable": "Symbol('D', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('D', commutative=True), Add(Symbol('D', commutative=True), Mul(Integer(2), cos(Symbol('y', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('D', commutative=True), Add(Mul(Integer(-1), Symbol('D', commutative=True)), Mul(Integer(2), Symbol('y', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(2)), exp(Symbol('y', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(2)), sin(Symbol('y', commutative=True)))", "Add(Mul(Symbol('D', commutative=True), Symbol('y', commutative=True)), sin(Symbol('y', commutative=True)))"]}, {"premise_expression": "\\log{(g t)}", "variable": "t", "positive": "t (\\log{(g t)} - 1)", "negatives": ["g (\\log{(g t)} - 1)", "g \\log{(t)}", "- \\cos{(g - t)}", "\\frac{t (2 g - t)}{2}"], "srepr_premise_expression": "log(Mul(Symbol('g', commutative=True), Symbol('t', commutative=True)))", "srepr_variable": "Symbol('t', commutative=True)", "srepr_positive": "Mul(Symbol('t', commutative=True), Add(log(Mul(Symbol('g', commutative=True), Symbol('t', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('g', commutative=True), Add(log(Mul(Symbol('g', commutative=True), Symbol('t', commutative=True))), Integer(-1)))", "Mul(Symbol('g', commutative=True), log(Symbol('t', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('g', commutative=True), Mul(Integer(-1), Symbol('t', commutative=True)))))", "Mul(Rational(1, 2), Symbol('t', commutative=True), Add(Mul(Integer(2), Symbol('g', commutative=True)), Mul(Integer(-1), Symbol('t', commutative=True))))"]}, {"premise_expression": "e^{S + g}", "variable": "g", "positive": "e^{S + g}", "negatives": ["\\frac{g (2 S + g)}{2}", "- S g + e^{g}", "g \\sin^{S}{(S)}", "\\frac{g (\\log{(g)} - 1)}{S}"], "srepr_premise_expression": "exp(Add(Symbol('S', commutative=True), Symbol('g', commutative=True)))", "srepr_variable": "Symbol('g', commutative=True)", "srepr_positive": "exp(Add(Symbol('S', commutative=True), Symbol('g', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Mul(Integer(2), Symbol('S', commutative=True)), Symbol('g', commutative=True)))", "Add(Mul(Integer(-1), Symbol('S', commutative=True), Symbol('g', commutative=True)), exp(Symbol('g', commutative=True)))", "Mul(Symbol('g', commutative=True), Pow(sin(Symbol('S', commutative=True)), Symbol('S', commutative=True)))", "Mul(Pow(Symbol('S', commutative=True), Integer(-1)), Symbol('g', commutative=True), Add(log(Symbol('g', commutative=True)), Integer(-1)))"]}, {"premise_expression": "B P + x", "variable": "P", "positive": "\\frac{P (B P + 2 x)}{2}", "negatives": ["\\frac{B (B P + 2 x)}{2}", "\\frac{x (2 B P + x)}{2}", "\\frac{P (- 2 B - P + 2 x)}{2}", "\\frac{B P^{2} x}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('B', commutative=True), Symbol('P', commutative=True)), Symbol('x', commutative=True))", "srepr_variable": "Symbol('P', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Mul(Symbol('B', commutative=True), Symbol('P', commutative=True)), Mul(Integer(2), Symbol('x', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('B', commutative=True), Add(Mul(Symbol('B', commutative=True), Symbol('P', commutative=True)), Mul(Integer(2), Symbol('x', commutative=True))))", "Mul(Rational(1, 2), Symbol('x', commutative=True), Add(Mul(Integer(2), Symbol('B', commutative=True), Symbol('P', commutative=True)), Symbol('x', commutative=True)))", "Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('B', commutative=True)), Mul(Integer(-1), Symbol('P', commutative=True)), Mul(Integer(2), Symbol('x', commutative=True))))", "Mul(Rational(1, 2), Symbol('B', commutative=True), Pow(Symbol('P', commutative=True), Integer(2)), Symbol('x', commutative=True))"]}, {"premise_expression": "h \\sin{(y)}", "variable": "h", "positive": "\\frac{h^{2} \\sin{(y)}}{2}", "negatives": ["\\frac{h^{2} \\log{(y)}}{2}", "h y + \\sin{(h)}", "\\frac{h (h - 2 y)}{2}", "- h \\cos{(y)}"], "srepr_premise_expression": "Mul(Symbol('h', commutative=True), sin(Symbol('y', commutative=True)))", "srepr_variable": "Symbol('h', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('h', commutative=True), Integer(2)), sin(Symbol('y', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('h', commutative=True), Integer(2)), log(Symbol('y', commutative=True)))", "Add(Mul(Symbol('h', commutative=True), Symbol('y', commutative=True)), sin(Symbol('h', commutative=True)))", "Mul(Rational(1, 2), Symbol('h', commutative=True), Add(Symbol('h', commutative=True), Mul(Integer(-1), Integer(2), Symbol('y', commutative=True))))", "Mul(Integer(-1), Symbol('h', commutative=True), cos(Symbol('y', commutative=True)))"]}, {"premise_expression": "k w - k", "variable": "w", "positive": "\\frac{k w (w - 2)}{2}", "negatives": ["\\frac{k^{2} (w - 1)}{2}", "\\frac{w^{2} e^{k}}{2}", "\\frac{w^{2} \\log{(k)}}{2}", "\\sin{(k + w)}"], "srepr_premise_expression": "Add(Mul(Symbol('k', commutative=True), Symbol('w', commutative=True)), Mul(Integer(-1), Symbol('k', commutative=True)))", "srepr_variable": "Symbol('w', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('k', commutative=True), Symbol('w', commutative=True), Add(Symbol('w', commutative=True), Integer(-2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('k', commutative=True), Integer(2)), Add(Symbol('w', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('w', commutative=True), Integer(2)), exp(Symbol('k', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('w', commutative=True), Integer(2)), log(Symbol('k', commutative=True)))", "sin(Add(Symbol('k', commutative=True), Symbol('w', commutative=True)))"]}, {"premise_expression": "\\log{(p - u)}", "variable": "u", "positive": "- p \\log{(- p + u)} + u \\log{(p - u)} - u", "negatives": ["p \\log{(p - u)} - p - u \\log{(p - u)}", "\\frac{u (- u + 2 e^{p})}{2}", "\\frac{u (\\log{(u)} - 1)}{p}", "\\frac{u (2 p + u)}{2}"], "srepr_premise_expression": "log(Add(Symbol('p', commutative=True), Mul(Integer(-1), Symbol('u', commutative=True))))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('p', commutative=True), log(Add(Mul(Integer(-1), Symbol('p', commutative=True)), Symbol('u', commutative=True)))), Mul(Symbol('u', commutative=True), log(Add(Symbol('p', commutative=True), Mul(Integer(-1), Symbol('u', commutative=True))))), Mul(Integer(-1), Symbol('u', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('p', commutative=True), log(Add(Symbol('p', commutative=True), Mul(Integer(-1), Symbol('u', commutative=True))))), Mul(Integer(-1), Symbol('p', commutative=True)), Mul(Integer(-1), Symbol('u', commutative=True), log(Add(Symbol('p', commutative=True), Mul(Integer(-1), Symbol('u', commutative=True))))))", "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(-1), Symbol('u', commutative=True)), Mul(Integer(2), exp(Symbol('p', commutative=True)))))", "Mul(Pow(Symbol('p', commutative=True), Integer(-1)), Symbol('u', commutative=True), Add(log(Symbol('u', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(2), Symbol('p', commutative=True)), Symbol('u', commutative=True)))"]}, {"premise_expression": "- S + Y", "variable": "Y", "positive": "\\frac{Y (- 2 S + Y)}{2}", "negatives": ["\\frac{S (- S + 2 Y)}{2}", "\\frac{Y^{2} \\cos{(S)}}{2}", "Y (\\log{(\\frac{S}{Y})} + 1)", "\\frac{\\sin{(Y)}}{S}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('S', commutative=True)), Symbol('Y', commutative=True))", "srepr_variable": "Symbol('Y', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('Y', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('S', commutative=True)), Symbol('Y', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Mul(Integer(-1), Symbol('S', commutative=True)), Mul(Integer(2), Symbol('Y', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('Y', commutative=True), Integer(2)), cos(Symbol('S', commutative=True)))", "Mul(Symbol('Y', commutative=True), Add(log(Mul(Symbol('S', commutative=True), Pow(Symbol('Y', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Pow(Symbol('S', commutative=True), Integer(-1)), sin(Symbol('Y', commutative=True)))"]}, {"premise_expression": "X - m", "variable": "X", "positive": "\\frac{X (X - 2 m)}{2}", "negatives": ["\\frac{m (2 X - m)}{2}", "\\sin{(X - m)}", "e^{X - m}", "\\cos{(X - m)}"], "srepr_premise_expression": "Add(Symbol('X', commutative=True), Mul(Integer(-1), Symbol('m', commutative=True)))", "srepr_variable": "Symbol('X', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('X', commutative=True), Add(Symbol('X', commutative=True), Mul(Integer(-1), Integer(2), Symbol('m', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Mul(Integer(2), Symbol('X', commutative=True)), Mul(Integer(-1), Symbol('m', commutative=True))))", "sin(Add(Symbol('X', commutative=True), Mul(Integer(-1), Symbol('m', commutative=True))))", "exp(Add(Symbol('X', commutative=True), Mul(Integer(-1), Symbol('m', commutative=True))))", "cos(Add(Symbol('X', commutative=True), Mul(Integer(-1), Symbol('m', commutative=True))))"]}, {"premise_expression": "g o^{2}", "variable": "o", "positive": "\\frac{g o^{3}}{3}", "negatives": ["\\frac{g^{2} o^{2}}{2}", "g e^{o}", "- g \\cos{(o)}", "\\frac{o (2 g - o)}{2}"], "srepr_premise_expression": "Mul(Symbol('g', commutative=True), Pow(Symbol('o', commutative=True), Integer(2)))", "srepr_variable": "Symbol('o', commutative=True)", "srepr_positive": "Mul(Rational(1, 3), Symbol('g', commutative=True), Pow(Symbol('o', commutative=True), Integer(3)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('g', commutative=True), Integer(2)), Pow(Symbol('o', commutative=True), Integer(2)))", "Mul(Symbol('g', commutative=True), exp(Symbol('o', commutative=True)))", "Mul(Integer(-1), Symbol('g', commutative=True), cos(Symbol('o', commutative=True)))", "Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Mul(Integer(2), Symbol('g', commutative=True)), Mul(Integer(-1), Symbol('o', commutative=True))))"]}, {"premise_expression": "Y \\log{(X)}", "variable": "X", "positive": "X Y (\\log{(X)} - 1)", "negatives": ["\\frac{Y^{2} \\log{(X)}}{2}", "X + Y \\log{(X)}", "- \\cos{(X + Y)}", "\\frac{X^{2}}{2 Y}"], "srepr_premise_expression": "Mul(Symbol('Y', commutative=True), log(Symbol('X', commutative=True)))", "srepr_variable": "Symbol('X', commutative=True)", "srepr_positive": "Mul(Symbol('X', commutative=True), Symbol('Y', commutative=True), Add(log(Symbol('X', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('Y', commutative=True), Integer(2)), log(Symbol('X', commutative=True)))", "Add(Symbol('X', commutative=True), Mul(Symbol('Y', commutative=True), log(Symbol('X', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('X', commutative=True), Symbol('Y', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('X', commutative=True), Integer(2)), Pow(Symbol('Y', commutative=True), Integer(-1)))"]}, {"premise_expression": "\\log{(\\frac{x}{F})}", "variable": "F", "positive": "F (\\log{(\\frac{x}{F})} + 1)", "negatives": ["x (\\log{(\\frac{x}{F})} - 1)", "\\frac{F^{2} \\log{(x)}}{2}", "e^{F + x}", "\\log{(F)} \\sin{(x)}"], "srepr_premise_expression": "log(Mul(Pow(Symbol('F', commutative=True), Integer(-1)), Symbol('x', commutative=True)))", "srepr_variable": "Symbol('F', commutative=True)", "srepr_positive": "Mul(Symbol('F', commutative=True), Add(log(Mul(Pow(Symbol('F', commutative=True), Integer(-1)), Symbol('x', commutative=True))), Integer(1)))", "srepr_negatives": ["Mul(Symbol('x', commutative=True), Add(log(Mul(Pow(Symbol('F', commutative=True), Integer(-1)), Symbol('x', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('F', commutative=True), Integer(2)), log(Symbol('x', commutative=True)))", "exp(Add(Symbol('F', commutative=True), Symbol('x', commutative=True)))", "Mul(log(Symbol('F', commutative=True)), sin(Symbol('x', commutative=True)))"]}, {"premise_expression": "\\sin^{I}{(P)}", "variable": "P", "positive": "\\int \\sin^{I}{(P)} dP", "negatives": ["\\frac{P (P + 2 \\sin{(I)})}{2}", "- I \\cos{(P)}", "\\frac{P^{2}}{2 I}", "\\frac{P^{2} \\log{(I)}}{2}"], "srepr_premise_expression": "Pow(sin(Symbol('P', commutative=True)), Symbol('I', commutative=True))", "srepr_variable": "Symbol('P', commutative=True)", "srepr_positive": "Integral(Pow(sin(Symbol('P', commutative=True)), Symbol('I', commutative=True)), Tuple(Symbol('P', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Symbol('P', commutative=True), Mul(Integer(2), sin(Symbol('I', commutative=True)))))", "Mul(Integer(-1), Symbol('I', commutative=True), cos(Symbol('P', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(-1)), Pow(Symbol('P', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2)), log(Symbol('I', commutative=True)))"]}, {"premise_expression": "L^{f} - M", "variable": "M", "positive": "\\frac{M (2 L^{f} - M)}{2}", "negatives": ["\\frac{M (- 2 L - M + 2 f)}{2}", "L f \\log{(M)}", "M f", "L M + \\frac{M^{2}}{2 f}"], "srepr_premise_expression": "Add(Pow(Symbol('L', commutative=True), Symbol('f', commutative=True)), Mul(Integer(-1), Symbol('M', commutative=True)))", "srepr_variable": "Symbol('M', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('M', commutative=True), Add(Mul(Integer(2), Pow(Symbol('L', commutative=True), Symbol('f', commutative=True))), Mul(Integer(-1), Symbol('M', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('M', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('L', commutative=True)), Mul(Integer(-1), Symbol('M', commutative=True)), Mul(Integer(2), Symbol('f', commutative=True))))", "Mul(Symbol('L', commutative=True), Symbol('f', commutative=True), log(Symbol('M', commutative=True)))", "Mul(Symbol('M', commutative=True), Symbol('f', commutative=True))", "Add(Mul(Symbol('L', commutative=True), Symbol('M', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('M', commutative=True), Integer(2)), Pow(Symbol('f', commutative=True), Integer(-1))))"]}, {"premise_expression": "e^{\\frac{m}{y}}", "variable": "m", "positive": "y e^{\\frac{m}{y}}", "negatives": ["- m y + e^{m}", "- \\cos{(m - y)}", "\\frac{m (m - 2 y)}{2}", "\\frac{m^{2} \\sin{(y)}}{2}"], "srepr_premise_expression": "exp(Mul(Symbol('m', commutative=True), Pow(Symbol('y', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('m', commutative=True)", "srepr_positive": "Mul(Symbol('y', commutative=True), exp(Mul(Symbol('m', commutative=True), Pow(Symbol('y', commutative=True), Integer(-1)))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('m', commutative=True), Symbol('y', commutative=True)), exp(Symbol('m', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('m', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True)))))", "Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Symbol('m', commutative=True), Mul(Integer(-1), Integer(2), Symbol('y', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('m', commutative=True), Integer(2)), sin(Symbol('y', commutative=True)))"]}, {"premise_expression": "\\frac{\\sin{(n)}}{C}", "variable": "C", "positive": "\\log{(C)} \\sin{(n)}", "negatives": ["n \\log{(C)}", "\\frac{C^{2} n}{2}", "- \\frac{\\cos{(n)}}{C}", "- C n - \\cos{(C)}"], "srepr_premise_expression": "Mul(Pow(Symbol('C', commutative=True), Integer(-1)), sin(Symbol('n', commutative=True)))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Mul(log(Symbol('C', commutative=True)), sin(Symbol('n', commutative=True)))", "srepr_negatives": ["Mul(Symbol('n', commutative=True), log(Symbol('C', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2)), Symbol('n', commutative=True))", "Mul(Integer(-1), Pow(Symbol('C', commutative=True), Integer(-1)), cos(Symbol('n', commutative=True)))", "Add(Mul(Integer(-1), Symbol('C', commutative=True), Symbol('n', commutative=True)), Mul(Integer(-1), cos(Symbol('C', commutative=True))))"]}, {"premise_expression": "\\frac{l}{c}", "variable": "l", "positive": "\\frac{l^{2}}{2 c}", "negatives": ["l \\log{(c)}", "\\frac{c l^{2}}{2}", "\\frac{l^{2} \\log{(c)}}{2}", "c \\log{(l)}"], "srepr_premise_expression": "Mul(Pow(Symbol('c', commutative=True), Integer(-1)), Symbol('l', commutative=True))", "srepr_variable": "Symbol('l', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('c', commutative=True), Integer(-1)), Pow(Symbol('l', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('l', commutative=True), log(Symbol('c', commutative=True)))", "Mul(Rational(1, 2), Symbol('c', commutative=True), Pow(Symbol('l', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('l', commutative=True), Integer(2)), log(Symbol('c', commutative=True)))", "Mul(Symbol('c', commutative=True), log(Symbol('l', commutative=True)))"]}, {"premise_expression": "\\log{(\\frac{T}{G})}", "variable": "G", "positive": "G (\\log{(\\frac{T}{G})} + 1)", "negatives": ["T (\\log{(\\frac{T}{G})} - 1)", "- e^{- G + T}", "\\sin{(G - T)}", "e^{G - T}"], "srepr_premise_expression": "log(Mul(Pow(Symbol('G', commutative=True), Integer(-1)), Symbol('T', commutative=True)))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Mul(Symbol('G', commutative=True), Add(log(Mul(Pow(Symbol('G', commutative=True), Integer(-1)), Symbol('T', commutative=True))), Integer(1)))", "srepr_negatives": ["Mul(Symbol('T', commutative=True), Add(log(Mul(Pow(Symbol('G', commutative=True), Integer(-1)), Symbol('T', commutative=True))), Integer(-1)))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('G', commutative=True)), Symbol('T', commutative=True))))", "sin(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('T', commutative=True))))", "exp(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('T', commutative=True))))"]}, {"premise_expression": "- m + \\cos{(B)}", "variable": "m", "positive": "\\frac{m (- m + 2 \\cos{(B)})}{2}", "negatives": ["\\frac{m (- m + 2 e^{B})}{2}", "m (- B + \\log{(m^{B})})", "- B m + \\sin{(B)}", "\\frac{B m^{2}}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('m', commutative=True)), cos(Symbol('B', commutative=True)))", "srepr_variable": "Symbol('m', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Mul(Integer(-1), Symbol('m', commutative=True)), Mul(Integer(2), cos(Symbol('B', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Mul(Integer(-1), Symbol('m', commutative=True)), Mul(Integer(2), exp(Symbol('B', commutative=True)))))", "Mul(Symbol('m', commutative=True), Add(Mul(Integer(-1), Symbol('B', commutative=True)), log(Pow(Symbol('m', commutative=True), Symbol('B', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('B', commutative=True), Symbol('m', commutative=True)), sin(Symbol('B', commutative=True)))", "Mul(Rational(1, 2), Symbol('B', commutative=True), Pow(Symbol('m', commutative=True), Integer(2)))"]}, {"premise_expression": "F + a + j", "variable": "a", "positive": "a (F + \\frac{a}{2} + j)", "negatives": ["\\frac{a (- 2 F + a + 2 j)}{2}", "\\frac{F (F + 2 a + 2 j)}{2}", "\\frac{j (2 F + 2 a + j)}{2}", "\\frac{a (4 F + a)}{2}"], "srepr_premise_expression": "Add(Symbol('F', commutative=True), Symbol('a', commutative=True), Symbol('j', commutative=True))", "srepr_variable": "Symbol('a', commutative=True)", "srepr_positive": "Mul(Symbol('a', commutative=True), Add(Symbol('F', commutative=True), Mul(Rational(1, 2), Symbol('a', commutative=True)), Symbol('j', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('a', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('F', commutative=True)), Symbol('a', commutative=True), Mul(Integer(2), Symbol('j', commutative=True))))", "Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Symbol('F', commutative=True), Mul(Integer(2), Symbol('a', commutative=True)), Mul(Integer(2), Symbol('j', commutative=True))))", "Mul(Rational(1, 2), Symbol('j', commutative=True), Add(Mul(Integer(2), Symbol('F', commutative=True)), Mul(Integer(2), Symbol('a', commutative=True)), Symbol('j', commutative=True)))", "Mul(Rational(1, 2), Symbol('a', commutative=True), Add(Mul(Integer(4), Symbol('F', commutative=True)), Symbol('a', commutative=True)))"]}, {"premise_expression": "- G + a m", "variable": "G", "positive": "\\frac{G (- G + 2 a m)}{2}", "negatives": ["\\frac{G (G + 2 a m)}{2}", "\\frac{m (- 2 G + a m)}{2}", "\\frac{a (- 2 G + a m)}{2}", "\\frac{G m (G + 2 a)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('G', commutative=True)), Mul(Symbol('a', commutative=True), Symbol('m', commutative=True)))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Mul(Integer(-1), Symbol('G', commutative=True)), Mul(Integer(2), Symbol('a', commutative=True), Symbol('m', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Symbol('G', commutative=True), Mul(Integer(2), Symbol('a', commutative=True), Symbol('m', commutative=True))))", "Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('G', commutative=True)), Mul(Symbol('a', commutative=True), Symbol('m', commutative=True))))", "Mul(Rational(1, 2), Symbol('a', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('G', commutative=True)), Mul(Symbol('a', commutative=True), Symbol('m', commutative=True))))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Symbol('m', commutative=True), Add(Symbol('G', commutative=True), Mul(Integer(2), Symbol('a', commutative=True))))"]}, {"premise_expression": "\\frac{P m}{s}", "variable": "P", "positive": "\\frac{P^{2} m}{2 s}", "negatives": ["\\frac{P m^{2}}{2 s}", "\\frac{P^{2} m^{2}}{2}", "P m \\log{(s)}", "\\frac{P^{2} (m + s)}{2}"], "srepr_premise_expression": "Mul(Symbol('P', commutative=True), Symbol('m', commutative=True), Pow(Symbol('s', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('P', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2)), Symbol('m', commutative=True), Pow(Symbol('s', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('P', commutative=True), Pow(Symbol('m', commutative=True), Integer(2)), Pow(Symbol('s', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2)), Pow(Symbol('m', commutative=True), Integer(2)))", "Mul(Symbol('P', commutative=True), Symbol('m', commutative=True), log(Symbol('s', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2)), Add(Symbol('m', commutative=True), Symbol('s', commutative=True)))"]}, {"premise_expression": "- Z + z", "variable": "z", "positive": "\\frac{z (- 2 Z + z)}{2}", "negatives": ["\\frac{Z (- Z + 2 z)}{2}", "e^{- Z + z}", "Z \\sin{(z)}", "Z e^{\\frac{z}{Z}}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('Z', commutative=True)), Symbol('z', commutative=True))", "srepr_variable": "Symbol('z', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('z', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('Z', commutative=True)), Symbol('z', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Mul(Integer(-1), Symbol('Z', commutative=True)), Mul(Integer(2), Symbol('z', commutative=True))))", "exp(Add(Mul(Integer(-1), Symbol('Z', commutative=True)), Symbol('z', commutative=True)))", "Mul(Symbol('Z', commutative=True), sin(Symbol('z', commutative=True)))", "Mul(Symbol('Z', commutative=True), exp(Mul(Pow(Symbol('Z', commutative=True), Integer(-1)), Symbol('z', commutative=True))))"]}, {"premise_expression": "E + y", "variable": "y", "positive": "\\frac{y (2 E + y)}{2}", "negatives": ["\\frac{E (E + 2 y)}{2}", "- e^{E - y}", "\\frac{y (\\log{(y)} - 1)}{E}", "- E \\cos{(y)}"], "srepr_premise_expression": "Add(Symbol('E', commutative=True), Symbol('y', commutative=True))", "srepr_variable": "Symbol('y', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('y', commutative=True), Add(Mul(Integer(2), Symbol('E', commutative=True)), Symbol('y', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('E', commutative=True), Add(Symbol('E', commutative=True), Mul(Integer(2), Symbol('y', commutative=True))))", "Mul(Integer(-1), exp(Add(Symbol('E', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True)))))", "Mul(Pow(Symbol('E', commutative=True), Integer(-1)), Symbol('y', commutative=True), Add(log(Symbol('y', commutative=True)), Integer(-1)))", "Mul(Integer(-1), Symbol('E', commutative=True), cos(Symbol('y', commutative=True)))"]}, {"premise_expression": "\\log{(G - g)}", "variable": "g", "positive": "- G \\log{(- G + g)} + g \\log{(G - g)} - g", "negatives": ["G \\log{(G - g)} - G - g \\log{(G - g)}", "\\log{(g)} \\cos{(G)}", "\\frac{g (2 G - g)}{2}", "\\cos{(G - g)}"], "srepr_premise_expression": "log(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('g', commutative=True))))", "srepr_variable": "Symbol('g', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('G', commutative=True), log(Add(Mul(Integer(-1), Symbol('G', commutative=True)), Symbol('g', commutative=True)))), Mul(Symbol('g', commutative=True), log(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('g', commutative=True))))), Mul(Integer(-1), Symbol('g', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('G', commutative=True), log(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('g', commutative=True))))), Mul(Integer(-1), Symbol('G', commutative=True)), Mul(Integer(-1), Symbol('g', commutative=True), log(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('g', commutative=True))))))", "Mul(log(Symbol('g', commutative=True)), cos(Symbol('G', commutative=True)))", "Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Mul(Integer(2), Symbol('G', commutative=True)), Mul(Integer(-1), Symbol('g', commutative=True))))", "cos(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('g', commutative=True))))"]}, {"premise_expression": "- R + r", "variable": "r", "positive": "\\frac{r (- 2 R + r)}{2}", "negatives": ["\\frac{r (2 R + r)}{2}", "\\frac{R (- R + 2 r)}{2}", "\\sin{(R + r)}", "- R r + \\sin{(r)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('R', commutative=True)), Symbol('r', commutative=True))", "srepr_variable": "Symbol('r', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('R', commutative=True)), Symbol('r', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(2), Symbol('R', commutative=True)), Symbol('r', commutative=True)))", "Mul(Rational(1, 2), Symbol('R', commutative=True), Add(Mul(Integer(-1), Symbol('R', commutative=True)), Mul(Integer(2), Symbol('r', commutative=True))))", "sin(Add(Symbol('R', commutative=True), Symbol('r', commutative=True)))", "Add(Mul(Integer(-1), Symbol('R', commutative=True), Symbol('r', commutative=True)), sin(Symbol('r', commutative=True)))"]}, {"premise_expression": "v + \\log{(c)}", "variable": "c", "positive": "c (v + \\log{(c)} - 1)", "negatives": ["\\frac{v (v + 2 \\log{(c)})}{2}", "\\cos{(c - v)}", "v \\log{(c)}", "- \\cos{(c - v)}"], "srepr_premise_expression": "Add(Symbol('v', commutative=True), log(Symbol('c', commutative=True)))", "srepr_variable": "Symbol('c', commutative=True)", "srepr_positive": "Mul(Symbol('c', commutative=True), Add(Symbol('v', commutative=True), log(Symbol('c', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('v', commutative=True), Add(Symbol('v', commutative=True), Mul(Integer(2), log(Symbol('c', commutative=True)))))", "cos(Add(Symbol('c', commutative=True), Mul(Integer(-1), Symbol('v', commutative=True))))", "Mul(Symbol('v', commutative=True), log(Symbol('c', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('c', commutative=True), Mul(Integer(-1), Symbol('v', commutative=True)))))"]}, {"premise_expression": "- V + \\cos{(J)}", "variable": "J", "positive": "- J V + \\sin{(J)}", "negatives": ["\\frac{J (J + 2 V)}{2}", "\\log{(J)} \\cos{(V)}", "\\frac{V (- V + 2 \\cos{(J)})}{2}", "\\frac{J (J + 2 e^{V})}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('V', commutative=True)), cos(Symbol('J', commutative=True)))", "srepr_variable": "Symbol('J', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('J', commutative=True), Symbol('V', commutative=True)), sin(Symbol('J', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('J', commutative=True), Add(Symbol('J', commutative=True), Mul(Integer(2), Symbol('V', commutative=True))))", "Mul(log(Symbol('J', commutative=True)), cos(Symbol('V', commutative=True)))", "Mul(Rational(1, 2), Symbol('V', commutative=True), Add(Mul(Integer(-1), Symbol('V', commutative=True)), Mul(Integer(2), cos(Symbol('J', commutative=True)))))", "Mul(Rational(1, 2), Symbol('J', commutative=True), Add(Symbol('J', commutative=True), Mul(Integer(2), exp(Symbol('V', commutative=True)))))"]}, {"premise_expression": "\\cos{(G + j)}", "variable": "j", "positive": "\\sin{(G + j)}", "negatives": ["\\frac{j (2 G + j)}{2}", "G \\log{(j)}", "- G \\cos{(j)}", "\\log{(G)} \\log{(j)}"], "srepr_premise_expression": "cos(Add(Symbol('G', commutative=True), Symbol('j', commutative=True)))", "srepr_variable": "Symbol('j', commutative=True)", "srepr_positive": "sin(Add(Symbol('G', commutative=True), Symbol('j', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('j', commutative=True), Add(Mul(Integer(2), Symbol('G', commutative=True)), Symbol('j', commutative=True)))", "Mul(Symbol('G', commutative=True), log(Symbol('j', commutative=True)))", "Mul(Integer(-1), Symbol('G', commutative=True), cos(Symbol('j', commutative=True)))", "Mul(log(Symbol('G', commutative=True)), log(Symbol('j', commutative=True)))"]}, {"premise_expression": "\\log{(C - K)}", "variable": "K", "positive": "- C \\log{(- C + K)} + K \\log{(C - K)} - K", "negatives": ["C \\log{(C - K)} - C - K \\log{(C - K)}", "K (- C + \\log{(K^{C})})", "K (\\log{(C K)} - 1)", "K (\\log{(\\frac{K}{C})} - 1)"], "srepr_premise_expression": "log(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('K', commutative=True))))", "srepr_variable": "Symbol('K', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('C', commutative=True), log(Add(Mul(Integer(-1), Symbol('C', commutative=True)), Symbol('K', commutative=True)))), Mul(Symbol('K', commutative=True), log(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('K', commutative=True))))), Mul(Integer(-1), Symbol('K', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('C', commutative=True), log(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('K', commutative=True))))), Mul(Integer(-1), Symbol('C', commutative=True)), Mul(Integer(-1), Symbol('K', commutative=True), log(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('K', commutative=True))))))", "Mul(Symbol('K', commutative=True), Add(Mul(Integer(-1), Symbol('C', commutative=True)), log(Pow(Symbol('K', commutative=True), Symbol('C', commutative=True)))))", "Mul(Symbol('K', commutative=True), Add(log(Mul(Symbol('C', commutative=True), Symbol('K', commutative=True))), Integer(-1)))", "Mul(Symbol('K', commutative=True), Add(log(Mul(Pow(Symbol('C', commutative=True), Integer(-1)), Symbol('K', commutative=True))), Integer(-1)))"]}, {"premise_expression": "G M", "variable": "M", "positive": "\\frac{G M^{2}}{2}", "negatives": ["\\frac{G^{2} M}{2}", "\\frac{M^{2}}{2 G}", "G M + \\sin{(M)}", "- \\cos{(G - M)}"], "srepr_premise_expression": "Mul(Symbol('G', commutative=True), Symbol('M', commutative=True))", "srepr_variable": "Symbol('M', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('G', commutative=True), Pow(Symbol('M', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(2)), Symbol('M', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(-1)), Pow(Symbol('M', commutative=True), Integer(2)))", "Add(Mul(Symbol('G', commutative=True), Symbol('M', commutative=True)), sin(Symbol('M', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('M', commutative=True)))))"]}, {"premise_expression": "\\frac{c}{Q}", "variable": "c", "positive": "\\frac{c^{2}}{2 Q}", "negatives": ["c \\log{(Q)}", "\\frac{c^{2} e^{Q}}{2}", "- \\frac{c^{2}}{2} + e^{c}", "c (- Q + \\log{(c^{Q})})"], "srepr_premise_expression": "Mul(Pow(Symbol('Q', commutative=True), Integer(-1)), Symbol('c', commutative=True))", "srepr_variable": "Symbol('c', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(-1)), Pow(Symbol('c', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('c', commutative=True), log(Symbol('Q', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('c', commutative=True), Integer(2)), exp(Symbol('Q', commutative=True)))", "Add(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('c', commutative=True), Integer(2))), exp(Symbol('c', commutative=True)))", "Mul(Symbol('c', commutative=True), Add(Mul(Integer(-1), Symbol('Q', commutative=True)), log(Pow(Symbol('c', commutative=True), Symbol('Q', commutative=True)))))"]}, {"premise_expression": "- w + \\cos{(U)}", "variable": "U", "positive": "- U w + \\sin{(U)}", "negatives": ["w \\log{(U)}", "e^{U + w}", "\\sin{(U + w)}", "\\frac{U (U - 2 w)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('w', commutative=True)), cos(Symbol('U', commutative=True)))", "srepr_variable": "Symbol('U', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('U', commutative=True), Symbol('w', commutative=True)), sin(Symbol('U', commutative=True)))", "srepr_negatives": ["Mul(Symbol('w', commutative=True), log(Symbol('U', commutative=True)))", "exp(Add(Symbol('U', commutative=True), Symbol('w', commutative=True)))", "sin(Add(Symbol('U', commutative=True), Symbol('w', commutative=True)))", "Mul(Rational(1, 2), Symbol('U', commutative=True), Add(Symbol('U', commutative=True), Mul(Integer(-1), Integer(2), Symbol('w', commutative=True))))"]}, {"premise_expression": "Q (- k + m)", "variable": "k", "positive": "\\frac{Q k (- k + 2 m)}{2}", "negatives": ["\\frac{Q^{2} (- k + m)}{2}", "\\frac{Q m (- 2 k + m)}{2}", "\\frac{k (2 Q^{m} + k)}{2}", "\\frac{k (2 Q + k + 2 m)}{2}"], "srepr_premise_expression": "Mul(Symbol('Q', commutative=True), Add(Mul(Integer(-1), Symbol('k', commutative=True)), Symbol('m', commutative=True)))", "srepr_variable": "Symbol('k', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('Q', commutative=True), Symbol('k', commutative=True), Add(Mul(Integer(-1), Symbol('k', commutative=True)), Mul(Integer(2), Symbol('m', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(2)), Add(Mul(Integer(-1), Symbol('k', commutative=True)), Symbol('m', commutative=True)))", "Mul(Rational(1, 2), Symbol('Q', commutative=True), Symbol('m', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('k', commutative=True)), Symbol('m', commutative=True)))", "Mul(Rational(1, 2), Symbol('k', commutative=True), Add(Mul(Integer(2), Pow(Symbol('Q', commutative=True), Symbol('m', commutative=True))), Symbol('k', commutative=True)))", "Mul(Rational(1, 2), Symbol('k', commutative=True), Add(Mul(Integer(2), Symbol('Q', commutative=True)), Symbol('k', commutative=True), Mul(Integer(2), Symbol('m', commutative=True))))"]}, {"premise_expression": "\\log{(H - h)}", "variable": "H", "positive": "H \\log{(H - h)} - H - h \\log{(H - h)}", "negatives": ["- H \\log{(- H + h)} + h \\log{(H - h)} - h", "H e^{\\frac{h}{H}} - h \\operatorname{Ei}{(\\frac{h}{H})}", "\\frac{H h (H - 2)}{2}", "- H h + \\sin{(H)}"], "srepr_premise_expression": "log(Add(Symbol('H', commutative=True), Mul(Integer(-1), Symbol('h', commutative=True))))", "srepr_variable": "Symbol('H', commutative=True)", "srepr_positive": "Add(Mul(Symbol('H', commutative=True), log(Add(Symbol('H', commutative=True), Mul(Integer(-1), Symbol('h', commutative=True))))), Mul(Integer(-1), Symbol('H', commutative=True)), Mul(Integer(-1), Symbol('h', commutative=True), log(Add(Symbol('H', commutative=True), Mul(Integer(-1), Symbol('h', commutative=True))))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('H', commutative=True), log(Add(Mul(Integer(-1), Symbol('H', commutative=True)), Symbol('h', commutative=True)))), Mul(Symbol('h', commutative=True), log(Add(Symbol('H', commutative=True), Mul(Integer(-1), Symbol('h', commutative=True))))), Mul(Integer(-1), Symbol('h', commutative=True)))", "Add(Mul(Symbol('H', commutative=True), exp(Mul(Pow(Symbol('H', commutative=True), Integer(-1)), Symbol('h', commutative=True)))), Mul(Integer(-1), Symbol('h', commutative=True), Ei(Mul(Pow(Symbol('H', commutative=True), Integer(-1)), Symbol('h', commutative=True)))))", "Mul(Rational(1, 2), Symbol('H', commutative=True), Symbol('h', commutative=True), Add(Symbol('H', commutative=True), Integer(-2)))", "Add(Mul(Integer(-1), Symbol('H', commutative=True), Symbol('h', commutative=True)), sin(Symbol('H', commutative=True)))"]}, {"premise_expression": "S y + v", "variable": "v", "positive": "\\frac{v (2 S y + v)}{2}", "negatives": ["\\frac{y (S y + 2 v)}{2}", "\\frac{S (S y + 2 v)}{2}", "\\frac{v (2 S + v)}{2 y}", "y^{S} \\log{(v)}"], "srepr_premise_expression": "Add(Mul(Symbol('S', commutative=True), Symbol('y', commutative=True)), Symbol('v', commutative=True))", "srepr_variable": "Symbol('v', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('v', commutative=True), Add(Mul(Integer(2), Symbol('S', commutative=True), Symbol('y', commutative=True)), Symbol('v', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('y', commutative=True), Add(Mul(Symbol('S', commutative=True), Symbol('y', commutative=True)), Mul(Integer(2), Symbol('v', commutative=True))))", "Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Mul(Symbol('S', commutative=True), Symbol('y', commutative=True)), Mul(Integer(2), Symbol('v', commutative=True))))", "Mul(Rational(1, 2), Symbol('v', commutative=True), Pow(Symbol('y', commutative=True), Integer(-1)), Add(Mul(Integer(2), Symbol('S', commutative=True)), Symbol('v', commutative=True)))", "Mul(Pow(Symbol('y', commutative=True), Symbol('S', commutative=True)), log(Symbol('v', commutative=True)))"]}, {"premise_expression": "- H + \\log{(l)}", "variable": "H", "positive": "\\frac{H (- H + 2 \\log{(l)})}{2}", "negatives": ["\\frac{H (H + 2 \\cos{(l)})}{2}", "\\frac{H (H + 2 l)}{2}", "\\frac{H (H + 4 l)}{2}", "l (- H + \\log{(l)} - 1)"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('H', commutative=True)), log(Symbol('l', commutative=True)))", "srepr_variable": "Symbol('H', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('H', commutative=True), Add(Mul(Integer(-1), Symbol('H', commutative=True)), Mul(Integer(2), log(Symbol('l', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('H', commutative=True), Add(Symbol('H', commutative=True), Mul(Integer(2), cos(Symbol('l', commutative=True)))))", "Mul(Rational(1, 2), Symbol('H', commutative=True), Add(Symbol('H', commutative=True), Mul(Integer(2), Symbol('l', commutative=True))))", "Mul(Rational(1, 2), Symbol('H', commutative=True), Add(Symbol('H', commutative=True), Mul(Integer(4), Symbol('l', commutative=True))))", "Mul(Symbol('l', commutative=True), Add(Mul(Integer(-1), Symbol('H', commutative=True)), log(Symbol('l', commutative=True)), Integer(-1)))"]}, {"premise_expression": "f + t", "variable": "f", "positive": "\\frac{f (f + 2 t)}{2}", "negatives": ["\\frac{f (- f + 2 t)}{2}", "\\frac{t (2 f + t)}{2}", "e^{f + t}", "f t + \\sin{(f)}"], "srepr_premise_expression": "Add(Symbol('f', commutative=True), Symbol('t', commutative=True))", "srepr_variable": "Symbol('f', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Symbol('f', commutative=True), Mul(Integer(2), Symbol('t', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Mul(Integer(-1), Symbol('f', commutative=True)), Mul(Integer(2), Symbol('t', commutative=True))))", "Mul(Rational(1, 2), Symbol('t', commutative=True), Add(Mul(Integer(2), Symbol('f', commutative=True)), Symbol('t', commutative=True)))", "exp(Add(Symbol('f', commutative=True), Symbol('t', commutative=True)))", "Add(Mul(Symbol('f', commutative=True), Symbol('t', commutative=True)), sin(Symbol('f', commutative=True)))"]}, {"premise_expression": "I + u", "variable": "u", "positive": "\\frac{u (2 I + u)}{2}", "negatives": ["\\frac{I (I + 2 u)}{2}", "\\sin{(I + u)}", "\\cos{(I - u)}", "u (\\log{(\\frac{I}{u})} + 1)"], "srepr_premise_expression": "Add(Symbol('I', commutative=True), Symbol('u', commutative=True))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(2), Symbol('I', commutative=True)), Symbol('u', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('I', commutative=True), Add(Symbol('I', commutative=True), Mul(Integer(2), Symbol('u', commutative=True))))", "sin(Add(Symbol('I', commutative=True), Symbol('u', commutative=True)))", "cos(Add(Symbol('I', commutative=True), Mul(Integer(-1), Symbol('u', commutative=True))))", "Mul(Symbol('u', commutative=True), Add(log(Mul(Symbol('I', commutative=True), Pow(Symbol('u', commutative=True), Integer(-1)))), Integer(1)))"]}, {"premise_expression": "r + e^{N}", "variable": "r", "positive": "\\frac{r (r + 2 e^{N})}{2}", "negatives": ["\\frac{r (r + 2 \\cos{(N)})}{2}", "N r + e^{N}", "N (r + \\log{(r)})", "r (\\log{(N r)} - 1)"], "srepr_premise_expression": "Add(Symbol('r', commutative=True), exp(Symbol('N', commutative=True)))", "srepr_variable": "Symbol('r', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Symbol('r', commutative=True), Mul(Integer(2), exp(Symbol('N', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Symbol('r', commutative=True), Mul(Integer(2), cos(Symbol('N', commutative=True)))))", "Add(Mul(Symbol('N', commutative=True), Symbol('r', commutative=True)), exp(Symbol('N', commutative=True)))", "Mul(Symbol('N', commutative=True), Add(Symbol('r', commutative=True), log(Symbol('r', commutative=True))))", "Mul(Symbol('r', commutative=True), Add(log(Mul(Symbol('N', commutative=True), Symbol('r', commutative=True))), Integer(-1)))"]}, {"premise_expression": "W X + k", "variable": "k", "positive": "\\frac{k (2 W X + k)}{2}", "negatives": ["\\frac{k (2 W + X k)}{2}", "\\frac{X (W X + 2 k)}{2}", "\\frac{W (W X + 2 k)}{2}", "\\frac{k (2 W - 2 X + k)}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('W', commutative=True), Symbol('X', commutative=True)), Symbol('k', commutative=True))", "srepr_variable": "Symbol('k', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('k', commutative=True), Add(Mul(Integer(2), Symbol('W', commutative=True), Symbol('X', commutative=True)), Symbol('k', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('k', commutative=True), Add(Mul(Integer(2), Symbol('W', commutative=True)), Mul(Symbol('X', commutative=True), Symbol('k', commutative=True))))", "Mul(Rational(1, 2), Symbol('X', commutative=True), Add(Mul(Symbol('W', commutative=True), Symbol('X', commutative=True)), Mul(Integer(2), Symbol('k', commutative=True))))", "Mul(Rational(1, 2), Symbol('W', commutative=True), Add(Mul(Symbol('W', commutative=True), Symbol('X', commutative=True)), Mul(Integer(2), Symbol('k', commutative=True))))", "Mul(Rational(1, 2), Symbol('k', commutative=True), Add(Mul(Integer(2), Symbol('W', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('X', commutative=True)), Symbol('k', commutative=True)))"]}, {"premise_expression": "e^{\\frac{u}{a}}", "variable": "u", "positive": "a e^{\\frac{u}{a}}", "negatives": ["e^{- a + u}", "\\frac{\\log{(u)}^{2}}{2}", "a u (\\log{(u)} - 1)", "a e^{\\frac{u}{a}} - u \\operatorname{Ei}{(\\frac{u}{a})}"], "srepr_premise_expression": "exp(Mul(Pow(Symbol('a', commutative=True), Integer(-1)), Symbol('u', commutative=True)))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "Mul(Symbol('a', commutative=True), exp(Mul(Pow(Symbol('a', commutative=True), Integer(-1)), Symbol('u', commutative=True))))", "srepr_negatives": ["exp(Add(Mul(Integer(-1), Symbol('a', commutative=True)), Symbol('u', commutative=True)))", "Mul(Rational(1, 2), Pow(log(Symbol('u', commutative=True)), Integer(2)))", "Mul(Symbol('a', commutative=True), Symbol('u', commutative=True), Add(log(Symbol('u', commutative=True)), Integer(-1)))", "Add(Mul(Symbol('a', commutative=True), exp(Mul(Pow(Symbol('a', commutative=True), Integer(-1)), Symbol('u', commutative=True)))), Mul(Integer(-1), Symbol('u', commutative=True), Ei(Mul(Pow(Symbol('a', commutative=True), Integer(-1)), Symbol('u', commutative=True)))))"]}, {"premise_expression": "a \\cos{(h)}", "variable": "a", "positive": "\\frac{a^{2} \\cos{(h)}}{2}", "negatives": ["\\frac{a^{2} h}{2}", "\\frac{a (- a + 2 \\cos{(h)})}{2}", "a \\sin{(h)}", "\\frac{a (a + 2 e^{h})}{2}"], "srepr_premise_expression": "Mul(Symbol('a', commutative=True), cos(Symbol('h', commutative=True)))", "srepr_variable": "Symbol('a', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('a', commutative=True), Integer(2)), cos(Symbol('h', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('a', commutative=True), Integer(2)), Symbol('h', commutative=True))", "Mul(Rational(1, 2), Symbol('a', commutative=True), Add(Mul(Integer(-1), Symbol('a', commutative=True)), Mul(Integer(2), cos(Symbol('h', commutative=True)))))", "Mul(Symbol('a', commutative=True), sin(Symbol('h', commutative=True)))", "Mul(Rational(1, 2), Symbol('a', commutative=True), Add(Symbol('a', commutative=True), Mul(Integer(2), exp(Symbol('h', commutative=True)))))"]}, {"premise_expression": "D - L", "variable": "D", "positive": "\\frac{D (D - 2 L)}{2}", "negatives": ["\\frac{D (D + 2 L)}{2}", "\\frac{L (2 D - L)}{2}", "\\frac{D (D + 2 \\sin{(L)})}{2}", "\\frac{D^{2} \\log{(L)}}{2}"], "srepr_premise_expression": "Add(Symbol('D', commutative=True), Mul(Integer(-1), Symbol('L', commutative=True)))", "srepr_variable": "Symbol('D', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('D', commutative=True), Add(Symbol('D', commutative=True), Mul(Integer(-1), Integer(2), Symbol('L', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('D', commutative=True), Add(Symbol('D', commutative=True), Mul(Integer(2), Symbol('L', commutative=True))))", "Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Mul(Integer(2), Symbol('D', commutative=True)), Mul(Integer(-1), Symbol('L', commutative=True))))", "Mul(Rational(1, 2), Symbol('D', commutative=True), Add(Symbol('D', commutative=True), Mul(Integer(2), sin(Symbol('L', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(2)), log(Symbol('L', commutative=True)))"]}, {"premise_expression": "- S + m", "variable": "S", "positive": "\\frac{S (- S + 2 m)}{2}", "negatives": ["\\frac{m (- 2 S + m)}{2}", "\\frac{S (S + 2 \\log{(m)})}{2}", "\\frac{S^{2} \\sin{(m)}}{2}", "\\sin{(S + m)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('S', commutative=True)), Symbol('m', commutative=True))", "srepr_variable": "Symbol('S', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Mul(Integer(-1), Symbol('S', commutative=True)), Mul(Integer(2), Symbol('m', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('S', commutative=True)), Symbol('m', commutative=True)))", "Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Symbol('S', commutative=True), Mul(Integer(2), log(Symbol('m', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('S', commutative=True), Integer(2)), sin(Symbol('m', commutative=True)))", "sin(Add(Symbol('S', commutative=True), Symbol('m', commutative=True)))"]}, {"premise_expression": "e^{- E + T}", "variable": "E", "positive": "- e^{- E + T}", "negatives": ["e^{- E + T}", "\\sin{(E + T)}", "T \\sin{(E)}", "\\frac{E^{2} T}{2}"], "srepr_premise_expression": "exp(Add(Mul(Integer(-1), Symbol('E', commutative=True)), Symbol('T', commutative=True)))", "srepr_variable": "Symbol('E', commutative=True)", "srepr_positive": "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('E', commutative=True)), Symbol('T', commutative=True))))", "srepr_negatives": ["exp(Add(Mul(Integer(-1), Symbol('E', commutative=True)), Symbol('T', commutative=True)))", "sin(Add(Symbol('E', commutative=True), Symbol('T', commutative=True)))", "Mul(Symbol('T', commutative=True), sin(Symbol('E', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('E', commutative=True), Integer(2)), Symbol('T', commutative=True))"]}, {"premise_expression": "P - W", "variable": "W", "positive": "\\frac{W (2 P - W)}{2}", "negatives": ["\\frac{P (P - 2 W)}{2}", "e^{P + W}", "- P \\cos{(W)}", "P e^{W}"], "srepr_premise_expression": "Add(Symbol('P', commutative=True), Mul(Integer(-1), Symbol('W', commutative=True)))", "srepr_variable": "Symbol('W', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('W', commutative=True), Add(Mul(Integer(2), Symbol('P', commutative=True)), Mul(Integer(-1), Symbol('W', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Symbol('P', commutative=True), Mul(Integer(-1), Integer(2), Symbol('W', commutative=True))))", "exp(Add(Symbol('P', commutative=True), Symbol('W', commutative=True)))", "Mul(Integer(-1), Symbol('P', commutative=True), cos(Symbol('W', commutative=True)))", "Mul(Symbol('P', commutative=True), exp(Symbol('W', commutative=True)))"]}, {"premise_expression": "\\log{(\\frac{s}{F})}", "variable": "s", "positive": "s (\\log{(\\frac{s}{F})} - 1)", "negatives": ["F (\\log{(\\frac{s}{F})} + 1)", "\\frac{s (\\log{(s)} - 1)}{F}", "F e^{\\frac{s}{F}}", "\\frac{s (2 F + s)}{2}"], "srepr_premise_expression": "log(Mul(Pow(Symbol('F', commutative=True), Integer(-1)), Symbol('s', commutative=True)))", "srepr_variable": "Symbol('s', commutative=True)", "srepr_positive": "Mul(Symbol('s', commutative=True), Add(log(Mul(Pow(Symbol('F', commutative=True), Integer(-1)), Symbol('s', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('F', commutative=True), Add(log(Mul(Pow(Symbol('F', commutative=True), Integer(-1)), Symbol('s', commutative=True))), Integer(1)))", "Mul(Pow(Symbol('F', commutative=True), Integer(-1)), Symbol('s', commutative=True), Add(log(Symbol('s', commutative=True)), Integer(-1)))", "Mul(Symbol('F', commutative=True), exp(Mul(Pow(Symbol('F', commutative=True), Integer(-1)), Symbol('s', commutative=True))))", "Mul(Rational(1, 2), Symbol('s', commutative=True), Add(Mul(Integer(2), Symbol('F', commutative=True)), Symbol('s', commutative=True)))"]}, {"premise_expression": "- \\sin{(I - l)}", "variable": "l", "positive": "- \\cos{(I - l)}", "negatives": ["\\cos{(I - l)}", "- e^{I - l}", "l (\\log{(I l)} - 1)", "l - \\frac{l^{2}}{2 I}"], "srepr_premise_expression": "Mul(Integer(-1), sin(Add(Symbol('I', commutative=True), Mul(Integer(-1), Symbol('l', commutative=True)))))", "srepr_variable": "Symbol('l', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('I', commutative=True), Mul(Integer(-1), Symbol('l', commutative=True)))))", "srepr_negatives": ["cos(Add(Symbol('I', commutative=True), Mul(Integer(-1), Symbol('l', commutative=True))))", "Mul(Integer(-1), exp(Add(Symbol('I', commutative=True), Mul(Integer(-1), Symbol('l', commutative=True)))))", "Mul(Symbol('l', commutative=True), Add(log(Mul(Symbol('I', commutative=True), Symbol('l', commutative=True))), Integer(-1)))", "Add(Symbol('l', commutative=True), Mul(Integer(-1), Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(-1)), Pow(Symbol('l', commutative=True), Integer(2))))"]}, {"premise_expression": "K L", "variable": "K", "positive": "\\frac{K^{2} L}{2}", "negatives": ["\\frac{K L^{2}}{2}", "\\frac{K^{2} \\log{(L)}}{2}", "\\frac{K (- K + 2 L)}{2}", "L \\sin{(K)}"], "srepr_premise_expression": "Mul(Symbol('K', commutative=True), Symbol('L', commutative=True))", "srepr_variable": "Symbol('K', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('K', commutative=True), Integer(2)), Symbol('L', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('K', commutative=True), Pow(Symbol('L', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('K', commutative=True), Integer(2)), log(Symbol('L', commutative=True)))", "Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Mul(Integer(-1), Symbol('K', commutative=True)), Mul(Integer(2), Symbol('L', commutative=True))))", "Mul(Symbol('L', commutative=True), sin(Symbol('K', commutative=True)))"]}, {"premise_expression": "g + \\cos{(h)}", "variable": "g", "positive": "\\frac{g (g + 2 \\cos{(h)})}{2}", "negatives": ["\\frac{g (g + 2 \\sin{(h)})}{2}", "g h + \\sin{(h)}", "\\sin{(g + h)}", "\\sin{(g - h)}"], "srepr_premise_expression": "Add(Symbol('g', commutative=True), cos(Symbol('h', commutative=True)))", "srepr_variable": "Symbol('g', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Symbol('g', commutative=True), Mul(Integer(2), cos(Symbol('h', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Symbol('g', commutative=True), Mul(Integer(2), sin(Symbol('h', commutative=True)))))", "Add(Mul(Symbol('g', commutative=True), Symbol('h', commutative=True)), sin(Symbol('h', commutative=True)))", "sin(Add(Symbol('g', commutative=True), Symbol('h', commutative=True)))", "sin(Add(Symbol('g', commutative=True), Mul(Integer(-1), Symbol('h', commutative=True))))"]}, {"premise_expression": "\\frac{I Z}{s}", "variable": "Z", "positive": "\\frac{I Z^{2}}{2 s}", "negatives": ["\\frac{I^{2} Z}{2 s}", "I Z \\log{(s)}", "\\frac{Z^{2} s}{2 I}", "- Z s + \\frac{Z^{2}}{2 I}"], "srepr_premise_expression": "Mul(Symbol('I', commutative=True), Symbol('Z', commutative=True), Pow(Symbol('s', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('Z', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('I', commutative=True), Pow(Symbol('Z', commutative=True), Integer(2)), Pow(Symbol('s', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(2)), Symbol('Z', commutative=True), Pow(Symbol('s', commutative=True), Integer(-1)))", "Mul(Symbol('I', commutative=True), Symbol('Z', commutative=True), log(Symbol('s', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(-1)), Pow(Symbol('Z', commutative=True), Integer(2)), Symbol('s', commutative=True))", "Add(Mul(Integer(-1), Symbol('Z', commutative=True), Symbol('s', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(-1)), Pow(Symbol('Z', commutative=True), Integer(2))))"]}, {"premise_expression": "\\cos{(C + y)}", "variable": "y", "positive": "\\sin{(C + y)}", "negatives": ["\\frac{y (2 C - y)}{2}", "C \\log{(y)}", "C y - \\cos{(y)}", "\\frac{y^{2} \\sin{(C)}}{2}"], "srepr_premise_expression": "cos(Add(Symbol('C', commutative=True), Symbol('y', commutative=True)))", "srepr_variable": "Symbol('y', commutative=True)", "srepr_positive": "sin(Add(Symbol('C', commutative=True), Symbol('y', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('y', commutative=True), Add(Mul(Integer(2), Symbol('C', commutative=True)), Mul(Integer(-1), Symbol('y', commutative=True))))", "Mul(Symbol('C', commutative=True), log(Symbol('y', commutative=True)))", "Add(Mul(Symbol('C', commutative=True), Symbol('y', commutative=True)), Mul(Integer(-1), cos(Symbol('y', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('y', commutative=True), Integer(2)), sin(Symbol('C', commutative=True)))"]}, {"premise_expression": "Q + w", "variable": "w", "positive": "\\frac{w (2 Q + w)}{2}", "negatives": ["\\frac{Q (Q + 2 w)}{2}", "\\frac{w^{2}}{2 Q}", "w \\sin{(1)}", "\\frac{w (- w + 2 \\sin{(Q)})}{2}"], "srepr_premise_expression": "Add(Symbol('Q', commutative=True), Symbol('w', commutative=True))", "srepr_variable": "Symbol('w', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('w', commutative=True), Add(Mul(Integer(2), Symbol('Q', commutative=True)), Symbol('w', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Symbol('Q', commutative=True), Mul(Integer(2), Symbol('w', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(-1)), Pow(Symbol('w', commutative=True), Integer(2)))", "Mul(Symbol('w', commutative=True), sin(Integer(1)))", "Mul(Rational(1, 2), Symbol('w', commutative=True), Add(Mul(Integer(-1), Symbol('w', commutative=True)), Mul(Integer(2), sin(Symbol('Q', commutative=True)))))"]}, {"premise_expression": "f + o", "variable": "o", "positive": "\\frac{o (2 f + o)}{2}", "negatives": ["\\frac{f (f + 2 o)}{2}", "e^{f + o}", "f e^{o}", "o (\\log{(\\frac{o}{f})} - 1)"], "srepr_premise_expression": "Add(Symbol('f', commutative=True), Symbol('o', commutative=True))", "srepr_variable": "Symbol('o', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Mul(Integer(2), Symbol('f', commutative=True)), Symbol('o', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Symbol('f', commutative=True), Mul(Integer(2), Symbol('o', commutative=True))))", "exp(Add(Symbol('f', commutative=True), Symbol('o', commutative=True)))", "Mul(Symbol('f', commutative=True), exp(Symbol('o', commutative=True)))", "Mul(Symbol('o', commutative=True), Add(log(Mul(Pow(Symbol('f', commutative=True), Integer(-1)), Symbol('o', commutative=True))), Integer(-1)))"]}, {"premise_expression": "W (N - T)", "variable": "W", "positive": "\\frac{W^{2} (N - T)}{2}", "negatives": ["\\frac{T W (2 N - T)}{2}", "\\frac{N W (N - 2 T)}{2}", "\\frac{W (2 N T - W)}{2}", "\\frac{N W (2 T + W)}{2}"], "srepr_premise_expression": "Mul(Symbol('W', commutative=True), Add(Symbol('N', commutative=True), Mul(Integer(-1), Symbol('T', commutative=True))))", "srepr_variable": "Symbol('W', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('W', commutative=True), Integer(2)), Add(Symbol('N', commutative=True), Mul(Integer(-1), Symbol('T', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('T', commutative=True), Symbol('W', commutative=True), Add(Mul(Integer(2), Symbol('N', commutative=True)), Mul(Integer(-1), Symbol('T', commutative=True))))", "Mul(Rational(1, 2), Symbol('N', commutative=True), Symbol('W', commutative=True), Add(Symbol('N', commutative=True), Mul(Integer(-1), Integer(2), Symbol('T', commutative=True))))", "Mul(Rational(1, 2), Symbol('W', commutative=True), Add(Mul(Integer(2), Symbol('N', commutative=True), Symbol('T', commutative=True)), Mul(Integer(-1), Symbol('W', commutative=True))))", "Mul(Rational(1, 2), Symbol('N', commutative=True), Symbol('W', commutative=True), Add(Mul(Integer(2), Symbol('T', commutative=True)), Symbol('W', commutative=True)))"]}, {"premise_expression": "\\frac{h}{o} - o", "variable": "o", "positive": "h \\log{(o)} - \\frac{o^{2}}{2}", "negatives": ["\\frac{h^{2}}{2 o} - h o", "\\frac{o (- 2 h + o)}{2}", "- h o - \\cos{(o)}", "\\frac{o^{2} \\log{(h)}}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('h', commutative=True), Pow(Symbol('o', commutative=True), Integer(-1))), Mul(Integer(-1), Symbol('o', commutative=True)))", "srepr_variable": "Symbol('o', commutative=True)", "srepr_positive": "Add(Mul(Symbol('h', commutative=True), log(Symbol('o', commutative=True))), Mul(Integer(-1), Rational(1, 2), Pow(Symbol('o', commutative=True), Integer(2))))", "srepr_negatives": ["Add(Mul(Rational(1, 2), Pow(Symbol('h', commutative=True), Integer(2)), Pow(Symbol('o', commutative=True), Integer(-1))), Mul(Integer(-1), Symbol('h', commutative=True), Symbol('o', commutative=True)))", "Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('h', commutative=True)), Symbol('o', commutative=True)))", "Add(Mul(Integer(-1), Symbol('h', commutative=True), Symbol('o', commutative=True)), Mul(Integer(-1), cos(Symbol('o', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('o', commutative=True), Integer(2)), log(Symbol('h', commutative=True)))"]}, {"premise_expression": "U + Y + r", "variable": "U", "positive": "U (\\frac{U}{2} + Y + r)", "negatives": ["\\frac{U (U + 2 Y - 2 r)}{2}", "\\frac{r (2 U + 2 Y + r)}{2}", "\\frac{Y (2 U + Y + 2 r)}{2}", "\\frac{U^{2} Y}{2 r}"], "srepr_premise_expression": "Add(Symbol('U', commutative=True), Symbol('Y', commutative=True), Symbol('r', commutative=True))", "srepr_variable": "Symbol('U', commutative=True)", "srepr_positive": "Mul(Symbol('U', commutative=True), Add(Mul(Rational(1, 2), Symbol('U', commutative=True)), Symbol('Y', commutative=True), Symbol('r', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('U', commutative=True), Add(Symbol('U', commutative=True), Mul(Integer(2), Symbol('Y', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('r', commutative=True))))", "Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(2), Symbol('U', commutative=True)), Mul(Integer(2), Symbol('Y', commutative=True)), Symbol('r', commutative=True)))", "Mul(Rational(1, 2), Symbol('Y', commutative=True), Add(Mul(Integer(2), Symbol('U', commutative=True)), Symbol('Y', commutative=True), Mul(Integer(2), Symbol('r', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('U', commutative=True), Integer(2)), Symbol('Y', commutative=True), Pow(Symbol('r', commutative=True), Integer(-1)))"]}, {"premise_expression": "\\log{(K + t)}", "variable": "K", "positive": "K \\log{(K + t)} - K + t \\log{(K + t)}", "negatives": ["K \\log{(K + t)} + t \\log{(K + t)} - t", "K \\cos{(\\frac{t}{K})} + t \\operatorname{Si}{(\\frac{t}{K})}", "\\frac{K (- K + 2 \\cos{(t)})}{2}", "K t (\\log{(K)} - 1)"], "srepr_premise_expression": "log(Add(Symbol('K', commutative=True), Symbol('t', commutative=True)))", "srepr_variable": "Symbol('K', commutative=True)", "srepr_positive": "Add(Mul(Symbol('K', commutative=True), log(Add(Symbol('K', commutative=True), Symbol('t', commutative=True)))), Mul(Integer(-1), Symbol('K', commutative=True)), Mul(Symbol('t', commutative=True), log(Add(Symbol('K', commutative=True), Symbol('t', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('K', commutative=True), log(Add(Symbol('K', commutative=True), Symbol('t', commutative=True)))), Mul(Symbol('t', commutative=True), log(Add(Symbol('K', commutative=True), Symbol('t', commutative=True)))), Mul(Integer(-1), Symbol('t', commutative=True)))", "Add(Mul(Symbol('K', commutative=True), cos(Mul(Pow(Symbol('K', commutative=True), Integer(-1)), Symbol('t', commutative=True)))), Mul(Symbol('t', commutative=True), Si(Mul(Pow(Symbol('K', commutative=True), Integer(-1)), Symbol('t', commutative=True)))))", "Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Mul(Integer(-1), Symbol('K', commutative=True)), Mul(Integer(2), cos(Symbol('t', commutative=True)))))", "Mul(Symbol('K', commutative=True), Symbol('t', commutative=True), Add(log(Symbol('K', commutative=True)), Integer(-1)))"]}, {"premise_expression": "- Z + a + h", "variable": "Z", "positive": "Z (- \\frac{Z}{2} + a + h)", "negatives": ["\\frac{Z (Z - 2 a - 2 h)}{2}", "\\frac{a (- 2 Z + a + 2 h)}{2}", "\\frac{h (- 2 Z + 2 a + h)}{2}", "\\frac{Z (Z a + 2 h)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('Z', commutative=True)), Symbol('a', commutative=True), Symbol('h', commutative=True))", "srepr_variable": "Symbol('Z', commutative=True)", "srepr_positive": "Mul(Symbol('Z', commutative=True), Add(Mul(Integer(-1), Rational(1, 2), Symbol('Z', commutative=True)), Symbol('a', commutative=True), Symbol('h', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Symbol('Z', commutative=True), Mul(Integer(-1), Integer(2), Symbol('a', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('h', commutative=True))))", "Mul(Rational(1, 2), Symbol('a', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('Z', commutative=True)), Symbol('a', commutative=True), Mul(Integer(2), Symbol('h', commutative=True))))", "Mul(Rational(1, 2), Symbol('h', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('Z', commutative=True)), Mul(Integer(2), Symbol('a', commutative=True)), Symbol('h', commutative=True)))", "Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Mul(Symbol('Z', commutative=True), Symbol('a', commutative=True)), Mul(Integer(2), Symbol('h', commutative=True))))"]}, {"premise_expression": "\\frac{E + t}{U}", "variable": "t", "positive": "\\frac{t (2 E + t)}{2 U}", "negatives": ["\\frac{E (E + 2 t)}{2 U}", "\\frac{E t (2 U - t)}{2}", "(E + t) \\log{(U)}", "\\frac{t (- 2 E + 2 U + t)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('U', commutative=True), Integer(-1)), Add(Symbol('E', commutative=True), Symbol('t', commutative=True)))", "srepr_variable": "Symbol('t', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('U', commutative=True), Integer(-1)), Symbol('t', commutative=True), Add(Mul(Integer(2), Symbol('E', commutative=True)), Symbol('t', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('E', commutative=True), Pow(Symbol('U', commutative=True), Integer(-1)), Add(Symbol('E', commutative=True), Mul(Integer(2), Symbol('t', commutative=True))))", "Mul(Rational(1, 2), Symbol('E', commutative=True), Symbol('t', commutative=True), Add(Mul(Integer(2), Symbol('U', commutative=True)), Mul(Integer(-1), Symbol('t', commutative=True))))", "Mul(Add(Symbol('E', commutative=True), Symbol('t', commutative=True)), log(Symbol('U', commutative=True)))", "Mul(Rational(1, 2), Symbol('t', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('E', commutative=True)), Mul(Integer(2), Symbol('U', commutative=True)), Symbol('t', commutative=True)))"]}, {"premise_expression": "E + T", "variable": "E", "positive": "\\frac{E (E + 2 T)}{2}", "negatives": ["\\frac{T (2 E + T)}{2}", "\\frac{E (E + 2 \\cos{(T)})}{2}", "\\sin{(E + T)}", "\\frac{E^{2} \\sin{(T)}}{2}"], "srepr_premise_expression": "Add(Symbol('E', commutative=True), Symbol('T', commutative=True))", "srepr_variable": "Symbol('E', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('E', commutative=True), Add(Symbol('E', commutative=True), Mul(Integer(2), Symbol('T', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('T', commutative=True), Add(Mul(Integer(2), Symbol('E', commutative=True)), Symbol('T', commutative=True)))", "Mul(Rational(1, 2), Symbol('E', commutative=True), Add(Symbol('E', commutative=True), Mul(Integer(2), cos(Symbol('T', commutative=True)))))", "sin(Add(Symbol('E', commutative=True), Symbol('T', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('E', commutative=True), Integer(2)), sin(Symbol('T', commutative=True)))"]}, {"premise_expression": "J - U", "variable": "U", "positive": "\\frac{U (2 J - U)}{2}", "negatives": ["\\frac{J (J - 2 U)}{2}", "e^{- J + U}", "e^{J + U}", "J \\log{(U)}"], "srepr_premise_expression": "Add(Symbol('J', commutative=True), Mul(Integer(-1), Symbol('U', commutative=True)))", "srepr_variable": "Symbol('U', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('U', commutative=True), Add(Mul(Integer(2), Symbol('J', commutative=True)), Mul(Integer(-1), Symbol('U', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('J', commutative=True), Add(Symbol('J', commutative=True), Mul(Integer(-1), Integer(2), Symbol('U', commutative=True))))", "exp(Add(Mul(Integer(-1), Symbol('J', commutative=True)), Symbol('U', commutative=True)))", "exp(Add(Symbol('J', commutative=True), Symbol('U', commutative=True)))", "Mul(Symbol('J', commutative=True), log(Symbol('U', commutative=True)))"]}, {"premise_expression": "- m + e^{v}", "variable": "v", "positive": "- m v + e^{v}", "negatives": ["m v + \\sin{(v)}", "\\frac{m (- m + 2 e^{v})}{2}", "e^{m + v}", "\\frac{v (- v + 2 e^{m})}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('m', commutative=True)), exp(Symbol('v', commutative=True)))", "srepr_variable": "Symbol('v', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('m', commutative=True), Symbol('v', commutative=True)), exp(Symbol('v', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('m', commutative=True), Symbol('v', commutative=True)), sin(Symbol('v', commutative=True)))", "Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Mul(Integer(-1), Symbol('m', commutative=True)), Mul(Integer(2), exp(Symbol('v', commutative=True)))))", "exp(Add(Symbol('m', commutative=True), Symbol('v', commutative=True)))", "Mul(Rational(1, 2), Symbol('v', commutative=True), Add(Mul(Integer(-1), Symbol('v', commutative=True)), Mul(Integer(2), exp(Symbol('m', commutative=True)))))"]}, {"premise_expression": "\\frac{\\log{(B)}}{y}", "variable": "B", "positive": "\\frac{B (\\log{(B)} - 1)}{y}", "negatives": ["B (\\log{(\\frac{y}{B})} + 1)", "\\frac{B (B - 2 y)}{2}", "\\log{(B)} \\log{(y)}", "\\frac{\\sin{(B)}}{y}"], "srepr_premise_expression": "Mul(Pow(Symbol('y', commutative=True), Integer(-1)), log(Symbol('B', commutative=True)))", "srepr_variable": "Symbol('B', commutative=True)", "srepr_positive": "Mul(Symbol('B', commutative=True), Pow(Symbol('y', commutative=True), Integer(-1)), Add(log(Symbol('B', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('B', commutative=True), Add(log(Mul(Pow(Symbol('B', commutative=True), Integer(-1)), Symbol('y', commutative=True))), Integer(1)))", "Mul(Rational(1, 2), Symbol('B', commutative=True), Add(Symbol('B', commutative=True), Mul(Integer(-1), Integer(2), Symbol('y', commutative=True))))", "Mul(log(Symbol('B', commutative=True)), log(Symbol('y', commutative=True)))", "Mul(Pow(Symbol('y', commutative=True), Integer(-1)), sin(Symbol('B', commutative=True)))"]}, {"premise_expression": "G - N", "variable": "G", "positive": "\\frac{G (G - 2 N)}{2}", "negatives": ["\\frac{N (2 G - N)}{2}", "\\frac{G^{2} N}{2}", "\\cos{(G - N)}", "G N + e^{G}"], "srepr_premise_expression": "Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('N', commutative=True)))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Symbol('G', commutative=True), Mul(Integer(-1), Integer(2), Symbol('N', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Mul(Integer(2), Symbol('G', commutative=True)), Mul(Integer(-1), Symbol('N', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(2)), Symbol('N', commutative=True))", "cos(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('N', commutative=True))))", "Add(Mul(Symbol('G', commutative=True), Symbol('N', commutative=True)), exp(Symbol('G', commutative=True)))"]}, {"premise_expression": "\\frac{\\cos{(R)}}{b}", "variable": "b", "positive": "\\log{(b)} \\cos{(R)}", "negatives": ["\\frac{b^{2} \\log{(R)}}{2}", "\\frac{\\sin{(R)}}{b}", "R e^{\\frac{b}{R}}", "\\frac{b (2 R + b)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('b', commutative=True), Integer(-1)), cos(Symbol('R', commutative=True)))", "srepr_variable": "Symbol('b', commutative=True)", "srepr_positive": "Mul(log(Symbol('b', commutative=True)), cos(Symbol('R', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('b', commutative=True), Integer(2)), log(Symbol('R', commutative=True)))", "Mul(Pow(Symbol('b', commutative=True), Integer(-1)), sin(Symbol('R', commutative=True)))", "Mul(Symbol('R', commutative=True), exp(Mul(Pow(Symbol('R', commutative=True), Integer(-1)), Symbol('b', commutative=True))))", "Mul(Rational(1, 2), Symbol('b', commutative=True), Add(Mul(Integer(2), Symbol('R', commutative=True)), Symbol('b', commutative=True)))"]}, {"premise_expression": "\\cos{(A - S)}", "variable": "A", "positive": "\\sin{(A - S)}", "negatives": ["- \\sin{(A - S)}", "- \\frac{\\cos{(A)}}{S}", "S e^{A}", "S \\log{(A)}"], "srepr_premise_expression": "cos(Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('S', commutative=True))))", "srepr_variable": "Symbol('A', commutative=True)", "srepr_positive": "sin(Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('S', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('S', commutative=True)))))", "Mul(Integer(-1), Pow(Symbol('S', commutative=True), Integer(-1)), cos(Symbol('A', commutative=True)))", "Mul(Symbol('S', commutative=True), exp(Symbol('A', commutative=True)))", "Mul(Symbol('S', commutative=True), log(Symbol('A', commutative=True)))"]}, {"premise_expression": "\\frac{\\log{(a)}}{F}", "variable": "a", "positive": "\\frac{a (\\log{(a)} - 1)}{F}", "negatives": ["a (\\log{(\\frac{F}{a})} + 1)", "\\log{(F)} \\log{(a)}", "\\sin{(F + a)}", "a (- F + \\log{(F)})"], "srepr_premise_expression": "Mul(Pow(Symbol('F', commutative=True), Integer(-1)), log(Symbol('a', commutative=True)))", "srepr_variable": "Symbol('a', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('F', commutative=True), Integer(-1)), Symbol('a', commutative=True), Add(log(Symbol('a', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('a', commutative=True), Add(log(Mul(Symbol('F', commutative=True), Pow(Symbol('a', commutative=True), Integer(-1)))), Integer(1)))", "Mul(log(Symbol('F', commutative=True)), log(Symbol('a', commutative=True)))", "sin(Add(Symbol('F', commutative=True), Symbol('a', commutative=True)))", "Mul(Symbol('a', commutative=True), Add(Mul(Integer(-1), Symbol('F', commutative=True)), log(Symbol('F', commutative=True))))"]}, {"premise_expression": "A + U", "variable": "U", "positive": "\\frac{U (2 A + U)}{2}", "negatives": ["\\frac{U (2 A - U)}{2}", "\\frac{A (A + 2 U)}{2}", "\\frac{U^{2} \\log{(A)}}{2}", "\\cos{(A - U)}"], "srepr_premise_expression": "Add(Symbol('A', commutative=True), Symbol('U', commutative=True))", "srepr_variable": "Symbol('U', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('U', commutative=True), Add(Mul(Integer(2), Symbol('A', commutative=True)), Symbol('U', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('U', commutative=True), Add(Mul(Integer(2), Symbol('A', commutative=True)), Mul(Integer(-1), Symbol('U', commutative=True))))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Symbol('A', commutative=True), Mul(Integer(2), Symbol('U', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('U', commutative=True), Integer(2)), log(Symbol('A', commutative=True)))", "cos(Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('U', commutative=True))))"]}, {"premise_expression": "\\log{(E - I)}", "variable": "I", "positive": "- E \\log{(- E + I)} + I \\log{(E - I)} - I", "negatives": ["- E \\log{(- E + I)} + I \\log{(- E + I)} - I", "E \\log{(E - I)} - E - I \\log{(E - I)}", "I (- E + \\log{(I^{E})})", "- E I + \\sin{(I)}"], "srepr_premise_expression": "log(Add(Symbol('E', commutative=True), Mul(Integer(-1), Symbol('I', commutative=True))))", "srepr_variable": "Symbol('I', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('E', commutative=True), log(Add(Mul(Integer(-1), Symbol('E', commutative=True)), Symbol('I', commutative=True)))), Mul(Symbol('I', commutative=True), log(Add(Symbol('E', commutative=True), Mul(Integer(-1), Symbol('I', commutative=True))))), Mul(Integer(-1), Symbol('I', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('E', commutative=True), log(Add(Mul(Integer(-1), Symbol('E', commutative=True)), Symbol('I', commutative=True)))), Mul(Symbol('I', commutative=True), log(Add(Mul(Integer(-1), Symbol('E', commutative=True)), Symbol('I', commutative=True)))), Mul(Integer(-1), Symbol('I', commutative=True)))", "Add(Mul(Symbol('E', commutative=True), log(Add(Symbol('E', commutative=True), Mul(Integer(-1), Symbol('I', commutative=True))))), Mul(Integer(-1), Symbol('E', commutative=True)), Mul(Integer(-1), Symbol('I', commutative=True), log(Add(Symbol('E', commutative=True), Mul(Integer(-1), Symbol('I', commutative=True))))))", "Mul(Symbol('I', commutative=True), Add(Mul(Integer(-1), Symbol('E', commutative=True)), log(Pow(Symbol('I', commutative=True), Symbol('E', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('E', commutative=True), Symbol('I', commutative=True)), sin(Symbol('I', commutative=True)))"]}, {"premise_expression": "\\log{(B^{a})}", "variable": "B", "positive": "B (- a + \\log{(B^{a})})", "negatives": ["\\frac{B (B + 2 \\cos{(a)})}{2}", "\\frac{a^{2} \\log{(B)}}{2}", "- \\frac{\\cos{(B)}}{a}", "- \\cos{(B + a)}"], "srepr_premise_expression": "log(Pow(Symbol('B', commutative=True), Symbol('a', commutative=True)))", "srepr_variable": "Symbol('B', commutative=True)", "srepr_positive": "Mul(Symbol('B', commutative=True), Add(Mul(Integer(-1), Symbol('a', commutative=True)), log(Pow(Symbol('B', commutative=True), Symbol('a', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('B', commutative=True), Add(Symbol('B', commutative=True), Mul(Integer(2), cos(Symbol('a', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('a', commutative=True), Integer(2)), log(Symbol('B', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('a', commutative=True), Integer(-1)), cos(Symbol('B', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('B', commutative=True), Symbol('a', commutative=True))))"]}, {"premise_expression": "\\log{(- B + M)}", "variable": "M", "positive": "- B \\log{(- B + M)} + M \\log{(- B + M)} - M", "negatives": ["B \\log{(- B + M)} - B - M \\log{(B - M)}", "B M (\\log{(M)} - 1)", "e^{B} \\log{(M)}", "- B M - \\cos{(M)}"], "srepr_premise_expression": "log(Add(Mul(Integer(-1), Symbol('B', commutative=True)), Symbol('M', commutative=True)))", "srepr_variable": "Symbol('M', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('B', commutative=True), log(Add(Mul(Integer(-1), Symbol('B', commutative=True)), Symbol('M', commutative=True)))), Mul(Symbol('M', commutative=True), log(Add(Mul(Integer(-1), Symbol('B', commutative=True)), Symbol('M', commutative=True)))), Mul(Integer(-1), Symbol('M', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('B', commutative=True), log(Add(Mul(Integer(-1), Symbol('B', commutative=True)), Symbol('M', commutative=True)))), Mul(Integer(-1), Symbol('B', commutative=True)), Mul(Integer(-1), Symbol('M', commutative=True), log(Add(Symbol('B', commutative=True), Mul(Integer(-1), Symbol('M', commutative=True))))))", "Mul(Symbol('B', commutative=True), Symbol('M', commutative=True), Add(log(Symbol('M', commutative=True)), Integer(-1)))", "Mul(exp(Symbol('B', commutative=True)), log(Symbol('M', commutative=True)))", "Add(Mul(Integer(-1), Symbol('B', commutative=True), Symbol('M', commutative=True)), Mul(Integer(-1), cos(Symbol('M', commutative=True))))"]}, {"premise_expression": "\\cos{(M + Y)}", "variable": "M", "positive": "\\sin{(M + Y)}", "negatives": ["\\frac{M^{2}}{2 Y}", "Y \\log{(M)}", "- Y \\cos{(M)}", "- M Y + e^{M}"], "srepr_premise_expression": "cos(Add(Symbol('M', commutative=True), Symbol('Y', commutative=True)))", "srepr_variable": "Symbol('M', commutative=True)", "srepr_positive": "sin(Add(Symbol('M', commutative=True), Symbol('Y', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('M', commutative=True), Integer(2)), Pow(Symbol('Y', commutative=True), Integer(-1)))", "Mul(Symbol('Y', commutative=True), log(Symbol('M', commutative=True)))", "Mul(Integer(-1), Symbol('Y', commutative=True), cos(Symbol('M', commutative=True)))", "Add(Mul(Integer(-1), Symbol('M', commutative=True), Symbol('Y', commutative=True)), exp(Symbol('M', commutative=True)))"]}, {"premise_expression": "v + w", "variable": "v", "positive": "\\frac{v (v + 2 w)}{2}", "negatives": ["\\frac{w (2 v + w)}{2}", "e^{v + w}", "\\frac{v^{2} \\log{(w)}}{2}", "v (- w + \\log{(v^{w})})"], "srepr_premise_expression": "Add(Symbol('v', commutative=True), Symbol('w', commutative=True))", "srepr_variable": "Symbol('v', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('v', commutative=True), Add(Symbol('v', commutative=True), Mul(Integer(2), Symbol('w', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('w', commutative=True), Add(Mul(Integer(2), Symbol('v', commutative=True)), Symbol('w', commutative=True)))", "exp(Add(Symbol('v', commutative=True), Symbol('w', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('v', commutative=True), Integer(2)), log(Symbol('w', commutative=True)))", "Mul(Symbol('v', commutative=True), Add(Mul(Integer(-1), Symbol('w', commutative=True)), log(Pow(Symbol('v', commutative=True), Symbol('w', commutative=True)))))"]}, {"premise_expression": "\\frac{S}{u}", "variable": "u", "positive": "S \\log{(u)}", "negatives": ["\\frac{S^{2}}{2 u}", "S u + e^{u}", "e^{- S + u}", "\\frac{u (2 S + u)}{2}"], "srepr_premise_expression": "Mul(Symbol('S', commutative=True), Pow(Symbol('u', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "Mul(Symbol('S', commutative=True), log(Symbol('u', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('S', commutative=True), Integer(2)), Pow(Symbol('u', commutative=True), Integer(-1)))", "Add(Mul(Symbol('S', commutative=True), Symbol('u', commutative=True)), exp(Symbol('u', commutative=True)))", "exp(Add(Mul(Integer(-1), Symbol('S', commutative=True)), Symbol('u', commutative=True)))", "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(2), Symbol('S', commutative=True)), Symbol('u', commutative=True)))"]}, {"premise_expression": "- A + x", "variable": "x", "positive": "\\frac{x (- 2 A + x)}{2}", "negatives": ["\\frac{A (- A + 2 x)}{2}", "\\frac{x^{2} \\log{(A)}}{2}", "- \\sin{(A - x)}", "\\frac{x^{2}}{2 A}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('A', commutative=True)), Symbol('x', commutative=True))", "srepr_variable": "Symbol('x', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('x', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('A', commutative=True)), Symbol('x', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Mul(Integer(-1), Symbol('A', commutative=True)), Mul(Integer(2), Symbol('x', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('x', commutative=True), Integer(2)), log(Symbol('A', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('x', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(-1)), Pow(Symbol('x', commutative=True), Integer(2)))"]}, {"premise_expression": "\\frac{I T}{h}", "variable": "T", "positive": "\\frac{I T^{2}}{2 h}", "negatives": ["\\frac{I^{2} T}{2 h}", "\\frac{T^{2}}{2 I h}", "I T \\log{(h)}", "\\frac{I T^{2} h}{2}"], "srepr_premise_expression": "Mul(Symbol('I', commutative=True), Symbol('T', commutative=True), Pow(Symbol('h', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('T', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('I', commutative=True), Pow(Symbol('T', commutative=True), Integer(2)), Pow(Symbol('h', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(2)), Symbol('T', commutative=True), Pow(Symbol('h', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(-1)), Pow(Symbol('T', commutative=True), Integer(2)), Pow(Symbol('h', commutative=True), Integer(-1)))", "Mul(Symbol('I', commutative=True), Symbol('T', commutative=True), log(Symbol('h', commutative=True)))", "Mul(Rational(1, 2), Symbol('I', commutative=True), Pow(Symbol('T', commutative=True), Integer(2)), Symbol('h', commutative=True))"]}, {"premise_expression": "A + H", "variable": "H", "positive": "\\frac{H (2 A + H)}{2}", "negatives": ["\\frac{A (A + 2 H)}{2}", "\\frac{H^{2} \\sin{(A)}}{2}", "\\frac{H^{2} \\log{(A)}}{2}", "- \\sin{(A - H)}"], "srepr_premise_expression": "Add(Symbol('A', commutative=True), Symbol('H', commutative=True))", "srepr_variable": "Symbol('H', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('H', commutative=True), Add(Mul(Integer(2), Symbol('A', commutative=True)), Symbol('H', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Symbol('A', commutative=True), Mul(Integer(2), Symbol('H', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('H', commutative=True), Integer(2)), sin(Symbol('A', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('H', commutative=True), Integer(2)), log(Symbol('A', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('H', commutative=True)))))"]}, {"premise_expression": "- V + \\cos{(z)}", "variable": "V", "positive": "\\frac{V (- V + 2 \\cos{(z)})}{2}", "negatives": ["\\frac{V^{2} \\log{(z)}}{2}", "V (- z + \\log{(V^{z})})", "- V z - \\cos{(V)}", "- V z + \\sin{(z)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('V', commutative=True)), cos(Symbol('z', commutative=True)))", "srepr_variable": "Symbol('V', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('V', commutative=True), Add(Mul(Integer(-1), Symbol('V', commutative=True)), Mul(Integer(2), cos(Symbol('z', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('V', commutative=True), Integer(2)), log(Symbol('z', commutative=True)))", "Mul(Symbol('V', commutative=True), Add(Mul(Integer(-1), Symbol('z', commutative=True)), log(Pow(Symbol('V', commutative=True), Symbol('z', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('V', commutative=True), Symbol('z', commutative=True)), Mul(Integer(-1), cos(Symbol('V', commutative=True))))", "Add(Mul(Integer(-1), Symbol('V', commutative=True), Symbol('z', commutative=True)), sin(Symbol('z', commutative=True)))"]}, {"premise_expression": "S o", "variable": "o", "positive": "\\frac{S o^{2}}{2}", "negatives": ["\\frac{S^{2} o}{2}", "\\frac{o (- 2 S + o)}{2}", "- e^{S - o}", "\\log{(o)} \\cos{(S)}"], "srepr_premise_expression": "Mul(Symbol('S', commutative=True), Symbol('o', commutative=True))", "srepr_variable": "Symbol('o', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('S', commutative=True), Pow(Symbol('o', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('S', commutative=True), Integer(2)), Symbol('o', commutative=True))", "Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('S', commutative=True)), Symbol('o', commutative=True)))", "Mul(Integer(-1), exp(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('o', commutative=True)))))", "Mul(log(Symbol('o', commutative=True)), cos(Symbol('S', commutative=True)))"]}, {"premise_expression": "- a + t + z", "variable": "z", "positive": "z (- a + t + \\frac{z}{2})", "negatives": ["\\frac{z (2 a + 2 t - z)}{2}", "\\frac{a (- a + 2 t + 2 z)}{2}", "\\frac{t (- 2 a + t + 2 z)}{2}", "z (a + t^{2})"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('a', commutative=True)), Symbol('t', commutative=True), Symbol('z', commutative=True))", "srepr_variable": "Symbol('z', commutative=True)", "srepr_positive": "Mul(Symbol('z', commutative=True), Add(Mul(Integer(-1), Symbol('a', commutative=True)), Symbol('t', commutative=True), Mul(Rational(1, 2), Symbol('z', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('z', commutative=True), Add(Mul(Integer(2), Symbol('a', commutative=True)), Mul(Integer(2), Symbol('t', commutative=True)), Mul(Integer(-1), Symbol('z', commutative=True))))", "Mul(Rational(1, 2), Symbol('a', commutative=True), Add(Mul(Integer(-1), Symbol('a', commutative=True)), Mul(Integer(2), Symbol('t', commutative=True)), Mul(Integer(2), Symbol('z', commutative=True))))", "Mul(Rational(1, 2), Symbol('t', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('a', commutative=True)), Symbol('t', commutative=True), Mul(Integer(2), Symbol('z', commutative=True))))", "Mul(Symbol('z', commutative=True), Add(Symbol('a', commutative=True), Pow(Symbol('t', commutative=True), Integer(2))))"]}, {"premise_expression": "\\sin{(H + y)}", "variable": "H", "positive": "- \\cos{(H + y)}", "negatives": ["\\cos{(H - y)}", "\\frac{H y (H - 2 y)}{2}", "\\log{(H)} \\log{(y)}", "\\log{(H)} \\sin{(y)}"], "srepr_premise_expression": "sin(Add(Symbol('H', commutative=True), Symbol('y', commutative=True)))", "srepr_variable": "Symbol('H', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('H', commutative=True), Symbol('y', commutative=True))))", "srepr_negatives": ["cos(Add(Symbol('H', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True))))", "Mul(Rational(1, 2), Symbol('H', commutative=True), Symbol('y', commutative=True), Add(Symbol('H', commutative=True), Mul(Integer(-1), Integer(2), Symbol('y', commutative=True))))", "Mul(log(Symbol('H', commutative=True)), log(Symbol('y', commutative=True)))", "Mul(log(Symbol('H', commutative=True)), sin(Symbol('y', commutative=True)))"]}, {"premise_expression": "- w + \\cos{(k)}", "variable": "k", "positive": "- k w + \\sin{(k)}", "negatives": ["w e^{k}", "w \\log{(k)}", "k (- w + \\log{(k^{w})})", "\\sin{(k + w)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('w', commutative=True)), cos(Symbol('k', commutative=True)))", "srepr_variable": "Symbol('k', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('k', commutative=True), Symbol('w', commutative=True)), sin(Symbol('k', commutative=True)))", "srepr_negatives": ["Mul(Symbol('w', commutative=True), exp(Symbol('k', commutative=True)))", "Mul(Symbol('w', commutative=True), log(Symbol('k', commutative=True)))", "Mul(Symbol('k', commutative=True), Add(Mul(Integer(-1), Symbol('w', commutative=True)), log(Pow(Symbol('k', commutative=True), Symbol('w', commutative=True)))))", "sin(Add(Symbol('k', commutative=True), Symbol('w', commutative=True)))"]}, {"premise_expression": "- a + \\sin{(q)}", "variable": "q", "positive": "- a q - \\cos{(q)}", "negatives": ["- a q + e^{q}", "a \\log{(q)}", "\\log{(q)} \\cos{(a)}", "- e^{a - q}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('a', commutative=True)), sin(Symbol('q', commutative=True)))", "srepr_variable": "Symbol('q', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('a', commutative=True), Symbol('q', commutative=True)), Mul(Integer(-1), cos(Symbol('q', commutative=True))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('a', commutative=True), Symbol('q', commutative=True)), exp(Symbol('q', commutative=True)))", "Mul(Symbol('a', commutative=True), log(Symbol('q', commutative=True)))", "Mul(log(Symbol('q', commutative=True)), cos(Symbol('a', commutative=True)))", "Mul(Integer(-1), exp(Add(Symbol('a', commutative=True), Mul(Integer(-1), Symbol('q', commutative=True)))))"]}, {"premise_expression": "\\frac{E w}{Q}", "variable": "E", "positive": "\\frac{E^{2} w}{2 Q}", "negatives": ["\\frac{E w^{2}}{2 Q}", "E w \\log{(Q)}", "\\frac{E (E + 2 Q + 2 w)}{2}", "- E Q + w \\log{(E)}"], "srepr_premise_expression": "Mul(Symbol('E', commutative=True), Pow(Symbol('Q', commutative=True), Integer(-1)), Symbol('w', commutative=True))", "srepr_variable": "Symbol('E', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('E', commutative=True), Integer(2)), Pow(Symbol('Q', commutative=True), Integer(-1)), Symbol('w', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('E', commutative=True), Pow(Symbol('Q', commutative=True), Integer(-1)), Pow(Symbol('w', commutative=True), Integer(2)))", "Mul(Symbol('E', commutative=True), Symbol('w', commutative=True), log(Symbol('Q', commutative=True)))", "Mul(Rational(1, 2), Symbol('E', commutative=True), Add(Symbol('E', commutative=True), Mul(Integer(2), Symbol('Q', commutative=True)), Mul(Integer(2), Symbol('w', commutative=True))))", "Add(Mul(Integer(-1), Symbol('E', commutative=True), Symbol('Q', commutative=True)), Mul(Symbol('w', commutative=True), log(Symbol('E', commutative=True))))"]}, {"premise_expression": "D + w", "variable": "w", "positive": "\\frac{w (2 D + w)}{2}", "negatives": ["\\frac{D (D + 2 w)}{2}", "\\frac{w^{2} e^{D}}{2}", "e^{D + w}", "- D w - \\cos{(w)}"], "srepr_premise_expression": "Add(Symbol('D', commutative=True), Symbol('w', commutative=True))", "srepr_variable": "Symbol('w', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('w', commutative=True), Add(Mul(Integer(2), Symbol('D', commutative=True)), Symbol('w', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('D', commutative=True), Add(Symbol('D', commutative=True), Mul(Integer(2), Symbol('w', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('w', commutative=True), Integer(2)), exp(Symbol('D', commutative=True)))", "exp(Add(Symbol('D', commutative=True), Symbol('w', commutative=True)))", "Add(Mul(Integer(-1), Symbol('D', commutative=True), Symbol('w', commutative=True)), Mul(Integer(-1), cos(Symbol('w', commutative=True))))"]}, {"premise_expression": "e^{- B + T}", "variable": "T", "positive": "e^{- B + T}", "negatives": ["- e^{- B + T}", "- \\cos{(B - T)}", "\\frac{T (2 B + T)}{2}", "e^{B} \\log{(T)}"], "srepr_premise_expression": "exp(Add(Mul(Integer(-1), Symbol('B', commutative=True)), Symbol('T', commutative=True)))", "srepr_variable": "Symbol('T', commutative=True)", "srepr_positive": "exp(Add(Mul(Integer(-1), Symbol('B', commutative=True)), Symbol('T', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('B', commutative=True)), Symbol('T', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('B', commutative=True), Mul(Integer(-1), Symbol('T', commutative=True)))))", "Mul(Rational(1, 2), Symbol('T', commutative=True), Add(Mul(Integer(2), Symbol('B', commutative=True)), Symbol('T', commutative=True)))", "Mul(exp(Symbol('B', commutative=True)), log(Symbol('T', commutative=True)))"]}, {"premise_expression": "E v w", "variable": "v", "positive": "\\frac{E v^{2} w}{2}", "negatives": ["\\frac{E v w^{2}}{2}", "\\frac{E^{2} v w}{2}", "\\frac{E v^{2}}{2 w}", "w^{E} \\log{(v)}"], "srepr_premise_expression": "Mul(Symbol('E', commutative=True), Symbol('v', commutative=True), Symbol('w', commutative=True))", "srepr_variable": "Symbol('v', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('E', commutative=True), Pow(Symbol('v', commutative=True), Integer(2)), Symbol('w', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('E', commutative=True), Symbol('v', commutative=True), Pow(Symbol('w', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('E', commutative=True), Integer(2)), Symbol('v', commutative=True), Symbol('w', commutative=True))", "Mul(Rational(1, 2), Symbol('E', commutative=True), Pow(Symbol('v', commutative=True), Integer(2)), Pow(Symbol('w', commutative=True), Integer(-1)))", "Mul(Pow(Symbol('w', commutative=True), Symbol('E', commutative=True)), log(Symbol('v', commutative=True)))"]}, {"premise_expression": "K + X - y", "variable": "K", "positive": "K (\\frac{K}{2} + X - y)", "negatives": ["\\frac{K (K - 2 X + 2 y)}{2}", "\\frac{X (2 K + X - 2 y)}{2}", "\\frac{y (2 K + 2 X - y)}{2}", "\\frac{K^{2} y}{2 X}"], "srepr_premise_expression": "Add(Symbol('K', commutative=True), Symbol('X', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True)))", "srepr_variable": "Symbol('K', commutative=True)", "srepr_positive": "Mul(Symbol('K', commutative=True), Add(Mul(Rational(1, 2), Symbol('K', commutative=True)), Symbol('X', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Symbol('K', commutative=True), Mul(Integer(-1), Integer(2), Symbol('X', commutative=True)), Mul(Integer(2), Symbol('y', commutative=True))))", "Mul(Rational(1, 2), Symbol('X', commutative=True), Add(Mul(Integer(2), Symbol('K', commutative=True)), Symbol('X', commutative=True), Mul(Integer(-1), Integer(2), Symbol('y', commutative=True))))", "Mul(Rational(1, 2), Symbol('y', commutative=True), Add(Mul(Integer(2), Symbol('K', commutative=True)), Mul(Integer(2), Symbol('X', commutative=True)), Mul(Integer(-1), Symbol('y', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('K', commutative=True), Integer(2)), Pow(Symbol('X', commutative=True), Integer(-1)), Symbol('y', commutative=True))"]}, {"premise_expression": "S V", "variable": "V", "positive": "\\frac{S V^{2}}{2}", "negatives": ["\\frac{S^{2} V}{2}", "\\frac{V^{2}}{2 S}", "- \\frac{\\cos{(V)}}{S}", "\\cos{(S - V)}"], "srepr_premise_expression": "Mul(Symbol('S', commutative=True), Symbol('V', commutative=True))", "srepr_variable": "Symbol('V', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('S', commutative=True), Pow(Symbol('V', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('S', commutative=True), Integer(2)), Symbol('V', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('S', commutative=True), Integer(-1)), Pow(Symbol('V', commutative=True), Integer(2)))", "Mul(Integer(-1), Pow(Symbol('S', commutative=True), Integer(-1)), cos(Symbol('V', commutative=True)))", "cos(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('V', commutative=True))))"]}, {"premise_expression": "\\frac{M}{j}", "variable": "M", "positive": "\\frac{M^{2}}{2 j}", "negatives": ["M \\log{(j)}", "j \\log{(M)}", "- \\cos{(M + j)}", "M (\\log{(M j)} - 1)"], "srepr_premise_expression": "Mul(Symbol('M', commutative=True), Pow(Symbol('j', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('M', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('M', commutative=True), Integer(2)), Pow(Symbol('j', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('M', commutative=True), log(Symbol('j', commutative=True)))", "Mul(Symbol('j', commutative=True), log(Symbol('M', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('M', commutative=True), Symbol('j', commutative=True))))", "Mul(Symbol('M', commutative=True), Add(log(Mul(Symbol('M', commutative=True), Symbol('j', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\frac{\\sin{(n)}}{F}", "variable": "F", "positive": "\\log{(F)} \\sin{(n)}", "negatives": ["F n + \\sin{(F)}", "\\frac{F^{2} \\sin{(n)}}{2}", "- \\cos{(F - n)}", "F (\\log{(\\frac{F}{n})} - 1)"], "srepr_premise_expression": "Mul(Pow(Symbol('F', commutative=True), Integer(-1)), sin(Symbol('n', commutative=True)))", "srepr_variable": "Symbol('F', commutative=True)", "srepr_positive": "Mul(log(Symbol('F', commutative=True)), sin(Symbol('n', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('F', commutative=True), Symbol('n', commutative=True)), sin(Symbol('F', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('F', commutative=True), Integer(2)), sin(Symbol('n', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('F', commutative=True), Mul(Integer(-1), Symbol('n', commutative=True)))))", "Mul(Symbol('F', commutative=True), Add(log(Mul(Symbol('F', commutative=True), Pow(Symbol('n', commutative=True), Integer(-1)))), Integer(-1)))"]}, {"premise_expression": "I - r", "variable": "r", "positive": "\\frac{r (2 I - r)}{2}", "negatives": ["\\frac{r (- 2 I + r)}{2}", "\\frac{I (I - 2 r)}{2}", "\\frac{r^{2} e^{I}}{2}", "\\frac{\\sin{(r)}}{I}"], "srepr_premise_expression": "Add(Symbol('I', commutative=True), Mul(Integer(-1), Symbol('r', commutative=True)))", "srepr_variable": "Symbol('r', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(2), Symbol('I', commutative=True)), Mul(Integer(-1), Symbol('r', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('I', commutative=True)), Symbol('r', commutative=True)))", "Mul(Rational(1, 2), Symbol('I', commutative=True), Add(Symbol('I', commutative=True), Mul(Integer(-1), Integer(2), Symbol('r', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('r', commutative=True), Integer(2)), exp(Symbol('I', commutative=True)))", "Mul(Pow(Symbol('I', commutative=True), Integer(-1)), sin(Symbol('r', commutative=True)))"]}, {"premise_expression": "\\cos{(\\frac{z}{D})}", "variable": "D", "positive": "D \\cos{(\\frac{z}{D})} + z \\operatorname{Si}{(\\frac{z}{D})}", "negatives": ["\\frac{D (D + 2 \\sin{(z)})}{2}", "\\frac{D (D - 2 z)}{2}", "\\log{(D)} \\log{(z)}", "D (- z + \\log{(D^{z})})"], "srepr_premise_expression": "cos(Mul(Pow(Symbol('D', commutative=True), Integer(-1)), Symbol('z', commutative=True)))", "srepr_variable": "Symbol('D', commutative=True)", "srepr_positive": "Add(Mul(Symbol('D', commutative=True), cos(Mul(Pow(Symbol('D', commutative=True), Integer(-1)), Symbol('z', commutative=True)))), Mul(Symbol('z', commutative=True), Si(Mul(Pow(Symbol('D', commutative=True), Integer(-1)), Symbol('z', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('D', commutative=True), Add(Symbol('D', commutative=True), Mul(Integer(2), sin(Symbol('z', commutative=True)))))", "Mul(Rational(1, 2), Symbol('D', commutative=True), Add(Symbol('D', commutative=True), Mul(Integer(-1), Integer(2), Symbol('z', commutative=True))))", "Mul(log(Symbol('D', commutative=True)), log(Symbol('z', commutative=True)))", "Mul(Symbol('D', commutative=True), Add(Mul(Integer(-1), Symbol('z', commutative=True)), log(Pow(Symbol('D', commutative=True), Symbol('z', commutative=True)))))"]}, {"premise_expression": "f - m", "variable": "f", "positive": "\\frac{f (f - 2 m)}{2}", "negatives": ["\\frac{m (2 f - m)}{2}", "\\frac{f^{2} m}{2}", "\\sin{(f + m)}", "f m - \\cos{(f)}"], "srepr_premise_expression": "Add(Symbol('f', commutative=True), Mul(Integer(-1), Symbol('m', commutative=True)))", "srepr_variable": "Symbol('f', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Symbol('f', commutative=True), Mul(Integer(-1), Integer(2), Symbol('m', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Mul(Integer(2), Symbol('f', commutative=True)), Mul(Integer(-1), Symbol('m', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('f', commutative=True), Integer(2)), Symbol('m', commutative=True))", "sin(Add(Symbol('f', commutative=True), Symbol('m', commutative=True)))", "Add(Mul(Symbol('f', commutative=True), Symbol('m', commutative=True)), Mul(Integer(-1), cos(Symbol('f', commutative=True))))"]}, {"premise_expression": "e^{- G + h}", "variable": "h", "positive": "e^{- G + h}", "negatives": ["- e^{- G + h}", "\\cos{(G - h)}", "- \\cos{(G + h)}", "\\frac{h (- 2 G + h)}{2}"], "srepr_premise_expression": "exp(Add(Mul(Integer(-1), Symbol('G', commutative=True)), Symbol('h', commutative=True)))", "srepr_variable": "Symbol('h', commutative=True)", "srepr_positive": "exp(Add(Mul(Integer(-1), Symbol('G', commutative=True)), Symbol('h', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('G', commutative=True)), Symbol('h', commutative=True))))", "cos(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('h', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('G', commutative=True), Symbol('h', commutative=True))))", "Mul(Rational(1, 2), Symbol('h', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('G', commutative=True)), Symbol('h', commutative=True)))"]}, {"premise_expression": "K j", "variable": "K", "positive": "\\frac{K^{2} j}{2}", "negatives": ["\\frac{K j^{2}}{2}", "\\frac{K^{2} \\log{(j)}}{2}", "\\frac{K (K + 2 j)}{2}", "K \\sin{(1)}"], "srepr_premise_expression": "Mul(Symbol('K', commutative=True), Symbol('j', commutative=True))", "srepr_variable": "Symbol('K', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('K', commutative=True), Integer(2)), Symbol('j', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('K', commutative=True), Pow(Symbol('j', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('K', commutative=True), Integer(2)), log(Symbol('j', commutative=True)))", "Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Symbol('K', commutative=True), Mul(Integer(2), Symbol('j', commutative=True))))", "Mul(Symbol('K', commutative=True), sin(Integer(1)))"]}, {"premise_expression": "- F + G", "variable": "G", "positive": "\\frac{G (- 2 F + G)}{2}", "negatives": ["\\frac{F (- F + 2 G)}{2}", "- e^{F - G}", "\\frac{G (- G + 2 \\log{(F)})}{2}", "G (- F + \\log{(G^{F})})"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('F', commutative=True)), Symbol('G', commutative=True))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('F', commutative=True)), Symbol('G', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Mul(Integer(-1), Symbol('F', commutative=True)), Mul(Integer(2), Symbol('G', commutative=True))))", "Mul(Integer(-1), exp(Add(Symbol('F', commutative=True), Mul(Integer(-1), Symbol('G', commutative=True)))))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Mul(Integer(-1), Symbol('G', commutative=True)), Mul(Integer(2), log(Symbol('F', commutative=True)))))", "Mul(Symbol('G', commutative=True), Add(Mul(Integer(-1), Symbol('F', commutative=True)), log(Pow(Symbol('G', commutative=True), Symbol('F', commutative=True)))))"]}, {"premise_expression": "J + h + y", "variable": "y", "positive": "y (J + h + \\frac{y}{2})", "negatives": ["\\frac{y (2 J - 2 h + y)}{2}", "\\frac{J (J + 2 h + 2 y)}{2}", "\\frac{h (2 J + h + 2 y)}{2}", "\\frac{y (2 J h + y)}{2}"], "srepr_premise_expression": "Add(Symbol('J', commutative=True), Symbol('h', commutative=True), Symbol('y', commutative=True))", "srepr_variable": "Symbol('y', commutative=True)", "srepr_positive": "Mul(Symbol('y', commutative=True), Add(Symbol('J', commutative=True), Symbol('h', commutative=True), Mul(Rational(1, 2), Symbol('y', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('y', commutative=True), Add(Mul(Integer(2), Symbol('J', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('h', commutative=True)), Symbol('y', commutative=True)))", "Mul(Rational(1, 2), Symbol('J', commutative=True), Add(Symbol('J', commutative=True), Mul(Integer(2), Symbol('h', commutative=True)), Mul(Integer(2), Symbol('y', commutative=True))))", "Mul(Rational(1, 2), Symbol('h', commutative=True), Add(Mul(Integer(2), Symbol('J', commutative=True)), Symbol('h', commutative=True), Mul(Integer(2), Symbol('y', commutative=True))))", "Mul(Rational(1, 2), Symbol('y', commutative=True), Add(Mul(Integer(2), Symbol('J', commutative=True), Symbol('h', commutative=True)), Symbol('y', commutative=True)))"]}, {"premise_expression": "\\frac{\\sin{(G)}}{S}", "variable": "G", "positive": "- \\frac{\\cos{(G)}}{S}", "negatives": ["S e^{G}", "\\frac{\\sin{(2 G)}}{2}", "\\frac{G^{2} \\cos{(S)}}{2}", "\\sin{(G + S)}"], "srepr_premise_expression": "Mul(Pow(Symbol('S', commutative=True), Integer(-1)), sin(Symbol('G', commutative=True)))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Mul(Integer(-1), Pow(Symbol('S', commutative=True), Integer(-1)), cos(Symbol('G', commutative=True)))", "srepr_negatives": ["Mul(Symbol('S', commutative=True), exp(Symbol('G', commutative=True)))", "Mul(Rational(1, 2), sin(Mul(Integer(2), Symbol('G', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(2)), cos(Symbol('S', commutative=True)))", "sin(Add(Symbol('G', commutative=True), Symbol('S', commutative=True)))"]}, {"premise_expression": "J + Z", "variable": "Z", "positive": "\\frac{Z (2 J + Z)}{2}", "negatives": ["\\frac{J (J + 2 Z)}{2}", "\\frac{Z^{2}}{2 J}", "\\frac{J Z^{2}}{2}", "Z (\\log{(\\frac{J}{Z})} + 1)"], "srepr_premise_expression": "Add(Symbol('J', commutative=True), Symbol('Z', commutative=True))", "srepr_variable": "Symbol('Z', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Mul(Integer(2), Symbol('J', commutative=True)), Symbol('Z', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('J', commutative=True), Add(Symbol('J', commutative=True), Mul(Integer(2), Symbol('Z', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('J', commutative=True), Integer(-1)), Pow(Symbol('Z', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('J', commutative=True), Pow(Symbol('Z', commutative=True), Integer(2)))", "Mul(Symbol('Z', commutative=True), Add(log(Mul(Symbol('J', commutative=True), Pow(Symbol('Z', commutative=True), Integer(-1)))), Integer(1)))"]}, {"premise_expression": "e^{\\frac{D}{g}}", "variable": "g", "positive": "- D \\operatorname{Ei}{(\\frac{D}{g})} + g e^{\\frac{D}{g}}", "negatives": ["D \\operatorname{Si}{(\\frac{D}{g})} + g \\cos{(\\frac{D}{g})}", "g e^{\\frac{D}{g}}", "D e^{g}", "\\frac{g (g + 2 \\sin{(D)})}{2}"], "srepr_premise_expression": "exp(Mul(Symbol('D', commutative=True), Pow(Symbol('g', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('g', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('D', commutative=True), Ei(Mul(Symbol('D', commutative=True), Pow(Symbol('g', commutative=True), Integer(-1))))), Mul(Symbol('g', commutative=True), exp(Mul(Symbol('D', commutative=True), Pow(Symbol('g', commutative=True), Integer(-1))))))", "srepr_negatives": ["Add(Mul(Symbol('D', commutative=True), Si(Mul(Symbol('D', commutative=True), Pow(Symbol('g', commutative=True), Integer(-1))))), Mul(Symbol('g', commutative=True), cos(Mul(Symbol('D', commutative=True), Pow(Symbol('g', commutative=True), Integer(-1))))))", "Mul(Symbol('g', commutative=True), exp(Mul(Symbol('D', commutative=True), Pow(Symbol('g', commutative=True), Integer(-1)))))", "Mul(Symbol('D', commutative=True), exp(Symbol('g', commutative=True)))", "Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Symbol('g', commutative=True), Mul(Integer(2), sin(Symbol('D', commutative=True)))))"]}, {"premise_expression": "\\frac{e^{M}}{A}", "variable": "A", "positive": "e^{M} \\log{(A)}", "negatives": ["- M \\cos{(A)}", "\\log{(A)} \\cos{(M)}", "e^{A - M}", "- e^{- A + M}"], "srepr_premise_expression": "Mul(Pow(Symbol('A', commutative=True), Integer(-1)), exp(Symbol('M', commutative=True)))", "srepr_variable": "Symbol('A', commutative=True)", "srepr_positive": "Mul(exp(Symbol('M', commutative=True)), log(Symbol('A', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Symbol('M', commutative=True), cos(Symbol('A', commutative=True)))", "Mul(log(Symbol('A', commutative=True)), cos(Symbol('M', commutative=True)))", "exp(Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('M', commutative=True))))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('A', commutative=True)), Symbol('M', commutative=True))))"]}, {"premise_expression": "e^{- R + c}", "variable": "c", "positive": "e^{- R + c}", "negatives": ["- e^{- R + c}", "R e^{\\frac{c}{R}}", "R c - \\cos{(c)}", "c (- R + \\log{(c^{R})})"], "srepr_premise_expression": "exp(Add(Mul(Integer(-1), Symbol('R', commutative=True)), Symbol('c', commutative=True)))", "srepr_variable": "Symbol('c', commutative=True)", "srepr_positive": "exp(Add(Mul(Integer(-1), Symbol('R', commutative=True)), Symbol('c', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('R', commutative=True)), Symbol('c', commutative=True))))", "Mul(Symbol('R', commutative=True), exp(Mul(Pow(Symbol('R', commutative=True), Integer(-1)), Symbol('c', commutative=True))))", "Add(Mul(Symbol('R', commutative=True), Symbol('c', commutative=True)), Mul(Integer(-1), cos(Symbol('c', commutative=True))))", "Mul(Symbol('c', commutative=True), Add(Mul(Integer(-1), Symbol('R', commutative=True)), log(Pow(Symbol('c', commutative=True), Symbol('R', commutative=True)))))"]}, {"premise_expression": "\\cos{(D + X)}", "variable": "D", "positive": "\\sin{(D + X)}", "negatives": ["\\frac{D^{2} \\log{(X)}}{2}", "\\frac{D (\\log{(D)} - 1)}{X}", "D X (\\log{(D)} - 1)", "D (\\log{(D X)} - 1)"], "srepr_premise_expression": "cos(Add(Symbol('D', commutative=True), Symbol('X', commutative=True)))", "srepr_variable": "Symbol('D', commutative=True)", "srepr_positive": "sin(Add(Symbol('D', commutative=True), Symbol('X', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(2)), log(Symbol('X', commutative=True)))", "Mul(Symbol('D', commutative=True), Pow(Symbol('X', commutative=True), Integer(-1)), Add(log(Symbol('D', commutative=True)), Integer(-1)))", "Mul(Symbol('D', commutative=True), Symbol('X', commutative=True), Add(log(Symbol('D', commutative=True)), Integer(-1)))", "Mul(Symbol('D', commutative=True), Add(log(Mul(Symbol('D', commutative=True), Symbol('X', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\log{(r^{f})}", "variable": "r", "positive": "r (- f + \\log{(r^{f})})", "negatives": ["\\frac{r (- r + 2 \\log{(f)})}{2}", "r \\log{(f)}^{f}", "\\frac{r (- 2 f + r)}{2}", "\\frac{r (r + 2 e^{f})}{2}"], "srepr_premise_expression": "log(Pow(Symbol('r', commutative=True), Symbol('f', commutative=True)))", "srepr_variable": "Symbol('r', commutative=True)", "srepr_positive": "Mul(Symbol('r', commutative=True), Add(Mul(Integer(-1), Symbol('f', commutative=True)), log(Pow(Symbol('r', commutative=True), Symbol('f', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(-1), Symbol('r', commutative=True)), Mul(Integer(2), log(Symbol('f', commutative=True)))))", "Mul(Symbol('r', commutative=True), Pow(log(Symbol('f', commutative=True)), Symbol('f', commutative=True)))", "Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('f', commutative=True)), Symbol('r', commutative=True)))", "Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Symbol('r', commutative=True), Mul(Integer(2), exp(Symbol('f', commutative=True)))))"]}, {"premise_expression": "X \\sin{(Z)}", "variable": "Z", "positive": "- X \\cos{(Z)}", "negatives": ["X \\log{(Z)}", "X \\sin{(Z)}", "- \\cos{(X + Z)}", "\\frac{X^{2} \\sin{(Z)}}{2}"], "srepr_premise_expression": "Mul(Symbol('X', commutative=True), sin(Symbol('Z', commutative=True)))", "srepr_variable": "Symbol('Z', commutative=True)", "srepr_positive": "Mul(Integer(-1), Symbol('X', commutative=True), cos(Symbol('Z', commutative=True)))", "srepr_negatives": ["Mul(Symbol('X', commutative=True), log(Symbol('Z', commutative=True)))", "Mul(Symbol('X', commutative=True), sin(Symbol('Z', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('X', commutative=True), Symbol('Z', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('X', commutative=True), Integer(2)), sin(Symbol('Z', commutative=True)))"]}, {"premise_expression": "Z (t - u)", "variable": "t", "positive": "\\frac{Z t (t - 2 u)}{2}", "negatives": ["\\frac{Z^{2} (t - u)}{2}", "\\frac{t (Z t - 2 u)}{2}", "\\frac{Z u (2 t - u)}{2}", "\\frac{t (Z t + 2 u)}{2}"], "srepr_premise_expression": "Mul(Symbol('Z', commutative=True), Add(Symbol('t', commutative=True), Mul(Integer(-1), Symbol('u', commutative=True))))", "srepr_variable": "Symbol('t', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('Z', commutative=True), Symbol('t', commutative=True), Add(Symbol('t', commutative=True), Mul(Integer(-1), Integer(2), Symbol('u', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('Z', commutative=True), Integer(2)), Add(Symbol('t', commutative=True), Mul(Integer(-1), Symbol('u', commutative=True))))", "Mul(Rational(1, 2), Symbol('t', commutative=True), Add(Mul(Symbol('Z', commutative=True), Symbol('t', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('u', commutative=True))))", "Mul(Rational(1, 2), Symbol('Z', commutative=True), Symbol('u', commutative=True), Add(Mul(Integer(2), Symbol('t', commutative=True)), Mul(Integer(-1), Symbol('u', commutative=True))))", "Mul(Rational(1, 2), Symbol('t', commutative=True), Add(Mul(Symbol('Z', commutative=True), Symbol('t', commutative=True)), Mul(Integer(2), Symbol('u', commutative=True))))"]}, {"premise_expression": "- F + S - Z", "variable": "F", "positive": "F (- \\frac{F}{2} + S - Z)", "negatives": ["\\frac{S (- 2 F + S - 2 Z)}{2}", "\\frac{Z (- 2 F + 2 S - Z)}{2}", "\\frac{F (- F - 2 S + 2 Z)}{2}", "\\frac{F^{2} (- S + Z)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('F', commutative=True)), Symbol('S', commutative=True), Mul(Integer(-1), Symbol('Z', commutative=True)))", "srepr_variable": "Symbol('F', commutative=True)", "srepr_positive": "Mul(Symbol('F', commutative=True), Add(Mul(Integer(-1), Rational(1, 2), Symbol('F', commutative=True)), Symbol('S', commutative=True), Mul(Integer(-1), Symbol('Z', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('F', commutative=True)), Symbol('S', commutative=True), Mul(Integer(-1), Integer(2), Symbol('Z', commutative=True))))", "Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('F', commutative=True)), Mul(Integer(2), Symbol('S', commutative=True)), Mul(Integer(-1), Symbol('Z', commutative=True))))", "Mul(Rational(1, 2), Symbol('F', commutative=True), Add(Mul(Integer(-1), Symbol('F', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('S', commutative=True)), Mul(Integer(2), Symbol('Z', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('F', commutative=True), Integer(2)), Add(Mul(Integer(-1), Symbol('S', commutative=True)), Symbol('Z', commutative=True)))"]}, {"premise_expression": "\\frac{A}{L}", "variable": "A", "positive": "\\frac{A^{2}}{2 L}", "negatives": ["A \\log{(L)}", "\\frac{A^{2}}{2 L} + A L", "\\sin{(A + L)}", "\\sin{(A - L)}"], "srepr_premise_expression": "Mul(Symbol('A', commutative=True), Pow(Symbol('L', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('A', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2)), Pow(Symbol('L', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('A', commutative=True), log(Symbol('L', commutative=True)))", "Add(Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2)), Pow(Symbol('L', commutative=True), Integer(-1))), Mul(Symbol('A', commutative=True), Symbol('L', commutative=True)))", "sin(Add(Symbol('A', commutative=True), Symbol('L', commutative=True)))", "sin(Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('L', commutative=True))))"]}, {"premise_expression": "A (W + q)", "variable": "A", "positive": "\\frac{A^{2} (W + q)}{2}", "negatives": ["\\frac{A^{2} (W - q)}{2}", "\\frac{A q (2 W + q)}{2}", "\\frac{A W (W + 2 q)}{2}", "\\frac{A W (- A + 2 q)}{2}"], "srepr_premise_expression": "Mul(Symbol('A', commutative=True), Add(Symbol('W', commutative=True), Symbol('q', commutative=True)))", "srepr_variable": "Symbol('A', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2)), Add(Symbol('W', commutative=True), Symbol('q', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2)), Add(Symbol('W', commutative=True), Mul(Integer(-1), Symbol('q', commutative=True))))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Symbol('q', commutative=True), Add(Mul(Integer(2), Symbol('W', commutative=True)), Symbol('q', commutative=True)))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Symbol('W', commutative=True), Add(Symbol('W', commutative=True), Mul(Integer(2), Symbol('q', commutative=True))))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Symbol('W', commutative=True), Add(Mul(Integer(-1), Symbol('A', commutative=True)), Mul(Integer(2), Symbol('q', commutative=True))))"]}, {"premise_expression": "\\log{(Y - z)}", "variable": "Y", "positive": "Y \\log{(Y - z)} - Y - z \\log{(Y - z)}", "negatives": ["- Y \\log{(- Y + z)} + z \\log{(Y - z)} - z", "\\log{(Y)} \\log{(z)}", "Y e^{\\frac{z}{Y}} - z \\operatorname{Ei}{(\\frac{z}{Y})}", "\\frac{Y (\\log{(Y)} - 1)}{z}"], "srepr_premise_expression": "log(Add(Symbol('Y', commutative=True), Mul(Integer(-1), Symbol('z', commutative=True))))", "srepr_variable": "Symbol('Y', commutative=True)", "srepr_positive": "Add(Mul(Symbol('Y', commutative=True), log(Add(Symbol('Y', commutative=True), Mul(Integer(-1), Symbol('z', commutative=True))))), Mul(Integer(-1), Symbol('Y', commutative=True)), Mul(Integer(-1), Symbol('z', commutative=True), log(Add(Symbol('Y', commutative=True), Mul(Integer(-1), Symbol('z', commutative=True))))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('Y', commutative=True), log(Add(Mul(Integer(-1), Symbol('Y', commutative=True)), Symbol('z', commutative=True)))), Mul(Symbol('z', commutative=True), log(Add(Symbol('Y', commutative=True), Mul(Integer(-1), Symbol('z', commutative=True))))), Mul(Integer(-1), Symbol('z', commutative=True)))", "Mul(log(Symbol('Y', commutative=True)), log(Symbol('z', commutative=True)))", "Add(Mul(Symbol('Y', commutative=True), exp(Mul(Pow(Symbol('Y', commutative=True), Integer(-1)), Symbol('z', commutative=True)))), Mul(Integer(-1), Symbol('z', commutative=True), Ei(Mul(Pow(Symbol('Y', commutative=True), Integer(-1)), Symbol('z', commutative=True)))))", "Mul(Symbol('Y', commutative=True), Pow(Symbol('z', commutative=True), Integer(-1)), Add(log(Symbol('Y', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\frac{e^{Q}}{W}", "variable": "W", "positive": "e^{Q} \\log{(W)}", "negatives": ["Q \\log{(W)}", "- Q W - \\cos{(W)}", "\\sin{(Q + W)}", "W \\cos{(1)}"], "srepr_premise_expression": "Mul(Pow(Symbol('W', commutative=True), Integer(-1)), exp(Symbol('Q', commutative=True)))", "srepr_variable": "Symbol('W', commutative=True)", "srepr_positive": "Mul(exp(Symbol('Q', commutative=True)), log(Symbol('W', commutative=True)))", "srepr_negatives": ["Mul(Symbol('Q', commutative=True), log(Symbol('W', commutative=True)))", "Add(Mul(Integer(-1), Symbol('Q', commutative=True), Symbol('W', commutative=True)), Mul(Integer(-1), cos(Symbol('W', commutative=True))))", "sin(Add(Symbol('Q', commutative=True), Symbol('W', commutative=True)))", "Mul(Symbol('W', commutative=True), cos(Integer(1)))"]}, {"premise_expression": "\\frac{S}{U}", "variable": "U", "positive": "S \\log{(U)}", "negatives": ["\\frac{S^{2}}{2 U}", "\\frac{U^{2} \\log{(S)}}{2}", "- S U - \\cos{(U)}", "e^{S + U}"], "srepr_premise_expression": "Mul(Symbol('S', commutative=True), Pow(Symbol('U', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('U', commutative=True)", "srepr_positive": "Mul(Symbol('S', commutative=True), log(Symbol('U', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('S', commutative=True), Integer(2)), Pow(Symbol('U', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('U', commutative=True), Integer(2)), log(Symbol('S', commutative=True)))", "Add(Mul(Integer(-1), Symbol('S', commutative=True), Symbol('U', commutative=True)), Mul(Integer(-1), cos(Symbol('U', commutative=True))))", "exp(Add(Symbol('S', commutative=True), Symbol('U', commutative=True)))"]}, {"premise_expression": "Y + f", "variable": "Y", "positive": "\\frac{Y (Y + 2 f)}{2}", "negatives": ["\\frac{Y (Y - 2 f)}{2}", "\\frac{f (2 Y + f)}{2}", "\\frac{Y (- Y + 2 \\log{(f)})}{2}", "\\frac{Y (- Y + 2 \\cos{(f)})}{2}"], "srepr_premise_expression": "Add(Symbol('Y', commutative=True), Symbol('f', commutative=True))", "srepr_variable": "Symbol('Y', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('Y', commutative=True), Add(Symbol('Y', commutative=True), Mul(Integer(2), Symbol('f', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('Y', commutative=True), Add(Symbol('Y', commutative=True), Mul(Integer(-1), Integer(2), Symbol('f', commutative=True))))", "Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Mul(Integer(2), Symbol('Y', commutative=True)), Symbol('f', commutative=True)))", "Mul(Rational(1, 2), Symbol('Y', commutative=True), Add(Mul(Integer(-1), Symbol('Y', commutative=True)), Mul(Integer(2), log(Symbol('f', commutative=True)))))", "Mul(Rational(1, 2), Symbol('Y', commutative=True), Add(Mul(Integer(-1), Symbol('Y', commutative=True)), Mul(Integer(2), cos(Symbol('f', commutative=True)))))"]}, {"premise_expression": "J + u", "variable": "u", "positive": "\\frac{u (2 J + u)}{2}", "negatives": ["\\frac{J (J + 2 u)}{2}", "\\sin{(J + u)}", "- J \\cos{(u)}", "\\frac{u (u + 2 \\cos{(J)})}{2}"], "srepr_premise_expression": "Add(Symbol('J', commutative=True), Symbol('u', commutative=True))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(2), Symbol('J', commutative=True)), Symbol('u', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('J', commutative=True), Add(Symbol('J', commutative=True), Mul(Integer(2), Symbol('u', commutative=True))))", "sin(Add(Symbol('J', commutative=True), Symbol('u', commutative=True)))", "Mul(Integer(-1), Symbol('J', commutative=True), cos(Symbol('u', commutative=True)))", "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Symbol('u', commutative=True), Mul(Integer(2), cos(Symbol('J', commutative=True)))))"]}, {"premise_expression": "\\frac{t}{I}", "variable": "t", "positive": "\\frac{t^{2}}{2 I}", "negatives": ["t \\log{(I)}", "\\cos{(I - t)}", "\\frac{t (- 2 I + t)}{2}", "- e^{I - t}"], "srepr_premise_expression": "Mul(Pow(Symbol('I', commutative=True), Integer(-1)), Symbol('t', commutative=True))", "srepr_variable": "Symbol('t', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(-1)), Pow(Symbol('t', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('t', commutative=True), log(Symbol('I', commutative=True)))", "cos(Add(Symbol('I', commutative=True), Mul(Integer(-1), Symbol('t', commutative=True))))", "Mul(Rational(1, 2), Symbol('t', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('I', commutative=True)), Symbol('t', commutative=True)))", "Mul(Integer(-1), exp(Add(Symbol('I', commutative=True), Mul(Integer(-1), Symbol('t', commutative=True)))))"]}, {"premise_expression": "e^{p^{h}}", "variable": "p", "positive": "\\frac{e^{- \\frac{i \\pi}{h}} \\gamma(\\frac{1}{h}, p^{h} e^{i \\pi})}{h}", "negatives": ["- h \\log{(- h + p)} + p \\log{(h - p)} - p", "\\frac{p (- p + 2 e^{h})}{2}", "h \\log{(h + p)} + p \\log{(h + p)} - p", "- h \\log{(- h + p)} + p \\log{(- h + p)} - p"], "srepr_premise_expression": "exp(Pow(Symbol('p', commutative=True), Symbol('h', commutative=True)))", "srepr_variable": "Symbol('p', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('h', commutative=True), Integer(-1)), exp(Mul(Integer(-1), I, pi, Pow(Symbol('h', commutative=True), Integer(-1)))), lowergamma(Pow(Symbol('h', commutative=True), Integer(-1)), Mul(Pow(Symbol('p', commutative=True), Symbol('h', commutative=True)), exp_polar(Mul(I, pi)))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('h', commutative=True), log(Add(Mul(Integer(-1), Symbol('h', commutative=True)), Symbol('p', commutative=True)))), Mul(Symbol('p', commutative=True), log(Add(Symbol('h', commutative=True), Mul(Integer(-1), Symbol('p', commutative=True))))), Mul(Integer(-1), Symbol('p', commutative=True)))", "Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Mul(Integer(-1), Symbol('p', commutative=True)), Mul(Integer(2), exp(Symbol('h', commutative=True)))))", "Add(Mul(Symbol('h', commutative=True), log(Add(Symbol('h', commutative=True), Symbol('p', commutative=True)))), Mul(Symbol('p', commutative=True), log(Add(Symbol('h', commutative=True), Symbol('p', commutative=True)))), Mul(Integer(-1), Symbol('p', commutative=True)))", "Add(Mul(Integer(-1), Symbol('h', commutative=True), log(Add(Mul(Integer(-1), Symbol('h', commutative=True)), Symbol('p', commutative=True)))), Mul(Symbol('p', commutative=True), log(Add(Mul(Integer(-1), Symbol('h', commutative=True)), Symbol('p', commutative=True)))), Mul(Integer(-1), Symbol('p', commutative=True)))"]}, {"premise_expression": "C + \\sin{(S)}", "variable": "C", "positive": "\\frac{C (C + 2 \\sin{(S)})}{2}", "negatives": ["C S - \\cos{(S)}", "C (- S + \\log{(C^{S})})", "\\sin{(C + S)}", "S \\sin{(C)}"], "srepr_premise_expression": "Add(Symbol('C', commutative=True), sin(Symbol('S', commutative=True)))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Symbol('C', commutative=True), Mul(Integer(2), sin(Symbol('S', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('C', commutative=True), Symbol('S', commutative=True)), Mul(Integer(-1), cos(Symbol('S', commutative=True))))", "Mul(Symbol('C', commutative=True), Add(Mul(Integer(-1), Symbol('S', commutative=True)), log(Pow(Symbol('C', commutative=True), Symbol('S', commutative=True)))))", "sin(Add(Symbol('C', commutative=True), Symbol('S', commutative=True)))", "Mul(Symbol('S', commutative=True), sin(Symbol('C', commutative=True)))"]}, {"premise_expression": "q + e^{I}", "variable": "I", "positive": "I q + e^{I}", "negatives": ["I q + \\sin{(I)}", "\\frac{q (q + 2 e^{I})}{2}", "\\frac{I^{2} e^{q}}{2}", "I (q + \\log{(I)} - 1)"], "srepr_premise_expression": "Add(Symbol('q', commutative=True), exp(Symbol('I', commutative=True)))", "srepr_variable": "Symbol('I', commutative=True)", "srepr_positive": "Add(Mul(Symbol('I', commutative=True), Symbol('q', commutative=True)), exp(Symbol('I', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('I', commutative=True), Symbol('q', commutative=True)), sin(Symbol('I', commutative=True)))", "Mul(Rational(1, 2), Symbol('q', commutative=True), Add(Symbol('q', commutative=True), Mul(Integer(2), exp(Symbol('I', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(2)), exp(Symbol('q', commutative=True)))", "Mul(Symbol('I', commutative=True), Add(Symbol('q', commutative=True), log(Symbol('I', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\frac{M}{p}", "variable": "M", "positive": "\\frac{M^{2}}{2 p}", "negatives": ["M \\log{(p)}", "\\frac{M^{2} \\log{(p)}}{2}", "e^{M - p}", "\\frac{M (M + 2 \\cos{(p)})}{2}"], "srepr_premise_expression": "Mul(Symbol('M', commutative=True), Pow(Symbol('p', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('M', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('M', commutative=True), Integer(2)), Pow(Symbol('p', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('M', commutative=True), log(Symbol('p', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('M', commutative=True), Integer(2)), log(Symbol('p', commutative=True)))", "exp(Add(Symbol('M', commutative=True), Mul(Integer(-1), Symbol('p', commutative=True))))", "Mul(Rational(1, 2), Symbol('M', commutative=True), Add(Symbol('M', commutative=True), Mul(Integer(2), cos(Symbol('p', commutative=True)))))"]}, {"premise_expression": "P f", "variable": "f", "positive": "\\frac{P f^{2}}{2}", "negatives": ["\\frac{P^{2} f}{2}", "e^{P + f}", "\\frac{f (\\log{(f)} - 1)}{P}", "f (\\log{(\\frac{P}{f})} + 1)"], "srepr_premise_expression": "Mul(Symbol('P', commutative=True), Symbol('f', commutative=True))", "srepr_variable": "Symbol('f', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('P', commutative=True), Pow(Symbol('f', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2)), Symbol('f', commutative=True))", "exp(Add(Symbol('P', commutative=True), Symbol('f', commutative=True)))", "Mul(Pow(Symbol('P', commutative=True), Integer(-1)), Symbol('f', commutative=True), Add(log(Symbol('f', commutative=True)), Integer(-1)))", "Mul(Symbol('f', commutative=True), Add(log(Mul(Symbol('P', commutative=True), Pow(Symbol('f', commutative=True), Integer(-1)))), Integer(1)))"]}, {"premise_expression": "T - Y", "variable": "T", "positive": "\\frac{T (T - 2 Y)}{2}", "negatives": ["\\frac{T (- T + 2 Y)}{2}", "\\frac{Y (2 T - Y)}{2}", "\\frac{T (T + 2 \\log{(Y)})}{2}", "\\frac{T^{2} \\log{(Y)}}{2}"], "srepr_premise_expression": "Add(Symbol('T', commutative=True), Mul(Integer(-1), Symbol('Y', commutative=True)))", "srepr_variable": "Symbol('T', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('T', commutative=True), Add(Symbol('T', commutative=True), Mul(Integer(-1), Integer(2), Symbol('Y', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('T', commutative=True), Add(Mul(Integer(-1), Symbol('T', commutative=True)), Mul(Integer(2), Symbol('Y', commutative=True))))", "Mul(Rational(1, 2), Symbol('Y', commutative=True), Add(Mul(Integer(2), Symbol('T', commutative=True)), Mul(Integer(-1), Symbol('Y', commutative=True))))", "Mul(Rational(1, 2), Symbol('T', commutative=True), Add(Symbol('T', commutative=True), Mul(Integer(2), log(Symbol('Y', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('T', commutative=True), Integer(2)), log(Symbol('Y', commutative=True)))"]}, {"premise_expression": "\\log{(b^{I})}", "variable": "b", "positive": "b (- I + \\log{(b^{I})})", "negatives": ["\\frac{I^{2} \\log{(b)}}{2}", "\\frac{b (2 I - b)}{2}", "- I b + e^{b}", "I \\sin{(b)}"], "srepr_premise_expression": "log(Pow(Symbol('b', commutative=True), Symbol('I', commutative=True)))", "srepr_variable": "Symbol('b', commutative=True)", "srepr_positive": "Mul(Symbol('b', commutative=True), Add(Mul(Integer(-1), Symbol('I', commutative=True)), log(Pow(Symbol('b', commutative=True), Symbol('I', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(2)), log(Symbol('b', commutative=True)))", "Mul(Rational(1, 2), Symbol('b', commutative=True), Add(Mul(Integer(2), Symbol('I', commutative=True)), Mul(Integer(-1), Symbol('b', commutative=True))))", "Add(Mul(Integer(-1), Symbol('I', commutative=True), Symbol('b', commutative=True)), exp(Symbol('b', commutative=True)))", "Mul(Symbol('I', commutative=True), sin(Symbol('b', commutative=True)))"]}, {"premise_expression": "R + \\sin{(p)}", "variable": "p", "positive": "R p - \\cos{(p)}", "negatives": ["- R p + e^{p}", "\\log{(R)} \\log{(p)}", "\\frac{R (R + 2 \\sin{(p)})}{2}", "\\frac{p^{2} \\log{(R)}}{2}"], "srepr_premise_expression": "Add(Symbol('R', commutative=True), sin(Symbol('p', commutative=True)))", "srepr_variable": "Symbol('p', commutative=True)", "srepr_positive": "Add(Mul(Symbol('R', commutative=True), Symbol('p', commutative=True)), Mul(Integer(-1), cos(Symbol('p', commutative=True))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('R', commutative=True), Symbol('p', commutative=True)), exp(Symbol('p', commutative=True)))", "Mul(log(Symbol('R', commutative=True)), log(Symbol('p', commutative=True)))", "Mul(Rational(1, 2), Symbol('R', commutative=True), Add(Symbol('R', commutative=True), Mul(Integer(2), sin(Symbol('p', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('p', commutative=True), Integer(2)), log(Symbol('R', commutative=True)))"]}, {"premise_expression": "- s + \\frac{t}{A}", "variable": "t", "positive": "- s t + \\frac{t^{2}}{2 A}", "negatives": ["- A s + t \\log{(A)}", "\\frac{s^{A} t^{2}}{2}", "\\frac{t^{2}}{2 A s}", "\\frac{A s t^{2}}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('s', commutative=True)), Mul(Pow(Symbol('A', commutative=True), Integer(-1)), Symbol('t', commutative=True)))", "srepr_variable": "Symbol('t', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('s', commutative=True), Symbol('t', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(-1)), Pow(Symbol('t', commutative=True), Integer(2))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('A', commutative=True), Symbol('s', commutative=True)), Mul(Symbol('t', commutative=True), log(Symbol('A', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('s', commutative=True), Symbol('A', commutative=True)), Pow(Symbol('t', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(-1)), Pow(Symbol('s', commutative=True), Integer(-1)), Pow(Symbol('t', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Symbol('s', commutative=True), Pow(Symbol('t', commutative=True), Integer(2)))"]}, {"premise_expression": "\\frac{A R}{v}", "variable": "A", "positive": "\\frac{A^{2} R}{2 v}", "negatives": ["\\frac{A R^{2}}{2 v}", "A R \\log{(v)}", "\\frac{A (A R + 2 v)}{2}", "v^{R} \\log{(A)}"], "srepr_premise_expression": "Mul(Symbol('A', commutative=True), Symbol('R', commutative=True), Pow(Symbol('v', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('A', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2)), Symbol('R', commutative=True), Pow(Symbol('v', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('A', commutative=True), Pow(Symbol('R', commutative=True), Integer(2)), Pow(Symbol('v', commutative=True), Integer(-1)))", "Mul(Symbol('A', commutative=True), Symbol('R', commutative=True), log(Symbol('v', commutative=True)))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Mul(Symbol('A', commutative=True), Symbol('R', commutative=True)), Mul(Integer(2), Symbol('v', commutative=True))))", "Mul(Pow(Symbol('v', commutative=True), Symbol('R', commutative=True)), log(Symbol('A', commutative=True)))"]}, {"premise_expression": "\\sin{(V - Z)}", "variable": "Z", "positive": "\\cos{(V - Z)}", "negatives": ["- \\cos{(V - Z)}", "- \\sin{(V - Z)}", "e^{- V + Z}", "- V Z - \\cos{(Z)}"], "srepr_premise_expression": "sin(Add(Symbol('V', commutative=True), Mul(Integer(-1), Symbol('Z', commutative=True))))", "srepr_variable": "Symbol('Z', commutative=True)", "srepr_positive": "cos(Add(Symbol('V', commutative=True), Mul(Integer(-1), Symbol('Z', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('V', commutative=True), Mul(Integer(-1), Symbol('Z', commutative=True)))))", "Mul(Integer(-1), sin(Add(Symbol('V', commutative=True), Mul(Integer(-1), Symbol('Z', commutative=True)))))", "exp(Add(Mul(Integer(-1), Symbol('V', commutative=True)), Symbol('Z', commutative=True)))", "Add(Mul(Integer(-1), Symbol('V', commutative=True), Symbol('Z', commutative=True)), Mul(Integer(-1), cos(Symbol('Z', commutative=True))))"]}, {"premise_expression": "Y - p + r", "variable": "p", "positive": "p (Y - \\frac{p}{2} + r)", "negatives": ["\\frac{Y (Y - 2 p + 2 r)}{2}", "\\frac{r (2 Y - 2 p + r)}{2}", "(Y - r) \\log{(p)}", "\\frac{p r (2 Y - p)}{2}"], "srepr_premise_expression": "Add(Symbol('Y', commutative=True), Mul(Integer(-1), Symbol('p', commutative=True)), Symbol('r', commutative=True))", "srepr_variable": "Symbol('p', commutative=True)", "srepr_positive": "Mul(Symbol('p', commutative=True), Add(Symbol('Y', commutative=True), Mul(Integer(-1), Rational(1, 2), Symbol('p', commutative=True)), Symbol('r', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('Y', commutative=True), Add(Symbol('Y', commutative=True), Mul(Integer(-1), Integer(2), Symbol('p', commutative=True)), Mul(Integer(2), Symbol('r', commutative=True))))", "Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(2), Symbol('Y', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('p', commutative=True)), Symbol('r', commutative=True)))", "Mul(Add(Symbol('Y', commutative=True), Mul(Integer(-1), Symbol('r', commutative=True))), log(Symbol('p', commutative=True)))", "Mul(Rational(1, 2), Symbol('p', commutative=True), Symbol('r', commutative=True), Add(Mul(Integer(2), Symbol('Y', commutative=True)), Mul(Integer(-1), Symbol('p', commutative=True))))"]}, {"premise_expression": "\\frac{- U + u}{L}", "variable": "L", "positive": "(- U + u) \\log{(L)}", "negatives": ["\\frac{U (- U + 2 u)}{2 L}", "\\frac{u (- 2 U + u)}{2 L}", "\\frac{u \\log{(L)}}{U}", "\\frac{L (- L + 2 u^{U})}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('L', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('U', commutative=True)), Symbol('u', commutative=True)))", "srepr_variable": "Symbol('L', commutative=True)", "srepr_positive": "Mul(Add(Mul(Integer(-1), Symbol('U', commutative=True)), Symbol('u', commutative=True)), log(Symbol('L', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(-1)), Symbol('U', commutative=True), Add(Mul(Integer(-1), Symbol('U', commutative=True)), Mul(Integer(2), Symbol('u', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(-1)), Symbol('u', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('U', commutative=True)), Symbol('u', commutative=True)))", "Mul(Pow(Symbol('U', commutative=True), Integer(-1)), Symbol('u', commutative=True), log(Symbol('L', commutative=True)))", "Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Mul(Integer(-1), Symbol('L', commutative=True)), Mul(Integer(2), Pow(Symbol('u', commutative=True), Symbol('U', commutative=True)))))"]}, {"premise_expression": "\\frac{Q}{D}", "variable": "D", "positive": "Q \\log{(D)}", "negatives": ["\\frac{Q^{2}}{2 D}", "\\frac{D^{2} \\log{(Q)}}{2}", "\\cos{(D - Q)}", "D Q (\\log{(D)} - 1)"], "srepr_premise_expression": "Mul(Pow(Symbol('D', commutative=True), Integer(-1)), Symbol('Q', commutative=True))", "srepr_variable": "Symbol('D', commutative=True)", "srepr_positive": "Mul(Symbol('Q', commutative=True), log(Symbol('D', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(-1)), Pow(Symbol('Q', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(2)), log(Symbol('Q', commutative=True)))", "cos(Add(Symbol('D', commutative=True), Mul(Integer(-1), Symbol('Q', commutative=True))))", "Mul(Symbol('D', commutative=True), Symbol('Q', commutative=True), Add(log(Symbol('D', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\sin{(B + a)}", "variable": "a", "positive": "- \\cos{(B + a)}", "negatives": ["B a - \\cos{(a)}", "a (\\log{(\\frac{a}{B})} - 1)", "\\frac{B a^{2}}{2}", "\\frac{a (- a + 2 \\sin{(B)})}{2}"], "srepr_premise_expression": "sin(Add(Symbol('B', commutative=True), Symbol('a', commutative=True)))", "srepr_variable": "Symbol('a', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('B', commutative=True), Symbol('a', commutative=True))))", "srepr_negatives": ["Add(Mul(Symbol('B', commutative=True), Symbol('a', commutative=True)), Mul(Integer(-1), cos(Symbol('a', commutative=True))))", "Mul(Symbol('a', commutative=True), Add(log(Mul(Pow(Symbol('B', commutative=True), Integer(-1)), Symbol('a', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('B', commutative=True), Pow(Symbol('a', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('a', commutative=True), Add(Mul(Integer(-1), Symbol('a', commutative=True)), Mul(Integer(2), sin(Symbol('B', commutative=True)))))"]}, {"premise_expression": "\\log{(\\frac{g}{u})}", "variable": "u", "positive": "u (\\log{(\\frac{g}{u})} + 1)", "negatives": ["g (\\log{(\\frac{g}{u})} - 1)", "g u (\\log{(u)} - 1)", "\\frac{u (2 g - u)}{2}", "\\frac{u (- u + 2 \\log{(g)})}{2}"], "srepr_premise_expression": "log(Mul(Symbol('g', commutative=True), Pow(Symbol('u', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "Mul(Symbol('u', commutative=True), Add(log(Mul(Symbol('g', commutative=True), Pow(Symbol('u', commutative=True), Integer(-1)))), Integer(1)))", "srepr_negatives": ["Mul(Symbol('g', commutative=True), Add(log(Mul(Symbol('g', commutative=True), Pow(Symbol('u', commutative=True), Integer(-1)))), Integer(-1)))", "Mul(Symbol('g', commutative=True), Symbol('u', commutative=True), Add(log(Symbol('u', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(2), Symbol('g', commutative=True)), Mul(Integer(-1), Symbol('u', commutative=True))))", "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(-1), Symbol('u', commutative=True)), Mul(Integer(2), log(Symbol('g', commutative=True)))))"]}, {"premise_expression": "- p + s", "variable": "s", "positive": "\\frac{s (- 2 p + s)}{2}", "negatives": ["\\frac{p (- p + 2 s)}{2}", "\\frac{s^{2} \\cos{(p)}}{2}", "- e^{p - s}", "s (\\log{(\\frac{p}{s})} + 1)"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('p', commutative=True)), Symbol('s', commutative=True))", "srepr_variable": "Symbol('s', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('s', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('p', commutative=True)), Symbol('s', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Mul(Integer(-1), Symbol('p', commutative=True)), Mul(Integer(2), Symbol('s', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('s', commutative=True), Integer(2)), cos(Symbol('p', commutative=True)))", "Mul(Integer(-1), exp(Add(Symbol('p', commutative=True), Mul(Integer(-1), Symbol('s', commutative=True)))))", "Mul(Symbol('s', commutative=True), Add(log(Mul(Symbol('p', commutative=True), Pow(Symbol('s', commutative=True), Integer(-1)))), Integer(1)))"]}, {"premise_expression": "x + \\log{(o)}", "variable": "o", "positive": "o (x + \\log{(o)} - 1)", "negatives": ["\\frac{o (\\log{(o)} - 1)}{x}", "o (\\log{(\\frac{o}{x})} - 1)", "\\frac{x (x + 2 \\log{(o)})}{2}", "e^{x} \\log{(o)}"], "srepr_premise_expression": "Add(Symbol('x', commutative=True), log(Symbol('o', commutative=True)))", "srepr_variable": "Symbol('o', commutative=True)", "srepr_positive": "Mul(Symbol('o', commutative=True), Add(Symbol('x', commutative=True), log(Symbol('o', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('o', commutative=True), Pow(Symbol('x', commutative=True), Integer(-1)), Add(log(Symbol('o', commutative=True)), Integer(-1)))", "Mul(Symbol('o', commutative=True), Add(log(Mul(Symbol('o', commutative=True), Pow(Symbol('x', commutative=True), Integer(-1)))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('x', commutative=True), Add(Symbol('x', commutative=True), Mul(Integer(2), log(Symbol('o', commutative=True)))))", "Mul(exp(Symbol('x', commutative=True)), log(Symbol('o', commutative=True)))"]}, {"premise_expression": "\\frac{Y}{I}", "variable": "I", "positive": "Y \\log{(I)}", "negatives": ["\\frac{Y^{2}}{2 I}", "\\log{(I)} \\sin{(Y)}", "I (\\log{(I Y)} - 1)", "I^{2} (\\frac{I}{3} - \\frac{Y}{2})"], "srepr_premise_expression": "Mul(Pow(Symbol('I', commutative=True), Integer(-1)), Symbol('Y', commutative=True))", "srepr_variable": "Symbol('I', commutative=True)", "srepr_positive": "Mul(Symbol('Y', commutative=True), log(Symbol('I', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(-1)), Pow(Symbol('Y', commutative=True), Integer(2)))", "Mul(log(Symbol('I', commutative=True)), sin(Symbol('Y', commutative=True)))", "Mul(Symbol('I', commutative=True), Add(log(Mul(Symbol('I', commutative=True), Symbol('Y', commutative=True))), Integer(-1)))", "Mul(Pow(Symbol('I', commutative=True), Integer(2)), Add(Mul(Rational(1, 3), Symbol('I', commutative=True)), Mul(Integer(-1), Rational(1, 2), Symbol('Y', commutative=True))))"]}, {"premise_expression": "- \\sin{(F - V)}", "variable": "F", "positive": "\\cos{(F - V)}", "negatives": ["- \\cos{(F - V)}", "- \\cos{(F + V)}", "- V \\cos{(F)}", "F (\\log{(\\frac{V}{F})} + 1)"], "srepr_premise_expression": "Mul(Integer(-1), sin(Add(Symbol('F', commutative=True), Mul(Integer(-1), Symbol('V', commutative=True)))))", "srepr_variable": "Symbol('F', commutative=True)", "srepr_positive": "cos(Add(Symbol('F', commutative=True), Mul(Integer(-1), Symbol('V', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('F', commutative=True), Mul(Integer(-1), Symbol('V', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('F', commutative=True), Symbol('V', commutative=True))))", "Mul(Integer(-1), Symbol('V', commutative=True), cos(Symbol('F', commutative=True)))", "Mul(Symbol('F', commutative=True), Add(log(Mul(Pow(Symbol('F', commutative=True), Integer(-1)), Symbol('V', commutative=True))), Integer(1)))"]}, {"premise_expression": "\\cos{(v - w)}", "variable": "v", "positive": "\\sin{(v - w)}", "negatives": ["- \\sin{(v - w)}", "\\cos{(v - w)}", "e^{w} \\log{(v)}", "\\frac{v^{2} e^{w}}{2}"], "srepr_premise_expression": "cos(Add(Symbol('v', commutative=True), Mul(Integer(-1), Symbol('w', commutative=True))))", "srepr_variable": "Symbol('v', commutative=True)", "srepr_positive": "sin(Add(Symbol('v', commutative=True), Mul(Integer(-1), Symbol('w', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('v', commutative=True), Mul(Integer(-1), Symbol('w', commutative=True)))))", "cos(Add(Symbol('v', commutative=True), Mul(Integer(-1), Symbol('w', commutative=True))))", "Mul(exp(Symbol('w', commutative=True)), log(Symbol('v', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('v', commutative=True), Integer(2)), exp(Symbol('w', commutative=True)))"]}, {"premise_expression": "\\frac{W - a}{y}", "variable": "y", "positive": "(W - a) \\log{(y)}", "negatives": ["W y + a \\log{(y)}", "\\frac{a (2 W - a)}{2 y}", "\\frac{W (W - 2 a)}{2 y}", "\\frac{y (2 W - 2 a - y)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('y', commutative=True), Integer(-1)), Add(Symbol('W', commutative=True), Mul(Integer(-1), Symbol('a', commutative=True))))", "srepr_variable": "Symbol('y', commutative=True)", "srepr_positive": "Mul(Add(Symbol('W', commutative=True), Mul(Integer(-1), Symbol('a', commutative=True))), log(Symbol('y', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('W', commutative=True), Symbol('y', commutative=True)), Mul(Symbol('a', commutative=True), log(Symbol('y', commutative=True))))", "Mul(Rational(1, 2), Symbol('a', commutative=True), Pow(Symbol('y', commutative=True), Integer(-1)), Add(Mul(Integer(2), Symbol('W', commutative=True)), Mul(Integer(-1), Symbol('a', commutative=True))))", "Mul(Rational(1, 2), Symbol('W', commutative=True), Pow(Symbol('y', commutative=True), Integer(-1)), Add(Symbol('W', commutative=True), Mul(Integer(-1), Integer(2), Symbol('a', commutative=True))))", "Mul(Rational(1, 2), Symbol('y', commutative=True), Add(Mul(Integer(2), Symbol('W', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('a', commutative=True)), Mul(Integer(-1), Symbol('y', commutative=True))))"]}, {"premise_expression": "- o + \\sin{(V)}", "variable": "o", "positive": "\\frac{o (- o + 2 \\sin{(V)})}{2}", "negatives": ["\\frac{o (- o + 2 \\cos{(V)})}{2}", "- V o - \\cos{(V)}", "\\frac{o^{2}}{2 V}", "\\log{(o)} \\cos{(V)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('o', commutative=True)), sin(Symbol('V', commutative=True)))", "srepr_variable": "Symbol('o', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Mul(Integer(-1), Symbol('o', commutative=True)), Mul(Integer(2), sin(Symbol('V', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Mul(Integer(-1), Symbol('o', commutative=True)), Mul(Integer(2), cos(Symbol('V', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('V', commutative=True), Symbol('o', commutative=True)), Mul(Integer(-1), cos(Symbol('V', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('V', commutative=True), Integer(-1)), Pow(Symbol('o', commutative=True), Integer(2)))", "Mul(log(Symbol('o', commutative=True)), cos(Symbol('V', commutative=True)))"]}, {"premise_expression": "\\frac{- T + q}{q}", "variable": "T", "positive": "- \\frac{T^{2}}{2 q} + T", "negatives": ["- T \\log{(q)} + q", "\\frac{T^{2} q}{2}", "\\frac{T^{2} e^{q}}{2}", "\\frac{T (T + 2 q)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('q', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('T', commutative=True)), Symbol('q', commutative=True)))", "srepr_variable": "Symbol('T', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('T', commutative=True), Integer(2)), Pow(Symbol('q', commutative=True), Integer(-1))), Symbol('T', commutative=True))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('T', commutative=True), log(Symbol('q', commutative=True))), Symbol('q', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('T', commutative=True), Integer(2)), Symbol('q', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('T', commutative=True), Integer(2)), exp(Symbol('q', commutative=True)))", "Mul(Rational(1, 2), Symbol('T', commutative=True), Add(Symbol('T', commutative=True), Mul(Integer(2), Symbol('q', commutative=True))))"]}, {"premise_expression": "a n", "variable": "a", "positive": "\\frac{a^{2} n}{2}", "negatives": ["\\frac{a n^{2}}{2}", "\\frac{a^{2}}{2 n}", "\\log{(a)} \\sin{(n)}", "\\frac{a (a + 2 \\sin{(n)})}{2}"], "srepr_premise_expression": "Mul(Symbol('a', commutative=True), Symbol('n', commutative=True))", "srepr_variable": "Symbol('a', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('a', commutative=True), Integer(2)), Symbol('n', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('a', commutative=True), Pow(Symbol('n', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('a', commutative=True), Integer(2)), Pow(Symbol('n', commutative=True), Integer(-1)))", "Mul(log(Symbol('a', commutative=True)), sin(Symbol('n', commutative=True)))", "Mul(Rational(1, 2), Symbol('a', commutative=True), Add(Symbol('a', commutative=True), Mul(Integer(2), sin(Symbol('n', commutative=True)))))"]}, {"premise_expression": "\\frac{A y}{j}", "variable": "A", "positive": "\\frac{A^{2} y}{2 j}", "negatives": ["\\frac{A y^{2}}{2 j}", "\\frac{A^{2} j y}{2}", "A y \\log{(j)}", "\\frac{A^{2} (- j + y)}{2}"], "srepr_premise_expression": "Mul(Symbol('A', commutative=True), Pow(Symbol('j', commutative=True), Integer(-1)), Symbol('y', commutative=True))", "srepr_variable": "Symbol('A', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2)), Pow(Symbol('j', commutative=True), Integer(-1)), Symbol('y', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('A', commutative=True), Pow(Symbol('j', commutative=True), Integer(-1)), Pow(Symbol('y', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2)), Symbol('j', commutative=True), Symbol('y', commutative=True))", "Mul(Symbol('A', commutative=True), Symbol('y', commutative=True), log(Symbol('j', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2)), Add(Mul(Integer(-1), Symbol('j', commutative=True)), Symbol('y', commutative=True)))"]}, {"premise_expression": "\\log{(k + w)}", "variable": "k", "positive": "k \\log{(k + w)} - k + w \\log{(k + w)}", "negatives": ["k \\log{(k + w)} + w \\log{(k + w)} - w", "\\log{(k)} \\sin{(w)}", "k (- k + w)", "- k w - \\cos{(k)}"], "srepr_premise_expression": "log(Add(Symbol('k', commutative=True), Symbol('w', commutative=True)))", "srepr_variable": "Symbol('k', commutative=True)", "srepr_positive": "Add(Mul(Symbol('k', commutative=True), log(Add(Symbol('k', commutative=True), Symbol('w', commutative=True)))), Mul(Integer(-1), Symbol('k', commutative=True)), Mul(Symbol('w', commutative=True), log(Add(Symbol('k', commutative=True), Symbol('w', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('k', commutative=True), log(Add(Symbol('k', commutative=True), Symbol('w', commutative=True)))), Mul(Symbol('w', commutative=True), log(Add(Symbol('k', commutative=True), Symbol('w', commutative=True)))), Mul(Integer(-1), Symbol('w', commutative=True)))", "Mul(log(Symbol('k', commutative=True)), sin(Symbol('w', commutative=True)))", "Mul(Symbol('k', commutative=True), Add(Mul(Integer(-1), Symbol('k', commutative=True)), Symbol('w', commutative=True)))", "Add(Mul(Integer(-1), Symbol('k', commutative=True), Symbol('w', commutative=True)), Mul(Integer(-1), cos(Symbol('k', commutative=True))))"]}, {"premise_expression": "\\frac{S}{r}", "variable": "S", "positive": "\\frac{S^{2}}{2 r}", "negatives": ["S \\log{(r)}", "S (S + r)", "r \\sin{(S)}", "r \\log{(S)}"], "srepr_premise_expression": "Mul(Symbol('S', commutative=True), Pow(Symbol('r', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('S', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('S', commutative=True), Integer(2)), Pow(Symbol('r', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('S', commutative=True), log(Symbol('r', commutative=True)))", "Mul(Symbol('S', commutative=True), Add(Symbol('S', commutative=True), Symbol('r', commutative=True)))", "Mul(Symbol('r', commutative=True), sin(Symbol('S', commutative=True)))", "Mul(Symbol('r', commutative=True), log(Symbol('S', commutative=True)))"]}, {"premise_expression": "Q (R + r)", "variable": "r", "positive": "\\frac{Q r (2 R + r)}{2}", "negatives": ["\\frac{Q^{2} (R + r)}{2}", "\\frac{Q R (R + 2 r)}{2}", "\\frac{r^{2} (Q + R)}{2}", "\\frac{r (- 2 R + r)}{2 Q}"], "srepr_premise_expression": "Mul(Symbol('Q', commutative=True), Add(Symbol('R', commutative=True), Symbol('r', commutative=True)))", "srepr_variable": "Symbol('r', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('Q', commutative=True), Symbol('r', commutative=True), Add(Mul(Integer(2), Symbol('R', commutative=True)), Symbol('r', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(2)), Add(Symbol('R', commutative=True), Symbol('r', commutative=True)))", "Mul(Rational(1, 2), Symbol('Q', commutative=True), Symbol('R', commutative=True), Add(Symbol('R', commutative=True), Mul(Integer(2), Symbol('r', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('r', commutative=True), Integer(2)), Add(Symbol('Q', commutative=True), Symbol('R', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(-1)), Symbol('r', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('R', commutative=True)), Symbol('r', commutative=True)))"]}, {"premise_expression": "P (p + s)", "variable": "P", "positive": "\\frac{P^{2} (p + s)}{2}", "negatives": ["\\frac{P s (2 p + s)}{2}", "\\frac{P p (p + 2 s)}{2}", "\\frac{P p (P + 2 s)}{2}", "\\frac{P p (P - 2 s)}{2}"], "srepr_premise_expression": "Mul(Symbol('P', commutative=True), Add(Symbol('p', commutative=True), Symbol('s', commutative=True)))", "srepr_variable": "Symbol('P', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2)), Add(Symbol('p', commutative=True), Symbol('s', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('P', commutative=True), Symbol('s', commutative=True), Add(Mul(Integer(2), Symbol('p', commutative=True)), Symbol('s', commutative=True)))", "Mul(Rational(1, 2), Symbol('P', commutative=True), Symbol('p', commutative=True), Add(Symbol('p', commutative=True), Mul(Integer(2), Symbol('s', commutative=True))))", "Mul(Rational(1, 2), Symbol('P', commutative=True), Symbol('p', commutative=True), Add(Symbol('P', commutative=True), Mul(Integer(2), Symbol('s', commutative=True))))", "Mul(Rational(1, 2), Symbol('P', commutative=True), Symbol('p', commutative=True), Add(Symbol('P', commutative=True), Mul(Integer(-1), Integer(2), Symbol('s', commutative=True))))"]}, {"premise_expression": "o + \\sin{(Y)}", "variable": "o", "positive": "\\frac{o (o + 2 \\sin{(Y)})}{2}", "negatives": ["\\frac{o^{2} \\log{(Y)}}{2}", "Y o - \\cos{(Y)}", "\\frac{o (2 Y - o)}{2}", "o (- Y + \\log{(o^{Y})})"], "srepr_premise_expression": "Add(Symbol('o', commutative=True), sin(Symbol('Y', commutative=True)))", "srepr_variable": "Symbol('o', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Symbol('o', commutative=True), Mul(Integer(2), sin(Symbol('Y', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('o', commutative=True), Integer(2)), log(Symbol('Y', commutative=True)))", "Add(Mul(Symbol('Y', commutative=True), Symbol('o', commutative=True)), Mul(Integer(-1), cos(Symbol('Y', commutative=True))))", "Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Mul(Integer(2), Symbol('Y', commutative=True)), Mul(Integer(-1), Symbol('o', commutative=True))))", "Mul(Symbol('o', commutative=True), Add(Mul(Integer(-1), Symbol('Y', commutative=True)), log(Pow(Symbol('o', commutative=True), Symbol('Y', commutative=True)))))"]}, {"premise_expression": "\\log{(\\frac{l}{v})}", "variable": "l", "positive": "l (\\log{(\\frac{l}{v})} - 1)", "negatives": ["v (\\log{(\\frac{l}{v})} + 1)", "v \\log{(l)}", "\\frac{l (l - 2 v)}{2}", "\\log{(l)} \\sin{(v)}"], "srepr_premise_expression": "log(Mul(Symbol('l', commutative=True), Pow(Symbol('v', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('l', commutative=True)", "srepr_positive": "Mul(Symbol('l', commutative=True), Add(log(Mul(Symbol('l', commutative=True), Pow(Symbol('v', commutative=True), Integer(-1)))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('v', commutative=True), Add(log(Mul(Symbol('l', commutative=True), Pow(Symbol('v', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Symbol('v', commutative=True), log(Symbol('l', commutative=True)))", "Mul(Rational(1, 2), Symbol('l', commutative=True), Add(Symbol('l', commutative=True), Mul(Integer(-1), Integer(2), Symbol('v', commutative=True))))", "Mul(log(Symbol('l', commutative=True)), sin(Symbol('v', commutative=True)))"]}, {"premise_expression": "K + \\sin{(P)}", "variable": "K", "positive": "\\frac{K (K + 2 \\sin{(P)})}{2}", "negatives": ["\\frac{K (- K + 2 \\sin{(P)})}{2}", "\\frac{K (K + 2 e^{P})}{2}", "\\frac{K (- K + 2 \\cos{(P)})}{2}", "K P - \\cos{(P)}"], "srepr_premise_expression": "Add(Symbol('K', commutative=True), sin(Symbol('P', commutative=True)))", "srepr_variable": "Symbol('K', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Symbol('K', commutative=True), Mul(Integer(2), sin(Symbol('P', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Mul(Integer(-1), Symbol('K', commutative=True)), Mul(Integer(2), sin(Symbol('P', commutative=True)))))", "Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Symbol('K', commutative=True), Mul(Integer(2), exp(Symbol('P', commutative=True)))))", "Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Mul(Integer(-1), Symbol('K', commutative=True)), Mul(Integer(2), cos(Symbol('P', commutative=True)))))", "Add(Mul(Symbol('K', commutative=True), Symbol('P', commutative=True)), Mul(Integer(-1), cos(Symbol('P', commutative=True))))"]}, {"premise_expression": "\\frac{\\cos{(J)}}{P}", "variable": "J", "positive": "\\frac{\\sin{(J)}}{P}", "negatives": ["\\frac{J^{2} \\sin{(P)}}{2}", "\\log{(P)} \\cos{(J)}", "- J P + e^{J}", "\\int \\cos^{P}{(J)} dJ"], "srepr_premise_expression": "Mul(Pow(Symbol('P', commutative=True), Integer(-1)), cos(Symbol('J', commutative=True)))", "srepr_variable": "Symbol('J', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('P', commutative=True), Integer(-1)), sin(Symbol('J', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('J', commutative=True), Integer(2)), sin(Symbol('P', commutative=True)))", "Mul(log(Symbol('P', commutative=True)), cos(Symbol('J', commutative=True)))", "Add(Mul(Integer(-1), Symbol('J', commutative=True), Symbol('P', commutative=True)), exp(Symbol('J', commutative=True)))", "Integral(Pow(cos(Symbol('J', commutative=True)), Symbol('P', commutative=True)), Tuple(Symbol('J', commutative=True)))"]}, {"premise_expression": "E - y", "variable": "E", "positive": "\\frac{E (E - 2 y)}{2}", "negatives": ["\\frac{y (2 E - y)}{2}", "\\frac{E (E + 2 \\log{(y)})}{2}", "\\frac{E (- E + 2 \\sin{(y)})}{2}", "\\sin{(E - y)}"], "srepr_premise_expression": "Add(Symbol('E', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True)))", "srepr_variable": "Symbol('E', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('E', commutative=True), Add(Symbol('E', commutative=True), Mul(Integer(-1), Integer(2), Symbol('y', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('y', commutative=True), Add(Mul(Integer(2), Symbol('E', commutative=True)), Mul(Integer(-1), Symbol('y', commutative=True))))", "Mul(Rational(1, 2), Symbol('E', commutative=True), Add(Symbol('E', commutative=True), Mul(Integer(2), log(Symbol('y', commutative=True)))))", "Mul(Rational(1, 2), Symbol('E', commutative=True), Add(Mul(Integer(-1), Symbol('E', commutative=True)), Mul(Integer(2), sin(Symbol('y', commutative=True)))))", "sin(Add(Symbol('E', commutative=True), Mul(Integer(-1), Symbol('y', commutative=True))))"]}, {"premise_expression": "a + r", "variable": "a", "positive": "\\frac{a (a + 2 r)}{2}", "negatives": ["\\frac{r (2 a + r)}{2}", "\\frac{a^{2} \\cos{(r)}}{2}", "\\frac{a^{2} \\log{(r)}}{2}", "- e^{- a + r}"], "srepr_premise_expression": "Add(Symbol('a', commutative=True), Symbol('r', commutative=True))", "srepr_variable": "Symbol('a', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('a', commutative=True), Add(Symbol('a', commutative=True), Mul(Integer(2), Symbol('r', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(2), Symbol('a', commutative=True)), Symbol('r', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('a', commutative=True), Integer(2)), cos(Symbol('r', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('a', commutative=True), Integer(2)), log(Symbol('r', commutative=True)))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('a', commutative=True)), Symbol('r', commutative=True))))"]}, {"premise_expression": "e^{t^{l}}", "variable": "t", "positive": "\\frac{e^{- \\frac{i \\pi}{l}} \\gamma(\\frac{1}{l}, t^{l} e^{i \\pi})}{l}", "negatives": ["\\int (l - t)^{t} dt", "- l \\log{(- l + t)} + t \\log{(l - t)} - t", "l \\operatorname{Si}{(\\frac{l}{t})} + t \\cos{(\\frac{l}{t})}", "\\log{(t)} \\cos{(l)}"], "srepr_premise_expression": "exp(Pow(Symbol('t', commutative=True), Symbol('l', commutative=True)))", "srepr_variable": "Symbol('t', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('l', commutative=True), Integer(-1)), exp(Mul(Integer(-1), I, pi, Pow(Symbol('l', commutative=True), Integer(-1)))), lowergamma(Pow(Symbol('l', commutative=True), Integer(-1)), Mul(Pow(Symbol('t', commutative=True), Symbol('l', commutative=True)), exp_polar(Mul(I, pi)))))", "srepr_negatives": ["NonElementaryIntegral(Pow(Add(Symbol('l', commutative=True), Mul(Integer(-1), Symbol('t', commutative=True))), Symbol('t', commutative=True)), Tuple(Symbol('t', commutative=True)))", "Add(Mul(Integer(-1), Symbol('l', commutative=True), log(Add(Mul(Integer(-1), Symbol('l', commutative=True)), Symbol('t', commutative=True)))), Mul(Symbol('t', commutative=True), log(Add(Symbol('l', commutative=True), Mul(Integer(-1), Symbol('t', commutative=True))))), Mul(Integer(-1), Symbol('t', commutative=True)))", "Add(Mul(Symbol('l', commutative=True), Si(Mul(Symbol('l', commutative=True), Pow(Symbol('t', commutative=True), Integer(-1))))), Mul(Symbol('t', commutative=True), cos(Mul(Symbol('l', commutative=True), Pow(Symbol('t', commutative=True), Integer(-1))))))", "Mul(log(Symbol('t', commutative=True)), cos(Symbol('l', commutative=True)))"]}, {"premise_expression": "\\sin{(l - n)}", "variable": "n", "positive": "\\cos{(l - n)}", "negatives": ["- \\cos{(l - n)}", "- l \\cos{(n)}", "\\frac{n^{2} \\log{(l)}}{2}", "\\frac{n^{2} e^{l}}{2}"], "srepr_premise_expression": "sin(Add(Symbol('l', commutative=True), Mul(Integer(-1), Symbol('n', commutative=True))))", "srepr_variable": "Symbol('n', commutative=True)", "srepr_positive": "cos(Add(Symbol('l', commutative=True), Mul(Integer(-1), Symbol('n', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('l', commutative=True), Mul(Integer(-1), Symbol('n', commutative=True)))))", "Mul(Integer(-1), Symbol('l', commutative=True), cos(Symbol('n', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('n', commutative=True), Integer(2)), log(Symbol('l', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('n', commutative=True), Integer(2)), exp(Symbol('l', commutative=True)))"]}, {"premise_expression": "- v + e^{u}", "variable": "v", "positive": "\\frac{v (- v + 2 e^{u})}{2}", "negatives": ["\\frac{v (- v + 2 \\sin{(u)})}{2}", "- u v + e^{u}", "\\frac{v^{2}}{2 u}", "- u v + \\sin{(v)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('v', commutative=True)), exp(Symbol('u', commutative=True)))", "srepr_variable": "Symbol('v', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('v', commutative=True), Add(Mul(Integer(-1), Symbol('v', commutative=True)), Mul(Integer(2), exp(Symbol('u', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('v', commutative=True), Add(Mul(Integer(-1), Symbol('v', commutative=True)), Mul(Integer(2), sin(Symbol('u', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('u', commutative=True), Symbol('v', commutative=True)), exp(Symbol('u', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('u', commutative=True), Integer(-1)), Pow(Symbol('v', commutative=True), Integer(2)))", "Add(Mul(Integer(-1), Symbol('u', commutative=True), Symbol('v', commutative=True)), sin(Symbol('v', commutative=True)))"]}, {"premise_expression": "\\log{(- u + x)}", "variable": "x", "positive": "- u \\log{(- u + x)} + x \\log{(- u + x)} - x", "negatives": ["u \\log{(- u + x)} - u - x \\log{(u - x)}", "\\log{(u)} \\log{(x)}", "x (\\log{(u x)} - 1)", "x (\\log{(\\frac{u}{x})} + 1)"], "srepr_premise_expression": "log(Add(Mul(Integer(-1), Symbol('u', commutative=True)), Symbol('x', commutative=True)))", "srepr_variable": "Symbol('x', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('u', commutative=True), log(Add(Mul(Integer(-1), Symbol('u', commutative=True)), Symbol('x', commutative=True)))), Mul(Symbol('x', commutative=True), log(Add(Mul(Integer(-1), Symbol('u', commutative=True)), Symbol('x', commutative=True)))), Mul(Integer(-1), Symbol('x', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('u', commutative=True), log(Add(Mul(Integer(-1), Symbol('u', commutative=True)), Symbol('x', commutative=True)))), Mul(Integer(-1), Symbol('u', commutative=True)), Mul(Integer(-1), Symbol('x', commutative=True), log(Add(Symbol('u', commutative=True), Mul(Integer(-1), Symbol('x', commutative=True))))))", "Mul(log(Symbol('u', commutative=True)), log(Symbol('x', commutative=True)))", "Mul(Symbol('x', commutative=True), Add(log(Mul(Symbol('u', commutative=True), Symbol('x', commutative=True))), Integer(-1)))", "Mul(Symbol('x', commutative=True), Add(log(Mul(Symbol('u', commutative=True), Pow(Symbol('x', commutative=True), Integer(-1)))), Integer(1)))"]}, {"premise_expression": "R + g - h", "variable": "h", "positive": "h (R + g - \\frac{h}{2})", "negatives": ["\\frac{h (- 2 R - 2 g + h)}{2}", "\\frac{R (R + 2 g - 2 h)}{2}", "\\frac{g (2 R + g - 2 h)}{2}", "\\frac{h (- 2 R + 2 g - h)}{2}"], "srepr_premise_expression": "Add(Symbol('R', commutative=True), Symbol('g', commutative=True), Mul(Integer(-1), Symbol('h', commutative=True)))", "srepr_variable": "Symbol('h', commutative=True)", "srepr_positive": "Mul(Symbol('h', commutative=True), Add(Symbol('R', commutative=True), Symbol('g', commutative=True), Mul(Integer(-1), Rational(1, 2), Symbol('h', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('h', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('R', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('g', commutative=True)), Symbol('h', commutative=True)))", "Mul(Rational(1, 2), Symbol('R', commutative=True), Add(Symbol('R', commutative=True), Mul(Integer(2), Symbol('g', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('h', commutative=True))))", "Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Mul(Integer(2), Symbol('R', commutative=True)), Symbol('g', commutative=True), Mul(Integer(-1), Integer(2), Symbol('h', commutative=True))))", "Mul(Rational(1, 2), Symbol('h', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('R', commutative=True)), Mul(Integer(2), Symbol('g', commutative=True)), Mul(Integer(-1), Symbol('h', commutative=True))))"]}, {"premise_expression": "C - V + r", "variable": "C", "positive": "C (\\frac{C}{2} - V + r)", "negatives": ["\\frac{C (C + 2 V - 2 r)}{2}", "\\frac{V (2 C - V + 2 r)}{2}", "\\frac{r (2 C - 2 V + r)}{2}", "\\frac{C^{2} (V - r)}{2}"], "srepr_premise_expression": "Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('V', commutative=True)), Symbol('r', commutative=True))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Mul(Symbol('C', commutative=True), Add(Mul(Rational(1, 2), Symbol('C', commutative=True)), Mul(Integer(-1), Symbol('V', commutative=True)), Symbol('r', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Symbol('C', commutative=True), Mul(Integer(2), Symbol('V', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('r', commutative=True))))", "Mul(Rational(1, 2), Symbol('V', commutative=True), Add(Mul(Integer(2), Symbol('C', commutative=True)), Mul(Integer(-1), Symbol('V', commutative=True)), Mul(Integer(2), Symbol('r', commutative=True))))", "Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(2), Symbol('C', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('V', commutative=True)), Symbol('r', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2)), Add(Symbol('V', commutative=True), Mul(Integer(-1), Symbol('r', commutative=True))))"]}, {"premise_expression": "\\cos{(\\frac{B}{h})}", "variable": "h", "positive": "B \\operatorname{Si}{(\\frac{B}{h})} + h \\cos{(\\frac{B}{h})}", "negatives": ["\\frac{h (h + 2 \\cos{(B)})}{2}", "h (B + \\sin{(B)})", "\\log{(h)} \\sin{(B)}", "\\frac{h (2 B - h)}{2}"], "srepr_premise_expression": "cos(Mul(Symbol('B', commutative=True), Pow(Symbol('h', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('h', commutative=True)", "srepr_positive": "Add(Mul(Symbol('B', commutative=True), Si(Mul(Symbol('B', commutative=True), Pow(Symbol('h', commutative=True), Integer(-1))))), Mul(Symbol('h', commutative=True), cos(Mul(Symbol('B', commutative=True), Pow(Symbol('h', commutative=True), Integer(-1))))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('h', commutative=True), Add(Symbol('h', commutative=True), Mul(Integer(2), cos(Symbol('B', commutative=True)))))", "Mul(Symbol('h', commutative=True), Add(Symbol('B', commutative=True), sin(Symbol('B', commutative=True))))", "Mul(log(Symbol('h', commutative=True)), sin(Symbol('B', commutative=True)))", "Mul(Rational(1, 2), Symbol('h', commutative=True), Add(Mul(Integer(2), Symbol('B', commutative=True)), Mul(Integer(-1), Symbol('h', commutative=True))))"]}, {"premise_expression": "\\log{(X t)}", "variable": "t", "positive": "t (\\log{(X t)} - 1)", "negatives": ["X (\\log{(X t)} - 1)", "X \\log{(t)}", "\\cos{(X - t)}", "\\frac{t (- 2 X + t)}{2}"], "srepr_premise_expression": "log(Mul(Symbol('X', commutative=True), Symbol('t', commutative=True)))", "srepr_variable": "Symbol('t', commutative=True)", "srepr_positive": "Mul(Symbol('t', commutative=True), Add(log(Mul(Symbol('X', commutative=True), Symbol('t', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('X', commutative=True), Add(log(Mul(Symbol('X', commutative=True), Symbol('t', commutative=True))), Integer(-1)))", "Mul(Symbol('X', commutative=True), log(Symbol('t', commutative=True)))", "cos(Add(Symbol('X', commutative=True), Mul(Integer(-1), Symbol('t', commutative=True))))", "Mul(Rational(1, 2), Symbol('t', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('X', commutative=True)), Symbol('t', commutative=True)))"]}, {"premise_expression": "U u", "variable": "U", "positive": "\\frac{U^{2} u}{2}", "negatives": ["\\frac{U u^{2}}{2}", "\\frac{U (U - 2 u)}{2}", "\\sin{(U + u)}", "U (\\log{(U u)} - 1)"], "srepr_premise_expression": "Mul(Symbol('U', commutative=True), Symbol('u', commutative=True))", "srepr_variable": "Symbol('U', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('U', commutative=True), Integer(2)), Symbol('u', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('U', commutative=True), Pow(Symbol('u', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('U', commutative=True), Add(Symbol('U', commutative=True), Mul(Integer(-1), Integer(2), Symbol('u', commutative=True))))", "sin(Add(Symbol('U', commutative=True), Symbol('u', commutative=True)))", "Mul(Symbol('U', commutative=True), Add(log(Mul(Symbol('U', commutative=True), Symbol('u', commutative=True))), Integer(-1)))"]}, {"premise_expression": "c e^{s}", "variable": "c", "positive": "\\frac{c^{2} e^{s}}{2}", "negatives": ["\\frac{c^{2} \\log{(s)}}{2}", "c e^{s}", "\\frac{c (- c + 2 \\cos{(s)})}{2}", "- c s + \\sin{(c)}"], "srepr_premise_expression": "Mul(Symbol('c', commutative=True), exp(Symbol('s', commutative=True)))", "srepr_variable": "Symbol('c', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('c', commutative=True), Integer(2)), exp(Symbol('s', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('c', commutative=True), Integer(2)), log(Symbol('s', commutative=True)))", "Mul(Symbol('c', commutative=True), exp(Symbol('s', commutative=True)))", "Mul(Rational(1, 2), Symbol('c', commutative=True), Add(Mul(Integer(-1), Symbol('c', commutative=True)), Mul(Integer(2), cos(Symbol('s', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('c', commutative=True), Symbol('s', commutative=True)), sin(Symbol('c', commutative=True)))"]}, {"premise_expression": "t \\log{(Y)}", "variable": "Y", "positive": "Y t (\\log{(Y)} - 1)", "negatives": ["\\frac{t^{2} \\log{(Y)}}{2}", "\\sin{(Y + t)}", "\\frac{Y^{2}}{2 t}", "\\frac{Y^{2} e^{t}}{2}"], "srepr_premise_expression": "Mul(Symbol('t', commutative=True), log(Symbol('Y', commutative=True)))", "srepr_variable": "Symbol('Y', commutative=True)", "srepr_positive": "Mul(Symbol('Y', commutative=True), Symbol('t', commutative=True), Add(log(Symbol('Y', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('t', commutative=True), Integer(2)), log(Symbol('Y', commutative=True)))", "sin(Add(Symbol('Y', commutative=True), Symbol('t', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('Y', commutative=True), Integer(2)), Pow(Symbol('t', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('Y', commutative=True), Integer(2)), exp(Symbol('t', commutative=True)))"]}, {"premise_expression": "D \\log{(H)}", "variable": "H", "positive": "D H (\\log{(H)} - 1)", "negatives": ["H (\\log{(\\frac{H}{D})} - 1)", "\\frac{D^{2} \\log{(H)}}{2}", "- D H + e^{H}", "- \\frac{\\cos{(H)}}{D}"], "srepr_premise_expression": "Mul(Symbol('D', commutative=True), log(Symbol('H', commutative=True)))", "srepr_variable": "Symbol('H', commutative=True)", "srepr_positive": "Mul(Symbol('D', commutative=True), Symbol('H', commutative=True), Add(log(Symbol('H', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('H', commutative=True), Add(log(Mul(Pow(Symbol('D', commutative=True), Integer(-1)), Symbol('H', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(2)), log(Symbol('H', commutative=True)))", "Add(Mul(Integer(-1), Symbol('D', commutative=True), Symbol('H', commutative=True)), exp(Symbol('H', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('D', commutative=True), Integer(-1)), cos(Symbol('H', commutative=True)))"]}, {"premise_expression": "Q - o", "variable": "Q", "positive": "\\frac{Q (Q - 2 o)}{2}", "negatives": ["\\frac{o (2 Q - o)}{2}", "\\frac{Q (Q + 2 \\cos{(o)})}{2}", "\\frac{Q^{2} \\cos{(o)}}{2}", "e^{Q - o}"], "srepr_premise_expression": "Add(Symbol('Q', commutative=True), Mul(Integer(-1), Symbol('o', commutative=True)))", "srepr_variable": "Symbol('Q', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Symbol('Q', commutative=True), Mul(Integer(-1), Integer(2), Symbol('o', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Mul(Integer(2), Symbol('Q', commutative=True)), Mul(Integer(-1), Symbol('o', commutative=True))))", "Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Symbol('Q', commutative=True), Mul(Integer(2), cos(Symbol('o', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(2)), cos(Symbol('o', commutative=True)))", "exp(Add(Symbol('Q', commutative=True), Mul(Integer(-1), Symbol('o', commutative=True))))"]}, {"premise_expression": "\\frac{Q}{I}", "variable": "Q", "positive": "\\frac{Q^{2}}{2 I}", "negatives": ["Q \\log{(I)}", "\\frac{Q^{2} \\cos{(I)}}{2}", "\\frac{Q (2 I + Q)}{2}", "- \\cos{(I + Q)}"], "srepr_premise_expression": "Mul(Pow(Symbol('I', commutative=True), Integer(-1)), Symbol('Q', commutative=True))", "srepr_variable": "Symbol('Q', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(-1)), Pow(Symbol('Q', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('Q', commutative=True), log(Symbol('I', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(2)), cos(Symbol('I', commutative=True)))", "Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Mul(Integer(2), Symbol('I', commutative=True)), Symbol('Q', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('I', commutative=True), Symbol('Q', commutative=True))))"]}, {"premise_expression": "\\sin{(c - k)}", "variable": "c", "positive": "- \\cos{(c - k)}", "negatives": ["\\cos{(c - k)}", "e^{c + k}", "c \\cos{(1)}", "k e^{\\frac{c}{k}}"], "srepr_premise_expression": "sin(Add(Symbol('c', commutative=True), Mul(Integer(-1), Symbol('k', commutative=True))))", "srepr_variable": "Symbol('c', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('c', commutative=True), Mul(Integer(-1), Symbol('k', commutative=True)))))", "srepr_negatives": ["cos(Add(Symbol('c', commutative=True), Mul(Integer(-1), Symbol('k', commutative=True))))", "exp(Add(Symbol('c', commutative=True), Symbol('k', commutative=True)))", "Mul(Symbol('c', commutative=True), cos(Integer(1)))", "Mul(Symbol('k', commutative=True), exp(Mul(Symbol('c', commutative=True), Pow(Symbol('k', commutative=True), Integer(-1)))))"]}, {"premise_expression": "g + e^{v}", "variable": "g", "positive": "\\frac{g (g + 2 e^{v})}{2}", "negatives": ["\\frac{g (- g + 2 e^{v})}{2}", "\\frac{g (- g + 2 \\sin{(v)})}{2}", "\\frac{g^{2} e^{v}}{2}", "g v + e^{v}"], "srepr_premise_expression": "Add(Symbol('g', commutative=True), exp(Symbol('v', commutative=True)))", "srepr_variable": "Symbol('g', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Symbol('g', commutative=True), Mul(Integer(2), exp(Symbol('v', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Mul(Integer(-1), Symbol('g', commutative=True)), Mul(Integer(2), exp(Symbol('v', commutative=True)))))", "Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Mul(Integer(-1), Symbol('g', commutative=True)), Mul(Integer(2), sin(Symbol('v', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('g', commutative=True), Integer(2)), exp(Symbol('v', commutative=True)))", "Add(Mul(Symbol('g', commutative=True), Symbol('v', commutative=True)), exp(Symbol('v', commutative=True)))"]}, {"premise_expression": "\\log{(V f)}", "variable": "f", "positive": "f (\\log{(V f)} - 1)", "negatives": ["V (\\log{(V f)} - 1)", "\\frac{f^{2} \\log{(V)}}{2}", "\\log{(f)} \\cos{(V)}", "e^{V + f}"], "srepr_premise_expression": "log(Mul(Symbol('V', commutative=True), Symbol('f', commutative=True)))", "srepr_variable": "Symbol('f', commutative=True)", "srepr_positive": "Mul(Symbol('f', commutative=True), Add(log(Mul(Symbol('V', commutative=True), Symbol('f', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('V', commutative=True), Add(log(Mul(Symbol('V', commutative=True), Symbol('f', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('f', commutative=True), Integer(2)), log(Symbol('V', commutative=True)))", "Mul(log(Symbol('f', commutative=True)), cos(Symbol('V', commutative=True)))", "exp(Add(Symbol('V', commutative=True), Symbol('f', commutative=True)))"]}, {"premise_expression": "\\frac{V}{t}", "variable": "V", "positive": "\\frac{V^{2}}{2 t}", "negatives": ["V \\log{(t)}", "\\frac{V^{2} \\sin{(t)}}{2}", "\\frac{V (V + 2 t)}{2}", "- \\cos{(V + t)}"], "srepr_premise_expression": "Mul(Symbol('V', commutative=True), Pow(Symbol('t', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('V', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('V', commutative=True), Integer(2)), Pow(Symbol('t', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('V', commutative=True), log(Symbol('t', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('V', commutative=True), Integer(2)), sin(Symbol('t', commutative=True)))", "Mul(Rational(1, 2), Symbol('V', commutative=True), Add(Symbol('V', commutative=True), Mul(Integer(2), Symbol('t', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('V', commutative=True), Symbol('t', commutative=True))))"]}, {"premise_expression": "w \\sin{(U)}", "variable": "w", "positive": "\\frac{w^{2} \\sin{(U)}}{2}", "negatives": ["- w \\cos{(U)}", "U e^{\\frac{w}{U}}", "\\frac{w (- w + 2 \\cos{(U)})}{2}", "e^{- U + w}"], "srepr_premise_expression": "Mul(Symbol('w', commutative=True), sin(Symbol('U', commutative=True)))", "srepr_variable": "Symbol('w', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('w', commutative=True), Integer(2)), sin(Symbol('U', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Symbol('w', commutative=True), cos(Symbol('U', commutative=True)))", "Mul(Symbol('U', commutative=True), exp(Mul(Pow(Symbol('U', commutative=True), Integer(-1)), Symbol('w', commutative=True))))", "Mul(Rational(1, 2), Symbol('w', commutative=True), Add(Mul(Integer(-1), Symbol('w', commutative=True)), Mul(Integer(2), cos(Symbol('U', commutative=True)))))", "exp(Add(Mul(Integer(-1), Symbol('U', commutative=True)), Symbol('w', commutative=True)))"]}, {"premise_expression": "K M c", "variable": "K", "positive": "\\frac{K^{2} M c}{2}", "negatives": ["\\frac{K M^{2} c}{2}", "\\frac{K M c^{2}}{2}", "\\frac{K (K + 2 M c)}{2}", "\\frac{K (- K + 2 M c)}{2}"], "srepr_premise_expression": "Mul(Symbol('K', commutative=True), Symbol('M', commutative=True), Symbol('c', commutative=True))", "srepr_variable": "Symbol('K', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('K', commutative=True), Integer(2)), Symbol('M', commutative=True), Symbol('c', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('K', commutative=True), Pow(Symbol('M', commutative=True), Integer(2)), Symbol('c', commutative=True))", "Mul(Rational(1, 2), Symbol('K', commutative=True), Symbol('M', commutative=True), Pow(Symbol('c', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Symbol('K', commutative=True), Mul(Integer(2), Symbol('M', commutative=True), Symbol('c', commutative=True))))", "Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Mul(Integer(-1), Symbol('K', commutative=True)), Mul(Integer(2), Symbol('M', commutative=True), Symbol('c', commutative=True))))"]}, {"premise_expression": "\\frac{e^{b}}{E}", "variable": "E", "positive": "e^{b} \\log{(E)}", "negatives": ["b \\sin{(E)}", "- \\frac{\\cos{(E)}}{b}", "E b (\\log{(E)} - 1)", "\\sin{(E - b)}"], "srepr_premise_expression": "Mul(Pow(Symbol('E', commutative=True), Integer(-1)), exp(Symbol('b', commutative=True)))", "srepr_variable": "Symbol('E', commutative=True)", "srepr_positive": "Mul(exp(Symbol('b', commutative=True)), log(Symbol('E', commutative=True)))", "srepr_negatives": ["Mul(Symbol('b', commutative=True), sin(Symbol('E', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('b', commutative=True), Integer(-1)), cos(Symbol('E', commutative=True)))", "Mul(Symbol('E', commutative=True), Symbol('b', commutative=True), Add(log(Symbol('E', commutative=True)), Integer(-1)))", "sin(Add(Symbol('E', commutative=True), Mul(Integer(-1), Symbol('b', commutative=True))))"]}, {"premise_expression": "I j", "variable": "I", "positive": "\\frac{I^{2} j}{2}", "negatives": ["\\frac{I j^{2}}{2}", "\\frac{I (I + 2 j)}{2}", "\\frac{I (- I + 2 j)}{2}", "- j \\cos{(I)}"], "srepr_premise_expression": "Mul(Symbol('I', commutative=True), Symbol('j', commutative=True))", "srepr_variable": "Symbol('I', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(2)), Symbol('j', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('I', commutative=True), Pow(Symbol('j', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('I', commutative=True), Add(Symbol('I', commutative=True), Mul(Integer(2), Symbol('j', commutative=True))))", "Mul(Rational(1, 2), Symbol('I', commutative=True), Add(Mul(Integer(-1), Symbol('I', commutative=True)), Mul(Integer(2), Symbol('j', commutative=True))))", "Mul(Integer(-1), Symbol('j', commutative=True), cos(Symbol('I', commutative=True)))"]}, {"premise_expression": "\\cos{(\\frac{J}{S})}", "variable": "S", "positive": "J \\operatorname{Si}{(\\frac{J}{S})} + S \\cos{(\\frac{J}{S})}", "negatives": ["- J \\cos{(S)}", "- \\cos{(J + S)}", "- J \\log{(- J + S)} + S \\log{(J - S)} - S", "\\frac{S^{2}}{2 J}"], "srepr_premise_expression": "cos(Mul(Symbol('J', commutative=True), Pow(Symbol('S', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('S', commutative=True)", "srepr_positive": "Add(Mul(Symbol('J', commutative=True), Si(Mul(Symbol('J', commutative=True), Pow(Symbol('S', commutative=True), Integer(-1))))), Mul(Symbol('S', commutative=True), cos(Mul(Symbol('J', commutative=True), Pow(Symbol('S', commutative=True), Integer(-1))))))", "srepr_negatives": ["Mul(Integer(-1), Symbol('J', commutative=True), cos(Symbol('S', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('J', commutative=True), Symbol('S', commutative=True))))", "Add(Mul(Integer(-1), Symbol('J', commutative=True), log(Add(Mul(Integer(-1), Symbol('J', commutative=True)), Symbol('S', commutative=True)))), Mul(Symbol('S', commutative=True), log(Add(Symbol('J', commutative=True), Mul(Integer(-1), Symbol('S', commutative=True))))), Mul(Integer(-1), Symbol('S', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('J', commutative=True), Integer(-1)), Pow(Symbol('S', commutative=True), Integer(2)))"]}, {"premise_expression": "\\log{(m x)}", "variable": "x", "positive": "x (\\log{(m x)} - 1)", "negatives": ["m (\\log{(m x)} - 1)", "x (\\log{(\\frac{x}{m})} - 1)", "- \\cos{(m + x)}", "- e^{m - x}"], "srepr_premise_expression": "log(Mul(Symbol('m', commutative=True), Symbol('x', commutative=True)))", "srepr_variable": "Symbol('x', commutative=True)", "srepr_positive": "Mul(Symbol('x', commutative=True), Add(log(Mul(Symbol('m', commutative=True), Symbol('x', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('m', commutative=True), Add(log(Mul(Symbol('m', commutative=True), Symbol('x', commutative=True))), Integer(-1)))", "Mul(Symbol('x', commutative=True), Add(log(Mul(Pow(Symbol('m', commutative=True), Integer(-1)), Symbol('x', commutative=True))), Integer(-1)))", "Mul(Integer(-1), cos(Add(Symbol('m', commutative=True), Symbol('x', commutative=True))))", "Mul(Integer(-1), exp(Add(Symbol('m', commutative=True), Mul(Integer(-1), Symbol('x', commutative=True)))))"]}, {"premise_expression": "- Z + g", "variable": "g", "positive": "\\frac{g (- 2 Z + g)}{2}", "negatives": ["\\frac{Z (- Z + 2 g)}{2}", "\\frac{g (- g + 2 \\cos{(Z)})}{2}", "- \\frac{\\cos{(g)}}{Z}", "g (\\log{(Z g)} - 1)"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('Z', commutative=True)), Symbol('g', commutative=True))", "srepr_variable": "Symbol('g', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('Z', commutative=True)), Symbol('g', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Mul(Integer(-1), Symbol('Z', commutative=True)), Mul(Integer(2), Symbol('g', commutative=True))))", "Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Mul(Integer(-1), Symbol('g', commutative=True)), Mul(Integer(2), cos(Symbol('Z', commutative=True)))))", "Mul(Integer(-1), Pow(Symbol('Z', commutative=True), Integer(-1)), cos(Symbol('g', commutative=True)))", "Mul(Symbol('g', commutative=True), Add(log(Mul(Symbol('Z', commutative=True), Symbol('g', commutative=True))), Integer(-1)))"]}, {"premise_expression": "h q", "variable": "q", "positive": "\\frac{h q^{2}}{2}", "negatives": ["\\frac{h^{2} q}{2}", "\\frac{q^{2}}{2 h}", "h \\sin{(q)}", "h \\log{(q)}"], "srepr_premise_expression": "Mul(Symbol('h', commutative=True), Symbol('q', commutative=True))", "srepr_variable": "Symbol('q', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('h', commutative=True), Pow(Symbol('q', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('h', commutative=True), Integer(2)), Symbol('q', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('h', commutative=True), Integer(-1)), Pow(Symbol('q', commutative=True), Integer(2)))", "Mul(Symbol('h', commutative=True), sin(Symbol('q', commutative=True)))", "Mul(Symbol('h', commutative=True), log(Symbol('q', commutative=True)))"]}, {"premise_expression": "\\cos{(S - c)}", "variable": "S", "positive": "\\sin{(S - c)}", "negatives": ["- \\sin{(S - c)}", "\\frac{S (S + 2 c)}{2}", "S (\\log{(\\frac{c}{S})} + 1)", "\\frac{S^{2} \\sin{(c)}}{2}"], "srepr_premise_expression": "cos(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('c', commutative=True))))", "srepr_variable": "Symbol('S', commutative=True)", "srepr_positive": "sin(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('c', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('c', commutative=True)))))", "Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Symbol('S', commutative=True), Mul(Integer(2), Symbol('c', commutative=True))))", "Mul(Symbol('S', commutative=True), Add(log(Mul(Pow(Symbol('S', commutative=True), Integer(-1)), Symbol('c', commutative=True))), Integer(1)))", "Mul(Rational(1, 2), Pow(Symbol('S', commutative=True), Integer(2)), sin(Symbol('c', commutative=True)))"]}, {"premise_expression": "E T", "variable": "E", "positive": "\\frac{E^{2} T}{2}", "negatives": ["\\frac{E T^{2}}{2}", "\\frac{E^{2}}{2 T}", "T \\log{(E)}", "- T \\cos{(E)}"], "srepr_premise_expression": "Mul(Symbol('E', commutative=True), Symbol('T', commutative=True))", "srepr_variable": "Symbol('E', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('E', commutative=True), Integer(2)), Symbol('T', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('E', commutative=True), Pow(Symbol('T', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('E', commutative=True), Integer(2)), Pow(Symbol('T', commutative=True), Integer(-1)))", "Mul(Symbol('T', commutative=True), log(Symbol('E', commutative=True)))", "Mul(Integer(-1), Symbol('T', commutative=True), cos(Symbol('E', commutative=True)))"]}, {"premise_expression": "F I", "variable": "I", "positive": "\\frac{F I^{2}}{2}", "negatives": ["\\frac{F^{2} I}{2}", "F e^{\\frac{I}{F}}", "0", "\\frac{I (2 F + I)}{2}"], "srepr_premise_expression": "Mul(Symbol('F', commutative=True), Symbol('I', commutative=True))", "srepr_variable": "Symbol('I', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('F', commutative=True), Pow(Symbol('I', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('F', commutative=True), Integer(2)), Symbol('I', commutative=True))", "Mul(Symbol('F', commutative=True), exp(Mul(Pow(Symbol('F', commutative=True), Integer(-1)), Symbol('I', commutative=True))))", "Integer(0)", "Mul(Rational(1, 2), Symbol('I', commutative=True), Add(Mul(Integer(2), Symbol('F', commutative=True)), Symbol('I', commutative=True)))"]}, {"premise_expression": "\\sin^{j}{(I)}", "variable": "I", "positive": "\\int \\sin^{j}{(I)} dI", "negatives": ["I (\\log{(I j)} - 1)", "e^{I + j}", "\\frac{I (I - 2 j)}{2}", "\\frac{I (- I + 2 e^{j})}{2}"], "srepr_premise_expression": "Pow(sin(Symbol('I', commutative=True)), Symbol('j', commutative=True))", "srepr_variable": "Symbol('I', commutative=True)", "srepr_positive": "Integral(Pow(sin(Symbol('I', commutative=True)), Symbol('j', commutative=True)), Tuple(Symbol('I', commutative=True)))", "srepr_negatives": ["Mul(Symbol('I', commutative=True), Add(log(Mul(Symbol('I', commutative=True), Symbol('j', commutative=True))), Integer(-1)))", "exp(Add(Symbol('I', commutative=True), Symbol('j', commutative=True)))", "Mul(Rational(1, 2), Symbol('I', commutative=True), Add(Symbol('I', commutative=True), Mul(Integer(-1), Integer(2), Symbol('j', commutative=True))))", "Mul(Rational(1, 2), Symbol('I', commutative=True), Add(Mul(Integer(-1), Symbol('I', commutative=True)), Mul(Integer(2), exp(Symbol('j', commutative=True)))))"]}, {"premise_expression": "\\sin^{L}{(A)}", "variable": "A", "positive": "\\int \\sin^{L}{(A)} dA", "negatives": ["e^{A - L}", "A (\\log{(\\frac{A}{L})} - 1)", "L \\log{(A)}", "\\frac{A^{2}}{2 L}"], "srepr_premise_expression": "Pow(sin(Symbol('A', commutative=True)), Symbol('L', commutative=True))", "srepr_variable": "Symbol('A', commutative=True)", "srepr_positive": "Integral(Pow(sin(Symbol('A', commutative=True)), Symbol('L', commutative=True)), Tuple(Symbol('A', commutative=True)))", "srepr_negatives": ["exp(Add(Symbol('A', commutative=True), Mul(Integer(-1), Symbol('L', commutative=True))))", "Mul(Symbol('A', commutative=True), Add(log(Mul(Symbol('A', commutative=True), Pow(Symbol('L', commutative=True), Integer(-1)))), Integer(-1)))", "Mul(Symbol('L', commutative=True), log(Symbol('A', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2)), Pow(Symbol('L', commutative=True), Integer(-1)))"]}, {"premise_expression": "e^{c + q}", "variable": "c", "positive": "e^{c + q}", "negatives": ["\\sin{(c - q)}", "q e^{\\frac{c}{q}}", "\\frac{c^{2} q}{2}", "\\frac{c^{2} \\log{(q)}}{2}"], "srepr_premise_expression": "exp(Add(Symbol('c', commutative=True), Symbol('q', commutative=True)))", "srepr_variable": "Symbol('c', commutative=True)", "srepr_positive": "exp(Add(Symbol('c', commutative=True), Symbol('q', commutative=True)))", "srepr_negatives": ["sin(Add(Symbol('c', commutative=True), Mul(Integer(-1), Symbol('q', commutative=True))))", "Mul(Symbol('q', commutative=True), exp(Mul(Symbol('c', commutative=True), Pow(Symbol('q', commutative=True), Integer(-1)))))", "Mul(Rational(1, 2), Pow(Symbol('c', commutative=True), Integer(2)), Symbol('q', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('c', commutative=True), Integer(2)), log(Symbol('q', commutative=True)))"]}, {"premise_expression": "\\log{(D u)}", "variable": "u", "positive": "u (\\log{(D u)} - 1)", "negatives": ["D (\\log{(D u)} - 1)", "u (- D + \\log{(u)} - 1)", "\\frac{u (2 D - u)}{2}", "\\log{(u)} \\sin{(D)}"], "srepr_premise_expression": "log(Mul(Symbol('D', commutative=True), Symbol('u', commutative=True)))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "Mul(Symbol('u', commutative=True), Add(log(Mul(Symbol('D', commutative=True), Symbol('u', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('D', commutative=True), Add(log(Mul(Symbol('D', commutative=True), Symbol('u', commutative=True))), Integer(-1)))", "Mul(Symbol('u', commutative=True), Add(Mul(Integer(-1), Symbol('D', commutative=True)), log(Symbol('u', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(2), Symbol('D', commutative=True)), Mul(Integer(-1), Symbol('u', commutative=True))))", "Mul(log(Symbol('u', commutative=True)), sin(Symbol('D', commutative=True)))"]}, {"premise_expression": "L + N", "variable": "N", "positive": "\\frac{N (2 L + N)}{2}", "negatives": ["\\frac{L (L + 2 N)}{2}", "e^{L + N}", "- e^{L - N}", "\\frac{N^{2}}{2 L}"], "srepr_premise_expression": "Add(Symbol('L', commutative=True), Symbol('N', commutative=True))", "srepr_variable": "Symbol('N', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Mul(Integer(2), Symbol('L', commutative=True)), Symbol('N', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Symbol('L', commutative=True), Mul(Integer(2), Symbol('N', commutative=True))))", "exp(Add(Symbol('L', commutative=True), Symbol('N', commutative=True)))", "Mul(Integer(-1), exp(Add(Symbol('L', commutative=True), Mul(Integer(-1), Symbol('N', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(-1)), Pow(Symbol('N', commutative=True), Integer(2)))"]}, {"premise_expression": "- w + \\sin{(l)}", "variable": "l", "positive": "- l w - \\cos{(l)}", "negatives": ["l w - \\cos{(l)}", "\\frac{l (l + 2 w)}{2}", "e^{l - w}", "\\frac{l (- l + 2 w)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('w', commutative=True)), sin(Symbol('l', commutative=True)))", "srepr_variable": "Symbol('l', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('l', commutative=True), Symbol('w', commutative=True)), Mul(Integer(-1), cos(Symbol('l', commutative=True))))", "srepr_negatives": ["Add(Mul(Symbol('l', commutative=True), Symbol('w', commutative=True)), Mul(Integer(-1), cos(Symbol('l', commutative=True))))", "Mul(Rational(1, 2), Symbol('l', commutative=True), Add(Symbol('l', commutative=True), Mul(Integer(2), Symbol('w', commutative=True))))", "exp(Add(Symbol('l', commutative=True), Mul(Integer(-1), Symbol('w', commutative=True))))", "Mul(Rational(1, 2), Symbol('l', commutative=True), Add(Mul(Integer(-1), Symbol('l', commutative=True)), Mul(Integer(2), Symbol('w', commutative=True))))"]}, {"premise_expression": "H U", "variable": "H", "positive": "\\frac{H^{2} U}{2}", "negatives": ["\\frac{H U^{2}}{2}", "\\frac{H^{2} e^{U}}{2}", "H", "H U + e^{H}"], "srepr_premise_expression": "Mul(Symbol('H', commutative=True), Symbol('U', commutative=True))", "srepr_variable": "Symbol('H', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('H', commutative=True), Integer(2)), Symbol('U', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('H', commutative=True), Pow(Symbol('U', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('H', commutative=True), Integer(2)), exp(Symbol('U', commutative=True)))", "Symbol('H', commutative=True)", "Add(Mul(Symbol('H', commutative=True), Symbol('U', commutative=True)), exp(Symbol('H', commutative=True)))"]}, {"premise_expression": "G a", "variable": "G", "positive": "\\frac{G^{2} a}{2}", "negatives": ["\\frac{G a^{2}}{2}", "\\sin{(G - a)}", "\\log{(G)} \\cos{(a)}", "\\frac{G (G + 2 e^{a})}{2}"], "srepr_premise_expression": "Mul(Symbol('G', commutative=True), Symbol('a', commutative=True))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(2)), Symbol('a', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('G', commutative=True), Pow(Symbol('a', commutative=True), Integer(2)))", "sin(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('a', commutative=True))))", "Mul(log(Symbol('G', commutative=True)), cos(Symbol('a', commutative=True)))", "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Symbol('G', commutative=True), Mul(Integer(2), exp(Symbol('a', commutative=True)))))"]}, {"premise_expression": "\\frac{F}{n}", "variable": "F", "positive": "\\frac{F^{2}}{2 n}", "negatives": ["F \\log{(n)}", "\\frac{F^{2} \\cos{(n)}}{2}", "F n + e^{F}", "F (\\log{(F n)} - 1)"], "srepr_premise_expression": "Mul(Symbol('F', commutative=True), Pow(Symbol('n', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('F', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('F', commutative=True), Integer(2)), Pow(Symbol('n', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('F', commutative=True), log(Symbol('n', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('F', commutative=True), Integer(2)), cos(Symbol('n', commutative=True)))", "Add(Mul(Symbol('F', commutative=True), Symbol('n', commutative=True)), exp(Symbol('F', commutative=True)))", "Mul(Symbol('F', commutative=True), Add(log(Mul(Symbol('F', commutative=True), Symbol('n', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\frac{\\sin{(P)}}{Y}", "variable": "P", "positive": "- \\frac{\\cos{(P)}}{Y}", "negatives": ["- Y \\cos{(P)}", "\\sin{(P - Y)}", "\\log{(P)} \\log{(Y)}", "\\log{(Y)} \\sin{(P)}"], "srepr_premise_expression": "Mul(Pow(Symbol('Y', commutative=True), Integer(-1)), sin(Symbol('P', commutative=True)))", "srepr_variable": "Symbol('P', commutative=True)", "srepr_positive": "Mul(Integer(-1), Pow(Symbol('Y', commutative=True), Integer(-1)), cos(Symbol('P', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Symbol('Y', commutative=True), cos(Symbol('P', commutative=True)))", "sin(Add(Symbol('P', commutative=True), Mul(Integer(-1), Symbol('Y', commutative=True))))", "Mul(log(Symbol('P', commutative=True)), log(Symbol('Y', commutative=True)))", "Mul(log(Symbol('Y', commutative=True)), sin(Symbol('P', commutative=True)))"]}, {"premise_expression": "g \\cos{(k)}", "variable": "g", "positive": "\\frac{g^{2} \\cos{(k)}}{2}", "negatives": ["\\frac{g^{2} k}{2}", "\\frac{g (g + 2 k)}{2}", "\\frac{g^{2}}{2 k}", "g \\sin{(k)}"], "srepr_premise_expression": "Mul(Symbol('g', commutative=True), cos(Symbol('k', commutative=True)))", "srepr_variable": "Symbol('g', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('g', commutative=True), Integer(2)), cos(Symbol('k', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('g', commutative=True), Integer(2)), Symbol('k', commutative=True))", "Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Symbol('g', commutative=True), Mul(Integer(2), Symbol('k', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('g', commutative=True), Integer(2)), Pow(Symbol('k', commutative=True), Integer(-1)))", "Mul(Symbol('g', commutative=True), sin(Symbol('k', commutative=True)))"]}, {"premise_expression": "M + N", "variable": "N", "positive": "\\frac{N (2 M + N)}{2}", "negatives": ["\\frac{M (M + 2 N)}{2}", "- e^{M - N}", "\\frac{N^{2}}{2 M}", "- M \\cos{(N)}"], "srepr_premise_expression": "Add(Symbol('M', commutative=True), Symbol('N', commutative=True))", "srepr_variable": "Symbol('N', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Mul(Integer(2), Symbol('M', commutative=True)), Symbol('N', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('M', commutative=True), Add(Symbol('M', commutative=True), Mul(Integer(2), Symbol('N', commutative=True))))", "Mul(Integer(-1), exp(Add(Symbol('M', commutative=True), Mul(Integer(-1), Symbol('N', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('M', commutative=True), Integer(-1)), Pow(Symbol('N', commutative=True), Integer(2)))", "Mul(Integer(-1), Symbol('M', commutative=True), cos(Symbol('N', commutative=True)))"]}, {"premise_expression": "T (H - V)", "variable": "V", "positive": "\\frac{T V (2 H - V)}{2}", "negatives": ["\\frac{T^{2} (H - V)}{2}", "\\frac{H V (2 T + V)}{2}", "\\frac{H T (H - 2 V)}{2}", "\\frac{H V (V + 2)}{2}"], "srepr_premise_expression": "Mul(Symbol('T', commutative=True), Add(Symbol('H', commutative=True), Mul(Integer(-1), Symbol('V', commutative=True))))", "srepr_variable": "Symbol('V', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('T', commutative=True), Symbol('V', commutative=True), Add(Mul(Integer(2), Symbol('H', commutative=True)), Mul(Integer(-1), Symbol('V', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('T', commutative=True), Integer(2)), Add(Symbol('H', commutative=True), Mul(Integer(-1), Symbol('V', commutative=True))))", "Mul(Rational(1, 2), Symbol('H', commutative=True), Symbol('V', commutative=True), Add(Mul(Integer(2), Symbol('T', commutative=True)), Symbol('V', commutative=True)))", "Mul(Rational(1, 2), Symbol('H', commutative=True), Symbol('T', commutative=True), Add(Symbol('H', commutative=True), Mul(Integer(-1), Integer(2), Symbol('V', commutative=True))))", "Mul(Rational(1, 2), Symbol('H', commutative=True), Symbol('V', commutative=True), Add(Symbol('V', commutative=True), Integer(2)))"]}, {"premise_expression": "- n + \\log{(q)}", "variable": "q", "positive": "q (- n + \\log{(q)} - 1)", "negatives": ["q (\\log{(\\frac{q}{n})} - 1)", "\\frac{n (- n + 2 \\log{(q)})}{2}", "n \\sin{(q)}", "n e^{\\frac{q}{n}}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('n', commutative=True)), log(Symbol('q', commutative=True)))", "srepr_variable": "Symbol('q', commutative=True)", "srepr_positive": "Mul(Symbol('q', commutative=True), Add(Mul(Integer(-1), Symbol('n', commutative=True)), log(Symbol('q', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('q', commutative=True), Add(log(Mul(Pow(Symbol('n', commutative=True), Integer(-1)), Symbol('q', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('n', commutative=True), Add(Mul(Integer(-1), Symbol('n', commutative=True)), Mul(Integer(2), log(Symbol('q', commutative=True)))))", "Mul(Symbol('n', commutative=True), sin(Symbol('q', commutative=True)))", "Mul(Symbol('n', commutative=True), exp(Mul(Pow(Symbol('n', commutative=True), Integer(-1)), Symbol('q', commutative=True))))"]}, {"premise_expression": "\\cos{(k - n)}", "variable": "k", "positive": "\\sin{(k - n)}", "negatives": ["- \\sin{(k - n)}", "\\sin{(k + n)}", "\\cos{(k - n)}", "\\frac{\\sin{(k)}}{n}"], "srepr_premise_expression": "cos(Add(Symbol('k', commutative=True), Mul(Integer(-1), Symbol('n', commutative=True))))", "srepr_variable": "Symbol('k', commutative=True)", "srepr_positive": "sin(Add(Symbol('k', commutative=True), Mul(Integer(-1), Symbol('n', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('k', commutative=True), Mul(Integer(-1), Symbol('n', commutative=True)))))", "sin(Add(Symbol('k', commutative=True), Symbol('n', commutative=True)))", "cos(Add(Symbol('k', commutative=True), Mul(Integer(-1), Symbol('n', commutative=True))))", "Mul(Pow(Symbol('n', commutative=True), Integer(-1)), sin(Symbol('k', commutative=True)))"]}, {"premise_expression": "\\log{(t^{k})}", "variable": "t", "positive": "t (- k + \\log{(t^{k})})", "negatives": ["\\log{(k)} \\log{(t)}", "\\frac{t (t + 2 \\log{(t)} - 2)}{2}", "\\frac{k^{2} \\log{(t)}}{2}", "k e^{t}"], "srepr_premise_expression": "log(Pow(Symbol('t', commutative=True), Symbol('k', commutative=True)))", "srepr_variable": "Symbol('t', commutative=True)", "srepr_positive": "Mul(Symbol('t', commutative=True), Add(Mul(Integer(-1), Symbol('k', commutative=True)), log(Pow(Symbol('t', commutative=True), Symbol('k', commutative=True)))))", "srepr_negatives": ["Mul(log(Symbol('k', commutative=True)), log(Symbol('t', commutative=True)))", "Mul(Rational(1, 2), Symbol('t', commutative=True), Add(Symbol('t', commutative=True), Mul(Integer(2), log(Symbol('t', commutative=True))), Integer(-2)))", "Mul(Rational(1, 2), Pow(Symbol('k', commutative=True), Integer(2)), log(Symbol('t', commutative=True)))", "Mul(Symbol('k', commutative=True), exp(Symbol('t', commutative=True)))"]}, {"premise_expression": "\\frac{e^{C}}{l}", "variable": "l", "positive": "e^{C} \\log{(l)}", "negatives": ["\\log{(C)} \\log{(l)}", "- e^{C - l}", "\\log{(l)} \\sin{(C)}", "C \\sin{(l)}"], "srepr_premise_expression": "Mul(Pow(Symbol('l', commutative=True), Integer(-1)), exp(Symbol('C', commutative=True)))", "srepr_variable": "Symbol('l', commutative=True)", "srepr_positive": "Mul(exp(Symbol('C', commutative=True)), log(Symbol('l', commutative=True)))", "srepr_negatives": ["Mul(log(Symbol('C', commutative=True)), log(Symbol('l', commutative=True)))", "Mul(Integer(-1), exp(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('l', commutative=True)))))", "Mul(log(Symbol('l', commutative=True)), sin(Symbol('C', commutative=True)))", "Mul(Symbol('C', commutative=True), sin(Symbol('l', commutative=True)))"]}, {"premise_expression": "q w", "variable": "w", "positive": "\\frac{q w^{2}}{2}", "negatives": ["\\frac{q^{2} w}{2}", "\\frac{w^{2}}{2 q}", "0", "q w + \\sin{(w)}"], "srepr_premise_expression": "Mul(Symbol('q', commutative=True), Symbol('w', commutative=True))", "srepr_variable": "Symbol('w', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('q', commutative=True), Pow(Symbol('w', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('q', commutative=True), Integer(2)), Symbol('w', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('q', commutative=True), Integer(-1)), Pow(Symbol('w', commutative=True), Integer(2)))", "Integer(0)", "Add(Mul(Symbol('q', commutative=True), Symbol('w', commutative=True)), sin(Symbol('w', commutative=True)))"]}, {"premise_expression": "f s", "variable": "s", "positive": "\\frac{f s^{2}}{2}", "negatives": ["\\frac{f^{2} s}{2}", "\\frac{s (- 2 f + s)}{2}", "s (\\log{(f s)} - 1)", "s (\\log{(\\frac{f}{s})} + 1)"], "srepr_premise_expression": "Mul(Symbol('f', commutative=True), Symbol('s', commutative=True))", "srepr_variable": "Symbol('s', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('f', commutative=True), Pow(Symbol('s', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('f', commutative=True), Integer(2)), Symbol('s', commutative=True))", "Mul(Rational(1, 2), Symbol('s', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('f', commutative=True)), Symbol('s', commutative=True)))", "Mul(Symbol('s', commutative=True), Add(log(Mul(Symbol('f', commutative=True), Symbol('s', commutative=True))), Integer(-1)))", "Mul(Symbol('s', commutative=True), Add(log(Mul(Symbol('f', commutative=True), Pow(Symbol('s', commutative=True), Integer(-1)))), Integer(1)))"]}, {"premise_expression": "J + V", "variable": "V", "positive": "\\frac{V (2 J + V)}{2}", "negatives": ["\\frac{V (- 2 J + V)}{2}", "\\frac{J (J + 2 V)}{2}", "\\cos{(J - V)}", "\\frac{V^{2}}{2 J}"], "srepr_premise_expression": "Add(Symbol('J', commutative=True), Symbol('V', commutative=True))", "srepr_variable": "Symbol('V', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('V', commutative=True), Add(Mul(Integer(2), Symbol('J', commutative=True)), Symbol('V', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('V', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('J', commutative=True)), Symbol('V', commutative=True)))", "Mul(Rational(1, 2), Symbol('J', commutative=True), Add(Symbol('J', commutative=True), Mul(Integer(2), Symbol('V', commutative=True))))", "cos(Add(Symbol('J', commutative=True), Mul(Integer(-1), Symbol('V', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('J', commutative=True), Integer(-1)), Pow(Symbol('V', commutative=True), Integer(2)))"]}, {"premise_expression": "- r + \\log{(Z)}", "variable": "r", "positive": "\\frac{r (- r + 2 \\log{(Z)})}{2}", "negatives": ["\\frac{r (- r + 2 \\cos{(Z)})}{2}", "\\frac{r (- r + 2 \\sin{(Z)})}{2}", "Z (- r + \\log{(Z)} - 1)", "\\frac{r^{2} \\cos{(Z)}}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('r', commutative=True)), log(Symbol('Z', commutative=True)))", "srepr_variable": "Symbol('r', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(-1), Symbol('r', commutative=True)), Mul(Integer(2), log(Symbol('Z', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(-1), Symbol('r', commutative=True)), Mul(Integer(2), cos(Symbol('Z', commutative=True)))))", "Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(-1), Symbol('r', commutative=True)), Mul(Integer(2), sin(Symbol('Z', commutative=True)))))", "Mul(Symbol('Z', commutative=True), Add(Mul(Integer(-1), Symbol('r', commutative=True)), log(Symbol('Z', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('r', commutative=True), Integer(2)), cos(Symbol('Z', commutative=True)))"]}, {"premise_expression": "j \\log{(m)}", "variable": "m", "positive": "j m (\\log{(m)} - 1)", "negatives": ["m (- j + \\log{(m)} - 1)", "\\frac{j^{2} \\log{(m)}}{2}", "e^{j} \\log{(m)}", "- \\sin{(j - m)}"], "srepr_premise_expression": "Mul(Symbol('j', commutative=True), log(Symbol('m', commutative=True)))", "srepr_variable": "Symbol('m', commutative=True)", "srepr_positive": "Mul(Symbol('j', commutative=True), Symbol('m', commutative=True), Add(log(Symbol('m', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('m', commutative=True), Add(Mul(Integer(-1), Symbol('j', commutative=True)), log(Symbol('m', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('j', commutative=True), Integer(2)), log(Symbol('m', commutative=True)))", "Mul(exp(Symbol('j', commutative=True)), log(Symbol('m', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('j', commutative=True), Mul(Integer(-1), Symbol('m', commutative=True)))))"]}, {"premise_expression": "\\frac{o}{H}", "variable": "H", "positive": "o \\log{(H)}", "negatives": ["\\frac{o^{2}}{2 H}", "\\frac{\\log{(H)}^{2}}{2}", "- \\cos{(H + o)}", "e^{H + o}"], "srepr_premise_expression": "Mul(Pow(Symbol('H', commutative=True), Integer(-1)), Symbol('o', commutative=True))", "srepr_variable": "Symbol('H', commutative=True)", "srepr_positive": "Mul(Symbol('o', commutative=True), log(Symbol('H', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('H', commutative=True), Integer(-1)), Pow(Symbol('o', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(log(Symbol('H', commutative=True)), Integer(2)))", "Mul(Integer(-1), cos(Add(Symbol('H', commutative=True), Symbol('o', commutative=True))))", "exp(Add(Symbol('H', commutative=True), Symbol('o', commutative=True)))"]}, {"premise_expression": "\\frac{v}{Q T}", "variable": "v", "positive": "\\frac{v^{2}}{2 Q T}", "negatives": ["v (- 2 Q + T)", "\\frac{v \\log{(Q)}}{T}", "\\frac{v \\log{(T)}}{Q}", "Q^{T} \\log{(v)}"], "srepr_premise_expression": "Mul(Pow(Symbol('Q', commutative=True), Integer(-1)), Pow(Symbol('T', commutative=True), Integer(-1)), Symbol('v', commutative=True))", "srepr_variable": "Symbol('v', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(-1)), Pow(Symbol('T', commutative=True), Integer(-1)), Pow(Symbol('v', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('v', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('Q', commutative=True)), Symbol('T', commutative=True)))", "Mul(Pow(Symbol('T', commutative=True), Integer(-1)), Symbol('v', commutative=True), log(Symbol('Q', commutative=True)))", "Mul(Pow(Symbol('Q', commutative=True), Integer(-1)), Symbol('v', commutative=True), log(Symbol('T', commutative=True)))", "Mul(Pow(Symbol('Q', commutative=True), Symbol('T', commutative=True)), log(Symbol('v', commutative=True)))"]}, {"premise_expression": "(U^{A})^{U}", "variable": "U", "positive": "\\int (U^{A})^{U} dU", "negatives": ["\\int \\cos^{A}{(U)} dU", "\\sin{(A + U)}", "U (\\log{(A U)} - 1)", "A \\sin{(U)}"], "srepr_premise_expression": "Pow(Pow(Symbol('U', commutative=True), Symbol('A', commutative=True)), Symbol('U', commutative=True))", "srepr_variable": "Symbol('U', commutative=True)", "srepr_positive": "NonElementaryIntegral(Pow(Pow(Symbol('U', commutative=True), Symbol('A', commutative=True)), Symbol('U', commutative=True)), Tuple(Symbol('U', commutative=True)))", "srepr_negatives": ["Integral(Pow(cos(Symbol('U', commutative=True)), Symbol('A', commutative=True)), Tuple(Symbol('U', commutative=True)))", "sin(Add(Symbol('A', commutative=True), Symbol('U', commutative=True)))", "Mul(Symbol('U', commutative=True), Add(log(Mul(Symbol('A', commutative=True), Symbol('U', commutative=True))), Integer(-1)))", "Mul(Symbol('A', commutative=True), sin(Symbol('U', commutative=True)))"]}, {"premise_expression": "- L + P", "variable": "P", "positive": "\\frac{P (- 2 L + P)}{2}", "negatives": ["\\frac{L (- L + 2 P)}{2}", "e^{L + P}", "- \\sin{(L - P)}", "- e^{L - P}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('L', commutative=True)), Symbol('P', commutative=True))", "srepr_variable": "Symbol('P', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('L', commutative=True)), Symbol('P', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Mul(Integer(-1), Symbol('L', commutative=True)), Mul(Integer(2), Symbol('P', commutative=True))))", "exp(Add(Symbol('L', commutative=True), Symbol('P', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('L', commutative=True), Mul(Integer(-1), Symbol('P', commutative=True)))))", "Mul(Integer(-1), exp(Add(Symbol('L', commutative=True), Mul(Integer(-1), Symbol('P', commutative=True)))))"]}, {"premise_expression": "o^{r} u", "variable": "u", "positive": "\\frac{o^{r} u^{2}}{2}", "negatives": ["- o u + \\frac{u^{2}}{2 r}", "\\frac{u^{2}}{2 o r}", "\\frac{u^{2} (o + r)}{2}", "\\frac{o u (- 2 r + u)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('o', commutative=True), Symbol('r', commutative=True)), Symbol('u', commutative=True))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('o', commutative=True), Symbol('r', commutative=True)), Pow(Symbol('u', commutative=True), Integer(2)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('o', commutative=True), Symbol('u', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('r', commutative=True), Integer(-1)), Pow(Symbol('u', commutative=True), Integer(2))))", "Mul(Rational(1, 2), Pow(Symbol('o', commutative=True), Integer(-1)), Pow(Symbol('r', commutative=True), Integer(-1)), Pow(Symbol('u', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('u', commutative=True), Integer(2)), Add(Symbol('o', commutative=True), Symbol('r', commutative=True)))", "Mul(Rational(1, 2), Symbol('o', commutative=True), Symbol('u', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('r', commutative=True)), Symbol('u', commutative=True)))"]}, {"premise_expression": "- u + x", "variable": "u", "positive": "\\frac{u (- u + 2 x)}{2}", "negatives": ["\\frac{u (u + 2 x)}{2}", "\\frac{x (- 2 u + x)}{2}", "u x + \\sin{(u)}", "\\cos{(u - x)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('u', commutative=True)), Symbol('x', commutative=True))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(-1), Symbol('u', commutative=True)), Mul(Integer(2), Symbol('x', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Symbol('u', commutative=True), Mul(Integer(2), Symbol('x', commutative=True))))", "Mul(Rational(1, 2), Symbol('x', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('u', commutative=True)), Symbol('x', commutative=True)))", "Add(Mul(Symbol('u', commutative=True), Symbol('x', commutative=True)), sin(Symbol('u', commutative=True)))", "cos(Add(Symbol('u', commutative=True), Mul(Integer(-1), Symbol('x', commutative=True))))"]}, {"premise_expression": "Y p", "variable": "Y", "positive": "\\frac{Y^{2} p}{2}", "negatives": ["\\frac{Y p^{2}}{2}", "\\frac{Y^{2} \\sin{(p)}}{2}", "p \\log{(Y)}", "p e^{\\frac{Y}{p}}"], "srepr_premise_expression": "Mul(Symbol('Y', commutative=True), Symbol('p', commutative=True))", "srepr_variable": "Symbol('Y', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('Y', commutative=True), Integer(2)), Symbol('p', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('Y', commutative=True), Pow(Symbol('p', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('Y', commutative=True), Integer(2)), sin(Symbol('p', commutative=True)))", "Mul(Symbol('p', commutative=True), log(Symbol('Y', commutative=True)))", "Mul(Symbol('p', commutative=True), exp(Mul(Symbol('Y', commutative=True), Pow(Symbol('p', commutative=True), Integer(-1)))))"]}, {"premise_expression": "q + \\log{(u)}", "variable": "u", "positive": "u (q + \\log{(u)} - 1)", "negatives": ["u (\\log{(\\frac{u}{q})} - 1)", "\\frac{u (\\log{(u)} - 1)}{q}", "\\frac{q (q + 2 \\log{(u)})}{2}", "q \\log{(u)}"], "srepr_premise_expression": "Add(Symbol('q', commutative=True), log(Symbol('u', commutative=True)))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "Mul(Symbol('u', commutative=True), Add(Symbol('q', commutative=True), log(Symbol('u', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('u', commutative=True), Add(log(Mul(Pow(Symbol('q', commutative=True), Integer(-1)), Symbol('u', commutative=True))), Integer(-1)))", "Mul(Pow(Symbol('q', commutative=True), Integer(-1)), Symbol('u', commutative=True), Add(log(Symbol('u', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('q', commutative=True), Add(Symbol('q', commutative=True), Mul(Integer(2), log(Symbol('u', commutative=True)))))", "Mul(Symbol('q', commutative=True), log(Symbol('u', commutative=True)))"]}, {"premise_expression": "u + z", "variable": "z", "positive": "\\frac{z (2 u + z)}{2}", "negatives": ["\\frac{u (u + 2 z)}{2}", "\\frac{z^{2} \\log{(u)}}{2}", "\\frac{z^{2} \\cos{(u)}}{2}", "\\sin{(u + z)}"], "srepr_premise_expression": "Add(Symbol('u', commutative=True), Symbol('z', commutative=True))", "srepr_variable": "Symbol('z', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('z', commutative=True), Add(Mul(Integer(2), Symbol('u', commutative=True)), Symbol('z', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Symbol('u', commutative=True), Mul(Integer(2), Symbol('z', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('z', commutative=True), Integer(2)), log(Symbol('u', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('z', commutative=True), Integer(2)), cos(Symbol('u', commutative=True)))", "sin(Add(Symbol('u', commutative=True), Symbol('z', commutative=True)))"]}, {"premise_expression": "\\cos{(Z - v)}", "variable": "Z", "positive": "\\sin{(Z - v)}", "negatives": ["- \\sin{(Z - v)}", "- \\cos{(Z - v)}", "\\frac{Z (Z - 2 v)}{2}", "- \\frac{v}{Z}"], "srepr_premise_expression": "cos(Add(Symbol('Z', commutative=True), Mul(Integer(-1), Symbol('v', commutative=True))))", "srepr_variable": "Symbol('Z', commutative=True)", "srepr_positive": "sin(Add(Symbol('Z', commutative=True), Mul(Integer(-1), Symbol('v', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('Z', commutative=True), Mul(Integer(-1), Symbol('v', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('Z', commutative=True), Mul(Integer(-1), Symbol('v', commutative=True)))))", "Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Symbol('Z', commutative=True), Mul(Integer(-1), Integer(2), Symbol('v', commutative=True))))", "Mul(Integer(-1), Pow(Symbol('Z', commutative=True), Integer(-1)), Symbol('v', commutative=True))"]}, {"premise_expression": "- h + e^{m}", "variable": "h", "positive": "\\frac{h (- h + 2 e^{m})}{2}", "negatives": ["\\frac{h (- h + 2 \\log{(m)})}{2}", "\\frac{h (- h + 2 \\sin{(m)})}{2}", "- h m + e^{m}", "\\frac{h^{2}}{2 m}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('h', commutative=True)), exp(Symbol('m', commutative=True)))", "srepr_variable": "Symbol('h', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('h', commutative=True), Add(Mul(Integer(-1), Symbol('h', commutative=True)), Mul(Integer(2), exp(Symbol('m', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('h', commutative=True), Add(Mul(Integer(-1), Symbol('h', commutative=True)), Mul(Integer(2), log(Symbol('m', commutative=True)))))", "Mul(Rational(1, 2), Symbol('h', commutative=True), Add(Mul(Integer(-1), Symbol('h', commutative=True)), Mul(Integer(2), sin(Symbol('m', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('h', commutative=True), Symbol('m', commutative=True)), exp(Symbol('m', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('h', commutative=True), Integer(2)), Pow(Symbol('m', commutative=True), Integer(-1)))"]}, {"premise_expression": "l + \\frac{b}{J}", "variable": "l", "positive": "\\frac{l^{2}}{2} + \\frac{b l}{J}", "negatives": ["\\frac{l (2 J + b l)}{2}", "\\frac{l^{2} (- J + b)}{2}", "J l + b \\log{(J)}", "\\frac{l (J l - 2 b)}{2}"], "srepr_premise_expression": "Add(Symbol('l', commutative=True), Mul(Pow(Symbol('J', commutative=True), Integer(-1)), Symbol('b', commutative=True)))", "srepr_variable": "Symbol('l', commutative=True)", "srepr_positive": "Add(Mul(Rational(1, 2), Pow(Symbol('l', commutative=True), Integer(2))), Mul(Pow(Symbol('J', commutative=True), Integer(-1)), Symbol('b', commutative=True), Symbol('l', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('l', commutative=True), Add(Mul(Integer(2), Symbol('J', commutative=True)), Mul(Symbol('b', commutative=True), Symbol('l', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('l', commutative=True), Integer(2)), Add(Mul(Integer(-1), Symbol('J', commutative=True)), Symbol('b', commutative=True)))", "Add(Mul(Symbol('J', commutative=True), Symbol('l', commutative=True)), Mul(Symbol('b', commutative=True), log(Symbol('J', commutative=True))))", "Mul(Rational(1, 2), Symbol('l', commutative=True), Add(Mul(Symbol('J', commutative=True), Symbol('l', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('b', commutative=True))))"]}, {"premise_expression": "\\log{(E b)}", "variable": "b", "positive": "b (\\log{(E b)} - 1)", "negatives": ["E (\\log{(E b)} - 1)", "E b (\\log{(b)} - 1)", "- \\cos{(E - b)}", "\\frac{b^{2} \\log{(E)}}{2}"], "srepr_premise_expression": "log(Mul(Symbol('E', commutative=True), Symbol('b', commutative=True)))", "srepr_variable": "Symbol('b', commutative=True)", "srepr_positive": "Mul(Symbol('b', commutative=True), Add(log(Mul(Symbol('E', commutative=True), Symbol('b', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('E', commutative=True), Add(log(Mul(Symbol('E', commutative=True), Symbol('b', commutative=True))), Integer(-1)))", "Mul(Symbol('E', commutative=True), Symbol('b', commutative=True), Add(log(Symbol('b', commutative=True)), Integer(-1)))", "Mul(Integer(-1), cos(Add(Symbol('E', commutative=True), Mul(Integer(-1), Symbol('b', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('b', commutative=True), Integer(2)), log(Symbol('E', commutative=True)))"]}, {"premise_expression": "- F + g + r", "variable": "F", "positive": "F (- \\frac{F}{2} + g + r)", "negatives": ["\\frac{r (- 2 F + 2 g + r)}{2}", "\\frac{g (- 2 F + g + 2 r)}{2}", "\\frac{F^{2} (g + r)}{2}", "\\frac{F g (- F + 2 r)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('F', commutative=True)), Symbol('g', commutative=True), Symbol('r', commutative=True))", "srepr_variable": "Symbol('F', commutative=True)", "srepr_positive": "Mul(Symbol('F', commutative=True), Add(Mul(Integer(-1), Rational(1, 2), Symbol('F', commutative=True)), Symbol('g', commutative=True), Symbol('r', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('F', commutative=True)), Mul(Integer(2), Symbol('g', commutative=True)), Symbol('r', commutative=True)))", "Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('F', commutative=True)), Symbol('g', commutative=True), Mul(Integer(2), Symbol('r', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('F', commutative=True), Integer(2)), Add(Symbol('g', commutative=True), Symbol('r', commutative=True)))", "Mul(Rational(1, 2), Symbol('F', commutative=True), Symbol('g', commutative=True), Add(Mul(Integer(-1), Symbol('F', commutative=True)), Mul(Integer(2), Symbol('r', commutative=True))))"]}, {"premise_expression": "\\log{(B h)}", "variable": "h", "positive": "h (\\log{(B h)} - 1)", "negatives": ["B (\\log{(B h)} - 1)", "\\frac{h (2 B - h)}{2}", "- \\sin{(B - h)}", "\\frac{h (2 B + h)}{2}"], "srepr_premise_expression": "log(Mul(Symbol('B', commutative=True), Symbol('h', commutative=True)))", "srepr_variable": "Symbol('h', commutative=True)", "srepr_positive": "Mul(Symbol('h', commutative=True), Add(log(Mul(Symbol('B', commutative=True), Symbol('h', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('B', commutative=True), Add(log(Mul(Symbol('B', commutative=True), Symbol('h', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('h', commutative=True), Add(Mul(Integer(2), Symbol('B', commutative=True)), Mul(Integer(-1), Symbol('h', commutative=True))))", "Mul(Integer(-1), sin(Add(Symbol('B', commutative=True), Mul(Integer(-1), Symbol('h', commutative=True)))))", "Mul(Rational(1, 2), Symbol('h', commutative=True), Add(Mul(Integer(2), Symbol('B', commutative=True)), Symbol('h', commutative=True)))"]}, {"premise_expression": "U \\cos{(S)}", "variable": "S", "positive": "U \\sin{(S)}", "negatives": ["- \\frac{\\cos{(S)}}{U}", "\\frac{U^{2} \\cos{(S)}}{2}", "- S U + e^{S}", "\\log{(S)} \\cos{(U)}"], "srepr_premise_expression": "Mul(Symbol('U', commutative=True), cos(Symbol('S', commutative=True)))", "srepr_variable": "Symbol('S', commutative=True)", "srepr_positive": "Mul(Symbol('U', commutative=True), sin(Symbol('S', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Pow(Symbol('U', commutative=True), Integer(-1)), cos(Symbol('S', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('U', commutative=True), Integer(2)), cos(Symbol('S', commutative=True)))", "Add(Mul(Integer(-1), Symbol('S', commutative=True), Symbol('U', commutative=True)), exp(Symbol('S', commutative=True)))", "Mul(log(Symbol('S', commutative=True)), cos(Symbol('U', commutative=True)))"]}, {"premise_expression": "e^{s + z}", "variable": "s", "positive": "e^{s + z}", "negatives": ["\\sin{(s - z)}", "- \\cos{(s + z)}", "- \\cos{(s - z)}", "z e^{\\frac{s}{z}}"], "srepr_premise_expression": "exp(Add(Symbol('s', commutative=True), Symbol('z', commutative=True)))", "srepr_variable": "Symbol('s', commutative=True)", "srepr_positive": "exp(Add(Symbol('s', commutative=True), Symbol('z', commutative=True)))", "srepr_negatives": ["sin(Add(Symbol('s', commutative=True), Mul(Integer(-1), Symbol('z', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('s', commutative=True), Symbol('z', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('s', commutative=True), Mul(Integer(-1), Symbol('z', commutative=True)))))", "Mul(Symbol('z', commutative=True), exp(Mul(Symbol('s', commutative=True), Pow(Symbol('z', commutative=True), Integer(-1)))))"]}, {"premise_expression": "\\frac{p}{w}", "variable": "w", "positive": "p \\log{(w)}", "negatives": ["\\frac{p^{2}}{2 w}", "\\frac{p w^{2}}{2}", "\\frac{w^{2} \\log{(p)}}{2}", "- p w + e^{w}"], "srepr_premise_expression": "Mul(Symbol('p', commutative=True), Pow(Symbol('w', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('w', commutative=True)", "srepr_positive": "Mul(Symbol('p', commutative=True), log(Symbol('w', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('p', commutative=True), Integer(2)), Pow(Symbol('w', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Symbol('p', commutative=True), Pow(Symbol('w', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('w', commutative=True), Integer(2)), log(Symbol('p', commutative=True)))", "Add(Mul(Integer(-1), Symbol('p', commutative=True), Symbol('w', commutative=True)), exp(Symbol('w', commutative=True)))"]}, {"premise_expression": "- P + s", "variable": "P", "positive": "\\frac{P (- P + 2 s)}{2}", "negatives": ["\\frac{P (P + 2 s)}{2}", "\\frac{s (- 2 P + s)}{2}", "\\frac{P (P + 2 \\cos{(s)})}{2}", "P (\\log{(P s)} - 1)"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('P', commutative=True)), Symbol('s', commutative=True))", "srepr_variable": "Symbol('P', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Mul(Integer(-1), Symbol('P', commutative=True)), Mul(Integer(2), Symbol('s', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Symbol('P', commutative=True), Mul(Integer(2), Symbol('s', commutative=True))))", "Mul(Rational(1, 2), Symbol('s', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('P', commutative=True)), Symbol('s', commutative=True)))", "Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Symbol('P', commutative=True), Mul(Integer(2), cos(Symbol('s', commutative=True)))))", "Mul(Symbol('P', commutative=True), Add(log(Mul(Symbol('P', commutative=True), Symbol('s', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\frac{A}{B}", "variable": "A", "positive": "\\frac{A^{2}}{2 B}", "negatives": ["A \\log{(B)}", "\\frac{A^{2} \\sin{(B)}}{2}", "e^{A + B}", "\\sin{(A + B)}"], "srepr_premise_expression": "Mul(Symbol('A', commutative=True), Pow(Symbol('B', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('A', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2)), Pow(Symbol('B', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('A', commutative=True), log(Symbol('B', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2)), sin(Symbol('B', commutative=True)))", "exp(Add(Symbol('A', commutative=True), Symbol('B', commutative=True)))", "sin(Add(Symbol('A', commutative=True), Symbol('B', commutative=True)))"]}, {"premise_expression": "\\frac{j}{B}", "variable": "B", "positive": "j \\log{(B)}", "negatives": ["\\frac{j^{2}}{2 B}", "\\log{(B)} \\log{(j)}", "- \\frac{j}{B}", "- \\cos{(B - j)}"], "srepr_premise_expression": "Mul(Pow(Symbol('B', commutative=True), Integer(-1)), Symbol('j', commutative=True))", "srepr_variable": "Symbol('B', commutative=True)", "srepr_positive": "Mul(Symbol('j', commutative=True), log(Symbol('B', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('B', commutative=True), Integer(-1)), Pow(Symbol('j', commutative=True), Integer(2)))", "Mul(log(Symbol('B', commutative=True)), log(Symbol('j', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('B', commutative=True), Integer(-1)), Symbol('j', commutative=True))", "Mul(Integer(-1), cos(Add(Symbol('B', commutative=True), Mul(Integer(-1), Symbol('j', commutative=True)))))"]}, {"premise_expression": "e^{B + E}", "variable": "E", "positive": "e^{B + E}", "negatives": ["- \\cos{(B + E)}", "B \\sin{(E)}", "E (B + \\sin{(B)})", "\\frac{E^{2}}{2 B}"], "srepr_premise_expression": "exp(Add(Symbol('B', commutative=True), Symbol('E', commutative=True)))", "srepr_variable": "Symbol('E', commutative=True)", "srepr_positive": "exp(Add(Symbol('B', commutative=True), Symbol('E', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('B', commutative=True), Symbol('E', commutative=True))))", "Mul(Symbol('B', commutative=True), sin(Symbol('E', commutative=True)))", "Mul(Symbol('E', commutative=True), Add(Symbol('B', commutative=True), sin(Symbol('B', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('B', commutative=True), Integer(-1)), Pow(Symbol('E', commutative=True), Integer(2)))"]}, {"premise_expression": "H - u", "variable": "u", "positive": "\\frac{u (2 H - u)}{2}", "negatives": ["\\frac{u (- 2 H + u)}{2}", "\\frac{H (H - 2 u)}{2}", "u (H + u)", "\\frac{H u^{2}}{2}"], "srepr_premise_expression": "Add(Symbol('H', commutative=True), Mul(Integer(-1), Symbol('u', commutative=True)))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(2), Symbol('H', commutative=True)), Mul(Integer(-1), Symbol('u', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('H', commutative=True)), Symbol('u', commutative=True)))", "Mul(Rational(1, 2), Symbol('H', commutative=True), Add(Symbol('H', commutative=True), Mul(Integer(-1), Integer(2), Symbol('u', commutative=True))))", "Mul(Symbol('u', commutative=True), Add(Symbol('H', commutative=True), Symbol('u', commutative=True)))", "Mul(Rational(1, 2), Symbol('H', commutative=True), Pow(Symbol('u', commutative=True), Integer(2)))"]}, {"premise_expression": "\\log{(y^{l})}", "variable": "l", "positive": "\\frac{l^{2} \\log{(y)}}{2}", "negatives": ["\\frac{l^{2} \\sin{(y)}}{2}", "\\log{(l)} \\cos{(y)}", "l (\\log{(l y)} - 1)", "y (- l + \\log{(y^{l})})"], "srepr_premise_expression": "log(Pow(Symbol('y', commutative=True), Symbol('l', commutative=True)))", "srepr_variable": "Symbol('l', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('l', commutative=True), Integer(2)), log(Symbol('y', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('l', commutative=True), Integer(2)), sin(Symbol('y', commutative=True)))", "Mul(log(Symbol('l', commutative=True)), cos(Symbol('y', commutative=True)))", "Mul(Symbol('l', commutative=True), Add(log(Mul(Symbol('l', commutative=True), Symbol('y', commutative=True))), Integer(-1)))", "Mul(Symbol('y', commutative=True), Add(Mul(Integer(-1), Symbol('l', commutative=True)), log(Pow(Symbol('y', commutative=True), Symbol('l', commutative=True)))))"]}, {"premise_expression": "f + e^{h}", "variable": "f", "positive": "\\frac{f (f + 2 e^{h})}{2}", "negatives": ["\\frac{f (f + 2 \\log{(h)})}{2}", "\\frac{f (f + 2 \\sin{(h)})}{2}", "\\frac{f (- f + 2 \\cos{(h)})}{2}", "f h + e^{h}"], "srepr_premise_expression": "Add(Symbol('f', commutative=True), exp(Symbol('h', commutative=True)))", "srepr_variable": "Symbol('f', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Symbol('f', commutative=True), Mul(Integer(2), exp(Symbol('h', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Symbol('f', commutative=True), Mul(Integer(2), log(Symbol('h', commutative=True)))))", "Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Symbol('f', commutative=True), Mul(Integer(2), sin(Symbol('h', commutative=True)))))", "Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Mul(Integer(-1), Symbol('f', commutative=True)), Mul(Integer(2), cos(Symbol('h', commutative=True)))))", "Add(Mul(Symbol('f', commutative=True), Symbol('h', commutative=True)), exp(Symbol('h', commutative=True)))"]}, {"premise_expression": "q + \\log{(F)}", "variable": "q", "positive": "\\frac{q (q + 2 \\log{(F)})}{2}", "negatives": ["\\frac{q (q + 2 \\cos{(F)})}{2}", "F (q + \\log{(F)} - 1)", "\\frac{q (2 F + q)}{2}", "- F q - \\cos{(q)}"], "srepr_premise_expression": "Add(Symbol('q', commutative=True), log(Symbol('F', commutative=True)))", "srepr_variable": "Symbol('q', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('q', commutative=True), Add(Symbol('q', commutative=True), Mul(Integer(2), log(Symbol('F', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('q', commutative=True), Add(Symbol('q', commutative=True), Mul(Integer(2), cos(Symbol('F', commutative=True)))))", "Mul(Symbol('F', commutative=True), Add(Symbol('q', commutative=True), log(Symbol('F', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('q', commutative=True), Add(Mul(Integer(2), Symbol('F', commutative=True)), Symbol('q', commutative=True)))", "Add(Mul(Integer(-1), Symbol('F', commutative=True), Symbol('q', commutative=True)), Mul(Integer(-1), cos(Symbol('q', commutative=True))))"]}, {"premise_expression": "- A + I J", "variable": "A", "positive": "\\frac{A (- A + 2 I J)}{2}", "negatives": ["\\frac{A I (- A + 2 J)}{2}", "\\frac{J (- 2 A + I J)}{2}", "\\frac{I (- 2 A + I J)}{2}", "\\frac{A^{2} I J}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('A', commutative=True)), Mul(Symbol('I', commutative=True), Symbol('J', commutative=True)))", "srepr_variable": "Symbol('A', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Mul(Integer(-1), Symbol('A', commutative=True)), Mul(Integer(2), Symbol('I', commutative=True), Symbol('J', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('A', commutative=True), Symbol('I', commutative=True), Add(Mul(Integer(-1), Symbol('A', commutative=True)), Mul(Integer(2), Symbol('J', commutative=True))))", "Mul(Rational(1, 2), Symbol('J', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('A', commutative=True)), Mul(Symbol('I', commutative=True), Symbol('J', commutative=True))))", "Mul(Rational(1, 2), Symbol('I', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('A', commutative=True)), Mul(Symbol('I', commutative=True), Symbol('J', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2)), Symbol('I', commutative=True), Symbol('J', commutative=True))"]}, {"premise_expression": "\\log{(\\frac{b}{k})}", "variable": "b", "positive": "b (\\log{(\\frac{b}{k})} - 1)", "negatives": ["b (\\log{(b k)} - 1)", "k (\\log{(\\frac{b}{k})} + 1)", "\\frac{b (b - 2 k)}{2}", "b (- k + \\log{(b^{k})})"], "srepr_premise_expression": "log(Mul(Symbol('b', commutative=True), Pow(Symbol('k', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('b', commutative=True)", "srepr_positive": "Mul(Symbol('b', commutative=True), Add(log(Mul(Symbol('b', commutative=True), Pow(Symbol('k', commutative=True), Integer(-1)))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('b', commutative=True), Add(log(Mul(Symbol('b', commutative=True), Symbol('k', commutative=True))), Integer(-1)))", "Mul(Symbol('k', commutative=True), Add(log(Mul(Symbol('b', commutative=True), Pow(Symbol('k', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Rational(1, 2), Symbol('b', commutative=True), Add(Symbol('b', commutative=True), Mul(Integer(-1), Integer(2), Symbol('k', commutative=True))))", "Mul(Symbol('b', commutative=True), Add(Mul(Integer(-1), Symbol('k', commutative=True)), log(Pow(Symbol('b', commutative=True), Symbol('k', commutative=True)))))"]}, {"premise_expression": "k (D + E)", "variable": "E", "positive": "\\frac{E k (2 D + E)}{2}", "negatives": ["\\frac{k^{2} (D + E)}{2}", "\\frac{E (2 D k + E)}{2}", "\\frac{D k (D + 2 E)}{2}", "\\frac{E (2 D k - E)}{2}"], "srepr_premise_expression": "Mul(Symbol('k', commutative=True), Add(Symbol('D', commutative=True), Symbol('E', commutative=True)))", "srepr_variable": "Symbol('E', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('E', commutative=True), Symbol('k', commutative=True), Add(Mul(Integer(2), Symbol('D', commutative=True)), Symbol('E', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('k', commutative=True), Integer(2)), Add(Symbol('D', commutative=True), Symbol('E', commutative=True)))", "Mul(Rational(1, 2), Symbol('E', commutative=True), Add(Mul(Integer(2), Symbol('D', commutative=True), Symbol('k', commutative=True)), Symbol('E', commutative=True)))", "Mul(Rational(1, 2), Symbol('D', commutative=True), Symbol('k', commutative=True), Add(Symbol('D', commutative=True), Mul(Integer(2), Symbol('E', commutative=True))))", "Mul(Rational(1, 2), Symbol('E', commutative=True), Add(Mul(Integer(2), Symbol('D', commutative=True), Symbol('k', commutative=True)), Mul(Integer(-1), Symbol('E', commutative=True))))"]}, {"premise_expression": "m \\sin{(I)}", "variable": "m", "positive": "\\frac{m^{2} \\sin{(I)}}{2}", "negatives": ["\\frac{m (- 2 I + m)}{2}", "- m \\cos{(I)}", "I \\log{(m)}", "I e^{\\frac{m}{I}}"], "srepr_premise_expression": "Mul(Symbol('m', commutative=True), sin(Symbol('I', commutative=True)))", "srepr_variable": "Symbol('m', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('m', commutative=True), Integer(2)), sin(Symbol('I', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('I', commutative=True)), Symbol('m', commutative=True)))", "Mul(Integer(-1), Symbol('m', commutative=True), cos(Symbol('I', commutative=True)))", "Mul(Symbol('I', commutative=True), log(Symbol('m', commutative=True)))", "Mul(Symbol('I', commutative=True), exp(Mul(Pow(Symbol('I', commutative=True), Integer(-1)), Symbol('m', commutative=True))))"]}, {"premise_expression": "\\log{(L u)}", "variable": "u", "positive": "u (\\log{(L u)} - 1)", "negatives": ["L (\\log{(L u)} - 1)", "u (\\log{(\\frac{L}{u})} + 1)", "u (L + \\log{(u)} - 1)", "\\frac{u^{2}}{2 L}"], "srepr_premise_expression": "log(Mul(Symbol('L', commutative=True), Symbol('u', commutative=True)))", "srepr_variable": "Symbol('u', commutative=True)", "srepr_positive": "Mul(Symbol('u', commutative=True), Add(log(Mul(Symbol('L', commutative=True), Symbol('u', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('L', commutative=True), Add(log(Mul(Symbol('L', commutative=True), Symbol('u', commutative=True))), Integer(-1)))", "Mul(Symbol('u', commutative=True), Add(log(Mul(Symbol('L', commutative=True), Pow(Symbol('u', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Symbol('u', commutative=True), Add(Symbol('L', commutative=True), log(Symbol('u', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(-1)), Pow(Symbol('u', commutative=True), Integer(2)))"]}, {"premise_expression": "\\frac{L}{m}", "variable": "L", "positive": "\\frac{L^{2}}{2 m}", "negatives": ["L \\log{(m)}", "m e^{\\frac{L}{m}}", "\\frac{L^{2} \\log{(m)}}{2}", "\\sin{(L - m)}"], "srepr_premise_expression": "Mul(Symbol('L', commutative=True), Pow(Symbol('m', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('L', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(2)), Pow(Symbol('m', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('L', commutative=True), log(Symbol('m', commutative=True)))", "Mul(Symbol('m', commutative=True), exp(Mul(Symbol('L', commutative=True), Pow(Symbol('m', commutative=True), Integer(-1)))))", "Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(2)), log(Symbol('m', commutative=True)))", "sin(Add(Symbol('L', commutative=True), Mul(Integer(-1), Symbol('m', commutative=True))))"]}, {"premise_expression": "P + b", "variable": "P", "positive": "\\frac{P (P + 2 b)}{2}", "negatives": ["\\frac{b (2 P + b)}{2}", "\\frac{P^{2} e^{b}}{2}", "\\frac{P^{2} \\sin{(b)}}{2}", "e^{P - b}"], "srepr_premise_expression": "Add(Symbol('P', commutative=True), Symbol('b', commutative=True))", "srepr_variable": "Symbol('P', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Symbol('P', commutative=True), Mul(Integer(2), Symbol('b', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('b', commutative=True), Add(Mul(Integer(2), Symbol('P', commutative=True)), Symbol('b', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2)), exp(Symbol('b', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2)), sin(Symbol('b', commutative=True)))", "exp(Add(Symbol('P', commutative=True), Mul(Integer(-1), Symbol('b', commutative=True))))"]}, {"premise_expression": "\\cos{(\\frac{R}{P})}", "variable": "P", "positive": "P \\cos{(\\frac{R}{P})} + R \\operatorname{Si}{(\\frac{R}{P})}", "negatives": ["P R + e^{P}", "P R + \\sin{(P)}", "\\frac{P (- P + 2 e^{R})}{2}", "\\log{(P)} \\log{(R)}"], "srepr_premise_expression": "cos(Mul(Pow(Symbol('P', commutative=True), Integer(-1)), Symbol('R', commutative=True)))", "srepr_variable": "Symbol('P', commutative=True)", "srepr_positive": "Add(Mul(Symbol('P', commutative=True), cos(Mul(Pow(Symbol('P', commutative=True), Integer(-1)), Symbol('R', commutative=True)))), Mul(Symbol('R', commutative=True), Si(Mul(Pow(Symbol('P', commutative=True), Integer(-1)), Symbol('R', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('P', commutative=True), Symbol('R', commutative=True)), exp(Symbol('P', commutative=True)))", "Add(Mul(Symbol('P', commutative=True), Symbol('R', commutative=True)), sin(Symbol('P', commutative=True)))", "Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Mul(Integer(-1), Symbol('P', commutative=True)), Mul(Integer(2), exp(Symbol('R', commutative=True)))))", "Mul(log(Symbol('P', commutative=True)), log(Symbol('R', commutative=True)))"]}, {"premise_expression": "v + z", "variable": "v", "positive": "\\frac{v (v + 2 z)}{2}", "negatives": ["\\frac{v (- v + 2 z)}{2}", "\\frac{z (2 v + z)}{2}", "\\frac{v (v + 2 \\cos{(z)})}{2}", "\\frac{v^{2} \\sin{(z)}}{2}"], "srepr_premise_expression": "Add(Symbol('v', commutative=True), Symbol('z', commutative=True))", "srepr_variable": "Symbol('v', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('v', commutative=True), Add(Symbol('v', commutative=True), Mul(Integer(2), Symbol('z', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('v', commutative=True), Add(Mul(Integer(-1), Symbol('v', commutative=True)), Mul(Integer(2), Symbol('z', commutative=True))))", "Mul(Rational(1, 2), Symbol('z', commutative=True), Add(Mul(Integer(2), Symbol('v', commutative=True)), Symbol('z', commutative=True)))", "Mul(Rational(1, 2), Symbol('v', commutative=True), Add(Symbol('v', commutative=True), Mul(Integer(2), cos(Symbol('z', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('v', commutative=True), Integer(2)), sin(Symbol('z', commutative=True)))"]}, {"premise_expression": "t e^{v}", "variable": "v", "positive": "t e^{v}", "negatives": ["t v + e^{v}", "\\frac{t^{2} e^{v}}{2}", "\\frac{t v^{2}}{2}", "- \\sin{(t - v)}"], "srepr_premise_expression": "Mul(Symbol('t', commutative=True), exp(Symbol('v', commutative=True)))", "srepr_variable": "Symbol('v', commutative=True)", "srepr_positive": "Mul(Symbol('t', commutative=True), exp(Symbol('v', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('t', commutative=True), Symbol('v', commutative=True)), exp(Symbol('v', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('t', commutative=True), Integer(2)), exp(Symbol('v', commutative=True)))", "Mul(Rational(1, 2), Symbol('t', commutative=True), Pow(Symbol('v', commutative=True), Integer(2)))", "Mul(Integer(-1), sin(Add(Symbol('t', commutative=True), Mul(Integer(-1), Symbol('v', commutative=True)))))"]}, {"premise_expression": "m \\sin{(M)}", "variable": "M", "positive": "- m \\cos{(M)}", "negatives": ["M m - \\cos{(M)}", "\\frac{m^{2} \\sin{(M)}}{2}", "\\log{(M)} \\log{(m)}", "M m (\\log{(M)} - 1)"], "srepr_premise_expression": "Mul(Symbol('m', commutative=True), sin(Symbol('M', commutative=True)))", "srepr_variable": "Symbol('M', commutative=True)", "srepr_positive": "Mul(Integer(-1), Symbol('m', commutative=True), cos(Symbol('M', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('M', commutative=True), Symbol('m', commutative=True)), Mul(Integer(-1), cos(Symbol('M', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('m', commutative=True), Integer(2)), sin(Symbol('M', commutative=True)))", "Mul(log(Symbol('M', commutative=True)), log(Symbol('m', commutative=True)))", "Mul(Symbol('M', commutative=True), Symbol('m', commutative=True), Add(log(Symbol('M', commutative=True)), Integer(-1)))"]}, {"premise_expression": "Q U", "variable": "U", "positive": "\\frac{Q U^{2}}{2}", "negatives": ["\\frac{Q^{2} U}{2}", "\\frac{U^{2}}{2 Q}", "U \\sin{(1)}", "- Q U + e^{U}"], "srepr_premise_expression": "Mul(Symbol('Q', commutative=True), Symbol('U', commutative=True))", "srepr_variable": "Symbol('U', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('Q', commutative=True), Pow(Symbol('U', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(2)), Symbol('U', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('Q', commutative=True), Integer(-1)), Pow(Symbol('U', commutative=True), Integer(2)))", "Mul(Symbol('U', commutative=True), sin(Integer(1)))", "Add(Mul(Integer(-1), Symbol('Q', commutative=True), Symbol('U', commutative=True)), exp(Symbol('U', commutative=True)))"]}, {"premise_expression": "- t + w", "variable": "w", "positive": "\\frac{w (- 2 t + w)}{2}", "negatives": ["\\frac{w (2 t + w)}{2}", "\\frac{t (- t + 2 w)}{2}", "\\frac{w (- w + 2 e^{t})}{2}", "- \\frac{\\cos{(w)}}{t}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('t', commutative=True)), Symbol('w', commutative=True))", "srepr_variable": "Symbol('w', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('w', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('t', commutative=True)), Symbol('w', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('w', commutative=True), Add(Mul(Integer(2), Symbol('t', commutative=True)), Symbol('w', commutative=True)))", "Mul(Rational(1, 2), Symbol('t', commutative=True), Add(Mul(Integer(-1), Symbol('t', commutative=True)), Mul(Integer(2), Symbol('w', commutative=True))))", "Mul(Rational(1, 2), Symbol('w', commutative=True), Add(Mul(Integer(-1), Symbol('w', commutative=True)), Mul(Integer(2), exp(Symbol('t', commutative=True)))))", "Mul(Integer(-1), Pow(Symbol('t', commutative=True), Integer(-1)), cos(Symbol('w', commutative=True)))"]}, {"premise_expression": "\\log{(X + a)}", "variable": "X", "positive": "X \\log{(X + a)} - X + a \\log{(X + a)}", "negatives": ["X \\log{(X + a)} + a \\log{(X + a)} - a", "\\frac{X (X + 2 \\log{(a)})}{2}", "X (\\log{(X a)} - 1)", "e^{a} \\log{(X)}"], "srepr_premise_expression": "log(Add(Symbol('X', commutative=True), Symbol('a', commutative=True)))", "srepr_variable": "Symbol('X', commutative=True)", "srepr_positive": "Add(Mul(Symbol('X', commutative=True), log(Add(Symbol('X', commutative=True), Symbol('a', commutative=True)))), Mul(Integer(-1), Symbol('X', commutative=True)), Mul(Symbol('a', commutative=True), log(Add(Symbol('X', commutative=True), Symbol('a', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('X', commutative=True), log(Add(Symbol('X', commutative=True), Symbol('a', commutative=True)))), Mul(Symbol('a', commutative=True), log(Add(Symbol('X', commutative=True), Symbol('a', commutative=True)))), Mul(Integer(-1), Symbol('a', commutative=True)))", "Mul(Rational(1, 2), Symbol('X', commutative=True), Add(Symbol('X', commutative=True), Mul(Integer(2), log(Symbol('a', commutative=True)))))", "Mul(Symbol('X', commutative=True), Add(log(Mul(Symbol('X', commutative=True), Symbol('a', commutative=True))), Integer(-1)))", "Mul(exp(Symbol('a', commutative=True)), log(Symbol('X', commutative=True)))"]}, {"premise_expression": "\\frac{S}{z}", "variable": "S", "positive": "\\frac{S^{2}}{2 z}", "negatives": ["\\frac{S^{2}}{2 z} + S", "S \\log{(z)}", "z e^{\\frac{S}{z}}", "\\frac{S (S - 2 z)}{2}"], "srepr_premise_expression": "Mul(Symbol('S', commutative=True), Pow(Symbol('z', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('S', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('S', commutative=True), Integer(2)), Pow(Symbol('z', commutative=True), Integer(-1)))", "srepr_negatives": ["Add(Mul(Rational(1, 2), Pow(Symbol('S', commutative=True), Integer(2)), Pow(Symbol('z', commutative=True), Integer(-1))), Symbol('S', commutative=True))", "Mul(Symbol('S', commutative=True), log(Symbol('z', commutative=True)))", "Mul(Symbol('z', commutative=True), exp(Mul(Symbol('S', commutative=True), Pow(Symbol('z', commutative=True), Integer(-1)))))", "Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Symbol('S', commutative=True), Mul(Integer(-1), Integer(2), Symbol('z', commutative=True))))"]}, {"premise_expression": "Q + t", "variable": "t", "positive": "\\frac{t (2 Q + t)}{2}", "negatives": ["\\frac{t (2 Q - t)}{2}", "\\frac{Q (Q + 2 t)}{2}", "\\sin{(Q + t)}", "- \\cos{(Q - t)}"], "srepr_premise_expression": "Add(Symbol('Q', commutative=True), Symbol('t', commutative=True))", "srepr_variable": "Symbol('t', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('t', commutative=True), Add(Mul(Integer(2), Symbol('Q', commutative=True)), Symbol('t', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('t', commutative=True), Add(Mul(Integer(2), Symbol('Q', commutative=True)), Mul(Integer(-1), Symbol('t', commutative=True))))", "Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Symbol('Q', commutative=True), Mul(Integer(2), Symbol('t', commutative=True))))", "sin(Add(Symbol('Q', commutative=True), Symbol('t', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('Q', commutative=True), Mul(Integer(-1), Symbol('t', commutative=True)))))"]}, {"premise_expression": "\\cos{(K + W)}", "variable": "K", "positive": "\\sin{(K + W)}", "negatives": ["- \\cos{(K + W)}", "- e^{- K + W}", "K \\sin{(1)}", "\\frac{K^{2}}{2 W}"], "srepr_premise_expression": "cos(Add(Symbol('K', commutative=True), Symbol('W', commutative=True)))", "srepr_variable": "Symbol('K', commutative=True)", "srepr_positive": "sin(Add(Symbol('K', commutative=True), Symbol('W', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('K', commutative=True), Symbol('W', commutative=True))))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('K', commutative=True)), Symbol('W', commutative=True))))", "Mul(Symbol('K', commutative=True), sin(Integer(1)))", "Mul(Rational(1, 2), Pow(Symbol('K', commutative=True), Integer(2)), Pow(Symbol('W', commutative=True), Integer(-1)))"]}, {"premise_expression": "- B + L", "variable": "B", "positive": "\\frac{B (- B + 2 L)}{2}", "negatives": ["\\frac{B (B - 2 L)}{2}", "\\frac{L (- 2 B + L)}{2}", "\\frac{B^{2}}{2 L}", "\\sin{(B + L)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('B', commutative=True)), Symbol('L', commutative=True))", "srepr_variable": "Symbol('B', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('B', commutative=True), Add(Mul(Integer(-1), Symbol('B', commutative=True)), Mul(Integer(2), Symbol('L', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('B', commutative=True), Add(Symbol('B', commutative=True), Mul(Integer(-1), Integer(2), Symbol('L', commutative=True))))", "Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('B', commutative=True)), Symbol('L', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('B', commutative=True), Integer(2)), Pow(Symbol('L', commutative=True), Integer(-1)))", "sin(Add(Symbol('B', commutative=True), Symbol('L', commutative=True)))"]}, {"premise_expression": "B + V", "variable": "B", "positive": "\\frac{B (B + 2 V)}{2}", "negatives": ["\\frac{V (2 B + V)}{2}", "\\frac{B (B + 2 e^{V})}{2}", "\\frac{B^{2} \\sin{(V)}}{2}", "\\cos{(B - V)}"], "srepr_premise_expression": "Add(Symbol('B', commutative=True), Symbol('V', commutative=True))", "srepr_variable": "Symbol('B', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('B', commutative=True), Add(Symbol('B', commutative=True), Mul(Integer(2), Symbol('V', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('V', commutative=True), Add(Mul(Integer(2), Symbol('B', commutative=True)), Symbol('V', commutative=True)))", "Mul(Rational(1, 2), Symbol('B', commutative=True), Add(Symbol('B', commutative=True), Mul(Integer(2), exp(Symbol('V', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('B', commutative=True), Integer(2)), sin(Symbol('V', commutative=True)))", "cos(Add(Symbol('B', commutative=True), Mul(Integer(-1), Symbol('V', commutative=True))))"]}, {"premise_expression": "Z + \\cos{(x)}", "variable": "x", "positive": "Z x + \\sin{(x)}", "negatives": ["\\frac{Z x^{2}}{2}", "\\frac{Z (Z + 2 \\cos{(x)})}{2}", "- \\cos{(Z - x)}", "\\frac{x^{2}}{2 Z}"], "srepr_premise_expression": "Add(Symbol('Z', commutative=True), cos(Symbol('x', commutative=True)))", "srepr_variable": "Symbol('x', commutative=True)", "srepr_positive": "Add(Mul(Symbol('Z', commutative=True), Symbol('x', commutative=True)), sin(Symbol('x', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('Z', commutative=True), Pow(Symbol('x', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Symbol('Z', commutative=True), Mul(Integer(2), cos(Symbol('x', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('Z', commutative=True), Mul(Integer(-1), Symbol('x', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('Z', commutative=True), Integer(-1)), Pow(Symbol('x', commutative=True), Integer(2)))"]}, {"premise_expression": "Z + f^{S}", "variable": "Z", "positive": "\\frac{Z (Z + 2 f^{S})}{2}", "negatives": ["\\frac{S Z}{f} + \\frac{Z^{2}}{2}", "\\frac{Z (2 S + Z - 2 f)}{2}", "\\frac{Z (2 S + Z + 2 f)}{2}", "\\frac{Z^{2} f}{2 S}"], "srepr_premise_expression": "Add(Symbol('Z', commutative=True), Pow(Symbol('f', commutative=True), Symbol('S', commutative=True)))", "srepr_variable": "Symbol('Z', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Symbol('Z', commutative=True), Mul(Integer(2), Pow(Symbol('f', commutative=True), Symbol('S', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('S', commutative=True), Symbol('Z', commutative=True), Pow(Symbol('f', commutative=True), Integer(-1))), Mul(Rational(1, 2), Pow(Symbol('Z', commutative=True), Integer(2))))", "Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Mul(Integer(2), Symbol('S', commutative=True)), Symbol('Z', commutative=True), Mul(Integer(-1), Integer(2), Symbol('f', commutative=True))))", "Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Mul(Integer(2), Symbol('S', commutative=True)), Symbol('Z', commutative=True), Mul(Integer(2), Symbol('f', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('S', commutative=True), Integer(-1)), Pow(Symbol('Z', commutative=True), Integer(2)), Symbol('f', commutative=True))"]}, {"premise_expression": "E + H", "variable": "H", "positive": "\\frac{H (2 E + H)}{2}", "negatives": ["\\frac{E (E + 2 H)}{2}", "\\frac{H^{2} \\sin{(E)}}{2}", "\\sin{(E + H)}", "e^{E + H}"], "srepr_premise_expression": "Add(Symbol('E', commutative=True), Symbol('H', commutative=True))", "srepr_variable": "Symbol('H', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('H', commutative=True), Add(Mul(Integer(2), Symbol('E', commutative=True)), Symbol('H', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('E', commutative=True), Add(Symbol('E', commutative=True), Mul(Integer(2), Symbol('H', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('H', commutative=True), Integer(2)), sin(Symbol('E', commutative=True)))", "sin(Add(Symbol('E', commutative=True), Symbol('H', commutative=True)))", "exp(Add(Symbol('E', commutative=True), Symbol('H', commutative=True)))"]}, {"premise_expression": "\\log{(V X)}", "variable": "V", "positive": "V (\\log{(V X)} - 1)", "negatives": ["X (\\log{(V X)} - 1)", "\\frac{V (V + 2 X)}{2}", "\\log{(V)} \\sin{(X)}", "e^{V + X}"], "srepr_premise_expression": "log(Mul(Symbol('V', commutative=True), Symbol('X', commutative=True)))", "srepr_variable": "Symbol('V', commutative=True)", "srepr_positive": "Mul(Symbol('V', commutative=True), Add(log(Mul(Symbol('V', commutative=True), Symbol('X', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('X', commutative=True), Add(log(Mul(Symbol('V', commutative=True), Symbol('X', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('V', commutative=True), Add(Symbol('V', commutative=True), Mul(Integer(2), Symbol('X', commutative=True))))", "Mul(log(Symbol('V', commutative=True)), sin(Symbol('X', commutative=True)))", "exp(Add(Symbol('V', commutative=True), Symbol('X', commutative=True)))"]}, {"premise_expression": "X s", "variable": "s", "positive": "\\frac{X s^{2}}{2}", "negatives": ["\\frac{X^{2} s}{2}", "\\frac{s^{2}}{2 X}", "\\frac{s (2 X - s)}{2}", "\\frac{s^{2} \\log{(X)}}{2}"], "srepr_premise_expression": "Mul(Symbol('X', commutative=True), Symbol('s', commutative=True))", "srepr_variable": "Symbol('s', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('X', commutative=True), Pow(Symbol('s', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('X', commutative=True), Integer(2)), Symbol('s', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('X', commutative=True), Integer(-1)), Pow(Symbol('s', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('s', commutative=True), Add(Mul(Integer(2), Symbol('X', commutative=True)), Mul(Integer(-1), Symbol('s', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('s', commutative=True), Integer(2)), log(Symbol('X', commutative=True)))"]}, {"premise_expression": "- I + \\sin{(s)}", "variable": "I", "positive": "\\frac{I (- I + 2 \\sin{(s)})}{2}", "negatives": ["\\frac{I (I + 2 \\sin{(s)})}{2}", "\\frac{I (I + 2 s)}{2}", "\\frac{I^{2} \\sin{(s)}}{2}", "- I s - \\cos{(s)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('I', commutative=True)), sin(Symbol('s', commutative=True)))", "srepr_variable": "Symbol('I', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('I', commutative=True), Add(Mul(Integer(-1), Symbol('I', commutative=True)), Mul(Integer(2), sin(Symbol('s', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('I', commutative=True), Add(Symbol('I', commutative=True), Mul(Integer(2), sin(Symbol('s', commutative=True)))))", "Mul(Rational(1, 2), Symbol('I', commutative=True), Add(Symbol('I', commutative=True), Mul(Integer(2), Symbol('s', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(2)), sin(Symbol('s', commutative=True)))", "Add(Mul(Integer(-1), Symbol('I', commutative=True), Symbol('s', commutative=True)), Mul(Integer(-1), cos(Symbol('s', commutative=True))))"]}, {"premise_expression": "r e^{b}", "variable": "r", "positive": "\\frac{r^{2} e^{b}}{2}", "negatives": ["r e^{b}", "b r + e^{r}", "\\frac{r (r + 2 \\cos{(b)})}{2}", "e^{- b + r}"], "srepr_premise_expression": "Mul(Symbol('r', commutative=True), exp(Symbol('b', commutative=True)))", "srepr_variable": "Symbol('r', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('r', commutative=True), Integer(2)), exp(Symbol('b', commutative=True)))", "srepr_negatives": ["Mul(Symbol('r', commutative=True), exp(Symbol('b', commutative=True)))", "Add(Mul(Symbol('b', commutative=True), Symbol('r', commutative=True)), exp(Symbol('r', commutative=True)))", "Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Symbol('r', commutative=True), Mul(Integer(2), cos(Symbol('b', commutative=True)))))", "exp(Add(Mul(Integer(-1), Symbol('b', commutative=True)), Symbol('r', commutative=True)))"]}, {"premise_expression": "\\frac{\\log{(c)}}{z}", "variable": "z", "positive": "\\log{(c)} \\log{(z)}", "negatives": ["c \\log{(z)}", "- c z - \\cos{(z)}", "\\frac{c (\\log{(c)} - 1)}{z}", "c z + \\sin{(z)}"], "srepr_premise_expression": "Mul(Pow(Symbol('z', commutative=True), Integer(-1)), log(Symbol('c', commutative=True)))", "srepr_variable": "Symbol('z', commutative=True)", "srepr_positive": "Mul(log(Symbol('c', commutative=True)), log(Symbol('z', commutative=True)))", "srepr_negatives": ["Mul(Symbol('c', commutative=True), log(Symbol('z', commutative=True)))", "Add(Mul(Integer(-1), Symbol('c', commutative=True), Symbol('z', commutative=True)), Mul(Integer(-1), cos(Symbol('z', commutative=True))))", "Mul(Symbol('c', commutative=True), Pow(Symbol('z', commutative=True), Integer(-1)), Add(log(Symbol('c', commutative=True)), Integer(-1)))", "Add(Mul(Symbol('c', commutative=True), Symbol('z', commutative=True)), sin(Symbol('z', commutative=True)))"]}, {"premise_expression": "\\frac{- c + w}{G}", "variable": "c", "positive": "\\frac{c (- c + 2 w)}{2 G}", "negatives": ["\\frac{w (- 2 c + w)}{2 G}", "G c + \\frac{c^{2}}{2 w}", "\\frac{c (2 G + c)}{2 w}", "(- c + w) \\log{(G)}"], "srepr_premise_expression": "Mul(Pow(Symbol('G', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('c', commutative=True)), Symbol('w', commutative=True)))", "srepr_variable": "Symbol('c', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(-1)), Symbol('c', commutative=True), Add(Mul(Integer(-1), Symbol('c', commutative=True)), Mul(Integer(2), Symbol('w', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(-1)), Symbol('w', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('c', commutative=True)), Symbol('w', commutative=True)))", "Add(Mul(Symbol('G', commutative=True), Symbol('c', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('c', commutative=True), Integer(2)), Pow(Symbol('w', commutative=True), Integer(-1))))", "Mul(Rational(1, 2), Symbol('c', commutative=True), Pow(Symbol('w', commutative=True), Integer(-1)), Add(Mul(Integer(2), Symbol('G', commutative=True)), Symbol('c', commutative=True)))", "Mul(Add(Mul(Integer(-1), Symbol('c', commutative=True)), Symbol('w', commutative=True)), log(Symbol('G', commutative=True)))"]}, {"premise_expression": "\\frac{g}{b}", "variable": "b", "positive": "g \\log{(b)}", "negatives": ["\\frac{g^{2}}{2 b}", "\\log{(b)} \\log{(g)}", "\\frac{b^{2} \\cos{(g)}}{2}", "b (\\log{(b g)} - 1)"], "srepr_premise_expression": "Mul(Pow(Symbol('b', commutative=True), Integer(-1)), Symbol('g', commutative=True))", "srepr_variable": "Symbol('b', commutative=True)", "srepr_positive": "Mul(Symbol('g', commutative=True), log(Symbol('b', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('b', commutative=True), Integer(-1)), Pow(Symbol('g', commutative=True), Integer(2)))", "Mul(log(Symbol('b', commutative=True)), log(Symbol('g', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('b', commutative=True), Integer(2)), cos(Symbol('g', commutative=True)))", "Mul(Symbol('b', commutative=True), Add(log(Mul(Symbol('b', commutative=True), Symbol('g', commutative=True))), Integer(-1)))"]}, {"premise_expression": "e^{\\frac{p}{H}}", "variable": "H", "positive": "H e^{\\frac{p}{H}} - p \\operatorname{Ei}{(\\frac{p}{H})}", "negatives": ["H e^{\\frac{p}{H}}", "e^{H + p}", "H (\\log{(\\frac{p}{H})} + 1)", "\\frac{H (H + 2 \\log{(p)})}{2}"], "srepr_premise_expression": "exp(Mul(Pow(Symbol('H', commutative=True), Integer(-1)), Symbol('p', commutative=True)))", "srepr_variable": "Symbol('H', commutative=True)", "srepr_positive": "Add(Mul(Symbol('H', commutative=True), exp(Mul(Pow(Symbol('H', commutative=True), Integer(-1)), Symbol('p', commutative=True)))), Mul(Integer(-1), Symbol('p', commutative=True), Ei(Mul(Pow(Symbol('H', commutative=True), Integer(-1)), Symbol('p', commutative=True)))))", "srepr_negatives": ["Mul(Symbol('H', commutative=True), exp(Mul(Pow(Symbol('H', commutative=True), Integer(-1)), Symbol('p', commutative=True))))", "exp(Add(Symbol('H', commutative=True), Symbol('p', commutative=True)))", "Mul(Symbol('H', commutative=True), Add(log(Mul(Pow(Symbol('H', commutative=True), Integer(-1)), Symbol('p', commutative=True))), Integer(1)))", "Mul(Rational(1, 2), Symbol('H', commutative=True), Add(Symbol('H', commutative=True), Mul(Integer(2), log(Symbol('p', commutative=True)))))"]}, {"premise_expression": "B + G", "variable": "G", "positive": "\\frac{G (2 B + G)}{2}", "negatives": ["\\frac{B (B + 2 G)}{2}", "e^{- B + G}", "\\frac{G^{2}}{2 B}", "\\frac{\\sin{(G)}}{B}"], "srepr_premise_expression": "Add(Symbol('B', commutative=True), Symbol('G', commutative=True))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('G', commutative=True), Add(Mul(Integer(2), Symbol('B', commutative=True)), Symbol('G', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('B', commutative=True), Add(Symbol('B', commutative=True), Mul(Integer(2), Symbol('G', commutative=True))))", "exp(Add(Mul(Integer(-1), Symbol('B', commutative=True)), Symbol('G', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('B', commutative=True), Integer(-1)), Pow(Symbol('G', commutative=True), Integer(2)))", "Mul(Pow(Symbol('B', commutative=True), Integer(-1)), sin(Symbol('G', commutative=True)))"]}, {"premise_expression": "\\frac{B}{Y}", "variable": "B", "positive": "\\frac{B^{2}}{2 Y}", "negatives": ["B \\log{(Y)}", "\\frac{B (- B + 2 Y)}{2}", "\\tilde{\\infty} B", "\\log{(B)} \\log{(Y)}"], "srepr_premise_expression": "Mul(Symbol('B', commutative=True), Pow(Symbol('Y', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('B', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('B', commutative=True), Integer(2)), Pow(Symbol('Y', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('B', commutative=True), log(Symbol('Y', commutative=True)))", "Mul(Rational(1, 2), Symbol('B', commutative=True), Add(Mul(Integer(-1), Symbol('B', commutative=True)), Mul(Integer(2), Symbol('Y', commutative=True))))", "Mul(zoo, Symbol('B', commutative=True))", "Mul(log(Symbol('B', commutative=True)), log(Symbol('Y', commutative=True)))"]}, {"premise_expression": "\\log{(F - N)}", "variable": "F", "positive": "F \\log{(F - N)} - F - N \\log{(F - N)}", "negatives": ["- F \\log{(- F + N)} + N \\log{(F - N)} - N", "F (N + \\log{(F)} - 1)", "F \\cos{(\\frac{N}{F})} + N \\operatorname{Si}{(\\frac{N}{F})}", "F N - \\cos{(F)}"], "srepr_premise_expression": "log(Add(Symbol('F', commutative=True), Mul(Integer(-1), Symbol('N', commutative=True))))", "srepr_variable": "Symbol('F', commutative=True)", "srepr_positive": "Add(Mul(Symbol('F', commutative=True), log(Add(Symbol('F', commutative=True), Mul(Integer(-1), Symbol('N', commutative=True))))), Mul(Integer(-1), Symbol('F', commutative=True)), Mul(Integer(-1), Symbol('N', commutative=True), log(Add(Symbol('F', commutative=True), Mul(Integer(-1), Symbol('N', commutative=True))))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('F', commutative=True), log(Add(Mul(Integer(-1), Symbol('F', commutative=True)), Symbol('N', commutative=True)))), Mul(Symbol('N', commutative=True), log(Add(Symbol('F', commutative=True), Mul(Integer(-1), Symbol('N', commutative=True))))), Mul(Integer(-1), Symbol('N', commutative=True)))", "Mul(Symbol('F', commutative=True), Add(Symbol('N', commutative=True), log(Symbol('F', commutative=True)), Integer(-1)))", "Add(Mul(Symbol('F', commutative=True), cos(Mul(Pow(Symbol('F', commutative=True), Integer(-1)), Symbol('N', commutative=True)))), Mul(Symbol('N', commutative=True), Si(Mul(Pow(Symbol('F', commutative=True), Integer(-1)), Symbol('N', commutative=True)))))", "Add(Mul(Symbol('F', commutative=True), Symbol('N', commutative=True)), Mul(Integer(-1), cos(Symbol('F', commutative=True))))"]}, {"premise_expression": "- Y + \\sin{(z)}", "variable": "Y", "positive": "\\frac{Y (- Y + 2 \\sin{(z)})}{2}", "negatives": ["\\frac{Y (- Y + 2 e^{z})}{2}", "- Y z - \\cos{(z)}", "\\frac{Y^{2} z}{2}", "Y \\sin{(2 z)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('Y', commutative=True)), sin(Symbol('z', commutative=True)))", "srepr_variable": "Symbol('Y', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('Y', commutative=True), Add(Mul(Integer(-1), Symbol('Y', commutative=True)), Mul(Integer(2), sin(Symbol('z', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('Y', commutative=True), Add(Mul(Integer(-1), Symbol('Y', commutative=True)), Mul(Integer(2), exp(Symbol('z', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('Y', commutative=True), Symbol('z', commutative=True)), Mul(Integer(-1), cos(Symbol('z', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('Y', commutative=True), Integer(2)), Symbol('z', commutative=True))", "Mul(Symbol('Y', commutative=True), sin(Mul(Integer(2), Symbol('z', commutative=True))))"]}, {"premise_expression": "- C + e^{Q}", "variable": "C", "positive": "\\frac{C (- C + 2 e^{Q})}{2}", "negatives": ["- C Q + e^{Q}", "\\frac{C^{2} \\sin{(Q)}}{2}", "- e^{- C + Q}", "C Q - \\cos{(C)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('C', commutative=True)), exp(Symbol('Q', commutative=True)))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Mul(Integer(-1), Symbol('C', commutative=True)), Mul(Integer(2), exp(Symbol('Q', commutative=True)))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('C', commutative=True), Symbol('Q', commutative=True)), exp(Symbol('Q', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2)), sin(Symbol('Q', commutative=True)))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('C', commutative=True)), Symbol('Q', commutative=True))))", "Add(Mul(Symbol('C', commutative=True), Symbol('Q', commutative=True)), Mul(Integer(-1), cos(Symbol('C', commutative=True))))"]}, {"premise_expression": "\\sin{(Q + R)}", "variable": "Q", "positive": "- \\cos{(Q + R)}", "negatives": ["- \\cos{(Q - R)}", "e^{Q + R}", "\\frac{Q (Q - 2 R)}{2}", "\\log{(Q)} \\sin{(R)}"], "srepr_premise_expression": "sin(Add(Symbol('Q', commutative=True), Symbol('R', commutative=True)))", "srepr_variable": "Symbol('Q', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('Q', commutative=True), Symbol('R', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('Q', commutative=True), Mul(Integer(-1), Symbol('R', commutative=True)))))", "exp(Add(Symbol('Q', commutative=True), Symbol('R', commutative=True)))", "Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Symbol('Q', commutative=True), Mul(Integer(-1), Integer(2), Symbol('R', commutative=True))))", "Mul(log(Symbol('Q', commutative=True)), sin(Symbol('R', commutative=True)))"]}, {"premise_expression": "\\cos{(c + y)}", "variable": "c", "positive": "\\sin{(c + y)}", "negatives": ["y \\sin{(c)}", "\\frac{c (c + 2 y)}{2}", "\\frac{c (- c + 2 \\log{(y)})}{2}", "\\int \\sin^{y}{(c)} dc"], "srepr_premise_expression": "cos(Add(Symbol('c', commutative=True), Symbol('y', commutative=True)))", "srepr_variable": "Symbol('c', commutative=True)", "srepr_positive": "sin(Add(Symbol('c', commutative=True), Symbol('y', commutative=True)))", "srepr_negatives": ["Mul(Symbol('y', commutative=True), sin(Symbol('c', commutative=True)))", "Mul(Rational(1, 2), Symbol('c', commutative=True), Add(Symbol('c', commutative=True), Mul(Integer(2), Symbol('y', commutative=True))))", "Mul(Rational(1, 2), Symbol('c', commutative=True), Add(Mul(Integer(-1), Symbol('c', commutative=True)), Mul(Integer(2), log(Symbol('y', commutative=True)))))", "Integral(Pow(sin(Symbol('c', commutative=True)), Symbol('y', commutative=True)), Tuple(Symbol('c', commutative=True)))"]}, {"premise_expression": "H + p + r", "variable": "p", "positive": "p (H + \\frac{p}{2} + r)", "negatives": ["\\frac{p (- 2 H + p + 2 r)}{2}", "\\frac{p (2 H - p + 2 r)}{2}", "\\frac{H (H + 2 p + 2 r)}{2}", "\\frac{r (2 H + 2 p + r)}{2}"], "srepr_premise_expression": "Add(Symbol('H', commutative=True), Symbol('p', commutative=True), Symbol('r', commutative=True))", "srepr_variable": "Symbol('p', commutative=True)", "srepr_positive": "Mul(Symbol('p', commutative=True), Add(Symbol('H', commutative=True), Mul(Rational(1, 2), Symbol('p', commutative=True)), Symbol('r', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('H', commutative=True)), Symbol('p', commutative=True), Mul(Integer(2), Symbol('r', commutative=True))))", "Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Mul(Integer(2), Symbol('H', commutative=True)), Mul(Integer(-1), Symbol('p', commutative=True)), Mul(Integer(2), Symbol('r', commutative=True))))", "Mul(Rational(1, 2), Symbol('H', commutative=True), Add(Symbol('H', commutative=True), Mul(Integer(2), Symbol('p', commutative=True)), Mul(Integer(2), Symbol('r', commutative=True))))", "Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(2), Symbol('H', commutative=True)), Mul(Integer(2), Symbol('p', commutative=True)), Symbol('r', commutative=True)))"]}, {"premise_expression": "e^{S - q}", "variable": "S", "positive": "e^{S - q}", "negatives": ["- e^{S - q}", "e^{S + q}", "S q (\\log{(S)} - 1)", "\\frac{S^{2} q}{2}"], "srepr_premise_expression": "exp(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('q', commutative=True))))", "srepr_variable": "Symbol('S', commutative=True)", "srepr_positive": "exp(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('q', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('q', commutative=True)))))", "exp(Add(Symbol('S', commutative=True), Symbol('q', commutative=True)))", "Mul(Symbol('S', commutative=True), Symbol('q', commutative=True), Add(log(Symbol('S', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('S', commutative=True), Integer(2)), Symbol('q', commutative=True))"]}, {"premise_expression": "F e^{n}", "variable": "n", "positive": "F e^{n}", "negatives": ["F \\log{(n)}", "\\frac{F^{2} e^{n}}{2}", "e^{F + n}", "\\frac{n^{2}}{2 F}"], "srepr_premise_expression": "Mul(Symbol('F', commutative=True), exp(Symbol('n', commutative=True)))", "srepr_variable": "Symbol('n', commutative=True)", "srepr_positive": "Mul(Symbol('F', commutative=True), exp(Symbol('n', commutative=True)))", "srepr_negatives": ["Mul(Symbol('F', commutative=True), log(Symbol('n', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('F', commutative=True), Integer(2)), exp(Symbol('n', commutative=True)))", "exp(Add(Symbol('F', commutative=True), Symbol('n', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('F', commutative=True), Integer(-1)), Pow(Symbol('n', commutative=True), Integer(2)))"]}, {"premise_expression": "n e^{y}", "variable": "n", "positive": "\\frac{n^{2} e^{y}}{2}", "negatives": ["n e^{y}", "\\frac{n^{2} y}{2}", "\\frac{n^{2}}{2 y}", "y \\log{(n)}"], "srepr_premise_expression": "Mul(Symbol('n', commutative=True), exp(Symbol('y', commutative=True)))", "srepr_variable": "Symbol('n', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('n', commutative=True), Integer(2)), exp(Symbol('y', commutative=True)))", "srepr_negatives": ["Mul(Symbol('n', commutative=True), exp(Symbol('y', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('n', commutative=True), Integer(2)), Symbol('y', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('n', commutative=True), Integer(2)), Pow(Symbol('y', commutative=True), Integer(-1)))", "Mul(Symbol('y', commutative=True), log(Symbol('n', commutative=True)))"]}, {"premise_expression": "\\frac{K}{a m}", "variable": "K", "positive": "\\frac{K^{2}}{2 a m}", "negatives": ["\\frac{K^{2} a}{2 m}", "\\frac{K^{2} m^{a}}{2}", "\\frac{K \\log{(a)}}{m}", "\\frac{K \\log{(m)}}{a}"], "srepr_premise_expression": "Mul(Symbol('K', commutative=True), Pow(Symbol('a', commutative=True), Integer(-1)), Pow(Symbol('m', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('K', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('K', commutative=True), Integer(2)), Pow(Symbol('a', commutative=True), Integer(-1)), Pow(Symbol('m', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('K', commutative=True), Integer(2)), Symbol('a', commutative=True), Pow(Symbol('m', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('K', commutative=True), Integer(2)), Pow(Symbol('m', commutative=True), Symbol('a', commutative=True)))", "Mul(Symbol('K', commutative=True), Pow(Symbol('m', commutative=True), Integer(-1)), log(Symbol('a', commutative=True)))", "Mul(Symbol('K', commutative=True), Pow(Symbol('a', commutative=True), Integer(-1)), log(Symbol('m', commutative=True)))"]}, {"premise_expression": "b + j - v", "variable": "v", "positive": "v (b + j - \\frac{v}{2})", "negatives": ["\\frac{j (2 b + j - 2 v)}{2}", "\\frac{b (b + 2 j - 2 v)}{2}", "\\frac{v (2 b j - v)}{2}", "(b - j) \\log{(v)}"], "srepr_premise_expression": "Add(Symbol('b', commutative=True), Symbol('j', commutative=True), Mul(Integer(-1), Symbol('v', commutative=True)))", "srepr_variable": "Symbol('v', commutative=True)", "srepr_positive": "Mul(Symbol('v', commutative=True), Add(Symbol('b', commutative=True), Symbol('j', commutative=True), Mul(Integer(-1), Rational(1, 2), Symbol('v', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('j', commutative=True), Add(Mul(Integer(2), Symbol('b', commutative=True)), Symbol('j', commutative=True), Mul(Integer(-1), Integer(2), Symbol('v', commutative=True))))", "Mul(Rational(1, 2), Symbol('b', commutative=True), Add(Symbol('b', commutative=True), Mul(Integer(2), Symbol('j', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('v', commutative=True))))", "Mul(Rational(1, 2), Symbol('v', commutative=True), Add(Mul(Integer(2), Symbol('b', commutative=True), Symbol('j', commutative=True)), Mul(Integer(-1), Symbol('v', commutative=True))))", "Mul(Add(Symbol('b', commutative=True), Mul(Integer(-1), Symbol('j', commutative=True))), log(Symbol('v', commutative=True)))"]}, {"premise_expression": "\\log{(R^{q})}", "variable": "R", "positive": "R (- q + \\log{(R^{q})})", "negatives": ["\\frac{R (R + 2 \\log{(q)})}{2}", "q \\log{(R)}", "\\frac{q^{2} \\log{(R)}}{2}", "R (\\log{(\\frac{q}{R})} + 1)"], "srepr_premise_expression": "log(Pow(Symbol('R', commutative=True), Symbol('q', commutative=True)))", "srepr_variable": "Symbol('R', commutative=True)", "srepr_positive": "Mul(Symbol('R', commutative=True), Add(Mul(Integer(-1), Symbol('q', commutative=True)), log(Pow(Symbol('R', commutative=True), Symbol('q', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('R', commutative=True), Add(Symbol('R', commutative=True), Mul(Integer(2), log(Symbol('q', commutative=True)))))", "Mul(Symbol('q', commutative=True), log(Symbol('R', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('q', commutative=True), Integer(2)), log(Symbol('R', commutative=True)))", "Mul(Symbol('R', commutative=True), Add(log(Mul(Pow(Symbol('R', commutative=True), Integer(-1)), Symbol('q', commutative=True))), Integer(1)))"]}, {"premise_expression": "\\frac{e^{q}}{A}", "variable": "A", "positive": "e^{q} \\log{(A)}", "negatives": ["- A q + e^{A}", "- A q + \\sin{(A)}", "A q (\\log{(A)} - 1)", "\\frac{A (A - 2 q)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('A', commutative=True), Integer(-1)), exp(Symbol('q', commutative=True)))", "srepr_variable": "Symbol('A', commutative=True)", "srepr_positive": "Mul(exp(Symbol('q', commutative=True)), log(Symbol('A', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('A', commutative=True), Symbol('q', commutative=True)), exp(Symbol('A', commutative=True)))", "Add(Mul(Integer(-1), Symbol('A', commutative=True), Symbol('q', commutative=True)), sin(Symbol('A', commutative=True)))", "Mul(Symbol('A', commutative=True), Symbol('q', commutative=True), Add(log(Symbol('A', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Symbol('A', commutative=True), Mul(Integer(-1), Integer(2), Symbol('q', commutative=True))))"]}, {"premise_expression": "E + x^{k}", "variable": "E", "positive": "\\frac{E (E + 2 x^{k})}{2}", "negatives": ["\\frac{E (E + 2 k^{x})}{2}", "\\frac{E (E k + 2 x)}{2}", "\\frac{E (k + x)}{x}", "\\frac{E^{2} x}{2 k}"], "srepr_premise_expression": "Add(Symbol('E', commutative=True), Pow(Symbol('x', commutative=True), Symbol('k', commutative=True)))", "srepr_variable": "Symbol('E', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('E', commutative=True), Add(Symbol('E', commutative=True), Mul(Integer(2), Pow(Symbol('x', commutative=True), Symbol('k', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('E', commutative=True), Add(Symbol('E', commutative=True), Mul(Integer(2), Pow(Symbol('k', commutative=True), Symbol('x', commutative=True)))))", "Mul(Rational(1, 2), Symbol('E', commutative=True), Add(Mul(Symbol('E', commutative=True), Symbol('k', commutative=True)), Mul(Integer(2), Symbol('x', commutative=True))))", "Mul(Symbol('E', commutative=True), Pow(Symbol('x', commutative=True), Integer(-1)), Add(Symbol('k', commutative=True), Symbol('x', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('E', commutative=True), Integer(2)), Pow(Symbol('k', commutative=True), Integer(-1)), Symbol('x', commutative=True))"]}, {"premise_expression": "\\frac{K}{u v}", "variable": "v", "positive": "\\frac{K \\log{(v)}}{u}", "negatives": ["\\frac{K \\log{(u)}}{v}", "K u \\log{(v)}", "(K + u) \\log{(v)}", "\\frac{K^{2}}{2 u v}"], "srepr_premise_expression": "Mul(Symbol('K', commutative=True), Pow(Symbol('u', commutative=True), Integer(-1)), Pow(Symbol('v', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('v', commutative=True)", "srepr_positive": "Mul(Symbol('K', commutative=True), Pow(Symbol('u', commutative=True), Integer(-1)), log(Symbol('v', commutative=True)))", "srepr_negatives": ["Mul(Symbol('K', commutative=True), Pow(Symbol('v', commutative=True), Integer(-1)), log(Symbol('u', commutative=True)))", "Mul(Symbol('K', commutative=True), Symbol('u', commutative=True), log(Symbol('v', commutative=True)))", "Mul(Add(Symbol('K', commutative=True), Symbol('u', commutative=True)), log(Symbol('v', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('K', commutative=True), Integer(2)), Pow(Symbol('u', commutative=True), Integer(-1)), Pow(Symbol('v', commutative=True), Integer(-1)))"]}, {"premise_expression": "\\frac{n}{J}", "variable": "n", "positive": "\\frac{n^{2}}{2 J}", "negatives": ["n \\log{(J)}", "J \\log{(n)}", "- \\frac{\\cos{(n)}}{J}", "\\frac{n (- 2 J + n)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('J', commutative=True), Integer(-1)), Symbol('n', commutative=True))", "srepr_variable": "Symbol('n', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('J', commutative=True), Integer(-1)), Pow(Symbol('n', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('n', commutative=True), log(Symbol('J', commutative=True)))", "Mul(Symbol('J', commutative=True), log(Symbol('n', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('J', commutative=True), Integer(-1)), cos(Symbol('n', commutative=True)))", "Mul(Rational(1, 2), Symbol('n', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('J', commutative=True)), Symbol('n', commutative=True)))"]}, {"premise_expression": "- A + Z + g", "variable": "g", "positive": "g (- A + Z + \\frac{g}{2})", "negatives": ["\\frac{g (2 A + 2 Z - g)}{2}", "\\frac{A (- A + 2 Z + 2 g)}{2}", "\\frac{Z (- 2 A + Z + 2 g)}{2}", "g (A + \\frac{g^{2}}{3})"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('A', commutative=True)), Symbol('Z', commutative=True), Symbol('g', commutative=True))", "srepr_variable": "Symbol('g', commutative=True)", "srepr_positive": "Mul(Symbol('g', commutative=True), Add(Mul(Integer(-1), Symbol('A', commutative=True)), Symbol('Z', commutative=True), Mul(Rational(1, 2), Symbol('g', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Mul(Integer(2), Symbol('A', commutative=True)), Mul(Integer(2), Symbol('Z', commutative=True)), Mul(Integer(-1), Symbol('g', commutative=True))))", "Mul(Rational(1, 2), Symbol('A', commutative=True), Add(Mul(Integer(-1), Symbol('A', commutative=True)), Mul(Integer(2), Symbol('Z', commutative=True)), Mul(Integer(2), Symbol('g', commutative=True))))", "Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('A', commutative=True)), Symbol('Z', commutative=True), Mul(Integer(2), Symbol('g', commutative=True))))", "Mul(Symbol('g', commutative=True), Add(Symbol('A', commutative=True), Mul(Rational(1, 3), Pow(Symbol('g', commutative=True), Integer(2)))))"]}, {"premise_expression": "e^{z^{Y}}", "variable": "z", "positive": "\\frac{e^{- \\frac{i \\pi}{Y}} \\gamma(\\frac{1}{Y}, z^{Y} e^{i \\pi})}{Y}", "negatives": ["- Y \\operatorname{Ei}{(\\frac{Y}{z})} + z e^{\\frac{Y}{z}}", "\\frac{z (- 2 Y + z)}{2}", "z (\\log{(\\frac{Y}{z})} + 1)", "- e^{Y - z}"], "srepr_premise_expression": "exp(Pow(Symbol('z', commutative=True), Symbol('Y', commutative=True)))", "srepr_variable": "Symbol('z', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('Y', commutative=True), Integer(-1)), exp(Mul(Integer(-1), I, pi, Pow(Symbol('Y', commutative=True), Integer(-1)))), lowergamma(Pow(Symbol('Y', commutative=True), Integer(-1)), Mul(Pow(Symbol('z', commutative=True), Symbol('Y', commutative=True)), exp_polar(Mul(I, pi)))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('Y', commutative=True), Ei(Mul(Symbol('Y', commutative=True), Pow(Symbol('z', commutative=True), Integer(-1))))), Mul(Symbol('z', commutative=True), exp(Mul(Symbol('Y', commutative=True), Pow(Symbol('z', commutative=True), Integer(-1))))))", "Mul(Rational(1, 2), Symbol('z', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('Y', commutative=True)), Symbol('z', commutative=True)))", "Mul(Symbol('z', commutative=True), Add(log(Mul(Symbol('Y', commutative=True), Pow(Symbol('z', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Integer(-1), exp(Add(Symbol('Y', commutative=True), Mul(Integer(-1), Symbol('z', commutative=True)))))"]}, {"premise_expression": "J W", "variable": "J", "positive": "\\frac{J^{2} W}{2}", "negatives": ["\\frac{J W^{2}}{2}", "\\frac{J^{2} \\log{(W)}}{2}", "\\sin{(J - W)}", "\\log{(J)} \\log{(W)}"], "srepr_premise_expression": "Mul(Symbol('J', commutative=True), Symbol('W', commutative=True))", "srepr_variable": "Symbol('J', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('J', commutative=True), Integer(2)), Symbol('W', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('J', commutative=True), Pow(Symbol('W', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('J', commutative=True), Integer(2)), log(Symbol('W', commutative=True)))", "sin(Add(Symbol('J', commutative=True), Mul(Integer(-1), Symbol('W', commutative=True))))", "Mul(log(Symbol('J', commutative=True)), log(Symbol('W', commutative=True)))"]}, {"premise_expression": "E + \\cos{(F)}", "variable": "F", "positive": "E F + \\sin{(F)}", "negatives": ["E e^{\\frac{F}{E}}", "\\frac{E (E + 2 \\cos{(F)})}{2}", "- e^{E - F}", "- \\frac{\\cos{(F)}}{E}"], "srepr_premise_expression": "Add(Symbol('E', commutative=True), cos(Symbol('F', commutative=True)))", "srepr_variable": "Symbol('F', commutative=True)", "srepr_positive": "Add(Mul(Symbol('E', commutative=True), Symbol('F', commutative=True)), sin(Symbol('F', commutative=True)))", "srepr_negatives": ["Mul(Symbol('E', commutative=True), exp(Mul(Pow(Symbol('E', commutative=True), Integer(-1)), Symbol('F', commutative=True))))", "Mul(Rational(1, 2), Symbol('E', commutative=True), Add(Symbol('E', commutative=True), Mul(Integer(2), cos(Symbol('F', commutative=True)))))", "Mul(Integer(-1), exp(Add(Symbol('E', commutative=True), Mul(Integer(-1), Symbol('F', commutative=True)))))", "Mul(Integer(-1), Pow(Symbol('E', commutative=True), Integer(-1)), cos(Symbol('F', commutative=True)))"]}, {"premise_expression": "C + b", "variable": "C", "positive": "\\frac{C (C + 2 b)}{2}", "negatives": ["\\frac{b (2 C + b)}{2}", "\\frac{C (C + 2 e^{b})}{2}", "\\frac{C^{2}}{2 b}", "- \\cos{(C + b)}"], "srepr_premise_expression": "Add(Symbol('C', commutative=True), Symbol('b', commutative=True))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Symbol('C', commutative=True), Mul(Integer(2), Symbol('b', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('b', commutative=True), Add(Mul(Integer(2), Symbol('C', commutative=True)), Symbol('b', commutative=True)))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Symbol('C', commutative=True), Mul(Integer(2), exp(Symbol('b', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2)), Pow(Symbol('b', commutative=True), Integer(-1)))", "Mul(Integer(-1), cos(Add(Symbol('C', commutative=True), Symbol('b', commutative=True))))"]}, {"premise_expression": "\\frac{\\log{(L)}}{m}", "variable": "L", "positive": "\\frac{L (\\log{(L)} - 1)}{m}", "negatives": ["L (- m + \\log{(L)} - 1)", "- \\cos{(L - m)}", "\\log{(L)} \\log{(m)}", "- \\frac{\\cos{(L)}}{m}"], "srepr_premise_expression": "Mul(Pow(Symbol('m', commutative=True), Integer(-1)), log(Symbol('L', commutative=True)))", "srepr_variable": "Symbol('L', commutative=True)", "srepr_positive": "Mul(Symbol('L', commutative=True), Pow(Symbol('m', commutative=True), Integer(-1)), Add(log(Symbol('L', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('L', commutative=True), Add(Mul(Integer(-1), Symbol('m', commutative=True)), log(Symbol('L', commutative=True)), Integer(-1)))", "Mul(Integer(-1), cos(Add(Symbol('L', commutative=True), Mul(Integer(-1), Symbol('m', commutative=True)))))", "Mul(log(Symbol('L', commutative=True)), log(Symbol('m', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('m', commutative=True), Integer(-1)), cos(Symbol('L', commutative=True)))"]}, {"premise_expression": "- C + \\sin{(B)}", "variable": "C", "positive": "\\frac{C (- C + 2 \\sin{(B)})}{2}", "negatives": ["\\frac{C^{2} \\log{(B)}}{2}", "\\frac{C (2 B - C)}{2}", "- B C - \\cos{(B)}", "\\frac{B C (2 B - C)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('C', commutative=True)), sin(Symbol('B', commutative=True)))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Mul(Integer(-1), Symbol('C', commutative=True)), Mul(Integer(2), sin(Symbol('B', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2)), log(Symbol('B', commutative=True)))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Mul(Integer(2), Symbol('B', commutative=True)), Mul(Integer(-1), Symbol('C', commutative=True))))", "Add(Mul(Integer(-1), Symbol('B', commutative=True), Symbol('C', commutative=True)), Mul(Integer(-1), cos(Symbol('B', commutative=True))))", "Mul(Rational(1, 2), Symbol('B', commutative=True), Symbol('C', commutative=True), Add(Mul(Integer(2), Symbol('B', commutative=True)), Mul(Integer(-1), Symbol('C', commutative=True))))"]}, {"premise_expression": "g \\sin{(H)}", "variable": "g", "positive": "\\frac{g^{2} \\sin{(H)}}{2}", "negatives": ["\\frac{g^{2} e^{H}}{2}", "\\frac{g (- 2 H + g)}{2}", "- g \\cos{(H)}", "\\sin{(H + g)}"], "srepr_premise_expression": "Mul(Symbol('g', commutative=True), sin(Symbol('H', commutative=True)))", "srepr_variable": "Symbol('g', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('g', commutative=True), Integer(2)), sin(Symbol('H', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('g', commutative=True), Integer(2)), exp(Symbol('H', commutative=True)))", "Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('H', commutative=True)), Symbol('g', commutative=True)))", "Mul(Integer(-1), Symbol('g', commutative=True), cos(Symbol('H', commutative=True)))", "sin(Add(Symbol('H', commutative=True), Symbol('g', commutative=True)))"]}, {"premise_expression": "\\cos{(Q + j)}", "variable": "j", "positive": "\\sin{(Q + j)}", "negatives": ["- Q j + \\sin{(j)}", "j", "Q j - \\cos{(j)}", "\\log{(j)} \\cos{(Q)}"], "srepr_premise_expression": "cos(Add(Symbol('Q', commutative=True), Symbol('j', commutative=True)))", "srepr_variable": "Symbol('j', commutative=True)", "srepr_positive": "sin(Add(Symbol('Q', commutative=True), Symbol('j', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('Q', commutative=True), Symbol('j', commutative=True)), sin(Symbol('j', commutative=True)))", "Symbol('j', commutative=True)", "Add(Mul(Symbol('Q', commutative=True), Symbol('j', commutative=True)), Mul(Integer(-1), cos(Symbol('j', commutative=True))))", "Mul(log(Symbol('j', commutative=True)), cos(Symbol('Q', commutative=True)))"]}, {"premise_expression": "\\log{(- G + Z)}", "variable": "Z", "positive": "- G \\log{(- G + Z)} + Z \\log{(- G + Z)} - Z", "negatives": ["G \\log{(- G + Z)} - G - Z \\log{(G - Z)}", "G \\operatorname{Si}{(\\frac{G}{Z})} + Z \\cos{(\\frac{G}{Z})}", "Z (- G + \\log{(Z^{G})})", "\\frac{Z (- Z + 2 \\cos{(G)})}{2}"], "srepr_premise_expression": "log(Add(Mul(Integer(-1), Symbol('G', commutative=True)), Symbol('Z', commutative=True)))", "srepr_variable": "Symbol('Z', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('G', commutative=True), log(Add(Mul(Integer(-1), Symbol('G', commutative=True)), Symbol('Z', commutative=True)))), Mul(Symbol('Z', commutative=True), log(Add(Mul(Integer(-1), Symbol('G', commutative=True)), Symbol('Z', commutative=True)))), Mul(Integer(-1), Symbol('Z', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('G', commutative=True), log(Add(Mul(Integer(-1), Symbol('G', commutative=True)), Symbol('Z', commutative=True)))), Mul(Integer(-1), Symbol('G', commutative=True)), Mul(Integer(-1), Symbol('Z', commutative=True), log(Add(Symbol('G', commutative=True), Mul(Integer(-1), Symbol('Z', commutative=True))))))", "Add(Mul(Symbol('G', commutative=True), Si(Mul(Symbol('G', commutative=True), Pow(Symbol('Z', commutative=True), Integer(-1))))), Mul(Symbol('Z', commutative=True), cos(Mul(Symbol('G', commutative=True), Pow(Symbol('Z', commutative=True), Integer(-1))))))", "Mul(Symbol('Z', commutative=True), Add(Mul(Integer(-1), Symbol('G', commutative=True)), log(Pow(Symbol('Z', commutative=True), Symbol('G', commutative=True)))))", "Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Mul(Integer(-1), Symbol('Z', commutative=True)), Mul(Integer(2), cos(Symbol('G', commutative=True)))))"]}, {"premise_expression": "\\sin{(C + t)}", "variable": "C", "positive": "- \\cos{(C + t)}", "negatives": ["- \\cos{(C - t)}", "t \\sin{(C)}", "\\frac{C^{2} e^{t}}{2}", "\\frac{C (C + 2 e^{t})}{2}"], "srepr_premise_expression": "sin(Add(Symbol('C', commutative=True), Symbol('t', commutative=True)))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('C', commutative=True), Symbol('t', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('t', commutative=True)))))", "Mul(Symbol('t', commutative=True), sin(Symbol('C', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2)), exp(Symbol('t', commutative=True)))", "Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Symbol('C', commutative=True), Mul(Integer(2), exp(Symbol('t', commutative=True)))))"]}, {"premise_expression": "y + e^{H}", "variable": "y", "positive": "\\frac{y (y + 2 e^{H})}{2}", "negatives": ["H y + e^{H}", "y (\\log{(H y)} - 1)", "y (- H + \\log{(y)} - 1)", "\\sin{(H + y)}"], "srepr_premise_expression": "Add(Symbol('y', commutative=True), exp(Symbol('H', commutative=True)))", "srepr_variable": "Symbol('y', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('y', commutative=True), Add(Symbol('y', commutative=True), Mul(Integer(2), exp(Symbol('H', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('H', commutative=True), Symbol('y', commutative=True)), exp(Symbol('H', commutative=True)))", "Mul(Symbol('y', commutative=True), Add(log(Mul(Symbol('H', commutative=True), Symbol('y', commutative=True))), Integer(-1)))", "Mul(Symbol('y', commutative=True), Add(Mul(Integer(-1), Symbol('H', commutative=True)), log(Symbol('y', commutative=True)), Integer(-1)))", "sin(Add(Symbol('H', commutative=True), Symbol('y', commutative=True)))"]}, {"premise_expression": "\\log{(E M)}", "variable": "M", "positive": "M (\\log{(E M)} - 1)", "negatives": ["E (\\log{(E M)} - 1)", "M (\\log{(\\frac{E}{M})} + 1)", "M (\\log{(\\frac{M}{E})} - 1)", "- E \\log{(M)} + M"], "srepr_premise_expression": "log(Mul(Symbol('E', commutative=True), Symbol('M', commutative=True)))", "srepr_variable": "Symbol('M', commutative=True)", "srepr_positive": "Mul(Symbol('M', commutative=True), Add(log(Mul(Symbol('E', commutative=True), Symbol('M', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('E', commutative=True), Add(log(Mul(Symbol('E', commutative=True), Symbol('M', commutative=True))), Integer(-1)))", "Mul(Symbol('M', commutative=True), Add(log(Mul(Symbol('E', commutative=True), Pow(Symbol('M', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Symbol('M', commutative=True), Add(log(Mul(Pow(Symbol('E', commutative=True), Integer(-1)), Symbol('M', commutative=True))), Integer(-1)))", "Add(Mul(Integer(-1), Symbol('E', commutative=True), log(Symbol('M', commutative=True))), Symbol('M', commutative=True))"]}, {"premise_expression": "H + p", "variable": "p", "positive": "\\frac{p (2 H + p)}{2}", "negatives": ["\\frac{H (H + 2 p)}{2}", "\\frac{p^{2} \\sin{(H)}}{2}", "\\frac{p^{2} \\cos{(H)}}{2}", "- \\frac{\\cos{(p)}}{H}"], "srepr_premise_expression": "Add(Symbol('H', commutative=True), Symbol('p', commutative=True))", "srepr_variable": "Symbol('p', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Mul(Integer(2), Symbol('H', commutative=True)), Symbol('p', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('H', commutative=True), Add(Symbol('H', commutative=True), Mul(Integer(2), Symbol('p', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('p', commutative=True), Integer(2)), sin(Symbol('H', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('p', commutative=True), Integer(2)), cos(Symbol('H', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('H', commutative=True), Integer(-1)), cos(Symbol('p', commutative=True)))"]}, {"premise_expression": "E - T - a", "variable": "E", "positive": "E (\\frac{E}{2} - T - a)", "negatives": ["\\frac{a (2 E - 2 T - a)}{2}", "\\frac{T (2 E - T - 2 a)}{2}", "\\frac{E^{2}}{2 T a}", "- \\frac{E (E - 2 T)}{2 a}"], "srepr_premise_expression": "Add(Symbol('E', commutative=True), Mul(Integer(-1), Symbol('T', commutative=True)), Mul(Integer(-1), Symbol('a', commutative=True)))", "srepr_variable": "Symbol('E', commutative=True)", "srepr_positive": "Mul(Symbol('E', commutative=True), Add(Mul(Rational(1, 2), Symbol('E', commutative=True)), Mul(Integer(-1), Symbol('T', commutative=True)), Mul(Integer(-1), Symbol('a', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('a', commutative=True), Add(Mul(Integer(2), Symbol('E', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('T', commutative=True)), Mul(Integer(-1), Symbol('a', commutative=True))))", "Mul(Rational(1, 2), Symbol('T', commutative=True), Add(Mul(Integer(2), Symbol('E', commutative=True)), Mul(Integer(-1), Symbol('T', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('a', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('E', commutative=True), Integer(2)), Pow(Symbol('T', commutative=True), Integer(-1)), Pow(Symbol('a', commutative=True), Integer(-1)))", "Mul(Integer(-1), Rational(1, 2), Symbol('E', commutative=True), Pow(Symbol('a', commutative=True), Integer(-1)), Add(Symbol('E', commutative=True), Mul(Integer(-1), Integer(2), Symbol('T', commutative=True))))"]}, {"premise_expression": "\\log{(\\frac{H}{p})}", "variable": "p", "positive": "p (\\log{(\\frac{H}{p})} + 1)", "negatives": ["H (\\log{(\\frac{H}{p})} - 1)", "e^{- H + p}", "- \\sin{(H - p)}", "\\log{(p)} \\cos{(H)}"], "srepr_premise_expression": "log(Mul(Symbol('H', commutative=True), Pow(Symbol('p', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('p', commutative=True)", "srepr_positive": "Mul(Symbol('p', commutative=True), Add(log(Mul(Symbol('H', commutative=True), Pow(Symbol('p', commutative=True), Integer(-1)))), Integer(1)))", "srepr_negatives": ["Mul(Symbol('H', commutative=True), Add(log(Mul(Symbol('H', commutative=True), Pow(Symbol('p', commutative=True), Integer(-1)))), Integer(-1)))", "exp(Add(Mul(Integer(-1), Symbol('H', commutative=True)), Symbol('p', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('H', commutative=True), Mul(Integer(-1), Symbol('p', commutative=True)))))", "Mul(log(Symbol('p', commutative=True)), cos(Symbol('H', commutative=True)))"]}, {"premise_expression": "g + v", "variable": "g", "positive": "\\frac{g (g + 2 v)}{2}", "negatives": ["\\frac{v (2 g + v)}{2}", "\\frac{g (g + 2 \\cos{(v)})}{2}", "\\frac{g^{2} v}{2}", "\\frac{g^{2} \\log{(v)}}{2}"], "srepr_premise_expression": "Add(Symbol('g', commutative=True), Symbol('v', commutative=True))", "srepr_variable": "Symbol('g', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Symbol('g', commutative=True), Mul(Integer(2), Symbol('v', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('v', commutative=True), Add(Mul(Integer(2), Symbol('g', commutative=True)), Symbol('v', commutative=True)))", "Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Symbol('g', commutative=True), Mul(Integer(2), cos(Symbol('v', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('g', commutative=True), Integer(2)), Symbol('v', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('g', commutative=True), Integer(2)), log(Symbol('v', commutative=True)))"]}, {"premise_expression": "J + g", "variable": "J", "positive": "\\frac{J (J + 2 g)}{2}", "negatives": ["\\frac{g (2 J + g)}{2}", "- \\cos{(J + g)}", "J^{2} (\\frac{J}{3} - \\frac{g}{2})", "e^{g} \\log{(J)}"], "srepr_premise_expression": "Add(Symbol('J', commutative=True), Symbol('g', commutative=True))", "srepr_variable": "Symbol('J', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('J', commutative=True), Add(Symbol('J', commutative=True), Mul(Integer(2), Symbol('g', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('g', commutative=True), Add(Mul(Integer(2), Symbol('J', commutative=True)), Symbol('g', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('J', commutative=True), Symbol('g', commutative=True))))", "Mul(Pow(Symbol('J', commutative=True), Integer(2)), Add(Mul(Rational(1, 3), Symbol('J', commutative=True)), Mul(Integer(-1), Rational(1, 2), Symbol('g', commutative=True))))", "Mul(exp(Symbol('g', commutative=True)), log(Symbol('J', commutative=True)))"]}, {"premise_expression": "\\sin{(A + x)}", "variable": "A", "positive": "- \\cos{(A + x)}", "negatives": ["\\log{(A)} \\log{(x)}", "\\frac{A^{2}}{2 x}", "- A x + \\sin{(A)}", "A (- x + \\log{(A)} - 1)"], "srepr_premise_expression": "sin(Add(Symbol('A', commutative=True), Symbol('x', commutative=True)))", "srepr_variable": "Symbol('A', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('A', commutative=True), Symbol('x', commutative=True))))", "srepr_negatives": ["Mul(log(Symbol('A', commutative=True)), log(Symbol('x', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('A', commutative=True), Integer(2)), Pow(Symbol('x', commutative=True), Integer(-1)))", "Add(Mul(Integer(-1), Symbol('A', commutative=True), Symbol('x', commutative=True)), sin(Symbol('A', commutative=True)))", "Mul(Symbol('A', commutative=True), Add(Mul(Integer(-1), Symbol('x', commutative=True)), log(Symbol('A', commutative=True)), Integer(-1)))"]}, {"premise_expression": "- D + \\log{(a)}", "variable": "D", "positive": "\\frac{D (- D + 2 \\log{(a)})}{2}", "negatives": ["\\frac{D (- D + 2 \\cos{(a)})}{2}", "a (- D + \\log{(a)} - 1)", "D (D + a)", "\\sin{(D + a)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('D', commutative=True)), log(Symbol('a', commutative=True)))", "srepr_variable": "Symbol('D', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('D', commutative=True), Add(Mul(Integer(-1), Symbol('D', commutative=True)), Mul(Integer(2), log(Symbol('a', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('D', commutative=True), Add(Mul(Integer(-1), Symbol('D', commutative=True)), Mul(Integer(2), cos(Symbol('a', commutative=True)))))", "Mul(Symbol('a', commutative=True), Add(Mul(Integer(-1), Symbol('D', commutative=True)), log(Symbol('a', commutative=True)), Integer(-1)))", "Mul(Symbol('D', commutative=True), Add(Symbol('D', commutative=True), Symbol('a', commutative=True)))", "sin(Add(Symbol('D', commutative=True), Symbol('a', commutative=True)))"]}, {"premise_expression": "\\sin^{R}{(N)}", "variable": "N", "positive": "\\int \\sin^{R}{(N)} dN", "negatives": ["\\int \\log{(N)}^{N} dN", "- \\frac{\\cos{(N)}}{R}", "R e^{N}", "R \\log{(N)}"], "srepr_premise_expression": "Pow(sin(Symbol('N', commutative=True)), Symbol('R', commutative=True))", "srepr_variable": "Symbol('N', commutative=True)", "srepr_positive": "Integral(Pow(sin(Symbol('N', commutative=True)), Symbol('R', commutative=True)), Tuple(Symbol('N', commutative=True)))", "srepr_negatives": ["NonElementaryIntegral(Pow(log(Symbol('N', commutative=True)), Symbol('N', commutative=True)), Tuple(Symbol('N', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('R', commutative=True), Integer(-1)), cos(Symbol('N', commutative=True)))", "Mul(Symbol('R', commutative=True), exp(Symbol('N', commutative=True)))", "Mul(Symbol('R', commutative=True), log(Symbol('N', commutative=True)))"]}, {"premise_expression": "\\log{(b + h)}", "variable": "h", "positive": "b \\log{(b + h)} + h \\log{(b + h)} - h", "negatives": ["b \\log{(b + h)} - b + h \\log{(b + h)}", "\\log{(h)} \\cos{(b)}", "h (\\log{(b h)} - 1)", "\\frac{h (- h + 2 \\sin{(b)})}{2}"], "srepr_premise_expression": "log(Add(Symbol('b', commutative=True), Symbol('h', commutative=True)))", "srepr_variable": "Symbol('h', commutative=True)", "srepr_positive": "Add(Mul(Symbol('b', commutative=True), log(Add(Symbol('b', commutative=True), Symbol('h', commutative=True)))), Mul(Symbol('h', commutative=True), log(Add(Symbol('b', commutative=True), Symbol('h', commutative=True)))), Mul(Integer(-1), Symbol('h', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('b', commutative=True), log(Add(Symbol('b', commutative=True), Symbol('h', commutative=True)))), Mul(Integer(-1), Symbol('b', commutative=True)), Mul(Symbol('h', commutative=True), log(Add(Symbol('b', commutative=True), Symbol('h', commutative=True)))))", "Mul(log(Symbol('h', commutative=True)), cos(Symbol('b', commutative=True)))", "Mul(Symbol('h', commutative=True), Add(log(Mul(Symbol('b', commutative=True), Symbol('h', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('h', commutative=True), Add(Mul(Integer(-1), Symbol('h', commutative=True)), Mul(Integer(2), sin(Symbol('b', commutative=True)))))"]}, {"premise_expression": "\\frac{S}{G}", "variable": "G", "positive": "S \\log{(G)}", "negatives": ["\\frac{S^{2}}{2 G}", "\\log{(G)} \\log{(S)}", "G S (\\log{(G)} - 1)", "G (\\log{(\\frac{G}{S})} - 1)"], "srepr_premise_expression": "Mul(Pow(Symbol('G', commutative=True), Integer(-1)), Symbol('S', commutative=True))", "srepr_variable": "Symbol('G', commutative=True)", "srepr_positive": "Mul(Symbol('S', commutative=True), log(Symbol('G', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(-1)), Pow(Symbol('S', commutative=True), Integer(2)))", "Mul(log(Symbol('G', commutative=True)), log(Symbol('S', commutative=True)))", "Mul(Symbol('G', commutative=True), Symbol('S', commutative=True), Add(log(Symbol('G', commutative=True)), Integer(-1)))", "Mul(Symbol('G', commutative=True), Add(log(Mul(Symbol('G', commutative=True), Pow(Symbol('S', commutative=True), Integer(-1)))), Integer(-1)))"]}, {"premise_expression": "E (W + Z)", "variable": "Z", "positive": "\\frac{E Z (2 W + Z)}{2}", "negatives": ["\\frac{W Z (2 E + Z)}{2}", "\\frac{E^{2} (W + Z)}{2}", "\\frac{E W (W + 2 Z)}{2}", "\\frac{Z (2 E + W Z)}{2}"], "srepr_premise_expression": "Mul(Symbol('E', commutative=True), Add(Symbol('W', commutative=True), Symbol('Z', commutative=True)))", "srepr_variable": "Symbol('Z', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('E', commutative=True), Symbol('Z', commutative=True), Add(Mul(Integer(2), Symbol('W', commutative=True)), Symbol('Z', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('W', commutative=True), Symbol('Z', commutative=True), Add(Mul(Integer(2), Symbol('E', commutative=True)), Symbol('Z', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('E', commutative=True), Integer(2)), Add(Symbol('W', commutative=True), Symbol('Z', commutative=True)))", "Mul(Rational(1, 2), Symbol('E', commutative=True), Symbol('W', commutative=True), Add(Symbol('W', commutative=True), Mul(Integer(2), Symbol('Z', commutative=True))))", "Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Mul(Integer(2), Symbol('E', commutative=True)), Mul(Symbol('W', commutative=True), Symbol('Z', commutative=True))))"]}, {"premise_expression": "R (- l + t)", "variable": "R", "positive": "\\frac{R^{2} (- l + t)}{2}", "negatives": ["\\frac{R l (- l + 2 t)}{2}", "\\frac{R t (- 2 l + t)}{2}", "\\frac{R^{2} l^{t}}{2}", "\\frac{R^{2} l t}{2}"], "srepr_premise_expression": "Mul(Symbol('R', commutative=True), Add(Mul(Integer(-1), Symbol('l', commutative=True)), Symbol('t', commutative=True)))", "srepr_variable": "Symbol('R', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('R', commutative=True), Integer(2)), Add(Mul(Integer(-1), Symbol('l', commutative=True)), Symbol('t', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('R', commutative=True), Symbol('l', commutative=True), Add(Mul(Integer(-1), Symbol('l', commutative=True)), Mul(Integer(2), Symbol('t', commutative=True))))", "Mul(Rational(1, 2), Symbol('R', commutative=True), Symbol('t', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('l', commutative=True)), Symbol('t', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('R', commutative=True), Integer(2)), Pow(Symbol('l', commutative=True), Symbol('t', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('R', commutative=True), Integer(2)), Symbol('l', commutative=True), Symbol('t', commutative=True))"]}, {"premise_expression": "\\log{(\\frac{m}{Z})}", "variable": "Z", "positive": "Z (\\log{(\\frac{m}{Z})} + 1)", "negatives": ["m (\\log{(\\frac{m}{Z})} - 1)", "Z m (\\log{(Z)} - 1)", "Z (- m + \\log{(Z)} - 1)", "m \\log{(Z)}"], "srepr_premise_expression": "log(Mul(Pow(Symbol('Z', commutative=True), Integer(-1)), Symbol('m', commutative=True)))", "srepr_variable": "Symbol('Z', commutative=True)", "srepr_positive": "Mul(Symbol('Z', commutative=True), Add(log(Mul(Pow(Symbol('Z', commutative=True), Integer(-1)), Symbol('m', commutative=True))), Integer(1)))", "srepr_negatives": ["Mul(Symbol('m', commutative=True), Add(log(Mul(Pow(Symbol('Z', commutative=True), Integer(-1)), Symbol('m', commutative=True))), Integer(-1)))", "Mul(Symbol('Z', commutative=True), Symbol('m', commutative=True), Add(log(Symbol('Z', commutative=True)), Integer(-1)))", "Mul(Symbol('Z', commutative=True), Add(Mul(Integer(-1), Symbol('m', commutative=True)), log(Symbol('Z', commutative=True)), Integer(-1)))", "Mul(Symbol('m', commutative=True), log(Symbol('Z', commutative=True)))"]}, {"premise_expression": "\\log{(\\frac{b}{D})}", "variable": "D", "positive": "D (\\log{(\\frac{b}{D})} + 1)", "negatives": ["b (\\log{(\\frac{b}{D})} - 1)", "\\frac{D (\\log{(D)} - 1)}{b}", "D (- b + \\log{(D)} - 1)", "\\frac{D^{2} \\log{(b)}}{2}"], "srepr_premise_expression": "log(Mul(Pow(Symbol('D', commutative=True), Integer(-1)), Symbol('b', commutative=True)))", "srepr_variable": "Symbol('D', commutative=True)", "srepr_positive": "Mul(Symbol('D', commutative=True), Add(log(Mul(Pow(Symbol('D', commutative=True), Integer(-1)), Symbol('b', commutative=True))), Integer(1)))", "srepr_negatives": ["Mul(Symbol('b', commutative=True), Add(log(Mul(Pow(Symbol('D', commutative=True), Integer(-1)), Symbol('b', commutative=True))), Integer(-1)))", "Mul(Symbol('D', commutative=True), Pow(Symbol('b', commutative=True), Integer(-1)), Add(log(Symbol('D', commutative=True)), Integer(-1)))", "Mul(Symbol('D', commutative=True), Add(Mul(Integer(-1), Symbol('b', commutative=True)), log(Symbol('D', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('D', commutative=True), Integer(2)), log(Symbol('b', commutative=True)))"]}, {"premise_expression": "\\frac{\\cos{(l)}}{Y}", "variable": "Y", "positive": "\\log{(Y)} \\cos{(l)}", "negatives": ["\\frac{Y^{2} \\log{(l)}}{2}", "l e^{\\frac{Y}{l}}", "\\frac{\\sin{(l)}}{Y}", "Y (- l + e^{l})"], "srepr_premise_expression": "Mul(Pow(Symbol('Y', commutative=True), Integer(-1)), cos(Symbol('l', commutative=True)))", "srepr_variable": "Symbol('Y', commutative=True)", "srepr_positive": "Mul(log(Symbol('Y', commutative=True)), cos(Symbol('l', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('Y', commutative=True), Integer(2)), log(Symbol('l', commutative=True)))", "Mul(Symbol('l', commutative=True), exp(Mul(Symbol('Y', commutative=True), Pow(Symbol('l', commutative=True), Integer(-1)))))", "Mul(Pow(Symbol('Y', commutative=True), Integer(-1)), sin(Symbol('l', commutative=True)))", "Mul(Symbol('Y', commutative=True), Add(Mul(Integer(-1), Symbol('l', commutative=True)), exp(Symbol('l', commutative=True))))"]}, {"premise_expression": "\\log{(- L + Z)}", "variable": "Z", "positive": "- L \\log{(- L + Z)} + Z \\log{(- L + Z)} - Z", "negatives": ["L \\log{(- L + Z)} - L - Z \\log{(L - Z)}", "L Z (\\log{(Z)} - 1)", "\\frac{Z (Z + 2 \\cos{(L)})}{2}", "e^{L} \\log{(Z)}"], "srepr_premise_expression": "log(Add(Mul(Integer(-1), Symbol('L', commutative=True)), Symbol('Z', commutative=True)))", "srepr_variable": "Symbol('Z', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('L', commutative=True), log(Add(Mul(Integer(-1), Symbol('L', commutative=True)), Symbol('Z', commutative=True)))), Mul(Symbol('Z', commutative=True), log(Add(Mul(Integer(-1), Symbol('L', commutative=True)), Symbol('Z', commutative=True)))), Mul(Integer(-1), Symbol('Z', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('L', commutative=True), log(Add(Mul(Integer(-1), Symbol('L', commutative=True)), Symbol('Z', commutative=True)))), Mul(Integer(-1), Symbol('L', commutative=True)), Mul(Integer(-1), Symbol('Z', commutative=True), log(Add(Symbol('L', commutative=True), Mul(Integer(-1), Symbol('Z', commutative=True))))))", "Mul(Symbol('L', commutative=True), Symbol('Z', commutative=True), Add(log(Symbol('Z', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Symbol('Z', commutative=True), Mul(Integer(2), cos(Symbol('L', commutative=True)))))", "Mul(exp(Symbol('L', commutative=True)), log(Symbol('Z', commutative=True)))"]}, {"premise_expression": "K + e^{k}", "variable": "K", "positive": "\\frac{K (K + 2 e^{k})}{2}", "negatives": ["\\frac{K (K + 2 \\sin{(k)})}{2}", "\\frac{K (- K + 2 \\sin{(k)})}{2}", "K k + e^{k}", "\\frac{K^{2}}{2 k}"], "srepr_premise_expression": "Add(Symbol('K', commutative=True), exp(Symbol('k', commutative=True)))", "srepr_variable": "Symbol('K', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Symbol('K', commutative=True), Mul(Integer(2), exp(Symbol('k', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Symbol('K', commutative=True), Mul(Integer(2), sin(Symbol('k', commutative=True)))))", "Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Mul(Integer(-1), Symbol('K', commutative=True)), Mul(Integer(2), sin(Symbol('k', commutative=True)))))", "Add(Mul(Symbol('K', commutative=True), Symbol('k', commutative=True)), exp(Symbol('k', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('K', commutative=True), Integer(2)), Pow(Symbol('k', commutative=True), Integer(-1)))"]}, {"premise_expression": "\\sin^{t}{(x)}", "variable": "x", "positive": "\\int \\sin^{t}{(x)} dx", "negatives": ["\\sin{(t + x)}", "x (\\log{(t x)} - 1)", "t \\log{(x)}", "e^{- t + x}"], "srepr_premise_expression": "Pow(sin(Symbol('x', commutative=True)), Symbol('t', commutative=True))", "srepr_variable": "Symbol('x', commutative=True)", "srepr_positive": "Integral(Pow(sin(Symbol('x', commutative=True)), Symbol('t', commutative=True)), Tuple(Symbol('x', commutative=True)))", "srepr_negatives": ["sin(Add(Symbol('t', commutative=True), Symbol('x', commutative=True)))", "Mul(Symbol('x', commutative=True), Add(log(Mul(Symbol('t', commutative=True), Symbol('x', commutative=True))), Integer(-1)))", "Mul(Symbol('t', commutative=True), log(Symbol('x', commutative=True)))", "exp(Add(Mul(Integer(-1), Symbol('t', commutative=True)), Symbol('x', commutative=True)))"]}, {"premise_expression": "- K + \\sin{(I)}", "variable": "I", "positive": "- I K - \\cos{(I)}", "negatives": ["K \\log{(I)}", "\\frac{I (I - 2 K)}{2}", "\\frac{I^{2} K}{2}", "\\frac{I (- I + 2 K)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('K', commutative=True)), sin(Symbol('I', commutative=True)))", "srepr_variable": "Symbol('I', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('I', commutative=True), Symbol('K', commutative=True)), Mul(Integer(-1), cos(Symbol('I', commutative=True))))", "srepr_negatives": ["Mul(Symbol('K', commutative=True), log(Symbol('I', commutative=True)))", "Mul(Rational(1, 2), Symbol('I', commutative=True), Add(Symbol('I', commutative=True), Mul(Integer(-1), Integer(2), Symbol('K', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(2)), Symbol('K', commutative=True))", "Mul(Rational(1, 2), Symbol('I', commutative=True), Add(Mul(Integer(-1), Symbol('I', commutative=True)), Mul(Integer(2), Symbol('K', commutative=True))))"]}, {"premise_expression": "\\frac{\\cos{(m)}}{n}", "variable": "m", "positive": "\\frac{\\sin{(m)}}{n}", "negatives": ["e^{m - n}", "\\cos{(m - n)}", "\\frac{m^{2} n}{2}", "m n + \\sin{(m)}"], "srepr_premise_expression": "Mul(Pow(Symbol('n', commutative=True), Integer(-1)), cos(Symbol('m', commutative=True)))", "srepr_variable": "Symbol('m', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('n', commutative=True), Integer(-1)), sin(Symbol('m', commutative=True)))", "srepr_negatives": ["exp(Add(Symbol('m', commutative=True), Mul(Integer(-1), Symbol('n', commutative=True))))", "cos(Add(Symbol('m', commutative=True), Mul(Integer(-1), Symbol('n', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('m', commutative=True), Integer(2)), Symbol('n', commutative=True))", "Add(Mul(Symbol('m', commutative=True), Symbol('n', commutative=True)), sin(Symbol('m', commutative=True)))"]}, {"premise_expression": "L T", "variable": "T", "positive": "\\frac{L T^{2}}{2}", "negatives": ["\\frac{L^{2} T}{2}", "\\frac{T^{2}}{2 L}", "- L T - \\cos{(T)}", "\\log{(T)} \\sin{(L)}"], "srepr_premise_expression": "Mul(Symbol('L', commutative=True), Symbol('T', commutative=True))", "srepr_variable": "Symbol('T', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('L', commutative=True), Pow(Symbol('T', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(2)), Symbol('T', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(-1)), Pow(Symbol('T', commutative=True), Integer(2)))", "Add(Mul(Integer(-1), Symbol('L', commutative=True), Symbol('T', commutative=True)), Mul(Integer(-1), cos(Symbol('T', commutative=True))))", "Mul(log(Symbol('T', commutative=True)), sin(Symbol('L', commutative=True)))"]}, {"premise_expression": "\\frac{o - t}{G}", "variable": "t", "positive": "\\frac{t (2 o - t)}{2 G}", "negatives": ["\\frac{o (o - 2 t)}{2 G}", "\\frac{t (2 G - 2 o - t)}{2}", "(o - t) \\log{(G)}", "\\frac{t (2 G + 2 o + t)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('G', commutative=True), Integer(-1)), Add(Symbol('o', commutative=True), Mul(Integer(-1), Symbol('t', commutative=True))))", "srepr_variable": "Symbol('t', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(-1)), Symbol('t', commutative=True), Add(Mul(Integer(2), Symbol('o', commutative=True)), Mul(Integer(-1), Symbol('t', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(-1)), Symbol('o', commutative=True), Add(Symbol('o', commutative=True), Mul(Integer(-1), Integer(2), Symbol('t', commutative=True))))", "Mul(Rational(1, 2), Symbol('t', commutative=True), Add(Mul(Integer(2), Symbol('G', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('o', commutative=True)), Mul(Integer(-1), Symbol('t', commutative=True))))", "Mul(Add(Symbol('o', commutative=True), Mul(Integer(-1), Symbol('t', commutative=True))), log(Symbol('G', commutative=True)))", "Mul(Rational(1, 2), Symbol('t', commutative=True), Add(Mul(Integer(2), Symbol('G', commutative=True)), Mul(Integer(2), Symbol('o', commutative=True)), Symbol('t', commutative=True)))"]}, {"premise_expression": "\\cos{(\\frac{J}{x})}", "variable": "x", "positive": "J \\operatorname{Si}{(\\frac{J}{x})} + x \\cos{(\\frac{J}{x})}", "negatives": ["\\frac{x (x + 2 \\log{(J)})}{2}", "\\frac{x (- 2 J + x)}{2}", "J \\log{(J + x)} + x \\log{(J + x)} - x", "x (\\log{(J x)} - 1)"], "srepr_premise_expression": "cos(Mul(Symbol('J', commutative=True), Pow(Symbol('x', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('x', commutative=True)", "srepr_positive": "Add(Mul(Symbol('J', commutative=True), Si(Mul(Symbol('J', commutative=True), Pow(Symbol('x', commutative=True), Integer(-1))))), Mul(Symbol('x', commutative=True), cos(Mul(Symbol('J', commutative=True), Pow(Symbol('x', commutative=True), Integer(-1))))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('x', commutative=True), Add(Symbol('x', commutative=True), Mul(Integer(2), log(Symbol('J', commutative=True)))))", "Mul(Rational(1, 2), Symbol('x', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('J', commutative=True)), Symbol('x', commutative=True)))", "Add(Mul(Symbol('J', commutative=True), log(Add(Symbol('J', commutative=True), Symbol('x', commutative=True)))), Mul(Symbol('x', commutative=True), log(Add(Symbol('J', commutative=True), Symbol('x', commutative=True)))), Mul(Integer(-1), Symbol('x', commutative=True)))", "Mul(Symbol('x', commutative=True), Add(log(Mul(Symbol('J', commutative=True), Symbol('x', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\frac{T V}{c}", "variable": "T", "positive": "\\frac{T^{2} V}{2 c}", "negatives": ["\\frac{T^{2} c}{2 V}", "\\frac{T V^{2}}{2 c}", "T V \\log{(c)}", "\\frac{T^{2} (V + c)}{2}"], "srepr_premise_expression": "Mul(Symbol('T', commutative=True), Symbol('V', commutative=True), Pow(Symbol('c', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('T', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('T', commutative=True), Integer(2)), Symbol('V', commutative=True), Pow(Symbol('c', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('T', commutative=True), Integer(2)), Pow(Symbol('V', commutative=True), Integer(-1)), Symbol('c', commutative=True))", "Mul(Rational(1, 2), Symbol('T', commutative=True), Pow(Symbol('V', commutative=True), Integer(2)), Pow(Symbol('c', commutative=True), Integer(-1)))", "Mul(Symbol('T', commutative=True), Symbol('V', commutative=True), log(Symbol('c', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('T', commutative=True), Integer(2)), Add(Symbol('V', commutative=True), Symbol('c', commutative=True)))"]}, {"premise_expression": "\\frac{T + w}{C}", "variable": "T", "positive": "\\frac{T (T + 2 w)}{2 C}", "negatives": ["\\frac{w (2 T + w)}{2 C}", "\\frac{T^{2} w}{2 C}", "\\frac{T (2 C - T)}{2 w}", "\\frac{T (C T - 2 w)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('C', commutative=True), Integer(-1)), Add(Symbol('T', commutative=True), Symbol('w', commutative=True)))", "srepr_variable": "Symbol('T', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(-1)), Symbol('T', commutative=True), Add(Symbol('T', commutative=True), Mul(Integer(2), Symbol('w', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(-1)), Symbol('w', commutative=True), Add(Mul(Integer(2), Symbol('T', commutative=True)), Symbol('w', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(-1)), Pow(Symbol('T', commutative=True), Integer(2)), Symbol('w', commutative=True))", "Mul(Rational(1, 2), Symbol('T', commutative=True), Pow(Symbol('w', commutative=True), Integer(-1)), Add(Mul(Integer(2), Symbol('C', commutative=True)), Mul(Integer(-1), Symbol('T', commutative=True))))", "Mul(Rational(1, 2), Symbol('T', commutative=True), Add(Mul(Symbol('C', commutative=True), Symbol('T', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('w', commutative=True))))"]}, {"premise_expression": "- X + u", "variable": "X", "positive": "\\frac{X (- X + 2 u)}{2}", "negatives": ["\\frac{u (- 2 X + u)}{2}", "\\frac{X (- X + 2 \\cos{(u)})}{2}", "\\frac{X (X + 2 \\sin{(u)})}{2}", "\\frac{X (X + 2 \\cos{(u)})}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('X', commutative=True)), Symbol('u', commutative=True))", "srepr_variable": "Symbol('X', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('X', commutative=True), Add(Mul(Integer(-1), Symbol('X', commutative=True)), Mul(Integer(2), Symbol('u', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('X', commutative=True)), Symbol('u', commutative=True)))", "Mul(Rational(1, 2), Symbol('X', commutative=True), Add(Mul(Integer(-1), Symbol('X', commutative=True)), Mul(Integer(2), cos(Symbol('u', commutative=True)))))", "Mul(Rational(1, 2), Symbol('X', commutative=True), Add(Symbol('X', commutative=True), Mul(Integer(2), sin(Symbol('u', commutative=True)))))", "Mul(Rational(1, 2), Symbol('X', commutative=True), Add(Symbol('X', commutative=True), Mul(Integer(2), cos(Symbol('u', commutative=True)))))"]}, {"premise_expression": "\\frac{P}{y} + j", "variable": "j", "positive": "\\frac{P j}{y} + \\frac{j^{2}}{2}", "negatives": ["\\frac{P j}{y} - \\frac{j^{2}}{2}", "\\frac{j (P j + 2 y)}{2}", "P \\log{(y)} + j y", "\\frac{P^{2}}{2 y} + P j"], "srepr_premise_expression": "Add(Mul(Symbol('P', commutative=True), Pow(Symbol('y', commutative=True), Integer(-1))), Symbol('j', commutative=True))", "srepr_variable": "Symbol('j', commutative=True)", "srepr_positive": "Add(Mul(Symbol('P', commutative=True), Symbol('j', commutative=True), Pow(Symbol('y', commutative=True), Integer(-1))), Mul(Rational(1, 2), Pow(Symbol('j', commutative=True), Integer(2))))", "srepr_negatives": ["Add(Mul(Symbol('P', commutative=True), Symbol('j', commutative=True), Pow(Symbol('y', commutative=True), Integer(-1))), Mul(Integer(-1), Rational(1, 2), Pow(Symbol('j', commutative=True), Integer(2))))", "Mul(Rational(1, 2), Symbol('j', commutative=True), Add(Mul(Symbol('P', commutative=True), Symbol('j', commutative=True)), Mul(Integer(2), Symbol('y', commutative=True))))", "Add(Mul(Symbol('P', commutative=True), log(Symbol('y', commutative=True))), Mul(Symbol('j', commutative=True), Symbol('y', commutative=True)))", "Add(Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2)), Pow(Symbol('y', commutative=True), Integer(-1))), Mul(Symbol('P', commutative=True), Symbol('j', commutative=True)))"]}, {"premise_expression": "\\frac{k}{j}", "variable": "j", "positive": "k \\log{(j)}", "negatives": ["\\frac{k^{2}}{2 j}", "k e^{\\frac{j}{k}}", "e^{j + k}", "\\frac{j (\\log{(j)} - 1)}{k}"], "srepr_premise_expression": "Mul(Pow(Symbol('j', commutative=True), Integer(-1)), Symbol('k', commutative=True))", "srepr_variable": "Symbol('j', commutative=True)", "srepr_positive": "Mul(Symbol('k', commutative=True), log(Symbol('j', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('j', commutative=True), Integer(-1)), Pow(Symbol('k', commutative=True), Integer(2)))", "Mul(Symbol('k', commutative=True), exp(Mul(Symbol('j', commutative=True), Pow(Symbol('k', commutative=True), Integer(-1)))))", "exp(Add(Symbol('j', commutative=True), Symbol('k', commutative=True)))", "Mul(Symbol('j', commutative=True), Pow(Symbol('k', commutative=True), Integer(-1)), Add(log(Symbol('j', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\log{(- c + s)}", "variable": "c", "positive": "c \\log{(- c + s)} - c - s \\log{(c - s)}", "negatives": ["- c \\log{(- c + s)} + s \\log{(- c + s)} - s", "c (- s + \\log{(c)} - 1)", "\\frac{c (c + 2 \\log{(c)} - 2)}{2}", "- c s - \\cos{(c)}"], "srepr_premise_expression": "log(Add(Mul(Integer(-1), Symbol('c', commutative=True)), Symbol('s', commutative=True)))", "srepr_variable": "Symbol('c', commutative=True)", "srepr_positive": "Add(Mul(Symbol('c', commutative=True), log(Add(Mul(Integer(-1), Symbol('c', commutative=True)), Symbol('s', commutative=True)))), Mul(Integer(-1), Symbol('c', commutative=True)), Mul(Integer(-1), Symbol('s', commutative=True), log(Add(Symbol('c', commutative=True), Mul(Integer(-1), Symbol('s', commutative=True))))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('c', commutative=True), log(Add(Mul(Integer(-1), Symbol('c', commutative=True)), Symbol('s', commutative=True)))), Mul(Symbol('s', commutative=True), log(Add(Mul(Integer(-1), Symbol('c', commutative=True)), Symbol('s', commutative=True)))), Mul(Integer(-1), Symbol('s', commutative=True)))", "Mul(Symbol('c', commutative=True), Add(Mul(Integer(-1), Symbol('s', commutative=True)), log(Symbol('c', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('c', commutative=True), Add(Symbol('c', commutative=True), Mul(Integer(2), log(Symbol('c', commutative=True))), Integer(-2)))", "Add(Mul(Integer(-1), Symbol('c', commutative=True), Symbol('s', commutative=True)), Mul(Integer(-1), cos(Symbol('c', commutative=True))))"]}, {"premise_expression": "K^{Z} - P", "variable": "P", "positive": "\\frac{P (2 K^{Z} - P)}{2}", "negatives": ["\\frac{P (2 K Z + P)}{2}", "\\frac{P^{2} (K - Z)}{2}", "\\frac{P (K P - 2 Z)}{2}", "\\frac{K P}{Z} - \\frac{P^{2}}{2}"], "srepr_premise_expression": "Add(Pow(Symbol('K', commutative=True), Symbol('Z', commutative=True)), Mul(Integer(-1), Symbol('P', commutative=True)))", "srepr_variable": "Symbol('P', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Mul(Integer(2), Pow(Symbol('K', commutative=True), Symbol('Z', commutative=True))), Mul(Integer(-1), Symbol('P', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Mul(Integer(2), Symbol('K', commutative=True), Symbol('Z', commutative=True)), Symbol('P', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2)), Add(Symbol('K', commutative=True), Mul(Integer(-1), Symbol('Z', commutative=True))))", "Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Mul(Symbol('K', commutative=True), Symbol('P', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('Z', commutative=True))))", "Add(Mul(Symbol('K', commutative=True), Symbol('P', commutative=True), Pow(Symbol('Z', commutative=True), Integer(-1))), Mul(Integer(-1), Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2))))"]}, {"premise_expression": "- M + j", "variable": "j", "positive": "\\frac{j (- 2 M + j)}{2}", "negatives": ["\\frac{M (- M + 2 j)}{2}", "\\frac{j^{2} \\log{(M)}}{2}", "- \\cos{(M + j)}", "e^{M + j}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('M', commutative=True)), Symbol('j', commutative=True))", "srepr_variable": "Symbol('j', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('j', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('M', commutative=True)), Symbol('j', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('M', commutative=True), Add(Mul(Integer(-1), Symbol('M', commutative=True)), Mul(Integer(2), Symbol('j', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('j', commutative=True), Integer(2)), log(Symbol('M', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('M', commutative=True), Symbol('j', commutative=True))))", "exp(Add(Symbol('M', commutative=True), Symbol('j', commutative=True)))"]}, {"premise_expression": "\\frac{M - Q}{N}", "variable": "Q", "positive": "\\frac{Q (2 M - Q)}{2 N}", "negatives": ["- \\frac{Q (2 M - Q)}{2 N}", "\\frac{M (M - 2 Q)}{2 N}", "(M - Q) \\log{(N)}", "\\frac{Q (- 2 M - 2 N + Q)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('N', commutative=True), Integer(-1)), Add(Symbol('M', commutative=True), Mul(Integer(-1), Symbol('Q', commutative=True))))", "srepr_variable": "Symbol('Q', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('N', commutative=True), Integer(-1)), Symbol('Q', commutative=True), Add(Mul(Integer(2), Symbol('M', commutative=True)), Mul(Integer(-1), Symbol('Q', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), Rational(1, 2), Pow(Symbol('N', commutative=True), Integer(-1)), Symbol('Q', commutative=True), Add(Mul(Integer(2), Symbol('M', commutative=True)), Mul(Integer(-1), Symbol('Q', commutative=True))))", "Mul(Rational(1, 2), Symbol('M', commutative=True), Pow(Symbol('N', commutative=True), Integer(-1)), Add(Symbol('M', commutative=True), Mul(Integer(-1), Integer(2), Symbol('Q', commutative=True))))", "Mul(Add(Symbol('M', commutative=True), Mul(Integer(-1), Symbol('Q', commutative=True))), log(Symbol('N', commutative=True)))", "Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('M', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('N', commutative=True)), Symbol('Q', commutative=True)))"]}, {"premise_expression": "\\frac{Y}{k} - m", "variable": "k", "positive": "Y \\log{(k)} - k m", "negatives": ["\\frac{Y^{2}}{2 k} - Y m", "\\frac{Y m}{k} - \\frac{m^{2}}{2}", "\\frac{Y k}{m} - \\frac{k^{2}}{2}", "\\frac{k (2 Y + k m)}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('Y', commutative=True), Pow(Symbol('k', commutative=True), Integer(-1))), Mul(Integer(-1), Symbol('m', commutative=True)))", "srepr_variable": "Symbol('k', commutative=True)", "srepr_positive": "Add(Mul(Symbol('Y', commutative=True), log(Symbol('k', commutative=True))), Mul(Integer(-1), Symbol('k', commutative=True), Symbol('m', commutative=True)))", "srepr_negatives": ["Add(Mul(Rational(1, 2), Pow(Symbol('Y', commutative=True), Integer(2)), Pow(Symbol('k', commutative=True), Integer(-1))), Mul(Integer(-1), Symbol('Y', commutative=True), Symbol('m', commutative=True)))", "Add(Mul(Symbol('Y', commutative=True), Pow(Symbol('k', commutative=True), Integer(-1)), Symbol('m', commutative=True)), Mul(Integer(-1), Rational(1, 2), Pow(Symbol('m', commutative=True), Integer(2))))", "Add(Mul(Symbol('Y', commutative=True), Symbol('k', commutative=True), Pow(Symbol('m', commutative=True), Integer(-1))), Mul(Integer(-1), Rational(1, 2), Pow(Symbol('k', commutative=True), Integer(2))))", "Mul(Rational(1, 2), Symbol('k', commutative=True), Add(Mul(Integer(2), Symbol('Y', commutative=True)), Mul(Symbol('k', commutative=True), Symbol('m', commutative=True))))"]}, {"premise_expression": "f + u", "variable": "f", "positive": "\\frac{f (f + 2 u)}{2}", "negatives": ["\\frac{f (f - 2 u)}{2}", "\\frac{u (2 f + u)}{2}", "\\frac{f (f + 2 \\log{(u)})}{2}", "- f u + e^{f}"], "srepr_premise_expression": "Add(Symbol('f', commutative=True), Symbol('u', commutative=True))", "srepr_variable": "Symbol('f', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Symbol('f', commutative=True), Mul(Integer(2), Symbol('u', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Symbol('f', commutative=True), Mul(Integer(-1), Integer(2), Symbol('u', commutative=True))))", "Mul(Rational(1, 2), Symbol('u', commutative=True), Add(Mul(Integer(2), Symbol('f', commutative=True)), Symbol('u', commutative=True)))", "Mul(Rational(1, 2), Symbol('f', commutative=True), Add(Symbol('f', commutative=True), Mul(Integer(2), log(Symbol('u', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('f', commutative=True), Symbol('u', commutative=True)), exp(Symbol('f', commutative=True)))"]}, {"premise_expression": "Z \\sin{(c)}", "variable": "Z", "positive": "\\frac{Z^{2} \\sin{(c)}}{2}", "negatives": ["\\frac{Z^{2} c}{2}", "- Z \\cos{(c)}", "\\log{(Z)} \\sin{(c)}", "\\frac{Z (Z + 2 \\cos{(c)})}{2}"], "srepr_premise_expression": "Mul(Symbol('Z', commutative=True), sin(Symbol('c', commutative=True)))", "srepr_variable": "Symbol('Z', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('Z', commutative=True), Integer(2)), sin(Symbol('c', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('Z', commutative=True), Integer(2)), Symbol('c', commutative=True))", "Mul(Integer(-1), Symbol('Z', commutative=True), cos(Symbol('c', commutative=True)))", "Mul(log(Symbol('Z', commutative=True)), sin(Symbol('c', commutative=True)))", "Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Symbol('Z', commutative=True), Mul(Integer(2), cos(Symbol('c', commutative=True)))))"]}, {"premise_expression": "e^{\\frac{o}{D}}", "variable": "o", "positive": "D e^{\\frac{o}{D}}", "negatives": ["D e^{o}", "D o + e^{o}", "- \\cos{(D - o)}", "o (\\log{(\\frac{o}{D})} - 1)"], "srepr_premise_expression": "exp(Mul(Pow(Symbol('D', commutative=True), Integer(-1)), Symbol('o', commutative=True)))", "srepr_variable": "Symbol('o', commutative=True)", "srepr_positive": "Mul(Symbol('D', commutative=True), exp(Mul(Pow(Symbol('D', commutative=True), Integer(-1)), Symbol('o', commutative=True))))", "srepr_negatives": ["Mul(Symbol('D', commutative=True), exp(Symbol('o', commutative=True)))", "Add(Mul(Symbol('D', commutative=True), Symbol('o', commutative=True)), exp(Symbol('o', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('D', commutative=True), Mul(Integer(-1), Symbol('o', commutative=True)))))", "Mul(Symbol('o', commutative=True), Add(log(Mul(Pow(Symbol('D', commutative=True), Integer(-1)), Symbol('o', commutative=True))), Integer(-1)))"]}, {"premise_expression": "B C - P", "variable": "B", "positive": "\\frac{B (B C - 2 P)}{2}", "negatives": ["\\frac{C (B C - 2 P)}{2}", "\\frac{P (2 B C - P)}{2}", "\\frac{B^{2} C}{2 P}", "- \\frac{B (B - 2 P)}{2 C}"], "srepr_premise_expression": "Add(Mul(Symbol('B', commutative=True), Symbol('C', commutative=True)), Mul(Integer(-1), Symbol('P', commutative=True)))", "srepr_variable": "Symbol('B', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('B', commutative=True), Add(Mul(Symbol('B', commutative=True), Symbol('C', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('P', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('C', commutative=True), Add(Mul(Symbol('B', commutative=True), Symbol('C', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('P', commutative=True))))", "Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Mul(Integer(2), Symbol('B', commutative=True), Symbol('C', commutative=True)), Mul(Integer(-1), Symbol('P', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('B', commutative=True), Integer(2)), Symbol('C', commutative=True), Pow(Symbol('P', commutative=True), Integer(-1)))", "Mul(Integer(-1), Rational(1, 2), Symbol('B', commutative=True), Pow(Symbol('C', commutative=True), Integer(-1)), Add(Symbol('B', commutative=True), Mul(Integer(-1), Integer(2), Symbol('P', commutative=True))))"]}, {"premise_expression": "- h + o", "variable": "o", "positive": "\\frac{o (- 2 h + o)}{2}", "negatives": ["\\frac{h (- h + 2 o)}{2}", "e^{- h + o}", "- \\cos{(h + o)}", "\\frac{o (o + 2 e^{h})}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('h', commutative=True)), Symbol('o', commutative=True))", "srepr_variable": "Symbol('o', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('h', commutative=True)), Symbol('o', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('h', commutative=True), Add(Mul(Integer(-1), Symbol('h', commutative=True)), Mul(Integer(2), Symbol('o', commutative=True))))", "exp(Add(Mul(Integer(-1), Symbol('h', commutative=True)), Symbol('o', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('h', commutative=True), Symbol('o', commutative=True))))", "Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Symbol('o', commutative=True), Mul(Integer(2), exp(Symbol('h', commutative=True)))))"]}, {"premise_expression": "e^{P + a}", "variable": "P", "positive": "e^{P + a}", "negatives": ["\\frac{P (P + 2 a)}{2}", "\\frac{P^{2}}{2 a}", "- P a + e^{P}", "\\frac{P^{2} e^{a}}{2}"], "srepr_premise_expression": "exp(Add(Symbol('P', commutative=True), Symbol('a', commutative=True)))", "srepr_variable": "Symbol('P', commutative=True)", "srepr_positive": "exp(Add(Symbol('P', commutative=True), Symbol('a', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Symbol('P', commutative=True), Mul(Integer(2), Symbol('a', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2)), Pow(Symbol('a', commutative=True), Integer(-1)))", "Add(Mul(Integer(-1), Symbol('P', commutative=True), Symbol('a', commutative=True)), exp(Symbol('P', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2)), exp(Symbol('a', commutative=True)))"]}, {"premise_expression": "- p + \\log{(b)}", "variable": "p", "positive": "\\frac{p (- p + 2 \\log{(b)})}{2}", "negatives": ["\\frac{p (- p + 2 \\sin{(b)})}{2}", "b (- p + \\log{(b)} - 1)", "\\frac{p (2 b - p)}{2}", "b \\operatorname{Si}{(\\frac{b}{p})} + p \\cos{(\\frac{b}{p})}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('p', commutative=True)), log(Symbol('b', commutative=True)))", "srepr_variable": "Symbol('p', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Mul(Integer(-1), Symbol('p', commutative=True)), Mul(Integer(2), log(Symbol('b', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Mul(Integer(-1), Symbol('p', commutative=True)), Mul(Integer(2), sin(Symbol('b', commutative=True)))))", "Mul(Symbol('b', commutative=True), Add(Mul(Integer(-1), Symbol('p', commutative=True)), log(Symbol('b', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Mul(Integer(2), Symbol('b', commutative=True)), Mul(Integer(-1), Symbol('p', commutative=True))))", "Add(Mul(Symbol('b', commutative=True), Si(Mul(Symbol('b', commutative=True), Pow(Symbol('p', commutative=True), Integer(-1))))), Mul(Symbol('p', commutative=True), cos(Mul(Symbol('b', commutative=True), Pow(Symbol('p', commutative=True), Integer(-1))))))"]}, {"premise_expression": "S + a", "variable": "a", "positive": "\\frac{a (2 S + a)}{2}", "negatives": ["\\frac{S (S + 2 a)}{2}", "- \\cos{(S + a)}", "- e^{S - a}", "a (\\log{(\\frac{S}{a})} + 1)"], "srepr_premise_expression": "Add(Symbol('S', commutative=True), Symbol('a', commutative=True))", "srepr_variable": "Symbol('a', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('a', commutative=True), Add(Mul(Integer(2), Symbol('S', commutative=True)), Symbol('a', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('S', commutative=True), Add(Symbol('S', commutative=True), Mul(Integer(2), Symbol('a', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('S', commutative=True), Symbol('a', commutative=True))))", "Mul(Integer(-1), exp(Add(Symbol('S', commutative=True), Mul(Integer(-1), Symbol('a', commutative=True)))))", "Mul(Symbol('a', commutative=True), Add(log(Mul(Symbol('S', commutative=True), Pow(Symbol('a', commutative=True), Integer(-1)))), Integer(1)))"]}, {"premise_expression": "\\log{(\\frac{q}{W})}", "variable": "q", "positive": "q (\\log{(\\frac{q}{W})} - 1)", "negatives": ["W (\\log{(\\frac{q}{W})} + 1)", "W q (\\log{(q)} - 1)", "\\frac{q (q + 2 \\cos{(W)})}{2}", "\\frac{q (- q + 2 \\log{(W)})}{2}"], "srepr_premise_expression": "log(Mul(Pow(Symbol('W', commutative=True), Integer(-1)), Symbol('q', commutative=True)))", "srepr_variable": "Symbol('q', commutative=True)", "srepr_positive": "Mul(Symbol('q', commutative=True), Add(log(Mul(Pow(Symbol('W', commutative=True), Integer(-1)), Symbol('q', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('W', commutative=True), Add(log(Mul(Pow(Symbol('W', commutative=True), Integer(-1)), Symbol('q', commutative=True))), Integer(1)))", "Mul(Symbol('W', commutative=True), Symbol('q', commutative=True), Add(log(Symbol('q', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('q', commutative=True), Add(Symbol('q', commutative=True), Mul(Integer(2), cos(Symbol('W', commutative=True)))))", "Mul(Rational(1, 2), Symbol('q', commutative=True), Add(Mul(Integer(-1), Symbol('q', commutative=True)), Mul(Integer(2), log(Symbol('W', commutative=True)))))"]}, {"premise_expression": "\\log{(- E + W)}", "variable": "W", "positive": "- E \\log{(- E + W)} + W \\log{(- E + W)} - W", "negatives": ["E \\log{(- E + W)} - E - W \\log{(E - W)}", "W (\\log{(E W)} - 1)", "E W (\\log{(W)} - 1)", "\\sin{(E + W)}"], "srepr_premise_expression": "log(Add(Mul(Integer(-1), Symbol('E', commutative=True)), Symbol('W', commutative=True)))", "srepr_variable": "Symbol('W', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('E', commutative=True), log(Add(Mul(Integer(-1), Symbol('E', commutative=True)), Symbol('W', commutative=True)))), Mul(Symbol('W', commutative=True), log(Add(Mul(Integer(-1), Symbol('E', commutative=True)), Symbol('W', commutative=True)))), Mul(Integer(-1), Symbol('W', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('E', commutative=True), log(Add(Mul(Integer(-1), Symbol('E', commutative=True)), Symbol('W', commutative=True)))), Mul(Integer(-1), Symbol('E', commutative=True)), Mul(Integer(-1), Symbol('W', commutative=True), log(Add(Symbol('E', commutative=True), Mul(Integer(-1), Symbol('W', commutative=True))))))", "Mul(Symbol('W', commutative=True), Add(log(Mul(Symbol('E', commutative=True), Symbol('W', commutative=True))), Integer(-1)))", "Mul(Symbol('E', commutative=True), Symbol('W', commutative=True), Add(log(Symbol('W', commutative=True)), Integer(-1)))", "sin(Add(Symbol('E', commutative=True), Symbol('W', commutative=True)))"]}, {"premise_expression": "o (F - Y)", "variable": "o", "positive": "\\frac{o^{2} (F - Y)}{2}", "negatives": ["\\frac{Y o (2 F - Y)}{2}", "\\frac{F o (F - 2 Y)}{2}", "\\frac{o (2 F^{Y} - o)}{2}", "\\frac{Y o (2 F + o)}{2}"], "srepr_premise_expression": "Mul(Symbol('o', commutative=True), Add(Symbol('F', commutative=True), Mul(Integer(-1), Symbol('Y', commutative=True))))", "srepr_variable": "Symbol('o', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('o', commutative=True), Integer(2)), Add(Symbol('F', commutative=True), Mul(Integer(-1), Symbol('Y', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('Y', commutative=True), Symbol('o', commutative=True), Add(Mul(Integer(2), Symbol('F', commutative=True)), Mul(Integer(-1), Symbol('Y', commutative=True))))", "Mul(Rational(1, 2), Symbol('F', commutative=True), Symbol('o', commutative=True), Add(Symbol('F', commutative=True), Mul(Integer(-1), Integer(2), Symbol('Y', commutative=True))))", "Mul(Rational(1, 2), Symbol('o', commutative=True), Add(Mul(Integer(2), Pow(Symbol('F', commutative=True), Symbol('Y', commutative=True))), Mul(Integer(-1), Symbol('o', commutative=True))))", "Mul(Rational(1, 2), Symbol('Y', commutative=True), Symbol('o', commutative=True), Add(Mul(Integer(2), Symbol('F', commutative=True)), Symbol('o', commutative=True)))"]}, {"premise_expression": "\\cos{(H + h)}", "variable": "H", "positive": "\\sin{(H + h)}", "negatives": ["- \\cos{(H + h)}", "\\frac{H^{2}}{2 h}", "- \\frac{\\cos{(H)}}{h}", "H (\\log{(\\frac{h}{H})} + 1)"], "srepr_premise_expression": "cos(Add(Symbol('H', commutative=True), Symbol('h', commutative=True)))", "srepr_variable": "Symbol('H', commutative=True)", "srepr_positive": "sin(Add(Symbol('H', commutative=True), Symbol('h', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('H', commutative=True), Symbol('h', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('H', commutative=True), Integer(2)), Pow(Symbol('h', commutative=True), Integer(-1)))", "Mul(Integer(-1), Pow(Symbol('h', commutative=True), Integer(-1)), cos(Symbol('H', commutative=True)))", "Mul(Symbol('H', commutative=True), Add(log(Mul(Pow(Symbol('H', commutative=True), Integer(-1)), Symbol('h', commutative=True))), Integer(1)))"]}, {"premise_expression": "\\cos{(P - S)}", "variable": "P", "positive": "\\sin{(P - S)}", "negatives": ["- \\sin{(P - S)}", "e^{P - S}", "\\frac{P (P - 2 S)}{2}", "\\log{(P)} \\cos{(S)}"], "srepr_premise_expression": "cos(Add(Symbol('P', commutative=True), Mul(Integer(-1), Symbol('S', commutative=True))))", "srepr_variable": "Symbol('P', commutative=True)", "srepr_positive": "sin(Add(Symbol('P', commutative=True), Mul(Integer(-1), Symbol('S', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('P', commutative=True), Mul(Integer(-1), Symbol('S', commutative=True)))))", "exp(Add(Symbol('P', commutative=True), Mul(Integer(-1), Symbol('S', commutative=True))))", "Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Symbol('P', commutative=True), Mul(Integer(-1), Integer(2), Symbol('S', commutative=True))))", "Mul(log(Symbol('P', commutative=True)), cos(Symbol('S', commutative=True)))"]}, {"premise_expression": "P + \\log{(R)}", "variable": "P", "positive": "\\frac{P (P + 2 \\log{(R)})}{2}", "negatives": ["R (P + \\log{(R)} - 1)", "\\frac{P^{2} e^{R}}{2}", "\\log{(P)} \\log{(R)}", "\\sin{(P + R)}"], "srepr_premise_expression": "Add(Symbol('P', commutative=True), log(Symbol('R', commutative=True)))", "srepr_variable": "Symbol('P', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Symbol('P', commutative=True), Mul(Integer(2), log(Symbol('R', commutative=True)))))", "srepr_negatives": ["Mul(Symbol('R', commutative=True), Add(Symbol('P', commutative=True), log(Symbol('R', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('P', commutative=True), Integer(2)), exp(Symbol('R', commutative=True)))", "Mul(log(Symbol('P', commutative=True)), log(Symbol('R', commutative=True)))", "sin(Add(Symbol('P', commutative=True), Symbol('R', commutative=True)))"]}, {"premise_expression": "\\frac{\\cos{(V)}}{l}", "variable": "V", "positive": "\\frac{\\sin{(V)}}{l}", "negatives": ["\\sin{(V - l)}", "\\cos{(V - l)}", "\\log{(l)} \\cos{(V)}", "\\frac{V (- V + 2 l)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('l', commutative=True), Integer(-1)), cos(Symbol('V', commutative=True)))", "srepr_variable": "Symbol('V', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('l', commutative=True), Integer(-1)), sin(Symbol('V', commutative=True)))", "srepr_negatives": ["sin(Add(Symbol('V', commutative=True), Mul(Integer(-1), Symbol('l', commutative=True))))", "cos(Add(Symbol('V', commutative=True), Mul(Integer(-1), Symbol('l', commutative=True))))", "Mul(log(Symbol('l', commutative=True)), cos(Symbol('V', commutative=True)))", "Mul(Rational(1, 2), Symbol('V', commutative=True), Add(Mul(Integer(-1), Symbol('V', commutative=True)), Mul(Integer(2), Symbol('l', commutative=True))))"]}, {"premise_expression": "N + p", "variable": "p", "positive": "\\frac{p (2 N + p)}{2}", "negatives": ["\\frac{p (2 N - p)}{2}", "\\frac{N (N + 2 p)}{2}", "\\frac{p^{2}}{2 N}", "N \\log{(p)}"], "srepr_premise_expression": "Add(Symbol('N', commutative=True), Symbol('p', commutative=True))", "srepr_variable": "Symbol('p', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Mul(Integer(2), Symbol('N', commutative=True)), Symbol('p', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Mul(Integer(2), Symbol('N', commutative=True)), Mul(Integer(-1), Symbol('p', commutative=True))))", "Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Symbol('N', commutative=True), Mul(Integer(2), Symbol('p', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('N', commutative=True), Integer(-1)), Pow(Symbol('p', commutative=True), Integer(2)))", "Mul(Symbol('N', commutative=True), log(Symbol('p', commutative=True)))"]}, {"premise_expression": "\\log{(Y g)}", "variable": "Y", "positive": "Y (\\log{(Y g)} - 1)", "negatives": ["g (\\log{(Y g)} - 1)", "Y (g + \\log{(Y)} - 1)", "\\frac{Y^{2} \\log{(g)}}{2}", "\\frac{Y^{2} \\sin{(g)}}{2}"], "srepr_premise_expression": "log(Mul(Symbol('Y', commutative=True), Symbol('g', commutative=True)))", "srepr_variable": "Symbol('Y', commutative=True)", "srepr_positive": "Mul(Symbol('Y', commutative=True), Add(log(Mul(Symbol('Y', commutative=True), Symbol('g', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('g', commutative=True), Add(log(Mul(Symbol('Y', commutative=True), Symbol('g', commutative=True))), Integer(-1)))", "Mul(Symbol('Y', commutative=True), Add(Symbol('g', commutative=True), log(Symbol('Y', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('Y', commutative=True), Integer(2)), log(Symbol('g', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('Y', commutative=True), Integer(2)), sin(Symbol('g', commutative=True)))"]}, {"premise_expression": "p (s + z)", "variable": "z", "positive": "\\frac{p z (2 s + z)}{2}", "negatives": ["\\frac{p^{2} (s + z)}{2}", "\\frac{p s (s + 2 z)}{2}", "\\frac{z (2 s + z)}{2 p}", "\\frac{p z^{2}}{2 s}"], "srepr_premise_expression": "Mul(Symbol('p', commutative=True), Add(Symbol('s', commutative=True), Symbol('z', commutative=True)))", "srepr_variable": "Symbol('z', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('p', commutative=True), Symbol('z', commutative=True), Add(Mul(Integer(2), Symbol('s', commutative=True)), Symbol('z', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('p', commutative=True), Integer(2)), Add(Symbol('s', commutative=True), Symbol('z', commutative=True)))", "Mul(Rational(1, 2), Symbol('p', commutative=True), Symbol('s', commutative=True), Add(Symbol('s', commutative=True), Mul(Integer(2), Symbol('z', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('p', commutative=True), Integer(-1)), Symbol('z', commutative=True), Add(Mul(Integer(2), Symbol('s', commutative=True)), Symbol('z', commutative=True)))", "Mul(Rational(1, 2), Symbol('p', commutative=True), Pow(Symbol('s', commutative=True), Integer(-1)), Pow(Symbol('z', commutative=True), Integer(2)))"]}, {"premise_expression": "P - w", "variable": "w", "positive": "\\frac{w (2 P - w)}{2}", "negatives": ["\\frac{w (- 2 P + w)}{2}", "\\frac{P (P - 2 w)}{2}", "\\sin{(P + w)}", "w (\\log{(\\frac{w}{P})} - 1)"], "srepr_premise_expression": "Add(Symbol('P', commutative=True), Mul(Integer(-1), Symbol('w', commutative=True)))", "srepr_variable": "Symbol('w', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('w', commutative=True), Add(Mul(Integer(2), Symbol('P', commutative=True)), Mul(Integer(-1), Symbol('w', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('w', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('P', commutative=True)), Symbol('w', commutative=True)))", "Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Symbol('P', commutative=True), Mul(Integer(-1), Integer(2), Symbol('w', commutative=True))))", "sin(Add(Symbol('P', commutative=True), Symbol('w', commutative=True)))", "Mul(Symbol('w', commutative=True), Add(log(Mul(Pow(Symbol('P', commutative=True), Integer(-1)), Symbol('w', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\frac{v}{z}", "variable": "z", "positive": "v \\log{(z)}", "negatives": ["\\frac{v^{2}}{2 z}", "- v z + e^{z}", "- \\cos{(v + z)}", "\\log{(z)} \\cos{(v)}"], "srepr_premise_expression": "Mul(Symbol('v', commutative=True), Pow(Symbol('z', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('z', commutative=True)", "srepr_positive": "Mul(Symbol('v', commutative=True), log(Symbol('z', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('v', commutative=True), Integer(2)), Pow(Symbol('z', commutative=True), Integer(-1)))", "Add(Mul(Integer(-1), Symbol('v', commutative=True), Symbol('z', commutative=True)), exp(Symbol('z', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('v', commutative=True), Symbol('z', commutative=True))))", "Mul(log(Symbol('z', commutative=True)), cos(Symbol('v', commutative=True)))"]}, {"premise_expression": "\\frac{\\sin{(m)}}{z}", "variable": "z", "positive": "\\log{(z)} \\sin{(m)}", "negatives": ["\\frac{\\sin{(z)}}{m}", "- \\frac{\\cos{(m)}}{z}", "\\frac{z^{2} \\log{(m)}}{2}", "z (\\log{(m z)} - 1)"], "srepr_premise_expression": "Mul(Pow(Symbol('z', commutative=True), Integer(-1)), sin(Symbol('m', commutative=True)))", "srepr_variable": "Symbol('z', commutative=True)", "srepr_positive": "Mul(log(Symbol('z', commutative=True)), sin(Symbol('m', commutative=True)))", "srepr_negatives": ["Mul(Pow(Symbol('m', commutative=True), Integer(-1)), sin(Symbol('z', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('z', commutative=True), Integer(-1)), cos(Symbol('m', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('z', commutative=True), Integer(2)), log(Symbol('m', commutative=True)))", "Mul(Symbol('z', commutative=True), Add(log(Mul(Symbol('m', commutative=True), Symbol('z', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\log{(Z^{G})}", "variable": "Z", "positive": "Z (- G + \\log{(Z^{G})})", "negatives": ["\\frac{Z (- Z + 2 \\sin{(G)})}{2}", "G Z + e^{Z}", "\\frac{G^{2} \\log{(Z)}}{2}", "\\sin{(G + Z)}"], "srepr_premise_expression": "log(Pow(Symbol('Z', commutative=True), Symbol('G', commutative=True)))", "srepr_variable": "Symbol('Z', commutative=True)", "srepr_positive": "Mul(Symbol('Z', commutative=True), Add(Mul(Integer(-1), Symbol('G', commutative=True)), log(Pow(Symbol('Z', commutative=True), Symbol('G', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Mul(Integer(-1), Symbol('Z', commutative=True)), Mul(Integer(2), sin(Symbol('G', commutative=True)))))", "Add(Mul(Symbol('G', commutative=True), Symbol('Z', commutative=True)), exp(Symbol('Z', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('G', commutative=True), Integer(2)), log(Symbol('Z', commutative=True)))", "sin(Add(Symbol('G', commutative=True), Symbol('Z', commutative=True)))"]}, {"premise_expression": "K (h + t)", "variable": "K", "positive": "\\frac{K^{2} (h + t)}{2}", "negatives": ["\\frac{K t (2 h + t)}{2}", "\\frac{K h (h + 2 t)}{2}", "\\frac{K h (K + 2 t)}{2}", "\\frac{K^{2} h}{2 t}"], "srepr_premise_expression": "Mul(Symbol('K', commutative=True), Add(Symbol('h', commutative=True), Symbol('t', commutative=True)))", "srepr_variable": "Symbol('K', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('K', commutative=True), Integer(2)), Add(Symbol('h', commutative=True), Symbol('t', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('K', commutative=True), Symbol('t', commutative=True), Add(Mul(Integer(2), Symbol('h', commutative=True)), Symbol('t', commutative=True)))", "Mul(Rational(1, 2), Symbol('K', commutative=True), Symbol('h', commutative=True), Add(Symbol('h', commutative=True), Mul(Integer(2), Symbol('t', commutative=True))))", "Mul(Rational(1, 2), Symbol('K', commutative=True), Symbol('h', commutative=True), Add(Symbol('K', commutative=True), Mul(Integer(2), Symbol('t', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('K', commutative=True), Integer(2)), Symbol('h', commutative=True), Pow(Symbol('t', commutative=True), Integer(-1)))"]}, {"premise_expression": "\\frac{r}{J}", "variable": "r", "positive": "\\frac{r^{2}}{2 J}", "negatives": ["r \\log{(J)}", "\\frac{r (- 2 J + r)}{2}", "- e^{J - r}", "\\frac{r (- r + 2 e^{J})}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('J', commutative=True), Integer(-1)), Symbol('r', commutative=True))", "srepr_variable": "Symbol('r', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('J', commutative=True), Integer(-1)), Pow(Symbol('r', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('r', commutative=True), log(Symbol('J', commutative=True)))", "Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('J', commutative=True)), Symbol('r', commutative=True)))", "Mul(Integer(-1), exp(Add(Symbol('J', commutative=True), Mul(Integer(-1), Symbol('r', commutative=True)))))", "Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(-1), Symbol('r', commutative=True)), Mul(Integer(2), exp(Symbol('J', commutative=True)))))"]}, {"premise_expression": "P + Q c", "variable": "Q", "positive": "\\frac{Q (2 P + Q c)}{2}", "negatives": ["\\frac{c (2 P + Q c)}{2}", "\\frac{Q (P Q + 2 c)}{2}", "\\frac{P (P + 2 Q c)}{2}", "\\frac{Q (- 2 P + Q + 2 c)}{2}"], "srepr_premise_expression": "Add(Symbol('P', commutative=True), Mul(Symbol('Q', commutative=True), Symbol('c', commutative=True)))", "srepr_variable": "Symbol('Q', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Mul(Integer(2), Symbol('P', commutative=True)), Mul(Symbol('Q', commutative=True), Symbol('c', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('c', commutative=True), Add(Mul(Integer(2), Symbol('P', commutative=True)), Mul(Symbol('Q', commutative=True), Symbol('c', commutative=True))))", "Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Mul(Symbol('P', commutative=True), Symbol('Q', commutative=True)), Mul(Integer(2), Symbol('c', commutative=True))))", "Mul(Rational(1, 2), Symbol('P', commutative=True), Add(Symbol('P', commutative=True), Mul(Integer(2), Symbol('Q', commutative=True), Symbol('c', commutative=True))))", "Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('P', commutative=True)), Symbol('Q', commutative=True), Mul(Integer(2), Symbol('c', commutative=True))))"]}, {"premise_expression": "\\log{(Z - v)}", "variable": "Z", "positive": "Z \\log{(Z - v)} - Z - v \\log{(Z - v)}", "negatives": ["- Z \\log{(- Z + v)} + v \\log{(Z - v)} - v", "Z e^{\\frac{v}{Z}} - v \\operatorname{Ei}{(\\frac{v}{Z})}", "- Z v - \\cos{(Z)}", "\\frac{Z (Z + 2 \\cos{(v)})}{2}"], "srepr_premise_expression": "log(Add(Symbol('Z', commutative=True), Mul(Integer(-1), Symbol('v', commutative=True))))", "srepr_variable": "Symbol('Z', commutative=True)", "srepr_positive": "Add(Mul(Symbol('Z', commutative=True), log(Add(Symbol('Z', commutative=True), Mul(Integer(-1), Symbol('v', commutative=True))))), Mul(Integer(-1), Symbol('Z', commutative=True)), Mul(Integer(-1), Symbol('v', commutative=True), log(Add(Symbol('Z', commutative=True), Mul(Integer(-1), Symbol('v', commutative=True))))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('Z', commutative=True), log(Add(Mul(Integer(-1), Symbol('Z', commutative=True)), Symbol('v', commutative=True)))), Mul(Symbol('v', commutative=True), log(Add(Symbol('Z', commutative=True), Mul(Integer(-1), Symbol('v', commutative=True))))), Mul(Integer(-1), Symbol('v', commutative=True)))", "Add(Mul(Symbol('Z', commutative=True), exp(Mul(Pow(Symbol('Z', commutative=True), Integer(-1)), Symbol('v', commutative=True)))), Mul(Integer(-1), Symbol('v', commutative=True), Ei(Mul(Pow(Symbol('Z', commutative=True), Integer(-1)), Symbol('v', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('Z', commutative=True), Symbol('v', commutative=True)), Mul(Integer(-1), cos(Symbol('Z', commutative=True))))", "Mul(Rational(1, 2), Symbol('Z', commutative=True), Add(Symbol('Z', commutative=True), Mul(Integer(2), cos(Symbol('v', commutative=True)))))"]}, {"premise_expression": "- L + s", "variable": "s", "positive": "\\frac{s (- 2 L + s)}{2}", "negatives": ["\\frac{L (- L + 2 s)}{2}", "\\frac{s^{2} \\log{(L)}}{2}", "\\frac{s (s + 2 e^{L})}{2}", "\\frac{s (- s + 2 \\cos{(L)})}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('L', commutative=True)), Symbol('s', commutative=True))", "srepr_variable": "Symbol('s', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('s', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('L', commutative=True)), Symbol('s', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Mul(Integer(-1), Symbol('L', commutative=True)), Mul(Integer(2), Symbol('s', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('s', commutative=True), Integer(2)), log(Symbol('L', commutative=True)))", "Mul(Rational(1, 2), Symbol('s', commutative=True), Add(Symbol('s', commutative=True), Mul(Integer(2), exp(Symbol('L', commutative=True)))))", "Mul(Rational(1, 2), Symbol('s', commutative=True), Add(Mul(Integer(-1), Symbol('s', commutative=True)), Mul(Integer(2), cos(Symbol('L', commutative=True)))))"]}, {"premise_expression": "\\frac{e^{l}}{V}", "variable": "V", "positive": "e^{l} \\log{(V)}", "negatives": ["l \\log{(V)}", "e^{V + l}", "V l + e^{V}", "V l + \\sin{(V)}"], "srepr_premise_expression": "Mul(Pow(Symbol('V', commutative=True), Integer(-1)), exp(Symbol('l', commutative=True)))", "srepr_variable": "Symbol('V', commutative=True)", "srepr_positive": "Mul(exp(Symbol('l', commutative=True)), log(Symbol('V', commutative=True)))", "srepr_negatives": ["Mul(Symbol('l', commutative=True), log(Symbol('V', commutative=True)))", "exp(Add(Symbol('V', commutative=True), Symbol('l', commutative=True)))", "Add(Mul(Symbol('V', commutative=True), Symbol('l', commutative=True)), exp(Symbol('V', commutative=True)))", "Add(Mul(Symbol('V', commutative=True), Symbol('l', commutative=True)), sin(Symbol('V', commutative=True)))"]}, {"premise_expression": "R + \\sin{(F)}", "variable": "R", "positive": "\\frac{R (R + 2 \\sin{(F)})}{2}", "negatives": ["\\frac{R (R + 2 \\log{(F)})}{2}", "\\frac{R^{2} \\log{(F)}}{2}", "F R - \\cos{(F)}", "R (F + \\log{(R)} - 1)"], "srepr_premise_expression": "Add(Symbol('R', commutative=True), sin(Symbol('F', commutative=True)))", "srepr_variable": "Symbol('R', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('R', commutative=True), Add(Symbol('R', commutative=True), Mul(Integer(2), sin(Symbol('F', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('R', commutative=True), Add(Symbol('R', commutative=True), Mul(Integer(2), log(Symbol('F', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('R', commutative=True), Integer(2)), log(Symbol('F', commutative=True)))", "Add(Mul(Symbol('F', commutative=True), Symbol('R', commutative=True)), Mul(Integer(-1), cos(Symbol('F', commutative=True))))", "Mul(Symbol('R', commutative=True), Add(Symbol('F', commutative=True), log(Symbol('R', commutative=True)), Integer(-1)))"]}, {"premise_expression": "K + m", "variable": "m", "positive": "\\frac{m (2 K + m)}{2}", "negatives": ["\\frac{K (K + 2 m)}{2}", "\\frac{m^{2} \\log{(K)}}{2}", "- \\frac{\\cos{(m)}}{K}", "K e^{m}"], "srepr_premise_expression": "Add(Symbol('K', commutative=True), Symbol('m', commutative=True))", "srepr_variable": "Symbol('m', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Mul(Integer(2), Symbol('K', commutative=True)), Symbol('m', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Symbol('K', commutative=True), Mul(Integer(2), Symbol('m', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('m', commutative=True), Integer(2)), log(Symbol('K', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('K', commutative=True), Integer(-1)), cos(Symbol('m', commutative=True)))", "Mul(Symbol('K', commutative=True), exp(Symbol('m', commutative=True)))"]}, {"premise_expression": "I - Q + s", "variable": "I", "positive": "I (\\frac{I}{2} - Q + s)", "negatives": ["\\frac{I (I - 2 Q - 2 s)}{2}", "\\frac{Q (2 I - Q + 2 s)}{2}", "\\frac{s (2 I - 2 Q + s)}{2}", "\\frac{I^{2} (- Q + s)}{2}"], "srepr_premise_expression": "Add(Symbol('I', commutative=True), Mul(Integer(-1), Symbol('Q', commutative=True)), Symbol('s', commutative=True))", "srepr_variable": "Symbol('I', commutative=True)", "srepr_positive": "Mul(Symbol('I', commutative=True), Add(Mul(Rational(1, 2), Symbol('I', commutative=True)), Mul(Integer(-1), Symbol('Q', commutative=True)), Symbol('s', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('I', commutative=True), Add(Symbol('I', commutative=True), Mul(Integer(-1), Integer(2), Symbol('Q', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('s', commutative=True))))", "Mul(Rational(1, 2), Symbol('Q', commutative=True), Add(Mul(Integer(2), Symbol('I', commutative=True)), Mul(Integer(-1), Symbol('Q', commutative=True)), Mul(Integer(2), Symbol('s', commutative=True))))", "Mul(Rational(1, 2), Symbol('s', commutative=True), Add(Mul(Integer(2), Symbol('I', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('Q', commutative=True)), Symbol('s', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('I', commutative=True), Integer(2)), Add(Mul(Integer(-1), Symbol('Q', commutative=True)), Symbol('s', commutative=True)))"]}, {"premise_expression": "- b + \\frac{j}{U}", "variable": "U", "positive": "- U b + j \\log{(U)}", "negatives": ["(b + j) \\log{(U)}", "b^{j} \\log{(U)}", "- b j + \\frac{j^{2}}{2 U}", "\\frac{U (U + 2 j)}{2 b}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('b', commutative=True)), Mul(Pow(Symbol('U', commutative=True), Integer(-1)), Symbol('j', commutative=True)))", "srepr_variable": "Symbol('U', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('U', commutative=True), Symbol('b', commutative=True)), Mul(Symbol('j', commutative=True), log(Symbol('U', commutative=True))))", "srepr_negatives": ["Mul(Add(Symbol('b', commutative=True), Symbol('j', commutative=True)), log(Symbol('U', commutative=True)))", "Mul(Pow(Symbol('b', commutative=True), Symbol('j', commutative=True)), log(Symbol('U', commutative=True)))", "Add(Mul(Integer(-1), Symbol('b', commutative=True), Symbol('j', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('U', commutative=True), Integer(-1)), Pow(Symbol('j', commutative=True), Integer(2))))", "Mul(Rational(1, 2), Symbol('U', commutative=True), Pow(Symbol('b', commutative=True), Integer(-1)), Add(Symbol('U', commutative=True), Mul(Integer(2), Symbol('j', commutative=True))))"]}, {"premise_expression": "- K + k", "variable": "k", "positive": "\\frac{k (- 2 K + k)}{2}", "negatives": ["\\frac{k (2 K - k)}{2}", "\\frac{K (- K + 2 k)}{2}", "\\frac{k^{2} \\log{(K)}}{2}", "\\sin{(K + k)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('K', commutative=True)), Symbol('k', commutative=True))", "srepr_variable": "Symbol('k', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('k', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('K', commutative=True)), Symbol('k', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('k', commutative=True), Add(Mul(Integer(2), Symbol('K', commutative=True)), Mul(Integer(-1), Symbol('k', commutative=True))))", "Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Mul(Integer(-1), Symbol('K', commutative=True)), Mul(Integer(2), Symbol('k', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('k', commutative=True), Integer(2)), log(Symbol('K', commutative=True)))", "sin(Add(Symbol('K', commutative=True), Symbol('k', commutative=True)))"]}, {"premise_expression": "C D", "variable": "C", "positive": "\\frac{C^{2} D}{2}", "negatives": ["\\frac{C D^{2}}{2}", "\\frac{C^{2} \\log{(D)}}{2}", "\\sin{(C - D)}", "e^{C - D}"], "srepr_premise_expression": "Mul(Symbol('C', commutative=True), Symbol('D', commutative=True))", "srepr_variable": "Symbol('C', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2)), Symbol('D', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('C', commutative=True), Pow(Symbol('D', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('C', commutative=True), Integer(2)), log(Symbol('D', commutative=True)))", "sin(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('D', commutative=True))))", "exp(Add(Symbol('C', commutative=True), Mul(Integer(-1), Symbol('D', commutative=True))))"]}, {"premise_expression": "L b", "variable": "L", "positive": "\\frac{L^{2} b}{2}", "negatives": ["\\frac{L b^{2}}{2}", "\\frac{L (L - 2 b)}{2}", "b \\sin{(L)}", "- b \\cos{(L)}"], "srepr_premise_expression": "Mul(Symbol('L', commutative=True), Symbol('b', commutative=True))", "srepr_variable": "Symbol('L', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(2)), Symbol('b', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('L', commutative=True), Pow(Symbol('b', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Symbol('L', commutative=True), Mul(Integer(-1), Integer(2), Symbol('b', commutative=True))))", "Mul(Symbol('b', commutative=True), sin(Symbol('L', commutative=True)))", "Mul(Integer(-1), Symbol('b', commutative=True), cos(Symbol('L', commutative=True)))"]}, {"premise_expression": "K - M", "variable": "M", "positive": "\\frac{M (2 K - M)}{2}", "negatives": ["\\frac{K (K - 2 M)}{2}", "\\frac{M^{2} \\log{(K)}}{2}", "\\frac{M^{2} \\sin{(K)}}{2}", "\\cos{(K - M)}"], "srepr_premise_expression": "Add(Symbol('K', commutative=True), Mul(Integer(-1), Symbol('M', commutative=True)))", "srepr_variable": "Symbol('M', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('M', commutative=True), Add(Mul(Integer(2), Symbol('K', commutative=True)), Mul(Integer(-1), Symbol('M', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('K', commutative=True), Add(Symbol('K', commutative=True), Mul(Integer(-1), Integer(2), Symbol('M', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('M', commutative=True), Integer(2)), log(Symbol('K', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('M', commutative=True), Integer(2)), sin(Symbol('K', commutative=True)))", "cos(Add(Symbol('K', commutative=True), Mul(Integer(-1), Symbol('M', commutative=True))))"]}, {"premise_expression": "- R + p", "variable": "p", "positive": "\\frac{p (- 2 R + p)}{2}", "negatives": ["\\frac{R (- R + 2 p)}{2}", "- \\cos{(R + p)}", "\\frac{p^{2}}{2 R}", "\\frac{p (p + 2 e^{R})}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('R', commutative=True)), Symbol('p', commutative=True))", "srepr_variable": "Symbol('p', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('R', commutative=True)), Symbol('p', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('R', commutative=True), Add(Mul(Integer(-1), Symbol('R', commutative=True)), Mul(Integer(2), Symbol('p', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('R', commutative=True), Symbol('p', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('R', commutative=True), Integer(-1)), Pow(Symbol('p', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Symbol('p', commutative=True), Mul(Integer(2), exp(Symbol('R', commutative=True)))))"]}, {"premise_expression": "L \\log{(D)}", "variable": "L", "positive": "\\frac{L^{2} \\log{(D)}}{2}", "negatives": ["\\frac{L^{2} \\cos{(D)}}{2}", "\\frac{L^{2} \\sin{(D)}}{2}", "\\frac{L (- 2 D + L)}{2}", "D L (\\log{(D)} - 1)"], "srepr_premise_expression": "Mul(Symbol('L', commutative=True), log(Symbol('D', commutative=True)))", "srepr_variable": "Symbol('L', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(2)), log(Symbol('D', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(2)), cos(Symbol('D', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('L', commutative=True), Integer(2)), sin(Symbol('D', commutative=True)))", "Mul(Rational(1, 2), Symbol('L', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('D', commutative=True)), Symbol('L', commutative=True)))", "Mul(Symbol('D', commutative=True), Symbol('L', commutative=True), Add(log(Symbol('D', commutative=True)), Integer(-1)))"]}, {"premise_expression": "N \\log{(Y)}", "variable": "N", "positive": "\\frac{N^{2} \\log{(Y)}}{2}", "negatives": ["N Y (\\log{(Y)} - 1)", "\\frac{N (N + 2 \\cos{(Y)})}{2}", "N (\\log{(\\frac{N}{Y})} - 1)", "\\frac{N (- N + 2 \\sin{(Y)})}{2}"], "srepr_premise_expression": "Mul(Symbol('N', commutative=True), log(Symbol('Y', commutative=True)))", "srepr_variable": "Symbol('N', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('N', commutative=True), Integer(2)), log(Symbol('Y', commutative=True)))", "srepr_negatives": ["Mul(Symbol('N', commutative=True), Symbol('Y', commutative=True), Add(log(Symbol('Y', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Symbol('N', commutative=True), Mul(Integer(2), cos(Symbol('Y', commutative=True)))))", "Mul(Symbol('N', commutative=True), Add(log(Mul(Symbol('N', commutative=True), Pow(Symbol('Y', commutative=True), Integer(-1)))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('N', commutative=True), Add(Mul(Integer(-1), Symbol('N', commutative=True)), Mul(Integer(2), sin(Symbol('Y', commutative=True)))))"]}, {"premise_expression": "v x", "variable": "x", "positive": "\\frac{v x^{2}}{2}", "negatives": ["\\frac{v^{2} x}{2}", "- v \\cos{(x)}", "\\frac{x (2 v + x)}{2}", "- v x + \\sin{(x)}"], "srepr_premise_expression": "Mul(Symbol('v', commutative=True), Symbol('x', commutative=True))", "srepr_variable": "Symbol('x', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('v', commutative=True), Pow(Symbol('x', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('v', commutative=True), Integer(2)), Symbol('x', commutative=True))", "Mul(Integer(-1), Symbol('v', commutative=True), cos(Symbol('x', commutative=True)))", "Mul(Rational(1, 2), Symbol('x', commutative=True), Add(Mul(Integer(2), Symbol('v', commutative=True)), Symbol('x', commutative=True)))", "Add(Mul(Integer(-1), Symbol('v', commutative=True), Symbol('x', commutative=True)), sin(Symbol('x', commutative=True)))"]}, {"premise_expression": "B - X + c", "variable": "X", "positive": "X (B - \\frac{X}{2} + c)", "negatives": ["\\frac{B (B - 2 X + 2 c)}{2}", "\\frac{c (2 B - 2 X + c)}{2}", "\\frac{X (B + c)}{c}", "\\frac{X^{2}}{2 B c}"], "srepr_premise_expression": "Add(Symbol('B', commutative=True), Mul(Integer(-1), Symbol('X', commutative=True)), Symbol('c', commutative=True))", "srepr_variable": "Symbol('X', commutative=True)", "srepr_positive": "Mul(Symbol('X', commutative=True), Add(Symbol('B', commutative=True), Mul(Integer(-1), Rational(1, 2), Symbol('X', commutative=True)), Symbol('c', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('B', commutative=True), Add(Symbol('B', commutative=True), Mul(Integer(-1), Integer(2), Symbol('X', commutative=True)), Mul(Integer(2), Symbol('c', commutative=True))))", "Mul(Rational(1, 2), Symbol('c', commutative=True), Add(Mul(Integer(2), Symbol('B', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('X', commutative=True)), Symbol('c', commutative=True)))", "Mul(Symbol('X', commutative=True), Pow(Symbol('c', commutative=True), Integer(-1)), Add(Symbol('B', commutative=True), Symbol('c', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('B', commutative=True), Integer(-1)), Pow(Symbol('X', commutative=True), Integer(2)), Pow(Symbol('c', commutative=True), Integer(-1)))"]}, {"premise_expression": "\\frac{w}{T}", "variable": "T", "positive": "w \\log{(T)}", "negatives": ["\\frac{w^{2}}{2 T}", "- \\cos{(T + w)}", "T (\\log{(\\frac{T}{w})} - 1)", "T (\\log{(T w)} - 1)"], "srepr_premise_expression": "Mul(Pow(Symbol('T', commutative=True), Integer(-1)), Symbol('w', commutative=True))", "srepr_variable": "Symbol('T', commutative=True)", "srepr_positive": "Mul(Symbol('w', commutative=True), log(Symbol('T', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('T', commutative=True), Integer(-1)), Pow(Symbol('w', commutative=True), Integer(2)))", "Mul(Integer(-1), cos(Add(Symbol('T', commutative=True), Symbol('w', commutative=True))))", "Mul(Symbol('T', commutative=True), Add(log(Mul(Symbol('T', commutative=True), Pow(Symbol('w', commutative=True), Integer(-1)))), Integer(-1)))", "Mul(Symbol('T', commutative=True), Add(log(Mul(Symbol('T', commutative=True), Symbol('w', commutative=True))), Integer(-1)))"]}, {"premise_expression": "- I + \\log{(m)}", "variable": "m", "positive": "m (- I + \\log{(m)} - 1)", "negatives": ["\\frac{I (- I + 2 \\log{(m)})}{2}", "\\frac{m (m + 2 \\cos{(I)})}{2}", "\\sin{(I + m)}", "\\log{(m)} \\cos{(I)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('I', commutative=True)), log(Symbol('m', commutative=True)))", "srepr_variable": "Symbol('m', commutative=True)", "srepr_positive": "Mul(Symbol('m', commutative=True), Add(Mul(Integer(-1), Symbol('I', commutative=True)), log(Symbol('m', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('I', commutative=True), Add(Mul(Integer(-1), Symbol('I', commutative=True)), Mul(Integer(2), log(Symbol('m', commutative=True)))))", "Mul(Rational(1, 2), Symbol('m', commutative=True), Add(Symbol('m', commutative=True), Mul(Integer(2), cos(Symbol('I', commutative=True)))))", "sin(Add(Symbol('I', commutative=True), Symbol('m', commutative=True)))", "Mul(log(Symbol('m', commutative=True)), cos(Symbol('I', commutative=True)))"]}, {"premise_expression": "\\frac{w}{Y}", "variable": "w", "positive": "\\frac{w^{2}}{2 Y}", "negatives": ["w \\log{(Y)}", "Y e^{\\frac{w}{Y}}", "Y \\log{(w)}", "\\sin{(Y + w)}"], "srepr_premise_expression": "Mul(Pow(Symbol('Y', commutative=True), Integer(-1)), Symbol('w', commutative=True))", "srepr_variable": "Symbol('w', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('Y', commutative=True), Integer(-1)), Pow(Symbol('w', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('w', commutative=True), log(Symbol('Y', commutative=True)))", "Mul(Symbol('Y', commutative=True), exp(Mul(Pow(Symbol('Y', commutative=True), Integer(-1)), Symbol('w', commutative=True))))", "Mul(Symbol('Y', commutative=True), log(Symbol('w', commutative=True)))", "sin(Add(Symbol('Y', commutative=True), Symbol('w', commutative=True)))"]}, {"premise_expression": "\\frac{z}{V}", "variable": "V", "positive": "z \\log{(V)}", "negatives": ["\\frac{z^{2}}{2 V}", "\\frac{\\sin{(V)}}{z}", "- \\cos{(V + z)}", "- e^{- V + z}"], "srepr_premise_expression": "Mul(Pow(Symbol('V', commutative=True), Integer(-1)), Symbol('z', commutative=True))", "srepr_variable": "Symbol('V', commutative=True)", "srepr_positive": "Mul(Symbol('z', commutative=True), log(Symbol('V', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('V', commutative=True), Integer(-1)), Pow(Symbol('z', commutative=True), Integer(2)))", "Mul(Pow(Symbol('z', commutative=True), Integer(-1)), sin(Symbol('V', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('V', commutative=True), Symbol('z', commutative=True))))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('V', commutative=True)), Symbol('z', commutative=True))))"]}, {"premise_expression": "\\cos{(T + r)}", "variable": "r", "positive": "\\sin{(T + r)}", "negatives": ["- \\sin{(T - r)}", "- \\cos{(T + r)}", "\\frac{r (2 T - r)}{2}", "\\frac{r^{2}}{2 T}"], "srepr_premise_expression": "cos(Add(Symbol('T', commutative=True), Symbol('r', commutative=True)))", "srepr_variable": "Symbol('r', commutative=True)", "srepr_positive": "sin(Add(Symbol('T', commutative=True), Symbol('r', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('T', commutative=True), Mul(Integer(-1), Symbol('r', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('T', commutative=True), Symbol('r', commutative=True))))", "Mul(Rational(1, 2), Symbol('r', commutative=True), Add(Mul(Integer(2), Symbol('T', commutative=True)), Mul(Integer(-1), Symbol('r', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('T', commutative=True), Integer(-1)), Pow(Symbol('r', commutative=True), Integer(2)))"]}, {"premise_expression": "j z", "variable": "z", "positive": "\\frac{j z^{2}}{2}", "negatives": ["\\frac{j^{2} z}{2}", "j \\log{(z)}", "\\frac{\\sin{(z)}}{j}", "- j \\cos{(z)}"], "srepr_premise_expression": "Mul(Symbol('j', commutative=True), Symbol('z', commutative=True))", "srepr_variable": "Symbol('z', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('j', commutative=True), Pow(Symbol('z', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('j', commutative=True), Integer(2)), Symbol('z', commutative=True))", "Mul(Symbol('j', commutative=True), log(Symbol('z', commutative=True)))", "Mul(Pow(Symbol('j', commutative=True), Integer(-1)), sin(Symbol('z', commutative=True)))", "Mul(Integer(-1), Symbol('j', commutative=True), cos(Symbol('z', commutative=True)))"]}, {"premise_expression": "- p + z", "variable": "z", "positive": "\\frac{z (- 2 p + z)}{2}", "negatives": ["\\frac{z (2 p - z)}{2}", "\\frac{p (- p + 2 z)}{2}", "- \\sin{(p - z)}", "\\frac{z (z + 2 \\sin{(p)})}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('p', commutative=True)), Symbol('z', commutative=True))", "srepr_variable": "Symbol('z', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('z', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('p', commutative=True)), Symbol('z', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('z', commutative=True), Add(Mul(Integer(2), Symbol('p', commutative=True)), Mul(Integer(-1), Symbol('z', commutative=True))))", "Mul(Rational(1, 2), Symbol('p', commutative=True), Add(Mul(Integer(-1), Symbol('p', commutative=True)), Mul(Integer(2), Symbol('z', commutative=True))))", "Mul(Integer(-1), sin(Add(Symbol('p', commutative=True), Mul(Integer(-1), Symbol('z', commutative=True)))))", "Mul(Rational(1, 2), Symbol('z', commutative=True), Add(Symbol('z', commutative=True), Mul(Integer(2), sin(Symbol('p', commutative=True)))))"]}]