[{"premise_expression": "\\frac{\\omega - \\xi}{\\psi}", "variable": "\\xi", "positive": "\\frac{\\xi (2 \\omega - \\xi)}{2 \\psi}", "negatives": ["\\frac{\\omega (\\omega - 2 \\xi)}{2 \\psi}", "\\frac{\\xi (2 \\omega^{\\psi} - \\xi)}{2}", "\\frac{\\xi (2 \\psi + \\xi)}{2 \\omega}", "(\\omega - \\xi) \\log{(\\psi)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Pow(Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True))), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\psi', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))), log(Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\alpha - \\beta + \\omega", "variable": "\\omega", "positive": "\\omega (\\alpha - \\beta + \\frac{\\omega}{2})", "negatives": ["\\frac{\\omega (2 \\alpha + 2 \\beta - \\omega)}{2}", "\\frac{\\alpha (\\alpha - 2 \\beta + 2 \\omega)}{2}", "\\frac{\\beta (2 \\alpha - \\beta + 2 \\omega)}{2}", "\\frac{\\omega (\\alpha \\omega + 2 \\beta)}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\beta', commutative=True))))"]}, {"premise_expression": "\\chi + \\sin{(\\delta)}", "variable": "\\chi", "positive": "\\frac{\\chi (\\chi + 2 \\sin{(\\delta)})}{2}", "negatives": ["\\frac{\\chi (\\chi + 2 e^{\\delta})}{2}", "\\frac{\\chi (\\chi - 2 \\delta)}{2}", "\\chi \\delta + \\sin{(\\chi)}", "\\frac{\\chi^{2} e^{\\delta}}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), sin(Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), sin(Symbol('\\\\delta', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), exp(Symbol('\\\\delta', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True))))", "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True)), sin(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), exp(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\alpha \\pi", "variable": "\\pi", "positive": "\\frac{\\alpha \\pi^{2}}{2}", "negatives": ["\\frac{\\alpha^{2} \\pi}{2}", "\\frac{\\pi^{2} \\log{(\\alpha)}}{2}", "\\frac{\\pi (- 2 \\alpha + \\pi)}{2}", "\\alpha \\log{(\\pi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\pi', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), log(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "- \\gamma + \\log{(\\pi)}", "variable": "\\pi", "positive": "\\pi (- \\gamma + \\log{(\\pi)} - 1)", "negatives": ["\\pi (\\log{(\\frac{\\pi}{\\gamma})} - 1)", "\\frac{\\gamma (- \\gamma + 2 \\log{(\\pi)})}{2}", "\\frac{\\pi (\\pi + 2 \\log{(\\gamma)})}{2}", "e^{\\gamma} \\log{(\\pi)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), log(Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), log(Symbol('\\\\pi', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\pi', commutative=True), Add(log(Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), log(Symbol('\\\\pi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), log(Symbol('\\\\gamma', commutative=True)))))", "Mul(exp(Symbol('\\\\gamma', commutative=True)), log(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\log{(- \\beta + \\chi)}", "variable": "\\chi", "positive": "- \\beta \\log{(- \\beta + \\chi)} + \\chi \\log{(- \\beta + \\chi)} - \\chi", "negatives": ["\\beta \\log{(- \\beta + \\chi)} - \\beta - \\chi \\log{(\\beta - \\chi)}", "\\beta \\chi (\\log{(\\chi)} - 1)", "\\chi (- \\beta + \\sin{(\\beta)})", "\\chi (\\log{(\\frac{\\chi}{\\beta})} - 1)"], "srepr_premise_expression": "log(Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\chi', commutative=True)))), Mul(Symbol('\\\\chi', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\chi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\beta', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\chi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Symbol('\\\\chi', commutative=True), log(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True))))))", "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True), Add(log(Symbol('\\\\chi', commutative=True)), Integer(-1)))", "Mul(Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), sin(Symbol('\\\\beta', commutative=True))))", "Mul(Symbol('\\\\chi', commutative=True), Add(log(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\chi', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\log{(\\beta + \\gamma)}", "variable": "\\gamma", "positive": "\\beta \\log{(\\beta + \\gamma)} + \\gamma \\log{(\\beta + \\gamma)} - \\gamma", "negatives": ["\\beta \\log{(\\beta + \\gamma)} - \\beta + \\gamma \\log{(\\beta + \\gamma)}", "\\gamma (\\log{(\\frac{\\beta}{\\gamma})} + 1)", "\\frac{\\gamma (\\gamma + 2 \\sin{(\\beta)})}{2}", "\\gamma (- \\beta + \\log{(\\gamma^{\\beta})})"], "srepr_premise_expression": "log(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\beta', commutative=True), log(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)))), Mul(Symbol('\\\\gamma', commutative=True), log(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)))), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\beta', commutative=True), log(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)))), Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Symbol('\\\\gamma', commutative=True), log(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)))))", "Mul(Symbol('\\\\gamma', commutative=True), Add(log(Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), sin(Symbol('\\\\beta', commutative=True)))))", "Mul(Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), log(Pow(Symbol('\\\\gamma', commutative=True), Symbol('\\\\beta', commutative=True)))))"]}, {"premise_expression": "\\frac{\\cos{(\\beta)}}{\\omega}", "variable": "\\omega", "positive": "\\log{(\\omega)} \\cos{(\\beta)}", "negatives": ["\\beta \\omega + \\sin{(\\omega)}", "\\cos{(\\beta - \\omega)}", "\\frac{\\sin{(\\beta)}}{\\omega}", "\\omega (\\log{(\\frac{\\beta}{\\omega})} + 1)"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), cos(Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(log(Symbol('\\\\omega', commutative=True)), cos(Symbol('\\\\beta', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True)), sin(Symbol('\\\\omega', commutative=True)))", "cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), sin(Symbol('\\\\beta', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), Add(log(Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))), Integer(1)))"]}, {"premise_expression": "- \\delta + \\psi", "variable": "\\psi", "positive": "\\frac{\\psi (- 2 \\delta + \\psi)}{2}", "negatives": ["\\frac{\\delta (- \\delta + 2 \\psi)}{2}", "\\frac{\\psi^{2}}{2 \\delta}", "\\frac{\\psi^{2} \\log{(\\delta)}}{2}", "\\delta \\psi + e^{\\psi}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), log(Symbol('\\\\delta', commutative=True)))", "Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\psi', commutative=True)), exp(Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\frac{\\gamma}{\\beta \\chi}", "variable": "\\chi", "positive": "\\frac{\\gamma \\log{(\\chi)}}{\\beta}", "negatives": ["\\frac{\\gamma \\log{(\\beta)}}{\\chi}", "\\beta \\gamma \\log{(\\chi)}", "\\beta^{\\gamma} \\log{(\\chi)}", "\\frac{\\gamma^{2}}{2 \\beta \\chi}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\beta', commutative=True)))", "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\chi', commutative=True)))", "Mul(Pow(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)), log(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)))"]}, {"premise_expression": "\\sin{(\\alpha - \\gamma)}", "variable": "\\gamma", "positive": "\\cos{(\\alpha - \\gamma)}", "negatives": ["- \\cos{(\\alpha - \\gamma)}", "\\alpha \\log{(\\gamma)}", "\\frac{\\gamma (\\log{(\\gamma)} - 1)}{\\alpha}", "\\frac{\\alpha \\gamma^{2}}{2}"], "srepr_premise_expression": "sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))))", "Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True), Add(log(Symbol('\\\\gamma', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)))"]}, {"premise_expression": "\\frac{\\omega + \\xi}{\\omega}", "variable": "\\xi", "positive": "\\xi + \\frac{\\xi^{2}}{2 \\omega}", "negatives": ["\\omega + \\xi \\log{(\\omega)}", "\\frac{\\omega \\xi^{2}}{2}", "\\frac{\\omega \\xi^{3}}{3}", "- \\omega \\xi + e^{\\xi}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Add(Symbol('\\\\xi', commutative=True), Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Integer(2))))", "srepr_negatives": ["Add(Symbol('\\\\omega', commutative=True), Mul(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Mul(Rational(1, 3), Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(3)))", "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True)), exp(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\beta - \\xi", "variable": "\\beta", "positive": "\\frac{\\beta (\\beta - 2 \\xi)}{2}", "negatives": ["\\frac{\\xi (2 \\beta - \\xi)}{2}", "\\sin{(\\beta - \\xi)}", "e^{\\beta + \\xi}", "- \\cos{(\\beta - \\xi)}"], "srepr_premise_expression": "Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "sin(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "exp(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))))"]}, {"premise_expression": "\\sigma \\xi^{\\chi}", "variable": "\\sigma", "positive": "\\frac{\\sigma^{2} \\xi^{\\chi}}{2}", "negatives": ["\\frac{\\chi \\sigma^{2} \\xi}{2}", "\\frac{\\sigma^{2} \\xi^{2}}{2}", "\\frac{\\sigma^{2}}{2 \\xi} + \\sigma", "\\frac{\\sigma (\\chi \\sigma + 2 \\xi)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\sigma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Add(Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))), Symbol('\\\\sigma', commutative=True))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\cos{(\\frac{\\chi}{\\gamma})}", "variable": "\\gamma", "positive": "\\chi \\operatorname{Si}{(\\frac{\\chi}{\\gamma})} + \\gamma \\cos{(\\frac{\\chi}{\\gamma})}", "negatives": ["\\gamma (\\log{(\\frac{\\chi}{\\gamma})} + 1)", "\\frac{\\gamma (\\log{(\\gamma)} - 1)}{\\chi}", "\\chi \\gamma - \\cos{(\\gamma)}", "\\frac{\\gamma (\\gamma + 2 \\cos{(\\chi)})}{2}"], "srepr_premise_expression": "cos(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\chi', commutative=True), Si(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1))))), Mul(Symbol('\\\\gamma', commutative=True), cos(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1))))))", "srepr_negatives": ["Mul(Symbol('\\\\gamma', commutative=True), Add(log(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True), Add(log(Symbol('\\\\gamma', commutative=True)), Integer(-1)))", "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), cos(Symbol('\\\\chi', commutative=True)))))"]}, {"premise_expression": "\\frac{- \\chi + \\omega}{\\sigma}", "variable": "\\chi", "positive": "\\frac{\\chi (- \\chi + 2 \\omega)}{2 \\sigma}", "negatives": ["\\frac{\\omega (- 2 \\chi + \\omega)}{2 \\sigma}", "\\frac{\\chi (\\chi + 2 \\omega \\sigma)}{2}", "\\frac{\\chi \\omega (\\chi + 2 \\sigma)}{2}", "(- \\chi + \\omega) \\log{(\\sigma)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\omega', commutative=True)), log(Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\log{(\\frac{\\pi}{\\sigma})}", "variable": "\\pi", "positive": "\\pi (\\log{(\\frac{\\pi}{\\sigma})} - 1)", "negatives": ["\\pi (\\log{(\\pi \\sigma)} - 1)", "\\sigma (\\log{(\\frac{\\pi}{\\sigma})} + 1)", "\\pi (\\log{(\\frac{\\sigma}{\\pi})} + 1)", "\\pi (- \\sigma + \\log{(\\pi)} - 1)"], "srepr_premise_expression": "log(Mul(Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\pi', commutative=True), Add(log(Mul(Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\pi', commutative=True), Add(log(Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\sigma', commutative=True), Add(log(Mul(Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Symbol('\\\\pi', commutative=True), Add(log(Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))), Integer(1)))", "Mul(Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), log(Symbol('\\\\pi', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\cos{(\\alpha + \\xi)}", "variable": "\\alpha", "positive": "\\sin{(\\alpha + \\xi)}", "negatives": ["e^{\\alpha + \\xi}", "\\alpha \\sin{(1)}", "\\frac{\\alpha (- \\alpha + 2 \\xi)}{2}", "\\frac{\\alpha^{2} \\xi}{2}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "sin(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["exp(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), sin(Integer(1)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))"]}, {"premise_expression": "\\frac{\\beta}{\\alpha}", "variable": "\\beta", "positive": "\\frac{\\beta^{2}}{2 \\alpha}", "negatives": ["\\beta \\log{(\\alpha)}", "\\alpha e^{\\beta}", "\\frac{\\beta (2 \\alpha - \\beta)}{2}", "- \\cos{(\\alpha - \\beta)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\beta', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\beta', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('\\\\beta', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), exp(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\beta', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\beta', commutative=True)))))"]}, {"premise_expression": "- \\beta + \\sin{(\\psi)}", "variable": "\\psi", "positive": "- \\beta \\psi - \\cos{(\\psi)}", "negatives": ["\\log{(\\beta)} \\log{(\\psi)}", "e^{\\beta + \\psi}", "\\beta \\psi (\\log{(\\psi)} - 1)", "\\frac{\\psi^{2}}{2 \\beta}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), sin(Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(log(Symbol('\\\\beta', commutative=True)), log(Symbol('\\\\psi', commutative=True)))", "exp(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\psi', commutative=True)))", "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\psi', commutative=True), Add(log(Symbol('\\\\psi', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))"]}, {"premise_expression": "\\pi + \\psi", "variable": "\\psi", "positive": "\\frac{\\psi (2 \\pi + \\psi)}{2}", "negatives": ["\\frac{\\psi (2 \\pi - \\psi)}{2}", "\\frac{\\pi (\\pi + 2 \\psi)}{2}", "\\frac{\\psi^{2} \\log{(\\pi)}}{2}", "\\pi \\log{(\\psi)}"], "srepr_premise_expression": "Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), log(Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\gamma + \\cos{(\\sigma)}", "variable": "\\sigma", "positive": "\\gamma \\sigma + \\sin{(\\sigma)}", "negatives": ["- \\gamma \\cos{(\\sigma)}", "\\log{(\\sigma)} \\sin{(\\gamma)}", "\\frac{\\sigma (\\sigma + 2 \\sin{(\\gamma)})}{2}", "\\frac{\\sigma (- \\sigma + 2 \\sin{(\\gamma)})}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\gamma', commutative=True), cos(Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True)), sin(Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), cos(Symbol('\\\\sigma', commutative=True)))", "Mul(log(Symbol('\\\\sigma', commutative=True)), sin(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(2), sin(Symbol('\\\\gamma', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\gamma', commutative=True)))))"]}, {"premise_expression": "\\frac{\\psi}{\\omega}", "variable": "\\omega", "positive": "\\psi \\log{(\\omega)}", "negatives": ["\\frac{\\psi^{2}}{2 \\omega}", "\\frac{\\omega^{2} \\psi}{2}", "\\frac{\\omega^{2} \\log{(\\psi)}}{2}", "\\frac{\\omega (\\log{(\\omega)} - 1)}{\\psi}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\psi', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), log(Symbol('\\\\psi', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Add(log(Symbol('\\\\omega', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\omega + \\pi", "variable": "\\pi", "positive": "\\frac{\\pi (2 \\omega + \\pi)}{2}", "negatives": ["\\frac{\\omega (\\omega + 2 \\pi)}{2}", "\\frac{\\pi^{2} e^{\\omega}}{2}", "e^{- \\omega + \\pi}", "\\frac{\\pi (\\log{(\\pi)} - 1)}{\\omega}"], "srepr_premise_expression": "Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), exp(Symbol('\\\\omega', commutative=True)))", "exp(Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True), Add(log(Symbol('\\\\pi', commutative=True)), Integer(-1)))"]}, {"premise_expression": "- \\gamma + \\omega", "variable": "\\omega", "positive": "\\frac{\\omega (- 2 \\gamma + \\omega)}{2}", "negatives": ["\\frac{\\gamma (- \\gamma + 2 \\omega)}{2}", "\\frac{\\omega^{2} \\sin{(\\gamma)}}{2}", "\\sin{(\\gamma + \\omega)}", "- \\sin{(\\gamma - \\omega)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), sin(Symbol('\\\\gamma', commutative=True)))", "sin(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))))"]}, {"premise_expression": "\\frac{\\alpha}{\\xi}", "variable": "\\alpha", "positive": "\\frac{\\alpha^{2}}{2 \\xi}", "negatives": ["\\alpha \\log{(\\xi)}", "\\frac{\\alpha^{2} \\sin{(\\xi)}}{2}", "\\cos{(\\alpha - \\xi)}", "\\frac{\\alpha^{2} (\\xi - 1)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), sin(Symbol('\\\\xi', commutative=True)))", "cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Add(Symbol('\\\\xi', commutative=True), Integer(-1)))"]}, {"premise_expression": "\\frac{\\sin{(\\xi)}}{\\sigma}", "variable": "\\sigma", "positive": "\\log{(\\sigma)} \\sin{(\\xi)}", "negatives": ["- \\frac{\\cos{(\\sigma)}}{\\xi}", "e^{\\sigma - \\xi}", "\\sigma (\\log{(\\sigma \\xi)} - 1)", "- \\frac{\\cos{(\\xi)}}{\\sigma}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), sin(Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(log(Symbol('\\\\sigma', commutative=True)), sin(Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), cos(Symbol('\\\\sigma', commutative=True)))", "exp(Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Symbol('\\\\sigma', commutative=True), Add(log(Mul(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True))), Integer(-1)))", "Mul(Integer(-1), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), cos(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\cos{(\\alpha - \\xi)}", "variable": "\\xi", "positive": "- \\sin{(\\alpha - \\xi)}", "negatives": ["\\sin{(\\alpha - \\xi)}", "- \\cos{(\\alpha - \\xi)}", "e^{\\alpha + \\xi}", "\\alpha \\xi + e^{\\xi}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Integer(-1), sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))))", "srepr_negatives": ["sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))))", "exp(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True)))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True)), exp(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "e^{\\frac{\\delta}{\\omega}}", "variable": "\\delta", "positive": "\\omega e^{\\frac{\\delta}{\\omega}}", "negatives": ["e^{\\delta - \\omega}", "- e^{- \\delta + \\omega}", "\\frac{\\sin{(\\delta)}}{\\omega}", "\\frac{\\delta (\\delta + 2 \\omega)}{2}"], "srepr_premise_expression": "exp(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\omega', commutative=True), exp(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))))", "srepr_negatives": ["exp(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\omega', commutative=True))))", "Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), sin(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))"]}, {"premise_expression": "\\beta \\psi", "variable": "\\psi", "positive": "\\frac{\\beta \\psi^{2}}{2}", "negatives": ["\\frac{\\beta^{2} \\psi}{2}", "\\frac{\\psi (2 \\beta + \\psi)}{2}", "\\beta e^{\\psi}", "e^{- \\beta + \\psi}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Symbol('\\\\beta', commutative=True), exp(Symbol('\\\\psi', commutative=True)))", "exp(Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\alpha + \\psi", "variable": "\\alpha", "positive": "\\frac{\\alpha (\\alpha + 2 \\psi)}{2}", "negatives": ["\\frac{\\psi (2 \\alpha + \\psi)}{2}", "\\frac{\\alpha^{2} \\log{(\\psi)}}{2}", "- \\cos{(\\alpha - \\psi)}", "\\frac{\\alpha^{2} \\psi}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), log(Symbol('\\\\psi', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))"]}, {"premise_expression": "e^{\\alpha + \\pi}", "variable": "\\pi", "positive": "e^{\\alpha + \\pi}", "negatives": ["\\frac{\\pi (2 \\alpha - \\pi)}{2}", "\\alpha \\pi + e^{\\pi}", "\\log{(\\alpha)} \\log{(\\pi)}", "\\frac{\\pi^{2} e^{\\alpha}}{2}"], "srepr_premise_expression": "exp(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "exp(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)), exp(Symbol('\\\\pi', commutative=True)))", "Mul(log(Symbol('\\\\alpha', commutative=True)), log(Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), exp(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\frac{\\cos{(\\beta)}}{\\chi}", "variable": "\\beta", "positive": "\\frac{\\sin{(\\beta)}}{\\chi}", "negatives": ["\\frac{\\beta^{3} \\chi}{3}", "\\chi \\log{(\\beta)}", "- \\cos{(\\beta + \\chi)}", "\\frac{\\beta (\\beta - 2 \\chi)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), cos(Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), sin(Symbol('\\\\beta', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 3), Pow(Symbol('\\\\beta', commutative=True), Integer(3)), Symbol('\\\\chi', commutative=True))", "Mul(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\beta', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True))))"]}, {"premise_expression": "\\psi e^{\\xi}", "variable": "\\psi", "positive": "\\frac{\\psi^{2} e^{\\xi}}{2}", "negatives": ["\\frac{\\psi^{2} \\log{(\\xi)}}{2}", "\\psi e^{\\xi}", "\\frac{\\psi (\\psi + 2 \\xi)}{2}", "e^{\\psi + \\xi}"], "srepr_premise_expression": "Mul(Symbol('\\\\psi', commutative=True), exp(Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), exp(Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), log(Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\psi', commutative=True), exp(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "exp(Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\beta + \\log{(\\sigma)}", "variable": "\\sigma", "positive": "\\sigma (\\beta + \\log{(\\sigma)} - 1)", "negatives": ["\\frac{\\sigma (\\log{(\\sigma)} - 1)}{\\beta}", "\\sigma (\\log{(\\frac{\\beta}{\\sigma})} + 1)", "\\frac{\\beta (\\beta + 2 \\log{(\\sigma)})}{2}", "\\beta \\sigma - \\cos{(\\sigma)}"], "srepr_premise_expression": "Add(Symbol('\\\\beta', commutative=True), log(Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\beta', commutative=True), log(Symbol('\\\\sigma', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True), Add(log(Symbol('\\\\sigma', commutative=True)), Integer(-1)))", "Mul(Symbol('\\\\sigma', commutative=True), Add(log(Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), log(Symbol('\\\\sigma', commutative=True)))))", "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "- \\beta + e^{\\omega}", "variable": "\\omega", "positive": "- \\beta \\omega + e^{\\omega}", "negatives": ["\\beta \\omega + e^{\\omega}", "\\beta e^{\\frac{\\omega}{\\beta}}", "\\frac{\\beta (- \\beta + 2 e^{\\omega})}{2}", "\\frac{\\omega (\\omega + 2 e^{\\beta})}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), exp(Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True)), exp(Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True)), exp(Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\beta', commutative=True), exp(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\omega', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), exp(Symbol('\\\\beta', commutative=True)))))"]}, {"premise_expression": "\\omega - \\pi", "variable": "\\omega", "positive": "\\frac{\\omega (\\omega - 2 \\pi)}{2}", "negatives": ["\\frac{\\pi (2 \\omega - \\pi)}{2}", "\\frac{\\omega^{2} e^{\\pi}}{2}", "\\frac{\\omega^{2} \\log{(\\pi)}}{2}", "\\sin{(\\omega - \\pi)}"], "srepr_premise_expression": "Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), exp(Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), log(Symbol('\\\\pi', commutative=True)))", "sin(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\frac{\\gamma}{\\psi}", "variable": "\\psi", "positive": "\\gamma \\log{(\\psi)}", "negatives": ["\\gamma \\sin{(\\psi)}", "\\gamma e^{\\psi}", "\\frac{\\gamma^{2}}{2 \\psi}", "\\gamma \\psi - \\cos{(\\psi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\gamma', commutative=True), sin(Symbol('\\\\psi', commutative=True)))", "Mul(Symbol('\\\\gamma', commutative=True), exp(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))", "Add(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "\\log{(\\alpha + \\omega)}", "variable": "\\alpha", "positive": "\\alpha \\log{(\\alpha + \\omega)} - \\alpha + \\omega \\log{(\\alpha + \\omega)}", "negatives": ["\\alpha \\log{(\\alpha + \\omega)} + \\omega \\log{(\\alpha + \\omega)} - \\omega", "\\frac{\\alpha (- \\alpha + 2 \\log{(\\omega)})}{2}", "\\frac{\\alpha (\\alpha + 2 \\sin{(\\omega)})}{2}", "\\omega \\log{(\\alpha)}"], "srepr_premise_expression": "log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\alpha', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)))), Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Symbol('\\\\omega', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\alpha', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)))), Mul(Symbol('\\\\omega', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)))), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), log(Symbol('\\\\omega', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), sin(Symbol('\\\\omega', commutative=True)))))", "Mul(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\delta \\sigma + \\psi", "variable": "\\delta", "positive": "\\frac{\\delta (\\delta \\sigma + 2 \\psi)}{2}", "negatives": ["\\frac{\\sigma (\\delta \\sigma + 2 \\psi)}{2}", "\\frac{\\delta (\\delta \\sigma - 2 \\psi)}{2}", "\\frac{\\psi (2 \\delta \\sigma + \\psi)}{2}", "\\frac{\\delta (- \\delta - 2 \\psi + 2 \\sigma)}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True)), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\frac{\\log{(\\pi)}}{\\xi}", "variable": "\\pi", "positive": "\\frac{\\pi (\\log{(\\pi)} - 1)}{\\xi}", "negatives": ["\\pi \\xi (\\log{(\\pi)} - 1)", "\\pi (\\log{(\\frac{\\xi}{\\pi})} + 1)", "\\cos{(\\pi - \\xi)}", "\\log{(\\pi)} \\log{(\\xi)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), log(Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), Add(log(Symbol('\\\\pi', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True), Add(log(Symbol('\\\\pi', commutative=True)), Integer(-1)))", "Mul(Symbol('\\\\pi', commutative=True), Add(log(Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))), Integer(1)))", "cos(Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(log(Symbol('\\\\pi', commutative=True)), log(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "- \\beta + \\chi", "variable": "\\chi", "positive": "\\frac{\\chi (- 2 \\beta + \\chi)}{2}", "negatives": ["\\frac{\\beta (- \\beta + 2 \\chi)}{2}", "\\frac{\\chi (\\chi + 2 \\sin{(\\beta)})}{2}", "\\frac{\\chi^{2} \\log{(\\beta)}}{2}", "\\chi (\\log{(\\beta \\chi)} - 1)"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\chi', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\chi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), sin(Symbol('\\\\beta', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), log(Symbol('\\\\beta', commutative=True)))", "Mul(Symbol('\\\\chi', commutative=True), Add(log(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True))), Integer(-1)))"]}, {"premise_expression": "- \\pi + \\xi", "variable": "\\pi", "positive": "\\frac{\\pi (- \\pi + 2 \\xi)}{2}", "negatives": ["\\frac{\\xi (- 2 \\pi + \\xi)}{2}", "\\frac{\\pi^{2} \\cos{(\\xi)}}{2}", "\\frac{\\pi^{2} e^{\\xi}}{2}", "\\cos{(\\pi - \\xi)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), cos(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), exp(Symbol('\\\\xi', commutative=True)))", "cos(Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "e^{\\omega^{\\alpha}}", "variable": "\\omega", "positive": "\\frac{e^{- \\frac{i \\pi}{\\alpha}} \\gamma(\\frac{1}{\\alpha}, \\omega^{\\alpha} e^{i \\pi})}{\\alpha}", "negatives": ["\\alpha \\log{(\\alpha + \\omega)} + \\omega \\log{(\\alpha + \\omega)} - \\omega", "\\frac{\\omega (\\log{(\\omega)} - 1)}{\\alpha}", "\\frac{\\omega (\\omega + 2 \\sin{(\\alpha)})}{2}", "- e^{\\alpha - \\omega}"], "srepr_premise_expression": "exp(Pow(Symbol('\\\\omega', commutative=True), Symbol('\\\\alpha', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), exp(Mul(Integer(-1), I, pi, Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)))), lowergamma(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Mul(Pow(Symbol('\\\\omega', commutative=True), Symbol('\\\\alpha', commutative=True)), exp_polar(Mul(I, pi)))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\alpha', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)))), Mul(Symbol('\\\\omega', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)))), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))", "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True), Add(log(Symbol('\\\\omega', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), sin(Symbol('\\\\alpha', commutative=True)))))", "Mul(Integer(-1), exp(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))))"]}, {"premise_expression": "\\frac{\\beta \\omega}{\\alpha}", "variable": "\\beta", "positive": "\\frac{\\beta^{2} \\omega}{2 \\alpha}", "negatives": ["\\frac{\\beta \\omega^{2}}{2 \\alpha}", "\\beta \\omega \\log{(\\alpha)}", "\\frac{\\beta (2 \\alpha + \\beta)}{2 \\omega}", "\\frac{\\beta (- 2 \\alpha + \\beta \\omega)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\omega', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True))))"]}, {"premise_expression": "\\beta \\omega - \\xi", "variable": "\\beta", "positive": "\\frac{\\beta (\\beta \\omega - 2 \\xi)}{2}", "negatives": ["\\frac{\\omega (\\beta \\omega - 2 \\xi)}{2}", "\\frac{\\xi (2 \\beta \\omega - \\xi)}{2}", "\\frac{\\beta^{2} (\\omega + \\xi)}{2}", "\\frac{\\beta^{2}}{2} + \\frac{\\beta \\omega}{\\xi}"], "srepr_premise_expression": "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True)))", "Add(Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2))), Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))"]}, {"premise_expression": "\\frac{\\omega \\psi}{\\pi}", "variable": "\\omega", "positive": "\\frac{\\omega^{2} \\psi}{2 \\pi}", "negatives": ["\\frac{\\omega \\psi^{2}}{2 \\pi}", "\\omega \\psi \\log{(\\pi)}", "\\frac{\\omega (\\omega \\psi - 2 \\pi)}{2}", "\\frac{\\omega (\\omega \\pi + 2 \\psi)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True), log(Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "e^{\\frac{\\delta}{\\alpha}}", "variable": "\\alpha", "positive": "\\alpha e^{\\frac{\\delta}{\\alpha}} - \\delta \\operatorname{Ei}{(\\frac{\\delta}{\\alpha})}", "negatives": ["\\alpha \\cos{(\\frac{\\delta}{\\alpha})} + \\delta \\operatorname{Si}{(\\frac{\\delta}{\\alpha})}", "\\alpha e^{\\frac{\\delta}{\\alpha}}", "\\frac{\\alpha (\\alpha + 2 \\delta)}{2}", "\\frac{\\alpha (- \\alpha + 2 \\delta)}{2}"], "srepr_premise_expression": "exp(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\alpha', commutative=True), exp(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True)))), Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Ei(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\alpha', commutative=True), cos(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True)))), Mul(Symbol('\\\\delta', commutative=True), Si(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True)))))", "Mul(Symbol('\\\\alpha', commutative=True), exp(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\delta', commutative=True))))"]}, {"premise_expression": "\\alpha + \\psi", "variable": "\\psi", "positive": "\\frac{\\psi (2 \\alpha + \\psi)}{2}", "negatives": ["\\frac{\\alpha (\\alpha + 2 \\psi)}{2}", "\\frac{\\psi^{2} e^{\\alpha}}{2}", "\\frac{\\psi^{2} \\cos{(\\alpha)}}{2}", "\\psi \\cos{(2 \\alpha)}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), exp(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), cos(Symbol('\\\\alpha', commutative=True)))", "Mul(Symbol('\\\\psi', commutative=True), cos(Mul(Integer(2), Symbol('\\\\alpha', commutative=True))))"]}, {"premise_expression": "\\omega + \\pi", "variable": "\\pi", "positive": "\\frac{\\pi (2 \\omega + \\pi)}{2}", "negatives": ["\\frac{\\omega (\\omega + 2 \\pi)}{2}", "\\frac{\\pi (\\pi + 2 \\sin{(\\omega)})}{2}", "\\frac{\\pi (\\pi + 2 e^{\\omega})}{2}", "\\frac{\\pi (- \\pi + 2 \\cos{(\\omega)})}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), sin(Symbol('\\\\omega', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), exp(Symbol('\\\\omega', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\omega', commutative=True)))))"]}, {"premise_expression": "\\alpha - \\beta", "variable": "\\alpha", "positive": "\\frac{\\alpha (\\alpha - 2 \\beta)}{2}", "negatives": ["\\frac{\\alpha (\\alpha + 2 \\beta)}{2}", "\\frac{\\beta (2 \\alpha - \\beta)}{2}", "\\frac{\\alpha^{2} \\cos{(\\beta)}}{2}", "\\frac{\\alpha (- \\alpha + 2 \\sin{(\\beta)})}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\beta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\beta', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), cos(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\beta', commutative=True)))))"]}, {"premise_expression": "- \\delta + \\pi", "variable": "\\delta", "positive": "\\frac{\\delta (- \\delta + 2 \\pi)}{2}", "negatives": ["\\frac{\\pi (- 2 \\delta + \\pi)}{2}", "\\frac{\\delta (\\log{(\\delta)} - 1)}{\\pi}", "\\frac{\\delta^{2}}{2} - \\cos{(\\delta)}", "e^{\\pi} \\log{(\\delta)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Add(log(Symbol('\\\\delta', commutative=True)), Integer(-1)))", "Add(Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2))), Mul(Integer(-1), cos(Symbol('\\\\delta', commutative=True))))", "Mul(exp(Symbol('\\\\pi', commutative=True)), log(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "- \\pi + \\sigma", "variable": "\\pi", "positive": "\\frac{\\pi (- \\pi + 2 \\sigma)}{2}", "negatives": ["\\frac{\\pi (\\pi + 2 \\sigma)}{2}", "\\frac{\\sigma (- 2 \\pi + \\sigma)}{2}", "\\frac{\\pi^{2} \\sin{(\\sigma)}}{2}", "\\frac{\\pi^{2} e^{\\sigma}}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), sin(Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), exp(Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\gamma + \\omega", "variable": "\\gamma", "positive": "\\frac{\\gamma (\\gamma + 2 \\omega)}{2}", "negatives": ["\\frac{\\omega (2 \\gamma + \\omega)}{2}", "\\frac{\\gamma^{2} e^{\\omega}}{2}", "\\omega \\log{(\\gamma)}", "\\gamma (\\log{(\\frac{\\omega}{\\gamma})} + 1)"], "srepr_premise_expression": "Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), exp(Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "Mul(Symbol('\\\\gamma', commutative=True), Add(log(Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True))), Integer(1)))"]}, {"premise_expression": "\\log{(\\sigma^{\\chi})}", "variable": "\\sigma", "positive": "\\sigma (- \\chi + \\log{(\\sigma^{\\chi})})", "negatives": ["\\sigma (\\log{(\\chi \\sigma)} - 1)", "\\frac{\\sigma^{2} \\log{(\\chi)}}{2}", "\\sigma (\\log{(\\frac{\\sigma}{\\chi})} - 1)", "\\frac{\\chi^{2} \\log{(\\sigma)}}{2}"], "srepr_premise_expression": "log(Pow(Symbol('\\\\sigma', commutative=True), Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), log(Pow(Symbol('\\\\sigma', commutative=True), Symbol('\\\\chi', commutative=True)))))", "srepr_negatives": ["Mul(Symbol('\\\\sigma', commutative=True), Add(log(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\sigma', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), log(Symbol('\\\\chi', commutative=True)))", "Mul(Symbol('\\\\sigma', commutative=True), Add(log(Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), log(Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\frac{\\alpha}{\\omega}", "variable": "\\omega", "positive": "\\alpha \\log{(\\omega)}", "negatives": ["\\frac{\\alpha^{2}}{2 \\omega}", "\\alpha \\omega + e^{\\omega}", "\\alpha \\omega + \\sin{(\\omega)}", "- \\alpha \\omega + \\sin{(\\omega)}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)), exp(Symbol('\\\\omega', commutative=True)))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)), sin(Symbol('\\\\omega', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)), sin(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\frac{\\sin{(\\gamma)}}{\\omega}", "variable": "\\gamma", "positive": "- \\frac{\\cos{(\\gamma)}}{\\omega}", "negatives": ["- \\cos{(\\gamma - \\omega)}", "- \\omega \\cos{(\\gamma)}", "\\frac{\\gamma^{2} \\cos{(\\omega)}}{2}", "- e^{- \\gamma + \\omega}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), sin(Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Integer(-1), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), cos(Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))))", "Mul(Integer(-1), Symbol('\\\\omega', commutative=True), cos(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), cos(Symbol('\\\\omega', commutative=True)))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\omega', commutative=True))))"]}, {"premise_expression": "- \\omega + \\pi", "variable": "\\pi", "positive": "\\frac{\\pi (- 2 \\omega + \\pi)}{2}", "negatives": ["\\frac{\\omega (- \\omega + 2 \\pi)}{2}", "- \\sin{(\\omega - \\pi)}", "\\cos{(\\omega - \\pi)}", "- \\omega \\pi - \\cos{(\\pi)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Integer(-1), sin(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))", "cos(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\frac{\\cos{(\\psi)}}{\\chi}", "variable": "\\psi", "positive": "\\frac{\\sin{(\\psi)}}{\\chi}", "negatives": ["\\frac{\\chi \\psi^{2}}{2}", "\\frac{\\psi^{2} \\sin{(\\chi)}}{2}", "e^{- \\chi + \\psi}", "e^{\\chi + \\psi}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), cos(Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), sin(Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), sin(Symbol('\\\\chi', commutative=True)))", "exp(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\psi', commutative=True)))", "exp(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\alpha + \\sigma + \\xi", "variable": "\\alpha", "positive": "\\alpha (\\frac{\\alpha}{2} + \\sigma + \\xi)", "negatives": ["\\frac{\\alpha (- \\alpha - 2 \\sigma + 2 \\xi)}{2}", "\\frac{\\xi (2 \\alpha + 2 \\sigma + \\xi)}{2}", "\\frac{\\sigma (2 \\alpha + \\sigma + 2 \\xi)}{2}", "\\frac{\\alpha^{2} (- \\sigma + \\xi)}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\alpha', commutative=True), Add(Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\sigma', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\cos{(\\gamma + \\xi)}", "variable": "\\gamma", "positive": "\\sin{(\\gamma + \\xi)}", "negatives": ["\\sin{(\\gamma - \\xi)}", "- \\cos{(\\gamma + \\xi)}", "e^{\\gamma - \\xi}", "\\xi \\sin{(\\gamma)}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "sin(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["sin(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True))))", "exp(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Symbol('\\\\xi', commutative=True), sin(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\gamma \\omega", "variable": "\\omega", "positive": "\\frac{\\gamma \\omega^{2}}{2}", "negatives": ["\\frac{\\gamma^{2} \\omega}{2}", "\\sin{(\\gamma + \\omega)}", "\\frac{\\omega (- 2 \\gamma + \\omega)}{2}", "- \\gamma \\omega - \\cos{(\\omega)}"], "srepr_premise_expression": "Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Symbol('\\\\omega', commutative=True))", "sin(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\omega', commutative=True))))"]}, {"premise_expression": "\\frac{\\pi}{\\psi}", "variable": "\\pi", "positive": "\\frac{\\pi^{2}}{2 \\psi}", "negatives": ["\\pi \\log{(\\psi)}", "\\frac{\\pi^{2} \\log{(\\psi)}}{2}", "\\frac{\\pi (\\pi + 2 \\psi)}{2}", "- \\cos{(\\pi + \\psi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), log(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "\\pi + \\xi", "variable": "\\xi", "positive": "\\frac{\\xi (2 \\pi + \\xi)}{2}", "negatives": ["\\frac{\\pi (\\pi + 2 \\xi)}{2}", "\\frac{\\xi^{2} \\sin{(\\pi)}}{2}", "\\frac{\\xi (\\log{(\\xi)} - 1)}{\\pi}", "- \\frac{\\cos{(\\xi)}}{\\pi}"], "srepr_premise_expression": "Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), sin(Symbol('\\\\pi', commutative=True)))", "Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True), Add(log(Symbol('\\\\xi', commutative=True)), Integer(-1)))", "Mul(Integer(-1), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), cos(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "e^{- \\gamma + \\xi}", "variable": "\\xi", "positive": "e^{- \\gamma + \\xi}", "negatives": ["- e^{- \\gamma + \\xi}", "\\gamma e^{\\frac{\\xi}{\\gamma}}", "\\gamma \\xi - \\cos{(\\xi)}", "- \\gamma \\xi - \\cos{(\\xi)}"], "srepr_premise_expression": "exp(Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "exp(Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\xi', commutative=True))))", "Mul(Symbol('\\\\gamma', commutative=True), exp(Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))))", "Add(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\xi', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\frac{\\omega}{\\alpha}", "variable": "\\alpha", "positive": "\\omega \\log{(\\alpha)}", "negatives": ["- \\omega \\cos{(\\alpha)}", "\\frac{\\omega^{2}}{2 \\alpha}", "\\frac{\\alpha^{2}}{2 \\omega}", "- \\cos{(\\alpha - \\omega)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Symbol('\\\\omega', commutative=True), cos(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))))"]}, {"premise_expression": "\\frac{\\sigma - \\xi}{\\beta}", "variable": "\\beta", "positive": "(\\sigma - \\xi) \\log{(\\beta)}", "negatives": ["\\frac{\\xi (2 \\sigma - \\xi)}{2 \\beta}", "\\frac{\\sigma (\\sigma - 2 \\xi)}{2 \\beta}", "\\frac{\\beta (- \\beta + 2 \\xi^{\\sigma})}{2}", "\\frac{\\beta \\xi (\\beta + 2 \\sigma)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))), log(Symbol('\\\\beta', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Pow(Symbol('\\\\xi', commutative=True), Symbol('\\\\sigma', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\chi e^{\\pi}", "variable": "\\chi", "positive": "\\frac{\\chi^{2} e^{\\pi}}{2}", "negatives": ["\\frac{\\chi^{2} \\log{(\\pi)}}{2}", "\\chi e^{\\pi}", "\\frac{\\chi \\pi (\\chi + 2 \\pi)}{2}", "\\chi \\pi + \\sin{(\\chi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), exp(Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), exp(Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), log(Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\chi', commutative=True), exp(Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True)), sin(Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "\\pi (\\beta - \\delta)", "variable": "\\beta", "positive": "\\frac{\\beta \\pi (\\beta - 2 \\delta)}{2}", "negatives": ["\\frac{\\beta \\pi (\\beta + 2 \\delta)}{2}", "\\frac{\\delta \\pi (2 \\beta - \\delta)}{2}", "\\frac{\\pi^{2} (\\beta - \\delta)}{2}", "\\frac{\\beta (\\beta \\pi + 2 \\delta)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), Symbol('\\\\delta', commutative=True))))"]}, {"premise_expression": "\\cos{(\\chi - \\xi)}", "variable": "\\chi", "positive": "\\sin{(\\chi - \\xi)}", "negatives": ["- \\sin{(\\chi - \\xi)}", "\\frac{\\sin{(\\chi)}}{\\xi}", "e^{\\chi + \\xi}", "\\frac{\\chi (\\chi - 2 \\xi)}{2}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "sin(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))))", "Mul(Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), sin(Symbol('\\\\chi', commutative=True)))", "exp(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\frac{\\pi}{\\chi}", "variable": "\\pi", "positive": "\\frac{\\pi^{2}}{2 \\chi}", "negatives": ["\\pi \\log{(\\chi)}", "\\frac{\\pi (2 \\chi + \\pi)}{2}", "- \\sin{(\\chi - \\pi)}", "\\frac{\\pi (4 \\chi - \\pi)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(4), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "- \\xi + \\log{(\\delta)}", "variable": "\\xi", "positive": "\\frac{\\xi (- \\xi + 2 \\log{(\\delta)})}{2}", "negatives": ["\\delta (- \\xi + \\log{(\\delta)} - 1)", "\\delta \\log{(\\xi)}", "\\xi (\\log{(\\delta \\xi)} - 1)", "\\delta \\log{(\\delta + \\xi)} + \\xi \\log{(\\delta + \\xi)} - \\xi"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), log(Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), log(Symbol('\\\\delta', commutative=True)))))", "srepr_negatives": ["Mul(Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), log(Symbol('\\\\delta', commutative=True)), Integer(-1)))", "Mul(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\xi', commutative=True), Add(log(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True))), Integer(-1)))", "Add(Mul(Symbol('\\\\delta', commutative=True), log(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True)))), Mul(Symbol('\\\\xi', commutative=True), log(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\log{(\\frac{\\alpha}{\\pi})}", "variable": "\\alpha", "positive": "\\alpha (\\log{(\\frac{\\alpha}{\\pi})} - 1)", "negatives": ["\\alpha (\\log{(\\alpha \\pi)} - 1)", "\\pi (\\log{(\\frac{\\alpha}{\\pi})} + 1)", "\\alpha (- \\pi + \\log{(\\alpha)} - 1)", "\\log{(\\alpha)} \\log{(\\pi)}"], "srepr_premise_expression": "log(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\alpha', commutative=True), Add(log(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\alpha', commutative=True), Add(log(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\pi', commutative=True), Add(log(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), log(Symbol('\\\\alpha', commutative=True)), Integer(-1)))", "Mul(log(Symbol('\\\\alpha', commutative=True)), log(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\frac{\\sigma}{\\alpha}", "variable": "\\sigma", "positive": "\\frac{\\sigma^{2}}{2 \\alpha}", "negatives": ["\\sigma \\log{(\\alpha)}", "\\frac{\\alpha \\sigma^{2}}{2}", "\\alpha \\sin{(\\sigma)}", "\\alpha \\sigma - \\cos{(\\sigma)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "Mul(Symbol('\\\\alpha', commutative=True), sin(Symbol('\\\\sigma', commutative=True)))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\gamma + \\sigma", "variable": "\\sigma", "positive": "\\frac{\\sigma (2 \\gamma + \\sigma)}{2}", "negatives": ["\\frac{\\gamma (\\gamma + 2 \\sigma)}{2}", "\\frac{\\sigma^{2} (\\gamma + 1)}{2}", "\\sin{(\\gamma + \\sigma)}", "\\cos{(\\gamma - \\sigma)}"], "srepr_premise_expression": "Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), Add(Symbol('\\\\gamma', commutative=True), Integer(1)))", "sin(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True)))", "cos(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "e^{\\frac{\\delta}{\\chi}}", "variable": "\\chi", "positive": "\\chi e^{\\frac{\\delta}{\\chi}} - \\delta \\operatorname{Ei}{(\\frac{\\delta}{\\chi})}", "negatives": ["\\frac{\\chi (\\chi + 2 e^{\\delta})}{2}", "\\chi e^{\\frac{\\delta}{\\chi}}", "\\frac{\\chi (- \\chi + 2 \\sin{(\\delta)})}{2}", "\\frac{\\chi (\\chi + 2 \\sin{(\\delta)})}{2}"], "srepr_premise_expression": "exp(Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\chi', commutative=True), exp(Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True)))), Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Ei(Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), exp(Symbol('\\\\delta', commutative=True)))))", "Mul(Symbol('\\\\chi', commutative=True), exp(Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\delta', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), sin(Symbol('\\\\delta', commutative=True)))))"]}, {"premise_expression": "\\log{(- \\gamma + \\pi)}", "variable": "\\gamma", "positive": "\\gamma \\log{(- \\gamma + \\pi)} - \\gamma - \\pi \\log{(\\gamma - \\pi)}", "negatives": ["- \\gamma \\log{(- \\gamma + \\pi)} + \\pi \\log{(- \\gamma + \\pi)} - \\pi", "\\frac{\\gamma (- \\gamma + 2 \\log{(\\pi)})}{2}", "\\frac{\\gamma (\\gamma + 2 \\cos{(\\pi)})}{2}", "- \\cos{(\\gamma - \\pi)}"], "srepr_premise_expression": "log(Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\gamma', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), Symbol('\\\\pi', commutative=True), log(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True)))), Mul(Symbol('\\\\pi', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), log(Symbol('\\\\pi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), cos(Symbol('\\\\pi', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))"]}, {"premise_expression": "e^{- \\gamma + \\sigma}", "variable": "\\sigma", "positive": "e^{- \\gamma + \\sigma}", "negatives": ["- e^{- \\gamma + \\sigma}", "- \\cos{(\\gamma + \\sigma)}", "\\frac{\\sigma (2 \\gamma + \\sigma)}{2}", "\\gamma \\sigma + e^{\\sigma}"], "srepr_premise_expression": "exp(Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "exp(Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\sigma', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Add(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True)), exp(Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\chi \\cos{(\\pi)}", "variable": "\\chi", "positive": "\\frac{\\chi^{2} \\cos{(\\pi)}}{2}", "negatives": ["\\frac{\\chi^{2} \\log{(\\pi)}}{2}", "\\frac{\\chi^{2} \\pi}{2}", "\\frac{\\chi^{2}}{2 \\pi}", "\\chi \\sin{(\\pi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), cos(Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), cos(Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), log(Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\pi', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))", "Mul(Symbol('\\\\chi', commutative=True), sin(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\frac{\\beta}{\\xi} - \\omega", "variable": "\\omega", "positive": "\\frac{\\beta \\omega}{\\xi} - \\frac{\\omega^{2}}{2}", "negatives": ["\\frac{\\beta \\omega^{2} \\xi}{2}", "- \\beta \\omega + \\frac{\\omega^{2}}{2 \\xi}", "\\omega (\\xi + \\xi^{\\beta})", "\\beta \\log{(\\xi)} - \\omega \\xi"], "srepr_premise_expression": "Add(Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))), Mul(Integer(-1), Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))", "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))", "Mul(Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\xi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Symbol('\\\\beta', commutative=True))))", "Add(Mul(Symbol('\\\\beta', commutative=True), log(Symbol('\\\\xi', commutative=True))), Mul(Integer(-1), Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\beta \\sin{(\\xi)}", "variable": "\\xi", "positive": "- \\beta \\cos{(\\xi)}", "negatives": ["- \\cos{(\\beta + \\xi)}", "\\cos{(\\beta - \\xi)}", "\\frac{\\beta^{2} \\sin{(\\xi)}}{2}", "e^{\\beta + \\xi}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), sin(Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Integer(-1), Symbol('\\\\beta', commutative=True), cos(Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True))))", "cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), sin(Symbol('\\\\xi', commutative=True)))", "exp(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\log{(\\alpha + \\pi)}", "variable": "\\pi", "positive": "\\alpha \\log{(\\alpha + \\pi)} + \\pi \\log{(\\alpha + \\pi)} - \\pi", "negatives": ["\\alpha \\log{(\\alpha + \\pi)} - \\alpha + \\pi \\log{(\\alpha + \\pi)}", "\\log{(\\pi)} \\cos{(\\alpha)}", "\\alpha \\pi + e^{\\pi}", "\\frac{\\pi (2 \\alpha + \\pi)}{2}"], "srepr_premise_expression": "log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\alpha', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)))), Mul(Symbol('\\\\pi', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\alpha', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Symbol('\\\\pi', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)))))", "Mul(log(Symbol('\\\\pi', commutative=True)), cos(Symbol('\\\\alpha', commutative=True)))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)), exp(Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\alpha \\cos{(\\chi)}", "variable": "\\chi", "positive": "\\alpha \\sin{(\\chi)}", "negatives": ["\\alpha e^{\\chi}", "- \\alpha \\chi + \\sin{(\\chi)}", "\\frac{\\alpha \\chi^{2}}{2}", "\\frac{\\alpha^{2} \\cos{(\\chi)}}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), cos(Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\alpha', commutative=True), sin(Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\alpha', commutative=True), exp(Symbol('\\\\chi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)), sin(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), cos(Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "\\alpha \\delta", "variable": "\\alpha", "positive": "\\frac{\\alpha^{2} \\delta}{2}", "negatives": ["\\frac{\\alpha \\delta^{2}}{2}", "\\delta \\log{(\\alpha)}", "\\delta e^{\\frac{\\alpha}{\\delta}}", "\\frac{\\alpha^{2} \\cos{(\\delta)}}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\delta', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\delta', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(2)))", "Mul(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "Mul(Symbol('\\\\delta', commutative=True), exp(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), cos(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\frac{\\sigma}{\\gamma}", "variable": "\\sigma", "positive": "\\frac{\\sigma^{2}}{2 \\gamma}", "negatives": ["\\sigma \\log{(\\gamma)}", "\\frac{\\sigma^{2} \\log{(\\gamma)}}{2}", "- \\gamma \\cos{(\\sigma)}", "\\frac{\\sin{(\\sigma)}}{\\gamma}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), log(Symbol('\\\\gamma', commutative=True)))", "Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), cos(Symbol('\\\\sigma', commutative=True)))", "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), sin(Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\log{(\\alpha^{\\chi})}", "variable": "\\chi", "positive": "\\frac{\\chi^{2} \\log{(\\alpha)}}{2}", "negatives": ["\\alpha \\chi - \\cos{(\\chi)}", "\\frac{\\chi (- \\chi + 2 \\cos{(\\alpha)})}{2}", "\\alpha \\chi + e^{\\chi}", "\\sin{(\\alpha + \\chi)}"], "srepr_premise_expression": "log(Pow(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), log(Symbol('\\\\alpha', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\chi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\alpha', commutative=True)))))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)), exp(Symbol('\\\\chi', commutative=True)))", "sin(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "\\gamma \\omega", "variable": "\\gamma", "positive": "\\frac{\\gamma^{2} \\omega}{2}", "negatives": ["\\frac{\\gamma \\omega^{2}}{2}", "\\omega \\sin{(\\gamma)}", "\\frac{\\gamma (\\gamma - 2 \\omega)}{2}", "- \\gamma \\omega - \\cos{(\\gamma)}"], "srepr_premise_expression": "Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Symbol('\\\\omega', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "Mul(Symbol('\\\\omega', commutative=True), sin(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\gamma', commutative=True))))"]}, {"premise_expression": "e^{\\gamma - \\pi}", "variable": "\\gamma", "positive": "e^{\\gamma - \\pi}", "negatives": ["- e^{\\gamma - \\pi}", "- \\cos{(\\gamma - \\pi)}", "\\gamma (- \\pi + \\log{(\\pi)})", "\\gamma \\pi + \\sin{(\\gamma)}"], "srepr_premise_expression": "exp(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "exp(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))", "Mul(Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), log(Symbol('\\\\pi', commutative=True))))", "Add(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True)), sin(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "- \\sigma + \\xi", "variable": "\\sigma", "positive": "\\frac{\\sigma (- \\sigma + 2 \\xi)}{2}", "negatives": ["\\frac{\\xi (- 2 \\sigma + \\xi)}{2}", "\\frac{\\sigma^{2} \\sin{(\\xi)}}{2}", "- e^{- \\sigma + \\xi}", "\\frac{\\sigma (\\log{(\\sigma)} - 1)}{\\xi}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), sin(Symbol('\\\\xi', commutative=True)))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), Symbol('\\\\xi', commutative=True))))", "Mul(Symbol('\\\\sigma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), Add(log(Symbol('\\\\sigma', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\sin^{\\xi}{(\\sigma)}", "variable": "\\sigma", "positive": "\\int \\sin^{\\xi}{(\\sigma)} d\\sigma", "negatives": ["\\operatorname{NonElementaryIntegral}{((\\frac{\\sigma}{\\xi})^{\\sigma},( \\sigma))}", "\\sin{(\\sigma + \\xi)}", "\\sigma \\xi + \\sin{(\\sigma)}", "\\log{(\\sigma)} \\log{(\\xi)}"], "srepr_premise_expression": "Pow(sin(Symbol('\\\\sigma', commutative=True)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Integral(Pow(sin(Symbol('\\\\sigma', commutative=True)), Symbol('\\\\xi', commutative=True)), Tuple(Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Function('NonElementaryIntegral')(Pow(Mul(Symbol('\\\\sigma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))), Symbol('\\\\sigma', commutative=True)), Tuple(Symbol('\\\\sigma', commutative=True)))", "sin(Add(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True)))", "Add(Mul(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True)), sin(Symbol('\\\\sigma', commutative=True)))", "Mul(log(Symbol('\\\\sigma', commutative=True)), log(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\chi \\log{(\\gamma)}", "variable": "\\gamma", "positive": "\\chi \\gamma (\\log{(\\gamma)} - 1)", "negatives": ["\\frac{\\chi^{2} \\log{(\\gamma)}}{2}", "\\frac{\\chi \\gamma (\\gamma + 2)}{2}", "- \\cos{(\\chi - \\gamma)}", "\\cos{(\\chi - \\gamma)}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True), Add(log(Symbol('\\\\gamma', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), log(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Integer(2)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))))", "cos(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))"]}, {"premise_expression": "\\delta \\sigma \\xi", "variable": "\\delta", "positive": "\\frac{\\delta^{2} \\sigma \\xi}{2}", "negatives": ["\\frac{\\delta \\sigma^{2} \\xi}{2}", "\\frac{\\delta \\sigma \\xi^{2}}{2}", "\\frac{\\delta^{2} \\sigma}{2 \\xi}", "\\sigma \\xi \\log{(\\delta)}"], "srepr_premise_expression": "Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Symbol('\\\\sigma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "Mul(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True), log(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\alpha \\psi", "variable": "\\alpha", "positive": "\\frac{\\alpha^{2} \\psi}{2}", "negatives": ["\\frac{\\alpha \\psi^{2}}{2}", "\\psi e^{\\alpha}", "\\alpha \\psi e^{\\psi}", "\\frac{\\alpha (\\alpha + 2 \\psi)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "Mul(Symbol('\\\\psi', commutative=True), exp(Symbol('\\\\alpha', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True), exp(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "- \\pi + \\frac{\\omega}{\\beta}", "variable": "\\beta", "positive": "- \\beta \\pi + \\omega \\log{(\\beta)}", "negatives": ["- \\omega \\pi + \\frac{\\omega^{2}}{2 \\beta}", "- \\frac{\\pi^{2}}{2} + \\frac{\\omega \\pi}{\\beta}", "\\frac{\\beta^{2}}{2} + \\frac{\\beta \\pi}{\\omega}", "\\frac{\\beta (- \\beta + 2 \\omega \\pi)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\beta', commutative=True))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Pow(Symbol('\\\\omega', commutative=True), Integer(2))))", "Add(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2))), Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)))", "Add(Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2))), Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\omega \\xi", "variable": "\\xi", "positive": "\\frac{\\omega \\xi^{2}}{2}", "negatives": ["\\frac{\\omega^{2} \\xi}{2}", "\\frac{\\xi (- 2 \\omega + \\xi)}{2}", "\\frac{\\xi (2 \\omega - \\xi)}{2}", "\\omega e^{\\frac{\\xi}{\\omega}}"], "srepr_premise_expression": "Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Symbol('\\\\omega', commutative=True), exp(Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "- \\beta + \\log{(\\alpha)}", "variable": "\\beta", "positive": "\\frac{\\beta (- \\beta + 2 \\log{(\\alpha)})}{2}", "negatives": ["\\frac{\\beta (\\beta + 2 \\log{(\\alpha)})}{2}", "\\alpha (- \\beta + \\log{(\\alpha)} - 1)", "\\log{(\\alpha)} \\log{(\\beta)}", "\\frac{\\alpha^{2} \\beta^{2}}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), log(Symbol('\\\\alpha', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), log(Symbol('\\\\alpha', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), log(Symbol('\\\\alpha', commutative=True)))))", "Mul(Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), log(Symbol('\\\\alpha', commutative=True)), Integer(-1)))", "Mul(log(Symbol('\\\\alpha', commutative=True)), log(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\beta', commutative=True), Integer(2)))"]}, {"premise_expression": "\\beta \\chi + \\delta", "variable": "\\delta", "positive": "\\frac{\\delta (2 \\beta \\chi + \\delta)}{2}", "negatives": ["\\frac{\\chi \\delta (2 \\beta + \\delta)}{2}", "\\frac{\\beta (\\beta \\chi + 2 \\delta)}{2}", "\\frac{\\chi (\\beta \\chi + 2 \\delta)}{2}", "\\frac{\\beta \\chi \\delta^{2}}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True)), Symbol('\\\\delta', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True)), Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(2)))"]}, {"premise_expression": "\\frac{\\beta}{\\gamma}", "variable": "\\gamma", "positive": "\\beta \\log{(\\gamma)}", "negatives": ["\\frac{\\beta^{2}}{2 \\gamma}", "- \\cos{(\\beta - \\gamma)}", "\\log{(\\gamma)} \\cos{(\\beta)}", "\\frac{\\gamma (\\log{(\\gamma)} - 1)}{\\beta}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\beta', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))))", "Mul(log(Symbol('\\\\gamma', commutative=True)), cos(Symbol('\\\\beta', commutative=True)))", "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True), Add(log(Symbol('\\\\gamma', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\psi + \\log{(\\gamma)}", "variable": "\\gamma", "positive": "\\gamma (\\psi + \\log{(\\gamma)} - 1)", "negatives": ["\\gamma (- \\psi + \\log{(\\gamma^{\\psi})})", "\\frac{\\psi (\\psi + 2 \\log{(\\gamma)})}{2}", "\\frac{\\gamma (\\gamma + 2 \\log{(\\psi)})}{2}", "\\psi \\log{(\\gamma)}"], "srepr_premise_expression": "Add(Symbol('\\\\psi', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\psi', commutative=True), log(Symbol('\\\\gamma', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), log(Pow(Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(2), log(Symbol('\\\\gamma', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), log(Symbol('\\\\psi', commutative=True)))))", "Mul(Symbol('\\\\psi', commutative=True), log(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "e^{\\beta + \\xi}", "variable": "\\beta", "positive": "e^{\\beta + \\xi}", "negatives": ["- \\cos{(\\beta + \\xi)}", "\\sin{(\\beta - \\xi)}", "- \\beta \\xi - \\cos{(\\beta)}", "\\frac{\\beta (\\beta + 2 e^{\\xi})}{2}"], "srepr_premise_expression": "exp(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "exp(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True))))", "sin(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\beta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), exp(Symbol('\\\\xi', commutative=True)))))"]}, {"premise_expression": "\\beta - \\gamma", "variable": "\\gamma", "positive": "\\frac{\\gamma (2 \\beta - \\gamma)}{2}", "negatives": ["\\frac{\\beta (\\beta - 2 \\gamma)}{2}", "\\frac{\\beta \\gamma^{2}}{2}", "\\sin{(\\beta + \\gamma)}", "\\frac{\\gamma^{2} \\sin{(\\beta)}}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)))", "sin(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), sin(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "\\chi - \\omega", "variable": "\\omega", "positive": "\\frac{\\omega (2 \\chi - \\omega)}{2}", "negatives": ["\\frac{\\chi (\\chi - 2 \\omega)}{2}", "- \\cos{(\\chi - \\omega)}", "- e^{\\chi - \\omega}", "\\frac{\\omega (\\omega + 2 e^{\\chi})}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))))", "Mul(Integer(-1), exp(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), exp(Symbol('\\\\chi', commutative=True)))))"]}, {"premise_expression": "\\chi - \\sigma", "variable": "\\sigma", "positive": "\\frac{\\sigma (2 \\chi - \\sigma)}{2}", "negatives": ["\\frac{\\sigma (2 \\chi + \\sigma)}{2}", "\\frac{\\sigma (- 2 \\chi + \\sigma)}{2}", "\\frac{\\chi (\\chi - 2 \\sigma)}{2}", "\\frac{\\sigma (- \\sigma + 2 \\sin{(\\chi)})}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\chi', commutative=True)))))"]}, {"premise_expression": "\\omega (\\chi - \\delta)", "variable": "\\delta", "positive": "\\frac{\\delta \\omega (2 \\chi - \\delta)}{2}", "negatives": ["\\frac{\\omega^{2} (\\chi - \\delta)}{2}", "\\frac{\\chi \\omega (\\chi - 2 \\delta)}{2}", "\\frac{\\delta (- \\delta + 2 \\omega^{\\chi})}{2}", "\\frac{\\delta (\\delta + 2 \\omega^{\\chi})}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), Pow(Symbol('\\\\omega', commutative=True), Symbol('\\\\chi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), Pow(Symbol('\\\\omega', commutative=True), Symbol('\\\\chi', commutative=True)))))"]}, {"premise_expression": "\\gamma + \\xi", "variable": "\\gamma", "positive": "\\frac{\\gamma (\\gamma + 2 \\xi)}{2}", "negatives": ["\\frac{\\gamma (\\gamma - 2 \\xi)}{2}", "\\frac{\\xi (2 \\gamma + \\xi)}{2}", "\\frac{\\gamma (\\gamma + 2 \\log{(\\xi)})}{2}", "\\frac{\\gamma (- \\gamma + 2 \\sin{(\\xi)})}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), log(Symbol('\\\\xi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\xi', commutative=True)))))"]}, {"premise_expression": "\\beta \\delta + \\omega", "variable": "\\delta", "positive": "\\frac{\\delta (\\beta \\delta + 2 \\omega)}{2}", "negatives": ["\\frac{\\beta (\\beta \\delta + 2 \\omega)}{2}", "\\frac{\\omega (2 \\beta \\delta + \\omega)}{2}", "\\frac{\\delta (\\delta + 2 \\omega^{\\omega})}{2}", "\\frac{\\beta \\delta^{2} \\omega}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True)), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), Pow(Symbol('\\\\omega', commutative=True), Symbol('\\\\omega', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Symbol('\\\\omega', commutative=True))"]}, {"premise_expression": "\\sin{(\\chi + \\delta)}", "variable": "\\delta", "positive": "- \\cos{(\\chi + \\delta)}", "negatives": ["\\log{(\\chi)} \\log{(\\delta)}", "\\delta", "\\chi^{2} \\delta", "\\delta (- \\chi + e^{\\chi})"], "srepr_premise_expression": "sin(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True))))", "srepr_negatives": ["Mul(log(Symbol('\\\\chi', commutative=True)), log(Symbol('\\\\delta', commutative=True)))", "Symbol('\\\\delta', commutative=True)", "Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\delta', commutative=True))", "Mul(Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), exp(Symbol('\\\\chi', commutative=True))))"]}, {"premise_expression": "\\alpha \\omega", "variable": "\\alpha", "positive": "\\frac{\\alpha^{2} \\omega}{2}", "negatives": ["\\frac{\\alpha \\omega^{2}}{2}", "e^{\\alpha - \\omega}", "- \\alpha \\omega - \\cos{(\\alpha)}", "e^{\\omega} \\log{(\\alpha)}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\omega', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "exp(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\alpha', commutative=True))))", "Mul(exp(Symbol('\\\\omega', commutative=True)), log(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "- \\gamma + \\pi - \\xi", "variable": "\\xi", "positive": "\\frac{\\xi (- 2 \\gamma + 2 \\pi - \\xi)}{2}", "negatives": ["\\frac{\\gamma (- \\gamma + 2 \\pi - 2 \\xi)}{2}", "\\frac{\\pi (- 2 \\gamma + \\pi - 2 \\xi)}{2}", "\\frac{\\xi (2 \\gamma + 2 \\pi - \\xi)}{2}", "\\frac{\\xi^{2} (\\gamma + \\pi)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\omega - \\sigma", "variable": "\\omega", "positive": "\\frac{\\omega (\\omega - 2 \\sigma)}{2}", "negatives": ["\\frac{\\sigma (2 \\omega - \\sigma)}{2}", "\\frac{\\omega (- \\omega + 2 \\sin{(\\sigma)})}{2}", "\\frac{\\omega^{2}}{2 \\sigma}", "- \\cos{(\\omega - \\sigma)}"], "srepr_premise_expression": "Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\sigma', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))"]}, {"premise_expression": "- \\pi - \\psi + \\xi", "variable": "\\pi", "positive": "\\frac{\\pi (- \\pi - 2 \\psi + 2 \\xi)}{2}", "negatives": ["\\frac{\\psi (- 2 \\pi - \\psi + 2 \\xi)}{2}", "\\frac{\\xi (- 2 \\pi - 2 \\psi + \\xi)}{2}", "\\frac{\\pi (\\pi \\xi + 2 \\psi)}{2}", "\\frac{\\pi (- \\pi + 2 \\xi^{\\psi})}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), Pow(Symbol('\\\\xi', commutative=True), Symbol('\\\\psi', commutative=True)))))"]}, {"premise_expression": "\\frac{\\pi}{\\beta}", "variable": "\\pi", "positive": "\\frac{\\pi^{2}}{2 \\beta}", "negatives": ["\\pi \\log{(\\beta)}", "\\beta e^{\\pi}", "\\frac{\\pi^{2} e^{\\beta}}{2}", "e^{\\beta + \\pi}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\beta', commutative=True)))", "Mul(Symbol('\\\\beta', commutative=True), exp(Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), exp(Symbol('\\\\beta', commutative=True)))", "exp(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\log{(\\gamma \\pi)}", "variable": "\\pi", "positive": "\\pi (\\log{(\\gamma \\pi)} - 1)", "negatives": ["\\gamma (\\log{(\\gamma \\pi)} - 1)", "\\pi (\\log{(\\frac{\\pi}{\\gamma})} - 1)", "\\gamma \\pi (\\log{(\\pi)} - 1)", "- \\cos{(\\gamma - \\pi)}"], "srepr_premise_expression": "log(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\pi', commutative=True), Add(log(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\gamma', commutative=True), Add(log(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\pi', commutative=True), Add(log(Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True), Add(log(Symbol('\\\\pi', commutative=True)), Integer(-1)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))"]}, {"premise_expression": "\\beta \\pi", "variable": "\\beta", "positive": "\\frac{\\beta^{2} \\pi}{2}", "negatives": ["\\frac{\\beta \\pi^{2}}{2}", "\\frac{\\beta^{2} \\log{(\\pi)}}{2}", "\\frac{\\beta^{2} (\\pi - 1)}{2}", "\\frac{\\beta (- \\beta + 2 \\log{(\\pi)})}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\pi', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), log(Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Add(Symbol('\\\\pi', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), log(Symbol('\\\\pi', commutative=True)))))"]}, {"premise_expression": "- \\beta + \\delta", "variable": "\\beta", "positive": "\\frac{\\beta (- \\beta + 2 \\delta)}{2}", "negatives": ["\\frac{\\delta (- 2 \\beta + \\delta)}{2}", "\\frac{\\beta^{2} \\sin{(\\delta)}}{2}", "\\frac{\\beta \\delta (\\beta + 2)}{2}", "\\frac{\\beta^{2}}{2 \\delta}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\delta', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\delta', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), sin(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)))"]}, {"premise_expression": "\\beta \\sin{(\\alpha)}", "variable": "\\beta", "positive": "\\frac{\\beta^{2} \\sin{(\\alpha)}}{2}", "negatives": ["\\frac{\\alpha^{2} \\beta^{2}}{2}", "- \\beta \\cos{(\\alpha)}", "\\alpha \\log{(\\beta)}", "e^{- \\alpha + \\beta}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), sin(Symbol('\\\\alpha', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), sin(Symbol('\\\\alpha', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\beta', commutative=True), Integer(2)))", "Mul(Integer(-1), Symbol('\\\\beta', commutative=True), cos(Symbol('\\\\alpha', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\beta', commutative=True)))", "exp(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "\\beta \\delta", "variable": "\\beta", "positive": "\\frac{\\beta^{2} \\delta}{2}", "negatives": ["\\frac{\\beta \\delta^{2}}{2}", "\\frac{\\beta (- \\beta + 2 \\delta)}{2}", "\\frac{\\beta^{2} \\sin{(\\delta)}}{2}", "\\frac{\\beta (\\beta - 2 \\delta)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\delta', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), sin(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True))))"]}, {"premise_expression": "\\frac{\\alpha + \\sigma}{\\beta}", "variable": "\\alpha", "positive": "\\frac{\\alpha (\\alpha + 2 \\sigma)}{2 \\beta}", "negatives": ["- \\frac{\\alpha (- \\alpha + 2 \\sigma)}{2 \\beta}", "\\frac{\\sigma (2 \\alpha + \\sigma)}{2 \\beta}", "\\frac{\\alpha (\\alpha \\beta + 2 \\sigma)}{2}", "\\frac{\\alpha (\\alpha + 2 \\beta + 2 \\sigma)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\chi + \\frac{\\psi}{\\omega}", "variable": "\\psi", "positive": "\\chi \\psi + \\frac{\\psi^{2}}{2 \\omega}", "negatives": ["\\chi \\omega + \\psi \\log{(\\omega)}", "\\frac{\\psi (2 \\chi - \\psi)}{2 \\omega}", "\\frac{\\psi (2 \\chi + 2 \\omega + \\psi)}{2}", "\\frac{\\chi^{2}}{2} + \\frac{\\chi \\psi}{\\omega}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Pow(Symbol('\\\\psi', commutative=True), Integer(2))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Symbol('\\\\psi', commutative=True), log(Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Add(Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2))), Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "e^{\\chi - \\gamma}", "variable": "\\gamma", "positive": "- e^{\\chi - \\gamma}", "negatives": ["e^{\\chi - \\gamma}", "\\frac{\\sin{(\\gamma)}}{\\chi}", "\\log{(\\gamma)} \\cos{(\\chi)}", "\\chi \\gamma + e^{\\gamma}"], "srepr_premise_expression": "exp(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Integer(-1), exp(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))))", "srepr_negatives": ["exp(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), sin(Symbol('\\\\gamma', commutative=True)))", "Mul(log(Symbol('\\\\gamma', commutative=True)), cos(Symbol('\\\\chi', commutative=True)))", "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True)), exp(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "- \\chi + \\cos{(\\psi)}", "variable": "\\chi", "positive": "\\frac{\\chi (- \\chi + 2 \\cos{(\\psi)})}{2}", "negatives": ["- \\chi \\psi + \\sin{(\\psi)}", "\\frac{\\chi^{2}}{2 \\psi}", "\\frac{\\chi^{2}}{2} + \\sin{(\\chi)}", "\\frac{\\chi^{2} \\psi^{2}}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), cos(Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\psi', commutative=True)))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True)), sin(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))", "Add(Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2))), sin(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))"]}, {"premise_expression": "\\cos{(\\delta - \\omega)}", "variable": "\\omega", "positive": "- \\sin{(\\delta - \\omega)}", "negatives": ["\\sin{(\\delta - \\omega)}", "\\sin{(\\delta + \\omega)}", "\\delta \\sin{(\\omega)}", "\\frac{\\omega (- 2 \\delta + \\omega)}{2}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Integer(-1), sin(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))))", "srepr_negatives": ["sin(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "sin(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\delta', commutative=True), sin(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "- \\chi + \\cos{(\\delta)}", "variable": "\\chi", "positive": "\\frac{\\chi (- \\chi + 2 \\cos{(\\delta)})}{2}", "negatives": ["\\frac{\\chi (\\chi + 2 e^{\\delta})}{2}", "\\frac{\\chi (- \\chi + 2 \\delta)}{2}", "\\frac{\\chi^{2} \\log{(\\delta)}}{2}", "\\frac{\\chi^{2} \\sin{(\\delta)}}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), cos(Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\delta', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), exp(Symbol('\\\\delta', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), log(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), sin(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "- \\chi + \\sin{(\\beta)}", "variable": "\\beta", "positive": "- \\beta \\chi - \\cos{(\\beta)}", "negatives": ["- \\beta \\chi + e^{\\beta}", "- \\chi \\cos{(\\beta)}", "e^{\\beta - \\chi}", "\\cos{(\\beta - \\chi)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), sin(Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\beta', commutative=True))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True)), exp(Symbol('\\\\beta', commutative=True)))", "Mul(Integer(-1), Symbol('\\\\chi', commutative=True), cos(Symbol('\\\\beta', commutative=True)))", "exp(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True))))", "cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True))))"]}, {"premise_expression": "- \\chi + \\omega", "variable": "\\chi", "positive": "\\frac{\\chi (- \\chi + 2 \\omega)}{2}", "negatives": ["\\frac{\\omega (- 2 \\chi + \\omega)}{2}", "\\frac{\\chi (\\chi + 2 e^{\\omega})}{2}", "e^{\\chi + \\omega}", "\\frac{\\chi^{2}}{2 \\omega}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), exp(Symbol('\\\\omega', commutative=True)))))", "exp(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))"]}, {"premise_expression": "\\frac{\\sin{(\\sigma)}}{\\xi}", "variable": "\\sigma", "positive": "- \\frac{\\cos{(\\sigma)}}{\\xi}", "negatives": ["\\xi e^{\\sigma}", "- \\sigma \\xi + \\sin{(\\sigma)}", "\\log{(\\xi)} \\sin{(\\sigma)}", "\\log{(\\sigma)} \\log{(\\xi)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), sin(Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Integer(-1), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), cos(Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\xi', commutative=True), exp(Symbol('\\\\sigma', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True)), sin(Symbol('\\\\sigma', commutative=True)))", "Mul(log(Symbol('\\\\xi', commutative=True)), sin(Symbol('\\\\sigma', commutative=True)))", "Mul(log(Symbol('\\\\sigma', commutative=True)), log(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\log{(\\frac{\\delta}{\\beta})}", "variable": "\\delta", "positive": "\\delta (\\log{(\\frac{\\delta}{\\beta})} - 1)", "negatives": ["\\beta (\\log{(\\frac{\\delta}{\\beta})} + 1)", "\\frac{\\delta (\\log{(\\delta)} - 1)}{\\beta}", "\\delta (\\beta + \\log{(\\delta)} - 1)", "- \\cos{(\\beta - \\delta)}"], "srepr_premise_expression": "log(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\delta', commutative=True), Add(log(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\beta', commutative=True), Add(log(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True))), Integer(1)))", "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True), Add(log(Symbol('\\\\delta', commutative=True)), Integer(-1)))", "Mul(Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\beta', commutative=True), log(Symbol('\\\\delta', commutative=True)), Integer(-1)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)))))"]}, {"premise_expression": "- \\gamma + e^{\\omega}", "variable": "\\omega", "positive": "- \\gamma \\omega + e^{\\omega}", "negatives": ["\\gamma \\omega + e^{\\omega}", "\\frac{\\gamma (- \\gamma + 2 e^{\\omega})}{2}", "\\log{(\\omega)} \\cos{(\\gamma)}", "\\frac{\\omega^{2}}{2 \\gamma}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), exp(Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True)), exp(Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True)), exp(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\omega', commutative=True)))))", "Mul(log(Symbol('\\\\omega', commutative=True)), cos(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))"]}, {"premise_expression": "- \\alpha + \\frac{\\gamma}{\\beta}", "variable": "\\alpha", "positive": "- \\frac{\\alpha^{2}}{2} + \\frac{\\alpha \\gamma}{\\beta}", "negatives": ["\\frac{\\alpha \\gamma (- \\alpha + 2 \\beta)}{2}", "\\frac{\\alpha^{2}}{2} + \\frac{\\alpha \\beta}{\\gamma}", "- \\alpha \\beta + \\gamma \\log{(\\beta)}", "\\frac{\\alpha (- \\alpha + 2 \\beta + 2 \\gamma)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2))), Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\beta', commutative=True))))", "Add(Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2))), Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1))))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True)), Mul(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\beta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\gamma', commutative=True))))"]}, {"premise_expression": "\\beta \\delta", "variable": "\\beta", "positive": "\\frac{\\beta^{2} \\delta}{2}", "negatives": ["\\frac{\\beta \\delta^{2}}{2}", "- \\delta \\cos{(\\beta)}", "\\frac{\\sin{(\\beta)}}{\\delta}", "\\sin{(\\beta - \\delta)}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\delta', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(2)))", "Mul(Integer(-1), Symbol('\\\\delta', commutative=True), cos(Symbol('\\\\beta', commutative=True)))", "Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), sin(Symbol('\\\\beta', commutative=True)))", "sin(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))"]}, {"premise_expression": "\\cos{(\\beta + \\delta)}", "variable": "\\delta", "positive": "\\sin{(\\beta + \\delta)}", "negatives": ["\\beta \\log{(\\delta)}", "\\beta e^{\\frac{\\delta}{\\beta}}", "\\frac{\\delta^{2}}{2 \\beta}", "\\delta (- \\beta + \\log{(\\delta^{\\beta})})"], "srepr_premise_expression": "cos(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "sin(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\beta', commutative=True), log(Symbol('\\\\delta', commutative=True)))", "Mul(Symbol('\\\\beta', commutative=True), exp(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Pow(Symbol('\\\\delta', commutative=True), Integer(2)))", "Mul(Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), log(Pow(Symbol('\\\\delta', commutative=True), Symbol('\\\\beta', commutative=True)))))"]}, {"premise_expression": "\\frac{\\alpha}{\\pi}", "variable": "\\alpha", "positive": "\\frac{\\alpha^{2}}{2 \\pi}", "negatives": ["\\alpha \\log{(\\pi)}", "\\frac{\\alpha^{2} \\log{(\\pi)}}{2}", "\\frac{\\alpha^{2} \\sin{(\\pi)}}{2}", "\\frac{\\alpha (- \\alpha + 2 \\pi)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), log(Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), sin(Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "- \\sin{(\\beta - \\gamma)}", "variable": "\\beta", "positive": "\\cos{(\\beta - \\gamma)}", "negatives": ["- \\cos{(\\beta - \\gamma)}", "- \\frac{\\cos{(\\beta)}}{\\gamma}", "\\frac{\\beta (\\beta - 2 \\gamma)}{2}", "\\beta \\gamma - \\cos{(\\beta)}"], "srepr_premise_expression": "Mul(Integer(-1), sin(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))))", "Mul(Integer(-1), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), cos(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True))))", "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\beta', commutative=True))))"]}, {"premise_expression": "\\omega + \\log{(\\delta)}", "variable": "\\omega", "positive": "\\frac{\\omega (\\omega + 2 \\log{(\\delta)})}{2}", "negatives": ["\\frac{\\omega (- \\omega + 2 \\log{(\\delta)})}{2}", "\\delta (\\omega + \\log{(\\delta)} - 1)", "\\frac{\\omega^{2} \\cos{(\\delta)}}{2}", "\\frac{\\omega^{2} e^{\\delta}}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), log(Symbol('\\\\delta', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), log(Symbol('\\\\delta', commutative=True)))))", "Mul(Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\delta', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), cos(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), exp(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "- \\delta + \\xi", "variable": "\\xi", "positive": "\\frac{\\xi (- 2 \\delta + \\xi)}{2}", "negatives": ["\\frac{\\xi (2 \\delta - \\xi)}{2}", "\\frac{\\delta (- \\delta + 2 \\xi)}{2}", "\\frac{\\xi^{2} \\log{(\\delta)}}{2}", "e^{- \\delta + \\xi}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), log(Symbol('\\\\delta', commutative=True)))", "exp(Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\sigma \\cos{(\\beta)}", "variable": "\\sigma", "positive": "\\frac{\\sigma^{2} \\cos{(\\beta)}}{2}", "negatives": ["\\frac{\\sigma^{2} \\sin{(\\beta)}}{2}", "\\beta \\sigma \\sin{(\\beta)}", "\\sigma \\sin{(\\beta)}", "\\frac{\\sigma (- \\sigma + 2 \\log{(\\beta)})}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\sigma', commutative=True), cos(Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), cos(Symbol('\\\\beta', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), sin(Symbol('\\\\beta', commutative=True)))", "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True), sin(Symbol('\\\\beta', commutative=True)))", "Mul(Symbol('\\\\sigma', commutative=True), sin(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), Mul(Integer(2), log(Symbol('\\\\beta', commutative=True)))))"]}, {"premise_expression": "\\gamma \\omega", "variable": "\\omega", "positive": "\\frac{\\gamma \\omega^{2}}{2}", "negatives": ["\\frac{\\gamma^{2} \\omega}{2}", "0", "\\log{(\\omega)} \\cos{(\\gamma)}", "- \\cos{(\\gamma + \\omega)}"], "srepr_premise_expression": "Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Symbol('\\\\omega', commutative=True))", "Integer(0)", "Mul(log(Symbol('\\\\omega', commutative=True)), cos(Symbol('\\\\gamma', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True))))"]}, {"premise_expression": "\\cos^{\\alpha}{(\\xi)}", "variable": "\\xi", "positive": "\\int \\cos^{\\alpha}{(\\xi)} d\\xi", "negatives": ["\\xi (\\log{(\\frac{\\xi}{\\alpha})} - 1)", "\\frac{\\xi (- \\xi + 2 \\cos{(\\alpha)})}{2}", "\\frac{\\xi (2 \\alpha + \\xi)}{2}", "\\frac{\\xi (- \\xi + 2 \\log{(\\alpha)})}{2}"], "srepr_premise_expression": "Pow(cos(Symbol('\\\\xi', commutative=True)), Symbol('\\\\alpha', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Integral(Pow(cos(Symbol('\\\\xi', commutative=True)), Symbol('\\\\alpha', commutative=True)), Tuple(Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\xi', commutative=True), Add(log(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\alpha', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), log(Symbol('\\\\alpha', commutative=True)))))"]}, {"premise_expression": "\\delta \\sin{(\\chi)}", "variable": "\\chi", "positive": "- \\delta \\cos{(\\chi)}", "negatives": ["\\delta \\sin{(\\chi)}", "- \\chi \\delta + \\sin{(\\chi)}", "\\frac{\\chi^{2} \\delta}{2}", "\\frac{\\delta^{2} \\sin{(\\chi)}}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\delta', commutative=True), sin(Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Integer(-1), Symbol('\\\\delta', commutative=True), cos(Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\delta', commutative=True), sin(Symbol('\\\\chi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True)), sin(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\delta', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), sin(Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "\\frac{\\alpha}{\\psi} + \\delta", "variable": "\\delta", "positive": "\\frac{\\alpha \\delta}{\\psi} + \\frac{\\delta^{2}}{2}", "negatives": ["\\frac{\\delta (\\alpha \\delta + 2 \\psi)}{2}", "\\frac{\\delta (2 \\alpha - \\delta + 2 \\psi)}{2}", "\\frac{\\delta (- 2 \\alpha + \\delta \\psi)}{2}", "\\frac{\\alpha \\delta^{2} \\psi}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1))), Symbol('\\\\delta', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1))), Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))"]}, {"premise_expression": "\\frac{\\sin{(\\beta)}}{\\xi}", "variable": "\\beta", "positive": "- \\frac{\\cos{(\\beta)}}{\\xi}", "negatives": ["\\frac{\\beta^{2} \\xi}{2}", "\\sin{(\\beta - \\xi)}", "\\frac{\\beta^{2} \\log{(\\xi)}}{2}", "\\frac{\\beta (- \\beta + 2 \\xi)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), sin(Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Integer(-1), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), cos(Symbol('\\\\beta', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))", "sin(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), log(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\alpha \\cos{(\\omega)}", "variable": "\\alpha", "positive": "\\frac{\\alpha^{2} \\cos{(\\omega)}}{2}", "negatives": ["\\frac{\\alpha^{2} \\log{(\\omega)}}{2}", "\\frac{\\alpha (- \\alpha + 2 \\cos{(\\omega)})}{2}", "- \\frac{\\cos{(\\alpha)}}{\\omega}", "\\alpha \\sin{(\\omega)}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), cos(Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), cos(Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), log(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\omega', commutative=True)))))", "Mul(Integer(-1), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), cos(Symbol('\\\\alpha', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), sin(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\gamma \\sigma", "variable": "\\sigma", "positive": "\\frac{\\gamma \\sigma^{2}}{2}", "negatives": ["\\frac{\\gamma^{2} \\sigma}{2}", "\\frac{\\sigma^{2} \\log{(\\gamma)}}{2}", "\\frac{\\sigma (2 \\gamma - \\sigma)}{2}", "\\gamma \\sigma + e^{\\sigma}"], "srepr_premise_expression": "Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Symbol('\\\\sigma', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), log(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Add(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True)), exp(Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "- \\beta + \\pi", "variable": "\\pi", "positive": "\\frac{\\pi (- 2 \\beta + \\pi)}{2}", "negatives": ["\\frac{\\beta (- \\beta + 2 \\pi)}{2}", "\\frac{\\beta \\pi^{2}}{2}", "- \\sin{(\\beta - \\pi)}", "\\cos{(\\beta - \\pi)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "Mul(Integer(-1), sin(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))", "cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "- \\alpha + \\delta + \\psi", "variable": "\\delta", "positive": "\\delta (- \\alpha + \\frac{\\delta}{2} + \\psi)", "negatives": ["\\frac{\\psi (- 2 \\alpha + 2 \\delta + \\psi)}{2}", "\\frac{\\alpha (- \\alpha + 2 \\delta + 2 \\psi)}{2}", "\\frac{\\delta^{2} (\\alpha + \\psi)}{2}", "\\frac{\\delta (\\alpha \\delta + 2 \\psi)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\delta', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "\\sigma \\xi", "variable": "\\xi", "positive": "\\frac{\\sigma \\xi^{2}}{2}", "negatives": ["\\frac{\\sigma^{2} \\xi}{2}", "\\sigma \\sin{(\\xi)}", "\\frac{\\xi^{2} \\cos{(\\sigma)}}{2}", "\\cos{(\\sigma - \\xi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))", "Mul(Symbol('\\\\sigma', commutative=True), sin(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), cos(Symbol('\\\\sigma', commutative=True)))", "cos(Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\delta + \\psi", "variable": "\\delta", "positive": "\\frac{\\delta (\\delta + 2 \\psi)}{2}", "negatives": ["\\frac{\\delta (\\delta - 2 \\psi)}{2}", "\\frac{\\psi (2 \\delta + \\psi)}{2}", "\\frac{\\delta (- \\delta + 2 \\log{(\\psi)})}{2}", "\\frac{\\delta^{2} \\sin{(\\psi)}}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), log(Symbol('\\\\psi', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), sin(Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\frac{e^{\\gamma}}{\\xi}", "variable": "\\xi", "positive": "e^{\\gamma} \\log{(\\xi)}", "negatives": ["\\gamma e^{\\xi}", "\\xi (e^{\\gamma})^{\\gamma}", "- e^{\\gamma - \\xi}", "- \\gamma \\xi - \\cos{(\\xi)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), exp(Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(exp(Symbol('\\\\gamma', commutative=True)), log(Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\gamma', commutative=True), exp(Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\xi', commutative=True), Pow(exp(Symbol('\\\\gamma', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "Mul(Integer(-1), exp(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\frac{\\beta}{\\gamma \\pi}", "variable": "\\beta", "positive": "\\frac{\\beta^{2}}{2 \\gamma \\pi}", "negatives": ["\\frac{\\beta^{2} \\pi}{2 \\gamma}", "\\frac{\\beta^{2} \\gamma}{2 \\pi}", "\\frac{\\beta \\log{(\\pi)}}{\\gamma}", "\\frac{\\beta \\log{(\\gamma)}}{\\pi}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))", "Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), log(Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), log(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\frac{\\alpha}{\\delta} + \\pi", "variable": "\\delta", "positive": "\\alpha \\log{(\\delta)} + \\delta \\pi", "negatives": ["\\frac{\\alpha^{2}}{2 \\delta} + \\alpha \\pi", "\\frac{\\alpha \\pi}{\\delta} + \\frac{\\pi^{2}}{2}", "(\\alpha + \\pi) \\log{(\\delta)}", "\\frac{\\delta (- 2 \\alpha + \\delta)}{2 \\pi}"], "srepr_premise_expression": "Add(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(-1))), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\delta', commutative=True))), Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Add(Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\delta', commutative=True), Integer(-1))), Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2))))", "Mul(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)), log(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\sigma \\cos{(\\delta)}", "variable": "\\sigma", "positive": "\\frac{\\sigma^{2} \\cos{(\\delta)}}{2}", "negatives": ["\\frac{\\sigma^{2} \\log{(\\delta)}}{2}", "\\frac{\\delta \\sigma^{2}}{2}", "\\sigma \\sin{(\\delta)}", "\\frac{\\sigma (\\sigma + 2 \\sin{(\\delta)})}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\sigma', commutative=True), cos(Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), cos(Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), log(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "Mul(Symbol('\\\\sigma', commutative=True), sin(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(2), sin(Symbol('\\\\delta', commutative=True)))))"]}, {"premise_expression": "\\beta - \\delta", "variable": "\\delta", "positive": "\\frac{\\delta (2 \\beta - \\delta)}{2}", "negatives": ["\\frac{\\beta (\\beta - 2 \\delta)}{2}", "\\frac{\\delta^{2} \\log{(\\beta)}}{2}", "\\beta \\delta + e^{\\delta}", "- \\beta \\delta - \\cos{(\\delta)}"], "srepr_premise_expression": "Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), log(Symbol('\\\\beta', commutative=True)))", "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True)), exp(Symbol('\\\\delta', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\delta', commutative=True))))"]}, {"premise_expression": "\\frac{\\omega}{\\psi}", "variable": "\\omega", "positive": "\\frac{\\omega^{2}}{2 \\psi}", "negatives": ["\\omega \\log{(\\psi)}", "- \\frac{\\cos{(\\omega)}}{\\psi}", "\\frac{\\sin{(\\omega)}}{\\psi}", "e^{\\omega - \\psi}"], "srepr_premise_expression": "Mul(Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\psi', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), cos(Symbol('\\\\omega', commutative=True)))", "Mul(Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), sin(Symbol('\\\\omega', commutative=True)))", "exp(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "- \\alpha + \\sin{(\\omega)}", "variable": "\\alpha", "positive": "\\frac{\\alpha (- \\alpha + 2 \\sin{(\\omega)})}{2}", "negatives": ["\\alpha \\omega + \\sin{(\\alpha)}", "\\frac{\\alpha \\omega (\\alpha - 2)}{2}", "- \\alpha \\omega - \\cos{(\\omega)}", "\\frac{\\alpha^{2} \\omega}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), sin(Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\omega', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)), sin(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Integer(-2)))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\omega', commutative=True))"]}, {"premise_expression": "\\alpha \\xi", "variable": "\\xi", "positive": "\\frac{\\alpha \\xi^{2}}{2}", "negatives": ["\\frac{\\alpha^{2} \\xi}{2}", "\\alpha \\sin{(\\xi)}", "\\frac{\\xi^{2} (\\alpha + 1)}{2 \\alpha}", "\\log{(\\alpha)} \\log{(\\xi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))", "Mul(Symbol('\\\\alpha', commutative=True), sin(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), Add(Symbol('\\\\alpha', commutative=True), Integer(1)))", "Mul(log(Symbol('\\\\alpha', commutative=True)), log(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "- \\chi + \\gamma", "variable": "\\chi", "positive": "\\frac{\\chi (- \\chi + 2 \\gamma)}{2}", "negatives": ["\\frac{\\gamma (- 2 \\chi + \\gamma)}{2}", "\\frac{\\chi^{2} \\cos{(\\gamma)}}{2}", "\\sin{(\\chi - \\gamma)}", "- \\cos{(\\chi - \\gamma)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\gamma', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\gamma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), cos(Symbol('\\\\gamma', commutative=True)))", "sin(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))))"]}, {"premise_expression": "\\frac{\\beta}{\\alpha}", "variable": "\\alpha", "positive": "\\beta \\log{(\\alpha)}", "negatives": ["\\frac{\\beta^{2}}{2 \\alpha}", "\\beta e^{\\frac{\\alpha}{\\beta}}", "\\alpha \\beta (\\log{(\\alpha)} - 1)", "e^{\\alpha - \\beta}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\beta', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\beta', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\beta', commutative=True), Integer(2)))", "Mul(Symbol('\\\\beta', commutative=True), exp(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)))))", "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True), Add(log(Symbol('\\\\alpha', commutative=True)), Integer(-1)))", "exp(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\beta', commutative=True))))"]}, {"premise_expression": "\\beta e^{\\psi}", "variable": "\\beta", "positive": "\\frac{\\beta^{2} e^{\\psi}}{2}", "negatives": ["\\beta e^{\\psi}", "\\frac{\\beta^{2} \\psi}{2}", "\\frac{\\beta (\\beta + 2 \\psi)}{2}", "\\frac{\\beta (- \\beta + 2 \\log{(\\psi)})}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), exp(Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), exp(Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\beta', commutative=True), exp(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), log(Symbol('\\\\psi', commutative=True)))))"]}, {"premise_expression": "\\alpha + e^{\\beta}", "variable": "\\beta", "positive": "\\alpha \\beta + e^{\\beta}", "negatives": ["\\alpha \\beta + \\sin{(\\beta)}", "\\frac{\\alpha (\\alpha + 2 e^{\\beta})}{2}", "\\frac{\\beta^{2} e^{\\alpha}}{2}", "\\frac{\\beta^{2}}{2 \\alpha}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), exp(Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True)), exp(Symbol('\\\\beta', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True)), sin(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), exp(Symbol('\\\\beta', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), exp(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\beta', commutative=True), Integer(2)))"]}, {"premise_expression": "\\frac{\\delta}{\\pi}", "variable": "\\delta", "positive": "\\frac{\\delta^{2}}{2 \\pi}", "negatives": ["\\delta \\log{(\\pi)}", "\\frac{\\delta^{2} \\pi}{2}", "\\frac{\\delta (\\delta + 2 \\log{(\\pi)})}{2}", "\\frac{\\delta (- \\delta + 2 \\cos{(\\pi)})}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Symbol('\\\\pi', commutative=True))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), log(Symbol('\\\\pi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\pi', commutative=True)))))"]}, {"premise_expression": "\\chi - \\psi", "variable": "\\psi", "positive": "\\frac{\\psi (2 \\chi - \\psi)}{2}", "negatives": ["\\frac{\\chi (\\chi - 2 \\psi)}{2}", "\\frac{\\psi (- \\psi + 2 \\sin{(\\chi)})}{2}", "\\frac{\\psi (\\psi + 2 e^{\\chi})}{2}", "\\psi \\sin{(2 \\chi)}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\chi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(2), exp(Symbol('\\\\chi', commutative=True)))))", "Mul(Symbol('\\\\psi', commutative=True), sin(Mul(Integer(2), Symbol('\\\\chi', commutative=True))))"]}, {"premise_expression": "- \\pi + \\psi - \\xi", "variable": "\\xi", "positive": "\\frac{\\xi (- 2 \\pi + 2 \\psi - \\xi)}{2}", "negatives": ["\\frac{\\xi (2 \\pi^{\\psi} - \\xi)}{2}", "\\frac{\\xi (2 \\psi^{\\pi} - \\xi)}{2}", "\\frac{\\psi (- 2 \\pi + \\psi - 2 \\xi)}{2}", "\\frac{\\pi (- \\pi + 2 \\psi - 2 \\xi)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Pow(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True))), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Pow(Symbol('\\\\psi', commutative=True), Symbol('\\\\pi', commutative=True))), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True)), Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\frac{e^{\\gamma}}{\\psi}", "variable": "\\psi", "positive": "e^{\\gamma} \\log{(\\psi)}", "negatives": ["- \\gamma \\psi + e^{\\psi}", "\\frac{\\psi (2 \\gamma + \\psi)}{2}", "\\frac{\\psi (2 \\gamma - \\psi)}{2}", "\\psi (- \\gamma + \\log{(\\psi)} - 1)"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), exp(Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(exp(Symbol('\\\\gamma', commutative=True)), log(Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True)), exp(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), log(Symbol('\\\\psi', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\omega \\sigma", "variable": "\\omega", "positive": "\\frac{\\omega^{2} \\sigma}{2}", "negatives": ["\\frac{\\omega \\sigma^{2}}{2}", "\\sigma e^{\\omega}", "- \\frac{\\cos{(\\omega)}}{\\sigma}", "\\frac{\\omega^{2} \\log{(\\sigma)}}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Symbol('\\\\sigma', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "Mul(Symbol('\\\\sigma', commutative=True), exp(Symbol('\\\\omega', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), cos(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), log(Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "e^{\\beta^{\\gamma}}", "variable": "\\beta", "positive": "\\frac{e^{- \\frac{i \\pi}{\\gamma}} \\gamma(\\frac{1}{\\gamma}, \\beta^{\\gamma} e^{i \\pi})}{\\gamma}", "negatives": ["\\beta (- \\gamma + \\log{(\\beta^{\\gamma})})", "\\frac{\\beta (\\beta + 2 \\log{(\\gamma)})}{2}", "\\frac{\\beta^{2} e^{\\gamma}}{2}", "\\int \\cos^{\\gamma}{(\\beta)} d\\beta"], "srepr_premise_expression": "exp(Pow(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), exp(Mul(Integer(-1), I, pi, Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)))), lowergamma(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Mul(Pow(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)), exp_polar(Mul(I, pi)))))", "srepr_negatives": ["Mul(Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), log(Pow(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), log(Symbol('\\\\gamma', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), exp(Symbol('\\\\gamma', commutative=True)))", "Integral(Pow(cos(Symbol('\\\\beta', commutative=True)), Symbol('\\\\gamma', commutative=True)), Tuple(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "\\gamma + e^{\\sigma}", "variable": "\\sigma", "positive": "\\gamma \\sigma + e^{\\sigma}", "negatives": ["\\gamma e^{\\sigma}", "\\gamma \\sigma - \\cos{(\\sigma)}", "\\frac{\\gamma (\\gamma + 2 e^{\\sigma})}{2}", "e^{\\gamma} \\log{(\\sigma)}"], "srepr_premise_expression": "Add(Symbol('\\\\gamma', commutative=True), exp(Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True)), exp(Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\gamma', commutative=True), exp(Symbol('\\\\sigma', commutative=True)))", "Add(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), exp(Symbol('\\\\sigma', commutative=True)))))", "Mul(exp(Symbol('\\\\gamma', commutative=True)), log(Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\sin{(\\beta - \\psi)}", "variable": "\\psi", "positive": "\\cos{(\\beta - \\psi)}", "negatives": ["- \\cos{(\\beta - \\psi)}", "e^{- \\beta + \\psi}", "- \\frac{\\cos{(\\psi)}}{\\beta}", "\\beta \\sin{(\\psi)}"], "srepr_premise_expression": "sin(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))", "exp(Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), cos(Symbol('\\\\psi', commutative=True)))", "Mul(Symbol('\\\\beta', commutative=True), sin(Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\frac{\\alpha}{\\xi}", "variable": "\\xi", "positive": "\\alpha \\log{(\\xi)}", "negatives": ["\\frac{\\alpha^{2}}{2 \\xi}", "e^{\\alpha} \\log{(\\xi)}", "\\xi", "\\frac{\\xi^{2} \\log{(\\alpha)}}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "Mul(exp(Symbol('\\\\alpha', commutative=True)), log(Symbol('\\\\xi', commutative=True)))", "Symbol('\\\\xi', commutative=True)", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), log(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "e^{\\alpha - \\delta}", "variable": "\\alpha", "positive": "e^{\\alpha - \\delta}", "negatives": ["- e^{\\alpha - \\delta}", "- \\cos{(\\alpha + \\delta)}", "\\sin{(\\alpha - \\delta)}", "\\frac{\\alpha^{2} \\log{(\\delta)}}{2}"], "srepr_premise_expression": "exp(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "exp(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\delta', commutative=True))))", "sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), log(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\log{(\\psi \\sigma)}", "variable": "\\sigma", "positive": "\\sigma (\\log{(\\psi \\sigma)} - 1)", "negatives": ["\\psi (\\log{(\\psi \\sigma)} - 1)", "\\frac{\\sigma (2 \\psi - \\sigma)}{2}", "e^{\\psi} \\log{(\\sigma)}", "\\frac{\\sigma (\\sigma + 2 \\log{(\\psi)})}{2}"], "srepr_premise_expression": "log(Mul(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\sigma', commutative=True), Add(log(Mul(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\psi', commutative=True), Add(log(Mul(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(exp(Symbol('\\\\psi', commutative=True)), log(Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(2), log(Symbol('\\\\psi', commutative=True)))))"]}, {"premise_expression": "\\log{(\\gamma \\xi)}", "variable": "\\gamma", "positive": "\\gamma (\\log{(\\gamma \\xi)} - 1)", "negatives": ["\\xi (\\log{(\\gamma \\xi)} - 1)", "\\frac{\\gamma (\\log{(\\gamma)} - 1)}{\\xi}", "- \\cos{(\\gamma + \\xi)}", "\\sin{(\\gamma + \\xi)}"], "srepr_premise_expression": "log(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\gamma', commutative=True), Add(log(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\xi', commutative=True), Add(log(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), Add(log(Symbol('\\\\gamma', commutative=True)), Integer(-1)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True))))", "sin(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\log{(\\delta - \\gamma)}", "variable": "\\delta", "positive": "\\delta \\log{(\\delta - \\gamma)} - \\delta - \\gamma \\log{(\\delta - \\gamma)}", "negatives": ["- \\delta \\log{(- \\delta + \\gamma)} + \\gamma \\log{(\\delta - \\gamma)} - \\gamma", "\\frac{\\delta (- \\delta + 2 \\log{(\\gamma)})}{2}", "\\delta \\cos{(\\frac{\\gamma}{\\delta})} + \\gamma \\operatorname{Si}{(\\frac{\\gamma}{\\delta})}", "- e^{- \\delta + \\gamma}"], "srepr_premise_expression": "log(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\delta', commutative=True), log(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), log(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\gamma', commutative=True)))), Mul(Symbol('\\\\gamma', commutative=True), log(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), log(Symbol('\\\\gamma', commutative=True)))))", "Add(Mul(Symbol('\\\\delta', commutative=True), cos(Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True)))), Mul(Symbol('\\\\gamma', commutative=True), Si(Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True)))))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\gamma', commutative=True))))"]}, {"premise_expression": "e^{\\frac{\\alpha}{\\psi}}", "variable": "\\alpha", "positive": "\\psi e^{\\frac{\\alpha}{\\psi}}", "negatives": ["\\sin{(\\alpha - \\psi)}", "\\frac{\\alpha^{2} \\log{(\\psi)}}{2}", "\\alpha (\\log{(\\alpha \\psi)} - 1)", "\\log{(\\alpha)} \\cos{(\\psi)}"], "srepr_premise_expression": "exp(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\psi', commutative=True), exp(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))))", "srepr_negatives": ["sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), log(Symbol('\\\\psi', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), Add(log(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True))), Integer(-1)))", "Mul(log(Symbol('\\\\alpha', commutative=True)), cos(Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\omega + \\psi", "variable": "\\omega", "positive": "\\frac{\\omega (\\omega + 2 \\psi)}{2}", "negatives": ["\\frac{\\omega (- \\omega + 2 \\psi)}{2}", "\\frac{\\psi (2 \\omega + \\psi)}{2}", "\\frac{\\omega (- \\omega + 2 e^{\\psi})}{2}", "\\frac{\\omega (- \\omega + 2 \\sin{(\\psi)})}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\psi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\psi', commutative=True)))))"]}, {"premise_expression": "\\log{(\\alpha \\xi)}", "variable": "\\alpha", "positive": "\\alpha (\\log{(\\alpha \\xi)} - 1)", "negatives": ["\\xi (\\log{(\\alpha \\xi)} - 1)", "\\alpha (\\log{(\\frac{\\xi}{\\alpha})} + 1)", "\\alpha (\\log{(\\frac{\\alpha}{\\xi})} - 1)", "- \\cos{(\\alpha + \\xi)}"], "srepr_premise_expression": "log(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\alpha', commutative=True), Add(log(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\xi', commutative=True), Add(log(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\alpha', commutative=True), Add(log(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))), Integer(1)))", "Mul(Symbol('\\\\alpha', commutative=True), Add(log(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))), Integer(-1)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\log{(\\frac{\\pi}{\\gamma})}", "variable": "\\pi", "positive": "\\pi (\\log{(\\frac{\\pi}{\\gamma})} - 1)", "negatives": ["\\gamma (\\log{(\\frac{\\pi}{\\gamma})} + 1)", "\\log{(\\pi)} \\sin{(\\gamma)}", "\\gamma e^{\\frac{\\pi}{\\gamma}}", "\\frac{\\pi^{2} \\log{(\\gamma)}}{2}"], "srepr_premise_expression": "log(Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\pi', commutative=True), Add(log(Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\gamma', commutative=True), Add(log(Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))), Integer(1)))", "Mul(log(Symbol('\\\\pi', commutative=True)), sin(Symbol('\\\\gamma', commutative=True)))", "Mul(Symbol('\\\\gamma', commutative=True), exp(Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), log(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\delta - \\xi", "variable": "\\delta", "positive": "\\frac{\\delta (\\delta - 2 \\xi)}{2}", "negatives": ["\\frac{\\xi (2 \\delta - \\xi)}{2}", "\\frac{\\delta^{2}}{2 \\xi}", "\\cos{(\\delta - \\xi)}", "\\frac{\\delta (- \\delta + 2 e^{\\xi})}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\xi', commutative=True)))))"]}, {"premise_expression": "e^{- \\chi + \\omega}", "variable": "\\omega", "positive": "e^{- \\chi + \\omega}", "negatives": ["- e^{- \\chi + \\omega}", "\\frac{\\chi \\omega (\\omega + 2)}{2}", "\\frac{\\omega^{2} \\log{(\\chi)}}{2}", "- \\chi \\log{(- \\chi + \\omega)} + \\omega \\log{(\\chi - \\omega)} - \\omega"], "srepr_premise_expression": "exp(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "exp(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), log(Symbol('\\\\chi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\omega', commutative=True)))), Mul(Symbol('\\\\omega', commutative=True), log(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\sin^{\\xi}{(\\beta)}", "variable": "\\beta", "positive": "\\int \\sin^{\\xi}{(\\beta)} d\\beta", "negatives": ["e^{\\xi} \\log{(\\beta)}", "\\beta \\log{(\\xi^{\\xi})}", "\\beta (\\log{(\\frac{\\beta}{\\xi})} - 1)", "\\xi e^{\\beta}"], "srepr_premise_expression": "Pow(sin(Symbol('\\\\beta', commutative=True)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Integral(Pow(sin(Symbol('\\\\beta', commutative=True)), Symbol('\\\\xi', commutative=True)), Tuple(Symbol('\\\\beta', commutative=True)))", "srepr_negatives": ["Mul(exp(Symbol('\\\\xi', commutative=True)), log(Symbol('\\\\beta', commutative=True)))", "Mul(Symbol('\\\\beta', commutative=True), log(Pow(Symbol('\\\\xi', commutative=True), Symbol('\\\\xi', commutative=True))))", "Mul(Symbol('\\\\beta', commutative=True), Add(log(Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))), Integer(-1)))", "Mul(Symbol('\\\\xi', commutative=True), exp(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "\\psi + \\sigma", "variable": "\\sigma", "positive": "\\frac{\\sigma (2 \\psi + \\sigma)}{2}", "negatives": ["\\frac{\\psi (\\psi + 2 \\sigma)}{2}", "\\cos{(\\psi - \\sigma)}", "\\psi e^{\\frac{\\sigma}{\\psi}}", "- \\psi \\operatorname{Ei}{(\\frac{\\psi}{\\sigma})} + \\sigma e^{\\frac{\\psi}{\\sigma}}"], "srepr_premise_expression": "Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\psi', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "cos(Add(Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Symbol('\\\\psi', commutative=True), exp(Mul(Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True), Ei(Mul(Symbol('\\\\psi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1))))), Mul(Symbol('\\\\sigma', commutative=True), exp(Mul(Symbol('\\\\psi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1))))))"]}, {"premise_expression": "\\sigma + \\log{(\\delta)}", "variable": "\\sigma", "positive": "\\frac{\\sigma (\\sigma + 2 \\log{(\\delta)})}{2}", "negatives": ["\\frac{\\sigma (- \\sigma + 2 e^{\\delta})}{2}", "\\frac{\\sigma^{2} \\log{(\\delta)}}{2}", "\\delta (\\sigma + \\log{(\\delta)} - 1)", "\\frac{\\sigma^{2} \\sin{(\\delta)}}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(2), log(Symbol('\\\\delta', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\delta', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), log(Symbol('\\\\delta', commutative=True)))", "Mul(Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\delta', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), sin(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\frac{\\log{(\\delta)}}{\\sigma}", "variable": "\\delta", "positive": "\\frac{\\delta (\\log{(\\delta)} - 1)}{\\sigma}", "negatives": ["\\delta (\\log{(\\delta \\sigma)} - 1)", "\\log{(\\delta)} \\log{(\\sigma)}", "\\frac{\\delta^{2} \\log{(\\sigma)}}{2}", "\\frac{\\delta (- \\delta + 2 \\sigma)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), log(Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Add(log(Symbol('\\\\delta', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\delta', commutative=True), Add(log(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True))), Integer(-1)))", "Mul(log(Symbol('\\\\delta', commutative=True)), log(Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), log(Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\cos{(\\frac{\\alpha}{\\chi})}", "variable": "\\chi", "positive": "\\alpha \\operatorname{Si}{(\\frac{\\alpha}{\\chi})} + \\chi \\cos{(\\frac{\\alpha}{\\chi})}", "negatives": ["- \\alpha \\operatorname{Ei}{(\\frac{\\alpha}{\\chi})} + \\chi e^{\\frac{\\alpha}{\\chi}}", "\\chi (\\log{(\\frac{\\alpha}{\\chi})} + 1)", "\\frac{\\chi (2 \\alpha + \\chi)}{2}", "\\frac{\\chi (\\chi + 2 \\log{(\\alpha)})}{2}"], "srepr_premise_expression": "cos(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\alpha', commutative=True), Si(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(-1))))), Mul(Symbol('\\\\chi', commutative=True), cos(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(-1))))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Ei(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(-1))))), Mul(Symbol('\\\\chi', commutative=True), exp(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(-1))))))", "Mul(Symbol('\\\\chi', commutative=True), Add(log(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), log(Symbol('\\\\alpha', commutative=True)))))"]}, {"premise_expression": "- \\xi + e^{\\pi}", "variable": "\\xi", "positive": "\\frac{\\xi (- \\xi + 2 e^{\\pi})}{2}", "negatives": ["\\frac{\\xi (\\xi + 2 \\log{(\\pi)})}{2}", "- \\pi \\xi + e^{\\pi}", "\\frac{\\xi (4 \\pi + \\xi)}{2}", "e^{\\pi + \\xi}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), exp(Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\pi', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\xi', commutative=True), Mul(Integer(2), log(Symbol('\\\\pi', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True)), exp(Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(4), Symbol('\\\\pi', commutative=True)), Symbol('\\\\xi', commutative=True)))", "exp(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\frac{\\beta}{\\sigma} - \\xi", "variable": "\\sigma", "positive": "\\beta \\log{(\\sigma)} - \\sigma \\xi", "negatives": ["\\beta \\xi \\log{(\\sigma)}", "\\frac{\\beta^{2}}{2 \\sigma} - \\beta \\xi", "\\beta^{\\xi} \\log{(\\sigma)}", "- \\beta \\sigma + \\frac{\\sigma^{2}}{2 \\xi}"], "srepr_premise_expression": "Add(Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1))), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\beta', commutative=True), log(Symbol('\\\\sigma', commutative=True))), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True), log(Symbol('\\\\sigma', commutative=True)))", "Add(Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1))), Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True)))", "Mul(Pow(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True)), log(Symbol('\\\\sigma', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))"]}, {"premise_expression": "\\frac{\\chi}{\\delta} - \\pi", "variable": "\\chi", "positive": "\\frac{\\chi^{2}}{2 \\delta} - \\chi \\pi", "negatives": ["\\chi \\log{(\\delta)} - \\delta \\pi", "\\frac{\\chi (\\chi + 2 \\delta)}{2 \\pi}", "\\frac{\\chi^{2} \\pi^{2}}{2}", "\\frac{\\chi^{2} \\pi^{\\delta}}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(-1))), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Add(Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Pow(Symbol('\\\\delta', commutative=True), Integer(-1))), Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\delta', commutative=True))), Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Pow(Symbol('\\\\pi', commutative=True), Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\alpha \\cos{(\\psi)}", "variable": "\\alpha", "positive": "\\frac{\\alpha^{2} \\cos{(\\psi)}}{2}", "negatives": ["\\alpha \\sin{(\\psi)}", "\\log{(\\alpha)} \\cos{(\\psi)}", "\\log{(\\alpha)} \\log{(\\psi)}", "- \\alpha \\psi + e^{\\alpha}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), cos(Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), cos(Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\alpha', commutative=True), sin(Symbol('\\\\psi', commutative=True)))", "Mul(log(Symbol('\\\\alpha', commutative=True)), cos(Symbol('\\\\psi', commutative=True)))", "Mul(log(Symbol('\\\\alpha', commutative=True)), log(Symbol('\\\\psi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True)), exp(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\sin{(\\beta - \\xi)}", "variable": "\\xi", "positive": "\\cos{(\\beta - \\xi)}", "negatives": ["- \\cos{(\\beta - \\xi)}", "- e^{\\beta - \\xi}", "\\beta \\xi + \\sin{(\\xi)}", "\\frac{\\beta \\xi^{2}}{2}"], "srepr_premise_expression": "sin(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))))", "Mul(Integer(-1), exp(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))))", "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True)), sin(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))"]}, {"premise_expression": "\\gamma \\sigma", "variable": "\\sigma", "positive": "\\frac{\\gamma \\sigma^{2}}{2}", "negatives": ["\\frac{\\gamma^{2} \\sigma}{2}", "\\frac{\\sigma (2 \\gamma - \\sigma)}{2}", "- \\gamma \\sigma + \\sin{(\\sigma)}", "e^{\\gamma + \\sigma}"], "srepr_premise_expression": "Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Symbol('\\\\sigma', commutative=True))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True)), sin(Symbol('\\\\sigma', commutative=True)))", "exp(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\frac{\\omega}{\\xi}", "variable": "\\xi", "positive": "\\omega \\log{(\\xi)}", "negatives": ["\\frac{\\omega^{2}}{2 \\xi}", "\\log{(\\omega)} \\log{(\\xi)}", "\\omega \\xi - \\cos{(\\xi)}", "\\frac{\\xi^{2}}{2 \\omega}"], "srepr_premise_expression": "Mul(Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "Mul(log(Symbol('\\\\omega', commutative=True)), log(Symbol('\\\\xi', commutative=True)))", "Add(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))"]}, {"premise_expression": "\\pi \\psi", "variable": "\\psi", "positive": "\\frac{\\pi \\psi^{2}}{2}", "negatives": ["\\frac{\\pi^{2} \\psi}{2}", "\\frac{\\psi^{2}}{2 \\pi}", "\\frac{\\psi (2 \\pi - \\psi)}{2}", "- \\sin{(\\pi - \\psi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(Integer(-1), sin(Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))"]}, {"premise_expression": "e^{- \\chi + \\omega}", "variable": "\\omega", "positive": "e^{- \\chi + \\omega}", "negatives": ["- e^{- \\chi + \\omega}", "\\chi e^{\\frac{\\omega}{\\chi}}", "\\frac{\\omega (- 2 \\chi + \\omega)}{2}", "\\chi \\omega e^{\\chi}"], "srepr_premise_expression": "exp(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "exp(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\omega', commutative=True))))", "Mul(Symbol('\\\\chi', commutative=True), exp(Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True), exp(Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "\\omega \\cos{(\\xi)}", "variable": "\\xi", "positive": "\\omega \\sin{(\\xi)}", "negatives": ["\\omega \\log{(\\xi)}", "- \\omega \\cos{(\\xi)}", "\\omega e^{\\frac{\\xi}{\\omega}}", "\\frac{\\omega^{2} \\cos{(\\xi)}}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\omega', commutative=True), cos(Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\omega', commutative=True), sin(Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\xi', commutative=True)))", "Mul(Integer(-1), Symbol('\\\\omega', commutative=True), cos(Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), exp(Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), cos(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\beta + \\omega", "variable": "\\beta", "positive": "\\frac{\\beta (\\beta + 2 \\omega)}{2}", "negatives": ["\\frac{\\omega (2 \\beta + \\omega)}{2}", "\\frac{\\beta^{2} e^{\\omega}}{2}", "e^{\\beta - \\omega}", "\\frac{\\beta (\\log{(\\beta)} - 1)}{\\omega}"], "srepr_premise_expression": "Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), exp(Symbol('\\\\omega', commutative=True)))", "exp(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Add(log(Symbol('\\\\beta', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\chi \\sigma", "variable": "\\chi", "positive": "\\frac{\\chi^{2} \\sigma}{2}", "negatives": ["\\frac{\\chi \\sigma^{2}}{2}", "\\frac{\\chi^{2}}{2 \\sigma}", "\\frac{\\chi (\\chi - 2 \\sigma)}{2}", "\\frac{\\chi (\\chi + 2 \\sigma)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\sigma', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\frac{- \\alpha + \\xi}{\\beta}", "variable": "\\xi", "positive": "\\frac{\\xi (- 2 \\alpha + \\xi)}{2 \\beta}", "negatives": ["\\frac{\\xi (2 \\beta + \\xi)}{2 \\alpha}", "\\frac{\\alpha (- \\alpha + 2 \\xi)}{2 \\beta}", "\\frac{\\xi (2 \\alpha - 2 \\beta + \\xi)}{2}", "(- \\alpha + \\xi) \\log{(\\beta)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\xi', commutative=True)), log(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "\\frac{\\beta}{\\psi}", "variable": "\\psi", "positive": "\\beta \\log{(\\psi)}", "negatives": ["\\frac{\\beta^{2}}{2 \\psi}", "\\beta \\psi - \\cos{(\\psi)}", "- \\cos{(\\beta + \\psi)}", "\\psi (\\log{(\\frac{\\beta}{\\psi})} + 1)"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\beta', commutative=True), log(Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))", "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\psi', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\psi', commutative=True))))", "Mul(Symbol('\\\\psi', commutative=True), Add(log(Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))), Integer(1)))"]}, {"premise_expression": "\\gamma \\xi", "variable": "\\xi", "positive": "\\frac{\\gamma \\xi^{2}}{2}", "negatives": ["\\frac{\\gamma^{2} \\xi}{2}", "\\frac{\\xi^{2} (\\gamma - 1)}{2}", "\\gamma e^{\\frac{\\xi}{\\gamma}}", "\\frac{\\xi (\\xi + 2 \\log{(\\gamma)})}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), Add(Symbol('\\\\gamma', commutative=True), Integer(-1)))", "Mul(Symbol('\\\\gamma', commutative=True), exp(Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\xi', commutative=True), Mul(Integer(2), log(Symbol('\\\\gamma', commutative=True)))))"]}, {"premise_expression": "\\sigma \\xi", "variable": "\\xi", "positive": "\\frac{\\sigma \\xi^{2}}{2}", "negatives": ["\\frac{\\sigma^{2} \\xi}{2}", "\\sigma \\xi + \\sin{(\\xi)}", "\\frac{\\xi (2 \\sigma + \\xi)}{2}", "\\frac{\\xi (2 \\sigma - \\xi)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))", "Add(Mul(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True)), sin(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\sigma', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\frac{\\beta}{\\omega}", "variable": "\\omega", "positive": "\\beta \\log{(\\omega)}", "negatives": ["\\frac{\\beta^{2}}{2 \\omega}", "\\omega (\\beta + \\omega)", "- \\frac{\\cos{(\\omega)}}{\\beta}", "\\sin{(\\beta + \\omega)}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\beta', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))", "Mul(Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), cos(Symbol('\\\\omega', commutative=True)))", "sin(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\chi \\gamma", "variable": "\\gamma", "positive": "\\frac{\\chi \\gamma^{2}}{2}", "negatives": ["\\frac{\\chi^{2} \\gamma}{2}", "\\frac{\\gamma^{2} \\log{(\\chi)}}{2}", "\\frac{\\gamma (- 2 \\chi + \\gamma)}{2}", "\\chi e^{\\gamma}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\gamma', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), log(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "Mul(Symbol('\\\\chi', commutative=True), exp(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\frac{\\alpha}{\\gamma}", "variable": "\\gamma", "positive": "\\alpha \\log{(\\gamma)}", "negatives": ["\\frac{\\alpha^{2}}{2 \\gamma}", "\\alpha \\gamma - \\cos{(\\gamma)}", "\\gamma (\\log{(\\frac{\\gamma}{\\alpha})} - 1)", "\\gamma (\\log{(\\alpha \\gamma)} - 1)"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\gamma', commutative=True))))", "Mul(Symbol('\\\\gamma', commutative=True), Add(log(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\gamma', commutative=True), Add(log(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True))), Integer(-1)))"]}, {"premise_expression": "- \\alpha + \\psi", "variable": "\\alpha", "positive": "\\frac{\\alpha (- \\alpha + 2 \\psi)}{2}", "negatives": ["\\frac{\\psi (- 2 \\alpha + \\psi)}{2}", "\\frac{\\alpha (- \\alpha + 2 \\log{(\\psi)})}{2}", "\\frac{\\alpha^{2} e^{\\psi}}{2}", "- \\alpha \\psi + e^{\\alpha}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), log(Symbol('\\\\psi', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), exp(Symbol('\\\\psi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True)), exp(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\frac{\\gamma}{\\alpha}", "variable": "\\alpha", "positive": "\\gamma \\log{(\\alpha)}", "negatives": ["- \\gamma \\cos{(\\alpha)}", "\\frac{\\gamma^{2}}{2 \\alpha}", "\\frac{\\alpha^{2} \\gamma}{2}", "\\alpha \\gamma + \\sin{(\\alpha)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), cos(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\gamma', commutative=True))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True)), sin(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\chi \\sigma", "variable": "\\chi", "positive": "\\frac{\\chi^{2} \\sigma}{2}", "negatives": ["\\frac{\\chi \\sigma^{2}}{2}", "\\frac{\\chi^{2}}{2 \\sigma}", "- \\cos{(\\chi - \\sigma)}", "- \\cos{(\\chi + \\sigma)}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\sigma', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "e^{\\beta + \\gamma}", "variable": "\\gamma", "positive": "e^{\\beta + \\gamma}", "negatives": ["e^{- \\beta + \\gamma}", "\\cos{(\\beta - \\gamma)}", "\\frac{\\gamma (2 \\beta - \\gamma)}{2}", "\\beta \\gamma (\\log{(\\gamma)} - 1)"], "srepr_premise_expression": "exp(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "exp(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["exp(Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True), Add(log(Symbol('\\\\gamma', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\alpha \\sin{(\\sigma)}", "variable": "\\alpha", "positive": "\\frac{\\alpha^{2} \\sin{(\\sigma)}}{2}", "negatives": ["\\frac{\\alpha (\\alpha - 2 \\sigma)}{2}", "- \\alpha \\cos{(\\sigma)}", "e^{\\alpha - \\sigma}", "\\alpha (- \\sigma + \\log{(\\alpha^{\\sigma})})"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), sin(Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), sin(Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), cos(Symbol('\\\\sigma', commutative=True)))", "exp(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), log(Pow(Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True)))))"]}, {"premise_expression": "\\log{(\\gamma \\xi)}", "variable": "\\gamma", "positive": "\\gamma (\\log{(\\gamma \\xi)} - 1)", "negatives": ["\\xi (\\log{(\\gamma \\xi)} - 1)", "\\xi \\log{(\\gamma)}", "\\sin{(\\gamma - \\xi)}", "- e^{- \\gamma + \\xi}"], "srepr_premise_expression": "log(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\gamma', commutative=True), Add(log(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\xi', commutative=True), Add(log(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "sin(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "- \\chi + \\psi", "variable": "\\chi", "positive": "\\frac{\\chi (- \\chi + 2 \\psi)}{2}", "negatives": ["\\frac{\\psi (- 2 \\chi + \\psi)}{2}", "\\frac{\\chi^{2} \\psi}{2}", "\\chi (\\log{(\\chi \\psi)} - 1)", "\\psi \\sin{(\\chi)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))", "Mul(Symbol('\\\\chi', commutative=True), Add(log(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\psi', commutative=True), sin(Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "\\gamma + \\sigma", "variable": "\\gamma", "positive": "\\frac{\\gamma (\\gamma + 2 \\sigma)}{2}", "negatives": ["\\frac{\\gamma (\\gamma - 2 \\sigma)}{2}", "\\frac{\\sigma (2 \\gamma + \\sigma)}{2}", "e^{\\gamma - \\sigma}", "e^{\\gamma + \\sigma}"], "srepr_premise_expression": "Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "exp(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "exp(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\frac{\\log{(\\delta)}}{\\beta}", "variable": "\\beta", "positive": "\\log{(\\beta)} \\log{(\\delta)}", "negatives": ["\\log{(\\beta)} \\cos{(\\delta)}", "e^{\\beta + \\delta}", "\\frac{\\delta (\\log{(\\delta)} - 1)}{\\beta}", "\\frac{\\beta^{2} \\cos{(\\delta)}}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), log(Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(log(Symbol('\\\\beta', commutative=True)), log(Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Mul(log(Symbol('\\\\beta', commutative=True)), cos(Symbol('\\\\delta', commutative=True)))", "exp(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True)))", "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True), Add(log(Symbol('\\\\delta', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), cos(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\frac{\\sin{(\\omega)}}{\\xi}", "variable": "\\omega", "positive": "- \\frac{\\cos{(\\omega)}}{\\xi}", "negatives": ["- \\omega \\xi - \\cos{(\\omega)}", "\\frac{\\omega^{2} \\log{(\\xi)}}{2}", "\\frac{\\omega^{2} \\sin{(\\xi)}}{2}", "\\log{(\\xi)} \\sin{(\\omega)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), sin(Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Integer(-1), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), cos(Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), log(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), sin(Symbol('\\\\xi', commutative=True)))", "Mul(log(Symbol('\\\\xi', commutative=True)), sin(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\beta + \\log{(\\psi)}", "variable": "\\beta", "positive": "\\frac{\\beta (\\beta + 2 \\log{(\\psi)})}{2}", "negatives": ["\\frac{\\beta (\\beta + 2 \\sin{(\\psi)})}{2}", "\\frac{\\beta (\\beta - 2 \\psi)}{2}", "\\psi (\\beta + \\log{(\\psi)} - 1)", "\\beta (\\psi + e^{\\psi})"], "srepr_premise_expression": "Add(Symbol('\\\\beta', commutative=True), log(Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), log(Symbol('\\\\psi', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), sin(Symbol('\\\\psi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\beta', commutative=True), log(Symbol('\\\\psi', commutative=True)), Integer(-1)))", "Mul(Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\psi', commutative=True), exp(Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "\\sin{(\\omega - \\pi)}", "variable": "\\pi", "positive": "\\cos{(\\omega - \\pi)}", "negatives": ["- \\cos{(\\omega - \\pi)}", "- \\sin{(\\omega - \\pi)}", "\\frac{\\pi (2 \\omega + \\pi)}{2}", "\\omega \\pi + \\sin{(\\pi)}"], "srepr_premise_expression": "sin(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "cos(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))", "Mul(Integer(-1), sin(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Add(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)), sin(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\chi \\gamma", "variable": "\\chi", "positive": "\\frac{\\chi^{2} \\gamma}{2}", "negatives": ["\\frac{\\chi \\gamma^{2}}{2}", "\\chi \\cos{(1)}", "0", "\\frac{\\chi^{2} \\log{(\\gamma)}}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\gamma', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)))", "Mul(Symbol('\\\\chi', commutative=True), cos(Integer(1)))", "Integer(0)", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), log(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "e^{\\sigma - \\xi}", "variable": "\\sigma", "positive": "e^{\\sigma - \\xi}", "negatives": ["- e^{\\sigma - \\xi}", "\\xi e^{\\sigma}", "\\xi \\log{(\\sigma)}", "\\frac{\\sin{(\\sigma)}}{\\xi}"], "srepr_premise_expression": "exp(Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "exp(Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))))", "Mul(Symbol('\\\\xi', commutative=True), exp(Symbol('\\\\sigma', commutative=True)))", "Mul(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\sigma', commutative=True)))", "Mul(Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), sin(Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "e^{\\frac{\\beta}{\\xi}}", "variable": "\\beta", "positive": "\\xi e^{\\frac{\\beta}{\\xi}}", "negatives": ["e^{\\beta + \\xi}", "\\frac{\\beta^{2}}{2 \\xi}", "\\frac{\\beta^{2} e^{\\xi}}{2}", "\\frac{\\beta^{2} \\xi}{2}"], "srepr_premise_expression": "exp(Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\xi', commutative=True), exp(Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))))", "srepr_negatives": ["exp(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), exp(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))"]}, {"premise_expression": "\\alpha - \\beta", "variable": "\\beta", "positive": "\\frac{\\beta (2 \\alpha - \\beta)}{2}", "negatives": ["\\frac{\\alpha \\beta (- 2 \\alpha + \\beta)}{2}", "\\frac{\\alpha (\\alpha - 2 \\beta)}{2}", "\\frac{\\beta^{2} \\log{(\\alpha)}}{2}", "e^{\\alpha + \\beta}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\beta', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), log(Symbol('\\\\alpha', commutative=True)))", "exp(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "\\log{(\\pi + \\psi)}", "variable": "\\psi", "positive": "\\pi \\log{(\\pi + \\psi)} + \\psi \\log{(\\pi + \\psi)} - \\psi", "negatives": ["- \\pi \\log{(- \\pi + \\psi)} + \\psi \\log{(\\pi - \\psi)} - \\psi", "\\pi \\log{(\\pi + \\psi)} - \\pi + \\psi \\log{(\\pi + \\psi)}", "\\psi (- \\pi + \\log{(\\psi^{\\pi})})", "\\frac{\\psi (- \\psi + 2 \\cos{(\\pi)})}{2}"], "srepr_premise_expression": "log(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\pi', commutative=True), log(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)))), Mul(Symbol('\\\\psi', commutative=True), log(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Symbol('\\\\psi', commutative=True)))), Mul(Symbol('\\\\psi', commutative=True), log(Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))", "Add(Mul(Symbol('\\\\pi', commutative=True), log(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Symbol('\\\\psi', commutative=True), log(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)))))", "Mul(Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), log(Pow(Symbol('\\\\psi', commutative=True), Symbol('\\\\pi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\pi', commutative=True)))))"]}, {"premise_expression": "\\alpha - \\beta + \\chi", "variable": "\\alpha", "positive": "\\alpha (\\frac{\\alpha}{2} - \\beta + \\chi)", "negatives": ["\\frac{\\alpha (\\alpha + 2 \\beta + 2 \\chi)}{2}", "\\frac{\\chi (2 \\alpha - 2 \\beta + \\chi)}{2}", "\\frac{\\beta (2 \\alpha - \\beta + 2 \\chi)}{2}", "\\frac{\\alpha (\\alpha \\chi - 2 \\beta)}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\chi', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\alpha', commutative=True), Add(Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\chi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\chi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True))))"]}, {"premise_expression": "- \\beta + \\chi", "variable": "\\chi", "positive": "\\frac{\\chi (- 2 \\beta + \\chi)}{2}", "negatives": ["\\frac{\\beta (- \\beta + 2 \\chi)}{2}", "\\frac{\\chi (\\log{(\\chi)} - 1)}{\\beta}", "\\frac{\\chi (- \\chi + 2 \\log{(\\beta)})}{2}", "\\beta \\chi + e^{\\chi}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\chi', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\chi', commutative=True))))", "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\chi', commutative=True), Add(log(Symbol('\\\\chi', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), log(Symbol('\\\\beta', commutative=True)))))", "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True)), exp(Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "- \\alpha + \\psi", "variable": "\\alpha", "positive": "\\frac{\\alpha (- \\alpha + 2 \\psi)}{2}", "negatives": ["\\frac{\\psi (- 2 \\alpha + \\psi)}{2}", "e^{\\alpha + \\psi}", "\\frac{\\alpha^{2} \\log{(\\psi)}}{2}", "\\frac{\\alpha (\\log{(\\alpha)} - 1)}{\\psi}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\psi', commutative=True)))", "exp(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), log(Symbol('\\\\psi', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Add(log(Symbol('\\\\alpha', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\alpha \\beta", "variable": "\\alpha", "positive": "\\frac{\\alpha^{2} \\beta}{2}", "negatives": ["\\frac{\\alpha \\beta^{2}}{2}", "\\frac{\\alpha^{2} \\sin{(\\beta)}}{2}", "\\frac{\\alpha^{2} \\log{(\\beta)}}{2}", "\\beta \\log{(\\alpha)}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\beta', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\beta', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), sin(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), log(Symbol('\\\\beta', commutative=True)))", "Mul(Symbol('\\\\beta', commutative=True), log(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\log{(\\frac{\\pi}{\\gamma})}", "variable": "\\pi", "positive": "\\pi (\\log{(\\frac{\\pi}{\\gamma})} - 1)", "negatives": ["\\gamma (\\log{(\\frac{\\pi}{\\gamma})} + 1)", "\\pi (\\log{(\\frac{\\gamma}{\\pi})} + 1)", "\\gamma \\pi (\\log{(\\pi)} - 1)", "e^{- \\gamma + \\pi}"], "srepr_premise_expression": "log(Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\pi', commutative=True), Add(log(Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\gamma', commutative=True), Add(log(Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))), Integer(1)))", "Mul(Symbol('\\\\pi', commutative=True), Add(log(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True), Add(log(Symbol('\\\\pi', commutative=True)), Integer(-1)))", "exp(Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\beta + \\sigma", "variable": "\\sigma", "positive": "\\frac{\\sigma (2 \\beta + \\sigma)}{2}", "negatives": ["\\frac{\\beta (\\beta + 2 \\sigma)}{2}", "\\frac{\\sigma (\\sigma + 2 \\sin{(\\beta)})}{2}", "\\frac{\\sigma^{2}}{2 \\beta}", "e^{\\beta + \\sigma}"], "srepr_premise_expression": "Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(2), sin(Symbol('\\\\beta', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "exp(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\alpha \\xi", "variable": "\\xi", "positive": "\\frac{\\alpha \\xi^{2}}{2}", "negatives": ["\\frac{\\alpha^{2} \\xi}{2}", "\\frac{\\xi (2 \\alpha - \\xi)}{2}", "- \\frac{\\cos{(\\xi)}}{\\alpha}", "e^{- \\alpha + \\xi}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Integer(-1), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), cos(Symbol('\\\\xi', commutative=True)))", "exp(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\log{(\\sigma^{\\omega})}", "variable": "\\omega", "positive": "\\frac{\\omega^{2} \\log{(\\sigma)}}{2}", "negatives": ["\\frac{\\omega (\\omega + 2 \\sigma)}{2}", "\\frac{\\omega (\\omega - 2 \\sigma)}{2}", "- \\omega \\sigma - \\cos{(\\omega)}", "\\sigma (- \\omega + \\log{(\\sigma^{\\omega})})"], "srepr_premise_expression": "log(Pow(Symbol('\\\\sigma', commutative=True), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), log(Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\omega', commutative=True))))", "Mul(Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), log(Pow(Symbol('\\\\sigma', commutative=True), Symbol('\\\\omega', commutative=True)))))"]}, {"premise_expression": "e^{- \\beta + \\psi}", "variable": "\\beta", "positive": "- e^{- \\beta + \\psi}", "negatives": ["e^{- \\beta + \\psi}", "\\psi \\log{(\\beta)}", "\\beta \\sin{(\\psi^{\\psi})}", "\\psi \\sin{(\\beta)}"], "srepr_premise_expression": "exp(Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["exp(Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Symbol('\\\\psi', commutative=True), log(Symbol('\\\\beta', commutative=True)))", "Mul(Symbol('\\\\beta', commutative=True), sin(Pow(Symbol('\\\\psi', commutative=True), Symbol('\\\\psi', commutative=True))))", "Mul(Symbol('\\\\psi', commutative=True), sin(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "\\log{(\\psi^{\\chi})}", "variable": "\\psi", "positive": "\\psi (- \\chi + \\log{(\\psi^{\\chi})})", "negatives": ["\\psi (- \\chi + \\log{(\\psi)} - 1)", "\\chi \\psi + e^{\\psi}", "\\frac{\\chi^{2} \\log{(\\psi)}}{2}", "\\psi (\\log{(\\frac{\\chi}{\\psi})} + 1)"], "srepr_premise_expression": "log(Pow(Symbol('\\\\psi', commutative=True), Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), log(Pow(Symbol('\\\\psi', commutative=True), Symbol('\\\\chi', commutative=True)))))", "srepr_negatives": ["Mul(Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), log(Symbol('\\\\psi', commutative=True)), Integer(-1)))", "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True)), exp(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), log(Symbol('\\\\psi', commutative=True)))", "Mul(Symbol('\\\\psi', commutative=True), Add(log(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))), Integer(1)))"]}, {"premise_expression": "\\alpha \\pi^{\\sigma}", "variable": "\\alpha", "positive": "\\frac{\\alpha^{2} \\pi^{\\sigma}}{2}", "negatives": ["\\frac{\\alpha^{2} \\pi \\sigma}{2}", "\\frac{\\alpha^{2} \\pi}{2 \\sigma}", "\\frac{\\alpha^{2} \\sigma}{2 \\pi}", "\\frac{\\alpha^{2}}{2 \\pi} + \\alpha \\sigma"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))", "Add(Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1))), Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "- \\xi + \\log{(\\pi)}", "variable": "\\pi", "positive": "\\pi (- \\xi + \\log{(\\pi)} - 1)", "negatives": ["\\pi (\\log{(\\frac{\\pi}{\\xi})} - 1)", "\\frac{\\xi (- \\xi + 2 \\log{(\\pi)})}{2}", "\\xi \\log{(\\pi)}", "e^{\\pi + \\xi}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), log(Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), log(Symbol('\\\\pi', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\pi', commutative=True), Add(log(Mul(Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), log(Symbol('\\\\pi', commutative=True)))))", "Mul(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\pi', commutative=True)))", "exp(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\sin{(\\frac{\\xi}{\\beta})}", "variable": "\\beta", "positive": "\\beta \\sin{(\\frac{\\xi}{\\beta})} - \\frac{\\xi \\log{(\\frac{\\xi^{2}}{\\beta^{2}})}}{2} + \\xi \\log{(\\frac{\\xi}{\\beta})} - \\xi \\operatorname{Ci}{(\\frac{\\xi}{\\beta})}", "negatives": ["\\beta \\log{(\\beta + \\xi)} - \\beta + \\xi \\log{(\\beta + \\xi)}", "(- \\log{(\\beta)})^{- \\xi} \\log{(\\beta)}^{\\xi} \\Gamma(\\xi + 1, - \\log{(\\beta)})", "\\beta (\\log{(\\beta \\xi)} - 1)", "\\beta (\\log{(\\frac{\\xi}{\\beta})} + 1)"], "srepr_premise_expression": "sin(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\beta', commutative=True), sin(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True)))), Mul(Integer(-1), Rational(1, 2), Symbol('\\\\xi', commutative=True), log(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-2)), Pow(Symbol('\\\\xi', commutative=True), Integer(2))))), Mul(Symbol('\\\\xi', commutative=True), log(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\xi', commutative=True), Ci(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\beta', commutative=True), log(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Symbol('\\\\xi', commutative=True), log(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True)))))", "Mul(Pow(Mul(Integer(-1), log(Symbol('\\\\beta', commutative=True))), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))), Pow(log(Symbol('\\\\beta', commutative=True)), Symbol('\\\\xi', commutative=True)), uppergamma(Add(Symbol('\\\\xi', commutative=True), Integer(1)), Mul(Integer(-1), log(Symbol('\\\\beta', commutative=True)))))", "Mul(Symbol('\\\\beta', commutative=True), Add(log(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\beta', commutative=True), Add(log(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))), Integer(1)))"]}, {"premise_expression": "\\sigma \\xi", "variable": "\\xi", "positive": "\\frac{\\sigma \\xi^{2}}{2}", "negatives": ["\\frac{\\sigma^{2} \\xi}{2}", "\\sigma \\log{(\\xi)}", "\\sigma \\xi + \\sin{(\\xi)}", "\\frac{\\xi^{2} \\log{(\\sigma)}}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))", "Mul(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\xi', commutative=True)))", "Add(Mul(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True)), sin(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), log(Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\cos{(\\alpha + \\chi)}", "variable": "\\alpha", "positive": "\\sin{(\\alpha + \\chi)}", "negatives": ["\\sin{(\\alpha - \\chi)}", "\\frac{\\alpha (- \\alpha + 2 \\chi)}{2}", "\\frac{\\alpha^{2} \\chi}{2}", "\\frac{\\alpha (\\log{(\\alpha)} - 1)}{\\chi}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "sin(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\chi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\chi', commutative=True))", "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Add(log(Symbol('\\\\alpha', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\frac{\\psi}{\\alpha \\beta}", "variable": "\\psi", "positive": "\\frac{\\psi^{2}}{2 \\alpha \\beta}", "negatives": ["- \\alpha \\psi + \\frac{\\psi^{2}}{2 \\beta}", "\\frac{\\psi^{2} (\\alpha + \\beta)}{2}", "\\frac{\\psi \\log{(\\beta)}}{\\alpha}", "\\frac{\\psi \\log{(\\alpha)}}{\\beta}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Pow(Symbol('\\\\psi', commutative=True), Integer(2))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True)))", "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True), log(Symbol('\\\\beta', commutative=True)))", "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True), log(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "- \\sigma + \\sin{(\\beta)}", "variable": "\\sigma", "positive": "\\frac{\\sigma (- \\sigma + 2 \\sin{(\\beta)})}{2}", "negatives": ["\\frac{\\sigma (\\sigma + 2 e^{\\beta})}{2}", "- \\beta \\sigma - \\cos{(\\beta)}", "\\beta \\sigma - \\cos{(\\sigma)}", "\\sigma (\\log{(2 \\sigma)} - 1)"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), sin(Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\beta', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(2), exp(Symbol('\\\\beta', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\beta', commutative=True))))", "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\sigma', commutative=True))))", "Mul(Symbol('\\\\sigma', commutative=True), Add(log(Mul(Integer(2), Symbol('\\\\sigma', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\frac{\\chi}{\\omega}", "variable": "\\chi", "positive": "\\frac{\\chi^{2}}{2 \\omega}", "negatives": ["\\chi \\log{(\\omega)}", "\\omega e^{\\frac{\\chi}{\\omega}}", "\\sin{(\\chi + \\omega)}", "\\frac{\\chi (\\chi + 2 \\omega)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), exp(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))))", "sin(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))"]}, {"premise_expression": "e^{\\alpha + \\beta}", "variable": "\\alpha", "positive": "e^{\\alpha + \\beta}", "negatives": ["\\cos{(\\alpha - \\beta)}", "\\sin{(\\alpha - \\beta)}", "\\frac{\\alpha (\\alpha + 2 \\beta)}{2}", "\\log{(\\alpha)} \\cos{(\\beta)}"], "srepr_premise_expression": "exp(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "exp(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True)))", "srepr_negatives": ["cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\beta', commutative=True))))", "sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\beta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\beta', commutative=True))))", "Mul(log(Symbol('\\\\alpha', commutative=True)), cos(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "\\cos^{\\xi}{(\\gamma)}", "variable": "\\gamma", "positive": "\\int \\cos^{\\xi}{(\\gamma)} d\\gamma", "negatives": ["- \\frac{\\cos{(\\gamma)}}{\\xi}", "\\xi e^{\\frac{\\gamma}{\\xi}}", "\\gamma (\\log{(\\gamma \\xi)} - 1)", "\\frac{\\gamma^{2} \\log{(\\xi)}}{2}"], "srepr_premise_expression": "Pow(cos(Symbol('\\\\gamma', commutative=True)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Integral(Pow(cos(Symbol('\\\\gamma', commutative=True)), Symbol('\\\\xi', commutative=True)), Tuple(Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), cos(Symbol('\\\\gamma', commutative=True)))", "Mul(Symbol('\\\\xi', commutative=True), exp(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))))", "Mul(Symbol('\\\\gamma', commutative=True), Add(log(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), log(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "e^{\\frac{\\xi}{\\chi}}", "variable": "\\xi", "positive": "\\chi e^{\\frac{\\xi}{\\chi}}", "negatives": ["\\chi e^{\\xi}", "- e^{\\chi - \\xi}", "\\frac{\\xi^{2}}{2 \\chi}", "- \\frac{\\cos{(\\xi)}}{\\chi}"], "srepr_premise_expression": "exp(Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\chi', commutative=True), exp(Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Symbol('\\\\chi', commutative=True), exp(Symbol('\\\\xi', commutative=True)))", "Mul(Integer(-1), exp(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Mul(Integer(-1), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), cos(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "- \\sin{(\\psi - \\sigma)}", "variable": "\\sigma", "positive": "- \\cos{(\\psi - \\sigma)}", "negatives": ["\\cos{(\\psi - \\sigma)}", "e^{\\psi + \\sigma}", "- \\psi \\sigma - \\cos{(\\sigma)}", "\\sigma (\\log{(\\frac{\\psi}{\\sigma})} + 1)"], "srepr_premise_expression": "Mul(Integer(-1), sin(Add(Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))", "srepr_negatives": ["cos(Add(Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "exp(Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\sigma', commutative=True))))", "Mul(Symbol('\\\\sigma', commutative=True), Add(log(Mul(Symbol('\\\\psi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))), Integer(1)))"]}, {"premise_expression": "\\chi \\sigma", "variable": "\\chi", "positive": "\\frac{\\chi^{2} \\sigma}{2}", "negatives": ["\\frac{\\chi \\sigma^{2}}{2}", "\\frac{\\chi^{2} \\log{(\\sigma)}}{2}", "\\sigma \\log{(\\chi)}", "e^{\\sigma} \\log{(\\chi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\sigma', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), log(Symbol('\\\\sigma', commutative=True)))", "Mul(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\chi', commutative=True)))", "Mul(exp(Symbol('\\\\sigma', commutative=True)), log(Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "\\cos^{\\chi}{(\\psi)}", "variable": "\\psi", "positive": "\\int \\cos^{\\chi}{(\\psi)} d\\psi", "negatives": ["- \\cos{(\\chi + \\psi)}", "- \\cos{(\\chi - \\psi)}", "\\frac{\\psi^{2}}{2 \\chi}", "\\frac{\\psi (2 \\chi - \\psi)}{2}"], "srepr_premise_expression": "Pow(cos(Symbol('\\\\psi', commutative=True)), Symbol('\\\\chi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Integral(Pow(cos(Symbol('\\\\psi', commutative=True)), Symbol('\\\\chi', commutative=True)), Tuple(Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "\\frac{\\psi + \\xi}{\\alpha}", "variable": "\\xi", "positive": "\\frac{\\xi (2 \\psi + \\xi)}{2 \\alpha}", "negatives": ["\\frac{\\xi (2 \\psi - \\xi)}{2 \\alpha}", "\\frac{\\psi (\\psi + 2 \\xi)}{2 \\alpha}", "\\frac{\\xi (2 \\psi^{\\alpha} + \\xi)}{2}", "(\\psi + \\xi) \\log{(\\alpha)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\psi', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Pow(Symbol('\\\\psi', commutative=True), Symbol('\\\\alpha', commutative=True))), Symbol('\\\\xi', commutative=True)))", "Mul(Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\xi', commutative=True)), log(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\cos^{\\alpha}{(\\pi)}", "variable": "\\pi", "positive": "\\int \\cos^{\\alpha}{(\\pi)} d\\pi", "negatives": ["\\log{(\\alpha)} \\log{(\\pi)}", "- \\frac{\\cos{(\\pi)}}{\\alpha}", "- \\alpha \\pi - \\cos{(\\pi)}", "\\alpha \\pi - \\cos{(\\pi)}"], "srepr_premise_expression": "Pow(cos(Symbol('\\\\pi', commutative=True)), Symbol('\\\\alpha', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Integral(Pow(cos(Symbol('\\\\pi', commutative=True)), Symbol('\\\\alpha', commutative=True)), Tuple(Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(log(Symbol('\\\\alpha', commutative=True)), log(Symbol('\\\\pi', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), cos(Symbol('\\\\pi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\pi', commutative=True))))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\log{(\\delta^{\\gamma})}", "variable": "\\delta", "positive": "\\delta (- \\gamma + \\log{(\\delta^{\\gamma})})", "negatives": ["\\frac{\\delta (- \\delta + 2 \\sin{(\\gamma)})}{2}", "- \\delta \\gamma - \\cos{(\\delta)}", "\\gamma \\log{(\\delta)}", "\\frac{\\gamma^{2} \\log{(\\delta)}}{2}"], "srepr_premise_expression": "log(Pow(Symbol('\\\\delta', commutative=True), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), log(Pow(Symbol('\\\\delta', commutative=True), Symbol('\\\\gamma', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\gamma', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\delta', commutative=True))))", "Mul(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), log(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\frac{\\gamma \\sigma}{\\omega}", "variable": "\\gamma", "positive": "\\frac{\\gamma^{2} \\sigma}{2 \\omega}", "negatives": ["\\frac{\\gamma \\sigma^{2}}{2 \\omega}", "\\frac{\\gamma^{2}}{2 \\omega \\sigma}", "\\gamma \\sigma \\log{(\\omega)}", "\\frac{\\gamma (- \\gamma + 2 \\sigma)}{2 \\omega}"], "srepr_premise_expression": "Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "e^{\\gamma - \\sigma}", "variable": "\\sigma", "positive": "- e^{\\gamma - \\sigma}", "negatives": ["e^{\\gamma - \\sigma}", "- \\cos{(\\gamma + \\sigma)}", "\\frac{\\sigma (- 2 \\gamma + \\sigma)}{2}", "\\gamma \\sigma - \\cos{(\\sigma)}"], "srepr_premise_expression": "exp(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Integer(-1), exp(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))", "srepr_negatives": ["exp(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Add(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "- \\omega + \\log{(\\delta)}", "variable": "\\omega", "positive": "\\frac{\\omega (- \\omega + 2 \\log{(\\delta)})}{2}", "negatives": ["\\frac{\\omega (- \\omega + 2 \\sin{(\\delta)})}{2}", "\\delta (- \\omega + \\log{(\\delta)} - 1)", "\\frac{\\omega (2 \\delta - \\omega)}{2}", "\\frac{\\delta \\omega^{2}}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), log(Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), log(Symbol('\\\\delta', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\delta', commutative=True)))))", "Mul(Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), log(Symbol('\\\\delta', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))"]}, {"premise_expression": "\\frac{\\pi}{\\xi}", "variable": "\\xi", "positive": "\\pi \\log{(\\xi)}", "negatives": ["\\frac{\\pi^{2}}{2 \\xi}", "\\frac{\\sin{(\\xi)}}{\\pi}", "\\frac{\\sin{(2 \\xi)}}{2}", "\\xi (\\log{(\\frac{\\xi}{\\pi})} - 1)"], "srepr_premise_expression": "Mul(Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), sin(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), sin(Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Symbol('\\\\xi', commutative=True), Add(log(Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\alpha + \\xi", "variable": "\\xi", "positive": "\\frac{\\xi (2 \\alpha + \\xi)}{2}", "negatives": ["\\frac{\\alpha (\\alpha + 2 \\xi)}{2}", "\\frac{\\xi^{2} \\log{(\\alpha)}}{2}", "- \\cos{(\\alpha + \\xi)}", "\\alpha \\log{(\\xi)} + \\xi"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), log(Symbol('\\\\alpha', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True))))", "Add(Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\xi', commutative=True))), Symbol('\\\\xi', commutative=True))"]}, {"premise_expression": "\\sin{(\\sigma + \\xi)}", "variable": "\\sigma", "positive": "- \\cos{(\\sigma + \\xi)}", "negatives": ["- \\cos{(\\sigma - \\xi)}", "e^{\\sigma + \\xi}", "\\xi \\log{(\\sigma)}", "\\sigma \\xi + e^{\\sigma}"], "srepr_premise_expression": "sin(Add(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))))", "exp(Add(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\sigma', commutative=True)))", "Add(Mul(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True)), exp(Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\log{(- \\alpha + \\pi)}", "variable": "\\pi", "positive": "- \\alpha \\log{(- \\alpha + \\pi)} + \\pi \\log{(- \\alpha + \\pi)} - \\pi", "negatives": ["\\alpha \\log{(- \\alpha + \\pi)} - \\alpha - \\pi \\log{(\\alpha - \\pi)}", "\\log{(\\alpha)} \\log{(\\pi)}", "e^{\\alpha} \\log{(\\pi)}", "- \\alpha \\pi - \\cos{(\\pi)}"], "srepr_premise_expression": "log(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\pi', commutative=True)))), Mul(Symbol('\\\\pi', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\pi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\alpha', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\pi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\pi', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))))", "Mul(log(Symbol('\\\\alpha', commutative=True)), log(Symbol('\\\\pi', commutative=True)))", "Mul(exp(Symbol('\\\\alpha', commutative=True)), log(Symbol('\\\\pi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\sin{(\\delta - \\omega)}", "variable": "\\omega", "positive": "\\cos{(\\delta - \\omega)}", "negatives": ["- \\cos{(\\delta - \\omega)}", "- \\cos{(\\delta + \\omega)}", "- \\sin{(\\delta - \\omega)}", "- \\delta \\cos{(\\omega)}"], "srepr_premise_expression": "sin(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True))))", "Mul(Integer(-1), sin(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))))", "Mul(Integer(-1), Symbol('\\\\delta', commutative=True), cos(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\alpha + \\beta", "variable": "\\alpha", "positive": "\\frac{\\alpha (\\alpha + 2 \\beta)}{2}", "negatives": ["\\frac{\\beta (2 \\alpha + \\beta)}{2}", "\\frac{\\alpha^{2} e^{\\beta}}{2}", "- \\cos{(\\alpha - \\beta)}", "\\frac{\\sin{(\\alpha)}}{\\beta}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\beta', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), exp(Symbol('\\\\beta', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\beta', commutative=True)))))", "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), sin(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\frac{e^{\\pi}}{\\delta}", "variable": "\\delta", "positive": "e^{\\pi} \\log{(\\delta)}", "negatives": ["\\log{(\\delta)} \\cos{(\\pi)}", "e^{\\delta + \\pi}", "\\delta (\\pi + \\pi^{\\pi})", "\\frac{\\sin{(\\delta)}}{\\pi}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), exp(Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(exp(Symbol('\\\\pi', commutative=True)), log(Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Mul(log(Symbol('\\\\delta', commutative=True)), cos(Symbol('\\\\pi', commutative=True)))", "exp(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Symbol('\\\\pi', commutative=True))))", "Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), sin(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\sin{(\\delta - \\psi)}", "variable": "\\delta", "positive": "- \\cos{(\\delta - \\psi)}", "negatives": ["\\cos{(\\delta - \\psi)}", "- \\frac{\\cos{(\\delta)}}{\\psi}", "\\frac{\\delta^{2}}{2 \\psi}", "\\delta (\\log{(\\frac{\\psi}{\\delta})} + 1)"], "srepr_premise_expression": "sin(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))", "srepr_negatives": ["cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(Integer(-1), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), cos(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))", "Mul(Symbol('\\\\delta', commutative=True), Add(log(Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True))), Integer(1)))"]}, {"premise_expression": "\\frac{- \\gamma + \\pi}{\\xi}", "variable": "\\pi", "positive": "\\frac{\\pi (- 2 \\gamma + \\pi)}{2 \\xi}", "negatives": ["- \\frac{\\gamma (\\gamma - 2 \\pi)}{2 \\xi}", "\\frac{\\pi (2 \\gamma + \\pi + 2 \\xi)}{2}", "(- \\gamma + \\pi) \\log{(\\xi)}", "\\frac{\\pi^{2} (\\gamma - \\xi)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Rational(1, 2), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True)), log(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\log{(- \\delta + \\omega)}", "variable": "\\omega", "positive": "- \\delta \\log{(- \\delta + \\omega)} + \\omega \\log{(- \\delta + \\omega)} - \\omega", "negatives": ["\\delta \\log{(- \\delta + \\omega)} - \\delta - \\omega \\log{(\\delta - \\omega)}", "- \\delta \\operatorname{Ei}{(\\frac{\\delta}{\\omega})} + \\omega e^{\\frac{\\delta}{\\omega}}", "\\log{(\\delta)} \\log{(\\omega)}", "\\log{(\\omega)} \\cos{(\\delta)}"], "srepr_premise_expression": "log(Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\omega', commutative=True)))), Mul(Symbol('\\\\omega', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\omega', commutative=True)))), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\delta', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\omega', commutative=True)))), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Symbol('\\\\omega', commutative=True), log(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))))", "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Ei(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1))))), Mul(Symbol('\\\\omega', commutative=True), exp(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1))))))", "Mul(log(Symbol('\\\\delta', commutative=True)), log(Symbol('\\\\omega', commutative=True)))", "Mul(log(Symbol('\\\\omega', commutative=True)), cos(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\alpha + \\cos{(\\sigma)}", "variable": "\\alpha", "positive": "\\frac{\\alpha (\\alpha + 2 \\cos{(\\sigma)})}{2}", "negatives": ["\\frac{\\alpha (\\alpha + 2 \\log{(\\sigma)})}{2}", "\\frac{\\alpha (- \\alpha + 2 e^{\\sigma})}{2}", "\\frac{\\alpha (- \\alpha + 2 \\sigma)}{2}", "\\alpha \\sigma + \\sin{(\\sigma)}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), cos(Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), cos(Symbol('\\\\sigma', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), log(Symbol('\\\\sigma', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\sigma', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True)), sin(Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\alpha - \\chi - \\gamma", "variable": "\\gamma", "positive": "\\frac{\\gamma (2 \\alpha - 2 \\chi - \\gamma)}{2}", "negatives": ["\\frac{\\chi (2 \\alpha - \\chi - 2 \\gamma)}{2}", "\\frac{\\gamma (\\alpha \\gamma - 2 \\chi)}{2}", "\\frac{\\alpha (\\alpha - 2 \\chi - 2 \\gamma)}{2}", "\\frac{\\gamma (2 \\chi + \\gamma)}{2 \\alpha}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\beta + \\chi + \\psi", "variable": "\\psi", "positive": "\\psi (\\beta + \\chi + \\frac{\\psi}{2})", "negatives": ["\\frac{\\psi (- 2 \\beta + 2 \\chi - \\psi)}{2}", "\\frac{\\beta (\\beta + 2 \\chi + 2 \\psi)}{2}", "\\frac{\\chi (2 \\beta + \\chi + 2 \\psi)}{2}", "\\frac{\\psi (2 \\chi + \\psi)}{2 \\beta}"], "srepr_premise_expression": "Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True), Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\beta (\\chi + \\xi)", "variable": "\\beta", "positive": "\\frac{\\beta^{2} (\\chi + \\xi)}{2}", "negatives": ["\\frac{\\beta \\xi (2 \\chi + \\xi)}{2}", "\\frac{\\beta \\chi (\\chi + 2 \\xi)}{2}", "\\frac{\\beta (- \\beta + 2 \\chi \\xi)}{2}", "\\frac{\\beta \\chi (\\beta + 2 \\xi)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\omega + \\xi", "variable": "\\xi", "positive": "\\frac{\\xi (2 \\omega + \\xi)}{2}", "negatives": ["\\frac{\\omega (\\omega + 2 \\xi)}{2}", "\\frac{\\omega \\xi^{2}}{2}", "\\frac{\\xi^{2} \\log{(\\omega)}}{2}", "e^{- \\omega + \\xi}"], "srepr_premise_expression": "Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), log(Symbol('\\\\omega', commutative=True)))", "exp(Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "e^{- \\chi + \\psi}", "variable": "\\psi", "positive": "e^{- \\chi + \\psi}", "negatives": ["- e^{- \\chi + \\psi}", "- e^{\\chi - \\psi}", "\\chi e^{\\psi}", "\\frac{\\psi (- 2 \\chi + \\psi)}{2}"], "srepr_premise_expression": "exp(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "exp(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\psi', commutative=True))))", "Mul(Integer(-1), exp(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))", "Mul(Symbol('\\\\chi', commutative=True), exp(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\log{(- \\beta + \\gamma)}", "variable": "\\gamma", "positive": "- \\beta \\log{(- \\beta + \\gamma)} + \\gamma \\log{(- \\beta + \\gamma)} - \\gamma", "negatives": ["\\beta \\log{(- \\beta + \\gamma)} - \\beta - \\gamma \\log{(\\beta - \\gamma)}", "\\gamma (- \\beta + \\log{(\\gamma)} - 1)", "\\frac{\\gamma (- \\gamma + 2 \\log{(\\beta)})}{2}", "\\gamma (\\log{(\\frac{\\beta}{\\gamma})} + 1)"], "srepr_premise_expression": "log(Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\gamma', commutative=True)))), Mul(Symbol('\\\\gamma', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\gamma', commutative=True)))), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\beta', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\gamma', commutative=True)))), Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), log(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))))", "Mul(Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), log(Symbol('\\\\gamma', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), log(Symbol('\\\\beta', commutative=True)))))", "Mul(Symbol('\\\\gamma', commutative=True), Add(log(Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)))), Integer(1)))"]}, {"premise_expression": "\\alpha \\pi", "variable": "\\pi", "positive": "\\frac{\\alpha \\pi^{2}}{2}", "negatives": ["\\frac{\\alpha^{2} \\pi}{2}", "\\frac{\\pi^{2}}{2 \\alpha}", "\\frac{\\pi (2 \\alpha + \\pi)}{2}", "\\frac{\\pi^{2} \\cos{(\\alpha)}}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\pi', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), cos(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "e^{\\frac{\\psi}{\\omega}}", "variable": "\\omega", "positive": "\\omega e^{\\frac{\\psi}{\\omega}} - \\psi \\operatorname{Ei}{(\\frac{\\psi}{\\omega})}", "negatives": ["\\omega \\cos{(\\frac{\\psi}{\\omega})} + \\psi \\operatorname{Si}{(\\frac{\\psi}{\\omega})}", "\\omega e^{\\frac{\\psi}{\\omega}}", "\\omega \\psi + \\sin{(\\omega)}", "\\omega (\\log{(\\frac{\\omega}{\\psi})} - 1)"], "srepr_premise_expression": "exp(Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\omega', commutative=True), exp(Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\psi', commutative=True), Ei(Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\omega', commutative=True), cos(Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True)))), Mul(Symbol('\\\\psi', commutative=True), Si(Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True)))))", "Mul(Symbol('\\\\omega', commutative=True), exp(Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True))))", "Add(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True)), sin(Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), Add(log(Mul(Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))), Integer(-1)))"]}, {"premise_expression": "\\frac{\\delta - \\xi}{\\omega}", "variable": "\\delta", "positive": "\\frac{\\delta (\\delta - 2 \\xi)}{2 \\omega}", "negatives": ["\\frac{\\xi (2 \\delta - \\xi)}{2 \\omega}", "\\frac{\\delta (- \\delta + 2 \\omega - 2 \\xi)}{2}", "(\\delta - \\xi) \\log{(\\omega)}", "\\frac{\\delta (\\delta + 2 \\omega + 2 \\xi)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))), log(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "- \\gamma + \\psi", "variable": "\\gamma", "positive": "\\frac{\\gamma (- \\gamma + 2 \\psi)}{2}", "negatives": ["\\frac{\\psi (- 2 \\gamma + \\psi)}{2}", "- e^{- \\gamma + \\psi}", "\\frac{\\gamma (\\log{(\\gamma)} - 1)}{\\psi}", "\\gamma (\\log{(\\gamma \\psi)} - 1)"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\psi', commutative=True))))", "Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Add(log(Symbol('\\\\gamma', commutative=True)), Integer(-1)))", "Mul(Symbol('\\\\gamma', commutative=True), Add(log(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\frac{\\gamma}{\\xi}", "variable": "\\gamma", "positive": "\\frac{\\gamma^{2}}{2 \\xi}", "negatives": ["\\gamma \\log{(\\xi)}", "\\gamma^{2}", "\\frac{\\gamma (- \\gamma + 2 \\xi)}{2}", "\\gamma (\\log{(\\frac{\\gamma}{\\xi})} - 1)"], "srepr_premise_expression": "Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\xi', commutative=True)))", "Pow(Symbol('\\\\gamma', commutative=True), Integer(2))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Symbol('\\\\gamma', commutative=True), Add(log(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))), Integer(-1)))"]}, {"premise_expression": "\\sin{(\\alpha + \\omega)}", "variable": "\\alpha", "positive": "- \\cos{(\\alpha + \\omega)}", "negatives": ["\\frac{\\alpha (- \\alpha + 2 \\omega)}{2}", "\\omega \\log{(\\alpha)}", "\\alpha \\omega + \\sin{(\\alpha)}", "\\frac{\\alpha \\log{(\\omega)}}{\\omega}"], "srepr_premise_expression": "sin(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)), sin(Symbol('\\\\alpha', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), log(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "- \\gamma + \\pi", "variable": "\\pi", "positive": "\\frac{\\pi (- 2 \\gamma + \\pi)}{2}", "negatives": ["\\frac{\\gamma (- \\gamma + 2 \\pi)}{2}", "\\frac{\\pi (- \\pi + 2 \\cos{(\\gamma)})}{2}", "\\frac{\\pi (\\log{(\\pi)} - 1)}{\\gamma}", "e^{\\gamma} \\log{(\\pi)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\gamma', commutative=True)))))", "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True), Add(log(Symbol('\\\\pi', commutative=True)), Integer(-1)))", "Mul(exp(Symbol('\\\\gamma', commutative=True)), log(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\frac{\\xi}{\\gamma}", "variable": "\\xi", "positive": "\\frac{\\xi^{2}}{2 \\gamma}", "negatives": ["\\xi \\log{(\\gamma)}", "\\gamma e^{\\xi}", "- \\sin{(\\gamma - \\xi)}", "\\xi (\\log{(\\frac{\\xi}{\\gamma})} - 1)"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "Mul(Symbol('\\\\gamma', commutative=True), exp(Symbol('\\\\xi', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))))", "Mul(Symbol('\\\\xi', commutative=True), Add(log(Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\beta - \\pi", "variable": "\\beta", "positive": "\\frac{\\beta (\\beta - 2 \\pi)}{2}", "negatives": ["\\frac{\\pi (2 \\beta - \\pi)}{2}", "\\sin{(\\beta - \\pi)}", "\\beta \\pi + e^{\\beta}", "- \\pi \\cos{(\\beta)}"], "srepr_premise_expression": "Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "sin(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\pi', commutative=True)), exp(Symbol('\\\\beta', commutative=True)))", "Mul(Integer(-1), Symbol('\\\\pi', commutative=True), cos(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "\\frac{\\log{(\\alpha)}}{\\omega}", "variable": "\\omega", "positive": "\\log{(\\alpha)} \\log{(\\omega)}", "negatives": ["- \\cos{(\\alpha + \\omega)}", "\\alpha (- \\omega + \\log{(\\omega)})", "- \\alpha \\omega - \\cos{(\\omega)}", "\\frac{\\alpha (\\log{(\\alpha)} - 1)}{\\omega}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), log(Symbol('\\\\alpha', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(log(Symbol('\\\\alpha', commutative=True)), log(Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True))))", "Mul(Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), log(Symbol('\\\\omega', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\omega', commutative=True))))", "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Add(log(Symbol('\\\\alpha', commutative=True)), Integer(-1)))"]}, {"premise_expression": "- \\omega + \\sigma", "variable": "\\sigma", "positive": "\\frac{\\sigma (- 2 \\omega + \\sigma)}{2}", "negatives": ["\\frac{\\sigma (2 \\omega - \\sigma)}{2}", "\\frac{\\omega (- \\omega + 2 \\sigma)}{2}", "\\frac{\\sigma^{2} \\log{(\\omega)}}{2}", "e^{- \\omega + \\sigma}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), log(Symbol('\\\\omega', commutative=True)))", "exp(Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "- \\delta + \\xi", "variable": "\\xi", "positive": "\\frac{\\xi (- 2 \\delta + \\xi)}{2}", "negatives": ["\\frac{\\xi (2 \\delta - \\xi)}{2}", "\\frac{\\delta (- \\delta + 2 \\xi)}{2}", "\\frac{\\xi^{2} \\log{(\\delta)}}{2}", "- \\cos{(\\delta - \\xi)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), log(Symbol('\\\\delta', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))))"]}, {"premise_expression": "- \\omega + e^{\\pi}", "variable": "\\pi", "positive": "- \\omega \\pi + e^{\\pi}", "negatives": ["- \\omega \\pi + \\sin{(\\pi)}", "\\omega \\sin{(\\pi)}", "\\frac{\\omega (- \\omega + 2 e^{\\pi})}{2}", "- e^{\\omega - \\pi}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), exp(Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)), exp(Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)), sin(Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), sin(Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\pi', commutative=True)))))", "Mul(Integer(-1), exp(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))"]}, {"premise_expression": "\\beta - \\delta", "variable": "\\delta", "positive": "\\frac{\\delta (2 \\beta - \\delta)}{2}", "negatives": ["\\frac{\\beta (\\beta - 2 \\delta)}{2}", "\\frac{\\delta (- \\delta + 2 e^{\\beta})}{2}", "\\frac{\\delta (\\delta + 2 \\sin{(\\beta)})}{2}", "\\sin{(\\beta + \\delta)}"], "srepr_premise_expression": "Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\beta', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), sin(Symbol('\\\\beta', commutative=True)))))", "sin(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\frac{\\xi}{\\sigma}", "variable": "\\xi", "positive": "\\frac{\\xi^{2}}{2 \\sigma}", "negatives": ["\\xi \\log{(\\sigma)}", "\\frac{\\sigma \\xi^{2}}{2}", "\\frac{\\xi^{2} (\\sigma + 1)}{2 \\sigma}", "- \\frac{\\cos{(\\xi)}}{\\sigma}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), Add(Symbol('\\\\sigma', commutative=True), Integer(1)))", "Mul(Integer(-1), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), cos(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\gamma - \\psi", "variable": "\\gamma", "positive": "\\frac{\\gamma (\\gamma - 2 \\psi)}{2}", "negatives": ["\\frac{\\psi (2 \\gamma - \\psi)}{2}", "\\frac{\\gamma^{2} \\psi}{2}", "\\frac{\\gamma (\\gamma + 2 \\sin{(\\psi)})}{2}", "\\sin{(\\gamma - \\psi)}"], "srepr_premise_expression": "Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), sin(Symbol('\\\\psi', commutative=True)))))", "sin(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "\\cos{(\\frac{\\xi}{\\delta})}", "variable": "\\delta", "positive": "\\delta \\cos{(\\frac{\\xi}{\\delta})} + \\xi \\operatorname{Si}{(\\frac{\\xi}{\\delta})}", "negatives": ["\\frac{\\delta (- \\delta + 2 \\cos{(\\xi)})}{2}", "- \\delta \\xi - \\cos{(\\delta)}", "\\delta \\xi + e^{\\delta}", "\\frac{\\delta (- \\delta + 2 e^{\\xi})}{2}"], "srepr_premise_expression": "cos(Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\delta', commutative=True), cos(Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True)))), Mul(Symbol('\\\\xi', commutative=True), Si(Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\xi', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\delta', commutative=True))))", "Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True)), exp(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\xi', commutative=True)))))"]}, {"premise_expression": "\\log{(\\psi^{\\pi})}", "variable": "\\pi", "positive": "\\frac{\\pi^{2} \\log{(\\psi)}}{2}", "negatives": ["\\psi \\log{(\\pi)}", "\\frac{\\pi (- \\pi + 2 \\log{(\\psi)})}{2}", "\\pi \\psi (\\log{(\\pi)} - 1)", "e^{\\psi} \\log{(\\pi)}"], "srepr_premise_expression": "log(Pow(Symbol('\\\\psi', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), log(Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\psi', commutative=True), log(Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), log(Symbol('\\\\psi', commutative=True)))))", "Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True), Add(log(Symbol('\\\\pi', commutative=True)), Integer(-1)))", "Mul(exp(Symbol('\\\\psi', commutative=True)), log(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\cos{(\\alpha - \\pi)}", "variable": "\\pi", "positive": "- \\sin{(\\alpha - \\pi)}", "negatives": ["\\sin{(\\alpha - \\pi)}", "- \\frac{\\cos{(\\pi)}}{\\alpha}", "\\alpha \\pi (\\log{(\\pi)} - 1)", "\\log{(\\pi)} \\sin{(\\alpha)}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Integer(-1), sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))", "srepr_negatives": ["sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "Mul(Integer(-1), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), cos(Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True), Add(log(Symbol('\\\\pi', commutative=True)), Integer(-1)))", "Mul(log(Symbol('\\\\pi', commutative=True)), sin(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\frac{\\chi}{\\gamma}", "variable": "\\chi", "positive": "\\frac{\\chi^{2}}{2 \\gamma}", "negatives": ["\\chi \\log{(\\gamma)}", "\\frac{\\chi^{2} \\gamma}{2}", "\\sin{(\\chi - \\gamma)}", "- \\cos{(\\chi - \\gamma)}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\gamma', commutative=True))", "sin(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))))"]}, {"premise_expression": "- \\psi + \\log{(\\xi)}", "variable": "\\xi", "positive": "\\xi (- \\psi + \\log{(\\xi)} - 1)", "negatives": ["\\frac{\\psi (- \\psi + 2 \\log{(\\xi)})}{2}", "\\log{(\\psi)} \\log{(\\xi)}", "\\frac{\\xi (- \\xi + 2 e^{\\psi})}{2}", "\\sin{(\\psi + \\xi)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), log(Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), log(Symbol('\\\\xi', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), log(Symbol('\\\\xi', commutative=True)))))", "Mul(log(Symbol('\\\\psi', commutative=True)), log(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\psi', commutative=True)))))", "sin(Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\cos{(\\psi - \\sigma)}", "variable": "\\sigma", "positive": "- \\sin{(\\psi - \\sigma)}", "negatives": ["\\sin{(\\psi - \\sigma)}", "\\cos{(\\psi - \\sigma)}", "\\psi \\sin{(\\sigma)}", "- e^{\\psi - \\sigma}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Integer(-1), sin(Add(Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))", "srepr_negatives": ["sin(Add(Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "cos(Add(Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Symbol('\\\\psi', commutative=True), sin(Symbol('\\\\sigma', commutative=True)))", "Mul(Integer(-1), exp(Add(Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))"]}, {"premise_expression": "e^{- \\alpha + \\gamma}", "variable": "\\gamma", "positive": "e^{- \\alpha + \\gamma}", "negatives": ["- e^{- \\alpha + \\gamma}", "\\sin{(\\alpha + \\gamma)}", "- \\cos{(\\alpha + \\gamma)}", "\\alpha e^{\\gamma}"], "srepr_premise_expression": "exp(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "exp(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\gamma', commutative=True))))", "sin(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True))))", "Mul(Symbol('\\\\alpha', commutative=True), exp(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\frac{\\beta \\gamma}{\\xi}", "variable": "\\xi", "positive": "\\beta \\gamma \\log{(\\xi)}", "negatives": ["\\gamma^{\\beta} \\log{(\\xi)}", "\\frac{\\beta \\log{(\\xi)}}{\\gamma}", "\\frac{\\beta \\gamma^{2}}{2 \\xi}", "(- \\beta + \\gamma) \\log{(\\xi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Pow(Symbol('\\\\gamma', commutative=True), Symbol('\\\\beta', commutative=True)), log(Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), log(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "Mul(Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\gamma', commutative=True)), log(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\beta + \\psi \\sigma", "variable": "\\sigma", "positive": "\\frac{\\sigma (2 \\beta + \\psi \\sigma)}{2}", "negatives": ["\\frac{\\psi (2 \\beta + \\psi \\sigma)}{2}", "\\frac{\\sigma (\\beta \\sigma - 2 \\psi)}{2}", "\\frac{\\beta (\\beta + 2 \\psi \\sigma)}{2}", "\\frac{\\sigma^{2} (\\beta + \\psi)}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\beta', commutative=True), Mul(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\gamma + \\psi", "variable": "\\gamma", "positive": "\\frac{\\gamma (\\gamma + 2 \\psi)}{2}", "negatives": ["\\frac{\\psi (2 \\gamma + \\psi)}{2}", "\\frac{\\gamma^{2} \\psi}{2}", "\\frac{\\gamma^{2} \\cos{(\\psi)}}{2}", "\\gamma \\psi + e^{\\gamma}"], "srepr_premise_expression": "Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), cos(Symbol('\\\\psi', commutative=True)))", "Add(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True)), exp(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\cos{(\\beta - \\delta)}", "variable": "\\delta", "positive": "- \\sin{(\\beta - \\delta)}", "negatives": ["\\sin{(\\beta - \\delta)}", "\\frac{\\delta (2 \\beta + \\delta)}{2}", "\\beta \\log{(\\delta)}", "\\frac{\\beta \\delta^{2}}{2}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Integer(-1), sin(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)))))", "srepr_negatives": ["sin(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\delta', commutative=True)))", "Mul(Symbol('\\\\beta', commutative=True), log(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(2)))"]}, {"premise_expression": "- \\delta + \\gamma + \\xi", "variable": "\\xi", "positive": "\\xi (- \\delta + \\gamma + \\frac{\\xi}{2})", "negatives": ["\\frac{\\delta (- \\delta + 2 \\gamma + 2 \\xi)}{2}", "\\frac{\\gamma (- 2 \\delta + \\gamma + 2 \\xi)}{2}", "\\frac{\\xi (- 2 \\delta + \\gamma \\xi)}{2}", "\\frac{\\xi (\\delta \\xi + 2 \\gamma)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\gamma', commutative=True), Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\gamma', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True)), Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), Symbol('\\\\gamma', commutative=True))))"]}, {"premise_expression": "\\alpha + \\xi", "variable": "\\alpha", "positive": "\\frac{\\alpha (\\alpha + 2 \\xi)}{2}", "negatives": ["\\frac{\\xi (2 \\alpha + \\xi)}{2}", "\\xi \\sin{(\\alpha)}", "\\frac{\\alpha (\\alpha + 2 e^{\\xi})}{2}", "\\log{(\\alpha)} \\log{(\\xi)}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\xi', commutative=True), sin(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), exp(Symbol('\\\\xi', commutative=True)))))", "Mul(log(Symbol('\\\\alpha', commutative=True)), log(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\beta \\xi", "variable": "\\beta", "positive": "\\frac{\\beta^{2} \\xi}{2}", "negatives": ["\\frac{\\beta \\xi^{2}}{2}", "\\frac{\\beta^{2}}{2 \\xi}", "\\beta \\xi + e^{\\beta}", "e^{\\beta - \\xi}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True)), exp(Symbol('\\\\beta', commutative=True)))", "exp(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\frac{\\log{(\\omega)}}{\\gamma}", "variable": "\\omega", "positive": "\\frac{\\omega (\\log{(\\omega)} - 1)}{\\gamma}", "negatives": ["\\omega (\\log{(\\gamma \\omega)} - 1)", "\\frac{\\omega (2 \\gamma - \\omega)}{2}", "\\frac{\\omega (- 2 \\gamma + \\omega)}{2}", "\\log{(\\gamma)} \\log{(\\omega)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), log(Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True), Add(log(Symbol('\\\\omega', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\omega', commutative=True), Add(log(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Mul(log(Symbol('\\\\gamma', commutative=True)), log(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\delta + \\sin{(\\psi)}", "variable": "\\delta", "positive": "\\frac{\\delta (\\delta + 2 \\sin{(\\psi)})}{2}", "negatives": ["\\frac{\\delta^{2} \\log{(\\psi)}}{2}", "\\delta \\psi - \\cos{(\\psi)}", "\\frac{\\delta (- \\delta + 2 \\psi)}{2}", "\\delta (\\psi + \\log{(\\delta)} - 1)"], "srepr_premise_expression": "Add(Symbol('\\\\delta', commutative=True), sin(Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), sin(Symbol('\\\\psi', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), log(Symbol('\\\\psi', commutative=True)))", "Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\psi', commutative=True), log(Symbol('\\\\delta', commutative=True)), Integer(-1)))"]}, {"premise_expression": "- \\omega + \\sigma^{\\psi}", "variable": "\\omega", "positive": "\\frac{\\omega (- \\omega + 2 \\sigma^{\\psi})}{2}", "negatives": ["\\frac{\\omega \\sigma (- \\omega + 2 \\psi)}{2}", "\\frac{\\omega (\\omega - 2 \\psi + 2 \\sigma)}{2}", "\\frac{\\omega^{2} (\\psi + \\sigma)}{2}", "\\frac{\\omega (\\omega + 2 \\psi + 2 \\sigma)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Pow(Symbol('\\\\sigma', commutative=True), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Pow(Symbol('\\\\sigma', commutative=True), Symbol('\\\\psi', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\chi + \\psi + \\sigma", "variable": "\\psi", "positive": "\\psi (\\chi + \\frac{\\psi}{2} + \\sigma)", "negatives": ["\\frac{\\chi (\\chi + 2 \\psi + 2 \\sigma)}{2}", "\\frac{\\sigma (2 \\chi + 2 \\psi + \\sigma)}{2}", "\\frac{\\psi (- 2 \\chi + \\psi \\sigma)}{2}", "\\frac{\\chi \\psi^{2}}{2 \\sigma}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))"]}, {"premise_expression": "\\sin^{\\delta}{(\\gamma)}", "variable": "\\gamma", "positive": "\\int \\sin^{\\delta}{(\\gamma)} d\\gamma", "negatives": ["\\operatorname{NonElementaryIntegral}{((\\gamma^{\\delta})^{\\gamma},( \\gamma))}", "- \\sin{(\\delta - \\gamma)}", "- \\delta \\gamma + \\sin{(\\gamma)}", "\\delta \\gamma + \\sin{(\\gamma)}"], "srepr_premise_expression": "Pow(sin(Symbol('\\\\gamma', commutative=True)), Symbol('\\\\delta', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Integral(Pow(sin(Symbol('\\\\gamma', commutative=True)), Symbol('\\\\delta', commutative=True)), Tuple(Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Function('NonElementaryIntegral')(Pow(Pow(Symbol('\\\\gamma', commutative=True), Symbol('\\\\delta', commutative=True)), Symbol('\\\\gamma', commutative=True)), Tuple(Symbol('\\\\gamma', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Symbol('\\\\gamma', commutative=True)), sin(Symbol('\\\\gamma', commutative=True)))", "Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\gamma', commutative=True)), sin(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\beta + \\chi", "variable": "\\beta", "positive": "\\frac{\\beta (\\beta + 2 \\chi)}{2}", "negatives": ["\\frac{\\chi (2 \\beta + \\chi)}{2}", "\\frac{\\beta^{2} e^{\\chi}}{2}", "\\frac{\\beta^{2} \\log{(\\chi)}}{2}", "\\frac{\\beta^{2} \\chi}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\chi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), exp(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), log(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\chi', commutative=True))"]}, {"premise_expression": "\\frac{\\pi}{\\sigma}", "variable": "\\sigma", "positive": "\\pi \\log{(\\sigma)}", "negatives": ["\\frac{\\pi^{2}}{2 \\sigma}", "- \\pi \\sigma - \\cos{(\\sigma)}", "\\log{(\\sigma)} \\sin{(\\pi)}", "\\frac{\\pi \\sigma (\\sigma - 2)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\sigma', commutative=True))))", "Mul(log(Symbol('\\\\sigma', commutative=True)), sin(Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\sigma', commutative=True), Integer(-2)))"]}, {"premise_expression": "- \\alpha + \\omega + \\psi", "variable": "\\psi", "positive": "\\psi (- \\alpha + \\omega + \\frac{\\psi}{2})", "negatives": ["\\frac{\\psi (2 \\alpha + 2 \\omega + \\psi)}{2}", "\\frac{\\psi (2 \\alpha - 2 \\omega - \\psi)}{2}", "\\frac{\\omega (- 2 \\alpha + \\omega + 2 \\psi)}{2}", "\\frac{\\alpha (- \\alpha + 2 \\omega + 2 \\psi)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\omega', commutative=True), Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "- \\gamma + \\log{(\\alpha)}", "variable": "\\alpha", "positive": "\\alpha (- \\gamma + \\log{(\\alpha)} - 1)", "negatives": ["\\alpha (\\log{(\\alpha \\gamma)} - 1)", "\\frac{\\gamma (- \\gamma + 2 \\log{(\\alpha)})}{2}", "\\alpha (\\gamma + \\sin{(\\gamma)})", "\\frac{\\alpha (\\alpha + 2 \\gamma)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), log(Symbol('\\\\alpha', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), log(Symbol('\\\\alpha', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\alpha', commutative=True), Add(log(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), log(Symbol('\\\\alpha', commutative=True)))))", "Mul(Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\gamma', commutative=True), sin(Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\gamma', commutative=True))))"]}, {"premise_expression": "\\log{(\\omega^{\\chi})}", "variable": "\\chi", "positive": "\\frac{\\chi^{2} \\log{(\\omega)}}{2}", "negatives": ["\\frac{\\chi (\\chi - 2 \\omega)}{2}", "\\frac{\\chi (- \\chi + 2 \\cos{(\\omega)})}{2}", "\\chi (- \\omega + \\log{(\\chi^{\\omega})})", "\\omega (- \\chi + \\log{(\\omega^{\\chi})})"], "srepr_premise_expression": "log(Pow(Symbol('\\\\omega', commutative=True), Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), log(Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\omega', commutative=True)))))", "Mul(Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), log(Pow(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True)))))", "Mul(Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), log(Pow(Symbol('\\\\omega', commutative=True), Symbol('\\\\chi', commutative=True)))))"]}, {"premise_expression": "\\delta + \\gamma + \\psi", "variable": "\\delta", "positive": "\\delta (\\frac{\\delta}{2} + \\gamma + \\psi)", "negatives": ["\\frac{\\delta (\\delta + 2 \\gamma - 2 \\psi)}{2}", "\\frac{\\delta (\\delta - 2 \\gamma + 2 \\psi)}{2}", "\\frac{\\psi (2 \\delta + 2 \\gamma + \\psi)}{2}", "\\frac{\\gamma (2 \\delta + \\gamma + 2 \\psi)}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\delta', commutative=True), Add(Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\gamma', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "\\log{(- \\sigma + \\xi)}", "variable": "\\xi", "positive": "- \\sigma \\log{(- \\sigma + \\xi)} + \\xi \\log{(- \\sigma + \\xi)} - \\xi", "negatives": ["\\sigma \\log{(- \\sigma + \\xi)} - \\sigma - \\xi \\log{(\\sigma - \\xi)}", "\\sigma \\operatorname{Si}{(\\frac{\\sigma}{\\xi})} + \\xi \\cos{(\\frac{\\sigma}{\\xi})}", "\\xi (- \\sigma + \\log{(\\xi^{\\sigma})})", "\\xi (\\log{(\\sigma \\xi)} - 1)"], "srepr_premise_expression": "log(Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), Symbol('\\\\xi', commutative=True)))), Mul(Symbol('\\\\xi', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), Symbol('\\\\xi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\sigma', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), Symbol('\\\\xi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True), log(Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))))", "Add(Mul(Symbol('\\\\sigma', commutative=True), Si(Mul(Symbol('\\\\sigma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))), Mul(Symbol('\\\\xi', commutative=True), cos(Mul(Symbol('\\\\sigma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))))", "Mul(Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), log(Pow(Symbol('\\\\xi', commutative=True), Symbol('\\\\sigma', commutative=True)))))", "Mul(Symbol('\\\\xi', commutative=True), Add(log(Mul(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True))), Integer(-1)))"]}, {"premise_expression": "e^{\\frac{\\beta}{\\alpha}}", "variable": "\\alpha", "positive": "\\alpha e^{\\frac{\\beta}{\\alpha}} - \\beta \\operatorname{Ei}{(\\frac{\\beta}{\\alpha})}", "negatives": ["\\frac{\\alpha (- \\alpha + 2 e^{\\beta})}{2}", "\\alpha e^{\\frac{\\beta}{\\alpha}}", "- \\alpha \\beta - \\cos{(\\alpha)}", "\\frac{\\alpha (\\alpha + 2 \\log{(\\beta)})}{2}"], "srepr_premise_expression": "exp(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\alpha', commutative=True), exp(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\beta', commutative=True)))), Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Ei(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\beta', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\beta', commutative=True)))))", "Mul(Symbol('\\\\alpha', commutative=True), exp(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\beta', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\alpha', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), log(Symbol('\\\\beta', commutative=True)))))"]}, {"premise_expression": "\\frac{\\chi + \\gamma}{\\psi}", "variable": "\\chi", "positive": "\\frac{\\chi (\\chi + 2 \\gamma)}{2 \\psi}", "negatives": ["\\frac{\\gamma (2 \\chi + \\gamma)}{2 \\psi}", "\\frac{\\chi (\\chi + 2 \\gamma^{\\psi})}{2}", "\\frac{\\chi \\gamma (\\chi + 2)}{2}", "(\\chi + \\gamma) \\log{(\\psi)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\gamma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Pow(Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\chi', commutative=True), Integer(2)))", "Mul(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True)), log(Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "- \\alpha + \\delta + \\omega", "variable": "\\alpha", "positive": "\\alpha (- \\frac{\\alpha}{2} + \\delta + \\omega)", "negatives": ["\\frac{\\alpha (\\alpha + 2 \\delta - 2 \\omega)}{2}", "\\frac{\\delta (- 2 \\alpha + \\delta + 2 \\omega)}{2}", "\\frac{\\omega (- 2 \\alpha + 2 \\delta + \\omega)}{2}", "\\alpha (\\frac{\\alpha^{2}}{3} - \\delta)"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Rational(1, 2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\delta', commutative=True), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), Add(Mul(Rational(1, 3), Pow(Symbol('\\\\alpha', commutative=True), Integer(2))), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))"]}, {"premise_expression": "\\omega (\\chi + \\xi)", "variable": "\\chi", "positive": "\\frac{\\chi \\omega (\\chi + 2 \\xi)}{2}", "negatives": ["\\frac{\\chi \\omega (\\chi + 2)}{2}", "\\frac{\\omega^{2} (\\chi + \\xi)}{2}", "\\frac{\\omega \\xi (2 \\chi + \\xi)}{2}", "\\frac{\\chi (\\chi \\xi + 2 \\omega)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\chi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))"]}, {"premise_expression": "\\alpha + \\frac{\\sigma}{\\gamma}", "variable": "\\sigma", "positive": "\\alpha \\sigma + \\frac{\\sigma^{2}}{2 \\gamma}", "negatives": ["\\alpha \\gamma + \\sigma \\log{(\\gamma)}", "- \\frac{\\sigma (2 \\alpha - \\sigma)}{2 \\gamma}", "\\frac{\\alpha^{2}}{2} + \\frac{\\alpha \\sigma}{\\gamma}", "\\frac{\\alpha \\log{(\\sigma)}}{\\gamma}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Integer(2))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True)), Mul(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\gamma', commutative=True))))", "Mul(Integer(-1), Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Add(Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2))), Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), log(Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\alpha + \\beta", "variable": "\\beta", "positive": "\\frac{\\beta (2 \\alpha + \\beta)}{2}", "negatives": ["\\frac{\\alpha (\\alpha + 2 \\beta)}{2}", "- \\cos{(\\alpha - \\beta)}", "\\beta (\\log{(\\frac{\\alpha}{\\beta})} + 1)", "\\frac{\\beta (\\beta + 2 e^{\\alpha})}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\beta', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\beta', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\beta', commutative=True)))))", "Mul(Symbol('\\\\beta', commutative=True), Add(log(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), exp(Symbol('\\\\alpha', commutative=True)))))"]}, {"premise_expression": "- \\sin{(\\delta - \\omega)}", "variable": "\\delta", "positive": "\\cos{(\\delta - \\omega)}", "negatives": ["- \\cos{(\\delta - \\omega)}", "- \\cos{(\\delta + \\omega)}", "e^{\\delta + \\omega}", "\\frac{\\delta (\\delta + 2 \\omega)}{2}"], "srepr_premise_expression": "Mul(Integer(-1), sin(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True))))", "exp(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))"]}, {"premise_expression": "- \\sin{(\\gamma - \\pi)}", "variable": "\\pi", "positive": "- \\cos{(\\gamma - \\pi)}", "negatives": ["\\cos{(\\gamma - \\pi)}", "- \\cos{(\\gamma + \\pi)}", "\\pi (\\log{(\\frac{\\pi}{\\gamma})} - 1)", "\\frac{\\pi (- 2 \\gamma + \\pi)}{2}"], "srepr_premise_expression": "Mul(Integer(-1), sin(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))", "srepr_negatives": ["cos(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True))))", "Mul(Symbol('\\\\pi', commutative=True), Add(log(Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "e^{\\frac{\\psi}{\\xi}}", "variable": "\\psi", "positive": "\\xi e^{\\frac{\\psi}{\\xi}}", "negatives": ["- \\psi \\xi + e^{\\psi}", "\\frac{\\psi (\\psi + 2 \\xi)}{2}", "\\frac{\\psi^{2} \\sin{(\\xi)}}{2}", "\\frac{\\psi (- \\psi + 2 \\xi)}{2}"], "srepr_premise_expression": "exp(Mul(Symbol('\\\\psi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\xi', commutative=True), exp(Mul(Symbol('\\\\psi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True), Symbol('\\\\xi', commutative=True)), exp(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), sin(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\frac{\\beta}{\\omega}", "variable": "\\beta", "positive": "\\frac{\\beta^{2}}{2 \\omega}", "negatives": ["\\beta \\log{(\\omega)}", "\\frac{\\beta (\\beta + 2 \\omega)}{2}", "\\frac{\\beta^{2} \\log{(\\omega)}}{2}", "\\sin{(\\beta + \\omega)}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\beta', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), log(Symbol('\\\\omega', commutative=True)))", "sin(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "- \\chi + \\gamma + \\pi", "variable": "\\chi", "positive": "\\chi (- \\frac{\\chi}{2} + \\gamma + \\pi)", "negatives": ["\\frac{\\chi (- \\chi - 2 \\gamma + 2 \\pi)}{2}", "\\frac{\\chi (\\chi - 2 \\gamma + 2 \\pi)}{2}", "\\frac{\\pi (- 2 \\chi + 2 \\gamma + \\pi)}{2}", "\\frac{\\gamma (- 2 \\chi + \\gamma + 2 \\pi)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Rational(1, 2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\gamma', commutative=True), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\sin{(\\omega + \\xi)}", "variable": "\\xi", "positive": "- \\cos{(\\omega + \\xi)}", "negatives": ["- e^{\\omega - \\xi}", "\\xi (- \\omega + \\xi)", "\\frac{\\omega \\xi (\\xi - 2)}{2}", "\\omega \\xi - \\cos{(\\xi)}"], "srepr_premise_expression": "sin(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))))", "Mul(Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\xi', commutative=True), Integer(-2)))", "Add(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\frac{\\xi}{\\delta}", "variable": "\\delta", "positive": "\\xi \\log{(\\delta)}", "negatives": ["\\frac{\\xi^{2}}{2 \\delta}", "\\delta \\xi - \\cos{(\\delta)}", "\\frac{\\delta^{2} \\xi}{2}", "\\frac{\\sin{(\\delta)}}{\\xi}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))", "Mul(Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), sin(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\frac{\\beta}{\\chi}", "variable": "\\beta", "positive": "\\frac{\\beta^{2}}{2 \\chi}", "negatives": ["\\beta \\log{(\\chi)}", "\\chi e^{\\frac{\\beta}{\\chi}}", "\\frac{\\beta^{2} \\log{(\\chi)}}{2}", "\\frac{\\beta^{2} (\\chi - 1)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\beta', commutative=True), log(Symbol('\\\\chi', commutative=True)))", "Mul(Symbol('\\\\chi', commutative=True), exp(Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), log(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Add(Symbol('\\\\chi', commutative=True), Integer(-1)))"]}, {"premise_expression": "\\log{(\\alpha - \\pi)}", "variable": "\\alpha", "positive": "\\alpha \\log{(\\alpha - \\pi)} - \\alpha - \\pi \\log{(\\alpha - \\pi)}", "negatives": ["- \\alpha \\log{(- \\alpha + \\pi)} + \\pi \\log{(\\alpha - \\pi)} - \\pi", "\\frac{\\alpha (- \\alpha + 2 \\cos{(\\pi)})}{2}", "- \\pi \\cos{(\\alpha)}", "\\alpha \\sin{(\\pi^{\\pi})}"], "srepr_premise_expression": "log(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\alpha', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))), Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\pi', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\pi', commutative=True)))), Mul(Symbol('\\\\pi', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\pi', commutative=True)))))", "Mul(Integer(-1), Symbol('\\\\pi', commutative=True), cos(Symbol('\\\\alpha', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), sin(Pow(Symbol('\\\\pi', commutative=True), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\frac{\\delta}{\\xi}", "variable": "\\delta", "positive": "\\frac{\\delta^{2}}{2 \\xi}", "negatives": ["\\delta \\log{(\\xi)}", "\\frac{\\delta (- \\delta + 2 \\xi)}{2}", "- \\delta \\xi + e^{\\delta}", "\\delta e^{\\frac{\\xi}{\\delta}} - \\xi \\operatorname{Ei}{(\\frac{\\xi}{\\delta})}"], "srepr_premise_expression": "Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True)), exp(Symbol('\\\\delta', commutative=True)))", "Add(Mul(Symbol('\\\\delta', commutative=True), exp(Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\xi', commutative=True), Ei(Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True)))))"]}, {"premise_expression": "\\xi (\\gamma + \\pi)", "variable": "\\xi", "positive": "\\frac{\\xi^{2} (\\gamma + \\pi)}{2}", "negatives": ["\\frac{\\xi^{2} (- \\gamma + \\pi)}{2}", "\\frac{\\gamma \\xi (\\gamma + 2 \\pi)}{2}", "\\frac{\\pi \\xi (2 \\gamma + \\pi)}{2}", "\\frac{\\xi^{2}}{2 \\gamma \\pi}"], "srepr_premise_expression": "Mul(Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))"]}, {"premise_expression": "\\frac{\\sin{(\\chi)}}{\\xi}", "variable": "\\xi", "positive": "\\log{(\\xi)} \\sin{(\\chi)}", "negatives": ["\\log{(\\xi)} \\cos{(\\chi)}", "e^{\\chi} \\log{(\\xi)}", "- \\sin{(\\chi - \\xi)}", "- \\cos{(\\chi + \\xi)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), sin(Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(log(Symbol('\\\\xi', commutative=True)), sin(Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(log(Symbol('\\\\xi', commutative=True)), cos(Symbol('\\\\chi', commutative=True)))", "Mul(exp(Symbol('\\\\chi', commutative=True)), log(Symbol('\\\\xi', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\xi + \\log{(\\omega)}", "variable": "\\omega", "positive": "\\omega (\\xi + \\log{(\\omega)} - 1)", "negatives": ["\\omega (- \\xi + \\log{(\\omega)} - 1)", "\\frac{\\xi (\\xi + 2 \\log{(\\omega)})}{2}", "\\frac{\\omega^{2} \\log{(\\xi)}}{2}", "\\frac{\\omega (\\omega + 2 \\cos{(\\xi)})}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\omega', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), log(Symbol('\\\\omega', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\xi', commutative=True), Mul(Integer(2), log(Symbol('\\\\omega', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), log(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), cos(Symbol('\\\\xi', commutative=True)))))"]}, {"premise_expression": "\\omega \\psi", "variable": "\\psi", "positive": "\\frac{\\omega \\psi^{2}}{2}", "negatives": ["\\frac{\\omega^{2} \\psi}{2}", "\\frac{\\psi^{2} \\cos{(\\omega)}}{2}", "\\frac{\\psi (- 2 \\omega + \\psi)}{2}", "\\log{(\\psi)} \\cos{(\\omega)}"], "srepr_premise_expression": "Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), cos(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(log(Symbol('\\\\psi', commutative=True)), cos(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "- \\gamma + \\sin{(\\omega)}", "variable": "\\omega", "positive": "- \\gamma \\omega - \\cos{(\\omega)}", "negatives": ["\\gamma \\omega - \\cos{(\\omega)}", "\\frac{\\omega^{2} \\sin{(\\gamma)}}{2}", "\\frac{\\gamma (- \\gamma + 2 \\sin{(\\omega)})}{2}", "\\frac{\\sin{(\\omega)}}{\\gamma}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), sin(Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), sin(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\omega', commutative=True)))))", "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), sin(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\log{(\\alpha + \\chi)}", "variable": "\\alpha", "positive": "\\alpha \\log{(\\alpha + \\chi)} - \\alpha + \\chi \\log{(\\alpha + \\chi)}", "negatives": ["\\alpha \\log{(\\alpha + \\chi)} + \\chi \\log{(\\alpha + \\chi)} - \\chi", "\\alpha (\\chi + \\log{(\\alpha)} - 1)", "\\log{(\\alpha)} \\cos{(\\chi)}", "\\frac{\\alpha (\\alpha + 2 e^{\\chi})}{2}"], "srepr_premise_expression": "log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\alpha', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Symbol('\\\\chi', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\alpha', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)))), Mul(Symbol('\\\\chi', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\chi', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\alpha', commutative=True)), Integer(-1)))", "Mul(log(Symbol('\\\\alpha', commutative=True)), cos(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), exp(Symbol('\\\\chi', commutative=True)))))"]}, {"premise_expression": "\\alpha + \\gamma", "variable": "\\gamma", "positive": "\\frac{\\gamma (2 \\alpha + \\gamma)}{2}", "negatives": ["\\frac{\\alpha (\\alpha + 2 \\gamma)}{2}", "\\frac{\\gamma^{2} e^{\\alpha}}{2}", "\\alpha \\gamma - \\cos{(\\gamma)}", "\\frac{\\gamma (\\log{(\\gamma)} - 1)}{\\alpha}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), exp(Symbol('\\\\alpha', commutative=True)))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\gamma', commutative=True))))", "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True), Add(log(Symbol('\\\\gamma', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\log{(\\beta + \\chi)}", "variable": "\\beta", "positive": "\\beta \\log{(\\beta + \\chi)} - \\beta + \\chi \\log{(\\beta + \\chi)}", "negatives": ["\\beta \\log{(\\beta + \\chi)} + \\chi \\log{(\\beta + \\chi)} - \\chi", "\\beta (\\log{(\\beta \\chi)} - 1)", "\\frac{\\beta (- \\beta + 2 e^{\\chi})}{2}", "- \\cos{(\\beta + \\chi)}"], "srepr_premise_expression": "log(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\beta', commutative=True), log(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Symbol('\\\\chi', commutative=True), log(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\beta', commutative=True), log(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True)))), Mul(Symbol('\\\\chi', commutative=True), log(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\chi', commutative=True)))", "Mul(Symbol('\\\\beta', commutative=True), Add(log(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\chi', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True))))"]}, {"premise_expression": "- \\alpha + \\chi", "variable": "\\chi", "positive": "\\frac{\\chi (- 2 \\alpha + \\chi)}{2}", "negatives": ["\\frac{\\chi (2 \\alpha + \\chi)}{2}", "\\frac{\\alpha (- \\alpha + 2 \\chi)}{2}", "- \\sin{(\\alpha - \\chi)}", "\\frac{\\chi^{2} \\log{(\\alpha)}}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\chi', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\chi', commutative=True))))", "Mul(Integer(-1), sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), log(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\sin{(\\beta - \\omega)}", "variable": "\\omega", "positive": "\\cos{(\\beta - \\omega)}", "negatives": ["- \\cos{(\\beta - \\omega)}", "- \\frac{\\cos{(\\omega)}}{\\beta}", "\\frac{\\omega (2 \\beta + \\omega)}{2}", "- \\beta \\omega - \\cos{(\\omega)}"], "srepr_premise_expression": "sin(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))))", "Mul(Integer(-1), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), cos(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\omega', commutative=True))))"]}, {"premise_expression": "\\omega + \\xi", "variable": "\\xi", "positive": "\\frac{\\xi (2 \\omega + \\xi)}{2}", "negatives": ["\\frac{\\omega (\\omega + 2 \\xi)}{2}", "\\frac{\\xi^{2} \\log{(\\omega)}}{2}", "\\sin{(\\omega + \\xi)}", "- \\cos{(\\omega + \\xi)}"], "srepr_premise_expression": "Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), log(Symbol('\\\\omega', commutative=True)))", "sin(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\chi + \\gamma", "variable": "\\gamma", "positive": "\\frac{\\gamma (2 \\chi + \\gamma)}{2}", "negatives": ["\\frac{\\gamma (2 \\chi - \\gamma)}{2}", "\\frac{\\chi (\\chi + 2 \\gamma)}{2}", "\\chi \\gamma + \\sin{(\\gamma)}", "- \\chi \\gamma + \\sin{(\\gamma)}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\gamma', commutative=True))))", "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True)), sin(Symbol('\\\\gamma', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True)), sin(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "- \\alpha + \\sin{(\\beta)}", "variable": "\\alpha", "positive": "\\frac{\\alpha (- \\alpha + 2 \\sin{(\\beta)})}{2}", "negatives": ["\\frac{\\alpha (\\alpha - 2 \\beta)}{2}", "\\frac{\\alpha^{2} \\log{(\\beta)}}{2}", "- \\alpha \\beta - \\cos{(\\beta)}", "\\alpha \\cos{(\\frac{\\beta}{\\alpha})} + \\beta \\operatorname{Si}{(\\frac{\\beta}{\\alpha})}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), sin(Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\beta', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), log(Symbol('\\\\beta', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\beta', commutative=True))))", "Add(Mul(Symbol('\\\\alpha', commutative=True), cos(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\beta', commutative=True)))), Mul(Symbol('\\\\beta', commutative=True), Si(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\beta', commutative=True)))))"]}, {"premise_expression": "\\chi \\log{(\\gamma)}", "variable": "\\chi", "positive": "\\frac{\\chi^{2} \\log{(\\gamma)}}{2}", "negatives": ["\\frac{\\chi^{2} e^{\\gamma}}{2}", "\\gamma \\log{(\\chi)}", "\\frac{\\chi (\\chi - 2 \\gamma)}{2}", "\\chi \\gamma (\\log{(\\gamma)} - 1)"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), log(Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), exp(Symbol('\\\\gamma', commutative=True)))", "Mul(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True))))", "Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True), Add(log(Symbol('\\\\gamma', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\alpha \\omega", "variable": "\\omega", "positive": "\\frac{\\alpha \\omega^{2}}{2}", "negatives": ["\\frac{\\alpha^{2} \\omega}{2}", "\\frac{\\omega^{2}}{2 \\alpha^{2}}", "e^{- \\alpha + \\omega}", "\\frac{\\omega (\\omega + 2 e^{\\alpha})}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\omega', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-2)), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "exp(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), exp(Symbol('\\\\alpha', commutative=True)))))"]}, {"premise_expression": "\\frac{\\sin{(\\chi)}}{\\gamma}", "variable": "\\chi", "positive": "- \\frac{\\cos{(\\chi)}}{\\gamma}", "negatives": ["- \\gamma \\cos{(\\chi)}", "- \\chi \\gamma - \\cos{(\\chi)}", "\\frac{\\chi (\\chi - 2 \\gamma)}{2}", "e^{\\chi + \\gamma}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), sin(Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Integer(-1), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), cos(Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), cos(Symbol('\\\\chi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\chi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True))))", "exp(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\frac{\\log{(\\pi)}}{\\omega}", "variable": "\\pi", "positive": "\\frac{\\pi (\\log{(\\pi)} - 1)}{\\omega}", "negatives": ["\\pi (- \\omega + \\log{(\\pi)} - 1)", "\\frac{\\pi (- 2 \\omega + \\pi)}{2}", "\\log{(\\pi)} \\cos{(\\omega)}", "\\log{(\\omega)} \\log{(\\pi)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), log(Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True), Add(log(Symbol('\\\\pi', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), log(Symbol('\\\\pi', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(log(Symbol('\\\\pi', commutative=True)), cos(Symbol('\\\\omega', commutative=True)))", "Mul(log(Symbol('\\\\omega', commutative=True)), log(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\log{(\\alpha^{\\pi})}", "variable": "\\alpha", "positive": "\\alpha (- \\pi + \\log{(\\alpha^{\\pi})})", "negatives": ["\\alpha \\pi + e^{\\alpha}", "\\pi \\log{(\\alpha)}", "\\frac{\\pi^{2} \\log{(\\alpha)}}{2}", "- \\cos{(\\alpha + \\pi)}"], "srepr_premise_expression": "log(Pow(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), log(Pow(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)), exp(Symbol('\\\\alpha', commutative=True)))", "Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), log(Symbol('\\\\alpha', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\gamma + \\pi", "variable": "\\gamma", "positive": "\\frac{\\gamma (\\gamma + 2 \\pi)}{2}", "negatives": ["\\frac{\\gamma (\\gamma - 2 \\pi)}{2}", "\\frac{\\pi (2 \\gamma + \\pi)}{2}", "\\sin{(\\gamma + \\pi)}", "\\frac{\\gamma^{2}}{2 \\pi}"], "srepr_premise_expression": "Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True)))", "sin(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))"]}, {"premise_expression": "e^{\\alpha + \\chi}", "variable": "\\chi", "positive": "e^{\\alpha + \\chi}", "negatives": ["- \\cos{(\\alpha + \\chi)}", "\\alpha e^{\\frac{\\chi}{\\alpha}}", "\\alpha \\chi + e^{\\chi}", "\\log{(\\chi)} \\cos{(\\alpha)}"], "srepr_premise_expression": "exp(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "exp(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True))))", "Mul(Symbol('\\\\alpha', commutative=True), exp(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\chi', commutative=True))))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)), exp(Symbol('\\\\chi', commutative=True)))", "Mul(log(Symbol('\\\\chi', commutative=True)), cos(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\gamma + \\sin{(\\pi)}", "variable": "\\gamma", "positive": "\\frac{\\gamma (\\gamma + 2 \\sin{(\\pi)})}{2}", "negatives": ["\\frac{\\gamma^{2} \\log{(\\pi)}}{2}", "\\gamma \\pi - \\cos{(\\pi)}", "\\cos{(\\gamma - \\pi)}", "\\gamma (\\log{(\\frac{\\gamma}{\\pi})} - 1)"], "srepr_premise_expression": "Add(Symbol('\\\\gamma', commutative=True), sin(Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), sin(Symbol('\\\\pi', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), log(Symbol('\\\\pi', commutative=True)))", "Add(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\pi', commutative=True))))", "cos(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "Mul(Symbol('\\\\gamma', commutative=True), Add(log(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))), Integer(-1)))"]}, {"premise_expression": "\\alpha + \\psi - \\sigma", "variable": "\\alpha", "positive": "\\alpha (\\frac{\\alpha}{2} + \\psi - \\sigma)", "negatives": ["\\frac{\\sigma (2 \\alpha + 2 \\psi - \\sigma)}{2}", "\\frac{\\psi (2 \\alpha + \\psi - 2 \\sigma)}{2}", "(\\psi + \\sigma) \\log{(\\alpha)}", "\\frac{\\alpha^{2}}{2 \\psi \\sigma}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\alpha', commutative=True), Add(Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True)), log(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))"]}, {"premise_expression": "\\chi + \\log{(\\alpha)}", "variable": "\\chi", "positive": "\\frac{\\chi (\\chi + 2 \\log{(\\alpha)})}{2}", "negatives": ["\\frac{\\chi (- \\chi + 2 \\sin{(\\alpha)})}{2}", "\\frac{\\chi^{2} \\log{(\\alpha)}}{2}", "\\alpha (\\chi + \\log{(\\alpha)} - 1)", "- \\alpha \\chi - \\cos{(\\chi)}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), log(Symbol('\\\\alpha', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\alpha', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), log(Symbol('\\\\alpha', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\alpha', commutative=True)), Integer(-1)))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\chi', commutative=True))))"]}, {"premise_expression": "\\frac{\\alpha \\beta}{\\pi}", "variable": "\\alpha", "positive": "\\frac{\\alpha^{2} \\beta}{2 \\pi}", "negatives": ["\\frac{\\alpha \\beta^{2}}{2 \\pi}", "\\frac{\\alpha^{2} \\beta \\pi}{2}", "\\alpha \\beta \\log{(\\pi)}", "\\pi^{\\beta} \\log{(\\alpha)}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\beta', commutative=True), Symbol('\\\\pi', commutative=True))", "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True), log(Symbol('\\\\pi', commutative=True)))", "Mul(Pow(Symbol('\\\\pi', commutative=True), Symbol('\\\\beta', commutative=True)), log(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "- \\delta + \\pi + \\psi", "variable": "\\delta", "positive": "\\delta (- \\frac{\\delta}{2} + \\pi + \\psi)", "negatives": ["\\frac{\\pi (- 2 \\delta + \\pi + 2 \\psi)}{2}", "\\frac{\\psi (- 2 \\delta + 2 \\pi + \\psi)}{2}", "\\frac{\\delta (\\delta + 2 \\pi \\psi)}{2}", "\\frac{\\delta (\\delta \\psi + 2 \\pi)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Rational(1, 2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\pi', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "- \\chi + e^{\\delta}", "variable": "\\delta", "positive": "- \\chi \\delta + e^{\\delta}", "negatives": ["\\chi e^{\\delta}", "\\chi \\log{(\\delta)}", "\\frac{\\chi (- \\chi + 2 e^{\\delta})}{2}", "e^{\\chi + \\delta}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), exp(Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True)), exp(Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\chi', commutative=True), exp(Symbol('\\\\delta', commutative=True)))", "Mul(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\delta', commutative=True)))))", "exp(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\chi \\omega", "variable": "\\omega", "positive": "\\frac{\\chi \\omega^{2}}{2}", "negatives": ["\\frac{\\chi^{2} \\omega}{2}", "\\frac{\\omega^{2}}{2 \\chi}", "\\chi \\log{(\\omega)}", "\\sin{(\\chi + \\omega)}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\omega', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "Mul(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "sin(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\frac{\\beta}{\\pi} - \\sigma", "variable": "\\pi", "positive": "\\beta \\log{(\\pi)} - \\pi \\sigma", "negatives": ["\\beta \\log{(\\pi)} + \\pi \\sigma", "\\frac{\\beta^{2}}{2 \\pi} - \\beta \\sigma", "\\frac{\\beta \\sigma}{\\pi} - \\frac{\\sigma^{2}}{2}", "\\frac{\\pi (2 \\beta \\sigma - \\pi)}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1))), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\beta', commutative=True), log(Symbol('\\\\pi', commutative=True))), Mul(Integer(-1), Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\beta', commutative=True), log(Symbol('\\\\pi', commutative=True))), Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True)))", "Add(Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1))), Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True)))", "Add(Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\log{(\\beta + \\delta)}", "variable": "\\delta", "positive": "\\beta \\log{(\\beta + \\delta)} + \\delta \\log{(\\beta + \\delta)} - \\delta", "negatives": ["\\beta \\log{(\\beta + \\delta)} - \\beta + \\delta \\log{(\\beta + \\delta)}", "- \\beta \\cos{(\\delta)}", "- \\sin{(\\beta - \\delta)}", "e^{\\beta + \\delta}"], "srepr_premise_expression": "log(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\beta', commutative=True), log(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True)))), Mul(Symbol('\\\\delta', commutative=True), log(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True)))), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\beta', commutative=True), log(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True)))), Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Symbol('\\\\delta', commutative=True), log(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True)))))", "Mul(Integer(-1), Symbol('\\\\beta', commutative=True), cos(Symbol('\\\\delta', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)))))", "exp(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\pi + \\sigma", "variable": "\\pi", "positive": "\\frac{\\pi (\\pi + 2 \\sigma)}{2}", "negatives": ["\\frac{\\sigma (2 \\pi + \\sigma)}{2}", "\\frac{\\pi (\\pi + 2 \\sin{(\\sigma)})}{2}", "\\frac{\\pi^{2} \\sigma}{2}", "e^{\\pi + \\sigma}"], "srepr_premise_expression": "Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), sin(Symbol('\\\\sigma', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), Symbol('\\\\sigma', commutative=True))", "exp(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\alpha \\delta", "variable": "\\alpha", "positive": "\\frac{\\alpha^{2} \\delta}{2}", "negatives": ["\\frac{\\alpha \\delta^{2}}{2}", "\\frac{\\alpha^{2} e^{\\delta}}{2}", "\\frac{\\alpha (\\alpha + 2 \\log{(\\delta)})}{2}", "\\alpha (- \\delta + \\log{(\\delta)})"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\delta', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\delta', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), exp(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), log(Symbol('\\\\delta', commutative=True)))))", "Mul(Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), log(Symbol('\\\\delta', commutative=True))))"]}, {"premise_expression": "e^{\\frac{\\omega}{\\delta}}", "variable": "\\omega", "positive": "\\delta e^{\\frac{\\omega}{\\delta}}", "negatives": ["\\delta \\log{(\\omega)}", "\\cos{(\\delta - \\omega)}", "e^{\\delta} \\log{(\\omega)}", "\\omega (\\log{(\\frac{\\omega}{\\delta})} - 1)"], "srepr_premise_expression": "exp(Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\delta', commutative=True), exp(Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Mul(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "Mul(exp(Symbol('\\\\delta', commutative=True)), log(Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), Add(log(Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\delta \\psi", "variable": "\\psi", "positive": "\\frac{\\delta \\psi^{2}}{2}", "negatives": ["\\frac{\\delta^{2} \\psi}{2}", "- \\frac{\\cos{(\\psi)}}{\\delta}", "\\frac{\\psi^{2} \\sin{(\\delta)}}{2}", "- \\cos{(\\delta - \\psi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))", "Mul(Integer(-1), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), cos(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), sin(Symbol('\\\\delta', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))"]}, {"premise_expression": "\\beta \\psi", "variable": "\\beta", "positive": "\\frac{\\beta^{2} \\psi}{2}", "negatives": ["\\frac{\\beta \\psi^{2}}{2}", "- \\beta \\psi + e^{\\beta}", "\\frac{\\beta (\\beta + 2 \\log{(\\psi)})}{2}", "\\frac{\\beta (- \\beta + 2 e^{\\psi})}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\psi', commutative=True)), exp(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), log(Symbol('\\\\psi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\psi', commutative=True)))))"]}, {"premise_expression": "\\alpha + \\sigma", "variable": "\\sigma", "positive": "\\frac{\\sigma (2 \\alpha + \\sigma)}{2}", "negatives": ["\\frac{\\alpha (\\alpha + 2 \\sigma)}{2}", "\\frac{\\sigma (\\log{(\\sigma)} - 1)}{\\alpha}", "- \\frac{\\cos{(\\sigma)}}{\\alpha}", "\\sigma (\\alpha + \\log{(\\sigma)} - 1)"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True), Add(log(Symbol('\\\\sigma', commutative=True)), Integer(-1)))", "Mul(Integer(-1), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), cos(Symbol('\\\\sigma', commutative=True)))", "Mul(Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\sigma', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\delta + e^{\\alpha}", "variable": "\\delta", "positive": "\\frac{\\delta (\\delta + 2 e^{\\alpha})}{2}", "negatives": ["\\frac{\\delta (- \\delta + 2 e^{\\alpha})}{2}", "\\alpha \\delta + e^{\\alpha}", "\\frac{\\delta (2 \\alpha + \\delta)}{2}", "\\alpha \\delta - \\cos{(\\delta)}"], "srepr_premise_expression": "Add(Symbol('\\\\delta', commutative=True), exp(Symbol('\\\\alpha', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), exp(Symbol('\\\\alpha', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\alpha', commutative=True)))))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\delta', commutative=True)), exp(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\delta', commutative=True)))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\delta', commutative=True))))"]}, {"premise_expression": "\\frac{e^{\\omega}}{\\psi}", "variable": "\\psi", "positive": "e^{\\omega} \\log{(\\psi)}", "negatives": ["- e^{\\omega - \\psi}", "\\psi (\\log{(\\omega \\psi)} - 1)", "\\psi (\\log{(\\frac{\\omega}{\\psi})} + 1)", "\\frac{\\psi (\\log{(\\psi)} - 1)}{\\omega}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), exp(Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(exp(Symbol('\\\\omega', commutative=True)), log(Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))", "Mul(Symbol('\\\\psi', commutative=True), Add(log(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\psi', commutative=True), Add(log(Mul(Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True), Add(log(Symbol('\\\\psi', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\omega \\xi", "variable": "\\xi", "positive": "\\frac{\\omega \\xi^{2}}{2}", "negatives": ["\\frac{\\omega^{2} \\xi}{2}", "\\frac{\\xi^{2} \\log{(\\omega)}}{2}", "\\frac{\\xi (2 \\omega + \\xi)}{2}", "\\frac{\\xi (2 \\omega - \\xi)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), log(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "- \\chi + \\log{(\\psi)}", "variable": "\\chi", "positive": "\\frac{\\chi (- \\chi + 2 \\log{(\\psi)})}{2}", "negatives": ["\\psi (- \\chi + \\log{(\\psi)} - 1)", "\\chi (- \\psi + e^{\\psi})", "\\frac{\\chi^{2} \\cos{(\\psi)}}{2}", "\\frac{\\chi (\\chi + 2 \\psi)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), log(Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), log(Symbol('\\\\psi', commutative=True)))))", "srepr_negatives": ["Mul(Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), log(Symbol('\\\\psi', commutative=True)), Integer(-1)))", "Mul(Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), exp(Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), cos(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "\\cos{(\\gamma - \\sigma)}", "variable": "\\sigma", "positive": "- \\sin{(\\gamma - \\sigma)}", "negatives": ["\\sin{(\\gamma - \\sigma)}", "e^{\\gamma + \\sigma}", "\\gamma \\sin{(\\sigma)}", "\\log{(\\gamma)} \\log{(\\sigma)}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Integer(-1), sin(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))", "srepr_negatives": ["sin(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "exp(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True)))", "Mul(Symbol('\\\\gamma', commutative=True), sin(Symbol('\\\\sigma', commutative=True)))", "Mul(log(Symbol('\\\\gamma', commutative=True)), log(Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\frac{\\delta}{\\alpha}", "variable": "\\alpha", "positive": "\\delta \\log{(\\alpha)}", "negatives": ["\\delta \\sin{(\\alpha)}", "\\frac{\\delta^{2}}{2 \\alpha}", "- \\cos{(\\alpha - \\delta)}", "\\alpha (\\log{(\\frac{\\delta}{\\alpha})} + 1)"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\delta', commutative=True), sin(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\delta', commutative=True), Integer(2)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)))))", "Mul(Symbol('\\\\alpha', commutative=True), Add(log(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True))), Integer(1)))"]}, {"premise_expression": "\\frac{\\omega}{\\pi}", "variable": "\\omega", "positive": "\\frac{\\omega^{2}}{2 \\pi}", "negatives": ["\\omega \\log{(\\pi)}", "\\pi \\sin{(\\omega)}", "e^{\\omega + \\pi}", "\\omega (\\log{(\\frac{\\pi}{\\omega})} + 1)"], "srepr_premise_expression": "Mul(Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\pi', commutative=True), sin(Symbol('\\\\omega', commutative=True)))", "exp(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), Add(log(Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))), Integer(1)))"]}, {"premise_expression": "\\cos{(\\alpha - \\chi)}", "variable": "\\chi", "positive": "- \\sin{(\\alpha - \\chi)}", "negatives": ["\\sin{(\\alpha - \\chi)}", "\\frac{\\chi (- 2 \\alpha + \\chi)}{2}", "\\alpha e^{\\chi}", "\\frac{\\chi (2 \\alpha - \\chi)}{2}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True))))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Integer(-1), sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True)))))", "srepr_negatives": ["sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\chi', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), exp(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\chi', commutative=True))))"]}, {"premise_expression": "e^{- \\chi + \\pi}", "variable": "\\chi", "positive": "- e^{- \\chi + \\pi}", "negatives": ["e^{- \\chi + \\pi}", "\\pi \\sin{(\\chi)}", "\\chi \\pi + e^{\\chi}", "\\log{(\\chi)} \\log{(\\pi)}"], "srepr_premise_expression": "exp(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["exp(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\pi', commutative=True), sin(Symbol('\\\\chi', commutative=True)))", "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True)), exp(Symbol('\\\\chi', commutative=True)))", "Mul(log(Symbol('\\\\chi', commutative=True)), log(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "- \\omega + \\pi", "variable": "\\omega", "positive": "\\frac{\\omega (- \\omega + 2 \\pi)}{2}", "negatives": ["\\frac{\\pi (- 2 \\omega + \\pi)}{2}", "\\frac{\\omega (- \\omega + 2 \\cos{(\\pi)})}{2}", "\\frac{\\omega^{2} \\log{(\\pi)}}{2}", "- \\omega \\pi + e^{\\omega}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\pi', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), log(Symbol('\\\\pi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)), exp(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "- \\psi + \\cos{(\\pi)}", "variable": "\\pi", "positive": "- \\pi \\psi + \\sin{(\\pi)}", "negatives": ["- \\pi \\psi + e^{\\pi}", "\\psi \\sin{(\\pi)}", "\\psi e^{\\pi}", "\\frac{\\sin{(\\pi)}}{\\psi}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), cos(Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)), sin(Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)), exp(Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\psi', commutative=True), sin(Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\psi', commutative=True), exp(Symbol('\\\\pi', commutative=True)))", "Mul(Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), sin(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "- \\alpha + \\beta", "variable": "\\beta", "positive": "\\frac{\\beta (- 2 \\alpha + \\beta)}{2}", "negatives": ["\\frac{\\alpha (- \\alpha + 2 \\beta)}{2}", "\\frac{\\beta (- \\beta + 2 \\cos{(\\alpha)})}{2}", "- \\cos{(\\alpha + \\beta)}", "- \\alpha \\beta + e^{\\beta}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\beta', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\beta', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\beta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\alpha', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True)), exp(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "- \\sin{(\\beta - \\psi)}", "variable": "\\psi", "positive": "- \\cos{(\\beta - \\psi)}", "negatives": ["\\cos{(\\beta - \\psi)}", "e^{- \\beta + \\psi}", "\\frac{\\psi (2 \\beta - \\psi)}{2}", "\\beta \\psi - \\cos{(\\psi)}"], "srepr_premise_expression": "Mul(Integer(-1), sin(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))", "srepr_negatives": ["cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "exp(Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "\\pi + \\log{(\\omega)}", "variable": "\\pi", "positive": "\\frac{\\pi (\\pi + 2 \\log{(\\omega)})}{2}", "negatives": ["\\frac{\\pi (- \\pi + 2 \\log{(\\omega)})}{2}", "\\frac{\\pi (- \\pi + 2 \\sin{(\\omega)})}{2}", "\\omega (\\pi + \\log{(\\omega)} - 1)", "\\frac{\\pi^{2} \\sin{(\\omega)}}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), log(Symbol('\\\\omega', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), log(Symbol('\\\\omega', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\omega', commutative=True)))))", "Mul(Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\omega', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), sin(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "e^{\\alpha - \\pi}", "variable": "\\alpha", "positive": "e^{\\alpha - \\pi}", "negatives": ["- e^{\\alpha - \\pi}", "\\sin{(\\alpha + \\pi)}", "- \\cos{(\\alpha - \\pi)}", "\\frac{\\alpha (\\alpha + 2 \\pi)}{2}"], "srepr_premise_expression": "exp(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "exp(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))", "sin(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\log{(\\psi^{\\beta})}", "variable": "\\beta", "positive": "\\frac{\\beta^{2} \\log{(\\psi)}}{2}", "negatives": ["\\psi \\log{(\\beta)}", "- \\psi \\cos{(\\beta)}", "\\frac{\\beta (\\beta + 2 \\sin{(\\psi)})}{2}", "\\psi (- \\beta + \\log{(\\psi^{\\beta})})"], "srepr_premise_expression": "log(Pow(Symbol('\\\\psi', commutative=True), Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), log(Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\psi', commutative=True), log(Symbol('\\\\beta', commutative=True)))", "Mul(Integer(-1), Symbol('\\\\psi', commutative=True), cos(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), sin(Symbol('\\\\psi', commutative=True)))))", "Mul(Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), log(Pow(Symbol('\\\\psi', commutative=True), Symbol('\\\\beta', commutative=True)))))"]}, {"premise_expression": "- \\gamma + \\pi", "variable": "\\gamma", "positive": "\\frac{\\gamma (- \\gamma + 2 \\pi)}{2}", "negatives": ["\\frac{\\gamma (\\gamma - 2 \\pi)}{2}", "\\frac{\\pi (- 2 \\gamma + \\pi)}{2}", "\\sin{(\\gamma + \\pi)}", "\\gamma \\pi + \\sin{(\\gamma)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True)))", "sin(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True)))", "Add(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True)), sin(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\log{(\\gamma \\pi)}", "variable": "\\gamma", "positive": "\\gamma (\\log{(\\gamma \\pi)} - 1)", "negatives": ["\\pi (\\log{(\\gamma \\pi)} - 1)", "\\frac{\\gamma^{2} \\log{(\\pi)}}{2}", "\\frac{\\gamma (- \\gamma + 2 \\pi)}{2}", "e^{\\gamma - \\pi}"], "srepr_premise_expression": "log(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\gamma', commutative=True), Add(log(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\pi', commutative=True), Add(log(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), log(Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "exp(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\alpha + \\chi", "variable": "\\alpha", "positive": "\\frac{\\alpha (\\alpha + 2 \\chi)}{2}", "negatives": ["\\frac{\\chi (2 \\alpha + \\chi)}{2}", "\\frac{\\alpha^{2} \\sin{(\\chi)}}{2}", "\\frac{\\alpha^{2} \\log{(\\chi)}}{2}", "\\frac{\\sin{(\\alpha)}}{\\chi}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\chi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), sin(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), log(Symbol('\\\\chi', commutative=True)))", "Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), sin(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\cos{(\\alpha - \\omega)}", "variable": "\\omega", "positive": "- \\sin{(\\alpha - \\omega)}", "negatives": ["\\sin{(\\alpha - \\omega)}", "\\frac{\\omega (2 \\alpha + \\omega)}{2}", "\\frac{\\alpha \\omega^{2}}{2}", "\\frac{\\omega^{2} \\log{(\\alpha)}}{2}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Integer(-1), sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))))", "srepr_negatives": ["sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), log(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\frac{\\pi}{\\chi}", "variable": "\\chi", "positive": "\\pi \\log{(\\chi)}", "negatives": ["\\frac{\\pi^{2}}{2 \\chi}", "\\frac{\\chi^{2} \\pi}{2}", "- \\cos{(\\chi - \\pi)}", "- \\cos{(\\chi + \\pi)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\pi', commutative=True))", "Mul(Integer(-1), cos(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\alpha \\xi", "variable": "\\xi", "positive": "\\frac{\\alpha \\xi^{2}}{2}", "negatives": ["\\frac{\\alpha^{2} \\xi}{2}", "\\frac{\\xi (- 2 \\alpha + \\xi)}{2}", "\\frac{\\xi (2 \\alpha + \\xi)}{2}", "\\alpha \\log{(\\xi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\frac{\\pi}{\\alpha}", "variable": "\\pi", "positive": "\\frac{\\pi^{2}}{2 \\alpha}", "negatives": ["\\pi \\log{(\\alpha)}", "\\frac{\\pi^{2} \\cos{(\\alpha)}}{2}", "- \\cos{(\\alpha + \\pi)}", "- \\cos{(\\alpha - \\pi)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), cos(Symbol('\\\\alpha', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))"]}, {"premise_expression": "\\chi \\xi + \\psi", "variable": "\\xi", "positive": "\\frac{\\xi (\\chi \\xi + 2 \\psi)}{2}", "negatives": ["\\frac{\\chi (\\chi \\xi + 2 \\psi)}{2}", "\\frac{\\psi (2 \\chi \\xi + \\psi)}{2}", "\\frac{\\xi (2 \\chi + 2 \\psi - \\xi)}{2}", "\\chi^{2} \\psi \\xi"], "srepr_premise_expression": "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True)), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True), Symbol('\\\\xi', commutative=True))"]}, {"premise_expression": "\\log{(- \\alpha + \\sigma)}", "variable": "\\sigma", "positive": "- \\alpha \\log{(- \\alpha + \\sigma)} + \\sigma \\log{(- \\alpha + \\sigma)} - \\sigma", "negatives": ["\\alpha \\log{(- \\alpha + \\sigma)} - \\alpha - \\sigma \\log{(\\alpha - \\sigma)}", "\\alpha \\operatorname{Si}{(\\frac{\\alpha}{\\sigma})} + \\sigma \\cos{(\\frac{\\alpha}{\\sigma})}", "\\sigma (- \\alpha + \\log{(\\sigma)} - 1)", "\\frac{\\sigma (- \\sigma + 2 \\log{(\\alpha)})}{2}"], "srepr_premise_expression": "log(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\sigma', commutative=True)))), Mul(Symbol('\\\\sigma', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\sigma', commutative=True)))), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\alpha', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\sigma', commutative=True)))), Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Si(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1))))), Mul(Symbol('\\\\sigma', commutative=True), cos(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1))))))", "Mul(Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), log(Symbol('\\\\sigma', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), Mul(Integer(2), log(Symbol('\\\\alpha', commutative=True)))))"]}, {"premise_expression": "\\log{(- \\beta + \\xi)}", "variable": "\\xi", "positive": "- \\beta \\log{(- \\beta + \\xi)} + \\xi \\log{(- \\beta + \\xi)} - \\xi", "negatives": ["\\beta \\log{(- \\beta + \\xi)} - \\beta - \\xi \\log{(\\beta - \\xi)}", "\\beta \\operatorname{Si}{(\\frac{\\beta}{\\xi})} + \\xi \\cos{(\\frac{\\beta}{\\xi})}", "\\frac{\\xi (- \\xi + 2 \\log{(\\beta)})}{2}", "\\xi (\\log{(\\frac{\\xi}{\\beta})} - 1)"], "srepr_premise_expression": "log(Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\xi', commutative=True)))), Mul(Symbol('\\\\xi', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\xi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\beta', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\xi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True), log(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))))", "Add(Mul(Symbol('\\\\beta', commutative=True), Si(Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))), Mul(Symbol('\\\\xi', commutative=True), cos(Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), log(Symbol('\\\\beta', commutative=True)))))", "Mul(Symbol('\\\\xi', commutative=True), Add(log(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\omega + \\cos{(\\psi)}", "variable": "\\omega", "positive": "\\frac{\\omega (\\omega + 2 \\cos{(\\psi)})}{2}", "negatives": ["\\frac{\\omega (\\omega + 2 \\log{(\\psi)})}{2}", "\\omega \\psi + \\sin{(\\psi)}", "\\frac{\\omega (\\omega + 2 \\psi)}{2}", "- \\psi \\cos{(\\omega)}"], "srepr_premise_expression": "Add(Symbol('\\\\omega', commutative=True), cos(Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), cos(Symbol('\\\\psi', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), log(Symbol('\\\\psi', commutative=True)))))", "Add(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True)), sin(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Integer(-1), Symbol('\\\\psi', commutative=True), cos(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\delta (- \\beta + \\xi)", "variable": "\\xi", "positive": "\\frac{\\delta \\xi (- 2 \\beta + \\xi)}{2}", "negatives": ["\\frac{\\delta \\xi (2 \\beta + \\xi)}{2}", "\\frac{\\delta \\xi (2 \\delta + \\xi)}{2}", "\\frac{\\delta^{2} (- \\beta + \\xi)}{2}", "\\frac{\\beta \\delta (- \\beta + 2 \\xi)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\chi \\omega", "variable": "\\omega", "positive": "\\frac{\\chi \\omega^{2}}{2}", "negatives": ["\\frac{\\chi^{2} \\omega}{2}", "\\frac{\\omega^{2}}{2 \\chi}", "\\chi e^{\\omega}", "\\frac{\\omega (2 \\chi - \\omega)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\omega', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "Mul(Symbol('\\\\chi', commutative=True), exp(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))"]}, {"premise_expression": "\\alpha \\delta", "variable": "\\alpha", "positive": "\\frac{\\alpha^{2} \\delta}{2}", "negatives": ["\\frac{\\alpha \\delta^{2}}{2}", "\\delta \\log{(\\alpha)}", "- \\frac{\\cos{(\\alpha)}}{\\delta}", "\\alpha \\delta - \\cos{(\\alpha)}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\delta', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\delta', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(2)))", "Mul(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), cos(Symbol('\\\\alpha', commutative=True)))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\alpha', commutative=True))))"]}, {"premise_expression": "\\sin{(\\frac{\\chi}{\\beta})}", "variable": "\\beta", "positive": "\\beta \\sin{(\\frac{\\chi}{\\beta})} - \\frac{\\chi \\log{(\\frac{\\chi^{2}}{\\beta^{2}})}}{2} + \\chi \\log{(\\frac{\\chi}{\\beta})} - \\chi \\operatorname{Ci}{(\\frac{\\chi}{\\beta})}", "negatives": ["\\beta \\log{(- \\beta + \\chi)} - \\beta - \\chi \\log{(\\beta - \\chi)}", "\\frac{\\beta (- \\beta + 2 \\log{(\\chi)})}{2}", "\\frac{\\beta (- \\beta + 2 \\cos{(\\chi)})}{2}", "\\frac{\\beta (\\beta + 2 \\sin{(\\chi)})}{2}"], "srepr_premise_expression": "sin(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\beta', commutative=True), sin(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\chi', commutative=True)))), Mul(Integer(-1), Rational(1, 2), Symbol('\\\\chi', commutative=True), log(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-2)), Pow(Symbol('\\\\chi', commutative=True), Integer(2))))), Mul(Symbol('\\\\chi', commutative=True), log(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\chi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Ci(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\chi', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\beta', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\chi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Symbol('\\\\chi', commutative=True), log(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True))))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), log(Symbol('\\\\chi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\chi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), sin(Symbol('\\\\chi', commutative=True)))))"]}, {"premise_expression": "\\frac{e^{\\alpha}}{\\beta}", "variable": "\\beta", "positive": "e^{\\alpha} \\log{(\\beta)}", "negatives": ["\\alpha \\beta + e^{\\beta}", "- \\alpha \\beta + e^{\\beta}", "- \\cos{(\\alpha + \\beta)}", "\\beta (\\alpha + \\log{(\\beta)} - 1)"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), exp(Symbol('\\\\alpha', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(exp(Symbol('\\\\alpha', commutative=True)), log(Symbol('\\\\beta', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True)), exp(Symbol('\\\\beta', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True)), exp(Symbol('\\\\beta', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True))))", "Mul(Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\beta', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\gamma + \\omega + \\sigma", "variable": "\\sigma", "positive": "\\sigma (\\gamma + \\omega + \\frac{\\sigma}{2})", "negatives": ["\\frac{\\sigma (2 \\gamma + 2 \\omega - \\sigma)}{2}", "\\frac{\\gamma (\\gamma + 2 \\omega + 2 \\sigma)}{2}", "\\frac{\\omega (2 \\gamma + \\omega + 2 \\sigma)}{2}", "\\frac{\\sigma^{2} (\\gamma + \\omega)}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True), Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\beta \\chi \\sigma", "variable": "\\beta", "positive": "\\frac{\\beta^{2} \\chi \\sigma}{2}", "negatives": ["\\frac{\\beta \\chi \\sigma^{2}}{2}", "\\frac{\\beta \\chi^{2} \\sigma}{2}", "\\frac{\\beta^{2}}{2 \\chi \\sigma}", "\\frac{\\beta^{2} (\\chi - \\sigma)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\chi', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\sigma', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\frac{\\chi}{\\omega}", "variable": "\\chi", "positive": "\\frac{\\chi^{2}}{2 \\omega}", "negatives": ["\\chi \\log{(\\omega)}", "\\omega e^{\\frac{\\chi}{\\omega}}", "\\frac{\\chi^{2} \\log{(\\omega)}}{2}", "\\frac{\\chi^{2} \\sin{(\\omega)}}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), exp(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), log(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), sin(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\chi + \\sigma", "variable": "\\sigma", "positive": "\\frac{\\sigma (2 \\chi + \\sigma)}{2}", "negatives": ["\\frac{\\sigma (2 \\chi - \\sigma)}{2}", "\\frac{\\chi (\\chi + 2 \\sigma)}{2}", "- \\cos{(\\chi + \\sigma)}", "- \\cos{(\\chi - \\sigma)}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\sigma', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))"]}, {"premise_expression": "\\log{(\\psi^{\\gamma})}", "variable": "\\gamma", "positive": "\\frac{\\gamma^{2} \\log{(\\psi)}}{2}", "negatives": ["\\frac{\\gamma^{2} \\sin{(\\psi)}}{2}", "\\frac{\\gamma (\\gamma + 2 \\log{(\\psi)})}{2}", "\\gamma (- \\gamma + \\psi)", "\\cos{(\\gamma - \\psi)}"], "srepr_premise_expression": "log(Pow(Symbol('\\\\psi', commutative=True), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), log(Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), sin(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), log(Symbol('\\\\psi', commutative=True)))))", "Mul(Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\psi', commutative=True)))", "cos(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "\\frac{\\delta}{\\beta \\omega}", "variable": "\\omega", "positive": "\\frac{\\delta \\log{(\\omega)}}{\\beta}", "negatives": ["\\frac{\\delta \\log{(\\beta)}}{\\omega}", "\\beta \\log{(\\omega)} + \\delta \\omega", "\\frac{\\delta^{\\beta} \\omega^{2}}{2}", "\\frac{\\delta^{2}}{2 \\beta \\omega}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), log(Symbol('\\\\beta', commutative=True)))", "Add(Mul(Symbol('\\\\beta', commutative=True), log(Symbol('\\\\omega', commutative=True))), Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Symbol('\\\\beta', commutative=True)), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))"]}, {"premise_expression": "- \\delta + \\cos{(\\psi)}", "variable": "\\psi", "positive": "- \\delta \\psi + \\sin{(\\psi)}", "negatives": ["\\delta \\psi + \\sin{(\\psi)}", "- \\delta \\psi + e^{\\psi}", "\\delta \\psi - \\cos{(\\psi)}", "\\frac{\\psi^{2}}{2 \\delta}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), cos(Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Symbol('\\\\psi', commutative=True)), sin(Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\psi', commutative=True)), sin(Symbol('\\\\psi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Symbol('\\\\psi', commutative=True)), exp(Symbol('\\\\psi', commutative=True)))", "Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))"]}, {"premise_expression": "\\log{(\\beta^{\\pi})}", "variable": "\\pi", "positive": "\\frac{\\pi^{2} \\log{(\\beta)}}{2}", "negatives": ["\\frac{\\pi (2 \\beta + \\pi)}{2}", "\\frac{\\pi (\\pi + 2 \\log{(\\beta)})}{2}", "\\frac{\\pi (\\pi + 2 \\sin{(\\beta)})}{2}", "\\beta e^{\\frac{\\pi}{\\beta}}"], "srepr_premise_expression": "log(Pow(Symbol('\\\\beta', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), log(Symbol('\\\\beta', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), log(Symbol('\\\\beta', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), sin(Symbol('\\\\beta', commutative=True)))))", "Mul(Symbol('\\\\beta', commutative=True), exp(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\frac{\\log{(\\alpha)}}{\\xi}", "variable": "\\alpha", "positive": "\\frac{\\alpha (\\log{(\\alpha)} - 1)}{\\xi}", "negatives": ["\\alpha (\\xi + \\log{(\\alpha)} - 1)", "\\log{(\\alpha)} \\log{(\\xi)}", "\\sin{(\\alpha + \\xi)}", "\\frac{\\alpha^{2} \\cos{(\\xi)}}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), log(Symbol('\\\\alpha', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), Add(log(Symbol('\\\\alpha', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\alpha', commutative=True)), Integer(-1)))", "Mul(log(Symbol('\\\\alpha', commutative=True)), log(Symbol('\\\\xi', commutative=True)))", "sin(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), cos(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\delta - \\sigma", "variable": "\\delta", "positive": "\\frac{\\delta (\\delta - 2 \\sigma)}{2}", "negatives": ["\\frac{\\sigma (2 \\delta - \\sigma)}{2}", "\\frac{\\delta (\\delta + 2 e^{\\sigma})}{2}", "- \\cos{(\\delta - \\sigma)}", "- \\cos{(\\delta + \\sigma)}"], "srepr_premise_expression": "Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), exp(Symbol('\\\\sigma', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\psi + \\sigma - \\xi", "variable": "\\psi", "positive": "\\psi (\\frac{\\psi}{2} + \\sigma - \\xi)", "negatives": ["\\frac{\\psi (- \\psi + 2 \\sigma + 2 \\xi)}{2}", "\\frac{\\sigma (2 \\psi + \\sigma - 2 \\xi)}{2}", "\\frac{\\xi (2 \\psi + 2 \\sigma - \\xi)}{2}", "\\frac{\\psi \\sigma (\\psi - 2 \\xi)}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\psi', commutative=True), Add(Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True)), Symbol('\\\\sigma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\psi', commutative=True)), Symbol('\\\\sigma', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\frac{\\log{(\\xi)}}{\\omega}", "variable": "\\xi", "positive": "\\frac{\\xi (\\log{(\\xi)} - 1)}{\\omega}", "negatives": ["\\log{(\\omega)} \\log{(\\xi)}", "\\frac{\\sin{(\\xi)}}{\\omega}", "\\omega \\sin{(\\xi)}", "\\sin{(\\omega + \\xi)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), log(Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True), Add(log(Symbol('\\\\xi', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(log(Symbol('\\\\omega', commutative=True)), log(Symbol('\\\\xi', commutative=True)))", "Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), sin(Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), sin(Symbol('\\\\xi', commutative=True)))", "sin(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "- \\sin{(\\alpha - \\xi)}", "variable": "\\xi", "positive": "- \\cos{(\\alpha - \\xi)}", "negatives": ["\\cos{(\\alpha - \\xi)}", "\\sin{(\\alpha + \\xi)}", "e^{\\alpha + \\xi}", "- \\alpha \\xi + \\sin{(\\xi)}"], "srepr_premise_expression": "Mul(Integer(-1), sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))))", "srepr_negatives": ["cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "sin(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True)))", "exp(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True)), sin(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\log{(\\omega \\sigma)}", "variable": "\\sigma", "positive": "\\sigma (\\log{(\\omega \\sigma)} - 1)", "negatives": ["\\omega (\\log{(\\omega \\sigma)} - 1)", "\\sigma (\\log{(\\frac{\\sigma}{\\omega})} - 1)", "\\frac{\\sigma (2 \\omega + \\sigma)}{2}", "\\frac{\\sigma (- 2 \\omega + \\sigma)}{2}"], "srepr_premise_expression": "log(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\sigma', commutative=True), Add(log(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\omega', commutative=True), Add(log(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\sigma', commutative=True), Add(log(Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "e^{\\chi + \\gamma}", "variable": "\\gamma", "positive": "e^{\\chi + \\gamma}", "negatives": ["\\log{(\\chi)} \\log{(\\gamma)}", "\\gamma (\\chi + \\log{(\\gamma)} - 1)", "\\frac{\\gamma (- \\gamma + 2 \\log{(\\chi)})}{2}", "\\chi \\log{(\\chi + \\gamma)} + \\gamma \\log{(\\chi + \\gamma)} - \\gamma"], "srepr_premise_expression": "exp(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "exp(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(log(Symbol('\\\\chi', commutative=True)), log(Symbol('\\\\gamma', commutative=True)))", "Mul(Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\gamma', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), log(Symbol('\\\\chi', commutative=True)))))", "Add(Mul(Symbol('\\\\chi', commutative=True), log(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True)))), Mul(Symbol('\\\\gamma', commutative=True), log(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True)))), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\omega \\sigma \\xi", "variable": "\\xi", "positive": "\\frac{\\omega \\sigma \\xi^{2}}{2}", "negatives": ["\\frac{\\sigma^{\\omega} \\xi^{2}}{2}", "\\frac{\\omega \\sigma^{2} \\xi}{2}", "\\frac{\\omega^{2} \\sigma \\xi}{2}", "0^{\\sigma} \\xi"], "srepr_premise_expression": "Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Symbol('\\\\omega', commutative=True)), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True))", "Mul(Pow(Integer(0), Symbol('\\\\sigma', commutative=True)), Symbol('\\\\xi', commutative=True))"]}, {"premise_expression": "\\cos{(\\chi - \\sigma)}", "variable": "\\sigma", "positive": "- \\sin{(\\chi - \\sigma)}", "negatives": ["\\sin{(\\chi - \\sigma)}", "\\frac{\\sigma^{2} (\\chi - 1)}{2}", "e^{\\chi} \\log{(\\sigma)}", "\\sigma"], "srepr_premise_expression": "cos(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Integer(-1), sin(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))", "srepr_negatives": ["sin(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), Add(Symbol('\\\\chi', commutative=True), Integer(-1)))", "Mul(exp(Symbol('\\\\chi', commutative=True)), log(Symbol('\\\\sigma', commutative=True)))", "Symbol('\\\\sigma', commutative=True)"]}, {"premise_expression": "\\frac{\\sin{(\\alpha)}}{\\psi}", "variable": "\\psi", "positive": "\\log{(\\psi)} \\sin{(\\alpha)}", "negatives": ["\\log{(\\alpha)} \\log{(\\psi)}", "\\cos{(\\alpha - \\psi)}", "- \\sin{(\\alpha - \\psi)}", "\\alpha \\log{(\\psi)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), sin(Symbol('\\\\alpha', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(log(Symbol('\\\\psi', commutative=True)), sin(Symbol('\\\\alpha', commutative=True)))", "srepr_negatives": ["Mul(log(Symbol('\\\\alpha', commutative=True)), log(Symbol('\\\\psi', commutative=True)))", "cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(Integer(-1), sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))", "Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\sin^{\\chi}{(\\gamma)}", "variable": "\\gamma", "positive": "\\int \\sin^{\\chi}{(\\gamma)} d\\gamma", "negatives": ["\\gamma (\\log{(\\gamma^{2})} - 2)", "- \\cos{(\\chi + \\gamma)}", "- \\cos{(\\chi - \\gamma)}", "\\gamma (- \\chi + \\log{(\\gamma)} - 1)"], "srepr_premise_expression": "Pow(sin(Symbol('\\\\gamma', commutative=True)), Symbol('\\\\chi', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Integral(Pow(sin(Symbol('\\\\gamma', commutative=True)), Symbol('\\\\chi', commutative=True)), Tuple(Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\gamma', commutative=True), Add(log(Pow(Symbol('\\\\gamma', commutative=True), Integer(2))), Integer(-2)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))))", "Mul(Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), log(Symbol('\\\\gamma', commutative=True)), Integer(-1)))"]}, {"premise_expression": "- \\chi + 2 \\gamma", "variable": "\\chi", "positive": "\\frac{\\chi (- \\chi + 4 \\gamma)}{2}", "negatives": ["\\gamma (- \\chi + \\gamma)", "- \\gamma \\cos{(\\chi)}", "\\frac{\\chi^{2}}{2 \\gamma}", "\\gamma e^{\\frac{\\chi}{\\gamma}}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(4), Symbol('\\\\gamma', commutative=True))))", "srepr_negatives": ["Mul(Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), cos(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)))", "Mul(Symbol('\\\\gamma', commutative=True), exp(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)))))"]}, {"premise_expression": "\\frac{\\alpha}{\\delta \\pi}", "variable": "\\pi", "positive": "\\frac{\\alpha \\log{(\\pi)}}{\\delta}", "negatives": ["\\frac{\\alpha \\log{(\\delta)}}{\\pi}", "\\frac{\\alpha^{2}}{2 \\delta \\pi}", "(\\alpha + \\delta) \\log{(\\pi)}", "\\frac{\\delta \\pi^{2}}{2 \\alpha}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), log(Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), log(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))", "Mul(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\delta', commutative=True)), log(Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))"]}, {"premise_expression": "\\frac{\\pi}{\\alpha}", "variable": "\\pi", "positive": "\\frac{\\pi^{2}}{2 \\alpha}", "negatives": ["\\pi \\log{(\\alpha)}", "\\alpha \\sin{(\\pi)}", "\\frac{\\pi (- 2 \\alpha + \\pi)}{2}", "- \\sin{(\\alpha - \\pi)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), sin(Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))"]}, {"premise_expression": "\\chi + \\sin{(\\sigma)}", "variable": "\\sigma", "positive": "\\chi \\sigma - \\cos{(\\sigma)}", "negatives": ["\\chi \\sigma + e^{\\sigma}", "\\frac{\\sigma (2 \\chi + \\sigma)}{2}", "\\frac{\\chi (\\chi + 2 \\sin{(\\sigma)})}{2}", "\\frac{\\chi \\sigma^{2}}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), sin(Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\sigma', commutative=True)), exp(Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), sin(Symbol('\\\\sigma', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))"]}, {"premise_expression": "\\sin{(\\alpha - \\psi)}", "variable": "\\psi", "positive": "\\cos{(\\alpha - \\psi)}", "negatives": ["- \\cos{(\\alpha - \\psi)}", "- e^{\\alpha - \\psi}", "\\frac{\\psi (2 \\alpha + \\psi)}{2}", "\\log{(\\alpha)} \\log{(\\psi)}"], "srepr_premise_expression": "sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))", "Mul(Integer(-1), exp(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(log(Symbol('\\\\alpha', commutative=True)), log(Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\cos{(\\beta - \\psi)}", "variable": "\\psi", "positive": "- \\sin{(\\beta - \\psi)}", "negatives": ["\\sin{(\\beta - \\psi)}", "\\frac{\\sin{(\\psi)}}{\\beta}", "- \\beta \\psi + \\sin{(\\psi)}", "\\frac{\\beta \\psi^{2}}{2}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Integer(-1), sin(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))", "srepr_negatives": ["sin(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), sin(Symbol('\\\\psi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\psi', commutative=True)), sin(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))"]}, {"premise_expression": "\\frac{\\omega}{\\gamma}", "variable": "\\gamma", "positive": "\\omega \\log{(\\gamma)}", "negatives": ["\\frac{\\omega^{2}}{2 \\gamma}", "\\gamma \\omega + \\sin{(\\gamma)}", "\\frac{\\gamma^{2} \\log{(\\omega)}}{2}", "- \\cos{(\\gamma + \\omega)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "Add(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True)), sin(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), log(Symbol('\\\\omega', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True))))"]}, {"premise_expression": "\\log{(- \\gamma + \\xi)}", "variable": "\\xi", "positive": "- \\gamma \\log{(- \\gamma + \\xi)} + \\xi \\log{(- \\gamma + \\xi)} - \\xi", "negatives": ["\\gamma \\log{(- \\gamma + \\xi)} - \\gamma - \\xi \\log{(\\gamma - \\xi)}", "- \\gamma \\operatorname{Ei}{(\\frac{\\gamma}{\\xi})} + \\xi e^{\\frac{\\gamma}{\\xi}}", "e^{- \\gamma + \\xi}", "\\int \\sin^{\\gamma}{(\\xi)} d\\xi"], "srepr_premise_expression": "log(Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\xi', commutative=True)))), Mul(Symbol('\\\\xi', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\xi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\gamma', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\xi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True), log(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))))", "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Ei(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))), Mul(Symbol('\\\\xi', commutative=True), exp(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))))", "exp(Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Integral(Pow(sin(Symbol('\\\\xi', commutative=True)), Symbol('\\\\gamma', commutative=True)), Tuple(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "e^{- \\gamma + \\pi}", "variable": "\\gamma", "positive": "- e^{- \\gamma + \\pi}", "negatives": ["e^{- \\gamma + \\pi}", "e^{\\pi} \\log{(\\gamma)}", "\\frac{\\gamma (\\gamma - 2 \\pi)}{2}", "\\pi \\log{(\\gamma)}"], "srepr_premise_expression": "exp(Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["exp(Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(exp(Symbol('\\\\pi', commutative=True)), log(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\alpha + \\cos{(\\xi)}", "variable": "\\xi", "positive": "\\alpha \\xi + \\sin{(\\xi)}", "negatives": ["\\log{(\\xi)} \\sin{(\\alpha)}", "\\xi (\\alpha + \\log{(\\xi)} - 1)", "\\frac{\\xi (2 \\alpha - \\xi)}{2}", "\\frac{\\xi (- \\xi + 2 \\sin{(\\alpha)})}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), cos(Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True)), sin(Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(log(Symbol('\\\\xi', commutative=True)), sin(Symbol('\\\\alpha', commutative=True)))", "Mul(Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\xi', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\alpha', commutative=True)))))"]}, {"premise_expression": "- \\beta + \\psi", "variable": "\\psi", "positive": "\\frac{\\psi (- 2 \\beta + \\psi)}{2}", "negatives": ["\\frac{\\psi (2 \\beta + \\psi)}{2}", "\\frac{\\beta (- \\beta + 2 \\psi)}{2}", "\\frac{\\beta \\psi^{2}}{2}", "\\frac{\\psi^{2}}{2 \\beta}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))"]}, {"premise_expression": "\\gamma \\pi", "variable": "\\pi", "positive": "\\frac{\\gamma \\pi^{2}}{2}", "negatives": ["\\frac{\\gamma^{2} \\pi}{2}", "\\gamma \\pi \\log{(\\gamma)}", "\\pi e^{\\gamma^{\\gamma}}", "\\frac{\\pi^{2} \\log{(\\gamma)}}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Symbol('\\\\pi', commutative=True))", "Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "Mul(Symbol('\\\\pi', commutative=True), exp(Pow(Symbol('\\\\gamma', commutative=True), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), log(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\chi + \\psi", "variable": "\\chi", "positive": "\\frac{\\chi (\\chi + 2 \\psi)}{2}", "negatives": ["\\frac{\\psi (2 \\chi + \\psi)}{2}", "\\frac{\\chi^{2} \\sin{(\\psi)}}{2}", "- \\chi \\psi + e^{\\chi}", "\\psi e^{\\frac{\\chi}{\\psi}}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), sin(Symbol('\\\\psi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True)), exp(Symbol('\\\\chi', commutative=True)))", "Mul(Symbol('\\\\psi', commutative=True), exp(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))))"]}, {"premise_expression": "\\omega \\cos{(\\pi)}", "variable": "\\omega", "positive": "\\frac{\\omega^{2} \\cos{(\\pi)}}{2}", "negatives": ["\\frac{\\omega^{2} \\log{(\\pi)}}{2}", "\\frac{\\omega (- \\omega + 2 \\pi)}{2}", "- \\pi \\cos{(\\omega)}", "\\omega \\sin{(\\pi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\omega', commutative=True), cos(Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), cos(Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), log(Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Integer(-1), Symbol('\\\\pi', commutative=True), cos(Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), sin(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\omega e^{\\xi}", "variable": "\\xi", "positive": "\\omega e^{\\xi}", "negatives": ["\\frac{\\omega^{2} e^{\\xi}}{2}", "\\xi e^{\\omega^{\\omega}}", "\\omega \\xi + \\sin{(\\xi)}", "\\omega \\xi - \\cos{(\\xi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\omega', commutative=True), exp(Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\omega', commutative=True), exp(Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), exp(Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\xi', commutative=True), exp(Pow(Symbol('\\\\omega', commutative=True), Symbol('\\\\omega', commutative=True))))", "Add(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True)), sin(Symbol('\\\\xi', commutative=True)))", "Add(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\omega + \\log{(\\beta)}", "variable": "\\beta", "positive": "\\beta (\\omega + \\log{(\\beta)} - 1)", "negatives": ["\\frac{\\omega (\\omega + 2 \\log{(\\beta)})}{2}", "\\frac{\\beta^{2} \\log{(\\omega)}}{2}", "e^{\\omega} \\log{(\\beta)}", "\\frac{\\beta (- \\beta + 2 \\omega)}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\beta', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), log(Symbol('\\\\beta', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), log(Symbol('\\\\omega', commutative=True)))", "Mul(exp(Symbol('\\\\omega', commutative=True)), log(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))"]}, {"premise_expression": "\\alpha \\xi", "variable": "\\xi", "positive": "\\frac{\\alpha \\xi^{2}}{2}", "negatives": ["\\frac{\\alpha^{2} \\xi}{2}", "- \\frac{\\cos{(\\xi)}}{\\alpha}", "\\frac{\\xi^{2} e^{\\alpha}}{2}", "e^{\\alpha + \\xi}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))", "Mul(Integer(-1), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), cos(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), exp(Symbol('\\\\alpha', commutative=True)))", "exp(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\delta e^{\\beta}", "variable": "\\beta", "positive": "\\delta e^{\\beta}", "negatives": ["\\frac{\\delta^{2} e^{\\beta}}{2}", "- \\frac{\\cos{(\\beta)}}{\\delta}", "- \\beta \\delta + \\sin{(\\beta)}", "\\frac{\\beta^{2} \\log{(\\delta)}}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\delta', commutative=True), exp(Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\delta', commutative=True), exp(Symbol('\\\\beta', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), exp(Symbol('\\\\beta', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), cos(Symbol('\\\\beta', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True)), sin(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), log(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\pi - \\xi", "variable": "\\xi", "positive": "\\frac{\\xi (2 \\pi - \\xi)}{2}", "negatives": ["\\frac{\\pi (\\pi - 2 \\xi)}{2}", "\\frac{\\xi^{2} \\log{(\\pi)}}{2}", "- \\cos{(\\pi + \\xi)}", "\\pi \\sin{(\\xi)}"], "srepr_premise_expression": "Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), log(Symbol('\\\\pi', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True))))", "Mul(Symbol('\\\\pi', commutative=True), sin(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\log{(\\gamma + \\xi)}", "variable": "\\gamma", "positive": "\\gamma \\log{(\\gamma + \\xi)} - \\gamma + \\xi \\log{(\\gamma + \\xi)}", "negatives": ["\\gamma \\log{(\\gamma - \\xi)} - \\gamma - \\xi \\log{(\\gamma - \\xi)}", "\\gamma \\log{(\\gamma + \\xi)} + \\xi \\log{(\\gamma + \\xi)} - \\xi", "\\gamma e^{\\frac{\\xi}{\\gamma}} - \\xi \\operatorname{Ei}{(\\frac{\\xi}{\\gamma})}", "\\gamma (- \\xi + \\log{(\\gamma)} - 1)"], "srepr_premise_expression": "log(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\gamma', commutative=True), log(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Symbol('\\\\xi', commutative=True), log(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\gamma', commutative=True), log(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True), log(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))))", "Add(Mul(Symbol('\\\\gamma', commutative=True), log(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)))), Mul(Symbol('\\\\xi', commutative=True), log(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "Add(Mul(Symbol('\\\\gamma', commutative=True), exp(Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\xi', commutative=True), Ei(Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True)))))", "Mul(Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), log(Symbol('\\\\gamma', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\xi + e^{\\gamma}", "variable": "\\gamma", "positive": "\\gamma \\xi + e^{\\gamma}", "negatives": ["\\frac{\\xi (\\xi + 2 e^{\\gamma})}{2}", "\\gamma \\cos{(\\xi^{\\xi})}", "e^{\\xi} \\log{(\\gamma)}", "\\sin{(\\gamma - \\xi)}"], "srepr_premise_expression": "Add(Symbol('\\\\xi', commutative=True), exp(Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)), exp(Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\xi', commutative=True), Mul(Integer(2), exp(Symbol('\\\\gamma', commutative=True)))))", "Mul(Symbol('\\\\gamma', commutative=True), cos(Pow(Symbol('\\\\xi', commutative=True), Symbol('\\\\xi', commutative=True))))", "Mul(exp(Symbol('\\\\xi', commutative=True)), log(Symbol('\\\\gamma', commutative=True)))", "sin(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\frac{\\cos{(\\alpha)}}{\\beta}", "variable": "\\alpha", "positive": "\\frac{\\sin{(\\alpha)}}{\\beta}", "negatives": ["e^{\\alpha + \\beta}", "\\log{(\\alpha)} \\log{(\\beta)}", "\\log{(\\beta)} \\cos{(\\alpha)}", "\\frac{\\alpha (\\log{(\\alpha)} - 1)}{\\beta}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), cos(Symbol('\\\\alpha', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), sin(Symbol('\\\\alpha', commutative=True)))", "srepr_negatives": ["exp(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True)))", "Mul(log(Symbol('\\\\alpha', commutative=True)), log(Symbol('\\\\beta', commutative=True)))", "Mul(log(Symbol('\\\\beta', commutative=True)), cos(Symbol('\\\\alpha', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Add(log(Symbol('\\\\alpha', commutative=True)), Integer(-1)))"]}, {"premise_expression": "- \\sin{(\\delta - \\psi)}", "variable": "\\psi", "positive": "- \\cos{(\\delta - \\psi)}", "negatives": ["\\cos{(\\delta - \\psi)}", "- e^{\\delta - \\psi}", "\\psi (\\log{(\\delta \\psi)} - 1)", "\\frac{\\psi (\\log{(\\psi)} - 1)}{\\delta}"], "srepr_premise_expression": "Mul(Integer(-1), sin(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))", "srepr_negatives": ["cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(Integer(-1), exp(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))", "Mul(Symbol('\\\\psi', commutative=True), Add(log(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\psi', commutative=True))), Integer(-1)))", "Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True), Add(log(Symbol('\\\\psi', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\frac{e^{\\sigma}}{\\omega}", "variable": "\\omega", "positive": "e^{\\sigma} \\log{(\\omega)}", "negatives": ["- \\cos{(\\omega - \\sigma)}", "\\frac{\\omega (\\omega - 2 \\sigma)}{2}", "\\frac{\\omega (\\omega + 2 \\sigma)}{2}", "\\frac{\\omega^{2}}{2 \\sigma}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), exp(Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(exp(Symbol('\\\\sigma', commutative=True)), log(Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))"]}, {"premise_expression": "\\log{(\\pi + \\psi)}", "variable": "\\psi", "positive": "\\pi \\log{(\\pi + \\psi)} + \\psi \\log{(\\pi + \\psi)} - \\psi", "negatives": ["\\pi \\log{(\\pi + \\psi)} - \\pi + \\psi \\log{(\\pi + \\psi)}", "\\psi (\\log{(\\pi \\psi)} - 1)", "\\frac{\\psi (\\psi + 2 \\sin{(\\pi)})}{2}", "\\pi \\psi + e^{\\psi}"], "srepr_premise_expression": "log(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\pi', commutative=True), log(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)))), Mul(Symbol('\\\\psi', commutative=True), log(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\pi', commutative=True), log(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Symbol('\\\\psi', commutative=True), log(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)))))", "Mul(Symbol('\\\\psi', commutative=True), Add(log(Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(2), sin(Symbol('\\\\pi', commutative=True)))))", "Add(Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)), exp(Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\xi e^{\\sigma}", "variable": "\\sigma", "positive": "\\xi e^{\\sigma}", "negatives": ["\\xi e^{\\frac{\\sigma}{\\xi}}", "\\frac{\\xi^{2} e^{\\sigma}}{2}", "\\frac{\\sigma^{2} \\log{(\\xi)}}{2}", "\\log{(\\sigma)} \\sin{(\\xi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\xi', commutative=True), exp(Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\xi', commutative=True), exp(Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\xi', commutative=True), exp(Mul(Symbol('\\\\sigma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), exp(Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), log(Symbol('\\\\xi', commutative=True)))", "Mul(log(Symbol('\\\\sigma', commutative=True)), sin(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\omega + \\xi", "variable": "\\xi", "positive": "\\frac{\\xi (2 \\omega + \\xi)}{2}", "negatives": ["\\frac{\\omega (\\omega + 2 \\xi)}{2}", "- \\cos{(\\omega + \\xi)}", "\\sin{(\\omega + \\xi)}", "e^{- \\omega + \\xi}"], "srepr_premise_expression": "Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True))))", "sin(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True)))", "exp(Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\cos{(\\alpha + \\chi)}", "variable": "\\chi", "positive": "\\sin{(\\alpha + \\chi)}", "negatives": ["e^{\\alpha + \\chi}", "\\frac{\\chi (2 \\alpha - \\chi)}{2}", "\\frac{\\chi (- 2 \\alpha + \\chi)}{2}", "- \\alpha \\operatorname{Ei}{(\\frac{\\alpha}{\\chi})} + \\chi e^{\\frac{\\alpha}{\\chi}}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "sin(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["exp(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\chi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\chi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Ei(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(-1))))), Mul(Symbol('\\\\chi', commutative=True), exp(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(-1))))))"]}, {"premise_expression": "e^{\\sigma^{\\omega}}", "variable": "\\sigma", "positive": "\\frac{e^{- \\frac{i \\pi}{\\omega}} \\gamma(\\frac{1}{\\omega}, \\sigma^{\\omega} e^{i \\pi})}{\\omega}", "negatives": ["- \\omega \\log{(- \\omega + \\sigma)} + \\sigma \\log{(- \\omega + \\sigma)} - \\sigma", "\\sigma (\\log{(\\omega \\sigma)} - 1)", "\\log{(\\sigma)} \\sin{(\\omega)}", "\\frac{\\sigma^{2} \\cos{(\\omega)}}{2}"], "srepr_premise_expression": "exp(Pow(Symbol('\\\\sigma', commutative=True), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), exp(Mul(Integer(-1), I, pi, Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))), lowergamma(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Mul(Pow(Symbol('\\\\sigma', commutative=True), Symbol('\\\\omega', commutative=True)), exp_polar(Mul(I, pi)))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Symbol('\\\\sigma', commutative=True)))), Mul(Symbol('\\\\sigma', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Symbol('\\\\sigma', commutative=True)))), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))", "Mul(Symbol('\\\\sigma', commutative=True), Add(log(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True))), Integer(-1)))", "Mul(log(Symbol('\\\\sigma', commutative=True)), sin(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), cos(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\beta \\sigma - \\xi", "variable": "\\sigma", "positive": "\\frac{\\sigma (\\beta \\sigma - 2 \\xi)}{2}", "negatives": ["\\frac{\\beta (\\beta \\sigma - 2 \\xi)}{2}", "\\frac{\\xi (2 \\beta \\sigma - \\xi)}{2}", "\\frac{\\beta \\sigma (\\sigma + 2 \\xi)}{2}", "\\frac{\\sigma \\xi (2 \\beta - \\sigma)}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\delta + e^{\\chi}", "variable": "\\chi", "positive": "\\chi \\delta + e^{\\chi}", "negatives": ["\\frac{\\delta (\\delta + 2 e^{\\chi})}{2}", "\\sin{(\\chi - \\delta)}", "\\log{(\\chi)} \\sin{(\\delta)}", "\\frac{\\chi (\\log{(\\chi)} - 1)}{\\delta}"], "srepr_premise_expression": "Add(Symbol('\\\\delta', commutative=True), exp(Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True)), exp(Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), exp(Symbol('\\\\chi', commutative=True)))))", "sin(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))", "Mul(log(Symbol('\\\\chi', commutative=True)), sin(Symbol('\\\\delta', commutative=True)))", "Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Add(log(Symbol('\\\\chi', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\psi + \\sigma", "variable": "\\psi", "positive": "\\frac{\\psi (\\psi + 2 \\sigma)}{2}", "negatives": ["\\frac{\\sigma (2 \\psi + \\sigma)}{2}", "- \\cos{(\\psi + \\sigma)}", "e^{\\psi - \\sigma}", "\\frac{\\psi^{2}}{2 \\sigma}"], "srepr_premise_expression": "Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\psi', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True))))", "exp(Add(Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))"]}, {"premise_expression": "e^{- \\pi + \\psi}", "variable": "\\psi", "positive": "e^{- \\pi + \\psi}", "negatives": ["- e^{- \\pi + \\psi}", "- \\sin{(\\pi - \\psi)}", "e^{\\pi} \\log{(\\psi)}", "\\frac{\\psi^{2}}{2 \\pi}"], "srepr_premise_expression": "exp(Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "exp(Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Symbol('\\\\psi', commutative=True))))", "Mul(Integer(-1), sin(Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))", "Mul(exp(Symbol('\\\\pi', commutative=True)), log(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))"]}, {"premise_expression": "- \\alpha + \\psi", "variable": "\\psi", "positive": "\\frac{\\psi (- 2 \\alpha + \\psi)}{2}", "negatives": ["\\frac{\\psi (2 \\alpha - \\psi)}{2}", "\\frac{\\alpha (- \\alpha + 2 \\psi)}{2}", "e^{- \\alpha + \\psi}", "e^{\\alpha + \\psi}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "exp(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\psi', commutative=True)))", "exp(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\frac{\\chi}{\\sigma}", "variable": "\\sigma", "positive": "\\chi \\log{(\\sigma)}", "negatives": ["\\frac{\\chi^{2}}{2 \\sigma}", "\\frac{\\sigma^{2}}{2 \\chi}", "- \\chi \\sigma + e^{\\sigma}", "\\sigma (\\log{(\\frac{\\sigma}{\\chi})} - 1)"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\sigma', commutative=True)), exp(Symbol('\\\\sigma', commutative=True)))", "Mul(Symbol('\\\\sigma', commutative=True), Add(log(Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\frac{\\delta \\xi}{\\sigma}", "variable": "\\delta", "positive": "\\frac{\\delta^{2} \\xi}{2 \\sigma}", "negatives": ["\\frac{\\delta \\xi^{2}}{2 \\sigma}", "\\delta \\xi \\log{(\\sigma)}", "\\frac{\\delta^{2} \\sigma \\xi}{2}", "\\sigma \\xi \\log{(\\delta)}"], "srepr_premise_expression": "Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True), log(Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True))", "Mul(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True), log(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\psi + \\cos{(\\omega)}", "variable": "\\psi", "positive": "\\frac{\\psi (\\psi + 2 \\cos{(\\omega)})}{2}", "negatives": ["\\omega \\psi + \\sin{(\\omega)}", "\\psi (- \\omega + \\log{(\\psi^{\\omega})})", "\\log{(\\psi)} \\sin{(\\omega)}", "\\psi (\\log{(\\frac{\\omega}{\\psi})} + 1)"], "srepr_premise_expression": "Add(Symbol('\\\\psi', commutative=True), cos(Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(2), cos(Symbol('\\\\omega', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True)), sin(Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), log(Pow(Symbol('\\\\psi', commutative=True), Symbol('\\\\omega', commutative=True)))))", "Mul(log(Symbol('\\\\psi', commutative=True)), sin(Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\psi', commutative=True), Add(log(Mul(Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))), Integer(1)))"]}, {"premise_expression": "- \\alpha + \\pi", "variable": "\\alpha", "positive": "\\frac{\\alpha (- \\alpha + 2 \\pi)}{2}", "negatives": ["\\frac{\\alpha (\\alpha - 2 \\pi)}{2}", "\\frac{\\pi (- 2 \\alpha + \\pi)}{2}", "\\frac{\\alpha^{2} \\log{(\\pi)}}{2}", "\\frac{\\alpha^{2} \\cos{(\\pi)}}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), log(Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), cos(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "- \\chi + e^{\\alpha}", "variable": "\\alpha", "positive": "- \\alpha \\chi + e^{\\alpha}", "negatives": ["- \\alpha \\chi + \\sin{(\\alpha)}", "\\alpha \\chi + \\sin{(\\alpha)}", "\\frac{\\chi (- \\chi + 2 e^{\\alpha})}{2}", "\\frac{\\alpha (\\alpha + 2 e^{\\chi})}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), exp(Symbol('\\\\alpha', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)), exp(Symbol('\\\\alpha', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)), sin(Symbol('\\\\alpha', commutative=True)))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)), sin(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\alpha', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), exp(Symbol('\\\\chi', commutative=True)))))"]}, {"premise_expression": "\\cos{(\\delta + \\omega)}", "variable": "\\delta", "positive": "\\sin{(\\delta + \\omega)}", "negatives": ["\\cos{(\\delta - \\omega)}", "\\frac{\\delta (\\delta + 2 \\omega)}{2}", "\\frac{\\delta (\\delta + 2 \\sin{(\\omega)})}{2}", "\\frac{\\delta (\\delta + 2 \\log{(\\omega)})}{2}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "sin(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), sin(Symbol('\\\\omega', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), log(Symbol('\\\\omega', commutative=True)))))"]}, {"premise_expression": "\\gamma + \\omega", "variable": "\\omega", "positive": "\\frac{\\omega (2 \\gamma + \\omega)}{2}", "negatives": ["\\frac{\\gamma (\\gamma + 2 \\omega)}{2}", "\\frac{\\omega (\\omega + 2 \\sin{(\\gamma)})}{2}", "\\frac{\\omega (- \\omega + 2 \\sin{(\\gamma)})}{2}", "\\frac{\\omega^{2} \\cos{(\\gamma)}}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), sin(Symbol('\\\\gamma', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\gamma', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), cos(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\gamma + \\xi", "variable": "\\xi", "positive": "\\frac{\\xi (2 \\gamma + \\xi)}{2}", "negatives": ["\\frac{\\gamma (\\gamma + 2 \\xi)}{2}", "\\frac{\\xi (- \\xi + 2 \\sin{(\\gamma)})}{2}", "\\sin{(\\gamma + \\xi)}", "e^{\\gamma + \\xi}"], "srepr_premise_expression": "Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\gamma', commutative=True)))))", "sin(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)))", "exp(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\gamma - \\xi", "variable": "\\xi", "positive": "\\frac{\\xi (2 \\gamma - \\xi)}{2}", "negatives": ["\\frac{\\gamma (\\gamma - 2 \\xi)}{2}", "\\frac{\\xi^{2} e^{\\gamma}}{2}", "- \\gamma \\xi + e^{\\xi}", "- \\gamma \\xi - \\cos{(\\xi)}"], "srepr_premise_expression": "Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), exp(Symbol('\\\\gamma', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)), exp(Symbol('\\\\xi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\log{(\\frac{\\gamma}{\\delta})}", "variable": "\\gamma", "positive": "\\gamma (\\log{(\\frac{\\gamma}{\\delta})} - 1)", "negatives": ["\\delta (\\log{(\\frac{\\gamma}{\\delta})} + 1)", "\\gamma (\\log{(\\delta \\gamma)} - 1)", "\\delta \\gamma (\\log{(\\gamma)} - 1)", "\\delta \\log{(\\gamma)}"], "srepr_premise_expression": "log(Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\gamma', commutative=True), Add(log(Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\delta', commutative=True), Add(log(Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True))), Integer(1)))", "Mul(Symbol('\\\\gamma', commutative=True), Add(log(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\gamma', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\gamma', commutative=True), Add(log(Symbol('\\\\gamma', commutative=True)), Integer(-1)))", "Mul(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\frac{\\omega - \\sigma}{\\beta}", "variable": "\\sigma", "positive": "\\frac{\\sigma (2 \\omega - \\sigma)}{2 \\beta}", "negatives": ["\\frac{\\sigma (2 \\omega + \\sigma)}{2 \\beta}", "\\frac{\\sigma (2 \\beta + \\sigma)}{2 \\omega}", "\\frac{\\omega (\\omega - 2 \\sigma)}{2 \\beta}", "\\frac{\\sigma (2 \\beta - 2 \\omega - \\sigma)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\omega + e^{\\xi}", "variable": "\\omega", "positive": "\\frac{\\omega (\\omega + 2 e^{\\xi})}{2}", "negatives": ["\\frac{\\omega (\\omega - 2 \\xi)}{2}", "\\omega \\xi + e^{\\xi}", "\\sin{(\\omega + \\xi)}", "\\sin{(\\omega - \\xi)}"], "srepr_premise_expression": "Add(Symbol('\\\\omega', commutative=True), exp(Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), exp(Symbol('\\\\xi', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "Add(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True)), exp(Symbol('\\\\xi', commutative=True)))", "sin(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True)))", "sin(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\cos{(\\frac{\\pi}{\\beta})}", "variable": "\\beta", "positive": "\\beta \\cos{(\\frac{\\pi}{\\beta})} + \\pi \\operatorname{Si}{(\\frac{\\pi}{\\beta})}", "negatives": ["\\beta e^{\\frac{\\pi}{\\beta}} - \\pi \\operatorname{Ei}{(\\frac{\\pi}{\\beta})}", "\\frac{\\beta (\\log{(\\beta)} - 1)}{\\pi}", "\\sin{(\\beta + \\pi)}", "- e^{- \\beta + \\pi}"], "srepr_premise_expression": "cos(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\beta', commutative=True), cos(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True)))), Mul(Symbol('\\\\pi', commutative=True), Si(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\beta', commutative=True), exp(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\pi', commutative=True), Ei(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True)))))", "Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Add(log(Symbol('\\\\beta', commutative=True)), Integer(-1)))", "sin(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\pi', commutative=True)))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\omega \\sigma", "variable": "\\omega", "positive": "\\frac{\\omega^{2} \\sigma}{2}", "negatives": ["\\frac{\\omega \\sigma^{2}}{2}", "\\frac{\\omega \\sigma (\\omega + 2)}{2}", "\\omega \\sigma - \\cos{(\\omega)}", "e^{\\omega - \\sigma}"], "srepr_premise_expression": "Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Symbol('\\\\sigma', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\omega', commutative=True), Integer(2)))", "Add(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\omega', commutative=True))))", "exp(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\beta^{\\delta} + \\sigma", "variable": "\\sigma", "positive": "\\frac{\\sigma (2 \\beta^{\\delta} + \\sigma)}{2}", "negatives": ["\\frac{\\sigma^{2} (\\beta + \\delta)}{2}", "\\frac{\\sigma (2 \\beta + 2 \\delta + \\sigma)}{2}", "\\frac{\\sigma (2 \\beta + 2 \\delta - \\sigma)}{2}", "\\frac{\\sigma (- 2 \\beta + 2 \\delta - \\sigma)}{2}"], "srepr_premise_expression": "Add(Pow(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True)), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Pow(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True))), Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "e^{\\beta - \\omega}", "variable": "\\beta", "positive": "e^{\\beta - \\omega}", "negatives": ["- e^{\\beta - \\omega}", "\\frac{\\beta (\\beta - 2 \\omega)}{2}", "\\frac{\\beta (\\beta + 2 \\omega)}{2}", "- \\omega \\cos{(\\beta)}"], "srepr_premise_expression": "exp(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "exp(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Integer(-1), Symbol('\\\\omega', commutative=True), cos(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "- \\alpha + \\chi - \\sigma", "variable": "\\sigma", "positive": "\\frac{\\sigma (- 2 \\alpha + 2 \\chi - \\sigma)}{2}", "negatives": ["\\frac{\\chi (- 2 \\alpha + \\chi - 2 \\sigma)}{2}", "\\frac{\\alpha (- \\alpha + 2 \\chi - 2 \\sigma)}{2}", "\\frac{\\sigma (4 \\chi - \\sigma)}{2}", "\\frac{\\alpha \\sigma (- 2 \\chi + \\sigma)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(4), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\omega \\log{(\\pi)}", "variable": "\\pi", "positive": "\\omega \\pi (\\log{(\\pi)} - 1)", "negatives": ["\\pi (\\log{(\\frac{\\omega}{\\pi})} + 1)", "\\frac{\\omega^{2} \\log{(\\pi)}}{2}", "e^{\\omega} \\log{(\\pi)}", "e^{\\omega + \\pi}"], "srepr_premise_expression": "Mul(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True), Add(log(Symbol('\\\\pi', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\pi', commutative=True), Add(log(Mul(Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), log(Symbol('\\\\pi', commutative=True)))", "Mul(exp(Symbol('\\\\omega', commutative=True)), log(Symbol('\\\\pi', commutative=True)))", "exp(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "- \\gamma - \\omega + \\xi", "variable": "\\xi", "positive": "\\xi (- \\gamma - \\omega + \\frac{\\xi}{2})", "negatives": ["\\frac{\\xi (2 \\gamma - 2 \\omega + \\xi)}{2}", "\\frac{\\gamma (- \\gamma - 2 \\omega + 2 \\xi)}{2}", "\\frac{\\omega (- 2 \\gamma - \\omega + 2 \\xi)}{2}", "\\frac{\\xi^{2}}{2} + \\frac{\\omega \\xi}{\\gamma}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Add(Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2))), Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\sin{(\\omega + \\pi)}", "variable": "\\omega", "positive": "- \\cos{(\\omega + \\pi)}", "negatives": ["- \\pi \\cos{(\\omega)}", "\\pi \\log{(\\omega)}", "\\pi e^{\\frac{\\omega}{\\pi}}", "\\omega (\\log{(\\frac{\\omega}{\\pi})} - 1)"], "srepr_premise_expression": "sin(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), Symbol('\\\\pi', commutative=True), cos(Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\pi', commutative=True), exp(Mul(Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))))", "Mul(Symbol('\\\\omega', commutative=True), Add(log(Mul(Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))), Integer(-1)))"]}, {"premise_expression": "- \\alpha + \\sin{(\\xi)}", "variable": "\\xi", "positive": "- \\alpha \\xi - \\cos{(\\xi)}", "negatives": ["\\alpha \\log{(\\xi)}", "\\frac{\\xi^{2} \\log{(\\alpha)}}{2}", "\\xi (\\alpha + \\log{(\\xi)} - 1)", "\\sin{(\\alpha + \\xi)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), sin(Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), log(Symbol('\\\\alpha', commutative=True)))", "Mul(Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\xi', commutative=True)), Integer(-1)))", "sin(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\gamma e^{\\sigma}", "variable": "\\sigma", "positive": "\\gamma e^{\\sigma}", "negatives": ["\\gamma e^{\\frac{\\sigma}{\\gamma}}", "\\frac{\\gamma^{2} e^{\\sigma}}{2}", "- \\frac{\\gamma}{\\sigma}", "\\frac{\\sigma^{2} e^{\\gamma}}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\gamma', commutative=True), exp(Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\gamma', commutative=True), exp(Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\gamma', commutative=True), exp(Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), exp(Symbol('\\\\sigma', commutative=True)))", "Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), exp(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "- \\omega + \\cos{(\\sigma)}", "variable": "\\omega", "positive": "\\frac{\\omega (- \\omega + 2 \\cos{(\\sigma)})}{2}", "negatives": ["\\frac{\\omega^{2} \\sin{(\\sigma)}}{2}", "- \\omega \\sigma + \\sin{(\\sigma)}", "\\frac{\\omega^{2}}{2 \\sigma}", "- \\omega \\sigma + \\sin{(\\omega)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), cos(Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\sigma', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), sin(Symbol('\\\\sigma', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True)), sin(Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True)), sin(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\omega \\cos{(\\beta)}", "variable": "\\beta", "positive": "\\omega \\sin{(\\beta)}", "negatives": ["\\frac{\\omega^{2} \\cos{(\\beta)}}{2}", "e^{\\omega} \\log{(\\beta)}", "\\frac{\\beta^{2} \\log{(\\omega)}}{2}", "\\beta (- \\omega + \\log{(\\beta)} - 1)"], "srepr_premise_expression": "Mul(Symbol('\\\\omega', commutative=True), cos(Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\omega', commutative=True), sin(Symbol('\\\\beta', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), cos(Symbol('\\\\beta', commutative=True)))", "Mul(exp(Symbol('\\\\omega', commutative=True)), log(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), log(Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), log(Symbol('\\\\beta', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\cos^{\\sigma}{(\\chi)}", "variable": "\\chi", "positive": "\\int \\cos^{\\sigma}{(\\chi)} d\\chi", "negatives": ["\\cos{(\\chi - \\sigma)}", "- \\cos{(\\chi + \\sigma)}", "\\chi \\sigma - \\cos{(\\chi)}", "- \\chi \\sigma - \\cos{(\\chi)}"], "srepr_premise_expression": "Pow(cos(Symbol('\\\\chi', commutative=True)), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Integral(Pow(cos(Symbol('\\\\chi', commutative=True)), Symbol('\\\\sigma', commutative=True)), Tuple(Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["cos(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\sigma', commutative=True))))", "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\chi', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\chi', commutative=True))))"]}, {"premise_expression": "\\pi \\sin{(\\psi)}", "variable": "\\pi", "positive": "\\frac{\\pi^{2} \\sin{(\\psi)}}{2}", "negatives": ["\\frac{\\pi (\\pi + 2 \\sin{(\\psi)})}{2}", "\\frac{\\pi (\\pi - 2 \\psi)}{2}", "- \\pi \\cos{(\\psi)}", "- \\frac{\\cos{(\\pi)}}{\\psi}"], "srepr_premise_expression": "Mul(Symbol('\\\\pi', commutative=True), sin(Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), sin(Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), sin(Symbol('\\\\psi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Integer(-1), Symbol('\\\\pi', commutative=True), cos(Symbol('\\\\psi', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), cos(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "e^{\\omega - \\psi}", "variable": "\\psi", "positive": "- e^{\\omega - \\psi}", "negatives": ["e^{\\omega - \\psi}", "\\frac{\\psi (2 \\omega - \\psi)}{2}", "\\frac{\\psi (2 \\omega + \\psi)}{2}", "\\psi (\\log{(\\frac{\\omega}{\\psi})} + 1)"], "srepr_premise_expression": "exp(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Integer(-1), exp(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))", "srepr_negatives": ["exp(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Symbol('\\\\psi', commutative=True), Add(log(Mul(Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))), Integer(1)))"]}, {"premise_expression": "\\xi + \\sin{(\\alpha)}", "variable": "\\alpha", "positive": "\\alpha \\xi - \\cos{(\\alpha)}", "negatives": ["- \\alpha \\xi + \\sin{(\\alpha)}", "\\frac{\\alpha^{2} \\cos{(\\xi)}}{2}", "\\cos{(\\alpha - \\xi)}", "\\frac{\\xi (\\xi + 2 \\sin{(\\alpha)})}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\xi', commutative=True), sin(Symbol('\\\\alpha', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\alpha', commutative=True))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True)), sin(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), cos(Symbol('\\\\xi', commutative=True)))", "cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\xi', commutative=True), Mul(Integer(2), sin(Symbol('\\\\alpha', commutative=True)))))"]}, {"premise_expression": "\\log{(\\omega + \\sigma)}", "variable": "\\sigma", "positive": "\\omega \\log{(\\omega + \\sigma)} + \\sigma \\log{(\\omega + \\sigma)} - \\sigma", "negatives": ["\\omega \\log{(\\omega + \\sigma)} - \\omega + \\sigma \\log{(\\omega + \\sigma)}", "\\sigma (- \\omega + \\log{(\\sigma^{\\omega})})", "\\frac{\\sigma (\\sigma + 2 \\cos{(\\omega)})}{2}", "- \\cos{(\\omega + \\sigma)}"], "srepr_premise_expression": "log(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\omega', commutative=True), log(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True)))), Mul(Symbol('\\\\sigma', commutative=True), log(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True)))), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\omega', commutative=True), log(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True)))), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Symbol('\\\\sigma', commutative=True), log(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True)))))", "Mul(Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), log(Pow(Symbol('\\\\sigma', commutative=True), Symbol('\\\\omega', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(2), cos(Symbol('\\\\omega', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "e^{\\omega - \\sigma}", "variable": "\\omega", "positive": "e^{\\omega - \\sigma}", "negatives": ["- e^{\\omega - \\sigma}", "- \\cos{(\\omega + \\sigma)}", "\\sigma \\log{(\\omega)}", "\\frac{\\omega (\\log{(\\omega)} - 1)}{\\sigma}"], "srepr_premise_expression": "exp(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "exp(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True))))", "Mul(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Add(log(Symbol('\\\\omega', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\alpha^{\\sigma} - \\delta", "variable": "\\delta", "positive": "\\frac{\\delta (2 \\alpha^{\\sigma} - \\delta)}{2}", "negatives": ["\\delta (\\alpha + \\sigma^{\\sigma})", "\\frac{\\delta (\\alpha \\delta - 2 \\sigma)}{2}", "\\frac{\\delta (2 \\alpha + \\delta - 2 \\sigma)}{2}", "\\frac{\\delta (- 2 \\alpha + \\delta - 2 \\sigma)}{2}"], "srepr_premise_expression": "Add(Pow(Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(2), Pow(Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True))), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))", "srepr_negatives": ["Mul(Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "e^{\\frac{\\omega}{\\xi}}", "variable": "\\omega", "positive": "\\xi e^{\\frac{\\omega}{\\xi}}", "negatives": ["\\xi \\sin{(\\omega)}", "\\frac{\\omega^{2}}{2 \\xi}", "\\sin{(\\omega - \\xi)}", "- \\cos{(\\omega + \\xi)}"], "srepr_premise_expression": "exp(Mul(Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\xi', commutative=True), exp(Mul(Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))))", "srepr_negatives": ["Mul(Symbol('\\\\xi', commutative=True), sin(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "sin(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\frac{e^{\\alpha}}{\\gamma}", "variable": "\\gamma", "positive": "e^{\\alpha} \\log{(\\gamma)}", "negatives": ["- \\sin{(\\alpha - \\gamma)}", "\\frac{\\alpha \\gamma^{2}}{2}", "- \\cos{(\\alpha + \\gamma)}", "\\frac{\\gamma (- 2 \\alpha + \\gamma)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), exp(Symbol('\\\\alpha', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(exp(Symbol('\\\\alpha', commutative=True)), log(Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\pi - \\xi", "variable": "\\xi", "positive": "\\frac{\\xi (2 \\pi - \\xi)}{2}", "negatives": ["\\frac{\\pi (\\pi - 2 \\xi)}{2}", "\\frac{\\xi (\\xi + 2 \\cos{(\\pi)})}{2}", "\\frac{\\xi^{2} \\log{(\\pi)}}{2}", "\\cos{(\\pi - \\xi)}"], "srepr_premise_expression": "Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\xi', commutative=True), Mul(Integer(2), cos(Symbol('\\\\pi', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), log(Symbol('\\\\pi', commutative=True)))", "cos(Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "e^{- \\psi + \\xi}", "variable": "\\psi", "positive": "- e^{- \\psi + \\xi}", "negatives": ["e^{- \\psi + \\xi}", "- \\cos{(\\psi - \\xi)}", "\\xi \\log{(\\psi)}", "\\log{(\\psi)} \\log{(\\xi)}"], "srepr_premise_expression": "exp(Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["exp(Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))))", "Mul(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\psi', commutative=True)))", "Mul(log(Symbol('\\\\psi', commutative=True)), log(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\beta \\sigma^{\\delta}", "variable": "\\beta", "positive": "\\frac{\\beta^{2} \\sigma^{\\delta}}{2}", "negatives": ["\\frac{\\beta^{2} \\delta \\sigma}{2}", "\\frac{\\beta^{2} \\sigma}{2 \\delta}", "\\frac{\\beta^{2} (\\delta - \\sigma)}{2}", "\\frac{\\delta \\log{(\\beta)}}{\\sigma}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), log(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "\\sin^{\\delta}{(\\omega)}", "variable": "\\omega", "positive": "\\int \\sin^{\\delta}{(\\omega)} d\\omega", "negatives": ["\\int \\cos^{\\delta}{(\\omega)} d\\omega", "\\log{(\\omega)} \\sin{(\\delta)}", "\\delta \\log{(\\omega)}", "\\frac{\\omega (\\omega + 2 e^{\\delta})}{2}"], "srepr_premise_expression": "Pow(sin(Symbol('\\\\omega', commutative=True)), Symbol('\\\\delta', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Integral(Pow(sin(Symbol('\\\\omega', commutative=True)), Symbol('\\\\delta', commutative=True)), Tuple(Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Integral(Pow(cos(Symbol('\\\\omega', commutative=True)), Symbol('\\\\delta', commutative=True)), Tuple(Symbol('\\\\omega', commutative=True)))", "Mul(log(Symbol('\\\\omega', commutative=True)), sin(Symbol('\\\\delta', commutative=True)))", "Mul(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), exp(Symbol('\\\\delta', commutative=True)))))"]}, {"premise_expression": "- \\chi + \\gamma", "variable": "\\chi", "positive": "\\frac{\\chi (- \\chi + 2 \\gamma)}{2}", "negatives": ["\\frac{\\gamma (- 2 \\chi + \\gamma)}{2}", "- e^{- \\chi + \\gamma}", "- \\cos{(\\chi - \\gamma)}", "\\frac{\\chi^{2} \\gamma}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\gamma', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\gamma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\gamma', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\gamma', commutative=True))"]}, {"premise_expression": "\\pi - \\xi", "variable": "\\xi", "positive": "\\frac{\\xi (2 \\pi - \\xi)}{2}", "negatives": ["\\frac{\\pi (\\pi - 2 \\xi)}{2}", "\\frac{\\xi (- \\xi + 2 \\cos{(\\pi)})}{2}", "\\frac{\\xi^{2} \\log{(\\pi)}}{2}", "e^{- \\pi + \\xi}"], "srepr_premise_expression": "Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\pi', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), log(Symbol('\\\\pi', commutative=True)))", "exp(Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "- \\psi + \\cos{(\\xi)}", "variable": "\\xi", "positive": "- \\psi \\xi + \\sin{(\\xi)}", "negatives": ["- \\psi \\xi - \\cos{(\\xi)}", "\\psi e^{\\xi}", "\\psi \\log{(\\xi)}", "\\psi e^{\\frac{\\xi}{\\psi}}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), cos(Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True), Symbol('\\\\xi', commutative=True)), sin(Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\xi', commutative=True))))", "Mul(Symbol('\\\\psi', commutative=True), exp(Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\psi', commutative=True), log(Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\psi', commutative=True), exp(Mul(Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\frac{\\alpha \\psi}{\\gamma}", "variable": "\\gamma", "positive": "\\alpha \\psi \\log{(\\gamma)}", "negatives": ["\\log{(\\gamma)}", "\\frac{\\alpha \\psi^{2}}{2 \\gamma}", "\\frac{\\alpha^{2} \\psi}{2 \\gamma}", "\\frac{\\alpha \\gamma^{2} \\psi}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["log(Symbol('\\\\gamma', commutative=True))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))"]}, {"premise_expression": "\\cos{(\\sigma - \\xi)}", "variable": "\\xi", "positive": "- \\sin{(\\sigma - \\xi)}", "negatives": ["\\sin{(\\sigma - \\xi)}", "\\operatorname{Ei}{(\\xi)}", "\\sigma e^{\\frac{\\xi}{\\sigma}}", "0"], "srepr_premise_expression": "cos(Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Integer(-1), sin(Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))))", "srepr_negatives": ["sin(Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Ei(Symbol('\\\\xi', commutative=True))", "Mul(Symbol('\\\\sigma', commutative=True), exp(Mul(Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))))", "Integer(0)"]}, {"premise_expression": "- \\xi + \\frac{\\chi}{\\beta}", "variable": "\\beta", "positive": "- \\beta \\xi + \\chi \\log{(\\beta)}", "negatives": ["\\chi^{\\xi} \\log{(\\beta)}", "- \\chi \\xi + \\frac{\\chi^{2}}{2 \\beta}", "- \\frac{\\xi^{2}}{2} + \\frac{\\chi \\xi}{\\beta}", "\\frac{\\beta^{2}}{2 \\chi \\xi}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\beta', commutative=True))))", "srepr_negatives": ["Mul(Pow(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True)), log(Symbol('\\\\beta', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Pow(Symbol('\\\\chi', commutative=True), Integer(2))))", "Add(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2))), Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))"]}, {"premise_expression": "\\frac{\\chi}{\\omega}", "variable": "\\chi", "positive": "\\frac{\\chi^{2}}{2 \\omega}", "negatives": ["\\chi \\log{(\\omega)}", "\\omega \\log{(\\chi)}", "\\frac{\\chi^{2} (\\omega - 1)}{2}", "\\cos{(\\chi - \\omega)}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Add(Symbol('\\\\omega', commutative=True), Integer(-1)))", "cos(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))"]}, {"premise_expression": "- \\beta - \\chi + \\delta", "variable": "\\delta", "positive": "\\delta (- \\beta - \\chi + \\frac{\\delta}{2})", "negatives": ["\\frac{\\delta (2 \\beta - 2 \\chi + \\delta)}{2}", "\\frac{\\delta (2 \\beta + 2 \\chi - \\delta)}{2}", "\\frac{\\beta (- \\beta - 2 \\chi + 2 \\delta)}{2}", "\\frac{\\chi (- 2 \\beta - \\chi + 2 \\delta)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\delta', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\delta', commutative=True))))"]}, {"premise_expression": "\\frac{\\pi}{\\xi}", "variable": "\\xi", "positive": "\\pi \\log{(\\xi)}", "negatives": ["\\frac{\\pi^{2}}{2 \\xi}", "\\frac{\\xi^{2} \\log{(\\pi)}}{2}", "\\xi (\\log{(\\frac{\\pi}{\\xi})} + 1)", "- e^{\\pi - \\xi}"], "srepr_premise_expression": "Mul(Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), log(Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\xi', commutative=True), Add(log(Mul(Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Integer(-1), exp(Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))))"]}, {"premise_expression": "\\frac{\\chi}{\\psi}", "variable": "\\chi", "positive": "\\frac{\\chi^{2}}{2 \\psi}", "negatives": ["\\chi \\log{(\\psi)}", "\\psi e^{\\frac{\\chi}{\\psi}}", "\\frac{\\chi^{2} \\psi}{2}", "\\frac{\\chi^{2} \\sin{(\\psi)}}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\psi', commutative=True)))", "Mul(Symbol('\\\\psi', commutative=True), exp(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), sin(Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\beta \\gamma + \\psi", "variable": "\\beta", "positive": "\\frac{\\beta (\\beta \\gamma + 2 \\psi)}{2}", "negatives": ["\\frac{\\gamma (\\beta \\gamma + 2 \\psi)}{2}", "\\frac{\\beta (\\beta \\psi + 2 \\gamma)}{2}", "\\frac{\\beta (- \\beta + 2 \\gamma \\psi)}{2}", "\\frac{\\psi (2 \\beta \\gamma + \\psi)}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\chi - \\sigma + \\xi", "variable": "\\xi", "positive": "\\xi (\\chi - \\sigma + \\frac{\\xi}{2})", "negatives": ["\\frac{\\xi (- 2 \\chi - 2 \\sigma + \\xi)}{2}", "\\frac{\\sigma (2 \\chi - \\sigma + 2 \\xi)}{2}", "\\frac{\\chi (\\chi - 2 \\sigma + 2 \\xi)}{2}", "\\frac{\\xi (\\chi \\xi + 2 \\sigma)}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\alpha + \\gamma \\omega", "variable": "\\alpha", "positive": "\\frac{\\alpha (\\alpha + 2 \\gamma \\omega)}{2}", "negatives": ["\\frac{\\alpha (\\alpha \\gamma + 2 \\omega)}{2}", "\\frac{\\gamma (2 \\alpha + \\gamma \\omega)}{2}", "\\frac{\\omega (2 \\alpha + \\gamma \\omega)}{2}", "\\frac{\\alpha \\omega (\\alpha - 2 \\gamma)}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True))))"]}, {"premise_expression": "\\omega + \\frac{\\delta}{\\chi}", "variable": "\\omega", "positive": "\\frac{\\omega^{2}}{2} + \\frac{\\delta \\omega}{\\chi}", "negatives": ["\\delta \\omega + \\frac{\\omega^{2}}{2 \\chi}", "\\frac{\\omega (2 \\chi - 2 \\delta + \\omega)}{2}", "\\frac{\\chi \\delta \\omega^{2}}{2}", "\\frac{\\chi \\omega^{2}}{2 \\delta}"], "srepr_premise_expression": "Add(Symbol('\\\\omega', commutative=True), Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Add(Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2))), Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Pow(Symbol('\\\\omega', commutative=True), Integer(2))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))"]}, {"premise_expression": "\\log{(\\alpha \\chi)}", "variable": "\\chi", "positive": "\\chi (\\log{(\\alpha \\chi)} - 1)", "negatives": ["\\alpha (\\log{(\\alpha \\chi)} - 1)", "- \\sin{(\\alpha - \\chi)}", "\\frac{\\chi (- 2 \\alpha + \\chi)}{2}", "\\sin{(\\alpha + \\chi)}"], "srepr_premise_expression": "log(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\chi', commutative=True), Add(log(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\alpha', commutative=True), Add(log(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True))), Integer(-1)))", "Mul(Integer(-1), sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\chi', commutative=True)))", "sin(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "\\beta \\delta + \\omega", "variable": "\\delta", "positive": "\\frac{\\delta (\\beta \\delta + 2 \\omega)}{2}", "negatives": ["\\frac{\\beta (\\beta \\delta + 2 \\omega)}{2}", "\\frac{\\omega (2 \\beta \\delta + \\omega)}{2}", "\\frac{\\delta^{2} (- \\beta + \\omega)}{2}", "\\frac{\\delta (- \\delta + 2 \\omega^{\\beta})}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True)), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), Pow(Symbol('\\\\omega', commutative=True), Symbol('\\\\beta', commutative=True)))))"]}, {"premise_expression": "\\sin{(\\chi - \\psi)}", "variable": "\\chi", "positive": "- \\cos{(\\chi - \\psi)}", "negatives": ["\\cos{(\\chi - \\psi)}", "\\psi \\sin{(\\chi)}", "\\log{(\\chi)} \\sin{(\\psi)}", "\\frac{\\chi^{2} \\log{(\\psi)}}{2}"], "srepr_premise_expression": "sin(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))", "srepr_negatives": ["cos(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(Symbol('\\\\psi', commutative=True), sin(Symbol('\\\\chi', commutative=True)))", "Mul(log(Symbol('\\\\chi', commutative=True)), sin(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), log(Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\sin{(\\psi + \\sigma)}", "variable": "\\psi", "positive": "- \\cos{(\\psi + \\sigma)}", "negatives": ["\\sigma e^{\\frac{\\psi}{\\sigma}}", "\\sigma e^{\\psi}", "\\frac{\\psi (\\log{(\\psi)} - 1)}{\\sigma}", "\\frac{\\psi^{2} \\log{(\\sigma)}}{2}"], "srepr_premise_expression": "sin(Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Symbol('\\\\sigma', commutative=True), exp(Mul(Symbol('\\\\psi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))))", "Mul(Symbol('\\\\sigma', commutative=True), exp(Symbol('\\\\psi', commutative=True)))", "Mul(Symbol('\\\\psi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Add(log(Symbol('\\\\psi', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), log(Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\chi \\gamma \\psi", "variable": "\\gamma", "positive": "\\frac{\\chi \\gamma^{2} \\psi}{2}", "negatives": ["\\frac{\\chi \\gamma \\psi^{2}}{2}", "\\frac{\\chi^{2} \\gamma \\psi}{2}", "\\frac{\\gamma^{2} \\psi}{2 \\chi}", "\\frac{\\chi \\log{(\\gamma)}}{\\psi}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))", "Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), log(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\frac{\\psi}{\\pi}", "variable": "\\pi", "positive": "\\psi \\log{(\\pi)}", "negatives": ["\\pi + \\psi \\log{(\\pi)}", "\\frac{\\psi^{2}}{2 \\pi}", "\\log{(\\pi)} \\log{(\\psi)}", "e^{\\psi} \\log{(\\pi)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\psi', commutative=True), log(Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Add(Symbol('\\\\pi', commutative=True), Mul(Symbol('\\\\psi', commutative=True), log(Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "Mul(log(Symbol('\\\\pi', commutative=True)), log(Symbol('\\\\psi', commutative=True)))", "Mul(exp(Symbol('\\\\psi', commutative=True)), log(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "- \\sin{(\\alpha - \\sigma)}", "variable": "\\alpha", "positive": "\\cos{(\\alpha - \\sigma)}", "negatives": ["- \\cos{(\\alpha - \\sigma)}", "\\sigma \\sin{(\\alpha)}", "\\alpha \\sigma + e^{\\alpha}", "\\frac{\\sin{(\\alpha)}}{\\sigma}"], "srepr_premise_expression": "Mul(Integer(-1), sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))", "Mul(Symbol('\\\\sigma', commutative=True), sin(Symbol('\\\\alpha', commutative=True)))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True)), exp(Symbol('\\\\alpha', commutative=True)))", "Mul(Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), sin(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\pi \\psi", "variable": "\\pi", "positive": "\\frac{\\pi^{2} \\psi}{2}", "negatives": ["\\frac{\\pi \\psi^{2}}{2}", "\\frac{\\pi^{2} \\psi^{2}}{2}", "\\frac{\\pi \\sin{(\\psi)}}{\\psi}", "\\frac{\\pi^{2} \\cos{(\\psi)}}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "Mul(Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), sin(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), cos(Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\cos{(\\psi - \\sigma)}", "variable": "\\sigma", "positive": "- \\sin{(\\psi - \\sigma)}", "negatives": ["\\sin{(\\psi - \\sigma)}", "\\cos{(\\psi - \\sigma)}", "- \\psi \\sigma - \\cos{(\\sigma)}", "\\frac{\\sigma^{2}}{2 \\psi}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Integer(-1), sin(Add(Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))", "srepr_negatives": ["sin(Add(Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "cos(Add(Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))"]}, {"premise_expression": "- \\psi + \\cos{(\\beta)}", "variable": "\\beta", "positive": "- \\beta \\psi + \\sin{(\\beta)}", "negatives": ["\\beta \\psi - \\cos{(\\beta)}", "e^{\\beta + \\psi}", "\\frac{\\beta^{2} \\log{(\\psi)}}{2}", "\\frac{\\psi (- \\psi + 2 \\cos{(\\beta)})}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), cos(Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\psi', commutative=True)), sin(Symbol('\\\\beta', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\beta', commutative=True))))", "exp(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), log(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\beta', commutative=True)))))"]}, {"premise_expression": "\\pi \\sigma", "variable": "\\sigma", "positive": "\\frac{\\pi \\sigma^{2}}{2}", "negatives": ["\\frac{\\pi^{2} \\sigma}{2}", "\\pi \\sin{(\\sigma)}", "- \\sin{(\\pi - \\sigma)}", "e^{\\pi + \\sigma}"], "srepr_premise_expression": "Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), Symbol('\\\\sigma', commutative=True))", "Mul(Symbol('\\\\pi', commutative=True), sin(Symbol('\\\\sigma', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))", "exp(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\chi + \\cos{(\\beta)}", "variable": "\\beta", "positive": "\\beta \\chi + \\sin{(\\beta)}", "negatives": ["\\beta \\chi + e^{\\beta}", "\\frac{\\sin{(\\beta)}}{\\chi}", "\\frac{\\beta \\chi (\\beta + 2 \\chi)}{2}", "\\frac{\\chi (\\chi + 2 \\cos{(\\beta)})}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), cos(Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True)), sin(Symbol('\\\\beta', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True)), exp(Symbol('\\\\beta', commutative=True)))", "Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), sin(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\chi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), cos(Symbol('\\\\beta', commutative=True)))))"]}, {"premise_expression": "\\frac{\\sigma}{\\alpha}", "variable": "\\alpha", "positive": "\\sigma \\log{(\\alpha)}", "negatives": ["- \\sigma \\cos{(\\alpha)}", "\\frac{\\sigma^{2}}{2 \\alpha}", "\\frac{\\alpha^{2} \\log{(\\sigma)}}{2}", "\\alpha \\sigma + \\sin{(\\alpha)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Symbol('\\\\sigma', commutative=True), cos(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), log(Symbol('\\\\sigma', commutative=True)))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True)), sin(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\log{(- \\beta + \\omega)}", "variable": "\\beta", "positive": "\\beta \\log{(- \\beta + \\omega)} - \\beta - \\omega \\log{(\\beta - \\omega)}", "negatives": ["- \\beta \\log{(- \\beta + \\omega)} + \\omega \\log{(- \\beta + \\omega)} - \\omega", "\\beta e^{\\frac{\\omega}{\\beta}} - \\omega \\operatorname{Ei}{(\\frac{\\omega}{\\beta})}", "- \\beta \\omega - \\cos{(\\beta)}", "- \\cos{(\\beta - \\omega)}"], "srepr_premise_expression": "log(Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\beta', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\omega', commutative=True)))), Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Symbol('\\\\omega', commutative=True), log(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\omega', commutative=True)))), Mul(Symbol('\\\\omega', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\omega', commutative=True)))), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))", "Add(Mul(Symbol('\\\\beta', commutative=True), exp(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True)))), Mul(Integer(-1), Symbol('\\\\omega', commutative=True), Ei(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\beta', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))))"]}, {"premise_expression": "- \\beta + \\gamma \\psi", "variable": "\\beta", "positive": "\\frac{\\beta (- \\beta + 2 \\gamma \\psi)}{2}", "negatives": ["\\frac{\\beta (- \\beta + 2 \\gamma^{\\psi})}{2}", "\\frac{\\gamma (- 2 \\beta + \\gamma \\psi)}{2}", "\\frac{\\psi (- 2 \\beta + \\gamma \\psi)}{2}", "\\frac{\\beta \\gamma (\\beta + 2 \\psi)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Pow(Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "\\beta - \\psi", "variable": "\\psi", "positive": "\\frac{\\psi (2 \\beta - \\psi)}{2}", "negatives": ["\\frac{\\psi (2 \\beta + \\psi)}{2}", "\\frac{\\beta (\\beta - 2 \\psi)}{2}", "\\beta \\psi - \\cos{(\\psi)}", "\\log{(\\psi)} \\cos{(\\beta)}"], "srepr_premise_expression": "Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))", "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\psi', commutative=True))))", "Mul(log(Symbol('\\\\psi', commutative=True)), cos(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "- \\delta + e^{\\chi}", "variable": "\\chi", "positive": "- \\chi \\delta + e^{\\chi}", "negatives": ["- \\chi \\delta + \\sin{(\\chi)}", "\\delta \\log{(\\chi)}", "\\frac{\\delta (- \\delta + 2 e^{\\chi})}{2}", "e^{\\chi - \\delta}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), exp(Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True)), exp(Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True)), sin(Symbol('\\\\chi', commutative=True)))", "Mul(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\chi', commutative=True)))))", "exp(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))"]}, {"premise_expression": "\\cos{(\\alpha - \\gamma)}", "variable": "\\gamma", "positive": "- \\sin{(\\alpha - \\gamma)}", "negatives": ["\\sin{(\\alpha - \\gamma)}", "\\frac{\\sin{(\\gamma)}}{\\alpha}", "\\alpha \\gamma - \\cos{(\\gamma)}", "\\gamma (\\log{(\\frac{\\gamma}{\\alpha})} - 1)"], "srepr_premise_expression": "cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Integer(-1), sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))))", "srepr_negatives": ["sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), sin(Symbol('\\\\gamma', commutative=True)))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\gamma', commutative=True))))", "Mul(Symbol('\\\\gamma', commutative=True), Add(log(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\frac{\\omega}{\\beta \\chi}", "variable": "\\beta", "positive": "\\frac{\\omega \\log{(\\beta)}}{\\chi}", "negatives": ["\\frac{\\omega \\log{(\\chi)}}{\\beta}", "\\beta \\omega", "\\frac{\\beta^{2}}{2}", "\\frac{\\omega^{2}}{2 \\beta \\chi}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True), log(Symbol('\\\\beta', commutative=True)))", "srepr_negatives": ["Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True), log(Symbol('\\\\chi', commutative=True)))", "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))"]}, {"premise_expression": "\\log{(\\frac{\\xi}{\\sigma})}", "variable": "\\xi", "positive": "\\xi (\\log{(\\frac{\\xi}{\\sigma})} - 1)", "negatives": ["\\sigma (\\log{(\\frac{\\xi}{\\sigma})} + 1)", "\\xi (\\log{(\\frac{\\sigma}{\\xi})} + 1)", "\\xi (- \\sigma + \\log{(\\xi)} - 1)", "- \\sin{(\\sigma - \\xi)}"], "srepr_premise_expression": "log(Mul(Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\xi', commutative=True), Add(log(Mul(Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\sigma', commutative=True), Add(log(Mul(Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))), Integer(1)))", "Mul(Symbol('\\\\xi', commutative=True), Add(log(Mul(Symbol('\\\\sigma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), log(Symbol('\\\\xi', commutative=True)), Integer(-1)))", "Mul(Integer(-1), sin(Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))))"]}, {"premise_expression": "\\delta + \\log{(\\gamma)}", "variable": "\\delta", "positive": "\\frac{\\delta (\\delta + 2 \\log{(\\gamma)})}{2}", "negatives": ["\\frac{\\delta (- \\delta + 2 \\log{(\\gamma)})}{2}", "\\frac{\\delta (\\delta - 2 \\gamma)}{2}", "\\gamma (\\delta + \\log{(\\gamma)} - 1)", "\\frac{\\delta^{2} e^{\\gamma}}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), log(Symbol('\\\\gamma', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), log(Symbol('\\\\gamma', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True))))", "Mul(Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\gamma', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), exp(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\chi \\delta", "variable": "\\delta", "positive": "\\frac{\\chi \\delta^{2}}{2}", "negatives": ["\\frac{\\chi^{2} \\delta}{2}", "\\frac{\\delta^{2}}{2 \\chi}", "- \\frac{\\cos{(\\delta)}}{\\chi}", "- \\chi \\delta - \\cos{(\\delta)}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\delta', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Pow(Symbol('\\\\delta', commutative=True), Integer(2)))", "Mul(Integer(-1), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), cos(Symbol('\\\\delta', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\delta', commutative=True))))"]}, {"premise_expression": "e^{\\frac{\\gamma}{\\chi}}", "variable": "\\chi", "positive": "\\chi e^{\\frac{\\gamma}{\\chi}} - \\gamma \\operatorname{Ei}{(\\frac{\\gamma}{\\chi})}", "negatives": ["\\chi \\gamma + e^{\\chi}", "\\frac{\\chi (- \\chi + 2 e^{\\gamma})}{2}", "\\chi e^{\\frac{\\gamma}{\\chi}}", "\\frac{\\chi (\\chi + 2 \\gamma)}{2}"], "srepr_premise_expression": "exp(Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\chi', commutative=True), exp(Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True)))), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Ei(Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True)), exp(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\gamma', commutative=True)))))", "Mul(Symbol('\\\\chi', commutative=True), exp(Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\gamma', commutative=True))))"]}, {"premise_expression": "\\log{(\\sigma^{\\chi})}", "variable": "\\chi", "positive": "\\frac{\\chi^{2} \\log{(\\sigma)}}{2}", "negatives": ["\\frac{\\chi^{2} e^{\\sigma}}{2}", "\\frac{\\chi (\\chi + 2 \\sin{(\\sigma)})}{2}", "\\sin{(\\chi + \\sigma)}", "\\chi (- \\sigma + \\log{(\\chi^{\\sigma})})"], "srepr_premise_expression": "log(Pow(Symbol('\\\\sigma', commutative=True), Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), log(Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), exp(Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), sin(Symbol('\\\\sigma', commutative=True)))))", "sin(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\sigma', commutative=True)))", "Mul(Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), log(Pow(Symbol('\\\\chi', commutative=True), Symbol('\\\\sigma', commutative=True)))))"]}, {"premise_expression": "\\frac{\\omega}{\\sigma}", "variable": "\\omega", "positive": "\\frac{\\omega^{2}}{2 \\sigma}", "negatives": ["\\omega \\log{(\\sigma)}", "\\frac{\\omega^{2} \\log{(\\sigma)}}{2}", "\\frac{\\omega^{2} (1 - \\sigma)}{2 \\sigma}", "- \\cos{(\\omega + \\sigma)}"], "srepr_premise_expression": "Mul(Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), log(Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Add(Integer(1), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\log{(\\alpha + \\omega)}", "variable": "\\alpha", "positive": "\\alpha \\log{(\\alpha + \\omega)} - \\alpha + \\omega \\log{(\\alpha + \\omega)}", "negatives": ["\\alpha \\log{(\\alpha + \\omega)} + \\omega \\log{(\\alpha + \\omega)} - \\omega", "\\alpha (\\omega + \\log{(\\alpha)} - 1)", "\\alpha (\\log{(\\alpha \\omega)} - 1)", "\\frac{\\alpha (- \\alpha + 2 \\sin{(\\omega)})}{2}"], "srepr_premise_expression": "log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\alpha', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)))), Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Symbol('\\\\omega', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\alpha', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)))), Mul(Symbol('\\\\omega', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)))), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\alpha', commutative=True)), Integer(-1)))", "Mul(Symbol('\\\\alpha', commutative=True), Add(log(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\omega', commutative=True)))))"]}, {"premise_expression": "\\frac{\\alpha}{\\beta}", "variable": "\\beta", "positive": "\\alpha \\log{(\\beta)}", "negatives": ["\\frac{\\alpha^{2}}{2 \\beta}", "- \\cos{(\\alpha + \\beta)}", "- \\alpha \\beta + e^{\\beta}", "\\beta (\\log{(\\alpha \\beta)} - 1)"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\beta', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True)), exp(Symbol('\\\\beta', commutative=True)))", "Mul(Symbol('\\\\beta', commutative=True), Add(log(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True))), Integer(-1)))"]}, {"premise_expression": "e^{\\frac{\\alpha}{\\pi}}", "variable": "\\alpha", "positive": "\\pi e^{\\frac{\\alpha}{\\pi}}", "negatives": ["- \\cos{(\\alpha - \\pi)}", "- \\cos{(\\alpha + \\pi)}", "\\frac{\\alpha (\\alpha - 2 \\pi)}{2}", "\\alpha \\pi (\\log{(\\alpha)} - 1)"], "srepr_premise_expression": "exp(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\pi', commutative=True), exp(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True), Add(log(Symbol('\\\\alpha', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\frac{\\beta}{\\alpha}", "variable": "\\alpha", "positive": "\\beta \\log{(\\alpha)}", "negatives": ["\\beta e^{\\alpha}", "\\frac{\\beta^{2}}{2 \\alpha}", "\\frac{\\alpha^{2}}{2 \\beta}", "\\alpha \\beta (\\log{(\\alpha)} - 1)"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\beta', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\beta', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\beta', commutative=True), exp(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\beta', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)))", "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True), Add(log(Symbol('\\\\alpha', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\gamma + \\psi", "variable": "\\psi", "positive": "\\frac{\\psi (2 \\gamma + \\psi)}{2}", "negatives": ["\\frac{\\gamma (\\gamma + 2 \\psi)}{2}", "\\frac{\\psi (- \\psi + 2 \\log{(\\gamma)})}{2}", "\\frac{\\psi^{2} \\log{(\\gamma)}}{2}", "e^{- \\gamma + \\psi}"], "srepr_premise_expression": "Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), log(Symbol('\\\\gamma', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), log(Symbol('\\\\gamma', commutative=True)))", "exp(Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\beta + \\gamma", "variable": "\\beta", "positive": "\\frac{\\beta (\\beta + 2 \\gamma)}{2}", "negatives": ["\\frac{\\gamma (2 \\beta + \\gamma)}{2}", "\\gamma \\sin{(\\beta)}", "\\frac{\\sin{(\\beta)}}{\\gamma}", "- \\frac{\\cos{(\\beta)}}{\\gamma}"], "srepr_premise_expression": "Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\gamma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "Mul(Symbol('\\\\gamma', commutative=True), sin(Symbol('\\\\beta', commutative=True)))", "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), sin(Symbol('\\\\beta', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), cos(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "\\delta + \\pi", "variable": "\\pi", "positive": "\\frac{\\pi (2 \\delta + \\pi)}{2}", "negatives": ["\\frac{\\delta (\\delta + 2 \\pi)}{2}", "\\frac{\\pi^{2} \\cos{(\\delta)}}{2}", "\\frac{\\pi^{2} \\log{(\\delta)}}{2}", "e^{\\delta + \\pi}"], "srepr_premise_expression": "Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), cos(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), log(Symbol('\\\\delta', commutative=True)))", "exp(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\beta \\chi", "variable": "\\chi", "positive": "\\frac{\\beta \\chi^{2}}{2}", "negatives": ["\\frac{\\beta^{2} \\chi}{2}", "\\frac{\\chi (- 2 \\beta + \\chi)}{2}", "\\beta \\chi - \\cos{(\\chi)}", "- \\beta \\chi - \\cos{(\\chi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\chi', commutative=True))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\chi', commutative=True)))", "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\chi', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\chi', commutative=True))))"]}, {"premise_expression": "\\alpha + \\beta + \\omega", "variable": "\\beta", "positive": "\\beta (\\alpha + \\frac{\\beta}{2} + \\omega)", "negatives": ["\\frac{\\alpha (\\alpha + 2 \\beta + 2 \\omega)}{2}", "\\frac{\\omega (2 \\alpha + 2 \\beta + \\omega)}{2}", "\\frac{\\beta (\\beta + 2 \\omega)}{2 \\alpha}", "(\\alpha + \\omega) \\log{(\\beta)}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)), log(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "- \\psi + \\sin{(\\pi)}", "variable": "\\psi", "positive": "\\frac{\\psi (- \\psi + 2 \\sin{(\\pi)})}{2}", "negatives": ["\\frac{\\psi^{2} \\sin{(\\pi)}}{2}", "\\log{(\\psi)} \\sin{(\\pi)}", "- \\pi \\psi - \\cos{(\\pi)}", "\\sin{(\\pi + \\psi)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), sin(Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\pi', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), sin(Symbol('\\\\pi', commutative=True)))", "Mul(log(Symbol('\\\\psi', commutative=True)), sin(Symbol('\\\\pi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\pi', commutative=True))))", "sin(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\sin{(\\delta - \\omega)}", "variable": "\\omega", "positive": "\\cos{(\\delta - \\omega)}", "negatives": ["- \\cos{(\\delta - \\omega)}", "e^{\\delta + \\omega}", "\\frac{\\omega (- 2 \\delta + \\omega)}{2}", "\\omega (\\delta + \\log{(\\omega)} - 1)"], "srepr_premise_expression": "sin(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))))", "exp(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\omega', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\psi \\sin{(\\pi)}", "variable": "\\psi", "positive": "\\frac{\\psi^{2} \\sin{(\\pi)}}{2}", "negatives": ["- \\psi \\cos{(\\pi)}", "\\frac{\\psi (2 \\pi - \\psi)}{2}", "\\frac{\\psi (- \\psi + 2 e^{\\pi})}{2}", "e^{\\pi + \\psi}"], "srepr_premise_expression": "Mul(Symbol('\\\\psi', commutative=True), sin(Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), sin(Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Symbol('\\\\psi', commutative=True), cos(Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\pi', commutative=True)))))", "exp(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\log{(- \\delta + \\xi)}", "variable": "\\xi", "positive": "- \\delta \\log{(- \\delta + \\xi)} + \\xi \\log{(- \\delta + \\xi)} - \\xi", "negatives": ["\\delta \\log{(- \\delta + \\xi)} - \\delta - \\xi \\log{(\\delta - \\xi)}", "\\xi (\\log{(\\delta \\xi)} - 1)", "\\log{(\\xi)} \\cos{(\\delta)}", "\\log{(\\xi)} \\sin{(\\delta)}"], "srepr_premise_expression": "log(Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\xi', commutative=True)))), Mul(Symbol('\\\\xi', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\xi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\delta', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\xi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True), log(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))))", "Mul(Symbol('\\\\xi', commutative=True), Add(log(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True))), Integer(-1)))", "Mul(log(Symbol('\\\\xi', commutative=True)), cos(Symbol('\\\\delta', commutative=True)))", "Mul(log(Symbol('\\\\xi', commutative=True)), sin(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\cos^{\\chi}{(\\sigma)}", "variable": "\\sigma", "positive": "\\int \\cos^{\\chi}{(\\sigma)} d\\sigma", "negatives": ["\\sigma (\\chi + \\log{(\\sigma)} - 1)", "\\frac{\\sigma (\\log{(\\sigma)} - 1)}{\\chi}", "\\frac{\\sigma (- \\sigma + 2 \\cos{(\\chi)})}{2}", "\\frac{\\sigma^{2} \\log{(\\chi)}}{2}"], "srepr_premise_expression": "Pow(cos(Symbol('\\\\sigma', commutative=True)), Symbol('\\\\chi', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Integral(Pow(cos(Symbol('\\\\sigma', commutative=True)), Symbol('\\\\chi', commutative=True)), Tuple(Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\sigma', commutative=True)), Integer(-1)))", "Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True), Add(log(Symbol('\\\\sigma', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\chi', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), log(Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "\\chi + e^{\\pi}", "variable": "\\chi", "positive": "\\frac{\\chi (\\chi + 2 e^{\\pi})}{2}", "negatives": ["\\frac{\\chi (- \\chi + 2 \\log{(\\pi)})}{2}", "\\chi \\pi + e^{\\pi}", "\\frac{\\chi (\\chi - 2 \\pi)}{2}", "- \\chi \\pi + \\sin{(\\chi)}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), exp(Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), exp(Symbol('\\\\pi', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), log(Symbol('\\\\pi', commutative=True)))))", "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True)), exp(Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True)), sin(Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "\\gamma + \\psi", "variable": "\\gamma", "positive": "\\frac{\\gamma (\\gamma + 2 \\psi)}{2}", "negatives": ["\\frac{\\gamma (\\gamma - 2 \\psi)}{2}", "\\frac{\\gamma (- \\gamma + 2 \\psi)}{2}", "\\frac{\\psi (2 \\gamma + \\psi)}{2}", "\\frac{\\gamma (- \\gamma + 2 \\cos{(\\psi)})}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\psi', commutative=True)))))"]}, {"premise_expression": "- \\beta + \\pi", "variable": "\\pi", "positive": "\\frac{\\pi (- 2 \\beta + \\pi)}{2}", "negatives": ["\\frac{\\pi (2 \\beta - \\pi)}{2}", "\\frac{\\beta (- \\beta + 2 \\pi)}{2}", "\\frac{\\beta \\pi^{2}}{2}", "- \\sin{(\\beta - \\pi)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "Mul(Integer(-1), sin(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))"]}, {"premise_expression": "e^{\\frac{\\delta}{\\omega}}", "variable": "\\omega", "positive": "- \\delta \\operatorname{Ei}{(\\frac{\\delta}{\\omega})} + \\omega e^{\\frac{\\delta}{\\omega}}", "negatives": ["\\delta \\omega + e^{\\omega}", "\\frac{\\omega (- \\omega + 2 e^{\\delta})}{2}", "\\frac{\\omega (\\omega + 2 e^{\\delta})}{2}", "\\omega e^{\\frac{\\delta}{\\omega}}"], "srepr_premise_expression": "exp(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Ei(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1))))), Mul(Symbol('\\\\omega', commutative=True), exp(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1))))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True)), exp(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\delta', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), exp(Symbol('\\\\delta', commutative=True)))))", "Mul(Symbol('\\\\omega', commutative=True), exp(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))))"]}, {"premise_expression": "\\omega - \\sigma", "variable": "\\omega", "positive": "\\frac{\\omega (\\omega - 2 \\sigma)}{2}", "negatives": ["\\frac{\\sigma (2 \\omega - \\sigma)}{2}", "\\omega \\sin{(\\sigma^{\\sigma})}", "- e^{- \\omega + \\sigma}", "\\frac{\\sin{(\\omega)}}{\\sigma}"], "srepr_premise_expression": "Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Symbol('\\\\omega', commutative=True), sin(Pow(Symbol('\\\\sigma', commutative=True), Symbol('\\\\sigma', commutative=True))))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Symbol('\\\\sigma', commutative=True))))", "Mul(Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), sin(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\gamma \\psi", "variable": "\\gamma", "positive": "\\frac{\\gamma^{2} \\psi}{2}", "negatives": ["\\frac{\\gamma \\psi^{2}}{2}", "\\frac{\\gamma^{2} e^{\\psi}}{2}", "\\frac{\\gamma (\\gamma - 2 \\psi)}{2}", "- \\gamma \\psi - \\cos{(\\gamma)}"], "srepr_premise_expression": "Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), exp(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\gamma', commutative=True))))"]}, {"premise_expression": "\\pi \\psi", "variable": "\\pi", "positive": "\\frac{\\pi^{2} \\psi}{2}", "negatives": ["\\frac{\\pi \\psi^{2}}{2}", "\\psi \\log{(\\pi)}", "e^{\\pi - \\psi}", "\\frac{\\pi (- \\pi + 2 \\log{(\\psi)})}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "Mul(Symbol('\\\\psi', commutative=True), log(Symbol('\\\\pi', commutative=True)))", "exp(Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), log(Symbol('\\\\psi', commutative=True)))))"]}, {"premise_expression": "\\frac{\\xi}{\\delta}", "variable": "\\delta", "positive": "\\xi \\log{(\\delta)}", "negatives": ["\\frac{\\xi^{2}}{2 \\delta}", "\\frac{\\delta^{3} \\xi}{3}", "\\delta \\xi (\\log{(\\delta)} - 1)", "- \\cos{(\\delta + \\xi)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Mul(Rational(1, 3), Pow(Symbol('\\\\delta', commutative=True), Integer(3)), Symbol('\\\\xi', commutative=True))", "Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True), Add(log(Symbol('\\\\delta', commutative=True)), Integer(-1)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\log{(\\alpha + \\omega)}", "variable": "\\omega", "positive": "\\alpha \\log{(\\alpha + \\omega)} + \\omega \\log{(\\alpha + \\omega)} - \\omega", "negatives": ["\\alpha \\log{(\\alpha + \\omega)} - \\alpha + \\omega \\log{(\\alpha + \\omega)}", "\\alpha \\omega (\\log{(\\omega)} - 1)", "\\frac{\\omega (- \\omega + 2 e^{\\alpha})}{2}", "\\omega (- \\alpha + \\log{(\\omega^{\\alpha})})"], "srepr_premise_expression": "log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\alpha', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)))), Mul(Symbol('\\\\omega', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)))), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\alpha', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)))), Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Symbol('\\\\omega', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)))))", "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True), Add(log(Symbol('\\\\omega', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\alpha', commutative=True)))))", "Mul(Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), log(Pow(Symbol('\\\\omega', commutative=True), Symbol('\\\\alpha', commutative=True)))))"]}, {"premise_expression": "\\frac{\\pi}{\\alpha}", "variable": "\\alpha", "positive": "\\pi \\log{(\\alpha)}", "negatives": ["\\pi \\sin{(\\alpha)}", "\\frac{\\pi^{2}}{2 \\alpha}", "\\frac{\\alpha^{2} \\pi}{2}", "\\frac{\\alpha^{2} \\log{(\\pi)}}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\pi', commutative=True), sin(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\pi', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), log(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\cos{(\\chi + \\xi)}", "variable": "\\xi", "positive": "\\sin{(\\chi + \\xi)}", "negatives": ["\\frac{\\xi (- 2 \\chi + \\xi)}{2}", "\\log{(\\xi)} \\sin{(\\chi)}", "- \\chi \\cos{(\\xi)}", "\\frac{\\xi^{2} \\log{(\\chi)}}{2}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "sin(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(log(Symbol('\\\\xi', commutative=True)), sin(Symbol('\\\\chi', commutative=True)))", "Mul(Integer(-1), Symbol('\\\\chi', commutative=True), cos(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), log(Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "\\frac{\\pi}{\\beta}", "variable": "\\beta", "positive": "\\pi \\log{(\\beta)}", "negatives": ["\\frac{\\pi^{2}}{2 \\beta}", "e^{\\pi} \\log{(\\beta)}", "e \\beta", "\\frac{\\beta^{2}}{2 \\pi}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\beta', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "Mul(exp(Symbol('\\\\pi', commutative=True)), log(Symbol('\\\\beta', commutative=True)))", "Mul(E, Symbol('\\\\beta', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))"]}, {"premise_expression": "\\psi \\sigma", "variable": "\\sigma", "positive": "\\frac{\\psi \\sigma^{2}}{2}", "negatives": ["\\frac{\\psi^{2} \\sigma}{2}", "\\frac{\\sigma (- 2 \\psi + \\sigma)}{2}", "\\frac{\\sigma (2 \\psi - \\sigma)}{2}", "\\psi e^{\\frac{\\sigma}{\\psi}}"], "srepr_premise_expression": "Mul(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), Symbol('\\\\sigma', commutative=True))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Symbol('\\\\psi', commutative=True), exp(Mul(Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "- \\omega + \\sigma", "variable": "\\omega", "positive": "\\frac{\\omega (- \\omega + 2 \\sigma)}{2}", "negatives": ["\\frac{\\sigma (- 2 \\omega + \\sigma)}{2}", "\\frac{\\omega^{2} \\cos{(\\sigma)}}{2}", "\\sin{(\\omega - \\sigma)}", "- \\cos{(\\omega + \\sigma)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), cos(Symbol('\\\\sigma', commutative=True)))", "sin(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\sin{(\\beta + \\gamma)}", "variable": "\\beta", "positive": "- \\cos{(\\beta + \\gamma)}", "negatives": ["\\sin{(\\beta - \\gamma)}", "e^{\\beta - \\gamma}", "\\beta \\gamma - \\cos{(\\beta)}", "\\beta (\\log{(\\beta \\gamma)} - 1)"], "srepr_premise_expression": "sin(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True))))", "srepr_negatives": ["sin(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "exp(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\beta', commutative=True))))", "Mul(Symbol('\\\\beta', commutative=True), Add(log(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\gamma \\log{(\\sigma)}", "variable": "\\gamma", "positive": "\\frac{\\gamma^{2} \\log{(\\sigma)}}{2}", "negatives": ["\\sigma \\log{(\\gamma)}", "\\frac{\\gamma^{2}}{2 \\sigma}", "\\frac{\\gamma (\\gamma + 2 \\sigma)}{2}", "\\gamma \\sigma (\\log{(\\sigma)} - 1)"], "srepr_premise_expression": "Mul(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), log(Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True), Add(log(Symbol('\\\\sigma', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\pi \\cos{(\\alpha)}", "variable": "\\alpha", "positive": "\\pi \\sin{(\\alpha)}", "negatives": ["\\pi \\log{(\\alpha)}", "\\frac{\\sin{(\\alpha)}}{\\pi}", "\\log{(\\alpha)} \\sin{(\\pi)}", "\\frac{\\pi^{2} \\cos{(\\alpha)}}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\pi', commutative=True), cos(Symbol('\\\\alpha', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\pi', commutative=True), sin(Symbol('\\\\alpha', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), sin(Symbol('\\\\alpha', commutative=True)))", "Mul(log(Symbol('\\\\alpha', commutative=True)), sin(Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), cos(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "- \\sin{(\\omega - \\sigma)}", "variable": "\\sigma", "positive": "- \\cos{(\\omega - \\sigma)}", "negatives": ["\\cos{(\\omega - \\sigma)}", "- e^{\\omega - \\sigma}", "e^{- \\omega + \\sigma}", "\\omega \\sin{(\\sigma)}"], "srepr_premise_expression": "Mul(Integer(-1), sin(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))", "srepr_negatives": ["cos(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Integer(-1), exp(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))", "exp(Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), sin(Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\chi - \\xi", "variable": "\\xi", "positive": "\\frac{\\xi (2 \\chi - \\xi)}{2}", "negatives": ["\\frac{\\chi (\\chi - 2 \\xi)}{2}", "\\frac{\\xi^{2} \\log{(\\chi)}}{2}", "\\frac{\\chi \\xi^{2}}{2}", "\\frac{\\xi (\\xi + 2 \\cos{(\\chi)})}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), log(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\xi', commutative=True), Mul(Integer(2), cos(Symbol('\\\\chi', commutative=True)))))"]}, {"premise_expression": "\\frac{\\sigma}{\\alpha \\pi}", "variable": "\\sigma", "positive": "\\frac{\\sigma^{2}}{2 \\alpha \\pi}", "negatives": ["\\frac{\\pi \\sigma^{2}}{2 \\alpha}", "\\frac{\\pi \\sigma^{3}}{3}", "\\frac{\\sigma \\log{(\\pi)}}{\\alpha}", "\\frac{\\sigma \\log{(\\alpha)}}{\\pi}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "Mul(Rational(1, 3), Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(3)))", "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\pi', commutative=True)))", "Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\alpha + \\omega - \\psi", "variable": "\\alpha", "positive": "\\alpha (\\frac{\\alpha}{2} + \\omega - \\psi)", "negatives": ["\\frac{\\alpha (\\alpha - 2 \\omega - 2 \\psi)}{2}", "\\frac{\\psi (2 \\alpha + 2 \\omega - \\psi)}{2}", "\\frac{\\omega (2 \\alpha + \\omega - 2 \\psi)}{2}", "- \\frac{\\alpha^{2}}{2} + \\frac{\\alpha \\psi}{\\omega}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\alpha', commutative=True), Add(Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))", "Add(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2))), Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\omega + \\cos{(\\delta)}", "variable": "\\omega", "positive": "\\frac{\\omega (\\omega + 2 \\cos{(\\delta)})}{2}", "negatives": ["\\delta \\omega - \\cos{(\\omega)}", "\\delta \\omega + \\sin{(\\delta)}", "\\frac{\\delta \\omega^{2}}{2}", "\\frac{\\omega^{2}}{2 \\delta}"], "srepr_premise_expression": "Add(Symbol('\\\\omega', commutative=True), cos(Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), cos(Symbol('\\\\delta', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\omega', commutative=True))))", "Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True)), sin(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))"]}, {"premise_expression": "- \\delta + \\frac{\\psi}{\\chi}", "variable": "\\chi", "positive": "- \\chi \\delta + \\psi \\log{(\\chi)}", "negatives": ["\\delta \\psi \\log{(\\chi)}", "- \\delta \\psi + \\frac{\\psi^{2}}{2 \\chi}", "\\frac{\\chi (\\chi + 2 \\psi)}{2 \\delta}", "\\frac{\\chi^{2} \\psi^{\\delta}}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True)), Mul(Symbol('\\\\psi', commutative=True), log(Symbol('\\\\chi', commutative=True))))", "srepr_negatives": ["Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\psi', commutative=True), log(Symbol('\\\\chi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Pow(Symbol('\\\\psi', commutative=True), Integer(2))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Pow(Symbol('\\\\psi', commutative=True), Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\log{(\\xi^{\\gamma})}", "variable": "\\gamma", "positive": "\\frac{\\gamma^{2} \\log{(\\xi)}}{2}", "negatives": ["\\frac{\\gamma (\\gamma - 2 \\xi)}{2}", "\\frac{\\gamma (\\gamma + 2 \\xi)}{2}", "\\xi \\sin{(\\gamma)}", "\\gamma \\xi + e^{\\gamma}"], "srepr_premise_expression": "log(Pow(Symbol('\\\\xi', commutative=True), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), log(Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Symbol('\\\\xi', commutative=True), sin(Symbol('\\\\gamma', commutative=True)))", "Add(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)), exp(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\cos{(\\beta - \\omega)}", "variable": "\\omega", "positive": "- \\sin{(\\beta - \\omega)}", "negatives": ["\\sin{(\\beta - \\omega)}", "\\beta \\sin{(\\omega)}", "- \\beta \\cos{(\\omega)}", "\\frac{\\omega (\\log{(\\omega)} - 1)}{\\beta}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Integer(-1), sin(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))))", "srepr_negatives": ["sin(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "Mul(Symbol('\\\\beta', commutative=True), sin(Symbol('\\\\omega', commutative=True)))", "Mul(Integer(-1), Symbol('\\\\beta', commutative=True), cos(Symbol('\\\\omega', commutative=True)))", "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True), Add(log(Symbol('\\\\omega', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\chi \\omega", "variable": "\\omega", "positive": "\\frac{\\chi \\omega^{2}}{2}", "negatives": ["\\frac{\\chi^{2} \\omega}{2}", "\\frac{\\omega^{2}}{2 \\chi}", "\\chi \\log{(\\omega)}", "- \\frac{\\cos{(\\omega)}}{\\chi}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\omega', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "Mul(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), cos(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\cos{(\\alpha - \\delta)}", "variable": "\\alpha", "positive": "\\sin{(\\alpha - \\delta)}", "negatives": ["- \\sin{(\\alpha - \\delta)}", "\\frac{\\sin{(\\alpha)}}{\\delta}", "- \\cos{(\\alpha - \\delta)}", "- \\frac{\\cos{(\\alpha)}}{\\delta}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)))))", "Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), sin(Symbol('\\\\alpha', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)))))", "Mul(Integer(-1), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), cos(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\psi + \\sin{(\\omega)}", "variable": "\\omega", "positive": "\\omega \\psi - \\cos{(\\omega)}", "negatives": ["\\omega \\psi + e^{\\omega}", "- \\omega \\psi + \\sin{(\\omega)}", "\\psi \\log{(\\omega)}", "\\frac{\\psi (\\psi + 2 \\sin{(\\omega)})}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\psi', commutative=True), sin(Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True)), exp(Symbol('\\\\omega', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True)), sin(Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\psi', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(2), sin(Symbol('\\\\omega', commutative=True)))))"]}, {"premise_expression": "\\pi + \\cos{(\\alpha)}", "variable": "\\pi", "positive": "\\frac{\\pi (\\pi + 2 \\cos{(\\alpha)})}{2}", "negatives": ["\\alpha \\pi - \\cos{(\\pi)}", "\\frac{\\pi^{2} e^{\\alpha}}{2}", "\\alpha \\pi + \\sin{(\\alpha)}", "- \\alpha \\pi + \\sin{(\\pi)}"], "srepr_premise_expression": "Add(Symbol('\\\\pi', commutative=True), cos(Symbol('\\\\alpha', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), cos(Symbol('\\\\alpha', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), exp(Symbol('\\\\alpha', commutative=True)))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)), sin(Symbol('\\\\alpha', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)), sin(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\frac{\\cos{(\\chi)}}{\\delta}", "variable": "\\chi", "positive": "\\frac{\\sin{(\\chi)}}{\\delta}", "negatives": ["\\sin{(\\chi + \\delta)}", "\\log{(\\chi)} \\log{(\\delta)}", "\\log{(\\chi)} \\sin{(\\delta)}", "\\frac{\\chi^{2} e^{\\delta}}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), cos(Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), sin(Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["sin(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True)))", "Mul(log(Symbol('\\\\chi', commutative=True)), log(Symbol('\\\\delta', commutative=True)))", "Mul(log(Symbol('\\\\chi', commutative=True)), sin(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), exp(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\frac{\\delta}{\\gamma}", "variable": "\\delta", "positive": "\\frac{\\delta^{2}}{2 \\gamma}", "negatives": ["\\delta \\log{(\\gamma)}", "\\delta \\cos{(\\gamma^{2})}", "\\gamma e^{\\delta}", "\\frac{\\sin{(\\delta)}}{\\gamma}"], "srepr_premise_expression": "Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "Mul(Symbol('\\\\delta', commutative=True), cos(Pow(Symbol('\\\\gamma', commutative=True), Integer(2))))", "Mul(Symbol('\\\\gamma', commutative=True), exp(Symbol('\\\\delta', commutative=True)))", "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), sin(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\log{(\\psi \\sigma)}", "variable": "\\sigma", "positive": "\\sigma (\\log{(\\psi \\sigma)} - 1)", "negatives": ["\\psi (\\log{(\\psi \\sigma)} - 1)", "e^{\\psi + \\sigma}", "\\psi \\sin{(\\sigma)}", "\\frac{\\psi \\sigma^{2}}{2}"], "srepr_premise_expression": "log(Mul(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\sigma', commutative=True), Add(log(Mul(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\psi', commutative=True), Add(log(Mul(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True))), Integer(-1)))", "exp(Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True)))", "Mul(Symbol('\\\\psi', commutative=True), sin(Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))"]}, {"premise_expression": "\\frac{\\pi^{\\psi}}{\\gamma}", "variable": "\\gamma", "positive": "\\pi^{\\psi} \\log{(\\gamma)}", "negatives": ["\\pi \\psi \\log{(\\gamma)}", "\\frac{\\psi \\log{(\\gamma)}}{\\pi}", "(\\pi + \\psi) \\log{(\\gamma)}", "\\frac{\\gamma^{2} \\pi}{2 \\psi}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Pow(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)), log(Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "Mul(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)), log(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))"]}, {"premise_expression": "- \\chi + \\psi", "variable": "\\chi", "positive": "\\frac{\\chi (- \\chi + 2 \\psi)}{2}", "negatives": ["\\frac{\\psi (- 2 \\chi + \\psi)}{2}", "\\frac{\\chi^{2} \\log{(\\psi)}}{2}", "\\frac{\\chi^{2} \\sin{(\\psi)}}{2}", "\\sin{(\\chi - \\psi)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), log(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), sin(Symbol('\\\\psi', commutative=True)))", "sin(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "\\delta + \\gamma", "variable": "\\gamma", "positive": "\\frac{\\gamma (2 \\delta + \\gamma)}{2}", "negatives": ["\\frac{\\delta (\\delta + 2 \\gamma)}{2}", "- \\delta \\gamma + \\sin{(\\gamma)}", "\\gamma (\\log{(\\delta \\gamma)} - 1)", "- \\frac{\\cos{(\\gamma)}}{\\delta}"], "srepr_premise_expression": "Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\gamma', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), Symbol('\\\\gamma', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Symbol('\\\\gamma', commutative=True)), sin(Symbol('\\\\gamma', commutative=True)))", "Mul(Symbol('\\\\gamma', commutative=True), Add(log(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\gamma', commutative=True))), Integer(-1)))", "Mul(Integer(-1), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), cos(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\sin{(\\chi - \\omega)}", "variable": "\\chi", "positive": "- \\cos{(\\chi - \\omega)}", "negatives": ["\\cos{(\\chi - \\omega)}", "- \\omega \\cos{(\\chi)}", "\\log{(\\chi)} \\cos{(\\omega)}", "\\log{(\\chi)} \\log{(\\omega)}"], "srepr_premise_expression": "sin(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))))", "srepr_negatives": ["cos(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "Mul(Integer(-1), Symbol('\\\\omega', commutative=True), cos(Symbol('\\\\chi', commutative=True)))", "Mul(log(Symbol('\\\\chi', commutative=True)), cos(Symbol('\\\\omega', commutative=True)))", "Mul(log(Symbol('\\\\chi', commutative=True)), log(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\frac{\\delta}{\\pi} - \\sigma", "variable": "\\pi", "positive": "\\delta \\log{(\\pi)} - \\pi \\sigma", "negatives": ["\\frac{\\delta^{2}}{2 \\pi} - \\delta \\sigma", "\\frac{\\pi (2 \\delta \\sigma + \\pi)}{2}", "\\frac{\\delta \\sigma}{\\pi} - \\frac{\\sigma^{2}}{2}", "- \\frac{\\pi (- 2 \\delta + \\pi)}{2 \\sigma}"], "srepr_premise_expression": "Add(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1))), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\pi', commutative=True))), Mul(Integer(-1), Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Add(Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1))), Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Add(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2))))", "Mul(Integer(-1), Rational(1, 2), Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\delta \\sin{(\\beta)}", "variable": "\\delta", "positive": "\\frac{\\delta^{2} \\sin{(\\beta)}}{2}", "negatives": ["- \\delta \\cos{(\\beta)}", "- \\beta \\delta + \\sin{(\\delta)}", "\\frac{\\delta (\\delta + 2 \\log{(\\beta)})}{2}", "- \\frac{\\cos{(\\delta)}}{\\beta}"], "srepr_premise_expression": "Mul(Symbol('\\\\delta', commutative=True), sin(Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), sin(Symbol('\\\\beta', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Symbol('\\\\delta', commutative=True), cos(Symbol('\\\\beta', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True)), sin(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), log(Symbol('\\\\beta', commutative=True)))))", "Mul(Integer(-1), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), cos(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\frac{\\beta}{\\alpha}", "variable": "\\alpha", "positive": "\\beta \\log{(\\alpha)}", "negatives": ["\\frac{\\beta^{2}}{2 \\alpha}", "\\frac{\\alpha (\\alpha + 2 \\log{(\\beta)})}{2}", "\\frac{\\alpha (- \\alpha + 2 \\log{(\\beta)})}{2}", "\\alpha \\cos{(\\frac{\\beta}{\\alpha})} + \\beta \\operatorname{Si}{(\\frac{\\beta}{\\alpha})}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\beta', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\beta', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\beta', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), log(Symbol('\\\\beta', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), log(Symbol('\\\\beta', commutative=True)))))", "Add(Mul(Symbol('\\\\alpha', commutative=True), cos(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\beta', commutative=True)))), Mul(Symbol('\\\\beta', commutative=True), Si(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\beta', commutative=True)))))"]}, {"premise_expression": "- \\beta + \\sin{(\\pi)}", "variable": "\\pi", "positive": "- \\beta \\pi - \\cos{(\\pi)}", "negatives": ["\\beta \\pi + e^{\\pi}", "\\log{(\\pi)} \\cos{(\\beta)}", "- e^{\\beta - \\pi}", "e^{\\beta + \\pi}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), sin(Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\pi', commutative=True)), exp(Symbol('\\\\pi', commutative=True)))", "Mul(log(Symbol('\\\\pi', commutative=True)), cos(Symbol('\\\\beta', commutative=True)))", "Mul(Integer(-1), exp(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))", "exp(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\sin{(\\alpha + \\psi)}", "variable": "\\psi", "positive": "- \\cos{(\\alpha + \\psi)}", "negatives": ["- \\frac{\\cos{(\\psi)}}{\\alpha}", "\\alpha \\psi - \\cos{(\\psi)}", "\\alpha e^{\\psi}", "\\frac{\\psi^{2} \\log{(\\alpha)}}{2}"], "srepr_premise_expression": "sin(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), cos(Symbol('\\\\psi', commutative=True)))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\psi', commutative=True))))", "Mul(Symbol('\\\\alpha', commutative=True), exp(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), log(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\log{(\\gamma + \\psi)}", "variable": "\\gamma", "positive": "\\gamma \\log{(\\gamma + \\psi)} - \\gamma + \\psi \\log{(\\gamma + \\psi)}", "negatives": ["\\gamma \\log{(\\gamma + \\psi)} + \\psi \\log{(\\gamma + \\psi)} - \\psi", "\\frac{\\gamma (- \\gamma + 2 \\cos{(\\psi)})}{2}", "\\frac{\\gamma \\psi (\\gamma + 2)}{2}", "\\frac{\\gamma^{2} \\log{(\\psi)}}{2}"], "srepr_premise_expression": "log(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\gamma', commutative=True), log(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Symbol('\\\\psi', commutative=True), log(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\gamma', commutative=True), log(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True)))), Mul(Symbol('\\\\psi', commutative=True), log(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\psi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), log(Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\beta \\gamma", "variable": "\\gamma", "positive": "\\frac{\\beta \\gamma^{2}}{2}", "negatives": ["\\frac{\\beta^{2} \\gamma}{2}", "\\frac{\\gamma^{2} e^{\\beta}}{2}", "- \\cos{(\\beta + \\gamma)}", "\\log{(\\beta)} \\log{(\\gamma)}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\gamma', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), exp(Symbol('\\\\beta', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True))))", "Mul(log(Symbol('\\\\beta', commutative=True)), log(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\log{(\\psi \\xi)}", "variable": "\\xi", "positive": "\\xi (\\log{(\\psi \\xi)} - 1)", "negatives": ["\\psi (\\log{(\\psi \\xi)} - 1)", "\\log{(\\psi)} \\log{(\\xi)}", "\\frac{\\xi (2 \\psi + \\xi)}{2}", "e^{\\psi + \\xi}"], "srepr_premise_expression": "log(Mul(Symbol('\\\\psi', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\xi', commutative=True), Add(log(Mul(Symbol('\\\\psi', commutative=True), Symbol('\\\\xi', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\psi', commutative=True), Add(log(Mul(Symbol('\\\\psi', commutative=True), Symbol('\\\\xi', commutative=True))), Integer(-1)))", "Mul(log(Symbol('\\\\psi', commutative=True)), log(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\psi', commutative=True)), Symbol('\\\\xi', commutative=True)))", "exp(Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\frac{\\xi}{\\delta}", "variable": "\\delta", "positive": "\\xi \\log{(\\delta)}", "negatives": ["\\xi e^{\\delta}", "\\frac{\\xi^{2}}{2 \\delta}", "- \\delta \\xi - \\cos{(\\delta)}", "- \\cos{(\\delta + \\xi)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\xi', commutative=True), exp(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\delta', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "e^{\\frac{\\beta}{\\sigma}}", "variable": "\\beta", "positive": "\\sigma e^{\\frac{\\beta}{\\sigma}}", "negatives": ["\\sigma e^{\\beta}", "- \\sigma \\cos{(\\beta)}", "\\frac{\\beta^{2} \\cos{(\\sigma)}}{2}", "- \\beta \\operatorname{Ei}{(\\frac{\\beta}{\\sigma})} + \\sigma e^{\\frac{\\beta}{\\sigma}}"], "srepr_premise_expression": "exp(Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\sigma', commutative=True), exp(Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))))", "srepr_negatives": ["Mul(Symbol('\\\\sigma', commutative=True), exp(Symbol('\\\\beta', commutative=True)))", "Mul(Integer(-1), Symbol('\\\\sigma', commutative=True), cos(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), cos(Symbol('\\\\sigma', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Ei(Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1))))), Mul(Symbol('\\\\sigma', commutative=True), exp(Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1))))))"]}, {"premise_expression": "\\alpha + \\gamma", "variable": "\\alpha", "positive": "\\frac{\\alpha (\\alpha + 2 \\gamma)}{2}", "negatives": ["\\frac{\\gamma (2 \\alpha + \\gamma)}{2}", "\\frac{\\alpha^{2}}{2 \\gamma}", "\\frac{\\alpha^{2} \\cos{(\\gamma)}}{2}", "\\frac{\\sin{(\\alpha)}}{\\gamma}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\gamma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), cos(Symbol('\\\\gamma', commutative=True)))", "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), sin(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\frac{\\sin{(\\gamma)}}{\\beta}", "variable": "\\gamma", "positive": "- \\frac{\\cos{(\\gamma)}}{\\beta}", "negatives": ["\\beta \\gamma - \\cos{(\\gamma)}", "\\beta^{2} \\gamma", "\\frac{\\gamma^{2}}{2 \\beta}", "- e^{\\beta - \\gamma}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), sin(Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Integer(-1), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), cos(Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\gamma', commutative=True))))", "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\gamma', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)))", "Mul(Integer(-1), exp(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))))"]}, {"premise_expression": "\\delta \\omega", "variable": "\\delta", "positive": "\\frac{\\delta^{2} \\omega}{2}", "negatives": ["\\frac{\\delta \\omega^{2}}{2}", "\\omega \\sin{(\\delta)}", "- \\frac{\\cos{(\\delta)}}{\\omega}", "\\delta \\cos^{\\omega}{(\\omega)}"], "srepr_premise_expression": "Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Symbol('\\\\omega', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "Mul(Symbol('\\\\omega', commutative=True), sin(Symbol('\\\\delta', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), cos(Symbol('\\\\delta', commutative=True)))", "Mul(Symbol('\\\\delta', commutative=True), Pow(cos(Symbol('\\\\omega', commutative=True)), Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "- \\pi + \\frac{\\sigma}{\\alpha}", "variable": "\\sigma", "positive": "- \\pi \\sigma + \\frac{\\sigma^{2}}{2 \\alpha}", "negatives": ["- \\alpha \\pi + \\sigma \\log{(\\alpha)}", "- \\frac{\\sigma^{2}}{2} + \\frac{\\pi \\sigma}{\\alpha}", "- \\frac{\\pi^{2}}{2} + \\frac{\\pi \\sigma}{\\alpha}", "\\frac{\\sigma (- 2 \\alpha - 2 \\pi + \\sigma)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Integer(2))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\alpha', commutative=True))))", "Add(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2))), Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True)))", "Add(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2))), Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True)), Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\omega - \\psi", "variable": "\\omega", "positive": "\\frac{\\omega (\\omega - 2 \\psi)}{2}", "negatives": ["\\frac{\\omega (\\omega + 2 \\psi)}{2}", "\\frac{\\psi (2 \\omega - \\psi)}{2}", "\\frac{\\omega (\\omega + 2 e^{\\psi})}{2}", "\\sin{(\\omega - \\psi)}"], "srepr_premise_expression": "Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), exp(Symbol('\\\\psi', commutative=True)))))", "sin(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "\\frac{\\xi}{\\gamma}", "variable": "\\gamma", "positive": "\\xi \\log{(\\gamma)}", "negatives": ["- \\xi \\cos{(\\gamma)}", "\\frac{\\xi^{2}}{2 \\gamma}", "- \\gamma \\xi + \\sin{(\\gamma)}", "\\log{(\\gamma)} \\cos{(\\xi)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Symbol('\\\\xi', commutative=True), cos(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)), sin(Symbol('\\\\gamma', commutative=True)))", "Mul(log(Symbol('\\\\gamma', commutative=True)), cos(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\cos{(\\frac{\\delta}{\\pi})}", "variable": "\\pi", "positive": "\\delta \\operatorname{Si}{(\\frac{\\delta}{\\pi})} + \\pi \\cos{(\\frac{\\delta}{\\pi})}", "negatives": ["- \\delta \\operatorname{Ei}{(\\frac{\\delta}{\\pi})} + \\pi e^{\\frac{\\delta}{\\pi}}", "- \\cos{(\\delta - \\pi)}", "\\frac{\\pi (2 \\delta + \\pi)}{2}", "\\frac{\\pi (- 2 \\delta + \\pi)}{2}"], "srepr_premise_expression": "cos(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\delta', commutative=True), Si(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1))))), Mul(Symbol('\\\\pi', commutative=True), cos(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1))))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Ei(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1))))), Mul(Symbol('\\\\pi', commutative=True), exp(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1))))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\psi + \\sigma", "variable": "\\psi", "positive": "\\frac{\\psi (\\psi + 2 \\sigma)}{2}", "negatives": ["\\frac{\\psi (- \\psi + 2 \\sigma)}{2}", "\\frac{\\sigma (2 \\psi + \\sigma)}{2}", "\\frac{\\psi (- \\psi + 2 \\sin{(\\sigma)})}{2}", "e^{\\psi + \\sigma}"], "srepr_premise_expression": "Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\psi', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\sigma', commutative=True)))))", "exp(Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\delta \\xi", "variable": "\\xi", "positive": "\\frac{\\delta \\xi^{2}}{2}", "negatives": ["\\frac{\\delta^{2} \\xi}{2}", "\\delta \\log{(\\xi)}", "\\delta e^{\\xi}", "\\frac{\\xi^{2} \\log{(\\delta)}}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))", "Mul(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\delta', commutative=True), exp(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), log(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "- \\gamma + \\cos{(\\pi)}", "variable": "\\gamma", "positive": "\\frac{\\gamma (- \\gamma + 2 \\cos{(\\pi)})}{2}", "negatives": ["\\frac{\\gamma (- \\gamma + 2 e^{\\pi})}{2}", "\\frac{\\gamma (\\gamma + 2 \\pi)}{2}", "\\gamma (\\gamma + \\pi)", "\\frac{\\gamma^{2} e^{\\pi}}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), cos(Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\pi', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\pi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), exp(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\frac{\\alpha}{\\omega}", "variable": "\\omega", "positive": "\\alpha \\log{(\\omega)}", "negatives": ["\\alpha e^{\\omega}", "\\omega \\cos{(1)}", "\\frac{\\alpha^{2}}{2 \\omega}", "\\cos{(\\alpha - \\omega)}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\alpha', commutative=True), exp(Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), cos(Integer(1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))", "cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))"]}, {"premise_expression": "- \\delta + \\log{(\\alpha)}", "variable": "\\alpha", "positive": "\\alpha (- \\delta + \\log{(\\alpha)} - 1)", "negatives": ["\\frac{\\delta (- \\delta + 2 \\log{(\\alpha)})}{2}", "\\sin{(\\alpha - \\delta)}", "\\log{(\\alpha)} \\log{(\\delta)}", "\\frac{\\alpha^{2} \\delta}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), log(Symbol('\\\\alpha', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), log(Symbol('\\\\alpha', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), log(Symbol('\\\\alpha', commutative=True)))))", "sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))", "Mul(log(Symbol('\\\\alpha', commutative=True)), log(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\delta', commutative=True))"]}, {"premise_expression": "\\pi + \\sin{(\\omega)}", "variable": "\\omega", "positive": "\\omega \\pi - \\cos{(\\omega)}", "negatives": ["\\omega \\cos{(1)}", "\\frac{\\omega^{3} \\pi}{3}", "\\frac{\\omega^{2} \\pi}{2}", "\\frac{\\pi (\\pi + 2 \\sin{(\\omega)})}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\pi', commutative=True), sin(Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Mul(Symbol('\\\\omega', commutative=True), cos(Integer(1)))", "Mul(Rational(1, 3), Pow(Symbol('\\\\omega', commutative=True), Integer(3)), Symbol('\\\\pi', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Symbol('\\\\pi', commutative=True))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), sin(Symbol('\\\\omega', commutative=True)))))"]}, {"premise_expression": "\\chi + \\psi", "variable": "\\chi", "positive": "\\frac{\\chi (\\chi + 2 \\psi)}{2}", "negatives": ["\\frac{\\chi (\\chi - 2 \\psi)}{2}", "\\frac{\\psi (2 \\chi + \\psi)}{2}", "\\sin{(\\chi - \\psi)}", "\\chi (- \\psi + \\log{(\\chi^{\\psi})})"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\psi', commutative=True)))", "sin(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), log(Pow(Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True)))))"]}, {"premise_expression": "\\log{(\\alpha \\beta)}", "variable": "\\alpha", "positive": "\\alpha (\\log{(\\alpha \\beta)} - 1)", "negatives": ["\\beta (\\log{(\\alpha \\beta)} - 1)", "\\alpha (\\log{(\\frac{\\alpha}{\\beta})} - 1)", "\\log{(\\alpha)} \\log{(\\beta)}", "\\frac{\\alpha^{2}}{2 \\beta}"], "srepr_premise_expression": "log(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\alpha', commutative=True), Add(log(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\beta', commutative=True), Add(log(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\alpha', commutative=True), Add(log(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)))), Integer(-1)))", "Mul(log(Symbol('\\\\alpha', commutative=True)), log(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)))"]}, {"premise_expression": "- \\chi + e^{\\sigma}", "variable": "\\sigma", "positive": "- \\chi \\sigma + e^{\\sigma}", "negatives": ["\\frac{\\chi (- \\chi + 2 e^{\\sigma})}{2}", "e^{\\chi + \\sigma}", "\\log{(\\chi)} \\log{(\\sigma)}", "\\frac{\\sigma (- 2 \\chi + \\sigma)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), exp(Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\sigma', commutative=True)), exp(Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\sigma', commutative=True)))))", "exp(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\sigma', commutative=True)))", "Mul(log(Symbol('\\\\chi', commutative=True)), log(Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\alpha \\chi", "variable": "\\alpha", "positive": "\\frac{\\alpha^{2} \\chi}{2}", "negatives": ["\\frac{\\alpha \\chi^{2}}{2}", "\\chi e^{\\alpha}", "e^{\\alpha + \\chi}", "e^{\\chi} \\log{(\\alpha)}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\chi', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(2)))", "Mul(Symbol('\\\\chi', commutative=True), exp(Symbol('\\\\alpha', commutative=True)))", "exp(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)))", "Mul(exp(Symbol('\\\\chi', commutative=True)), log(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\frac{\\alpha}{\\chi}", "variable": "\\alpha", "positive": "\\frac{\\alpha^{2}}{2 \\chi}", "negatives": ["\\alpha \\log{(\\chi)}", "\\frac{\\alpha^{2} \\log{(\\chi)}}{2}", "\\sin{(\\alpha + \\chi)}", "\\frac{\\alpha (\\alpha + 2 \\chi)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), log(Symbol('\\\\chi', commutative=True)))", "sin(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\chi', commutative=True))))"]}, {"premise_expression": "\\log{(\\psi - \\sigma)}", "variable": "\\sigma", "positive": "- \\psi \\log{(- \\psi + \\sigma)} + \\sigma \\log{(\\psi - \\sigma)} - \\sigma", "negatives": ["- \\psi \\log{(- \\psi + \\sigma)} + \\sigma \\log{(- \\psi + \\sigma)} - \\sigma", "\\psi \\log{(\\psi - \\sigma)} - \\psi - \\sigma \\log{(\\psi - \\sigma)}", "- \\psi \\operatorname{Ei}{(\\frac{\\psi}{\\sigma})} + \\sigma e^{\\frac{\\psi}{\\sigma}}", "\\sigma (- \\psi + \\log{(\\sigma)} - 1)"], "srepr_premise_expression": "log(Add(Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Symbol('\\\\sigma', commutative=True)))), Mul(Symbol('\\\\sigma', commutative=True), log(Add(Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Symbol('\\\\sigma', commutative=True)))), Mul(Symbol('\\\\sigma', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Symbol('\\\\sigma', commutative=True)))), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))", "Add(Mul(Symbol('\\\\psi', commutative=True), log(Add(Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True), log(Add(Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))))", "Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True), Ei(Mul(Symbol('\\\\psi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1))))), Mul(Symbol('\\\\sigma', commutative=True), exp(Mul(Symbol('\\\\psi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1))))))", "Mul(Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), log(Symbol('\\\\sigma', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\chi + \\gamma", "variable": "\\chi", "positive": "\\frac{\\chi (\\chi + 2 \\gamma)}{2}", "negatives": ["\\frac{\\chi (- \\chi + 2 \\gamma)}{2}", "\\frac{\\gamma (2 \\chi + \\gamma)}{2}", "\\frac{\\chi (- \\chi + 2 e^{\\gamma})}{2}", "e^{\\chi + \\gamma}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\gamma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\gamma', commutative=True)))))", "exp(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\frac{\\alpha}{\\omega} - \\gamma", "variable": "\\alpha", "positive": "\\frac{\\alpha^{2}}{2 \\omega} - \\alpha \\gamma", "negatives": ["\\alpha \\log{(\\omega)} - \\gamma \\omega", "\\frac{\\alpha^{2} \\gamma}{2 \\omega}", "\\frac{\\alpha^{2}}{2 \\gamma \\omega}", "\\frac{\\alpha^{2} \\gamma \\omega}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1))), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Add(Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\omega', commutative=True), Integer(-1))), Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\omega', commutative=True))), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True))"]}, {"premise_expression": "\\beta \\cos{(\\omega)}", "variable": "\\beta", "positive": "\\frac{\\beta^{2} \\cos{(\\omega)}}{2}", "negatives": ["\\frac{\\beta^{2} \\sin{(\\omega)}}{2}", "\\beta \\sin{(\\omega)}", "\\omega \\log{(\\beta)}", "\\int \\sin^{\\omega}{(\\beta)} d\\beta"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), cos(Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), cos(Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), sin(Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\beta', commutative=True), sin(Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\beta', commutative=True)))", "Integral(Pow(sin(Symbol('\\\\beta', commutative=True)), Symbol('\\\\omega', commutative=True)), Tuple(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "\\omega - \\pi", "variable": "\\pi", "positive": "\\frac{\\pi (2 \\omega - \\pi)}{2}", "negatives": ["\\frac{\\omega (\\omega - 2 \\pi)}{2}", "\\frac{\\pi^{2} \\cos{(\\omega)}}{2}", "\\pi (- \\omega + \\log{(\\pi^{\\omega})})", "\\pi (\\log{(\\frac{\\pi}{\\omega})} - 1)"], "srepr_premise_expression": "Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), cos(Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), log(Pow(Symbol('\\\\pi', commutative=True), Symbol('\\\\omega', commutative=True)))))", "Mul(Symbol('\\\\pi', commutative=True), Add(log(Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\pi + \\cos{(\\omega)}", "variable": "\\omega", "positive": "\\omega \\pi + \\sin{(\\omega)}", "negatives": ["- \\omega \\pi + e^{\\omega}", "\\frac{\\omega^{2}}{2} + e^{\\omega}", "\\frac{\\pi (\\pi + 2 \\cos{(\\omega)})}{2}", "e^{\\omega - \\pi}"], "srepr_premise_expression": "Add(Symbol('\\\\pi', commutative=True), cos(Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)), sin(Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)), exp(Symbol('\\\\omega', commutative=True)))", "Add(Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2))), exp(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), cos(Symbol('\\\\omega', commutative=True)))))", "exp(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\omega \\pi", "variable": "\\pi", "positive": "\\frac{\\omega \\pi^{2}}{2}", "negatives": ["\\frac{\\omega^{2} \\pi}{2}", "\\frac{\\pi (2 \\omega + \\pi)}{2}", "\\omega e^{\\pi}", "\\omega \\sin{(\\pi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Symbol('\\\\pi', commutative=True))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), exp(Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), sin(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\beta + \\psi", "variable": "\\beta", "positive": "\\frac{\\beta (\\beta + 2 \\psi)}{2}", "negatives": ["\\frac{\\psi (2 \\beta + \\psi)}{2}", "- \\cos{(\\beta + \\psi)}", "\\frac{\\beta^{2}}{2 \\psi}", "\\operatorname{Ei}{(\\beta)}"], "srepr_premise_expression": "Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))", "Ei(Symbol('\\\\beta', commutative=True))"]}, {"premise_expression": "\\gamma \\pi", "variable": "\\gamma", "positive": "\\frac{\\gamma^{2} \\pi}{2}", "negatives": ["\\frac{\\gamma \\pi^{2}}{2}", "- \\pi \\cos{(\\gamma)}", "\\cos{(\\gamma - \\pi)}", "- \\cos{(\\gamma - \\pi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Symbol('\\\\pi', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "Mul(Integer(-1), Symbol('\\\\pi', commutative=True), cos(Symbol('\\\\gamma', commutative=True)))", "cos(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))"]}, {"premise_expression": "\\alpha (\\gamma + \\pi)", "variable": "\\pi", "positive": "\\frac{\\alpha \\pi (2 \\gamma + \\pi)}{2}", "negatives": ["\\frac{\\alpha^{2} (\\gamma + \\pi)}{2}", "\\frac{\\alpha \\gamma (\\gamma + 2 \\pi)}{2}", "\\frac{\\pi^{2} (\\alpha + \\gamma)}{2}", "\\frac{\\pi (2 \\alpha^{\\gamma} - \\pi)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Pow(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True))), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\frac{\\sin{(\\xi)}}{\\sigma}", "variable": "\\xi", "positive": "- \\frac{\\cos{(\\xi)}}{\\sigma}", "negatives": ["\\frac{\\sin{(\\xi)}}{\\sigma}", "- \\cos{(\\sigma + \\xi)}", "\\sigma e^{\\xi}", "\\sigma e^{\\frac{\\xi}{\\sigma}}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), sin(Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Integer(-1), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), cos(Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), sin(Symbol('\\\\xi', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True))))", "Mul(Symbol('\\\\sigma', commutative=True), exp(Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\sigma', commutative=True), exp(Mul(Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\xi + \\cos{(\\delta)}", "variable": "\\xi", "positive": "\\frac{\\xi (\\xi + 2 \\cos{(\\delta)})}{2}", "negatives": ["\\frac{\\xi^{2} \\log{(\\delta)}}{2}", "\\frac{\\xi^{2} e^{\\delta}}{2}", "\\delta \\xi + \\sin{(\\delta)}", "\\xi (\\log{(2 \\xi)} - 1)"], "srepr_premise_expression": "Add(Symbol('\\\\xi', commutative=True), cos(Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\xi', commutative=True), Mul(Integer(2), cos(Symbol('\\\\delta', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), log(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), exp(Symbol('\\\\delta', commutative=True)))", "Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True)), sin(Symbol('\\\\delta', commutative=True)))", "Mul(Symbol('\\\\xi', commutative=True), Add(log(Mul(Integer(2), Symbol('\\\\xi', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\beta - \\xi", "variable": "\\xi", "positive": "\\frac{\\xi (2 \\beta - \\xi)}{2}", "negatives": ["\\frac{\\beta (\\beta - 2 \\xi)}{2}", "\\frac{\\xi (\\log{(\\xi)} - 1)}{\\beta}", "\\frac{\\xi^{2}}{2 \\beta}", "\\beta e^{\\xi}"], "srepr_premise_expression": "Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True), Add(log(Symbol('\\\\xi', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Mul(Symbol('\\\\beta', commutative=True), exp(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "- \\beta + \\pi + \\xi", "variable": "\\pi", "positive": "\\pi (- \\beta + \\frac{\\pi}{2} + \\xi)", "negatives": ["\\frac{\\pi (2 \\beta - \\pi - 2 \\xi)}{2}", "\\frac{\\beta (- \\beta + 2 \\pi + 2 \\xi)}{2}", "\\frac{\\xi (- 2 \\beta + 2 \\pi + \\xi)}{2}", "\\frac{\\pi (- 2 \\beta + \\pi \\xi)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\omega \\xi", "variable": "\\xi", "positive": "\\frac{\\omega \\xi^{2}}{2}", "negatives": ["\\frac{\\omega^{2} \\xi}{2}", "\\omega \\log{(\\xi)}", "- \\frac{\\cos{(\\xi)}}{\\omega}", "\\frac{\\xi (2 \\omega - \\xi)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))", "Mul(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\xi', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), cos(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "- \\psi - \\sigma + \\xi", "variable": "\\psi", "positive": "\\psi (- \\frac{\\psi}{2} - \\sigma + \\xi)", "negatives": ["\\frac{\\sigma (- 2 \\psi - \\sigma + 2 \\xi)}{2}", "\\frac{\\xi (- 2 \\psi - 2 \\sigma + \\xi)}{2}", "\\psi (\\sigma - 2 \\xi)", "\\frac{\\psi (\\psi \\xi + 2 \\sigma)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Rational(1, 2), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Symbol('\\\\psi', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\beta \\log{(\\delta)}", "variable": "\\delta", "positive": "\\beta \\delta (\\log{(\\delta)} - 1)", "negatives": ["\\delta (\\log{(\\beta \\delta)} - 1)", "\\delta (\\log{(\\frac{\\beta}{\\delta})} + 1)", "\\frac{\\beta^{2} \\log{(\\delta)}}{2}", "\\frac{\\delta^{2} \\log{(\\beta)}}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), log(Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True), Add(log(Symbol('\\\\delta', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\delta', commutative=True), Add(log(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\delta', commutative=True), Add(log(Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), log(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), log(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "\\pi + \\xi", "variable": "\\xi", "positive": "\\frac{\\xi (2 \\pi + \\xi)}{2}", "negatives": ["\\frac{\\pi (\\pi + 2 \\xi)}{2}", "\\frac{\\xi (\\log{(\\xi)} - 1)}{\\pi}", "- \\pi \\cos{(\\xi)}", "\\log{(\\pi)} \\log{(\\xi)}"], "srepr_premise_expression": "Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True), Add(log(Symbol('\\\\xi', commutative=True)), Integer(-1)))", "Mul(Integer(-1), Symbol('\\\\pi', commutative=True), cos(Symbol('\\\\xi', commutative=True)))", "Mul(log(Symbol('\\\\pi', commutative=True)), log(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\chi (\\gamma - \\sigma)", "variable": "\\gamma", "positive": "\\frac{\\chi \\gamma (\\gamma - 2 \\sigma)}{2}", "negatives": ["\\frac{\\chi^{2} (\\gamma - \\sigma)}{2}", "\\frac{\\gamma (\\chi \\gamma - 2 \\sigma)}{2}", "\\frac{\\chi \\sigma (2 \\gamma - \\sigma)}{2}", "\\frac{\\gamma (\\chi \\gamma + 2 \\sigma)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "- \\gamma + \\sin{(\\chi)}", "variable": "\\chi", "positive": "- \\chi \\gamma - \\cos{(\\chi)}", "negatives": ["\\frac{\\chi^{2} \\cos{(\\gamma)}}{2}", "- \\frac{\\cos{(\\chi)}}{\\gamma}", "\\frac{\\chi (\\chi - 2 \\gamma)}{2}", "e^{\\chi - \\gamma}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), sin(Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\chi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), cos(Symbol('\\\\gamma', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), cos(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True))))", "exp(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))"]}, {"premise_expression": "\\gamma - \\pi", "variable": "\\pi", "positive": "\\frac{\\pi (2 \\gamma - \\pi)}{2}", "negatives": ["\\frac{\\gamma (\\gamma - 2 \\pi)}{2}", "\\frac{\\pi^{2} e^{\\gamma}}{2}", "\\cos{(\\gamma - \\pi)}", "\\gamma \\log{(\\pi)}"], "srepr_premise_expression": "Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), exp(Symbol('\\\\gamma', commutative=True)))", "cos(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "Mul(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "- \\beta + \\log{(\\chi)}", "variable": "\\chi", "positive": "\\chi (- \\beta + \\log{(\\chi)} - 1)", "negatives": ["\\frac{\\beta (- \\beta + 2 \\log{(\\chi)})}{2}", "\\frac{\\chi (2 \\beta - \\chi)}{2}", "\\cos{(\\beta - \\chi)}", "\\sin{(\\beta + \\chi)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), log(Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), log(Symbol('\\\\chi', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), log(Symbol('\\\\chi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Symbol('\\\\chi', commutative=True))))", "cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True))))", "sin(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "\\log{(\\pi^{\\omega})}", "variable": "\\pi", "positive": "\\pi (- \\omega + \\log{(\\pi^{\\omega})})", "negatives": ["\\frac{\\pi (- \\pi + 2 \\cos{(\\omega)})}{2}", "- \\omega \\pi + e^{\\pi}", "\\pi (\\log{(\\frac{\\pi}{\\omega})} - 1)", "\\frac{\\omega^{2} \\log{(\\pi)}}{2}"], "srepr_premise_expression": "log(Pow(Symbol('\\\\pi', commutative=True), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), log(Pow(Symbol('\\\\pi', commutative=True), Symbol('\\\\omega', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\omega', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)), exp(Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\pi', commutative=True), Add(log(Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), log(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\pi - \\sigma", "variable": "\\pi", "positive": "\\frac{\\pi (\\pi - 2 \\sigma)}{2}", "negatives": ["\\frac{\\sigma (2 \\pi - \\sigma)}{2}", "\\frac{\\pi^{2} \\cos{(\\sigma)}}{2}", "\\sin{(\\pi - \\sigma)}", "\\frac{\\pi (- \\pi + 2 \\cos{(\\sigma)})}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), cos(Symbol('\\\\sigma', commutative=True)))", "sin(Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\sigma', commutative=True)))))"]}, {"premise_expression": "\\delta + \\gamma + \\omega", "variable": "\\gamma", "positive": "\\gamma (\\delta + \\frac{\\gamma}{2} + \\omega)", "negatives": ["\\frac{\\gamma (- 2 \\delta + \\gamma + 2 \\omega)}{2}", "\\frac{\\omega (2 \\delta + 2 \\gamma + \\omega)}{2}", "\\frac{\\delta (\\delta + 2 \\gamma + 2 \\omega)}{2}", "\\frac{\\gamma^{2} (- \\delta + \\omega)}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\gamma', commutative=True), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\frac{\\sigma}{\\gamma}", "variable": "\\gamma", "positive": "\\sigma \\log{(\\gamma)}", "negatives": ["\\sigma \\sin{(\\gamma)}", "\\frac{\\sigma^{2}}{2 \\gamma}", "\\frac{\\gamma^{2} \\sigma}{2}", "\\frac{\\gamma^{2}}{2 \\sigma}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\sigma', commutative=True), sin(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Symbol('\\\\sigma', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))"]}, {"premise_expression": "- \\alpha + \\beta", "variable": "\\alpha", "positive": "\\frac{\\alpha (- \\alpha + 2 \\beta)}{2}", "negatives": ["\\frac{\\beta (- 2 \\alpha + \\beta)}{2}", "- \\cos{(\\alpha - \\beta)}", "\\beta \\log{(\\alpha)}", "\\frac{\\alpha (\\alpha + 2 \\sin{(\\beta)})}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\beta', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\beta', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\beta', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\beta', commutative=True)))))", "Mul(Symbol('\\\\beta', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), sin(Symbol('\\\\beta', commutative=True)))))"]}, {"premise_expression": "- \\omega + \\sigma", "variable": "\\sigma", "positive": "\\frac{\\sigma (- 2 \\omega + \\sigma)}{2}", "negatives": ["\\frac{\\omega (- \\omega + 2 \\sigma)}{2}", "\\frac{\\sigma^{2} \\cos{(\\omega)}}{2}", "\\sin{(\\omega + \\sigma)}", "e^{\\omega + \\sigma}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), cos(Symbol('\\\\omega', commutative=True)))", "sin(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True)))", "exp(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\omega \\sigma", "variable": "\\sigma", "positive": "\\frac{\\omega \\sigma^{2}}{2}", "negatives": ["\\frac{\\omega^{2} \\sigma}{2}", "\\frac{\\sigma^{2}}{2 \\omega}", "\\sigma", "- \\sin{(\\omega - \\sigma)}"], "srepr_premise_expression": "Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Symbol('\\\\sigma', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "Symbol('\\\\sigma', commutative=True)", "Mul(Integer(-1), sin(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))"]}, {"premise_expression": "\\frac{\\chi}{\\xi}", "variable": "\\chi", "positive": "\\frac{\\chi^{2}}{2 \\xi}", "negatives": ["\\chi \\log{(\\xi)}", "\\frac{\\chi^{2} \\log{(\\xi)}}{2}", "\\frac{\\chi (- \\chi + 2 \\xi)}{2}", "\\log{(\\chi)} \\log{(\\xi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), log(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(log(Symbol('\\\\chi', commutative=True)), log(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\xi \\log{(\\psi)}", "variable": "\\psi", "positive": "\\psi \\xi (\\log{(\\psi)} - 1)", "negatives": ["\\psi (- \\xi + \\log{(\\psi)} - 1)", "\\frac{\\xi^{2} \\log{(\\psi)}}{2}", "\\cos{(\\psi - \\xi)}", "\\frac{\\psi^{2} \\log{(\\xi)}}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\psi', commutative=True), Symbol('\\\\xi', commutative=True), Add(log(Symbol('\\\\psi', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), log(Symbol('\\\\psi', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), log(Symbol('\\\\psi', commutative=True)))", "cos(Add(Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), log(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "- \\alpha - \\beta + \\omega", "variable": "\\beta", "positive": "\\beta (- \\alpha - \\frac{\\beta}{2} + \\omega)", "negatives": ["\\frac{\\alpha (- \\alpha - 2 \\beta + 2 \\omega)}{2}", "\\frac{\\omega (- 2 \\alpha - 2 \\beta + \\omega)}{2}", "\\frac{\\beta (- 2 \\alpha + \\beta \\omega)}{2}", "\\frac{\\beta (- \\beta + 2 \\omega^{\\alpha})}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Rational(1, 2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Pow(Symbol('\\\\omega', commutative=True), Symbol('\\\\alpha', commutative=True)))))"]}, {"premise_expression": "e^{\\omega - \\pi}", "variable": "\\omega", "positive": "e^{\\omega - \\pi}", "negatives": ["- e^{\\omega - \\pi}", "\\omega (\\log{(\\frac{\\omega}{\\pi})} - 1)", "- \\omega \\pi - \\cos{(\\omega)}", "\\omega \\pi + \\sin{(\\omega)}"], "srepr_premise_expression": "exp(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "exp(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))", "Mul(Symbol('\\\\omega', commutative=True), Add(log(Mul(Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))), Integer(-1)))", "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\omega', commutative=True))))", "Add(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)), sin(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\pi + \\sin{(\\beta)}", "variable": "\\beta", "positive": "\\beta \\pi - \\cos{(\\beta)}", "negatives": ["\\pi \\log{(\\beta)}", "\\frac{\\beta^{2}}{2 \\pi}", "\\frac{\\beta^{2} \\log{(\\pi)}}{2}", "\\beta e^{2 \\pi}"], "srepr_premise_expression": "Add(Symbol('\\\\pi', commutative=True), sin(Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\beta', commutative=True))))", "srepr_negatives": ["Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), log(Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\beta', commutative=True), exp(Mul(Integer(2), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\xi \\cos{(\\chi)}", "variable": "\\xi", "positive": "\\frac{\\xi^{2} \\cos{(\\chi)}}{2}", "negatives": ["\\xi \\sin{(\\chi)}", "\\frac{\\sin{(\\xi)}}{\\chi}", "- \\cos{(\\chi + \\xi)}", "e^{\\chi + \\xi}"], "srepr_premise_expression": "Mul(Symbol('\\\\xi', commutative=True), cos(Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), cos(Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\xi', commutative=True), sin(Symbol('\\\\chi', commutative=True)))", "Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), sin(Symbol('\\\\xi', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True))))", "exp(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\xi + \\sin{(\\psi)}", "variable": "\\psi", "positive": "\\psi \\xi - \\cos{(\\psi)}", "negatives": ["- \\frac{\\cos{(\\psi)}}{\\xi}", "\\frac{\\xi (\\xi + 2 \\sin{(\\psi)})}{2}", "\\frac{\\psi^{2} \\log{(\\xi)}}{2}", "\\psi (- \\xi + \\log{(\\psi^{\\xi})})"], "srepr_premise_expression": "Add(Symbol('\\\\xi', commutative=True), sin(Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\psi', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), cos(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\xi', commutative=True), Mul(Integer(2), sin(Symbol('\\\\psi', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), log(Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), log(Pow(Symbol('\\\\psi', commutative=True), Symbol('\\\\xi', commutative=True)))))"]}, {"premise_expression": "\\psi + \\xi", "variable": "\\psi", "positive": "\\frac{\\psi (\\psi + 2 \\xi)}{2}", "negatives": ["\\frac{\\xi (2 \\psi + \\xi)}{2}", "\\frac{\\psi^{2} \\cos{(\\xi)}}{2}", "\\frac{\\psi^{2} \\log{(\\xi)}}{2}", "\\frac{\\psi \\xi (\\psi - 2)}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\psi', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), cos(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), log(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Integer(-2)))"]}, {"premise_expression": "- \\sin{(\\delta - \\gamma)}", "variable": "\\delta", "positive": "\\cos{(\\delta - \\gamma)}", "negatives": ["- \\cos{(\\delta - \\gamma)}", "- \\cos{(\\delta + \\gamma)}", "\\delta \\gamma - \\cos{(\\delta)}", "- \\delta \\gamma - \\cos{(\\delta)}"], "srepr_premise_expression": "Mul(Integer(-1), sin(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\gamma', commutative=True))))", "Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\delta', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\delta', commutative=True))))"]}, {"premise_expression": "\\pi \\log{(\\gamma)}", "variable": "\\gamma", "positive": "\\gamma \\pi (\\log{(\\gamma)} - 1)", "negatives": ["\\frac{\\pi^{2} \\log{(\\gamma)}}{2}", "\\gamma \\pi - \\cos{(\\gamma)}", "- e^{- \\gamma + \\pi}", "\\log{(\\gamma)} \\cos{(\\pi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True), Add(log(Symbol('\\\\gamma', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), log(Symbol('\\\\gamma', commutative=True)))", "Add(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\gamma', commutative=True))))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True))))", "Mul(log(Symbol('\\\\gamma', commutative=True)), cos(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\chi \\omega", "variable": "\\chi", "positive": "\\frac{\\chi^{2} \\omega}{2}", "negatives": ["\\frac{\\chi \\omega^{2}}{2}", "\\frac{\\chi^{2} \\sin{(\\omega)}}{2}", "\\chi", "e^{\\chi + \\omega}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\omega', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), sin(Symbol('\\\\omega', commutative=True)))", "Symbol('\\\\chi', commutative=True)", "exp(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\beta - \\xi", "variable": "\\beta", "positive": "\\frac{\\beta (\\beta - 2 \\xi)}{2}", "negatives": ["\\frac{\\xi (2 \\beta - \\xi)}{2}", "\\frac{\\beta^{2} \\xi}{2}", "\\sin{(\\beta - \\xi)}", "\\frac{\\beta (- \\beta + 2 e^{\\xi})}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))", "sin(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\xi', commutative=True)))))"]}, {"premise_expression": "\\delta + \\frac{\\psi}{\\sigma}", "variable": "\\sigma", "positive": "\\delta \\sigma + \\psi \\log{(\\sigma)}", "negatives": ["\\delta \\psi + \\frac{\\psi^{2}}{2 \\sigma}", "\\frac{\\delta \\log{(\\sigma)}}{\\psi}", "\\frac{\\delta^{2}}{2} + \\frac{\\delta \\psi}{\\sigma}", "\\frac{\\delta^{\\psi} \\sigma^{2}}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\delta', commutative=True), Mul(Symbol('\\\\psi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Symbol('\\\\psi', commutative=True), log(Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1))))", "Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), log(Symbol('\\\\sigma', commutative=True)))", "Add(Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2))), Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\psi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Symbol('\\\\psi', commutative=True)), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))"]}, {"premise_expression": "\\cos{(\\gamma + \\sigma)}", "variable": "\\sigma", "positive": "\\sin{(\\gamma + \\sigma)}", "negatives": ["e^{- \\gamma + \\sigma}", "\\gamma e^{\\sigma}", "e^{\\gamma} \\log{(\\sigma)}", "- \\gamma \\sigma + \\sin{(\\sigma)}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "sin(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["exp(Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Symbol('\\\\gamma', commutative=True), exp(Symbol('\\\\sigma', commutative=True)))", "Mul(exp(Symbol('\\\\gamma', commutative=True)), log(Symbol('\\\\sigma', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True)), sin(Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\frac{\\xi^{\\omega}}{\\gamma}", "variable": "\\gamma", "positive": "\\xi^{\\omega} \\log{(\\gamma)}", "negatives": ["\\frac{\\gamma^{2} \\xi}{2 \\omega}", "\\frac{\\gamma^{2} \\omega}{2 \\xi}", "\\frac{\\gamma^{2} \\omega \\xi}{2}", "\\frac{\\gamma \\omega (\\gamma - 2)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('\\\\xi', commutative=True), Symbol('\\\\omega', commutative=True)), log(Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Integer(-2)))"]}, {"premise_expression": "\\alpha + \\chi + \\delta", "variable": "\\alpha", "positive": "\\alpha (\\frac{\\alpha}{2} + \\chi + \\delta)", "negatives": ["\\frac{\\alpha (- \\alpha + 2 \\chi - 2 \\delta)}{2}", "\\frac{\\chi (2 \\alpha + \\chi + 2 \\delta)}{2}", "\\frac{\\delta (2 \\alpha + 2 \\chi + \\delta)}{2}", "\\frac{\\alpha (\\alpha + 2 \\chi \\delta)}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\alpha', commutative=True), Add(Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True))))"]}, {"premise_expression": "\\psi (- \\omega + \\pi)", "variable": "\\omega", "positive": "\\frac{\\omega \\psi (- \\omega + 2 \\pi)}{2}", "negatives": ["\\frac{\\psi^{2} (- \\omega + \\pi)}{2}", "\\frac{\\pi \\psi (- 2 \\omega + \\pi)}{2}", "\\frac{\\omega^{2} (\\pi + \\psi)}{2}", "\\frac{\\omega^{2} (- \\pi + \\psi)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\log{(\\psi^{\\sigma})}", "variable": "\\sigma", "positive": "\\frac{\\sigma^{2} \\log{(\\psi)}}{2}", "negatives": ["\\frac{\\sigma^{2} e^{\\psi}}{2}", "\\frac{\\sigma (\\log{(\\sigma)} - 1)}{\\psi}", "\\log{(\\sigma)} \\sin{(\\psi)}", "\\psi (- \\sigma + \\log{(\\psi^{\\sigma})})"], "srepr_premise_expression": "log(Pow(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), log(Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), exp(Symbol('\\\\psi', commutative=True)))", "Mul(Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True), Add(log(Symbol('\\\\sigma', commutative=True)), Integer(-1)))", "Mul(log(Symbol('\\\\sigma', commutative=True)), sin(Symbol('\\\\psi', commutative=True)))", "Mul(Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), log(Pow(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True)))))"]}, {"premise_expression": "\\frac{\\beta}{\\omega}", "variable": "\\beta", "positive": "\\frac{\\beta^{2}}{2 \\omega}", "negatives": ["\\beta \\log{(\\omega)}", "\\frac{\\beta^{2} \\omega}{2}", "\\omega \\sin{(\\beta)}", "e^{\\beta - \\omega}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\beta', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\omega', commutative=True))", "Mul(Symbol('\\\\omega', commutative=True), sin(Symbol('\\\\beta', commutative=True)))", "exp(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))"]}, {"premise_expression": "\\log{(\\omega^{\\beta})}", "variable": "\\beta", "positive": "\\frac{\\beta^{2} \\log{(\\omega)}}{2}", "negatives": ["\\frac{\\beta^{2} \\omega}{2}", "\\omega \\log{(\\beta)}", "- \\omega \\cos{(\\beta)}", "\\omega \\sin{(\\beta)}"], "srepr_premise_expression": "log(Pow(Symbol('\\\\omega', commutative=True), Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), log(Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\omega', commutative=True))", "Mul(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\beta', commutative=True)))", "Mul(Integer(-1), Symbol('\\\\omega', commutative=True), cos(Symbol('\\\\beta', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), sin(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "- \\sin{(\\alpha - \\psi)}", "variable": "\\psi", "positive": "- \\cos{(\\alpha - \\psi)}", "negatives": ["\\cos{(\\alpha - \\psi)}", "- \\sin{(\\alpha - \\psi)}", "\\alpha \\psi (\\log{(\\psi)} - 1)", "- \\alpha \\psi + e^{\\psi}"], "srepr_premise_expression": "Mul(Integer(-1), sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))", "srepr_negatives": ["cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(Integer(-1), sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))", "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True), Add(log(Symbol('\\\\psi', commutative=True)), Integer(-1)))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True)), exp(Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\psi + \\xi", "variable": "\\psi", "positive": "\\frac{\\psi (\\psi + 2 \\xi)}{2}", "negatives": ["\\frac{\\psi (- \\psi + 2 \\xi)}{2}", "\\frac{\\xi (2 \\psi + \\xi)}{2}", "\\frac{\\psi (\\psi + 2 \\log{(\\xi)})}{2}", "\\frac{\\psi (- \\psi + 2 \\cos{(\\xi)})}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\psi', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(2), log(Symbol('\\\\xi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\xi', commutative=True)))))"]}, {"premise_expression": "- \\beta + e^{\\xi}", "variable": "\\beta", "positive": "\\frac{\\beta (- \\beta + 2 e^{\\xi})}{2}", "negatives": ["\\frac{\\beta (- \\beta + 2 \\xi)}{2}", "- \\beta \\xi + e^{\\xi}", "\\frac{\\beta^{2} \\log{(\\xi)}}{2}", "\\beta \\xi (\\log{(\\beta)} - 1)"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), exp(Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\xi', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True)), exp(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), log(Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True), Add(log(Symbol('\\\\beta', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\frac{\\cos{(\\alpha)}}{\\pi}", "variable": "\\pi", "positive": "\\log{(\\pi)} \\cos{(\\alpha)}", "negatives": ["\\cos{(\\alpha - \\pi)}", "- \\cos{(\\alpha - \\pi)}", "\\frac{\\sin{(\\alpha)}}{\\pi}", "\\frac{\\pi (\\pi + 2 \\cos{(\\alpha)})}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), cos(Symbol('\\\\alpha', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(log(Symbol('\\\\pi', commutative=True)), cos(Symbol('\\\\alpha', commutative=True)))", "srepr_negatives": ["cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))", "Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), sin(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), cos(Symbol('\\\\alpha', commutative=True)))))"]}, {"premise_expression": "\\omega - \\pi", "variable": "\\omega", "positive": "\\frac{\\omega (\\omega - 2 \\pi)}{2}", "negatives": ["\\frac{\\pi (2 \\omega - \\pi)}{2}", "\\frac{\\omega^{2} \\log{(\\pi)}}{2}", "e^{\\omega + \\pi}", "\\omega (\\log{(\\frac{\\pi}{\\omega})} + 1)"], "srepr_premise_expression": "Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), log(Symbol('\\\\pi', commutative=True)))", "exp(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), Add(log(Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))), Integer(1)))"]}, {"premise_expression": "\\log{(- \\delta + \\gamma)}", "variable": "\\delta", "positive": "\\delta \\log{(- \\delta + \\gamma)} - \\delta - \\gamma \\log{(\\delta - \\gamma)}", "negatives": ["- \\delta \\log{(- \\delta + \\gamma)} + \\gamma \\log{(- \\delta + \\gamma)} - \\gamma", "- \\cos{(\\delta - \\gamma)}", "- e^{- \\delta + \\gamma}", "e^{\\delta + \\gamma}"], "srepr_premise_expression": "log(Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\delta', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\gamma', commutative=True)))), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), log(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\gamma', commutative=True)))), Mul(Symbol('\\\\gamma', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\gamma', commutative=True)))), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\gamma', commutative=True))))", "exp(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\omega^{2} \\xi", "variable": "\\omega", "positive": "\\frac{\\omega^{3} \\xi}{3}", "negatives": ["\\frac{\\omega^{2} \\xi^{2}}{2}", "\\omega", "\\omega \\xi + \\sin{(\\omega)}", "\\cos{(\\omega - \\xi)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 3), Pow(Symbol('\\\\omega', commutative=True), Integer(3)), Symbol('\\\\xi', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Symbol('\\\\omega', commutative=True)", "Add(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True)), sin(Symbol('\\\\omega', commutative=True)))", "cos(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "e^{\\chi + \\xi}", "variable": "\\chi", "positive": "e^{\\chi + \\xi}", "negatives": ["e^{\\chi - \\xi}", "\\xi e^{\\frac{\\chi}{\\xi}}", "\\frac{\\chi (- \\chi + 2 \\xi)}{2}", "\\chi \\xi + e^{\\chi}"], "srepr_premise_expression": "exp(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "exp(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["exp(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Symbol('\\\\xi', commutative=True), exp(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True)), exp(Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "\\frac{e^{\\xi}}{\\alpha}", "variable": "\\alpha", "positive": "e^{\\xi} \\log{(\\alpha)}", "negatives": ["\\alpha \\xi - \\cos{(\\alpha)}", "- \\cos{(\\alpha + \\xi)}", "\\alpha \\xi + \\sin{(\\alpha)}", "\\alpha (\\xi + \\log{(\\alpha)} - 1)"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), exp(Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(exp(Symbol('\\\\xi', commutative=True)), log(Symbol('\\\\alpha', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\alpha', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True))))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True)), sin(Symbol('\\\\alpha', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\alpha', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\sin^{\\alpha}{(\\sigma)}", "variable": "\\sigma", "positive": "\\int \\sin^{\\alpha}{(\\sigma)} d\\sigma", "negatives": ["\\log{(\\sigma)} \\sin{(\\alpha)}", "\\log{(\\sigma)} \\cos{(\\alpha)}", "e^{\\alpha + \\sigma}", "\\frac{\\sigma (\\log{(\\sigma)} - 1)}{\\alpha}"], "srepr_premise_expression": "Pow(sin(Symbol('\\\\sigma', commutative=True)), Symbol('\\\\alpha', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Integral(Pow(sin(Symbol('\\\\sigma', commutative=True)), Symbol('\\\\alpha', commutative=True)), Tuple(Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(log(Symbol('\\\\sigma', commutative=True)), sin(Symbol('\\\\alpha', commutative=True)))", "Mul(log(Symbol('\\\\sigma', commutative=True)), cos(Symbol('\\\\alpha', commutative=True)))", "exp(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True)))", "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True), Add(log(Symbol('\\\\sigma', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\alpha + \\delta", "variable": "\\alpha", "positive": "\\frac{\\alpha (\\alpha + 2 \\delta)}{2}", "negatives": ["\\frac{\\alpha (\\alpha - 2 \\delta)}{2}", "\\frac{\\delta (2 \\alpha + \\delta)}{2}", "\\frac{\\alpha^{2} \\log{(\\delta)}}{2}", "\\sin{(\\alpha + \\delta)}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\delta', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\delta', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), log(Symbol('\\\\delta', commutative=True)))", "sin(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\frac{\\gamma}{\\alpha}", "variable": "\\alpha", "positive": "\\gamma \\log{(\\alpha)}", "negatives": ["\\frac{\\gamma^{2}}{2 \\alpha}", "\\frac{\\alpha^{2} \\gamma}{2}", "- \\alpha \\gamma + e^{\\alpha}", "- \\alpha \\gamma + \\sin{(\\alpha)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\gamma', commutative=True))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True)), exp(Symbol('\\\\alpha', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True)), sin(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\sigma + \\log{(\\beta)}", "variable": "\\beta", "positive": "\\beta (\\sigma + \\log{(\\beta)} - 1)", "negatives": ["\\frac{\\sigma (\\sigma + 2 \\log{(\\beta)})}{2}", "\\frac{\\beta^{2} \\log{(\\sigma)}}{2}", "\\frac{\\beta (\\beta + 2 \\cos{(\\sigma)})}{2}", "\\frac{\\beta (\\beta + 2 \\sin{(\\sigma)})}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\beta', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(2), log(Symbol('\\\\beta', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), log(Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), cos(Symbol('\\\\sigma', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), sin(Symbol('\\\\sigma', commutative=True)))))"]}, {"premise_expression": "\\log{(\\chi \\psi)}", "variable": "\\chi", "positive": "\\chi (\\log{(\\chi \\psi)} - 1)", "negatives": ["\\psi (\\log{(\\chi \\psi)} - 1)", "e^{\\chi - \\psi}", "\\sin{(\\chi + \\psi)}", "- \\chi \\psi - \\cos{(\\chi)}"], "srepr_premise_expression": "log(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\chi', commutative=True), Add(log(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\psi', commutative=True), Add(log(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True))), Integer(-1)))", "exp(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "sin(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\chi', commutative=True))))"]}, {"premise_expression": "- \\beta + \\chi", "variable": "\\beta", "positive": "\\frac{\\beta (- \\beta + 2 \\chi)}{2}", "negatives": ["\\frac{\\chi (- 2 \\beta + \\chi)}{2}", "\\frac{\\beta^{2} \\cos{(\\chi)}}{2}", "\\frac{\\beta^{2} \\sin{(\\chi)}}{2}", "\\chi^{2} \\log{(\\beta)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\chi', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\chi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), cos(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), sin(Symbol('\\\\chi', commutative=True)))", "Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(2)), log(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "\\alpha + \\omega", "variable": "\\omega", "positive": "\\frac{\\omega (2 \\alpha + \\omega)}{2}", "negatives": ["\\frac{\\omega (- 2 \\alpha + \\omega)}{2}", "\\frac{\\alpha (\\alpha + 2 \\omega)}{2}", "\\omega \\cos{(2 \\alpha)}", "\\frac{\\omega^{2} e^{\\alpha}}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Symbol('\\\\omega', commutative=True), cos(Mul(Integer(2), Symbol('\\\\alpha', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), exp(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\pi \\xi", "variable": "\\pi", "positive": "\\frac{\\pi^{2} \\xi}{2}", "negatives": ["\\frac{\\pi \\xi^{2}}{2}", "\\frac{\\pi^{2}}{2 \\xi}", "e^{\\pi + \\xi}", "e^{\\pi - \\xi}"], "srepr_premise_expression": "Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "exp(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True)))", "exp(Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\log{(\\chi^{\\alpha})}", "variable": "\\chi", "positive": "\\chi (- \\alpha + \\log{(\\chi^{\\alpha})})", "negatives": ["\\alpha \\chi + e^{\\chi}", "\\frac{\\chi (2 \\alpha - \\chi)}{2}", "- \\alpha \\chi - \\cos{(\\chi)}", "\\frac{\\alpha^{2} \\log{(\\chi)}}{2}"], "srepr_premise_expression": "log(Pow(Symbol('\\\\chi', commutative=True), Symbol('\\\\alpha', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), log(Pow(Symbol('\\\\chi', commutative=True), Symbol('\\\\alpha', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)), exp(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\chi', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\chi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), log(Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "\\psi + \\xi", "variable": "\\psi", "positive": "\\frac{\\psi (\\psi + 2 \\xi)}{2}", "negatives": ["\\frac{\\xi (2 \\psi + \\xi)}{2}", "\\frac{\\psi^{2} \\xi}{2}", "\\frac{\\psi^{2} \\log{(\\xi)}}{2}", "\\frac{\\psi (\\log{(\\psi)} - 1)}{\\xi}"], "srepr_premise_expression": "Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\psi', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), log(Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\psi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), Add(log(Symbol('\\\\psi', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\sin^{\\pi}{(\\delta)}", "variable": "\\delta", "positive": "\\int \\sin^{\\pi}{(\\delta)} d\\delta", "negatives": ["\\int \\cos^{\\pi}{(\\delta)} d\\delta", "- \\delta \\pi + \\sin{(\\delta)}", "e^{\\delta + \\pi}", "\\delta \\pi - \\cos{(\\delta)}"], "srepr_premise_expression": "Pow(sin(Symbol('\\\\delta', commutative=True)), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Integral(Pow(sin(Symbol('\\\\delta', commutative=True)), Symbol('\\\\pi', commutative=True)), Tuple(Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Integral(Pow(cos(Symbol('\\\\delta', commutative=True)), Symbol('\\\\pi', commutative=True)), Tuple(Symbol('\\\\delta', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True)), sin(Symbol('\\\\delta', commutative=True)))", "exp(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True)))", "Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\delta', commutative=True))))"]}, {"premise_expression": "\\beta \\sin{(\\omega)}", "variable": "\\beta", "positive": "\\frac{\\beta^{2} \\sin{(\\omega)}}{2}", "negatives": ["- \\beta \\cos{(\\omega)}", "e^{\\beta + \\omega}", "\\beta (\\log{(\\frac{\\beta}{\\omega})} - 1)", "\\frac{\\beta (\\log{(\\beta)} - 1)}{\\omega}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), sin(Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), sin(Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Symbol('\\\\beta', commutative=True), cos(Symbol('\\\\omega', commutative=True)))", "exp(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\beta', commutative=True), Add(log(Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))), Integer(-1)))", "Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Add(log(Symbol('\\\\beta', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\sigma + e^{\\xi}", "variable": "\\xi", "positive": "\\sigma \\xi + e^{\\xi}", "negatives": ["- \\sigma \\xi + e^{\\xi}", "\\frac{\\sigma (\\sigma + 2 e^{\\xi})}{2}", "e^{\\sigma + \\xi}", "- e^{\\sigma - \\xi}"], "srepr_premise_expression": "Add(Symbol('\\\\sigma', commutative=True), exp(Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True)), exp(Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True)), exp(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(2), exp(Symbol('\\\\xi', commutative=True)))))", "exp(Add(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True)))", "Mul(Integer(-1), exp(Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))))"]}, {"premise_expression": "\\frac{\\beta}{\\delta}", "variable": "\\delta", "positive": "\\beta \\log{(\\delta)}", "negatives": ["\\frac{\\beta^{2}}{2 \\delta}", "- \\cos{(\\beta + \\delta)}", "\\cos{(\\beta - \\delta)}", "\\delta + \\frac{\\delta^{2}}{2 \\beta}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\beta', commutative=True), log(Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True))))", "cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))", "Add(Symbol('\\\\delta', commutative=True), Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Pow(Symbol('\\\\delta', commutative=True), Integer(2))))"]}, {"premise_expression": "\\frac{\\chi}{\\xi}", "variable": "\\chi", "positive": "\\frac{\\chi^{2}}{2 \\xi}", "negatives": ["\\chi \\log{(\\xi)}", "- \\cos{(\\chi + \\xi)}", "\\chi \\xi + \\sin{(\\chi)}", "\\chi (\\log{(\\frac{\\chi}{\\xi})} - 1)"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\xi', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True))))", "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True)), sin(Symbol('\\\\chi', commutative=True)))", "Mul(Symbol('\\\\chi', commutative=True), Add(log(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))), Integer(-1)))"]}, {"premise_expression": "\\gamma \\omega", "variable": "\\gamma", "positive": "\\frac{\\gamma^{2} \\omega}{2}", "negatives": ["\\frac{\\gamma \\omega^{2}}{2}", "\\frac{\\gamma (- \\gamma + 2 \\omega)}{2}", "\\sin{(\\gamma + \\omega)}", "\\frac{\\gamma (\\gamma - 2 \\omega)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Symbol('\\\\omega', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "sin(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True))))"]}, {"premise_expression": "\\cos{(\\delta - \\pi)}", "variable": "\\pi", "positive": "- \\sin{(\\delta - \\pi)}", "negatives": ["\\sin{(\\delta - \\pi)}", "\\cos{(\\delta - \\pi)}", "\\frac{\\sin{(\\pi)}}{\\delta}", "\\frac{\\delta \\pi (\\pi - 2)}{2}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Integer(-1), sin(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))", "srepr_negatives": ["sin(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), sin(Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Integer(-2)))"]}, {"premise_expression": "\\delta + \\cos{(\\gamma)}", "variable": "\\delta", "positive": "\\frac{\\delta (\\delta + 2 \\cos{(\\gamma)})}{2}", "negatives": ["\\delta \\gamma + \\sin{(\\gamma)}", "\\frac{\\delta (\\delta + 2 \\gamma)}{2}", "\\frac{\\delta (\\delta - 2 \\gamma)}{2}", "\\frac{\\delta^{2} \\gamma}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\delta', commutative=True), cos(Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), cos(Symbol('\\\\gamma', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\gamma', commutative=True)), sin(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Symbol('\\\\gamma', commutative=True))"]}, {"premise_expression": "\\alpha - \\chi + \\omega", "variable": "\\omega", "positive": "\\omega (\\alpha - \\chi + \\frac{\\omega}{2})", "negatives": ["\\frac{\\omega (2 \\alpha + 2 \\chi + \\omega)}{2}", "\\frac{\\omega (2 \\alpha + 2 \\chi - \\omega)}{2}", "\\frac{\\alpha (\\alpha - 2 \\chi + 2 \\omega)}{2}", "\\frac{\\chi (2 \\alpha - \\chi + 2 \\omega)}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))"]}, {"premise_expression": "\\alpha - \\chi + \\sigma", "variable": "\\chi", "positive": "\\chi (\\alpha - \\frac{\\chi}{2} + \\sigma)", "negatives": ["\\frac{\\chi (- 2 \\alpha + \\chi + 2 \\sigma)}{2}", "\\frac{\\sigma (2 \\alpha - 2 \\chi + \\sigma)}{2}", "\\frac{\\alpha (\\alpha - 2 \\chi + 2 \\sigma)}{2}", "\\frac{\\chi (2 \\alpha^{\\sigma} - \\chi)}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Rational(1, 2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(2), Pow(Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True))), Mul(Integer(-1), Symbol('\\\\chi', commutative=True))))"]}, {"premise_expression": "\\alpha \\chi", "variable": "\\chi", "positive": "\\frac{\\alpha \\chi^{2}}{2}", "negatives": ["\\frac{\\alpha^{2} \\chi}{2}", "\\frac{\\chi^{2} \\sin{(\\alpha)}}{2}", "\\frac{\\chi (2 \\alpha + \\chi)}{2}", "\\alpha \\log{(\\chi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\chi', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), sin(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\chi', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "\\sin{(\\omega + \\sigma)}", "variable": "\\sigma", "positive": "- \\cos{(\\omega + \\sigma)}", "negatives": ["e^{\\omega + \\sigma}", "- \\omega \\cos{(\\sigma)}", "\\omega \\log{(\\sigma)}", "\\sigma (\\log{(\\frac{\\sigma}{\\omega})} - 1)"], "srepr_premise_expression": "sin(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["exp(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True)))", "Mul(Integer(-1), Symbol('\\\\omega', commutative=True), cos(Symbol('\\\\sigma', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\sigma', commutative=True)))", "Mul(Symbol('\\\\sigma', commutative=True), Add(log(Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\frac{\\cos{(\\delta)}}{\\sigma}", "variable": "\\sigma", "positive": "\\log{(\\sigma)} \\cos{(\\delta)}", "negatives": ["\\delta \\sigma - \\cos{(\\sigma)}", "\\frac{\\sin{(\\sigma)}}{\\delta}", "\\frac{\\sin{(\\delta)}}{\\sigma}", "e^{\\delta + \\sigma}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), cos(Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(log(Symbol('\\\\sigma', commutative=True)), cos(Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\sigma', commutative=True))))", "Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), sin(Symbol('\\\\sigma', commutative=True)))", "Mul(Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), sin(Symbol('\\\\delta', commutative=True)))", "exp(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\log{(\\sigma^{\\chi})}", "variable": "\\chi", "positive": "\\frac{\\chi^{2} \\log{(\\sigma)}}{2}", "negatives": ["\\frac{\\chi (\\chi + 2 \\sigma)}{2}", "\\sigma \\log{(\\chi)}", "\\frac{\\chi (- \\chi + 2 \\sin{(\\sigma)})}{2}", "\\chi (\\sigma + \\log{(\\chi)} - 1)"], "srepr_premise_expression": "log(Pow(Symbol('\\\\sigma', commutative=True), Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), log(Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\sigma', commutative=True)))))", "Mul(Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\chi', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\frac{\\alpha}{\\xi}", "variable": "\\xi", "positive": "\\alpha \\log{(\\xi)}", "negatives": ["\\alpha \\log{(\\xi)} + \\xi", "\\frac{\\alpha^{2}}{2 \\xi}", "- \\frac{\\cos{(\\xi)}}{\\alpha}", "\\alpha \\xi + e^{\\xi}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\xi', commutative=True))), Symbol('\\\\xi', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "Mul(Integer(-1), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), cos(Symbol('\\\\xi', commutative=True)))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True)), exp(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\omega + \\xi", "variable": "\\xi", "positive": "\\frac{\\xi (2 \\omega + \\xi)}{2}", "negatives": ["\\frac{\\omega (\\omega + 2 \\xi)}{2}", "e^{- \\omega + \\xi}", "\\cos{(\\omega - \\xi)}", "\\omega \\xi - \\cos{(\\xi)}"], "srepr_premise_expression": "Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "exp(Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Symbol('\\\\xi', commutative=True)))", "cos(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Add(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\cos{(\\frac{\\pi}{\\omega})}", "variable": "\\omega", "positive": "\\omega \\cos{(\\frac{\\pi}{\\omega})} + \\pi \\operatorname{Si}{(\\frac{\\pi}{\\omega})}", "negatives": ["\\omega e^{\\frac{\\pi}{\\omega}} - \\pi \\operatorname{Ei}{(\\frac{\\pi}{\\omega})}", "\\frac{\\omega (\\omega + 2 \\pi)}{2}", "\\frac{\\omega (- \\omega + 2 e^{\\pi})}{2}", "\\frac{\\omega (\\omega - 2 \\pi)}{2}"], "srepr_premise_expression": "cos(Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\omega', commutative=True), cos(Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True)))), Mul(Symbol('\\\\pi', commutative=True), Si(Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\omega', commutative=True), exp(Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\pi', commutative=True), Ei(Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\pi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "- \\omega + \\frac{\\pi}{\\psi}", "variable": "\\omega", "positive": "- \\frac{\\omega^{2}}{2} + \\frac{\\omega \\pi}{\\psi}", "negatives": ["\\frac{\\omega \\psi (- \\omega + 2 \\pi)}{2}", "\\frac{\\omega^{2} (\\pi + \\psi)}{2}", "\\frac{\\omega^{2}}{2 \\psi} - \\omega \\pi", "- \\omega \\pi + \\frac{\\pi^{2}}{2 \\psi}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2))), Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)))", "Add(Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Pow(Symbol('\\\\psi', commutative=True), Integer(-1))), Mul(Integer(-1), Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), Pow(Symbol('\\\\psi', commutative=True), Integer(-1))))"]}, {"premise_expression": "- \\psi + \\sigma \\xi", "variable": "\\sigma", "positive": "\\frac{\\sigma (- 2 \\psi + \\sigma \\xi)}{2}", "negatives": ["\\frac{\\xi (- 2 \\psi + \\sigma \\xi)}{2}", "\\frac{\\sigma (\\psi \\sigma + 2 \\xi)}{2}", "\\frac{\\psi (- \\psi + 2 \\sigma \\xi)}{2}", "\\frac{\\sigma^{2} (\\psi + \\xi)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True)), Mul(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True)), Mul(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\xi e^{\\sigma}", "variable": "\\sigma", "positive": "\\xi e^{\\sigma}", "negatives": ["- \\xi \\cos{(\\sigma)}", "\\frac{\\xi^{2} e^{\\sigma}}{2}", "- \\sigma \\xi - \\cos{(\\sigma)}", "\\frac{\\sigma (\\sigma - 2 \\xi)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\xi', commutative=True), exp(Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\xi', commutative=True), exp(Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Symbol('\\\\xi', commutative=True), cos(Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), exp(Symbol('\\\\sigma', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\frac{\\alpha}{\\chi} - \\delta", "variable": "\\alpha", "positive": "\\frac{\\alpha^{2}}{2 \\chi} - \\alpha \\delta", "negatives": ["\\alpha \\log{(\\chi)} - \\chi \\delta", "\\frac{\\alpha^{2} \\delta}{2 \\chi}", "- \\alpha \\chi + \\delta \\log{(\\alpha)}", "\\frac{\\alpha \\delta}{\\chi} - \\frac{\\delta^{2}}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(-1))), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Add(Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\chi', commutative=True), Integer(-1))), Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\chi', commutative=True))), Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)), Mul(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\alpha', commutative=True))))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2))))"]}, {"premise_expression": "\\beta - \\pi + \\psi", "variable": "\\psi", "positive": "\\psi (\\beta - \\pi + \\frac{\\psi}{2})", "negatives": ["\\frac{\\psi (2 \\beta + 2 \\pi + \\psi)}{2}", "\\frac{\\pi (2 \\beta - \\pi + 2 \\psi)}{2}", "\\frac{\\beta (\\beta - 2 \\pi + 2 \\psi)}{2}", "\\frac{\\psi (\\beta \\psi - 2 \\pi)}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\frac{\\gamma}{\\chi}", "variable": "\\chi", "positive": "\\gamma \\log{(\\chi)}", "negatives": ["\\frac{\\gamma^{2}}{2 \\chi}", "- \\frac{\\cos{(\\chi)}}{\\gamma}", "- \\cos{(\\chi - \\gamma)}", "\\chi (\\log{(\\frac{\\chi}{\\gamma})} - 1)"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)))", "Mul(Integer(-1), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), cos(Symbol('\\\\chi', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))))", "Mul(Symbol('\\\\chi', commutative=True), Add(log(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)))), Integer(-1)))"]}, {"premise_expression": "- \\alpha + \\psi", "variable": "\\alpha", "positive": "\\frac{\\alpha (- \\alpha + 2 \\psi)}{2}", "negatives": ["\\frac{\\alpha (\\alpha + 2 \\psi)}{2}", "\\frac{\\psi (- 2 \\alpha + \\psi)}{2}", "- \\cos{(\\alpha - \\psi)}", "\\frac{\\alpha^{2}}{2 \\psi}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))"]}, {"premise_expression": "\\alpha - \\xi", "variable": "\\xi", "positive": "\\frac{\\xi (2 \\alpha - \\xi)}{2}", "negatives": ["\\frac{\\alpha (\\alpha - 2 \\xi)}{2}", "\\frac{\\xi^{2} e^{\\alpha}}{2}", "\\frac{\\xi (\\xi + 2 \\log{(\\alpha)})}{2}", "\\log{(\\alpha)} \\log{(\\xi)}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), exp(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\xi', commutative=True), Mul(Integer(2), log(Symbol('\\\\alpha', commutative=True)))))", "Mul(log(Symbol('\\\\alpha', commutative=True)), log(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\frac{\\sin{(\\xi)}}{\\gamma}", "variable": "\\gamma", "positive": "\\log{(\\gamma)} \\sin{(\\xi)}", "negatives": ["- \\frac{\\cos{(\\xi)}}{\\gamma}", "- \\cos{(\\gamma - \\xi)}", "\\sin{(\\gamma + \\xi)}", "\\frac{\\gamma^{2} \\log{(\\xi)}}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), sin(Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(log(Symbol('\\\\gamma', commutative=True)), sin(Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), cos(Symbol('\\\\xi', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))))", "sin(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), log(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\beta + \\chi", "variable": "\\chi", "positive": "\\frac{\\chi (2 \\beta + \\chi)}{2}", "negatives": ["\\frac{\\beta (\\beta + 2 \\chi)}{2}", "\\frac{\\chi^{2} e^{\\beta}}{2}", "e^{\\beta + \\chi}", "\\cos{(\\beta - \\chi)}"], "srepr_premise_expression": "Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\chi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), exp(Symbol('\\\\beta', commutative=True)))", "exp(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True)))", "cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True))))"]}, {"premise_expression": "\\frac{\\alpha}{\\beta}", "variable": "\\alpha", "positive": "\\frac{\\alpha^{2}}{2 \\beta}", "negatives": ["\\alpha \\log{(\\beta)}", "\\frac{\\alpha^{2} \\log{(\\beta)}}{2}", "\\frac{\\alpha (\\alpha - 2 \\beta)}{2}", "\\alpha (\\log{(\\frac{\\alpha}{\\beta})} - 1)"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), log(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True))))", "Mul(Symbol('\\\\alpha', commutative=True), Add(log(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)))), Integer(-1)))"]}, {"premise_expression": "- \\beta + \\gamma + \\pi", "variable": "\\gamma", "positive": "\\gamma (- \\beta + \\frac{\\gamma}{2} + \\pi)", "negatives": ["\\frac{\\gamma (2 \\beta - \\gamma - 2 \\pi)}{2}", "\\frac{\\pi (- 2 \\beta + 2 \\gamma + \\pi)}{2}", "\\frac{\\beta (- \\beta + 2 \\gamma + 2 \\pi)}{2}", "\\frac{\\gamma (- 2 \\beta - \\gamma + 2 \\pi)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\gamma + e^{\\pi}", "variable": "\\pi", "positive": "\\gamma \\pi + e^{\\pi}", "negatives": ["\\frac{\\gamma (\\gamma + 2 e^{\\pi})}{2}", "\\frac{\\gamma \\pi^{2}}{2}", "\\frac{\\pi^{2}}{2 \\gamma}", "\\frac{\\pi (- 2 \\gamma + \\pi)}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\gamma', commutative=True), exp(Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True)), exp(Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), exp(Symbol('\\\\pi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\chi - \\gamma", "variable": "\\gamma", "positive": "\\frac{\\gamma (2 \\chi - \\gamma)}{2}", "negatives": ["\\frac{\\chi (\\chi - 2 \\gamma)}{2}", "\\frac{\\gamma^{2} \\cos{(\\chi)}}{2}", "- \\sin{(\\chi - \\gamma)}", "e^{- \\chi + \\gamma}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), cos(Symbol('\\\\chi', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))))", "exp(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "- \\omega + \\sin{(\\beta)}", "variable": "\\beta", "positive": "- \\beta \\omega - \\cos{(\\beta)}", "negatives": ["\\omega \\log{(\\beta)}", "\\frac{\\beta^{2} \\log{(\\omega)}}{2}", "\\frac{\\omega (- \\omega + 2 \\sin{(\\beta)})}{2}", "\\beta (\\omega + \\log{(\\beta)} - 1)"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), sin(Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\beta', commutative=True))))", "srepr_negatives": ["Mul(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), log(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\beta', commutative=True)))))", "Mul(Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\beta', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\beta \\psi", "variable": "\\beta", "positive": "\\frac{\\beta^{2} \\psi}{2}", "negatives": ["\\frac{\\beta \\psi^{2}}{2}", "\\beta \\psi^{\\psi}", "\\beta e^{\\psi^{\\psi}}", "e^{\\beta - \\psi}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Symbol('\\\\psi', commutative=True)))", "Mul(Symbol('\\\\beta', commutative=True), exp(Pow(Symbol('\\\\psi', commutative=True), Symbol('\\\\psi', commutative=True))))", "exp(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "\\pi + \\sin{(\\beta)}", "variable": "\\beta", "positive": "\\beta \\pi - \\cos{(\\beta)}", "negatives": ["\\beta \\pi + e^{\\beta}", "- \\beta \\pi + \\sin{(\\beta)}", "\\frac{\\beta^{2} \\cos{(\\pi)}}{2}", "\\log{(\\beta)} \\cos{(\\pi)}"], "srepr_premise_expression": "Add(Symbol('\\\\pi', commutative=True), sin(Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\beta', commutative=True))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\pi', commutative=True)), exp(Symbol('\\\\beta', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\pi', commutative=True)), sin(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), cos(Symbol('\\\\pi', commutative=True)))", "Mul(log(Symbol('\\\\beta', commutative=True)), cos(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\omega + e^{\\sigma}", "variable": "\\sigma", "positive": "\\omega \\sigma + e^{\\sigma}", "negatives": ["\\frac{\\omega (\\omega + 2 e^{\\sigma})}{2}", "\\omega \\log{(\\sigma)}", "\\cos{(\\omega - \\sigma)}", "\\frac{\\sigma (\\sigma + 2 \\cos{(\\omega)})}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\omega', commutative=True), exp(Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True)), exp(Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), exp(Symbol('\\\\sigma', commutative=True)))))", "Mul(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\sigma', commutative=True)))", "cos(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(2), cos(Symbol('\\\\omega', commutative=True)))))"]}, {"premise_expression": "\\frac{\\psi}{\\chi}", "variable": "\\chi", "positive": "\\psi \\log{(\\chi)}", "negatives": ["\\frac{\\psi^{2}}{2 \\chi}", "\\frac{\\chi^{3} \\psi}{3}", "\\chi \\psi - \\cos{(\\chi)}", "- \\chi \\psi - \\cos{(\\chi)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\psi', commutative=True), log(Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "Mul(Rational(1, 3), Pow(Symbol('\\\\chi', commutative=True), Integer(3)), Symbol('\\\\psi', commutative=True))", "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\chi', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\chi', commutative=True))))"]}, {"premise_expression": "\\frac{\\sigma}{\\alpha}", "variable": "\\sigma", "positive": "\\frac{\\sigma^{2}}{2 \\alpha}", "negatives": ["\\sigma \\log{(\\alpha)}", "\\alpha e^{\\frac{\\sigma}{\\alpha}}", "\\frac{\\sigma (2 \\alpha - \\sigma)}{2}", "\\log{(\\sigma)} \\sin{(\\alpha)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), exp(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(log(Symbol('\\\\sigma', commutative=True)), sin(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "e^{\\alpha + \\delta}", "variable": "\\delta", "positive": "e^{\\alpha + \\delta}", "negatives": ["\\alpha e^{\\delta}", "\\alpha \\delta + \\sin{(\\delta)}", "- \\alpha \\delta + e^{\\delta}", "\\log{(\\delta)} \\cos{(\\alpha)}"], "srepr_premise_expression": "exp(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "exp(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\alpha', commutative=True), exp(Symbol('\\\\delta', commutative=True)))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\delta', commutative=True)), sin(Symbol('\\\\delta', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\delta', commutative=True)), exp(Symbol('\\\\delta', commutative=True)))", "Mul(log(Symbol('\\\\delta', commutative=True)), cos(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\chi \\log{(\\gamma)}", "variable": "\\chi", "positive": "\\frac{\\chi^{2} \\log{(\\gamma)}}{2}", "negatives": ["\\frac{\\chi (\\chi + 2 \\log{(\\gamma)})}{2}", "\\frac{\\chi^{2}}{2 \\gamma}", "\\chi \\gamma (\\log{(\\gamma)} - 1)", "\\frac{\\chi (- \\chi + 2 \\gamma)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), log(Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), log(Symbol('\\\\gamma', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)))", "Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True), Add(log(Symbol('\\\\gamma', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\gamma', commutative=True))))"]}, {"premise_expression": "- \\pi + \\frac{\\xi}{\\gamma}", "variable": "\\gamma", "positive": "- \\gamma \\pi + \\xi \\log{(\\gamma)}", "negatives": ["\\pi \\xi \\log{(\\gamma)}", "- \\pi \\xi + \\frac{\\xi^{2}}{2 \\gamma}", "\\frac{\\xi \\log{(\\gamma)}}{\\pi}", "- \\frac{\\pi^{2}}{2} + \\frac{\\pi \\xi}{\\gamma}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\gamma', commutative=True))))", "srepr_negatives": ["Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Integer(2))))", "Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "Add(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2))), Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\frac{\\xi}{\\psi}", "variable": "\\xi", "positive": "\\frac{\\xi^{2}}{2 \\psi}", "negatives": ["\\xi \\log{(\\psi)}", "\\psi e^{\\xi}", "\\frac{\\xi (- 2 \\psi + \\xi)}{2}", "\\log{(\\xi)} \\sin{(\\psi)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\psi', commutative=True)))", "Mul(Symbol('\\\\psi', commutative=True), exp(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(log(Symbol('\\\\xi', commutative=True)), sin(Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\frac{\\alpha}{\\pi}", "variable": "\\alpha", "positive": "\\frac{\\alpha^{2}}{2 \\pi}", "negatives": ["\\alpha \\log{(\\pi)}", "\\frac{\\alpha^{2} \\pi}{2}", "\\frac{\\alpha^{2} \\log{(\\pi)}}{2}", "e^{\\alpha - \\pi}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\pi', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), log(Symbol('\\\\pi', commutative=True)))", "exp(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\gamma + e^{\\alpha}", "variable": "\\alpha", "positive": "\\alpha \\gamma + e^{\\alpha}", "negatives": ["- \\alpha \\gamma + e^{\\alpha}", "\\alpha \\gamma + \\sin{(\\alpha)}", "\\gamma e^{\\frac{\\alpha}{\\gamma}}", "\\frac{\\gamma (\\gamma + 2 e^{\\alpha})}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\gamma', commutative=True), exp(Symbol('\\\\alpha', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True)), exp(Symbol('\\\\alpha', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True)), exp(Symbol('\\\\alpha', commutative=True)))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True)), sin(Symbol('\\\\alpha', commutative=True)))", "Mul(Symbol('\\\\gamma', commutative=True), exp(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), exp(Symbol('\\\\alpha', commutative=True)))))"]}, {"premise_expression": "- \\psi + e^{\\gamma}", "variable": "\\psi", "positive": "\\frac{\\psi (- \\psi + 2 e^{\\gamma})}{2}", "negatives": ["\\frac{\\psi (- \\psi + 2 \\sin{(\\gamma)})}{2}", "- \\gamma \\psi + e^{\\gamma}", "\\gamma \\psi + e^{\\psi}", "\\frac{\\psi e^{\\gamma}}{\\gamma}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), exp(Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\gamma', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\gamma', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True)), exp(Symbol('\\\\gamma', commutative=True)))", "Add(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True)), exp(Symbol('\\\\psi', commutative=True)))", "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True), exp(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\gamma \\log{(\\chi)}", "variable": "\\chi", "positive": "\\chi \\gamma (\\log{(\\chi)} - 1)", "negatives": ["\\chi (\\log{(\\frac{\\chi}{\\gamma})} - 1)", "\\frac{\\gamma^{2} \\log{(\\chi)}}{2}", "\\log{(\\chi)} \\sin{(\\gamma)}", "- \\frac{\\cos{(\\chi)}}{\\gamma}"], "srepr_premise_expression": "Mul(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True), Add(log(Symbol('\\\\chi', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\chi', commutative=True), Add(log(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)))), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), log(Symbol('\\\\chi', commutative=True)))", "Mul(log(Symbol('\\\\chi', commutative=True)), sin(Symbol('\\\\gamma', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), cos(Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "\\log{(\\delta \\pi)}", "variable": "\\pi", "positive": "\\pi (\\log{(\\delta \\pi)} - 1)", "negatives": ["\\delta (\\log{(\\delta \\pi)} - 1)", "\\log{(\\delta)} \\log{(\\pi)}", "\\log{(\\pi)} \\cos{(\\delta)}", "e^{\\delta + \\pi}"], "srepr_premise_expression": "log(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\pi', commutative=True), Add(log(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\delta', commutative=True), Add(log(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True))), Integer(-1)))", "Mul(log(Symbol('\\\\delta', commutative=True)), log(Symbol('\\\\pi', commutative=True)))", "Mul(log(Symbol('\\\\pi', commutative=True)), cos(Symbol('\\\\delta', commutative=True)))", "exp(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\log{(\\omega^{\\psi})}", "variable": "\\omega", "positive": "\\omega (- \\psi + \\log{(\\omega^{\\psi})})", "negatives": ["\\frac{\\omega (- \\omega + 2 \\sin{(\\psi)})}{2}", "e^{\\omega - \\psi}", "\\frac{\\psi^{2} \\log{(\\omega)}}{2}", "- \\omega \\psi - \\cos{(\\omega)}"], "srepr_premise_expression": "log(Pow(Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), log(Pow(Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\psi', commutative=True)))))", "exp(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), log(Symbol('\\\\omega', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\omega', commutative=True))))"]}, {"premise_expression": "\\log{(\\alpha \\xi)}", "variable": "\\xi", "positive": "\\xi (\\log{(\\alpha \\xi)} - 1)", "negatives": ["\\alpha (\\log{(\\alpha \\xi)} - 1)", "- \\cos{(\\alpha - \\xi)}", "- \\cos{(\\alpha + \\xi)}", "\\frac{\\xi (- 2 \\alpha + \\xi)}{2}"], "srepr_premise_expression": "log(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\xi', commutative=True), Add(log(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\alpha', commutative=True), Add(log(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True))), Integer(-1)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\alpha - \\gamma - \\psi", "variable": "\\gamma", "positive": "\\gamma (\\alpha - \\frac{\\gamma}{2} - \\psi)", "negatives": ["\\frac{\\psi (2 \\alpha - 2 \\gamma - \\psi)}{2}", "\\frac{\\alpha (\\alpha - 2 \\gamma - 2 \\psi)}{2}", "\\gamma (1 - \\alpha)", "\\frac{\\gamma (2 \\alpha \\psi - \\gamma)}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Rational(1, 2), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Symbol('\\\\gamma', commutative=True), Add(Integer(1), Mul(Integer(-1), Symbol('\\\\alpha', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))"]}, {"premise_expression": "\\frac{\\sigma}{\\beta}", "variable": "\\beta", "positive": "\\sigma \\log{(\\beta)}", "negatives": ["\\frac{\\sigma^{2}}{2 \\beta}", "\\frac{\\beta^{2} \\sigma}{2}", "\\frac{\\beta^{2}}{2 \\sigma}", "- \\cos{(\\beta + \\sigma)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\beta', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\sigma', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "e^{\\alpha^{\\pi}}", "variable": "\\alpha", "positive": "\\frac{e^{- \\frac{i \\pi}{\\pi}} \\gamma(\\frac{1}{\\pi}, \\alpha^{\\pi} e^{i \\pi})}{\\pi}", "negatives": ["\\alpha (\\log{(\\frac{\\alpha}{\\pi})} - 1)", "\\frac{\\alpha (- \\alpha + 2 \\cos{(\\pi)})}{2}", "\\frac{\\alpha (\\alpha - 4 \\pi)}{2}", "e^{\\alpha - \\pi}"], "srepr_premise_expression": "exp(Pow(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), exp(Mul(Integer(-1), I, pi, Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))), lowergamma(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Mul(Pow(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)), exp_polar(Mul(I, pi)))))", "srepr_negatives": ["Mul(Symbol('\\\\alpha', commutative=True), Add(log(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\pi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Integer(4), Symbol('\\\\pi', commutative=True))))", "exp(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\alpha + \\log{(\\psi)}", "variable": "\\alpha", "positive": "\\frac{\\alpha (\\alpha + 2 \\log{(\\psi)})}{2}", "negatives": ["\\frac{\\alpha (\\alpha + 2 e^{\\psi})}{2}", "\\psi (\\alpha + \\log{(\\psi)} - 1)", "\\frac{\\alpha (\\alpha - 2 \\psi)}{2}", "\\frac{\\alpha (- \\alpha + 2 \\psi)}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), log(Symbol('\\\\psi', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), exp(Symbol('\\\\psi', commutative=True)))))", "Mul(Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\psi', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "\\chi + \\omega", "variable": "\\chi", "positive": "\\frac{\\chi (\\chi + 2 \\omega)}{2}", "negatives": ["\\frac{\\omega (2 \\chi + \\omega)}{2}", "e^{\\chi + \\omega}", "\\frac{\\chi^{2} \\omega}{2}", "\\frac{\\chi (\\chi + 2 \\sin{(\\omega)})}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\omega', commutative=True)))", "exp(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\omega', commutative=True))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), sin(Symbol('\\\\omega', commutative=True)))))"]}, {"premise_expression": "\\frac{\\cos{(\\sigma)}}{\\alpha}", "variable": "\\alpha", "positive": "\\log{(\\alpha)} \\cos{(\\sigma)}", "negatives": ["\\frac{\\sin{(\\sigma)}}{\\alpha}", "e^{\\alpha - \\sigma}", "- \\alpha \\sigma + e^{\\alpha}", "e^{\\alpha + \\sigma}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), cos(Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(log(Symbol('\\\\alpha', commutative=True)), cos(Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), sin(Symbol('\\\\sigma', commutative=True)))", "exp(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True)), exp(Symbol('\\\\alpha', commutative=True)))", "exp(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\frac{\\omega}{\\pi}", "variable": "\\omega", "positive": "\\frac{\\omega^{2}}{2 \\pi}", "negatives": ["\\omega \\log{(\\pi)}", "\\omega (\\omega + \\pi)", "\\frac{\\omega^{2} \\log{(\\pi)}}{2}", "\\omega (\\log{(\\frac{\\omega}{\\pi})} - 1)"], "srepr_premise_expression": "Mul(Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), log(Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), Add(log(Mul(Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))), Integer(-1)))"]}, {"premise_expression": "- \\xi + e^{\\gamma}", "variable": "\\xi", "positive": "\\frac{\\xi (- \\xi + 2 e^{\\gamma})}{2}", "negatives": ["- \\gamma \\xi + e^{\\gamma}", "\\frac{\\xi^{2}}{2 \\gamma}", "\\xi e^{2 \\gamma}", "\\gamma \\xi - \\cos{(\\xi)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), exp(Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\gamma', commutative=True)))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)), exp(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Mul(Symbol('\\\\xi', commutative=True), exp(Mul(Integer(2), Symbol('\\\\gamma', commutative=True))))", "Add(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\chi - \\pi", "variable": "\\pi", "positive": "\\frac{\\pi (2 \\chi - \\pi)}{2}", "negatives": ["\\frac{\\pi (2 \\chi + \\pi)}{2}", "\\frac{\\chi (\\chi - 2 \\pi)}{2}", "\\frac{\\pi^{2} \\sin{(\\chi)}}{2}", "- \\cos{(\\chi + \\pi)}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), sin(Symbol('\\\\chi', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\frac{\\log{(\\chi)}}{\\pi}", "variable": "\\pi", "positive": "\\log{(\\chi)} \\log{(\\pi)}", "negatives": ["e^{\\chi + \\pi}", "\\frac{\\pi (\\log{(\\pi)} - 1)}{\\chi}", "\\chi e^{\\frac{\\pi}{\\chi}}", "\\frac{\\chi (\\log{(\\chi)} - 1)}{\\pi}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), log(Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(log(Symbol('\\\\chi', commutative=True)), log(Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["exp(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True)))", "Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True), Add(log(Symbol('\\\\pi', commutative=True)), Integer(-1)))", "Mul(Symbol('\\\\chi', commutative=True), exp(Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))))", "Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Add(log(Symbol('\\\\chi', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\chi + \\frac{\\omega}{\\sigma}", "variable": "\\sigma", "positive": "\\chi \\sigma + \\omega \\log{(\\sigma)}", "negatives": ["\\chi \\log{(\\sigma)} - \\omega \\sigma", "\\chi \\omega + \\frac{\\omega^{2}}{2 \\sigma}", "\\frac{\\sigma (2 \\omega + \\sigma)}{2 \\chi}", "\\frac{\\chi^{2}}{2} + \\frac{\\chi \\omega}{\\sigma}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), Mul(Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\sigma', commutative=True))), Mul(Integer(-1), Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True)))", "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Add(Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2))), Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1))))"]}, {"premise_expression": "\\log{(\\omega^{\\alpha})}", "variable": "\\alpha", "positive": "\\frac{\\alpha^{2} \\log{(\\omega)}}{2}", "negatives": ["\\frac{\\alpha (- \\alpha + 2 \\log{(\\omega)})}{2}", "\\frac{\\sin{(2 \\alpha)}}{2}", "\\omega e^{\\alpha}", "\\omega (- \\alpha + \\log{(\\omega^{\\alpha})})"], "srepr_premise_expression": "log(Pow(Symbol('\\\\omega', commutative=True), Symbol('\\\\alpha', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), log(Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), log(Symbol('\\\\omega', commutative=True)))))", "Mul(Rational(1, 2), sin(Mul(Integer(2), Symbol('\\\\alpha', commutative=True))))", "Mul(Symbol('\\\\omega', commutative=True), exp(Symbol('\\\\alpha', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), log(Pow(Symbol('\\\\omega', commutative=True), Symbol('\\\\alpha', commutative=True)))))"]}, {"premise_expression": "\\frac{\\sin{(\\delta)}}{\\beta}", "variable": "\\beta", "positive": "\\log{(\\beta)} \\sin{(\\delta)}", "negatives": ["- \\frac{\\cos{(\\delta)}}{\\beta}", "\\frac{\\beta (- \\beta + 2 \\delta)}{2}", "- \\beta \\delta - \\cos{(\\beta)}", "\\frac{\\beta (- \\beta + 2 \\log{(\\delta)})}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), sin(Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(log(Symbol('\\\\beta', commutative=True)), sin(Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), cos(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\delta', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\beta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), log(Symbol('\\\\delta', commutative=True)))))"]}, {"premise_expression": "- \\gamma + \\omega", "variable": "\\gamma", "positive": "\\frac{\\gamma (- \\gamma + 2 \\omega)}{2}", "negatives": ["\\frac{\\gamma (\\gamma + 2 \\omega)}{2}", "\\frac{\\omega (- 2 \\gamma + \\omega)}{2}", "- e^{- \\gamma + \\omega}", "\\frac{\\gamma^{2} \\cos{(\\omega)}}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), cos(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\log{(\\alpha + \\delta)}", "variable": "\\alpha", "positive": "\\alpha \\log{(\\alpha + \\delta)} - \\alpha + \\delta \\log{(\\alpha + \\delta)}", "negatives": ["\\alpha \\log{(\\alpha + \\delta)} + \\delta \\log{(\\alpha + \\delta)} - \\delta", "\\alpha (- \\delta + \\log{(\\alpha)} - 1)", "\\alpha (\\delta + \\log{(\\alpha)} - 1)", "\\frac{\\alpha (- \\alpha + 2 \\delta)}{2}"], "srepr_premise_expression": "log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\alpha', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\delta', commutative=True)))), Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Symbol('\\\\delta', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\delta', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\alpha', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\delta', commutative=True)))), Mul(Symbol('\\\\delta', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\delta', commutative=True)))), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), log(Symbol('\\\\alpha', commutative=True)), Integer(-1)))", "Mul(Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\alpha', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\delta', commutative=True))))"]}, {"premise_expression": "\\frac{\\beta}{\\alpha}", "variable": "\\alpha", "positive": "\\beta \\log{(\\alpha)}", "negatives": ["\\beta e^{\\alpha}", "\\frac{\\beta^{2}}{2 \\alpha}", "\\log{(\\alpha)} \\log{(\\beta)}", "\\frac{\\alpha^{2} \\beta}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\beta', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\beta', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\beta', commutative=True), exp(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\beta', commutative=True), Integer(2)))", "Mul(log(Symbol('\\\\alpha', commutative=True)), log(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\beta', commutative=True))"]}, {"premise_expression": "\\beta + \\chi", "variable": "\\chi", "positive": "\\frac{\\chi (2 \\beta + \\chi)}{2}", "negatives": ["\\frac{\\beta (\\beta + 2 \\chi)}{2}", "\\frac{\\chi^{2} \\cos{(\\beta)}}{2}", "e^{- \\beta + \\chi}", "\\beta \\chi - \\cos{(\\chi)}"], "srepr_premise_expression": "Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\chi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), cos(Symbol('\\\\beta', commutative=True)))", "exp(Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\chi', commutative=True)))", "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\chi', commutative=True))))"]}, {"premise_expression": "\\xi e^{\\sigma}", "variable": "\\sigma", "positive": "\\xi e^{\\sigma}", "negatives": ["\\frac{\\xi^{2} e^{\\sigma}}{2}", "\\frac{\\sigma^{2} \\xi}{2}", "\\frac{\\sin{(\\sigma)}}{\\xi}", "- \\cos{(\\sigma + \\xi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\xi', commutative=True), exp(Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\xi', commutative=True), exp(Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), exp(Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))", "Mul(Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), sin(Symbol('\\\\sigma', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\log{(\\frac{\\xi}{\\gamma})}", "variable": "\\xi", "positive": "\\xi (\\log{(\\frac{\\xi}{\\gamma})} - 1)", "negatives": ["\\gamma (\\log{(\\frac{\\xi}{\\gamma})} + 1)", "\\frac{\\xi (\\log{(\\xi)} - 1)}{\\gamma}", "\\gamma \\log{(\\xi)}", "\\cos{(\\gamma - \\xi)}"], "srepr_premise_expression": "log(Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\xi', commutative=True), Add(log(Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\gamma', commutative=True), Add(log(Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))), Integer(1)))", "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True), Add(log(Symbol('\\\\xi', commutative=True)), Integer(-1)))", "Mul(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\xi', commutative=True)))", "cos(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "- \\omega + e^{\\gamma}", "variable": "\\omega", "positive": "\\frac{\\omega (- \\omega + 2 e^{\\gamma})}{2}", "negatives": ["\\frac{\\omega (- \\omega + 2 \\cos{(\\gamma)})}{2}", "- \\gamma \\omega + e^{\\gamma}", "\\frac{\\omega (- 2 \\gamma + \\omega)}{2}", "- \\gamma \\omega + e^{\\omega}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), exp(Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\gamma', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\gamma', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True)), exp(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True)), exp(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\frac{\\beta}{\\sigma}", "variable": "\\beta", "positive": "\\frac{\\beta^{2}}{2 \\sigma}", "negatives": ["\\beta \\log{(\\sigma)}", "\\frac{\\beta (- \\beta + 2 \\sigma)}{2}", "\\beta \\sigma - \\cos{(\\beta)}", "0"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\beta', commutative=True), log(Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\beta', commutative=True))))", "Integer(0)"]}, {"premise_expression": "\\frac{\\cos{(\\beta)}}{\\gamma}", "variable": "\\beta", "positive": "\\frac{\\sin{(\\beta)}}{\\gamma}", "negatives": ["\\log{(\\gamma)} \\cos{(\\beta)}", "\\frac{\\beta (\\beta + 2 \\sin{(\\gamma)})}{2}", "\\beta (\\log{(\\frac{\\gamma}{\\beta})} + 1)", "\\frac{\\beta (- \\beta + 2 \\sin{(\\gamma)})}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), cos(Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), sin(Symbol('\\\\beta', commutative=True)))", "srepr_negatives": ["Mul(log(Symbol('\\\\gamma', commutative=True)), cos(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), sin(Symbol('\\\\gamma', commutative=True)))))", "Mul(Symbol('\\\\beta', commutative=True), Add(log(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True))), Integer(1)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\gamma', commutative=True)))))"]}, {"premise_expression": "- \\xi + \\sin{(\\gamma)}", "variable": "\\gamma", "positive": "- \\gamma \\xi - \\cos{(\\gamma)}", "negatives": ["\\gamma \\xi - \\cos{(\\gamma)}", "e^{\\xi} \\log{(\\gamma)}", "\\cos{(\\gamma - \\xi)}", "- \\cos{(\\gamma + \\xi)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), sin(Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\gamma', commutative=True))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\gamma', commutative=True))))", "Mul(exp(Symbol('\\\\xi', commutative=True)), log(Symbol('\\\\gamma', commutative=True)))", "cos(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\xi e^{\\alpha}", "variable": "\\xi", "positive": "\\frac{\\xi^{2} e^{\\alpha}}{2}", "negatives": ["\\frac{\\xi^{2} \\log{(\\alpha)}}{2}", "\\xi e^{\\alpha}", "\\alpha e^{\\frac{\\xi}{\\alpha}}", "\\frac{\\alpha \\xi^{2}}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\xi', commutative=True), exp(Symbol('\\\\alpha', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), exp(Symbol('\\\\alpha', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), log(Symbol('\\\\alpha', commutative=True)))", "Mul(Symbol('\\\\xi', commutative=True), exp(Symbol('\\\\alpha', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), exp(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))"]}, {"premise_expression": "\\alpha + \\chi", "variable": "\\chi", "positive": "\\frac{\\chi (2 \\alpha + \\chi)}{2}", "negatives": ["\\frac{\\chi (2 \\alpha - \\chi)}{2}", "\\frac{\\alpha (\\alpha + 2 \\chi)}{2}", "- e^{\\alpha - \\chi}", "\\frac{\\chi^{2}}{2} + \\sin{(\\chi)}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\chi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\chi', commutative=True))))", "Mul(Integer(-1), exp(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True)))))", "Add(Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2))), sin(Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "\\alpha + \\chi", "variable": "\\alpha", "positive": "\\frac{\\alpha (\\alpha + 2 \\chi)}{2}", "negatives": ["\\frac{\\alpha (- \\alpha + 2 \\chi)}{2}", "\\frac{\\chi (2 \\alpha + \\chi)}{2}", "\\frac{\\alpha^{2} \\cos{(\\chi)}}{2}", "\\sin{(\\alpha - \\chi)}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\chi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\chi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), cos(Symbol('\\\\chi', commutative=True)))", "sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True))))"]}, {"premise_expression": "\\log{(\\chi \\delta)}", "variable": "\\delta", "positive": "\\delta (\\log{(\\chi \\delta)} - 1)", "negatives": ["\\chi (\\log{(\\chi \\delta)} - 1)", "\\delta (\\log{(\\frac{\\chi}{\\delta})} + 1)", "\\delta (\\log{(\\frac{\\delta}{\\chi})} - 1)", "\\delta (\\chi + \\log{(\\delta)} - 1)"], "srepr_premise_expression": "log(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\delta', commutative=True), Add(log(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\chi', commutative=True), Add(log(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\delta', commutative=True), Add(log(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Symbol('\\\\delta', commutative=True), Add(log(Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\delta', commutative=True)), Integer(-1)))"]}, {"premise_expression": "- \\beta + \\sigma", "variable": "\\beta", "positive": "\\frac{\\beta (- \\beta + 2 \\sigma)}{2}", "negatives": ["\\frac{\\sigma (- 2 \\beta + \\sigma)}{2}", "e^{\\beta + \\sigma}", "e^{\\sigma} \\log{(\\beta)}", "\\frac{\\beta (\\beta + 2 e^{\\sigma})}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "exp(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True)))", "Mul(exp(Symbol('\\\\sigma', commutative=True)), log(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), exp(Symbol('\\\\sigma', commutative=True)))))"]}, {"premise_expression": "\\gamma \\log{(\\delta)}", "variable": "\\gamma", "positive": "\\frac{\\gamma^{2} \\log{(\\delta)}}{2}", "negatives": ["\\frac{\\gamma^{2} \\cos{(\\delta)}}{2}", "\\frac{\\gamma^{2} \\sin{(\\delta)}}{2}", "\\frac{\\gamma (2 \\delta - \\gamma)}{2}", "\\frac{\\gamma (2 \\delta + \\gamma)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), log(Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), cos(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), sin(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\alpha e^{\\sigma}", "variable": "\\sigma", "positive": "\\alpha e^{\\sigma}", "negatives": ["\\frac{\\alpha^{2} e^{\\sigma}}{2}", "\\log{(\\alpha)} \\log{(\\sigma)}", "- \\cos{(\\alpha + \\sigma)}", "\\frac{\\sigma^{2} \\sin{(\\alpha)}}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), exp(Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\alpha', commutative=True), exp(Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), exp(Symbol('\\\\sigma', commutative=True)))", "Mul(log(Symbol('\\\\alpha', commutative=True)), log(Symbol('\\\\sigma', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), sin(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\alpha + e^{\\omega}", "variable": "\\omega", "positive": "\\alpha \\omega + e^{\\omega}", "negatives": ["\\alpha \\omega - \\cos{(\\omega)}", "\\frac{\\alpha (\\alpha + 2 e^{\\omega})}{2}", "\\cos{(\\alpha - \\omega)}", "\\frac{\\alpha \\omega^{2}}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), exp(Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)), exp(Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), exp(Symbol('\\\\omega', commutative=True)))))", "cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))"]}, {"premise_expression": "\\cos{(\\frac{\\delta}{\\omega})}", "variable": "\\omega", "positive": "\\delta \\operatorname{Si}{(\\frac{\\delta}{\\omega})} + \\omega \\cos{(\\frac{\\delta}{\\omega})}", "negatives": ["- \\delta \\operatorname{Ei}{(\\frac{\\delta}{\\omega})} + \\omega e^{\\frac{\\delta}{\\omega}}", "\\omega (\\log{(\\frac{\\delta}{\\omega})} + 1)", "\\frac{\\omega (2 \\delta - \\omega)}{2}", "\\delta \\omega - \\cos{(\\omega)}"], "srepr_premise_expression": "cos(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\delta', commutative=True), Si(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1))))), Mul(Symbol('\\\\omega', commutative=True), cos(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1))))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Ei(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1))))), Mul(Symbol('\\\\omega', commutative=True), exp(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1))))))", "Mul(Symbol('\\\\omega', commutative=True), Add(log(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\omega', commutative=True))))"]}, {"premise_expression": "\\chi \\pi \\sigma", "variable": "\\chi", "positive": "\\frac{\\chi^{2} \\pi \\sigma}{2}", "negatives": ["\\frac{\\chi \\pi^{2} \\sigma}{2}", "\\frac{\\chi \\pi \\sigma^{2}}{2}", "\\frac{\\chi^{2} \\pi}{2 \\sigma}", "\\frac{\\pi \\log{(\\chi)}}{\\sigma}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), Symbol('\\\\sigma', commutative=True))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "Mul(Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), log(Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "\\frac{\\psi}{\\alpha}", "variable": "\\alpha", "positive": "\\psi \\log{(\\alpha)}", "negatives": ["\\frac{\\psi^{2}}{2 \\alpha}", "\\psi (\\alpha + \\log{(\\alpha)})", "\\alpha \\psi - \\cos{(\\alpha)}", "- \\cos{(\\alpha - \\psi)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\psi', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "Mul(Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\alpha', commutative=True))))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\alpha', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))"]}, {"premise_expression": "- \\delta + \\sin{(\\sigma)}", "variable": "\\delta", "positive": "\\frac{\\delta (- \\delta + 2 \\sin{(\\sigma)})}{2}", "negatives": ["\\frac{\\delta^{2} \\sin{(\\sigma)}}{2}", "\\frac{\\delta^{2} \\cos{(\\sigma)}}{2}", "- \\delta \\sigma - \\cos{(\\sigma)}", "\\frac{\\delta^{2}}{2 \\sigma}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), sin(Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\sigma', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), sin(Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), cos(Symbol('\\\\sigma', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))"]}, {"premise_expression": "\\frac{\\beta^{\\chi}}{\\sigma}", "variable": "\\sigma", "positive": "\\beta^{\\chi} \\log{(\\sigma)}", "negatives": ["\\beta \\chi \\log{(\\sigma)}", "\\frac{\\beta \\sigma^{2}}{2 \\chi}", "\\frac{\\beta \\chi \\sigma^{2}}{2}", "\\frac{\\beta^{\\chi} \\sigma^{2}}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True)), log(Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True), log(Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True)), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))"]}, {"premise_expression": "\\alpha - \\sigma", "variable": "\\alpha", "positive": "\\frac{\\alpha (\\alpha - 2 \\sigma)}{2}", "negatives": ["\\frac{\\alpha (- \\alpha + 2 \\sigma)}{2}", "\\frac{\\sigma (2 \\alpha - \\sigma)}{2}", "\\frac{\\alpha (\\alpha + 2 \\sin{(\\sigma)})}{2}", "\\frac{\\alpha (\\alpha + 2 e^{\\sigma})}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), sin(Symbol('\\\\sigma', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), exp(Symbol('\\\\sigma', commutative=True)))))"]}, {"premise_expression": "\\log{(- \\delta + \\gamma)}", "variable": "\\delta", "positive": "\\delta \\log{(- \\delta + \\gamma)} - \\delta - \\gamma \\log{(\\delta - \\gamma)}", "negatives": ["\\delta \\log{(\\delta - \\gamma)} - \\delta - \\gamma \\log{(\\delta - \\gamma)}", "- \\delta \\log{(- \\delta + \\gamma)} + \\gamma \\log{(- \\delta + \\gamma)} - \\gamma", "\\delta (- \\gamma + \\log{(\\delta)} - 1)", "\\log{(\\delta)} \\cos{(\\gamma)}"], "srepr_premise_expression": "log(Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\delta', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\gamma', commutative=True)))), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), log(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\delta', commutative=True), log(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), log(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))))", "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\gamma', commutative=True)))), Mul(Symbol('\\\\gamma', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\gamma', commutative=True)))), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))", "Mul(Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), log(Symbol('\\\\delta', commutative=True)), Integer(-1)))", "Mul(log(Symbol('\\\\delta', commutative=True)), cos(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "- \\pi + \\sigma", "variable": "\\pi", "positive": "\\frac{\\pi (- \\pi + 2 \\sigma)}{2}", "negatives": ["\\frac{\\sigma (- 2 \\pi + \\sigma)}{2}", "- e^{- \\pi + \\sigma}", "\\cos{(\\pi - \\sigma)}", "e^{\\pi + \\sigma}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Symbol('\\\\sigma', commutative=True))))", "cos(Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "exp(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\log{(\\frac{\\pi}{\\psi})}", "variable": "\\psi", "positive": "\\psi (\\log{(\\frac{\\pi}{\\psi})} + 1)", "negatives": ["\\pi (\\log{(\\frac{\\pi}{\\psi})} - 1)", "\\frac{\\psi^{2} \\log{(\\pi)}}{2}", "\\sin{(\\pi + \\psi)}", "\\frac{\\psi (2 \\pi + \\psi)}{2}"], "srepr_premise_expression": "log(Mul(Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\psi', commutative=True), Add(log(Mul(Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))), Integer(1)))", "srepr_negatives": ["Mul(Symbol('\\\\pi', commutative=True), Add(log(Mul(Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), log(Symbol('\\\\pi', commutative=True)))", "sin(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "- \\sigma + \\sin{(\\alpha)}", "variable": "\\sigma", "positive": "\\frac{\\sigma (- \\sigma + 2 \\sin{(\\alpha)})}{2}", "negatives": ["\\frac{\\sigma (\\sigma + 2 \\sin{(\\alpha)})}{2}", "\\frac{\\sigma (2 \\alpha - \\sigma)}{2}", "- \\alpha \\sigma - \\cos{(\\alpha)}", "\\sin{(\\alpha + \\sigma)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), sin(Symbol('\\\\alpha', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\alpha', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(2), sin(Symbol('\\\\alpha', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\alpha', commutative=True))))", "sin(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "e^{\\frac{\\delta}{\\sigma}}", "variable": "\\delta", "positive": "\\sigma e^{\\frac{\\delta}{\\sigma}}", "negatives": ["- \\sigma \\cos{(\\delta)}", "\\frac{\\delta^{2} \\log{(\\sigma)}}{2}", "\\delta \\sigma - \\cos{(\\delta)}", "\\delta (\\log{(\\delta \\sigma)} - 1)"], "srepr_premise_expression": "exp(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\sigma', commutative=True), exp(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))))", "srepr_negatives": ["Mul(Integer(-1), Symbol('\\\\sigma', commutative=True), cos(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), log(Symbol('\\\\sigma', commutative=True)))", "Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\delta', commutative=True))))", "Mul(Symbol('\\\\delta', commutative=True), Add(log(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\chi + \\psi + \\xi", "variable": "\\xi", "positive": "\\xi (\\chi + \\psi + \\frac{\\xi}{2})", "negatives": ["\\frac{\\xi (2 \\chi - 2 \\psi + \\xi)}{2}", "\\frac{\\xi (- 2 \\chi + 2 \\psi + \\xi)}{2}", "\\frac{\\psi (2 \\chi + \\psi + 2 \\xi)}{2}", "\\frac{\\chi (\\chi + 2 \\psi + 2 \\xi)}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True), Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\psi', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\frac{\\cos{(\\psi)}}{\\gamma}", "variable": "\\gamma", "positive": "\\log{(\\gamma)} \\cos{(\\psi)}", "negatives": ["\\gamma \\psi - \\cos{(\\gamma)}", "- \\cos{(\\gamma + \\psi)}", "\\frac{\\gamma^{2} \\log{(\\psi)}}{2}", "\\frac{\\sin{(\\psi)}}{\\gamma}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), cos(Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(log(Symbol('\\\\gamma', commutative=True)), cos(Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\gamma', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), log(Symbol('\\\\psi', commutative=True)))", "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), sin(Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\log{(\\delta \\sigma)}", "variable": "\\sigma", "positive": "\\sigma (\\log{(\\delta \\sigma)} - 1)", "negatives": ["\\delta (\\log{(\\delta \\sigma)} - 1)", "\\frac{\\sigma (2 \\delta + \\sigma)}{2}", "- e^{\\delta - \\sigma}", "\\delta \\sigma - \\cos{(\\sigma)}"], "srepr_premise_expression": "log(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\sigma', commutative=True), Add(log(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\delta', commutative=True), Add(log(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Integer(-1), exp(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))", "Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\beta \\psi", "variable": "\\beta", "positive": "\\frac{\\beta^{2} \\psi}{2}", "negatives": ["\\frac{\\beta \\psi^{2}}{2}", "\\cos{(\\beta - \\psi)}", "\\sin{(\\beta + \\psi)}", "\\log{(\\beta)} \\sin{(\\psi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "sin(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\psi', commutative=True)))", "Mul(log(Symbol('\\\\beta', commutative=True)), sin(Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\frac{e^{\\xi}}{\\omega}", "variable": "\\omega", "positive": "e^{\\xi} \\log{(\\omega)}", "negatives": ["\\xi^{2} \\log{(\\omega)}", "\\omega (\\xi + \\log{(\\xi)})", "- e^{- \\omega + \\xi}", "- \\omega \\xi + e^{\\omega}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), exp(Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(exp(Symbol('\\\\xi', commutative=True)), log(Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Pow(Symbol('\\\\xi', commutative=True), Integer(2)), log(Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\xi', commutative=True))))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Symbol('\\\\xi', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True)), exp(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\frac{\\delta}{\\pi}", "variable": "\\delta", "positive": "\\frac{\\delta^{2}}{2 \\pi}", "negatives": ["\\delta \\log{(\\pi)}", "\\delta^{2} (\\frac{\\delta}{3} + \\frac{\\pi}{2})", "\\sin{(\\delta + \\pi)}", "\\sin{(\\delta - \\pi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\pi', commutative=True)))", "Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Add(Mul(Rational(1, 3), Symbol('\\\\delta', commutative=True)), Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True))))", "sin(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True)))", "sin(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\frac{\\sin{(\\psi)}}{\\pi}", "variable": "\\pi", "positive": "\\log{(\\pi)} \\sin{(\\psi)}", "negatives": ["\\frac{\\pi^{2} e^{\\psi}}{2}", "- \\frac{\\cos{(\\psi)}}{\\pi}", "\\sin{(\\pi + \\psi)}", "- \\cos{(\\pi + \\psi)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), sin(Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(log(Symbol('\\\\pi', commutative=True)), sin(Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), exp(Symbol('\\\\psi', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), cos(Symbol('\\\\psi', commutative=True)))", "sin(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "\\alpha - \\xi", "variable": "\\xi", "positive": "\\frac{\\xi (2 \\alpha - \\xi)}{2}", "negatives": ["\\frac{\\xi (2 \\alpha + \\xi)}{2}", "\\frac{\\alpha (\\alpha - 2 \\xi)}{2}", "\\frac{\\xi^{2} \\log{(\\alpha)}}{2}", "\\frac{\\xi^{2} e^{\\alpha}}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), log(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), exp(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\frac{- \\gamma + \\sigma}{\\sigma}", "variable": "\\sigma", "positive": "- \\gamma \\log{(\\sigma)} + \\sigma", "negatives": ["- \\frac{\\gamma^{2}}{2 \\sigma} + \\gamma", "\\gamma e^{\\frac{\\sigma}{\\gamma}}", "\\sigma (- \\gamma + \\log{(\\sigma)} - 1)", "- e^{\\gamma - \\sigma}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\sigma', commutative=True))), Symbol('\\\\sigma', commutative=True))", "srepr_negatives": ["Add(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1))), Symbol('\\\\gamma', commutative=True))", "Mul(Symbol('\\\\gamma', commutative=True), exp(Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))))", "Mul(Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), log(Symbol('\\\\sigma', commutative=True)), Integer(-1)))", "Mul(Integer(-1), exp(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))"]}, {"premise_expression": "\\gamma \\omega", "variable": "\\gamma", "positive": "\\frac{\\gamma^{2} \\omega}{2}", "negatives": ["\\frac{\\gamma \\omega^{2}}{2}", "\\frac{\\gamma (- \\gamma + 2 \\omega)}{2}", "\\cos{(\\gamma - \\omega)}", "- \\gamma \\omega + e^{\\gamma}"], "srepr_premise_expression": "Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Symbol('\\\\omega', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "cos(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True)), exp(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\sin{(\\alpha - \\omega)}", "variable": "\\alpha", "positive": "- \\cos{(\\alpha - \\omega)}", "negatives": ["\\cos{(\\alpha - \\omega)}", "- \\frac{\\cos{(\\alpha)}}{\\omega}", "\\frac{\\sin{(\\alpha)}}{\\omega}", "\\frac{\\alpha (\\alpha + 2 \\omega)}{2}"], "srepr_premise_expression": "sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))))", "srepr_negatives": ["cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "Mul(Integer(-1), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), cos(Symbol('\\\\alpha', commutative=True)))", "Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), sin(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))"]}, {"premise_expression": "\\sin{(\\alpha - \\psi)}", "variable": "\\psi", "positive": "\\cos{(\\alpha - \\psi)}", "negatives": ["- \\cos{(\\alpha - \\psi)}", "\\psi", "\\frac{\\alpha \\psi^{2}}{2}", "e^{\\alpha} \\log{(\\psi)}"], "srepr_premise_expression": "sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))", "Symbol('\\\\psi', commutative=True)", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "Mul(exp(Symbol('\\\\alpha', commutative=True)), log(Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "- \\alpha + e^{\\xi}", "variable": "\\alpha", "positive": "\\frac{\\alpha (- \\alpha + 2 e^{\\xi})}{2}", "negatives": ["\\frac{\\alpha (\\alpha + 2 \\log{(\\xi)})}{2}", "- \\alpha \\xi + e^{\\xi}", "\\frac{\\alpha (\\alpha - 2 \\xi)}{2}", "\\frac{\\alpha^{2}}{2 \\xi}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), exp(Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\xi', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), log(Symbol('\\\\xi', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True)), exp(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))"]}, {"premise_expression": "\\frac{\\sin{(\\omega)}}{\\gamma}", "variable": "\\gamma", "positive": "\\log{(\\gamma)} \\sin{(\\omega)}", "negatives": ["\\gamma (\\gamma - \\omega)", "\\frac{\\gamma^{2}}{2 \\omega}", "- \\frac{\\cos{(\\omega)}}{\\gamma}", "\\frac{\\gamma (\\gamma + 2 \\omega)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), sin(Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(log(Symbol('\\\\gamma', commutative=True)), sin(Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))", "Mul(Integer(-1), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), cos(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))"]}, {"premise_expression": "\\beta - \\delta + \\xi", "variable": "\\xi", "positive": "\\xi (\\beta - \\delta + \\frac{\\xi}{2})", "negatives": ["\\frac{\\xi (2 \\beta + 2 \\delta + \\xi)}{2}", "\\frac{\\beta (\\beta - 2 \\delta + 2 \\xi)}{2}", "\\frac{\\delta (2 \\beta - \\delta + 2 \\xi)}{2}", "\\frac{\\xi (2 \\beta - \\xi)}{2 \\delta}"], "srepr_premise_expression": "Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\log{(\\gamma + \\sigma)}", "variable": "\\gamma", "positive": "\\gamma \\log{(\\gamma + \\sigma)} - \\gamma + \\sigma \\log{(\\gamma + \\sigma)}", "negatives": ["\\gamma \\log{(- \\gamma + \\sigma)} - \\gamma - \\sigma \\log{(\\gamma - \\sigma)}", "\\gamma \\log{(\\gamma - \\sigma)} - \\gamma - \\sigma \\log{(\\gamma - \\sigma)}", "\\gamma \\log{(\\gamma + \\sigma)} + \\sigma \\log{(\\gamma + \\sigma)} - \\sigma", "\\gamma (- \\sigma + \\log{(\\gamma)} - 1)"], "srepr_premise_expression": "log(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\gamma', commutative=True), log(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True)))), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Symbol('\\\\sigma', commutative=True), log(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\gamma', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\sigma', commutative=True)))), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True), log(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))))", "Add(Mul(Symbol('\\\\gamma', commutative=True), log(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True), log(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))))", "Add(Mul(Symbol('\\\\gamma', commutative=True), log(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True)))), Mul(Symbol('\\\\sigma', commutative=True), log(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True)))), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))", "Mul(Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), log(Symbol('\\\\gamma', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\frac{\\delta \\gamma}{\\psi}", "variable": "\\delta", "positive": "\\frac{\\delta^{2} \\gamma}{2 \\psi}", "negatives": ["\\frac{\\delta \\gamma^{2}}{2 \\psi}", "\\delta \\gamma \\log{(\\psi)}", "2 \\delta \\gamma \\psi", "\\delta \\psi (\\gamma + \\psi)"], "srepr_premise_expression": "Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))", "Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\psi', commutative=True)))", "Mul(Integer(2), Symbol('\\\\delta', commutative=True), Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True))", "Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\frac{\\log{(\\beta)}}{\\xi}", "variable": "\\xi", "positive": "\\log{(\\beta)} \\log{(\\xi)}", "negatives": ["- \\beta \\cos{(\\xi)}", "- \\cos{(\\beta + \\xi)}", "- \\beta \\xi - \\cos{(\\xi)}", "\\frac{\\beta (\\log{(\\beta)} - 1)}{\\xi}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), log(Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(log(Symbol('\\\\beta', commutative=True)), log(Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Symbol('\\\\beta', commutative=True), cos(Symbol('\\\\xi', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\xi', commutative=True))))", "Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), Add(log(Symbol('\\\\beta', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\frac{\\alpha}{\\omega}", "variable": "\\omega", "positive": "\\alpha \\log{(\\omega)}", "negatives": ["\\frac{\\alpha^{2}}{2 \\omega}", "\\alpha e^{\\frac{\\omega}{\\alpha}}", "\\frac{\\omega^{2} \\log{(\\alpha)}}{2}", "\\sin{(\\alpha + \\omega)}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))", "Mul(Symbol('\\\\alpha', commutative=True), exp(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), log(Symbol('\\\\alpha', commutative=True)))", "sin(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\cos{(\\alpha + \\chi)}", "variable": "\\alpha", "positive": "\\sin{(\\alpha + \\chi)}", "negatives": ["e^{\\alpha - \\chi}", "\\frac{\\alpha (\\alpha + 2 \\chi)}{2}", "\\frac{\\alpha^{2} \\chi}{2}", "\\frac{\\alpha^{3} \\chi}{3}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "sin(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["exp(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\chi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\chi', commutative=True))", "Mul(Rational(1, 3), Pow(Symbol('\\\\alpha', commutative=True), Integer(3)), Symbol('\\\\chi', commutative=True))"]}, {"premise_expression": "\\cos{(\\frac{\\chi}{\\beta})}", "variable": "\\beta", "positive": "\\beta \\cos{(\\frac{\\chi}{\\beta})} + \\chi \\operatorname{Si}{(\\frac{\\chi}{\\beta})}", "negatives": ["\\beta e^{\\frac{\\chi}{\\beta}} - \\chi \\operatorname{Ei}{(\\frac{\\chi}{\\beta})}", "\\frac{\\beta (\\beta + 2 \\log{(\\chi)})}{2}", "\\frac{\\beta^{2}}{2 \\chi} - \\beta \\chi", "\\log{(\\beta)} \\log{(\\chi)}"], "srepr_premise_expression": "cos(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\beta', commutative=True), cos(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\chi', commutative=True)))), Mul(Symbol('\\\\chi', commutative=True), Si(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\chi', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\beta', commutative=True), exp(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\chi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Ei(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\chi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), log(Symbol('\\\\chi', commutative=True)))))", "Add(Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\chi', commutative=True), Integer(-1))), Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True)))", "Mul(log(Symbol('\\\\beta', commutative=True)), log(Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "\\gamma + \\sigma", "variable": "\\gamma", "positive": "\\frac{\\gamma (\\gamma + 2 \\sigma)}{2}", "negatives": ["\\frac{\\gamma (- \\gamma + 2 \\sigma)}{2}", "\\frac{\\sigma (2 \\gamma + \\sigma)}{2}", "\\frac{\\gamma^{2} \\log{(\\sigma)}}{2}", "\\sin{(\\gamma - \\sigma)}"], "srepr_premise_expression": "Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), log(Symbol('\\\\sigma', commutative=True)))", "sin(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\gamma \\xi", "variable": "\\gamma", "positive": "\\frac{\\gamma^{2} \\xi}{2}", "negatives": ["\\frac{\\gamma \\xi^{2}}{2}", "\\xi \\log{(\\gamma)}", "\\frac{\\gamma (\\gamma + 2 \\xi)}{2}", "- \\gamma \\xi + \\sin{(\\gamma)}"], "srepr_premise_expression": "Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Mul(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)), sin(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "- \\psi + \\sin{(\\delta)}", "variable": "\\psi", "positive": "\\frac{\\psi (- \\psi + 2 \\sin{(\\delta)})}{2}", "negatives": ["\\frac{\\psi (\\psi + 2 \\sin{(\\delta)})}{2}", "\\delta \\psi + \\sin{(\\psi)}", "\\frac{\\psi^{2} e^{\\delta}}{2}", "- \\delta \\psi - \\cos{(\\delta)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), sin(Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\delta', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(2), sin(Symbol('\\\\delta', commutative=True)))))", "Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\psi', commutative=True)), sin(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), exp(Symbol('\\\\delta', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\delta', commutative=True))))"]}, {"premise_expression": "\\cos{(\\frac{\\gamma}{\\sigma})}", "variable": "\\sigma", "positive": "\\gamma \\operatorname{Si}{(\\frac{\\gamma}{\\sigma})} + \\sigma \\cos{(\\frac{\\gamma}{\\sigma})}", "negatives": ["\\log{(\\sigma)} \\sin{(\\gamma)}", "\\sigma (\\log{(\\gamma \\sigma)} - 1)", "\\log{(\\sigma)} \\cos{(\\gamma)}", "e^{\\gamma + \\sigma}"], "srepr_premise_expression": "cos(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\gamma', commutative=True), Si(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1))))), Mul(Symbol('\\\\sigma', commutative=True), cos(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1))))))", "srepr_negatives": ["Mul(log(Symbol('\\\\sigma', commutative=True)), sin(Symbol('\\\\gamma', commutative=True)))", "Mul(Symbol('\\\\sigma', commutative=True), Add(log(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True))), Integer(-1)))", "Mul(log(Symbol('\\\\sigma', commutative=True)), cos(Symbol('\\\\gamma', commutative=True)))", "exp(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\gamma \\xi", "variable": "\\gamma", "positive": "\\frac{\\gamma^{2} \\xi}{2}", "negatives": ["\\frac{\\gamma \\xi^{2}}{2}", "\\frac{\\gamma^{2} \\sin{(\\xi)}}{2}", "\\gamma (2 \\xi)^{\\xi}", "\\frac{\\gamma (\\gamma + 2 \\xi)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), sin(Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\gamma', commutative=True), Pow(Mul(Integer(2), Symbol('\\\\xi', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\chi - \\pi", "variable": "\\pi", "positive": "\\frac{\\pi (2 \\chi - \\pi)}{2}", "negatives": ["\\frac{\\chi (\\chi - 2 \\pi)}{2}", "- e^{\\chi - \\pi}", "\\pi (- \\chi + \\log{(\\pi)} - 1)", "\\chi \\log{(\\pi)}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Integer(-1), exp(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))", "Mul(Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), log(Symbol('\\\\pi', commutative=True)), Integer(-1)))", "Mul(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\psi + e^{\\omega}", "variable": "\\psi", "positive": "\\frac{\\psi (\\psi + 2 e^{\\omega})}{2}", "negatives": ["\\frac{\\psi (\\psi + 2 \\log{(\\omega)})}{2}", "\\frac{\\psi (- \\psi + 2 \\cos{(\\omega)})}{2}", "\\omega \\psi + e^{\\omega}", "\\frac{\\psi (2 \\omega + \\psi)}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\psi', commutative=True), exp(Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(2), exp(Symbol('\\\\omega', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(2), log(Symbol('\\\\omega', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\omega', commutative=True)))))", "Add(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True)), exp(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\cos{(\\alpha + \\gamma)}", "variable": "\\gamma", "positive": "\\sin{(\\alpha + \\gamma)}", "negatives": ["- \\cos{(\\alpha + \\gamma)}", "\\frac{\\gamma (2 \\alpha + \\gamma)}{2}", "\\alpha e^{\\frac{\\gamma}{\\alpha}}", "\\alpha \\log{(\\gamma)}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "sin(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), exp(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True))))", "Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\chi \\omega", "variable": "\\chi", "positive": "\\frac{\\chi^{2} \\omega}{2}", "negatives": ["\\frac{\\chi \\omega^{2}}{2}", "\\frac{\\chi^{2} e^{\\omega}}{2}", "\\frac{\\chi^{2}}{2 \\omega}", "\\cos{(\\chi - \\omega)}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\omega', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), exp(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))", "cos(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))"]}, {"premise_expression": "\\chi \\gamma \\psi", "variable": "\\psi", "positive": "\\frac{\\chi \\gamma \\psi^{2}}{2}", "negatives": ["\\frac{\\chi^{2} \\gamma \\psi}{2}", "\\frac{\\gamma^{\\chi} \\psi^{2}}{2}", "\\frac{\\chi \\gamma^{2} \\psi}{2}", "\\frac{\\psi^{2} (- \\chi + \\gamma)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Symbol('\\\\chi', commutative=True)), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\log{(\\sigma^{\\pi})}", "variable": "\\pi", "positive": "\\frac{\\pi^{2} \\log{(\\sigma)}}{2}", "negatives": ["\\frac{\\pi^{2} \\sin{(\\sigma)}}{2}", "\\frac{\\pi (\\pi + 2 \\log{(\\sigma)})}{2}", "\\frac{\\pi (- \\pi + 2 \\sigma)}{2}", "\\frac{\\pi \\sin{(\\sigma)}}{\\sigma}"], "srepr_premise_expression": "log(Pow(Symbol('\\\\sigma', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), log(Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), sin(Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), log(Symbol('\\\\sigma', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), sin(Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\delta - \\gamma", "variable": "\\delta", "positive": "\\frac{\\delta (\\delta - 2 \\gamma)}{2}", "negatives": ["\\frac{\\gamma (2 \\delta - \\gamma)}{2}", "\\frac{\\delta^{2} e^{\\gamma}}{2}", "- \\frac{\\cos{(\\delta)}}{\\gamma}", "- \\delta \\gamma + e^{\\delta}"], "srepr_premise_expression": "Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), exp(Symbol('\\\\gamma', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), cos(Symbol('\\\\delta', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Symbol('\\\\gamma', commutative=True)), exp(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\log{(- \\chi + \\xi)}", "variable": "\\chi", "positive": "\\chi \\log{(- \\chi + \\xi)} - \\chi - \\xi \\log{(\\chi - \\xi)}", "negatives": ["- \\chi \\log{(- \\chi + \\xi)} + \\xi \\log{(- \\chi + \\xi)} - \\xi", "\\frac{\\chi (- \\chi + 2 e^{\\xi})}{2}", "- \\chi \\xi + \\sin{(\\chi)}", "\\frac{\\chi (\\chi + 2 e^{\\xi})}{2}"], "srepr_premise_expression": "log(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\chi', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\xi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True), log(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\xi', commutative=True)))), Mul(Symbol('\\\\xi', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\xi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\xi', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True)), sin(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), exp(Symbol('\\\\xi', commutative=True)))))"]}, {"premise_expression": "- \\alpha + \\delta", "variable": "\\alpha", "positive": "\\frac{\\alpha (- \\alpha + 2 \\delta)}{2}", "negatives": ["\\frac{\\delta (- 2 \\alpha + \\delta)}{2}", "\\frac{\\alpha (\\alpha + 2 e^{\\delta})}{2}", "\\frac{\\alpha (\\alpha + 2 \\log{(\\delta)})}{2}", "- \\frac{\\cos{(\\alpha)}}{\\delta}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\delta', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\delta', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), exp(Symbol('\\\\delta', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), log(Symbol('\\\\delta', commutative=True)))))", "Mul(Integer(-1), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), cos(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\frac{\\delta}{\\sigma}", "variable": "\\delta", "positive": "\\frac{\\delta^{2}}{2 \\sigma}", "negatives": ["\\delta \\log{(\\sigma)}", "\\frac{\\delta (\\delta - 2 \\sigma)}{2}", "\\frac{\\delta^{2} e^{\\sigma}}{2}", "\\frac{\\sin{(\\delta)}}{\\sigma}"], "srepr_premise_expression": "Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), exp(Symbol('\\\\sigma', commutative=True)))", "Mul(Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), sin(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\beta \\cos{(\\pi)}", "variable": "\\pi", "positive": "\\beta \\sin{(\\pi)}", "negatives": ["- \\beta \\pi + \\sin{(\\pi)}", "\\beta \\pi + e^{\\pi}", "\\frac{\\beta^{2} \\cos{(\\pi)}}{2}", "- \\cos{(\\beta - \\pi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), cos(Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\beta', commutative=True), sin(Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\pi', commutative=True)), sin(Symbol('\\\\pi', commutative=True)))", "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\pi', commutative=True)), exp(Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), cos(Symbol('\\\\pi', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))"]}, {"premise_expression": "\\frac{\\beta}{\\omega \\sigma}", "variable": "\\beta", "positive": "\\frac{\\beta^{2}}{2 \\omega \\sigma}", "negatives": ["\\frac{\\beta^{2} \\omega}{2 \\sigma}", "\\frac{\\beta \\log{(\\sigma)}}{\\omega}", "\\frac{\\beta \\log{(\\omega)}}{\\sigma}", "\\frac{\\beta^{2}}{2 \\omega} - \\beta \\sigma"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), log(Symbol('\\\\sigma', commutative=True)))", "Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), log(Symbol('\\\\omega', commutative=True)))", "Add(Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\omega', commutative=True), Integer(-1))), Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\chi \\log{(\\gamma)}", "variable": "\\gamma", "positive": "\\chi \\gamma (\\log{(\\gamma)} - 1)", "negatives": ["\\frac{\\chi^{2} \\log{(\\gamma)}}{2}", "\\frac{\\gamma^{2} \\log{(\\chi)}}{2}", "\\chi \\gamma + \\sin{(\\gamma)}", "e^{\\chi} \\log{(\\gamma)}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True), Add(log(Symbol('\\\\gamma', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), log(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), log(Symbol('\\\\chi', commutative=True)))", "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True)), sin(Symbol('\\\\gamma', commutative=True)))", "Mul(exp(Symbol('\\\\chi', commutative=True)), log(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\gamma (\\beta + \\sigma)", "variable": "\\sigma", "positive": "\\frac{\\gamma \\sigma (2 \\beta + \\sigma)}{2}", "negatives": ["\\frac{\\gamma^{2} (\\beta + \\sigma)}{2}", "\\frac{\\beta \\gamma (\\beta + 2 \\sigma)}{2}", "\\frac{\\sigma (2 \\gamma^{\\beta} - \\sigma)}{2}", "\\frac{\\sigma (2 \\gamma + \\sigma)}{2 \\beta}"], "srepr_premise_expression": "Mul(Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Pow(Symbol('\\\\gamma', commutative=True), Symbol('\\\\beta', commutative=True))), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\log{(\\chi \\sigma)}", "variable": "\\chi", "positive": "\\chi (\\log{(\\chi \\sigma)} - 1)", "negatives": ["\\sigma (\\log{(\\chi \\sigma)} - 1)", "- e^{- \\chi + \\sigma}", "\\sigma e^{\\frac{\\chi}{\\sigma}}", "\\frac{\\chi (\\chi + 2 \\cos{(\\sigma)})}{2}"], "srepr_premise_expression": "log(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\chi', commutative=True), Add(log(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\sigma', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\sigma', commutative=True), Add(log(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\sigma', commutative=True))), Integer(-1)))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\sigma', commutative=True))))", "Mul(Symbol('\\\\sigma', commutative=True), exp(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), cos(Symbol('\\\\sigma', commutative=True)))))"]}, {"premise_expression": "\\cos{(\\chi + \\omega)}", "variable": "\\chi", "positive": "\\sin{(\\chi + \\omega)}", "negatives": ["\\frac{\\chi (\\chi - 2 \\omega)}{2}", "\\chi (\\log{(\\frac{\\chi}{\\omega})} - 1)", "\\frac{\\chi^{2} \\log{(\\omega)}}{2}", "\\frac{\\chi^{2} \\sin{(\\omega)}}{2}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "sin(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Symbol('\\\\chi', commutative=True), Add(log(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), log(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), sin(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\alpha - \\sigma", "variable": "\\alpha", "positive": "\\frac{\\alpha (\\alpha - 2 \\sigma)}{2}", "negatives": ["\\frac{\\alpha (\\alpha + 2 \\sigma)}{2}", "\\frac{\\alpha (- \\alpha + 2 \\sigma)}{2}", "\\frac{\\sigma (2 \\alpha - \\sigma)}{2}", "\\sin{(\\alpha + \\sigma)}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "sin(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\alpha + \\pi + \\psi", "variable": "\\alpha", "positive": "\\alpha (\\frac{\\alpha}{2} + \\pi + \\psi)", "negatives": ["\\frac{\\alpha (- \\alpha + 2 \\pi + 2 \\psi)}{2}", "\\frac{\\psi (2 \\alpha + 2 \\pi + \\psi)}{2}", "\\frac{\\pi (2 \\alpha + \\pi + 2 \\psi)}{2}", "\\frac{\\alpha (\\alpha + 2 \\psi)}{2 \\pi}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\alpha', commutative=True), Add(Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\pi', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "\\cos{(\\gamma - \\xi)}", "variable": "\\xi", "positive": "- \\sin{(\\gamma - \\xi)}", "negatives": ["\\sin{(\\gamma - \\xi)}", "\\cos{(\\gamma - \\xi)}", "\\xi \\sin{(2 \\gamma)}", "\\gamma \\log{(\\xi)}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Integer(-1), sin(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))))", "srepr_negatives": ["sin(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "cos(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Symbol('\\\\xi', commutative=True), sin(Mul(Integer(2), Symbol('\\\\gamma', commutative=True))))", "Mul(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\log{(\\alpha + \\beta)}", "variable": "\\alpha", "positive": "\\alpha \\log{(\\alpha + \\beta)} - \\alpha + \\beta \\log{(\\alpha + \\beta)}", "negatives": ["\\alpha \\log{(\\alpha + \\beta)} + \\beta \\log{(\\alpha + \\beta)} - \\beta", "\\frac{\\alpha (- \\alpha + 2 \\beta)}{2}", "\\frac{\\alpha (- \\alpha + 2 e^{\\beta})}{2}", "\\frac{\\alpha (\\alpha + 2 \\sin{(\\beta)})}{2}"], "srepr_premise_expression": "log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\alpha', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True)))), Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Symbol('\\\\beta', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\alpha', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True)))), Mul(Symbol('\\\\beta', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True)))), Mul(Integer(-1), Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\beta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\beta', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), sin(Symbol('\\\\beta', commutative=True)))))"]}, {"premise_expression": "- \\pi + \\cos{(\\psi)}", "variable": "\\pi", "positive": "\\frac{\\pi (- \\pi + 2 \\cos{(\\psi)})}{2}", "negatives": ["\\frac{\\pi (- \\pi + 2 \\log{(\\psi)})}{2}", "\\frac{\\pi (- \\pi + 2 e^{\\psi})}{2}", "\\frac{\\pi (\\pi + 2 e^{\\psi})}{2}", "\\frac{\\pi (\\pi - 2 \\psi)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), cos(Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\psi', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), log(Symbol('\\\\psi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\psi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), exp(Symbol('\\\\psi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "\\frac{\\beta}{\\alpha}", "variable": "\\alpha", "positive": "\\beta \\log{(\\alpha)}", "negatives": ["\\beta e^{\\alpha}", "\\frac{\\beta^{2}}{2 \\alpha}", "\\alpha \\beta - \\cos{(\\alpha)}", "\\log{(\\alpha)} \\sin{(\\beta)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\beta', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\beta', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\beta', commutative=True), exp(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\beta', commutative=True), Integer(2)))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\alpha', commutative=True))))", "Mul(log(Symbol('\\\\alpha', commutative=True)), sin(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "\\alpha + \\pi + \\psi", "variable": "\\alpha", "positive": "\\alpha (\\frac{\\alpha}{2} + \\pi + \\psi)", "negatives": ["\\frac{\\alpha (\\alpha - 2 \\pi + 2 \\psi)}{2}", "\\frac{\\psi (2 \\alpha + 2 \\pi + \\psi)}{2}", "\\frac{\\pi (2 \\alpha + \\pi + 2 \\psi)}{2}", "\\frac{\\alpha^{2} (- \\pi + \\psi)}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\alpha', commutative=True), Add(Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\pi', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\cos{(\\delta + \\omega)}", "variable": "\\omega", "positive": "\\sin{(\\delta + \\omega)}", "negatives": ["\\delta \\omega - \\cos{(\\omega)}", "\\omega (\\log{(\\frac{\\omega}{\\delta})} - 1)", "\\omega (- \\delta + \\log{(\\omega)} - 1)", "\\int \\cos^{\\delta}{(\\omega)} d\\omega"], "srepr_premise_expression": "cos(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "sin(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\omega', commutative=True))))", "Mul(Symbol('\\\\omega', commutative=True), Add(log(Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), log(Symbol('\\\\omega', commutative=True)), Integer(-1)))", "Integral(Pow(cos(Symbol('\\\\omega', commutative=True)), Symbol('\\\\delta', commutative=True)), Tuple(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\cos{(\\chi - \\pi)}", "variable": "\\pi", "positive": "- \\sin{(\\chi - \\pi)}", "negatives": ["\\sin{(\\chi - \\pi)}", "\\sin{(\\chi + \\pi)}", "\\frac{\\chi \\pi (\\pi - 2)}{2}", "\\pi (\\log{(\\chi \\pi)} - 1)"], "srepr_premise_expression": "cos(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Integer(-1), sin(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))", "srepr_negatives": ["sin(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "sin(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Integer(-2)))", "Mul(Symbol('\\\\pi', commutative=True), Add(log(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True))), Integer(-1)))"]}, {"premise_expression": "- \\alpha + \\log{(\\chi)}", "variable": "\\alpha", "positive": "\\frac{\\alpha (- \\alpha + 2 \\log{(\\chi)})}{2}", "negatives": ["\\frac{\\alpha (- \\alpha + 2 \\cos{(\\chi)})}{2}", "\\frac{\\alpha^{2} \\log{(\\chi)}}{2}", "\\chi (- \\alpha + \\log{(\\chi)} - 1)", "\\alpha \\chi + \\sin{(\\alpha)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), log(Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), log(Symbol('\\\\chi', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\chi', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), log(Symbol('\\\\chi', commutative=True)))", "Mul(Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), log(Symbol('\\\\chi', commutative=True)), Integer(-1)))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)), sin(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\omega \\sigma", "variable": "\\omega", "positive": "\\frac{\\omega^{2} \\sigma}{2}", "negatives": ["\\frac{\\omega \\sigma^{2}}{2}", "\\sigma \\log{(\\omega)}", "\\sigma e^{\\omega}", "\\omega (e^{\\sigma})^{\\sigma}"], "srepr_premise_expression": "Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Symbol('\\\\sigma', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "Mul(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\sigma', commutative=True), exp(Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), Pow(exp(Symbol('\\\\sigma', commutative=True)), Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\log{(\\beta - \\omega)}", "variable": "\\omega", "positive": "- \\beta \\log{(- \\beta + \\omega)} + \\omega \\log{(\\beta - \\omega)} - \\omega", "negatives": ["- \\beta \\log{(- \\beta + \\omega)} + \\omega \\log{(- \\beta + \\omega)} - \\omega", "\\beta \\log{(\\beta - \\omega)} - \\beta - \\omega \\log{(\\beta - \\omega)}", "\\omega (- \\beta + \\log{(\\omega^{\\beta})})", "\\frac{\\omega (\\omega + 2 \\cos{(\\beta)})}{2}"], "srepr_premise_expression": "log(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\omega', commutative=True)))), Mul(Symbol('\\\\omega', commutative=True), log(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\omega', commutative=True)))), Mul(Symbol('\\\\omega', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\omega', commutative=True)))), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))", "Add(Mul(Symbol('\\\\beta', commutative=True), log(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))), Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Symbol('\\\\omega', commutative=True), log(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))))", "Mul(Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), log(Pow(Symbol('\\\\omega', commutative=True), Symbol('\\\\beta', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), cos(Symbol('\\\\beta', commutative=True)))))"]}, {"premise_expression": "\\sin^{\\alpha}{(\\omega)}", "variable": "\\omega", "positive": "\\int \\sin^{\\alpha}{(\\omega)} d\\omega", "negatives": ["\\alpha \\sin{(\\omega)}", "\\frac{\\omega (\\omega + 2 \\sin{(\\alpha)})}{2}", "\\omega (\\log{(\\frac{\\alpha}{\\omega})} + 1)", "\\omega (- \\alpha + \\log{(\\omega)} - 1)"], "srepr_premise_expression": "Pow(sin(Symbol('\\\\omega', commutative=True)), Symbol('\\\\alpha', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Integral(Pow(sin(Symbol('\\\\omega', commutative=True)), Symbol('\\\\alpha', commutative=True)), Tuple(Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\alpha', commutative=True), sin(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), sin(Symbol('\\\\alpha', commutative=True)))))", "Mul(Symbol('\\\\omega', commutative=True), Add(log(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), log(Symbol('\\\\omega', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\sigma \\xi", "variable": "\\sigma", "positive": "\\frac{\\sigma^{2} \\xi}{2}", "negatives": ["\\frac{\\sigma \\xi^{2}}{2}", "\\xi e^{\\sigma}", "\\sigma \\cos{(1)}", "\\frac{\\sigma^{2} \\cos{(\\xi)}}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Mul(Symbol('\\\\xi', commutative=True), exp(Symbol('\\\\sigma', commutative=True)))", "Mul(Symbol('\\\\sigma', commutative=True), cos(Integer(1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), cos(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\chi + \\log{(\\beta)}", "variable": "\\beta", "positive": "\\beta (\\chi + \\log{(\\beta)} - 1)", "negatives": ["\\beta (- \\chi + \\log{(\\beta^{\\chi})})", "\\beta (\\log{(\\beta \\chi)} - 1)", "\\frac{\\chi (\\chi + 2 \\log{(\\beta)})}{2}", "\\frac{\\beta \\chi (\\beta - 2)}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\beta', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), log(Pow(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True)))))", "Mul(Symbol('\\\\beta', commutative=True), Add(log(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), log(Symbol('\\\\beta', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\beta', commutative=True), Integer(-2)))"]}, {"premise_expression": "\\sin{(\\gamma - \\pi)}", "variable": "\\gamma", "positive": "- \\cos{(\\gamma - \\pi)}", "negatives": ["\\cos{(\\gamma - \\pi)}", "\\sin{(\\gamma - \\pi)}", "\\frac{\\gamma^{2}}{2 \\pi}", "\\frac{\\gamma^{2} \\log{(\\pi)}}{2}"], "srepr_premise_expression": "sin(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))", "srepr_negatives": ["cos(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "sin(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), log(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\gamma + \\psi", "variable": "\\psi", "positive": "\\frac{\\psi (2 \\gamma + \\psi)}{2}", "negatives": ["\\frac{\\gamma (\\gamma + 2 \\psi)}{2}", "e^{- \\gamma + \\psi}", "\\cos{(\\gamma - \\psi)}", "\\frac{\\psi (\\psi + 2 \\cos{(\\gamma)})}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "exp(Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\psi', commutative=True)))", "cos(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(2), cos(Symbol('\\\\gamma', commutative=True)))))"]}, {"premise_expression": "- \\gamma + \\omega \\xi", "variable": "\\gamma", "positive": "\\frac{\\gamma (- \\gamma + 2 \\omega \\xi)}{2}", "negatives": ["\\frac{\\omega (- 2 \\gamma + \\omega \\xi)}{2}", "\\frac{\\xi (- 2 \\gamma + \\omega \\xi)}{2}", "\\frac{\\gamma (\\gamma \\xi + 2 \\omega)}{2}", "\\frac{\\gamma (- \\omega + \\xi)}{\\xi}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\alpha \\pi", "variable": "\\pi", "positive": "\\frac{\\alpha \\pi^{2}}{2}", "negatives": ["\\frac{\\alpha^{2} \\pi}{2}", "\\frac{\\pi^{2} \\cos{(\\alpha)}}{2}", "\\frac{\\pi (2 \\alpha - \\pi)}{2}", "\\alpha e^{\\frac{\\pi}{\\alpha}}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\pi', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), cos(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "Mul(Symbol('\\\\alpha', commutative=True), exp(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\cos^{\\psi}{(\\sigma)}", "variable": "\\sigma", "positive": "\\int \\cos^{\\psi}{(\\sigma)} d\\sigma", "negatives": ["- \\psi \\sigma - \\cos{(\\sigma)}", "- \\psi \\cos{(\\sigma)}", "e^{\\psi + \\sigma}", "\\sigma (\\log{(\\frac{\\psi}{\\sigma})} + 1)"], "srepr_premise_expression": "Pow(cos(Symbol('\\\\sigma', commutative=True)), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Integral(Pow(cos(Symbol('\\\\sigma', commutative=True)), Symbol('\\\\psi', commutative=True)), Tuple(Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\sigma', commutative=True))))", "Mul(Integer(-1), Symbol('\\\\psi', commutative=True), cos(Symbol('\\\\sigma', commutative=True)))", "exp(Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True)))", "Mul(Symbol('\\\\sigma', commutative=True), Add(log(Mul(Symbol('\\\\psi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))), Integer(1)))"]}, {"premise_expression": "\\log{(\\gamma \\xi)}", "variable": "\\gamma", "positive": "\\gamma (\\log{(\\gamma \\xi)} - 1)", "negatives": ["\\xi (\\log{(\\gamma \\xi)} - 1)", "\\gamma (\\log{(\\frac{\\xi}{\\gamma})} + 1)", "\\gamma (- \\xi + \\log{(\\gamma)} - 1)", "\\sin{(\\gamma - \\xi)}"], "srepr_premise_expression": "log(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\gamma', commutative=True), Add(log(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\xi', commutative=True), Add(log(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\gamma', commutative=True), Add(log(Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))), Integer(1)))", "Mul(Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), log(Symbol('\\\\gamma', commutative=True)), Integer(-1)))", "sin(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\log{(\\psi \\xi)}", "variable": "\\xi", "positive": "\\xi (\\log{(\\psi \\xi)} - 1)", "negatives": ["\\psi (\\log{(\\psi \\xi)} - 1)", "\\psi \\xi (\\log{(\\xi)} - 1)", "\\xi (- \\psi + \\log{(\\xi)} - 1)", "\\frac{\\xi^{2} \\log{(\\psi)}}{2}"], "srepr_premise_expression": "log(Mul(Symbol('\\\\psi', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\xi', commutative=True), Add(log(Mul(Symbol('\\\\psi', commutative=True), Symbol('\\\\xi', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\psi', commutative=True), Add(log(Mul(Symbol('\\\\psi', commutative=True), Symbol('\\\\xi', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\psi', commutative=True), Symbol('\\\\xi', commutative=True), Add(log(Symbol('\\\\xi', commutative=True)), Integer(-1)))", "Mul(Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), log(Symbol('\\\\xi', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), log(Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\sigma \\xi", "variable": "\\sigma", "positive": "\\frac{\\sigma^{2} \\xi}{2}", "negatives": ["\\frac{\\sigma \\xi^{2}}{2}", "\\frac{\\sigma^{2} e^{\\xi}}{2}", "\\frac{\\sigma (\\sigma + 2 \\xi)}{2}", "\\sin{(\\sigma - \\xi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), exp(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "sin(Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\frac{\\psi}{\\delta}", "variable": "\\delta", "positive": "\\psi \\log{(\\delta)}", "negatives": ["\\psi \\sin{(\\delta)}", "\\frac{\\psi^{2}}{2 \\delta}", "\\delta \\sin{(1)}", "- \\cos{(\\delta - \\psi)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\psi', commutative=True), log(Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\psi', commutative=True), sin(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "Mul(Symbol('\\\\delta', commutative=True), sin(Integer(1)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))"]}, {"premise_expression": "\\cos{(\\beta - \\pi)}", "variable": "\\pi", "positive": "- \\sin{(\\beta - \\pi)}", "negatives": ["\\sin{(\\beta - \\pi)}", "\\pi \\log{(2 \\beta)}", "\\frac{\\pi^{2}}{2 \\beta}", "- \\beta \\cos{(\\pi)}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Integer(-1), sin(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))", "srepr_negatives": ["sin(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "Mul(Symbol('\\\\pi', commutative=True), log(Mul(Integer(2), Symbol('\\\\beta', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "Mul(Integer(-1), Symbol('\\\\beta', commutative=True), cos(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\beta + \\frac{\\chi}{\\xi}", "variable": "\\chi", "positive": "\\beta \\chi + \\frac{\\chi^{2}}{2 \\xi}", "negatives": ["\\beta \\xi + \\chi \\log{(\\xi)}", "\\frac{\\chi^{2} (\\beta + \\xi)}{2}", "\\frac{\\chi (- 2 \\beta + \\chi \\xi)}{2}", "\\frac{\\beta \\chi^{2} \\xi}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\beta', commutative=True), Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))"]}, {"premise_expression": "- \\gamma + \\omega + \\pi", "variable": "\\pi", "positive": "\\pi (- \\gamma + \\omega + \\frac{\\pi}{2})", "negatives": ["\\frac{\\pi (2 \\gamma + 2 \\omega + \\pi)}{2}", "\\frac{\\omega (- 2 \\gamma + \\omega + 2 \\pi)}{2}", "\\frac{\\gamma (- \\gamma + 2 \\omega + 2 \\pi)}{2}", "\\frac{\\pi (\\gamma + \\omega)}{\\omega}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\omega', commutative=True), Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\log{(\\chi^{\\xi})}", "variable": "\\xi", "positive": "\\frac{\\xi^{2} \\log{(\\chi)}}{2}", "negatives": ["\\frac{\\xi^{2} \\sin{(\\chi)}}{2}", "\\frac{\\xi (2 \\chi + \\xi)}{2}", "\\chi \\log{(\\xi)} - \\xi", "\\xi (\\log{(\\chi \\xi)} - 1)"], "srepr_premise_expression": "log(Pow(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), log(Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), sin(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Add(Mul(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\xi', commutative=True))), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\xi', commutative=True), Add(log(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True))), Integer(-1)))"]}, {"premise_expression": "e^{\\beta - \\psi}", "variable": "\\beta", "positive": "e^{\\beta - \\psi}", "negatives": ["- e^{\\beta - \\psi}", "- \\cos{(\\beta - \\psi)}", "\\frac{\\beta (\\beta - 2 \\psi)}{2}", "- \\frac{\\cos{(\\beta)}}{\\psi}"], "srepr_premise_expression": "exp(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "exp(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Integer(-1), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), cos(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "\\cos{(\\frac{\\gamma}{\\sigma})}", "variable": "\\sigma", "positive": "\\gamma \\operatorname{Si}{(\\frac{\\gamma}{\\sigma})} + \\sigma \\cos{(\\frac{\\gamma}{\\sigma})}", "negatives": ["\\gamma \\sigma - \\cos{(\\sigma)}", "\\frac{\\sigma (- \\sigma + 2 \\cos{(\\gamma)})}{2}", "- \\gamma \\sigma - \\cos{(\\sigma)}", "\\frac{\\sigma (\\sigma + 2 e^{\\gamma})}{2}"], "srepr_premise_expression": "cos(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\gamma', commutative=True), Si(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1))))), Mul(Symbol('\\\\sigma', commutative=True), cos(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1))))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\gamma', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(2), exp(Symbol('\\\\gamma', commutative=True)))))"]}, {"premise_expression": "\\alpha \\beta", "variable": "\\alpha", "positive": "\\frac{\\alpha^{2} \\beta}{2}", "negatives": ["\\frac{\\alpha \\beta^{2}}{2}", "\\frac{\\alpha^{2} (\\beta - 1)}{2}", "\\frac{\\alpha (\\alpha + 2 \\beta)}{2}", "\\alpha (\\alpha + \\beta)"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\beta', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\beta', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Add(Symbol('\\\\beta', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\beta', commutative=True))))", "Mul(Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "\\beta \\omega + \\sigma", "variable": "\\beta", "positive": "\\frac{\\beta (\\beta \\omega + 2 \\sigma)}{2}", "negatives": ["\\frac{\\omega (\\beta \\omega + 2 \\sigma)}{2}", "\\frac{\\sigma (2 \\beta \\omega + \\sigma)}{2}", "\\frac{\\beta^{2} (- \\omega + \\sigma)}{2}", "\\beta (2 \\omega - \\sigma)"], "srepr_premise_expression": "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True)), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Symbol('\\\\beta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\cos{(\\frac{\\alpha}{\\pi})}", "variable": "\\pi", "positive": "\\alpha \\operatorname{Si}{(\\frac{\\alpha}{\\pi})} + \\pi \\cos{(\\frac{\\alpha}{\\pi})}", "negatives": ["- \\cos{(\\alpha + \\pi)}", "\\frac{\\pi (- \\pi + 2 \\sin{(\\alpha)})}{2}", "- \\cos{(\\alpha - \\pi)}", "\\frac{\\pi (- \\pi + 2 \\cos{(\\alpha)})}{2}"], "srepr_premise_expression": "cos(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\alpha', commutative=True), Si(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1))))), Mul(Symbol('\\\\pi', commutative=True), cos(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1))))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\alpha', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\alpha', commutative=True)))))"]}, {"premise_expression": "\\beta + \\gamma", "variable": "\\beta", "positive": "\\frac{\\beta (\\beta + 2 \\gamma)}{2}", "negatives": ["\\frac{\\beta (\\beta - 2 \\gamma)}{2}", "\\frac{\\gamma (2 \\beta + \\gamma)}{2}", "\\frac{\\beta^{2} \\gamma}{2}", "\\gamma \\log{(\\beta)}"], "srepr_premise_expression": "Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\gamma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\gamma', commutative=True))", "Mul(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "\\log{(\\beta - \\pi)}", "variable": "\\beta", "positive": "\\beta \\log{(\\beta - \\pi)} - \\beta - \\pi \\log{(\\beta - \\pi)}", "negatives": ["- \\beta \\log{(- \\beta + \\pi)} + \\pi \\log{(\\beta - \\pi)} - \\pi", "e^{\\pi} \\log{(\\beta)}", "\\beta (\\log{(\\frac{\\beta}{\\pi})} - 1)", "\\beta \\pi + e^{\\beta}"], "srepr_premise_expression": "log(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\beta', commutative=True), log(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))), Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Symbol('\\\\pi', commutative=True), log(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\pi', commutative=True)))), Mul(Symbol('\\\\pi', commutative=True), log(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))", "Mul(exp(Symbol('\\\\pi', commutative=True)), log(Symbol('\\\\beta', commutative=True)))", "Mul(Symbol('\\\\beta', commutative=True), Add(log(Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))), Integer(-1)))", "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\pi', commutative=True)), exp(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "- \\beta + e^{\\gamma}", "variable": "\\gamma", "positive": "- \\beta \\gamma + e^{\\gamma}", "negatives": ["\\beta \\gamma + e^{\\gamma}", "\\beta e^{\\gamma}", "\\frac{\\beta (- \\beta + 2 e^{\\gamma})}{2}", "- \\cos{(\\beta + \\gamma)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), exp(Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)), exp(Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)), exp(Symbol('\\\\gamma', commutative=True)))", "Mul(Symbol('\\\\beta', commutative=True), exp(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\gamma', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True))))"]}, {"premise_expression": "- \\alpha + e^{\\psi}", "variable": "\\psi", "positive": "- \\alpha \\psi + e^{\\psi}", "negatives": ["\\alpha \\psi - \\cos{(\\psi)}", "\\frac{\\alpha (- \\alpha + 2 e^{\\psi})}{2}", "\\frac{\\psi (\\psi + 2 e^{\\alpha})}{2}", "e^{\\alpha + \\psi}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), exp(Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True)), exp(Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\psi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(2), exp(Symbol('\\\\alpha', commutative=True)))))", "exp(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\log{(\\frac{\\beta}{\\xi})}", "variable": "\\beta", "positive": "\\beta (\\log{(\\frac{\\beta}{\\xi})} - 1)", "negatives": ["\\xi (\\log{(\\frac{\\beta}{\\xi})} + 1)", "\\sin{(\\beta + \\xi)}", "\\frac{\\beta (\\beta + 2 \\sin{(\\xi)})}{2}", "\\beta \\xi + e^{\\beta}"], "srepr_premise_expression": "log(Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\beta', commutative=True), Add(log(Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\xi', commutative=True), Add(log(Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))), Integer(1)))", "sin(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), sin(Symbol('\\\\xi', commutative=True)))))", "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True)), exp(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "\\beta \\pi", "variable": "\\beta", "positive": "\\frac{\\beta^{2} \\pi}{2}", "negatives": ["\\frac{\\beta \\pi^{2}}{2}", "\\log{(\\beta)} \\log{(\\pi)}", "- \\cos{(\\beta + \\pi)}", "\\frac{\\beta (\\beta + 2 \\cos{(\\pi)})}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\pi', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "Mul(log(Symbol('\\\\beta', commutative=True)), log(Symbol('\\\\pi', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), cos(Symbol('\\\\pi', commutative=True)))))"]}, {"premise_expression": "\\frac{\\sin{(\\pi)}}{\\beta}", "variable": "\\pi", "positive": "- \\frac{\\cos{(\\pi)}}{\\beta}", "negatives": ["\\cos{(\\beta - \\pi)}", "\\beta e^{\\pi}", "\\frac{\\pi^{2} \\log{(\\beta)}}{2}", "\\log{(\\pi)} \\sin{(\\beta)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), sin(Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Integer(-1), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), cos(Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "Mul(Symbol('\\\\beta', commutative=True), exp(Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), log(Symbol('\\\\beta', commutative=True)))", "Mul(log(Symbol('\\\\pi', commutative=True)), sin(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "- \\delta + \\sigma", "variable": "\\delta", "positive": "\\frac{\\delta (- \\delta + 2 \\sigma)}{2}", "negatives": ["\\frac{\\sigma (- 2 \\delta + \\sigma)}{2}", "\\frac{\\delta^{2} e^{\\sigma}}{2}", "- \\cos{(\\delta + \\sigma)}", "- \\frac{\\cos{(\\delta)}}{\\sigma}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), exp(Symbol('\\\\sigma', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True))))", "Mul(Integer(-1), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), cos(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\log{(\\frac{\\xi}{\\pi})}", "variable": "\\xi", "positive": "\\xi (\\log{(\\frac{\\xi}{\\pi})} - 1)", "negatives": ["\\pi (\\log{(\\frac{\\xi}{\\pi})} + 1)", "\\cos{(\\pi - \\xi)}", "\\sin{(\\pi + \\xi)}", "\\frac{\\xi (2 \\pi + \\xi)}{2}"], "srepr_premise_expression": "log(Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\xi', commutative=True), Add(log(Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\pi', commutative=True), Add(log(Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))), Integer(1)))", "cos(Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "sin(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "- \\pi + e^{\\gamma}", "variable": "\\gamma", "positive": "- \\gamma \\pi + e^{\\gamma}", "negatives": ["- \\gamma \\pi + \\sin{(\\gamma)}", "\\frac{\\pi (- \\pi + 2 e^{\\gamma})}{2}", "\\pi \\log{(\\gamma)}", "\\frac{\\gamma^{2}}{2 \\pi}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), exp(Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True)), exp(Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True)), sin(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\gamma', commutative=True)))))", "Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))"]}, {"premise_expression": "- \\chi + \\delta", "variable": "\\delta", "positive": "\\frac{\\delta (- 2 \\chi + \\delta)}{2}", "negatives": ["\\frac{\\chi (- \\chi + 2 \\delta)}{2}", "\\frac{\\delta (\\delta + 2 \\sin{(\\chi)})}{2}", "\\frac{\\delta^{2} \\log{(\\chi)}}{2}", "\\frac{\\delta^{2} \\sin{(\\chi)}}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\delta', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), sin(Symbol('\\\\chi', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), log(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), sin(Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "\\beta \\gamma", "variable": "\\beta", "positive": "\\frac{\\beta^{2} \\gamma}{2}", "negatives": ["\\frac{\\beta \\gamma^{2}}{2}", "\\frac{\\beta (- \\beta + 2 \\gamma)}{2}", "\\gamma e^{\\beta}", "- \\gamma \\cos{(\\beta)}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\gamma', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\gamma', commutative=True))))", "Mul(Symbol('\\\\gamma', commutative=True), exp(Symbol('\\\\beta', commutative=True)))", "Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), cos(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "\\cos{(\\omega + \\xi)}", "variable": "\\xi", "positive": "\\sin{(\\omega + \\xi)}", "negatives": ["\\cos{(\\omega - \\xi)}", "- \\cos{(\\omega - \\xi)}", "\\omega e^{\\xi}", "\\omega \\log{(\\xi)}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "sin(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["cos(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))))", "Mul(Symbol('\\\\omega', commutative=True), exp(Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "- \\alpha + \\beta", "variable": "\\alpha", "positive": "\\frac{\\alpha (- \\alpha + 2 \\beta)}{2}", "negatives": ["\\frac{\\beta (- 2 \\alpha + \\beta)}{2}", "\\frac{\\alpha (\\alpha + 2 \\cos{(\\beta)})}{2}", "\\frac{\\alpha^{2} \\beta}{2}", "\\frac{\\alpha^{2} \\cos{(\\beta)}}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\beta', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\beta', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), cos(Symbol('\\\\beta', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\beta', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), cos(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "- \\pi + \\sigma^{\\gamma}", "variable": "\\pi", "positive": "\\frac{\\pi (- \\pi + 2 \\sigma^{\\gamma})}{2}", "negatives": ["- \\frac{\\pi (\\pi - 2 \\sigma)}{2 \\gamma}", "\\frac{\\pi (\\pi - 2 \\sigma)}{2 \\gamma}", "\\frac{\\pi (- 2 \\gamma + \\pi - 2 \\sigma)}{2}", "\\frac{\\pi \\sigma (2 \\gamma + \\pi)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Pow(Symbol('\\\\sigma', commutative=True), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), Pow(Symbol('\\\\sigma', commutative=True), Symbol('\\\\gamma', commutative=True)))))", "srepr_negatives": ["Mul(Integer(-1), Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\xi + \\frac{\\pi}{\\delta}", "variable": "\\pi", "positive": "\\pi \\xi + \\frac{\\pi^{2}}{2 \\delta}", "negatives": ["\\delta \\xi + \\pi \\log{(\\delta)}", "\\delta \\pi + \\xi \\log{(\\pi)}", "\\frac{\\pi (2 \\delta + \\pi \\xi)}{2}", "\\frac{\\xi^{2}}{2} + \\frac{\\pi \\xi}{\\delta}"], "srepr_premise_expression": "Add(Symbol('\\\\xi', commutative=True), Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Pow(Symbol('\\\\pi', commutative=True), Integer(2))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\delta', commutative=True))))", "Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True))))", "Add(Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2))), Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "e^{\\alpha + \\pi}", "variable": "\\alpha", "positive": "e^{\\alpha + \\pi}", "negatives": ["\\pi e^{\\alpha}", "- \\pi \\cos{(\\alpha)}", "- \\frac{\\cos{(\\alpha)}}{\\pi}", "\\alpha (\\log{(\\frac{\\alpha}{\\pi})} - 1)"], "srepr_premise_expression": "exp(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "exp(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\pi', commutative=True), exp(Symbol('\\\\alpha', commutative=True)))", "Mul(Integer(-1), Symbol('\\\\pi', commutative=True), cos(Symbol('\\\\alpha', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), cos(Symbol('\\\\alpha', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), Add(log(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))), Integer(-1)))"]}, {"premise_expression": "- \\chi + \\cos{(\\pi)}", "variable": "\\pi", "positive": "- \\chi \\pi + \\sin{(\\pi)}", "negatives": ["- \\chi \\pi - \\cos{(\\pi)}", "\\chi \\pi - \\cos{(\\pi)}", "\\frac{\\pi^{2} \\sin{(\\chi)}}{2}", "\\frac{\\sin{(\\pi)}}{\\chi}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), cos(Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True)), sin(Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\pi', commutative=True))))", "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), sin(Symbol('\\\\chi', commutative=True)))", "Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), sin(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\sin{(\\alpha + \\chi)}", "variable": "\\chi", "positive": "- \\cos{(\\alpha + \\chi)}", "negatives": ["- \\alpha \\chi + \\sin{(\\chi)}", "\\alpha e^{\\chi}", "\\frac{\\chi^{2}}{2 \\alpha}", "\\chi (\\log{(\\frac{\\chi}{\\alpha})} - 1)"], "srepr_premise_expression": "sin(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)), sin(Symbol('\\\\chi', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), exp(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\chi', commutative=True), Integer(2)))", "Mul(Symbol('\\\\chi', commutative=True), Add(log(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\chi', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\frac{\\xi}{\\sigma}", "variable": "\\xi", "positive": "\\frac{\\xi^{2}}{2 \\sigma}", "negatives": ["\\xi \\log{(\\sigma)}", "\\frac{\\sigma \\xi^{2}}{2}", "\\frac{\\xi (2 \\sigma + \\xi)}{2}", "\\sin{(\\sigma + \\xi)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\sigma', commutative=True)), Symbol('\\\\xi', commutative=True)))", "sin(Add(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\chi + \\pi", "variable": "\\chi", "positive": "\\frac{\\chi (\\chi + 2 \\pi)}{2}", "negatives": ["\\frac{\\chi (- \\chi + 2 \\pi)}{2}", "\\frac{\\pi (2 \\chi + \\pi)}{2}", "\\frac{\\chi^{2}}{2 \\pi}", "\\frac{\\chi^{2} \\pi}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\pi', commutative=True))"]}, {"premise_expression": "\\cos^{\\xi}{(\\pi)}", "variable": "\\pi", "positive": "\\int \\cos^{\\xi}{(\\pi)} d\\pi", "negatives": ["e^{\\xi} \\log{(\\pi)}", "- e^{- \\pi + \\xi}", "\\sin{(\\pi - \\xi)}", "\\frac{\\pi (- \\pi + 2 \\xi)}{2}"], "srepr_premise_expression": "Pow(cos(Symbol('\\\\pi', commutative=True)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Integral(Pow(cos(Symbol('\\\\pi', commutative=True)), Symbol('\\\\xi', commutative=True)), Tuple(Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(exp(Symbol('\\\\xi', commutative=True)), log(Symbol('\\\\pi', commutative=True)))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Symbol('\\\\xi', commutative=True))))", "sin(Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\frac{\\log{(\\psi)}}{\\pi}", "variable": "\\pi", "positive": "\\log{(\\pi)} \\log{(\\psi)}", "negatives": ["e^{\\pi + \\psi}", "\\frac{\\psi (\\log{(\\psi)} - 1)}{\\pi}", "\\psi e^{\\frac{\\pi}{\\psi}}", "- \\frac{\\cos{(\\pi)}}{\\psi}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), log(Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(log(Symbol('\\\\pi', commutative=True)), log(Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["exp(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)))", "Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True), Add(log(Symbol('\\\\psi', commutative=True)), Integer(-1)))", "Mul(Symbol('\\\\psi', commutative=True), exp(Mul(Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))))", "Mul(Integer(-1), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), cos(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "- \\sin{(\\chi - \\sigma)}", "variable": "\\sigma", "positive": "- \\cos{(\\chi - \\sigma)}", "negatives": ["\\cos{(\\chi - \\sigma)}", "- \\chi \\cos{(\\sigma)}", "2 \\chi \\sigma", "\\frac{\\sigma (2 \\chi - \\sigma)}{2}"], "srepr_premise_expression": "Mul(Integer(-1), sin(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))", "srepr_negatives": ["cos(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Integer(-1), Symbol('\\\\chi', commutative=True), cos(Symbol('\\\\sigma', commutative=True)))", "Mul(Integer(2), Symbol('\\\\chi', commutative=True), Symbol('\\\\sigma', commutative=True))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\frac{- \\chi + \\omega}{\\xi}", "variable": "\\chi", "positive": "\\frac{\\chi (- \\chi + 2 \\omega)}{2 \\xi}", "negatives": ["\\frac{\\chi (\\chi + 2 \\omega)}{2 \\xi}", "\\frac{\\omega (- 2 \\chi + \\omega)}{2 \\xi}", "\\frac{\\chi (- \\chi + 2 \\xi^{\\omega})}{2}", "\\frac{\\chi \\xi (\\chi - 2 \\omega)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Pow(Symbol('\\\\xi', commutative=True), Symbol('\\\\omega', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True))))"]}, {"premise_expression": "\\psi \\xi", "variable": "\\psi", "positive": "\\frac{\\psi^{2} \\xi}{2}", "negatives": ["\\frac{\\psi \\xi^{2}}{2}", "\\frac{\\psi^{2}}{2 \\xi}", "\\frac{\\psi (\\psi - 2 \\xi)}{2}", "\\xi e^{\\psi}"], "srepr_premise_expression": "Mul(Symbol('\\\\psi', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Symbol('\\\\xi', commutative=True), exp(Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\gamma + \\pi", "variable": "\\pi", "positive": "\\frac{\\pi (2 \\gamma + \\pi)}{2}", "negatives": ["\\frac{\\gamma (\\gamma + 2 \\pi)}{2}", "\\frac{\\pi^{2} e^{\\gamma}}{2}", "\\cos{(\\gamma - \\pi)}", "\\frac{\\pi^{2} (\\gamma - 1)}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), exp(Symbol('\\\\gamma', commutative=True)))", "cos(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), Add(Symbol('\\\\gamma', commutative=True), Integer(-1)))"]}, {"premise_expression": "\\beta + \\omega", "variable": "\\omega", "positive": "\\frac{\\omega (2 \\beta + \\omega)}{2}", "negatives": ["\\frac{\\beta (\\beta + 2 \\omega)}{2}", "\\frac{\\omega^{2} \\log{(\\beta)}}{2}", "- \\cos{(\\beta + \\omega)}", "- \\sin{(\\beta - \\omega)}"], "srepr_premise_expression": "Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), log(Symbol('\\\\beta', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True))))", "Mul(Integer(-1), sin(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))))"]}, {"premise_expression": "\\frac{\\cos{(\\sigma)}}{\\pi}", "variable": "\\sigma", "positive": "\\frac{\\sin{(\\sigma)}}{\\pi}", "negatives": ["\\pi \\sin{(\\sigma)}", "\\pi e^{\\sigma}", "- \\pi \\cos{(\\sigma)}", "\\pi \\sigma + \\sin{(\\sigma)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), cos(Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), sin(Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\pi', commutative=True), sin(Symbol('\\\\sigma', commutative=True)))", "Mul(Symbol('\\\\pi', commutative=True), exp(Symbol('\\\\sigma', commutative=True)))", "Mul(Integer(-1), Symbol('\\\\pi', commutative=True), cos(Symbol('\\\\sigma', commutative=True)))", "Add(Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True)), sin(Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "- \\sin{(\\alpha - \\chi)}", "variable": "\\alpha", "positive": "\\cos{(\\alpha - \\chi)}", "negatives": ["- \\cos{(\\alpha - \\chi)}", "\\sin{(\\alpha + \\chi)}", "\\sin{(\\alpha - \\chi)}", "e^{\\alpha + \\chi}"], "srepr_premise_expression": "Mul(Integer(-1), sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True)))))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True)))))", "sin(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)))", "sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True))))", "exp(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "\\log{(\\chi \\pi)}", "variable": "\\pi", "positive": "\\pi (\\log{(\\chi \\pi)} - 1)", "negatives": ["\\chi (\\log{(\\chi \\pi)} - 1)", "\\pi (\\log{(\\frac{\\chi}{\\pi})} + 1)", "\\frac{\\pi^{2} (\\chi - 1)}{2}", "\\pi (- \\chi + \\log{(\\pi^{\\chi})})"], "srepr_premise_expression": "log(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\pi', commutative=True), Add(log(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\chi', commutative=True), Add(log(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\pi', commutative=True), Add(log(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), Add(Symbol('\\\\chi', commutative=True), Integer(-1)))", "Mul(Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), log(Pow(Symbol('\\\\pi', commutative=True), Symbol('\\\\chi', commutative=True)))))"]}, {"premise_expression": "\\beta \\xi", "variable": "\\xi", "positive": "\\frac{\\beta \\xi^{2}}{2}", "negatives": ["\\frac{\\beta^{2} \\xi}{2}", "\\frac{\\xi^{2}}{2 \\beta}", "\\frac{\\xi (2 \\beta + \\xi)}{2}", "- \\frac{\\cos{(\\xi)}}{\\beta}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), cos(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\alpha \\omega", "variable": "\\omega", "positive": "\\frac{\\alpha \\omega^{2}}{2}", "negatives": ["\\frac{\\alpha^{2} \\omega}{2}", "\\frac{\\omega^{2} \\log{(\\alpha)}}{2}", "- \\sin{(\\alpha - \\omega)}", "\\alpha \\omega + e^{\\omega}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\omega', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), log(Symbol('\\\\alpha', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)), exp(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\log{(\\pi + \\psi)}", "variable": "\\pi", "positive": "\\pi \\log{(\\pi + \\psi)} - \\pi + \\psi \\log{(\\pi + \\psi)}", "negatives": ["\\pi \\log{(\\pi + \\psi)} + \\psi \\log{(\\pi + \\psi)} - \\psi", "\\pi (- \\psi + \\log{(\\pi^{\\psi})})", "\\frac{\\pi (\\pi - 2 \\psi)}{2}", "\\psi \\log{(\\pi)}"], "srepr_premise_expression": "log(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\pi', commutative=True), log(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Symbol('\\\\psi', commutative=True), log(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\pi', commutative=True), log(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)))), Mul(Symbol('\\\\psi', commutative=True), log(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))", "Mul(Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), log(Pow(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Symbol('\\\\psi', commutative=True), log(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\psi + e^{\\omega}", "variable": "\\psi", "positive": "\\frac{\\psi (\\psi + 2 e^{\\omega})}{2}", "negatives": ["\\frac{\\psi (\\psi + 2 \\cos{(\\omega)})}{2}", "\\frac{\\psi (- \\psi + 2 \\sin{(\\omega)})}{2}", "\\omega \\psi + e^{\\omega}", "\\frac{\\psi (2 \\omega - \\psi)}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\psi', commutative=True), exp(Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(2), exp(Symbol('\\\\omega', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(2), cos(Symbol('\\\\omega', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\omega', commutative=True)))))", "Add(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True)), exp(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "\\log{(\\delta \\sigma)}", "variable": "\\delta", "positive": "\\delta (\\log{(\\delta \\sigma)} - 1)", "negatives": ["\\sigma (\\log{(\\delta \\sigma)} - 1)", "\\frac{\\delta (\\delta + 2 \\cos{(\\sigma)})}{2}", "\\frac{\\delta (\\delta + 2 \\sin{(\\sigma)})}{2}", "\\frac{\\delta (- \\delta + 2 \\sin{(\\sigma)})}{2}"], "srepr_premise_expression": "log(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\delta', commutative=True), Add(log(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\sigma', commutative=True), Add(log(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), cos(Symbol('\\\\sigma', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), sin(Symbol('\\\\sigma', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\sigma', commutative=True)))))"]}, {"premise_expression": "- \\alpha + \\xi", "variable": "\\alpha", "positive": "\\frac{\\alpha (- \\alpha + 2 \\xi)}{2}", "negatives": ["\\frac{\\xi (- 2 \\alpha + \\xi)}{2}", "\\sin{(\\alpha - \\xi)}", "\\frac{\\alpha^{2} \\xi}{2}", "\\frac{\\alpha^{2}}{2 \\xi}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\xi', commutative=True)))", "sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))"]}, {"premise_expression": "\\log{(- \\alpha + \\xi)}", "variable": "\\xi", "positive": "- \\alpha \\log{(- \\alpha + \\xi)} + \\xi \\log{(- \\alpha + \\xi)} - \\xi", "negatives": ["\\alpha \\log{(- \\alpha + \\xi)} - \\alpha - \\xi \\log{(\\alpha - \\xi)}", "\\frac{\\xi (- \\xi + 2 \\log{(\\alpha)})}{2}", "- \\alpha \\xi - \\cos{(\\xi)}", "\\frac{\\xi (\\xi + 2 e^{\\alpha})}{2}"], "srepr_premise_expression": "log(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\xi', commutative=True)))), Mul(Symbol('\\\\xi', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\xi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\alpha', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\xi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), log(Symbol('\\\\alpha', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\xi', commutative=True), Mul(Integer(2), exp(Symbol('\\\\alpha', commutative=True)))))"]}, {"premise_expression": "\\sigma + \\xi", "variable": "\\sigma", "positive": "\\frac{\\sigma (\\sigma + 2 \\xi)}{2}", "negatives": ["\\frac{\\xi (2 \\sigma + \\xi)}{2}", "\\frac{\\sigma^{2} \\sin{(\\xi)}}{2}", "\\frac{\\sigma^{2} (1 - \\xi)}{2 \\xi}", "\\frac{\\sigma^{2} \\xi}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\sigma', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), sin(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), Add(Integer(1), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))"]}, {"premise_expression": "- \\sigma + \\sin{(\\chi)}", "variable": "\\sigma", "positive": "\\frac{\\sigma (- \\sigma + 2 \\sin{(\\chi)})}{2}", "negatives": ["\\frac{\\sigma (- \\sigma + 2 \\log{(\\chi)})}{2}", "\\frac{\\sigma^{2} e^{\\chi}}{2}", "\\log{(\\sigma)} \\sin{(\\chi)}", "- \\chi \\sigma - \\cos{(\\chi)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), sin(Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\chi', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), Mul(Integer(2), log(Symbol('\\\\chi', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), exp(Symbol('\\\\chi', commutative=True)))", "Mul(log(Symbol('\\\\sigma', commutative=True)), sin(Symbol('\\\\chi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\chi', commutative=True))))"]}, {"premise_expression": "\\alpha + \\sigma + \\xi", "variable": "\\xi", "positive": "\\xi (\\alpha + \\sigma + \\frac{\\xi}{2})", "negatives": ["\\frac{\\xi (- 2 \\alpha + 2 \\sigma + \\xi)}{2}", "\\frac{\\sigma (2 \\alpha + \\sigma + 2 \\xi)}{2}", "\\frac{\\alpha (\\alpha + 2 \\sigma + 2 \\xi)}{2}", "\\xi (\\alpha + \\xi)"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True), Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\sigma', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\cos{(\\omega + \\sigma)}", "variable": "\\omega", "positive": "\\sin{(\\omega + \\sigma)}", "negatives": ["\\sin{(\\omega - \\sigma)}", "\\omega \\sigma - \\cos{(\\omega)}", "e^{\\sigma} \\log{(\\omega)}", "\\omega \\sigma + e^{\\omega}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "sin(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["sin(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Add(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\omega', commutative=True))))", "Mul(exp(Symbol('\\\\sigma', commutative=True)), log(Symbol('\\\\omega', commutative=True)))", "Add(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True)), exp(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\frac{\\gamma \\omega}{\\alpha}", "variable": "\\alpha", "positive": "\\gamma \\omega \\log{(\\alpha)}", "negatives": ["\\frac{\\gamma \\omega^{2}}{2 \\alpha}", "(- \\gamma + \\omega) \\log{(\\alpha)}", "\\frac{\\gamma^{2} \\omega}{2 \\alpha}", "\\frac{\\alpha^{2} \\gamma}{2 \\omega}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "Mul(Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\omega', commutative=True)), log(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Symbol('\\\\omega', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))"]}, {"premise_expression": "\\log{(- \\beta + \\pi)}", "variable": "\\pi", "positive": "- \\beta \\log{(- \\beta + \\pi)} + \\pi \\log{(- \\beta + \\pi)} - \\pi", "negatives": ["\\beta \\log{(- \\beta + \\pi)} - \\beta - \\pi \\log{(\\beta - \\pi)}", "\\pi (- \\beta + \\log{(\\pi)} - 1)", "\\beta \\pi (\\log{(\\pi)} - 1)", "- \\beta \\operatorname{Ei}{(\\frac{\\beta}{\\pi})} + \\pi e^{\\frac{\\beta}{\\pi}}"], "srepr_premise_expression": "log(Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\pi', commutative=True)))), Mul(Symbol('\\\\pi', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\pi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\beta', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\pi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Symbol('\\\\pi', commutative=True), log(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))))", "Mul(Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), log(Symbol('\\\\pi', commutative=True)), Integer(-1)))", "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\pi', commutative=True), Add(log(Symbol('\\\\pi', commutative=True)), Integer(-1)))", "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Ei(Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1))))), Mul(Symbol('\\\\pi', commutative=True), exp(Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1))))))"]}, {"premise_expression": "\\log{(\\alpha - \\pi)}", "variable": "\\pi", "positive": "- \\alpha \\log{(- \\alpha + \\pi)} + \\pi \\log{(\\alpha - \\pi)} - \\pi", "negatives": ["\\alpha \\log{(\\alpha - \\pi)} - \\alpha - \\pi \\log{(\\alpha - \\pi)}", "\\pi (- \\alpha + \\log{(\\pi^{\\alpha})})", "\\log{(\\pi)} \\cos{(\\alpha)}", "\\frac{\\pi (- \\pi + 2 \\sin{(\\alpha)})}{2}"], "srepr_premise_expression": "log(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\pi', commutative=True)))), Mul(Symbol('\\\\pi', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\alpha', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))), Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\pi', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))))", "Mul(Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), log(Pow(Symbol('\\\\pi', commutative=True), Symbol('\\\\alpha', commutative=True)))))", "Mul(log(Symbol('\\\\pi', commutative=True)), cos(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\alpha', commutative=True)))))"]}, {"premise_expression": "- \\omega + e^{\\chi}", "variable": "\\omega", "positive": "\\frac{\\omega (- \\omega + 2 e^{\\chi})}{2}", "negatives": ["- \\chi \\omega + e^{\\chi}", "\\chi \\omega + e^{\\omega}", "\\frac{\\omega^{2} \\cos{(\\chi)}}{2}", "\\cos{(\\chi - \\omega)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), exp(Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\chi', commutative=True)))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True)), exp(Symbol('\\\\chi', commutative=True)))", "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True)), exp(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), cos(Symbol('\\\\chi', commutative=True)))", "cos(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))"]}, {"premise_expression": "\\alpha - \\gamma", "variable": "\\alpha", "positive": "\\frac{\\alpha (\\alpha - 2 \\gamma)}{2}", "negatives": ["\\frac{\\gamma (2 \\alpha - \\gamma)}{2}", "\\frac{\\alpha^{2} \\log{(\\gamma)}}{2}", "\\sin{(\\alpha - \\gamma)}", "- \\cos{(\\alpha - \\gamma)}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), log(Symbol('\\\\gamma', commutative=True)))", "sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))))"]}, {"premise_expression": "\\pi + \\xi", "variable": "\\pi", "positive": "\\frac{\\pi (\\pi + 2 \\xi)}{2}", "negatives": ["\\frac{\\xi (2 \\pi + \\xi)}{2}", "\\frac{\\pi^{2} \\sin{(\\xi)}}{2}", "\\frac{\\pi^{2}}{2 \\xi}", "\\frac{\\sin{(\\pi)}}{\\xi}"], "srepr_premise_expression": "Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), sin(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "Mul(Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), sin(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\frac{\\cos{(\\alpha)}}{\\xi}", "variable": "\\alpha", "positive": "\\frac{\\sin{(\\alpha)}}{\\xi}", "negatives": ["\\xi e^{\\frac{\\alpha}{\\xi}}", "- \\cos{(\\alpha + \\xi)}", "\\log{(\\alpha)} \\sin{(\\xi)}", "\\log{(\\xi)} \\cos{(\\alpha)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), cos(Symbol('\\\\alpha', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), sin(Symbol('\\\\alpha', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\xi', commutative=True), exp(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True))))", "Mul(log(Symbol('\\\\alpha', commutative=True)), sin(Symbol('\\\\xi', commutative=True)))", "Mul(log(Symbol('\\\\xi', commutative=True)), cos(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\pi + \\sigma", "variable": "\\pi", "positive": "\\frac{\\pi (\\pi + 2 \\sigma)}{2}", "negatives": ["\\frac{\\sigma (2 \\pi + \\sigma)}{2}", "\\frac{\\pi (- \\pi + 2 e^{\\sigma})}{2}", "- \\cos{(\\pi + \\sigma)}", "- \\pi \\sigma + e^{\\pi}"], "srepr_premise_expression": "Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\sigma', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True)), exp(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\frac{\\sigma}{\\delta}", "variable": "\\sigma", "positive": "\\frac{\\sigma^{2}}{2 \\delta}", "negatives": ["\\sigma \\log{(\\delta)}", "\\delta e^{\\frac{\\sigma}{\\delta}}", "\\delta e^{\\sigma}", "\\frac{\\sigma \\cos{(\\delta)}}{\\delta}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\delta', commutative=True)))", "Mul(Symbol('\\\\delta', commutative=True), exp(Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))))", "Mul(Symbol('\\\\delta', commutative=True), exp(Symbol('\\\\sigma', commutative=True)))", "Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True), cos(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\alpha + \\cos{(\\gamma)}", "variable": "\\gamma", "positive": "\\alpha \\gamma + \\sin{(\\gamma)}", "negatives": ["- \\alpha \\cos{(\\gamma)}", "\\alpha \\log{(\\gamma)}", "\\sin{(\\alpha + \\gamma)}", "\\frac{\\alpha (\\alpha + 2 \\cos{(\\gamma)})}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), cos(Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True)), sin(Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), cos(Symbol('\\\\gamma', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "sin(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), cos(Symbol('\\\\gamma', commutative=True)))))"]}, {"premise_expression": "\\chi + \\psi", "variable": "\\psi", "positive": "\\frac{\\psi (2 \\chi + \\psi)}{2}", "negatives": ["\\frac{\\chi (\\chi + 2 \\psi)}{2}", "- \\sin{(\\chi - \\psi)}", "\\cos{(\\chi - \\psi)}", "\\chi \\sin{(\\psi)}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Integer(-1), sin(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))", "cos(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(Symbol('\\\\chi', commutative=True), sin(Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\alpha \\psi", "variable": "\\alpha", "positive": "\\frac{\\alpha^{2} \\psi}{2}", "negatives": ["\\frac{\\alpha \\psi^{2}}{2}", "\\psi \\log{(\\alpha)}", "\\sin{(\\alpha - \\psi)}", "e^{\\alpha - \\psi}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "Mul(Symbol('\\\\psi', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "exp(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "- \\chi + \\sin{(\\gamma)}", "variable": "\\chi", "positive": "\\frac{\\chi (- \\chi + 2 \\sin{(\\gamma)})}{2}", "negatives": ["\\frac{\\chi (- \\chi + 2 \\cos{(\\gamma)})}{2}", "\\frac{\\chi (\\chi - 2 \\gamma)}{2}", "- \\chi \\gamma - \\cos{(\\gamma)}", "\\frac{\\chi^{2} \\gamma}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), sin(Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\gamma', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\gamma', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\gamma', commutative=True))"]}, {"premise_expression": "\\xi + \\sin{(\\chi)}", "variable": "\\chi", "positive": "\\chi \\xi - \\cos{(\\chi)}", "negatives": ["\\sin{(\\chi + \\xi)}", "\\cos{(\\chi - \\xi)}", "\\frac{\\xi (\\xi + 2 \\sin{(\\chi)})}{2}", "\\frac{\\chi^{2} \\sin{(\\xi)}}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\xi', commutative=True), sin(Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\chi', commutative=True))))", "srepr_negatives": ["sin(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True)))", "cos(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\xi', commutative=True), Mul(Integer(2), sin(Symbol('\\\\chi', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), sin(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\frac{\\chi \\xi}{\\gamma}", "variable": "\\xi", "positive": "\\frac{\\chi \\xi^{2}}{2 \\gamma}", "negatives": ["\\frac{\\chi^{2} \\xi}{2 \\gamma}", "\\frac{\\xi^{2}}{2 \\chi \\gamma}", "\\chi \\xi \\log{(\\gamma)}", "\\chi \\gamma \\log{(\\xi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\sigma + \\sin{(\\chi)}", "variable": "\\sigma", "positive": "\\frac{\\sigma (\\sigma + 2 \\sin{(\\chi)})}{2}", "negatives": ["\\frac{\\sigma^{2} \\log{(\\chi)}}{2}", "\\chi \\sigma - \\cos{(\\chi)}", "\\frac{\\sigma (2 \\chi - \\sigma)}{2}", "\\sigma (\\chi + \\log{(\\sigma)} - 1)"], "srepr_premise_expression": "Add(Symbol('\\\\sigma', commutative=True), sin(Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(2), sin(Symbol('\\\\chi', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), log(Symbol('\\\\chi', commutative=True)))", "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\chi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\sigma', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\alpha \\chi", "variable": "\\chi", "positive": "\\frac{\\alpha \\chi^{2}}{2}", "negatives": ["\\frac{\\alpha^{2} \\chi}{2}", "\\frac{\\chi^{2} e^{\\alpha}}{2}", "\\frac{\\sin{(\\chi)}}{\\alpha}", "- \\frac{\\cos{(\\chi)}}{\\alpha}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\chi', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), exp(Symbol('\\\\alpha', commutative=True)))", "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), sin(Symbol('\\\\chi', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), cos(Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "\\log{(\\frac{\\omega}{\\delta})}", "variable": "\\omega", "positive": "\\omega (\\log{(\\frac{\\omega}{\\delta})} - 1)", "negatives": ["\\delta (\\log{(\\frac{\\omega}{\\delta})} + 1)", "\\delta \\omega (\\log{(\\omega)} - 1)", "\\omega (- \\delta + \\log{(\\omega)} - 1)", "\\frac{\\omega^{2} \\log{(\\delta)}}{2}"], "srepr_premise_expression": "log(Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\omega', commutative=True), Add(log(Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\delta', commutative=True), Add(log(Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True))), Integer(1)))", "Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True), Add(log(Symbol('\\\\omega', commutative=True)), Integer(-1)))", "Mul(Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), log(Symbol('\\\\omega', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), log(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\frac{\\pi}{\\alpha}", "variable": "\\alpha", "positive": "\\pi \\log{(\\alpha)}", "negatives": ["\\frac{\\pi^{2}}{2 \\alpha}", "\\alpha \\pi + e^{\\alpha}", "- \\cos{(\\alpha - \\pi)}", "\\cos{(\\alpha - \\pi)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)), exp(Symbol('\\\\alpha', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))", "cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "e^{\\sigma + \\xi}", "variable": "\\xi", "positive": "e^{\\sigma + \\xi}", "negatives": ["- \\cos{(\\sigma + \\xi)}", "\\sigma \\xi + e^{\\xi}", "- \\sigma \\xi + \\sin{(\\xi)}", "\\frac{\\sin{(\\xi)}}{\\sigma}"], "srepr_premise_expression": "exp(Add(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "exp(Add(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True))))", "Add(Mul(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True)), exp(Symbol('\\\\xi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True)), sin(Symbol('\\\\xi', commutative=True)))", "Mul(Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), sin(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\sin{(\\delta - \\sigma)}", "variable": "\\sigma", "positive": "\\cos{(\\delta - \\sigma)}", "negatives": ["- \\cos{(\\delta - \\sigma)}", "e^{- \\delta + \\sigma}", "- \\frac{\\cos{(\\sigma)}}{\\delta}", "\\frac{\\sigma (\\log{(\\sigma)} - 1)}{\\delta}"], "srepr_premise_expression": "sin(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))", "exp(Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), cos(Symbol('\\\\sigma', commutative=True)))", "Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True), Add(log(Symbol('\\\\sigma', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\frac{\\psi - \\sigma}{\\pi}", "variable": "\\sigma", "positive": "\\frac{\\sigma (2 \\psi - \\sigma)}{2 \\pi}", "negatives": ["\\frac{\\sigma (2 \\psi + \\sigma)}{2 \\pi}", "- \\frac{\\psi (- \\psi + 2 \\sigma)}{2 \\pi}", "\\frac{\\sigma (2 \\psi^{\\pi} - \\sigma)}{2}", "\\frac{\\sigma (2 \\pi \\psi - \\sigma)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\psi', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Integer(-1), Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Pow(Symbol('\\\\psi', commutative=True), Symbol('\\\\pi', commutative=True))), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\sin^{\\pi}{(\\xi)}", "variable": "\\xi", "positive": "\\int \\sin^{\\pi}{(\\xi)} d\\xi", "negatives": ["\\pi \\xi (\\log{(\\xi)} - 1)", "\\log{(\\xi)} \\cos{(\\pi)}", "\\pi \\log{(\\xi)}", "\\frac{\\xi (2 \\pi - \\xi)}{2}"], "srepr_premise_expression": "Pow(sin(Symbol('\\\\xi', commutative=True)), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Integral(Pow(sin(Symbol('\\\\xi', commutative=True)), Symbol('\\\\pi', commutative=True)), Tuple(Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True), Add(log(Symbol('\\\\xi', commutative=True)), Integer(-1)))", "Mul(log(Symbol('\\\\xi', commutative=True)), cos(Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\cos{(\\frac{\\gamma}{\\xi})}", "variable": "\\xi", "positive": "\\gamma \\operatorname{Si}{(\\frac{\\gamma}{\\xi})} + \\xi \\cos{(\\frac{\\gamma}{\\xi})}", "negatives": ["\\frac{\\xi (- \\xi + 2 \\sin{(\\gamma)})}{2}", "- \\gamma \\xi - \\cos{(\\xi)}", "e^{\\gamma} \\log{(\\xi)}", "e^{- \\gamma + \\xi}"], "srepr_premise_expression": "cos(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\gamma', commutative=True), Si(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))), Mul(Symbol('\\\\xi', commutative=True), cos(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\gamma', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\xi', commutative=True))))", "Mul(exp(Symbol('\\\\gamma', commutative=True)), log(Symbol('\\\\xi', commutative=True)))", "exp(Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\beta + \\sin{(\\delta)}", "variable": "\\delta", "positive": "\\beta \\delta - \\cos{(\\delta)}", "negatives": ["\\frac{\\delta^{2} \\cos{(\\beta)}}{2}", "\\beta \\sin{(\\delta)}", "\\frac{\\delta (\\delta + 2 \\cos{(\\beta)})}{2}", "\\frac{\\beta (\\beta + 2 \\sin{(\\delta)})}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\beta', commutative=True), sin(Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\delta', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), cos(Symbol('\\\\beta', commutative=True)))", "Mul(Symbol('\\\\beta', commutative=True), sin(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), cos(Symbol('\\\\beta', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), sin(Symbol('\\\\delta', commutative=True)))))"]}, {"premise_expression": "\\pi + \\psi", "variable": "\\pi", "positive": "\\frac{\\pi (\\pi + 2 \\psi)}{2}", "negatives": ["\\frac{\\psi (2 \\pi + \\psi)}{2}", "\\frac{\\pi^{2} \\log{(\\psi)}}{2}", "e^{\\pi - \\psi}", "- \\cos{(\\pi - \\psi)}"], "srepr_premise_expression": "Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), log(Symbol('\\\\psi', commutative=True)))", "exp(Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))"]}, {"premise_expression": "\\frac{\\xi}{\\pi}", "variable": "\\xi", "positive": "\\frac{\\xi^{2}}{2 \\pi}", "negatives": ["\\xi \\log{(\\pi)}", "\\frac{\\xi^{2} \\sin{(\\pi)}}{2}", "- \\frac{\\cos{(\\xi)}}{\\pi}", "- e^{\\pi - \\xi}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), sin(Symbol('\\\\pi', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), cos(Symbol('\\\\xi', commutative=True)))", "Mul(Integer(-1), exp(Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))))"]}, {"premise_expression": "\\chi + \\omega", "variable": "\\omega", "positive": "\\frac{\\omega (2 \\chi + \\omega)}{2}", "negatives": ["\\frac{\\chi (\\chi + 2 \\omega)}{2}", "- \\cos{(\\chi + \\omega)}", "\\frac{\\omega^{2}}{2 \\chi}", "\\omega (\\log{(\\frac{\\chi}{\\omega})} + 1)"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "Mul(Symbol('\\\\omega', commutative=True), Add(log(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))), Integer(1)))"]}, {"premise_expression": "\\chi + \\log{(\\xi)}", "variable": "\\chi", "positive": "\\frac{\\chi (\\chi + 2 \\log{(\\xi)})}{2}", "negatives": ["\\frac{\\chi (- \\chi + 2 e^{\\xi})}{2}", "\\frac{\\chi^{2} \\log{(\\xi)}}{2}", "\\xi (\\chi + \\log{(\\xi)} - 1)", "\\chi (- \\xi + \\log{(\\chi^{\\xi})})"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), log(Symbol('\\\\xi', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\xi', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), log(Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\xi', commutative=True)), Integer(-1)))", "Mul(Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), log(Pow(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True)))))"]}, {"premise_expression": "\\delta - \\omega", "variable": "\\delta", "positive": "\\frac{\\delta (\\delta - 2 \\omega)}{2}", "negatives": ["\\frac{\\omega (2 \\delta - \\omega)}{2}", "\\frac{\\delta^{2} \\omega}{2}", "\\frac{\\delta (- \\delta + 2 e^{\\omega})}{2}", "\\frac{\\delta^{2} \\log{(\\omega)}}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Symbol('\\\\omega', commutative=True))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\omega', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), log(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\frac{\\sigma^{\\xi}}{\\pi}", "variable": "\\pi", "positive": "\\sigma^{\\xi} \\log{(\\pi)}", "negatives": ["(\\sigma - \\xi) \\log{(\\pi)}", "\\frac{\\pi \\sigma (\\pi + 2 \\sigma)}{2}", "\\frac{\\pi (\\pi \\sigma + 2 \\xi)}{2}", "\\frac{\\pi (- \\pi + 2 \\sigma + 2 \\xi)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True)), log(Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))), log(Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\frac{\\delta \\xi}{\\omega}", "variable": "\\delta", "positive": "\\frac{\\delta^{2} \\xi}{2 \\omega}", "negatives": ["\\frac{\\delta \\xi^{2}}{2 \\omega}", "\\delta \\xi \\log{(\\omega)}", "\\frac{\\delta (\\delta \\xi + 2 \\omega)}{2}", "\\delta (\\xi + 1)"], "srepr_premise_expression": "Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\xi', commutative=True), Integer(1)))"]}, {"premise_expression": "\\log{(\\frac{\\gamma}{\\delta})}", "variable": "\\gamma", "positive": "\\gamma (\\log{(\\frac{\\gamma}{\\delta})} - 1)", "negatives": ["\\delta (\\log{(\\frac{\\gamma}{\\delta})} + 1)", "\\gamma (\\log{(\\frac{\\delta}{\\gamma})} + 1)", "- \\sin{(\\delta - \\gamma)}", "e^{\\delta + \\gamma}"], "srepr_premise_expression": "log(Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\gamma', commutative=True), Add(log(Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\delta', commutative=True), Add(log(Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True))), Integer(1)))", "Mul(Symbol('\\\\gamma', commutative=True), Add(log(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Integer(-1), sin(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))))", "exp(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\sin^{\\omega}{(\\delta)}", "variable": "\\delta", "positive": "\\int \\sin^{\\omega}{(\\delta)} d\\delta", "negatives": ["\\int \\cos^{\\omega}{(\\delta)} d\\delta", "- \\cos{(\\delta + \\omega)}", "\\frac{\\delta (\\delta + 2 \\sin{(\\omega)})}{2}", "\\frac{\\delta^{2} \\omega}{2}"], "srepr_premise_expression": "Pow(sin(Symbol('\\\\delta', commutative=True)), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Integral(Pow(sin(Symbol('\\\\delta', commutative=True)), Symbol('\\\\omega', commutative=True)), Tuple(Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Integral(Pow(cos(Symbol('\\\\delta', commutative=True)), Symbol('\\\\omega', commutative=True)), Tuple(Symbol('\\\\delta', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), sin(Symbol('\\\\omega', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Symbol('\\\\omega', commutative=True))"]}, {"premise_expression": "\\alpha - \\chi", "variable": "\\chi", "positive": "\\frac{\\chi (2 \\alpha - \\chi)}{2}", "negatives": ["\\frac{\\chi (- 2 \\alpha + \\chi)}{2}", "\\frac{\\alpha (\\alpha - 2 \\chi)}{2}", "\\frac{\\chi^{2} \\log{(\\alpha)}}{2}", "\\frac{\\chi^{2} \\cos{(\\alpha)}}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\chi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), log(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), cos(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\beta + \\omega", "variable": "\\beta", "positive": "\\frac{\\beta (\\beta + 2 \\omega)}{2}", "negatives": ["\\frac{\\omega (2 \\beta + \\omega)}{2}", "- \\beta \\omega + \\sin{(\\beta)}", "- \\cos{(\\beta - \\omega)}", "- \\frac{\\cos{(\\beta)}}{\\omega}"], "srepr_premise_expression": "Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True)), sin(Symbol('\\\\beta', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))))", "Mul(Integer(-1), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), cos(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "\\pi + \\sin{(\\chi)}", "variable": "\\pi", "positive": "\\frac{\\pi (\\pi + 2 \\sin{(\\chi)})}{2}", "negatives": ["\\frac{\\pi (\\pi + 2 \\cos{(\\chi)})}{2}", "\\frac{\\pi (- 2 \\chi + \\pi)}{2}", "\\chi \\pi - \\cos{(\\chi)}", "\\sin{(\\chi + \\pi)}"], "srepr_premise_expression": "Add(Symbol('\\\\pi', commutative=True), sin(Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), sin(Symbol('\\\\chi', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), cos(Symbol('\\\\chi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\chi', commutative=True))))", "sin(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "e^{\\alpha + \\beta}", "variable": "\\alpha", "positive": "e^{\\alpha + \\beta}", "negatives": ["\\frac{\\alpha (\\alpha + 2 \\beta)}{2}", "\\beta \\log{(\\alpha)}", "\\log{(\\alpha)} \\log{(\\beta)}", "\\frac{\\alpha^{2} \\beta}{2}"], "srepr_premise_expression": "exp(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "exp(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\beta', commutative=True))))", "Mul(Symbol('\\\\beta', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "Mul(log(Symbol('\\\\alpha', commutative=True)), log(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\beta', commutative=True))"]}, {"premise_expression": "\\psi + \\cos{(\\beta)}", "variable": "\\beta", "positive": "\\beta \\psi + \\sin{(\\beta)}", "negatives": ["- \\beta \\psi + e^{\\beta}", "\\beta \\psi - \\cos{(\\beta)}", "\\frac{\\beta^{2}}{2 \\psi}", "\\beta (- \\psi + \\log{(\\beta^{\\psi})})"], "srepr_premise_expression": "Add(Symbol('\\\\psi', commutative=True), cos(Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\psi', commutative=True)), sin(Symbol('\\\\beta', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\psi', commutative=True)), exp(Symbol('\\\\beta', commutative=True)))", "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\beta', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))", "Mul(Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), log(Pow(Symbol('\\\\beta', commutative=True), Symbol('\\\\psi', commutative=True)))))"]}, {"premise_expression": "e^{\\frac{\\beta}{\\alpha}}", "variable": "\\alpha", "positive": "\\alpha e^{\\frac{\\beta}{\\alpha}} - \\beta \\operatorname{Ei}{(\\frac{\\beta}{\\alpha})}", "negatives": ["\\alpha e^{\\frac{\\beta}{\\alpha}}", "- \\alpha \\beta + e^{\\alpha}", "\\frac{\\alpha (\\alpha + 2 e^{\\beta})}{2}", "\\sin{(\\alpha - \\beta)}"], "srepr_premise_expression": "exp(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\alpha', commutative=True), exp(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\beta', commutative=True)))), Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Ei(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\beta', commutative=True)))))", "srepr_negatives": ["Mul(Symbol('\\\\alpha', commutative=True), exp(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\beta', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True)), exp(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), exp(Symbol('\\\\beta', commutative=True)))))", "sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\beta', commutative=True))))"]}, {"premise_expression": "\\alpha + \\beta \\gamma", "variable": "\\alpha", "positive": "\\frac{\\alpha (\\alpha + 2 \\beta \\gamma)}{2}", "negatives": ["\\frac{\\beta (2 \\alpha + \\beta \\gamma)}{2}", "\\frac{\\gamma (2 \\alpha + \\beta \\gamma)}{2}", "\\frac{\\alpha^{2}}{2 \\beta \\gamma}", "\\frac{\\alpha (\\alpha + 2 \\gamma^{\\beta})}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Pow(Symbol('\\\\gamma', commutative=True), Symbol('\\\\beta', commutative=True)))))"]}, {"premise_expression": "\\gamma \\sin{(\\alpha)}", "variable": "\\gamma", "positive": "\\frac{\\gamma^{2} \\sin{(\\alpha)}}{2}", "negatives": ["\\frac{\\gamma^{2} \\log{(\\alpha)}}{2}", "\\frac{\\gamma (2 \\alpha + \\gamma)}{2}", "\\frac{\\gamma^{2}}{2 \\alpha}", "- \\gamma \\cos{(\\alpha)}"], "srepr_premise_expression": "Mul(Symbol('\\\\gamma', commutative=True), sin(Symbol('\\\\alpha', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), sin(Symbol('\\\\alpha', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), log(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)))", "Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), cos(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "- \\xi + e^{\\pi}", "variable": "\\pi", "positive": "- \\pi \\xi + e^{\\pi}", "negatives": ["- \\pi \\xi + \\sin{(\\pi)}", "\\frac{\\xi (- \\xi + 2 e^{\\pi})}{2}", "\\frac{\\pi^{2} e^{\\xi}}{2}", "\\pi - \\xi \\log{(\\pi)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), exp(Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True)), exp(Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True)), sin(Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\pi', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), exp(Symbol('\\\\xi', commutative=True)))", "Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True), log(Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\delta - \\psi", "variable": "\\delta", "positive": "\\frac{\\delta (\\delta - 2 \\psi)}{2}", "negatives": ["\\frac{\\psi (2 \\delta - \\psi)}{2}", "e^{\\delta - \\psi}", "\\frac{\\delta^{2} \\log{(\\psi)}}{2}", "\\frac{\\delta^{2} \\cos{(\\psi)}}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "exp(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), log(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), cos(Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "e^{\\alpha^{\\sigma}}", "variable": "\\alpha", "positive": "\\frac{e^{- \\frac{i \\pi}{\\sigma}} \\gamma(\\frac{1}{\\sigma}, \\alpha^{\\sigma} e^{i \\pi})}{\\sigma}", "negatives": ["\\frac{\\alpha (- \\alpha + 2 e^{\\sigma})}{2}", "\\frac{\\alpha^{2} \\log{(\\sigma)}}{2}", "\\alpha \\sigma (\\log{(\\alpha)} - 1)", "\\frac{\\alpha (\\alpha + 2 \\sigma)}{2}"], "srepr_premise_expression": "exp(Pow(Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), exp(Mul(Integer(-1), I, pi, Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))), lowergamma(Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Mul(Pow(Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True)), exp_polar(Mul(I, pi)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\sigma', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), log(Symbol('\\\\sigma', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True), Add(log(Symbol('\\\\alpha', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\cos{(\\frac{\\xi}{\\delta})}", "variable": "\\delta", "positive": "\\delta \\cos{(\\frac{\\xi}{\\delta})} + \\xi \\operatorname{Si}{(\\frac{\\xi}{\\delta})}", "negatives": ["\\frac{\\delta (\\delta + 2 \\xi)}{2}", "- \\cos{(\\delta - \\xi)}", "\\frac{\\delta (- \\delta + 2 \\sin{(\\xi)})}{2}", "e^{\\delta + \\xi}"], "srepr_premise_expression": "cos(Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\delta', commutative=True), cos(Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True)))), Mul(Symbol('\\\\xi', commutative=True), Si(Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\xi', commutative=True)))))", "exp(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\frac{\\alpha}{\\delta}", "variable": "\\alpha", "positive": "\\frac{\\alpha^{2}}{2 \\delta}", "negatives": ["\\alpha \\log{(\\delta)}", "\\frac{\\alpha^{2} \\log{(\\delta)}}{2}", "\\frac{\\alpha^{2} \\cos{(\\delta)}}{2}", "\\frac{\\alpha (\\alpha + 2 e^{\\delta})}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), log(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), cos(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), exp(Symbol('\\\\delta', commutative=True)))))"]}, {"premise_expression": "\\frac{\\alpha + \\chi}{\\sigma}", "variable": "\\alpha", "positive": "\\frac{\\alpha (\\alpha + 2 \\chi)}{2 \\sigma}", "negatives": ["\\frac{\\chi (2 \\alpha + \\chi)}{2 \\sigma}", "\\frac{\\alpha (- \\alpha - 2 \\chi + 2 \\sigma)}{2}", "\\frac{\\alpha^{2} \\sigma}{2 \\chi}", "(\\alpha + \\chi) \\log{(\\sigma)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\chi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))", "Mul(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)), log(Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\omega + \\xi", "variable": "\\xi", "positive": "\\frac{\\xi (2 \\omega + \\xi)}{2}", "negatives": ["\\frac{\\omega (\\omega + 2 \\xi)}{2}", "\\frac{\\xi (\\xi + 2 \\log{(\\omega)})}{2}", "\\sin{(\\omega + \\xi)}", "- \\frac{\\cos{(\\xi)}}{\\omega}"], "srepr_premise_expression": "Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\xi', commutative=True), Mul(Integer(2), log(Symbol('\\\\omega', commutative=True)))))", "sin(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), cos(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\frac{\\alpha}{\\psi}", "variable": "\\alpha", "positive": "\\frac{\\alpha^{2}}{2 \\psi}", "negatives": ["\\alpha \\log{(\\psi)}", "\\frac{\\sin{(\\alpha)}}{\\psi}", "\\sin{(\\alpha - \\psi)}", "\\log{(\\alpha)} \\sin{(\\psi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\psi', commutative=True)))", "Mul(Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), sin(Symbol('\\\\alpha', commutative=True)))", "sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(log(Symbol('\\\\alpha', commutative=True)), sin(Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "e^{\\alpha + \\gamma}", "variable": "\\gamma", "positive": "e^{\\alpha + \\gamma}", "negatives": ["\\cos{(\\alpha - \\gamma)}", "\\frac{\\gamma (2 \\alpha + \\gamma)}{2}", "\\frac{\\gamma^{2}}{2 \\alpha}", "\\log{(\\gamma)} \\sin{(\\alpha)}"], "srepr_premise_expression": "exp(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "exp(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)))", "Mul(log(Symbol('\\\\gamma', commutative=True)), sin(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\frac{\\log{(\\chi)}}{\\delta}", "variable": "\\chi", "positive": "\\frac{\\chi (\\log{(\\chi)} - 1)}{\\delta}", "negatives": ["\\chi + \\delta \\log{(\\chi)}", "\\chi (- \\delta + \\log{(\\chi)} - 1)", "\\delta \\log{(\\chi)}", "\\log{(\\chi)} \\log{(\\delta)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), log(Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Add(log(Symbol('\\\\chi', commutative=True)), Integer(-1)))", "srepr_negatives": ["Add(Symbol('\\\\chi', commutative=True), Mul(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\chi', commutative=True))))", "Mul(Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), log(Symbol('\\\\chi', commutative=True)), Integer(-1)))", "Mul(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\chi', commutative=True)))", "Mul(log(Symbol('\\\\chi', commutative=True)), log(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "e^{- \\alpha + \\xi}", "variable": "\\xi", "positive": "e^{- \\alpha + \\xi}", "negatives": ["- e^{- \\alpha + \\xi}", "- e^{\\alpha - \\xi}", "\\sin{(\\alpha + \\xi)}", "\\frac{\\xi (2 \\alpha + \\xi)}{2}"], "srepr_premise_expression": "exp(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "exp(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\xi', commutative=True))))", "Mul(Integer(-1), exp(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))))", "sin(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\frac{\\log{(\\gamma)}}{\\alpha}", "variable": "\\alpha", "positive": "\\log{(\\alpha)} \\log{(\\gamma)}", "negatives": ["\\cos{(\\alpha - \\gamma)}", "- \\cos{(\\alpha + \\gamma)}", "\\frac{\\gamma (\\log{(\\gamma)} - 1)}{\\alpha}", "\\alpha \\gamma + \\sin{(\\alpha)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), log(Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(log(Symbol('\\\\alpha', commutative=True)), log(Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True))))", "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True), Add(log(Symbol('\\\\gamma', commutative=True)), Integer(-1)))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True)), sin(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\frac{\\chi}{\\sigma}", "variable": "\\sigma", "positive": "\\chi \\log{(\\sigma)}", "negatives": ["\\frac{\\chi^{2}}{2 \\sigma}", "\\frac{\\chi \\sigma^{2}}{2}", "- \\chi \\sigma - \\cos{(\\sigma)}", "e^{- \\chi + \\sigma}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\sigma', commutative=True))))", "exp(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\gamma \\sin{(\\pi)}", "variable": "\\gamma", "positive": "\\frac{\\gamma^{2} \\sin{(\\pi)}}{2}", "negatives": ["\\frac{\\gamma (- \\gamma + 2 \\sin{(\\pi)})}{2}", "- \\gamma \\cos{(\\pi)}", "- \\cos{(\\gamma + \\pi)}", "\\gamma (\\log{(\\frac{\\gamma}{\\pi})} - 1)"], "srepr_premise_expression": "Mul(Symbol('\\\\gamma', commutative=True), sin(Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), sin(Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\pi', commutative=True)))))", "Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), cos(Symbol('\\\\pi', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True))))", "Mul(Symbol('\\\\gamma', commutative=True), Add(log(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))), Integer(-1)))"]}, {"premise_expression": "\\log{(\\frac{\\pi}{\\sigma})}", "variable": "\\sigma", "positive": "\\sigma (\\log{(\\frac{\\pi}{\\sigma})} + 1)", "negatives": ["\\pi (\\log{(\\frac{\\pi}{\\sigma})} - 1)", "\\pi \\sigma (\\log{(\\sigma)} - 1)", "- \\cos{(\\pi + \\sigma)}", "\\sin{(\\pi + \\sigma)}"], "srepr_premise_expression": "log(Mul(Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\sigma', commutative=True), Add(log(Mul(Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))), Integer(1)))", "srepr_negatives": ["Mul(Symbol('\\\\pi', commutative=True), Add(log(Mul(Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))), Integer(-1)))", "Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True), Add(log(Symbol('\\\\sigma', commutative=True)), Integer(-1)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True))))", "sin(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\pi - \\xi", "variable": "\\pi", "positive": "\\frac{\\pi (\\pi - 2 \\xi)}{2}", "negatives": ["\\frac{\\xi (2 \\pi - \\xi)}{2}", "\\frac{\\pi^{2} \\log{(\\xi)}}{2}", "\\frac{\\pi^{2}}{2 \\xi}", "\\frac{\\pi^{2} \\cos{(\\xi)}}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), log(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), cos(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\cos{(\\frac{\\delta}{\\sigma})}", "variable": "\\sigma", "positive": "\\delta \\operatorname{Si}{(\\frac{\\delta}{\\sigma})} + \\sigma \\cos{(\\frac{\\delta}{\\sigma})}", "negatives": ["\\frac{\\sigma (2 \\delta + \\sigma)}{2}", "- \\delta \\sigma + \\sin{(\\sigma)}", "\\frac{\\sigma (- 2 \\delta + \\sigma)}{2}", "- \\sin{(\\delta - \\sigma)}"], "srepr_premise_expression": "cos(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\delta', commutative=True), Si(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1))))), Mul(Symbol('\\\\sigma', commutative=True), cos(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1))))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True)), sin(Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))"]}, {"premise_expression": "\\sin{(\\frac{\\sigma}{\\psi})}", "variable": "\\psi", "positive": "\\psi \\sin{(\\frac{\\sigma}{\\psi})} - \\frac{\\sigma \\log{(\\frac{\\sigma^{2}}{\\psi^{2}})}}{2} + \\sigma \\log{(\\frac{\\sigma}{\\psi})} - \\sigma \\operatorname{Ci}{(\\frac{\\sigma}{\\psi})}", "negatives": ["\\psi \\log{(\\psi + \\sigma)} - \\psi + \\sigma \\log{(\\psi + \\sigma)}", "\\psi (- \\sigma + \\log{(\\psi^{\\sigma})})", "\\frac{\\psi (- \\psi + 2 \\log{(\\sigma)})}{2}", "\\frac{\\psi (- \\psi + 2 e^{\\sigma})}{2}"], "srepr_premise_expression": "sin(Mul(Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\psi', commutative=True), sin(Mul(Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True)))), Mul(Integer(-1), Rational(1, 2), Symbol('\\\\sigma', commutative=True), log(Mul(Pow(Symbol('\\\\psi', commutative=True), Integer(-2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(2))))), Mul(Symbol('\\\\sigma', commutative=True), log(Mul(Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True)))), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True), Ci(Mul(Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\psi', commutative=True), log(Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True)))), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Symbol('\\\\sigma', commutative=True), log(Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True)))))", "Mul(Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), log(Pow(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), log(Symbol('\\\\sigma', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\sigma', commutative=True)))))"]}, {"premise_expression": "\\psi - \\sigma", "variable": "\\psi", "positive": "\\frac{\\psi (\\psi - 2 \\sigma)}{2}", "negatives": ["\\frac{\\sigma (2 \\psi - \\sigma)}{2}", "\\frac{\\psi^{2} \\cos{(\\sigma)}}{2}", "\\cos{(\\psi - \\sigma)}", "\\sin{(\\psi - \\sigma)}"], "srepr_premise_expression": "Add(Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), cos(Symbol('\\\\sigma', commutative=True)))", "cos(Add(Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "sin(Add(Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\alpha \\sin{(\\beta)}", "variable": "\\beta", "positive": "- \\alpha \\cos{(\\beta)}", "negatives": ["\\alpha \\beta \\log{(\\alpha)}", "- \\alpha \\beta + \\sin{(\\beta)}", "\\log{(\\beta)} \\cos{(\\alpha)}", "\\frac{\\alpha^{2} \\sin{(\\beta)}}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), sin(Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), cos(Symbol('\\\\beta', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True)), sin(Symbol('\\\\beta', commutative=True)))", "Mul(log(Symbol('\\\\beta', commutative=True)), cos(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), sin(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "\\chi + \\xi", "variable": "\\xi", "positive": "\\frac{\\xi (2 \\chi + \\xi)}{2}", "negatives": ["\\frac{\\chi (\\chi + 2 \\xi)}{2}", "\\frac{\\xi^{2} \\log{(\\chi)}}{2}", "- \\cos{(\\chi + \\xi)}", "\\frac{\\chi \\xi^{2}}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), log(Symbol('\\\\chi', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))"]}, {"premise_expression": "\\cos{(\\beta - \\psi)}", "variable": "\\beta", "positive": "\\sin{(\\beta - \\psi)}", "negatives": ["- \\sin{(\\beta - \\psi)}", "\\frac{\\sin{(\\beta)}}{\\psi}", "- \\cos{(\\beta + \\psi)}", "\\psi \\sin{(\\beta)}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "sin(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))", "Mul(Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), sin(Symbol('\\\\beta', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\psi', commutative=True))))", "Mul(Symbol('\\\\psi', commutative=True), sin(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "\\frac{\\psi}{\\sigma}", "variable": "\\psi", "positive": "\\frac{\\psi^{2}}{2 \\sigma}", "negatives": ["\\psi \\log{(\\sigma)}", "\\sigma e^{\\frac{\\psi}{\\sigma}}", "- \\sigma \\cos{(\\psi)}", "\\psi"], "srepr_premise_expression": "Mul(Symbol('\\\\psi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\psi', commutative=True), log(Symbol('\\\\sigma', commutative=True)))", "Mul(Symbol('\\\\sigma', commutative=True), exp(Mul(Symbol('\\\\psi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))))", "Mul(Integer(-1), Symbol('\\\\sigma', commutative=True), cos(Symbol('\\\\psi', commutative=True)))", "Symbol('\\\\psi', commutative=True)"]}, {"premise_expression": "\\omega e^{\\sigma}", "variable": "\\sigma", "positive": "\\omega e^{\\sigma}", "negatives": ["\\frac{\\omega^{2} e^{\\sigma}}{2}", "\\frac{\\sigma^{2} \\sin{(\\omega)}}{2}", "\\sigma (\\omega + \\log{(\\sigma)} - 1)", "\\frac{\\sigma (\\sigma + 2 \\sin{(\\omega)})}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\omega', commutative=True), exp(Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\omega', commutative=True), exp(Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), exp(Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), sin(Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\sigma', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(2), sin(Symbol('\\\\omega', commutative=True)))))"]}, {"premise_expression": "\\frac{\\beta}{\\gamma}", "variable": "\\gamma", "positive": "\\beta \\log{(\\gamma)}", "negatives": ["\\frac{\\beta^{2}}{2 \\gamma}", "\\beta \\gamma + \\sin{(\\gamma)}", "- \\cos{(\\beta - \\gamma)}", "- \\beta \\gamma + \\sin{(\\gamma)}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\beta', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)))", "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)), sin(Symbol('\\\\gamma', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)), sin(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\gamma \\psi", "variable": "\\psi", "positive": "\\frac{\\gamma \\psi^{2}}{2}", "negatives": ["\\frac{\\gamma^{2} \\psi}{2}", "\\gamma e^{\\frac{\\psi}{\\gamma}}", "\\gamma \\log{(\\psi)}", "e^{\\gamma + \\psi}"], "srepr_premise_expression": "Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))", "Mul(Symbol('\\\\gamma', commutative=True), exp(Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True))))", "Mul(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\psi', commutative=True)))", "exp(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\frac{\\beta}{\\psi \\sigma}", "variable": "\\psi", "positive": "\\frac{\\beta \\log{(\\psi)}}{\\sigma}", "negatives": ["\\frac{\\beta \\log{(\\sigma)}}{\\psi}", "\\frac{\\sigma \\log{(\\psi)}}{\\beta}", "\\beta \\sigma \\log{(\\psi)}", "\\frac{\\beta \\psi^{2} \\sigma}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), log(Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), log(Symbol('\\\\sigma', commutative=True)))", "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\psi', commutative=True)))", "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), Symbol('\\\\sigma', commutative=True))"]}, {"premise_expression": "\\log{(\\omega^{\\sigma})}", "variable": "\\omega", "positive": "\\omega (- \\sigma + \\log{(\\omega^{\\sigma})})", "negatives": ["\\frac{\\omega (\\omega - 2 \\sigma)}{2}", "\\frac{\\sigma^{2} \\log{(\\omega)}}{2}", "\\frac{\\omega^{2}}{2 \\sigma}", "\\omega (\\log{(\\frac{\\sigma}{\\omega})} + 1)"], "srepr_premise_expression": "log(Pow(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), log(Pow(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), log(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "Mul(Symbol('\\\\omega', commutative=True), Add(log(Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))), Integer(1)))"]}, {"premise_expression": "\\frac{\\omega}{\\beta}", "variable": "\\beta", "positive": "\\omega \\log{(\\beta)}", "negatives": ["\\frac{\\omega^{2}}{2 \\beta}", "\\beta \\omega + e^{\\beta}", "- \\cos{(\\beta + \\omega)}", "\\frac{\\beta (- \\beta + 2 \\omega)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\beta', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True)), exp(Symbol('\\\\beta', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))"]}, {"premise_expression": "\\chi \\sigma", "variable": "\\sigma", "positive": "\\frac{\\chi \\sigma^{2}}{2}", "negatives": ["\\frac{\\chi^{2} \\sigma}{2}", "\\frac{\\sin{(\\sigma)}}{\\chi}", "\\chi \\sigma + e^{\\sigma}", "\\frac{\\sigma (2 \\chi - \\sigma)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\sigma', commutative=True))", "Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), sin(Symbol('\\\\sigma', commutative=True)))", "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\sigma', commutative=True)), exp(Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "e^{\\frac{\\psi}{\\xi}}", "variable": "\\psi", "positive": "\\xi e^{\\frac{\\psi}{\\xi}}", "negatives": ["\\frac{\\psi^{2} \\xi}{2}", "e^{\\psi - \\xi}", "\\log{(\\psi)} \\sin{(\\xi)}", "- \\psi \\operatorname{Ei}{(\\frac{\\psi}{\\xi})} + \\xi e^{\\frac{\\psi}{\\xi}}"], "srepr_premise_expression": "exp(Mul(Symbol('\\\\psi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\xi', commutative=True), exp(Mul(Symbol('\\\\psi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))", "exp(Add(Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(log(Symbol('\\\\psi', commutative=True)), sin(Symbol('\\\\xi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True), Ei(Mul(Symbol('\\\\psi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))), Mul(Symbol('\\\\xi', commutative=True), exp(Mul(Symbol('\\\\psi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))))"]}, {"premise_expression": "\\frac{e^{\\gamma}}{\\pi}", "variable": "\\pi", "positive": "e^{\\gamma} \\log{(\\pi)}", "negatives": ["e^{- \\gamma + \\pi}", "- \\gamma \\pi + e^{\\pi}", "\\gamma \\pi (\\log{(\\pi)} - 1)", "\\frac{\\pi (- 2 \\gamma + \\pi)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), exp(Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(exp(Symbol('\\\\gamma', commutative=True)), log(Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["exp(Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True)), exp(Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True), Add(log(Symbol('\\\\pi', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\frac{\\pi - \\sigma}{\\delta}", "variable": "\\sigma", "positive": "\\frac{\\sigma (2 \\pi - \\sigma)}{2 \\delta}", "negatives": ["- \\frac{\\pi (- \\pi + 2 \\sigma)}{2 \\delta}", "\\frac{\\sigma (\\delta \\sigma - 2 \\pi)}{2}", "- \\frac{\\sigma (2 \\delta - \\sigma)}{2 \\pi}", "\\sigma (\\pi - \\sigma)"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Integer(-1), Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "- \\sin{(\\omega - \\xi)}", "variable": "\\xi", "positive": "- \\cos{(\\omega - \\xi)}", "negatives": ["\\cos{(\\omega - \\xi)}", "- \\omega \\cos{(\\xi)}", "- \\omega \\xi + e^{\\xi}", "\\frac{\\xi (\\log{(\\xi)} - 1)}{\\omega}"], "srepr_premise_expression": "Mul(Integer(-1), sin(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))))", "srepr_negatives": ["cos(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Integer(-1), Symbol('\\\\omega', commutative=True), cos(Symbol('\\\\xi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True)), exp(Symbol('\\\\xi', commutative=True)))", "Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True), Add(log(Symbol('\\\\xi', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\beta \\log{(\\delta)}", "variable": "\\delta", "positive": "\\beta \\delta (\\log{(\\delta)} - 1)", "negatives": ["\\delta (\\beta + \\log{(\\delta)} - 1)", "\\beta \\log{(\\delta)}", "\\frac{\\beta^{2} \\log{(\\delta)}}{2}", "\\frac{\\delta^{2}}{2 \\beta}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), log(Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True), Add(log(Symbol('\\\\delta', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\beta', commutative=True), log(Symbol('\\\\delta', commutative=True)), Integer(-1)))", "Mul(Symbol('\\\\beta', commutative=True), log(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), log(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Pow(Symbol('\\\\delta', commutative=True), Integer(2)))"]}, {"premise_expression": "\\frac{\\chi}{\\omega}", "variable": "\\omega", "positive": "\\chi \\log{(\\omega)}", "negatives": ["\\frac{\\chi^{2}}{2 \\omega}", "e^{\\chi} \\log{(\\omega)}", "\\chi e^{\\frac{\\omega}{\\chi}}", "\\sin{(\\chi + \\omega)}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))", "Mul(exp(Symbol('\\\\chi', commutative=True)), log(Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\chi', commutative=True), exp(Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True))))", "sin(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\beta \\omega", "variable": "\\omega", "positive": "\\frac{\\beta \\omega^{2}}{2}", "negatives": ["\\frac{\\beta^{2} \\omega}{2}", "e \\omega", "\\frac{\\beta \\omega (2 \\beta + \\omega)}{2}", "\\beta \\omega - \\cos{(\\omega)}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\omega', commutative=True))", "Mul(E, Symbol('\\\\omega', commutative=True))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\omega', commutative=True))))"]}, {"premise_expression": "\\beta + \\chi", "variable": "\\beta", "positive": "\\frac{\\beta (\\beta + 2 \\chi)}{2}", "negatives": ["\\frac{\\chi (2 \\beta + \\chi)}{2}", "\\frac{\\beta (- \\beta + 2 \\cos{(\\chi)})}{2}", "\\frac{\\beta^{2} \\sin{(\\chi)}}{2}", "\\beta (\\log{(\\beta \\chi)} - 1)"], "srepr_premise_expression": "Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\chi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\chi', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), sin(Symbol('\\\\chi', commutative=True)))", "Mul(Symbol('\\\\beta', commutative=True), Add(log(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\alpha - \\psi", "variable": "\\psi", "positive": "\\frac{\\psi (2 \\alpha - \\psi)}{2}", "negatives": ["\\frac{\\alpha (\\alpha - 2 \\psi)}{2}", "e^{- \\alpha + \\psi}", "\\frac{\\psi (\\log{(\\psi)} - 1)}{\\alpha}", "\\frac{\\psi (\\psi + 2 \\cos{(\\alpha)})}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))", "exp(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True), Add(log(Symbol('\\\\psi', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(2), cos(Symbol('\\\\alpha', commutative=True)))))"]}, {"premise_expression": "\\chi + \\sigma", "variable": "\\chi", "positive": "\\frac{\\chi (\\chi + 2 \\sigma)}{2}", "negatives": ["\\frac{\\sigma (2 \\chi + \\sigma)}{2}", "- \\cos{(\\chi + \\sigma)}", "\\sigma \\log{(\\chi)}", "\\sigma \\sin{(\\chi)}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\sigma', commutative=True))))", "Mul(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\chi', commutative=True)))", "Mul(Symbol('\\\\sigma', commutative=True), sin(Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "\\psi \\cos{(\\alpha)}", "variable": "\\psi", "positive": "\\frac{\\psi^{2} \\cos{(\\alpha)}}{2}", "negatives": ["\\frac{\\psi (2 \\alpha + \\psi)}{2}", "\\frac{\\psi^{2}}{2 \\alpha}", "\\psi \\sin{(\\alpha)}", "\\frac{\\psi (- \\psi + 2 \\log{(\\alpha)})}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\psi', commutative=True), cos(Symbol('\\\\alpha', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), cos(Symbol('\\\\alpha', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "Mul(Symbol('\\\\psi', commutative=True), sin(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), log(Symbol('\\\\alpha', commutative=True)))))"]}, {"premise_expression": "\\sin{(\\chi + \\pi)}", "variable": "\\chi", "positive": "- \\cos{(\\chi + \\pi)}", "negatives": ["\\pi \\log{(\\chi)}", "\\frac{\\chi^{2} \\pi}{2}", "\\chi (\\pi + \\log{(\\chi)} - 1)", "\\frac{\\chi (- \\chi + 2 \\log{(\\pi)})}{2}"], "srepr_premise_expression": "sin(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\pi', commutative=True))", "Mul(Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\chi', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), log(Symbol('\\\\pi', commutative=True)))))"]}, {"premise_expression": "\\alpha \\delta - \\gamma", "variable": "\\delta", "positive": "\\frac{\\delta (\\alpha \\delta - 2 \\gamma)}{2}", "negatives": ["\\frac{\\alpha (\\alpha \\delta - 2 \\gamma)}{2}", "\\frac{\\gamma (2 \\alpha \\delta - \\gamma)}{2}", "\\frac{\\delta (2 \\alpha^{\\gamma} + \\delta)}{2}", "\\frac{\\alpha \\delta}{\\gamma} - \\frac{\\delta^{2}}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(2), Pow(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True))), Symbol('\\\\delta', commutative=True)))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1))), Mul(Integer(-1), Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2))))"]}, {"premise_expression": "\\cos{(\\alpha + \\chi)}", "variable": "\\alpha", "positive": "\\sin{(\\alpha + \\chi)}", "negatives": ["e^{\\alpha - \\chi}", "- \\frac{\\cos{(\\alpha)}}{\\chi}", "\\alpha \\chi e^{\\chi}", "- \\alpha \\chi - \\cos{(\\alpha)}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "sin(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["exp(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True))))", "Mul(Integer(-1), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), cos(Symbol('\\\\alpha', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True), exp(Symbol('\\\\chi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\alpha', commutative=True))))"]}, {"premise_expression": "\\frac{\\cos{(\\chi)}}{\\psi}", "variable": "\\psi", "positive": "\\log{(\\psi)} \\cos{(\\chi)}", "negatives": ["\\frac{\\psi^{2} \\log{(\\chi)}}{2}", "\\frac{\\sin{(\\chi)}}{\\psi}", "\\psi (\\log{(\\frac{\\chi}{\\psi})} + 1)", "\\frac{\\psi (2 \\chi - \\psi)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), cos(Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(log(Symbol('\\\\psi', commutative=True)), cos(Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), log(Symbol('\\\\chi', commutative=True)))", "Mul(Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), sin(Symbol('\\\\chi', commutative=True)))", "Mul(Symbol('\\\\psi', commutative=True), Add(log(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "\\frac{\\beta \\gamma}{\\omega}", "variable": "\\gamma", "positive": "\\frac{\\beta \\gamma^{2}}{2 \\omega}", "negatives": ["\\frac{\\beta^{2} \\gamma}{2 \\omega}", "\\beta \\gamma \\log{(\\omega)}", "\\frac{\\gamma (\\beta \\gamma - 2 \\omega)}{2}", "\\frac{\\gamma (\\beta \\gamma + 2 \\omega)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))", "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))"]}, {"premise_expression": "\\sin{(\\beta + \\gamma)}", "variable": "\\beta", "positive": "- \\cos{(\\beta + \\gamma)}", "negatives": ["\\gamma \\sin{(\\beta)}", "\\beta (\\gamma + \\log{(\\beta)} - 1)", "\\beta e^{\\frac{\\gamma}{\\beta}} - \\gamma \\operatorname{Ei}{(\\frac{\\gamma}{\\beta})}", "\\int \\sin^{\\gamma}{(\\beta)} d\\beta"], "srepr_premise_expression": "sin(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True))))", "srepr_negatives": ["Mul(Symbol('\\\\gamma', commutative=True), sin(Symbol('\\\\beta', commutative=True)))", "Mul(Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\beta', commutative=True)), Integer(-1)))", "Add(Mul(Symbol('\\\\beta', commutative=True), exp(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True)))), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Ei(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True)))))", "Integral(Pow(sin(Symbol('\\\\beta', commutative=True)), Symbol('\\\\gamma', commutative=True)), Tuple(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "\\cos{(\\delta - \\omega)}", "variable": "\\delta", "positive": "\\sin{(\\delta - \\omega)}", "negatives": ["- \\sin{(\\delta - \\omega)}", "\\frac{\\delta (\\delta - 2 \\omega)}{2}", "\\delta \\cos{(\\omega^{\\omega})}", "\\delta^{2} (- \\frac{\\delta}{3} + \\frac{\\omega}{2})"], "srepr_premise_expression": "cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "sin(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Symbol('\\\\delta', commutative=True), cos(Pow(Symbol('\\\\omega', commutative=True), Symbol('\\\\omega', commutative=True))))", "Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Add(Mul(Integer(-1), Rational(1, 3), Symbol('\\\\delta', commutative=True)), Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True))))"]}, {"premise_expression": "- \\delta + \\sin{(\\chi)}", "variable": "\\delta", "positive": "\\frac{\\delta (- \\delta + 2 \\sin{(\\chi)})}{2}", "negatives": ["\\frac{\\delta (\\delta + 2 \\cos{(\\chi)})}{2}", "- \\chi \\delta - \\cos{(\\chi)}", "\\chi \\delta + e^{\\delta}", "\\chi \\delta - \\cos{(\\delta)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), sin(Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\chi', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), cos(Symbol('\\\\chi', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\chi', commutative=True))))", "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True)), exp(Symbol('\\\\delta', commutative=True)))", "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\delta', commutative=True))))"]}, {"premise_expression": "\\frac{\\chi}{\\delta}", "variable": "\\chi", "positive": "\\frac{\\chi^{2}}{2 \\delta}", "negatives": ["\\chi \\log{(\\delta)}", "- \\frac{\\chi^{2}}{2 \\delta} + \\chi", "\\frac{\\chi (- \\chi + 2 \\delta)}{2}", "e^{\\chi - \\delta}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\delta', commutative=True)))", "Add(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Pow(Symbol('\\\\delta', commutative=True), Integer(-1))), Symbol('\\\\chi', commutative=True))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\delta', commutative=True))))", "exp(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))"]}, {"premise_expression": "\\chi \\sin{(\\omega)}", "variable": "\\chi", "positive": "\\frac{\\chi^{2} \\sin{(\\omega)}}{2}", "negatives": ["\\frac{\\chi^{2} \\log{(\\omega)}}{2}", "\\frac{\\chi^{2} \\omega}{2}", "\\frac{\\chi (- \\chi + 2 \\sin{(\\omega)})}{2}", "- \\chi \\cos{(\\omega)}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), sin(Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), sin(Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), log(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\omega', commutative=True))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\omega', commutative=True)))))", "Mul(Integer(-1), Symbol('\\\\chi', commutative=True), cos(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\frac{\\cos{(\\chi)}}{\\gamma}", "variable": "\\gamma", "positive": "\\log{(\\gamma)} \\cos{(\\chi)}", "negatives": ["\\gamma \\cos{(2 \\chi)}", "- \\frac{\\cos{(\\gamma)}}{\\chi}", "\\frac{\\sin{(\\chi)}}{\\gamma}", "- \\cos{(\\chi + \\gamma)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), cos(Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(log(Symbol('\\\\gamma', commutative=True)), cos(Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\gamma', commutative=True), cos(Mul(Integer(2), Symbol('\\\\chi', commutative=True))))", "Mul(Integer(-1), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), cos(Symbol('\\\\gamma', commutative=True)))", "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), sin(Symbol('\\\\chi', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True))))"]}, {"premise_expression": "\\chi \\log{(\\pi)}", "variable": "\\chi", "positive": "\\frac{\\chi^{2} \\log{(\\pi)}}{2}", "negatives": ["\\frac{\\chi^{2} \\pi^{2}}{2}", "\\pi \\log{(\\chi)}", "\\chi \\pi (\\log{(\\pi)} - 1)", "\\frac{\\chi (- \\chi + 2 \\pi)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), log(Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\chi', commutative=True)))", "Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True), Add(log(Symbol('\\\\pi', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\log{(\\chi \\gamma)}", "variable": "\\gamma", "positive": "\\gamma (\\log{(\\chi \\gamma)} - 1)", "negatives": ["\\chi (\\log{(\\chi \\gamma)} - 1)", "\\gamma (- \\chi + \\log{(\\gamma)} - 1)", "\\cos{(\\chi - \\gamma)}", "\\frac{\\gamma (- 2 \\chi + \\gamma)}{2}"], "srepr_premise_expression": "log(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\gamma', commutative=True), Add(log(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\chi', commutative=True), Add(log(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), log(Symbol('\\\\gamma', commutative=True)), Integer(-1)))", "cos(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\frac{\\alpha}{\\beta}", "variable": "\\beta", "positive": "\\alpha \\log{(\\beta)}", "negatives": ["\\alpha e^{\\beta}", "\\frac{\\alpha^{2}}{2 \\beta}", "\\alpha e^{\\frac{\\beta}{\\alpha}}", "\\beta"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\beta', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\alpha', commutative=True), exp(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)))", "Mul(Symbol('\\\\alpha', commutative=True), exp(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\beta', commutative=True))))", "Symbol('\\\\beta', commutative=True)"]}, {"premise_expression": "\\omega (- \\beta + \\delta)", "variable": "\\delta", "positive": "\\frac{\\delta \\omega (- 2 \\beta + \\delta)}{2}", "negatives": ["\\frac{\\delta (- 2 \\beta + \\delta \\omega)}{2}", "\\frac{\\beta \\omega (- \\beta + 2 \\delta)}{2}", "\\frac{\\omega^{2} (- \\beta + \\delta)}{2}", "\\frac{\\delta^{2} \\omega^{\\beta}}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Pow(Symbol('\\\\omega', commutative=True), Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "- \\xi + \\sin{(\\beta)}", "variable": "\\beta", "positive": "- \\beta \\xi - \\cos{(\\beta)}", "negatives": ["- \\beta \\xi + \\sin{(\\beta)}", "\\frac{\\beta^{2} \\cos{(\\xi)}}{2}", "e^{\\xi} \\log{(\\beta)}", "\\frac{\\beta (\\beta - 2 \\xi)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), sin(Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\beta', commutative=True))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True)), sin(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), cos(Symbol('\\\\xi', commutative=True)))", "Mul(exp(Symbol('\\\\xi', commutative=True)), log(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\cos{(\\alpha + \\beta)}", "variable": "\\beta", "positive": "\\sin{(\\alpha + \\beta)}", "negatives": ["- \\sin{(\\alpha - \\beta)}", "- e^{\\alpha - \\beta}", "\\alpha \\sin{(\\beta)}", "\\frac{\\beta (2 \\alpha - \\beta)}{2}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "sin(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\beta', commutative=True)))))", "Mul(Integer(-1), exp(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\beta', commutative=True)))))", "Mul(Symbol('\\\\alpha', commutative=True), sin(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\beta', commutative=True))))"]}, {"premise_expression": "\\frac{\\psi}{\\alpha \\delta}", "variable": "\\delta", "positive": "\\frac{\\psi \\log{(\\delta)}}{\\alpha}", "negatives": ["\\frac{\\psi \\log{(\\alpha)}}{\\delta}", "\\frac{\\alpha \\log{(\\delta)}}{\\psi}", "\\alpha^{\\psi} \\log{(\\delta)}", "\\frac{\\delta^{2}}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True), log(Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), log(Symbol('\\\\delta', commutative=True)))", "Mul(Pow(Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True)), log(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)))"]}, {"premise_expression": "\\chi e^{\\alpha}", "variable": "\\alpha", "positive": "\\chi e^{\\alpha}", "negatives": ["\\frac{\\chi^{2} e^{\\alpha}}{2}", "\\frac{\\alpha^{2} \\chi}{2}", "e^{\\alpha - \\chi}", "\\log{(\\alpha)} \\sin{(\\chi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), exp(Symbol('\\\\alpha', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\chi', commutative=True), exp(Symbol('\\\\alpha', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), exp(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\chi', commutative=True))", "exp(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True))))", "Mul(log(Symbol('\\\\alpha', commutative=True)), sin(Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "e^{\\frac{\\omega}{\\beta}}", "variable": "\\beta", "positive": "\\beta e^{\\frac{\\omega}{\\beta}} - \\omega \\operatorname{Ei}{(\\frac{\\omega}{\\beta})}", "negatives": ["\\beta e^{\\frac{\\omega}{\\beta}}", "e^{\\beta + \\omega}", "\\frac{\\beta \\omega (- \\beta + 2 \\omega)}{2}", "\\frac{\\beta (\\beta + 2 \\omega)}{2}"], "srepr_premise_expression": "exp(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\beta', commutative=True), exp(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True)))), Mul(Integer(-1), Symbol('\\\\omega', commutative=True), Ei(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True)))))", "srepr_negatives": ["Mul(Symbol('\\\\beta', commutative=True), exp(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True))))", "exp(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))"]}, {"premise_expression": "\\chi - \\delta + \\sigma", "variable": "\\chi", "positive": "\\chi (\\frac{\\chi}{2} - \\delta + \\sigma)", "negatives": ["\\frac{\\delta (2 \\chi - \\delta + 2 \\sigma)}{2}", "\\frac{\\sigma (2 \\chi - 2 \\delta + \\sigma)}{2}", "\\frac{\\chi (\\chi \\sigma - 2 \\delta)}{2}", "\\frac{\\chi (\\chi + 2 \\delta^{\\sigma})}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\chi', commutative=True), Add(Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Pow(Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True)))))"]}, {"premise_expression": "\\alpha + \\beta", "variable": "\\alpha", "positive": "\\frac{\\alpha (\\alpha + 2 \\beta)}{2}", "negatives": ["\\frac{\\alpha (\\alpha - 2 \\beta)}{2}", "\\frac{\\beta (2 \\alpha + \\beta)}{2}", "\\cos{(\\alpha - \\beta)}", "\\sin{(\\alpha - \\beta)}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\beta', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\beta', commutative=True)))", "cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\beta', commutative=True))))", "sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\beta', commutative=True))))"]}, {"premise_expression": "\\beta \\omega + \\delta", "variable": "\\beta", "positive": "\\frac{\\beta (\\beta \\omega + 2 \\delta)}{2}", "negatives": ["\\frac{\\omega (\\beta \\omega + 2 \\delta)}{2}", "\\frac{\\beta (\\beta \\omega - 2 \\delta)}{2}", "\\frac{\\delta (2 \\beta \\omega + \\delta)}{2}", "\\frac{\\beta^{2} (\\delta + \\omega)}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True)), Symbol('\\\\delta', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\delta', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True)), Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "- \\alpha + \\gamma", "variable": "\\gamma", "positive": "\\frac{\\gamma (- 2 \\alpha + \\gamma)}{2}", "negatives": ["\\frac{\\alpha (- \\alpha + 2 \\gamma)}{2}", "\\frac{\\gamma (\\gamma + 2 \\sin{(\\alpha)})}{2}", "\\frac{\\gamma^{2} \\sin{(\\alpha)}}{2}", "\\frac{\\gamma^{2} e^{\\alpha}}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\gamma', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), sin(Symbol('\\\\alpha', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), sin(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), exp(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\beta \\sin{(\\xi)}", "variable": "\\xi", "positive": "- \\beta \\cos{(\\xi)}", "negatives": ["\\beta \\log{(\\xi)}", "\\frac{\\beta \\xi^{2}}{2}", "\\frac{\\beta^{2} \\sin{(\\xi)}}{2}", "e^{\\beta + \\xi}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), sin(Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Integer(-1), Symbol('\\\\beta', commutative=True), cos(Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\beta', commutative=True), log(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), sin(Symbol('\\\\xi', commutative=True)))", "exp(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "- \\psi + \\cos{(\\pi)}", "variable": "\\pi", "positive": "- \\pi \\psi + \\sin{(\\pi)}", "negatives": ["\\frac{\\pi^{2} \\sin{(\\psi)}}{2}", "\\frac{\\pi^{2}}{2 \\psi}", "\\sin{(\\pi - \\psi)}", "\\log{(\\pi)} \\log{(\\psi)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), cos(Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)), sin(Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), sin(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))", "sin(Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(log(Symbol('\\\\pi', commutative=True)), log(Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\frac{\\omega}{\\delta}", "variable": "\\omega", "positive": "\\frac{\\omega^{2}}{2 \\delta}", "negatives": ["\\omega \\log{(\\delta)}", "\\frac{\\omega (- \\omega + 2 \\sin{(\\delta)})}{2}", "\\delta \\operatorname{Si}{(\\frac{\\delta}{\\omega})} + \\omega \\cos{(\\frac{\\delta}{\\omega})}", "\\int \\cos^{\\delta}{(\\omega)} d\\omega"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\delta', commutative=True)))))", "Add(Mul(Symbol('\\\\delta', commutative=True), Si(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1))))), Mul(Symbol('\\\\omega', commutative=True), cos(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1))))))", "Integral(Pow(cos(Symbol('\\\\omega', commutative=True)), Symbol('\\\\delta', commutative=True)), Tuple(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\delta \\gamma", "variable": "\\gamma", "positive": "\\frac{\\delta \\gamma^{2}}{2}", "negatives": ["\\frac{\\delta^{2} \\gamma}{2}", "\\frac{\\gamma^{2}}{2 \\delta}", "\\frac{\\gamma^{2} e^{\\delta}}{2}", "\\sin{(\\delta + \\gamma)}"], "srepr_premise_expression": "Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\gamma', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Symbol('\\\\gamma', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), exp(Symbol('\\\\delta', commutative=True)))", "sin(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\frac{\\alpha \\pi}{\\xi}", "variable": "\\pi", "positive": "\\frac{\\alpha \\pi^{2}}{2 \\xi}", "negatives": ["\\frac{\\alpha^{2} \\pi}{2 \\xi}", "\\frac{\\alpha \\pi^{2} \\xi}{2}", "\\alpha \\pi \\log{(\\xi)}", "\\frac{\\pi (- 2 \\alpha - \\pi + 2 \\xi)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))", "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True), log(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\frac{\\beta}{\\omega}", "variable": "\\omega", "positive": "\\beta \\log{(\\omega)}", "negatives": ["\\omega \\cos{(1)}", "\\frac{\\beta^{2}}{2 \\omega}", "\\frac{\\beta \\omega^{2}}{2}", "\\beta \\omega (\\log{(\\omega)} - 1)"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\beta', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\omega', commutative=True), cos(Integer(1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True), Add(log(Symbol('\\\\omega', commutative=True)), Integer(-1)))"]}, {"premise_expression": "e^{\\frac{\\gamma}{\\beta}}", "variable": "\\beta", "positive": "\\beta e^{\\frac{\\gamma}{\\beta}} - \\gamma \\operatorname{Ei}{(\\frac{\\gamma}{\\beta})}", "negatives": ["- \\beta \\gamma + e^{\\beta}", "\\frac{\\beta (- \\beta + 2 e^{\\gamma})}{2}", "\\beta e^{\\frac{\\gamma}{\\beta}}", "\\beta \\gamma + \\sin{(\\beta)}"], "srepr_premise_expression": "exp(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\beta', commutative=True), exp(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True)))), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Ei(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True)))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)), exp(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\gamma', commutative=True)))))", "Mul(Symbol('\\\\beta', commutative=True), exp(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True))))", "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)), sin(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "\\chi \\psi", "variable": "\\chi", "positive": "\\frac{\\chi^{2} \\psi}{2}", "negatives": ["\\frac{\\chi \\psi^{2}}{2}", "\\frac{\\chi (\\chi + 2 \\psi)}{2}", "\\frac{\\chi (- \\chi + 2 \\psi)}{2}", "\\frac{\\chi^{2} (\\psi + 1)}{2 \\psi}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Add(Symbol('\\\\psi', commutative=True), Integer(1)))"]}, {"premise_expression": "e^{\\frac{\\gamma}{\\chi}}", "variable": "\\gamma", "positive": "\\chi e^{\\frac{\\gamma}{\\chi}}", "negatives": ["\\cos{(\\chi - \\gamma)}", "- \\chi \\gamma - \\cos{(\\gamma)}", "\\frac{\\gamma^{2} \\sin{(\\chi)}}{2}", "\\chi e^{\\frac{\\gamma}{\\chi}} - \\gamma \\operatorname{Ei}{(\\frac{\\gamma}{\\chi})}"], "srepr_premise_expression": "exp(Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\chi', commutative=True), exp(Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True))))", "srepr_negatives": ["cos(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), sin(Symbol('\\\\chi', commutative=True)))", "Add(Mul(Symbol('\\\\chi', commutative=True), exp(Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True)))), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Ei(Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True)))))"]}, {"premise_expression": "\\frac{\\delta}{\\omega}", "variable": "\\omega", "positive": "\\delta \\log{(\\omega)}", "negatives": ["\\frac{\\delta^{2}}{2 \\omega}", "\\frac{\\delta \\omega^{2}}{2}", "- \\cos{(\\delta + \\omega)}", "\\frac{\\omega^{2} \\log{(\\delta)}}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), log(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\cos^{\\delta}{(\\gamma)}", "variable": "\\gamma", "positive": "\\int \\cos^{\\delta}{(\\gamma)} d\\gamma", "negatives": ["\\delta \\log{(\\gamma)}", "\\frac{\\gamma^{2}}{2 \\delta}", "\\delta e^{\\gamma}", "\\frac{\\gamma (2 \\delta + \\gamma)}{2}"], "srepr_premise_expression": "Pow(cos(Symbol('\\\\gamma', commutative=True)), Symbol('\\\\delta', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Integral(Pow(cos(Symbol('\\\\gamma', commutative=True)), Symbol('\\\\delta', commutative=True)), Tuple(Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)))", "Mul(Symbol('\\\\delta', commutative=True), exp(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\omega e^{\\chi}", "variable": "\\chi", "positive": "\\omega e^{\\chi}", "negatives": ["\\omega \\sin{(\\chi)}", "\\frac{\\omega^{2} e^{\\chi}}{2}", "- \\frac{\\cos{(\\chi)}}{\\omega}", "\\sin{(\\chi + \\omega)}"], "srepr_premise_expression": "Mul(Symbol('\\\\omega', commutative=True), exp(Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\omega', commutative=True), exp(Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\omega', commutative=True), sin(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), exp(Symbol('\\\\chi', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), cos(Symbol('\\\\chi', commutative=True)))", "sin(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\frac{\\pi}{\\alpha}", "variable": "\\pi", "positive": "\\frac{\\pi^{2}}{2 \\alpha}", "negatives": ["\\pi \\log{(\\alpha)}", "\\frac{\\alpha \\pi^{2}}{2}", "\\frac{\\pi (- 2 \\alpha + \\pi)}{2}", "e^{\\alpha + \\pi}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\pi', commutative=True)))", "exp(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\log{(\\pi \\psi)}", "variable": "\\pi", "positive": "\\pi (\\log{(\\pi \\psi)} - 1)", "negatives": ["\\psi (\\log{(\\pi \\psi)} - 1)", "\\frac{\\pi (\\log{(\\pi)} - 1)}{\\psi}", "- \\cos{(\\pi - \\psi)}", "\\psi \\log{(\\pi)}"], "srepr_premise_expression": "log(Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\pi', commutative=True), Add(log(Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\psi', commutative=True), Add(log(Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Add(log(Symbol('\\\\pi', commutative=True)), Integer(-1)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))", "Mul(Symbol('\\\\psi', commutative=True), log(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "- \\sin{(\\beta - \\omega)}", "variable": "\\omega", "positive": "- \\cos{(\\beta - \\omega)}", "negatives": ["\\cos{(\\beta - \\omega)}", "e^{- \\beta + \\omega}", "\\frac{\\omega (2 \\beta - \\omega)}{2}", "\\omega (\\log{(\\beta \\omega)} - 1)"], "srepr_premise_expression": "Mul(Integer(-1), sin(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))))", "srepr_negatives": ["cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "exp(Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "Mul(Symbol('\\\\omega', commutative=True), Add(log(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\beta - \\sigma", "variable": "\\sigma", "positive": "\\frac{\\sigma (2 \\beta - \\sigma)}{2}", "negatives": ["\\frac{\\beta (\\beta - 2 \\sigma)}{2}", "\\frac{\\beta \\sigma^{2}}{2}", "\\sigma (\\log{(\\beta \\sigma)} - 1)", "\\frac{\\sigma (\\sigma + 2 \\sin{(\\beta)})}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "Mul(Symbol('\\\\sigma', commutative=True), Add(log(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(2), sin(Symbol('\\\\beta', commutative=True)))))"]}, {"premise_expression": "- \\delta + \\sigma", "variable": "\\delta", "positive": "\\frac{\\delta (- \\delta + 2 \\sigma)}{2}", "negatives": ["\\frac{\\sigma (- 2 \\delta + \\sigma)}{2}", "\\frac{\\delta (\\delta + 2 e^{\\sigma})}{2}", "\\frac{\\delta^{2} \\log{(\\sigma)}}{2}", "- e^{- \\delta + \\sigma}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), exp(Symbol('\\\\sigma', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), log(Symbol('\\\\sigma', commutative=True)))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\frac{\\log{(\\chi)}}{\\alpha}", "variable": "\\chi", "positive": "\\frac{\\chi (\\log{(\\chi)} - 1)}{\\alpha}", "negatives": ["- \\cos{(\\alpha - \\chi)}", "\\log{(\\alpha)} \\log{(\\chi)}", "\\log{(\\chi)} \\sin{(\\alpha)}", "- \\cos{(\\alpha + \\chi)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), log(Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\chi', commutative=True), Add(log(Symbol('\\\\chi', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True)))))", "Mul(log(Symbol('\\\\alpha', commutative=True)), log(Symbol('\\\\chi', commutative=True)))", "Mul(log(Symbol('\\\\chi', commutative=True)), sin(Symbol('\\\\alpha', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True))))"]}, {"premise_expression": "e^{\\frac{\\delta}{\\omega}}", "variable": "\\delta", "positive": "\\omega e^{\\frac{\\delta}{\\omega}}", "negatives": ["\\frac{\\delta^{2} \\omega}{2}", "\\frac{\\sin{(\\delta)}}{\\omega}", "- \\delta \\omega - \\cos{(\\delta)}", "\\sin{(\\delta + \\omega)}"], "srepr_premise_expression": "exp(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\omega', commutative=True), exp(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Symbol('\\\\omega', commutative=True))", "Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), sin(Symbol('\\\\delta', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\delta', commutative=True))))", "sin(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\sin{(\\sigma - \\xi)}", "variable": "\\xi", "positive": "\\cos{(\\sigma - \\xi)}", "negatives": ["- \\cos{(\\sigma - \\xi)}", "\\frac{\\xi (2 \\sigma + \\xi)}{2}", "\\frac{\\xi^{2}}{2 \\sigma}", "\\xi (\\log{(\\sigma \\xi)} - 1)"], "srepr_premise_expression": "sin(Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "cos(Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\sigma', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Mul(Symbol('\\\\xi', commutative=True), Add(log(Mul(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True))), Integer(-1)))"]}, {"premise_expression": "- \\omega + e^{\\beta}", "variable": "\\beta", "positive": "- \\beta \\omega + e^{\\beta}", "negatives": ["\\frac{\\omega (- \\omega + 2 e^{\\beta})}{2}", "\\sin{(\\beta + \\omega)}", "\\frac{\\beta^{2}}{2 \\omega}", "\\frac{\\beta^{2} \\log{(\\omega)}}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), exp(Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True)), exp(Symbol('\\\\beta', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\beta', commutative=True)))))", "sin(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), log(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\log{(\\chi)}^{\\alpha}", "variable": "\\chi", "positive": "(- \\log{(\\chi)})^{- \\alpha} \\log{(\\chi)}^{\\alpha} \\Gamma(\\alpha + 1, - \\log{(\\chi)})", "negatives": ["- \\alpha \\log{(- \\alpha + \\chi)} + \\chi \\log{(- \\alpha + \\chi)} - \\chi", "\\chi (\\log{(\\alpha \\chi)} - 1)", "\\chi (\\alpha + \\log{(\\chi)} - 1)", "\\frac{\\chi (\\log{(\\chi)} - 1)}{\\alpha}"], "srepr_premise_expression": "Pow(log(Symbol('\\\\chi', commutative=True)), Symbol('\\\\alpha', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Pow(Mul(Integer(-1), log(Symbol('\\\\chi', commutative=True))), Mul(Integer(-1), Symbol('\\\\alpha', commutative=True))), Pow(log(Symbol('\\\\chi', commutative=True)), Symbol('\\\\alpha', commutative=True)), uppergamma(Add(Symbol('\\\\alpha', commutative=True), Integer(1)), Mul(Integer(-1), log(Symbol('\\\\chi', commutative=True)))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\chi', commutative=True)))), Mul(Symbol('\\\\chi', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\chi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\chi', commutative=True)))", "Mul(Symbol('\\\\chi', commutative=True), Add(log(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\chi', commutative=True)), Integer(-1)))", "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\chi', commutative=True), Add(log(Symbol('\\\\chi', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\frac{\\gamma}{\\xi} - \\pi", "variable": "\\gamma", "positive": "\\frac{\\gamma^{2}}{2 \\xi} - \\gamma \\pi", "negatives": ["\\gamma \\log{(\\xi)} - \\pi \\xi", "\\frac{\\gamma (\\gamma + 2 \\pi)}{2 \\xi}", "\\frac{\\gamma^{2} \\pi \\xi}{2}", "\\frac{\\gamma \\pi}{\\xi} - \\frac{\\pi^{2}}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Add(Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\xi', commutative=True))), Mul(Integer(-1), Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True))", "Add(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))), Mul(Integer(-1), Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2))))"]}, {"premise_expression": "\\beta (\\chi + \\pi)", "variable": "\\beta", "positive": "\\frac{\\beta^{2} (\\chi + \\pi)}{2}", "negatives": ["\\frac{\\beta^{2} (- \\chi + \\pi)}{2}", "\\frac{\\beta \\chi (\\chi + 2 \\pi)}{2}", "\\frac{\\beta (\\beta \\chi + 2 \\pi)}{2}", "\\frac{\\beta \\pi (2 \\chi + \\pi)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\frac{\\chi}{\\xi}", "variable": "\\xi", "positive": "\\chi \\log{(\\xi)}", "negatives": ["\\frac{\\chi^{2}}{2 \\xi}", "\\log{(\\chi)} \\log{(\\xi)}", "\\frac{\\xi^{2} \\log{(\\chi)}}{2}", "\\cos{(\\chi - \\xi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "Mul(log(Symbol('\\\\chi', commutative=True)), log(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), log(Symbol('\\\\chi', commutative=True)))", "cos(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "e^{- \\delta + \\gamma}", "variable": "\\delta", "positive": "- e^{- \\delta + \\gamma}", "negatives": ["e^{- \\delta + \\gamma}", "\\frac{\\delta (- \\delta + 2 \\gamma)}{2}", "\\log{(\\delta)} \\sin{(\\gamma)}", "\\frac{\\delta^{2} \\sin{(\\gamma)}}{2}"], "srepr_premise_expression": "exp(Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\gamma', commutative=True))))", "srepr_negatives": ["exp(Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), Symbol('\\\\gamma', commutative=True))))", "Mul(log(Symbol('\\\\delta', commutative=True)), sin(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), sin(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\frac{\\pi}{\\gamma}", "variable": "\\pi", "positive": "\\frac{\\pi^{2}}{2 \\gamma}", "negatives": ["\\pi \\log{(\\gamma)}", "\\gamma \\sin{(\\pi)}", "- \\frac{\\cos{(\\pi)}}{\\gamma}", "- \\cos{(\\gamma - \\pi)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "Mul(Symbol('\\\\gamma', commutative=True), sin(Symbol('\\\\pi', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), cos(Symbol('\\\\pi', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))"]}, {"premise_expression": "\\frac{\\alpha}{\\omega}", "variable": "\\omega", "positive": "\\alpha \\log{(\\omega)}", "negatives": ["\\frac{\\alpha^{2}}{2 \\omega}", "\\frac{\\alpha \\omega^{2}}{2}", "- \\sin{(\\alpha - \\omega)}", "\\frac{\\omega^{2} e^{\\alpha}}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "Mul(Integer(-1), sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), exp(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\delta + \\psi", "variable": "\\delta", "positive": "\\frac{\\delta (\\delta + 2 \\psi)}{2}", "negatives": ["\\frac{\\psi (2 \\delta + \\psi)}{2}", "\\delta (\\psi + \\cos{(\\psi)})", "\\frac{\\delta^{2}}{2 \\psi}", "\\delta \\psi + e^{\\delta}"], "srepr_premise_expression": "Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\psi', commutative=True), cos(Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))", "Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\psi', commutative=True)), exp(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\frac{\\delta}{\\omega}", "variable": "\\delta", "positive": "\\frac{\\delta^{2}}{2 \\omega}", "negatives": ["\\delta \\log{(\\omega)}", "\\frac{\\delta^{2} \\omega}{2}", "\\omega \\sin{(\\delta)}", "\\sin{(\\delta + \\omega)}"], "srepr_premise_expression": "Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Symbol('\\\\omega', commutative=True))", "Mul(Symbol('\\\\omega', commutative=True), sin(Symbol('\\\\delta', commutative=True)))", "sin(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\frac{\\log{(\\beta)}}{\\xi}", "variable": "\\beta", "positive": "\\frac{\\beta (\\log{(\\beta)} - 1)}{\\xi}", "negatives": ["\\log{(\\beta)} \\log{(\\xi)}", "\\frac{\\beta (\\beta + 2 \\xi)}{2}", "\\frac{\\beta (- \\beta + 2 \\xi)}{2}", "\\frac{\\sin{(\\beta)}}{\\xi}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), log(Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), Add(log(Symbol('\\\\beta', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(log(Symbol('\\\\beta', commutative=True)), log(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), sin(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "\\log{(- \\chi + \\delta)}", "variable": "\\chi", "positive": "\\chi \\log{(- \\chi + \\delta)} - \\chi - \\delta \\log{(\\chi - \\delta)}", "negatives": ["\\chi \\log{(\\chi - \\delta)} - \\chi - \\delta \\log{(\\chi - \\delta)}", "- \\chi \\log{(- \\chi + \\delta)} + \\delta \\log{(- \\chi + \\delta)} - \\delta", "\\chi e^{\\frac{\\delta}{\\chi}} - \\delta \\operatorname{Ei}{(\\frac{\\delta}{\\chi})}", "\\chi (\\delta + \\log{(\\chi)} - 1)"], "srepr_premise_expression": "log(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\chi', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\delta', commutative=True)))), Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\delta', commutative=True), log(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\chi', commutative=True), log(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))), Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\delta', commutative=True), log(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))))", "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\delta', commutative=True)))), Mul(Symbol('\\\\delta', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\delta', commutative=True)))), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)))", "Add(Mul(Symbol('\\\\chi', commutative=True), exp(Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True)))), Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Ei(Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True)))))", "Mul(Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\chi', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\frac{\\gamma}{\\beta}", "variable": "\\beta", "positive": "\\gamma \\log{(\\beta)}", "negatives": ["\\frac{\\gamma^{2}}{2 \\beta}", "\\cos{(\\beta - \\gamma)}", "0", "\\frac{\\beta^{2} \\sin{(\\gamma)}}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\beta', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)))", "cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "Integer(0)", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), sin(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\log{(\\frac{\\omega}{\\xi})}", "variable": "\\omega", "positive": "\\omega (\\log{(\\frac{\\omega}{\\xi})} - 1)", "negatives": ["\\xi (\\log{(\\frac{\\omega}{\\xi})} + 1)", "\\frac{\\omega^{2} \\log{(\\xi)}}{2}", "\\sin{(\\omega - \\xi)}", "- \\cos{(\\omega + \\xi)}"], "srepr_premise_expression": "log(Mul(Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\omega', commutative=True), Add(log(Mul(Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\xi', commutative=True), Add(log(Mul(Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), log(Symbol('\\\\xi', commutative=True)))", "sin(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\frac{\\alpha}{\\omega}", "variable": "\\omega", "positive": "\\alpha \\log{(\\omega)}", "negatives": ["- \\alpha \\cos{(\\omega)}", "\\frac{\\alpha^{2}}{2 \\omega}", "e^{\\alpha} \\log{(\\omega)}", "\\alpha e^{\\frac{\\omega}{\\alpha}}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), cos(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))", "Mul(exp(Symbol('\\\\alpha', commutative=True)), log(Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), exp(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True))))"]}, {"premise_expression": "\\chi + \\cos{(\\omega)}", "variable": "\\omega", "positive": "\\chi \\omega + \\sin{(\\omega)}", "negatives": ["\\chi \\log{(\\omega)}", "\\log{(\\omega)} \\sin{(\\chi)}", "\\frac{\\chi (\\chi + 2 \\cos{(\\omega)})}{2}", "\\log{(\\chi)} \\log{(\\omega)}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), cos(Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True)), sin(Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "Mul(log(Symbol('\\\\omega', commutative=True)), sin(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), cos(Symbol('\\\\omega', commutative=True)))))", "Mul(log(Symbol('\\\\chi', commutative=True)), log(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\pi (\\beta - \\chi)", "variable": "\\chi", "positive": "\\frac{\\chi \\pi (2 \\beta - \\chi)}{2}", "negatives": ["\\frac{\\pi^{2} (\\beta - \\chi)}{2}", "\\frac{\\beta \\pi (\\beta - 2 \\chi)}{2}", "\\frac{\\chi (2 \\beta + \\chi - 2 \\pi)}{2}", "\\frac{\\beta \\chi^{2}}{2 \\pi}"], "srepr_premise_expression": "Mul(Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True))))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Symbol('\\\\chi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))"]}, {"premise_expression": "\\omega + \\frac{\\sigma}{\\pi}", "variable": "\\pi", "positive": "\\omega \\pi + \\sigma \\log{(\\pi)}", "negatives": ["\\omega \\sigma + \\frac{\\sigma^{2}}{2 \\pi}", "\\frac{\\omega^{2}}{2} + \\frac{\\omega \\sigma}{\\pi}", "\\frac{\\pi (\\omega \\pi + 2 \\sigma)}{2}", "\\frac{\\pi (\\omega \\pi - 2 \\sigma)}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\omega', commutative=True), Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Integer(2))))", "Add(Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2))), Mul(Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\frac{\\psi}{\\gamma}", "variable": "\\psi", "positive": "\\frac{\\psi^{2}}{2 \\gamma}", "negatives": ["\\psi \\log{(\\gamma)}", "\\frac{\\psi^{2} e^{\\gamma}}{2}", "\\gamma e^{\\psi}", "e^{\\gamma + \\psi}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('\\\\psi', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), exp(Symbol('\\\\gamma', commutative=True)))", "Mul(Symbol('\\\\gamma', commutative=True), exp(Symbol('\\\\psi', commutative=True)))", "exp(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\frac{\\gamma - \\pi}{\\gamma}", "variable": "\\pi", "positive": "\\pi - \\frac{\\pi^{2}}{2 \\gamma}", "negatives": ["\\gamma - \\pi \\log{(\\gamma)}", "\\frac{\\gamma \\pi^{2}}{2}", "- \\gamma \\cos{(\\pi)}", "\\gamma \\log{(\\pi)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Pow(Symbol('\\\\pi', commutative=True), Integer(2))))", "srepr_negatives": ["Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True), log(Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), cos(Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\frac{\\psi}{\\gamma}", "variable": "\\psi", "positive": "\\frac{\\psi^{2}}{2 \\gamma}", "negatives": ["\\psi \\log{(\\gamma)}", "\\frac{\\psi^{2} e^{\\gamma}}{2}", "e^{- \\gamma + \\psi}", "\\gamma \\psi + \\sin{(\\psi)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('\\\\psi', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), exp(Symbol('\\\\gamma', commutative=True)))", "exp(Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Add(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True)), sin(Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\alpha - \\pi + \\sigma", "variable": "\\pi", "positive": "\\pi (\\alpha - \\frac{\\pi}{2} + \\sigma)", "negatives": ["\\frac{\\pi (2 \\alpha - \\pi - 2 \\sigma)}{2}", "\\frac{\\sigma (2 \\alpha - 2 \\pi + \\sigma)}{2}", "\\frac{\\alpha (\\alpha - 2 \\pi + 2 \\sigma)}{2}", "\\frac{\\pi (\\alpha \\pi + 2 \\sigma)}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Rational(1, 2), Symbol('\\\\pi', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\omega \\xi", "variable": "\\xi", "positive": "\\frac{\\omega \\xi^{2}}{2}", "negatives": ["\\frac{\\omega^{2} \\xi}{2}", "\\omega \\log{(\\xi)}", "\\frac{\\xi^{2} \\sin{(\\omega)}}{2}", "\\omega \\xi - \\cos{(\\xi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))", "Mul(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), sin(Symbol('\\\\omega', commutative=True)))", "Add(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "e^{\\delta + \\sigma}", "variable": "\\delta", "positive": "e^{\\delta + \\sigma}", "negatives": ["- e^{- \\delta + \\sigma}", "\\sin{(\\delta + \\sigma)}", "\\log{(\\delta)} \\cos{(\\sigma)}", "\\frac{\\delta^{2} \\log{(\\sigma)}}{2}"], "srepr_premise_expression": "exp(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "exp(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\sigma', commutative=True))))", "sin(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True)))", "Mul(log(Symbol('\\\\delta', commutative=True)), cos(Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), log(Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\cos{(\\delta - \\omega)}", "variable": "\\delta", "positive": "\\sin{(\\delta - \\omega)}", "negatives": ["- \\sin{(\\delta - \\omega)}", "\\omega \\sin{(\\delta)}", "- \\omega \\cos{(\\delta)}", "\\omega \\log{(\\delta)}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "sin(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))))", "Mul(Symbol('\\\\omega', commutative=True), sin(Symbol('\\\\delta', commutative=True)))", "Mul(Integer(-1), Symbol('\\\\omega', commutative=True), cos(Symbol('\\\\delta', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\frac{\\sin{(\\chi)}}{\\psi}", "variable": "\\psi", "positive": "\\log{(\\psi)} \\sin{(\\chi)}", "negatives": ["\\chi \\log{(\\psi)}", "- \\frac{\\cos{(\\chi)}}{\\psi}", "\\psi (\\log{(\\chi \\psi)} - 1)", "e^{\\chi + \\psi}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), sin(Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(log(Symbol('\\\\psi', commutative=True)), sin(Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\psi', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), cos(Symbol('\\\\chi', commutative=True)))", "Mul(Symbol('\\\\psi', commutative=True), Add(log(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True))), Integer(-1)))", "exp(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\cos{(\\frac{\\chi}{\\pi})}", "variable": "\\pi", "positive": "\\chi \\operatorname{Si}{(\\frac{\\chi}{\\pi})} + \\pi \\cos{(\\frac{\\chi}{\\pi})}", "negatives": ["\\frac{\\pi (- \\pi + 2 \\log{(\\chi)})}{2}", "\\pi (\\chi - \\pi)", "- \\sin{(\\chi - \\pi)}", "\\frac{\\pi (2 \\chi - \\pi)}{2}"], "srepr_premise_expression": "cos(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\chi', commutative=True), Si(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1))))), Mul(Symbol('\\\\pi', commutative=True), cos(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1))))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), log(Symbol('\\\\chi', commutative=True)))))", "Mul(Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "Mul(Integer(-1), sin(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\frac{\\chi}{\\beta}", "variable": "\\chi", "positive": "\\frac{\\chi^{2}}{2 \\beta}", "negatives": ["\\chi \\log{(\\beta)}", "\\frac{\\chi^{2} \\log{(\\beta)}}{2}", "\\frac{\\chi^{2} \\sin{(\\beta)}}{2}", "\\beta \\chi - \\cos{(\\chi)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\chi', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Pow(Symbol('\\\\chi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), log(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), sin(Symbol('\\\\beta', commutative=True)))", "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\chi', commutative=True))))"]}, {"premise_expression": "\\frac{\\sigma}{\\pi}", "variable": "\\pi", "positive": "\\sigma \\log{(\\pi)}", "negatives": ["\\frac{\\sigma^{2}}{2 \\pi}", "\\cos{(\\pi - \\sigma)}", "\\pi (\\log{(\\frac{\\sigma}{\\pi})} + 1)", "\\frac{\\pi^{2}}{2} + \\sigma \\log{(\\pi)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "cos(Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Symbol('\\\\pi', commutative=True), Add(log(Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))), Integer(1)))", "Add(Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2))), Mul(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\frac{\\cos{(\\beta)}}{\\omega}", "variable": "\\omega", "positive": "\\log{(\\omega)} \\cos{(\\beta)}", "negatives": ["\\beta e^{\\omega}", "\\omega (\\log{(\\frac{\\omega}{\\beta})} - 1)", "\\frac{\\sin{(\\beta)}}{\\omega}", "\\beta e^{\\frac{\\omega}{\\beta}}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), cos(Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(log(Symbol('\\\\omega', commutative=True)), cos(Symbol('\\\\beta', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\beta', commutative=True), exp(Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), Add(log(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True))), Integer(-1)))", "Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), sin(Symbol('\\\\beta', commutative=True)))", "Mul(Symbol('\\\\beta', commutative=True), exp(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True))))"]}, {"premise_expression": "\\log{(\\pi + \\psi)}", "variable": "\\pi", "positive": "\\pi \\log{(\\pi + \\psi)} - \\pi + \\psi \\log{(\\pi + \\psi)}", "negatives": ["\\pi \\log{(\\pi - \\psi)} - \\pi - \\psi \\log{(\\pi - \\psi)}", "\\pi \\log{(\\pi + \\psi)} + \\psi \\log{(\\pi + \\psi)} - \\psi", "\\frac{\\pi (- \\pi + 2 \\cos{(\\psi)})}{2}", "e^{\\psi} \\log{(\\pi)}"], "srepr_premise_expression": "log(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\pi', commutative=True), log(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Symbol('\\\\psi', commutative=True), log(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\pi', commutative=True), log(Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), Symbol('\\\\psi', commutative=True), log(Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))))", "Add(Mul(Symbol('\\\\pi', commutative=True), log(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)))), Mul(Symbol('\\\\psi', commutative=True), log(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\psi', commutative=True)))))", "Mul(exp(Symbol('\\\\psi', commutative=True)), log(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\gamma \\psi", "variable": "\\gamma", "positive": "\\frac{\\gamma^{2} \\psi}{2}", "negatives": ["\\frac{\\gamma \\psi^{2}}{2}", "\\frac{\\gamma (\\gamma + 2 \\psi)}{2}", "\\cos{(\\gamma - \\psi)}", "- \\gamma \\psi + \\sin{(\\gamma)}"], "srepr_premise_expression": "Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "cos(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True)), sin(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\frac{\\delta}{\\chi}", "variable": "\\delta", "positive": "\\frac{\\delta^{2}}{2 \\chi}", "negatives": ["\\delta \\log{(\\chi)}", "\\chi \\sin{(\\delta)}", "\\delta (- \\chi + \\log{(\\delta^{\\chi})})", "\\frac{\\delta (\\delta + 2 e^{\\chi})}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Pow(Symbol('\\\\delta', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\chi', commutative=True)))", "Mul(Symbol('\\\\chi', commutative=True), sin(Symbol('\\\\delta', commutative=True)))", "Mul(Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), log(Pow(Symbol('\\\\delta', commutative=True), Symbol('\\\\chi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), exp(Symbol('\\\\chi', commutative=True)))))"]}, {"premise_expression": "\\frac{\\alpha}{\\omega}", "variable": "\\alpha", "positive": "\\frac{\\alpha^{2}}{2 \\omega}", "negatives": ["\\alpha \\log{(\\omega)}", "\\omega e^{\\frac{\\alpha}{\\omega}}", "\\omega \\log{(\\alpha)}", "\\frac{\\alpha (\\alpha - 2 \\omega)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), exp(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))))", "Mul(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True))))"]}, {"premise_expression": "\\log{(\\alpha + \\gamma)}", "variable": "\\gamma", "positive": "\\alpha \\log{(\\alpha + \\gamma)} + \\gamma \\log{(\\alpha + \\gamma)} - \\gamma", "negatives": ["\\alpha \\log{(\\alpha + \\gamma)} - \\alpha + \\gamma \\log{(\\alpha + \\gamma)}", "\\frac{\\gamma (\\gamma + 2 \\log{(\\alpha)})}{2}", "\\gamma (\\log{(\\alpha \\gamma)} - 1)", "\\alpha \\operatorname{Si}{(\\frac{\\alpha}{\\gamma})} + \\gamma \\cos{(\\frac{\\alpha}{\\gamma})}"], "srepr_premise_expression": "log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\alpha', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True)))), Mul(Symbol('\\\\gamma', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True)))), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\alpha', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True)))), Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Symbol('\\\\gamma', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), log(Symbol('\\\\alpha', commutative=True)))))", "Mul(Symbol('\\\\gamma', commutative=True), Add(log(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True))), Integer(-1)))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Si(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1))))), Mul(Symbol('\\\\gamma', commutative=True), cos(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1))))))"]}, {"premise_expression": "\\beta + \\cos{(\\pi)}", "variable": "\\pi", "positive": "\\beta \\pi + \\sin{(\\pi)}", "negatives": ["- \\beta \\pi - \\cos{(\\pi)}", "\\beta \\log{(\\pi)}", "- e^{\\beta - \\pi}", "\\beta e^{\\frac{\\pi}{\\beta}}"], "srepr_premise_expression": "Add(Symbol('\\\\beta', commutative=True), cos(Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\pi', commutative=True)), sin(Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\pi', commutative=True))))", "Mul(Symbol('\\\\beta', commutative=True), log(Symbol('\\\\pi', commutative=True)))", "Mul(Integer(-1), exp(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))", "Mul(Symbol('\\\\beta', commutative=True), exp(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\gamma + e^{\\pi}", "variable": "\\gamma", "positive": "\\frac{\\gamma (\\gamma + 2 e^{\\pi})}{2}", "negatives": ["\\frac{\\gamma (\\gamma + 2 \\pi)}{2}", "\\frac{\\gamma (\\gamma - 2 \\pi)}{2}", "\\gamma \\pi + e^{\\pi}", "- \\gamma \\pi + e^{\\gamma}"], "srepr_premise_expression": "Add(Symbol('\\\\gamma', commutative=True), exp(Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), exp(Symbol('\\\\pi', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True))))", "Add(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True)), exp(Symbol('\\\\pi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True)), exp(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "- \\psi + \\sin{(\\pi)}", "variable": "\\psi", "positive": "\\frac{\\psi (- \\psi + 2 \\sin{(\\pi)})}{2}", "negatives": ["- \\pi \\psi - \\cos{(\\pi)}", "\\psi (- \\pi + \\log{(\\psi)} - 1)", "\\frac{\\sin{(\\psi)}}{\\pi}", "- \\pi \\operatorname{Ei}{(\\frac{\\pi}{\\psi})} + \\psi e^{\\frac{\\pi}{\\psi}}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), sin(Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\pi', commutative=True)))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\pi', commutative=True))))", "Mul(Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), log(Symbol('\\\\psi', commutative=True)), Integer(-1)))", "Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), sin(Symbol('\\\\psi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True), Ei(Mul(Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1))))), Mul(Symbol('\\\\psi', commutative=True), exp(Mul(Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1))))))"]}, {"premise_expression": "\\sin^{\\alpha}{(\\sigma)}", "variable": "\\sigma", "positive": "\\int \\sin^{\\alpha}{(\\sigma)} d\\sigma", "negatives": ["\\sigma (\\alpha + \\log{(\\sigma)} - 1)", "\\sigma (- \\alpha + \\log{(\\sigma^{\\alpha})})", "\\sigma (\\log{(\\alpha \\sigma)} - 1)", "\\cos{(\\alpha - \\sigma)}"], "srepr_premise_expression": "Pow(sin(Symbol('\\\\sigma', commutative=True)), Symbol('\\\\alpha', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Integral(Pow(sin(Symbol('\\\\sigma', commutative=True)), Symbol('\\\\alpha', commutative=True)), Tuple(Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\sigma', commutative=True)), Integer(-1)))", "Mul(Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), log(Pow(Symbol('\\\\sigma', commutative=True), Symbol('\\\\alpha', commutative=True)))))", "Mul(Symbol('\\\\sigma', commutative=True), Add(log(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True))), Integer(-1)))", "cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "- \\delta + \\cos{(\\gamma)}", "variable": "\\gamma", "positive": "- \\delta \\gamma + \\sin{(\\gamma)}", "negatives": ["\\frac{\\gamma (- \\gamma + 2 \\sin{(\\delta)})}{2}", "\\frac{\\gamma (2 \\delta + \\gamma)}{2}", "\\frac{\\delta (- \\delta + 2 \\cos{(\\gamma)})}{2}", "\\frac{\\gamma^{2} e^{\\delta}}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), cos(Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Symbol('\\\\gamma', commutative=True)), sin(Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\delta', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\gamma', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), exp(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\log{(\\frac{\\omega}{\\delta})}", "variable": "\\omega", "positive": "\\omega (\\log{(\\frac{\\omega}{\\delta})} - 1)", "negatives": ["\\delta (\\log{(\\frac{\\omega}{\\delta})} + 1)", "\\cos{(\\delta - \\omega)}", "\\frac{\\omega (2 \\delta - \\omega)}{2}", "\\sin{(\\delta + \\omega)}"], "srepr_premise_expression": "log(Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\omega', commutative=True), Add(log(Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\delta', commutative=True), Add(log(Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True))), Integer(1)))", "cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "sin(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\frac{\\alpha}{\\xi}", "variable": "\\alpha", "positive": "\\frac{\\alpha^{2}}{2 \\xi}", "negatives": ["\\alpha \\log{(\\xi)}", "\\frac{\\alpha^{2} e^{\\xi}}{2}", "\\frac{\\alpha (- \\alpha + 2 \\xi)}{2}", "e^{\\alpha + \\xi}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), exp(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "exp(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\frac{\\pi}{\\chi}", "variable": "\\chi", "positive": "\\pi \\log{(\\chi)}", "negatives": ["\\frac{\\pi^{2}}{2 \\chi}", "\\operatorname{Si}{(\\chi)}", "\\frac{\\chi^{2}}{2 \\pi}", "- \\chi \\pi - \\cos{(\\chi)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "Si(Symbol('\\\\chi', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))", "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\chi', commutative=True))))"]}, {"premise_expression": "\\alpha - \\xi", "variable": "\\xi", "positive": "\\frac{\\xi (2 \\alpha - \\xi)}{2}", "negatives": ["\\frac{\\alpha (\\alpha - 2 \\xi)}{2}", "\\frac{\\xi (- \\xi + 2 \\log{(\\alpha)})}{2}", "\\frac{\\xi^{2} \\log{(\\alpha)}}{2}", "\\frac{\\xi^{2} \\sin{(\\alpha)}}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), log(Symbol('\\\\alpha', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), log(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), sin(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\frac{e^{\\sigma}}{\\beta}", "variable": "\\beta", "positive": "e^{\\sigma} \\log{(\\beta)}", "negatives": ["\\beta \\sigma - \\cos{(\\beta)}", "- \\cos{(\\beta - \\sigma)}", "- \\beta \\sigma + e^{\\beta}", "- \\frac{\\cos{(\\beta)}}{\\sigma}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), exp(Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(exp(Symbol('\\\\sigma', commutative=True)), log(Symbol('\\\\beta', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\beta', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True)), exp(Symbol('\\\\beta', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), cos(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "\\pi e^{\\sigma}", "variable": "\\sigma", "positive": "\\pi e^{\\sigma}", "negatives": ["\\frac{\\pi^{2} e^{\\sigma}}{2}", "- \\pi \\sigma + e^{\\sigma}", "e^{\\pi + \\sigma}", "\\frac{\\sigma^{2}}{2 \\pi}"], "srepr_premise_expression": "Mul(Symbol('\\\\pi', commutative=True), exp(Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\pi', commutative=True), exp(Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), exp(Symbol('\\\\sigma', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True)), exp(Symbol('\\\\sigma', commutative=True)))", "exp(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))"]}, {"premise_expression": "\\frac{\\sigma}{\\gamma}", "variable": "\\gamma", "positive": "\\sigma \\log{(\\gamma)}", "negatives": ["\\frac{\\sigma^{2}}{2 \\gamma}", "\\frac{\\gamma^{2} \\sigma}{2}", "0", "\\gamma (\\log{(\\gamma \\sigma)} - 1)"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Symbol('\\\\sigma', commutative=True))", "Integer(0)", "Mul(Symbol('\\\\gamma', commutative=True), Add(log(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True))), Integer(-1)))"]}, {"premise_expression": "- \\chi - \\omega + \\pi", "variable": "\\chi", "positive": "\\frac{\\chi (- \\chi - 2 \\omega + 2 \\pi)}{2}", "negatives": ["\\frac{\\chi (- \\chi + 2 \\omega + 2 \\pi)}{2}", "\\frac{\\pi (- 2 \\chi - 2 \\omega + \\pi)}{2}", "\\frac{\\omega (- 2 \\chi - \\omega + 2 \\pi)}{2}", "\\frac{\\chi (\\chi + 2 \\pi^{2})}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))))"]}, {"premise_expression": "\\chi \\log{(\\omega)}", "variable": "\\chi", "positive": "\\frac{\\chi^{2} \\log{(\\omega)}}{2}", "negatives": ["\\frac{\\chi (\\chi - 2 \\omega)}{2}", "\\frac{\\chi^{2}}{2 \\omega}", "\\chi \\omega (\\log{(\\omega)} - 1)", "\\omega \\sin{(\\chi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), log(Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))", "Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True), Add(log(Symbol('\\\\omega', commutative=True)), Integer(-1)))", "Mul(Symbol('\\\\omega', commutative=True), sin(Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "\\frac{e^{\\alpha}}{\\psi}", "variable": "\\psi", "positive": "e^{\\alpha} \\log{(\\psi)}", "negatives": ["\\log{(\\alpha)} \\log{(\\psi)}", "\\psi (\\alpha + \\log{(\\psi)} - 1)", "\\psi (\\log{(\\frac{\\psi}{\\alpha})} - 1)", "0"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), exp(Symbol('\\\\alpha', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(exp(Symbol('\\\\alpha', commutative=True)), log(Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(log(Symbol('\\\\alpha', commutative=True)), log(Symbol('\\\\psi', commutative=True)))", "Mul(Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\psi', commutative=True)), Integer(-1)))", "Mul(Symbol('\\\\psi', commutative=True), Add(log(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True))), Integer(-1)))", "Integer(0)"]}, {"premise_expression": "\\log{(\\pi^{\\omega})}", "variable": "\\omega", "positive": "\\frac{\\omega^{2} \\log{(\\pi)}}{2}", "negatives": ["\\pi \\log{(\\omega)}", "- \\frac{\\omega^{2}}{2} + \\pi \\log{(\\omega)}", "\\omega (\\log{(\\frac{\\pi}{\\omega})} + 1)", "- \\omega \\pi + \\sin{(\\omega)}"], "srepr_premise_expression": "log(Pow(Symbol('\\\\pi', commutative=True), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), log(Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "Add(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2))), Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\omega', commutative=True))))", "Mul(Symbol('\\\\omega', commutative=True), Add(log(Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))), Integer(1)))", "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)), sin(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\frac{\\beta}{\\chi}", "variable": "\\beta", "positive": "\\frac{\\beta^{2}}{2 \\chi}", "negatives": ["\\beta \\log{(\\chi)}", "\\frac{\\beta^{2} \\chi}{2}", "\\frac{\\beta (\\beta - 2 \\chi)}{2}", "\\cos{(\\beta - \\chi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\beta', commutative=True), log(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\chi', commutative=True))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True))))", "cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True))))"]}, {"premise_expression": "- \\omega + e^{\\pi}", "variable": "\\pi", "positive": "- \\omega \\pi + e^{\\pi}", "negatives": ["\\frac{\\pi^{2} e^{\\omega}}{2}", "\\frac{\\omega (- \\omega + 2 e^{\\pi})}{2}", "\\frac{\\pi (2 \\omega + \\pi)}{2}", "\\frac{\\pi (\\pi + 2 e^{\\omega})}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), exp(Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)), exp(Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), exp(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\pi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), exp(Symbol('\\\\omega', commutative=True)))))"]}, {"premise_expression": "\\log{(\\omega + \\pi)}", "variable": "\\pi", "positive": "\\omega \\log{(\\omega + \\pi)} + \\pi \\log{(\\omega + \\pi)} - \\pi", "negatives": ["\\omega \\log{(\\omega + \\pi)} - \\omega + \\pi \\log{(\\omega + \\pi)}", "\\log{(\\omega)} \\log{(\\pi)}", "\\pi (- \\omega + \\log{(\\pi)} - 1)", "\\frac{\\pi^{2} \\log{(\\omega)}}{2}"], "srepr_premise_expression": "log(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\omega', commutative=True), log(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)))), Mul(Symbol('\\\\pi', commutative=True), log(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\omega', commutative=True), log(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Symbol('\\\\pi', commutative=True), log(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)))))", "Mul(log(Symbol('\\\\omega', commutative=True)), log(Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), log(Symbol('\\\\pi', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), log(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "- \\chi + \\omega + \\pi", "variable": "\\pi", "positive": "\\pi (- \\chi + \\omega + \\frac{\\pi}{2})", "negatives": ["\\frac{\\pi (2 \\chi + 2 \\omega + \\pi)}{2}", "\\frac{\\pi (2 \\chi - 2 \\omega - \\pi)}{2}", "\\frac{\\chi (- \\chi + 2 \\omega + 2 \\pi)}{2}", "\\frac{\\omega (- 2 \\chi + \\omega + 2 \\pi)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\omega', commutative=True), Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\frac{\\xi}{\\sigma}", "variable": "\\sigma", "positive": "\\xi \\log{(\\sigma)}", "negatives": ["\\frac{\\xi^{2}}{2 \\sigma}", "e^{\\sigma + \\xi}", "\\log{(\\sigma)} \\sin{(\\xi)}", "\\sigma (\\log{(\\sigma \\xi)} - 1)"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "exp(Add(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True)))", "Mul(log(Symbol('\\\\sigma', commutative=True)), sin(Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\sigma', commutative=True), Add(log(Mul(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True))), Integer(-1)))"]}, {"premise_expression": "e^{\\alpha - \\pi}", "variable": "\\alpha", "positive": "e^{\\alpha - \\pi}", "negatives": ["- e^{\\alpha - \\pi}", "- e^{- \\alpha + \\pi}", "- \\cos{(\\alpha - \\pi)}", "- \\alpha \\pi + e^{\\alpha}"], "srepr_premise_expression": "exp(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "exp(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\pi', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)), exp(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\chi \\gamma", "variable": "\\gamma", "positive": "\\frac{\\chi \\gamma^{2}}{2}", "negatives": ["\\frac{\\chi^{2} \\gamma}{2}", "\\gamma^{2}", "- \\chi \\cos{(\\gamma)}", "e^{- \\chi + \\gamma}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\gamma', commutative=True))", "Pow(Symbol('\\\\gamma', commutative=True), Integer(2))", "Mul(Integer(-1), Symbol('\\\\chi', commutative=True), cos(Symbol('\\\\gamma', commutative=True)))", "exp(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "- \\chi + \\pi", "variable": "\\pi", "positive": "\\frac{\\pi (- 2 \\chi + \\pi)}{2}", "negatives": ["\\frac{\\chi (- \\chi + 2 \\pi)}{2}", "\\frac{\\pi^{2} \\cos{(\\chi)}}{2}", "\\frac{\\pi^{2} \\log{(\\chi)}}{2}", "\\cos{(\\chi - \\pi)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), cos(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), log(Symbol('\\\\chi', commutative=True)))", "cos(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\beta \\omega - \\chi", "variable": "\\chi", "positive": "\\frac{\\chi (2 \\beta \\omega - \\chi)}{2}", "negatives": ["\\frac{\\chi (\\beta \\chi + 2 \\omega)}{2}", "\\frac{\\beta (\\beta \\omega - 2 \\chi)}{2}", "\\frac{\\omega (\\beta \\omega - 2 \\chi)}{2}", "\\frac{\\beta \\chi (\\chi - 2 \\omega)}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\chi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True))))"]}, {"premise_expression": "\\psi + \\sigma", "variable": "\\psi", "positive": "\\frac{\\psi (\\psi + 2 \\sigma)}{2}", "negatives": ["\\frac{\\sigma (2 \\psi + \\sigma)}{2}", "e^{\\psi - \\sigma}", "\\cos{(\\psi - \\sigma)}", "\\sigma e^{\\frac{\\psi}{\\sigma}}"], "srepr_premise_expression": "Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\psi', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "exp(Add(Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "cos(Add(Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Symbol('\\\\sigma', commutative=True), exp(Mul(Symbol('\\\\psi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))))"]}, {"premise_expression": "\\frac{\\psi}{\\alpha \\omega}", "variable": "\\psi", "positive": "\\frac{\\psi^{2}}{2 \\alpha \\omega}", "negatives": ["\\frac{\\alpha \\psi^{2}}{2 \\omega}", "\\frac{\\omega \\psi^{2}}{2 \\alpha}", "\\frac{\\psi \\log{(\\omega)}}{\\alpha}", "\\frac{\\psi \\log{(\\alpha)}}{\\omega}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True), log(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\frac{\\chi + \\psi}{\\xi}", "variable": "\\xi", "positive": "(\\chi + \\psi) \\log{(\\xi)}", "negatives": ["\\chi \\psi \\log{(\\xi)}", "\\frac{\\chi (\\chi + 2 \\psi)}{2 \\xi}", "\\frac{\\psi (2 \\chi + \\psi)}{2 \\xi}", "\\frac{\\xi (2 \\chi + 2 \\psi - \\xi)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True)), log(Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True), log(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\frac{e^{\\gamma}}{\\chi}", "variable": "\\chi", "positive": "e^{\\gamma} \\log{(\\chi)}", "negatives": ["\\gamma e^{\\frac{\\chi}{\\gamma}}", "\\sin{(\\chi - \\gamma)}", "\\chi (\\gamma + \\log{(\\chi)} - 1)", "\\frac{\\chi (\\chi + 2 \\gamma)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), exp(Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(exp(Symbol('\\\\gamma', commutative=True)), log(Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\gamma', commutative=True), exp(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)))))", "sin(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "Mul(Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\chi', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\gamma', commutative=True))))"]}, {"premise_expression": "\\frac{\\xi}{\\beta \\omega}", "variable": "\\omega", "positive": "\\frac{\\xi \\log{(\\omega)}}{\\beta}", "negatives": ["\\frac{\\xi \\log{(\\beta)}}{\\omega}", "\\frac{\\beta \\omega^{2} \\xi}{2}", "\\frac{\\xi^{2}}{2 \\beta \\omega}", "\\frac{\\omega^{2} \\xi}{2 \\beta}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True), log(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))"]}, {"premise_expression": "\\alpha - \\omega", "variable": "\\alpha", "positive": "\\frac{\\alpha (\\alpha - 2 \\omega)}{2}", "negatives": ["\\frac{\\omega (2 \\alpha - \\omega)}{2}", "\\frac{\\alpha (- \\alpha + 2 \\sin{(\\omega)})}{2}", "\\frac{\\alpha (- \\alpha + 2 \\log{(\\omega)})}{2}", "\\alpha (\\log{(\\alpha \\omega)} - 1)"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\omega', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), log(Symbol('\\\\omega', commutative=True)))))", "Mul(Symbol('\\\\alpha', commutative=True), Add(log(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True))), Integer(-1)))"]}, {"premise_expression": "- \\omega + \\log{(\\sigma)}", "variable": "\\omega", "positive": "\\frac{\\omega (- \\omega + 2 \\log{(\\sigma)})}{2}", "negatives": ["\\frac{\\omega (\\omega + 2 \\sin{(\\sigma)})}{2}", "\\frac{\\omega (- \\omega + 2 \\sigma)}{2}", "\\frac{\\omega (\\omega + 2 \\sigma)}{2}", "\\frac{\\omega^{2} \\log{(\\sigma)}}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), log(Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), log(Symbol('\\\\sigma', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), sin(Symbol('\\\\sigma', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), log(Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "e^{\\frac{\\gamma}{\\omega}}", "variable": "\\gamma", "positive": "\\omega e^{\\frac{\\gamma}{\\omega}}", "negatives": ["e^{\\gamma - \\omega}", "\\tilde{\\infty} \\gamma", "- \\gamma \\operatorname{Ei}{(\\frac{\\gamma}{\\omega})} + \\omega e^{\\frac{\\gamma}{\\omega}}", "\\frac{\\gamma (\\gamma + 2 e^{\\omega})}{2}"], "srepr_premise_expression": "exp(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\omega', commutative=True), exp(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))))", "srepr_negatives": ["exp(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "Mul(zoo, Symbol('\\\\gamma', commutative=True))", "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Ei(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1))))), Mul(Symbol('\\\\omega', commutative=True), exp(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1))))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), exp(Symbol('\\\\omega', commutative=True)))))"]}, {"premise_expression": "- \\delta + e^{\\beta}", "variable": "\\beta", "positive": "- \\beta \\delta + e^{\\beta}", "negatives": ["- \\beta \\delta + \\sin{(\\beta)}", "- \\delta \\cos{(\\beta)}", "\\frac{\\delta (- \\delta + 2 e^{\\beta})}{2}", "\\frac{\\beta (\\beta + 2 e^{\\delta})}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), exp(Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True)), exp(Symbol('\\\\beta', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True)), sin(Symbol('\\\\beta', commutative=True)))", "Mul(Integer(-1), Symbol('\\\\delta', commutative=True), cos(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\beta', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), exp(Symbol('\\\\delta', commutative=True)))))"]}, {"premise_expression": "\\frac{\\log{(\\delta)}}{\\sigma}", "variable": "\\delta", "positive": "\\frac{\\delta (\\log{(\\delta)} - 1)}{\\sigma}", "negatives": ["\\log{(\\delta)} \\log{(\\sigma)}", "\\frac{\\sin{(\\delta)}}{\\sigma}", "\\delta (- \\sigma + \\log{(\\delta^{\\sigma})})", "\\frac{\\delta (\\delta + 2 \\sin{(\\sigma)})}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), log(Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Add(log(Symbol('\\\\delta', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(log(Symbol('\\\\delta', commutative=True)), log(Symbol('\\\\sigma', commutative=True)))", "Mul(Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), sin(Symbol('\\\\delta', commutative=True)))", "Mul(Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), log(Pow(Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), sin(Symbol('\\\\sigma', commutative=True)))))"]}, {"premise_expression": "e^{\\gamma - \\sigma}", "variable": "\\sigma", "positive": "- e^{\\gamma - \\sigma}", "negatives": ["e^{\\gamma - \\sigma}", "- \\cos{(\\gamma + \\sigma)}", "\\frac{\\sigma (2 \\gamma - \\sigma)}{2}", "- \\gamma \\sigma + e^{\\sigma}"], "srepr_premise_expression": "exp(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Integer(-1), exp(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))", "srepr_negatives": ["exp(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True)), exp(Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\log{(\\psi + \\sigma)}", "variable": "\\sigma", "positive": "\\psi \\log{(\\psi + \\sigma)} + \\sigma \\log{(\\psi + \\sigma)} - \\sigma", "negatives": ["\\psi \\log{(\\psi + \\sigma)} - \\psi + \\sigma \\log{(\\psi + \\sigma)}", "\\sigma (\\psi + \\log{(\\sigma)} - 1)", "\\frac{\\sigma (- \\sigma + 2 \\cos{(\\psi)})}{2}", "\\sigma (\\log{(\\psi \\sigma)} - 1)"], "srepr_premise_expression": "log(Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\psi', commutative=True), log(Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True)))), Mul(Symbol('\\\\sigma', commutative=True), log(Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True)))), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\psi', commutative=True), log(Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True)))), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Symbol('\\\\sigma', commutative=True), log(Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True)))))", "Mul(Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\psi', commutative=True), log(Symbol('\\\\sigma', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\psi', commutative=True)))))", "Mul(Symbol('\\\\sigma', commutative=True), Add(log(Mul(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\alpha + e^{\\gamma}", "variable": "\\gamma", "positive": "\\alpha \\gamma + e^{\\gamma}", "negatives": ["- \\alpha \\gamma + e^{\\gamma}", "\\frac{\\alpha (\\alpha + 2 e^{\\gamma})}{2}", "\\frac{\\gamma (2 \\alpha + \\gamma)}{2}", "\\alpha \\log{(\\gamma)}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), exp(Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True)), exp(Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True)), exp(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), exp(Symbol('\\\\gamma', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\frac{\\alpha}{\\beta \\sigma}", "variable": "\\beta", "positive": "\\frac{\\alpha \\log{(\\beta)}}{\\sigma}", "negatives": ["\\frac{\\alpha \\log{(\\sigma)}}{\\beta}", "\\frac{\\alpha^{2}}{2 \\beta \\sigma}", "\\alpha \\beta \\sigma^{\\sigma}", "(- \\alpha + \\sigma) \\log{(\\beta)}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), log(Symbol('\\\\beta', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), log(Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Symbol('\\\\sigma', commutative=True)))", "Mul(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\sigma', commutative=True)), log(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "\\sigma \\log{(\\delta)}", "variable": "\\delta", "positive": "\\delta \\sigma (\\log{(\\delta)} - 1)", "negatives": ["\\frac{\\sigma^{2} \\log{(\\delta)}}{2}", "\\frac{\\delta^{2} \\log{(\\sigma)}}{2}", "\\cos{(\\delta - \\sigma)}", "\\frac{\\delta^{2}}{2 \\sigma}"], "srepr_premise_expression": "Mul(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True), Add(log(Symbol('\\\\delta', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), log(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), log(Symbol('\\\\sigma', commutative=True)))", "cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))"]}, {"premise_expression": "- \\gamma + \\psi \\sigma", "variable": "\\sigma", "positive": "\\frac{\\sigma (- 2 \\gamma + \\psi \\sigma)}{2}", "negatives": ["\\frac{\\psi (- 2 \\gamma + \\psi \\sigma)}{2}", "\\frac{\\psi \\sigma (- 2 \\gamma + \\sigma)}{2}", "\\frac{\\gamma (- \\gamma + 2 \\psi \\sigma)}{2}", "\\frac{\\sigma^{2} (\\gamma + \\psi)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\frac{\\beta}{\\alpha \\chi}", "variable": "\\chi", "positive": "\\frac{\\beta \\log{(\\chi)}}{\\alpha}", "negatives": ["\\frac{\\beta \\log{(\\alpha)}}{\\chi}", "\\frac{\\alpha \\beta \\chi^{2}}{2}", "\\frac{\\beta^{2}}{2 \\alpha \\chi}", "\\frac{\\beta \\chi^{2}}{2 \\alpha}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\beta', commutative=True), log(Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), log(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(2)))"]}, {"premise_expression": "\\chi + e^{\\gamma}", "variable": "\\gamma", "positive": "\\chi \\gamma + e^{\\gamma}", "negatives": ["\\chi e^{\\frac{\\gamma}{\\chi}}", "\\frac{\\chi (\\chi + 2 e^{\\gamma})}{2}", "\\frac{\\gamma^{2} e^{\\chi}}{2}", "\\frac{\\gamma^{2}}{2 \\chi}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), exp(Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True)), exp(Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\chi', commutative=True), exp(Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), exp(Symbol('\\\\gamma', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), exp(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)))"]}, {"premise_expression": "\\frac{\\sin{(\\pi)}}{\\gamma}", "variable": "\\pi", "positive": "- \\frac{\\cos{(\\pi)}}{\\gamma}", "negatives": ["\\cos{(\\gamma - \\pi)}", "\\frac{\\pi^{2}}{2 \\gamma}", "\\frac{\\pi (\\log{(\\pi)} - 1)}{\\gamma}", "\\log{(\\gamma)} \\sin{(\\pi)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), sin(Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Integer(-1), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), cos(Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["cos(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True), Add(log(Symbol('\\\\pi', commutative=True)), Integer(-1)))", "Mul(log(Symbol('\\\\gamma', commutative=True)), sin(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\omega \\sin{(\\pi)}", "variable": "\\omega", "positive": "\\frac{\\omega^{2} \\sin{(\\pi)}}{2}", "negatives": ["\\frac{\\omega^{2} \\cos{(\\pi)}}{2}", "\\frac{\\omega^{2} (\\pi - 1)}{2}", "\\frac{\\omega (\\omega + 2 \\sin{(\\pi)})}{2}", "- \\omega \\cos{(\\pi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\omega', commutative=True), sin(Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), sin(Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), cos(Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Add(Symbol('\\\\pi', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), sin(Symbol('\\\\pi', commutative=True)))))", "Mul(Integer(-1), Symbol('\\\\omega', commutative=True), cos(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\gamma - \\xi", "variable": "\\gamma", "positive": "\\frac{\\gamma (\\gamma - 2 \\xi)}{2}", "negatives": ["\\frac{\\gamma (\\gamma + 2 \\xi)}{2}", "\\frac{\\xi (2 \\gamma - \\xi)}{2}", "\\frac{\\gamma (\\gamma + 2 \\log{(\\xi)})}{2}", "\\gamma \\sin{(\\xi^{\\xi})}"], "srepr_premise_expression": "Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), log(Symbol('\\\\xi', commutative=True)))))", "Mul(Symbol('\\\\gamma', commutative=True), sin(Pow(Symbol('\\\\xi', commutative=True), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\sigma + \\log{(\\delta)}", "variable": "\\sigma", "positive": "\\frac{\\sigma (\\sigma + 2 \\log{(\\delta)})}{2}", "negatives": ["\\frac{\\sigma (- \\sigma + 2 \\sin{(\\delta)})}{2}", "\\delta (\\sigma + \\log{(\\delta)} - 1)", "\\delta \\sigma - \\cos{(\\sigma)}", "\\delta \\log{(\\sigma)}"], "srepr_premise_expression": "Add(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(2), log(Symbol('\\\\delta', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\delta', commutative=True)))))", "Mul(Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\delta', commutative=True)), Integer(-1)))", "Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\sigma', commutative=True))))", "Mul(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "- \\omega + \\pi", "variable": "\\pi", "positive": "\\frac{\\pi (- 2 \\omega + \\pi)}{2}", "negatives": ["\\frac{\\omega (- \\omega + 2 \\pi)}{2}", "\\frac{\\omega \\pi^{2}}{2}", "\\frac{\\pi (- \\pi + 2 \\cos{(\\omega)})}{2}", "\\frac{\\pi^{2} \\cos{(\\omega)}}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\omega', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), cos(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\chi \\psi", "variable": "\\psi", "positive": "\\frac{\\chi \\psi^{2}}{2}", "negatives": ["\\frac{\\chi^{2} \\psi}{2}", "\\frac{\\psi^{2}}{2 \\chi}", "\\chi \\log{(\\psi)}", "\\frac{\\psi^{2} \\sin{(\\chi)}}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "Mul(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), sin(Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "- \\omega + \\sigma + \\xi", "variable": "\\xi", "positive": "\\xi (- \\omega + \\sigma + \\frac{\\xi}{2})", "negatives": ["\\frac{\\sigma (- 2 \\omega + \\sigma + 2 \\xi)}{2}", "\\frac{\\omega (- \\omega + 2 \\sigma + 2 \\xi)}{2}", "\\frac{\\xi^{2} (\\omega + \\sigma)}{2}", "\\frac{\\xi (- 2 \\omega + \\xi)}{2 \\sigma}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Symbol('\\\\sigma', commutative=True), Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\sigma', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\frac{\\sin{(\\pi)}}{\\delta}", "variable": "\\pi", "positive": "- \\frac{\\cos{(\\pi)}}{\\delta}", "negatives": ["\\delta \\log{(\\pi)}", "\\delta e^{\\frac{\\pi}{\\delta}}", "\\delta \\pi - \\cos{(\\pi)}", "- \\sin{(\\delta - \\pi)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), sin(Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Integer(-1), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), cos(Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\delta', commutative=True), exp(Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))))", "Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\pi', commutative=True))))", "Mul(Integer(-1), sin(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))"]}, {"premise_expression": "\\sin{(\\beta - \\gamma)}", "variable": "\\gamma", "positive": "\\cos{(\\beta - \\gamma)}", "negatives": ["- \\cos{(\\beta - \\gamma)}", "\\sin{(\\beta + \\gamma)}", "\\beta \\log{(\\gamma)}", "\\gamma"], "srepr_premise_expression": "sin(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))))", "sin(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)))", "Mul(Symbol('\\\\beta', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "Symbol('\\\\gamma', commutative=True)"]}, {"premise_expression": "\\xi + e^{\\alpha}", "variable": "\\xi", "positive": "\\frac{\\xi (\\xi + 2 e^{\\alpha})}{2}", "negatives": ["\\frac{\\xi (\\xi + 2 \\sin{(\\alpha)})}{2}", "\\alpha \\xi + e^{\\alpha}", "\\xi (- \\alpha + \\log{(\\xi^{\\alpha})})", "e^{- \\alpha + \\xi}"], "srepr_premise_expression": "Add(Symbol('\\\\xi', commutative=True), exp(Symbol('\\\\alpha', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\xi', commutative=True), Mul(Integer(2), exp(Symbol('\\\\alpha', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\xi', commutative=True), Mul(Integer(2), sin(Symbol('\\\\alpha', commutative=True)))))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True)), exp(Symbol('\\\\alpha', commutative=True)))", "Mul(Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), log(Pow(Symbol('\\\\xi', commutative=True), Symbol('\\\\alpha', commutative=True)))))", "exp(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "- \\gamma + \\pi", "variable": "\\pi", "positive": "\\frac{\\pi (- 2 \\gamma + \\pi)}{2}", "negatives": ["\\frac{\\gamma (- \\gamma + 2 \\pi)}{2}", "\\frac{\\pi (- \\pi + 2 \\log{(\\gamma)})}{2}", "- \\sin{(\\gamma - \\pi)}", "\\sin{(\\gamma + \\pi)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), log(Symbol('\\\\gamma', commutative=True)))))", "Mul(Integer(-1), sin(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))", "sin(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\frac{- \\pi + \\psi}{\\omega}", "variable": "\\pi", "positive": "\\frac{\\pi (- \\pi + 2 \\psi)}{2 \\omega}", "negatives": ["\\frac{\\psi (- 2 \\pi + \\psi)}{2 \\omega}", "\\frac{\\pi (2 \\omega \\psi - \\pi)}{2}", "\\frac{\\pi (2 \\omega + \\pi \\psi)}{2}", "(- \\pi + \\psi) \\log{(\\omega)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True))))", "Mul(Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Symbol('\\\\psi', commutative=True)), log(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\frac{\\sigma}{\\psi}", "variable": "\\sigma", "positive": "\\frac{\\sigma^{2}}{2 \\psi}", "negatives": ["\\sigma \\log{(\\psi)}", "\\frac{\\sigma (2 \\psi + \\sigma)}{2}", "e^{- \\psi + \\sigma}", "\\sin{(\\psi + \\sigma)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\psi', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "exp(Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "sin(Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\beta \\sin{(\\chi)}", "variable": "\\beta", "positive": "\\frac{\\beta^{2} \\sin{(\\chi)}}{2}", "negatives": ["\\frac{\\sin{(\\beta)}}{\\chi}", "- \\beta \\cos{(\\chi)}", "\\frac{\\beta^{2} \\chi}{2}", "\\log{(\\beta)} \\cos{(\\chi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), sin(Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), sin(Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), sin(Symbol('\\\\beta', commutative=True)))", "Mul(Integer(-1), Symbol('\\\\beta', commutative=True), cos(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\chi', commutative=True))", "Mul(log(Symbol('\\\\beta', commutative=True)), cos(Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "\\psi + \\frac{\\pi}{\\alpha}", "variable": "\\pi", "positive": "\\pi \\psi + \\frac{\\pi^{2}}{2 \\alpha}", "negatives": ["\\alpha \\psi + \\pi \\log{(\\alpha)}", "\\frac{\\pi^{2}}{2 \\alpha \\psi}", "\\frac{\\pi^{2} (\\alpha - \\psi)}{2}", "\\pi^{2} (- \\frac{\\alpha}{2} + \\frac{\\pi}{3})"], "srepr_premise_expression": "Add(Symbol('\\\\psi', commutative=True), Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\pi', commutative=True), Integer(2))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\alpha', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(2)), Add(Mul(Integer(-1), Rational(1, 2), Symbol('\\\\alpha', commutative=True)), Mul(Rational(1, 3), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\frac{\\delta}{\\psi}", "variable": "\\delta", "positive": "\\frac{\\delta^{2}}{2 \\psi}", "negatives": ["\\delta \\log{(\\psi)}", "\\frac{\\delta^{2} \\cos{(\\psi)}}{2}", "- \\frac{\\cos{(\\delta)}}{\\psi}", "\\delta \\psi + e^{\\delta}"], "srepr_premise_expression": "Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), cos(Symbol('\\\\psi', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), cos(Symbol('\\\\delta', commutative=True)))", "Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\psi', commutative=True)), exp(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\frac{\\pi + \\psi}{\\omega}", "variable": "\\omega", "positive": "(\\pi + \\psi) \\log{(\\omega)}", "negatives": ["\\omega - \\pi \\log{(\\omega)}", "- \\omega \\psi + \\pi \\log{(\\omega)}", "\\frac{\\pi (\\pi + 2 \\psi)}{2 \\omega}", "\\frac{\\psi (2 \\pi + \\psi)}{2 \\omega}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)), log(Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True), log(Symbol('\\\\omega', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\log{(\\sigma^{\\beta})}", "variable": "\\beta", "positive": "\\frac{\\beta^{2} \\log{(\\sigma)}}{2}", "negatives": ["\\frac{\\beta (- \\beta + 2 \\log{(\\sigma)})}{2}", "\\frac{\\beta^{2}}{2 \\sigma}", "\\beta (\\log{(\\frac{\\beta}{\\sigma})} - 1)", "\\sigma (- \\beta + \\log{(\\sigma^{\\beta})})"], "srepr_premise_expression": "log(Pow(Symbol('\\\\sigma', commutative=True), Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), log(Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), log(Symbol('\\\\sigma', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "Mul(Symbol('\\\\beta', commutative=True), Add(log(Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))), Integer(-1)))", "Mul(Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), log(Pow(Symbol('\\\\sigma', commutative=True), Symbol('\\\\beta', commutative=True)))))"]}, {"premise_expression": "- \\beta + \\pi", "variable": "\\pi", "positive": "\\frac{\\pi (- 2 \\beta + \\pi)}{2}", "negatives": ["\\frac{\\beta (- \\beta + 2 \\pi)}{2}", "\\frac{\\beta \\pi^{2}}{2}", "\\frac{\\pi (\\pi + 2 \\cos{(\\beta)})}{2}", "- \\sin{(\\beta - \\pi)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), cos(Symbol('\\\\beta', commutative=True)))))", "Mul(Integer(-1), sin(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))"]}, {"premise_expression": "\\log{(\\frac{\\omega}{\\pi})}", "variable": "\\pi", "positive": "\\pi (\\log{(\\frac{\\omega}{\\pi})} + 1)", "negatives": ["\\omega (\\log{(\\frac{\\omega}{\\pi})} - 1)", "\\omega \\log{(\\pi)}", "\\frac{\\pi^{2}}{2 \\omega}", "\\omega e^{\\pi}"], "srepr_premise_expression": "log(Mul(Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\pi', commutative=True), Add(log(Mul(Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))), Integer(1)))", "srepr_negatives": ["Mul(Symbol('\\\\omega', commutative=True), Add(log(Mul(Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))), Integer(-1)))", "Mul(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "Mul(Symbol('\\\\omega', commutative=True), exp(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\frac{\\psi}{\\xi}", "variable": "\\psi", "positive": "\\frac{\\psi^{2}}{2 \\xi}", "negatives": ["\\psi \\log{(\\xi)}", "\\frac{\\psi (\\psi + 2 \\xi)}{2}", "\\frac{\\psi^{2} \\sin{(\\xi)}}{2}", "e^{\\psi + \\xi}"], "srepr_premise_expression": "Mul(Symbol('\\\\psi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\psi', commutative=True), log(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), sin(Symbol('\\\\xi', commutative=True)))", "exp(Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\log{(\\delta - \\psi)}", "variable": "\\psi", "positive": "- \\delta \\log{(- \\delta + \\psi)} + \\psi \\log{(\\delta - \\psi)} - \\psi", "negatives": ["\\delta \\log{(\\delta - \\psi)} - \\delta - \\psi \\log{(\\delta - \\psi)}", "\\psi (- \\delta + \\log{(\\psi^{\\delta})})", "\\frac{\\psi (- \\psi + 2 \\log{(\\delta)})}{2}", "\\psi (\\log{(\\frac{\\delta}{\\psi})} + 1)"], "srepr_premise_expression": "log(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\psi', commutative=True)))), Mul(Symbol('\\\\psi', commutative=True), log(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\delta', commutative=True), log(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Symbol('\\\\psi', commutative=True), log(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))))", "Mul(Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), log(Pow(Symbol('\\\\psi', commutative=True), Symbol('\\\\delta', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), log(Symbol('\\\\delta', commutative=True)))))", "Mul(Symbol('\\\\psi', commutative=True), Add(log(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))), Integer(1)))"]}, {"premise_expression": "- \\gamma + \\pi + \\sigma", "variable": "\\sigma", "positive": "\\sigma (- \\gamma + \\pi + \\frac{\\sigma}{2})", "negatives": ["\\frac{\\sigma (2 \\gamma + 2 \\pi + \\sigma)}{2}", "\\frac{\\pi (- 2 \\gamma + \\pi + 2 \\sigma)}{2}", "\\frac{\\gamma (- \\gamma + 2 \\pi + 2 \\sigma)}{2}", "\\pi \\sigma + \\frac{\\sigma^{2}}{2 \\gamma}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True), Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Add(Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Integer(2))))"]}, {"premise_expression": "\\frac{\\gamma}{\\delta}", "variable": "\\delta", "positive": "\\gamma \\log{(\\delta)}", "negatives": ["- \\gamma \\cos{(\\delta)}", "\\frac{\\gamma^{2}}{2 \\delta}", "\\log{(\\delta)} \\log{(\\gamma)}", "- \\delta \\gamma + e^{\\delta}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), cos(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)))", "Mul(log(Symbol('\\\\delta', commutative=True)), log(Symbol('\\\\gamma', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Symbol('\\\\gamma', commutative=True)), exp(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\chi \\omega - \\gamma", "variable": "\\chi", "positive": "\\frac{\\chi (\\chi \\omega - 2 \\gamma)}{2}", "negatives": ["\\frac{\\omega (\\chi \\omega - 2 \\gamma)}{2}", "\\frac{\\gamma (2 \\chi \\omega - \\gamma)}{2}", "\\frac{\\chi \\gamma (\\chi - 2 \\omega)}{2}", "\\chi \\omega + \\gamma \\log{(\\chi)}"], "srepr_premise_expression": "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True))))", "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\chi', commutative=True))))"]}, {"premise_expression": "- \\gamma + \\sin{(\\omega)}", "variable": "\\gamma", "positive": "\\frac{\\gamma (- \\gamma + 2 \\sin{(\\omega)})}{2}", "negatives": ["\\frac{\\gamma (- \\gamma + 2 \\log{(\\gamma)} - 2)}{2}", "- \\gamma \\omega - \\cos{(\\omega)}", "\\sin{(\\gamma + \\omega)}", "e^{\\gamma + \\omega}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), sin(Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\omega', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), log(Symbol('\\\\gamma', commutative=True))), Integer(-2)))", "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\omega', commutative=True))))", "sin(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True)))", "exp(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "e^{\\omega + \\psi}", "variable": "\\omega", "positive": "e^{\\omega + \\psi}", "negatives": ["\\sin{(\\omega + \\psi)}", "\\frac{\\omega (- \\omega + 2 \\psi)}{2}", "\\log{(\\omega)} \\cos{(\\psi)}", "- \\psi \\cos{(\\omega)}"], "srepr_premise_expression": "exp(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "exp(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["sin(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(log(Symbol('\\\\omega', commutative=True)), cos(Symbol('\\\\psi', commutative=True)))", "Mul(Integer(-1), Symbol('\\\\psi', commutative=True), cos(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\omega + \\psi", "variable": "\\omega", "positive": "\\frac{\\omega (\\omega + 2 \\psi)}{2}", "negatives": ["\\frac{\\omega (\\omega - 2 \\psi)}{2}", "\\frac{\\psi (2 \\omega + \\psi)}{2}", "\\frac{\\omega^{2} \\log{(\\psi)}}{2}", "\\omega \\cos{(\\psi^{2})}"], "srepr_premise_expression": "Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), log(Symbol('\\\\psi', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), cos(Pow(Symbol('\\\\psi', commutative=True), Integer(2))))"]}, {"premise_expression": "\\chi \\psi", "variable": "\\chi", "positive": "\\frac{\\chi^{2} \\psi}{2}", "negatives": ["\\frac{\\chi \\psi^{2}}{2}", "\\chi \\psi + \\sin{(\\chi)}", "- \\chi \\psi + \\sin{(\\chi)}", "\\frac{\\chi (\\chi - 2 \\psi)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True)), sin(Symbol('\\\\chi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True)), sin(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "\\pi e^{\\delta}", "variable": "\\delta", "positive": "\\pi e^{\\delta}", "negatives": ["\\delta \\pi + e^{\\delta}", "\\frac{\\pi^{2} e^{\\delta}}{2}", "- \\delta \\pi + e^{\\delta}", "\\frac{\\delta^{2} e^{\\pi}}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\pi', commutative=True), exp(Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\pi', commutative=True), exp(Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True)), exp(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), exp(Symbol('\\\\delta', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True)), exp(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), exp(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\pi \\xi", "variable": "\\pi", "positive": "\\frac{\\pi^{2} \\xi}{2}", "negatives": ["\\frac{\\pi \\xi^{2}}{2}", "\\pi \\cos{(\\xi^{\\xi})}", "\\frac{\\pi (\\pi + 2 \\sin{(\\xi)})}{2}", "\\frac{\\pi (\\pi + 2 e^{\\xi})}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Mul(Symbol('\\\\pi', commutative=True), cos(Pow(Symbol('\\\\xi', commutative=True), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), sin(Symbol('\\\\xi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), exp(Symbol('\\\\xi', commutative=True)))))"]}, {"premise_expression": "- \\delta + \\cos{(\\pi)}", "variable": "\\pi", "positive": "- \\delta \\pi + \\sin{(\\pi)}", "negatives": ["\\delta \\pi - \\cos{(\\pi)}", "- \\sin{(\\delta - \\pi)}", "\\frac{\\pi^{2} \\cos{(\\delta)}}{2}", "\\frac{\\delta (- \\delta + 2 \\cos{(\\pi)})}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), cos(Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True)), sin(Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\pi', commutative=True))))", "Mul(Integer(-1), sin(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), cos(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\pi', commutative=True)))))"]}, {"premise_expression": "\\frac{\\sigma}{\\alpha}", "variable": "\\sigma", "positive": "\\frac{\\sigma^{2}}{2 \\alpha}", "negatives": ["\\sigma \\log{(\\alpha)}", "- \\sin{(\\alpha - \\sigma)}", "\\cos{(\\alpha - \\sigma)}", "\\frac{\\sigma (\\sigma + 2 \\log{(\\alpha)})}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))", "cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(2), log(Symbol('\\\\alpha', commutative=True)))))"]}, {"premise_expression": "- \\chi + \\delta", "variable": "\\chi", "positive": "\\frac{\\chi (- \\chi + 2 \\delta)}{2}", "negatives": ["\\frac{\\chi (\\chi + 2 \\delta)}{2}", "\\frac{\\delta (- 2 \\chi + \\delta)}{2}", "\\sin{(\\chi - \\delta)}", "\\frac{\\chi^{2} \\delta}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\delta', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\delta', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\delta', commutative=True)))", "sin(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\delta', commutative=True))"]}, {"premise_expression": "\\sigma (\\chi + \\gamma)", "variable": "\\gamma", "positive": "\\frac{\\gamma \\sigma (2 \\chi + \\gamma)}{2}", "negatives": ["\\frac{\\chi \\gamma (\\gamma + 2 \\sigma)}{2}", "\\frac{\\chi \\gamma (- \\gamma + 2 \\sigma)}{2}", "\\frac{\\chi \\sigma (\\chi + 2 \\gamma)}{2}", "\\frac{\\sigma^{2} (\\chi + \\gamma)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "- \\beta + \\xi", "variable": "\\xi", "positive": "\\frac{\\xi (- 2 \\beta + \\xi)}{2}", "negatives": ["\\frac{\\xi (2 \\beta + \\xi)}{2}", "\\frac{\\beta \\xi (2 \\beta + \\xi)}{2}", "\\frac{\\beta (- \\beta + 2 \\xi)}{2}", "\\beta \\xi + \\sin{(\\xi)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True)), sin(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\frac{\\chi \\pi}{\\omega}", "variable": "\\chi", "positive": "\\frac{\\chi^{2} \\pi}{2 \\omega}", "negatives": ["\\frac{\\chi \\pi^{2}}{2 \\omega}", "\\frac{\\chi^{2}}{2 \\omega \\pi}", "\\chi \\pi \\log{(\\omega)}", "\\frac{\\chi^{2}}{2 \\pi} + \\chi \\omega"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))", "Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "Add(Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1))), Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "- \\beta + \\sin{(\\xi)}", "variable": "\\beta", "positive": "\\frac{\\beta (- \\beta + 2 \\sin{(\\xi)})}{2}", "negatives": ["\\frac{\\beta^{2} \\cos{(\\xi)}}{2}", "- \\beta \\xi - \\cos{(\\xi)}", "\\beta (- \\xi + \\log{(\\beta)} - 1)", "- \\beta \\xi - \\cos{(\\beta)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), sin(Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\xi', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), cos(Symbol('\\\\xi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\xi', commutative=True))))", "Mul(Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), log(Symbol('\\\\beta', commutative=True)), Integer(-1)))", "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\beta', commutative=True))))"]}, {"premise_expression": "\\frac{- \\gamma + \\pi}{\\alpha}", "variable": "\\gamma", "positive": "\\frac{\\gamma (- \\gamma + 2 \\pi)}{2 \\alpha}", "negatives": ["\\frac{\\pi (- 2 \\gamma + \\pi)}{2 \\alpha}", "(- \\gamma + \\pi) \\log{(\\alpha)}", "\\frac{\\alpha \\gamma^{2}}{2 \\pi}", "- \\alpha \\gamma + \\pi \\log{(\\gamma)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True)), log(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True)), Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\gamma', commutative=True))))"]}, {"premise_expression": "\\frac{\\psi^{\\beta}}{\\pi}", "variable": "\\pi", "positive": "\\psi^{\\beta} \\log{(\\pi)}", "negatives": ["\\frac{\\beta \\pi^{2} \\psi}{2}", "\\beta \\pi + \\psi \\log{(\\pi)}", "\\frac{\\pi^{2} (- \\beta + \\psi)}{2}", "\\frac{\\pi (2 \\beta^{\\psi} - \\pi)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Pow(Symbol('\\\\psi', commutative=True), Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('\\\\psi', commutative=True), Symbol('\\\\beta', commutative=True)), log(Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))", "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Symbol('\\\\psi', commutative=True), log(Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Pow(Symbol('\\\\beta', commutative=True), Symbol('\\\\psi', commutative=True))), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\frac{\\gamma \\psi}{\\delta}", "variable": "\\psi", "positive": "\\frac{\\gamma \\psi^{2}}{2 \\delta}", "negatives": ["\\frac{\\gamma^{2} \\psi}{2 \\delta}", "\\gamma \\psi \\log{(\\delta)}", "\\frac{\\gamma \\psi (2 \\delta - \\psi)}{2}", "\\frac{\\psi (\\delta \\psi - 2 \\gamma)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))", "Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True), log(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True))))"]}, {"premise_expression": "\\frac{\\omega}{\\delta}", "variable": "\\delta", "positive": "\\omega \\log{(\\delta)}", "negatives": ["\\omega \\sin{(\\delta)}", "\\frac{\\omega^{2}}{2 \\delta}", "\\frac{\\delta^{2} \\log{(\\omega)}}{2}", "\\frac{\\delta^{2} \\omega}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\omega', commutative=True), sin(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), log(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Symbol('\\\\omega', commutative=True))"]}, {"premise_expression": "\\frac{\\chi \\gamma}{\\beta}", "variable": "\\gamma", "positive": "\\frac{\\chi \\gamma^{2}}{2 \\beta}", "negatives": ["\\frac{\\chi^{2} \\gamma}{2 \\beta}", "\\chi \\gamma \\log{(\\beta)}", "\\beta \\gamma + \\frac{\\gamma^{2}}{2 \\chi}", "\\frac{\\beta^{\\chi} \\gamma^{2}}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\gamma', commutative=True))", "Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\beta', commutative=True)))", "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Pow(Symbol('\\\\gamma', commutative=True), Integer(2))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True)), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)))"]}, {"premise_expression": "\\log{(\\delta + \\omega)}", "variable": "\\delta", "positive": "\\delta \\log{(\\delta + \\omega)} - \\delta + \\omega \\log{(\\delta + \\omega)}", "negatives": ["\\delta \\log{(\\delta + \\omega)} + \\omega \\log{(\\delta + \\omega)} - \\omega", "\\delta e^{\\frac{\\omega}{\\delta}} - \\omega \\operatorname{Ei}{(\\frac{\\omega}{\\delta})}", "\\delta (\\log{(\\delta \\omega)} - 1)", "\\delta (\\log{(\\frac{\\omega}{\\delta})} + 1)"], "srepr_premise_expression": "log(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\delta', commutative=True), log(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True)))), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Symbol('\\\\omega', commutative=True), log(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\delta', commutative=True), log(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True)))), Mul(Symbol('\\\\omega', commutative=True), log(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True)))), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))", "Add(Mul(Symbol('\\\\delta', commutative=True), exp(Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True)))), Mul(Integer(-1), Symbol('\\\\omega', commutative=True), Ei(Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True)))))", "Mul(Symbol('\\\\delta', commutative=True), Add(log(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\delta', commutative=True), Add(log(Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True))), Integer(1)))"]}, {"premise_expression": "\\frac{\\chi \\omega}{\\xi}", "variable": "\\omega", "positive": "\\frac{\\chi \\omega^{2}}{2 \\xi}", "negatives": ["\\frac{\\chi^{2} \\omega}{2 \\xi}", "\\frac{\\chi \\omega^{2} \\xi}{2}", "\\chi \\omega \\log{(\\xi)}", "\\frac{\\omega (\\chi \\omega - 2 \\xi)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))", "Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True), log(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "- \\chi + \\omega", "variable": "\\chi", "positive": "\\frac{\\chi (- \\chi + 2 \\omega)}{2}", "negatives": ["\\frac{\\omega (- 2 \\chi + \\omega)}{2}", "\\omega \\log{(\\chi)}", "\\frac{\\chi (\\chi + 2 \\log{(\\omega)})}{2}", "\\chi \\omega + \\sin{(\\chi)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), log(Symbol('\\\\omega', commutative=True)))))", "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True)), sin(Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "- \\beta + \\gamma", "variable": "\\beta", "positive": "\\frac{\\beta (- \\beta + 2 \\gamma)}{2}", "negatives": ["\\frac{\\gamma (- 2 \\beta + \\gamma)}{2}", "\\frac{\\beta^{2} e^{\\gamma}}{2}", "\\frac{\\beta^{2} \\log{(\\gamma)}}{2}", "\\frac{\\beta (\\log{(\\beta)} - 1)}{\\gamma}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\gamma', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\gamma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), exp(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), log(Symbol('\\\\gamma', commutative=True)))", "Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Add(log(Symbol('\\\\beta', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\alpha \\sigma", "variable": "\\sigma", "positive": "\\frac{\\alpha \\sigma^{2}}{2}", "negatives": ["\\frac{\\alpha^{2} \\sigma}{2}", "\\frac{\\sigma \\cos{(\\alpha)}}{\\alpha}", "\\sigma e^{\\alpha^{2}}", "\\alpha e^{\\sigma}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\sigma', commutative=True))", "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True), cos(Symbol('\\\\alpha', commutative=True)))", "Mul(Symbol('\\\\sigma', commutative=True), exp(Pow(Symbol('\\\\alpha', commutative=True), Integer(2))))", "Mul(Symbol('\\\\alpha', commutative=True), exp(Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\xi \\log{(\\beta)}", "variable": "\\beta", "positive": "\\beta \\xi (\\log{(\\beta)} - 1)", "negatives": ["\\frac{\\xi^{2} \\log{(\\beta)}}{2}", "\\beta \\xi - \\cos{(\\beta)}", "\\xi e^{\\beta}", "e^{\\xi} \\log{(\\beta)}"], "srepr_premise_expression": "Mul(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True), Add(log(Symbol('\\\\beta', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), log(Symbol('\\\\beta', commutative=True)))", "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\beta', commutative=True))))", "Mul(Symbol('\\\\xi', commutative=True), exp(Symbol('\\\\beta', commutative=True)))", "Mul(exp(Symbol('\\\\xi', commutative=True)), log(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "2 \\alpha - \\xi", "variable": "\\xi", "positive": "\\frac{\\xi (4 \\alpha - \\xi)}{2}", "negatives": ["\\alpha (\\alpha - \\xi)", "\\frac{\\xi^{2} \\log{(\\alpha)}}{2}", "e^{\\alpha + \\xi}", "\\frac{\\xi (\\log{(\\xi)} - 1)}{\\alpha}"], "srepr_premise_expression": "Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(4), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), log(Symbol('\\\\alpha', commutative=True)))", "exp(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True)))", "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True), Add(log(Symbol('\\\\xi', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\frac{\\omega - \\psi}{\\alpha}", "variable": "\\alpha", "positive": "(\\omega - \\psi) \\log{(\\alpha)}", "negatives": ["- \\frac{\\omega (- \\omega + 2 \\psi)}{2 \\alpha}", "- \\frac{\\psi (- 2 \\omega + \\psi)}{2 \\alpha}", "\\frac{\\alpha (\\alpha + 2 \\omega + 2 \\psi)}{2}", "\\frac{\\alpha (\\alpha - 2 \\omega - 2 \\psi)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))), log(Symbol('\\\\alpha', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Integer(-1), Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "\\frac{e^{\\pi}}{\\sigma}", "variable": "\\sigma", "positive": "e^{\\pi} \\log{(\\sigma)}", "negatives": ["\\pi \\log{(\\sigma)}", "e^{\\pi + \\sigma}", "- e^{\\pi - \\sigma}", "\\sigma \\log{(\\pi^{\\pi})}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), exp(Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(exp(Symbol('\\\\pi', commutative=True)), log(Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\sigma', commutative=True)))", "exp(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True)))", "Mul(Integer(-1), exp(Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))", "Mul(Symbol('\\\\sigma', commutative=True), log(Pow(Symbol('\\\\pi', commutative=True), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "- \\delta + \\sigma", "variable": "\\sigma", "positive": "\\frac{\\sigma (- 2 \\delta + \\sigma)}{2}", "negatives": ["\\frac{\\delta (- \\delta + 2 \\sigma)}{2}", "- \\cos{(\\delta + \\sigma)}", "\\sin{(\\delta + \\sigma)}", "- \\sin{(\\delta - \\sigma)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True))))", "sin(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))"]}, {"premise_expression": "\\sin{(\\gamma + \\sigma)}", "variable": "\\sigma", "positive": "- \\cos{(\\gamma + \\sigma)}", "negatives": ["- \\gamma \\cos{(\\sigma)}", "\\gamma \\log{(\\sigma)}", "\\frac{\\sigma (2 \\gamma - \\sigma)}{2}", "\\gamma \\sigma - \\cos{(\\sigma)}"], "srepr_premise_expression": "sin(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), cos(Symbol('\\\\sigma', commutative=True)))", "Mul(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Add(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\frac{\\pi}{\\psi}", "variable": "\\psi", "positive": "\\pi \\log{(\\psi)}", "negatives": ["\\pi e^{\\psi}", "\\frac{\\pi^{2}}{2 \\psi}", "- \\cos{(\\pi + \\psi)}", "\\sin{(\\pi + \\psi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\pi', commutative=True), exp(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True))))", "sin(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "e^{\\psi + \\sigma}", "variable": "\\sigma", "positive": "e^{\\psi + \\sigma}", "negatives": ["\\psi e^{\\frac{\\sigma}{\\psi}}", "e^{\\psi} \\log{(\\sigma)}", "\\frac{\\sigma (\\sigma + 2 \\sin{(\\psi)})}{2}", "\\frac{\\sigma (- \\sigma + 2 \\sin{(\\psi)})}{2}"], "srepr_premise_expression": "exp(Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "exp(Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\psi', commutative=True), exp(Mul(Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))))", "Mul(exp(Symbol('\\\\psi', commutative=True)), log(Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(2), sin(Symbol('\\\\psi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\psi', commutative=True)))))"]}, {"premise_expression": "e^{\\psi + \\sigma}", "variable": "\\psi", "positive": "e^{\\psi + \\sigma}", "negatives": ["\\frac{\\psi (\\psi - 2 \\sigma)}{2}", "- \\psi \\sigma + \\sin{(\\psi)}", "\\frac{\\psi^{2} \\log{(\\sigma)}}{2}", "\\psi \\cos{(\\frac{\\sigma}{\\psi})} + \\sigma \\operatorname{Si}{(\\frac{\\sigma}{\\psi})}"], "srepr_premise_expression": "exp(Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "exp(Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True)), sin(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), log(Symbol('\\\\sigma', commutative=True)))", "Add(Mul(Symbol('\\\\psi', commutative=True), cos(Mul(Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True)))), Mul(Symbol('\\\\sigma', commutative=True), Si(Mul(Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True)))))"]}, {"premise_expression": "\\gamma - \\pi - \\xi", "variable": "\\pi", "positive": "\\frac{\\pi (2 \\gamma - \\pi - 2 \\xi)}{2}", "negatives": ["\\frac{\\xi (2 \\gamma - 2 \\pi - \\xi)}{2}", "\\frac{\\pi (\\gamma \\pi - 2 \\xi)}{2}", "\\frac{\\gamma (\\gamma - 2 \\pi - 2 \\xi)}{2}", "\\frac{\\pi^{2} (\\gamma + \\xi)}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\frac{\\beta}{\\delta}", "variable": "\\beta", "positive": "\\frac{\\beta^{2}}{2 \\delta}", "negatives": ["\\beta \\log{(\\delta)}", "\\frac{\\beta^{2} \\delta}{2}", "\\frac{\\beta^{2} (\\delta - 1)}{2}", "\\frac{\\beta (\\beta + 2 \\delta)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\beta', commutative=True), log(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\delta', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Add(Symbol('\\\\delta', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\delta', commutative=True))))"]}, {"premise_expression": "\\xi \\log{(\\sigma)}", "variable": "\\xi", "positive": "\\frac{\\xi^{2} \\log{(\\sigma)}}{2}", "negatives": ["\\frac{\\xi^{2} e^{\\sigma}}{2}", "\\sigma \\xi (\\log{(\\sigma)} - 1)", "e^{\\sigma} \\log{(\\xi)}", "- \\sigma \\xi - \\cos{(\\xi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), log(Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), exp(Symbol('\\\\sigma', commutative=True)))", "Mul(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True), Add(log(Symbol('\\\\sigma', commutative=True)), Integer(-1)))", "Mul(exp(Symbol('\\\\sigma', commutative=True)), log(Symbol('\\\\xi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\beta + \\gamma \\sigma", "variable": "\\beta", "positive": "\\frac{\\beta (\\beta + 2 \\gamma \\sigma)}{2}", "negatives": ["\\frac{\\gamma (2 \\beta + \\gamma \\sigma)}{2}", "\\frac{\\sigma (2 \\beta + \\gamma \\sigma)}{2}", "\\beta (\\beta - \\gamma)", "\\frac{\\beta^{2} \\gamma^{\\sigma}}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\beta', commutative=True), Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True))))", "Mul(Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\delta - \\omega", "variable": "\\omega", "positive": "\\frac{\\omega (2 \\delta - \\omega)}{2}", "negatives": ["\\frac{\\delta (\\delta - 2 \\omega)}{2}", "\\frac{\\omega (\\omega + 2 e^{\\delta})}{2}", "e^{\\delta + \\omega}", "- \\cos{(\\delta + \\omega)}"], "srepr_premise_expression": "Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), exp(Symbol('\\\\delta', commutative=True)))))", "exp(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True))))"]}, {"premise_expression": "\\log{(\\gamma)}^{\\alpha}", "variable": "\\gamma", "positive": "(- \\log{(\\gamma)})^{- \\alpha} \\log{(\\gamma)}^{\\alpha} \\Gamma(\\alpha + 1, - \\log{(\\gamma)})", "negatives": ["- \\alpha \\log{(- \\alpha + \\gamma)} + \\gamma \\log{(- \\alpha + \\gamma)} - \\gamma", "\\log{(\\gamma)} \\cos{(\\alpha)}", "\\alpha \\gamma + \\sin{(\\gamma)}", "\\frac{e^{- \\frac{i \\pi}{\\alpha}} \\gamma(\\frac{1}{\\alpha}, \\gamma^{\\alpha} e^{i \\pi})}{\\alpha}"], "srepr_premise_expression": "Pow(log(Symbol('\\\\gamma', commutative=True)), Symbol('\\\\alpha', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Pow(Mul(Integer(-1), log(Symbol('\\\\gamma', commutative=True))), Mul(Integer(-1), Symbol('\\\\alpha', commutative=True))), Pow(log(Symbol('\\\\gamma', commutative=True)), Symbol('\\\\alpha', commutative=True)), uppergamma(Add(Symbol('\\\\alpha', commutative=True), Integer(1)), Mul(Integer(-1), log(Symbol('\\\\gamma', commutative=True)))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\gamma', commutative=True)))), Mul(Symbol('\\\\gamma', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\gamma', commutative=True)))), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))", "Mul(log(Symbol('\\\\gamma', commutative=True)), cos(Symbol('\\\\alpha', commutative=True)))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True)), sin(Symbol('\\\\gamma', commutative=True)))", "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), exp(Mul(Integer(-1), I, pi, Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)))), lowergamma(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Mul(Pow(Symbol('\\\\gamma', commutative=True), Symbol('\\\\alpha', commutative=True)), exp_polar(Mul(I, pi)))))"]}, {"premise_expression": "e^{\\alpha - \\xi}", "variable": "\\alpha", "positive": "e^{\\alpha - \\xi}", "negatives": ["- e^{\\alpha - \\xi}", "\\sin{(\\alpha - \\xi)}", "\\xi \\sin{(\\alpha)}", "\\alpha \\xi + e^{\\alpha}"], "srepr_premise_expression": "exp(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "exp(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))))", "sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Symbol('\\\\xi', commutative=True), sin(Symbol('\\\\alpha', commutative=True)))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True)), exp(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\sin^{\\gamma}{(\\psi)}", "variable": "\\psi", "positive": "\\int \\sin^{\\gamma}{(\\psi)} d\\psi", "negatives": ["- \\gamma \\psi + \\sin{(\\psi)}", "e^{- \\gamma + \\psi}", "e^{\\gamma + \\psi}", "\\frac{\\psi (- \\psi + 2 e^{\\gamma})}{2}"], "srepr_premise_expression": "Pow(sin(Symbol('\\\\psi', commutative=True)), Symbol('\\\\gamma', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Integral(Pow(sin(Symbol('\\\\psi', commutative=True)), Symbol('\\\\gamma', commutative=True)), Tuple(Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True)), sin(Symbol('\\\\psi', commutative=True)))", "exp(Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\psi', commutative=True)))", "exp(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\gamma', commutative=True)))))"]}, {"premise_expression": "\\frac{\\alpha}{\\psi}", "variable": "\\alpha", "positive": "\\frac{\\alpha^{2}}{2 \\psi}", "negatives": ["\\alpha \\log{(\\psi)}", "\\frac{\\alpha^{2} \\psi}{2}", "e^{\\alpha + \\psi}", "\\frac{\\alpha (- \\alpha + 2 \\sin{(\\psi)})}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))", "exp(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\psi', commutative=True)))))"]}, {"premise_expression": "\\omega + \\sin{(\\delta)}", "variable": "\\delta", "positive": "\\delta \\omega - \\cos{(\\delta)}", "negatives": ["\\frac{\\delta^{2} \\log{(\\omega)}}{2}", "\\frac{\\delta (\\delta + 2 \\omega)}{2}", "\\delta \\sin{(2 \\omega)}", "\\frac{\\delta^{2}}{2 \\omega}"], "srepr_premise_expression": "Add(Symbol('\\\\omega', commutative=True), sin(Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\delta', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), log(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Symbol('\\\\delta', commutative=True), sin(Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))"]}, {"premise_expression": "\\chi + \\pi", "variable": "\\pi", "positive": "\\frac{\\pi (2 \\chi + \\pi)}{2}", "negatives": ["\\frac{\\chi (\\chi + 2 \\pi)}{2}", "e^{- \\chi + \\pi}", "\\frac{\\sin{(\\pi)}}{\\chi}", "\\frac{\\pi (- \\pi + 2 \\sin{(\\chi)})}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "exp(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), sin(Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\chi', commutative=True)))))"]}, {"premise_expression": "\\beta \\delta + \\xi", "variable": "\\delta", "positive": "\\frac{\\delta (\\beta \\delta + 2 \\xi)}{2}", "negatives": ["\\frac{\\beta (\\beta \\delta + 2 \\xi)}{2}", "\\frac{\\delta (\\beta \\delta - 2 \\xi)}{2}", "\\frac{\\xi (2 \\beta \\delta + \\xi)}{2}", "\\frac{\\delta \\xi (2 \\beta + \\delta)}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "- \\gamma + \\log{(\\chi)}", "variable": "\\chi", "positive": "\\chi (- \\gamma + \\log{(\\chi)} - 1)", "negatives": ["\\chi \\gamma (\\log{(\\chi)} - 1)", "\\frac{\\gamma (- \\gamma + 2 \\log{(\\chi)})}{2}", "\\chi \\gamma - \\cos{(\\chi)}", "\\frac{\\chi (- \\chi + 2 \\gamma)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), log(Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), log(Symbol('\\\\chi', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True), Add(log(Symbol('\\\\chi', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), log(Symbol('\\\\chi', commutative=True)))))", "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\chi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\gamma', commutative=True))))"]}, {"premise_expression": "\\gamma - \\pi + \\xi", "variable": "\\xi", "positive": "\\xi (\\gamma - \\pi + \\frac{\\xi}{2})", "negatives": ["\\frac{\\xi (2 \\gamma + 2 \\pi - \\xi)}{2}", "\\frac{\\pi (2 \\gamma - \\pi + 2 \\xi)}{2}", "\\frac{\\gamma (\\gamma - 2 \\pi + 2 \\xi)}{2}", "- \\gamma \\xi + \\frac{\\xi^{2}}{2 \\pi}"], "srepr_premise_expression": "Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Integer(2))))"]}, {"premise_expression": "\\cos^{\\omega}{(\\beta)}", "variable": "\\beta", "positive": "\\int \\cos^{\\omega}{(\\beta)} d\\beta", "negatives": ["- \\cos{(\\beta + \\omega)}", "e^{\\beta - \\omega}", "\\frac{\\beta (\\beta - 2 \\omega)}{2}", "\\frac{\\beta^{2}}{2} + \\omega \\log{(\\beta)}"], "srepr_premise_expression": "Pow(cos(Symbol('\\\\beta', commutative=True)), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Integral(Pow(cos(Symbol('\\\\beta', commutative=True)), Symbol('\\\\omega', commutative=True)), Tuple(Symbol('\\\\beta', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True))))", "exp(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True))))", "Add(Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2))), Mul(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\beta', commutative=True))))"]}, {"premise_expression": "- \\delta + \\cos{(\\xi)}", "variable": "\\delta", "positive": "\\frac{\\delta (- \\delta + 2 \\cos{(\\xi)})}{2}", "negatives": ["- \\delta \\xi + \\sin{(\\xi)}", "\\delta \\xi + e^{\\delta}", "\\delta (\\xi + \\log{(\\delta)} - 1)", "- \\xi \\cos{(\\delta)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), cos(Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\xi', commutative=True)))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True)), sin(Symbol('\\\\xi', commutative=True)))", "Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True)), exp(Symbol('\\\\delta', commutative=True)))", "Mul(Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\delta', commutative=True)), Integer(-1)))", "Mul(Integer(-1), Symbol('\\\\xi', commutative=True), cos(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\pi^{\\alpha} + \\xi", "variable": "\\xi", "positive": "\\frac{\\xi (2 \\pi^{\\alpha} + \\xi)}{2}", "negatives": ["\\frac{\\alpha \\xi (2 \\pi + \\xi)}{2}", "\\frac{\\xi (2 \\pi + \\xi)}{2 \\alpha}", "\\frac{\\alpha \\pi \\xi^{2}}{2}", "\\frac{\\xi^{2} (\\alpha + \\pi)}{2}"], "srepr_premise_expression": "Add(Pow(Symbol('\\\\pi', commutative=True), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Pow(Symbol('\\\\pi', commutative=True), Symbol('\\\\alpha', commutative=True))), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\log{(\\alpha - \\gamma)}", "variable": "\\gamma", "positive": "- \\alpha \\log{(- \\alpha + \\gamma)} + \\gamma \\log{(\\alpha - \\gamma)} - \\gamma", "negatives": ["- \\alpha \\log{(- \\alpha + \\gamma)} + \\gamma \\log{(- \\alpha + \\gamma)} - \\gamma", "\\alpha \\log{(\\alpha - \\gamma)} - \\alpha - \\gamma \\log{(\\alpha - \\gamma)}", "\\gamma (\\alpha + \\log{(\\gamma)} - 1)", "- \\alpha \\gamma - \\cos{(\\gamma)}"], "srepr_premise_expression": "log(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\gamma', commutative=True)))), Mul(Symbol('\\\\gamma', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\gamma', commutative=True)))), Mul(Symbol('\\\\gamma', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\gamma', commutative=True)))), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))", "Add(Mul(Symbol('\\\\alpha', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))), Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))))", "Mul(Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\gamma', commutative=True)), Integer(-1)))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\gamma', commutative=True))))"]}, {"premise_expression": "\\beta \\psi", "variable": "\\psi", "positive": "\\frac{\\beta \\psi^{2}}{2}", "negatives": ["\\frac{\\beta^{2} \\psi}{2}", "- \\beta \\psi + \\sin{(\\psi)}", "\\log{(\\psi)} \\cos{(\\beta)}", "- \\cos{(\\beta + \\psi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))", "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\psi', commutative=True)), sin(Symbol('\\\\psi', commutative=True)))", "Mul(log(Symbol('\\\\psi', commutative=True)), cos(Symbol('\\\\beta', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "\\alpha e^{\\chi}", "variable": "\\chi", "positive": "\\alpha e^{\\chi}", "negatives": ["- \\alpha \\cos{(\\chi)}", "\\frac{\\alpha^{2} e^{\\chi}}{2}", "- \\alpha \\chi + e^{\\chi}", "\\frac{\\chi^{2}}{2 \\alpha}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), exp(Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\alpha', commutative=True), exp(Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), cos(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), exp(Symbol('\\\\chi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)), exp(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\chi', commutative=True), Integer(2)))"]}, {"premise_expression": "\\sin^{\\beta}{(\\omega)}", "variable": "\\omega", "positive": "\\int \\sin^{\\beta}{(\\omega)} d\\omega", "negatives": ["- \\sin{(\\beta - \\omega)}", "\\omega \\sin{(2 \\beta)}", "\\log{(\\omega)} \\cos{(\\beta)}", "\\omega (- \\beta + \\log{(\\omega^{\\beta})})"], "srepr_premise_expression": "Pow(sin(Symbol('\\\\omega', commutative=True)), Symbol('\\\\beta', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Integral(Pow(sin(Symbol('\\\\omega', commutative=True)), Symbol('\\\\beta', commutative=True)), Tuple(Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))))", "Mul(Symbol('\\\\omega', commutative=True), sin(Mul(Integer(2), Symbol('\\\\beta', commutative=True))))", "Mul(log(Symbol('\\\\omega', commutative=True)), cos(Symbol('\\\\beta', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), log(Pow(Symbol('\\\\omega', commutative=True), Symbol('\\\\beta', commutative=True)))))"]}, {"premise_expression": "\\sigma \\sin{(\\psi)}", "variable": "\\sigma", "positive": "\\frac{\\sigma^{2} \\sin{(\\psi)}}{2}", "negatives": ["\\frac{\\sigma^{2} \\cos{(\\psi)}}{2}", "\\frac{\\sigma^{2} \\log{(\\psi)}}{2}", "\\frac{\\sigma^{2} e^{\\psi}}{2}", "- \\sigma \\cos{(\\psi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\sigma', commutative=True), sin(Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), sin(Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), cos(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), log(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), exp(Symbol('\\\\psi', commutative=True)))", "Mul(Integer(-1), Symbol('\\\\sigma', commutative=True), cos(Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "e^{- \\delta + \\gamma}", "variable": "\\gamma", "positive": "e^{- \\delta + \\gamma}", "negatives": ["- e^{- \\delta + \\gamma}", "- \\cos{(\\delta - \\gamma)}", "\\frac{\\gamma (- 2 \\delta + \\gamma)}{2}", "\\log{(\\gamma)} \\sin{(\\delta)}"], "srepr_premise_expression": "exp(Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "exp(Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\gamma', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "Mul(log(Symbol('\\\\gamma', commutative=True)), sin(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\delta \\psi", "variable": "\\psi", "positive": "\\frac{\\delta \\psi^{2}}{2}", "negatives": ["\\frac{\\delta^{2} \\psi}{2}", "\\frac{\\psi^{2}}{2 \\delta}", "\\psi + \\frac{\\psi^{2}}{2 \\delta}", "\\cos{(\\delta - \\psi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "Add(Symbol('\\\\psi', commutative=True), Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Pow(Symbol('\\\\psi', commutative=True), Integer(2))))", "cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "\\omega e^{\\gamma}", "variable": "\\omega", "positive": "\\frac{\\omega^{2} e^{\\gamma}}{2}", "negatives": ["\\frac{\\omega^{2} \\sin{(\\gamma)}}{2}", "\\omega e^{\\gamma}", "\\gamma \\omega + e^{\\omega}", "\\frac{\\sin{(\\omega)}}{\\gamma}"], "srepr_premise_expression": "Mul(Symbol('\\\\omega', commutative=True), exp(Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), exp(Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), sin(Symbol('\\\\gamma', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), exp(Symbol('\\\\gamma', commutative=True)))", "Add(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True)), exp(Symbol('\\\\omega', commutative=True)))", "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), sin(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "e^{\\frac{\\pi}{\\gamma}}", "variable": "\\gamma", "positive": "\\gamma e^{\\frac{\\pi}{\\gamma}} - \\pi \\operatorname{Ei}{(\\frac{\\pi}{\\gamma})}", "negatives": ["\\gamma e^{\\frac{\\pi}{\\gamma}}", "\\gamma \\sin{(\\gamma)} + \\cos{(\\gamma)}", "\\gamma \\pi - \\cos{(\\gamma)}", "\\frac{\\gamma (\\gamma - 2 \\pi)}{2}"], "srepr_premise_expression": "exp(Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\gamma', commutative=True), exp(Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\pi', commutative=True), Ei(Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True)))))", "srepr_negatives": ["Mul(Symbol('\\\\gamma', commutative=True), exp(Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))))", "Add(Mul(Symbol('\\\\gamma', commutative=True), sin(Symbol('\\\\gamma', commutative=True))), cos(Symbol('\\\\gamma', commutative=True)))", "Add(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "- \\delta + \\pi", "variable": "\\pi", "positive": "\\frac{\\pi (- 2 \\delta + \\pi)}{2}", "negatives": ["\\frac{\\delta (- \\delta + 2 \\pi)}{2}", "\\frac{\\pi (\\pi + 2 \\log{(\\delta)})}{2}", "\\frac{\\pi^{2} \\cos{(\\delta)}}{2}", "\\frac{\\pi (- \\pi + 2 \\log{(\\delta)})}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), log(Symbol('\\\\delta', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), cos(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), log(Symbol('\\\\delta', commutative=True)))))"]}, {"premise_expression": "\\frac{\\delta \\xi}{\\gamma}", "variable": "\\xi", "positive": "\\frac{\\delta \\xi^{2}}{2 \\gamma}", "negatives": ["\\frac{\\delta^{2} \\xi}{2 \\gamma}", "\\delta \\xi \\log{(\\gamma)}", "\\frac{\\xi (2 \\delta + \\xi)}{2 \\gamma}", "\\delta \\gamma \\log{(\\xi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))", "Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\chi \\xi", "variable": "\\xi", "positive": "\\frac{\\chi \\xi^{2}}{2}", "negatives": ["\\frac{\\chi^{2} \\xi}{2}", "\\frac{\\xi (2 \\chi + \\xi)}{2}", "\\frac{\\xi^{2} e^{\\chi}}{2}", "\\frac{\\xi (- 2 \\chi + \\xi)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), exp(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\alpha + \\chi \\omega", "variable": "\\omega", "positive": "\\frac{\\omega (2 \\alpha + \\chi \\omega)}{2}", "negatives": ["\\frac{\\chi (2 \\alpha + \\chi \\omega)}{2}", "\\frac{\\omega^{2} (\\alpha + \\chi)}{2}", "\\frac{\\chi \\omega (2 \\alpha + \\omega)}{2}", "\\frac{\\alpha (\\alpha + 2 \\chi \\omega)}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True))))"]}, {"premise_expression": "- \\delta + \\frac{\\omega}{\\gamma}", "variable": "\\gamma", "positive": "- \\delta \\gamma + \\omega \\log{(\\gamma)}", "negatives": ["\\delta \\log{(\\gamma)} + \\gamma \\omega", "(- \\delta + \\omega) \\log{(\\gamma)}", "\\delta \\omega \\log{(\\gamma)}", "- \\delta \\omega + \\frac{\\omega^{2}}{2 \\gamma}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Symbol('\\\\gamma', commutative=True)), Mul(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\gamma', commutative=True))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\gamma', commutative=True))), Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True)))", "Mul(Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\omega', commutative=True)), log(Symbol('\\\\gamma', commutative=True)))", "Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Pow(Symbol('\\\\omega', commutative=True), Integer(2))))"]}, {"premise_expression": "- \\sin{(\\gamma - \\psi)}", "variable": "\\psi", "positive": "- \\cos{(\\gamma - \\psi)}", "negatives": ["\\cos{(\\gamma - \\psi)}", "- \\sin{(\\gamma - \\psi)}", "- \\frac{\\cos{(\\psi)}}{\\gamma}", "e^{- \\gamma + \\psi}"], "srepr_premise_expression": "Mul(Integer(-1), sin(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))", "srepr_negatives": ["cos(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(Integer(-1), sin(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))", "Mul(Integer(-1), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), cos(Symbol('\\\\psi', commutative=True)))", "exp(Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\sigma e^{\\gamma}", "variable": "\\sigma", "positive": "\\frac{\\sigma^{2} e^{\\gamma}}{2}", "negatives": ["\\frac{\\sigma^{2} \\log{(\\gamma)}}{2}", "\\sigma e^{\\gamma}", "\\gamma e^{\\frac{\\sigma}{\\gamma}}", "\\sigma \\sin^{\\gamma}{(\\gamma)}"], "srepr_premise_expression": "Mul(Symbol('\\\\sigma', commutative=True), exp(Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), exp(Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), log(Symbol('\\\\gamma', commutative=True)))", "Mul(Symbol('\\\\sigma', commutative=True), exp(Symbol('\\\\gamma', commutative=True)))", "Mul(Symbol('\\\\gamma', commutative=True), exp(Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))))", "Mul(Symbol('\\\\sigma', commutative=True), Pow(sin(Symbol('\\\\gamma', commutative=True)), Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "- \\sin{(\\gamma - \\psi)}", "variable": "\\psi", "positive": "- \\cos{(\\gamma - \\psi)}", "negatives": ["\\cos{(\\gamma - \\psi)}", "- \\cos{(\\gamma + \\psi)}", "\\sin{(\\gamma + \\psi)}", "\\frac{\\sin{(\\psi)}}{\\gamma}"], "srepr_premise_expression": "Mul(Integer(-1), sin(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))", "srepr_negatives": ["cos(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True))))", "sin(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True)))", "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), sin(Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\gamma - \\sigma", "variable": "\\gamma", "positive": "\\frac{\\gamma (\\gamma - 2 \\sigma)}{2}", "negatives": ["\\frac{\\sigma (2 \\gamma - \\sigma)}{2}", "\\sigma \\sin{(\\gamma)}", "\\frac{\\gamma^{2} \\sigma}{2}", "\\gamma \\sigma + \\sin{(\\gamma)}"], "srepr_premise_expression": "Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Symbol('\\\\sigma', commutative=True), sin(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Symbol('\\\\sigma', commutative=True))", "Add(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True)), sin(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "- \\alpha + e^{\\psi}", "variable": "\\alpha", "positive": "\\frac{\\alpha (- \\alpha + 2 e^{\\psi})}{2}", "negatives": ["\\frac{\\alpha (- \\alpha + 2 \\cos{(\\psi)})}{2}", "\\frac{\\alpha (\\alpha + 2 \\psi)}{2}", "- \\alpha \\psi + e^{\\psi}", "\\sin{(\\alpha + \\psi)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), exp(Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\psi', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\psi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True)), exp(Symbol('\\\\psi', commutative=True)))", "sin(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\log{(\\alpha^{\\chi})}", "variable": "\\chi", "positive": "\\frac{\\chi^{2} \\log{(\\alpha)}}{2}", "negatives": ["\\frac{\\chi \\sin{(\\alpha)}}{\\alpha}", "\\frac{\\chi (- \\chi + 2 e^{\\alpha})}{2}", "\\chi (- \\alpha + \\log{(\\chi^{\\alpha})})", "\\alpha (- \\chi + \\log{(\\alpha^{\\chi})})"], "srepr_premise_expression": "log(Pow(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), log(Symbol('\\\\alpha', commutative=True)))", "srepr_negatives": ["Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\chi', commutative=True), sin(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\alpha', commutative=True)))))", "Mul(Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), log(Pow(Symbol('\\\\chi', commutative=True), Symbol('\\\\alpha', commutative=True)))))", "Mul(Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), log(Pow(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)))))"]}, {"premise_expression": "\\frac{\\beta}{\\gamma \\psi}", "variable": "\\beta", "positive": "\\frac{\\beta^{2}}{2 \\gamma \\psi}", "negatives": ["\\frac{\\beta \\log{(\\gamma)}}{\\psi}", "\\frac{\\beta^{2}}{2} + \\frac{\\beta \\psi}{\\gamma}", "\\frac{\\beta \\log{(\\psi)}}{\\gamma}", "\\frac{\\beta \\psi (\\beta + 2 \\gamma)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), log(Symbol('\\\\gamma', commutative=True)))", "Add(Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2))), Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True)))", "Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), log(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\gamma', commutative=True))))"]}, {"premise_expression": "\\pi \\psi", "variable": "\\pi", "positive": "\\frac{\\pi^{2} \\psi}{2}", "negatives": ["\\frac{\\pi \\psi^{2}}{2}", "\\frac{\\pi^{2}}{2 \\psi}", "\\frac{\\pi (\\pi - 2 \\psi)}{2}", "\\pi \\psi + e^{\\pi}"], "srepr_premise_expression": "Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))", "Add(Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)), exp(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\frac{\\chi}{\\alpha}", "variable": "\\alpha", "positive": "\\chi \\log{(\\alpha)}", "negatives": ["\\frac{\\chi^{2}}{2 \\alpha}", "\\frac{\\alpha^{2} \\cos{(\\chi)}}{2}", "e^{\\alpha - \\chi}", "\\alpha (\\log{(\\alpha \\chi)} - 1)"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\chi', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\chi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), cos(Symbol('\\\\chi', commutative=True)))", "exp(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True))))", "Mul(Symbol('\\\\alpha', commutative=True), Add(log(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\frac{\\alpha}{\\gamma}", "variable": "\\alpha", "positive": "\\frac{\\alpha^{2}}{2 \\gamma}", "negatives": ["\\alpha \\log{(\\gamma)}", "\\gamma \\sin{(\\alpha)}", "\\frac{\\alpha (- \\alpha + 2 \\gamma)}{2}", "\\sin{(\\alpha + \\gamma)}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "Mul(Symbol('\\\\gamma', commutative=True), sin(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\gamma', commutative=True))))", "sin(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\frac{\\cos{(\\delta)}}{\\sigma}", "variable": "\\sigma", "positive": "\\log{(\\sigma)} \\cos{(\\delta)}", "negatives": ["e^{\\delta} \\log{(\\sigma)}", "\\frac{\\sigma^{2} \\cos{(\\delta)}}{2}", "\\frac{\\sin{(\\sigma)}}{\\delta}", "\\sigma (\\delta + \\sigma)"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), cos(Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(log(Symbol('\\\\sigma', commutative=True)), cos(Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Mul(exp(Symbol('\\\\delta', commutative=True)), log(Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), cos(Symbol('\\\\delta', commutative=True)))", "Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), sin(Symbol('\\\\sigma', commutative=True)))", "Mul(Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\chi + \\pi", "variable": "\\chi", "positive": "\\frac{\\chi (\\chi + 2 \\pi)}{2}", "negatives": ["\\frac{\\pi (2 \\chi + \\pi)}{2}", "\\frac{\\chi (\\chi + 2 e^{\\pi})}{2}", "\\frac{\\chi (- \\chi + 2 \\sin{(\\pi)})}{2}", "\\sin{(\\chi - \\pi)}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), exp(Symbol('\\\\pi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\pi', commutative=True)))))", "sin(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\cos{(\\pi + \\xi)}", "variable": "\\xi", "positive": "\\sin{(\\pi + \\xi)}", "negatives": ["e^{- \\pi + \\xi}", "\\pi \\sin{(\\xi)}", "\\frac{\\xi (2 \\pi + \\xi)}{2}", "\\frac{\\xi (2 \\pi - \\xi)}{2}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "sin(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["exp(Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\pi', commutative=True), sin(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "- \\psi + \\frac{\\sigma}{\\alpha}", "variable": "\\alpha", "positive": "- \\alpha \\psi + \\sigma \\log{(\\alpha)}", "negatives": ["\\alpha + \\sigma \\log{(\\alpha)}", "- \\psi \\sigma + \\frac{\\sigma^{2}}{2 \\alpha}", "- \\frac{\\psi^{2}}{2} + \\frac{\\psi \\sigma}{\\alpha}", "\\frac{\\alpha^{2} \\psi \\sigma}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\alpha', commutative=True))))", "srepr_negatives": ["Add(Symbol('\\\\alpha', commutative=True), Mul(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\alpha', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Integer(2))))", "Add(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2))), Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True))"]}, {"premise_expression": "\\frac{\\log{(\\beta)}}{\\xi}", "variable": "\\xi", "positive": "\\log{(\\beta)} \\log{(\\xi)}", "negatives": ["\\log{(\\xi)} \\cos{(\\beta)}", "\\xi \\log{(\\beta^{\\beta})}", "- \\frac{\\cos{(\\xi)}}{\\beta}", "\\frac{\\xi^{2} e^{\\beta}}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), log(Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(log(Symbol('\\\\beta', commutative=True)), log(Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(log(Symbol('\\\\xi', commutative=True)), cos(Symbol('\\\\beta', commutative=True)))", "Mul(Symbol('\\\\xi', commutative=True), log(Pow(Symbol('\\\\beta', commutative=True), Symbol('\\\\beta', commutative=True))))", "Mul(Integer(-1), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), cos(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), exp(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "\\gamma \\xi", "variable": "\\gamma", "positive": "\\frac{\\gamma^{2} \\xi}{2}", "negatives": ["\\frac{\\gamma \\xi^{2}}{2}", "2 \\gamma \\xi", "\\frac{\\gamma^{2} \\cos{(\\xi)}}{2}", "\\frac{\\gamma (\\gamma - 2 \\xi)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Mul(Integer(2), Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), cos(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\chi - \\pi", "variable": "\\chi", "positive": "\\frac{\\chi (\\chi - 2 \\pi)}{2}", "negatives": ["\\frac{\\chi (- \\chi + 2 \\pi)}{2}", "\\frac{\\pi (2 \\chi - \\pi)}{2}", "\\sin{(\\chi - \\pi)}", "\\chi \\pi - \\cos{(\\chi)}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "sin(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\chi', commutative=True))))"]}, {"premise_expression": "- \\sigma + e^{\\beta}", "variable": "\\sigma", "positive": "\\frac{\\sigma (- \\sigma + 2 e^{\\beta})}{2}", "negatives": ["- \\beta \\sigma + e^{\\beta}", "- \\beta \\sigma + e^{\\sigma}", "\\frac{\\sigma^{2} \\sin{(\\beta)}}{2}", "- \\beta \\operatorname{Ei}{(\\frac{\\beta}{\\sigma})} + \\sigma e^{\\frac{\\beta}{\\sigma}}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), exp(Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\beta', commutative=True)))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True)), exp(Symbol('\\\\beta', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True)), exp(Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), sin(Symbol('\\\\beta', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Ei(Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1))))), Mul(Symbol('\\\\sigma', commutative=True), exp(Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1))))))"]}, {"premise_expression": "\\frac{\\gamma}{\\chi}", "variable": "\\gamma", "positive": "\\frac{\\gamma^{2}}{2 \\chi}", "negatives": ["\\gamma \\log{(\\chi)}", "\\frac{\\gamma (2 \\chi - \\gamma)}{2}", "\\frac{\\gamma (2 \\chi + \\gamma)}{2}", "- \\cos{(\\chi + \\gamma)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True))))"]}, {"premise_expression": "\\gamma e^{\\chi}", "variable": "\\gamma", "positive": "\\frac{\\gamma^{2} e^{\\chi}}{2}", "negatives": ["\\gamma e^{\\chi}", "\\frac{\\gamma (- 2 \\chi + \\gamma)}{2}", "\\frac{\\chi \\gamma^{2}}{2}", "- e^{\\chi - \\gamma}"], "srepr_premise_expression": "Mul(Symbol('\\\\gamma', commutative=True), exp(Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), exp(Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\gamma', commutative=True), exp(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)))", "Mul(Integer(-1), exp(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))))"]}, {"premise_expression": "\\alpha \\log{(\\delta)}", "variable": "\\alpha", "positive": "\\frac{\\alpha^{2} \\log{(\\delta)}}{2}", "negatives": ["\\alpha \\delta (\\log{(\\delta)} - 1)", "\\frac{\\alpha (- \\alpha + 2 \\delta)}{2}", "\\frac{\\alpha (\\alpha + 2 \\sin{(\\delta)})}{2}", "- \\frac{\\cos{(\\alpha)}}{\\delta}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), log(Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\delta', commutative=True), Add(log(Symbol('\\\\delta', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), sin(Symbol('\\\\delta', commutative=True)))))", "Mul(Integer(-1), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), cos(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "- \\omega + \\frac{\\sigma}{\\xi}", "variable": "\\omega", "positive": "- \\frac{\\omega^{2}}{2} + \\frac{\\omega \\sigma}{\\xi}", "negatives": ["\\frac{\\omega \\xi (\\omega + 2 \\sigma)}{2}", "\\frac{\\omega \\sigma (\\omega - 2 \\xi)}{2}", "\\frac{\\omega^{2} \\xi}{2 \\sigma}", "\\frac{\\omega (\\omega + 2 \\xi^{\\sigma})}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Symbol('\\\\sigma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2))), Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), Pow(Symbol('\\\\xi', commutative=True), Symbol('\\\\sigma', commutative=True)))))"]}, {"premise_expression": "\\frac{\\pi}{\\delta}", "variable": "\\delta", "positive": "\\pi \\log{(\\delta)}", "negatives": ["\\frac{\\pi^{2}}{2 \\delta}", "- \\frac{\\cos{(\\delta)}}{\\pi}", "- \\cos{(\\delta + \\pi)}", "- \\delta \\pi + \\sin{(\\delta)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "Mul(Integer(-1), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), cos(Symbol('\\\\delta', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True)), sin(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\beta \\omega", "variable": "\\beta", "positive": "\\frac{\\beta^{2} \\omega}{2}", "negatives": ["\\frac{\\beta \\omega^{2}}{2}", "\\frac{\\beta (- \\beta + 2 \\omega)}{2}", "- \\omega \\cos{(\\beta)}", "- \\beta \\omega + e^{\\beta}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\omega', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Integer(-1), Symbol('\\\\omega', commutative=True), cos(Symbol('\\\\beta', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True)), exp(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "- \\chi + \\cos{(\\beta)}", "variable": "\\beta", "positive": "- \\beta \\chi + \\sin{(\\beta)}", "negatives": ["\\beta \\chi + \\sin{(\\beta)}", "\\cos{(\\beta - \\chi)}", "\\chi e^{\\frac{\\beta}{\\chi}}", "\\frac{\\chi (- \\chi + 2 \\cos{(\\beta)})}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), cos(Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True)), sin(Symbol('\\\\beta', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True)), sin(Symbol('\\\\beta', commutative=True)))", "cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True))))", "Mul(Symbol('\\\\chi', commutative=True), exp(Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\beta', commutative=True)))))"]}, {"premise_expression": "\\chi + e^{\\omega}", "variable": "\\chi", "positive": "\\frac{\\chi (\\chi + 2 e^{\\omega})}{2}", "negatives": ["\\frac{\\chi (\\chi + 2 \\cos{(\\omega)})}{2}", "\\chi \\omega + e^{\\omega}", "\\sin{(\\chi + \\omega)}", "\\chi (- \\omega + \\log{(\\chi)} - 1)"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), exp(Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), exp(Symbol('\\\\omega', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), cos(Symbol('\\\\omega', commutative=True)))))", "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True)), exp(Symbol('\\\\omega', commutative=True)))", "sin(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), log(Symbol('\\\\chi', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\sigma (\\omega + \\xi)", "variable": "\\omega", "positive": "\\frac{\\omega \\sigma (\\omega + 2 \\xi)}{2}", "negatives": ["\\frac{\\sigma^{2} (\\omega + \\xi)}{2}", "\\frac{\\sigma \\xi (2 \\omega + \\xi)}{2}", "\\frac{\\omega (- \\omega + 2 \\sigma^{\\xi})}{2}", "\\frac{\\omega (- \\omega + 2 \\xi^{\\sigma})}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Pow(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Pow(Symbol('\\\\xi', commutative=True), Symbol('\\\\sigma', commutative=True)))))"]}, {"premise_expression": "\\chi + \\pi + \\sigma", "variable": "\\pi", "positive": "\\pi (\\chi + \\frac{\\pi}{2} + \\sigma)", "negatives": ["\\frac{\\sigma (2 \\chi + 2 \\pi + \\sigma)}{2}", "\\frac{\\chi (\\chi + 2 \\pi + 2 \\sigma)}{2}", "\\frac{\\chi \\pi}{\\sigma} - \\frac{\\pi^{2}}{2}", "\\pi (1 - \\chi)"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1))), Mul(Integer(-1), Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2))))", "Mul(Symbol('\\\\pi', commutative=True), Add(Integer(1), Mul(Integer(-1), Symbol('\\\\chi', commutative=True))))"]}, {"premise_expression": "- \\beta + \\psi", "variable": "\\psi", "positive": "\\frac{\\psi (- 2 \\beta + \\psi)}{2}", "negatives": ["\\frac{\\beta (- \\beta + 2 \\psi)}{2}", "e^{\\beta + \\psi}", "\\sin{(\\beta + \\psi)}", "\\beta e^{\\psi}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "exp(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\psi', commutative=True)))", "sin(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\psi', commutative=True)))", "Mul(Symbol('\\\\beta', commutative=True), exp(Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\sin{(\\chi + \\xi)}", "variable": "\\chi", "positive": "- \\cos{(\\chi + \\xi)}", "negatives": ["- \\chi \\xi + \\sin{(\\chi)}", "\\chi (\\log{(\\chi \\xi)} - 1)", "\\chi \\xi + e^{\\chi}", "\\chi \\xi + \\sin{(\\chi)}"], "srepr_premise_expression": "sin(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True)), sin(Symbol('\\\\chi', commutative=True)))", "Mul(Symbol('\\\\chi', commutative=True), Add(log(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True))), Integer(-1)))", "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True)), exp(Symbol('\\\\chi', commutative=True)))", "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True)), sin(Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "e^{\\frac{\\gamma}{\\psi}}", "variable": "\\psi", "positive": "- \\gamma \\operatorname{Ei}{(\\frac{\\gamma}{\\psi})} + \\psi e^{\\frac{\\gamma}{\\psi}}", "negatives": ["\\frac{\\psi (\\psi + 2 e^{\\gamma})}{2}", "\\psi e^{\\frac{\\gamma}{\\psi}}", "\\frac{\\psi (\\psi + 2 \\log{(\\gamma)})}{2}", "\\frac{\\psi (\\psi + 2 \\sin{(\\gamma)})}{2}"], "srepr_premise_expression": "exp(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Ei(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1))))), Mul(Symbol('\\\\psi', commutative=True), exp(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1))))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(2), exp(Symbol('\\\\gamma', commutative=True)))))", "Mul(Symbol('\\\\psi', commutative=True), exp(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(2), log(Symbol('\\\\gamma', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(2), sin(Symbol('\\\\gamma', commutative=True)))))"]}, {"premise_expression": "\\cos{(\\alpha + \\psi)}", "variable": "\\psi", "positive": "\\sin{(\\alpha + \\psi)}", "negatives": ["- \\cos{(\\alpha + \\psi)}", "\\frac{\\psi (- 2 \\alpha + \\psi)}{2}", "\\psi (\\log{(\\frac{\\alpha}{\\psi})} + 1)", "\\frac{\\psi (- \\psi + 2 \\log{(\\alpha)})}{2}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "sin(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Symbol('\\\\psi', commutative=True), Add(log(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), log(Symbol('\\\\alpha', commutative=True)))))"]}, {"premise_expression": "\\beta + \\xi", "variable": "\\beta", "positive": "\\frac{\\beta (\\beta + 2 \\xi)}{2}", "negatives": ["\\frac{\\beta (\\beta - 2 \\xi)}{2}", "\\frac{\\xi (2 \\beta + \\xi)}{2}", "e^{\\beta - \\xi}", "\\sin{(\\beta + \\xi)}"], "srepr_premise_expression": "Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\xi', commutative=True)))", "exp(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "sin(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\sin{(\\omega - \\pi)}", "variable": "\\omega", "positive": "- \\cos{(\\omega - \\pi)}", "negatives": ["\\cos{(\\omega - \\pi)}", "\\frac{\\omega (\\omega - 2 \\pi)}{2}", "\\frac{\\omega (\\omega + 2 \\pi)}{2}", "\\log{(\\omega)} \\cos{(\\pi)}"], "srepr_premise_expression": "sin(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))", "srepr_negatives": ["cos(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(log(Symbol('\\\\omega', commutative=True)), cos(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\frac{\\delta^{\\xi}}{\\omega}", "variable": "\\omega", "positive": "\\delta^{\\xi} \\log{(\\omega)}", "negatives": ["\\frac{\\delta \\omega^{2}}{2 \\xi}", "\\omega \\xi", "\\frac{\\omega^{2} (\\delta + \\xi)}{2}", "\\frac{\\delta \\omega}{\\xi} + \\frac{\\omega^{2}}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True)), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True)), log(Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True)))", "Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))), Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2))))"]}, {"premise_expression": "\\sin{(\\frac{\\psi}{\\omega})}", "variable": "\\omega", "positive": "\\omega \\sin{(\\frac{\\psi}{\\omega})} - \\frac{\\psi \\log{(\\frac{\\psi^{2}}{\\omega^{2}})}}{2} + \\psi \\log{(\\frac{\\psi}{\\omega})} - \\psi \\operatorname{Ci}{(\\frac{\\psi}{\\omega})}", "negatives": ["\\omega \\log{(\\omega + \\psi)} - \\omega + \\psi \\log{(\\omega + \\psi)}", "\\omega \\log{(- \\omega + \\psi)} - \\omega - \\psi \\log{(\\omega - \\psi)}", "\\omega \\log{(\\omega - \\psi)} - \\omega - \\psi \\log{(\\omega - \\psi)}", "\\log{(\\omega)} \\sin{(\\psi)}"], "srepr_premise_expression": "sin(Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\omega', commutative=True), sin(Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True)))), Mul(Integer(-1), Rational(1, 2), Symbol('\\\\psi', commutative=True), log(Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-2)), Pow(Symbol('\\\\psi', commutative=True), Integer(2))))), Mul(Symbol('\\\\psi', commutative=True), log(Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\psi', commutative=True), Ci(Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\omega', commutative=True), log(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Symbol('\\\\psi', commutative=True), log(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True)))))", "Add(Mul(Symbol('\\\\omega', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Symbol('\\\\psi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\psi', commutative=True), log(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))))", "Add(Mul(Symbol('\\\\omega', commutative=True), log(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\psi', commutative=True), log(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))))", "Mul(log(Symbol('\\\\omega', commutative=True)), sin(Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\alpha + \\cos{(\\omega)}", "variable": "\\alpha", "positive": "\\frac{\\alpha (\\alpha + 2 \\cos{(\\omega)})}{2}", "negatives": ["\\frac{\\alpha (\\alpha + 2 \\log{(\\omega)})}{2}", "\\frac{\\alpha (- \\alpha + 2 e^{\\omega})}{2}", "\\alpha \\omega + \\sin{(\\omega)}", "\\alpha (- \\omega + \\log{(\\alpha^{\\omega})})"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), cos(Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), cos(Symbol('\\\\omega', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), log(Symbol('\\\\omega', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\omega', commutative=True)))))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)), sin(Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), log(Pow(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)))))"]}, {"premise_expression": "\\sin{(\\pi - \\sigma)}", "variable": "\\pi", "positive": "- \\cos{(\\pi - \\sigma)}", "negatives": ["\\cos{(\\pi - \\sigma)}", "e^{\\pi + \\sigma}", "- e^{- \\pi + \\sigma}", "\\pi \\sin{(\\sigma^{2})}"], "srepr_premise_expression": "sin(Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))", "srepr_negatives": ["cos(Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "exp(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True)))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Symbol('\\\\sigma', commutative=True))))", "Mul(Symbol('\\\\pi', commutative=True), sin(Pow(Symbol('\\\\sigma', commutative=True), Integer(2))))"]}, {"premise_expression": "\\frac{\\pi \\psi}{\\gamma}", "variable": "\\psi", "positive": "\\frac{\\pi \\psi^{2}}{2 \\gamma}", "negatives": ["\\frac{\\pi^{2} \\psi}{2 \\gamma}", "\\pi \\psi \\log{(\\gamma)}", "\\frac{\\psi (2 \\gamma + \\pi \\psi)}{2}", "\\frac{\\psi (- 2 \\gamma + \\pi \\psi)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))", "Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "- \\omega + \\pi^{\\sigma}", "variable": "\\omega", "positive": "\\frac{\\omega (- \\omega + 2 \\pi^{\\sigma})}{2}", "negatives": ["\\frac{\\omega (- \\omega + 2 \\pi \\sigma)}{2}", "\\frac{\\omega (- \\omega - 2 \\pi + 2 \\sigma)}{2}", "\\frac{\\omega \\pi (\\omega - 2 \\sigma)}{2}", "\\frac{\\omega (\\omega + 2 \\sigma)}{2 \\pi}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Pow(Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Pow(Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\frac{\\alpha + \\xi}{\\chi}", "variable": "\\alpha", "positive": "\\frac{\\alpha (\\alpha + 2 \\xi)}{2 \\chi}", "negatives": ["\\frac{\\xi (2 \\alpha + \\xi)}{2 \\chi}", "\\frac{\\alpha (\\alpha \\xi + 2 \\chi)}{2}", "\\frac{\\alpha (- \\alpha + 2 \\chi \\xi)}{2}", "(\\alpha + \\xi) \\log{(\\chi)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), Symbol('\\\\chi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True))))", "Mul(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True)), log(Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "\\delta + \\pi", "variable": "\\delta", "positive": "\\frac{\\delta (\\delta + 2 \\pi)}{2}", "negatives": ["\\frac{\\delta (\\delta - 2 \\pi)}{2}", "\\frac{\\pi (2 \\delta + \\pi)}{2}", "\\frac{\\delta^{2} \\log{(\\pi)}}{2}", "\\sin{(\\delta - \\pi)}"], "srepr_premise_expression": "Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), log(Symbol('\\\\pi', commutative=True)))", "sin(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\alpha \\psi", "variable": "\\alpha", "positive": "\\frac{\\alpha^{2} \\psi}{2}", "negatives": ["\\frac{\\alpha \\psi^{2}}{2}", "\\frac{\\alpha^{2}}{2 \\psi}", "\\alpha \\log{(2 \\psi)}", "\\psi \\sin{(\\alpha)}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))", "Mul(Symbol('\\\\alpha', commutative=True), log(Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Symbol('\\\\psi', commutative=True), sin(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\frac{\\log{(\\delta)}}{\\beta}", "variable": "\\beta", "positive": "\\log{(\\beta)} \\log{(\\delta)}", "negatives": ["\\frac{\\beta^{2} \\log{(\\delta)}}{2}", "\\frac{\\delta (\\log{(\\delta)} - 1)}{\\beta}", "\\frac{\\sin{(\\beta)}}{\\delta}", "\\frac{\\beta (\\beta - 2 \\delta)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), log(Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(log(Symbol('\\\\beta', commutative=True)), log(Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), log(Symbol('\\\\delta', commutative=True)))", "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True), Add(log(Symbol('\\\\delta', commutative=True)), Integer(-1)))", "Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), sin(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True))))"]}, {"premise_expression": "\\frac{\\cos{(\\gamma)}}{\\psi}", "variable": "\\gamma", "positive": "\\frac{\\sin{(\\gamma)}}{\\psi}", "negatives": ["\\psi e^{\\frac{\\gamma}{\\psi}}", "\\log{(\\gamma)} \\cos{(\\psi)}", "\\frac{\\gamma (\\gamma + 2 \\psi)}{2}", "\\log{(\\psi)} \\cos{(\\gamma)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), cos(Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), sin(Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\psi', commutative=True), exp(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))))", "Mul(log(Symbol('\\\\gamma', commutative=True)), cos(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(log(Symbol('\\\\psi', commutative=True)), cos(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\sigma - \\xi", "variable": "\\xi", "positive": "\\frac{\\xi (2 \\sigma - \\xi)}{2}", "negatives": ["\\frac{\\xi (2 \\sigma + \\xi)}{2}", "\\frac{\\sigma (\\sigma - 2 \\xi)}{2}", "\\frac{\\sigma \\xi^{2}}{2}", "\\frac{\\xi^{2} \\log{(\\sigma)}}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\sigma', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), log(Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\chi - \\pi", "variable": "\\pi", "positive": "\\frac{\\pi (2 \\chi - \\pi)}{2}", "negatives": ["\\frac{\\chi (\\chi - 2 \\pi)}{2}", "\\frac{\\pi^{2} \\sin{(\\chi)}}{2}", "- \\cos{(\\chi - \\pi)}", "e^{\\chi + \\pi}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), sin(Symbol('\\\\chi', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))", "exp(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\sigma + \\sin{(\\pi)}", "variable": "\\sigma", "positive": "\\frac{\\sigma (\\sigma + 2 \\sin{(\\pi)})}{2}", "negatives": ["\\pi \\sigma - \\cos{(\\pi)}", "\\frac{\\sigma (2 \\pi + \\sigma)}{2}", "\\frac{\\sigma (2 \\pi - \\sigma)}{2}", "\\pi \\sigma - \\cos{(\\sigma)}"], "srepr_premise_expression": "Add(Symbol('\\\\sigma', commutative=True), sin(Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(2), sin(Symbol('\\\\pi', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Add(Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\frac{\\beta}{\\psi}", "variable": "\\psi", "positive": "\\beta \\log{(\\psi)}", "negatives": ["\\beta e^{\\psi}", "\\frac{\\beta^{2}}{2 \\psi}", "- \\frac{\\cos{(\\psi)}}{\\beta}", "\\frac{\\psi \\cos{(\\beta)}}{\\beta}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\beta', commutative=True), log(Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\beta', commutative=True), exp(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))", "Mul(Integer(-1), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), cos(Symbol('\\\\psi', commutative=True)))", "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True), cos(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "\\frac{\\xi}{\\psi}", "variable": "\\xi", "positive": "\\frac{\\xi^{2}}{2 \\psi}", "negatives": ["\\xi \\log{(\\psi)}", "\\frac{\\xi^{2} \\cos{(\\psi)}}{2}", "\\frac{\\xi^{2} \\log{(\\psi)}}{2}", "- \\sin{(\\psi - \\xi)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), cos(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), log(Symbol('\\\\psi', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))))"]}, {"premise_expression": "\\log{(\\gamma^{\\omega})}", "variable": "\\omega", "positive": "\\frac{\\omega^{2} \\log{(\\gamma)}}{2}", "negatives": ["\\gamma \\sin{(\\omega)}", "\\omega (\\log{(\\frac{\\omega}{\\gamma})} - 1)", "- \\cos{(\\gamma + \\omega)}", "\\gamma (- \\omega + \\log{(\\gamma^{\\omega})})"], "srepr_premise_expression": "log(Pow(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), log(Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\gamma', commutative=True), sin(Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), Add(log(Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True))), Integer(-1)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True))))", "Mul(Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), log(Pow(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True)))))"]}, {"premise_expression": "\\alpha \\beta", "variable": "\\beta", "positive": "\\frac{\\alpha \\beta^{2}}{2}", "negatives": ["\\frac{\\alpha^{2} \\beta}{2}", "\\beta^{2}", "\\frac{\\beta (- 2 \\alpha + \\beta)}{2}", "\\alpha \\beta + e^{\\beta}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\beta', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\beta', commutative=True))", "Pow(Symbol('\\\\beta', commutative=True), Integer(2))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\beta', commutative=True)))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True)), exp(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "- \\delta + \\log{(\\omega)}", "variable": "\\omega", "positive": "\\omega (- \\delta + \\log{(\\omega)} - 1)", "negatives": ["\\frac{\\delta (- \\delta + 2 \\log{(\\omega)})}{2}", "\\omega (\\log{(\\frac{\\delta}{\\omega})} + 1)", "\\frac{\\omega (2 \\delta + \\omega)}{2}", "- \\sin{(\\delta - \\omega)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), log(Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), log(Symbol('\\\\omega', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), log(Symbol('\\\\omega', commutative=True)))))", "Mul(Symbol('\\\\omega', commutative=True), Add(log(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))))"]}, {"premise_expression": "\\pi + \\log{(\\xi)}", "variable": "\\pi", "positive": "\\frac{\\pi (\\pi + 2 \\log{(\\xi)})}{2}", "negatives": ["\\frac{\\pi (\\pi + 2 \\cos{(\\xi)})}{2}", "\\frac{\\pi (\\pi + 2 \\xi)}{2}", "\\xi (\\pi + \\log{(\\xi)} - 1)", "\\pi \\xi + e^{\\pi}"], "srepr_premise_expression": "Add(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), log(Symbol('\\\\xi', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), cos(Symbol('\\\\xi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\xi', commutative=True)), Integer(-1)))", "Add(Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True)), exp(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "- \\chi + e^{\\psi}", "variable": "\\chi", "positive": "\\frac{\\chi (- \\chi + 2 e^{\\psi})}{2}", "negatives": ["- \\chi \\psi + e^{\\psi}", "\\frac{\\chi^{2} \\cos{(\\psi)}}{2}", "e^{\\chi + \\psi}", "- \\cos{(\\chi - \\psi)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), exp(Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\psi', commutative=True)))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True)), exp(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), cos(Symbol('\\\\psi', commutative=True)))", "exp(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))"]}, {"premise_expression": "\\xi \\log{(\\alpha)}", "variable": "\\xi", "positive": "\\frac{\\xi^{2} \\log{(\\alpha)}}{2}", "negatives": ["\\frac{\\xi^{2} e^{\\alpha}}{2}", "\\alpha \\xi (\\log{(\\alpha)} - 1)", "\\frac{\\xi (\\xi + 2 \\cos{(\\alpha)})}{2}", "\\alpha \\sin{(\\xi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), log(Symbol('\\\\alpha', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), exp(Symbol('\\\\alpha', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True), Add(log(Symbol('\\\\alpha', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\xi', commutative=True), Mul(Integer(2), cos(Symbol('\\\\alpha', commutative=True)))))", "Mul(Symbol('\\\\alpha', commutative=True), sin(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\frac{\\cos{(\\delta)}}{\\sigma}", "variable": "\\sigma", "positive": "\\log{(\\sigma)} \\cos{(\\delta)}", "negatives": ["\\frac{\\sigma (\\sigma + 2 \\cos{(\\delta)})}{2}", "\\frac{\\sin{(\\delta)}}{\\sigma}", "e^{\\delta + \\sigma}", "e^{- \\delta + \\sigma}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), cos(Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(log(Symbol('\\\\sigma', commutative=True)), cos(Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(2), cos(Symbol('\\\\delta', commutative=True)))))", "Mul(Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), sin(Symbol('\\\\delta', commutative=True)))", "exp(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True)))", "exp(Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\frac{\\psi}{\\chi}", "variable": "\\chi", "positive": "\\psi \\log{(\\chi)}", "negatives": ["\\psi e^{\\chi}", "\\frac{\\psi^{2}}{2 \\chi}", "\\frac{\\chi^{2} \\psi}{2}", "\\frac{\\chi^{2} \\cos{(\\psi)}}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\psi', commutative=True), log(Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\psi', commutative=True), exp(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), cos(Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\log{(\\psi)}^{\\alpha}", "variable": "\\psi", "positive": "(- \\log{(\\psi)})^{- \\alpha} \\log{(\\psi)}^{\\alpha} \\Gamma(\\alpha + 1, - \\log{(\\psi)})", "negatives": ["\\frac{\\psi (- \\psi + 2 \\log{(\\alpha)})}{2}", "- \\alpha \\psi + \\sin{(\\psi)}", "- \\cos{(\\alpha + \\psi)}", "e^{\\alpha + \\psi}"], "srepr_premise_expression": "Pow(log(Symbol('\\\\psi', commutative=True)), Symbol('\\\\alpha', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Pow(Mul(Integer(-1), log(Symbol('\\\\psi', commutative=True))), Mul(Integer(-1), Symbol('\\\\alpha', commutative=True))), Pow(log(Symbol('\\\\psi', commutative=True)), Symbol('\\\\alpha', commutative=True)), uppergamma(Add(Symbol('\\\\alpha', commutative=True), Integer(1)), Mul(Integer(-1), log(Symbol('\\\\psi', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), log(Symbol('\\\\alpha', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True)), sin(Symbol('\\\\psi', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True))))", "exp(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "e^{\\beta + \\xi}", "variable": "\\beta", "positive": "e^{\\beta + \\xi}", "negatives": ["\\xi e^{\\frac{\\beta}{\\xi}}", "\\xi e^{\\beta}", "\\frac{\\beta (\\beta + 2 \\xi)}{2}", "\\beta \\xi - \\cos{(\\beta)}"], "srepr_premise_expression": "exp(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "exp(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\xi', commutative=True), exp(Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))))", "Mul(Symbol('\\\\xi', commutative=True), exp(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\beta', commutative=True))))"]}, {"premise_expression": "\\frac{\\omega}{\\xi}", "variable": "\\xi", "positive": "\\omega \\log{(\\xi)}", "negatives": ["\\frac{\\omega^{2}}{2 \\xi}", "\\omega e^{\\frac{\\xi}{\\omega}}", "- \\frac{\\cos{(\\xi)}}{\\omega}", "\\frac{\\xi^{2} \\log{(\\omega)}}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "Mul(Symbol('\\\\omega', commutative=True), exp(Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))))", "Mul(Integer(-1), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), cos(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), log(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\frac{\\sin{(\\sigma)}}{\\psi}", "variable": "\\psi", "positive": "\\log{(\\psi)} \\sin{(\\sigma)}", "negatives": ["e^{\\sigma} \\log{(\\psi)}", "\\sin{(\\psi - \\sigma)}", "\\frac{\\psi (\\log{(\\psi)} - 1)}{\\sigma}", "- \\frac{\\cos{(\\sigma)}}{\\psi}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), sin(Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(log(Symbol('\\\\psi', commutative=True)), sin(Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(exp(Symbol('\\\\sigma', commutative=True)), log(Symbol('\\\\psi', commutative=True)))", "sin(Add(Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Symbol('\\\\psi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Add(log(Symbol('\\\\psi', commutative=True)), Integer(-1)))", "Mul(Integer(-1), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), cos(Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\xi e^{\\chi}", "variable": "\\xi", "positive": "\\frac{\\xi^{2} e^{\\chi}}{2}", "negatives": ["\\frac{\\xi^{2} \\log{(\\chi)}}{2}", "\\frac{\\xi^{2} \\sin{(\\chi)}}{2}", "\\xi e^{\\chi}", "\\frac{\\chi \\xi^{2}}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\xi', commutative=True), exp(Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), exp(Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), log(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), sin(Symbol('\\\\chi', commutative=True)))", "Mul(Symbol('\\\\xi', commutative=True), exp(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))"]}, {"premise_expression": "\\chi \\gamma", "variable": "\\chi", "positive": "\\frac{\\chi^{2} \\gamma}{2}", "negatives": ["\\frac{\\chi \\gamma^{2}}{2}", "\\frac{\\chi (\\chi + 2 \\gamma)}{2}", "\\sin{(\\chi + \\gamma)}", "\\cos{(\\chi - \\gamma)}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\gamma', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\gamma', commutative=True))))", "sin(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True)))", "cos(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))"]}, {"premise_expression": "\\frac{\\chi - \\pi}{\\delta}", "variable": "\\chi", "positive": "\\frac{\\chi (\\chi - 2 \\pi)}{2 \\delta}", "negatives": ["\\frac{\\pi (2 \\chi - \\pi)}{2 \\delta}", "\\frac{\\chi (\\chi + 2 \\delta \\pi)}{2}", "(\\chi - \\pi) \\log{(\\delta)}", "\\frac{\\chi (\\chi - 2 \\delta - 2 \\pi)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True))))", "Mul(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))), log(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\frac{- \\chi + \\xi}{\\beta}", "variable": "\\chi", "positive": "\\frac{\\chi (- \\chi + 2 \\xi)}{2 \\beta}", "negatives": ["\\frac{\\xi (- 2 \\chi + \\xi)}{2 \\beta}", "\\frac{\\beta \\chi (\\chi - 2 \\xi)}{2}", "(- \\chi + \\xi) \\log{(\\beta)}", "- \\chi \\xi + \\frac{\\chi^{2}}{2 \\beta}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\xi', commutative=True)), log(Symbol('\\\\beta', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Pow(Symbol('\\\\chi', commutative=True), Integer(2))))"]}, {"premise_expression": "(\\chi - \\gamma)^{\\chi}", "variable": "\\chi", "positive": "\\operatorname{NonElementaryIntegral}{((\\chi - \\gamma)^{\\chi},( \\chi))}", "negatives": ["\\sin{(\\chi - \\gamma)}", "- \\cos{(\\chi + \\gamma)}", "\\chi (\\log{(\\frac{\\chi}{\\gamma})} - 1)", "\\chi \\gamma - \\cos{(\\chi)}"], "srepr_premise_expression": "Pow(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))), Symbol('\\\\chi', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Function('NonElementaryIntegral')(Pow(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))), Symbol('\\\\chi', commutative=True)), Tuple(Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["sin(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True))))", "Mul(Symbol('\\\\chi', commutative=True), Add(log(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)))), Integer(-1)))", "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\chi', commutative=True))))"]}, {"premise_expression": "- \\delta + \\frac{\\sigma}{\\xi}", "variable": "\\xi", "positive": "- \\delta \\xi + \\sigma \\log{(\\xi)}", "negatives": ["- \\delta \\sigma + \\frac{\\sigma^{2}}{2 \\xi}", "\\sigma^{\\sigma} \\log{(\\xi)}", "\\frac{\\sigma \\log{(\\xi)}}{\\delta}", "- \\frac{\\delta^{2}}{2} + \\frac{\\delta \\sigma}{\\xi}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Symbol('\\\\sigma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))", "Mul(Pow(Symbol('\\\\sigma', commutative=True), Symbol('\\\\sigma', commutative=True)), log(Symbol('\\\\xi', commutative=True)))", "Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\xi', commutative=True)))", "Add(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2))), Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))"]}, {"premise_expression": "\\frac{\\psi - \\xi}{\\alpha}", "variable": "\\psi", "positive": "\\frac{\\psi (\\psi - 2 \\xi)}{2 \\alpha}", "negatives": ["\\frac{\\psi (\\psi + 2 \\xi)}{2 \\alpha}", "\\frac{\\xi (2 \\psi - \\xi)}{2 \\alpha}", "\\frac{\\psi (2 \\alpha \\xi - \\psi)}{2}", "\\frac{\\psi (2 \\alpha + \\psi \\xi)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Symbol('\\\\psi', commutative=True), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "e^{\\alpha - \\psi}", "variable": "\\alpha", "positive": "e^{\\alpha - \\psi}", "negatives": ["- e^{\\alpha - \\psi}", "\\sin{(\\alpha - \\psi)}", "\\psi \\sin{(\\alpha)}", "\\alpha \\psi + e^{\\alpha}"], "srepr_premise_expression": "exp(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "exp(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))", "sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(Symbol('\\\\psi', commutative=True), sin(Symbol('\\\\alpha', commutative=True)))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True)), exp(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\frac{\\delta}{\\sigma}", "variable": "\\sigma", "positive": "\\delta \\log{(\\sigma)}", "negatives": ["\\frac{\\delta^{2}}{2 \\sigma}", "\\sin{(\\delta + \\sigma)}", "- \\cos{(\\delta + \\sigma)}", "- \\delta \\sigma + e^{\\sigma}"], "srepr_premise_expression": "Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "sin(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True)), exp(Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "- \\delta + \\xi", "variable": "\\xi", "positive": "\\frac{\\xi (- 2 \\delta + \\xi)}{2}", "negatives": ["\\frac{\\delta (- \\delta + 2 \\xi)}{2}", "\\frac{\\xi^{2} \\sin{(\\delta)}}{2}", "- \\cos{(\\delta + \\xi)}", "\\frac{\\xi (- \\xi + 2 \\cos{(\\delta)})}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), sin(Symbol('\\\\delta', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\delta', commutative=True)))))"]}, {"premise_expression": "\\frac{\\chi}{\\pi} - \\pi", "variable": "\\pi", "positive": "\\chi \\log{(\\pi)} - \\frac{\\pi^{2}}{2}", "negatives": ["\\frac{\\chi^{2}}{2 \\pi} - \\chi \\pi", "\\frac{\\chi \\pi^{2}}{2}", "\\frac{\\pi (- \\pi + 2 e^{\\chi})}{2}", "\\chi \\pi (\\log{(\\pi)} - 1)"], "srepr_premise_expression": "Add(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1))), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\pi', commutative=True))), Mul(Integer(-1), Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2))))", "srepr_negatives": ["Add(Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1))), Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\chi', commutative=True)))))", "Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True), Add(log(Symbol('\\\\pi', commutative=True)), Integer(-1)))"]}, {"premise_expression": "e^{\\beta + \\xi}", "variable": "\\beta", "positive": "e^{\\beta + \\xi}", "negatives": ["\\sin{(\\beta - \\xi)}", "\\beta \\xi - \\cos{(\\beta)}", "\\beta (\\log{(\\frac{\\beta}{\\xi})} - 1)", "\\beta (\\log{(\\beta \\xi)} - 1)"], "srepr_premise_expression": "exp(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "exp(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["sin(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\beta', commutative=True))))", "Mul(Symbol('\\\\beta', commutative=True), Add(log(Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))), Integer(-1)))", "Mul(Symbol('\\\\beta', commutative=True), Add(log(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True))), Integer(-1)))"]}, {"premise_expression": "(\\alpha - \\sigma)^{\\sigma}", "variable": "\\sigma", "positive": "\\operatorname{NonElementaryIntegral}{((\\alpha - \\sigma)^{\\sigma},( \\sigma))}", "negatives": ["- e^{\\alpha - \\sigma}", "e^{\\alpha + \\sigma}", "\\log{(\\sigma)} \\sin{(\\alpha)}", "\\frac{\\sigma (2 \\alpha + \\sigma)}{2}"], "srepr_premise_expression": "Pow(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Function('NonElementaryIntegral')(Pow(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))), Symbol('\\\\sigma', commutative=True)), Tuple(Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))", "exp(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True)))", "Mul(log(Symbol('\\\\sigma', commutative=True)), sin(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\gamma + e^{\\pi}", "variable": "\\pi", "positive": "\\gamma \\pi + e^{\\pi}", "negatives": ["\\gamma e^{\\pi}", "- \\gamma \\pi - \\cos{(\\pi)}", "\\pi (\\gamma + \\sin{(\\gamma)})", "\\frac{\\gamma (\\gamma + 2 e^{\\pi})}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\gamma', commutative=True), exp(Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True)), exp(Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\gamma', commutative=True), exp(Symbol('\\\\pi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\pi', commutative=True))))", "Mul(Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\gamma', commutative=True), sin(Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), exp(Symbol('\\\\pi', commutative=True)))))"]}, {"premise_expression": "\\log{(- \\chi + \\omega)}", "variable": "\\chi", "positive": "\\chi \\log{(- \\chi + \\omega)} - \\chi - \\omega \\log{(\\chi - \\omega)}", "negatives": ["\\chi \\log{(\\chi - \\omega)} - \\chi - \\omega \\log{(\\chi - \\omega)}", "- \\chi \\log{(- \\chi + \\omega)} + \\omega \\log{(- \\chi + \\omega)} - \\omega", "\\chi (- \\omega + \\log{(\\chi^{\\omega})})", "\\chi (\\log{(\\chi \\omega)} - 1)"], "srepr_premise_expression": "log(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\chi', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\omega', commutative=True)))), Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\omega', commutative=True), log(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\chi', commutative=True), log(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))), Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\omega', commutative=True), log(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))))", "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\omega', commutative=True)))), Mul(Symbol('\\\\omega', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\omega', commutative=True)))), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), log(Pow(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True)))))", "Mul(Symbol('\\\\chi', commutative=True), Add(log(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\psi + \\sin{(\\delta)}", "variable": "\\delta", "positive": "\\delta \\psi - \\cos{(\\delta)}", "negatives": ["\\psi \\log{(\\delta)}", "\\psi e^{\\delta}", "e^{\\delta - \\psi}", "\\frac{\\psi (\\psi + 2 \\sin{(\\delta)})}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\psi', commutative=True), sin(Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\delta', commutative=True))))", "srepr_negatives": ["Mul(Symbol('\\\\psi', commutative=True), log(Symbol('\\\\delta', commutative=True)))", "Mul(Symbol('\\\\psi', commutative=True), exp(Symbol('\\\\delta', commutative=True)))", "exp(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(2), sin(Symbol('\\\\delta', commutative=True)))))"]}, {"premise_expression": "\\frac{\\gamma}{\\pi} + \\psi", "variable": "\\gamma", "positive": "\\frac{\\gamma^{2}}{2 \\pi} + \\gamma \\psi", "negatives": ["\\frac{\\gamma^{2}}{2 \\psi} + \\gamma \\pi", "\\gamma \\log{(\\pi)} + \\pi \\psi", "\\frac{\\gamma^{2}}{2} + \\frac{\\gamma \\pi}{\\psi}", "\\frac{\\gamma^{2} \\psi}{2 \\pi}"], "srepr_premise_expression": "Add(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1))), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Add(Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1))), Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Add(Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Pow(Symbol('\\\\psi', commutative=True), Integer(-1))), Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True)))", "Add(Mul(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\pi', commutative=True))), Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)))", "Add(Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2))), Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True))"]}, {"premise_expression": "\\log{(\\omega + \\pi)}", "variable": "\\omega", "positive": "\\omega \\log{(\\omega + \\pi)} - \\omega + \\pi \\log{(\\omega + \\pi)}", "negatives": ["\\omega \\log{(\\omega - \\pi)} - \\omega - \\pi \\log{(\\omega - \\pi)}", "\\omega \\log{(\\omega + \\pi)} + \\pi \\log{(\\omega + \\pi)} - \\pi", "\\omega (\\pi + \\log{(\\omega)} - 1)", "\\omega (\\log{(\\omega \\pi)} - 1)"], "srepr_premise_expression": "log(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\omega', commutative=True), log(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Symbol('\\\\pi', commutative=True), log(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\omega', commutative=True), log(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\pi', commutative=True), log(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))))", "Add(Mul(Symbol('\\\\omega', commutative=True), log(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)))), Mul(Symbol('\\\\pi', commutative=True), log(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\omega', commutative=True)), Integer(-1)))", "Mul(Symbol('\\\\omega', commutative=True), Add(log(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True))), Integer(-1)))"]}, {"premise_expression": "- \\omega + \\sigma", "variable": "\\sigma", "positive": "\\frac{\\sigma (- 2 \\omega + \\sigma)}{2}", "negatives": ["\\frac{\\omega (- \\omega + 2 \\sigma)}{2}", "\\frac{\\sigma^{2} \\log{(\\omega)}}{2}", "e^{\\omega + \\sigma}", "\\frac{\\sigma (- \\sigma + 2 e^{\\omega})}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), log(Symbol('\\\\omega', commutative=True)))", "exp(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\omega', commutative=True)))))"]}, {"premise_expression": "\\frac{\\delta}{\\gamma}", "variable": "\\delta", "positive": "\\frac{\\delta^{2}}{2 \\gamma}", "negatives": ["\\delta \\log{(\\gamma)}", "\\gamma \\sin{(\\delta)}", "\\delta", "\\log{(\\delta)} \\cos{(\\gamma)}"], "srepr_premise_expression": "Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "Mul(Symbol('\\\\gamma', commutative=True), sin(Symbol('\\\\delta', commutative=True)))", "Symbol('\\\\delta', commutative=True)", "Mul(log(Symbol('\\\\delta', commutative=True)), cos(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\frac{\\gamma - \\psi}{\\alpha}", "variable": "\\gamma", "positive": "\\frac{\\gamma (\\gamma - 2 \\psi)}{2 \\alpha}", "negatives": ["\\frac{\\gamma (- \\gamma + 2 \\psi)}{2 \\alpha}", "\\frac{\\gamma (2 \\alpha + \\gamma)}{2 \\psi}", "\\frac{\\psi (2 \\gamma - \\psi)}{2 \\alpha}", "\\frac{\\gamma^{2} (\\alpha + \\psi)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\sin{(\\sigma + \\xi)}", "variable": "\\xi", "positive": "- \\cos{(\\sigma + \\xi)}", "negatives": ["- \\sigma \\cos{(\\xi)}", "\\xi (\\log{(\\frac{\\sigma}{\\xi})} + 1)", "\\frac{\\xi^{2} \\log{(\\sigma)}}{2}", "\\xi (- \\sigma + \\log{(\\xi^{\\sigma})})"], "srepr_premise_expression": "sin(Add(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), Symbol('\\\\sigma', commutative=True), cos(Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\xi', commutative=True), Add(log(Mul(Symbol('\\\\sigma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), log(Symbol('\\\\sigma', commutative=True)))", "Mul(Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), log(Pow(Symbol('\\\\xi', commutative=True), Symbol('\\\\sigma', commutative=True)))))"]}, {"premise_expression": "\\gamma \\psi + \\omega", "variable": "\\gamma", "positive": "\\frac{\\gamma (\\gamma \\psi + 2 \\omega)}{2}", "negatives": ["\\frac{\\psi (\\gamma \\psi + 2 \\omega)}{2}", "\\frac{\\gamma (\\gamma \\omega + 2 \\psi)}{2}", "\\frac{\\omega (2 \\gamma \\psi + \\omega)}{2}", "\\frac{\\gamma \\omega (\\gamma + 2 \\psi)}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True)), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "\\frac{\\delta}{\\sigma}", "variable": "\\sigma", "positive": "\\delta \\log{(\\sigma)}", "negatives": ["\\frac{\\delta^{2}}{2 \\sigma}", "e^{\\delta} \\log{(\\sigma)}", "\\log{(\\delta)} \\log{(\\sigma)}", "\\frac{\\sigma^{2}}{2 \\delta}"], "srepr_premise_expression": "Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "Mul(exp(Symbol('\\\\delta', commutative=True)), log(Symbol('\\\\sigma', commutative=True)))", "Mul(log(Symbol('\\\\delta', commutative=True)), log(Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))"]}, {"premise_expression": "\\log{(\\frac{\\omega}{\\psi})}", "variable": "\\psi", "positive": "\\psi (\\log{(\\frac{\\omega}{\\psi})} + 1)", "negatives": ["\\omega (\\log{(\\frac{\\omega}{\\psi})} - 1)", "\\psi (\\log{(\\frac{\\psi}{\\omega})} - 1)", "\\frac{\\psi (\\log{(\\psi)} - 1)}{\\omega}", "\\log{(\\psi)} \\sin{(\\omega)}"], "srepr_premise_expression": "log(Mul(Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\psi', commutative=True), Add(log(Mul(Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))), Integer(1)))", "srepr_negatives": ["Mul(Symbol('\\\\omega', commutative=True), Add(log(Mul(Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))), Integer(-1)))", "Mul(Symbol('\\\\psi', commutative=True), Add(log(Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True))), Integer(-1)))", "Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True), Add(log(Symbol('\\\\psi', commutative=True)), Integer(-1)))", "Mul(log(Symbol('\\\\psi', commutative=True)), sin(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\frac{\\alpha}{\\delta}", "variable": "\\delta", "positive": "\\alpha \\log{(\\delta)}", "negatives": ["\\frac{\\alpha^{2}}{2 \\delta}", "- \\frac{\\cos{(\\delta)}}{\\alpha}", "\\frac{\\alpha \\delta^{2}}{2}", "\\delta (\\log{(\\frac{\\alpha}{\\delta})} + 1)"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)))", "Mul(Integer(-1), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), cos(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(2)))", "Mul(Symbol('\\\\delta', commutative=True), Add(log(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)))), Integer(1)))"]}, {"premise_expression": "- \\alpha + \\pi", "variable": "\\pi", "positive": "\\frac{\\pi (- 2 \\alpha + \\pi)}{2}", "negatives": ["\\frac{\\alpha (- \\alpha + 2 \\pi)}{2}", "\\frac{\\pi (\\pi + 2 \\cos{(\\alpha)})}{2}", "\\frac{\\pi (- \\pi + 2 \\log{(\\alpha)})}{2}", "- \\frac{\\pi^{2}}{2} + \\sin{(\\pi)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), cos(Symbol('\\\\alpha', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), log(Symbol('\\\\alpha', commutative=True)))))", "Add(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2))), sin(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\frac{\\omega}{\\alpha}", "variable": "\\omega", "positive": "\\frac{\\omega^{2}}{2 \\alpha}", "negatives": ["\\omega \\log{(\\alpha)}", "- \\alpha \\omega + \\frac{\\omega^{2}}{2 \\alpha}", "\\frac{\\omega^{2} \\log{(\\alpha)}}{2}", "\\frac{\\omega^{2} \\cos{(\\alpha)}}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\omega', commutative=True), Integer(2))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), log(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), cos(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\xi \\cos{(\\omega)}", "variable": "\\xi", "positive": "\\frac{\\xi^{2} \\cos{(\\omega)}}{2}", "negatives": ["\\frac{\\xi^{2} e^{\\omega}}{2}", "\\frac{\\xi (2 \\omega - \\xi)}{2}", "\\xi \\sin{(\\omega)}", "\\frac{\\xi (- \\xi + 2 \\log{(\\omega)})}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\xi', commutative=True), cos(Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), cos(Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), exp(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Symbol('\\\\xi', commutative=True), sin(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), log(Symbol('\\\\omega', commutative=True)))))"]}, {"premise_expression": "\\chi + \\frac{\\delta}{\\sigma}", "variable": "\\delta", "positive": "\\chi \\delta + \\frac{\\delta^{2}}{2 \\sigma}", "negatives": ["\\chi \\sigma + \\delta \\log{(\\sigma)}", "\\frac{\\delta^{2} \\sigma}{2 \\chi}", "\\delta (\\delta + \\sigma)", "\\frac{\\chi^{2}}{2} + \\frac{\\chi \\delta}{\\sigma}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Symbol('\\\\sigma', commutative=True))", "Mul(Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True)))", "Add(Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2))), Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1))))"]}, {"premise_expression": "\\frac{\\alpha}{\\chi}", "variable": "\\chi", "positive": "\\alpha \\log{(\\chi)}", "negatives": ["\\frac{\\alpha^{2}}{2 \\chi}", "\\frac{\\alpha \\chi^{2}}{2}", "- \\cos{(\\alpha + \\chi)}", "- \\cos{(\\alpha - \\chi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(2)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True)))))"]}, {"premise_expression": "\\psi \\sigma", "variable": "\\psi", "positive": "\\frac{\\psi^{2} \\sigma}{2}", "negatives": ["\\frac{\\psi \\sigma^{2}}{2}", "\\sigma \\log{(\\psi)}", "\\sigma \\sin{(\\psi)}", "\\frac{\\psi^{2} \\log{(\\sigma)}}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), Symbol('\\\\sigma', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "Mul(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\psi', commutative=True)))", "Mul(Symbol('\\\\sigma', commutative=True), sin(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), log(Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\pi \\psi - \\xi", "variable": "\\pi", "positive": "\\frac{\\pi (\\pi \\psi - 2 \\xi)}{2}", "negatives": ["\\frac{\\psi (\\pi \\psi - 2 \\xi)}{2}", "\\frac{\\pi (\\pi \\psi + 2 \\xi)}{2}", "\\frac{\\xi (2 \\pi \\psi - \\xi)}{2}", "\\frac{\\pi \\psi (- \\pi + 2 \\xi)}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "- \\beta + \\delta - \\gamma", "variable": "\\gamma", "positive": "\\gamma (- \\beta + \\delta - \\frac{\\gamma}{2})", "negatives": ["\\frac{\\gamma (- 2 \\beta + 2 \\delta + \\gamma)}{2}", "\\frac{\\delta (- 2 \\beta + \\delta - 2 \\gamma)}{2}", "\\frac{\\beta (- \\beta + 2 \\delta - 2 \\gamma)}{2}", "\\frac{\\gamma^{2}}{2 \\beta \\delta}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Rational(1, 2), Symbol('\\\\gamma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)))"]}, {"premise_expression": "\\sigma \\log{(\\alpha)}", "variable": "\\alpha", "positive": "\\alpha \\sigma (\\log{(\\alpha)} - 1)", "negatives": ["\\alpha (\\log{(\\alpha \\sigma)} - 1)", "\\frac{\\sigma^{2} \\log{(\\alpha)}}{2}", "\\log{(\\alpha)} \\cos{(\\sigma)}", "\\log{(\\alpha)} \\sin{(\\sigma)}"], "srepr_premise_expression": "Mul(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True), Add(log(Symbol('\\\\alpha', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\alpha', commutative=True), Add(log(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), log(Symbol('\\\\alpha', commutative=True)))", "Mul(log(Symbol('\\\\alpha', commutative=True)), cos(Symbol('\\\\sigma', commutative=True)))", "Mul(log(Symbol('\\\\alpha', commutative=True)), sin(Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\log{(\\frac{\\sigma}{\\xi})}", "variable": "\\sigma", "positive": "\\sigma (\\log{(\\frac{\\sigma}{\\xi})} - 1)", "negatives": ["\\xi (\\log{(\\frac{\\sigma}{\\xi})} + 1)", "\\sigma (- \\xi + \\log{(\\sigma)} - 1)", "\\sigma (- \\xi + \\log{(\\sigma^{\\xi})})", "\\sigma e^{2 \\xi}"], "srepr_premise_expression": "log(Mul(Symbol('\\\\sigma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\sigma', commutative=True), Add(log(Mul(Symbol('\\\\sigma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\xi', commutative=True), Add(log(Mul(Symbol('\\\\sigma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), log(Symbol('\\\\sigma', commutative=True)), Integer(-1)))", "Mul(Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), log(Pow(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True)))))", "Mul(Symbol('\\\\sigma', commutative=True), exp(Mul(Integer(2), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\alpha \\beta + \\sigma", "variable": "\\sigma", "positive": "\\frac{\\sigma (2 \\alpha \\beta + \\sigma)}{2}", "negatives": ["\\frac{\\beta (\\alpha \\beta + 2 \\sigma)}{2}", "\\frac{\\alpha (\\alpha \\beta + 2 \\sigma)}{2}", "\\frac{\\alpha \\beta \\sigma^{2}}{2}", "\\frac{\\sigma (- 2 \\beta + \\sigma)}{2 \\alpha}"], "srepr_premise_expression": "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True)), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "- \\delta + \\xi", "variable": "\\delta", "positive": "\\frac{\\delta (- \\delta + 2 \\xi)}{2}", "negatives": ["\\frac{\\xi (- 2 \\delta + \\xi)}{2}", "\\frac{\\delta^{2} \\log{(\\xi)}}{2}", "- e^{- \\delta + \\xi}", "\\xi \\sin{(\\delta)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), log(Symbol('\\\\xi', commutative=True)))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\xi', commutative=True))))", "Mul(Symbol('\\\\xi', commutative=True), sin(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\log{(\\alpha + \\gamma)}", "variable": "\\gamma", "positive": "\\alpha \\log{(\\alpha + \\gamma)} + \\gamma \\log{(\\alpha + \\gamma)} - \\gamma", "negatives": ["\\alpha \\log{(\\alpha + \\gamma)} - \\alpha + \\gamma \\log{(\\alpha + \\gamma)}", "\\frac{\\gamma (\\gamma + 2 \\log{(\\alpha)})}{2}", "\\gamma (\\log{(\\alpha \\gamma)} - 1)", "- \\alpha \\gamma + \\sin{(\\gamma)}"], "srepr_premise_expression": "log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\alpha', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True)))), Mul(Symbol('\\\\gamma', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True)))), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\alpha', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True)))), Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Symbol('\\\\gamma', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), log(Symbol('\\\\alpha', commutative=True)))))", "Mul(Symbol('\\\\gamma', commutative=True), Add(log(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True))), Integer(-1)))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True)), sin(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\cos^{\\gamma}{(\\psi)}", "variable": "\\psi", "positive": "\\int \\cos^{\\gamma}{(\\psi)} d\\psi", "negatives": ["e^{\\gamma} \\log{(\\psi)}", "\\frac{\\psi (- 2 \\gamma + \\psi)}{2}", "\\frac{\\gamma \\psi^{2}}{2}", "\\frac{\\psi (- \\psi + 2 \\log{(\\gamma)})}{2}"], "srepr_premise_expression": "Pow(cos(Symbol('\\\\psi', commutative=True)), Symbol('\\\\gamma', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Integral(Pow(cos(Symbol('\\\\psi', commutative=True)), Symbol('\\\\gamma', commutative=True)), Tuple(Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(exp(Symbol('\\\\gamma', commutative=True)), log(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), log(Symbol('\\\\gamma', commutative=True)))))"]}, {"premise_expression": "\\delta \\sigma", "variable": "\\delta", "positive": "\\frac{\\delta^{2} \\sigma}{2}", "negatives": ["\\frac{\\delta \\sigma^{2}}{2}", "\\frac{\\delta^{2} \\log{(\\sigma)}}{2}", "\\frac{\\delta (\\delta + 2 \\sigma)}{2}", "\\sigma e^{\\frac{\\delta}{\\sigma}}"], "srepr_premise_expression": "Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Symbol('\\\\sigma', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), log(Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Symbol('\\\\sigma', commutative=True), exp(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))))"]}, {"premise_expression": "\\alpha + \\chi", "variable": "\\chi", "positive": "\\frac{\\chi (2 \\alpha + \\chi)}{2}", "negatives": ["\\frac{\\alpha (\\alpha + 2 \\chi)}{2}", "\\frac{\\chi^{2} \\log{(\\alpha)}}{2}", "e^{- \\alpha + \\chi}", "\\sin{(\\alpha + \\chi)}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\chi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), log(Symbol('\\\\alpha', commutative=True)))", "exp(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\chi', commutative=True)))", "sin(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "\\cos{(\\frac{\\psi}{\\omega})}", "variable": "\\omega", "positive": "\\omega \\cos{(\\frac{\\psi}{\\omega})} + \\psi \\operatorname{Si}{(\\frac{\\psi}{\\omega})}", "negatives": ["\\omega (\\log{(\\frac{\\psi}{\\omega})} + 1)", "\\frac{\\omega \\psi (\\omega - 2 \\psi)}{2}", "\\frac{\\omega (\\omega + 2 \\cos{(\\psi)})}{2}", "- \\omega \\psi + \\sin{(\\omega)}"], "srepr_premise_expression": "cos(Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\omega', commutative=True), cos(Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True)))), Mul(Symbol('\\\\psi', commutative=True), Si(Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True)))))", "srepr_negatives": ["Mul(Symbol('\\\\omega', commutative=True), Add(log(Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True))), Integer(1)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), cos(Symbol('\\\\psi', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True)), sin(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "e^{\\frac{\\delta}{\\pi}}", "variable": "\\pi", "positive": "- \\delta \\operatorname{Ei}{(\\frac{\\delta}{\\pi})} + \\pi e^{\\frac{\\delta}{\\pi}}", "negatives": ["\\delta \\pi + e^{\\pi}", "\\pi e^{\\frac{\\delta}{\\pi}}", "- \\delta \\pi - \\cos{(\\pi)}", "\\delta \\pi + \\sin{(\\pi)}"], "srepr_premise_expression": "exp(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Ei(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1))))), Mul(Symbol('\\\\pi', commutative=True), exp(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1))))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True)), exp(Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\pi', commutative=True), exp(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))))", "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\pi', commutative=True))))", "Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True)), sin(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\frac{\\alpha \\gamma}{\\xi}", "variable": "\\xi", "positive": "\\alpha \\gamma \\log{(\\xi)}", "negatives": ["\\frac{\\alpha \\gamma^{2}}{2 \\xi}", "\\frac{\\alpha \\gamma \\xi^{2}}{2}", "\\frac{\\alpha^{2} \\gamma}{2 \\xi}", "\\frac{\\alpha^{2} \\xi}{\\gamma}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))"]}, {"premise_expression": "- \\psi + \\cos{(\\chi)}", "variable": "\\psi", "positive": "\\frac{\\psi (- \\psi + 2 \\cos{(\\chi)})}{2}", "negatives": ["\\frac{\\psi (- \\psi + 2 e^{\\chi})}{2}", "\\frac{\\psi^{2} \\cos{(\\chi)}}{2}", "\\psi (- \\chi + \\log{(\\psi^{\\chi})})", "- \\chi \\psi + \\sin{(\\chi)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), cos(Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\chi', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\chi', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), cos(Symbol('\\\\chi', commutative=True)))", "Mul(Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), log(Pow(Symbol('\\\\psi', commutative=True), Symbol('\\\\chi', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True)), sin(Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "\\sin{(\\chi - \\psi)}", "variable": "\\psi", "positive": "\\cos{(\\chi - \\psi)}", "negatives": ["- \\cos{(\\chi - \\psi)}", "- \\chi \\psi - \\cos{(\\psi)}", "e^{\\chi} \\log{(\\psi)}", "\\chi \\psi + \\sin{(\\psi)}"], "srepr_premise_expression": "sin(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "cos(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\psi', commutative=True))))", "Mul(exp(Symbol('\\\\chi', commutative=True)), log(Symbol('\\\\psi', commutative=True)))", "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True)), sin(Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\chi + \\pi", "variable": "\\chi", "positive": "\\frac{\\chi (\\chi + 2 \\pi)}{2}", "negatives": ["\\frac{\\pi (2 \\chi + \\pi)}{2}", "\\frac{\\chi (\\chi + 2 \\log{(\\pi)})}{2}", "\\cos{(\\chi - \\pi)}", "\\chi (- \\pi + \\log{(\\chi)} - 1)"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), log(Symbol('\\\\pi', commutative=True)))))", "cos(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "Mul(Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), log(Symbol('\\\\chi', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\log{(\\psi^{\\sigma})}", "variable": "\\psi", "positive": "\\psi (- \\sigma + \\log{(\\psi^{\\sigma})})", "negatives": ["\\frac{\\sigma^{2} \\log{(\\psi)}}{2}", "- \\psi \\sigma + \\sin{(\\psi)}", "\\psi (\\log{(\\psi \\sigma)} - 1)", "- \\frac{\\cos{(\\psi)}}{\\sigma}"], "srepr_premise_expression": "log(Pow(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), log(Pow(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), log(Symbol('\\\\psi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True)), sin(Symbol('\\\\psi', commutative=True)))", "Mul(Symbol('\\\\psi', commutative=True), Add(log(Mul(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True))), Integer(-1)))", "Mul(Integer(-1), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), cos(Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\beta \\delta", "variable": "\\beta", "positive": "\\frac{\\beta^{2} \\delta}{2}", "negatives": ["\\frac{\\beta \\delta^{2}}{2}", "\\frac{\\beta^{2}}{2 \\delta}", "- \\frac{\\cos{(\\beta)}}{\\delta}", "\\frac{\\beta^{2} (\\delta - 1)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\delta', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)))", "Mul(Integer(-1), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), cos(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Add(Symbol('\\\\delta', commutative=True), Integer(-1)))"]}, {"premise_expression": "\\alpha \\pi", "variable": "\\alpha", "positive": "\\frac{\\alpha^{2} \\pi}{2}", "negatives": ["\\frac{\\alpha \\pi^{2}}{2}", "\\frac{\\alpha^{2}}{2 \\pi}", "\\alpha (\\log{(\\alpha \\pi)} - 1)", "\\frac{\\alpha (- \\alpha + 2 e^{\\pi})}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\pi', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))", "Mul(Symbol('\\\\alpha', commutative=True), Add(log(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\pi', commutative=True)))))"]}, {"premise_expression": "\\chi (- \\beta + \\psi)", "variable": "\\psi", "positive": "\\frac{\\chi \\psi (- 2 \\beta + \\psi)}{2}", "negatives": ["\\frac{\\beta \\psi (2 \\chi + \\psi)}{2}", "\\frac{\\psi (- 2 \\beta + \\chi \\psi)}{2}", "\\frac{\\beta \\chi (- \\beta + 2 \\psi)}{2}", "\\frac{\\chi^{2} (- \\beta + \\psi)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\chi + \\cos{(\\gamma)}", "variable": "\\chi", "positive": "\\frac{\\chi (\\chi + 2 \\cos{(\\gamma)})}{2}", "negatives": ["\\frac{\\chi (- \\chi + 2 \\cos{(\\gamma)})}{2}", "\\chi \\gamma + \\sin{(\\gamma)}", "- \\chi \\gamma - \\cos{(\\chi)}", "\\chi \\gamma + \\sin{(\\chi)}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), cos(Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), cos(Symbol('\\\\gamma', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\gamma', commutative=True)))))", "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True)), sin(Symbol('\\\\gamma', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\chi', commutative=True))))", "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True)), sin(Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "\\omega \\xi", "variable": "\\omega", "positive": "\\frac{\\omega^{2} \\xi}{2}", "negatives": ["\\frac{\\omega \\xi^{2}}{2}", "\\frac{\\omega^{2} \\log{(\\xi)}}{2}", "\\frac{\\omega (\\omega + 2 \\xi)}{2}", "\\omega \\log{(\\omega + \\xi)} - \\omega + \\xi \\log{(\\omega + \\xi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), log(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Add(Mul(Symbol('\\\\omega', commutative=True), log(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Symbol('\\\\xi', commutative=True), log(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True)))))"]}, {"premise_expression": "\\omega \\cos{(\\delta)}", "variable": "\\omega", "positive": "\\frac{\\omega^{2} \\cos{(\\delta)}}{2}", "negatives": ["\\frac{\\omega^{2} \\sin{(\\delta)}}{2}", "\\omega \\sin{(\\delta)}", "\\frac{\\omega (\\omega + 2 e^{\\delta})}{2}", "- \\sin{(\\delta - \\omega)}"], "srepr_premise_expression": "Mul(Symbol('\\\\omega', commutative=True), cos(Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), cos(Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), sin(Symbol('\\\\delta', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), sin(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), exp(Symbol('\\\\delta', commutative=True)))))", "Mul(Integer(-1), sin(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))))"]}, {"premise_expression": "- \\sin{(\\gamma - \\omega)}", "variable": "\\gamma", "positive": "\\cos{(\\gamma - \\omega)}", "negatives": ["- \\cos{(\\gamma - \\omega)}", "\\omega e^{\\frac{\\gamma}{\\omega}}", "\\gamma (\\log{(\\frac{\\gamma}{\\omega})} - 1)", "\\log{(\\gamma)} \\cos{(\\omega)}"], "srepr_premise_expression": "Mul(Integer(-1), sin(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "cos(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))))", "Mul(Symbol('\\\\omega', commutative=True), exp(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))))", "Mul(Symbol('\\\\gamma', commutative=True), Add(log(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))), Integer(-1)))", "Mul(log(Symbol('\\\\gamma', commutative=True)), cos(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\cos^{\\beta}{(\\chi)}", "variable": "\\chi", "positive": "\\int \\cos^{\\beta}{(\\chi)} d\\chi", "negatives": ["e^{- \\beta + \\chi}", "- \\beta \\chi + \\sin{(\\chi)}", "\\frac{\\chi (\\chi + 2 e^{\\beta})}{2}", "\\frac{\\chi (- \\chi + 2 \\sin{(\\beta)})}{2}"], "srepr_premise_expression": "Pow(cos(Symbol('\\\\chi', commutative=True)), Symbol('\\\\beta', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Integral(Pow(cos(Symbol('\\\\chi', commutative=True)), Symbol('\\\\beta', commutative=True)), Tuple(Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["exp(Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\chi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True)), sin(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), exp(Symbol('\\\\beta', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\beta', commutative=True)))))"]}, {"premise_expression": "\\log{(\\frac{\\omega}{\\beta})}", "variable": "\\omega", "positive": "\\omega (\\log{(\\frac{\\omega}{\\beta})} - 1)", "negatives": ["\\beta (\\log{(\\frac{\\omega}{\\beta})} + 1)", "\\beta e^{\\omega}", "\\frac{\\omega (\\omega + 2 \\log{(\\beta)})}{2}", "\\frac{\\omega (\\omega + 2 \\sin{(\\beta)})}{2}"], "srepr_premise_expression": "log(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\omega', commutative=True), Add(log(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\beta', commutative=True), Add(log(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True))), Integer(1)))", "Mul(Symbol('\\\\beta', commutative=True), exp(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), log(Symbol('\\\\beta', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), sin(Symbol('\\\\beta', commutative=True)))))"]}, {"premise_expression": "\\cos{(\\alpha - \\delta)}", "variable": "\\delta", "positive": "- \\sin{(\\alpha - \\delta)}", "negatives": ["\\sin{(\\alpha - \\delta)}", "e^{- \\alpha + \\delta}", "\\frac{\\delta (2 \\alpha + \\delta)}{2}", "- \\alpha \\cos{(\\delta)}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Integer(-1), sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)))))", "srepr_negatives": ["sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))", "exp(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\delta', commutative=True)))", "Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), cos(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "- \\gamma + \\log{(\\xi)}", "variable": "\\xi", "positive": "\\xi (- \\gamma + \\log{(\\xi)} - 1)", "negatives": ["\\xi (\\log{(\\gamma \\xi)} - 1)", "\\frac{\\gamma (- \\gamma + 2 \\log{(\\xi)})}{2}", "\\xi (\\log{(\\frac{\\gamma}{\\xi})} + 1)", "\\gamma \\xi - \\cos{(\\xi)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), log(Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), log(Symbol('\\\\xi', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\xi', commutative=True), Add(log(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), log(Symbol('\\\\xi', commutative=True)))))", "Mul(Symbol('\\\\xi', commutative=True), Add(log(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))), Integer(1)))", "Add(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\omega + \\pi", "variable": "\\omega", "positive": "\\frac{\\omega (\\omega + 2 \\pi)}{2}", "negatives": ["\\frac{\\pi (2 \\omega + \\pi)}{2}", "\\frac{\\omega^{2} \\cos{(\\pi)}}{2}", "\\sin{(\\omega + \\pi)}", "\\frac{\\sin{(\\omega)}}{\\pi}"], "srepr_premise_expression": "Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), cos(Symbol('\\\\pi', commutative=True)))", "sin(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)))", "Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), sin(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\frac{- \\gamma + \\psi}{\\sigma}", "variable": "\\psi", "positive": "\\frac{\\psi (- 2 \\gamma + \\psi)}{2 \\sigma}", "negatives": ["\\frac{\\gamma (- \\gamma + 2 \\psi)}{2 \\sigma}", "\\frac{\\psi^{2} (\\gamma + \\sigma)}{2}", "(- \\gamma + \\psi) \\log{(\\sigma)}", "\\frac{\\psi (2 \\gamma + \\psi - 2 \\sigma)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True)))", "Mul(Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\psi', commutative=True)), log(Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\psi + \\xi", "variable": "\\psi", "positive": "\\frac{\\psi (\\psi + 2 \\xi)}{2}", "negatives": ["\\frac{\\psi (- \\psi + 2 \\xi)}{2}", "\\frac{\\xi (2 \\psi + \\xi)}{2}", "\\frac{\\psi^{2} \\sin{(\\xi)}}{2}", "\\frac{\\psi (\\log{(\\psi)} - 1)}{\\xi}"], "srepr_premise_expression": "Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\psi', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), sin(Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\psi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), Add(log(Symbol('\\\\psi', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\log{(\\omega \\pi)}", "variable": "\\omega", "positive": "\\omega (\\log{(\\omega \\pi)} - 1)", "negatives": ["\\pi (\\log{(\\omega \\pi)} - 1)", "\\pi \\log{(\\omega)}", "- e^{- \\omega + \\pi}", "\\omega (- \\pi + \\log{(\\omega^{\\pi})})"], "srepr_premise_expression": "log(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\omega', commutative=True), Add(log(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\pi', commutative=True), Add(log(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Symbol('\\\\pi', commutative=True))))", "Mul(Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), log(Pow(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)))))"]}, {"premise_expression": "\\beta + \\sigma", "variable": "\\sigma", "positive": "\\frac{\\sigma (2 \\beta + \\sigma)}{2}", "negatives": ["\\frac{\\sigma (2 \\beta - \\sigma)}{2}", "\\frac{\\beta (\\beta + 2 \\sigma)}{2}", "\\frac{\\sigma (\\sigma + 2 \\cos{(\\beta)})}{2}", "- \\beta \\sigma + e^{\\sigma}"], "srepr_premise_expression": "Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(2), cos(Symbol('\\\\beta', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True)), exp(Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\log{(\\omega + \\xi)}", "variable": "\\omega", "positive": "\\omega \\log{(\\omega + \\xi)} - \\omega + \\xi \\log{(\\omega + \\xi)}", "negatives": ["\\omega \\log{(\\omega + \\xi)} + \\xi \\log{(\\omega + \\xi)} - \\xi", "\\omega (- \\xi + \\log{(\\omega^{\\xi})})", "\\frac{\\omega (- \\omega + 2 e^{\\xi})}{2}", "\\frac{\\omega (- \\omega + 2 \\xi)}{2}"], "srepr_premise_expression": "log(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\omega', commutative=True), log(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Symbol('\\\\xi', commutative=True), log(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\omega', commutative=True), log(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True)))), Mul(Symbol('\\\\xi', commutative=True), log(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), log(Pow(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\xi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\log{(\\xi^{\\gamma})}", "variable": "\\xi", "positive": "\\xi (- \\gamma + \\log{(\\xi^{\\gamma})})", "negatives": ["\\frac{\\xi (2 \\gamma + \\xi)}{2}", "\\frac{\\xi (\\xi + 2 \\sin{(\\gamma)})}{2}", "\\frac{\\gamma^{2} \\log{(\\xi)}}{2}", "- \\cos{(\\gamma + \\xi)}"], "srepr_premise_expression": "log(Pow(Symbol('\\\\xi', commutative=True), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), log(Pow(Symbol('\\\\xi', commutative=True), Symbol('\\\\gamma', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\xi', commutative=True), Mul(Integer(2), sin(Symbol('\\\\gamma', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), log(Symbol('\\\\xi', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "- \\beta + \\sin{(\\chi)}", "variable": "\\beta", "positive": "\\frac{\\beta (- \\beta + 2 \\sin{(\\chi)})}{2}", "negatives": ["\\frac{\\beta (\\beta + 2 e^{\\chi})}{2}", "- \\beta \\chi - \\cos{(\\chi)}", "\\frac{\\beta^{2}}{2 \\chi}", "\\cos{(\\beta - \\chi)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), sin(Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\chi', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), exp(Symbol('\\\\chi', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\chi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)))", "cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True))))"]}, {"premise_expression": "\\cos{(\\beta - \\chi)}", "variable": "\\chi", "positive": "- \\sin{(\\beta - \\chi)}", "negatives": ["\\sin{(\\beta - \\chi)}", "\\beta \\sin{(\\chi)}", "\\frac{\\sin{(\\chi)}}{\\beta}", "- \\frac{\\cos{(\\chi)}}{\\beta}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True))))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Integer(-1), sin(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True)))))", "srepr_negatives": ["sin(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True))))", "Mul(Symbol('\\\\beta', commutative=True), sin(Symbol('\\\\chi', commutative=True)))", "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), sin(Symbol('\\\\chi', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), cos(Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "\\sin{(\\frac{\\chi}{\\xi})}", "variable": "\\xi", "positive": "\\chi \\log{(\\frac{\\chi}{\\xi})} - \\frac{\\chi \\log{(\\frac{\\chi^{2}}{\\xi^{2}})}}{2} - \\chi \\operatorname{Ci}{(\\frac{\\chi}{\\xi})} + \\xi \\sin{(\\frac{\\chi}{\\xi})}", "negatives": ["- \\chi \\log{(- \\chi + \\xi)} + \\xi \\log{(- \\chi + \\xi)} - \\xi", "\\chi \\log{(\\chi + \\xi)} + \\xi \\log{(\\chi + \\xi)} - \\xi", "\\xi (\\log{(\\chi \\xi)} - 1)", "\\frac{\\xi (\\xi + 2 e^{\\chi})}{2}"], "srepr_premise_expression": "sin(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\chi', commutative=True), log(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))), Mul(Integer(-1), Rational(1, 2), Symbol('\\\\chi', commutative=True), log(Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-2))))), Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Ci(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))), Mul(Symbol('\\\\xi', commutative=True), sin(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\xi', commutative=True)))), Mul(Symbol('\\\\xi', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\xi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "Add(Mul(Symbol('\\\\chi', commutative=True), log(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True)))), Mul(Symbol('\\\\xi', commutative=True), log(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\xi', commutative=True), Add(log(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\xi', commutative=True), Mul(Integer(2), exp(Symbol('\\\\chi', commutative=True)))))"]}, {"premise_expression": "\\frac{\\delta}{\\chi}", "variable": "\\chi", "positive": "\\delta \\log{(\\chi)}", "negatives": ["\\frac{\\delta^{2}}{2 \\chi}", "\\delta e^{\\frac{\\chi}{\\delta}}", "\\chi \\delta - \\cos{(\\chi)}", "\\cos{(\\chi - \\delta)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Pow(Symbol('\\\\delta', commutative=True), Integer(2)))", "Mul(Symbol('\\\\delta', commutative=True), exp(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)))))", "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\chi', commutative=True))))", "cos(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))"]}, {"premise_expression": "- \\omega + \\psi", "variable": "\\omega", "positive": "\\frac{\\omega (- \\omega + 2 \\psi)}{2}", "negatives": ["\\frac{\\omega (\\omega - 2 \\psi)}{2}", "\\frac{\\psi (- 2 \\omega + \\psi)}{2}", "\\frac{\\omega (- \\omega + 2 \\log{(\\psi)})}{2}", "\\frac{\\omega (- \\omega + 2 \\cos{(\\psi)})}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), log(Symbol('\\\\psi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\psi', commutative=True)))))"]}, {"premise_expression": "\\log{(\\gamma + \\psi)}", "variable": "\\gamma", "positive": "\\gamma \\log{(\\gamma + \\psi)} - \\gamma + \\psi \\log{(\\gamma + \\psi)}", "negatives": ["\\gamma \\log{(\\gamma - \\psi)} - \\gamma - \\psi \\log{(\\gamma - \\psi)}", "\\gamma \\log{(\\gamma + \\psi)} + \\psi \\log{(\\gamma + \\psi)} - \\psi", "\\frac{\\gamma (- \\gamma + 2 \\log{(\\psi)})}{2}", "\\gamma e^{\\frac{\\psi}{\\gamma}} - \\psi \\operatorname{Ei}{(\\frac{\\psi}{\\gamma})}"], "srepr_premise_expression": "log(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\gamma', commutative=True), log(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Symbol('\\\\psi', commutative=True), log(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\gamma', commutative=True), log(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), Symbol('\\\\psi', commutative=True), log(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))))", "Add(Mul(Symbol('\\\\gamma', commutative=True), log(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True)))), Mul(Symbol('\\\\psi', commutative=True), log(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), log(Symbol('\\\\psi', commutative=True)))))", "Add(Mul(Symbol('\\\\gamma', commutative=True), exp(Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\psi', commutative=True), Ei(Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True)))))"]}, {"premise_expression": "\\frac{\\delta^{\\psi}}{\\omega}", "variable": "\\omega", "positive": "\\delta^{\\psi} \\log{(\\omega)}", "negatives": ["\\delta^{2} \\log{(\\omega)}", "(- \\delta + \\psi) \\log{(\\omega)}", "\\frac{\\delta \\omega^{2} \\psi}{2}", "\\omega^{2} (- \\frac{\\delta}{2} + \\frac{\\omega}{3})"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\delta', commutative=True), Symbol('\\\\psi', commutative=True)), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('\\\\delta', commutative=True), Symbol('\\\\psi', commutative=True)), log(Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(2)), log(Symbol('\\\\omega', commutative=True)))", "Mul(Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\psi', commutative=True)), log(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))", "Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Add(Mul(Integer(-1), Rational(1, 2), Symbol('\\\\delta', commutative=True)), Mul(Rational(1, 3), Symbol('\\\\omega', commutative=True))))"]}, {"premise_expression": "\\pi + \\sin{(\\chi)}", "variable": "\\pi", "positive": "\\frac{\\pi (\\pi + 2 \\sin{(\\chi)})}{2}", "negatives": ["\\frac{\\pi (\\pi + 2 \\cos{(\\chi)})}{2}", "\\chi \\pi - \\cos{(\\chi)}", "- \\chi \\pi - \\cos{(\\pi)}", "- \\cos{(\\chi - \\pi)}"], "srepr_premise_expression": "Add(Symbol('\\\\pi', commutative=True), sin(Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), sin(Symbol('\\\\chi', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), cos(Symbol('\\\\chi', commutative=True)))))", "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\chi', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\pi', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))"]}, {"premise_expression": "\\frac{\\xi}{\\beta}", "variable": "\\xi", "positive": "\\frac{\\xi^{2}}{2 \\beta}", "negatives": ["\\xi \\log{(\\beta)}", "\\frac{\\beta \\xi^{2}}{2}", "\\sin{(\\beta + \\xi)}", "\\frac{\\xi (2 \\beta - \\xi)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "sin(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\sin^{\\gamma}{(\\beta)}", "variable": "\\beta", "positive": "\\int \\sin^{\\gamma}{(\\beta)} d\\beta", "negatives": ["\\beta (e^{\\gamma})^{\\gamma}", "\\beta (\\gamma + \\log{(\\beta)} - 1)", "e^{\\beta + \\gamma}", "- \\beta \\gamma + e^{\\beta}"], "srepr_premise_expression": "Pow(sin(Symbol('\\\\beta', commutative=True)), Symbol('\\\\gamma', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Integral(Pow(sin(Symbol('\\\\beta', commutative=True)), Symbol('\\\\gamma', commutative=True)), Tuple(Symbol('\\\\beta', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\beta', commutative=True), Pow(exp(Symbol('\\\\gamma', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "Mul(Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\beta', commutative=True)), Integer(-1)))", "exp(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)), exp(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "\\delta + \\omega + \\sigma", "variable": "\\sigma", "positive": "\\sigma (\\delta + \\omega + \\frac{\\sigma}{2})", "negatives": ["\\frac{\\sigma (2 \\delta + 2 \\omega - \\sigma)}{2}", "\\frac{\\sigma (- 2 \\delta - 2 \\omega + \\sigma)}{2}", "\\frac{\\omega (2 \\delta + \\omega + 2 \\sigma)}{2}", "\\frac{\\delta (\\delta + 2 \\omega + 2 \\sigma)}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True), Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\frac{\\alpha}{\\omega}", "variable": "\\omega", "positive": "\\alpha \\log{(\\omega)}", "negatives": ["\\frac{\\alpha^{2}}{2 \\omega}", "\\frac{\\alpha \\omega^{2}}{2}", "\\omega", "\\log{(\\alpha)} \\log{(\\omega)}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "Symbol('\\\\omega', commutative=True)", "Mul(log(Symbol('\\\\alpha', commutative=True)), log(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "e^{- \\beta + \\gamma}", "variable": "\\gamma", "positive": "e^{- \\beta + \\gamma}", "negatives": ["- e^{- \\beta + \\gamma}", "- \\sin{(\\beta - \\gamma)}", "- e^{\\beta - \\gamma}", "\\gamma \\log{(\\beta^{2})}"], "srepr_premise_expression": "exp(Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "exp(Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\gamma', commutative=True))))", "Mul(Integer(-1), sin(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))))", "Mul(Integer(-1), exp(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))))", "Mul(Symbol('\\\\gamma', commutative=True), log(Pow(Symbol('\\\\beta', commutative=True), Integer(2))))"]}, {"premise_expression": "e^{\\frac{\\chi}{\\pi}}", "variable": "\\pi", "positive": "- \\chi \\operatorname{Ei}{(\\frac{\\chi}{\\pi})} + \\pi e^{\\frac{\\chi}{\\pi}}", "negatives": ["\\pi e^{\\frac{\\chi}{\\pi}}", "\\chi e^{\\frac{\\pi}{\\chi}}", "e^{\\chi + \\pi}", "\\pi (\\log{(\\chi \\pi)} - 1)"], "srepr_premise_expression": "exp(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Ei(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1))))), Mul(Symbol('\\\\pi', commutative=True), exp(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1))))))", "srepr_negatives": ["Mul(Symbol('\\\\pi', commutative=True), exp(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))))", "Mul(Symbol('\\\\chi', commutative=True), exp(Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))))", "exp(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\pi', commutative=True), Add(log(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\omega + \\psi", "variable": "\\psi", "positive": "\\frac{\\psi (2 \\omega + \\psi)}{2}", "negatives": ["\\frac{\\omega (\\omega + 2 \\psi)}{2}", "\\frac{\\psi (\\psi + 2 e^{\\omega})}{2}", "\\frac{\\psi^{2}}{2 \\omega}", "\\cos{(\\omega - \\psi)}"], "srepr_premise_expression": "Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(2), exp(Symbol('\\\\omega', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "cos(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "\\sin^{\\beta}{(\\delta)}", "variable": "\\delta", "positive": "\\int \\sin^{\\beta}{(\\delta)} d\\delta", "negatives": ["e^{- \\beta + \\delta}", "e^{\\beta + \\delta}", "\\frac{\\delta^{2}}{2 \\beta}", "\\frac{\\delta^{2} \\log{(\\beta)}}{2}"], "srepr_premise_expression": "Pow(sin(Symbol('\\\\delta', commutative=True)), Symbol('\\\\beta', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Integral(Pow(sin(Symbol('\\\\delta', commutative=True)), Symbol('\\\\beta', commutative=True)), Tuple(Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["exp(Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\delta', commutative=True)))", "exp(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Pow(Symbol('\\\\delta', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), log(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "- \\sin{(\\alpha - \\sigma)}", "variable": "\\alpha", "positive": "\\cos{(\\alpha - \\sigma)}", "negatives": ["- \\cos{(\\alpha - \\sigma)}", "\\frac{\\alpha (\\alpha + 2 \\sigma)}{2}", "\\frac{e^{2 \\alpha}}{2}", "\\alpha (\\log{(\\frac{\\sigma}{\\alpha})} + 1)"], "srepr_premise_expression": "Mul(Integer(-1), sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), exp(Mul(Integer(2), Symbol('\\\\alpha', commutative=True))))", "Mul(Symbol('\\\\alpha', commutative=True), Add(log(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))), Integer(1)))"]}, {"premise_expression": "\\gamma + \\omega", "variable": "\\gamma", "positive": "\\frac{\\gamma (\\gamma + 2 \\omega)}{2}", "negatives": ["\\frac{\\omega (2 \\gamma + \\omega)}{2}", "\\cos{(\\gamma - \\omega)}", "\\sin{(\\gamma - \\omega)}", "\\frac{\\gamma (\\gamma + 2 e^{\\omega})}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\omega', commutative=True)))", "cos(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "sin(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), exp(Symbol('\\\\omega', commutative=True)))))"]}, {"premise_expression": "\\sin{(\\psi + \\xi)}", "variable": "\\xi", "positive": "- \\cos{(\\psi + \\xi)}", "negatives": ["\\psi e^{\\frac{\\xi}{\\psi}}", "\\log{(\\xi)} \\cos{(\\psi)}", "\\frac{\\xi^{2} \\sin{(\\psi)}}{2}", "\\frac{\\xi^{2} e^{\\psi}}{2}"], "srepr_premise_expression": "sin(Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Symbol('\\\\psi', commutative=True), exp(Mul(Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))))", "Mul(log(Symbol('\\\\xi', commutative=True)), cos(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), sin(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), exp(Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\frac{\\omega}{\\xi}", "variable": "\\xi", "positive": "\\omega \\log{(\\xi)}", "negatives": ["\\frac{\\omega^{2}}{2 \\xi}", "\\frac{\\sin{(\\xi)}}{\\omega}", "\\omega \\xi (\\log{(\\xi)} - 1)", "\\frac{\\xi (2 \\omega - \\xi)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), sin(Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True), Add(log(Symbol('\\\\xi', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\beta^{\\psi} + \\chi", "variable": "\\chi", "positive": "\\frac{\\chi (2 \\beta^{\\psi} + \\chi)}{2}", "negatives": ["\\frac{\\chi (2 \\beta \\psi + \\chi)}{2}", "\\frac{\\chi (\\chi + 2 \\psi)}{2 \\beta}", "\\frac{\\chi (2 \\beta - \\chi - 2 \\psi)}{2}", "\\frac{\\chi (- 2 \\beta + \\chi \\psi)}{2}"], "srepr_premise_expression": "Add(Pow(Symbol('\\\\beta', commutative=True), Symbol('\\\\psi', commutative=True)), Symbol('\\\\chi', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(2), Pow(Symbol('\\\\beta', commutative=True), Symbol('\\\\psi', commutative=True))), Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True), Symbol('\\\\psi', commutative=True)), Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "- \\delta + \\sin{(\\pi)}", "variable": "\\pi", "positive": "- \\delta \\pi - \\cos{(\\pi)}", "negatives": ["- \\delta \\pi + \\sin{(\\pi)}", "\\delta \\pi + \\sin{(\\pi)}", "\\delta (\\pi + \\log{(\\pi)})", "- \\frac{\\cos{(\\pi)}}{\\delta}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), sin(Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True)), sin(Symbol('\\\\pi', commutative=True)))", "Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True)), sin(Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\pi', commutative=True))))", "Mul(Integer(-1), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), cos(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "- \\alpha + \\psi", "variable": "\\alpha", "positive": "\\frac{\\alpha (- \\alpha + 2 \\psi)}{2}", "negatives": ["\\frac{\\alpha (\\alpha + 2 \\psi)}{2}", "\\alpha (- \\alpha + \\psi)", "\\frac{\\psi (- 2 \\alpha + \\psi)}{2}", "- e^{- \\alpha + \\psi}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "\\frac{\\xi}{\\psi}", "variable": "\\xi", "positive": "\\frac{\\xi^{2}}{2 \\psi}", "negatives": ["\\xi \\log{(\\psi)}", "\\frac{\\psi \\xi^{2}}{2}", "\\frac{\\sin{(\\xi)}}{\\psi}", "- \\cos{(\\psi - \\xi)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Mul(Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), sin(Symbol('\\\\xi', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))))"]}, {"premise_expression": "- \\chi + \\delta", "variable": "\\chi", "positive": "\\frac{\\chi (- \\chi + 2 \\delta)}{2}", "negatives": ["\\frac{\\delta (- 2 \\chi + \\delta)}{2}", "\\sin{(\\chi + \\delta)}", "\\chi \\delta + \\sin{(\\chi)}", "\\sin{(\\chi - \\delta)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\delta', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\delta', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\delta', commutative=True)))", "sin(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True)))", "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True)), sin(Symbol('\\\\chi', commutative=True)))", "sin(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))"]}, {"premise_expression": "\\log{(\\omega^{\\gamma})}", "variable": "\\omega", "positive": "\\omega (- \\gamma + \\log{(\\omega^{\\gamma})})", "negatives": ["\\frac{\\gamma^{2} \\log{(\\omega)}}{2}", "\\sin{(\\gamma + \\omega)}", "- \\frac{\\cos{(\\omega)}}{\\gamma}", "\\int \\sin^{\\gamma}{(\\omega)} d\\omega"], "srepr_premise_expression": "log(Pow(Symbol('\\\\omega', commutative=True), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), log(Pow(Symbol('\\\\omega', commutative=True), Symbol('\\\\gamma', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), log(Symbol('\\\\omega', commutative=True)))", "sin(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), cos(Symbol('\\\\omega', commutative=True)))", "Integral(Pow(sin(Symbol('\\\\omega', commutative=True)), Symbol('\\\\gamma', commutative=True)), Tuple(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\cos^{\\chi}{(\\gamma)}", "variable": "\\gamma", "positive": "\\int \\cos^{\\chi}{(\\gamma)} d\\gamma", "negatives": ["\\log{(\\gamma)} \\sin{(\\chi)}", "- \\chi \\cos{(\\gamma)}", "\\chi e^{\\frac{\\gamma}{\\chi}}", "\\frac{\\gamma^{2} \\cos{(\\chi)}}{2}"], "srepr_premise_expression": "Pow(cos(Symbol('\\\\gamma', commutative=True)), Symbol('\\\\chi', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Integral(Pow(cos(Symbol('\\\\gamma', commutative=True)), Symbol('\\\\chi', commutative=True)), Tuple(Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(log(Symbol('\\\\gamma', commutative=True)), sin(Symbol('\\\\chi', commutative=True)))", "Mul(Integer(-1), Symbol('\\\\chi', commutative=True), cos(Symbol('\\\\gamma', commutative=True)))", "Mul(Symbol('\\\\chi', commutative=True), exp(Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), cos(Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "\\delta + e^{\\psi}", "variable": "\\psi", "positive": "\\delta \\psi + e^{\\psi}", "negatives": ["\\delta e^{\\psi}", "\\frac{\\delta (\\delta + 2 e^{\\psi})}{2}", "\\delta \\log{(\\psi)}", "\\sin{(\\delta + \\psi)}"], "srepr_premise_expression": "Add(Symbol('\\\\delta', commutative=True), exp(Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\psi', commutative=True)), exp(Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\delta', commutative=True), exp(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), exp(Symbol('\\\\psi', commutative=True)))))", "Mul(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\psi', commutative=True)))", "sin(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\frac{\\alpha}{\\sigma}", "variable": "\\alpha", "positive": "\\frac{\\alpha^{2}}{2 \\sigma}", "negatives": ["\\alpha \\log{(\\sigma)}", "\\frac{\\alpha (\\alpha + 2 \\sigma)}{2}", "e^{\\alpha - \\sigma}", "\\frac{\\alpha^{2} (1 - \\sigma)}{2 \\sigma}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "exp(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Add(Integer(1), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "- \\beta + \\gamma", "variable": "\\beta", "positive": "\\frac{\\beta (- \\beta + 2 \\gamma)}{2}", "negatives": ["\\frac{\\gamma (- 2 \\beta + \\gamma)}{2}", "\\sin{(\\beta + \\gamma)}", "\\frac{\\beta^{2} \\gamma}{2}", "\\beta (\\log{(\\frac{\\gamma}{\\beta})} + 1)"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\gamma', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\gamma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "sin(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\gamma', commutative=True))", "Mul(Symbol('\\\\beta', commutative=True), Add(log(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True))), Integer(1)))"]}, {"premise_expression": "\\omega + \\pi + \\psi", "variable": "\\omega", "positive": "\\omega (\\frac{\\omega}{2} + \\pi + \\psi)", "negatives": ["\\frac{\\pi (2 \\omega + \\pi + 2 \\psi)}{2}", "\\frac{\\psi (2 \\omega + 2 \\pi + \\psi)}{2}", "\\frac{\\omega (\\omega \\pi - 2 \\psi)}{2}", "\\frac{\\omega (\\omega + 2 \\pi)}{2 \\psi}"], "srepr_premise_expression": "Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\omega', commutative=True), Add(Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\pi', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\frac{\\log{(\\delta)}}{\\beta}", "variable": "\\delta", "positive": "\\frac{\\delta (\\log{(\\delta)} - 1)}{\\beta}", "negatives": ["\\log{(\\beta)} \\log{(\\delta)}", "\\delta^{2} (- \\frac{\\beta}{2} + \\frac{\\delta}{3})", "\\frac{\\delta (2 \\beta + \\delta)}{2}", "e^{- \\beta + \\delta}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), log(Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True), Add(log(Symbol('\\\\delta', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(log(Symbol('\\\\beta', commutative=True)), log(Symbol('\\\\delta', commutative=True)))", "Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Add(Mul(Integer(-1), Rational(1, 2), Symbol('\\\\beta', commutative=True)), Mul(Rational(1, 3), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\delta', commutative=True)))", "exp(Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\beta (- \\gamma + \\omega)", "variable": "\\gamma", "positive": "\\frac{\\beta \\gamma (- \\gamma + 2 \\omega)}{2}", "negatives": ["\\frac{\\beta^{2} (- \\gamma + \\omega)}{2}", "\\frac{\\beta \\omega (- 2 \\gamma + \\omega)}{2}", "\\frac{\\gamma (2 \\beta \\omega + \\gamma)}{2}", "\\gamma (\\beta + \\gamma)"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "Mul(Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "- \\xi + \\sin{(\\pi)}", "variable": "\\xi", "positive": "\\frac{\\xi (- \\xi + 2 \\sin{(\\pi)})}{2}", "negatives": ["\\frac{\\xi (- \\xi + 2 e^{\\pi})}{2}", "\\frac{\\xi (2 \\pi + \\xi)}{2}", "\\frac{\\xi^{2} e^{\\pi}}{2}", "- \\pi \\xi - \\cos{(\\pi)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), sin(Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\pi', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\pi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), exp(Symbol('\\\\pi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\frac{\\omega + \\psi}{\\alpha}", "variable": "\\psi", "positive": "\\frac{\\psi (2 \\omega + \\psi)}{2 \\alpha}", "negatives": ["\\frac{\\psi (- 2 \\alpha + \\psi)}{2 \\omega}", "\\frac{\\omega (\\omega + 2 \\psi)}{2 \\alpha}", "\\frac{\\psi (2 \\alpha \\omega + \\psi)}{2}", "\\frac{\\omega \\psi (2 \\alpha + \\psi)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\alpha + \\omega + \\sigma", "variable": "\\alpha", "positive": "\\alpha (\\frac{\\alpha}{2} + \\omega + \\sigma)", "negatives": ["\\frac{\\alpha (- \\alpha + 2 \\omega - 2 \\sigma)}{2}", "\\frac{\\sigma (2 \\alpha + 2 \\omega + \\sigma)}{2}", "\\frac{\\omega (2 \\alpha + \\omega + 2 \\sigma)}{2}", "\\frac{\\alpha (\\alpha \\omega - 2 \\sigma)}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\alpha', commutative=True), Add(Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\frac{\\sin{(\\gamma)}}{\\beta}", "variable": "\\gamma", "positive": "- \\frac{\\cos{(\\gamma)}}{\\beta}", "negatives": ["\\beta \\sin{(\\gamma)}", "\\frac{\\gamma^{2} \\cos{(\\beta)}}{2}", "\\beta^{2} \\log{(\\gamma)}", "\\beta \\gamma + \\sin{(\\gamma)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), sin(Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Integer(-1), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), cos(Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\beta', commutative=True), sin(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), cos(Symbol('\\\\beta', commutative=True)))", "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(2)), log(Symbol('\\\\gamma', commutative=True)))", "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)), sin(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "e^{- \\chi + \\pi}", "variable": "\\pi", "positive": "e^{- \\chi + \\pi}", "negatives": ["- e^{- \\chi + \\pi}", "e^{\\chi + \\pi}", "- e^{\\chi - \\pi}", "\\chi e^{\\pi}"], "srepr_premise_expression": "exp(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "exp(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\pi', commutative=True))))", "exp(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True)))", "Mul(Integer(-1), exp(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))", "Mul(Symbol('\\\\chi', commutative=True), exp(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\alpha + \\psi", "variable": "\\alpha", "positive": "\\frac{\\alpha (\\alpha + 2 \\psi)}{2}", "negatives": ["\\frac{\\psi (2 \\alpha + \\psi)}{2}", "e^{\\alpha - \\psi}", "\\sin{(\\alpha - \\psi)}", "\\psi e^{\\alpha}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\psi', commutative=True)))", "exp(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(Symbol('\\\\psi', commutative=True), exp(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\frac{\\alpha}{\\beta}", "variable": "\\alpha", "positive": "\\frac{\\alpha^{2}}{2 \\beta}", "negatives": ["\\alpha \\log{(\\beta)}", "\\beta \\log{(\\alpha)}", "\\sin{(\\alpha + \\beta)}", "- e^{- \\alpha + \\beta}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\beta', commutative=True)))", "Mul(Symbol('\\\\beta', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "sin(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True)))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\beta', commutative=True))))"]}, {"premise_expression": "\\frac{\\psi}{\\alpha \\sigma}", "variable": "\\sigma", "positive": "\\frac{\\psi \\log{(\\sigma)}}{\\alpha}", "negatives": ["\\frac{\\psi \\log{(\\alpha)}}{\\sigma}", "\\frac{\\alpha \\log{(\\sigma)}}{\\psi}", "(\\alpha + \\psi) \\log{(\\sigma)}", "\\frac{\\alpha \\psi \\sigma^{2}}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True), log(Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\psi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), log(Symbol('\\\\alpha', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), log(Symbol('\\\\sigma', commutative=True)))", "Mul(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True)), log(Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))"]}, {"premise_expression": "\\frac{\\omega}{\\alpha}", "variable": "\\alpha", "positive": "\\omega \\log{(\\alpha)}", "negatives": ["\\frac{\\omega^{2}}{2 \\alpha}", "e^{\\omega} \\log{(\\alpha)}", "\\alpha \\omega - \\cos{(\\alpha)}", "\\alpha \\omega + \\sin{(\\alpha)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "Mul(exp(Symbol('\\\\omega', commutative=True)), log(Symbol('\\\\alpha', commutative=True)))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\alpha', commutative=True))))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)), sin(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "- \\sin{(\\delta - \\gamma)}", "variable": "\\gamma", "positive": "- \\cos{(\\delta - \\gamma)}", "negatives": ["\\cos{(\\delta - \\gamma)}", "- \\delta \\gamma - \\cos{(\\gamma)}", "\\frac{\\gamma (- 2 \\delta + \\gamma)}{2}", "\\delta \\gamma + e^{\\gamma}"], "srepr_premise_expression": "Mul(Integer(-1), sin(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))))", "srepr_negatives": ["cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\gamma', commutative=True)), exp(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\frac{\\sigma}{\\psi \\xi}", "variable": "\\psi", "positive": "\\frac{\\sigma \\log{(\\psi)}}{\\xi}", "negatives": ["\\frac{\\sigma \\log{(\\xi)}}{\\psi}", "\\sigma \\xi \\log{(\\psi)}", "\\frac{\\sigma^{2}}{2 \\psi \\xi}", "(\\sigma + \\xi) \\log{(\\psi)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\sigma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), log(Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True), log(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "Mul(Add(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True)), log(Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\cos^{\\omega}{(\\chi)}", "variable": "\\chi", "positive": "\\int \\cos^{\\omega}{(\\chi)} d\\chi", "negatives": ["\\int \\sin^{\\omega}{(\\chi)} d\\chi", "\\cos{(\\chi - \\omega)}", "\\chi (\\log{(\\chi \\omega)} - 1)", "\\omega e^{\\chi}"], "srepr_premise_expression": "Pow(cos(Symbol('\\\\chi', commutative=True)), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Integral(Pow(cos(Symbol('\\\\chi', commutative=True)), Symbol('\\\\omega', commutative=True)), Tuple(Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Integral(Pow(sin(Symbol('\\\\chi', commutative=True)), Symbol('\\\\omega', commutative=True)), Tuple(Symbol('\\\\chi', commutative=True)))", "cos(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "Mul(Symbol('\\\\chi', commutative=True), Add(log(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\omega', commutative=True), exp(Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "\\omega e^{\\alpha}", "variable": "\\alpha", "positive": "\\omega e^{\\alpha}", "negatives": ["\\frac{\\omega^{2} e^{\\alpha}}{2}", "\\alpha (\\log{(\\alpha \\omega)} - 1)", "\\alpha (\\omega + \\log{(\\alpha)} - 1)", "\\alpha (- \\omega + \\log{(\\alpha)} - 1)"], "srepr_premise_expression": "Mul(Symbol('\\\\omega', commutative=True), exp(Symbol('\\\\alpha', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\omega', commutative=True), exp(Symbol('\\\\alpha', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), exp(Symbol('\\\\alpha', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), Add(log(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\alpha', commutative=True)), Integer(-1)))", "Mul(Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), log(Symbol('\\\\alpha', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\psi + \\sigma", "variable": "\\sigma", "positive": "\\frac{\\sigma (2 \\psi + \\sigma)}{2}", "negatives": ["\\frac{\\psi (\\psi + 2 \\sigma)}{2}", "\\frac{\\sigma (\\sigma + 2 \\cos{(\\psi)})}{2}", "\\frac{\\sigma (\\sigma + 2 \\log{(\\psi)})}{2}", "\\psi \\sigma + \\sin{(\\sigma)}"], "srepr_premise_expression": "Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\psi', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(2), cos(Symbol('\\\\psi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(2), log(Symbol('\\\\psi', commutative=True)))))", "Add(Mul(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True)), sin(Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\frac{\\xi}{\\sigma}", "variable": "\\sigma", "positive": "\\xi \\log{(\\sigma)}", "negatives": ["- \\xi \\cos{(\\sigma)}", "\\frac{\\xi^{2}}{2 \\sigma}", "\\sigma \\xi - \\cos{(\\sigma)}", "\\frac{\\sigma^{2}}{2 \\xi}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Symbol('\\\\xi', commutative=True), cos(Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Add(Mul(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))"]}, {"premise_expression": "\\log{(\\alpha \\omega)}", "variable": "\\alpha", "positive": "\\alpha (\\log{(\\alpha \\omega)} - 1)", "negatives": ["\\omega (\\log{(\\alpha \\omega)} - 1)", "\\alpha (\\log{(\\frac{\\alpha}{\\omega})} - 1)", "\\omega \\log{(\\alpha)}", "\\frac{\\alpha^{2} \\log{(\\omega)}}{2}"], "srepr_premise_expression": "log(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\alpha', commutative=True), Add(log(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\omega', commutative=True), Add(log(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\alpha', commutative=True), Add(log(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))), Integer(-1)))", "Mul(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), log(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\frac{\\gamma}{\\beta}", "variable": "\\beta", "positive": "\\gamma \\log{(\\beta)}", "negatives": ["\\frac{\\gamma^{2}}{2 \\beta}", "\\beta \\gamma + \\sin{(\\beta)}", "\\frac{\\beta^{2}}{2 \\gamma}", "\\beta (\\log{(\\frac{\\beta}{\\gamma})} - 1)"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\beta', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)))", "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)), sin(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)))", "Mul(Symbol('\\\\beta', commutative=True), Add(log(Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)))), Integer(-1)))"]}, {"premise_expression": "\\gamma \\xi", "variable": "\\gamma", "positive": "\\frac{\\gamma^{2} \\xi}{2}", "negatives": ["\\frac{\\gamma \\xi^{2}}{2}", "\\xi \\sin{(\\gamma)}", "\\frac{\\sin{(\\gamma)}}{\\xi}", "\\cos{(\\gamma - \\xi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Mul(Symbol('\\\\xi', commutative=True), sin(Symbol('\\\\gamma', commutative=True)))", "Mul(Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), sin(Symbol('\\\\gamma', commutative=True)))", "cos(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "e^{\\beta - \\xi}", "variable": "\\beta", "positive": "e^{\\beta - \\xi}", "negatives": ["- e^{\\beta - \\xi}", "e^{\\beta + \\xi}", "\\frac{\\sin{(\\beta)}}{\\xi}", "\\frac{\\beta (\\beta - 2 \\xi)}{2}"], "srepr_premise_expression": "exp(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "exp(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))))", "exp(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True)))", "Mul(Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), sin(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "e^{- \\chi + \\xi}", "variable": "\\xi", "positive": "e^{- \\chi + \\xi}", "negatives": ["- e^{- \\chi + \\xi}", "- \\sin{(\\chi - \\xi)}", "\\frac{\\xi (2 \\chi - \\xi)}{2}", "\\chi \\sin{(\\xi)}"], "srepr_premise_expression": "exp(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "exp(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\xi', commutative=True))))", "Mul(Integer(-1), sin(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Symbol('\\\\chi', commutative=True), sin(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "- \\alpha + \\xi", "variable": "\\xi", "positive": "\\frac{\\xi (- 2 \\alpha + \\xi)}{2}", "negatives": ["\\frac{\\alpha (- \\alpha + 2 \\xi)}{2}", "e^{- \\alpha + \\xi}", "e^{\\alpha + \\xi}", "\\xi (- \\alpha + \\log{(\\alpha)})"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "exp(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\xi', commutative=True)))", "exp(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), log(Symbol('\\\\alpha', commutative=True))))"]}, {"premise_expression": "\\pi + \\log{(\\omega)}", "variable": "\\omega", "positive": "\\omega (\\pi + \\log{(\\omega)} - 1)", "negatives": ["\\frac{\\pi (\\pi + 2 \\log{(\\omega)})}{2}", "\\omega \\pi + e^{\\omega}", "\\frac{\\omega (- \\omega + 2 \\cos{(\\pi)})}{2}", "\\frac{\\omega (\\omega - 2 \\pi)}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\omega', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), log(Symbol('\\\\omega', commutative=True)))))", "Add(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)), exp(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\pi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\log{(\\gamma^{\\sigma})}", "variable": "\\sigma", "positive": "\\frac{\\sigma^{2} \\log{(\\gamma)}}{2}", "negatives": ["\\log{(\\gamma)} \\log{(\\sigma)}", "\\gamma \\sigma (\\log{(\\sigma)} - 1)", "\\sigma (\\gamma + \\log{(\\sigma)} - 1)", "- \\cos{(\\gamma - \\sigma)}"], "srepr_premise_expression": "log(Pow(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), log(Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(log(Symbol('\\\\gamma', commutative=True)), log(Symbol('\\\\sigma', commutative=True)))", "Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True), Add(log(Symbol('\\\\sigma', commutative=True)), Integer(-1)))", "Mul(Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\sigma', commutative=True)), Integer(-1)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))"]}, {"premise_expression": "\\cos{(\\pi + \\psi)}", "variable": "\\psi", "positive": "\\sin{(\\pi + \\psi)}", "negatives": ["\\frac{\\sin{(\\psi)}}{\\pi}", "\\frac{\\psi (2 \\pi + \\psi)}{2}", "\\frac{\\psi^{2}}{2 \\pi}", "\\pi e^{\\psi}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "sin(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), sin(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "Mul(Symbol('\\\\pi', commutative=True), exp(Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\frac{- \\omega + \\xi}{\\pi}", "variable": "\\omega", "positive": "\\frac{\\omega (- \\omega + 2 \\xi)}{2 \\pi}", "negatives": ["\\frac{\\omega (\\omega + 2 \\xi)}{2 \\pi}", "- \\frac{\\xi (2 \\omega - \\xi)}{2 \\pi}", "(- \\omega + \\xi) \\log{(\\pi)}", "\\frac{\\omega^{2}}{2 \\pi \\xi}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Integer(-1), Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Symbol('\\\\xi', commutative=True)), log(Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))"]}, {"premise_expression": "\\gamma - \\omega", "variable": "\\gamma", "positive": "\\frac{\\gamma (\\gamma - 2 \\omega)}{2}", "negatives": ["\\frac{\\omega (2 \\gamma - \\omega)}{2}", "- \\cos{(\\gamma + \\omega)}", "e^{\\gamma + \\omega}", "- \\frac{\\cos{(\\gamma)}}{\\omega}"], "srepr_premise_expression": "Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True))))", "exp(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), cos(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\log{(\\frac{\\pi}{\\beta})}", "variable": "\\pi", "positive": "\\pi (\\log{(\\frac{\\pi}{\\beta})} - 1)", "negatives": ["\\beta (\\log{(\\frac{\\pi}{\\beta})} + 1)", "\\frac{\\pi (2 \\beta + \\pi)}{2}", "\\sin{(\\beta + \\pi)}", "\\beta \\sin{(\\pi)}"], "srepr_premise_expression": "log(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\pi', commutative=True), Add(log(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\beta', commutative=True), Add(log(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))), Integer(1)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\pi', commutative=True)))", "sin(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\beta', commutative=True), sin(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\delta \\sigma", "variable": "\\delta", "positive": "\\frac{\\delta^{2} \\sigma}{2}", "negatives": ["\\frac{\\delta \\sigma^{2}}{2}", "\\sigma \\log{(\\delta)}", "- \\frac{\\cos{(\\delta)}}{\\sigma}", "\\frac{\\delta (- \\delta + 2 \\sigma)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Symbol('\\\\sigma', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "Mul(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\delta', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), cos(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "- \\delta + \\omega", "variable": "\\omega", "positive": "\\frac{\\omega (- 2 \\delta + \\omega)}{2}", "negatives": ["\\frac{\\omega (2 \\delta + \\omega)}{2}", "\\frac{\\delta (- \\delta + 2 \\omega)}{2}", "- \\cos{(\\delta - \\omega)}", "- \\frac{\\cos{(\\omega)}}{\\delta}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))))", "Mul(Integer(-1), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), cos(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\psi + \\log{(\\beta)}", "variable": "\\beta", "positive": "\\beta (\\psi + \\log{(\\beta)} - 1)", "negatives": ["\\frac{\\psi (\\psi + 2 \\log{(\\beta)})}{2}", "\\frac{\\beta (\\beta + 2 \\psi)}{2}", "\\psi \\log{(\\beta)}", "\\frac{\\beta (\\beta + 2 \\cos{(\\psi)})}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\psi', commutative=True), log(Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\psi', commutative=True), log(Symbol('\\\\beta', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(2), log(Symbol('\\\\beta', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Symbol('\\\\psi', commutative=True), log(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), cos(Symbol('\\\\psi', commutative=True)))))"]}, {"premise_expression": "\\frac{\\beta}{\\alpha}", "variable": "\\alpha", "positive": "\\beta \\log{(\\alpha)}", "negatives": ["\\frac{\\beta^{2}}{2 \\alpha}", "- \\cos{(\\alpha + \\beta)}", "\\alpha \\beta + \\sin{(\\alpha)}", "\\frac{\\alpha (\\alpha + 2 \\beta)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\beta', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\beta', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\beta', commutative=True), Integer(2)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True))))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True)), sin(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\beta', commutative=True))))"]}, {"premise_expression": "- \\beta + \\pi + \\psi", "variable": "\\psi", "positive": "\\psi (- \\beta + \\pi + \\frac{\\psi}{2})", "negatives": ["\\frac{\\psi (2 \\beta + 2 \\pi + \\psi)}{2}", "\\frac{\\psi (2 \\beta + 2 \\pi - \\psi)}{2}", "\\frac{\\beta (- \\beta + 2 \\pi + 2 \\psi)}{2}", "\\frac{\\pi (- 2 \\beta + \\pi + 2 \\psi)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\pi', commutative=True), Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\pi', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "\\sin{(\\omega + \\sigma)}", "variable": "\\omega", "positive": "- \\cos{(\\omega + \\sigma)}", "negatives": ["- e^{- \\omega + \\sigma}", "e^{\\omega + \\sigma}", "\\omega (\\log{(\\omega \\sigma)} - 1)", "\\frac{\\omega^{2}}{2 \\sigma}"], "srepr_premise_expression": "sin(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Symbol('\\\\sigma', commutative=True))))", "exp(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), Add(log(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))"]}, {"premise_expression": "\\frac{\\cos{(\\alpha)}}{\\chi}", "variable": "\\chi", "positive": "\\log{(\\chi)} \\cos{(\\alpha)}", "negatives": ["\\alpha \\log{(\\chi)}", "- \\frac{\\cos{(\\chi)}}{\\alpha}", "\\frac{\\chi (\\chi + 2 \\cos{(\\alpha)})}{2}", "\\alpha e^{\\chi}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), cos(Symbol('\\\\alpha', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(log(Symbol('\\\\chi', commutative=True)), cos(Symbol('\\\\alpha', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\chi', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), cos(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), cos(Symbol('\\\\alpha', commutative=True)))))", "Mul(Symbol('\\\\alpha', commutative=True), exp(Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "\\frac{\\omega}{\\psi}", "variable": "\\omega", "positive": "\\frac{\\omega^{2}}{2 \\psi}", "negatives": ["\\omega \\log{(\\psi)}", "\\psi \\log{(\\omega)}", "\\frac{\\omega^{2} e^{\\psi}}{2}", "\\frac{\\omega^{2} \\log{(\\psi)}}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\psi', commutative=True)))", "Mul(Symbol('\\\\psi', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), exp(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), log(Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "- \\alpha + \\cos{(\\gamma)}", "variable": "\\gamma", "positive": "- \\alpha \\gamma + \\sin{(\\gamma)}", "negatives": ["e^{\\alpha} \\log{(\\gamma)}", "\\frac{\\alpha \\gamma^{2}}{2}", "\\cos{(\\alpha - \\gamma)}", "\\frac{\\alpha (- \\alpha + 2 \\cos{(\\gamma)})}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), cos(Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True)), sin(Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(exp(Symbol('\\\\alpha', commutative=True)), log(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)))", "cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\gamma', commutative=True)))))"]}, {"premise_expression": "\\frac{\\alpha \\xi}{\\sigma}", "variable": "\\alpha", "positive": "\\frac{\\alpha^{2} \\xi}{2 \\sigma}", "negatives": ["\\frac{\\alpha \\xi^{2}}{2 \\sigma}", "\\frac{\\alpha^{2} \\sigma \\xi}{2}", "\\alpha \\xi \\log{(\\sigma)}", "\\frac{\\alpha (\\alpha \\xi - 2 \\sigma)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True))", "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True), log(Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\gamma \\log{(\\xi)}", "variable": "\\xi", "positive": "\\gamma \\xi (\\log{(\\xi)} - 1)", "negatives": ["\\xi (\\log{(\\frac{\\xi}{\\gamma})} - 1)", "\\frac{\\gamma^{2} \\log{(\\xi)}}{2}", "\\frac{\\xi^{2}}{2 \\gamma}", "- \\gamma \\xi - \\cos{(\\xi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True), Add(log(Symbol('\\\\xi', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\xi', commutative=True), Add(log(Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), log(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\xi \\log{(\\chi)}", "variable": "\\xi", "positive": "\\frac{\\xi^{2} \\log{(\\chi)}}{2}", "negatives": ["\\frac{\\xi (2 \\chi + \\xi)}{2}", "\\chi \\log{(\\xi)}", "\\chi \\xi (\\log{(\\chi)} - 1)", "- \\sin{(\\chi - \\xi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), log(Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True), Add(log(Symbol('\\\\chi', commutative=True)), Integer(-1)))", "Mul(Integer(-1), sin(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))))"]}, {"premise_expression": "\\log{(\\chi^{\\gamma})}", "variable": "\\gamma", "positive": "\\frac{\\gamma^{2} \\log{(\\chi)}}{2}", "negatives": ["\\log{(\\chi)} \\log{(\\gamma)}", "\\frac{\\gamma (\\gamma + 2 \\sin{(\\chi)})}{2}", "\\gamma (\\log{(\\chi \\gamma)} - 1)", "- \\chi \\gamma + e^{\\gamma}"], "srepr_premise_expression": "log(Pow(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), log(Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(log(Symbol('\\\\chi', commutative=True)), log(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), sin(Symbol('\\\\chi', commutative=True)))))", "Mul(Symbol('\\\\gamma', commutative=True), Add(log(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True))), Integer(-1)))", "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True)), exp(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\log{(\\alpha + \\pi)}", "variable": "\\alpha", "positive": "\\alpha \\log{(\\alpha + \\pi)} - \\alpha + \\pi \\log{(\\alpha + \\pi)}", "negatives": ["\\alpha \\log{(\\alpha + \\pi)} + \\pi \\log{(\\alpha + \\pi)} - \\pi", "\\frac{\\alpha (\\log{(\\alpha)} - 1)}{\\pi}", "\\alpha (\\log{(\\frac{\\pi}{\\alpha})} + 1)", "\\frac{\\alpha (- \\alpha + 2 \\sin{(\\pi)})}{2}"], "srepr_premise_expression": "log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\alpha', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Symbol('\\\\pi', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\alpha', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)))), Mul(Symbol('\\\\pi', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Add(log(Symbol('\\\\alpha', commutative=True)), Integer(-1)))", "Mul(Symbol('\\\\alpha', commutative=True), Add(log(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))), Integer(1)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\pi', commutative=True)))))"]}, {"premise_expression": "\\delta + \\cos{(\\gamma)}", "variable": "\\gamma", "positive": "\\delta \\gamma + \\sin{(\\gamma)}", "negatives": ["\\delta \\log{(\\gamma)}", "\\frac{\\gamma (- 2 \\delta + \\gamma)}{2}", "\\frac{\\delta (\\delta + 2 \\cos{(\\gamma)})}{2}", "\\sin{(\\delta + \\gamma)}"], "srepr_premise_expression": "Add(Symbol('\\\\delta', commutative=True), cos(Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\gamma', commutative=True)), sin(Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), cos(Symbol('\\\\gamma', commutative=True)))))", "sin(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\frac{\\gamma}{\\xi}", "variable": "\\xi", "positive": "\\gamma \\log{(\\xi)}", "negatives": ["\\frac{\\gamma^{2}}{2 \\xi}", "\\gamma \\xi - \\cos{(\\xi)}", "\\gamma \\xi + e^{\\xi}", "\\sin{(\\gamma + \\xi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "Add(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\xi', commutative=True))))", "Add(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)), exp(Symbol('\\\\xi', commutative=True)))", "sin(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\delta \\pi", "variable": "\\pi", "positive": "\\frac{\\delta \\pi^{2}}{2}", "negatives": ["\\frac{\\delta^{2} \\pi}{2}", "\\delta e^{\\frac{\\pi}{\\delta}}", "\\frac{\\pi (2 \\delta - \\pi)}{2}", "\\frac{\\pi (2 \\delta + \\pi)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Symbol('\\\\pi', commutative=True))", "Mul(Symbol('\\\\delta', commutative=True), exp(Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\frac{\\gamma}{\\beta}", "variable": "\\gamma", "positive": "\\frac{\\gamma^{2}}{2 \\beta}", "negatives": ["\\gamma \\log{(\\beta)}", "\\frac{\\gamma^{2} \\log{(\\beta)}}{2}", "\\frac{\\gamma (- 2 \\beta + \\gamma)}{2}", "\\frac{\\gamma (\\gamma + 2 e^{\\beta})}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), log(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), exp(Symbol('\\\\beta', commutative=True)))))"]}, {"premise_expression": "\\omega \\cos{(\\chi)}", "variable": "\\omega", "positive": "\\frac{\\omega^{2} \\cos{(\\chi)}}{2}", "negatives": ["\\frac{\\omega (2 \\chi + \\omega)}{2}", "\\frac{\\omega (- 2 \\chi + \\omega)}{2}", "\\omega \\sin{(\\chi)}", "\\frac{\\omega (\\omega + 2 \\log{(\\chi)})}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\omega', commutative=True), cos(Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), cos(Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), sin(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), log(Symbol('\\\\chi', commutative=True)))))"]}, {"premise_expression": "\\cos{(\\alpha - \\gamma)}", "variable": "\\gamma", "positive": "- \\sin{(\\alpha - \\gamma)}", "negatives": ["\\sin{(\\alpha - \\gamma)}", "e^{- \\alpha + \\gamma}", "\\cos{(\\alpha - \\gamma)}", "e^{\\alpha + \\gamma}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Integer(-1), sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))))", "srepr_negatives": ["sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "exp(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "exp(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\alpha e^{\\xi}", "variable": "\\xi", "positive": "\\alpha e^{\\xi}", "negatives": ["\\frac{\\alpha^{2} e^{\\xi}}{2}", "\\alpha \\xi + e^{\\xi}", "e^{\\alpha + \\xi}", "\\frac{\\alpha \\xi^{2}}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), exp(Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\alpha', commutative=True), exp(Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), exp(Symbol('\\\\xi', commutative=True)))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True)), exp(Symbol('\\\\xi', commutative=True)))", "exp(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))"]}, {"premise_expression": "- \\alpha + \\beta", "variable": "\\beta", "positive": "\\frac{\\beta (- 2 \\alpha + \\beta)}{2}", "negatives": ["\\frac{\\beta (2 \\alpha - \\beta)}{2}", "\\frac{\\alpha (- \\alpha + 2 \\beta)}{2}", "\\frac{\\beta (- \\beta + 2 \\cos{(\\alpha)})}{2}", "\\frac{\\beta^{2} \\log{(\\alpha)}}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\beta', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\beta', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\beta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\beta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\alpha', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), log(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\frac{\\chi}{\\sigma}", "variable": "\\sigma", "positive": "\\chi \\log{(\\sigma)}", "negatives": ["\\frac{\\chi^{2}}{2 \\sigma}", "\\cos{(\\chi - \\sigma)}", "\\frac{\\sigma^{2} \\cos{(\\chi)}}{2}", "\\frac{\\sigma (- \\sigma + 2 \\cos{(\\chi)})}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "cos(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), cos(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\chi', commutative=True)))))"]}, {"premise_expression": "\\delta \\psi", "variable": "\\delta", "positive": "\\frac{\\delta^{2} \\psi}{2}", "negatives": ["\\frac{\\delta \\psi^{2}}{2}", "\\frac{\\delta^{2} \\cos{(\\psi)}}{2}", "\\psi \\sin{(\\delta)}", "e^{\\delta - \\psi}"], "srepr_premise_expression": "Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), cos(Symbol('\\\\psi', commutative=True)))", "Mul(Symbol('\\\\psi', commutative=True), sin(Symbol('\\\\delta', commutative=True)))", "exp(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "\\delta + \\psi", "variable": "\\psi", "positive": "\\frac{\\psi (2 \\delta + \\psi)}{2}", "negatives": ["\\frac{\\delta (\\delta + 2 \\psi)}{2}", "\\frac{\\psi (\\psi + 2 \\cos{(\\delta)})}{2}", "\\frac{\\delta \\psi^{2}}{2}", "\\frac{\\psi^{2} \\cos{(\\delta)}}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(2), cos(Symbol('\\\\delta', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), cos(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\gamma \\log{(\\psi)}", "variable": "\\psi", "positive": "\\gamma \\psi (\\log{(\\psi)} - 1)", "negatives": ["\\gamma \\log{(\\psi)}", "\\frac{\\gamma^{2} \\log{(\\psi)}}{2}", "- \\cos{(\\gamma - \\psi)}", "e^{- \\gamma + \\psi}"], "srepr_premise_expression": "Mul(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True), Add(log(Symbol('\\\\psi', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), log(Symbol('\\\\psi', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))", "exp(Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\frac{\\sigma}{\\omega}", "variable": "\\sigma", "positive": "\\frac{\\sigma^{2}}{2 \\omega}", "negatives": ["\\sigma \\log{(\\omega)}", "\\omega e^{\\sigma}", "\\frac{\\sigma^{2} \\log{(\\omega)}}{2}", "\\sin{(\\omega + \\sigma)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), exp(Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), log(Symbol('\\\\omega', commutative=True)))", "sin(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\cos{(\\frac{\\alpha}{\\xi})}", "variable": "\\xi", "positive": "\\alpha \\operatorname{Si}{(\\frac{\\alpha}{\\xi})} + \\xi \\cos{(\\frac{\\alpha}{\\xi})}", "negatives": ["- \\alpha \\operatorname{Ei}{(\\frac{\\alpha}{\\xi})} + \\xi e^{\\frac{\\alpha}{\\xi}}", "\\frac{\\xi (- \\xi + 2 \\sin{(\\alpha)})}{2}", "\\frac{\\xi (2 \\alpha - \\xi)}{2}", "- \\cos{(\\alpha - \\xi)}"], "srepr_premise_expression": "cos(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\alpha', commutative=True), Si(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))), Mul(Symbol('\\\\xi', commutative=True), cos(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Ei(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))), Mul(Symbol('\\\\xi', commutative=True), exp(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\alpha', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))))"]}, {"premise_expression": "- \\beta + \\delta + \\sigma", "variable": "\\sigma", "positive": "\\sigma (- \\beta + \\delta + \\frac{\\sigma}{2})", "negatives": ["\\frac{\\beta (- \\beta + 2 \\delta + 2 \\sigma)}{2}", "\\frac{\\delta (- 2 \\beta + \\delta + 2 \\sigma)}{2}", "\\frac{\\sigma^{2}}{2} + \\frac{\\delta \\sigma}{\\beta}", "\\frac{\\beta \\sigma}{\\delta} + \\frac{\\sigma^{2}}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\delta', commutative=True), Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\delta', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Add(Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2))), Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True)))", "Add(Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2))))"]}, {"premise_expression": "\\cos{(\\omega + \\pi)}", "variable": "\\pi", "positive": "\\sin{(\\omega + \\pi)}", "negatives": ["e^{\\omega + \\pi}", "\\cos{(\\omega - \\pi)}", "\\omega \\sin{(\\pi)}", "\\log{(\\omega)} \\log{(\\pi)}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "sin(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["exp(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)))", "cos(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "Mul(Symbol('\\\\omega', commutative=True), sin(Symbol('\\\\pi', commutative=True)))", "Mul(log(Symbol('\\\\omega', commutative=True)), log(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "e^{- \\omega + \\psi}", "variable": "\\omega", "positive": "- e^{- \\omega + \\psi}", "negatives": ["e^{- \\omega + \\psi}", "\\sin{(\\omega + \\psi)}", "\\frac{\\omega (\\omega + 2 \\psi)}{2}", "\\omega (\\log{(\\frac{\\psi}{\\omega})} + 1)"], "srepr_premise_expression": "exp(Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["exp(Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Symbol('\\\\psi', commutative=True)))", "sin(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Symbol('\\\\omega', commutative=True), Add(log(Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True))), Integer(1)))"]}, {"premise_expression": "\\alpha - \\xi", "variable": "\\xi", "positive": "\\frac{\\xi (2 \\alpha - \\xi)}{2}", "negatives": ["\\frac{\\xi (4 \\alpha - \\xi)}{2}", "\\frac{\\alpha \\xi (2 \\alpha - \\xi)}{2}", "\\frac{\\alpha (\\alpha - 2 \\xi)}{2}", "\\frac{\\xi^{2} \\cos{(\\alpha)}}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(4), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), cos(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\cos{(\\chi - \\delta)}", "variable": "\\delta", "positive": "- \\sin{(\\chi - \\delta)}", "negatives": ["\\sin{(\\chi - \\delta)}", "\\frac{\\delta e^{\\chi}}{\\chi}", "\\frac{\\delta^{2} \\log{(\\chi)}}{2}", "e^{\\chi} \\log{(\\delta)}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Integer(-1), sin(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)))))", "srepr_negatives": ["sin(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))", "Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True), exp(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), log(Symbol('\\\\chi', commutative=True)))", "Mul(exp(Symbol('\\\\chi', commutative=True)), log(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\beta \\sigma", "variable": "\\sigma", "positive": "\\frac{\\beta \\sigma^{2}}{2}", "negatives": ["\\frac{\\beta^{2} \\sigma}{2}", "\\beta \\log{(\\sigma)}", "\\sigma", "\\frac{\\sigma (\\sigma + 2 e^{\\beta})}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\sigma', commutative=True))", "Mul(Symbol('\\\\beta', commutative=True), log(Symbol('\\\\sigma', commutative=True)))", "Symbol('\\\\sigma', commutative=True)", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(2), exp(Symbol('\\\\beta', commutative=True)))))"]}, {"premise_expression": "\\pi + \\sigma", "variable": "\\sigma", "positive": "\\frac{\\sigma (2 \\pi + \\sigma)}{2}", "negatives": ["\\frac{\\pi (\\pi + 2 \\sigma)}{2}", "\\frac{\\sigma^{2}}{2 \\pi}", "\\frac{\\sigma (\\sigma + 2 \\sin{(\\pi)})}{2}", "\\frac{\\sigma (- \\sigma + 2 e^{\\pi})}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(2), sin(Symbol('\\\\pi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\pi', commutative=True)))))"]}, {"premise_expression": "\\alpha \\omega", "variable": "\\alpha", "positive": "\\frac{\\alpha^{2} \\omega}{2}", "negatives": ["\\frac{\\alpha \\omega^{2}}{2}", "\\frac{\\alpha^{2}}{2 \\omega}", "e^{\\alpha + \\omega}", "- \\alpha \\omega + e^{\\alpha}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\omega', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))", "exp(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)), exp(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "- \\sin{(\\delta - \\psi)}", "variable": "\\delta", "positive": "\\cos{(\\delta - \\psi)}", "negatives": ["- \\cos{(\\delta - \\psi)}", "\\sin{(\\delta - \\psi)}", "e^{\\delta + \\psi}", "- e^{- \\delta + \\psi}"], "srepr_premise_expression": "Mul(Integer(-1), sin(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))", "sin(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "exp(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\psi', commutative=True)))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "- \\gamma + \\pi", "variable": "\\gamma", "positive": "\\frac{\\gamma (- \\gamma + 2 \\pi)}{2}", "negatives": ["\\frac{\\gamma (\\gamma + 2 \\pi)}{2}", "\\frac{\\gamma (\\gamma - 2 \\pi)}{2}", "\\frac{\\pi (- 2 \\gamma + \\pi)}{2}", "\\frac{\\gamma \\pi (\\gamma - 2)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Integer(-2)))"]}, {"premise_expression": "\\beta + \\delta", "variable": "\\delta", "positive": "\\frac{\\delta (2 \\beta + \\delta)}{2}", "negatives": ["\\frac{\\beta (\\beta + 2 \\delta)}{2}", "- \\sin{(\\beta - \\delta)}", "\\frac{\\delta (\\log{(\\delta)} - 1)}{\\beta}", "\\log{(\\beta)} \\log{(\\delta)}"], "srepr_premise_expression": "Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\delta', commutative=True))))", "Mul(Integer(-1), sin(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)))))", "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True), Add(log(Symbol('\\\\delta', commutative=True)), Integer(-1)))", "Mul(log(Symbol('\\\\beta', commutative=True)), log(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\frac{\\log{(\\psi)}}{\\delta}", "variable": "\\psi", "positive": "\\frac{\\psi (\\log{(\\psi)} - 1)}{\\delta}", "negatives": ["\\psi (\\log{(\\frac{\\psi}{\\delta})} - 1)", "\\psi (\\delta + \\log{(\\psi)} - 1)", "\\log{(\\delta)} \\log{(\\psi)}", "\\log{(\\psi)} \\cos{(\\delta)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), log(Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True), Add(log(Symbol('\\\\psi', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\psi', commutative=True), Add(log(Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\psi', commutative=True)), Integer(-1)))", "Mul(log(Symbol('\\\\delta', commutative=True)), log(Symbol('\\\\psi', commutative=True)))", "Mul(log(Symbol('\\\\psi', commutative=True)), cos(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\delta - \\sigma", "variable": "\\delta", "positive": "\\frac{\\delta (\\delta - 2 \\sigma)}{2}", "negatives": ["\\frac{\\sigma (2 \\delta - \\sigma)}{2}", "\\frac{\\delta (\\delta + 2 \\log{(\\sigma)})}{2}", "\\frac{\\delta (- \\delta + 2 \\cos{(\\sigma)})}{2}", "- \\cos{(\\delta + \\sigma)}"], "srepr_premise_expression": "Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), log(Symbol('\\\\sigma', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\sigma', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\log{(\\gamma + \\xi)}", "variable": "\\gamma", "positive": "\\gamma \\log{(\\gamma + \\xi)} - \\gamma + \\xi \\log{(\\gamma + \\xi)}", "negatives": ["\\gamma \\log{(\\gamma + \\xi)} + \\xi \\log{(\\gamma + \\xi)} - \\xi", "\\gamma \\cos{(\\frac{\\xi}{\\gamma})} + \\xi \\operatorname{Si}{(\\frac{\\xi}{\\gamma})}", "\\gamma e^{\\frac{\\xi}{\\gamma}} - \\xi \\operatorname{Ei}{(\\frac{\\xi}{\\gamma})}", "\\frac{\\gamma (\\gamma + 2 \\log{(\\xi)})}{2}"], "srepr_premise_expression": "log(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\gamma', commutative=True), log(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Symbol('\\\\xi', commutative=True), log(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\gamma', commutative=True), log(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)))), Mul(Symbol('\\\\xi', commutative=True), log(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "Add(Mul(Symbol('\\\\gamma', commutative=True), cos(Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True)))), Mul(Symbol('\\\\xi', commutative=True), Si(Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True)))))", "Add(Mul(Symbol('\\\\gamma', commutative=True), exp(Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\xi', commutative=True), Ei(Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), log(Symbol('\\\\xi', commutative=True)))))"]}, {"premise_expression": "e^{\\alpha - \\chi}", "variable": "\\chi", "positive": "- e^{\\alpha - \\chi}", "negatives": ["e^{\\alpha - \\chi}", "- \\cos{(\\alpha - \\chi)}", "\\frac{\\chi (2 \\alpha + \\chi)}{2}", "\\frac{\\chi^{2}}{2 \\alpha}"], "srepr_premise_expression": "exp(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True))))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Integer(-1), exp(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True)))))", "srepr_negatives": ["exp(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\chi', commutative=True), Integer(2)))"]}, {"premise_expression": "\\frac{\\pi}{\\gamma}", "variable": "\\gamma", "positive": "\\pi \\log{(\\gamma)}", "negatives": ["\\frac{\\pi^{2}}{2 \\gamma}", "\\log{(\\gamma)} \\log{(\\pi)}", "\\gamma \\pi + e^{\\gamma}", "- e^{- \\gamma + \\pi}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "Mul(log(Symbol('\\\\gamma', commutative=True)), log(Symbol('\\\\pi', commutative=True)))", "Add(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True)), exp(Symbol('\\\\gamma', commutative=True)))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\alpha \\sin{(\\chi)}", "variable": "\\alpha", "positive": "\\frac{\\alpha^{2} \\sin{(\\chi)}}{2}", "negatives": ["- \\alpha \\cos{(\\chi)}", "- \\cos{(\\alpha + \\chi)}", "- e^{- \\alpha + \\chi}", "\\alpha (\\log{(\\alpha \\chi)} - 1)"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), sin(Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), sin(Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), cos(Symbol('\\\\chi', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True))))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\chi', commutative=True))))", "Mul(Symbol('\\\\alpha', commutative=True), Add(log(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True))), Integer(-1)))"]}, {"premise_expression": "- \\beta + \\chi + \\xi", "variable": "\\beta", "positive": "\\beta (- \\frac{\\beta}{2} + \\chi + \\xi)", "negatives": ["\\frac{\\beta (- \\beta - 2 \\chi + 2 \\xi)}{2}", "\\frac{\\xi (- 2 \\beta + 2 \\chi + \\xi)}{2}", "\\frac{\\chi (- 2 \\beta + \\chi + 2 \\xi)}{2}", "\\frac{\\beta (\\beta \\xi + 2 \\chi)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Rational(1, 2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), Symbol('\\\\chi', commutative=True))))"]}, {"premise_expression": "- \\delta + \\omega", "variable": "\\omega", "positive": "\\frac{\\omega (- 2 \\delta + \\omega)}{2}", "negatives": ["\\frac{\\delta (- \\delta + 2 \\omega)}{2}", "\\frac{\\omega^{2} \\log{(\\delta)}}{2}", "\\frac{\\omega (- \\omega + 2 \\cos{(\\delta)})}{2}", "\\log{(\\omega)} \\sin{(\\delta)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), log(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\delta', commutative=True)))))", "Mul(log(Symbol('\\\\omega', commutative=True)), sin(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\frac{\\delta}{\\alpha}", "variable": "\\alpha", "positive": "\\delta \\log{(\\alpha)}", "negatives": ["\\delta e^{\\alpha}", "\\frac{\\delta^{2}}{2 \\alpha}", "\\frac{\\alpha^{2}}{2 \\delta}", "\\frac{\\alpha^{2} \\delta}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\delta', commutative=True), exp(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\delta', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\delta', commutative=True))"]}, {"premise_expression": "\\pi \\cos{(\\alpha)}", "variable": "\\alpha", "positive": "\\pi \\sin{(\\alpha)}", "negatives": ["\\frac{\\alpha^{2} \\pi}{2}", "\\sin{(\\alpha - \\pi)}", "\\frac{\\pi^{2} \\cos{(\\alpha)}}{2}", "- \\alpha \\pi + e^{\\alpha}"], "srepr_premise_expression": "Mul(Symbol('\\\\pi', commutative=True), cos(Symbol('\\\\alpha', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\pi', commutative=True), sin(Symbol('\\\\alpha', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\pi', commutative=True))", "sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), cos(Symbol('\\\\alpha', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)), exp(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "- \\xi + \\sin{(\\pi)}", "variable": "\\pi", "positive": "- \\pi \\xi - \\cos{(\\pi)}", "negatives": ["e^{\\xi} \\log{(\\pi)}", "e^{\\pi + \\xi}", "\\frac{\\pi^{2} \\log{(\\xi)}}{2}", "\\frac{\\pi (- \\pi + 2 \\cos{(\\xi)})}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), sin(Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(exp(Symbol('\\\\xi', commutative=True)), log(Symbol('\\\\pi', commutative=True)))", "exp(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), log(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\xi', commutative=True)))))"]}, {"premise_expression": "\\frac{\\sin{(\\xi)}}{\\psi}", "variable": "\\psi", "positive": "\\log{(\\psi)} \\sin{(\\xi)}", "negatives": ["- \\cos{(\\psi + \\xi)}", "\\xi \\log{(\\psi)}", "\\frac{\\psi (\\psi + 2 \\sin{(\\xi)})}{2}", "- \\frac{\\cos{(\\xi)}}{\\psi}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), sin(Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(log(Symbol('\\\\psi', commutative=True)), sin(Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\xi', commutative=True))))", "Mul(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(2), sin(Symbol('\\\\xi', commutative=True)))))", "Mul(Integer(-1), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), cos(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\log{(\\alpha - \\gamma)}", "variable": "\\alpha", "positive": "\\alpha \\log{(\\alpha - \\gamma)} - \\alpha - \\gamma \\log{(\\alpha - \\gamma)}", "negatives": ["- \\alpha \\log{(- \\alpha + \\gamma)} + \\gamma \\log{(\\alpha - \\gamma)} - \\gamma", "\\alpha \\cos{(\\frac{\\gamma}{\\alpha})} + \\gamma \\operatorname{Si}{(\\frac{\\gamma}{\\alpha})}", "\\log{(\\alpha)} \\log{(\\gamma)}", "- \\alpha \\gamma + \\sin{(\\alpha)}"], "srepr_premise_expression": "log(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\alpha', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))), Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\gamma', commutative=True)))), Mul(Symbol('\\\\gamma', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))", "Add(Mul(Symbol('\\\\alpha', commutative=True), cos(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True)))), Mul(Symbol('\\\\gamma', commutative=True), Si(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True)))))", "Mul(log(Symbol('\\\\alpha', commutative=True)), log(Symbol('\\\\gamma', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True)), sin(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "e^{\\frac{\\chi}{\\delta}}", "variable": "\\chi", "positive": "\\delta e^{\\frac{\\chi}{\\delta}}", "negatives": ["\\chi \\delta + e^{\\chi}", "\\frac{\\chi^{2}}{2 \\delta}", "\\sin{(\\chi + \\delta)}", "\\frac{\\chi^{2} \\cos{(\\delta)}}{2}"], "srepr_premise_expression": "exp(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\delta', commutative=True), exp(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True)), exp(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)))", "sin(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), cos(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\log{(\\frac{\\omega}{\\sigma})}", "variable": "\\sigma", "positive": "\\sigma (\\log{(\\frac{\\omega}{\\sigma})} + 1)", "negatives": ["\\omega (\\log{(\\frac{\\omega}{\\sigma})} - 1)", "\\sin{(\\omega + \\sigma)}", "- \\omega \\cos{(\\sigma)}", "\\frac{\\sigma (\\sigma + 2 \\log{(\\omega)})}{2}"], "srepr_premise_expression": "log(Mul(Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\sigma', commutative=True), Add(log(Mul(Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))), Integer(1)))", "srepr_negatives": ["Mul(Symbol('\\\\omega', commutative=True), Add(log(Mul(Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))), Integer(-1)))", "sin(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True)))", "Mul(Integer(-1), Symbol('\\\\omega', commutative=True), cos(Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(2), log(Symbol('\\\\omega', commutative=True)))))"]}, {"premise_expression": "- \\omega + \\log{(\\psi)}", "variable": "\\omega", "positive": "\\frac{\\omega (- \\omega + 2 \\log{(\\psi)})}{2}", "negatives": ["\\frac{\\omega (- \\omega + 2 \\psi)}{2}", "\\psi (- \\omega + \\log{(\\psi)} - 1)", "\\omega \\psi - \\cos{(\\omega)}", "\\omega (\\log{(\\omega \\psi)} - 1)"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), log(Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), log(Symbol('\\\\psi', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), log(Symbol('\\\\psi', commutative=True)), Integer(-1)))", "Add(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\omega', commutative=True))))", "Mul(Symbol('\\\\omega', commutative=True), Add(log(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True))), Integer(-1)))"]}, {"premise_expression": "- \\chi + \\delta", "variable": "\\delta", "positive": "\\frac{\\delta (- 2 \\chi + \\delta)}{2}", "negatives": ["\\frac{\\delta (2 \\chi + \\delta)}{2}", "\\frac{\\delta (2 \\chi - \\delta)}{2}", "\\frac{\\chi (- \\chi + 2 \\delta)}{2}", "- \\sin{(\\chi - \\delta)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\delta', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\delta', commutative=True))))", "Mul(Integer(-1), sin(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)))))"]}, {"premise_expression": "\\cos^{\\chi}{(\\pi)}", "variable": "\\pi", "positive": "\\int \\cos^{\\chi}{(\\pi)} d\\pi", "negatives": ["\\pi (- \\chi + \\log{(\\pi^{\\chi})})", "- \\chi \\pi - \\cos{(\\pi)}", "e^{\\chi + \\pi}", "\\frac{\\pi^{2} \\log{(\\chi)}}{2}"], "srepr_premise_expression": "Pow(cos(Symbol('\\\\pi', commutative=True)), Symbol('\\\\chi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Integral(Pow(cos(Symbol('\\\\pi', commutative=True)), Symbol('\\\\chi', commutative=True)), Tuple(Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), log(Pow(Symbol('\\\\pi', commutative=True), Symbol('\\\\chi', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\pi', commutative=True))))", "exp(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), log(Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "e^{\\frac{\\gamma}{\\sigma}}", "variable": "\\gamma", "positive": "\\sigma e^{\\frac{\\gamma}{\\sigma}}", "negatives": ["\\sigma \\sin{(\\gamma)}", "e^{\\gamma + \\sigma}", "\\frac{\\gamma^{2} \\cos{(\\sigma)}}{2}", "\\gamma (\\log{(\\frac{\\gamma}{\\sigma})} - 1)"], "srepr_premise_expression": "exp(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\sigma', commutative=True), exp(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))))", "srepr_negatives": ["Mul(Symbol('\\\\sigma', commutative=True), sin(Symbol('\\\\gamma', commutative=True)))", "exp(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), cos(Symbol('\\\\sigma', commutative=True)))", "Mul(Symbol('\\\\gamma', commutative=True), Add(log(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))), Integer(-1)))"]}, {"premise_expression": "e^{\\frac{\\gamma}{\\pi}}", "variable": "\\gamma", "positive": "\\pi e^{\\frac{\\gamma}{\\pi}}", "negatives": ["\\frac{\\gamma^{2} \\pi}{2}", "e^{\\gamma + \\pi}", "\\frac{\\gamma^{2} \\log{(\\pi)}}{2}", "- \\cos{(\\gamma - \\pi)}"], "srepr_premise_expression": "exp(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\pi', commutative=True), exp(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Symbol('\\\\pi', commutative=True))", "exp(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), log(Symbol('\\\\pi', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))"]}, {"premise_expression": "\\alpha + \\cos{(\\delta)}", "variable": "\\alpha", "positive": "\\frac{\\alpha (\\alpha + 2 \\cos{(\\delta)})}{2}", "negatives": ["\\frac{\\alpha (\\alpha + 2 \\log{(\\delta)})}{2}", "\\alpha \\delta + \\sin{(\\delta)}", "\\alpha \\delta + e^{\\alpha}", "\\log{(\\alpha)} \\log{(\\delta)}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), cos(Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), cos(Symbol('\\\\delta', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), log(Symbol('\\\\delta', commutative=True)))))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\delta', commutative=True)), sin(Symbol('\\\\delta', commutative=True)))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\delta', commutative=True)), exp(Symbol('\\\\alpha', commutative=True)))", "Mul(log(Symbol('\\\\alpha', commutative=True)), log(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\delta + \\psi", "variable": "\\psi", "positive": "\\frac{\\psi (2 \\delta + \\psi)}{2}", "negatives": ["\\frac{\\delta (\\delta + 2 \\psi)}{2}", "- \\sin{(\\delta - \\psi)}", "- \\cos{(\\delta - \\psi)}", "\\frac{\\psi (\\psi + 2 \\sin{(\\delta)})}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Integer(-1), sin(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(2), sin(Symbol('\\\\delta', commutative=True)))))"]}, {"premise_expression": "\\frac{\\pi}{\\sigma}", "variable": "\\sigma", "positive": "\\pi \\log{(\\sigma)}", "negatives": ["\\frac{\\pi^{2}}{2 \\sigma}", "\\pi \\sigma - \\cos{(\\sigma)}", "- \\cos{(\\pi + \\sigma)}", "\\cos{(\\pi - \\sigma)}"], "srepr_premise_expression": "Mul(Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "Add(Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\sigma', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True))))", "cos(Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\frac{\\beta}{\\omega}", "variable": "\\beta", "positive": "\\frac{\\beta^{2}}{2 \\omega}", "negatives": ["\\beta \\log{(\\omega)}", "\\frac{\\beta^{2} \\cos{(\\omega)}}{2}", "\\frac{\\sin{(\\beta)}}{\\omega}", "\\beta \\omega - \\cos{(\\beta)}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\beta', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), cos(Symbol('\\\\omega', commutative=True)))", "Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), sin(Symbol('\\\\beta', commutative=True)))", "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\beta', commutative=True))))"]}, {"premise_expression": "\\log{(\\frac{\\chi}{\\alpha})}", "variable": "\\alpha", "positive": "\\alpha (\\log{(\\frac{\\chi}{\\alpha})} + 1)", "negatives": ["\\chi (\\log{(\\frac{\\chi}{\\alpha})} - 1)", "\\alpha \\chi (\\log{(\\alpha)} - 1)", "\\frac{\\alpha (\\alpha + 2 \\chi)}{2}", "\\frac{\\alpha (\\alpha + 2 \\cos{(\\chi)})}{2}"], "srepr_premise_expression": "log(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\alpha', commutative=True), Add(log(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\chi', commutative=True))), Integer(1)))", "srepr_negatives": ["Mul(Symbol('\\\\chi', commutative=True), Add(log(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\chi', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True), Add(log(Symbol('\\\\alpha', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\chi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), cos(Symbol('\\\\chi', commutative=True)))))"]}, {"premise_expression": "- \\delta + \\cos{(\\omega)}", "variable": "\\delta", "positive": "\\frac{\\delta (- \\delta + 2 \\cos{(\\omega)})}{2}", "negatives": ["\\frac{\\delta (\\delta + 2 \\log{(\\omega)})}{2}", "\\frac{\\delta^{2} \\cos{(\\omega)}}{2}", "\\log{(\\delta)} \\cos{(\\omega)}", "- \\delta \\omega + \\sin{(\\omega)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), cos(Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\omega', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), log(Symbol('\\\\omega', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), cos(Symbol('\\\\omega', commutative=True)))", "Mul(log(Symbol('\\\\delta', commutative=True)), cos(Symbol('\\\\omega', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True)), sin(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\frac{\\sigma}{\\pi}", "variable": "\\pi", "positive": "\\sigma \\log{(\\pi)}", "negatives": ["\\sigma \\sin{(\\pi)}", "\\frac{\\sigma^{2}}{2 \\pi}", "\\frac{\\sin{(\\pi)}}{\\sigma}", "\\frac{\\pi (\\log{(\\pi)} - 1)}{\\sigma}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\sigma', commutative=True), sin(Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "Mul(Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), sin(Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Add(log(Symbol('\\\\pi', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\frac{\\pi}{\\delta}", "variable": "\\delta", "positive": "\\pi \\log{(\\delta)}", "negatives": ["\\frac{\\pi^{2}}{2 \\delta}", "\\frac{\\delta^{2} \\pi}{2}", "\\frac{\\delta^{2} \\log{(\\pi)}}{2}", "- \\cos{(\\delta + \\pi)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Symbol('\\\\pi', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), log(Symbol('\\\\pi', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\frac{\\cos{(\\xi)}}{\\beta}", "variable": "\\beta", "positive": "\\log{(\\beta)} \\cos{(\\xi)}", "negatives": ["e^{\\xi} \\log{(\\beta)}", "e^{\\beta + \\xi}", "\\frac{\\beta (\\beta + 2 \\cos{(\\xi)})}{2}", "\\frac{\\sin{(\\xi)}}{\\beta}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), cos(Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(log(Symbol('\\\\beta', commutative=True)), cos(Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(exp(Symbol('\\\\xi', commutative=True)), log(Symbol('\\\\beta', commutative=True)))", "exp(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), cos(Symbol('\\\\xi', commutative=True)))))", "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), sin(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\alpha^{\\chi} - \\beta", "variable": "\\beta", "positive": "\\frac{\\beta (2 \\alpha^{\\chi} - \\beta)}{2}", "negatives": ["\\frac{\\beta (2 \\alpha \\chi + \\beta)}{2}", "\\frac{\\beta \\chi (2 \\alpha - \\beta)}{2}", "\\frac{\\beta (- 2 \\alpha + \\beta \\chi)}{2}", "\\beta (2 \\alpha + \\chi)"], "srepr_premise_expression": "Add(Pow(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(2), Pow(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True))), Mul(Integer(-1), Symbol('\\\\beta', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)), Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\beta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True))))", "Mul(Symbol('\\\\beta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "- \\sin{(\\beta - \\chi)}", "variable": "\\beta", "positive": "\\cos{(\\beta - \\chi)}", "negatives": ["- \\cos{(\\beta - \\chi)}", "- \\chi \\cos{(\\beta)}", "\\frac{\\beta (\\log{(\\beta)} - 1)}{\\chi}", "\\beta (\\log{(\\beta^{2})} - 2)"], "srepr_premise_expression": "Mul(Integer(-1), sin(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True)))))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True)))))", "Mul(Integer(-1), Symbol('\\\\chi', commutative=True), cos(Symbol('\\\\beta', commutative=True)))", "Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Add(log(Symbol('\\\\beta', commutative=True)), Integer(-1)))", "Mul(Symbol('\\\\beta', commutative=True), Add(log(Pow(Symbol('\\\\beta', commutative=True), Integer(2))), Integer(-2)))"]}, {"premise_expression": "\\cos^{\\xi}{(\\alpha)}", "variable": "\\alpha", "positive": "\\int \\cos^{\\xi}{(\\alpha)} d\\alpha", "negatives": ["- \\frac{\\cos{(\\alpha)}}{\\xi}", "\\xi \\log{(\\alpha)}", "\\frac{\\alpha^{2} \\log{(\\xi)}}{2}", "\\frac{\\alpha (\\alpha - 2 \\xi)}{2}"], "srepr_premise_expression": "Pow(cos(Symbol('\\\\alpha', commutative=True)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Integral(Pow(cos(Symbol('\\\\alpha', commutative=True)), Symbol('\\\\xi', commutative=True)), Tuple(Symbol('\\\\alpha', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), cos(Symbol('\\\\alpha', commutative=True)))", "Mul(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), log(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\beta + \\delta + \\gamma", "variable": "\\beta", "positive": "\\beta (\\frac{\\beta}{2} + \\delta + \\gamma)", "negatives": ["\\frac{\\beta (\\beta + 2 \\delta - 2 \\gamma)}{2}", "\\frac{\\gamma (2 \\beta + 2 \\delta + \\gamma)}{2}", "\\frac{\\delta (2 \\beta + \\delta + 2 \\gamma)}{2}", "\\frac{\\beta (- \\beta + 2 \\gamma)}{2 \\delta}"], "srepr_premise_expression": "Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True), Symbol('\\\\gamma', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\beta', commutative=True), Add(Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\delta', commutative=True), Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\delta', commutative=True), Mul(Integer(2), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\gamma', commutative=True))))"]}, {"premise_expression": "\\frac{\\log{(\\omega)}}{\\xi}", "variable": "\\omega", "positive": "\\frac{\\omega (\\log{(\\omega)} - 1)}{\\xi}", "negatives": ["\\xi \\log{(\\omega)}", "\\log{(\\omega)} \\log{(\\xi)}", "\\frac{\\omega (- \\omega + 2 \\xi)}{2}", "e^{\\omega + \\xi}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), log(Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), Add(log(Symbol('\\\\omega', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "Mul(log(Symbol('\\\\omega', commutative=True)), log(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "exp(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\frac{\\delta}{\\chi \\sigma}", "variable": "\\chi", "positive": "\\frac{\\delta \\log{(\\chi)}}{\\sigma}", "negatives": ["\\frac{\\delta \\log{(\\sigma)}}{\\chi}", "\\frac{\\delta^{2}}{2 \\chi \\sigma}", "\\frac{\\chi (- \\chi + 2 \\delta \\sigma)}{2}", "- \\frac{\\chi^{2}}{2} + \\frac{\\chi \\sigma}{\\delta}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), log(Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True), log(Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True))))", "Add(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2))), Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\log{(\\alpha + \\sigma)}", "variable": "\\sigma", "positive": "\\alpha \\log{(\\alpha + \\sigma)} + \\sigma \\log{(\\alpha + \\sigma)} - \\sigma", "negatives": ["- \\alpha \\log{(- \\alpha + \\sigma)} + \\sigma \\log{(\\alpha - \\sigma)} - \\sigma", "\\alpha \\log{(\\alpha + \\sigma)} - \\alpha + \\sigma \\log{(\\alpha + \\sigma)}", "\\sigma (\\alpha + \\log{(\\sigma)} - 1)", "\\alpha \\sigma + e^{\\sigma}"], "srepr_premise_expression": "log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\alpha', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True)))), Mul(Symbol('\\\\sigma', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True)))), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\sigma', commutative=True)))), Mul(Symbol('\\\\sigma', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))", "Add(Mul(Symbol('\\\\alpha', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True)))), Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Symbol('\\\\sigma', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True)))))", "Mul(Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\sigma', commutative=True)), Integer(-1)))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True)), exp(Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\cos{(\\omega + \\pi)}", "variable": "\\pi", "positive": "\\sin{(\\omega + \\pi)}", "negatives": ["- \\cos{(\\omega + \\pi)}", "\\frac{\\pi (2 \\omega + \\pi)}{2}", "\\frac{\\pi (2 \\omega - \\pi)}{2}", "\\omega \\pi + e^{\\pi}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "sin(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "Add(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)), exp(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\frac{\\pi}{\\psi} - \\sigma", "variable": "\\sigma", "positive": "\\frac{\\pi \\sigma}{\\psi} - \\frac{\\sigma^{2}}{2}", "negatives": ["\\frac{\\sigma^{2}}{2} + \\frac{\\psi \\sigma}{\\pi}", "\\frac{\\sigma^{2} (\\pi - \\psi)}{2}", "\\frac{\\pi \\sigma (- 2 \\psi + \\sigma)}{2}", "\\frac{\\psi \\sigma (- 2 \\pi + \\sigma)}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1))), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2))))", "srepr_negatives": ["Add(Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2))), Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True)), Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\frac{\\delta + \\omega}{\\chi}", "variable": "\\delta", "positive": "\\frac{\\delta (\\delta + 2 \\omega)}{2 \\chi}", "negatives": ["\\frac{\\omega (2 \\delta + \\omega)}{2 \\chi}", "\\frac{\\delta (2 \\chi \\omega + \\delta)}{2}", "\\frac{\\delta \\omega (2 \\chi + \\delta)}{2}", "\\frac{\\delta (2 \\chi + \\delta \\omega)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True)), Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True))))"]}, {"premise_expression": "e^{\\frac{\\gamma}{\\psi}}", "variable": "\\psi", "positive": "- \\gamma \\operatorname{Ei}{(\\frac{\\gamma}{\\psi})} + \\psi e^{\\frac{\\gamma}{\\psi}}", "negatives": ["\\psi e^{\\frac{\\gamma}{\\psi}}", "e^{- \\gamma + \\psi}", "e^{\\gamma + \\psi}", "\\frac{\\psi (\\log{(\\psi)} - 1)}{\\gamma}"], "srepr_premise_expression": "exp(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Ei(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1))))), Mul(Symbol('\\\\psi', commutative=True), exp(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1))))))", "srepr_negatives": ["Mul(Symbol('\\\\psi', commutative=True), exp(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))))", "exp(Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\psi', commutative=True)))", "exp(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True)))", "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True), Add(log(Symbol('\\\\psi', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\gamma - \\pi", "variable": "\\gamma", "positive": "\\frac{\\gamma (\\gamma - 2 \\pi)}{2}", "negatives": ["\\frac{\\pi (2 \\gamma - \\pi)}{2}", "\\frac{\\gamma^{2}}{2 \\pi}", "e^{\\gamma - \\pi}", "- \\cos{(\\gamma + \\pi)}"], "srepr_premise_expression": "Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))", "exp(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "- \\omega + \\frac{\\xi}{\\gamma}", "variable": "\\gamma", "positive": "- \\gamma \\omega + \\xi \\log{(\\gamma)}", "negatives": ["- \\omega \\xi + \\frac{\\xi^{2}}{2 \\gamma}", "\\omega^{\\xi} \\log{(\\gamma)}", "\\omega \\xi \\log{(\\gamma)}", "- \\frac{\\omega^{2}}{2} + \\frac{\\omega \\xi}{\\gamma}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\gamma', commutative=True))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Integer(2))))", "Mul(Pow(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True)), log(Symbol('\\\\gamma', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "Add(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2))), Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\log{(\\frac{\\gamma}{\\sigma})}", "variable": "\\gamma", "positive": "\\gamma (\\log{(\\frac{\\gamma}{\\sigma})} - 1)", "negatives": ["\\sigma (\\log{(\\frac{\\gamma}{\\sigma})} + 1)", "\\sigma e^{\\frac{\\gamma}{\\sigma}}", "\\log{(\\gamma)} \\sin{(\\sigma)}", "\\frac{\\gamma (\\gamma - 2 \\sigma)}{2}"], "srepr_premise_expression": "log(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\gamma', commutative=True), Add(log(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\sigma', commutative=True), Add(log(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Symbol('\\\\sigma', commutative=True), exp(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))))", "Mul(log(Symbol('\\\\gamma', commutative=True)), sin(Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\log{(\\beta + \\gamma)}", "variable": "\\beta", "positive": "\\beta \\log{(\\beta + \\gamma)} - \\beta + \\gamma \\log{(\\beta + \\gamma)}", "negatives": ["\\beta \\log{(\\beta + \\gamma)} + \\gamma \\log{(\\beta + \\gamma)} - \\gamma", "\\beta \\gamma + e^{\\beta}", "\\beta \\gamma \\cos{(\\gamma)}", "e^{\\beta + \\gamma}"], "srepr_premise_expression": "log(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\beta', commutative=True), log(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)))), Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Symbol('\\\\gamma', commutative=True), log(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\beta', commutative=True), log(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)))), Mul(Symbol('\\\\gamma', commutative=True), log(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)))), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))", "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)), exp(Symbol('\\\\beta', commutative=True)))", "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True), cos(Symbol('\\\\gamma', commutative=True)))", "exp(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\chi \\pi", "variable": "\\pi", "positive": "\\frac{\\chi \\pi^{2}}{2}", "negatives": ["\\frac{\\chi^{2} \\pi}{2}", "\\frac{\\pi (- 2 \\chi + \\pi)}{2}", "e^{- \\chi + \\pi}", "e^{\\chi + \\pi}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\pi', commutative=True))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\pi', commutative=True)))", "exp(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\pi', commutative=True)))", "exp(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\frac{\\alpha}{\\chi}", "variable": "\\alpha", "positive": "\\frac{\\alpha^{2}}{2 \\chi}", "negatives": ["\\alpha \\log{(\\chi)}", "\\frac{\\alpha^{2} \\cos{(\\chi)}}{2}", "2 \\alpha \\chi", "\\cos{(\\alpha - \\chi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), cos(Symbol('\\\\chi', commutative=True)))", "Mul(Integer(2), Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True))", "cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True))))"]}, {"premise_expression": "\\pi + \\sigma", "variable": "\\pi", "positive": "\\frac{\\pi (\\pi + 2 \\sigma)}{2}", "negatives": ["\\frac{\\pi (- \\pi + 2 \\sigma)}{2}", "\\frac{\\sigma (2 \\pi + \\sigma)}{2}", "\\frac{\\pi^{2} \\sigma}{2}", "\\pi \\sigma + e^{\\pi}"], "srepr_premise_expression": "Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), Symbol('\\\\sigma', commutative=True))", "Add(Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True)), exp(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\log{(\\frac{\\sigma}{\\omega})}", "variable": "\\omega", "positive": "\\omega (\\log{(\\frac{\\sigma}{\\omega})} + 1)", "negatives": ["\\sigma (\\log{(\\frac{\\sigma}{\\omega})} - 1)", "\\frac{\\omega (\\log{(\\omega)} - 1)}{\\sigma}", "- \\cos{(\\omega + \\sigma)}", "\\omega e^{\\sigma^{\\sigma}}"], "srepr_premise_expression": "log(Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\omega', commutative=True), Add(log(Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))), Integer(1)))", "srepr_negatives": ["Mul(Symbol('\\\\sigma', commutative=True), Add(log(Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Add(log(Symbol('\\\\omega', commutative=True)), Integer(-1)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True))))", "Mul(Symbol('\\\\omega', commutative=True), exp(Pow(Symbol('\\\\sigma', commutative=True), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\log{(\\gamma + \\sigma)}", "variable": "\\gamma", "positive": "\\gamma \\log{(\\gamma + \\sigma)} - \\gamma + \\sigma \\log{(\\gamma + \\sigma)}", "negatives": ["\\gamma \\log{(\\gamma - \\sigma)} - \\gamma - \\sigma \\log{(\\gamma - \\sigma)}", "\\gamma \\log{(\\gamma + \\sigma)} + \\sigma \\log{(\\gamma + \\sigma)} - \\sigma", "\\gamma (\\log{(\\frac{\\gamma}{\\sigma})} - 1)", "\\gamma (\\log{(\\frac{\\sigma}{\\gamma})} + 1)"], "srepr_premise_expression": "log(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\gamma', commutative=True), log(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True)))), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Symbol('\\\\sigma', commutative=True), log(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\gamma', commutative=True), log(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True), log(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))))", "Add(Mul(Symbol('\\\\gamma', commutative=True), log(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True)))), Mul(Symbol('\\\\sigma', commutative=True), log(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True)))), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))", "Mul(Symbol('\\\\gamma', commutative=True), Add(log(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))), Integer(-1)))", "Mul(Symbol('\\\\gamma', commutative=True), Add(log(Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))), Integer(1)))"]}, {"premise_expression": "\\gamma \\pi", "variable": "\\gamma", "positive": "\\frac{\\gamma^{2} \\pi}{2}", "negatives": ["\\frac{\\gamma \\pi^{2}}{2}", "\\pi e^{\\frac{\\gamma}{\\pi}}", "\\log{(\\gamma)} \\cos{(\\pi)}", "\\log{(\\gamma)} \\log{(\\pi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Symbol('\\\\pi', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "Mul(Symbol('\\\\pi', commutative=True), exp(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))))", "Mul(log(Symbol('\\\\gamma', commutative=True)), cos(Symbol('\\\\pi', commutative=True)))", "Mul(log(Symbol('\\\\gamma', commutative=True)), log(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "- \\gamma + \\omega", "variable": "\\gamma", "positive": "\\frac{\\gamma (- \\gamma + 2 \\omega)}{2}", "negatives": ["\\frac{\\omega (- 2 \\gamma + \\omega)}{2}", "\\frac{\\gamma^{2} \\log{(\\omega)}}{2}", "e^{\\gamma - \\omega}", "- \\frac{\\cos{(\\gamma)}}{\\omega}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), log(Symbol('\\\\omega', commutative=True)))", "exp(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "Mul(Integer(-1), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), cos(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "- \\psi + \\xi", "variable": "\\psi", "positive": "\\frac{\\psi (- \\psi + 2 \\xi)}{2}", "negatives": ["\\frac{\\xi (- 2 \\psi + \\xi)}{2}", "\\cos{(\\psi - \\xi)}", "\\frac{\\psi (\\log{(\\psi)} - 1)}{\\xi}", "- \\xi \\cos{(\\psi)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True)), Symbol('\\\\xi', commutative=True)))", "cos(Add(Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Symbol('\\\\psi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), Add(log(Symbol('\\\\psi', commutative=True)), Integer(-1)))", "Mul(Integer(-1), Symbol('\\\\xi', commutative=True), cos(Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\delta + \\omega", "variable": "\\delta", "positive": "\\frac{\\delta (\\delta + 2 \\omega)}{2}", "negatives": ["\\frac{\\omega (2 \\delta + \\omega)}{2}", "\\frac{\\delta (\\delta + 2 \\log{(\\omega)})}{2}", "\\sin{(\\delta - \\omega)}", "\\frac{\\delta^{2}}{2 \\omega} + \\delta"], "srepr_premise_expression": "Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), log(Symbol('\\\\omega', commutative=True)))))", "sin(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "Add(Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Pow(Symbol('\\\\omega', commutative=True), Integer(-1))), Symbol('\\\\delta', commutative=True))"]}, {"premise_expression": "- \\chi + \\xi", "variable": "\\chi", "positive": "\\frac{\\chi (- \\chi + 2 \\xi)}{2}", "negatives": ["\\frac{\\xi (- 2 \\chi + \\xi)}{2}", "\\frac{\\chi^{2} \\xi}{2}", "\\sin{(\\chi + \\xi)}", "- \\cos{(\\chi + \\xi)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))", "sin(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\log{(\\chi \\delta)}", "variable": "\\delta", "positive": "\\delta (\\log{(\\chi \\delta)} - 1)", "negatives": ["\\chi (\\log{(\\chi \\delta)} - 1)", "\\delta (- \\chi + \\log{(\\delta)} - 1)", "\\frac{\\delta (2 \\chi + \\delta)}{2}", "\\chi^{\\chi} \\delta"], "srepr_premise_expression": "log(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\delta', commutative=True), Add(log(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\chi', commutative=True), Add(log(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), log(Symbol('\\\\delta', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\delta', commutative=True)))", "Mul(Pow(Symbol('\\\\chi', commutative=True), Symbol('\\\\chi', commutative=True)), Symbol('\\\\delta', commutative=True))"]}, {"premise_expression": "\\delta + e^{\\beta}", "variable": "\\beta", "positive": "\\beta \\delta + e^{\\beta}", "negatives": ["\\beta \\delta + \\sin{(\\beta)}", "\\beta (- \\delta + e^{\\delta})", "\\frac{\\delta (\\delta + 2 e^{\\beta})}{2}", "\\frac{\\beta (\\beta + 2 \\delta)}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\delta', commutative=True), exp(Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True)), exp(Symbol('\\\\beta', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True)), sin(Symbol('\\\\beta', commutative=True)))", "Mul(Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), exp(Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), exp(Symbol('\\\\beta', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\delta', commutative=True))))"]}, {"premise_expression": "\\frac{\\gamma}{\\alpha}", "variable": "\\alpha", "positive": "\\gamma \\log{(\\alpha)}", "negatives": ["\\frac{\\gamma^{2}}{2 \\alpha}", "\\alpha \\log{(\\gamma^{\\gamma})}", "\\alpha \\gamma (\\log{(\\alpha)} - 1)", "- \\alpha \\gamma + e^{\\alpha}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)))", "Mul(Symbol('\\\\alpha', commutative=True), log(Pow(Symbol('\\\\gamma', commutative=True), Symbol('\\\\gamma', commutative=True))))", "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True), Add(log(Symbol('\\\\alpha', commutative=True)), Integer(-1)))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True)), exp(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\psi - \\xi", "variable": "\\xi", "positive": "\\frac{\\xi (2 \\psi - \\xi)}{2}", "negatives": ["\\frac{\\psi (\\psi - 2 \\xi)}{2}", "\\frac{\\xi (- \\xi + 2 \\sin{(\\psi)})}{2}", "\\frac{\\xi^{2} e^{\\psi}}{2}", "e^{\\psi + \\xi}"], "srepr_premise_expression": "Add(Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\psi', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), exp(Symbol('\\\\psi', commutative=True)))", "exp(Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\frac{\\psi}{\\omega}", "variable": "\\psi", "positive": "\\frac{\\psi^{2}}{2 \\omega}", "negatives": ["\\psi \\log{(\\omega)}", "\\omega \\sin{(\\psi)}", "\\frac{\\psi (2 \\omega + \\psi)}{2}", "- \\sin{(\\omega - \\psi)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('\\\\psi', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), sin(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))"]}, {"premise_expression": "\\sin^{\\omega}{(\\sigma)}", "variable": "\\sigma", "positive": "\\int \\sin^{\\omega}{(\\sigma)} d\\sigma", "negatives": ["\\sin{(\\omega + \\sigma)}", "\\omega e^{\\frac{\\sigma}{\\omega}}", "\\cos{(\\omega - \\sigma)}", "\\frac{\\sigma^{2}}{2 \\omega}"], "srepr_premise_expression": "Pow(sin(Symbol('\\\\sigma', commutative=True)), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Integral(Pow(sin(Symbol('\\\\sigma', commutative=True)), Symbol('\\\\omega', commutative=True)), Tuple(Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["sin(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), exp(Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))))", "cos(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))"]}, {"premise_expression": "\\frac{\\psi}{\\chi}", "variable": "\\chi", "positive": "\\psi \\log{(\\chi)}", "negatives": ["\\frac{\\psi^{2}}{2 \\chi}", "e^{\\chi - \\psi}", "\\frac{\\chi (- \\chi + 2 \\psi)}{2}", "\\frac{\\chi^{2} \\sin{(\\psi)}}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\psi', commutative=True), log(Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "exp(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), sin(Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\alpha + \\frac{\\beta}{\\xi}", "variable": "\\xi", "positive": "\\alpha \\xi + \\beta \\log{(\\xi)}", "negatives": ["\\alpha \\beta + \\frac{\\beta^{2}}{2 \\xi}", "\\frac{\\alpha^{2}}{2} + \\frac{\\alpha \\beta}{\\xi}", "\\xi (\\beta + \\xi)", "\\frac{\\beta \\xi^{2}}{2 \\alpha}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Symbol('\\\\beta', commutative=True), log(Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))", "Add(Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2))), Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))", "Mul(Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))"]}, {"premise_expression": "\\delta + \\xi", "variable": "\\xi", "positive": "\\frac{\\xi (2 \\delta + \\xi)}{2}", "negatives": ["\\frac{\\delta (\\delta + 2 \\xi)}{2}", "\\frac{\\xi^{2} e^{\\delta}}{2}", "- \\cos{(\\delta + \\xi)}", "\\cos{(\\delta - \\xi)}"], "srepr_premise_expression": "Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), exp(Symbol('\\\\delta', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True))))", "cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\omega + e^{\\delta}", "variable": "\\omega", "positive": "\\frac{\\omega (\\omega + 2 e^{\\delta})}{2}", "negatives": ["\\frac{\\omega (\\omega + 2 \\sin{(\\delta)})}{2}", "\\delta \\omega + e^{\\delta}", "- \\sin{(\\delta - \\omega)}", "\\log{(\\omega)} \\sin{(\\delta)}"], "srepr_premise_expression": "Add(Symbol('\\\\omega', commutative=True), exp(Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), exp(Symbol('\\\\delta', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), sin(Symbol('\\\\delta', commutative=True)))))", "Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True)), exp(Symbol('\\\\delta', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))))", "Mul(log(Symbol('\\\\omega', commutative=True)), sin(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\cos^{\\psi}{(\\beta)}", "variable": "\\beta", "positive": "\\int \\cos^{\\psi}{(\\beta)} d\\beta", "negatives": ["- \\frac{\\cos{(\\beta)}}{\\psi}", "- \\beta \\psi + \\sin{(\\beta)}", "\\frac{\\beta (- \\beta + 2 \\psi)}{2}", "\\frac{\\beta^{2} (2 \\beta + 3)}{6}"], "srepr_premise_expression": "Pow(cos(Symbol('\\\\beta', commutative=True)), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Integral(Pow(cos(Symbol('\\\\beta', commutative=True)), Symbol('\\\\psi', commutative=True)), Tuple(Symbol('\\\\beta', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), cos(Symbol('\\\\beta', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\psi', commutative=True)), sin(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 6), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Integer(3)))"]}, {"premise_expression": "\\log{(\\frac{\\gamma}{\\sigma})}", "variable": "\\sigma", "positive": "\\sigma (\\log{(\\frac{\\gamma}{\\sigma})} + 1)", "negatives": ["\\gamma (\\log{(\\frac{\\gamma}{\\sigma})} - 1)", "\\log{(\\gamma)} \\log{(\\sigma)}", "\\frac{\\sigma^{2} \\log{(\\gamma)}}{2}", "\\log{(\\sigma)} \\sin{(\\gamma)}"], "srepr_premise_expression": "log(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\sigma', commutative=True), Add(log(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))), Integer(1)))", "srepr_negatives": ["Mul(Symbol('\\\\gamma', commutative=True), Add(log(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))), Integer(-1)))", "Mul(log(Symbol('\\\\gamma', commutative=True)), log(Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), log(Symbol('\\\\gamma', commutative=True)))", "Mul(log(Symbol('\\\\sigma', commutative=True)), sin(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\beta + e^{\\delta}", "variable": "\\beta", "positive": "\\frac{\\beta (\\beta + 2 e^{\\delta})}{2}", "negatives": ["\\frac{\\beta (\\beta + 2 \\sin{(\\delta)})}{2}", "\\beta \\delta + e^{\\delta}", "\\frac{\\beta (- \\beta + 2 \\delta)}{2}", "\\beta \\delta + \\sin{(\\beta)}"], "srepr_premise_expression": "Add(Symbol('\\\\beta', commutative=True), exp(Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), exp(Symbol('\\\\delta', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), sin(Symbol('\\\\delta', commutative=True)))))", "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True)), exp(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\delta', commutative=True))))", "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True)), sin(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "- \\pi + \\psi", "variable": "\\pi", "positive": "\\frac{\\pi (- \\pi + 2 \\psi)}{2}", "negatives": ["\\frac{\\psi (- 2 \\pi + \\psi)}{2}", "- \\cos{(\\pi + \\psi)}", "\\frac{\\pi^{2} \\psi}{2}", "\\frac{\\sin{(\\pi)}}{\\psi}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))", "Mul(Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), sin(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "- \\sigma + \\log{(\\delta)}", "variable": "\\delta", "positive": "\\delta (- \\sigma + \\log{(\\delta)} - 1)", "negatives": ["\\frac{\\sigma (- \\sigma + 2 \\log{(\\delta)})}{2}", "\\delta - \\sigma \\log{(\\delta)}", "\\frac{\\delta (- \\delta + 2 \\cos{(\\sigma)})}{2}", "- \\delta \\sigma - \\cos{(\\delta)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), log(Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), log(Symbol('\\\\delta', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), Mul(Integer(2), log(Symbol('\\\\delta', commutative=True)))))", "Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\sigma', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\delta', commutative=True))))"]}, {"premise_expression": "\\cos{(\\pi - \\sigma)}", "variable": "\\sigma", "positive": "- \\sin{(\\pi - \\sigma)}", "negatives": ["\\sin{(\\pi - \\sigma)}", "\\frac{\\sin{(\\sigma)}}{\\pi}", "- e^{\\pi - \\sigma}", "\\frac{\\sigma (2 \\pi + \\sigma)}{2}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Integer(-1), sin(Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))", "srepr_negatives": ["sin(Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), sin(Symbol('\\\\sigma', commutative=True)))", "Mul(Integer(-1), exp(Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\frac{\\pi - \\psi}{\\omega}", "variable": "\\pi", "positive": "\\frac{\\pi (\\pi - 2 \\psi)}{2 \\omega}", "negatives": ["\\frac{\\pi (2 \\omega - \\pi)}{2 \\psi}", "\\frac{\\psi (2 \\pi - \\psi)}{2 \\omega}", "(\\pi - \\psi) \\log{(\\omega)}", "\\frac{\\pi (2 \\omega + \\pi + 2 \\psi)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))), log(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\pi', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "\\beta \\sigma - \\psi", "variable": "\\sigma", "positive": "\\frac{\\sigma (\\beta \\sigma - 2 \\psi)}{2}", "negatives": ["\\frac{\\beta (\\beta \\sigma - 2 \\psi)}{2}", "\\frac{\\sigma (- 2 \\beta + \\psi \\sigma)}{2}", "\\frac{\\psi (2 \\beta \\sigma - \\psi)}{2}", "\\frac{\\psi \\sigma (- 2 \\beta + \\sigma)}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\frac{\\gamma^{\\psi}}{\\delta}", "variable": "\\delta", "positive": "\\gamma^{\\psi} \\log{(\\delta)}", "negatives": ["\\gamma \\psi \\log{(\\delta)}", "\\frac{\\delta \\gamma (\\delta + 2 \\psi)}{2}", "\\frac{\\delta (\\delta \\gamma + 2 \\psi)}{2}", "\\frac{\\delta (\\delta - 2 \\gamma + 2 \\psi)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Pow(Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True)), log(Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True), log(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "\\omega \\xi^{\\psi}", "variable": "\\omega", "positive": "\\frac{\\omega^{2} \\xi^{\\psi}}{2}", "negatives": ["\\frac{\\omega^{2} \\psi \\xi}{2}", "\\frac{\\omega^{2} \\psi}{2 \\xi}", "\\psi^{\\xi} \\log{(\\omega)}", "\\frac{\\omega (\\omega \\xi - 2 \\psi)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True), Symbol('\\\\xi', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "Mul(Pow(Symbol('\\\\psi', commutative=True), Symbol('\\\\xi', commutative=True)), log(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "\\frac{\\chi}{\\alpha}", "variable": "\\alpha", "positive": "\\chi \\log{(\\alpha)}", "negatives": ["\\frac{\\chi^{2}}{2 \\alpha}", "\\frac{\\alpha (\\log{(\\alpha)} - 1)}{\\chi}", "\\sin{(\\alpha + \\chi)}", "e^{\\alpha + \\chi}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\chi', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\chi', commutative=True), Integer(2)))", "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Add(log(Symbol('\\\\alpha', commutative=True)), Integer(-1)))", "sin(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)))", "exp(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "\\frac{\\alpha}{\\chi}", "variable": "\\chi", "positive": "\\alpha \\log{(\\chi)}", "negatives": ["\\alpha \\sin{(\\chi)}", "\\frac{\\alpha^{2}}{2 \\chi}", "\\frac{\\chi^{2} \\log{(\\alpha)}}{2}", "- \\cos{(\\alpha + \\chi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\alpha', commutative=True), sin(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), log(Symbol('\\\\alpha', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True))))"]}, {"premise_expression": "\\delta \\sigma", "variable": "\\sigma", "positive": "\\frac{\\delta \\sigma^{2}}{2}", "negatives": ["\\frac{\\delta^{2} \\sigma}{2}", "\\delta^{\\delta} \\sigma", "\\delta \\sigma + \\sin{(\\sigma)}", "- \\cos{(\\delta - \\sigma)}"], "srepr_premise_expression": "Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Symbol('\\\\sigma', commutative=True))", "Mul(Pow(Symbol('\\\\delta', commutative=True), Symbol('\\\\delta', commutative=True)), Symbol('\\\\sigma', commutative=True))", "Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True)), sin(Symbol('\\\\sigma', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))"]}, {"premise_expression": "- \\delta + \\sin{(\\beta)}", "variable": "\\delta", "positive": "\\frac{\\delta (- \\delta + 2 \\sin{(\\beta)})}{2}", "negatives": ["\\frac{\\delta (- \\delta + 2 e^{\\beta})}{2}", "- \\beta \\delta - \\cos{(\\beta)}", "- e^{\\beta - \\delta}", "- \\cos{(\\beta - \\delta)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), sin(Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\beta', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\beta', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\beta', commutative=True))))", "Mul(Integer(-1), exp(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)))))"]}, {"premise_expression": "\\pi + \\psi", "variable": "\\psi", "positive": "\\frac{\\psi (2 \\pi + \\psi)}{2}", "negatives": ["\\frac{\\pi (\\pi + 2 \\psi)}{2}", "\\frac{\\psi^{2} \\cos{(\\pi)}}{2}", "\\frac{\\psi^{2} e^{\\pi}}{2}", "- \\cos{(\\pi + \\psi)}"], "srepr_premise_expression": "Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), cos(Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), exp(Symbol('\\\\pi', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "\\cos^{\\alpha}{(\\xi)}", "variable": "\\xi", "positive": "\\int \\cos^{\\alpha}{(\\xi)} d\\xi", "negatives": ["\\log{(\\xi)} \\sin{(\\alpha)}", "- \\frac{\\cos{(\\xi)}}{\\alpha}", "\\alpha \\xi - \\cos{(\\xi)}", "- \\alpha \\xi - \\cos{(\\xi)}"], "srepr_premise_expression": "Pow(cos(Symbol('\\\\xi', commutative=True)), Symbol('\\\\alpha', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Integral(Pow(cos(Symbol('\\\\xi', commutative=True)), Symbol('\\\\alpha', commutative=True)), Tuple(Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(log(Symbol('\\\\xi', commutative=True)), sin(Symbol('\\\\alpha', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), cos(Symbol('\\\\xi', commutative=True)))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\xi', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\frac{e^{\\psi}}{\\sigma}", "variable": "\\sigma", "positive": "e^{\\psi} \\log{(\\sigma)}", "negatives": ["e^{\\psi + \\sigma}", "\\frac{\\sigma (2 \\psi - \\sigma)}{2}", "\\frac{\\sigma^{2} e^{\\psi}}{2}", "\\sigma (\\log{(\\psi \\sigma)} - 1)"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), exp(Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(exp(Symbol('\\\\psi', commutative=True)), log(Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["exp(Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), exp(Symbol('\\\\psi', commutative=True)))", "Mul(Symbol('\\\\sigma', commutative=True), Add(log(Mul(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\gamma + \\pi", "variable": "\\pi", "positive": "\\frac{\\pi (2 \\gamma + \\pi)}{2}", "negatives": ["\\frac{\\gamma (\\gamma + 2 \\pi)}{2}", "\\frac{\\pi^{2} e^{\\gamma}}{2}", "\\cos{(\\gamma - \\pi)}", "- \\cos{(\\gamma + \\pi)}"], "srepr_premise_expression": "Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), exp(Symbol('\\\\gamma', commutative=True)))", "cos(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\sigma \\xi", "variable": "\\xi", "positive": "\\frac{\\sigma \\xi^{2}}{2}", "negatives": ["\\frac{\\sigma^{2} \\xi}{2}", "\\sigma \\xi + e^{\\xi}", "\\xi^{2} (\\frac{\\sigma}{2} - \\frac{\\xi}{3})", "\\sigma \\xi (\\log{(\\xi)} - 1)"], "srepr_premise_expression": "Mul(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))", "Add(Mul(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True)), exp(Symbol('\\\\xi', commutative=True)))", "Mul(Pow(Symbol('\\\\xi', commutative=True), Integer(2)), Add(Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), Rational(1, 3), Symbol('\\\\xi', commutative=True))))", "Mul(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True), Add(log(Symbol('\\\\xi', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\delta - \\pi", "variable": "\\pi", "positive": "\\frac{\\pi (2 \\delta - \\pi)}{2}", "negatives": ["\\frac{\\delta (\\delta - 2 \\pi)}{2}", "- \\cos{(\\delta + \\pi)}", "\\pi (\\log{(\\delta \\pi)} - 1)", "\\frac{\\pi (- \\pi + 2 \\log{(\\delta)})}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True))))", "Mul(Symbol('\\\\pi', commutative=True), Add(log(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), log(Symbol('\\\\delta', commutative=True)))))"]}, {"premise_expression": "\\chi + \\psi", "variable": "\\psi", "positive": "\\frac{\\psi (2 \\chi + \\psi)}{2}", "negatives": ["\\frac{\\chi (\\chi + 2 \\psi)}{2}", "\\frac{\\psi^{2} \\sin{(\\chi)}}{2}", "\\frac{\\psi^{2} e^{\\chi}}{2}", "\\sin{(\\chi + \\psi)}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), sin(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), exp(Symbol('\\\\chi', commutative=True)))", "sin(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\frac{e^{\\chi}}{\\delta}", "variable": "\\delta", "positive": "e^{\\chi} \\log{(\\delta)}", "negatives": ["\\frac{\\delta (- 2 \\chi + \\delta)}{2}", "- \\frac{\\cos{(\\delta)}}{\\chi}", "\\frac{\\delta^{2} \\sin{(\\chi)}}{2}", "\\frac{\\delta^{2} e^{\\chi}}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), exp(Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(exp(Symbol('\\\\chi', commutative=True)), log(Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\delta', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), cos(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), sin(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), exp(Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "\\omega \\sigma", "variable": "\\sigma", "positive": "\\frac{\\omega \\sigma^{2}}{2}", "negatives": ["\\frac{\\omega^{2} \\sigma}{2}", "\\frac{\\sigma (2 \\omega - \\sigma)}{2}", "\\omega \\sin{(\\sigma)}", "- \\frac{\\cos{(\\sigma)}}{\\omega}"], "srepr_premise_expression": "Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Symbol('\\\\sigma', commutative=True))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Symbol('\\\\omega', commutative=True), sin(Symbol('\\\\sigma', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), cos(Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\alpha \\chi", "variable": "\\chi", "positive": "\\frac{\\alpha \\chi^{2}}{2}", "negatives": ["\\frac{\\alpha^{2} \\chi}{2}", "\\frac{\\chi^{2}}{2 \\alpha}", "- \\frac{\\cos{(\\chi)}}{\\alpha}", "- \\alpha \\chi + \\sin{(\\chi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\chi', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\chi', commutative=True), Integer(2)))", "Mul(Integer(-1), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), cos(Symbol('\\\\chi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)), sin(Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "\\sin{(\\beta - \\pi)}", "variable": "\\beta", "positive": "- \\cos{(\\beta - \\pi)}", "negatives": ["\\cos{(\\beta - \\pi)}", "\\sin{(\\beta + \\pi)}", "\\beta (\\log{(\\frac{\\beta}{\\pi})} - 1)", "\\frac{\\beta (- \\beta + 2 \\pi)}{2}"], "srepr_premise_expression": "sin(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))", "srepr_negatives": ["cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "sin(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\beta', commutative=True), Add(log(Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "- \\psi + \\sin{(\\alpha)}", "variable": "\\psi", "positive": "\\frac{\\psi (- \\psi + 2 \\sin{(\\alpha)})}{2}", "negatives": ["\\frac{\\psi^{2} e^{\\alpha}}{2}", "- \\alpha \\psi - \\cos{(\\alpha)}", "\\alpha \\psi + e^{\\psi}", "\\psi (\\alpha + \\log{(\\psi)} - 1)"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), sin(Symbol('\\\\alpha', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\alpha', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), exp(Symbol('\\\\alpha', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\alpha', commutative=True))))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True)), exp(Symbol('\\\\psi', commutative=True)))", "Mul(Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\psi', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\cos{(\\sigma + \\xi)}", "variable": "\\sigma", "positive": "\\sin{(\\sigma + \\xi)}", "negatives": ["e^{\\sigma + \\xi}", "\\frac{\\sigma (\\sigma - 2 \\xi)}{2}", "\\sigma \\xi (\\log{(\\sigma)} - 1)", "\\sigma (\\xi + \\log{(\\sigma)} - 1)"], "srepr_premise_expression": "cos(Add(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "sin(Add(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["exp(Add(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True), Add(log(Symbol('\\\\sigma', commutative=True)), Integer(-1)))", "Mul(Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\sigma', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\delta + \\pi", "variable": "\\delta", "positive": "\\frac{\\delta (\\delta + 2 \\pi)}{2}", "negatives": ["\\frac{\\delta (- \\delta + 2 \\pi)}{2}", "\\frac{\\pi (2 \\delta + \\pi)}{2}", "\\frac{\\delta^{2} \\log{(\\pi)}}{2}", "- \\cos{(\\delta + \\pi)}"], "srepr_premise_expression": "Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), log(Symbol('\\\\pi', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\frac{\\delta}{\\alpha}", "variable": "\\alpha", "positive": "\\delta \\log{(\\alpha)}", "negatives": ["\\frac{\\delta^{2}}{2 \\alpha}", "\\frac{\\alpha^{2} \\log{(\\delta)}}{2}", "e^{\\alpha + \\delta}", "\\frac{\\alpha (\\alpha - 2 \\delta)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\delta', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), log(Symbol('\\\\delta', commutative=True)))", "exp(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True))))"]}, {"premise_expression": "\\cos{(\\gamma - \\pi)}", "variable": "\\gamma", "positive": "\\sin{(\\gamma - \\pi)}", "negatives": ["- \\sin{(\\gamma - \\pi)}", "- \\frac{\\cos{(\\gamma)}}{\\pi}", "\\log{(\\gamma)} \\cos{(\\pi)}", "\\gamma \\pi - \\cos{(\\gamma)}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "sin(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))", "Mul(Integer(-1), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), cos(Symbol('\\\\gamma', commutative=True)))", "Mul(log(Symbol('\\\\gamma', commutative=True)), cos(Symbol('\\\\pi', commutative=True)))", "Add(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\gamma', commutative=True))))"]}, {"premise_expression": "\\frac{\\sigma}{\\delta}", "variable": "\\sigma", "positive": "\\frac{\\sigma^{2}}{2 \\delta}", "negatives": ["\\sigma \\log{(\\delta)}", "\\delta e^{\\frac{\\sigma}{\\delta}}", "\\delta \\log{(\\sigma)}", "\\delta \\sin{(\\sigma)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\delta', commutative=True)))", "Mul(Symbol('\\\\delta', commutative=True), exp(Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))))", "Mul(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\sigma', commutative=True)))", "Mul(Symbol('\\\\delta', commutative=True), sin(Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\alpha \\omega - \\sigma", "variable": "\\omega", "positive": "\\frac{\\omega (\\alpha \\omega - 2 \\sigma)}{2}", "negatives": ["\\frac{\\alpha (\\alpha \\omega - 2 \\sigma)}{2}", "\\frac{\\omega (2 \\alpha + \\omega \\sigma)}{2}", "\\frac{\\sigma (2 \\alpha \\omega - \\sigma)}{2}", "\\frac{\\alpha \\omega (\\omega + 2 \\sigma)}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\frac{\\alpha}{\\pi}", "variable": "\\alpha", "positive": "\\frac{\\alpha^{2}}{2 \\pi}", "negatives": ["\\alpha \\log{(\\pi)}", "\\frac{\\alpha^{2} \\log{(\\pi)}}{2}", "\\alpha (\\alpha + \\pi)", "- \\pi \\cos{(\\alpha)}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), log(Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)))", "Mul(Integer(-1), Symbol('\\\\pi', commutative=True), cos(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "e^{\\omega + \\pi}", "variable": "\\omega", "positive": "e^{\\omega + \\pi}", "negatives": ["- e^{- \\omega + \\pi}", "\\sin{(\\omega - \\pi)}", "\\log{(\\omega)} \\sin{(\\pi)}", "\\frac{\\omega^{2} \\pi}{2}"], "srepr_premise_expression": "exp(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "exp(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Symbol('\\\\pi', commutative=True))))", "sin(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "Mul(log(Symbol('\\\\omega', commutative=True)), sin(Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Symbol('\\\\pi', commutative=True))"]}, {"premise_expression": "\\frac{\\log{(\\chi)}}{\\psi}", "variable": "\\psi", "positive": "\\log{(\\chi)} \\log{(\\psi)}", "negatives": ["e^{\\chi} \\log{(\\psi)}", "\\psi \\log{(2 \\chi)}", "\\frac{\\sin{(\\psi)}}{\\chi}", "e^{- \\chi + \\psi}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), log(Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(log(Symbol('\\\\chi', commutative=True)), log(Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(exp(Symbol('\\\\chi', commutative=True)), log(Symbol('\\\\psi', commutative=True)))", "Mul(Symbol('\\\\psi', commutative=True), log(Mul(Integer(2), Symbol('\\\\chi', commutative=True))))", "Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), sin(Symbol('\\\\psi', commutative=True)))", "exp(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\beta \\log{(\\chi)}", "variable": "\\chi", "positive": "\\beta \\chi (\\log{(\\chi)} - 1)", "negatives": ["\\frac{\\beta^{2} \\log{(\\chi)}}{2}", "\\cos{(\\beta - \\chi)}", "\\beta \\sin{(\\chi)}", "\\log{(\\chi)} \\sin{(\\beta)}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), log(Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True), Add(log(Symbol('\\\\chi', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), log(Symbol('\\\\chi', commutative=True)))", "cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True))))", "Mul(Symbol('\\\\beta', commutative=True), sin(Symbol('\\\\chi', commutative=True)))", "Mul(log(Symbol('\\\\chi', commutative=True)), sin(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "\\log{(- \\gamma + \\xi)}", "variable": "\\xi", "positive": "- \\gamma \\log{(- \\gamma + \\xi)} + \\xi \\log{(- \\gamma + \\xi)} - \\xi", "negatives": ["\\gamma \\log{(- \\gamma + \\xi)} - \\gamma - \\xi \\log{(\\gamma - \\xi)}", "\\log{(\\xi)} \\cos{(\\gamma)}", "\\xi (\\log{(\\frac{\\gamma}{\\xi})} + 1)", "\\frac{\\xi (\\xi + 2 \\sin{(\\gamma)})}{2}"], "srepr_premise_expression": "log(Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\xi', commutative=True)))), Mul(Symbol('\\\\xi', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\xi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\gamma', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\xi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True), log(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))))", "Mul(log(Symbol('\\\\xi', commutative=True)), cos(Symbol('\\\\gamma', commutative=True)))", "Mul(Symbol('\\\\xi', commutative=True), Add(log(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\xi', commutative=True), Mul(Integer(2), sin(Symbol('\\\\gamma', commutative=True)))))"]}, {"premise_expression": "\\chi + \\gamma", "variable": "\\gamma", "positive": "\\frac{\\gamma (2 \\chi + \\gamma)}{2}", "negatives": ["\\frac{\\chi (\\chi + 2 \\gamma)}{2}", "\\cos{(\\chi - \\gamma)}", "\\chi \\log{(\\gamma)}", "\\frac{\\gamma (- \\gamma + 2 e^{\\chi})}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\gamma', commutative=True))))", "cos(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "Mul(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\chi', commutative=True)))))"]}, {"premise_expression": "e^{\\frac{\\gamma}{\\delta}}", "variable": "\\gamma", "positive": "\\delta e^{\\frac{\\gamma}{\\delta}}", "negatives": ["\\gamma e^{\\delta^{2}}", "\\log{(\\gamma)} \\sin{(\\delta)}", "\\frac{\\gamma (2 \\delta + \\gamma)}{2}", "\\delta e^{\\frac{\\gamma}{\\delta}} - \\gamma \\operatorname{Ei}{(\\frac{\\gamma}{\\delta})}"], "srepr_premise_expression": "exp(Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\delta', commutative=True), exp(Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True))))", "srepr_negatives": ["Mul(Symbol('\\\\gamma', commutative=True), exp(Pow(Symbol('\\\\delta', commutative=True), Integer(2))))", "Mul(log(Symbol('\\\\gamma', commutative=True)), sin(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "Add(Mul(Symbol('\\\\delta', commutative=True), exp(Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True)))), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Ei(Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True)))))"]}, {"premise_expression": "e^{\\delta + \\pi}", "variable": "\\pi", "positive": "e^{\\delta + \\pi}", "negatives": ["- e^{\\delta - \\pi}", "- \\sin{(\\delta - \\pi)}", "\\delta e^{\\frac{\\pi}{\\delta}}", "\\pi^{2} (\\frac{\\delta}{2} + \\frac{\\pi}{3})"], "srepr_premise_expression": "exp(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "exp(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))", "Mul(Integer(-1), sin(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))", "Mul(Symbol('\\\\delta', commutative=True), exp(Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))))", "Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(2)), Add(Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True)), Mul(Rational(1, 3), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\beta \\chi", "variable": "\\beta", "positive": "\\frac{\\beta^{2} \\chi}{2}", "negatives": ["\\frac{\\beta \\chi^{2}}{2}", "\\chi e^{\\frac{\\beta}{\\chi}}", "- \\cos{(\\beta + \\chi)}", "\\frac{\\beta (\\beta + 2 \\cos{(\\chi)})}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\chi', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(2)))", "Mul(Symbol('\\\\chi', commutative=True), exp(Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), cos(Symbol('\\\\chi', commutative=True)))))"]}, {"premise_expression": "\\beta + \\chi", "variable": "\\beta", "positive": "\\frac{\\beta (\\beta + 2 \\chi)}{2}", "negatives": ["\\frac{\\beta (- \\beta + 2 \\chi)}{2}", "\\frac{\\chi (2 \\beta + \\chi)}{2}", "\\frac{\\beta^{2} \\log{(\\chi)}}{2}", "\\frac{\\beta^{2} \\cos{(\\chi)}}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\chi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\chi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), log(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), cos(Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "\\log{(\\psi + \\xi)}", "variable": "\\xi", "positive": "\\psi \\log{(\\psi + \\xi)} + \\xi \\log{(\\psi + \\xi)} - \\xi", "negatives": ["\\psi \\log{(\\psi + \\xi)} - \\psi + \\xi \\log{(\\psi + \\xi)}", "\\frac{\\xi (- \\xi + 2 \\log{(\\psi)})}{2}", "\\xi (\\log{(\\frac{\\psi}{\\xi})} + 1)", "\\psi \\xi + \\sin{(\\xi)}"], "srepr_premise_expression": "log(Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\psi', commutative=True), log(Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\xi', commutative=True)))), Mul(Symbol('\\\\xi', commutative=True), log(Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\xi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\psi', commutative=True), log(Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\xi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Symbol('\\\\xi', commutative=True), log(Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\xi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), log(Symbol('\\\\psi', commutative=True)))))", "Mul(Symbol('\\\\xi', commutative=True), Add(log(Mul(Symbol('\\\\psi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))), Integer(1)))", "Add(Mul(Symbol('\\\\psi', commutative=True), Symbol('\\\\xi', commutative=True)), sin(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\alpha + \\frac{\\xi}{\\pi}", "variable": "\\pi", "positive": "\\alpha \\pi + \\xi \\log{(\\pi)}", "negatives": ["(- \\alpha + \\xi) \\log{(\\pi)}", "\\alpha \\xi + \\frac{\\xi^{2}}{2 \\pi}", "- \\pi \\xi + \\frac{\\pi^{2}}{2 \\alpha}", "\\frac{\\alpha^{2}}{2} + \\frac{\\alpha \\xi}{\\pi}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\xi', commutative=True)), log(Symbol('\\\\pi', commutative=True)))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Integer(2))))", "Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\pi', commutative=True), Integer(2))))", "Add(Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2))), Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\frac{\\omega}{\\gamma}", "variable": "\\gamma", "positive": "\\omega \\log{(\\gamma)}", "negatives": ["\\frac{\\omega^{2}}{2 \\gamma}", "- \\frac{\\cos{(\\gamma)}}{\\omega}", "\\frac{\\gamma^{2}}{2 \\omega}", "\\gamma \\omega (\\log{(\\gamma)} - 1)"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "Mul(Integer(-1), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), cos(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))", "Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True), Add(log(Symbol('\\\\gamma', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\chi + \\gamma", "variable": "\\chi", "positive": "\\frac{\\chi (\\chi + 2 \\gamma)}{2}", "negatives": ["\\frac{\\gamma (2 \\chi + \\gamma)}{2}", "e^{\\chi - \\gamma}", "\\sin{(\\chi + \\gamma)}", "\\sin{(\\chi - \\gamma)}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\gamma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "exp(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "sin(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True)))", "sin(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))"]}, {"premise_expression": "\\frac{\\xi}{\\pi}", "variable": "\\pi", "positive": "\\xi \\log{(\\pi)}", "negatives": ["\\frac{\\xi^{2}}{2 \\pi}", "\\xi e^{\\frac{\\pi}{\\xi}}", "\\pi \\xi + e^{\\pi}", "\\frac{\\pi^{2} \\log{(\\xi)}}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Mul(Symbol('\\\\xi', commutative=True), exp(Mul(Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))))", "Add(Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True)), exp(Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), log(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\frac{\\cos{(\\sigma)}}{\\xi}", "variable": "\\sigma", "positive": "\\frac{\\sin{(\\sigma)}}{\\xi}", "negatives": ["\\xi e^{\\frac{\\sigma}{\\xi}}", "- \\cos{(\\sigma + \\xi)}", "\\frac{\\sigma^{2} \\log{(\\xi)}}{2}", "\\log{(\\xi)} \\cos{(\\sigma)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), cos(Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), sin(Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\xi', commutative=True), exp(Mul(Symbol('\\\\sigma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), log(Symbol('\\\\xi', commutative=True)))", "Mul(log(Symbol('\\\\xi', commutative=True)), cos(Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\beta - \\gamma + \\sigma", "variable": "\\sigma", "positive": "\\sigma (\\beta - \\gamma + \\frac{\\sigma}{2})", "negatives": ["\\frac{\\beta (\\beta - 2 \\gamma + 2 \\sigma)}{2}", "\\frac{\\gamma (2 \\beta - \\gamma + 2 \\sigma)}{2}", "\\frac{\\sigma (2 \\beta \\gamma - \\sigma)}{2}", "\\frac{\\sigma (2 \\gamma^{\\beta} - \\sigma)}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Pow(Symbol('\\\\gamma', commutative=True), Symbol('\\\\beta', commutative=True))), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "e^{\\alpha^{\\chi}}", "variable": "\\alpha", "positive": "\\frac{e^{- \\frac{i \\pi}{\\chi}} \\gamma(\\frac{1}{\\chi}, \\alpha^{\\chi} e^{i \\pi})}{\\chi}", "negatives": ["\\operatorname{NonElementaryIntegral}{((\\alpha + \\chi)^{\\alpha},( \\alpha))}", "\\alpha (\\log{(\\alpha \\chi)} - 1)", "\\frac{\\alpha (\\log{(\\alpha)} - 1)}{\\chi}", "\\alpha (- \\chi + \\log{(\\alpha)} - 1)"], "srepr_premise_expression": "exp(Pow(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), exp(Mul(Integer(-1), I, pi, Pow(Symbol('\\\\chi', commutative=True), Integer(-1)))), lowergamma(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Mul(Pow(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)), exp_polar(Mul(I, pi)))))", "srepr_negatives": ["Function('NonElementaryIntegral')(Pow(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)), Symbol('\\\\alpha', commutative=True)), Tuple(Symbol('\\\\alpha', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), Add(log(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Add(log(Symbol('\\\\alpha', commutative=True)), Integer(-1)))", "Mul(Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), log(Symbol('\\\\alpha', commutative=True)), Integer(-1)))"]}, {"premise_expression": "- \\chi + \\psi", "variable": "\\chi", "positive": "\\frac{\\chi (- \\chi + 2 \\psi)}{2}", "negatives": ["\\frac{\\psi (- 2 \\chi + \\psi)}{2}", "\\frac{\\chi (\\chi + 2 \\log{(\\psi)})}{2}", "\\chi \\psi + \\sin{(\\chi)}", "\\chi \\psi + e^{\\chi}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), log(Symbol('\\\\psi', commutative=True)))))", "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True)), sin(Symbol('\\\\chi', commutative=True)))", "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True)), exp(Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "\\pi \\psi", "variable": "\\pi", "positive": "\\frac{\\pi^{2} \\psi}{2}", "negatives": ["\\frac{\\pi \\psi^{2}}{2}", "\\frac{\\pi^{2} e^{\\psi}}{2}", "\\psi \\sin{(\\pi)}", "\\psi e^{\\frac{\\pi}{\\psi}}"], "srepr_premise_expression": "Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), exp(Symbol('\\\\psi', commutative=True)))", "Mul(Symbol('\\\\psi', commutative=True), sin(Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\psi', commutative=True), exp(Mul(Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))))"]}, {"premise_expression": "\\frac{\\log{(\\xi)}}{\\delta}", "variable": "\\xi", "positive": "\\frac{\\xi (\\log{(\\xi)} - 1)}{\\delta}", "negatives": ["\\log{(\\delta)} \\log{(\\xi)}", "\\frac{\\xi (2 \\delta + \\xi)}{2}", "e^{- \\delta + \\xi}", "\\delta \\xi + e^{\\xi}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), log(Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True), Add(log(Symbol('\\\\xi', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(log(Symbol('\\\\delta', commutative=True)), log(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\xi', commutative=True)))", "exp(Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True)), exp(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "- \\beta + \\omega", "variable": "\\beta", "positive": "\\frac{\\beta (- \\beta + 2 \\omega)}{2}", "negatives": ["\\frac{\\omega (- 2 \\beta + \\omega)}{2}", "\\frac{\\beta (\\log{(\\beta)} - 1)}{\\omega}", "\\frac{\\beta^{2} \\omega}{2}", "\\omega e^{\\beta}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Add(log(Symbol('\\\\beta', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\omega', commutative=True))", "Mul(Symbol('\\\\omega', commutative=True), exp(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "- \\sin{(\\delta - \\sigma)}", "variable": "\\sigma", "positive": "- \\cos{(\\delta - \\sigma)}", "negatives": ["\\cos{(\\delta - \\sigma)}", "e^{\\delta + \\sigma}", "- \\frac{\\cos{(\\sigma)}}{\\delta}", "- \\delta \\sigma - \\cos{(\\sigma)}"], "srepr_premise_expression": "Mul(Integer(-1), sin(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))", "srepr_negatives": ["cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "exp(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), cos(Symbol('\\\\sigma', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\frac{\\gamma}{\\pi}", "variable": "\\gamma", "positive": "\\frac{\\gamma^{2}}{2 \\pi}", "negatives": ["\\gamma \\log{(\\pi)}", "\\pi \\sin{(\\gamma)}", "- \\cos{(\\gamma - \\pi)}", "\\log{(\\gamma)} \\sin{(\\pi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\pi', commutative=True), sin(Symbol('\\\\gamma', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))", "Mul(log(Symbol('\\\\gamma', commutative=True)), sin(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\chi (\\delta + \\xi)", "variable": "\\xi", "positive": "\\frac{\\chi \\xi (2 \\delta + \\xi)}{2}", "negatives": ["\\frac{\\chi^{2} (\\delta + \\xi)}{2}", "\\frac{\\chi \\delta (\\delta + 2 \\xi)}{2}", "\\frac{\\xi (\\chi \\xi - 2 \\delta)}{2}", "\\frac{\\xi (2 \\chi + \\delta \\xi)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\frac{\\pi}{\\sigma} + \\xi", "variable": "\\xi", "positive": "\\frac{\\pi \\xi}{\\sigma} + \\frac{\\xi^{2}}{2}", "negatives": ["\\frac{\\pi \\xi (2 \\sigma + \\xi)}{2}", "\\frac{\\pi \\sigma \\xi^{2}}{2}", "\\pi \\log{(\\sigma)} + \\sigma \\xi", "\\frac{\\pi^{2}}{2 \\sigma} + \\pi \\xi"], "srepr_premise_expression": "Add(Mul(Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1))), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\sigma', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Add(Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\sigma', commutative=True))), Mul(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True)))", "Add(Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1))), Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "- \\beta + \\cos{(\\sigma)}", "variable": "\\sigma", "positive": "- \\beta \\sigma + \\sin{(\\sigma)}", "negatives": ["- \\sin{(\\beta - \\sigma)}", "- \\cos{(\\beta - \\sigma)}", "e^{\\beta + \\sigma}", "\\frac{\\beta (- \\beta + 2 \\cos{(\\sigma)})}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), cos(Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True)), sin(Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))", "exp(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\sigma', commutative=True)))))"]}, {"premise_expression": "\\delta - \\sigma", "variable": "\\sigma", "positive": "\\frac{\\sigma (2 \\delta - \\sigma)}{2}", "negatives": ["\\frac{\\sigma (- 2 \\delta + \\sigma)}{2}", "\\frac{\\delta (\\delta - 2 \\sigma)}{2}", "\\frac{\\sigma (- \\sigma + 2 \\sin{(\\delta)})}{2}", "\\delta \\sigma + e^{\\sigma}"], "srepr_premise_expression": "Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\delta', commutative=True)))))", "Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True)), exp(Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\delta \\log{(\\xi)}", "variable": "\\delta", "positive": "\\frac{\\delta^{2} \\log{(\\xi)}}{2}", "negatives": ["\\frac{\\delta (\\delta + 2 \\log{(\\xi)})}{2}", "\\frac{\\delta (\\delta + 2 \\xi)}{2}", "\\delta \\xi (\\log{(\\xi)} - 1)", "\\frac{\\delta (- \\delta + 2 \\cos{(\\xi)})}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), log(Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), log(Symbol('\\\\xi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True), Add(log(Symbol('\\\\xi', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\xi', commutative=True)))))"]}, {"premise_expression": "\\gamma + \\log{(\\sigma)}", "variable": "\\gamma", "positive": "\\frac{\\gamma (\\gamma + 2 \\log{(\\sigma)})}{2}", "negatives": ["\\frac{\\gamma (\\gamma - 2 \\sigma)}{2}", "\\sigma (\\gamma + \\log{(\\sigma)} - 1)", "\\gamma (- \\sigma + \\log{(\\gamma)} - 1)", "\\frac{\\gamma^{2} \\sigma}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), log(Symbol('\\\\sigma', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\sigma', commutative=True)), Integer(-1)))", "Mul(Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), log(Symbol('\\\\gamma', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Symbol('\\\\sigma', commutative=True))"]}, {"premise_expression": "\\cos^{\\gamma}{(\\psi)}", "variable": "\\psi", "positive": "\\int \\cos^{\\gamma}{(\\psi)} d\\psi", "negatives": ["\\frac{\\sin{(\\psi)}}{\\gamma}", "- \\sin{(\\gamma - \\psi)}", "\\frac{\\psi (- 2 \\gamma + \\psi)}{2}", "- \\gamma \\psi + e^{\\psi}"], "srepr_premise_expression": "Pow(cos(Symbol('\\\\psi', commutative=True)), Symbol('\\\\gamma', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Integral(Pow(cos(Symbol('\\\\psi', commutative=True)), Symbol('\\\\gamma', commutative=True)), Tuple(Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), sin(Symbol('\\\\psi', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True)), exp(Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\frac{\\alpha + \\delta}{\\psi}", "variable": "\\delta", "positive": "\\frac{\\delta (2 \\alpha + \\delta)}{2 \\psi}", "negatives": ["\\frac{\\delta (2 \\alpha - \\delta)}{2 \\psi}", "\\frac{\\alpha (\\alpha + 2 \\delta)}{2 \\psi}", "\\frac{\\delta (\\alpha \\delta - 2 \\psi)}{2}", "(\\alpha + \\delta) \\log{(\\psi)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\delta', commutative=True)), log(Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\frac{\\delta}{\\xi}", "variable": "\\xi", "positive": "\\delta \\log{(\\xi)}", "negatives": ["\\frac{\\delta^{2}}{2 \\xi}", "- \\frac{\\cos{(\\xi)}}{\\delta}", "\\frac{\\xi^{2} \\log{(\\delta)}}{2}", "\\log{(\\xi)} \\sin{(\\delta)}"], "srepr_premise_expression": "Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "Mul(Integer(-1), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), cos(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), log(Symbol('\\\\delta', commutative=True)))", "Mul(log(Symbol('\\\\xi', commutative=True)), sin(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\beta + e^{\\xi}", "variable": "\\beta", "positive": "\\frac{\\beta (\\beta + 2 e^{\\xi})}{2}", "negatives": ["\\frac{\\beta^{2} e^{\\xi}}{2}", "\\beta \\xi + e^{\\xi}", "\\frac{\\beta^{2} \\cos{(\\xi)}}{2}", "- \\beta \\xi + \\sin{(\\beta)}"], "srepr_premise_expression": "Add(Symbol('\\\\beta', commutative=True), exp(Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), exp(Symbol('\\\\xi', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), exp(Symbol('\\\\xi', commutative=True)))", "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True)), exp(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), cos(Symbol('\\\\xi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True)), sin(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "\\log{(\\frac{\\beta}{\\gamma})}", "variable": "\\beta", "positive": "\\beta (\\log{(\\frac{\\beta}{\\gamma})} - 1)", "negatives": ["\\gamma (\\log{(\\frac{\\beta}{\\gamma})} + 1)", "\\frac{\\beta^{2} \\log{(\\gamma)}}{2}", "- e^{- \\beta + \\gamma}", "\\frac{\\beta (\\beta - 2 \\gamma)}{2}"], "srepr_premise_expression": "log(Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\beta', commutative=True), Add(log(Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\gamma', commutative=True), Add(log(Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), log(Symbol('\\\\gamma', commutative=True)))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True))))"]}, {"premise_expression": "- \\alpha + \\gamma", "variable": "\\gamma", "positive": "\\frac{\\gamma (- 2 \\alpha + \\gamma)}{2}", "negatives": ["\\frac{\\alpha (- \\alpha + 2 \\gamma)}{2}", "- \\alpha \\gamma + e^{\\gamma}", "\\gamma (\\log{(\\frac{\\gamma}{\\alpha})} - 1)", "- \\alpha \\gamma + \\sin{(\\gamma)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\gamma', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\gamma', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True)), exp(Symbol('\\\\gamma', commutative=True)))", "Mul(Symbol('\\\\gamma', commutative=True), Add(log(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True))), Integer(-1)))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True)), sin(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\alpha + \\frac{\\chi}{\\sigma}", "variable": "\\chi", "positive": "\\alpha \\chi + \\frac{\\chi^{2}}{2 \\sigma}", "negatives": ["\\alpha \\sigma + \\chi \\log{(\\sigma)}", "\\frac{\\chi (2 \\alpha + \\chi - 2 \\sigma)}{2}", "\\frac{\\chi^{2} \\sigma}{2 \\alpha}", "\\frac{\\alpha \\chi^{2} \\sigma}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\sigma', commutative=True))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\sigma', commutative=True))"]}, {"premise_expression": "\\frac{\\gamma}{\\xi}", "variable": "\\xi", "positive": "\\gamma \\log{(\\xi)}", "negatives": ["\\frac{\\gamma^{2}}{2 \\xi}", "- \\sin{(\\gamma - \\xi)}", "\\xi (\\log{(\\frac{\\xi}{\\gamma})} - 1)", "\\frac{\\xi (2 \\gamma - \\xi)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "Mul(Integer(-1), sin(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))))", "Mul(Symbol('\\\\xi', commutative=True), Add(log(Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "- \\sigma + \\xi", "variable": "\\sigma", "positive": "\\frac{\\sigma (- \\sigma + 2 \\xi)}{2}", "negatives": ["\\frac{\\sigma (\\sigma + 2 \\xi)}{2}", "\\frac{\\xi (- 2 \\sigma + \\xi)}{2}", "\\frac{\\sigma (\\sigma + 2 \\cos{(\\xi)})}{2}", "\\frac{\\sigma^{2}}{2 \\xi}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(2), cos(Symbol('\\\\xi', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))"]}, {"premise_expression": "- \\pi + e^{\\alpha}", "variable": "\\pi", "positive": "\\frac{\\pi (- \\pi + 2 e^{\\alpha})}{2}", "negatives": ["\\frac{\\pi (\\pi + 2 e^{\\alpha})}{2}", "\\frac{\\pi (\\pi + 2 \\sin{(\\alpha)})}{2}", "- \\alpha \\pi + e^{\\alpha}", "\\alpha e^{\\pi}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), exp(Symbol('\\\\alpha', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\alpha', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), exp(Symbol('\\\\alpha', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), sin(Symbol('\\\\alpha', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)), exp(Symbol('\\\\alpha', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), exp(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\beta + \\delta", "variable": "\\beta", "positive": "\\frac{\\beta (\\beta + 2 \\delta)}{2}", "negatives": ["\\frac{\\beta (- \\beta + 2 \\delta)}{2}", "\\frac{\\delta (2 \\beta + \\delta)}{2}", "\\frac{\\beta (\\beta + 2 \\cos{(\\delta)})}{2}", "\\frac{\\beta^{2} \\cos{(\\delta)}}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\delta', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), cos(Symbol('\\\\delta', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), cos(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\sin^{\\beta}{(\\delta)}", "variable": "\\delta", "positive": "\\int \\sin^{\\beta}{(\\delta)} d\\delta", "negatives": ["- \\sin{(\\beta - \\delta)}", "- \\beta \\delta + \\sin{(\\delta)}", "\\delta (- \\beta + \\log{(\\delta^{\\beta})})", "\\delta (\\log{(\\beta \\delta)} - 1)"], "srepr_premise_expression": "Pow(sin(Symbol('\\\\delta', commutative=True)), Symbol('\\\\beta', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Integral(Pow(sin(Symbol('\\\\delta', commutative=True)), Symbol('\\\\beta', commutative=True)), Tuple(Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True)), sin(Symbol('\\\\delta', commutative=True)))", "Mul(Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), log(Pow(Symbol('\\\\delta', commutative=True), Symbol('\\\\beta', commutative=True)))))", "Mul(Symbol('\\\\delta', commutative=True), Add(log(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\delta + \\xi", "variable": "\\xi", "positive": "\\frac{\\xi (2 \\delta + \\xi)}{2}", "negatives": ["\\frac{\\delta (\\delta + 2 \\xi)}{2}", "\\frac{\\xi^{2} \\log{(\\delta)}}{2}", "- \\delta \\cos{(\\xi)}", "\\frac{\\sin{(\\xi)}}{\\delta}"], "srepr_premise_expression": "Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), log(Symbol('\\\\delta', commutative=True)))", "Mul(Integer(-1), Symbol('\\\\delta', commutative=True), cos(Symbol('\\\\xi', commutative=True)))", "Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), sin(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\alpha + \\chi \\delta", "variable": "\\alpha", "positive": "\\frac{\\alpha (\\alpha + 2 \\chi \\delta)}{2}", "negatives": ["\\frac{\\chi (2 \\alpha + \\chi \\delta)}{2}", "\\frac{\\delta (2 \\alpha + \\chi \\delta)}{2}", "\\frac{\\alpha (\\alpha + 2 \\delta)}{2 \\chi}", "\\frac{\\alpha (\\alpha + 2 \\chi - 2 \\delta)}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True))))"]}, {"premise_expression": "- \\omega + \\sin{(\\beta)}", "variable": "\\beta", "positive": "- \\beta \\omega - \\cos{(\\beta)}", "negatives": ["- \\frac{\\cos{(\\beta)}}{\\omega}", "\\sin{(\\beta - \\omega)}", "\\frac{\\omega (- \\omega + 2 \\sin{(\\beta)})}{2}", "\\frac{\\beta (\\beta - 2 \\omega)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), sin(Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\beta', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), cos(Symbol('\\\\beta', commutative=True)))", "sin(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\beta', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True))))"]}, {"premise_expression": "\\chi + \\gamma", "variable": "\\chi", "positive": "\\frac{\\chi (\\chi + 2 \\gamma)}{2}", "negatives": ["\\frac{\\gamma (2 \\chi + \\gamma)}{2}", "\\frac{\\chi (\\chi + 2 \\cos{(\\gamma)})}{2}", "- \\chi \\gamma + \\sin{(\\chi)}", "- \\frac{\\cos{(\\chi)}}{\\gamma}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\gamma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), cos(Symbol('\\\\gamma', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True)), sin(Symbol('\\\\chi', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), cos(Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "- \\xi + \\cos{(\\sigma)}", "variable": "\\xi", "positive": "\\frac{\\xi (- \\xi + 2 \\cos{(\\sigma)})}{2}", "negatives": ["\\frac{\\xi^{2} \\log{(\\sigma)}}{2}", "\\frac{\\xi^{2} e^{\\sigma}}{2}", "- \\sigma \\xi + \\sin{(\\sigma)}", "\\cos{(\\sigma - \\xi)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), cos(Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\sigma', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), log(Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), exp(Symbol('\\\\sigma', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True)), sin(Symbol('\\\\sigma', commutative=True)))", "cos(Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "e^{\\chi - \\sigma}", "variable": "\\sigma", "positive": "- e^{\\chi - \\sigma}", "negatives": ["e^{\\chi - \\sigma}", "- \\cos{(\\chi + \\sigma)}", "\\frac{\\sigma (- 2 \\chi + \\sigma)}{2}", "\\chi \\sigma (\\log{(\\sigma)} - 1)"], "srepr_premise_expression": "exp(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Integer(-1), exp(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))", "srepr_negatives": ["exp(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\sigma', commutative=True), Add(log(Symbol('\\\\sigma', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\chi + \\frac{\\pi}{\\omega}", "variable": "\\omega", "positive": "\\chi \\omega + \\pi \\log{(\\omega)}", "negatives": ["\\chi \\pi + \\frac{\\pi^{2}}{2 \\omega}", "\\chi^{\\pi} \\log{(\\omega)}", "\\frac{\\chi^{2}}{2} + \\frac{\\chi \\pi}{\\omega}", "\\frac{\\omega (\\chi \\omega + 2 \\pi)}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Pow(Symbol('\\\\pi', commutative=True), Integer(2))))", "Mul(Pow(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True)), log(Symbol('\\\\omega', commutative=True)))", "Add(Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2))), Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "e^{\\beta + \\psi}", "variable": "\\psi", "positive": "e^{\\beta + \\psi}", "negatives": ["\\beta \\psi - \\cos{(\\psi)}", "\\psi (\\log{(\\frac{\\psi}{\\beta})} - 1)", "\\log{(\\psi)} \\cos{(\\beta)}", "\\frac{\\psi^{2} \\sin{(\\beta)}}{2}"], "srepr_premise_expression": "exp(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "exp(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\psi', commutative=True))))", "Mul(Symbol('\\\\psi', commutative=True), Add(log(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True))), Integer(-1)))", "Mul(log(Symbol('\\\\psi', commutative=True)), cos(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), sin(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "\\frac{\\alpha}{\\pi}", "variable": "\\pi", "positive": "\\alpha \\log{(\\pi)}", "negatives": ["\\frac{\\alpha^{2}}{2 \\pi}", "- \\cos{(\\alpha + \\pi)}", "\\sin{(\\alpha + \\pi)}", "\\pi (\\log{(\\frac{\\pi}{\\alpha})} - 1)"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True))))", "sin(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\pi', commutative=True), Add(log(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\cos{(\\delta - \\gamma)}", "variable": "\\gamma", "positive": "- \\sin{(\\delta - \\gamma)}", "negatives": ["\\sin{(\\delta - \\gamma)}", "\\sin{(\\delta + \\gamma)}", "e^{- \\delta + \\gamma}", "\\delta \\log{(\\gamma)}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Integer(-1), sin(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))))", "srepr_negatives": ["sin(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "sin(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\gamma', commutative=True)))", "exp(Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "Mul(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\alpha \\sin{(\\delta)}", "variable": "\\delta", "positive": "- \\alpha \\cos{(\\delta)}", "negatives": ["\\alpha \\log{(\\delta)}", "\\alpha \\delta - \\cos{(\\delta)}", "- \\alpha \\delta + \\sin{(\\delta)}", "\\frac{\\alpha^{2} \\sin{(\\delta)}}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), sin(Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), cos(Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\delta', commutative=True)))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\delta', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\delta', commutative=True)), sin(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), sin(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\frac{\\beta}{\\psi \\xi}", "variable": "\\beta", "positive": "\\frac{\\beta^{2}}{2 \\psi \\xi}", "negatives": ["\\frac{\\beta^{2} \\xi}{2 \\psi}", "\\frac{\\beta^{2} \\psi}{2 \\xi}", "\\frac{\\beta (\\beta + 2 \\psi \\xi)}{2}", "\\frac{\\beta \\log{(\\psi)}}{\\xi}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True), Symbol('\\\\xi', commutative=True))))", "Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), log(Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\cos{(\\chi + \\pi)}", "variable": "\\pi", "positive": "\\sin{(\\chi + \\pi)}", "negatives": ["- \\sin{(\\chi - \\pi)}", "- e^{\\chi - \\pi}", "\\chi \\sin{(\\pi)}", "\\pi \\sin{(\\pi)} + \\cos{(\\pi)}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "sin(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))", "Mul(Integer(-1), exp(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))", "Mul(Symbol('\\\\chi', commutative=True), sin(Symbol('\\\\pi', commutative=True)))", "Add(Mul(Symbol('\\\\pi', commutative=True), sin(Symbol('\\\\pi', commutative=True))), cos(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\beta \\delta - \\psi", "variable": "\\delta", "positive": "\\frac{\\delta (\\beta \\delta - 2 \\psi)}{2}", "negatives": ["\\frac{\\beta (\\beta \\delta - 2 \\psi)}{2}", "\\frac{\\psi (2 \\beta \\delta - \\psi)}{2}", "\\frac{\\delta (2 \\beta - \\delta - 2 \\psi)}{2}", "\\frac{\\delta (2 \\beta + \\delta + 2 \\psi)}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\delta', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "\\frac{\\delta \\omega}{\\gamma}", "variable": "\\omega", "positive": "\\frac{\\delta \\omega^{2}}{2 \\gamma}", "negatives": ["\\frac{\\delta^{2} \\omega}{2 \\gamma}", "\\frac{\\delta \\gamma \\omega^{2}}{2}", "\\delta \\omega \\log{(\\gamma)}", "\\frac{\\omega (2 \\gamma + \\omega)}{2 \\delta}"], "srepr_premise_expression": "Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\alpha + \\xi", "variable": "\\xi", "positive": "\\frac{\\xi (2 \\alpha + \\xi)}{2}", "negatives": ["\\frac{\\alpha (\\alpha + 2 \\xi)}{2}", "\\sin{(\\alpha + \\xi)}", "\\alpha \\log{(\\xi)}", "\\alpha e^{\\xi}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "sin(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), exp(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\sin{(\\delta + \\xi)}", "variable": "\\xi", "positive": "- \\cos{(\\delta + \\xi)}", "negatives": ["- \\delta \\cos{(\\xi)}", "\\frac{\\xi (2 \\delta + \\xi)}{2}", "\\delta \\log{(\\xi)}", "- \\delta \\xi - \\cos{(\\xi)}"], "srepr_premise_expression": "sin(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), Symbol('\\\\delta', commutative=True), cos(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\xi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\chi \\psi", "variable": "\\psi", "positive": "\\frac{\\chi \\psi^{2}}{2}", "negatives": ["\\frac{\\chi^{2} \\psi}{2}", "\\frac{\\psi^{2} \\sin{(\\chi)}}{2}", "\\cos{(\\chi - \\psi)}", "\\frac{\\psi (- \\psi + 2 \\sin{(\\chi)})}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), sin(Symbol('\\\\chi', commutative=True)))", "cos(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\chi', commutative=True)))))"]}, {"premise_expression": "\\frac{\\chi}{\\delta \\psi}", "variable": "\\chi", "positive": "\\frac{\\chi^{2}}{2 \\delta \\psi}", "negatives": ["\\frac{\\chi^{2} \\delta \\psi}{2}", "\\frac{\\chi^{2}}{2} + \\frac{\\chi \\delta}{\\psi}", "\\frac{\\chi \\log{(\\psi)}}{\\delta}", "\\frac{\\chi \\log{(\\delta)}}{\\psi}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\delta', commutative=True), Symbol('\\\\psi', commutative=True))", "Add(Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2))), Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1))))", "Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), log(Symbol('\\\\psi', commutative=True)))", "Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), log(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\sin{(\\alpha + \\gamma)}", "variable": "\\gamma", "positive": "- \\cos{(\\alpha + \\gamma)}", "negatives": ["\\sin{(\\alpha + \\gamma)}", "\\frac{\\gamma e^{\\alpha}}{\\alpha}", "\\alpha \\gamma (\\log{(\\gamma)} - 1)", "\\gamma (\\log{(\\frac{\\gamma}{\\alpha})} - 1)"], "srepr_premise_expression": "sin(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True))))", "srepr_negatives": ["sin(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True)))", "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True), exp(Symbol('\\\\alpha', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True), Add(log(Symbol('\\\\gamma', commutative=True)), Integer(-1)))", "Mul(Symbol('\\\\gamma', commutative=True), Add(log(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\frac{\\omega}{\\beta}", "variable": "\\omega", "positive": "\\frac{\\omega^{2}}{2 \\beta}", "negatives": ["\\omega \\log{(\\beta)}", "\\frac{\\omega (- 2 \\beta + \\omega)}{2}", "\\sin{(\\beta + \\omega)}", "\\frac{\\sin{(\\omega)}}{\\beta}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\omega', commutative=True)))", "sin(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True)))", "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), sin(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\pi + e^{\\xi}", "variable": "\\xi", "positive": "\\pi \\xi + e^{\\xi}", "negatives": ["\\frac{\\pi (\\pi + 2 e^{\\xi})}{2}", "\\frac{\\xi^{2} e^{\\pi}}{2}", "\\xi \\log{(2 \\pi)}", "\\frac{\\xi^{2} \\sin{(\\pi)}}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\pi', commutative=True), exp(Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True)), exp(Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), exp(Symbol('\\\\xi', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), exp(Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\xi', commutative=True), log(Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), sin(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\chi (- \\beta + \\delta)", "variable": "\\delta", "positive": "\\frac{\\chi \\delta (- 2 \\beta + \\delta)}{2}", "negatives": ["\\frac{\\chi^{2} (- \\beta + \\delta)}{2}", "\\frac{\\beta \\chi (- \\beta + 2 \\delta)}{2}", "\\frac{\\beta \\chi \\delta^{2}}{2}", "\\frac{\\delta^{2} (\\beta + \\chi)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "- \\beta + \\gamma", "variable": "\\gamma", "positive": "\\frac{\\gamma (- 2 \\beta + \\gamma)}{2}", "negatives": ["\\frac{\\beta (- \\beta + 2 \\gamma)}{2}", "\\frac{\\gamma (\\gamma + 2 \\cos{(\\beta)})}{2}", "\\frac{\\gamma^{2}}{2 \\beta}", "\\beta \\gamma + e^{\\gamma}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\gamma', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), cos(Symbol('\\\\beta', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)))", "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)), exp(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\log{(\\xi^{\\gamma})}", "variable": "\\xi", "positive": "\\xi (- \\gamma + \\log{(\\xi^{\\gamma})})", "negatives": ["\\xi (- \\gamma + \\log{(\\xi)} - 1)", "\\frac{\\xi (- \\xi + 2 \\log{(\\gamma)})}{2}", "\\gamma \\xi - \\cos{(\\xi)}", "\\frac{\\xi (\\xi + 2 \\cos{(\\gamma)})}{2}"], "srepr_premise_expression": "log(Pow(Symbol('\\\\xi', commutative=True), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), log(Pow(Symbol('\\\\xi', commutative=True), Symbol('\\\\gamma', commutative=True)))))", "srepr_negatives": ["Mul(Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), log(Symbol('\\\\xi', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), log(Symbol('\\\\gamma', commutative=True)))))", "Add(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\xi', commutative=True), Mul(Integer(2), cos(Symbol('\\\\gamma', commutative=True)))))"]}, {"premise_expression": "\\pi \\log{(\\omega)}", "variable": "\\omega", "positive": "\\omega \\pi (\\log{(\\omega)} - 1)", "negatives": ["\\omega (\\log{(\\omega \\pi)} - 1)", "\\frac{\\pi^{2} \\log{(\\omega)}}{2}", "- \\cos{(\\omega - \\pi)}", "\\pi e^{\\frac{\\omega}{\\pi}}"], "srepr_premise_expression": "Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True), Add(log(Symbol('\\\\omega', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\omega', commutative=True), Add(log(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), log(Symbol('\\\\omega', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))", "Mul(Symbol('\\\\pi', commutative=True), exp(Mul(Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))))"]}, {"premise_expression": "\\chi \\omega", "variable": "\\omega", "positive": "\\frac{\\chi \\omega^{2}}{2}", "negatives": ["\\frac{\\chi^{2} \\omega}{2}", "\\chi e^{\\frac{\\omega}{\\chi}}", "\\frac{\\omega (- 2 \\chi + \\omega)}{2}", "- \\chi \\omega + e^{\\omega}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\omega', commutative=True))", "Mul(Symbol('\\\\chi', commutative=True), exp(Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True)), exp(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\chi \\delta", "variable": "\\chi", "positive": "\\frac{\\chi^{2} \\delta}{2}", "negatives": ["\\frac{\\chi \\delta^{2}}{2}", "\\frac{\\chi (- \\chi + 2 \\delta)}{2}", "\\delta \\log{(\\chi)}", "e^{\\chi + \\delta}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\delta', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\delta', commutative=True))))", "Mul(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\chi', commutative=True)))", "exp(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\cos{(\\beta - \\psi)}", "variable": "\\beta", "positive": "\\sin{(\\beta - \\psi)}", "negatives": ["- \\sin{(\\beta - \\psi)}", "- e^{- \\beta + \\psi}", "\\beta \\psi (\\log{(\\beta)} - 1)", "\\beta (\\log{(\\beta \\psi)} - 1)"], "srepr_premise_expression": "cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "sin(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\psi', commutative=True))))", "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\psi', commutative=True), Add(log(Symbol('\\\\beta', commutative=True)), Integer(-1)))", "Mul(Symbol('\\\\beta', commutative=True), Add(log(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\psi', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\alpha + \\xi", "variable": "\\alpha", "positive": "\\frac{\\alpha (\\alpha + 2 \\xi)}{2}", "negatives": ["\\frac{\\alpha (\\alpha - 2 \\xi)}{2}", "\\frac{\\xi (2 \\alpha + \\xi)}{2}", "\\frac{\\alpha (\\alpha + 2 \\cos{(\\xi)})}{2}", "\\frac{\\alpha (- \\alpha + 2 \\log{(\\xi)})}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), cos(Symbol('\\\\xi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), log(Symbol('\\\\xi', commutative=True)))))"]}, {"premise_expression": "\\frac{\\delta}{\\alpha}", "variable": "\\alpha", "positive": "\\delta \\log{(\\alpha)}", "negatives": ["- \\delta \\cos{(\\alpha)}", "\\frac{\\delta^{2}}{2 \\alpha}", "\\frac{\\alpha^{2} \\delta}{2}", "- \\alpha \\delta - \\cos{(\\alpha)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Symbol('\\\\delta', commutative=True), cos(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\delta', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\delta', commutative=True))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\alpha', commutative=True))))"]}, {"premise_expression": "\\frac{\\pi \\xi}{\\omega}", "variable": "\\xi", "positive": "\\frac{\\pi \\xi^{2}}{2 \\omega}", "negatives": ["\\frac{\\pi^{2} \\xi}{2 \\omega}", "\\pi \\xi \\log{(\\omega)}", "\\frac{\\xi (2 \\pi - \\xi)}{2 \\omega}", "\\frac{\\xi (2 \\omega + \\pi \\xi)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))", "Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "- \\alpha + e^{\\psi}", "variable": "\\alpha", "positive": "\\frac{\\alpha (- \\alpha + 2 e^{\\psi})}{2}", "negatives": ["\\frac{\\alpha (\\alpha + 2 e^{\\psi})}{2}", "- \\alpha \\psi + e^{\\psi}", "\\frac{\\alpha^{2} \\sin{(\\psi)}}{2}", "- \\alpha \\psi + \\sin{(\\alpha)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), exp(Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\psi', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), exp(Symbol('\\\\psi', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True)), exp(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), sin(Symbol('\\\\psi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True)), sin(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\chi + \\delta - \\xi", "variable": "\\delta", "positive": "\\delta (\\chi + \\frac{\\delta}{2} - \\xi)", "negatives": ["\\frac{\\chi (\\chi + 2 \\delta - 2 \\xi)}{2}", "\\frac{\\xi (2 \\chi + 2 \\delta - \\xi)}{2}", "\\frac{\\delta (\\chi \\delta - 2 \\xi)}{2}", "\\frac{\\delta (\\delta + 2 \\xi)}{2 \\chi}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "(\\frac{\\chi}{\\sigma})^{\\chi}", "variable": "\\chi", "positive": "\\operatorname{NonElementaryIntegral}{((\\frac{\\chi}{\\sigma})^{\\chi},( \\chi))}", "negatives": ["\\chi (\\log{(\\chi \\sigma)} - 1)", "\\sin{(\\chi - \\sigma)}", "- \\cos{(\\chi - \\sigma)}", "- \\chi \\sigma - \\cos{(\\chi)}"], "srepr_premise_expression": "Pow(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1))), Symbol('\\\\chi', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Function('NonElementaryIntegral')(Pow(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1))), Symbol('\\\\chi', commutative=True)), Tuple(Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\chi', commutative=True), Add(log(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\sigma', commutative=True))), Integer(-1)))", "sin(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\chi', commutative=True))))"]}, {"premise_expression": "\\gamma + \\pi", "variable": "\\gamma", "positive": "\\frac{\\gamma (\\gamma + 2 \\pi)}{2}", "negatives": ["\\frac{\\pi (2 \\gamma + \\pi)}{2}", "- e^{- \\gamma + \\pi}", "\\frac{\\gamma (\\log{(\\gamma)} - 1)}{\\pi}", "\\frac{\\gamma^{2}}{2 \\pi}"], "srepr_premise_expression": "Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True))))", "Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Add(log(Symbol('\\\\gamma', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))"]}, {"premise_expression": "- \\pi + \\frac{\\delta}{\\alpha}", "variable": "\\pi", "positive": "- \\frac{\\pi^{2}}{2} + \\frac{\\delta \\pi}{\\alpha}", "negatives": ["\\frac{\\pi (2 \\alpha + 2 \\delta + \\pi)}{2}", "\\frac{\\delta \\pi (2 \\alpha + \\pi)}{2}", "- \\alpha \\pi + \\delta \\log{(\\alpha)}", "\\frac{\\pi (2 \\alpha \\delta - \\pi)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2))), Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\alpha', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "- \\psi - \\sigma + \\xi", "variable": "\\sigma", "positive": "\\sigma (- \\psi - \\frac{\\sigma}{2} + \\xi)", "negatives": ["\\frac{\\sigma (2 \\psi + \\sigma - 2 \\xi)}{2}", "\\frac{\\xi (- 2 \\psi - 2 \\sigma + \\xi)}{2}", "\\frac{\\psi (- \\psi - 2 \\sigma + 2 \\xi)}{2}", "\\sigma (\\psi^{\\xi} - \\xi)"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), Rational(1, 2), Symbol('\\\\sigma', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\psi', commutative=True)), Symbol('\\\\sigma', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Symbol('\\\\sigma', commutative=True), Add(Pow(Symbol('\\\\psi', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\alpha \\log{(\\omega)}", "variable": "\\alpha", "positive": "\\frac{\\alpha^{2} \\log{(\\omega)}}{2}", "negatives": ["\\frac{\\alpha^{2} e^{\\omega}}{2}", "\\frac{\\alpha (- \\alpha + 2 \\omega)}{2}", "\\alpha \\omega (\\log{(\\omega)} - 1)", "\\frac{\\alpha \\omega (\\alpha - 2)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), log(Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), exp(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True), Add(log(Symbol('\\\\omega', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Integer(-2)))"]}, {"premise_expression": "\\cos{(\\frac{\\gamma}{\\alpha})}", "variable": "\\alpha", "positive": "\\alpha \\cos{(\\frac{\\gamma}{\\alpha})} + \\gamma \\operatorname{Si}{(\\frac{\\gamma}{\\alpha})}", "negatives": ["- \\alpha \\gamma + \\sin{(\\alpha)}", "\\alpha (\\gamma + \\log{(\\alpha)} - 1)", "\\frac{\\alpha (- \\alpha + 2 \\gamma)}{2}", "\\gamma \\log{(\\alpha)}"], "srepr_premise_expression": "cos(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\alpha', commutative=True), cos(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True)))), Mul(Symbol('\\\\gamma', commutative=True), Si(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True)))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True)), sin(Symbol('\\\\alpha', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\alpha', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\gamma', commutative=True))))", "Mul(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\chi \\delta", "variable": "\\chi", "positive": "\\frac{\\chi^{2} \\delta}{2}", "negatives": ["\\frac{\\chi \\delta^{2}}{2}", "\\delta e^{\\frac{\\chi}{\\delta}}", "\\frac{\\chi (\\chi + 2 \\delta)}{2}", "\\frac{\\chi^{2} \\log{(\\delta)}}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\delta', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(2)))", "Mul(Symbol('\\\\delta', commutative=True), exp(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), log(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\frac{\\pi}{\\psi}", "variable": "\\psi", "positive": "\\pi \\log{(\\psi)}", "negatives": ["\\frac{\\pi^{2}}{2 \\psi}", "\\frac{\\psi (\\log{(\\psi)} - 1)}{\\pi}", "\\frac{\\psi^{2} e^{\\pi}}{2}", "\\frac{\\psi (\\psi + 2 \\log{(\\pi)})}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))", "Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True), Add(log(Symbol('\\\\psi', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), exp(Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(2), log(Symbol('\\\\pi', commutative=True)))))"]}, {"premise_expression": "\\cos^{\\chi}{(\\xi)}", "variable": "\\xi", "positive": "\\int \\cos^{\\chi}{(\\xi)} d\\xi", "negatives": ["\\xi (\\log{(\\frac{\\xi}{\\chi})} - 1)", "\\chi \\xi + e^{\\xi}", "- \\chi \\xi + e^{\\xi}", "\\chi \\operatorname{Si}{(\\frac{\\chi}{\\xi})} + \\xi \\cos{(\\frac{\\chi}{\\xi})}"], "srepr_premise_expression": "Pow(cos(Symbol('\\\\xi', commutative=True)), Symbol('\\\\chi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Integral(Pow(cos(Symbol('\\\\xi', commutative=True)), Symbol('\\\\chi', commutative=True)), Tuple(Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\xi', commutative=True), Add(log(Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))), Integer(-1)))", "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True)), exp(Symbol('\\\\xi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True)), exp(Symbol('\\\\xi', commutative=True)))", "Add(Mul(Symbol('\\\\chi', commutative=True), Si(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))), Mul(Symbol('\\\\xi', commutative=True), cos(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))))"]}, {"premise_expression": "\\cos{(\\alpha + \\delta)}", "variable": "\\alpha", "positive": "\\sin{(\\alpha + \\delta)}", "negatives": ["\\frac{\\sin{(\\alpha)}}{\\delta}", "- \\frac{\\cos{(\\alpha)}}{\\delta}", "\\alpha (\\log{(\\frac{\\delta}{\\alpha})} + 1)", "- \\alpha \\delta + \\sin{(\\alpha)}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "sin(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), sin(Symbol('\\\\alpha', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), cos(Symbol('\\\\alpha', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), Add(log(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True))), Integer(1)))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\delta', commutative=True)), sin(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\pi + \\sigma", "variable": "\\pi", "positive": "\\frac{\\pi (\\pi + 2 \\sigma)}{2}", "negatives": ["\\frac{\\sigma (2 \\pi + \\sigma)}{2}", "e^{\\pi + \\sigma}", "\\pi (\\log{(\\pi \\sigma)} - 1)", "\\frac{\\pi (- \\pi + 2 \\sin{(\\sigma)})}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "exp(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True)))", "Mul(Symbol('\\\\pi', commutative=True), Add(log(Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\sigma', commutative=True)))))"]}, {"premise_expression": "\\beta \\gamma", "variable": "\\beta", "positive": "\\frac{\\beta^{2} \\gamma}{2}", "negatives": ["\\frac{\\beta \\gamma^{2}}{2}", "\\frac{\\beta (\\beta + 2 \\gamma)}{2}", "\\sin{(\\beta - \\gamma)}", "e^{\\beta + \\gamma}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\gamma', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\gamma', commutative=True))))", "sin(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "exp(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "- \\psi + \\sin{(\\sigma)}", "variable": "\\psi", "positive": "\\frac{\\psi (- \\psi + 2 \\sin{(\\sigma)})}{2}", "negatives": ["- \\psi \\sigma - \\cos{(\\sigma)}", "\\frac{\\psi^{2}}{2 \\sigma}", "\\frac{\\psi (\\log{(\\psi)} - 1)}{\\sigma}", "\\sin{(\\psi + \\sigma)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), sin(Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\sigma', commutative=True)))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "Mul(Symbol('\\\\psi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Add(log(Symbol('\\\\psi', commutative=True)), Integer(-1)))", "sin(Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\omega^{\\sigma} \\xi", "variable": "\\xi", "positive": "\\frac{\\omega^{\\sigma} \\xi^{2}}{2}", "negatives": ["\\frac{\\omega \\xi (- 2 \\sigma + \\xi)}{2}", "\\frac{\\xi (- 2 \\omega + \\sigma \\xi)}{2}", "\\frac{\\xi (2 \\sigma + \\xi)}{2 \\omega}", "\\frac{\\xi (2 \\omega + \\xi)}{2 \\sigma}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True)), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\sigma', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\chi + e^{\\gamma}", "variable": "\\chi", "positive": "\\frac{\\chi (\\chi + 2 e^{\\gamma})}{2}", "negatives": ["\\frac{\\chi (\\chi + 2 \\cos{(\\gamma)})}{2}", "\\chi \\gamma + e^{\\gamma}", "\\frac{\\chi^{2}}{2 \\gamma} + \\chi", "- \\chi \\gamma - \\cos{(\\chi)}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), exp(Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), exp(Symbol('\\\\gamma', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), cos(Symbol('\\\\gamma', commutative=True)))))", "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True)), exp(Symbol('\\\\gamma', commutative=True)))", "Add(Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1))), Symbol('\\\\chi', commutative=True))", "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\chi', commutative=True))))"]}, {"premise_expression": "\\psi - \\xi", "variable": "\\xi", "positive": "\\frac{\\xi (2 \\psi - \\xi)}{2}", "negatives": ["\\frac{\\psi (\\psi - 2 \\xi)}{2}", "\\frac{\\xi (- \\xi + 2 \\cos{(\\psi)})}{2}", "\\sin{(\\psi + \\xi)}", "\\frac{\\xi^{2} (2 \\xi + 3)}{6}"], "srepr_premise_expression": "Add(Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\psi', commutative=True)))))", "sin(Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 6), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), Add(Mul(Integer(2), Symbol('\\\\xi', commutative=True)), Integer(3)))"]}, {"premise_expression": "\\sin{(\\beta + \\gamma)}", "variable": "\\beta", "positive": "- \\cos{(\\beta + \\gamma)}", "negatives": ["\\frac{\\beta (\\beta + 2 \\gamma)}{2}", "\\beta \\gamma - \\cos{(\\beta)}", "\\frac{\\beta^{2} \\log{(\\gamma)}}{2}", "\\frac{\\beta (\\beta + 2 e^{\\gamma})}{2}"], "srepr_premise_expression": "sin(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\gamma', commutative=True))))", "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\beta', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), log(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), exp(Symbol('\\\\gamma', commutative=True)))))"]}, {"premise_expression": "\\frac{\\log{(\\beta)}}{\\delta}", "variable": "\\delta", "positive": "\\log{(\\beta)} \\log{(\\delta)}", "negatives": ["\\frac{\\beta (\\log{(\\beta)} - 1)}{\\delta}", "\\delta (\\log{(\\beta \\delta)} - 1)", "\\beta \\delta (\\log{(\\delta)} - 1)", "\\delta (\\log{(\\frac{\\delta}{\\beta})} - 1)"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), log(Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(log(Symbol('\\\\beta', commutative=True)), log(Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Add(log(Symbol('\\\\beta', commutative=True)), Integer(-1)))", "Mul(Symbol('\\\\delta', commutative=True), Add(log(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True), Add(log(Symbol('\\\\delta', commutative=True)), Integer(-1)))", "Mul(Symbol('\\\\delta', commutative=True), Add(log(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\sigma (- \\gamma + \\pi)", "variable": "\\sigma", "positive": "\\frac{\\sigma^{2} (- \\gamma + \\pi)}{2}", "negatives": ["\\frac{\\gamma \\sigma (- \\gamma + 2 \\pi)}{2}", "\\frac{\\pi \\sigma (- 2 \\gamma + \\pi)}{2}", "\\frac{\\sigma (- 2 \\gamma + 2 \\pi + \\sigma)}{2}", "\\frac{\\gamma \\pi \\sigma^{2}}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))"]}, {"premise_expression": "\\gamma \\pi", "variable": "\\gamma", "positive": "\\frac{\\gamma^{2} \\pi}{2}", "negatives": ["\\frac{\\gamma^{2}}{2}", "\\frac{\\gamma \\pi^{2}}{2}", "\\frac{\\gamma^{2}}{2 \\pi}", "e^{\\gamma + \\pi}"], "srepr_premise_expression": "Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Symbol('\\\\pi', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))", "exp(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\sin{(\\alpha + \\omega)}", "variable": "\\omega", "positive": "- \\cos{(\\alpha + \\omega)}", "negatives": ["\\omega \\sin{(1)}", "\\frac{\\omega^{3}}{3}", "\\frac{\\omega (\\omega + 2 \\log{(\\alpha)})}{2}", "\\frac{\\omega (\\omega + 2 e^{\\alpha})}{2}"], "srepr_premise_expression": "sin(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Mul(Symbol('\\\\omega', commutative=True), sin(Integer(1)))", "Mul(Rational(1, 3), Pow(Symbol('\\\\omega', commutative=True), Integer(3)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), log(Symbol('\\\\alpha', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), exp(Symbol('\\\\alpha', commutative=True)))))"]}, {"premise_expression": "\\beta + \\xi", "variable": "\\beta", "positive": "\\frac{\\beta (\\beta + 2 \\xi)}{2}", "negatives": ["\\frac{\\beta (\\beta - 2 \\xi)}{2}", "\\frac{\\xi (2 \\beta + \\xi)}{2}", "\\frac{\\beta^{2} \\log{(\\xi)}}{2}", "e^{\\beta + \\xi}"], "srepr_premise_expression": "Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), log(Symbol('\\\\xi', commutative=True)))", "exp(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "- \\psi + \\frac{\\delta}{\\alpha}", "variable": "\\psi", "positive": "- \\frac{\\psi^{2}}{2} + \\frac{\\delta \\psi}{\\alpha}", "negatives": ["\\frac{\\alpha \\psi^{2}}{2 \\delta}", "\\frac{\\delta \\psi^{2}}{2 \\alpha}", "\\alpha \\log{(\\psi)} + \\delta \\psi", "- \\delta \\psi + \\frac{\\delta^{2}}{2 \\alpha}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2))), Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True), Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "Add(Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\psi', commutative=True))), Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\psi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\delta', commutative=True), Integer(2))))"]}, {"premise_expression": "\\gamma \\log{(\\psi)}", "variable": "\\gamma", "positive": "\\frac{\\gamma^{2} \\log{(\\psi)}}{2}", "negatives": ["\\frac{\\gamma (\\gamma - 2 \\psi)}{2}", "\\frac{\\gamma^{2}}{2 \\psi}", "\\gamma \\psi (\\log{(\\psi)} - 1)", "\\gamma (\\log{(\\frac{\\gamma}{\\psi})} - 1)"], "srepr_premise_expression": "Mul(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), log(Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))", "Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True), Add(log(Symbol('\\\\psi', commutative=True)), Integer(-1)))", "Mul(Symbol('\\\\gamma', commutative=True), Add(log(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))), Integer(-1)))"]}, {"premise_expression": "e^{\\xi^{\\gamma}}", "variable": "\\xi", "positive": "\\frac{e^{- \\frac{i \\pi}{\\gamma}} \\gamma(\\frac{1}{\\gamma}, \\xi^{\\gamma} e^{i \\pi})}{\\gamma}", "negatives": ["\\frac{\\xi (- \\xi + 2 \\log{(\\gamma)})}{2}", "\\gamma \\log{(\\gamma + \\xi)} + \\xi \\log{(\\gamma + \\xi)} - \\xi", "\\log{(\\xi)} \\cos{(\\gamma)}", "- \\gamma \\log{(- \\gamma + \\xi)} + \\xi \\log{(\\gamma - \\xi)} - \\xi"], "srepr_premise_expression": "exp(Pow(Symbol('\\\\xi', commutative=True), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), exp(Mul(Integer(-1), I, pi, Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)))), lowergamma(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Mul(Pow(Symbol('\\\\xi', commutative=True), Symbol('\\\\gamma', commutative=True)), exp_polar(Mul(I, pi)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), log(Symbol('\\\\gamma', commutative=True)))))", "Add(Mul(Symbol('\\\\gamma', commutative=True), log(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)))), Mul(Symbol('\\\\xi', commutative=True), log(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "Mul(log(Symbol('\\\\xi', commutative=True)), cos(Symbol('\\\\gamma', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\xi', commutative=True)))), Mul(Symbol('\\\\xi', commutative=True), log(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\chi e^{\\beta}", "variable": "\\beta", "positive": "\\chi e^{\\beta}", "negatives": ["\\frac{\\chi^{2} e^{\\beta}}{2}", "- e^{- \\beta + \\chi}", "\\beta \\chi + \\sin{(\\beta)}", "\\beta \\chi - \\cos{(\\beta)}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), exp(Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\chi', commutative=True), exp(Symbol('\\\\beta', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), exp(Symbol('\\\\beta', commutative=True)))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\chi', commutative=True))))", "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True)), sin(Symbol('\\\\beta', commutative=True)))", "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\beta', commutative=True))))"]}, {"premise_expression": "\\frac{\\cos{(\\delta)}}{\\chi}", "variable": "\\chi", "positive": "\\log{(\\chi)} \\cos{(\\delta)}", "negatives": ["- \\chi + \\delta \\log{(\\chi)}", "\\delta \\sin{(\\chi)}", "\\frac{\\sin{(\\delta)}}{\\chi}", "e^{\\chi - \\delta}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), cos(Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(log(Symbol('\\\\chi', commutative=True)), cos(Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\chi', commutative=True))))", "Mul(Symbol('\\\\delta', commutative=True), sin(Symbol('\\\\chi', commutative=True)))", "Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), sin(Symbol('\\\\delta', commutative=True)))", "exp(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))"]}, {"premise_expression": "\\frac{\\omega}{\\sigma}", "variable": "\\omega", "positive": "\\frac{\\omega^{2}}{2 \\sigma}", "negatives": ["\\omega \\log{(\\sigma)}", "\\frac{\\omega^{2} e^{\\sigma}}{2}", "\\sigma \\log{(\\omega)}", "\\cos{(\\omega - \\sigma)}"], "srepr_premise_expression": "Mul(Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), exp(Symbol('\\\\sigma', commutative=True)))", "Mul(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "cos(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\frac{\\gamma}{\\pi}", "variable": "\\pi", "positive": "\\gamma \\log{(\\pi)}", "negatives": ["\\frac{\\gamma^{2}}{2 \\pi}", "\\frac{\\sin{(\\pi)}}{\\gamma}", "\\frac{\\gamma \\pi^{2}}{2}", "\\cos{(\\gamma - \\pi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))", "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), sin(Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "cos(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\delta e^{\\chi}", "variable": "\\delta", "positive": "\\frac{\\delta^{2} e^{\\chi}}{2}", "negatives": ["\\delta e^{\\chi}", "\\frac{\\delta (2 \\chi + \\delta)}{2}", "\\frac{\\delta (\\delta + 2 e^{\\chi})}{2}", "\\frac{\\delta (\\delta + 2 \\cos{(\\chi)})}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\delta', commutative=True), exp(Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), exp(Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\delta', commutative=True), exp(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), exp(Symbol('\\\\chi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), cos(Symbol('\\\\chi', commutative=True)))))"]}, {"premise_expression": "\\cos{(\\frac{\\gamma}{\\delta})}", "variable": "\\delta", "positive": "\\delta \\cos{(\\frac{\\gamma}{\\delta})} + \\gamma \\operatorname{Si}{(\\frac{\\gamma}{\\delta})}", "negatives": ["\\delta \\gamma - \\cos{(\\delta)}", "\\log{(\\delta)} \\log{(\\gamma)}", "\\frac{\\delta (\\delta + 2 \\gamma)}{2}", "\\log{(\\delta)} \\sin{(\\gamma)}"], "srepr_premise_expression": "cos(Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\delta', commutative=True), cos(Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True)))), Mul(Symbol('\\\\gamma', commutative=True), Si(Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\delta', commutative=True))))", "Mul(log(Symbol('\\\\delta', commutative=True)), log(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), Symbol('\\\\gamma', commutative=True))))", "Mul(log(Symbol('\\\\delta', commutative=True)), sin(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\alpha \\omega - \\pi", "variable": "\\omega", "positive": "\\frac{\\omega (\\alpha \\omega - 2 \\pi)}{2}", "negatives": ["\\frac{\\alpha (\\alpha \\omega - 2 \\pi)}{2}", "\\frac{\\omega (- 2 \\alpha + \\omega \\pi)}{2}", "\\frac{\\pi (2 \\alpha \\omega - \\pi)}{2}", "\\frac{\\omega (2 \\alpha^{\\pi} + \\omega)}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Pow(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True))), Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\frac{\\chi}{\\pi} - \\omega", "variable": "\\pi", "positive": "\\chi \\log{(\\pi)} - \\omega \\pi", "negatives": ["\\chi \\omega \\log{(\\pi)}", "\\frac{\\chi^{2}}{2 \\pi} - \\chi \\omega", "\\frac{\\omega \\log{(\\pi)}}{\\chi}", "\\frac{\\chi \\omega}{\\pi} - \\frac{\\omega^{2}}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1))), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\pi', commutative=True))), Mul(Integer(-1), Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True), log(Symbol('\\\\pi', commutative=True)))", "Add(Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1))), Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True)))", "Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True), log(Symbol('\\\\pi', commutative=True)))", "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1))), Mul(Integer(-1), Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2))))"]}, {"premise_expression": "\\chi e^{\\gamma}", "variable": "\\chi", "positive": "\\frac{\\chi^{2} e^{\\gamma}}{2}", "negatives": ["\\frac{\\chi^{2} \\sin{(\\gamma)}}{2}", "\\frac{\\chi^{2} \\log{(\\gamma)}}{2}", "\\chi e^{\\gamma}", "\\frac{\\chi^{2} \\gamma}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), exp(Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), exp(Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), sin(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), log(Symbol('\\\\gamma', commutative=True)))", "Mul(Symbol('\\\\chi', commutative=True), exp(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\gamma', commutative=True))"]}, {"premise_expression": "\\alpha + \\chi \\xi", "variable": "\\chi", "positive": "\\frac{\\chi (2 \\alpha + \\chi \\xi)}{2}", "negatives": ["\\frac{\\xi (2 \\alpha + \\chi \\xi)}{2}", "\\frac{\\alpha (\\alpha + 2 \\chi \\xi)}{2}", "\\frac{\\chi (2 \\alpha + \\chi)}{2 \\xi}", "\\frac{\\chi (2 \\alpha + \\chi + 2 \\xi)}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\log{(\\beta + \\sigma)}", "variable": "\\beta", "positive": "\\beta \\log{(\\beta + \\sigma)} - \\beta + \\sigma \\log{(\\beta + \\sigma)}", "negatives": ["\\beta \\log{(\\beta + \\sigma)} + \\sigma \\log{(\\beta + \\sigma)} - \\sigma", "\\beta \\cos{(\\frac{\\sigma}{\\beta})} + \\sigma \\operatorname{Si}{(\\frac{\\sigma}{\\beta})}", "\\log{(\\beta)} \\sin{(\\sigma)}", "\\sin{(\\beta - \\sigma)}"], "srepr_premise_expression": "log(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\beta', commutative=True), log(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True)))), Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Symbol('\\\\sigma', commutative=True), log(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\beta', commutative=True), log(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True)))), Mul(Symbol('\\\\sigma', commutative=True), log(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True)))), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))", "Add(Mul(Symbol('\\\\beta', commutative=True), cos(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True)))), Mul(Symbol('\\\\sigma', commutative=True), Si(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True)))))", "Mul(log(Symbol('\\\\beta', commutative=True)), sin(Symbol('\\\\sigma', commutative=True)))", "sin(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\frac{\\alpha - \\chi}{\\gamma}", "variable": "\\chi", "positive": "\\frac{\\chi (2 \\alpha - \\chi)}{2 \\gamma}", "negatives": ["\\frac{\\alpha (\\alpha - 2 \\chi)}{2 \\gamma}", "\\frac{\\chi (2 \\alpha^{\\gamma} - \\chi)}{2}", "\\frac{\\chi (2 \\alpha \\gamma + \\chi)}{2}", "(\\alpha - \\chi) \\log{(\\gamma)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True))))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\chi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(2), Pow(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True))), Mul(Integer(-1), Symbol('\\\\chi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\chi', commutative=True)))", "Mul(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True))), log(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\delta - \\omega", "variable": "\\omega", "positive": "\\frac{\\omega (2 \\delta - \\omega)}{2}", "negatives": ["\\frac{\\delta (\\delta - 2 \\omega)}{2}", "\\sin{(\\delta + \\omega)}", "\\delta \\omega - \\cos{(\\omega)}", "\\frac{\\omega (\\omega + 2 \\sin{(\\delta)})}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True))))", "sin(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True)))", "Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), sin(Symbol('\\\\delta', commutative=True)))))"]}, {"premise_expression": "\\frac{- \\omega + \\pi}{\\sigma}", "variable": "\\omega", "positive": "\\frac{\\omega (- \\omega + 2 \\pi)}{2 \\sigma}", "negatives": ["\\frac{\\pi (- 2 \\omega + \\pi)}{2 \\sigma}", "\\frac{\\omega (- \\omega + 2 \\pi \\sigma)}{2}", "\\frac{\\omega \\sigma (\\omega + 2 \\pi)}{2}", "\\frac{\\omega (\\omega \\pi + 2 \\sigma)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\frac{e^{\\omega}}{\\alpha}", "variable": "\\alpha", "positive": "e^{\\omega} \\log{(\\alpha)}", "negatives": ["e^{\\alpha + \\omega}", "- \\cos{(\\alpha + \\omega)}", "- \\alpha \\omega + e^{\\alpha}", "- \\frac{\\cos{(\\alpha)}}{\\omega}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), exp(Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(exp(Symbol('\\\\omega', commutative=True)), log(Symbol('\\\\alpha', commutative=True)))", "srepr_negatives": ["exp(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)), exp(Symbol('\\\\alpha', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), cos(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\frac{\\delta}{\\omega} + \\gamma", "variable": "\\omega", "positive": "\\delta \\log{(\\omega)} + \\gamma \\omega", "negatives": ["\\frac{\\delta^{2}}{2 \\omega} + \\delta \\gamma", "\\frac{\\delta \\gamma}{\\omega} + \\frac{\\gamma^{2}}{2}", "\\frac{\\omega^{2}}{2} + \\frac{\\gamma \\omega}{\\delta}", "\\frac{\\omega (\\delta \\omega + 2 \\gamma)}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1))), Symbol('\\\\gamma', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\omega', commutative=True))), Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Add(Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Pow(Symbol('\\\\omega', commutative=True), Integer(-1))), Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\gamma', commutative=True)))", "Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1))), Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2))))", "Add(Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2))), Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\gamma', commutative=True))))"]}, {"premise_expression": "\\omega \\psi", "variable": "\\psi", "positive": "\\frac{\\omega \\psi^{2}}{2}", "negatives": ["\\frac{\\omega^{2} \\psi}{2}", "\\frac{\\psi (2 \\omega - \\psi)}{2}", "\\omega \\psi - \\cos{(\\psi)}", "- \\omega \\psi - \\cos{(\\psi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Add(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\psi', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "\\beta \\delta \\pi", "variable": "\\pi", "positive": "\\frac{\\beta \\delta \\pi^{2}}{2}", "negatives": ["\\frac{\\beta^{2} \\delta \\pi}{2}", "\\frac{\\beta \\delta^{2} \\pi}{2}", "\\frac{\\beta^{\\delta} \\pi^{2}}{2}", "\\beta \\delta \\log{(\\pi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Symbol('\\\\pi', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True)), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True), log(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\gamma (\\alpha + \\chi)", "variable": "\\chi", "positive": "\\frac{\\chi \\gamma (2 \\alpha + \\chi)}{2}", "negatives": ["\\frac{\\gamma^{2} (\\alpha + \\chi)}{2}", "\\frac{\\alpha \\gamma (\\alpha + 2 \\chi)}{2}", "\\frac{\\chi (\\alpha \\chi + 2 \\gamma)}{2}", "\\frac{\\chi^{2}}{2 \\alpha^{2}}"], "srepr_premise_expression": "Mul(Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\chi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-2)), Pow(Symbol('\\\\chi', commutative=True), Integer(2)))"]}, {"premise_expression": "\\log{(\\delta - \\psi)}", "variable": "\\delta", "positive": "\\delta \\log{(\\delta - \\psi)} - \\delta - \\psi \\log{(\\delta - \\psi)}", "negatives": ["- \\delta \\log{(- \\delta + \\psi)} + \\psi \\log{(\\delta - \\psi)} - \\psi", "\\frac{\\delta (- \\delta + 2 \\cos{(\\psi)})}{2}", "\\frac{\\delta (\\delta - 2 \\psi)}{2}", "\\frac{\\delta (\\delta + 2 \\psi)}{2}"], "srepr_premise_expression": "log(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\delta', commutative=True), log(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Symbol('\\\\psi', commutative=True), log(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\psi', commutative=True)))), Mul(Symbol('\\\\psi', commutative=True), log(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\psi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "\\omega - \\xi", "variable": "\\omega", "positive": "\\frac{\\omega (\\omega - 2 \\xi)}{2}", "negatives": ["\\frac{\\omega (\\omega + 2 \\xi)}{2}", "\\frac{\\xi (2 \\omega - \\xi)}{2}", "\\frac{\\omega^{2} \\log{(\\xi)}}{2}", "\\sin{(\\omega - \\xi)}"], "srepr_premise_expression": "Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), log(Symbol('\\\\xi', commutative=True)))", "sin(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\alpha + \\beta + \\gamma", "variable": "\\alpha", "positive": "\\alpha (\\frac{\\alpha}{2} + \\beta + \\gamma)", "negatives": ["\\frac{\\alpha (\\alpha + 2 \\beta - 2 \\gamma)}{2}", "\\frac{\\beta (2 \\alpha + \\beta + 2 \\gamma)}{2}", "\\frac{\\gamma (2 \\alpha + 2 \\beta + \\gamma)}{2}", "\\frac{\\alpha (\\alpha - 2 \\beta)}{2 \\gamma}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\alpha', commutative=True), Add(Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True))))"]}, {"premise_expression": "\\alpha - \\delta", "variable": "\\delta", "positive": "\\frac{\\delta (2 \\alpha - \\delta)}{2}", "negatives": ["\\frac{\\alpha (\\alpha - 2 \\delta)}{2}", "\\frac{\\alpha \\delta^{2}}{2}", "- e^{\\alpha - \\delta}", "\\alpha e^{\\delta}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(2)))", "Mul(Integer(-1), exp(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)))))", "Mul(Symbol('\\\\alpha', commutative=True), exp(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "e^{\\chi + \\pi}", "variable": "\\chi", "positive": "e^{\\chi + \\pi}", "negatives": ["- \\cos{(\\chi - \\pi)}", "\\frac{\\chi \\pi (\\chi + 2)}{2}", "- \\chi \\pi + \\sin{(\\chi)}", "\\chi \\pi + \\sin{(\\chi)}"], "srepr_premise_expression": "exp(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "exp(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Integer(2)))", "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True)), sin(Symbol('\\\\chi', commutative=True)))", "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True)), sin(Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "\\sin{(\\frac{\\pi}{\\alpha})}", "variable": "\\alpha", "positive": "\\alpha \\sin{(\\frac{\\pi}{\\alpha})} - \\frac{\\pi \\log{(\\frac{\\pi^{2}}{\\alpha^{2}})}}{2} + \\pi \\log{(\\frac{\\pi}{\\alpha})} - \\pi \\operatorname{Ci}{(\\frac{\\pi}{\\alpha})}", "negatives": ["\\alpha \\log{(\\alpha + \\pi)} - \\alpha + \\pi \\log{(\\alpha + \\pi)}", "\\alpha \\cos{(\\frac{\\pi}{\\alpha})} + \\pi \\operatorname{Si}{(\\frac{\\pi}{\\alpha})}", "\\alpha (\\log{(\\frac{\\pi}{\\alpha})} + 1)", "\\frac{\\alpha (- \\alpha + 2 \\log{(\\pi)})}{2}"], "srepr_premise_expression": "sin(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\alpha', commutative=True), sin(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True)))), Mul(Integer(-1), Rational(1, 2), Symbol('\\\\pi', commutative=True), log(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-2)), Pow(Symbol('\\\\pi', commutative=True), Integer(2))))), Mul(Symbol('\\\\pi', commutative=True), log(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\pi', commutative=True), Ci(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\alpha', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Symbol('\\\\pi', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)))))", "Add(Mul(Symbol('\\\\alpha', commutative=True), cos(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True)))), Mul(Symbol('\\\\pi', commutative=True), Si(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True)))))", "Mul(Symbol('\\\\alpha', commutative=True), Add(log(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))), Integer(1)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), log(Symbol('\\\\pi', commutative=True)))))"]}, {"premise_expression": "\\alpha \\pi", "variable": "\\pi", "positive": "\\frac{\\alpha \\pi^{2}}{2}", "negatives": ["\\frac{\\alpha^{2} \\pi}{2}", "\\frac{\\pi^{2} \\log{(\\alpha)}}{2}", "\\pi (\\alpha + \\sin{(\\alpha)})", "\\pi (- \\alpha + \\log{(\\pi)} - 1)"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\pi', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), log(Symbol('\\\\alpha', commutative=True)))", "Mul(Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\alpha', commutative=True), sin(Symbol('\\\\alpha', commutative=True))))", "Mul(Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), log(Symbol('\\\\pi', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\alpha \\beta \\chi", "variable": "\\chi", "positive": "\\frac{\\alpha \\beta \\chi^{2}}{2}", "negatives": ["\\frac{\\alpha^{2} \\beta \\chi}{2}", "\\frac{\\alpha \\beta^{2} \\chi}{2}", "\\frac{\\beta \\chi (2 \\alpha - \\chi)}{2}", "\\frac{\\chi (2 \\beta - \\chi)}{2 \\alpha}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\chi', commutative=True))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\chi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Symbol('\\\\chi', commutative=True))))"]}, {"premise_expression": "\\sigma e^{\\alpha}", "variable": "\\alpha", "positive": "\\sigma e^{\\alpha}", "negatives": ["\\frac{\\sigma^{2} e^{\\alpha}}{2}", "- e^{- \\alpha + \\sigma}", "\\frac{\\sin{(\\alpha)}}{\\sigma}", "\\frac{\\alpha^{2} e^{\\sigma}}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\sigma', commutative=True), exp(Symbol('\\\\alpha', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\sigma', commutative=True), exp(Symbol('\\\\alpha', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), exp(Symbol('\\\\alpha', commutative=True)))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\sigma', commutative=True))))", "Mul(Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), sin(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), exp(Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "e^{\\frac{\\chi}{\\beta}}", "variable": "\\chi", "positive": "\\beta e^{\\frac{\\chi}{\\beta}}", "negatives": ["- \\beta \\cos{(\\chi)}", "e \\chi", "(\\chi - 1) e^{\\chi}", "\\chi - \\frac{\\chi^{2}}{2 \\beta}"], "srepr_premise_expression": "exp(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\beta', commutative=True), exp(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\chi', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), Symbol('\\\\beta', commutative=True), cos(Symbol('\\\\chi', commutative=True)))", "Mul(E, Symbol('\\\\chi', commutative=True))", "Mul(Add(Symbol('\\\\chi', commutative=True), Integer(-1)), exp(Symbol('\\\\chi', commutative=True)))", "Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Pow(Symbol('\\\\chi', commutative=True), Integer(2))))"]}, {"premise_expression": "\\frac{\\delta}{\\gamma}", "variable": "\\delta", "positive": "\\frac{\\delta^{2}}{2 \\gamma}", "negatives": ["\\delta \\log{(\\gamma)}", "\\frac{\\delta^{2} \\gamma}{2}", "\\frac{\\delta^{2} \\sin{(\\gamma)}}{2}", "\\sin{(\\delta + \\gamma)}"], "srepr_premise_expression": "Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Symbol('\\\\gamma', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), sin(Symbol('\\\\gamma', commutative=True)))", "sin(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "e^{- \\alpha + \\chi}", "variable": "\\alpha", "positive": "- e^{- \\alpha + \\chi}", "negatives": ["e^{- \\alpha + \\chi}", "- \\alpha \\chi + \\sin{(\\alpha)}", "\\alpha \\chi + \\sin{(\\alpha)}", "\\log{(\\alpha)} \\log{(\\chi)}"], "srepr_premise_expression": "exp(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\chi', commutative=True))))", "srepr_negatives": ["exp(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\chi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)), sin(Symbol('\\\\alpha', commutative=True)))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)), sin(Symbol('\\\\alpha', commutative=True)))", "Mul(log(Symbol('\\\\alpha', commutative=True)), log(Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "- \\gamma + \\psi", "variable": "\\gamma", "positive": "\\frac{\\gamma (- \\gamma + 2 \\psi)}{2}", "negatives": ["\\frac{\\psi (- 2 \\gamma + \\psi)}{2}", "\\sin{(\\gamma - \\psi)}", "e^{\\gamma - \\psi}", "\\frac{\\gamma (- \\gamma + 2 \\log{(\\psi)})}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\psi', commutative=True)))", "sin(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "exp(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), log(Symbol('\\\\psi', commutative=True)))))"]}, {"premise_expression": "\\frac{\\gamma \\sigma}{\\xi}", "variable": "\\sigma", "positive": "\\frac{\\gamma \\sigma^{2}}{2 \\xi}", "negatives": ["\\frac{\\sigma^{2} \\xi}{2 \\gamma}", "\\frac{\\gamma^{2} \\sigma}{2 \\xi}", "\\gamma \\sigma \\log{(\\xi)}", "\\frac{\\sigma^{2} \\xi^{\\gamma}}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Symbol('\\\\sigma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\alpha + \\chi", "variable": "\\chi", "positive": "\\frac{\\chi (2 \\alpha + \\chi)}{2}", "negatives": ["\\frac{\\alpha (\\alpha + 2 \\chi)}{2}", "\\chi \\log{(2 \\alpha)}", "- \\alpha \\chi + \\sin{(\\chi)}", "\\log{(\\chi)} \\cos{(\\alpha)}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\chi', commutative=True))))", "Mul(Symbol('\\\\chi', commutative=True), log(Mul(Integer(2), Symbol('\\\\alpha', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)), sin(Symbol('\\\\chi', commutative=True)))", "Mul(log(Symbol('\\\\chi', commutative=True)), cos(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\gamma + \\cos{(\\xi)}", "variable": "\\gamma", "positive": "\\frac{\\gamma (\\gamma + 2 \\cos{(\\xi)})}{2}", "negatives": ["\\frac{\\gamma (- \\gamma + 2 \\xi)}{2}", "\\frac{\\gamma^{2} e^{\\xi}}{2}", "\\frac{\\gamma^{2} \\sin{(\\xi)}}{2}", "\\gamma \\xi + \\sin{(\\xi)}"], "srepr_premise_expression": "Add(Symbol('\\\\gamma', commutative=True), cos(Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), cos(Symbol('\\\\xi', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), exp(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), sin(Symbol('\\\\xi', commutative=True)))", "Add(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)), sin(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\log{(\\pi \\xi)}", "variable": "\\xi", "positive": "\\xi (\\log{(\\pi \\xi)} - 1)", "negatives": ["\\pi (\\log{(\\pi \\xi)} - 1)", "\\pi \\log{(\\xi)}", "- \\cos{(\\pi - \\xi)}", "\\frac{\\xi (2 \\pi - \\xi)}{2}"], "srepr_premise_expression": "log(Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\xi', commutative=True), Add(log(Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\pi', commutative=True), Add(log(Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\xi', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "e^{\\omega + \\xi}", "variable": "\\omega", "positive": "e^{\\omega + \\xi}", "negatives": ["\\frac{\\omega (\\omega + 2 \\xi)}{2}", "- \\omega \\xi + e^{\\omega}", "\\omega \\sin^{\\xi}{(\\xi)}", "\\frac{\\omega (\\log{(\\omega)} - 1)}{\\xi}"], "srepr_premise_expression": "exp(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "exp(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True)), exp(Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), Pow(sin(Symbol('\\\\xi', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), Add(log(Symbol('\\\\omega', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\beta \\xi + \\pi", "variable": "\\beta", "positive": "\\frac{\\beta (\\beta \\xi + 2 \\pi)}{2}", "negatives": ["\\frac{\\xi (\\beta \\xi + 2 \\pi)}{2}", "\\frac{\\pi (2 \\beta \\xi + \\pi)}{2}", "\\frac{\\beta (- \\beta + 2 \\pi - 2 \\xi)}{2}", "\\frac{\\beta^{2} \\pi \\xi}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True)), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True))"]}, {"premise_expression": "\\chi \\sin{(\\delta)}", "variable": "\\chi", "positive": "\\frac{\\chi^{2} \\sin{(\\delta)}}{2}", "negatives": ["\\frac{\\chi^{2} \\log{(\\delta)}}{2}", "\\chi \\delta + \\sin{(\\chi)}", "\\frac{\\chi (\\chi - 2 \\delta)}{2}", "- \\chi \\cos{(\\delta)}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), sin(Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), sin(Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), log(Symbol('\\\\delta', commutative=True)))", "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True)), sin(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True))))", "Mul(Integer(-1), Symbol('\\\\chi', commutative=True), cos(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\beta \\delta - \\beta", "variable": "\\delta", "positive": "\\frac{\\beta \\delta (\\delta - 2)}{2}", "negatives": ["\\frac{\\beta^{2} (\\delta - 1)}{2}", "\\frac{\\delta^{2} e^{\\beta}}{2}", "\\frac{\\delta^{2} \\log{(\\beta)}}{2}", "\\sin{(\\beta + \\delta)}"], "srepr_premise_expression": "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Integer(-2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Add(Symbol('\\\\delta', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), exp(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), log(Symbol('\\\\beta', commutative=True)))", "sin(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\log{(\\gamma - \\sigma)}", "variable": "\\sigma", "positive": "- \\gamma \\log{(- \\gamma + \\sigma)} + \\sigma \\log{(\\gamma - \\sigma)} - \\sigma", "negatives": ["\\gamma \\log{(\\gamma - \\sigma)} - \\gamma - \\sigma \\log{(\\gamma - \\sigma)}", "\\frac{\\sigma (- \\sigma + 2 e^{\\gamma})}{2}", "\\frac{\\sigma (\\log{(\\sigma)} - 1)}{\\gamma}", "\\frac{\\sigma (2 \\gamma + \\sigma)}{2}"], "srepr_premise_expression": "log(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\sigma', commutative=True)))), Mul(Symbol('\\\\sigma', commutative=True), log(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\gamma', commutative=True), log(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True), log(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\gamma', commutative=True)))))", "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True), Add(log(Symbol('\\\\sigma', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "- \\pi + \\xi", "variable": "\\xi", "positive": "\\frac{\\xi (- 2 \\pi + \\xi)}{2}", "negatives": ["\\frac{\\pi (- \\pi + 2 \\xi)}{2}", "\\frac{\\xi^{2} \\cos{(\\pi)}}{2}", "\\xi (\\log{(\\frac{\\pi}{\\xi})} + 1)", "\\frac{\\sin{(\\xi)}}{\\pi}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), cos(Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\xi', commutative=True), Add(log(Mul(Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), sin(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "- \\omega + \\pi", "variable": "\\pi", "positive": "\\frac{\\pi (- 2 \\omega + \\pi)}{2}", "negatives": ["\\frac{\\omega (- \\omega + 2 \\pi)}{2}", "- \\sin{(\\omega - \\pi)}", "e^{- \\omega + \\pi}", "\\cos{(\\omega - \\pi)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Integer(-1), sin(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))", "exp(Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Symbol('\\\\pi', commutative=True)))", "cos(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\beta^{2} \\psi", "variable": "\\beta", "positive": "\\frac{\\beta^{3} \\psi}{3}", "negatives": ["\\frac{\\beta^{2} \\psi^{2}}{2}", "\\psi e^{\\beta}", "- \\psi \\cos{(\\beta)}", "\\frac{\\beta (- \\beta + 2 \\psi)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 3), Pow(Symbol('\\\\beta', commutative=True), Integer(3)), Symbol('\\\\psi', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "Mul(Symbol('\\\\psi', commutative=True), exp(Symbol('\\\\beta', commutative=True)))", "Mul(Integer(-1), Symbol('\\\\psi', commutative=True), cos(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "\\pi \\log{(\\gamma)}", "variable": "\\gamma", "positive": "\\gamma \\pi (\\log{(\\gamma)} - 1)", "negatives": ["\\frac{\\pi^{2} \\log{(\\gamma)}}{2}", "\\gamma + \\pi \\log{(\\gamma)}", "- \\cos{(\\gamma + \\pi)}", "\\frac{\\gamma^{2}}{2 \\pi}"], "srepr_premise_expression": "Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True), Add(log(Symbol('\\\\gamma', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), log(Symbol('\\\\gamma', commutative=True)))", "Add(Symbol('\\\\gamma', commutative=True), Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\gamma', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))"]}, {"premise_expression": "\\log{(\\frac{\\omega}{\\chi})}", "variable": "\\chi", "positive": "\\chi (\\log{(\\frac{\\omega}{\\chi})} + 1)", "negatives": ["\\omega (\\log{(\\frac{\\omega}{\\chi})} - 1)", "\\frac{\\chi^{2} \\log{(\\omega)}}{2}", "e^{\\chi + \\omega}", "\\log{(\\chi)} \\sin{(\\omega)}"], "srepr_premise_expression": "log(Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\chi', commutative=True), Add(log(Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True))), Integer(1)))", "srepr_negatives": ["Mul(Symbol('\\\\omega', commutative=True), Add(log(Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), log(Symbol('\\\\omega', commutative=True)))", "exp(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True)))", "Mul(log(Symbol('\\\\chi', commutative=True)), sin(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\sin^{\\sigma}{(\\delta)}", "variable": "\\delta", "positive": "\\int \\sin^{\\sigma}{(\\delta)} d\\delta", "negatives": ["\\frac{\\delta (\\delta + 2 \\sin{(\\sigma)})}{2}", "- \\sigma \\cos{(\\delta)}", "\\frac{\\delta^{2}}{2 \\sigma}", "\\frac{\\delta^{2} \\log{(\\sigma)}}{2}"], "srepr_premise_expression": "Pow(sin(Symbol('\\\\delta', commutative=True)), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Integral(Pow(sin(Symbol('\\\\delta', commutative=True)), Symbol('\\\\sigma', commutative=True)), Tuple(Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), sin(Symbol('\\\\sigma', commutative=True)))))", "Mul(Integer(-1), Symbol('\\\\sigma', commutative=True), cos(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), log(Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "- \\alpha + \\pi^{\\beta}", "variable": "\\alpha", "positive": "\\frac{\\alpha (- \\alpha + 2 \\pi^{\\beta})}{2}", "negatives": ["\\frac{\\alpha (- \\alpha + 2 \\beta - 2 \\pi)}{2}", "\\beta \\pi \\log{(\\alpha)}", "\\alpha \\beta", "\\frac{\\alpha^{2}}{2 \\beta} + \\alpha \\pi"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Pow(Symbol('\\\\pi', commutative=True), Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Pow(Symbol('\\\\pi', commutative=True), Symbol('\\\\beta', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\pi', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True))", "Add(Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\beta', commutative=True), Integer(-1))), Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "e^{\\frac{\\omega}{\\gamma}}", "variable": "\\omega", "positive": "\\gamma e^{\\frac{\\omega}{\\gamma}}", "negatives": ["- \\gamma \\omega + e^{\\omega}", "- \\cos{(\\gamma - \\omega)}", "\\frac{\\omega (- 2 \\gamma + \\omega)}{2}", "\\frac{\\omega^{2} \\sin{(\\gamma)}}{2}"], "srepr_premise_expression": "exp(Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\gamma', commutative=True), exp(Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True)), exp(Symbol('\\\\omega', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), sin(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\frac{\\sin{(\\gamma)}}{\\sigma}", "variable": "\\sigma", "positive": "\\log{(\\sigma)} \\sin{(\\gamma)}", "negatives": ["\\gamma \\log{(\\sigma)}", "\\frac{\\gamma \\sigma^{2}}{2}", "- \\frac{\\cos{(\\gamma)}}{\\sigma}", "- \\gamma \\sigma - \\cos{(\\sigma)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), sin(Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(log(Symbol('\\\\sigma', commutative=True)), sin(Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "Mul(Integer(-1), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), cos(Symbol('\\\\gamma', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\frac{\\omega}{\\gamma}", "variable": "\\omega", "positive": "\\frac{\\omega^{2}}{2 \\gamma}", "negatives": ["\\omega \\log{(\\gamma)}", "\\frac{\\gamma \\omega^{2}}{2}", "\\frac{\\omega^{2} \\log{(\\gamma)}}{2}", "\\gamma \\log{(\\omega)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), log(Symbol('\\\\gamma', commutative=True)))", "Mul(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\log{(\\frac{\\delta}{\\psi})}", "variable": "\\psi", "positive": "\\psi (\\log{(\\frac{\\delta}{\\psi})} + 1)", "negatives": ["\\delta (\\log{(\\frac{\\delta}{\\psi})} - 1)", "- e^{\\delta - \\psi}", "- \\sin{(\\delta - \\psi)}", "e^{- \\delta + \\psi}"], "srepr_premise_expression": "log(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\psi', commutative=True), Add(log(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))), Integer(1)))", "srepr_negatives": ["Mul(Symbol('\\\\delta', commutative=True), Add(log(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))), Integer(-1)))", "Mul(Integer(-1), exp(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))", "Mul(Integer(-1), sin(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))", "exp(Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "- \\xi + \\cos{(\\psi)}", "variable": "\\xi", "positive": "\\frac{\\xi (- \\xi + 2 \\cos{(\\psi)})}{2}", "negatives": ["\\frac{\\xi (- \\xi + 2 e^{\\psi})}{2}", "\\xi (- \\psi + \\log{(\\xi^{\\psi})})", "- \\psi \\xi + \\sin{(\\psi)}", "\\frac{\\psi \\xi^{2}}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), cos(Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\psi', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\psi', commutative=True)))))", "Mul(Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), log(Pow(Symbol('\\\\xi', commutative=True), Symbol('\\\\psi', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True), Symbol('\\\\xi', commutative=True)), sin(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))"]}, {"premise_expression": "\\alpha + \\gamma + \\psi", "variable": "\\gamma", "positive": "\\gamma (\\alpha + \\frac{\\gamma}{2} + \\psi)", "negatives": ["\\frac{\\gamma (- 2 \\alpha + \\gamma + 2 \\psi)}{2}", "\\frac{\\alpha (\\alpha + 2 \\gamma + 2 \\psi)}{2}", "\\frac{\\psi (2 \\alpha + 2 \\gamma + \\psi)}{2}", "\\frac{\\gamma (4 \\alpha + \\gamma)}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\gamma', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(4), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\beta \\sigma - \\chi", "variable": "\\chi", "positive": "\\frac{\\chi (2 \\beta \\sigma - \\chi)}{2}", "negatives": ["\\frac{\\chi (2 \\beta \\sigma + \\chi)}{2}", "\\frac{\\sigma (\\beta \\sigma - 2 \\chi)}{2}", "\\frac{\\beta (\\beta \\sigma - 2 \\chi)}{2}", "\\frac{\\chi \\sigma (2 \\beta + \\chi)}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), Symbol('\\\\chi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True)), Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "\\frac{\\alpha \\sigma}{\\pi}", "variable": "\\sigma", "positive": "\\frac{\\alpha \\sigma^{2}}{2 \\pi}", "negatives": ["\\frac{\\alpha^{2} \\sigma}{2 \\pi}", "\\frac{\\alpha^{2} \\sigma^{2}}{2}", "\\alpha \\sigma \\log{(\\pi)}", "\\frac{\\sigma^{2} (\\alpha + \\pi)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "- \\sigma + \\xi", "variable": "\\xi", "positive": "\\frac{\\xi (- 2 \\sigma + \\xi)}{2}", "negatives": ["\\frac{\\sigma (- \\sigma + 2 \\xi)}{2}", "e^{- \\sigma + \\xi}", "\\sigma \\sin{(\\xi)}", "\\sigma e^{\\frac{\\xi}{\\sigma}}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "exp(Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\sigma', commutative=True), sin(Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\sigma', commutative=True), exp(Mul(Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\beta + \\pi", "variable": "\\pi", "positive": "\\frac{\\pi (2 \\beta + \\pi)}{2}", "negatives": ["\\frac{\\beta (\\beta + 2 \\pi)}{2}", "- e^{\\beta - \\pi}", "\\frac{\\pi (\\log{(\\pi)} - 1)}{\\beta}", "- \\beta \\cos{(\\pi)}"], "srepr_premise_expression": "Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Integer(-1), exp(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))", "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True), Add(log(Symbol('\\\\pi', commutative=True)), Integer(-1)))", "Mul(Integer(-1), Symbol('\\\\beta', commutative=True), cos(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\log{(- \\delta + \\sigma)}", "variable": "\\delta", "positive": "\\delta \\log{(- \\delta + \\sigma)} - \\delta - \\sigma \\log{(\\delta - \\sigma)}", "negatives": ["- \\delta \\log{(- \\delta + \\sigma)} + \\sigma \\log{(- \\delta + \\sigma)} - \\sigma", "\\log{(\\delta)} \\cos{(\\sigma)}", "\\frac{\\delta (- \\delta + 2 \\sigma)}{2}", "\\cos{(\\delta - \\sigma)}"], "srepr_premise_expression": "log(Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\delta', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\sigma', commutative=True)))), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True), log(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\sigma', commutative=True)))), Mul(Symbol('\\\\sigma', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\sigma', commutative=True)))), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))", "Mul(log(Symbol('\\\\delta', commutative=True)), cos(Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "- \\gamma + \\xi", "variable": "\\xi", "positive": "\\frac{\\xi (- 2 \\gamma + \\xi)}{2}", "negatives": ["\\frac{\\xi (2 \\gamma + \\xi)}{2}", "\\frac{\\gamma (- \\gamma + 2 \\xi)}{2}", "\\sin{(\\gamma + \\xi)}", "- \\gamma \\xi + \\sin{(\\xi)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "sin(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)), sin(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\xi + \\log{(\\psi)}", "variable": "\\psi", "positive": "\\psi (\\xi + \\log{(\\psi)} - 1)", "negatives": ["\\frac{\\xi (\\xi + 2 \\log{(\\psi)})}{2}", "\\cos{(\\psi - \\xi)}", "\\xi \\log{(\\psi)}", "- \\cos{(\\psi - \\xi)}"], "srepr_premise_expression": "Add(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\psi', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\xi', commutative=True), Mul(Integer(2), log(Symbol('\\\\psi', commutative=True)))))", "cos(Add(Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\psi', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))))"]}, {"premise_expression": "- \\beta + \\cos{(\\psi)}", "variable": "\\psi", "positive": "- \\beta \\psi + \\sin{(\\psi)}", "negatives": ["\\frac{\\psi (2 \\beta + \\psi)}{2}", "\\log{(\\psi)} \\cos{(\\beta)}", "\\frac{\\beta (- \\beta + 2 \\cos{(\\psi)})}{2}", "\\frac{\\psi (\\psi + 2 e^{\\beta})}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), cos(Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\psi', commutative=True)), sin(Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(log(Symbol('\\\\psi', commutative=True)), cos(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\psi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(2), exp(Symbol('\\\\beta', commutative=True)))))"]}, {"premise_expression": "\\cos{(\\gamma + \\omega)}", "variable": "\\omega", "positive": "\\sin{(\\gamma + \\omega)}", "negatives": ["\\frac{\\omega (2 \\gamma + \\omega)}{2}", "\\gamma \\log{(\\omega)}", "- \\gamma \\cos{(\\omega)}", "\\log{(\\gamma)} \\log{(\\omega)}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "sin(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), cos(Symbol('\\\\omega', commutative=True)))", "Mul(log(Symbol('\\\\gamma', commutative=True)), log(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\log{(- \\chi + \\gamma)}", "variable": "\\chi", "positive": "\\chi \\log{(- \\chi + \\gamma)} - \\chi - \\gamma \\log{(\\chi - \\gamma)}", "negatives": ["- \\chi \\log{(- \\chi + \\gamma)} + \\gamma \\log{(- \\chi + \\gamma)} - \\gamma", "\\chi (- \\gamma + \\log{(\\chi^{\\gamma})})", "\\chi (\\log{(\\chi \\gamma)} - 1)", "\\chi (\\log{(\\frac{\\chi}{\\gamma})} - 1)"], "srepr_premise_expression": "log(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\chi', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\gamma', commutative=True)))), Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), log(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\gamma', commutative=True)))), Mul(Symbol('\\\\gamma', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\gamma', commutative=True)))), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))", "Mul(Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), log(Pow(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True)))))", "Mul(Symbol('\\\\chi', commutative=True), Add(log(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\chi', commutative=True), Add(log(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)))), Integer(-1)))"]}, {"premise_expression": "\\delta \\psi", "variable": "\\psi", "positive": "\\frac{\\delta \\psi^{2}}{2}", "negatives": ["\\frac{\\delta^{2} \\psi}{2}", "\\frac{\\psi^{2}}{2 \\delta}", "\\delta \\psi + \\sin{(\\psi)}", "- \\cos{(\\delta - \\psi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\psi', commutative=True)), sin(Symbol('\\\\psi', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))"]}, {"premise_expression": "\\frac{\\pi}{\\alpha}", "variable": "\\pi", "positive": "\\frac{\\pi^{2}}{2 \\alpha}", "negatives": ["\\pi \\log{(\\alpha)}", "\\frac{\\pi^{2} e^{\\alpha}}{2}", "- \\frac{\\pi^{2}}{2} + e^{\\pi}", "\\pi (- \\alpha + \\log{(\\pi^{\\alpha})})"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), exp(Symbol('\\\\alpha', commutative=True)))", "Add(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2))), exp(Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), log(Pow(Symbol('\\\\pi', commutative=True), Symbol('\\\\alpha', commutative=True)))))"]}, {"premise_expression": "- \\sigma + \\cos{(\\beta)}", "variable": "\\beta", "positive": "- \\beta \\sigma + \\sin{(\\beta)}", "negatives": ["\\sigma \\log{(\\beta)}", "e^{\\beta + \\sigma}", "\\sin{(\\beta + \\sigma)}", "\\frac{\\beta (\\beta - 2 \\sigma)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), cos(Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True)), sin(Symbol('\\\\beta', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\beta', commutative=True)))", "exp(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True)))", "sin(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\alpha (- \\beta + \\pi)", "variable": "\\beta", "positive": "\\frac{\\alpha \\beta (- \\beta + 2 \\pi)}{2}", "negatives": ["\\frac{\\alpha^{2} (- \\beta + \\pi)}{2}", "\\frac{\\alpha \\pi (- 2 \\beta + \\pi)}{2}", "\\frac{\\beta (2 \\alpha^{\\pi} + \\beta)}{2}", "\\frac{\\beta (2 \\alpha + \\beta + 2 \\pi)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(2), Pow(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True))), Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\log{(\\pi - \\xi)}", "variable": "\\pi", "positive": "\\pi \\log{(\\pi - \\xi)} - \\pi - \\xi \\log{(\\pi - \\xi)}", "negatives": ["- \\pi \\log{(- \\pi + \\xi)} + \\xi \\log{(\\pi - \\xi)} - \\xi", "\\pi e^{\\frac{\\xi}{\\pi}} - \\xi \\operatorname{Ei}{(\\frac{\\xi}{\\pi})}", "\\frac{\\pi \\xi (\\pi - 2)}{2}", "- \\pi \\xi + \\sin{(\\pi)}"], "srepr_premise_expression": "log(Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\pi', commutative=True), log(Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True), log(Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Symbol('\\\\xi', commutative=True)))), Mul(Symbol('\\\\xi', commutative=True), log(Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "Add(Mul(Symbol('\\\\pi', commutative=True), exp(Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\xi', commutative=True), Ei(Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Integer(-2)))", "Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True)), sin(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\alpha + \\omega \\sigma", "variable": "\\alpha", "positive": "\\frac{\\alpha (\\alpha + 2 \\omega \\sigma)}{2}", "negatives": ["\\frac{\\omega (2 \\alpha + \\omega \\sigma)}{2}", "\\frac{\\sigma (2 \\alpha + \\omega \\sigma)}{2}", "\\frac{\\alpha (\\alpha + 2 \\sigma)}{2 \\omega}", "\\omega^{\\sigma} \\log{(\\alpha)}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Pow(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True)), log(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "- \\delta + \\log{(\\sigma)}", "variable": "\\delta", "positive": "\\frac{\\delta (- \\delta + 2 \\log{(\\sigma)})}{2}", "negatives": ["\\frac{\\delta (\\delta + 2 \\cos{(\\sigma)})}{2}", "\\frac{\\delta (\\delta + 2 \\sigma)}{2}", "\\frac{\\delta (\\delta + 4 \\sigma)}{2}", "\\sigma (- \\delta + \\log{(\\sigma)} - 1)"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), log(Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), log(Symbol('\\\\sigma', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), cos(Symbol('\\\\sigma', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(4), Symbol('\\\\sigma', commutative=True))))", "Mul(Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), log(Symbol('\\\\sigma', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\chi + \\delta", "variable": "\\chi", "positive": "\\frac{\\chi (\\chi + 2 \\delta)}{2}", "negatives": ["\\frac{\\chi (- \\chi + 2 \\delta)}{2}", "\\frac{\\delta (2 \\chi + \\delta)}{2}", "e^{\\chi + \\delta}", "\\chi \\delta + \\sin{(\\chi)}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\delta', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\delta', commutative=True)))", "exp(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True)))", "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True)), sin(Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "\\beta + \\gamma", "variable": "\\gamma", "positive": "\\frac{\\gamma (2 \\beta + \\gamma)}{2}", "negatives": ["\\frac{\\beta (\\beta + 2 \\gamma)}{2}", "\\sin{(\\beta + \\gamma)}", "\\cos{(\\beta - \\gamma)}", "\\gamma (\\log{(\\frac{\\beta}{\\gamma})} + 1)"], "srepr_premise_expression": "Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\gamma', commutative=True))))", "sin(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)))", "cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "Mul(Symbol('\\\\gamma', commutative=True), Add(log(Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)))), Integer(1)))"]}, {"premise_expression": "\\alpha + e^{\\beta}", "variable": "\\alpha", "positive": "\\frac{\\alpha (\\alpha + 2 e^{\\beta})}{2}", "negatives": ["\\frac{\\alpha (\\alpha + 2 \\cos{(\\beta)})}{2}", "\\alpha \\beta + e^{\\beta}", "\\beta (\\alpha + \\log{(\\alpha)})", "\\alpha (\\log{(\\alpha \\beta)} - 1)"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), exp(Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), exp(Symbol('\\\\beta', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), cos(Symbol('\\\\beta', commutative=True)))))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True)), exp(Symbol('\\\\beta', commutative=True)))", "Mul(Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\alpha', commutative=True))))", "Mul(Symbol('\\\\alpha', commutative=True), Add(log(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\delta + \\omega \\pi", "variable": "\\delta", "positive": "\\frac{\\delta (\\delta + 2 \\omega \\pi)}{2}", "negatives": ["\\frac{\\delta (\\delta \\omega + 2 \\pi)}{2}", "\\frac{\\omega (2 \\delta + \\omega \\pi)}{2}", "\\frac{\\pi (2 \\delta + \\omega \\pi)}{2}", "\\frac{\\delta (\\delta - 2 \\omega + 2 \\pi)}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\delta', commutative=True), Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "e^{\\frac{\\beta}{\\chi}}", "variable": "\\beta", "positive": "\\chi e^{\\frac{\\beta}{\\chi}}", "negatives": ["e^{\\beta - \\chi}", "\\frac{\\log{(\\beta)}^{2}}{2}", "\\beta \\chi (\\log{(\\beta)} - 1)", "- \\beta \\operatorname{Ei}{(\\frac{\\beta}{\\chi})} + \\chi e^{\\frac{\\beta}{\\chi}}"], "srepr_premise_expression": "exp(Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\chi', commutative=True), exp(Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)))))", "srepr_negatives": ["exp(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True))))", "Mul(Rational(1, 2), Pow(log(Symbol('\\\\beta', commutative=True)), Integer(2)))", "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True), Add(log(Symbol('\\\\beta', commutative=True)), Integer(-1)))", "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Ei(Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(-1))))), Mul(Symbol('\\\\chi', commutative=True), exp(Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(-1))))))"]}, {"premise_expression": "\\delta \\cos{(\\omega)}", "variable": "\\delta", "positive": "\\frac{\\delta^{2} \\cos{(\\omega)}}{2}", "negatives": ["\\frac{\\delta^{2} \\omega}{2}", "\\frac{\\delta (- \\delta + 2 \\cos{(\\omega)})}{2}", "\\delta \\sin{(\\omega)}", "\\frac{\\delta (\\delta + 2 e^{\\omega})}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\delta', commutative=True), cos(Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), cos(Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Symbol('\\\\omega', commutative=True))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\omega', commutative=True)))))", "Mul(Symbol('\\\\delta', commutative=True), sin(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), exp(Symbol('\\\\omega', commutative=True)))))"]}, {"premise_expression": "- \\delta + \\sigma", "variable": "\\sigma", "positive": "\\frac{\\sigma (- 2 \\delta + \\sigma)}{2}", "negatives": ["\\frac{\\sigma (2 \\delta + \\sigma)}{2}", "\\frac{\\delta (- \\delta + 2 \\sigma)}{2}", "\\frac{\\sigma (\\sigma + 2 \\sin{(\\delta)})}{2}", "\\frac{\\sigma^{2} \\log{(\\delta)}}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(2), sin(Symbol('\\\\delta', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), log(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\omega - \\sigma", "variable": "\\sigma", "positive": "\\frac{\\sigma (2 \\omega - \\sigma)}{2}", "negatives": ["\\frac{\\omega (\\omega - 2 \\sigma)}{2}", "\\frac{\\sigma (\\sigma + 2 \\log{(\\omega)})}{2}", "\\frac{\\sigma^{2} \\sin{(\\omega)}}{2}", "\\sin{(\\omega + \\sigma)}"], "srepr_premise_expression": "Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(2), log(Symbol('\\\\omega', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), sin(Symbol('\\\\omega', commutative=True)))", "sin(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "e^{- \\alpha + \\delta}", "variable": "\\alpha", "positive": "- e^{- \\alpha + \\delta}", "negatives": ["e^{- \\alpha + \\delta}", "\\sin{(\\alpha + \\delta)}", "\\delta \\sin{(\\alpha)}", "\\frac{\\alpha^{2} \\delta}{2}"], "srepr_premise_expression": "exp(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\delta', commutative=True))))", "srepr_negatives": ["exp(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\delta', commutative=True)))", "sin(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\delta', commutative=True)))", "Mul(Symbol('\\\\delta', commutative=True), sin(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\delta', commutative=True))"]}, {"premise_expression": "- \\gamma + \\pi", "variable": "\\gamma", "positive": "\\frac{\\gamma (- \\gamma + 2 \\pi)}{2}", "negatives": ["\\frac{\\pi (- 2 \\gamma + \\pi)}{2}", "e^{\\gamma + \\pi}", "- \\pi \\cos{(\\gamma)}", "\\pi e^{\\gamma}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True)))", "exp(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True)))", "Mul(Integer(-1), Symbol('\\\\pi', commutative=True), cos(Symbol('\\\\gamma', commutative=True)))", "Mul(Symbol('\\\\pi', commutative=True), exp(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\log{(\\frac{\\sigma}{\\xi})}", "variable": "\\sigma", "positive": "\\sigma (\\log{(\\frac{\\sigma}{\\xi})} - 1)", "negatives": ["\\xi (\\log{(\\frac{\\sigma}{\\xi})} + 1)", "\\frac{\\sigma (\\log{(\\sigma)} - 1)}{\\xi}", "\\xi e^{\\frac{\\sigma}{\\xi}}", "\\frac{\\sigma (\\sigma + 2 \\xi)}{2}"], "srepr_premise_expression": "log(Mul(Symbol('\\\\sigma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\sigma', commutative=True), Add(log(Mul(Symbol('\\\\sigma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\xi', commutative=True), Add(log(Mul(Symbol('\\\\sigma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Symbol('\\\\sigma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), Add(log(Symbol('\\\\sigma', commutative=True)), Integer(-1)))", "Mul(Symbol('\\\\xi', commutative=True), exp(Mul(Symbol('\\\\sigma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "- \\sin{(\\beta - \\omega)}", "variable": "\\omega", "positive": "- \\cos{(\\beta - \\omega)}", "negatives": ["\\cos{(\\beta - \\omega)}", "- e^{\\beta - \\omega}", "\\omega (\\log{(\\beta \\omega)} - 1)", "\\omega - \\frac{\\omega^{2}}{2 \\beta}"], "srepr_premise_expression": "Mul(Integer(-1), sin(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))))", "srepr_negatives": ["cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "Mul(Integer(-1), exp(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))))", "Mul(Symbol('\\\\omega', commutative=True), Add(log(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True))), Integer(-1)))", "Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Pow(Symbol('\\\\omega', commutative=True), Integer(2))))"]}, {"premise_expression": "\\gamma \\pi", "variable": "\\pi", "positive": "\\frac{\\gamma \\pi^{2}}{2}", "negatives": ["\\frac{\\gamma^{2} \\pi}{2}", "\\frac{\\pi^{2} \\log{(\\gamma)}}{2}", "\\frac{\\pi (2 \\gamma - \\pi)}{2}", "\\gamma \\sin{(\\pi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Symbol('\\\\pi', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), log(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "Mul(Symbol('\\\\gamma', commutative=True), sin(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\xi + \\cos{(\\psi)}", "variable": "\\xi", "positive": "\\frac{\\xi (\\xi + 2 \\cos{(\\psi)})}{2}", "negatives": ["\\frac{\\xi (\\xi + 2 \\sin{(\\psi)})}{2}", "\\psi \\xi + \\sin{(\\psi)}", "\\sin{(\\psi + \\xi)}", "- \\sin{(\\psi - \\xi)}"], "srepr_premise_expression": "Add(Symbol('\\\\xi', commutative=True), cos(Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\xi', commutative=True), Mul(Integer(2), cos(Symbol('\\\\psi', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\xi', commutative=True), Mul(Integer(2), sin(Symbol('\\\\psi', commutative=True)))))", "Add(Mul(Symbol('\\\\psi', commutative=True), Symbol('\\\\xi', commutative=True)), sin(Symbol('\\\\psi', commutative=True)))", "sin(Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\xi', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))))"]}, {"premise_expression": "\\frac{\\gamma \\xi}{\\delta}", "variable": "\\gamma", "positive": "\\frac{\\gamma^{2} \\xi}{2 \\delta}", "negatives": ["\\frac{\\gamma \\xi^{2}}{2 \\delta}", "\\gamma \\xi \\log{(\\delta)}", "\\frac{\\delta \\gamma^{2}}{2 \\xi}", "- \\delta \\gamma + \\frac{\\gamma^{2}}{2 \\xi}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True), log(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Symbol('\\\\gamma', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))"]}, {"premise_expression": "\\cos{(\\alpha + \\beta)}", "variable": "\\beta", "positive": "\\sin{(\\alpha + \\beta)}", "negatives": ["\\frac{\\beta (2 \\alpha - \\beta)}{2}", "\\alpha \\log{(\\beta)}", "\\alpha \\beta - \\cos{(\\beta)}", "\\frac{\\beta^{2} \\sin{(\\alpha)}}{2}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "sin(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\beta', commutative=True))))", "Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\beta', commutative=True)))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\beta', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), sin(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\beta + \\delta", "variable": "\\beta", "positive": "\\frac{\\beta (\\beta + 2 \\delta)}{2}", "negatives": ["\\frac{\\delta (2 \\beta + \\delta)}{2}", "\\frac{\\beta^{2}}{2 \\delta}", "\\beta \\sin{(1)}", "\\frac{\\beta (- \\beta + 2 \\sin{(\\delta)})}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\delta', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)))", "Mul(Symbol('\\\\beta', commutative=True), sin(Integer(1)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\delta', commutative=True)))))"]}, {"premise_expression": "\\chi + \\sigma", "variable": "\\sigma", "positive": "\\frac{\\sigma (2 \\chi + \\sigma)}{2}", "negatives": ["\\frac{\\chi (\\chi + 2 \\sigma)}{2}", "e^{\\chi + \\sigma}", "\\chi e^{\\sigma}", "\\sigma (\\log{(\\frac{\\sigma}{\\chi})} - 1)"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "exp(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\sigma', commutative=True)))", "Mul(Symbol('\\\\chi', commutative=True), exp(Symbol('\\\\sigma', commutative=True)))", "Mul(Symbol('\\\\sigma', commutative=True), Add(log(Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\psi (\\delta - \\omega)", "variable": "\\psi", "positive": "\\frac{\\psi^{2} (\\delta - \\omega)}{2}", "negatives": ["\\frac{\\omega \\psi (2 \\delta - \\omega)}{2}", "\\frac{\\delta \\psi (\\delta - 2 \\omega)}{2}", "\\frac{\\psi (2 \\delta \\omega - \\psi)}{2}", "\\frac{\\delta \\psi (2 \\omega + \\psi)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "- \\alpha + \\frac{\\omega}{\\alpha}", "variable": "\\alpha", "positive": "- \\frac{\\alpha^{2}}{2} + \\omega \\log{(\\alpha)}", "negatives": ["- \\alpha \\omega + \\frac{\\omega^{2}}{2 \\alpha}", "\\frac{\\alpha (\\alpha - 2 \\omega)}{2}", "- \\alpha \\omega - \\cos{(\\alpha)}", "\\frac{\\alpha^{2} \\log{(\\omega)}}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2))), Mul(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\alpha', commutative=True))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\omega', commutative=True), Integer(2))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\alpha', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), log(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\alpha + \\omega + \\psi", "variable": "\\psi", "positive": "\\psi (\\alpha + \\omega + \\frac{\\psi}{2})", "negatives": ["\\frac{\\psi (2 \\alpha - 2 \\omega + \\psi)}{2}", "\\frac{\\omega (2 \\alpha + \\omega + 2 \\psi)}{2}", "\\frac{\\alpha (\\alpha + 2 \\omega + 2 \\psi)}{2}", "\\frac{\\alpha \\psi^{2}}{2 \\omega}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True), Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))"]}, {"premise_expression": "\\log{(\\beta + \\sigma)}", "variable": "\\beta", "positive": "\\beta \\log{(\\beta + \\sigma)} - \\beta + \\sigma \\log{(\\beta + \\sigma)}", "negatives": ["\\beta \\log{(\\beta + \\sigma)} + \\sigma \\log{(\\beta + \\sigma)} - \\sigma", "\\beta \\cos{(\\frac{\\sigma}{\\beta})} + \\sigma \\operatorname{Si}{(\\frac{\\sigma}{\\beta})}", "\\frac{\\beta (- \\beta + 2 \\cos{(\\sigma)})}{2}", "\\beta \\sigma (\\log{(\\beta)} - 1)"], "srepr_premise_expression": "log(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\beta', commutative=True), log(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True)))), Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Symbol('\\\\sigma', commutative=True), log(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\beta', commutative=True), log(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True)))), Mul(Symbol('\\\\sigma', commutative=True), log(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True)))), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))", "Add(Mul(Symbol('\\\\beta', commutative=True), cos(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True)))), Mul(Symbol('\\\\sigma', commutative=True), Si(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\sigma', commutative=True)))))", "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True), Add(log(Symbol('\\\\beta', commutative=True)), Integer(-1)))"]}, {"premise_expression": "- \\chi + \\pi + \\psi", "variable": "\\chi", "positive": "\\chi (- \\frac{\\chi}{2} + \\pi + \\psi)", "negatives": ["\\frac{\\chi (\\chi - 2 \\pi - 2 \\psi)}{2}", "\\frac{\\psi (- 2 \\chi + 2 \\pi + \\psi)}{2}", "\\frac{\\pi (- 2 \\chi + \\pi + 2 \\psi)}{2}", "\\frac{\\chi (\\chi \\psi + 2 \\pi)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Rational(1, 2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\pi', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\frac{\\omega + \\xi}{\\pi}", "variable": "\\omega", "positive": "\\frac{\\omega (\\omega + 2 \\xi)}{2 \\pi}", "negatives": ["\\frac{\\xi (2 \\omega + \\xi)}{2 \\pi}", "\\frac{\\omega \\xi (- \\omega + 2 \\pi)}{2}", "(\\omega + \\xi) \\log{(\\pi)}", "\\frac{\\omega (\\omega + 2 \\pi - 2 \\xi)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True)), log(Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\psi + \\xi", "variable": "\\psi", "positive": "\\frac{\\psi (\\psi + 2 \\xi)}{2}", "negatives": ["\\frac{\\xi (2 \\psi + \\xi)}{2}", "\\frac{\\psi (\\psi + 2 \\cos{(\\xi)})}{2}", "\\sin{(\\psi + \\xi)}", "\\frac{\\psi^{2} \\sin{(\\xi)}}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\psi', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(2), cos(Symbol('\\\\xi', commutative=True)))))", "sin(Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), sin(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "- \\gamma + \\omega", "variable": "\\gamma", "positive": "\\frac{\\gamma (- \\gamma + 2 \\omega)}{2}", "negatives": ["\\frac{\\omega (- 2 \\gamma + \\omega)}{2}", "e^{\\gamma - \\omega}", "e^{\\gamma + \\omega}", "\\omega \\log{(\\gamma)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\omega', commutative=True)))", "exp(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "exp(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "- \\delta + e^{\\omega}", "variable": "\\omega", "positive": "- \\delta \\omega + e^{\\omega}", "negatives": ["\\delta \\omega + \\sin{(\\omega)}", "\\frac{\\delta (- \\delta + 2 e^{\\omega})}{2}", "e^{\\delta + \\omega}", "\\frac{\\omega (- \\omega + 2 e^{\\delta})}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), exp(Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True)), exp(Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True)), sin(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\omega', commutative=True)))))", "exp(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\delta', commutative=True)))))"]}, {"premise_expression": "\\frac{\\log{(\\xi)}}{\\alpha}", "variable": "\\xi", "positive": "\\frac{\\xi (\\log{(\\xi)} - 1)}{\\alpha}", "negatives": ["\\xi (\\log{(\\frac{\\alpha}{\\xi})} + 1)", "\\frac{\\xi (- 2 \\alpha + \\xi)}{2}", "\\log{(\\alpha)} \\log{(\\xi)}", "\\frac{\\sin{(\\xi)}}{\\alpha}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), log(Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True), Add(log(Symbol('\\\\xi', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\xi', commutative=True), Add(log(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(log(Symbol('\\\\alpha', commutative=True)), log(Symbol('\\\\xi', commutative=True)))", "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), sin(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\sigma - \\xi", "variable": "\\sigma", "positive": "\\frac{\\sigma (\\sigma - 2 \\xi)}{2}", "negatives": ["\\frac{\\xi (2 \\sigma - \\xi)}{2}", "\\frac{\\sigma^{2} \\xi}{2}", "\\cos{(\\sigma - \\xi)}", "\\sigma \\xi + e^{\\sigma}"], "srepr_premise_expression": "Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))", "cos(Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Add(Mul(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True)), exp(Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\frac{\\cos{(\\pi)}}{\\delta}", "variable": "\\delta", "positive": "\\log{(\\delta)} \\cos{(\\pi)}", "negatives": ["\\frac{\\delta^{2} \\log{(\\pi)}}{2}", "\\frac{\\sin{(\\pi)}}{\\delta}", "\\pi e^{\\frac{\\delta}{\\pi}}", "\\frac{\\delta (\\delta + 2 \\pi)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), cos(Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(log(Symbol('\\\\delta', commutative=True)), cos(Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), log(Symbol('\\\\pi', commutative=True)))", "Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), sin(Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\pi', commutative=True), exp(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\cos{(\\sigma - \\xi)}", "variable": "\\sigma", "positive": "\\sin{(\\sigma - \\xi)}", "negatives": ["- \\sin{(\\sigma - \\xi)}", "- \\frac{\\cos{(\\sigma)}}{\\xi}", "\\xi e^{\\sigma}", "\\xi \\log{(\\sigma)}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "sin(Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))))", "Mul(Integer(-1), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), cos(Symbol('\\\\sigma', commutative=True)))", "Mul(Symbol('\\\\xi', commutative=True), exp(Symbol('\\\\sigma', commutative=True)))", "Mul(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\frac{\\log{(\\alpha)}}{\\pi}", "variable": "\\alpha", "positive": "\\frac{\\alpha (\\log{(\\alpha)} - 1)}{\\pi}", "negatives": ["\\alpha (\\log{(\\frac{\\pi}{\\alpha})} + 1)", "\\log{(\\alpha)} \\log{(\\pi)}", "\\sin{(\\alpha + \\pi)}", "\\alpha (- \\pi + \\log{(\\pi)})"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), log(Symbol('\\\\alpha', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Add(log(Symbol('\\\\alpha', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\alpha', commutative=True), Add(log(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))), Integer(1)))", "Mul(log(Symbol('\\\\alpha', commutative=True)), log(Symbol('\\\\pi', commutative=True)))", "sin(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), log(Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\chi + \\pi", "variable": "\\chi", "positive": "\\frac{\\chi (\\chi + 2 \\pi)}{2}", "negatives": ["\\frac{\\chi (- \\chi + 2 \\pi)}{2}", "\\frac{\\pi (2 \\chi + \\pi)}{2}", "\\frac{\\chi^{2} \\log{(\\pi)}}{2}", "\\cos{(\\chi - \\pi)}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), log(Symbol('\\\\pi', commutative=True)))", "cos(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\log{(- \\sigma + \\xi)}", "variable": "\\sigma", "positive": "\\sigma \\log{(- \\sigma + \\xi)} - \\sigma - \\xi \\log{(\\sigma - \\xi)}", "negatives": ["\\sigma \\log{(\\sigma - \\xi)} - \\sigma - \\xi \\log{(\\sigma - \\xi)}", "- \\sigma \\log{(- \\sigma + \\xi)} + \\xi \\log{(- \\sigma + \\xi)} - \\xi", "\\sigma (- \\xi + \\log{(\\sigma^{\\xi})})", "- \\sigma \\xi + \\sin{(\\sigma)}"], "srepr_premise_expression": "log(Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\sigma', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), Symbol('\\\\xi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True), log(Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\sigma', commutative=True), log(Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True), log(Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))))", "Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), Symbol('\\\\xi', commutative=True)))), Mul(Symbol('\\\\xi', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), Symbol('\\\\xi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), log(Pow(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True)), sin(Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\log{(\\psi^{\\sigma})}", "variable": "\\psi", "positive": "\\psi (- \\sigma + \\log{(\\psi^{\\sigma})})", "negatives": ["\\frac{\\psi (\\psi + 2 \\cos{(\\sigma)})}{2}", "\\frac{\\sigma^{2} \\log{(\\psi)}}{2}", "- \\frac{\\cos{(\\psi)}}{\\sigma}", "- \\cos{(\\psi + \\sigma)}"], "srepr_premise_expression": "log(Pow(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), log(Pow(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(2), cos(Symbol('\\\\sigma', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), log(Symbol('\\\\psi', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), cos(Symbol('\\\\psi', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\log{(- \\alpha + \\omega)}", "variable": "\\omega", "positive": "- \\alpha \\log{(- \\alpha + \\omega)} + \\omega \\log{(- \\alpha + \\omega)} - \\omega", "negatives": ["\\alpha \\log{(- \\alpha + \\omega)} - \\alpha - \\omega \\log{(\\alpha - \\omega)}", "\\alpha \\omega (\\log{(\\omega)} - 1)", "e^{\\alpha} \\log{(\\omega)}", "- \\alpha \\omega - \\cos{(\\omega)}"], "srepr_premise_expression": "log(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\omega', commutative=True)))), Mul(Symbol('\\\\omega', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\omega', commutative=True)))), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\alpha', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\omega', commutative=True)))), Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\omega', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))))", "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True), Add(log(Symbol('\\\\omega', commutative=True)), Integer(-1)))", "Mul(exp(Symbol('\\\\alpha', commutative=True)), log(Symbol('\\\\omega', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\omega', commutative=True))))"]}, {"premise_expression": "\\cos{(\\gamma + \\pi)}", "variable": "\\pi", "positive": "\\sin{(\\gamma + \\pi)}", "negatives": ["\\frac{\\pi^{2}}{2 \\gamma}", "\\gamma \\log{(\\pi)}", "- \\gamma \\cos{(\\pi)}", "- \\gamma \\pi + e^{\\pi}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "sin(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "Mul(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\pi', commutative=True)))", "Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), cos(Symbol('\\\\pi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True)), exp(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\omega + \\sigma", "variable": "\\sigma", "positive": "\\frac{\\sigma (2 \\omega + \\sigma)}{2}", "negatives": ["\\frac{\\omega (\\omega + 2 \\sigma)}{2}", "e^{\\omega + \\sigma}", "\\frac{\\sigma^{2} \\log{(\\omega)}}{2}", "\\sigma (- \\omega + \\log{(\\sigma^{\\omega})})"], "srepr_premise_expression": "Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "exp(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), log(Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), log(Pow(Symbol('\\\\sigma', commutative=True), Symbol('\\\\omega', commutative=True)))))"]}, {"premise_expression": "\\frac{\\xi}{\\sigma}", "variable": "\\sigma", "positive": "\\xi \\log{(\\sigma)}", "negatives": ["\\frac{\\xi^{2}}{2 \\sigma}", "\\sigma \\xi + e^{\\sigma}", "e^{\\sigma - \\xi}", "\\frac{\\sigma (\\sigma + 2 \\xi)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Add(Mul(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True)), exp(Symbol('\\\\sigma', commutative=True)))", "exp(Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "- \\psi + \\sigma", "variable": "\\sigma", "positive": "\\frac{\\sigma (- 2 \\psi + \\sigma)}{2}", "negatives": ["\\frac{\\psi (- \\psi + 2 \\sigma)}{2}", "\\frac{\\sigma^{2} \\log{(\\psi)}}{2}", "- \\sin{(\\psi - \\sigma)}", "\\frac{\\sigma^{2}}{2 \\psi}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), log(Symbol('\\\\psi', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))"]}, {"premise_expression": "\\frac{\\beta \\delta}{\\psi}", "variable": "\\delta", "positive": "\\frac{\\beta \\delta^{2}}{2 \\psi}", "negatives": ["\\frac{\\beta^{2} \\delta}{2 \\psi}", "\\frac{\\delta^{2}}{2 \\beta \\psi}", "\\beta \\delta \\log{(\\psi)}", "\\frac{\\beta \\delta^{2} \\psi}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))", "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True), log(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))"]}, {"premise_expression": "\\delta + \\omega", "variable": "\\omega", "positive": "\\frac{\\omega (2 \\delta + \\omega)}{2}", "negatives": ["\\frac{\\delta (\\delta + 2 \\omega)}{2}", "\\frac{\\omega^{2} \\sin{(\\delta)}}{2}", "\\frac{\\omega^{2} \\log{(\\delta)}}{2}", "- \\sin{(\\delta - \\omega)}"], "srepr_premise_expression": "Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), sin(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), log(Symbol('\\\\delta', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))))"]}, {"premise_expression": "- \\pi + \\cos{(\\psi)}", "variable": "\\pi", "positive": "\\frac{\\pi (- \\pi + 2 \\cos{(\\psi)})}{2}", "negatives": ["\\frac{\\pi^{2} \\log{(\\psi)}}{2}", "\\pi (- \\psi + \\log{(\\pi^{\\psi})})", "- \\pi \\psi - \\cos{(\\pi)}", "- \\pi \\psi + \\sin{(\\psi)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), cos(Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\psi', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), log(Symbol('\\\\psi', commutative=True)))", "Mul(Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), log(Pow(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\pi', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)), sin(Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\omega \\psi", "variable": "\\omega", "positive": "\\frac{\\omega^{2} \\psi}{2}", "negatives": ["\\frac{\\omega \\psi^{2}}{2}", "\\frac{\\omega (\\omega - 2 \\psi)}{2}", "- e^{- \\omega + \\psi}", "\\log{(\\omega)} \\cos{(\\psi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Symbol('\\\\psi', commutative=True))))", "Mul(log(Symbol('\\\\omega', commutative=True)), cos(Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\chi - \\delta + \\psi", "variable": "\\chi", "positive": "\\chi (\\frac{\\chi}{2} - \\delta + \\psi)", "negatives": ["\\frac{\\chi (- \\chi + 2 \\delta + 2 \\psi)}{2}", "\\frac{\\delta (2 \\chi - \\delta + 2 \\psi)}{2}", "\\frac{\\psi (2 \\chi - 2 \\delta + \\psi)}{2}", "\\chi (\\delta + \\psi^{2})"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\chi', commutative=True), Add(Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(2))))"]}, {"premise_expression": "\\sin{(\\delta + \\gamma)}", "variable": "\\delta", "positive": "- \\cos{(\\delta + \\gamma)}", "negatives": ["\\cos{(\\delta - \\gamma)}", "\\frac{\\delta \\gamma (\\delta - 2 \\gamma)}{2}", "\\log{(\\delta)} \\log{(\\gamma)}", "\\log{(\\delta)} \\sin{(\\gamma)}"], "srepr_premise_expression": "sin(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\gamma', commutative=True))))", "srepr_negatives": ["cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True))))", "Mul(log(Symbol('\\\\delta', commutative=True)), log(Symbol('\\\\gamma', commutative=True)))", "Mul(log(Symbol('\\\\delta', commutative=True)), sin(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "- \\psi + \\cos{(\\alpha)}", "variable": "\\alpha", "positive": "- \\alpha \\psi + \\sin{(\\alpha)}", "negatives": ["\\psi e^{\\alpha}", "\\psi \\log{(\\alpha)}", "\\alpha (- \\psi + \\log{(\\alpha^{\\psi})})", "\\sin{(\\alpha + \\psi)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), cos(Symbol('\\\\alpha', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True)), sin(Symbol('\\\\alpha', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\psi', commutative=True), exp(Symbol('\\\\alpha', commutative=True)))", "Mul(Symbol('\\\\psi', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), log(Pow(Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True)))))", "sin(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "- \\gamma + \\sin{(\\pi)}", "variable": "\\pi", "positive": "- \\gamma \\pi - \\cos{(\\pi)}", "negatives": ["- \\gamma \\pi + e^{\\pi}", "\\gamma \\log{(\\pi)}", "\\log{(\\pi)} \\cos{(\\gamma)}", "- e^{\\gamma - \\pi}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), sin(Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True)), exp(Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\pi', commutative=True)))", "Mul(log(Symbol('\\\\pi', commutative=True)), cos(Symbol('\\\\gamma', commutative=True)))", "Mul(Integer(-1), exp(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))"]}, {"premise_expression": "\\frac{\\pi \\psi}{\\sigma}", "variable": "\\pi", "positive": "\\frac{\\pi^{2} \\psi}{2 \\sigma}", "negatives": ["\\frac{\\pi \\psi^{2}}{2 \\sigma}", "\\pi \\psi \\log{(\\sigma)}", "\\frac{\\pi (\\pi + 2 \\psi + 2 \\sigma)}{2}", "- \\pi \\sigma + \\psi \\log{(\\pi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True), log(Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Symbol('\\\\psi', commutative=True), log(Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\alpha + \\pi", "variable": "\\pi", "positive": "\\frac{\\pi (2 \\alpha + \\pi)}{2}", "negatives": ["\\frac{\\alpha (\\alpha + 2 \\pi)}{2}", "\\frac{\\pi^{2} e^{\\alpha}}{2}", "e^{\\alpha + \\pi}", "- \\alpha \\pi - \\cos{(\\pi)}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), exp(Symbol('\\\\alpha', commutative=True)))", "exp(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "e^{\\beta - \\sigma}", "variable": "\\beta", "positive": "e^{\\beta - \\sigma}", "negatives": ["- e^{\\beta - \\sigma}", "- \\cos{(\\beta - \\sigma)}", "\\frac{\\beta (\\beta + 2 \\sigma)}{2}", "e^{\\sigma} \\log{(\\beta)}"], "srepr_premise_expression": "exp(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "exp(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(exp(Symbol('\\\\sigma', commutative=True)), log(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "\\chi \\gamma \\omega", "variable": "\\omega", "positive": "\\frac{\\chi \\gamma \\omega^{2}}{2}", "negatives": ["\\frac{\\chi \\gamma^{2} \\omega}{2}", "\\frac{\\chi^{2} \\gamma \\omega}{2}", "\\frac{\\chi \\omega^{2}}{2 \\gamma}", "\\gamma^{\\chi} \\log{(\\omega)}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Symbol('\\\\omega', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "Mul(Pow(Symbol('\\\\gamma', commutative=True), Symbol('\\\\chi', commutative=True)), log(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\delta - \\omega + \\sigma", "variable": "\\sigma", "positive": "\\sigma (\\delta - \\omega + \\frac{\\sigma}{2})", "negatives": ["\\frac{\\sigma (- 2 \\delta + 2 \\omega + \\sigma)}{2}", "\\frac{\\delta (\\delta - 2 \\omega + 2 \\sigma)}{2}", "\\frac{\\omega (2 \\delta - \\omega + 2 \\sigma)}{2}", "\\frac{\\omega \\sigma^{2}}{2 \\delta}"], "srepr_premise_expression": "Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))"]}, {"premise_expression": "\\alpha \\beta", "variable": "\\beta", "positive": "\\frac{\\alpha \\beta^{2}}{2}", "negatives": ["\\frac{\\alpha^{2} \\beta}{2}", "\\frac{\\beta^{2}}{2 \\alpha}", "- \\frac{\\cos{(\\beta)}}{\\alpha}", "\\cos{(\\alpha - \\beta)}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\beta', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\beta', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\beta', commutative=True), Integer(2)))", "Mul(Integer(-1), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), cos(Symbol('\\\\beta', commutative=True)))", "cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\beta', commutative=True))))"]}, {"premise_expression": "\\frac{\\beta}{\\delta}", "variable": "\\beta", "positive": "\\frac{\\beta^{2}}{2 \\delta}", "negatives": ["\\beta \\log{(\\delta)}", "\\delta \\log{(\\beta)}", "- \\cos{(\\beta + \\delta)}", "\\beta (\\log{(\\beta \\delta)} - 1)"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\beta', commutative=True), log(Symbol('\\\\delta', commutative=True)))", "Mul(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\beta', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True))))", "Mul(Symbol('\\\\beta', commutative=True), Add(log(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\frac{\\sin{(\\chi)}}{\\omega}", "variable": "\\omega", "positive": "\\log{(\\omega)} \\sin{(\\chi)}", "negatives": ["\\chi \\omega + \\sin{(\\omega)}", "\\frac{\\omega^{2} \\sin{(\\chi)}}{2}", "- \\cos{(\\chi - \\omega)}", "\\omega (\\log{(\\frac{\\omega}{\\chi})} - 1)"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), sin(Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(log(Symbol('\\\\omega', commutative=True)), sin(Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True)), sin(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), sin(Symbol('\\\\chi', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))))", "Mul(Symbol('\\\\omega', commutative=True), Add(log(Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\omega - \\sigma", "variable": "\\sigma", "positive": "\\frac{\\sigma (2 \\omega - \\sigma)}{2}", "negatives": ["\\frac{\\sigma (- 2 \\omega + \\sigma)}{2}", "\\frac{\\omega (\\omega - 2 \\sigma)}{2}", "\\frac{\\sigma^{2} e^{\\omega}}{2}", "\\frac{\\sin{(\\sigma)}}{\\omega}"], "srepr_premise_expression": "Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), exp(Symbol('\\\\omega', commutative=True)))", "Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), sin(Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\cos{(\\frac{\\beta}{\\omega})}", "variable": "\\omega", "positive": "\\beta \\operatorname{Si}{(\\frac{\\beta}{\\omega})} + \\omega \\cos{(\\frac{\\beta}{\\omega})}", "negatives": ["\\frac{\\omega (\\omega + 2 \\sin{(\\beta)})}{2}", "\\frac{\\omega (- 2 \\beta + \\omega)}{2}", "\\log{(\\beta)} \\log{(\\omega)}", "\\omega (- \\beta + \\log{(\\omega^{\\beta})})"], "srepr_premise_expression": "cos(Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\beta', commutative=True), Si(Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1))))), Mul(Symbol('\\\\omega', commutative=True), cos(Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1))))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), sin(Symbol('\\\\beta', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Mul(log(Symbol('\\\\beta', commutative=True)), log(Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), log(Pow(Symbol('\\\\omega', commutative=True), Symbol('\\\\beta', commutative=True)))))"]}, {"premise_expression": "- \\alpha + \\chi", "variable": "\\chi", "positive": "\\frac{\\chi (- 2 \\alpha + \\chi)}{2}", "negatives": ["\\frac{\\alpha (- \\alpha + 2 \\chi)}{2}", "\\frac{\\alpha \\chi^{2}}{2}", "\\sin{(\\alpha + \\chi)}", "\\alpha \\chi - \\cos{(\\chi)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\chi', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\chi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(2)))", "sin(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\chi', commutative=True))))"]}, {"premise_expression": "e^{\\gamma - \\sigma}", "variable": "\\gamma", "positive": "e^{\\gamma - \\sigma}", "negatives": ["- e^{\\gamma - \\sigma}", "\\cos{(\\gamma - \\sigma)}", "- \\cos{(\\gamma + \\sigma)}", "\\frac{\\gamma (\\gamma - 2 \\sigma)}{2}"], "srepr_premise_expression": "exp(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "exp(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))", "cos(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\gamma \\omega", "variable": "\\gamma", "positive": "\\frac{\\gamma^{2} \\omega}{2}", "negatives": ["\\frac{\\gamma \\omega^{2}}{2}", "\\frac{\\gamma^{2} \\log{(\\omega)}}{2}", "\\frac{\\gamma (\\gamma + 2 \\omega)}{2}", "\\gamma \\sin{(1)}"], "srepr_premise_expression": "Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Symbol('\\\\omega', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), log(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Symbol('\\\\gamma', commutative=True), sin(Integer(1)))"]}, {"premise_expression": "- \\sigma + \\xi", "variable": "\\xi", "positive": "\\frac{\\xi (- 2 \\sigma + \\xi)}{2}", "negatives": ["\\frac{\\sigma (- \\sigma + 2 \\xi)}{2}", "- e^{\\sigma - \\xi}", "\\frac{\\xi (- \\xi + 2 \\log{(\\sigma)})}{2}", "\\xi (- \\sigma + \\log{(\\xi^{\\sigma})})"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Integer(-1), exp(Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), log(Symbol('\\\\sigma', commutative=True)))))", "Mul(Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), log(Pow(Symbol('\\\\xi', commutative=True), Symbol('\\\\sigma', commutative=True)))))"]}, {"premise_expression": "\\omega + \\psi + \\sigma", "variable": "\\omega", "positive": "\\omega (\\frac{\\omega}{2} + \\psi + \\sigma)", "negatives": ["\\frac{\\omega (\\omega - 2 \\psi + 2 \\sigma)}{2}", "\\frac{\\sigma (2 \\omega + 2 \\psi + \\sigma)}{2}", "\\frac{\\psi (2 \\omega + \\psi + 2 \\sigma)}{2}", "\\frac{\\omega (\\omega + 2 \\psi \\sigma)}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\omega', commutative=True), Add(Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\psi', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\frac{\\sin{(\\psi)}}{\\beta}", "variable": "\\psi", "positive": "- \\frac{\\cos{(\\psi)}}{\\beta}", "negatives": ["\\beta e^{\\psi}", "\\frac{\\sin{(2 \\psi)}}{2}", "\\frac{\\psi^{2} \\cos{(\\beta)}}{2}", "\\sin{(\\beta + \\psi)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), sin(Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Integer(-1), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), cos(Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\beta', commutative=True), exp(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), sin(Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), cos(Symbol('\\\\beta', commutative=True)))", "sin(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\omega + \\sigma", "variable": "\\sigma", "positive": "\\frac{\\sigma (2 \\omega + \\sigma)}{2}", "negatives": ["\\frac{\\omega (\\omega + 2 \\sigma)}{2}", "\\frac{\\sigma^{2}}{2 \\omega}", "\\frac{\\omega \\sigma^{2}}{2}", "\\sigma (\\log{(\\frac{\\omega}{\\sigma})} + 1)"], "srepr_premise_expression": "Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "Mul(Symbol('\\\\sigma', commutative=True), Add(log(Mul(Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))), Integer(1)))"]}, {"premise_expression": "e^{\\frac{\\sigma}{\\beta}}", "variable": "\\beta", "positive": "\\beta e^{\\frac{\\sigma}{\\beta}} - \\sigma \\operatorname{Ei}{(\\frac{\\sigma}{\\beta})}", "negatives": ["\\beta \\cos{(\\frac{\\sigma}{\\beta})} + \\sigma \\operatorname{Si}{(\\frac{\\sigma}{\\beta})}", "\\beta e^{\\frac{\\sigma}{\\beta}}", "\\sigma e^{\\beta}", "\\frac{\\beta (\\beta + 2 \\sin{(\\sigma)})}{2}"], "srepr_premise_expression": "exp(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\beta', commutative=True), exp(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True)))), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True), Ei(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\beta', commutative=True), cos(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True)))), Mul(Symbol('\\\\sigma', commutative=True), Si(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True)))))", "Mul(Symbol('\\\\beta', commutative=True), exp(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))))", "Mul(Symbol('\\\\sigma', commutative=True), exp(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), sin(Symbol('\\\\sigma', commutative=True)))))"]}, {"premise_expression": "\\frac{e^{\\gamma}}{\\pi}", "variable": "\\pi", "positive": "e^{\\gamma} \\log{(\\pi)}", "negatives": ["- \\gamma \\cos{(\\pi)}", "\\log{(\\pi)} \\cos{(\\gamma)}", "e^{- \\gamma + \\pi}", "- e^{\\gamma - \\pi}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), exp(Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(exp(Symbol('\\\\gamma', commutative=True)), log(Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), cos(Symbol('\\\\pi', commutative=True)))", "Mul(log(Symbol('\\\\pi', commutative=True)), cos(Symbol('\\\\gamma', commutative=True)))", "exp(Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(Integer(-1), exp(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))"]}, {"premise_expression": "e^{\\delta - \\omega}", "variable": "\\delta", "positive": "e^{\\delta - \\omega}", "negatives": ["- e^{\\delta - \\omega}", "\\omega e^{\\frac{\\delta}{\\omega}}", "\\delta \\omega - \\cos{(\\delta)}", "\\delta (- \\omega + \\log{(\\delta^{\\omega})})"], "srepr_premise_expression": "exp(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "exp(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))))", "Mul(Symbol('\\\\omega', commutative=True), exp(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))))", "Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\delta', commutative=True))))", "Mul(Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), log(Pow(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True)))))"]}, {"premise_expression": "\\cos{(\\pi + \\psi)}", "variable": "\\pi", "positive": "\\sin{(\\pi + \\psi)}", "negatives": ["\\frac{\\pi^{2} \\log{(\\psi)}}{2}", "\\frac{\\pi (\\log{(\\pi)} - 1)}{\\psi}", "\\pi \\psi (\\log{(\\pi)} - 1)", "\\pi (\\log{(\\pi \\psi)} - 1)"], "srepr_premise_expression": "cos(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "sin(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), log(Symbol('\\\\psi', commutative=True)))", "Mul(Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Add(log(Symbol('\\\\pi', commutative=True)), Integer(-1)))", "Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True), Add(log(Symbol('\\\\pi', commutative=True)), Integer(-1)))", "Mul(Symbol('\\\\pi', commutative=True), Add(log(Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\log{(\\gamma^{\\omega})}", "variable": "\\gamma", "positive": "\\gamma (- \\omega + \\log{(\\gamma^{\\omega})})", "negatives": ["\\frac{\\gamma (- \\gamma + 2 \\log{(\\omega)})}{2}", "\\gamma \\log{(\\omega)}^{\\omega}", "\\frac{\\gamma (\\gamma - 2 \\omega)}{2}", "\\frac{\\gamma (\\gamma + 2 e^{\\omega})}{2}"], "srepr_premise_expression": "log(Pow(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), log(Pow(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), log(Symbol('\\\\omega', commutative=True)))))", "Mul(Symbol('\\\\gamma', commutative=True), Pow(log(Symbol('\\\\omega', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), exp(Symbol('\\\\omega', commutative=True)))))"]}, {"premise_expression": "\\gamma \\sin{(\\chi)}", "variable": "\\chi", "positive": "- \\gamma \\cos{(\\chi)}", "negatives": ["\\gamma \\log{(\\chi)}", "\\gamma \\sin{(\\chi)}", "- \\cos{(\\chi + \\gamma)}", "\\frac{\\gamma^{2} \\sin{(\\chi)}}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\gamma', commutative=True), sin(Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), cos(Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\chi', commutative=True)))", "Mul(Symbol('\\\\gamma', commutative=True), sin(Symbol('\\\\chi', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), sin(Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "\\omega (\\gamma - \\sigma)", "variable": "\\gamma", "positive": "\\frac{\\gamma \\omega (\\gamma - 2 \\sigma)}{2}", "negatives": ["\\frac{\\omega^{2} (\\gamma - \\sigma)}{2}", "\\frac{\\gamma (\\gamma \\omega - 2 \\sigma)}{2}", "\\frac{\\omega \\sigma (2 \\gamma - \\sigma)}{2}", "\\frac{\\gamma (\\gamma \\omega + 2 \\sigma)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "- \\beta + \\chi - \\psi", "variable": "\\beta", "positive": "\\beta (- \\frac{\\beta}{2} + \\chi - \\psi)", "negatives": ["\\frac{\\chi (- 2 \\beta + \\chi - 2 \\psi)}{2}", "\\frac{\\psi (- 2 \\beta + 2 \\chi - \\psi)}{2}", "\\frac{\\beta (- \\beta - 2 \\chi + 2 \\psi)}{2}", "\\frac{\\beta^{2} (- \\chi + \\psi)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Rational(1, 2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\frac{\\alpha}{\\beta}", "variable": "\\alpha", "positive": "\\frac{\\alpha^{2}}{2 \\beta}", "negatives": ["\\alpha \\log{(\\beta)}", "\\frac{\\alpha^{2}}{2 \\beta} + \\alpha \\beta", "\\sin{(\\alpha + \\beta)}", "\\sin{(\\alpha - \\beta)}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\beta', commutative=True)))", "Add(Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\beta', commutative=True), Integer(-1))), Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True)))", "sin(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True)))", "sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\beta', commutative=True))))"]}, {"premise_expression": "\\gamma (\\pi + \\xi)", "variable": "\\gamma", "positive": "\\frac{\\gamma^{2} (\\pi + \\xi)}{2}", "negatives": ["\\frac{\\gamma^{2} (\\pi - \\xi)}{2}", "\\frac{\\gamma \\xi (2 \\pi + \\xi)}{2}", "\\frac{\\gamma \\pi (\\pi + 2 \\xi)}{2}", "\\frac{\\gamma \\pi (- \\gamma + 2 \\xi)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\log{(- \\pi + \\xi)}", "variable": "\\xi", "positive": "- \\pi \\log{(- \\pi + \\xi)} + \\xi \\log{(- \\pi + \\xi)} - \\xi", "negatives": ["\\pi \\log{(- \\pi + \\xi)} - \\pi - \\xi \\log{(\\pi - \\xi)}", "\\log{(\\pi)} \\log{(\\xi)}", "- \\pi \\operatorname{Ei}{(\\frac{\\pi}{\\xi})} + \\xi e^{\\frac{\\pi}{\\xi}}", "\\frac{\\xi (\\log{(\\xi)} - 1)}{\\pi}"], "srepr_premise_expression": "log(Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Symbol('\\\\xi', commutative=True)))), Mul(Symbol('\\\\xi', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Symbol('\\\\xi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\pi', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Symbol('\\\\xi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True), log(Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))))", "Mul(log(Symbol('\\\\pi', commutative=True)), log(Symbol('\\\\xi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True), Ei(Mul(Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))), Mul(Symbol('\\\\xi', commutative=True), exp(Mul(Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))))", "Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True), Add(log(Symbol('\\\\xi', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\frac{e^{\\alpha}}{\\sigma}", "variable": "\\sigma", "positive": "e^{\\alpha} \\log{(\\sigma)}", "negatives": ["\\alpha \\log{(\\sigma)}", "- \\alpha \\sigma - \\cos{(\\sigma)}", "\\sin{(\\alpha + \\sigma)}", "\\sigma \\cos{(1)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), exp(Symbol('\\\\alpha', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(exp(Symbol('\\\\alpha', commutative=True)), log(Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\sigma', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\sigma', commutative=True))))", "sin(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True)))", "Mul(Symbol('\\\\sigma', commutative=True), cos(Integer(1)))"]}, {"premise_expression": "\\frac{\\delta}{\\xi}", "variable": "\\xi", "positive": "\\delta \\log{(\\xi)}", "negatives": ["\\frac{\\delta^{2}}{2 \\xi}", "\\frac{\\xi^{2} \\log{(\\delta)}}{2}", "- \\delta \\xi - \\cos{(\\xi)}", "e^{\\delta + \\xi}"], "srepr_premise_expression": "Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), log(Symbol('\\\\delta', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\xi', commutative=True))))", "exp(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\chi + \\xi", "variable": "\\xi", "positive": "\\frac{\\xi (2 \\chi + \\xi)}{2}", "negatives": ["\\frac{\\xi (- 2 \\chi + \\xi)}{2}", "\\frac{\\chi (\\chi + 2 \\xi)}{2}", "\\frac{\\xi (- \\xi + 2 \\log{(\\chi)})}{2}", "\\frac{\\xi (- \\xi + 2 \\cos{(\\chi)})}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), log(Symbol('\\\\chi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\chi', commutative=True)))))"]}, {"premise_expression": "\\chi + \\xi", "variable": "\\xi", "positive": "\\frac{\\xi (2 \\chi + \\xi)}{2}", "negatives": ["\\frac{\\chi (\\chi + 2 \\xi)}{2}", "\\sin{(\\chi + \\xi)}", "- \\chi \\cos{(\\xi)}", "\\frac{\\xi (\\xi + 2 \\cos{(\\chi)})}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "sin(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True)))", "Mul(Integer(-1), Symbol('\\\\chi', commutative=True), cos(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\xi', commutative=True), Mul(Integer(2), cos(Symbol('\\\\chi', commutative=True)))))"]}, {"premise_expression": "\\frac{\\pi}{\\psi}", "variable": "\\pi", "positive": "\\frac{\\pi^{2}}{2 \\psi}", "negatives": ["\\pi \\log{(\\psi)}", "\\cos{(\\pi - \\psi)}", "\\frac{\\pi (\\pi - 2 \\psi)}{2}", "- e^{- \\pi + \\psi}"], "srepr_premise_expression": "Mul(Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\psi', commutative=True)))", "cos(Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "e^{\\psi^{\\sigma}}", "variable": "\\psi", "positive": "\\frac{e^{- \\frac{i \\pi}{\\sigma}} \\gamma(\\frac{1}{\\sigma}, \\psi^{\\sigma} e^{i \\pi})}{\\sigma}", "negatives": ["\\psi \\log{(- \\psi + \\sigma)} - \\psi - \\sigma \\log{(\\psi - \\sigma)}", "\\frac{\\psi (- \\psi + 2 e^{\\sigma})}{2}", "\\psi \\log{(\\psi + \\sigma)} - \\psi + \\sigma \\log{(\\psi + \\sigma)}", "\\psi \\log{(\\psi - \\sigma)} - \\psi - \\sigma \\log{(\\psi - \\sigma)}"], "srepr_premise_expression": "exp(Pow(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), exp(Mul(Integer(-1), I, pi, Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))), lowergamma(Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Mul(Pow(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True)), exp_polar(Mul(I, pi)))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\psi', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Symbol('\\\\sigma', commutative=True)))), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True), log(Add(Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\sigma', commutative=True)))))", "Add(Mul(Symbol('\\\\psi', commutative=True), log(Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True)))), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Symbol('\\\\sigma', commutative=True), log(Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True)))))", "Add(Mul(Symbol('\\\\psi', commutative=True), log(Add(Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True), log(Add(Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))))"]}, {"premise_expression": "\\alpha + \\sin{(\\psi)}", "variable": "\\alpha", "positive": "\\frac{\\alpha (\\alpha + 2 \\sin{(\\psi)})}{2}", "negatives": ["\\alpha \\psi - \\cos{(\\psi)}", "\\alpha (- \\psi + \\log{(\\alpha^{\\psi})})", "\\sin{(\\alpha + \\psi)}", "\\psi \\sin{(\\alpha)}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), sin(Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), sin(Symbol('\\\\psi', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\psi', commutative=True))))", "Mul(Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), log(Pow(Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True)))))", "sin(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True)))", "Mul(Symbol('\\\\psi', commutative=True), sin(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\psi + e^{\\delta}", "variable": "\\delta", "positive": "\\delta \\psi + e^{\\delta}", "negatives": ["\\delta \\psi + \\sin{(\\delta)}", "\\frac{\\psi (\\psi + 2 e^{\\delta})}{2}", "\\frac{\\delta^{2} e^{\\psi}}{2}", "\\delta (\\psi + \\log{(\\delta)} - 1)"], "srepr_premise_expression": "Add(Symbol('\\\\psi', commutative=True), exp(Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\psi', commutative=True)), exp(Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\psi', commutative=True)), sin(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(2), exp(Symbol('\\\\delta', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), exp(Symbol('\\\\psi', commutative=True)))", "Mul(Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\psi', commutative=True), log(Symbol('\\\\delta', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\frac{\\delta}{\\alpha}", "variable": "\\delta", "positive": "\\frac{\\delta^{2}}{2 \\alpha}", "negatives": ["\\delta \\log{(\\alpha)}", "\\frac{\\delta^{2} \\log{(\\alpha)}}{2}", "e^{- \\alpha + \\delta}", "\\frac{\\delta (\\delta + 2 \\cos{(\\alpha)})}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\delta', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), log(Symbol('\\\\alpha', commutative=True)))", "exp(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), cos(Symbol('\\\\alpha', commutative=True)))))"]}, {"premise_expression": "\\alpha \\sigma", "variable": "\\sigma", "positive": "\\frac{\\alpha \\sigma^{2}}{2}", "negatives": ["\\frac{\\alpha^{2} \\sigma}{2}", "e^{\\alpha + \\sigma}", "\\frac{\\sigma (\\log{(\\sigma)} - 1)}{\\alpha}", "\\sigma (\\log{(\\frac{\\alpha}{\\sigma})} + 1)"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\sigma', commutative=True))", "exp(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True)))", "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True), Add(log(Symbol('\\\\sigma', commutative=True)), Integer(-1)))", "Mul(Symbol('\\\\sigma', commutative=True), Add(log(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))), Integer(1)))"]}, {"premise_expression": "\\alpha - \\xi", "variable": "\\alpha", "positive": "\\frac{\\alpha (\\alpha - 2 \\xi)}{2}", "negatives": ["\\frac{\\alpha (- \\alpha + 2 \\xi)}{2}", "\\frac{\\xi (2 \\alpha - \\xi)}{2}", "\\frac{\\alpha (\\alpha + 2 \\log{(\\xi)})}{2}", "\\frac{\\alpha^{2} \\log{(\\xi)}}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), log(Symbol('\\\\xi', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), log(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\log{(\\delta^{\\alpha})}", "variable": "\\delta", "positive": "\\delta (- \\alpha + \\log{(\\delta^{\\alpha})})", "negatives": ["\\frac{\\alpha^{2} \\log{(\\delta)}}{2}", "\\frac{\\delta (2 \\alpha - \\delta)}{2}", "- \\alpha \\delta + e^{\\delta}", "\\alpha \\sin{(\\delta)}"], "srepr_premise_expression": "log(Pow(Symbol('\\\\delta', commutative=True), Symbol('\\\\alpha', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), log(Pow(Symbol('\\\\delta', commutative=True), Symbol('\\\\alpha', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), log(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\delta', commutative=True)), exp(Symbol('\\\\delta', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), sin(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\xi + \\sin{(\\beta)}", "variable": "\\beta", "positive": "\\beta \\xi - \\cos{(\\beta)}", "negatives": ["- \\beta \\xi + e^{\\beta}", "\\log{(\\beta)} \\log{(\\xi)}", "\\frac{\\xi (\\xi + 2 \\sin{(\\beta)})}{2}", "\\frac{\\beta^{2} \\log{(\\xi)}}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\xi', commutative=True), sin(Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\beta', commutative=True))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True)), exp(Symbol('\\\\beta', commutative=True)))", "Mul(log(Symbol('\\\\beta', commutative=True)), log(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\xi', commutative=True), Mul(Integer(2), sin(Symbol('\\\\beta', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), log(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "- \\psi + \\frac{\\omega}{\\chi}", "variable": "\\omega", "positive": "- \\omega \\psi + \\frac{\\omega^{2}}{2 \\chi}", "negatives": ["- \\chi \\psi + \\omega \\log{(\\chi)}", "\\frac{\\omega^{2} \\psi^{\\chi}}{2}", "\\frac{\\omega^{2}}{2 \\chi \\psi}", "\\frac{\\chi \\omega^{2} \\psi}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Pow(Symbol('\\\\omega', commutative=True), Integer(2))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\chi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Pow(Symbol('\\\\psi', commutative=True), Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))"]}, {"premise_expression": "\\frac{\\alpha \\xi}{\\chi}", "variable": "\\alpha", "positive": "\\frac{\\alpha^{2} \\xi}{2 \\chi}", "negatives": ["\\frac{\\alpha \\xi^{2}}{2 \\chi}", "\\alpha \\xi \\log{(\\chi)}", "\\frac{\\alpha (\\alpha \\xi + 2 \\chi)}{2}", "\\chi^{\\xi} \\log{(\\alpha)}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True), log(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), Symbol('\\\\chi', commutative=True))))", "Mul(Pow(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True)), log(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\sin{(\\delta - \\omega)}", "variable": "\\omega", "positive": "\\cos{(\\delta - \\omega)}", "negatives": ["- \\cos{(\\delta - \\omega)}", "- \\sin{(\\delta - \\omega)}", "e^{- \\delta + \\omega}", "- \\delta \\omega - \\cos{(\\omega)}"], "srepr_premise_expression": "sin(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))))", "Mul(Integer(-1), sin(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))))", "exp(Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\omega', commutative=True))))"]}, {"premise_expression": "- \\delta + \\omega + \\pi", "variable": "\\delta", "positive": "\\delta (- \\frac{\\delta}{2} + \\omega + \\pi)", "negatives": ["\\frac{\\pi (- 2 \\delta + 2 \\omega + \\pi)}{2}", "\\frac{\\omega (- 2 \\delta + \\omega + 2 \\pi)}{2}", "(- \\omega + \\pi) \\log{(\\delta)}", "\\frac{\\delta \\omega (- \\delta + 2 \\pi)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Rational(1, 2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Symbol('\\\\pi', commutative=True)), log(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\frac{\\alpha - \\gamma}{\\beta}", "variable": "\\beta", "positive": "(\\alpha - \\gamma) \\log{(\\beta)}", "negatives": ["\\frac{\\gamma (2 \\alpha - \\gamma)}{2 \\beta}", "\\frac{\\alpha (\\alpha - 2 \\gamma)}{2 \\beta}", "\\frac{\\alpha \\log{(\\beta)}}{\\gamma}", "\\frac{\\beta (2 \\alpha^{\\gamma} - \\beta)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))), log(Symbol('\\\\beta', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True))))", "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), log(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(2), Pow(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True))), Mul(Integer(-1), Symbol('\\\\beta', commutative=True))))"]}, {"premise_expression": "\\frac{\\delta}{\\alpha}", "variable": "\\alpha", "positive": "\\delta \\log{(\\alpha)}", "negatives": ["\\frac{\\delta^{2}}{2 \\alpha}", "\\frac{\\alpha^{2} \\log{(\\delta)}}{2}", "\\cos{(\\alpha - \\delta)}", "\\alpha \\delta (\\log{(\\alpha)} - 1)"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\delta', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), log(Symbol('\\\\delta', commutative=True)))", "cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))", "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\delta', commutative=True), Add(log(Symbol('\\\\alpha', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\sin{(\\beta + \\omega)}", "variable": "\\beta", "positive": "- \\cos{(\\beta + \\omega)}", "negatives": ["\\beta \\omega - \\cos{(\\beta)}", "\\beta (\\log{(\\frac{\\beta}{\\omega})} - 1)", "\\frac{\\beta^{2} \\omega}{2}", "\\frac{\\beta (- \\beta + 2 \\sin{(\\omega)})}{2}"], "srepr_premise_expression": "sin(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\beta', commutative=True))))", "Mul(Symbol('\\\\beta', commutative=True), Add(log(Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\omega', commutative=True))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\omega', commutative=True)))))"]}, {"premise_expression": "\\log{(\\frac{\\delta}{\\xi})}", "variable": "\\xi", "positive": "\\xi (\\log{(\\frac{\\delta}{\\xi})} + 1)", "negatives": ["\\delta (\\log{(\\frac{\\delta}{\\xi})} - 1)", "\\delta \\xi (\\log{(\\xi)} - 1)", "\\frac{\\xi (2 \\delta - \\xi)}{2}", "\\frac{\\xi (- \\xi + 2 \\log{(\\delta)})}{2}"], "srepr_premise_expression": "log(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\xi', commutative=True), Add(log(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))), Integer(1)))", "srepr_negatives": ["Mul(Symbol('\\\\delta', commutative=True), Add(log(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))), Integer(-1)))", "Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True), Add(log(Symbol('\\\\xi', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), log(Symbol('\\\\delta', commutative=True)))))"]}, {"premise_expression": "- \\alpha + \\delta", "variable": "\\delta", "positive": "\\frac{\\delta (- 2 \\alpha + \\delta)}{2}", "negatives": ["\\frac{\\alpha (- \\alpha + 2 \\delta)}{2}", "\\frac{\\delta^{2} \\cos{(\\alpha)}}{2}", "- e^{\\alpha - \\delta}", "\\delta (\\log{(\\frac{\\alpha}{\\delta})} + 1)"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\delta', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), cos(Symbol('\\\\alpha', commutative=True)))", "Mul(Integer(-1), exp(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)))))", "Mul(Symbol('\\\\delta', commutative=True), Add(log(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)))), Integer(1)))"]}, {"premise_expression": "\\psi + \\log{(\\delta)}", "variable": "\\delta", "positive": "\\delta (\\psi + \\log{(\\delta)} - 1)", "negatives": ["\\frac{\\delta (\\log{(\\delta)} - 1)}{\\psi}", "\\delta (\\log{(\\frac{\\delta}{\\psi})} - 1)", "\\frac{\\psi (\\psi + 2 \\log{(\\delta)})}{2}", "e^{\\psi} \\log{(\\delta)}"], "srepr_premise_expression": "Add(Symbol('\\\\psi', commutative=True), log(Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\psi', commutative=True), log(Symbol('\\\\delta', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Add(log(Symbol('\\\\delta', commutative=True)), Integer(-1)))", "Mul(Symbol('\\\\delta', commutative=True), Add(log(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(2), log(Symbol('\\\\delta', commutative=True)))))", "Mul(exp(Symbol('\\\\psi', commutative=True)), log(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\frac{\\chi}{\\alpha}", "variable": "\\alpha", "positive": "\\chi \\log{(\\alpha)}", "negatives": ["\\frac{\\chi^{2}}{2 \\alpha}", "\\log{(\\alpha)} \\sin{(\\chi)}", "\\alpha (\\log{(\\alpha \\chi)} - 1)", "\\alpha^{2} (\\frac{\\alpha}{3} - \\frac{\\chi}{2})"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\chi', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\chi', commutative=True), Integer(2)))", "Mul(log(Symbol('\\\\alpha', commutative=True)), sin(Symbol('\\\\chi', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), Add(log(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True))), Integer(-1)))", "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Add(Mul(Rational(1, 3), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Rational(1, 2), Symbol('\\\\chi', commutative=True))))"]}, {"premise_expression": "- \\sin{(\\psi - \\sigma)}", "variable": "\\psi", "positive": "\\cos{(\\psi - \\sigma)}", "negatives": ["- \\cos{(\\psi - \\sigma)}", "- \\cos{(\\psi + \\sigma)}", "- \\sigma \\cos{(\\psi)}", "\\psi (\\log{(\\frac{\\sigma}{\\psi})} + 1)"], "srepr_premise_expression": "Mul(Integer(-1), sin(Add(Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "cos(Add(Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True))))", "Mul(Integer(-1), Symbol('\\\\sigma', commutative=True), cos(Symbol('\\\\psi', commutative=True)))", "Mul(Symbol('\\\\psi', commutative=True), Add(log(Mul(Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))), Integer(1)))"]}, {"premise_expression": "\\cos{(\\chi - \\gamma)}", "variable": "\\gamma", "positive": "- \\sin{(\\chi - \\gamma)}", "negatives": ["\\sin{(\\chi - \\gamma)}", "\\cos{(\\chi - \\gamma)}", "e^{\\chi} \\log{(\\gamma)}", "\\frac{\\gamma^{2} e^{\\chi}}{2}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Integer(-1), sin(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))))", "srepr_negatives": ["sin(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "cos(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "Mul(exp(Symbol('\\\\chi', commutative=True)), log(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), exp(Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "\\frac{\\chi - \\psi}{\\pi}", "variable": "\\pi", "positive": "(\\chi - \\psi) \\log{(\\pi)}", "negatives": ["\\chi \\pi + \\psi \\log{(\\pi)}", "\\frac{\\psi (2 \\chi - \\psi)}{2 \\pi}", "\\frac{\\chi (\\chi - 2 \\psi)}{2 \\pi}", "\\frac{\\pi (2 \\chi - \\pi - 2 \\psi)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))), log(Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Symbol('\\\\psi', commutative=True), log(Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "- \\psi + \\sin{(\\alpha)}", "variable": "\\psi", "positive": "\\frac{\\psi (- \\psi + 2 \\sin{(\\alpha)})}{2}", "negatives": ["\\frac{\\psi (- \\psi + 2 \\cos{(\\alpha)})}{2}", "- \\alpha \\psi - \\cos{(\\alpha)}", "\\frac{\\psi^{2}}{2 \\alpha}", "\\log{(\\psi)} \\cos{(\\alpha)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), sin(Symbol('\\\\alpha', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\alpha', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\alpha', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\alpha', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "Mul(log(Symbol('\\\\psi', commutative=True)), cos(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\frac{- \\beta + \\chi}{\\chi}", "variable": "\\beta", "positive": "- \\frac{\\beta^{2}}{2 \\chi} + \\beta", "negatives": ["- \\beta \\log{(\\chi)} + \\chi", "\\frac{\\beta^{2} \\chi}{2}", "\\frac{\\beta^{2} e^{\\chi}}{2}", "\\frac{\\beta (\\beta + 2 \\chi)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\chi', commutative=True), Integer(-1))), Symbol('\\\\beta', commutative=True))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), log(Symbol('\\\\chi', commutative=True))), Symbol('\\\\chi', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\chi', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), exp(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\chi', commutative=True))))"]}, {"premise_expression": "\\beta \\pi", "variable": "\\pi", "positive": "\\frac{\\beta \\pi^{2}}{2}", "negatives": ["\\frac{\\beta^{2} \\pi}{2}", "\\frac{\\pi^{2}}{2 \\beta}", "\\log{(\\pi)} \\sin{(\\beta)}", "\\frac{\\pi (\\pi + 2 \\sin{(\\beta)})}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\pi', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "Mul(log(Symbol('\\\\pi', commutative=True)), sin(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), sin(Symbol('\\\\beta', commutative=True)))))"]}, {"premise_expression": "\\frac{\\beta \\xi}{\\pi}", "variable": "\\xi", "positive": "\\frac{\\beta \\xi^{2}}{2 \\pi}", "negatives": ["\\frac{\\beta^{2} \\xi}{2 \\pi}", "\\frac{\\beta \\pi \\xi^{2}}{2}", "\\beta \\xi \\log{(\\pi)}", "\\frac{\\xi^{2} (\\beta - \\pi)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True), log(Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\log{(\\chi + \\xi)}", "variable": "\\xi", "positive": "\\chi \\log{(\\chi + \\xi)} + \\xi \\log{(\\chi + \\xi)} - \\xi", "negatives": ["\\chi \\log{(\\chi + \\xi)} - \\chi + \\xi \\log{(\\chi + \\xi)}", "\\log{(\\xi)} \\sin{(\\chi)}", "\\xi (\\chi - \\xi)", "- \\chi \\xi - \\cos{(\\xi)}"], "srepr_premise_expression": "log(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\chi', commutative=True), log(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True)))), Mul(Symbol('\\\\xi', commutative=True), log(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\chi', commutative=True), log(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Symbol('\\\\xi', commutative=True), log(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True)))))", "Mul(log(Symbol('\\\\xi', commutative=True)), sin(Symbol('\\\\chi', commutative=True)))", "Mul(Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\frac{\\xi}{\\sigma}", "variable": "\\xi", "positive": "\\frac{\\xi^{2}}{2 \\sigma}", "negatives": ["\\xi \\log{(\\sigma)}", "\\xi (\\sigma + \\xi)", "\\sigma \\sin{(\\xi)}", "\\sigma \\log{(\\xi)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\sigma', commutative=True)))", "Mul(Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\sigma', commutative=True), sin(Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\psi (\\chi + \\omega)", "variable": "\\chi", "positive": "\\frac{\\chi \\psi (\\chi + 2 \\omega)}{2}", "negatives": ["\\frac{\\psi^{2} (\\chi + \\omega)}{2}", "\\frac{\\omega \\psi (2 \\chi + \\omega)}{2}", "\\frac{\\chi^{2} (\\omega + \\psi)}{2}", "\\frac{\\chi (\\chi - 2 \\omega)}{2 \\psi}"], "srepr_premise_expression": "Mul(Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True))))"]}, {"premise_expression": "\\xi (\\chi + \\omega)", "variable": "\\xi", "positive": "\\frac{\\xi^{2} (\\chi + \\omega)}{2}", "negatives": ["\\frac{\\omega \\xi (2 \\chi + \\omega)}{2}", "\\frac{\\chi \\xi (\\chi + 2 \\omega)}{2}", "\\frac{\\chi \\xi (2 \\omega + \\xi)}{2}", "\\frac{\\chi \\xi (- 2 \\omega + \\xi)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\sigma + \\sin{(\\alpha)}", "variable": "\\sigma", "positive": "\\frac{\\sigma (\\sigma + 2 \\sin{(\\alpha)})}{2}", "negatives": ["\\frac{\\sigma^{2} \\log{(\\alpha)}}{2}", "\\alpha \\sigma - \\cos{(\\alpha)}", "\\frac{\\sigma (2 \\alpha - \\sigma)}{2}", "\\sigma (- \\alpha + \\log{(\\sigma^{\\alpha})})"], "srepr_premise_expression": "Add(Symbol('\\\\sigma', commutative=True), sin(Symbol('\\\\alpha', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(2), sin(Symbol('\\\\alpha', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), log(Symbol('\\\\alpha', commutative=True)))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\alpha', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), log(Pow(Symbol('\\\\sigma', commutative=True), Symbol('\\\\alpha', commutative=True)))))"]}, {"premise_expression": "\\log{(\\frac{\\xi}{\\psi})}", "variable": "\\xi", "positive": "\\xi (\\log{(\\frac{\\xi}{\\psi})} - 1)", "negatives": ["\\psi (\\log{(\\frac{\\xi}{\\psi})} + 1)", "\\psi \\log{(\\xi)}", "\\frac{\\xi (- 2 \\psi + \\xi)}{2}", "\\log{(\\xi)} \\sin{(\\psi)}"], "srepr_premise_expression": "log(Mul(Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\xi', commutative=True), Add(log(Mul(Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\psi', commutative=True), Add(log(Mul(Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))), Integer(1)))", "Mul(Symbol('\\\\psi', commutative=True), log(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(log(Symbol('\\\\xi', commutative=True)), sin(Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\delta + \\sin{(\\chi)}", "variable": "\\delta", "positive": "\\frac{\\delta (\\delta + 2 \\sin{(\\chi)})}{2}", "negatives": ["\\frac{\\delta (- \\delta + 2 \\sin{(\\chi)})}{2}", "\\frac{\\delta (\\delta + 2 e^{\\chi})}{2}", "\\frac{\\delta (- \\delta + 2 \\cos{(\\chi)})}{2}", "\\chi \\delta - \\cos{(\\chi)}"], "srepr_premise_expression": "Add(Symbol('\\\\delta', commutative=True), sin(Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), sin(Symbol('\\\\chi', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\chi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), exp(Symbol('\\\\chi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\chi', commutative=True)))))", "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\chi', commutative=True))))"]}, {"premise_expression": "\\frac{\\cos{(\\pi)}}{\\delta}", "variable": "\\pi", "positive": "\\frac{\\sin{(\\pi)}}{\\delta}", "negatives": ["\\frac{\\pi^{2} \\sin{(\\delta)}}{2}", "\\log{(\\delta)} \\cos{(\\pi)}", "- \\delta \\pi + e^{\\pi}", "\\int \\cos^{\\delta}{(\\pi)} d\\pi"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), cos(Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), sin(Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), sin(Symbol('\\\\delta', commutative=True)))", "Mul(log(Symbol('\\\\delta', commutative=True)), cos(Symbol('\\\\pi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True)), exp(Symbol('\\\\pi', commutative=True)))", "Integral(Pow(cos(Symbol('\\\\pi', commutative=True)), Symbol('\\\\delta', commutative=True)), Tuple(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "- \\beta + \\gamma", "variable": "\\gamma", "positive": "\\frac{\\gamma (- 2 \\beta + \\gamma)}{2}", "negatives": ["\\frac{\\beta (- \\beta + 2 \\gamma)}{2}", "\\frac{\\gamma (\\gamma + 2 \\log{(\\beta)})}{2}", "\\frac{\\gamma (- \\gamma + 2 \\sin{(\\beta)})}{2}", "- \\sin{(\\beta - \\gamma)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\gamma', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), log(Symbol('\\\\beta', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\beta', commutative=True)))))", "Mul(Integer(-1), sin(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))))"]}, {"premise_expression": "\\omega + \\sigma", "variable": "\\sigma", "positive": "\\frac{\\sigma (2 \\omega + \\sigma)}{2}", "negatives": ["\\frac{\\omega (\\omega + 2 \\sigma)}{2}", "\\frac{\\sigma^{2} \\cos{(\\omega)}}{2}", "\\frac{\\sigma^{2} \\log{(\\omega)}}{2}", "- e^{\\omega - \\sigma}"], "srepr_premise_expression": "Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), cos(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), log(Symbol('\\\\omega', commutative=True)))", "Mul(Integer(-1), exp(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))"]}, {"premise_expression": "e^{\\xi^{\\omega}}", "variable": "\\xi", "positive": "\\frac{e^{- \\frac{i \\pi}{\\omega}} \\gamma(\\frac{1}{\\omega}, \\xi^{\\omega} e^{i \\pi})}{\\omega}", "negatives": ["\\operatorname{NonElementaryIntegral}{((\\omega - \\xi)^{\\xi},( \\xi))}", "- \\omega \\log{(- \\omega + \\xi)} + \\xi \\log{(\\omega - \\xi)} - \\xi", "\\omega \\operatorname{Si}{(\\frac{\\omega}{\\xi})} + \\xi \\cos{(\\frac{\\omega}{\\xi})}", "\\log{(\\xi)} \\cos{(\\omega)}"], "srepr_premise_expression": "exp(Pow(Symbol('\\\\xi', commutative=True), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), exp(Mul(Integer(-1), I, pi, Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))), lowergamma(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Mul(Pow(Symbol('\\\\xi', commutative=True), Symbol('\\\\omega', commutative=True)), exp_polar(Mul(I, pi)))))", "srepr_negatives": ["Function('NonElementaryIntegral')(Pow(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))), Symbol('\\\\xi', commutative=True)), Tuple(Symbol('\\\\xi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Symbol('\\\\xi', commutative=True)))), Mul(Symbol('\\\\xi', commutative=True), log(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "Add(Mul(Symbol('\\\\omega', commutative=True), Si(Mul(Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))), Mul(Symbol('\\\\xi', commutative=True), cos(Mul(Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))))", "Mul(log(Symbol('\\\\xi', commutative=True)), cos(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "- \\sin{(\\alpha - \\omega)}", "variable": "\\alpha", "positive": "\\cos{(\\alpha - \\omega)}", "negatives": ["- \\cos{(\\alpha - \\omega)}", "- \\omega \\cos{(\\alpha)}", "\\frac{\\alpha^{2} \\log{(\\omega)}}{2}", "\\frac{\\alpha^{2} e^{\\omega}}{2}"], "srepr_premise_expression": "Mul(Integer(-1), sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))))", "Mul(Integer(-1), Symbol('\\\\omega', commutative=True), cos(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), log(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), exp(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "- \\omega + e^{\\alpha}", "variable": "\\omega", "positive": "\\frac{\\omega (- \\omega + 2 e^{\\alpha})}{2}", "negatives": ["\\frac{\\omega (- \\omega + 2 \\sin{(\\alpha)})}{2}", "- \\alpha \\omega + e^{\\alpha}", "\\frac{\\omega^{2}}{2 \\alpha}", "- \\alpha \\omega + \\sin{(\\omega)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), exp(Symbol('\\\\alpha', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\alpha', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\alpha', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)), exp(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)), sin(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\log{(\\gamma - \\pi)}", "variable": "\\gamma", "positive": "\\gamma \\log{(\\gamma - \\pi)} - \\gamma - \\pi \\log{(\\gamma - \\pi)}", "negatives": ["- \\gamma \\log{(- \\gamma + \\pi)} + \\pi \\log{(\\gamma - \\pi)} - \\pi", "\\log{(\\gamma)} \\log{(\\pi)}", "\\gamma (\\log{(\\gamma \\pi)} - 1)", "\\gamma (\\log{(\\frac{\\pi}{\\gamma})} + 1)"], "srepr_premise_expression": "log(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\gamma', commutative=True), log(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), Symbol('\\\\pi', commutative=True), log(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True)))), Mul(Symbol('\\\\pi', commutative=True), log(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))", "Mul(log(Symbol('\\\\gamma', commutative=True)), log(Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\gamma', commutative=True), Add(log(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\gamma', commutative=True), Add(log(Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))), Integer(1)))"]}, {"premise_expression": "\\chi - \\gamma + \\omega", "variable": "\\gamma", "positive": "\\gamma (\\chi - \\frac{\\gamma}{2} + \\omega)", "negatives": ["\\frac{\\gamma (- 2 \\chi + \\gamma - 2 \\omega)}{2}", "\\frac{\\chi (\\chi - 2 \\gamma + 2 \\omega)}{2}", "\\frac{\\omega (2 \\chi - 2 \\gamma + \\omega)}{2}", "\\frac{\\gamma (- 2 \\chi - \\gamma + 2 \\omega)}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Rational(1, 2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))"]}, {"premise_expression": "\\alpha + \\omega - \\psi", "variable": "\\omega", "positive": "\\omega (\\alpha + \\frac{\\omega}{2} - \\psi)", "negatives": ["\\frac{\\omega (- 2 \\alpha + \\omega + 2 \\psi)}{2}", "\\frac{\\psi (2 \\alpha + 2 \\omega - \\psi)}{2}", "\\frac{\\alpha (\\alpha + 2 \\omega - 2 \\psi)}{2}", "\\frac{\\omega^{2} (- \\alpha + \\psi)}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\cos{(\\frac{\\gamma}{\\pi})}", "variable": "\\pi", "positive": "\\gamma \\operatorname{Si}{(\\frac{\\gamma}{\\pi})} + \\pi \\cos{(\\frac{\\gamma}{\\pi})}", "negatives": ["\\frac{\\pi (\\pi + 2 \\cos{(\\gamma)})}{2}", "\\pi (\\gamma + \\sin{(\\gamma)})", "\\log{(\\pi)} \\sin{(\\gamma)}", "\\frac{\\pi (2 \\gamma - \\pi)}{2}"], "srepr_premise_expression": "cos(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\gamma', commutative=True), Si(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1))))), Mul(Symbol('\\\\pi', commutative=True), cos(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1))))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), cos(Symbol('\\\\gamma', commutative=True)))))", "Mul(Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\gamma', commutative=True), sin(Symbol('\\\\gamma', commutative=True))))", "Mul(log(Symbol('\\\\pi', commutative=True)), sin(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\log{(\\omega \\psi)}", "variable": "\\omega", "positive": "\\omega (\\log{(\\omega \\psi)} - 1)", "negatives": ["\\psi (\\log{(\\omega \\psi)} - 1)", "\\psi \\log{(\\omega)}", "\\cos{(\\omega - \\psi)}", "\\frac{\\omega (\\omega - 2 \\psi)}{2}"], "srepr_premise_expression": "log(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\omega', commutative=True), Add(log(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\psi', commutative=True), Add(log(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\psi', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "cos(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "\\omega \\xi", "variable": "\\omega", "positive": "\\frac{\\omega^{2} \\xi}{2}", "negatives": ["\\frac{\\omega \\xi^{2}}{2}", "\\frac{\\omega (\\omega - 2 \\xi)}{2}", "\\sin{(\\omega + \\xi)}", "\\omega (\\log{(\\omega \\xi)} - 1)"], "srepr_premise_expression": "Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "sin(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), Add(log(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\pi e^{\\gamma}", "variable": "\\pi", "positive": "\\frac{\\pi^{2} e^{\\gamma}}{2}", "negatives": ["\\frac{\\pi^{2} \\log{(\\gamma)}}{2}", "\\pi e^{\\gamma}", "\\frac{\\pi (- \\pi + 2 \\cos{(\\gamma)})}{2}", "- \\gamma \\pi + \\sin{(\\pi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\pi', commutative=True), exp(Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), exp(Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), log(Symbol('\\\\gamma', commutative=True)))", "Mul(Symbol('\\\\pi', commutative=True), exp(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\gamma', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True)), sin(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\psi \\log{(\\sigma)}", "variable": "\\sigma", "positive": "\\psi \\sigma (\\log{(\\sigma)} - 1)", "negatives": ["\\frac{\\psi^{2} \\log{(\\sigma)}}{2}", "\\sin{(\\psi + \\sigma)}", "\\frac{\\sigma^{2}}{2 \\psi}", "\\frac{\\sigma^{2} e^{\\psi}}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\psi', commutative=True), log(Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True), Add(log(Symbol('\\\\sigma', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), log(Symbol('\\\\sigma', commutative=True)))", "sin(Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), exp(Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\xi \\log{(\\beta)}", "variable": "\\beta", "positive": "\\beta \\xi (\\log{(\\beta)} - 1)", "negatives": ["\\beta (\\log{(\\frac{\\beta}{\\xi})} - 1)", "\\frac{\\xi^{2} \\log{(\\beta)}}{2}", "- \\beta \\xi + e^{\\beta}", "- \\frac{\\cos{(\\beta)}}{\\xi}"], "srepr_premise_expression": "Mul(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True), Add(log(Symbol('\\\\beta', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\beta', commutative=True), Add(log(Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), log(Symbol('\\\\beta', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True)), exp(Symbol('\\\\beta', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), cos(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "\\chi - \\delta", "variable": "\\chi", "positive": "\\frac{\\chi (\\chi - 2 \\delta)}{2}", "negatives": ["\\frac{\\delta (2 \\chi - \\delta)}{2}", "\\frac{\\chi (\\chi + 2 \\cos{(\\delta)})}{2}", "\\frac{\\chi^{2} \\cos{(\\delta)}}{2}", "e^{\\chi - \\delta}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), cos(Symbol('\\\\delta', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), cos(Symbol('\\\\delta', commutative=True)))", "exp(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))"]}, {"premise_expression": "\\frac{\\sigma}{\\delta}", "variable": "\\sigma", "positive": "\\frac{\\sigma^{2}}{2 \\delta}", "negatives": ["\\sigma \\log{(\\delta)}", "\\frac{\\sigma^{2} \\cos{(\\delta)}}{2}", "\\frac{\\sigma (2 \\delta + \\sigma)}{2}", "- \\cos{(\\delta + \\sigma)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), cos(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "- \\sin{(\\gamma - \\pi)}", "variable": "\\pi", "positive": "- \\cos{(\\gamma - \\pi)}", "negatives": ["\\cos{(\\gamma - \\pi)}", "e^{\\gamma + \\pi}", "\\pi \\cos{(1)}", "\\gamma e^{\\frac{\\pi}{\\gamma}}"], "srepr_premise_expression": "Mul(Integer(-1), sin(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))", "srepr_negatives": ["cos(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "exp(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\pi', commutative=True), cos(Integer(1)))", "Mul(Symbol('\\\\gamma', commutative=True), exp(Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\chi + e^{\\xi}", "variable": "\\chi", "positive": "\\frac{\\chi (\\chi + 2 e^{\\xi})}{2}", "negatives": ["\\frac{\\chi (- \\chi + 2 e^{\\xi})}{2}", "\\frac{\\chi (- \\chi + 2 \\sin{(\\xi)})}{2}", "\\frac{\\chi^{2} e^{\\xi}}{2}", "\\chi \\xi + e^{\\xi}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), exp(Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), exp(Symbol('\\\\xi', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\xi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\xi', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), exp(Symbol('\\\\xi', commutative=True)))", "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True)), exp(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\log{(\\delta \\sigma)}", "variable": "\\sigma", "positive": "\\sigma (\\log{(\\delta \\sigma)} - 1)", "negatives": ["\\delta (\\log{(\\delta \\sigma)} - 1)", "\\frac{\\sigma^{2} \\log{(\\delta)}}{2}", "\\log{(\\sigma)} \\cos{(\\delta)}", "e^{\\delta + \\sigma}"], "srepr_premise_expression": "log(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\sigma', commutative=True), Add(log(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\delta', commutative=True), Add(log(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), log(Symbol('\\\\delta', commutative=True)))", "Mul(log(Symbol('\\\\sigma', commutative=True)), cos(Symbol('\\\\delta', commutative=True)))", "exp(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\frac{\\omega}{\\xi}", "variable": "\\omega", "positive": "\\frac{\\omega^{2}}{2 \\xi}", "negatives": ["\\omega \\log{(\\xi)}", "\\frac{\\omega^{2} \\sin{(\\xi)}}{2}", "\\frac{\\omega (\\omega + 2 \\xi)}{2}", "- \\cos{(\\omega + \\xi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), sin(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\chi \\sin{(\\delta)}", "variable": "\\chi", "positive": "\\frac{\\chi^{2} \\sin{(\\delta)}}{2}", "negatives": ["- \\chi \\cos{(\\delta)}", "\\delta e^{\\frac{\\chi}{\\delta}}", "\\frac{\\chi (- \\chi + 2 \\cos{(\\delta)})}{2}", "e^{\\chi - \\delta}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), sin(Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), sin(Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Symbol('\\\\chi', commutative=True), cos(Symbol('\\\\delta', commutative=True)))", "Mul(Symbol('\\\\delta', commutative=True), exp(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\delta', commutative=True)))))", "exp(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))"]}, {"premise_expression": "\\chi \\pi \\psi", "variable": "\\psi", "positive": "\\frac{\\chi \\pi \\psi^{2}}{2}", "negatives": ["\\frac{\\chi^{2} \\pi \\psi}{2}", "\\frac{\\chi \\pi^{2} \\psi}{2}", "\\frac{\\psi (2 \\chi \\pi + \\psi)}{2}", "\\frac{\\psi (2 \\chi \\pi - \\psi)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "\\frac{e^{\\alpha}}{\\beta}", "variable": "\\beta", "positive": "e^{\\alpha} \\log{(\\beta)}", "negatives": ["\\alpha \\sin{(\\beta)}", "- \\frac{\\cos{(\\beta)}}{\\alpha}", "\\alpha \\beta (\\log{(\\beta)} - 1)", "- \\sin{(\\alpha - \\beta)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), exp(Symbol('\\\\alpha', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(exp(Symbol('\\\\alpha', commutative=True)), log(Symbol('\\\\beta', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\alpha', commutative=True), sin(Symbol('\\\\beta', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), cos(Symbol('\\\\beta', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True), Add(log(Symbol('\\\\beta', commutative=True)), Integer(-1)))", "Mul(Integer(-1), sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\beta', commutative=True)))))"]}, {"premise_expression": "\\alpha \\delta", "variable": "\\alpha", "positive": "\\frac{\\alpha^{2} \\delta}{2}", "negatives": ["\\frac{\\alpha \\delta^{2}}{2}", "\\frac{\\alpha (\\alpha + 2 \\delta)}{2}", "\\frac{\\alpha (- \\alpha + 2 \\delta)}{2}", "- \\delta \\cos{(\\alpha)}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\delta', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\delta', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\delta', commutative=True))))", "Mul(Integer(-1), Symbol('\\\\delta', commutative=True), cos(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\cos{(\\frac{\\sigma}{\\psi})}", "variable": "\\psi", "positive": "\\psi \\cos{(\\frac{\\sigma}{\\psi})} + \\sigma \\operatorname{Si}{(\\frac{\\sigma}{\\psi})}", "negatives": ["- \\sigma \\cos{(\\psi)}", "- \\cos{(\\psi + \\sigma)}", "\\psi \\log{(- \\psi + \\sigma)} - \\psi - \\sigma \\log{(\\psi - \\sigma)}", "\\frac{\\psi^{2}}{2 \\sigma}"], "srepr_premise_expression": "cos(Mul(Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\psi', commutative=True), cos(Mul(Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True)))), Mul(Symbol('\\\\sigma', commutative=True), Si(Mul(Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True)))))", "srepr_negatives": ["Mul(Integer(-1), Symbol('\\\\sigma', commutative=True), cos(Symbol('\\\\psi', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True))))", "Add(Mul(Symbol('\\\\psi', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Symbol('\\\\sigma', commutative=True)))), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True), log(Add(Symbol('\\\\psi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))"]}, {"premise_expression": "\\log{(\\chi \\xi)}", "variable": "\\chi", "positive": "\\chi (\\log{(\\chi \\xi)} - 1)", "negatives": ["\\xi (\\log{(\\chi \\xi)} - 1)", "\\chi (\\log{(\\frac{\\chi}{\\xi})} - 1)", "- \\cos{(\\chi + \\xi)}", "- e^{- \\chi + \\xi}"], "srepr_premise_expression": "log(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\chi', commutative=True), Add(log(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\xi', commutative=True), Add(log(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\chi', commutative=True), Add(log(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))), Integer(-1)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True))))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "- \\chi + \\delta", "variable": "\\delta", "positive": "\\frac{\\delta (- 2 \\chi + \\delta)}{2}", "negatives": ["\\frac{\\chi (- \\chi + 2 \\delta)}{2}", "\\frac{\\delta (- \\delta + 2 \\cos{(\\chi)})}{2}", "- \\frac{\\cos{(\\delta)}}{\\chi}", "\\delta (\\log{(\\chi \\delta)} - 1)"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\delta', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\chi', commutative=True)))))", "Mul(Integer(-1), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), cos(Symbol('\\\\delta', commutative=True)))", "Mul(Symbol('\\\\delta', commutative=True), Add(log(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\alpha \\xi", "variable": "\\xi", "positive": "\\frac{\\alpha \\xi^{2}}{2}", "negatives": ["\\frac{\\alpha^{2} \\xi}{2}", "\\frac{\\xi^{2}}{2 \\alpha}", "\\alpha \\sin{(\\xi)}", "\\alpha \\log{(\\xi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Mul(Symbol('\\\\alpha', commutative=True), sin(Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\cos{(\\delta - \\xi)}", "variable": "\\xi", "positive": "- \\sin{(\\delta - \\xi)}", "negatives": ["\\sin{(\\delta - \\xi)}", "\\frac{\\xi (2 \\delta + \\xi)}{2}", "\\xi (\\log{(\\frac{\\delta}{\\xi})} + 1)", "\\frac{\\xi^{2} \\sin{(\\delta)}}{2}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Integer(-1), sin(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))))", "srepr_negatives": ["sin(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\xi', commutative=True), Add(log(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), sin(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\gamma \\omega", "variable": "\\omega", "positive": "\\frac{\\gamma \\omega^{2}}{2}", "negatives": ["\\frac{\\gamma^{2} \\omega}{2}", "\\frac{\\omega^{2}}{2 \\gamma}", "\\gamma \\log{(\\omega)}", "- \\gamma \\cos{(\\omega)}"], "srepr_premise_expression": "Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Symbol('\\\\omega', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "Mul(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), cos(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\alpha \\psi", "variable": "\\alpha", "positive": "\\frac{\\alpha^{2} \\psi}{2}", "negatives": ["\\frac{\\alpha \\psi^{2}}{2}", "\\psi e^{\\frac{\\alpha}{\\psi}}", "0", "\\frac{\\alpha (\\alpha + 2 \\psi)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "Mul(Symbol('\\\\psi', commutative=True), exp(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))))", "Integer(0)", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "\\sin^{\\alpha}{(\\omega)}", "variable": "\\omega", "positive": "\\int \\sin^{\\alpha}{(\\omega)} d\\omega", "negatives": ["\\omega (\\log{(\\alpha \\omega)} - 1)", "e^{\\alpha + \\omega}", "\\frac{\\omega (- 2 \\alpha + \\omega)}{2}", "\\frac{\\omega (- \\omega + 2 e^{\\alpha})}{2}"], "srepr_premise_expression": "Pow(sin(Symbol('\\\\omega', commutative=True)), Symbol('\\\\alpha', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Integral(Pow(sin(Symbol('\\\\omega', commutative=True)), Symbol('\\\\alpha', commutative=True)), Tuple(Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\omega', commutative=True), Add(log(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True))), Integer(-1)))", "exp(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\alpha', commutative=True)))))"]}, {"premise_expression": "\\sin^{\\gamma}{(\\chi)}", "variable": "\\chi", "positive": "\\int \\sin^{\\gamma}{(\\chi)} d\\chi", "negatives": ["e^{\\chi - \\gamma}", "\\chi (\\log{(\\frac{\\chi}{\\gamma})} - 1)", "\\gamma \\log{(\\chi)}", "\\frac{\\chi^{2}}{2 \\gamma}"], "srepr_premise_expression": "Pow(sin(Symbol('\\\\chi', commutative=True)), Symbol('\\\\gamma', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Integral(Pow(sin(Symbol('\\\\chi', commutative=True)), Symbol('\\\\gamma', commutative=True)), Tuple(Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["exp(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "Mul(Symbol('\\\\chi', commutative=True), Add(log(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)))), Integer(-1)))", "Mul(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)))"]}, {"premise_expression": "e^{\\alpha + \\chi}", "variable": "\\alpha", "positive": "e^{\\alpha + \\chi}", "negatives": ["\\sin{(\\alpha - \\chi)}", "\\chi e^{\\frac{\\alpha}{\\chi}}", "\\frac{\\alpha^{2} \\chi}{2}", "\\frac{\\alpha^{2} \\log{(\\chi)}}{2}"], "srepr_premise_expression": "exp(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "exp(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True))))", "Mul(Symbol('\\\\chi', commutative=True), exp(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\chi', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), log(Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "\\log{(\\beta \\xi)}", "variable": "\\xi", "positive": "\\xi (\\log{(\\beta \\xi)} - 1)", "negatives": ["\\beta (\\log{(\\beta \\xi)} - 1)", "\\xi (- \\beta + \\log{(\\xi)} - 1)", "\\frac{\\xi (2 \\beta - \\xi)}{2}", "\\log{(\\xi)} \\sin{(\\beta)}"], "srepr_premise_expression": "log(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\xi', commutative=True), Add(log(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\beta', commutative=True), Add(log(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), log(Symbol('\\\\xi', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(log(Symbol('\\\\xi', commutative=True)), sin(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "\\alpha + \\beta", "variable": "\\alpha", "positive": "\\frac{\\alpha (\\alpha + 2 \\beta)}{2}", "negatives": ["\\frac{\\beta (2 \\alpha + \\beta)}{2}", "e^{\\alpha + \\beta}", "- e^{- \\alpha + \\beta}", "\\frac{\\alpha^{2}}{2 \\beta}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\beta', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\beta', commutative=True)))", "exp(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True)))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\beta', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)))"]}, {"premise_expression": "- \\sigma + \\sin{(\\beta)}", "variable": "\\beta", "positive": "- \\beta \\sigma - \\cos{(\\beta)}", "negatives": ["\\beta \\sigma - \\cos{(\\beta)}", "\\frac{\\beta (\\beta + 2 \\sigma)}{2}", "e^{\\beta - \\sigma}", "\\frac{\\beta (- \\beta + 2 \\sigma)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), sin(Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\beta', commutative=True))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\beta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "exp(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\alpha \\gamma", "variable": "\\alpha", "positive": "\\frac{\\alpha^{2} \\gamma}{2}", "negatives": ["\\frac{\\alpha \\gamma^{2}}{2}", "\\frac{\\alpha^{2} e^{\\gamma}}{2}", "\\alpha", "\\alpha \\gamma + e^{\\alpha}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\gamma', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), exp(Symbol('\\\\gamma', commutative=True)))", "Symbol('\\\\alpha', commutative=True)", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True)), exp(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\alpha \\chi", "variable": "\\chi", "positive": "\\frac{\\alpha \\chi^{2}}{2}", "negatives": ["\\frac{\\alpha^{2} \\chi}{2}", "- \\sin{(\\alpha - \\chi)}", "\\log{(\\chi)} \\cos{(\\alpha)}", "\\frac{\\chi (\\chi + 2 e^{\\alpha})}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\chi', commutative=True))", "Mul(Integer(-1), sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True)))))", "Mul(log(Symbol('\\\\chi', commutative=True)), cos(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), exp(Symbol('\\\\alpha', commutative=True)))))"]}, {"premise_expression": "\\frac{\\pi}{\\delta}", "variable": "\\pi", "positive": "\\frac{\\pi^{2}}{2 \\delta}", "negatives": ["\\pi \\log{(\\delta)}", "\\frac{\\pi^{2} \\cos{(\\delta)}}{2}", "\\delta \\pi + e^{\\pi}", "\\pi (\\log{(\\delta \\pi)} - 1)"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), cos(Symbol('\\\\delta', commutative=True)))", "Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True)), exp(Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\pi', commutative=True), Add(log(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\frac{\\sin{(\\chi)}}{\\omega}", "variable": "\\chi", "positive": "- \\frac{\\cos{(\\chi)}}{\\omega}", "negatives": ["- \\omega \\cos{(\\chi)}", "\\sin{(\\chi - \\omega)}", "\\log{(\\chi)} \\log{(\\omega)}", "\\log{(\\omega)} \\sin{(\\chi)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), sin(Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Integer(-1), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), cos(Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Symbol('\\\\omega', commutative=True), cos(Symbol('\\\\chi', commutative=True)))", "sin(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "Mul(log(Symbol('\\\\chi', commutative=True)), log(Symbol('\\\\omega', commutative=True)))", "Mul(log(Symbol('\\\\omega', commutative=True)), sin(Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "\\alpha \\cos{(\\delta)}", "variable": "\\alpha", "positive": "\\frac{\\alpha^{2} \\cos{(\\delta)}}{2}", "negatives": ["\\frac{\\alpha^{2} \\delta}{2}", "\\frac{\\alpha (\\alpha + 2 \\delta)}{2}", "\\frac{\\alpha^{2}}{2 \\delta}", "\\alpha \\sin{(\\delta)}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), cos(Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), cos(Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\delta', commutative=True))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)))", "Mul(Symbol('\\\\alpha', commutative=True), sin(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\beta + \\chi", "variable": "\\chi", "positive": "\\frac{\\chi (2 \\beta + \\chi)}{2}", "negatives": ["\\frac{\\beta (\\beta + 2 \\chi)}{2}", "- e^{\\beta - \\chi}", "\\frac{\\chi^{2}}{2 \\beta}", "- \\beta \\cos{(\\chi)}"], "srepr_premise_expression": "Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\chi', commutative=True))))", "Mul(Integer(-1), exp(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Pow(Symbol('\\\\chi', commutative=True), Integer(2)))", "Mul(Integer(-1), Symbol('\\\\beta', commutative=True), cos(Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "\\xi (- \\alpha + \\chi)", "variable": "\\alpha", "positive": "\\frac{\\alpha \\xi (- \\alpha + 2 \\chi)}{2}", "negatives": ["\\frac{\\xi^{2} (- \\alpha + \\chi)}{2}", "\\frac{\\alpha \\chi (\\alpha + 2 \\xi)}{2}", "\\frac{\\chi \\xi (- 2 \\alpha + \\chi)}{2}", "\\frac{\\alpha \\chi (\\alpha + 2)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\chi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Integer(2)))"]}, {"premise_expression": "- \\pi + \\log{(\\psi)}", "variable": "\\psi", "positive": "\\psi (- \\pi + \\log{(\\psi)} - 1)", "negatives": ["\\psi (\\log{(\\frac{\\psi}{\\pi})} - 1)", "\\frac{\\pi (- \\pi + 2 \\log{(\\psi)})}{2}", "\\pi \\sin{(\\psi)}", "\\pi e^{\\frac{\\psi}{\\pi}}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), log(Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), log(Symbol('\\\\psi', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\psi', commutative=True), Add(log(Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), log(Symbol('\\\\psi', commutative=True)))))", "Mul(Symbol('\\\\pi', commutative=True), sin(Symbol('\\\\psi', commutative=True)))", "Mul(Symbol('\\\\pi', commutative=True), exp(Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "\\cos{(\\pi - \\sigma)}", "variable": "\\pi", "positive": "\\sin{(\\pi - \\sigma)}", "negatives": ["- \\sin{(\\pi - \\sigma)}", "\\sin{(\\pi + \\sigma)}", "\\cos{(\\pi - \\sigma)}", "\\frac{\\sin{(\\pi)}}{\\sigma}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "sin(Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))", "sin(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True)))", "cos(Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), sin(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\log{(\\sigma^{\\alpha})}", "variable": "\\sigma", "positive": "\\sigma (- \\alpha + \\log{(\\sigma^{\\alpha})})", "negatives": ["\\log{(\\alpha)} \\log{(\\sigma)}", "\\frac{\\sigma (\\sigma + 2 \\log{(\\sigma)} - 2)}{2}", "\\frac{\\alpha^{2} \\log{(\\sigma)}}{2}", "\\alpha e^{\\sigma}"], "srepr_premise_expression": "log(Pow(Symbol('\\\\sigma', commutative=True), Symbol('\\\\alpha', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), log(Pow(Symbol('\\\\sigma', commutative=True), Symbol('\\\\alpha', commutative=True)))))", "srepr_negatives": ["Mul(log(Symbol('\\\\alpha', commutative=True)), log(Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(2), log(Symbol('\\\\sigma', commutative=True))), Integer(-2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), log(Symbol('\\\\sigma', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), exp(Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\frac{e^{\\delta}}{\\psi}", "variable": "\\psi", "positive": "e^{\\delta} \\log{(\\psi)}", "negatives": ["\\log{(\\delta)} \\log{(\\psi)}", "- e^{\\delta - \\psi}", "\\log{(\\psi)} \\sin{(\\delta)}", "\\delta \\sin{(\\psi)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), exp(Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(exp(Symbol('\\\\delta', commutative=True)), log(Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(log(Symbol('\\\\delta', commutative=True)), log(Symbol('\\\\psi', commutative=True)))", "Mul(Integer(-1), exp(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))", "Mul(log(Symbol('\\\\psi', commutative=True)), sin(Symbol('\\\\delta', commutative=True)))", "Mul(Symbol('\\\\delta', commutative=True), sin(Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\alpha \\psi", "variable": "\\alpha", "positive": "\\frac{\\alpha^{2} \\psi}{2}", "negatives": ["\\frac{\\alpha \\psi^{2}}{2}", "\\frac{\\alpha^{2}}{2 \\psi}", "0", "\\alpha \\psi + \\sin{(\\alpha)}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))", "Integer(0)", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True)), sin(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\delta \\omega", "variable": "\\omega", "positive": "\\frac{\\delta \\omega^{2}}{2}", "negatives": ["\\frac{\\delta^{2} \\omega}{2}", "\\frac{\\omega (- 2 \\delta + \\omega)}{2}", "\\omega (\\log{(\\delta \\omega)} - 1)", "\\omega (\\log{(\\frac{\\delta}{\\omega})} + 1)"], "srepr_premise_expression": "Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Symbol('\\\\omega', commutative=True))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), Add(log(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\omega', commutative=True), Add(log(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))), Integer(1)))"]}, {"premise_expression": "\\gamma + \\pi", "variable": "\\gamma", "positive": "\\frac{\\gamma (\\gamma + 2 \\pi)}{2}", "negatives": ["\\frac{\\gamma (\\gamma - 2 \\pi)}{2}", "\\frac{\\pi (2 \\gamma + \\pi)}{2}", "\\cos{(\\gamma - \\pi)}", "\\frac{\\gamma^{2}}{2 \\pi}"], "srepr_premise_expression": "Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True)))", "cos(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))"]}, {"premise_expression": "- \\gamma + \\log{(\\pi)}", "variable": "\\gamma", "positive": "\\frac{\\gamma (- \\gamma + 2 \\log{(\\pi)})}{2}", "negatives": ["\\frac{\\gamma (- \\gamma + 2 \\cos{(\\pi)})}{2}", "\\frac{\\gamma (- \\gamma + 2 \\sin{(\\pi)})}{2}", "\\pi (- \\gamma + \\log{(\\pi)} - 1)", "\\frac{\\gamma^{2} \\cos{(\\pi)}}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), log(Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), log(Symbol('\\\\pi', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\pi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\pi', commutative=True)))))", "Mul(Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), log(Symbol('\\\\pi', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), cos(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\sigma \\log{(\\chi)}", "variable": "\\chi", "positive": "\\chi \\sigma (\\log{(\\chi)} - 1)", "negatives": ["\\chi (- \\sigma + \\log{(\\chi)} - 1)", "\\frac{\\sigma^{2} \\log{(\\chi)}}{2}", "e^{\\sigma} \\log{(\\chi)}", "\\sin{(\\chi - \\sigma)}"], "srepr_premise_expression": "Mul(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\sigma', commutative=True), Add(log(Symbol('\\\\chi', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), log(Symbol('\\\\chi', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), log(Symbol('\\\\chi', commutative=True)))", "Mul(exp(Symbol('\\\\sigma', commutative=True)), log(Symbol('\\\\chi', commutative=True)))", "sin(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\frac{\\beta}{\\pi}", "variable": "\\pi", "positive": "\\beta \\log{(\\pi)}", "negatives": ["\\frac{\\beta^{2}}{2 \\pi}", "\\frac{\\log{(\\pi)}^{2}}{2}", "- \\cos{(\\beta + \\pi)}", "e^{\\beta + \\pi}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\beta', commutative=True), log(Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Pow(log(Symbol('\\\\pi', commutative=True)), Integer(2)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\pi', commutative=True))))", "exp(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\frac{\\alpha}{\\omega \\psi}", "variable": "\\alpha", "positive": "\\frac{\\alpha^{2}}{2 \\omega \\psi}", "negatives": ["\\alpha (- 2 \\omega + \\psi)", "\\frac{\\alpha \\log{(\\omega)}}{\\psi}", "\\frac{\\alpha \\log{(\\psi)}}{\\omega}", "\\omega^{\\psi} \\log{(\\alpha)}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), log(Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), log(Symbol('\\\\psi', commutative=True)))", "Mul(Pow(Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True)), log(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "(\\delta^{\\chi})^{\\delta}", "variable": "\\delta", "positive": "\\operatorname{NonElementaryIntegral}{((\\delta^{\\chi})^{\\delta},( \\delta))}", "negatives": ["\\int \\cos^{\\chi}{(\\delta)} d\\delta", "\\sin{(\\chi + \\delta)}", "\\delta (\\log{(\\chi \\delta)} - 1)", "\\chi \\sin{(\\delta)}"], "srepr_premise_expression": "Pow(Pow(Symbol('\\\\delta', commutative=True), Symbol('\\\\chi', commutative=True)), Symbol('\\\\delta', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Function('NonElementaryIntegral')(Pow(Pow(Symbol('\\\\delta', commutative=True), Symbol('\\\\chi', commutative=True)), Symbol('\\\\delta', commutative=True)), Tuple(Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Integral(Pow(cos(Symbol('\\\\delta', commutative=True)), Symbol('\\\\chi', commutative=True)), Tuple(Symbol('\\\\delta', commutative=True)))", "sin(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True)))", "Mul(Symbol('\\\\delta', commutative=True), Add(log(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\chi', commutative=True), sin(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\chi - \\sigma", "variable": "\\chi", "positive": "\\frac{\\chi (\\chi - 2 \\sigma)}{2}", "negatives": ["\\frac{\\sigma (2 \\chi - \\sigma)}{2}", "e^{\\chi + \\sigma}", "\\sin{(\\chi - \\sigma)}", "- e^{- \\chi + \\sigma}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "exp(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\sigma', commutative=True)))", "sin(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\alpha \\omega^{\\psi}", "variable": "\\alpha", "positive": "\\frac{\\alpha^{2} \\omega^{\\psi}}{2}", "negatives": ["\\frac{\\alpha^{2}}{2 \\psi} - \\alpha \\omega", "\\frac{\\alpha^{2}}{2 \\omega \\psi}", "\\frac{\\alpha^{2} (\\omega + \\psi)}{2}", "\\frac{\\alpha \\omega (\\alpha - 2 \\psi)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Add(Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\psi', commutative=True), Integer(-1))), Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "- \\beta + \\omega", "variable": "\\beta", "positive": "\\frac{\\beta (- \\beta + 2 \\omega)}{2}", "negatives": ["\\frac{\\beta (\\beta + 2 \\omega)}{2}", "\\frac{\\omega (- 2 \\beta + \\omega)}{2}", "\\beta \\omega + \\sin{(\\beta)}", "\\cos{(\\beta - \\omega)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True)), sin(Symbol('\\\\beta', commutative=True)))", "cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))"]}, {"premise_expression": "\\chi \\xi", "variable": "\\chi", "positive": "\\frac{\\chi^{2} \\xi}{2}", "negatives": ["\\frac{\\chi \\xi^{2}}{2}", "\\frac{\\chi^{2} \\sin{(\\xi)}}{2}", "\\xi \\log{(\\chi)}", "\\xi e^{\\frac{\\chi}{\\xi}}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), sin(Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\chi', commutative=True)))", "Mul(Symbol('\\\\xi', commutative=True), exp(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))))"]}, {"premise_expression": "\\sigma + \\log{(\\xi)}", "variable": "\\xi", "positive": "\\xi (\\sigma + \\log{(\\xi)} - 1)", "negatives": ["\\xi (\\log{(\\frac{\\xi}{\\sigma})} - 1)", "\\frac{\\xi (\\log{(\\xi)} - 1)}{\\sigma}", "\\frac{\\sigma (\\sigma + 2 \\log{(\\xi)})}{2}", "\\sigma \\log{(\\xi)}"], "srepr_premise_expression": "Add(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\xi', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\xi', commutative=True), Add(log(Mul(Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))), Integer(-1)))", "Mul(Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True), Add(log(Symbol('\\\\xi', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(2), log(Symbol('\\\\xi', commutative=True)))))", "Mul(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\omega + \\sigma", "variable": "\\sigma", "positive": "\\frac{\\sigma (2 \\omega + \\sigma)}{2}", "negatives": ["\\frac{\\omega (\\omega + 2 \\sigma)}{2}", "\\frac{\\sigma^{2} \\log{(\\omega)}}{2}", "\\frac{\\sigma^{2} \\cos{(\\omega)}}{2}", "\\sin{(\\omega + \\sigma)}"], "srepr_premise_expression": "Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), log(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), cos(Symbol('\\\\omega', commutative=True)))", "sin(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\cos{(\\beta - \\delta)}", "variable": "\\beta", "positive": "\\sin{(\\beta - \\delta)}", "negatives": ["- \\sin{(\\beta - \\delta)}", "- \\cos{(\\beta - \\delta)}", "\\frac{\\beta (\\beta - 2 \\delta)}{2}", "- \\frac{\\delta}{\\beta}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "sin(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True))))", "Mul(Integer(-1), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True))"]}, {"premise_expression": "- \\alpha + e^{\\gamma}", "variable": "\\alpha", "positive": "\\frac{\\alpha (- \\alpha + 2 e^{\\gamma})}{2}", "negatives": ["\\frac{\\alpha (- \\alpha + 2 \\log{(\\gamma)})}{2}", "\\frac{\\alpha (- \\alpha + 2 \\sin{(\\gamma)})}{2}", "- \\alpha \\gamma + e^{\\gamma}", "\\frac{\\alpha^{2}}{2 \\gamma}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), exp(Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\gamma', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), log(Symbol('\\\\gamma', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\gamma', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True)), exp(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)))"]}, {"premise_expression": "\\alpha + \\frac{\\xi}{\\chi}", "variable": "\\alpha", "positive": "\\frac{\\alpha^{2}}{2} + \\frac{\\alpha \\xi}{\\chi}", "negatives": ["\\frac{\\alpha (\\alpha \\xi + 2 \\chi)}{2}", "\\frac{\\alpha^{2} (- \\chi + \\xi)}{2}", "\\alpha \\chi + \\xi \\log{(\\chi)}", "\\frac{\\alpha (\\alpha \\chi - 2 \\xi)}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Add(Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2))), Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), Symbol('\\\\chi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)), Mul(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\chi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\log{(\\beta \\psi)}", "variable": "\\beta", "positive": "\\beta (\\log{(\\beta \\psi)} - 1)", "negatives": ["\\psi (\\log{(\\beta \\psi)} - 1)", "\\beta \\psi (\\log{(\\beta)} - 1)", "- \\cos{(\\beta - \\psi)}", "\\frac{\\beta^{2} \\log{(\\psi)}}{2}"], "srepr_premise_expression": "log(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\beta', commutative=True), Add(log(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\psi', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\psi', commutative=True), Add(log(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\psi', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\psi', commutative=True), Add(log(Symbol('\\\\beta', commutative=True)), Integer(-1)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), log(Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\delta + \\pi - \\sigma", "variable": "\\sigma", "positive": "\\sigma (\\delta + \\pi - \\frac{\\sigma}{2})", "negatives": ["\\frac{\\pi (2 \\delta + \\pi - 2 \\sigma)}{2}", "\\frac{\\delta (\\delta + 2 \\pi - 2 \\sigma)}{2}", "\\frac{\\sigma^{2} (\\delta + \\pi)}{2}", "\\frac{\\delta \\sigma (2 \\pi - \\sigma)}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Rational(1, 2), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\log{(\\omega \\pi)}", "variable": "\\pi", "positive": "\\pi (\\log{(\\omega \\pi)} - 1)", "negatives": ["\\omega (\\log{(\\omega \\pi)} - 1)", "\\frac{\\pi (2 \\omega - \\pi)}{2}", "- \\sin{(\\omega - \\pi)}", "\\frac{\\pi (2 \\omega + \\pi)}{2}"], "srepr_premise_expression": "log(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\pi', commutative=True), Add(log(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\omega', commutative=True), Add(log(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "Mul(Integer(-1), sin(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\pi \\cos{(\\psi)}", "variable": "\\psi", "positive": "\\pi \\sin{(\\psi)}", "negatives": ["- \\frac{\\cos{(\\psi)}}{\\pi}", "\\frac{\\pi^{2} \\cos{(\\psi)}}{2}", "- \\pi \\psi + e^{\\psi}", "\\log{(\\psi)} \\cos{(\\pi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\pi', commutative=True), cos(Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\pi', commutative=True), sin(Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), cos(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), cos(Symbol('\\\\psi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)), exp(Symbol('\\\\psi', commutative=True)))", "Mul(log(Symbol('\\\\psi', commutative=True)), cos(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "e^{\\pi + \\psi}", "variable": "\\psi", "positive": "e^{\\pi + \\psi}", "negatives": ["- \\sin{(\\pi - \\psi)}", "- \\cos{(\\pi + \\psi)}", "- \\cos{(\\pi - \\psi)}", "\\pi e^{\\frac{\\psi}{\\pi}}"], "srepr_premise_expression": "exp(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "exp(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))", "Mul(Symbol('\\\\pi', commutative=True), exp(Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "\\frac{\\pi}{\\delta}", "variable": "\\delta", "positive": "\\pi \\log{(\\delta)}", "negatives": ["\\frac{\\pi^{2}}{2 \\delta}", "\\frac{\\delta^{2} \\pi}{2}", "\\frac{\\delta^{2} \\log{(\\pi)}}{2}", "- \\delta \\pi + e^{\\delta}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Symbol('\\\\pi', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), log(Symbol('\\\\pi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True)), exp(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\alpha - \\gamma", "variable": "\\gamma", "positive": "\\frac{\\gamma (2 \\alpha - \\gamma)}{2}", "negatives": ["\\frac{\\gamma (2 \\alpha + \\gamma)}{2}", "\\frac{\\alpha (\\alpha - 2 \\gamma)}{2}", "\\frac{\\gamma (\\gamma + 2 \\cos{(\\alpha)})}{2}", "\\gamma (\\log{(\\alpha \\gamma)} - 1)"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), cos(Symbol('\\\\alpha', commutative=True)))))", "Mul(Symbol('\\\\gamma', commutative=True), Add(log(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\frac{\\alpha}{\\xi}", "variable": "\\alpha", "positive": "\\frac{\\alpha^{2}}{2 \\xi}", "negatives": ["\\alpha \\log{(\\xi)}", "\\frac{\\alpha^{2} \\sin{(\\xi)}}{2}", "e^{\\alpha + \\xi}", "\\sin{(\\alpha + \\xi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), sin(Symbol('\\\\xi', commutative=True)))", "exp(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True)))", "sin(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\frac{\\chi}{\\sigma}", "variable": "\\sigma", "positive": "\\chi \\log{(\\sigma)}", "negatives": ["\\frac{\\chi^{2}}{2 \\sigma}", "\\log{(\\chi)} \\log{(\\sigma)}", "- \\frac{\\chi}{\\sigma}", "- \\cos{(\\chi - \\sigma)}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "Mul(log(Symbol('\\\\chi', commutative=True)), log(Symbol('\\\\sigma', commutative=True)))", "Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))))"]}, {"premise_expression": "e^{\\gamma + \\xi}", "variable": "\\xi", "positive": "e^{\\gamma + \\xi}", "negatives": ["- \\cos{(\\gamma + \\xi)}", "\\gamma \\sin{(\\xi)}", "\\xi (\\gamma + \\sin{(\\gamma)})", "\\frac{\\xi^{2}}{2 \\gamma}"], "srepr_premise_expression": "exp(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "exp(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True))))", "Mul(Symbol('\\\\gamma', commutative=True), sin(Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\gamma', commutative=True), sin(Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))"]}, {"premise_expression": "\\delta - \\psi", "variable": "\\psi", "positive": "\\frac{\\psi (2 \\delta - \\psi)}{2}", "negatives": ["\\frac{\\psi (- 2 \\delta + \\psi)}{2}", "\\frac{\\delta (\\delta - 2 \\psi)}{2}", "\\psi (\\delta + \\psi)", "\\frac{\\delta \\psi^{2}}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))"]}, {"premise_expression": "\\log{(\\alpha^{\\omega})}", "variable": "\\omega", "positive": "\\frac{\\omega^{2} \\log{(\\alpha)}}{2}", "negatives": ["\\frac{\\omega^{2} \\sin{(\\alpha)}}{2}", "\\log{(\\omega)} \\cos{(\\alpha)}", "\\omega (\\log{(\\alpha \\omega)} - 1)", "\\alpha (- \\omega + \\log{(\\alpha^{\\omega})})"], "srepr_premise_expression": "log(Pow(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), log(Symbol('\\\\alpha', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), sin(Symbol('\\\\alpha', commutative=True)))", "Mul(log(Symbol('\\\\omega', commutative=True)), cos(Symbol('\\\\alpha', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), Add(log(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), log(Pow(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)))))"]}, {"premise_expression": "\\xi + e^{\\delta}", "variable": "\\xi", "positive": "\\frac{\\xi (\\xi + 2 e^{\\delta})}{2}", "negatives": ["\\frac{\\xi (\\xi + 2 \\log{(\\delta)})}{2}", "\\frac{\\xi (\\xi + 2 \\sin{(\\delta)})}{2}", "\\frac{\\xi (- \\xi + 2 \\cos{(\\delta)})}{2}", "\\delta \\xi + e^{\\delta}"], "srepr_premise_expression": "Add(Symbol('\\\\xi', commutative=True), exp(Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\xi', commutative=True), Mul(Integer(2), exp(Symbol('\\\\delta', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\xi', commutative=True), Mul(Integer(2), log(Symbol('\\\\delta', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\xi', commutative=True), Mul(Integer(2), sin(Symbol('\\\\delta', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\delta', commutative=True)))))", "Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True)), exp(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\alpha + \\log{(\\beta)}", "variable": "\\alpha", "positive": "\\frac{\\alpha (\\alpha + 2 \\log{(\\beta)})}{2}", "negatives": ["\\frac{\\alpha (\\alpha + 2 \\cos{(\\beta)})}{2}", "\\beta (\\alpha + \\log{(\\beta)} - 1)", "\\frac{\\alpha (\\alpha + 2 \\beta)}{2}", "- \\alpha \\beta - \\cos{(\\alpha)}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), log(Symbol('\\\\beta', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), cos(Symbol('\\\\beta', commutative=True)))))", "Mul(Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\alpha', commutative=True), log(Symbol('\\\\beta', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\beta', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\alpha', commutative=True))))"]}, {"premise_expression": "- \\beta + \\pi \\sigma", "variable": "\\beta", "positive": "\\frac{\\beta (- \\beta + 2 \\pi \\sigma)}{2}", "negatives": ["\\frac{\\beta \\sigma (- \\beta + 2 \\pi)}{2}", "\\frac{\\pi (- 2 \\beta + \\pi \\sigma)}{2}", "\\frac{\\sigma (- 2 \\beta + \\pi \\sigma)}{2}", "\\frac{\\beta^{2} \\pi \\sigma}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True))"]}, {"premise_expression": "\\log{(\\frac{\\pi}{\\omega})}", "variable": "\\pi", "positive": "\\pi (\\log{(\\frac{\\pi}{\\omega})} - 1)", "negatives": ["\\pi (\\log{(\\omega \\pi)} - 1)", "\\omega (\\log{(\\frac{\\pi}{\\omega})} + 1)", "\\frac{\\pi (- 2 \\omega + \\pi)}{2}", "\\pi (- \\omega + \\log{(\\pi^{\\omega})})"], "srepr_premise_expression": "log(Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\pi', commutative=True), Add(log(Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\pi', commutative=True), Add(log(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\omega', commutative=True), Add(log(Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))), Integer(1)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), log(Pow(Symbol('\\\\pi', commutative=True), Symbol('\\\\omega', commutative=True)))))"]}, {"premise_expression": "\\sigma (\\omega + \\pi)", "variable": "\\omega", "positive": "\\frac{\\omega \\sigma (\\omega + 2 \\pi)}{2}", "negatives": ["\\frac{\\sigma^{2} (\\omega + \\pi)}{2}", "\\frac{\\omega (\\omega + 2 \\pi \\sigma)}{2}", "\\frac{\\pi \\sigma (2 \\omega + \\pi)}{2}", "\\frac{\\omega (- \\omega + 2 \\pi \\sigma)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\omega \\sin{(\\gamma)}", "variable": "\\omega", "positive": "\\frac{\\omega^{2} \\sin{(\\gamma)}}{2}", "negatives": ["\\frac{\\omega (- 2 \\gamma + \\omega)}{2}", "- \\omega \\cos{(\\gamma)}", "\\gamma \\log{(\\omega)}", "\\gamma e^{\\frac{\\omega}{\\gamma}}"], "srepr_premise_expression": "Mul(Symbol('\\\\omega', commutative=True), sin(Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), sin(Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Mul(Integer(-1), Symbol('\\\\omega', commutative=True), cos(Symbol('\\\\gamma', commutative=True)))", "Mul(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\gamma', commutative=True), exp(Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True))))"]}, {"premise_expression": "\\log{(\\omega \\xi)}", "variable": "\\omega", "positive": "\\omega (\\log{(\\omega \\xi)} - 1)", "negatives": ["\\xi (\\log{(\\omega \\xi)} - 1)", "\\omega (\\log{(\\frac{\\xi}{\\omega})} + 1)", "\\omega (\\xi + \\log{(\\omega)} - 1)", "\\frac{\\omega^{2}}{2 \\xi}"], "srepr_premise_expression": "log(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\omega', commutative=True), Add(log(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\xi', commutative=True), Add(log(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\omega', commutative=True), Add(log(Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))), Integer(1)))", "Mul(Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\omega', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))"]}, {"premise_expression": "\\frac{\\delta}{\\gamma}", "variable": "\\delta", "positive": "\\frac{\\delta^{2}}{2 \\gamma}", "negatives": ["\\delta \\log{(\\gamma)}", "\\gamma e^{\\frac{\\delta}{\\gamma}}", "\\frac{\\delta^{2} \\log{(\\gamma)}}{2}", "\\sin{(\\delta - \\gamma)}"], "srepr_premise_expression": "Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "Mul(Symbol('\\\\gamma', commutative=True), exp(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), log(Symbol('\\\\gamma', commutative=True)))", "sin(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))"]}, {"premise_expression": "\\alpha + \\pi", "variable": "\\pi", "positive": "\\frac{\\pi (2 \\alpha + \\pi)}{2}", "negatives": ["\\frac{\\alpha (\\alpha + 2 \\pi)}{2}", "\\frac{\\pi^{2} e^{\\alpha}}{2}", "\\frac{\\pi^{2} \\sin{(\\alpha)}}{2}", "e^{- \\alpha + \\pi}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), exp(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), sin(Symbol('\\\\alpha', commutative=True)))", "exp(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\cos{(\\frac{\\pi}{\\chi})}", "variable": "\\chi", "positive": "\\chi \\cos{(\\frac{\\pi}{\\chi})} + \\pi \\operatorname{Si}{(\\frac{\\pi}{\\chi})}", "negatives": ["\\chi \\pi + e^{\\chi}", "\\chi \\pi + \\sin{(\\chi)}", "\\frac{\\chi (- \\chi + 2 e^{\\pi})}{2}", "\\log{(\\chi)} \\log{(\\pi)}"], "srepr_premise_expression": "cos(Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\chi', commutative=True), cos(Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True)))), Mul(Symbol('\\\\pi', commutative=True), Si(Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True)), exp(Symbol('\\\\chi', commutative=True)))", "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True)), sin(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\pi', commutative=True)))))", "Mul(log(Symbol('\\\\chi', commutative=True)), log(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\beta + \\delta", "variable": "\\delta", "positive": "\\frac{\\delta (2 \\beta + \\delta)}{2}", "negatives": ["\\frac{\\delta (2 \\beta - \\delta)}{2}", "\\frac{\\beta (\\beta + 2 \\delta)}{2}", "\\frac{\\delta (\\delta + 2 \\cos{(\\beta)})}{2}", "\\frac{\\delta^{2} \\sin{(\\beta)}}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), cos(Symbol('\\\\beta', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), sin(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "\\pi e^{\\psi}", "variable": "\\psi", "positive": "\\pi e^{\\psi}", "negatives": ["\\pi \\psi + e^{\\psi}", "\\frac{\\pi^{2} e^{\\psi}}{2}", "\\frac{\\pi \\psi^{2}}{2}", "- \\sin{(\\pi - \\psi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\pi', commutative=True), exp(Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\pi', commutative=True), exp(Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)), exp(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), exp(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "Mul(Integer(-1), sin(Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))"]}, {"premise_expression": "\\chi \\sin{(\\delta)}", "variable": "\\delta", "positive": "- \\chi \\cos{(\\delta)}", "negatives": ["\\chi \\delta - \\cos{(\\delta)}", "\\frac{\\chi^{2} \\sin{(\\delta)}}{2}", "\\log{(\\chi)} \\log{(\\delta)}", "\\chi \\delta (\\log{(\\delta)} - 1)"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), sin(Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Integer(-1), Symbol('\\\\chi', commutative=True), cos(Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), sin(Symbol('\\\\delta', commutative=True)))", "Mul(log(Symbol('\\\\chi', commutative=True)), log(Symbol('\\\\delta', commutative=True)))", "Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True), Add(log(Symbol('\\\\delta', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\alpha \\sigma", "variable": "\\sigma", "positive": "\\frac{\\alpha \\sigma^{2}}{2}", "negatives": ["\\frac{\\alpha^{2} \\sigma}{2}", "\\frac{\\sigma^{2}}{2 \\alpha}", "\\sigma \\sin{(1)}", "- \\alpha \\sigma + e^{\\sigma}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\sigma', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "Mul(Symbol('\\\\sigma', commutative=True), sin(Integer(1)))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True)), exp(Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "- \\omega + \\xi", "variable": "\\xi", "positive": "\\frac{\\xi (- 2 \\omega + \\xi)}{2}", "negatives": ["\\frac{\\xi (2 \\omega + \\xi)}{2}", "\\frac{\\omega (- \\omega + 2 \\xi)}{2}", "\\frac{\\xi (- \\xi + 2 e^{\\omega})}{2}", "- \\frac{\\cos{(\\xi)}}{\\omega}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\omega', commutative=True)))))", "Mul(Integer(-1), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), cos(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\log{(\\chi + \\psi)}", "variable": "\\chi", "positive": "\\chi \\log{(\\chi + \\psi)} - \\chi + \\psi \\log{(\\chi + \\psi)}", "negatives": ["\\chi \\log{(\\chi + \\psi)} + \\psi \\log{(\\chi + \\psi)} - \\psi", "\\frac{\\chi (\\chi + 2 \\log{(\\psi)})}{2}", "\\chi (\\log{(\\chi \\psi)} - 1)", "e^{\\psi} \\log{(\\chi)}"], "srepr_premise_expression": "log(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\chi', commutative=True), log(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Symbol('\\\\psi', commutative=True), log(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\chi', commutative=True), log(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True)))), Mul(Symbol('\\\\psi', commutative=True), log(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), log(Symbol('\\\\psi', commutative=True)))))", "Mul(Symbol('\\\\chi', commutative=True), Add(log(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True))), Integer(-1)))", "Mul(exp(Symbol('\\\\psi', commutative=True)), log(Symbol('\\\\chi', commutative=True)))"]}, {"premise_expression": "\\frac{\\sigma}{\\gamma}", "variable": "\\sigma", "positive": "\\frac{\\sigma^{2}}{2 \\gamma}", "negatives": ["\\sigma + \\frac{\\sigma^{2}}{2 \\gamma}", "\\sigma \\log{(\\gamma)}", "\\gamma e^{\\frac{\\sigma}{\\gamma}}", "\\frac{\\sigma (- 2 \\gamma + \\sigma)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "srepr_negatives": ["Add(Symbol('\\\\sigma', commutative=True), Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Integer(2))))", "Mul(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "Mul(Symbol('\\\\gamma', commutative=True), exp(Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\delta + \\gamma", "variable": "\\gamma", "positive": "\\frac{\\gamma (2 \\delta + \\gamma)}{2}", "negatives": ["\\frac{\\gamma (2 \\delta - \\gamma)}{2}", "\\frac{\\delta (\\delta + 2 \\gamma)}{2}", "\\sin{(\\delta + \\gamma)}", "- \\cos{(\\delta - \\gamma)}"], "srepr_premise_expression": "Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\gamma', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), Symbol('\\\\gamma', commutative=True))))", "sin(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\gamma', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))))"]}, {"premise_expression": "\\cos{(\\beta + \\gamma)}", "variable": "\\gamma", "positive": "\\sin{(\\beta + \\gamma)}", "negatives": ["- \\cos{(\\beta + \\gamma)}", "- e^{\\beta - \\gamma}", "\\gamma \\sin{(1)}", "\\frac{\\gamma^{2}}{2 \\beta}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "sin(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True))))", "Mul(Integer(-1), exp(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))))", "Mul(Symbol('\\\\gamma', commutative=True), sin(Integer(1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)))"]}, {"premise_expression": "\\omega - \\pi", "variable": "\\pi", "positive": "\\frac{\\pi (2 \\omega - \\pi)}{2}", "negatives": ["\\frac{\\pi (- 2 \\omega + \\pi)}{2}", "\\frac{\\omega (\\omega - 2 \\pi)}{2}", "\\frac{\\pi^{2}}{2 \\omega}", "\\sin{(\\omega + \\pi)}"], "srepr_premise_expression": "Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "sin(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\alpha + \\pi", "variable": "\\pi", "positive": "\\frac{\\pi (2 \\alpha + \\pi)}{2}", "negatives": ["\\frac{\\alpha (\\alpha + 2 \\pi)}{2}", "\\frac{\\pi (\\pi + 2 e^{\\alpha})}{2}", "\\frac{\\pi^{2} \\sin{(\\alpha)}}{2}", "\\cos{(\\alpha - \\pi)}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), exp(Symbol('\\\\alpha', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), sin(Symbol('\\\\alpha', commutative=True)))", "cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\psi + \\cos{(\\alpha)}", "variable": "\\alpha", "positive": "\\alpha \\psi + \\sin{(\\alpha)}", "negatives": ["\\frac{\\alpha^{2} \\psi}{2}", "\\frac{\\psi (\\psi + 2 \\cos{(\\alpha)})}{2}", "- \\cos{(\\alpha - \\psi)}", "\\frac{\\alpha^{2}}{2 \\psi}"], "srepr_premise_expression": "Add(Symbol('\\\\psi', commutative=True), cos(Symbol('\\\\alpha', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True)), sin(Symbol('\\\\alpha', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\psi', commutative=True))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(2), cos(Symbol('\\\\alpha', commutative=True)))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))"]}, {"premise_expression": "\\beta^{\\pi} + \\omega", "variable": "\\omega", "positive": "\\frac{\\omega (2 \\beta^{\\pi} + \\omega)}{2}", "negatives": ["\\frac{\\omega^{2}}{2} + \\frac{\\omega \\pi}{\\beta}", "\\frac{\\omega (- 2 \\beta + \\omega + 2 \\pi)}{2}", "\\frac{\\omega (2 \\beta + \\omega + 2 \\pi)}{2}", "\\frac{\\beta \\omega^{2}}{2 \\pi}"], "srepr_premise_expression": "Add(Pow(Symbol('\\\\beta', commutative=True), Symbol('\\\\pi', commutative=True)), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Pow(Symbol('\\\\beta', commutative=True), Symbol('\\\\pi', commutative=True))), Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Add(Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2))), Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))"]}, {"premise_expression": "\\alpha + \\delta", "variable": "\\alpha", "positive": "\\frac{\\alpha (\\alpha + 2 \\delta)}{2}", "negatives": ["\\frac{\\delta (2 \\alpha + \\delta)}{2}", "\\frac{\\alpha^{2} \\sin{(\\delta)}}{2}", "\\sin{(\\alpha + \\delta)}", "e^{\\alpha + \\delta}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\delta', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\delta', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), sin(Symbol('\\\\delta', commutative=True)))", "sin(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\delta', commutative=True)))", "exp(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\log{(\\omega \\sigma)}", "variable": "\\sigma", "positive": "\\sigma (\\log{(\\omega \\sigma)} - 1)", "negatives": ["\\omega (\\log{(\\omega \\sigma)} - 1)", "\\frac{\\sigma (2 \\omega + \\sigma)}{2}", "\\log{(\\sigma)} \\sin{(\\omega)}", "e^{\\omega + \\sigma}"], "srepr_premise_expression": "log(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\sigma', commutative=True), Add(log(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\omega', commutative=True), Add(log(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(log(Symbol('\\\\sigma', commutative=True)), sin(Symbol('\\\\omega', commutative=True)))", "exp(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\delta \\omega", "variable": "\\omega", "positive": "\\frac{\\delta \\omega^{2}}{2}", "negatives": ["\\frac{\\delta^{2} \\omega}{2}", "\\frac{\\omega^{2}}{2 \\delta}", "\\frac{\\omega (2 \\delta - \\omega)}{2}", "\\frac{\\omega^{2} \\log{(\\delta)}}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Symbol('\\\\omega', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), log(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "- \\sigma + \\sin{(\\omega)}", "variable": "\\sigma", "positive": "\\frac{\\sigma (- \\sigma + 2 \\sin{(\\omega)})}{2}", "negatives": ["\\frac{\\sigma (\\sigma + 2 \\sin{(\\omega)})}{2}", "\\frac{\\sigma (2 \\omega + \\sigma)}{2}", "\\frac{\\sigma^{2} \\sin{(\\omega)}}{2}", "- \\omega \\sigma - \\cos{(\\omega)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), sin(Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\omega', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(2), sin(Symbol('\\\\omega', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), sin(Symbol('\\\\omega', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\omega', commutative=True))))"]}, {"premise_expression": "\\xi e^{\\beta}", "variable": "\\xi", "positive": "\\frac{\\xi^{2} e^{\\beta}}{2}", "negatives": ["\\xi e^{\\beta}", "\\beta \\xi + e^{\\xi}", "\\frac{\\xi (\\xi + 2 \\cos{(\\beta)})}{2}", "e^{- \\beta + \\xi}"], "srepr_premise_expression": "Mul(Symbol('\\\\xi', commutative=True), exp(Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), exp(Symbol('\\\\beta', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\xi', commutative=True), exp(Symbol('\\\\beta', commutative=True)))", "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\xi', commutative=True)), exp(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\xi', commutative=True), Mul(Integer(2), cos(Symbol('\\\\beta', commutative=True)))))", "exp(Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\frac{\\log{(\\sigma)}}{\\alpha}", "variable": "\\alpha", "positive": "\\log{(\\alpha)} \\log{(\\sigma)}", "negatives": ["\\sigma \\log{(\\alpha)}", "- \\alpha \\sigma - \\cos{(\\alpha)}", "\\frac{\\sigma (\\log{(\\sigma)} - 1)}{\\alpha}", "\\alpha \\sigma + \\sin{(\\alpha)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), log(Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(log(Symbol('\\\\alpha', commutative=True)), log(Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\alpha', commutative=True))))", "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True), Add(log(Symbol('\\\\sigma', commutative=True)), Integer(-1)))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True)), sin(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\frac{- \\chi + \\pi}{\\delta}", "variable": "\\chi", "positive": "\\frac{\\chi (- \\chi + 2 \\pi)}{2 \\delta}", "negatives": ["\\frac{\\pi (- 2 \\chi + \\pi)}{2 \\delta}", "\\frac{\\chi^{2}}{2 \\pi} + \\chi \\delta", "\\frac{\\chi (\\chi + 2 \\delta)}{2 \\pi}", "(- \\chi + \\pi) \\log{(\\delta)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Add(Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1))), Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\delta', commutative=True))))", "Mul(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\pi', commutative=True)), log(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\frac{\\xi}{\\sigma}", "variable": "\\sigma", "positive": "\\xi \\log{(\\sigma)}", "negatives": ["\\frac{\\xi^{2}}{2 \\sigma}", "\\log{(\\sigma)} \\log{(\\xi)}", "\\frac{\\sigma^{2} \\cos{(\\xi)}}{2}", "\\sigma (\\log{(\\sigma \\xi)} - 1)"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Mul(log(Symbol('\\\\sigma', commutative=True)), log(Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), cos(Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\sigma', commutative=True), Add(log(Mul(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True))), Integer(-1)))"]}, {"premise_expression": "e^{\\frac{\\psi}{\\xi}}", "variable": "\\xi", "positive": "- \\psi \\operatorname{Ei}{(\\frac{\\psi}{\\xi})} + \\xi e^{\\frac{\\psi}{\\xi}}", "negatives": ["\\xi e^{\\frac{\\psi}{\\xi}}", "e^{\\psi + \\xi}", "\\xi (\\log{(\\frac{\\psi}{\\xi})} + 1)", "\\frac{\\xi (\\xi + 2 \\log{(\\psi)})}{2}"], "srepr_premise_expression": "exp(Mul(Symbol('\\\\psi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True), Ei(Mul(Symbol('\\\\psi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))), Mul(Symbol('\\\\xi', commutative=True), exp(Mul(Symbol('\\\\psi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))))", "srepr_negatives": ["Mul(Symbol('\\\\xi', commutative=True), exp(Mul(Symbol('\\\\psi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))))", "exp(Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\xi', commutative=True), Add(log(Mul(Symbol('\\\\psi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\xi', commutative=True), Mul(Integer(2), log(Symbol('\\\\psi', commutative=True)))))"]}, {"premise_expression": "\\delta + \\pi", "variable": "\\pi", "positive": "\\frac{\\pi (2 \\delta + \\pi)}{2}", "negatives": ["\\frac{\\delta (\\delta + 2 \\pi)}{2}", "e^{- \\delta + \\pi}", "\\frac{\\pi^{2}}{2 \\delta}", "\\frac{\\sin{(\\pi)}}{\\delta}"], "srepr_premise_expression": "Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "exp(Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), sin(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\frac{\\delta}{\\alpha}", "variable": "\\delta", "positive": "\\frac{\\delta^{2}}{2 \\alpha}", "negatives": ["\\delta \\log{(\\alpha)}", "\\frac{\\delta (2 \\alpha - \\delta)}{2}", "\\tilde{\\infty} \\delta", "\\log{(\\alpha)} \\log{(\\delta)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\delta', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))", "Mul(zoo, Symbol('\\\\delta', commutative=True))", "Mul(log(Symbol('\\\\alpha', commutative=True)), log(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\log{(\\beta - \\delta)}", "variable": "\\beta", "positive": "\\beta \\log{(\\beta - \\delta)} - \\beta - \\delta \\log{(\\beta - \\delta)}", "negatives": ["- \\beta \\log{(- \\beta + \\delta)} + \\delta \\log{(\\beta - \\delta)} - \\delta", "\\beta (\\delta + \\log{(\\beta)} - 1)", "\\beta \\cos{(\\frac{\\delta}{\\beta})} + \\delta \\operatorname{Si}{(\\frac{\\delta}{\\beta})}", "\\beta \\delta - \\cos{(\\beta)}"], "srepr_premise_expression": "log(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\beta', commutative=True), log(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))), Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Symbol('\\\\delta', commutative=True), log(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\delta', commutative=True)))), Mul(Symbol('\\\\delta', commutative=True), log(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)))", "Mul(Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\delta', commutative=True), log(Symbol('\\\\beta', commutative=True)), Integer(-1)))", "Add(Mul(Symbol('\\\\beta', commutative=True), cos(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True)))), Mul(Symbol('\\\\delta', commutative=True), Si(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True)))))", "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\beta', commutative=True))))"]}, {"premise_expression": "- \\xi + \\sin{(\\pi)}", "variable": "\\xi", "positive": "\\frac{\\xi (- \\xi + 2 \\sin{(\\pi)})}{2}", "negatives": ["\\frac{\\xi (- \\xi + 2 e^{\\pi})}{2}", "- \\pi \\xi - \\cos{(\\pi)}", "\\frac{\\pi \\xi^{2}}{2}", "\\xi \\sin{(2 \\pi)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), sin(Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\pi', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\pi', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Mul(Symbol('\\\\xi', commutative=True), sin(Mul(Integer(2), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "- \\pi + e^{\\omega}", "variable": "\\pi", "positive": "\\frac{\\pi (- \\pi + 2 e^{\\omega})}{2}", "negatives": ["- \\omega \\pi + e^{\\omega}", "\\frac{\\pi^{2} \\sin{(\\omega)}}{2}", "- e^{\\omega - \\pi}", "\\omega \\pi - \\cos{(\\pi)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), exp(Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\omega', commutative=True)))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)), exp(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), sin(Symbol('\\\\omega', commutative=True)))", "Mul(Integer(-1), exp(Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))", "Add(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\sin{(\\delta + \\xi)}", "variable": "\\delta", "positive": "- \\cos{(\\delta + \\xi)}", "negatives": ["- \\cos{(\\delta - \\xi)}", "e^{\\delta + \\xi}", "\\frac{\\delta (\\delta - 2 \\xi)}{2}", "\\log{(\\delta)} \\sin{(\\xi)}"], "srepr_premise_expression": "sin(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))))", "exp(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(log(Symbol('\\\\delta', commutative=True)), sin(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\cos{(\\beta + \\gamma)}", "variable": "\\beta", "positive": "\\sin{(\\beta + \\gamma)}", "negatives": ["\\gamma \\sin{(\\beta)}", "\\frac{\\beta (\\beta + 2 \\gamma)}{2}", "\\frac{\\beta (- \\beta + 2 \\log{(\\gamma)})}{2}", "\\int \\sin^{\\gamma}{(\\beta)} d\\beta"], "srepr_premise_expression": "cos(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "sin(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\gamma', commutative=True), sin(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), log(Symbol('\\\\gamma', commutative=True)))))", "Integral(Pow(sin(Symbol('\\\\beta', commutative=True)), Symbol('\\\\gamma', commutative=True)), Tuple(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "\\beta + \\gamma + \\pi", "variable": "\\beta", "positive": "\\beta (\\frac{\\beta}{2} + \\gamma + \\pi)", "negatives": ["\\frac{\\beta (\\beta - 2 \\gamma + 2 \\pi)}{2}", "\\frac{\\beta (- \\beta + 2 \\gamma + 2 \\pi)}{2}", "\\frac{\\gamma (2 \\beta + \\gamma + 2 \\pi)}{2}", "\\frac{\\pi (2 \\beta + 2 \\gamma + \\pi)}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\beta', commutative=True), Add(Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\gamma', commutative=True), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "e^{\\beta - \\omega}", "variable": "\\beta", "positive": "e^{\\beta - \\omega}", "negatives": ["- e^{\\beta - \\omega}", "e^{\\beta + \\omega}", "\\beta \\omega (\\log{(\\beta)} - 1)", "\\frac{\\beta^{2} \\omega}{2}"], "srepr_premise_expression": "exp(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "exp(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), exp(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))))", "exp(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True), Add(log(Symbol('\\\\beta', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\omega', commutative=True))"]}, {"premise_expression": "\\sigma e^{\\chi}", "variable": "\\chi", "positive": "\\sigma e^{\\chi}", "negatives": ["\\sigma \\log{(\\chi)}", "\\frac{\\sigma^{2} e^{\\chi}}{2}", "e^{\\chi + \\sigma}", "\\frac{\\chi^{2}}{2 \\sigma}"], "srepr_premise_expression": "Mul(Symbol('\\\\sigma', commutative=True), exp(Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\sigma', commutative=True), exp(Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), exp(Symbol('\\\\chi', commutative=True)))", "exp(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))"]}, {"premise_expression": "\\delta e^{\\gamma}", "variable": "\\delta", "positive": "\\frac{\\delta^{2} e^{\\gamma}}{2}", "negatives": ["\\delta e^{\\gamma}", "\\frac{\\delta^{2} \\gamma}{2}", "\\frac{\\delta^{2}}{2 \\gamma}", "\\gamma \\log{(\\delta)}"], "srepr_premise_expression": "Mul(Symbol('\\\\delta', commutative=True), exp(Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), exp(Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\delta', commutative=True), exp(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Symbol('\\\\gamma', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)))", "Mul(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\frac{\\sigma}{\\alpha \\omega}", "variable": "\\sigma", "positive": "\\frac{\\sigma^{2}}{2 \\alpha \\omega}", "negatives": ["\\frac{\\omega \\sigma^{2}}{2 \\alpha}", "\\frac{\\alpha^{\\omega} \\sigma^{2}}{2}", "\\frac{\\sigma \\log{(\\omega)}}{\\alpha}", "\\frac{\\sigma \\log{(\\alpha)}}{\\omega}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "- \\alpha + \\beta + \\sigma", "variable": "\\alpha", "positive": "\\alpha (- \\frac{\\alpha}{2} + \\beta + \\sigma)", "negatives": ["\\frac{\\sigma (- 2 \\alpha + 2 \\beta + \\sigma)}{2}", "\\frac{\\beta (- 2 \\alpha + \\beta + 2 \\sigma)}{2}", "\\frac{\\alpha (- \\alpha + 2 \\beta \\sigma)}{2}", "(\\beta - \\sigma) \\log{(\\alpha)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Rational(1, 2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True))))", "Mul(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))), log(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\log{(\\psi^{\\chi})}", "variable": "\\psi", "positive": "\\psi (- \\chi + \\log{(\\psi^{\\chi})})", "negatives": ["\\frac{\\psi (\\psi + 2 \\log{(\\chi)})}{2}", "\\chi \\log{(\\psi)}", "\\frac{\\chi^{2} \\log{(\\psi)}}{2}", "\\psi (\\log{(\\frac{\\chi}{\\psi})} + 1)"], "srepr_premise_expression": "log(Pow(Symbol('\\\\psi', commutative=True), Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), log(Pow(Symbol('\\\\psi', commutative=True), Symbol('\\\\chi', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(2), log(Symbol('\\\\chi', commutative=True)))))", "Mul(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), log(Symbol('\\\\psi', commutative=True)))", "Mul(Symbol('\\\\psi', commutative=True), Add(log(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))), Integer(1)))"]}, {"premise_expression": "\\frac{e^{\\gamma}}{\\chi}", "variable": "\\chi", "positive": "e^{\\gamma} \\log{(\\chi)}", "negatives": ["- \\chi \\gamma + e^{\\chi}", "- \\chi \\gamma + \\sin{(\\chi)}", "\\chi \\gamma (\\log{(\\chi)} - 1)", "\\frac{\\chi (\\chi - 2 \\gamma)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), exp(Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(exp(Symbol('\\\\gamma', commutative=True)), log(Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True)), exp(Symbol('\\\\chi', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True)), sin(Symbol('\\\\chi', commutative=True)))", "Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\gamma', commutative=True), Add(log(Symbol('\\\\chi', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True))))"]}, {"premise_expression": "\\alpha + \\sigma^{\\beta}", "variable": "\\alpha", "positive": "\\frac{\\alpha (\\alpha + 2 \\sigma^{\\beta})}{2}", "negatives": ["\\frac{\\alpha (\\alpha + 2 \\beta^{\\sigma})}{2}", "\\frac{\\alpha (\\alpha \\beta + 2 \\sigma)}{2}", "\\frac{\\alpha (\\beta + \\sigma)}{\\sigma}", "\\frac{\\alpha^{2} \\sigma}{2 \\beta}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Pow(Symbol('\\\\sigma', commutative=True), Symbol('\\\\beta', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Pow(Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))"]}, {"premise_expression": "\\frac{\\sigma}{\\delta \\pi}", "variable": "\\delta", "positive": "\\frac{\\sigma \\log{(\\delta)}}{\\pi}", "negatives": ["\\frac{\\sigma \\log{(\\pi)}}{\\delta}", "\\pi \\sigma \\log{(\\delta)}", "(\\pi + \\sigma) \\log{(\\delta)}", "\\frac{\\sigma^{2}}{2 \\delta \\pi}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\delta', commutative=True)))", "Mul(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True)), log(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))"]}, {"premise_expression": "\\frac{\\omega}{\\pi}", "variable": "\\omega", "positive": "\\frac{\\omega^{2}}{2 \\pi}", "negatives": ["\\omega \\log{(\\pi)}", "\\pi \\log{(\\omega)}", "- \\frac{\\cos{(\\omega)}}{\\pi}", "\\frac{\\omega (\\omega - 2 \\pi)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), cos(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\pi + \\sigma - \\xi", "variable": "\\sigma", "positive": "\\sigma (\\pi + \\frac{\\sigma}{2} - \\xi)", "negatives": ["\\frac{\\sigma (2 \\pi - \\sigma + 2 \\xi)}{2}", "\\frac{\\xi (2 \\pi + 2 \\sigma - \\xi)}{2}", "\\frac{\\pi (\\pi + 2 \\sigma - 2 \\xi)}{2}", "\\sigma (\\frac{\\sigma^{2}}{3} + \\xi)"], "srepr_premise_expression": "Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Symbol('\\\\sigma', commutative=True), Add(Mul(Rational(1, 3), Pow(Symbol('\\\\sigma', commutative=True), Integer(2))), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "e^{\\gamma^{\\omega}}", "variable": "\\gamma", "positive": "\\frac{e^{- \\frac{i \\pi}{\\omega}} \\gamma(\\frac{1}{\\omega}, \\gamma^{\\omega} e^{i \\pi})}{\\omega}", "negatives": ["\\gamma e^{\\frac{\\omega}{\\gamma}} - \\omega \\operatorname{Ei}{(\\frac{\\omega}{\\gamma})}", "\\frac{\\gamma (\\gamma - 2 \\omega)}{2}", "\\gamma (\\log{(\\frac{\\omega}{\\gamma})} + 1)", "- e^{- \\gamma + \\omega}"], "srepr_premise_expression": "exp(Pow(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), exp(Mul(Integer(-1), I, pi, Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))), lowergamma(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Mul(Pow(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True)), exp_polar(Mul(I, pi)))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\gamma', commutative=True), exp(Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True)))), Mul(Integer(-1), Symbol('\\\\omega', commutative=True), Ei(Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Symbol('\\\\gamma', commutative=True), Add(log(Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True))), Integer(1)))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\omega', commutative=True))))"]}, {"premise_expression": "\\chi \\pi", "variable": "\\pi", "positive": "\\frac{\\chi \\pi^{2}}{2}", "negatives": ["\\frac{\\chi^{2} \\pi}{2}", "\\frac{\\pi^{2} \\log{(\\chi)}}{2}", "- \\sin{(\\chi - \\pi)}", "\\log{(\\chi)} \\log{(\\pi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\pi', commutative=True))", "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), log(Symbol('\\\\chi', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))))", "Mul(log(Symbol('\\\\chi', commutative=True)), log(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\sigma + \\cos{(\\alpha)}", "variable": "\\alpha", "positive": "\\alpha \\sigma + \\sin{(\\alpha)}", "negatives": ["\\sigma e^{\\frac{\\alpha}{\\sigma}}", "\\frac{\\sigma (\\sigma + 2 \\cos{(\\alpha)})}{2}", "- e^{- \\alpha + \\sigma}", "- \\frac{\\cos{(\\alpha)}}{\\sigma}"], "srepr_premise_expression": "Add(Symbol('\\\\sigma', commutative=True), cos(Symbol('\\\\alpha', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True)), sin(Symbol('\\\\alpha', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\sigma', commutative=True), exp(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(2), cos(Symbol('\\\\alpha', commutative=True)))))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\sigma', commutative=True))))", "Mul(Integer(-1), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), cos(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\omega + \\pi", "variable": "\\pi", "positive": "\\frac{\\pi (2 \\omega + \\pi)}{2}", "negatives": ["\\frac{\\omega (\\omega + 2 \\pi)}{2}", "\\frac{\\pi (\\pi + 2 e^{\\omega})}{2}", "\\frac{\\pi^{2}}{2 \\omega}", "- \\cos{(\\omega + \\pi)}"], "srepr_premise_expression": "Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), exp(Symbol('\\\\omega', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\frac{\\log{(\\omega)}}{\\gamma}", "variable": "\\omega", "positive": "\\frac{\\omega (\\log{(\\omega)} - 1)}{\\gamma}", "negatives": ["\\omega (- \\gamma + \\log{(\\omega)} - 1)", "- \\cos{(\\gamma - \\omega)}", "\\log{(\\gamma)} \\log{(\\omega)}", "- \\frac{\\cos{(\\omega)}}{\\gamma}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), log(Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True), Add(log(Symbol('\\\\omega', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), log(Symbol('\\\\omega', commutative=True)), Integer(-1)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))))", "Mul(log(Symbol('\\\\gamma', commutative=True)), log(Symbol('\\\\omega', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), cos(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "- \\delta + \\sin{(\\beta)}", "variable": "\\delta", "positive": "\\frac{\\delta (- \\delta + 2 \\sin{(\\beta)})}{2}", "negatives": ["\\frac{\\delta^{2} \\log{(\\beta)}}{2}", "\\frac{\\delta (2 \\beta - \\delta)}{2}", "- \\beta \\delta - \\cos{(\\beta)}", "\\frac{\\beta \\delta (2 \\beta - \\delta)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), sin(Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\beta', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), log(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\beta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))"]}, {"premise_expression": "\\gamma \\sin{(\\psi)}", "variable": "\\gamma", "positive": "\\frac{\\gamma^{2} \\sin{(\\psi)}}{2}", "negatives": ["\\frac{\\gamma^{2} e^{\\psi}}{2}", "\\frac{\\gamma (\\gamma - 2 \\psi)}{2}", "- \\gamma \\cos{(\\psi)}", "\\sin{(\\gamma + \\psi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\gamma', commutative=True), sin(Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), sin(Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), exp(Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), cos(Symbol('\\\\psi', commutative=True)))", "sin(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\cos{(\\sigma + \\xi)}", "variable": "\\xi", "positive": "\\sin{(\\sigma + \\xi)}", "negatives": ["- \\sigma \\xi + \\sin{(\\xi)}", "\\xi", "\\sigma \\xi - \\cos{(\\xi)}", "\\log{(\\xi)} \\cos{(\\sigma)}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "sin(Add(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True)), sin(Symbol('\\\\xi', commutative=True)))", "Symbol('\\\\xi', commutative=True)", "Add(Mul(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\xi', commutative=True))))", "Mul(log(Symbol('\\\\xi', commutative=True)), cos(Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\log{(\\alpha - \\omega)}", "variable": "\\alpha", "positive": "\\alpha \\log{(\\alpha - \\omega)} - \\alpha - \\omega \\log{(\\alpha - \\omega)}", "negatives": ["- \\alpha \\log{(- \\alpha + \\omega)} + \\omega \\log{(\\alpha - \\omega)} - \\omega", "\\alpha \\cos{(\\frac{\\omega}{\\alpha})} + \\omega \\operatorname{Si}{(\\frac{\\omega}{\\alpha})}", "\\alpha (- \\omega + \\log{(\\alpha^{\\omega})})", "\\frac{\\alpha (- \\alpha + 2 \\cos{(\\omega)})}{2}"], "srepr_premise_expression": "log(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\alpha', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))), Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\omega', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\omega', commutative=True)))), Mul(Symbol('\\\\omega', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))", "Add(Mul(Symbol('\\\\alpha', commutative=True), cos(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True)))), Mul(Symbol('\\\\omega', commutative=True), Si(Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True)))))", "Mul(Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), log(Pow(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\omega', commutative=True)))))"]}, {"premise_expression": "\\sin{(\\delta + \\gamma)}", "variable": "\\delta", "positive": "- \\cos{(\\delta + \\gamma)}", "negatives": ["- \\cos{(\\delta - \\gamma)}", "\\gamma \\sin{(\\delta)}", "\\frac{\\delta^{2} e^{\\gamma}}{2}", "\\frac{\\delta (\\delta + 2 e^{\\gamma})}{2}"], "srepr_premise_expression": "sin(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\gamma', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))))", "Mul(Symbol('\\\\gamma', commutative=True), sin(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), exp(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), exp(Symbol('\\\\gamma', commutative=True)))))"]}, {"premise_expression": "\\delta + e^{\\xi}", "variable": "\\delta", "positive": "\\frac{\\delta (\\delta + 2 e^{\\xi})}{2}", "negatives": ["\\delta \\xi + e^{\\xi}", "\\delta (\\log{(\\delta \\xi)} - 1)", "\\delta (- \\xi + \\log{(\\delta)} - 1)", "\\sin{(\\delta + \\xi)}"], "srepr_premise_expression": "Add(Symbol('\\\\delta', commutative=True), exp(Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), exp(Symbol('\\\\xi', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True)), exp(Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\delta', commutative=True), Add(log(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), log(Symbol('\\\\delta', commutative=True)), Integer(-1)))", "sin(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\log{(\\delta \\pi)}", "variable": "\\delta", "positive": "\\delta (\\log{(\\delta \\pi)} - 1)", "negatives": ["\\pi (\\log{(\\delta \\pi)} - 1)", "\\delta (\\log{(\\frac{\\pi}{\\delta})} + 1)", "\\delta (\\log{(\\frac{\\delta}{\\pi})} - 1)", "\\delta - \\pi \\log{(\\delta)}"], "srepr_premise_expression": "log(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\delta', commutative=True), Add(log(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\pi', commutative=True), Add(log(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\delta', commutative=True), Add(log(Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))), Integer(1)))", "Mul(Symbol('\\\\delta', commutative=True), Add(log(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))), Integer(-1)))", "Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True), log(Symbol('\\\\delta', commutative=True))))"]}, {"premise_expression": "\\omega + \\pi", "variable": "\\omega", "positive": "\\frac{\\omega (\\omega + 2 \\pi)}{2}", "negatives": ["\\frac{\\pi (2 \\omega + \\pi)}{2}", "\\frac{\\omega^{2} \\sin{(\\pi)}}{2}", "\\frac{\\omega^{2} \\cos{(\\pi)}}{2}", "- \\frac{\\cos{(\\omega)}}{\\pi}"], "srepr_premise_expression": "Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), sin(Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), cos(Symbol('\\\\pi', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), cos(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "- \\alpha + \\omega - \\pi", "variable": "\\omega", "positive": "\\omega (- \\alpha + \\frac{\\omega}{2} - \\pi)", "negatives": ["\\frac{\\alpha (- \\alpha + 2 \\omega - 2 \\pi)}{2}", "\\frac{\\pi (- 2 \\alpha + 2 \\omega - \\pi)}{2}", "\\frac{\\omega^{2}}{2 \\alpha \\pi}", "- \\frac{\\omega (\\omega - 2 \\pi)}{2 \\alpha}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))", "Mul(Integer(-1), Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\log{(\\frac{\\alpha}{\\omega})}", "variable": "\\omega", "positive": "\\omega (\\log{(\\frac{\\alpha}{\\omega})} + 1)", "negatives": ["\\alpha (\\log{(\\frac{\\alpha}{\\omega})} - 1)", "e^{- \\alpha + \\omega}", "- \\sin{(\\alpha - \\omega)}", "\\log{(\\omega)} \\cos{(\\alpha)}"], "srepr_premise_expression": "log(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\omega', commutative=True), Add(log(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))), Integer(1)))", "srepr_negatives": ["Mul(Symbol('\\\\alpha', commutative=True), Add(log(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))), Integer(-1)))", "exp(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Mul(Integer(-1), sin(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))))", "Mul(log(Symbol('\\\\omega', commutative=True)), cos(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\omega + \\psi", "variable": "\\psi", "positive": "\\frac{\\psi (2 \\omega + \\psi)}{2}", "negatives": ["\\frac{\\omega (\\omega + 2 \\psi)}{2}", "\\frac{\\psi (\\psi + 2 \\cos{(\\omega)})}{2}", "\\frac{\\omega \\psi^{2}}{2}", "\\frac{\\psi^{2} \\log{(\\omega)}}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(2), cos(Symbol('\\\\omega', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), log(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\gamma + \\sigma", "variable": "\\gamma", "positive": "\\frac{\\gamma (\\gamma + 2 \\sigma)}{2}", "negatives": ["\\frac{\\sigma (2 \\gamma + \\sigma)}{2}", "- \\cos{(\\gamma + \\sigma)}", "\\gamma^{2} (\\frac{\\gamma}{3} - \\frac{\\sigma}{2})", "e^{\\sigma} \\log{(\\gamma)}"], "srepr_premise_expression": "Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True))))", "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Add(Mul(Rational(1, 3), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), Rational(1, 2), Symbol('\\\\sigma', commutative=True))))", "Mul(exp(Symbol('\\\\sigma', commutative=True)), log(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\sin{(\\alpha + \\sigma)}", "variable": "\\alpha", "positive": "- \\cos{(\\alpha + \\sigma)}", "negatives": ["\\log{(\\alpha)} \\log{(\\sigma)}", "\\frac{\\alpha^{2}}{2 \\sigma}", "- \\alpha \\sigma + \\sin{(\\alpha)}", "\\alpha (- \\sigma + \\log{(\\alpha)} - 1)"], "srepr_premise_expression": "sin(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(log(Symbol('\\\\alpha', commutative=True)), log(Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True)), sin(Symbol('\\\\alpha', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), log(Symbol('\\\\alpha', commutative=True)), Integer(-1)))"]}, {"premise_expression": "- \\beta + \\log{(\\gamma)}", "variable": "\\beta", "positive": "\\frac{\\beta (- \\beta + 2 \\log{(\\gamma)})}{2}", "negatives": ["\\frac{\\beta (- \\beta + 2 \\cos{(\\gamma)})}{2}", "\\gamma (- \\beta + \\log{(\\gamma)} - 1)", "\\beta (\\beta + \\gamma)", "\\sin{(\\beta + \\gamma)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), log(Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), log(Symbol('\\\\gamma', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\gamma', commutative=True)))))", "Mul(Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), log(Symbol('\\\\gamma', commutative=True)), Integer(-1)))", "Mul(Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)))", "sin(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\sin^{\\omega}{(\\pi)}", "variable": "\\pi", "positive": "\\int \\sin^{\\omega}{(\\pi)} d\\pi", "negatives": ["\\operatorname{NonElementaryIntegral}{(\\log{(\\pi)}^{\\pi},( \\pi))}", "- \\frac{\\cos{(\\pi)}}{\\omega}", "\\omega e^{\\pi}", "\\omega \\log{(\\pi)}"], "srepr_premise_expression": "Pow(sin(Symbol('\\\\pi', commutative=True)), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Integral(Pow(sin(Symbol('\\\\pi', commutative=True)), Symbol('\\\\omega', commutative=True)), Tuple(Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Function('NonElementaryIntegral')(Pow(log(Symbol('\\\\pi', commutative=True)), Symbol('\\\\pi', commutative=True)), Tuple(Symbol('\\\\pi', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), cos(Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), exp(Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\log{(\\chi + \\delta)}", "variable": "\\chi", "positive": "\\chi \\log{(\\chi + \\delta)} - \\chi + \\delta \\log{(\\chi + \\delta)}", "negatives": ["\\chi \\log{(\\chi + \\delta)} + \\delta \\log{(\\chi + \\delta)} - \\delta", "\\log{(\\chi)} \\cos{(\\delta)}", "\\chi (\\log{(\\chi \\delta)} - 1)", "\\frac{\\chi (- \\chi + 2 \\sin{(\\delta)})}{2}"], "srepr_premise_expression": "log(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\chi', commutative=True), log(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True)))), Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Symbol('\\\\delta', commutative=True), log(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True)))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\chi', commutative=True), log(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True)))), Mul(Symbol('\\\\delta', commutative=True), log(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True)))), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)))", "Mul(log(Symbol('\\\\chi', commutative=True)), cos(Symbol('\\\\delta', commutative=True)))", "Mul(Symbol('\\\\chi', commutative=True), Add(log(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\delta', commutative=True)))))"]}, {"premise_expression": "\\frac{\\psi}{\\pi}", "variable": "\\pi", "positive": "\\psi \\log{(\\pi)}", "negatives": ["\\frac{\\psi^{2}}{2 \\pi}", "\\log{(\\pi)} \\log{(\\psi)}", "\\pi \\psi (\\log{(\\pi)} - 1)", "\\pi (\\log{(\\frac{\\pi}{\\psi})} - 1)"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\psi', commutative=True), log(Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "Mul(log(Symbol('\\\\pi', commutative=True)), log(Symbol('\\\\psi', commutative=True)))", "Mul(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True), Add(log(Symbol('\\\\pi', commutative=True)), Integer(-1)))", "Mul(Symbol('\\\\pi', commutative=True), Add(log(Mul(Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))), Integer(-1)))"]}, {"premise_expression": "\\psi (\\omega + \\pi)", "variable": "\\pi", "positive": "\\frac{\\pi \\psi (2 \\omega + \\pi)}{2}", "negatives": ["\\frac{\\omega \\pi (\\pi + 2 \\psi)}{2}", "\\frac{\\psi^{2} (\\omega + \\pi)}{2}", "\\frac{\\omega \\psi (\\omega + 2 \\pi)}{2}", "\\frac{\\pi (\\omega \\pi + 2 \\psi)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "\\xi (- \\gamma + \\psi)", "variable": "\\xi", "positive": "\\frac{\\xi^{2} (- \\gamma + \\psi)}{2}", "negatives": ["\\frac{\\gamma \\xi (- \\gamma + 2 \\psi)}{2}", "\\frac{\\psi \\xi (- 2 \\gamma + \\psi)}{2}", "\\frac{\\gamma^{\\psi} \\xi^{2}}{2}", "\\frac{\\gamma \\psi \\xi^{2}}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True)), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))"]}, {"premise_expression": "\\log{(\\frac{\\sigma}{\\beta})}", "variable": "\\beta", "positive": "\\beta (\\log{(\\frac{\\sigma}{\\beta})} + 1)", "negatives": ["\\sigma (\\log{(\\frac{\\sigma}{\\beta})} - 1)", "\\beta \\sigma (\\log{(\\beta)} - 1)", "\\beta (- \\sigma + \\log{(\\beta)} - 1)", "\\sigma \\log{(\\beta)}"], "srepr_premise_expression": "log(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\beta', commutative=True), Add(log(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))), Integer(1)))", "srepr_negatives": ["Mul(Symbol('\\\\sigma', commutative=True), Add(log(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True), Add(log(Symbol('\\\\beta', commutative=True)), Integer(-1)))", "Mul(Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), log(Symbol('\\\\beta', commutative=True)), Integer(-1)))", "Mul(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "\\log{(\\frac{\\gamma}{\\chi})}", "variable": "\\chi", "positive": "\\chi (\\log{(\\frac{\\gamma}{\\chi})} + 1)", "negatives": ["\\gamma (\\log{(\\frac{\\gamma}{\\chi})} - 1)", "\\frac{\\chi (\\log{(\\chi)} - 1)}{\\gamma}", "\\chi (- \\gamma + \\log{(\\chi)} - 1)", "\\frac{\\chi^{2} \\log{(\\gamma)}}{2}"], "srepr_premise_expression": "log(Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\chi', commutative=True), Add(log(Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True))), Integer(1)))", "srepr_negatives": ["Mul(Symbol('\\\\gamma', commutative=True), Add(log(Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Add(log(Symbol('\\\\chi', commutative=True)), Integer(-1)))", "Mul(Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), log(Symbol('\\\\chi', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), log(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\frac{\\cos{(\\pi)}}{\\gamma}", "variable": "\\gamma", "positive": "\\log{(\\gamma)} \\cos{(\\pi)}", "negatives": ["\\frac{\\gamma^{2} \\log{(\\pi)}}{2}", "\\pi e^{\\frac{\\gamma}{\\pi}}", "\\frac{\\sin{(\\pi)}}{\\gamma}", "\\gamma (- \\pi + e^{\\pi})"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), cos(Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(log(Symbol('\\\\gamma', commutative=True)), cos(Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), log(Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\pi', commutative=True), exp(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))))", "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), sin(Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), exp(Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\log{(\\alpha - \\chi)}", "variable": "\\alpha", "positive": "\\alpha \\log{(\\alpha - \\chi)} - \\alpha - \\chi \\log{(\\alpha - \\chi)}", "negatives": ["- \\alpha \\log{(- \\alpha + \\chi)} + \\chi \\log{(\\alpha - \\chi)} - \\chi", "\\alpha \\chi (\\log{(\\alpha)} - 1)", "\\frac{\\alpha (\\alpha + 2 \\cos{(\\chi)})}{2}", "e^{\\chi} \\log{(\\alpha)}"], "srepr_premise_expression": "log(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True))))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\alpha', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True))))), Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\chi', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True))))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\chi', commutative=True)))), Mul(Symbol('\\\\chi', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\chi', commutative=True))))), Mul(Integer(-1), Symbol('\\\\chi', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True), Add(log(Symbol('\\\\alpha', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), cos(Symbol('\\\\chi', commutative=True)))))", "Mul(exp(Symbol('\\\\chi', commutative=True)), log(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "\\alpha + e^{\\gamma}", "variable": "\\alpha", "positive": "\\frac{\\alpha (\\alpha + 2 e^{\\gamma})}{2}", "negatives": ["\\frac{\\alpha (\\alpha + 2 \\sin{(\\gamma)})}{2}", "\\frac{\\alpha (- \\alpha + 2 \\sin{(\\gamma)})}{2}", "\\alpha \\gamma + e^{\\gamma}", "\\frac{\\alpha^{2}}{2 \\gamma}"], "srepr_premise_expression": "Add(Symbol('\\\\alpha', commutative=True), exp(Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), exp(Symbol('\\\\gamma', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), sin(Symbol('\\\\gamma', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\gamma', commutative=True)))))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\gamma', commutative=True)), exp(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)))"]}, {"premise_expression": "\\sin^{\\pi}{(\\chi)}", "variable": "\\chi", "positive": "\\int \\sin^{\\pi}{(\\chi)} d\\chi", "negatives": ["\\sin{(\\chi + \\pi)}", "\\chi (\\log{(\\chi \\pi)} - 1)", "\\pi \\log{(\\chi)}", "e^{\\chi - \\pi}"], "srepr_premise_expression": "Pow(sin(Symbol('\\\\chi', commutative=True)), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Integral(Pow(sin(Symbol('\\\\chi', commutative=True)), Symbol('\\\\pi', commutative=True)), Tuple(Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["sin(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True)))", "Mul(Symbol('\\\\chi', commutative=True), Add(log(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\chi', commutative=True)))", "exp(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "- \\omega + \\sin{(\\pi)}", "variable": "\\pi", "positive": "- \\omega \\pi - \\cos{(\\pi)}", "negatives": ["\\omega \\log{(\\pi)}", "\\frac{\\pi (- 2 \\omega + \\pi)}{2}", "\\frac{\\omega \\pi^{2}}{2}", "\\frac{\\pi (2 \\omega - \\pi)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), sin(Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\pi', commutative=True))))", "srepr_negatives": ["Mul(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\frac{\\cos{(\\beta)}}{\\sigma}", "variable": "\\beta", "positive": "\\frac{\\sin{(\\beta)}}{\\sigma}", "negatives": ["e^{\\beta - \\sigma}", "\\cos{(\\beta - \\sigma)}", "\\frac{\\beta^{2} \\sigma}{2}", "\\beta \\sigma + \\sin{(\\beta)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), cos(Symbol('\\\\beta', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), sin(Symbol('\\\\beta', commutative=True)))", "srepr_negatives": ["exp(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\sigma', commutative=True))", "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\sigma', commutative=True)), sin(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "\\chi \\pi", "variable": "\\chi", "positive": "\\frac{\\chi^{2} \\pi}{2}", "negatives": ["\\frac{\\chi \\pi^{2}}{2}", "\\frac{\\chi^{2}}{2 \\pi}", "- \\chi \\pi - \\cos{(\\chi)}", "\\log{(\\chi)} \\sin{(\\pi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\pi', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))", "Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\chi', commutative=True))))", "Mul(log(Symbol('\\\\chi', commutative=True)), sin(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\frac{- \\omega + \\xi}{\\chi}", "variable": "\\omega", "positive": "\\frac{\\omega (- \\omega + 2 \\xi)}{2 \\chi}", "negatives": ["\\frac{\\xi (- 2 \\omega + \\xi)}{2 \\chi}", "\\frac{\\omega (2 \\chi - \\omega - 2 \\xi)}{2}", "(- \\omega + \\xi) \\log{(\\chi)}", "\\frac{\\omega (2 \\chi + \\omega + 2 \\xi)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Symbol('\\\\xi', commutative=True)), log(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\omega', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\cos{(\\frac{\\alpha}{\\psi})}", "variable": "\\psi", "positive": "\\alpha \\operatorname{Si}{(\\frac{\\alpha}{\\psi})} + \\psi \\cos{(\\frac{\\alpha}{\\psi})}", "negatives": ["\\frac{\\psi (\\psi + 2 \\log{(\\alpha)})}{2}", "\\frac{\\psi (- 2 \\alpha + \\psi)}{2}", "\\alpha \\log{(\\alpha + \\psi)} + \\psi \\log{(\\alpha + \\psi)} - \\psi", "\\psi (\\log{(\\alpha \\psi)} - 1)"], "srepr_premise_expression": "cos(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\alpha', commutative=True), Si(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1))))), Mul(Symbol('\\\\psi', commutative=True), cos(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1))))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(2), log(Symbol('\\\\alpha', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Add(Mul(Symbol('\\\\alpha', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True)))), Mul(Symbol('\\\\psi', commutative=True), log(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True)))), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))", "Mul(Symbol('\\\\psi', commutative=True), Add(log(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\frac{\\alpha \\psi}{\\delta}", "variable": "\\psi", "positive": "\\frac{\\alpha \\psi^{2}}{2 \\delta}", "negatives": ["\\frac{\\delta \\psi^{2}}{2 \\alpha}", "\\frac{\\alpha^{2} \\psi}{2 \\delta}", "\\alpha \\psi \\log{(\\delta)}", "\\frac{\\psi^{2} (\\alpha + \\delta)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True))", "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\psi', commutative=True), log(Symbol('\\\\delta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(2)), Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\frac{\\chi + \\xi}{\\alpha}", "variable": "\\chi", "positive": "\\frac{\\chi (\\chi + 2 \\xi)}{2 \\alpha}", "negatives": ["\\frac{\\xi (2 \\chi + \\xi)}{2 \\alpha}", "\\frac{\\chi^{2} \\xi}{2 \\alpha}", "\\frac{\\chi (2 \\alpha - \\chi)}{2 \\xi}", "\\frac{\\chi (\\alpha \\chi - 2 \\xi)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True)), Mul(Integer(-1), Symbol('\\\\chi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "- \\alpha + \\gamma", "variable": "\\alpha", "positive": "\\frac{\\alpha (- \\alpha + 2 \\gamma)}{2}", "negatives": ["\\frac{\\gamma (- 2 \\alpha + \\gamma)}{2}", "\\frac{\\alpha (- \\alpha + 2 \\cos{(\\gamma)})}{2}", "\\frac{\\alpha (\\alpha + 2 \\sin{(\\gamma)})}{2}", "\\frac{\\alpha (\\alpha + 2 \\cos{(\\gamma)})}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\gamma', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\gamma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\gamma', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), sin(Symbol('\\\\gamma', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), cos(Symbol('\\\\gamma', commutative=True)))))"]}, {"premise_expression": "\\frac{\\beta}{\\sigma} + \\omega", "variable": "\\omega", "positive": "\\frac{\\beta \\omega}{\\sigma} + \\frac{\\omega^{2}}{2}", "negatives": ["\\frac{\\beta \\omega}{\\sigma} - \\frac{\\omega^{2}}{2}", "\\frac{\\omega (\\beta \\omega + 2 \\sigma)}{2}", "\\beta \\log{(\\sigma)} + \\omega \\sigma", "\\frac{\\beta^{2}}{2 \\sigma} + \\beta \\omega"], "srepr_premise_expression": "Add(Mul(Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1))), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1))), Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2))))", "srepr_negatives": ["Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1))), Mul(Integer(-1), Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Add(Mul(Symbol('\\\\beta', commutative=True), log(Symbol('\\\\sigma', commutative=True))), Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True)))", "Add(Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1))), Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "\\frac{\\omega}{\\chi}", "variable": "\\chi", "positive": "\\omega \\log{(\\chi)}", "negatives": ["\\frac{\\omega^{2}}{2 \\chi}", "\\omega e^{\\frac{\\chi}{\\omega}}", "e^{\\chi + \\omega}", "\\frac{\\chi (\\log{(\\chi)} - 1)}{\\omega}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "Mul(Symbol('\\\\omega', commutative=True), exp(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))))", "exp(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Add(log(Symbol('\\\\chi', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\log{(\\pi - \\sigma)}", "variable": "\\sigma", "positive": "- \\pi \\log{(- \\pi + \\sigma)} + \\sigma \\log{(\\pi - \\sigma)} - \\sigma", "negatives": ["\\pi \\log{(\\pi - \\sigma)} - \\pi - \\sigma \\log{(\\pi - \\sigma)}", "\\sigma (- \\pi + \\log{(\\sigma)} - 1)", "\\frac{\\sigma (\\sigma + 2 \\log{(\\sigma)} - 2)}{2}", "- \\pi \\sigma - \\cos{(\\sigma)}"], "srepr_premise_expression": "log(Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Symbol('\\\\sigma', commutative=True)))), Mul(Symbol('\\\\sigma', commutative=True), log(Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Add(Mul(Symbol('\\\\pi', commutative=True), log(Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))), Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True), log(Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))))", "Mul(Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), log(Symbol('\\\\sigma', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Symbol('\\\\sigma', commutative=True), Mul(Integer(2), log(Symbol('\\\\sigma', commutative=True))), Integer(-2)))", "Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\gamma^{\\omega} - \\sigma", "variable": "\\sigma", "positive": "\\frac{\\sigma (2 \\gamma^{\\omega} - \\sigma)}{2}", "negatives": ["\\frac{\\sigma (2 \\gamma \\omega + \\sigma)}{2}", "\\frac{\\sigma^{2} (\\gamma - \\omega)}{2}", "\\frac{\\sigma (\\gamma \\sigma - 2 \\omega)}{2}", "\\frac{\\gamma \\sigma}{\\omega} - \\frac{\\sigma^{2}}{2}"], "srepr_premise_expression": "Add(Pow(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Pow(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True))), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True))))", "Add(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True)), Mul(Integer(-1), Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2))))"]}, {"premise_expression": "\\chi - \\sigma", "variable": "\\chi", "positive": "\\frac{\\chi (\\chi - 2 \\sigma)}{2}", "negatives": ["\\frac{\\sigma (2 \\chi - \\sigma)}{2}", "\\frac{\\chi^{2} \\log{(\\sigma)}}{2}", "- \\cos{(\\chi + \\sigma)}", "e^{\\chi + \\sigma}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), log(Symbol('\\\\sigma', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\sigma', commutative=True))))", "exp(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\frac{- \\chi + \\delta}{\\omega}", "variable": "\\chi", "positive": "\\frac{\\chi (- \\chi + 2 \\delta)}{2 \\omega}", "negatives": ["- \\frac{\\chi (- \\chi + 2 \\delta)}{2 \\omega}", "\\frac{\\delta (- 2 \\chi + \\delta)}{2 \\omega}", "(- \\chi + \\delta) \\log{(\\omega)}", "\\frac{\\chi (\\chi - 2 \\delta - 2 \\omega)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\delta', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\delta', commutative=True)))", "Mul(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\delta', commutative=True)), log(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True))))"]}, {"premise_expression": "- \\gamma + \\frac{\\pi}{\\omega}", "variable": "\\omega", "positive": "- \\gamma \\omega + \\pi \\log{(\\omega)}", "negatives": ["- \\gamma \\pi + \\frac{\\pi^{2}}{2 \\omega}", "- \\frac{\\gamma^{2}}{2} + \\frac{\\gamma \\pi}{\\omega}", "- \\frac{\\omega^{2}}{2} + \\frac{\\omega \\pi}{\\gamma}", "\\frac{\\omega (\\gamma \\omega + 2 \\pi)}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Pow(Symbol('\\\\pi', commutative=True), Integer(2))))", "Add(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2))), Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True)))", "Add(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2))), Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))"]}, {"premise_expression": "\\pi + \\psi", "variable": "\\pi", "positive": "\\frac{\\pi (\\pi + 2 \\psi)}{2}", "negatives": ["\\frac{\\pi (\\pi - 2 \\psi)}{2}", "\\frac{\\psi (2 \\pi + \\psi)}{2}", "\\frac{\\pi (\\pi + 2 \\log{(\\psi)})}{2}", "- \\pi \\psi + e^{\\pi}"], "srepr_premise_expression": "Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), log(Symbol('\\\\psi', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)), exp(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "\\delta \\sin{(\\chi)}", "variable": "\\delta", "positive": "\\frac{\\delta^{2} \\sin{(\\chi)}}{2}", "negatives": ["\\frac{\\chi \\delta^{2}}{2}", "- \\delta \\cos{(\\chi)}", "\\log{(\\delta)} \\sin{(\\chi)}", "\\frac{\\delta (\\delta + 2 \\cos{(\\chi)})}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\delta', commutative=True), sin(Symbol('\\\\chi', commutative=True)))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), sin(Symbol('\\\\chi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\delta', commutative=True), Integer(2)))", "Mul(Integer(-1), Symbol('\\\\delta', commutative=True), cos(Symbol('\\\\chi', commutative=True)))", "Mul(log(Symbol('\\\\delta', commutative=True)), sin(Symbol('\\\\chi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), cos(Symbol('\\\\chi', commutative=True)))))"]}, {"premise_expression": "e^{\\frac{\\omega}{\\beta}}", "variable": "\\omega", "positive": "\\beta e^{\\frac{\\omega}{\\beta}}", "negatives": ["\\beta e^{\\omega}", "\\beta \\omega + e^{\\omega}", "- \\cos{(\\beta - \\omega)}", "\\omega (\\log{(\\frac{\\omega}{\\beta})} - 1)"], "srepr_premise_expression": "exp(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\beta', commutative=True), exp(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Mul(Symbol('\\\\beta', commutative=True), exp(Symbol('\\\\omega', commutative=True)))", "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True)), exp(Symbol('\\\\omega', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True)))))", "Mul(Symbol('\\\\omega', commutative=True), Add(log(Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\omega', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\alpha \\pi - \\xi", "variable": "\\pi", "positive": "\\frac{\\pi (\\alpha \\pi - 2 \\xi)}{2}", "negatives": ["\\frac{\\alpha (\\alpha \\pi - 2 \\xi)}{2}", "\\frac{\\xi (2 \\alpha \\pi - \\xi)}{2}", "\\frac{\\alpha \\pi^{2}}{2 \\xi}", "- \\frac{\\pi (\\pi - 2 \\xi)}{2 \\alpha}"], "srepr_premise_expression": "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\alpha', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "Mul(Integer(-1), Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "- \\omega + \\psi", "variable": "\\psi", "positive": "\\frac{\\psi (- 2 \\omega + \\psi)}{2}", "negatives": ["\\frac{\\omega (- \\omega + 2 \\psi)}{2}", "e^{- \\omega + \\psi}", "- \\cos{(\\omega + \\psi)}", "\\frac{\\psi (\\psi + 2 e^{\\omega})}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "exp(Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\psi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Symbol('\\\\psi', commutative=True), Mul(Integer(2), exp(Symbol('\\\\omega', commutative=True)))))"]}, {"premise_expression": "e^{\\gamma + \\xi}", "variable": "\\gamma", "positive": "e^{\\gamma + \\xi}", "negatives": ["\\frac{\\gamma (\\gamma + 2 \\xi)}{2}", "\\frac{\\gamma^{2}}{2 \\xi}", "- \\gamma \\xi + e^{\\gamma}", "\\frac{\\gamma^{2} e^{\\xi}}{2}"], "srepr_premise_expression": "exp(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "exp(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))", "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)), exp(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), exp(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "- \\xi + \\log{(\\pi)}", "variable": "\\xi", "positive": "\\frac{\\xi (- \\xi + 2 \\log{(\\pi)})}{2}", "negatives": ["\\frac{\\xi (- \\xi + 2 \\sin{(\\pi)})}{2}", "\\pi (- \\xi + \\log{(\\pi)} - 1)", "\\frac{\\xi (2 \\pi - \\xi)}{2}", "\\pi \\operatorname{Si}{(\\frac{\\pi}{\\xi})} + \\xi \\cos{(\\frac{\\pi}{\\xi})}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), log(Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), log(Symbol('\\\\pi', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\pi', commutative=True)))))", "Mul(Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\xi', commutative=True)), log(Symbol('\\\\pi', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\pi', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Add(Mul(Symbol('\\\\pi', commutative=True), Si(Mul(Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))), Mul(Symbol('\\\\xi', commutative=True), cos(Mul(Symbol('\\\\pi', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1))))))"]}, {"premise_expression": "\\chi + \\psi", "variable": "\\psi", "positive": "\\frac{\\psi (2 \\chi + \\psi)}{2}", "negatives": ["\\frac{\\chi (\\chi + 2 \\psi)}{2}", "- \\cos{(\\chi + \\psi)}", "- e^{\\chi - \\psi}", "\\psi (\\log{(\\frac{\\chi}{\\psi})} + 1)"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True))))", "Mul(Integer(-1), exp(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))", "Mul(Symbol('\\\\psi', commutative=True), Add(log(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))), Integer(1)))"]}, {"premise_expression": "\\log{(\\frac{\\gamma}{\\psi})}", "variable": "\\gamma", "positive": "\\gamma (\\log{(\\frac{\\gamma}{\\psi})} - 1)", "negatives": ["\\psi (\\log{(\\frac{\\gamma}{\\psi})} + 1)", "\\gamma \\psi (\\log{(\\gamma)} - 1)", "\\frac{\\gamma (\\gamma + 2 \\cos{(\\psi)})}{2}", "\\frac{\\gamma (- \\gamma + 2 \\log{(\\psi)})}{2}"], "srepr_premise_expression": "log(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1))))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\gamma', commutative=True), Add(log(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\psi', commutative=True), Add(log(Mul(Symbol('\\\\gamma', commutative=True), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)))), Integer(1)))", "Mul(Symbol('\\\\gamma', commutative=True), Symbol('\\\\psi', commutative=True), Add(log(Symbol('\\\\gamma', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), cos(Symbol('\\\\psi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), log(Symbol('\\\\psi', commutative=True)))))"]}, {"premise_expression": "\\log{(\\chi - \\psi)}", "variable": "\\chi", "positive": "\\chi \\log{(\\chi - \\psi)} - \\chi - \\psi \\log{(\\chi - \\psi)}", "negatives": ["- \\chi \\log{(- \\chi + \\psi)} + \\psi \\log{(\\chi - \\psi)} - \\psi", "\\chi (\\log{(\\chi \\psi)} - 1)", "\\chi \\psi (\\log{(\\chi)} - 1)", "\\sin{(\\chi + \\psi)}"], "srepr_premise_expression": "log(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\chi', commutative=True), log(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))), Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\psi', commutative=True), log(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Symbol('\\\\psi', commutative=True)))), Mul(Symbol('\\\\psi', commutative=True), log(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True))))), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))", "Mul(Symbol('\\\\chi', commutative=True), Add(log(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True), Add(log(Symbol('\\\\chi', commutative=True)), Integer(-1)))", "sin(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\psi', commutative=True)))"]}, {"premise_expression": "\\pi (- \\beta + \\xi)", "variable": "\\pi", "positive": "\\frac{\\pi^{2} (- \\beta + \\xi)}{2}", "negatives": ["\\frac{\\beta \\pi (- \\beta + 2 \\xi)}{2}", "\\frac{\\pi \\xi (- 2 \\beta + \\xi)}{2}", "\\frac{\\pi (- \\pi + 2 \\xi^{\\beta})}{2}", "\\frac{\\beta \\pi (\\pi + 2 \\xi)}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Integer(2), Pow(Symbol('\\\\xi', commutative=True), Symbol('\\\\beta', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\pi', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))"]}, {"premise_expression": "\\cos{(\\omega + \\xi)}", "variable": "\\xi", "positive": "\\sin{(\\omega + \\xi)}", "negatives": ["- \\cos{(\\omega + \\xi)}", "\\frac{\\xi^{2}}{2 \\omega}", "- \\frac{\\cos{(\\xi)}}{\\omega}", "\\xi (\\log{(\\frac{\\omega}{\\xi})} + 1)"], "srepr_premise_expression": "cos(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "sin(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), cos(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Mul(Integer(-1), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), cos(Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\xi', commutative=True), Add(log(Mul(Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))), Integer(1)))"]}, {"premise_expression": "\\cos{(\\beta - \\gamma)}", "variable": "\\beta", "positive": "\\sin{(\\beta - \\gamma)}", "negatives": ["- \\sin{(\\beta - \\gamma)}", "e^{\\beta - \\gamma}", "\\frac{\\beta (\\beta - 2 \\gamma)}{2}", "\\log{(\\beta)} \\cos{(\\gamma)}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "sin(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))))", "exp(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True))))", "Mul(log(Symbol('\\\\beta', commutative=True)), cos(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\omega + \\log{(\\xi)}", "variable": "\\omega", "positive": "\\frac{\\omega (\\omega + 2 \\log{(\\xi)})}{2}", "negatives": ["\\xi (\\omega + \\log{(\\xi)} - 1)", "\\frac{\\omega^{2} e^{\\xi}}{2}", "\\log{(\\omega)} \\log{(\\xi)}", "\\sin{(\\omega + \\xi)}"], "srepr_premise_expression": "Add(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Symbol('\\\\omega', commutative=True), Mul(Integer(2), log(Symbol('\\\\xi', commutative=True)))))", "srepr_negatives": ["Mul(Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\omega', commutative=True), log(Symbol('\\\\xi', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), exp(Symbol('\\\\xi', commutative=True)))", "Mul(log(Symbol('\\\\omega', commutative=True)), log(Symbol('\\\\xi', commutative=True)))", "sin(Add(Symbol('\\\\omega', commutative=True), Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\frac{\\cos{(\\gamma)}}{\\chi}", "variable": "\\gamma", "positive": "\\frac{\\sin{(\\gamma)}}{\\chi}", "negatives": ["- \\sin{(\\chi - \\gamma)}", "\\cos{(\\chi - \\gamma)}", "\\log{(\\chi)} \\cos{(\\gamma)}", "\\frac{\\gamma (2 \\chi - \\gamma)}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), cos(Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Pow(Symbol('\\\\chi', commutative=True), Integer(-1)), sin(Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Integer(-1), sin(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))))", "cos(Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "Mul(log(Symbol('\\\\chi', commutative=True)), cos(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))"]}, {"premise_expression": "\\gamma + \\xi", "variable": "\\xi", "positive": "\\frac{\\xi (2 \\gamma + \\xi)}{2}", "negatives": ["\\frac{\\xi (2 \\gamma - \\xi)}{2}", "\\frac{\\gamma (\\gamma + 2 \\xi)}{2}", "\\frac{\\xi^{2}}{2 \\gamma}", "\\gamma \\log{(\\xi)}"], "srepr_premise_expression": "Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Mul(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\xi', commutative=True)))"]}, {"premise_expression": "\\log{(\\beta \\gamma)}", "variable": "\\gamma", "positive": "\\gamma (\\log{(\\beta \\gamma)} - 1)", "negatives": ["\\beta (\\log{(\\beta \\gamma)} - 1)", "\\gamma (\\beta + \\log{(\\gamma)} - 1)", "\\frac{\\gamma^{2} \\log{(\\beta)}}{2}", "\\frac{\\gamma^{2} \\sin{(\\beta)}}{2}"], "srepr_premise_expression": "log(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\gamma', commutative=True), Add(log(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True))), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\beta', commutative=True), Add(log(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True))), Integer(-1)))", "Mul(Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\beta', commutative=True), log(Symbol('\\\\gamma', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), log(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), sin(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "\\delta (\\gamma + \\xi)", "variable": "\\xi", "positive": "\\frac{\\delta \\xi (2 \\gamma + \\xi)}{2}", "negatives": ["\\frac{\\delta^{2} (\\gamma + \\xi)}{2}", "\\frac{\\delta \\gamma (\\gamma + 2 \\xi)}{2}", "\\frac{\\xi (2 \\gamma + \\xi)}{2 \\delta}", "\\frac{\\delta \\xi^{2}}{2 \\gamma}"], "srepr_premise_expression": "Mul(Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))"]}, {"premise_expression": "- \\alpha + \\omega", "variable": "\\alpha", "positive": "\\frac{\\alpha (- \\alpha + 2 \\omega)}{2}", "negatives": ["\\frac{\\alpha (\\alpha - 2 \\omega)}{2}", "\\frac{\\omega (- 2 \\alpha + \\omega)}{2}", "\\sin{(\\alpha + \\omega)}", "\\alpha (\\log{(\\frac{\\alpha}{\\omega})} - 1)"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\omega', commutative=True)))", "sin(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), Add(log(Mul(Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)))), Integer(-1)))"]}, {"premise_expression": "\\frac{\\sigma}{\\psi}", "variable": "\\psi", "positive": "\\sigma \\log{(\\psi)}", "negatives": ["\\frac{\\sigma^{2}}{2 \\psi}", "- \\psi \\sigma + e^{\\psi}", "- \\cos{(\\psi + \\sigma)}", "\\log{(\\psi)} \\cos{(\\sigma)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\psi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\psi', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True)), exp(Symbol('\\\\psi', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\psi', commutative=True), Symbol('\\\\sigma', commutative=True))))", "Mul(log(Symbol('\\\\psi', commutative=True)), cos(Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\frac{\\sin{(\\omega)}}{\\beta}", "variable": "\\beta", "positive": "\\log{(\\beta)} \\sin{(\\omega)}", "negatives": ["\\frac{\\sin{(\\beta)}}{\\omega}", "- \\frac{\\cos{(\\omega)}}{\\beta}", "\\frac{\\beta^{2} \\log{(\\omega)}}{2}", "\\beta (\\log{(\\beta \\omega)} - 1)"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), sin(Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(log(Symbol('\\\\beta', commutative=True)), sin(Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), sin(Symbol('\\\\beta', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), cos(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), log(Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\beta', commutative=True), Add(log(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\omega', commutative=True))), Integer(-1)))"]}, {"premise_expression": "\\log{(\\alpha^{\\sigma})}", "variable": "\\alpha", "positive": "\\alpha (- \\sigma + \\log{(\\alpha^{\\sigma})})", "negatives": ["\\frac{\\alpha (- \\alpha + 2 \\sin{(\\sigma)})}{2}", "\\alpha \\sigma + e^{\\alpha}", "\\frac{\\sigma^{2} \\log{(\\alpha)}}{2}", "\\sin{(\\alpha + \\sigma)}"], "srepr_premise_expression": "log(Pow(Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\sigma', commutative=True)), log(Pow(Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\sigma', commutative=True)))))", "Add(Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True)), exp(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), log(Symbol('\\\\alpha', commutative=True)))", "sin(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\pi (\\gamma + \\xi)", "variable": "\\pi", "positive": "\\frac{\\pi^{2} (\\gamma + \\xi)}{2}", "negatives": ["\\frac{\\gamma \\pi (\\gamma + 2 \\xi)}{2}", "\\frac{\\pi \\xi (2 \\gamma + \\xi)}{2}", "\\frac{\\pi \\xi (2 \\gamma + \\pi)}{2}", "\\frac{\\pi^{2} \\xi}{2 \\gamma}"], "srepr_premise_expression": "Mul(Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Symbol('\\\\pi', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\pi', commutative=True), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\pi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Pow(Symbol('\\\\pi', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))"]}, {"premise_expression": "\\frac{\\psi}{\\gamma}", "variable": "\\psi", "positive": "\\frac{\\psi^{2}}{2 \\gamma}", "negatives": ["\\psi \\log{(\\gamma)}", "\\frac{\\psi (- 2 \\gamma + \\psi)}{2}", "- e^{\\gamma - \\psi}", "\\frac{\\psi (- \\psi + 2 e^{\\gamma})}{2}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True))", "srepr_variable": "Symbol('\\\\psi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(-1)), Pow(Symbol('\\\\psi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Symbol('\\\\psi', commutative=True), log(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\psi', commutative=True)))", "Mul(Integer(-1), exp(Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(-1), Symbol('\\\\psi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\psi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\psi', commutative=True)), Mul(Integer(2), exp(Symbol('\\\\gamma', commutative=True)))))"]}, {"premise_expression": "\\beta \\chi + \\sigma", "variable": "\\chi", "positive": "\\frac{\\chi (\\beta \\chi + 2 \\sigma)}{2}", "negatives": ["\\frac{\\beta (\\beta \\chi + 2 \\sigma)}{2}", "\\frac{\\chi (2 \\beta + \\chi \\sigma)}{2}", "\\frac{\\sigma (2 \\beta \\chi + \\sigma)}{2}", "\\frac{\\chi (2 \\beta + \\chi - 2 \\sigma)}{2}"], "srepr_premise_expression": "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True)), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\sigma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True), Symbol('\\\\chi', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\log{(\\delta - \\gamma)}", "variable": "\\delta", "positive": "\\delta \\log{(\\delta - \\gamma)} - \\delta - \\gamma \\log{(\\delta - \\gamma)}", "negatives": ["- \\delta \\log{(- \\delta + \\gamma)} + \\gamma \\log{(\\delta - \\gamma)} - \\gamma", "\\delta e^{\\frac{\\gamma}{\\delta}} - \\gamma \\operatorname{Ei}{(\\frac{\\gamma}{\\delta})}", "- \\delta \\gamma - \\cos{(\\delta)}", "\\frac{\\delta (\\delta + 2 \\cos{(\\gamma)})}{2}"], "srepr_premise_expression": "log(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Add(Mul(Symbol('\\\\delta', commutative=True), log(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), log(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))))", "srepr_negatives": ["Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), log(Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\gamma', commutative=True)))), Mul(Symbol('\\\\gamma', commutative=True), log(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))", "Add(Mul(Symbol('\\\\delta', commutative=True), exp(Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True)))), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True), Ei(Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\gamma', commutative=True)))))", "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True), Symbol('\\\\gamma', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Symbol('\\\\delta', commutative=True), Mul(Integer(2), cos(Symbol('\\\\gamma', commutative=True)))))"]}, {"premise_expression": "\\chi - \\gamma", "variable": "\\chi", "positive": "\\frac{\\chi (\\chi - 2 \\gamma)}{2}", "negatives": ["\\frac{\\gamma (2 \\chi - \\gamma)}{2}", "\\frac{\\chi^{2} \\log{(\\gamma)}}{2}", "\\frac{\\chi (\\chi + 2 e^{\\gamma})}{2}", "\\frac{\\chi (- \\chi + 2 \\cos{(\\gamma)})}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\gamma', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), log(Symbol('\\\\gamma', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), exp(Symbol('\\\\gamma', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), cos(Symbol('\\\\gamma', commutative=True)))))"]}, {"premise_expression": "\\frac{e^{\\gamma}}{\\beta}", "variable": "\\beta", "positive": "e^{\\gamma} \\log{(\\beta)}", "negatives": ["\\gamma \\log{(\\beta)}", "e^{\\beta + \\gamma}", "\\beta \\gamma + e^{\\beta}", "\\beta \\gamma + \\sin{(\\beta)}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), exp(Symbol('\\\\gamma', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Mul(exp(Symbol('\\\\gamma', commutative=True)), log(Symbol('\\\\beta', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\gamma', commutative=True), log(Symbol('\\\\beta', commutative=True)))", "exp(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)))", "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)), exp(Symbol('\\\\beta', commutative=True)))", "Add(Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\gamma', commutative=True)), sin(Symbol('\\\\beta', commutative=True)))"]}, {"premise_expression": "\\chi + \\sin{(\\xi)}", "variable": "\\chi", "positive": "\\frac{\\chi (\\chi + 2 \\sin{(\\xi)})}{2}", "negatives": ["\\frac{\\chi (\\chi + 2 \\log{(\\xi)})}{2}", "\\frac{\\chi^{2} \\log{(\\xi)}}{2}", "\\chi \\xi - \\cos{(\\xi)}", "\\chi (\\xi + \\log{(\\chi)} - 1)"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), sin(Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), sin(Symbol('\\\\xi', commutative=True)))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), log(Symbol('\\\\xi', commutative=True)))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), log(Symbol('\\\\xi', commutative=True)))", "Add(Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\xi', commutative=True)), Mul(Integer(-1), cos(Symbol('\\\\xi', commutative=True))))", "Mul(Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\xi', commutative=True), log(Symbol('\\\\chi', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\gamma + \\omega", "variable": "\\gamma", "positive": "\\frac{\\gamma (\\gamma + 2 \\omega)}{2}", "negatives": ["\\frac{\\omega (2 \\gamma + \\omega)}{2}", "\\frac{\\gamma^{2} \\log{(\\omega)}}{2}", "- \\frac{\\cos{(\\gamma)}}{\\omega}", "\\omega e^{\\gamma}"], "srepr_premise_expression": "Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), Symbol('\\\\omega', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(2), Symbol('\\\\gamma', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\gamma', commutative=True), Integer(2)), log(Symbol('\\\\omega', commutative=True)))", "Mul(Integer(-1), Pow(Symbol('\\\\omega', commutative=True), Integer(-1)), cos(Symbol('\\\\gamma', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), exp(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\beta - \\delta + \\xi", "variable": "\\xi", "positive": "\\xi (\\beta - \\delta + \\frac{\\xi}{2})", "negatives": ["\\frac{\\xi (- 2 \\beta - 2 \\delta + \\xi)}{2}", "\\frac{\\delta (2 \\beta - \\delta + 2 \\xi)}{2}", "\\frac{\\beta (\\beta - 2 \\delta + 2 \\xi)}{2}", "\\frac{\\xi^{2} (\\beta - \\delta)}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\xi', commutative=True), Integer(2)), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))"]}, {"premise_expression": "- \\pi + \\frac{\\psi}{\\beta}", "variable": "\\beta", "positive": "- \\beta \\pi + \\psi \\log{(\\beta)}", "negatives": ["(\\pi + \\psi) \\log{(\\beta)}", "\\pi^{\\psi} \\log{(\\beta)}", "- \\pi \\psi + \\frac{\\psi^{2}}{2 \\beta}", "\\frac{\\beta (\\beta + 2 \\psi)}{2 \\pi}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True)), Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Symbol('\\\\psi', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True), Symbol('\\\\pi', commutative=True)), Mul(Symbol('\\\\psi', commutative=True), log(Symbol('\\\\beta', commutative=True))))", "srepr_negatives": ["Mul(Add(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)), log(Symbol('\\\\beta', commutative=True)))", "Mul(Pow(Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)), log(Symbol('\\\\beta', commutative=True)))", "Add(Mul(Integer(-1), Symbol('\\\\pi', commutative=True), Symbol('\\\\psi', commutative=True)), Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), Pow(Symbol('\\\\psi', commutative=True), Integer(2))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)), Add(Symbol('\\\\beta', commutative=True), Mul(Integer(2), Symbol('\\\\psi', commutative=True))))"]}, {"premise_expression": "- \\beta + \\delta", "variable": "\\delta", "positive": "\\frac{\\delta (- 2 \\beta + \\delta)}{2}", "negatives": ["\\frac{\\delta (2 \\beta - \\delta)}{2}", "\\frac{\\beta (- \\beta + 2 \\delta)}{2}", "\\frac{\\delta^{2} \\log{(\\beta)}}{2}", "\\sin{(\\beta + \\delta)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Symbol('\\\\delta', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\beta', commutative=True)), Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\beta', commutative=True)), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), log(Symbol('\\\\beta', commutative=True)))", "sin(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\delta', commutative=True)))"]}, {"premise_expression": "\\delta \\omega", "variable": "\\delta", "positive": "\\frac{\\delta^{2} \\omega}{2}", "negatives": ["\\frac{\\delta \\omega^{2}}{2}", "\\frac{\\delta^{2} \\log{(\\omega)}}{2}", "\\sin{(\\delta - \\omega)}", "e^{\\delta - \\omega}"], "srepr_premise_expression": "Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), Symbol('\\\\omega', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(2)), log(Symbol('\\\\omega', commutative=True)))", "sin(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))", "exp(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\omega', commutative=True))))"]}, {"premise_expression": "\\alpha \\omega", "variable": "\\omega", "positive": "\\frac{\\alpha \\omega^{2}}{2}", "negatives": ["\\frac{\\alpha^{2} \\omega}{2}", "\\frac{\\omega (- 2 \\alpha + \\omega)}{2}", "\\alpha \\sin{(\\omega)}", "- \\alpha \\cos{(\\omega)}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\omega', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\omega', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\omega', commutative=True))", "Mul(Rational(1, 2), Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\omega', commutative=True)))", "Mul(Symbol('\\\\alpha', commutative=True), sin(Symbol('\\\\omega', commutative=True)))", "Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), cos(Symbol('\\\\omega', commutative=True)))"]}, {"premise_expression": "- \\alpha + \\beta", "variable": "\\alpha", "positive": "\\frac{\\alpha (- \\alpha + 2 \\beta)}{2}", "negatives": ["\\frac{\\beta (- 2 \\alpha + \\beta)}{2}", "\\frac{\\alpha^{2} \\log{(\\beta)}}{2}", "\\frac{\\alpha^{2} \\sin{(\\beta)}}{2}", "\\cos{(\\alpha - \\beta)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\beta', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Mul(Integer(2), Symbol('\\\\beta', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), log(Symbol('\\\\beta', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), sin(Symbol('\\\\beta', commutative=True)))", "cos(Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(-1), Symbol('\\\\beta', commutative=True))))"]}, {"premise_expression": "\\chi - \\delta", "variable": "\\chi", "positive": "\\frac{\\chi (\\chi - 2 \\delta)}{2}", "negatives": ["\\frac{\\delta (2 \\chi - \\delta)}{2}", "- \\cos{(\\chi + \\delta)}", "\\frac{\\chi^{2}}{2 \\delta}", "\\frac{\\chi (\\chi + 2 e^{\\delta})}{2}"], "srepr_premise_expression": "Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Symbol('\\\\delta', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True))))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(2), Symbol('\\\\chi', commutative=True)), Mul(Integer(-1), Symbol('\\\\delta', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\delta', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), exp(Symbol('\\\\delta', commutative=True)))))"]}, {"premise_expression": "\\sigma \\log{(\\omega)}", "variable": "\\sigma", "positive": "\\frac{\\sigma^{2} \\log{(\\omega)}}{2}", "negatives": ["\\frac{\\sigma^{2} \\cos{(\\omega)}}{2}", "\\frac{\\sigma^{2} \\sin{(\\omega)}}{2}", "\\frac{\\sigma (- 2 \\omega + \\sigma)}{2}", "\\omega \\sigma (\\log{(\\omega)} - 1)"], "srepr_premise_expression": "Mul(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\omega', commutative=True)))", "srepr_variable": "Symbol('\\\\sigma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), log(Symbol('\\\\omega', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), cos(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)), sin(Symbol('\\\\omega', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\sigma', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), Symbol('\\\\sigma', commutative=True), Add(log(Symbol('\\\\omega', commutative=True)), Integer(-1)))"]}, {"premise_expression": "\\chi \\log{(\\sigma)}", "variable": "\\chi", "positive": "\\frac{\\chi^{2} \\log{(\\sigma)}}{2}", "negatives": ["\\chi \\sigma (\\log{(\\sigma)} - 1)", "\\frac{\\chi (\\chi + 2 \\cos{(\\sigma)})}{2}", "\\chi (\\log{(\\frac{\\chi}{\\sigma})} - 1)", "\\frac{\\chi (- \\chi + 2 \\sin{(\\sigma)})}{2}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\sigma', commutative=True)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), log(Symbol('\\\\sigma', commutative=True)))", "srepr_negatives": ["Mul(Symbol('\\\\chi', commutative=True), Symbol('\\\\sigma', commutative=True), Add(log(Symbol('\\\\sigma', commutative=True)), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Symbol('\\\\chi', commutative=True), Mul(Integer(2), cos(Symbol('\\\\sigma', commutative=True)))))", "Mul(Symbol('\\\\chi', commutative=True), Add(log(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))), Integer(-1)))", "Mul(Rational(1, 2), Symbol('\\\\chi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\chi', commutative=True)), Mul(Integer(2), sin(Symbol('\\\\sigma', commutative=True)))))"]}, {"premise_expression": "\\alpha \\xi", "variable": "\\alpha", "positive": "\\frac{\\alpha^{2} \\xi}{2}", "negatives": ["\\frac{\\alpha \\xi^{2}}{2}", "- \\xi \\cos{(\\alpha)}", "\\frac{\\alpha (\\alpha + 2 \\xi)}{2}", "- \\alpha \\xi + \\sin{(\\alpha)}"], "srepr_premise_expression": "Mul(Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(2)), Symbol('\\\\xi', commutative=True))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(2)))", "Mul(Integer(-1), Symbol('\\\\xi', commutative=True), cos(Symbol('\\\\alpha', commutative=True)))", "Mul(Rational(1, 2), Symbol('\\\\alpha', commutative=True), Add(Symbol('\\\\alpha', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True), Symbol('\\\\xi', commutative=True)), sin(Symbol('\\\\alpha', commutative=True)))"]}, {"premise_expression": "- \\omega + \\sigma + \\xi", "variable": "\\omega", "positive": "\\omega (- \\frac{\\omega}{2} + \\sigma + \\xi)", "negatives": ["\\frac{\\sigma (- 2 \\omega + \\sigma + 2 \\xi)}{2}", "\\frac{\\xi (- 2 \\omega + 2 \\sigma + \\xi)}{2}", "\\frac{\\omega (\\sigma + \\xi)}{\\xi}", "\\frac{\\omega^{2}}{2 \\sigma \\xi}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\omega', commutative=True)), Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True))", "srepr_variable": "Symbol('\\\\omega', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\omega', commutative=True), Add(Mul(Integer(-1), Rational(1, 2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\sigma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True)), Symbol('\\\\sigma', commutative=True), Mul(Integer(2), Symbol('\\\\xi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\omega', commutative=True)), Mul(Integer(2), Symbol('\\\\sigma', commutative=True)), Symbol('\\\\xi', commutative=True)))", "Mul(Symbol('\\\\omega', commutative=True), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)), Add(Symbol('\\\\sigma', commutative=True), Symbol('\\\\xi', commutative=True)))", "Mul(Rational(1, 2), Pow(Symbol('\\\\omega', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), Pow(Symbol('\\\\xi', commutative=True), Integer(-1)))"]}, {"premise_expression": "\\frac{\\pi}{\\delta}", "variable": "\\delta", "positive": "\\pi \\log{(\\delta)}", "negatives": ["\\frac{\\pi^{2}}{2 \\delta}", "- \\cos{(\\delta + \\pi)}", "\\delta (\\log{(\\frac{\\delta}{\\pi})} - 1)", "\\delta (\\log{(\\delta \\pi)} - 1)"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\delta', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\pi', commutative=True), log(Symbol('\\\\delta', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\delta', commutative=True), Integer(-1)), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True))))", "Mul(Symbol('\\\\delta', commutative=True), Add(log(Mul(Symbol('\\\\delta', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))), Integer(-1)))", "Mul(Symbol('\\\\delta', commutative=True), Add(log(Mul(Symbol('\\\\delta', commutative=True), Symbol('\\\\pi', commutative=True))), Integer(-1)))"]}, {"premise_expression": "- \\gamma + \\log{(\\xi)}", "variable": "\\xi", "positive": "\\xi (- \\gamma + \\log{(\\xi)} - 1)", "negatives": ["\\frac{\\gamma (- \\gamma + 2 \\log{(\\xi)})}{2}", "\\frac{\\xi (\\xi + 2 \\cos{(\\gamma)})}{2}", "\\sin{(\\gamma + \\xi)}", "\\log{(\\xi)} \\cos{(\\gamma)}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), log(Symbol('\\\\xi', commutative=True)))", "srepr_variable": "Symbol('\\\\xi', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\xi', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), log(Symbol('\\\\xi', commutative=True)), Integer(-1)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)), Mul(Integer(2), log(Symbol('\\\\xi', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\xi', commutative=True), Add(Symbol('\\\\xi', commutative=True), Mul(Integer(2), cos(Symbol('\\\\gamma', commutative=True)))))", "sin(Add(Symbol('\\\\gamma', commutative=True), Symbol('\\\\xi', commutative=True)))", "Mul(log(Symbol('\\\\xi', commutative=True)), cos(Symbol('\\\\gamma', commutative=True)))"]}, {"premise_expression": "\\frac{\\chi}{\\sigma}", "variable": "\\chi", "positive": "\\frac{\\chi^{2}}{2 \\sigma}", "negatives": ["\\chi \\log{(\\sigma)}", "\\sigma e^{\\frac{\\chi}{\\sigma}}", "\\sigma \\log{(\\chi)}", "\\sin{(\\chi + \\sigma)}"], "srepr_premise_expression": "Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "srepr_variable": "Symbol('\\\\chi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Pow(Symbol('\\\\chi', commutative=True), Integer(2)), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))", "srepr_negatives": ["Mul(Symbol('\\\\chi', commutative=True), log(Symbol('\\\\sigma', commutative=True)))", "Mul(Symbol('\\\\sigma', commutative=True), exp(Mul(Symbol('\\\\chi', commutative=True), Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)))))", "Mul(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\chi', commutative=True)))", "sin(Add(Symbol('\\\\chi', commutative=True), Symbol('\\\\sigma', commutative=True)))"]}, {"premise_expression": "\\frac{\\sigma}{\\alpha}", "variable": "\\alpha", "positive": "\\sigma \\log{(\\alpha)}", "negatives": ["\\frac{\\sigma^{2}}{2 \\alpha}", "\\frac{\\sin{(\\alpha)}}{\\sigma}", "- \\cos{(\\alpha + \\sigma)}", "- e^{- \\alpha + \\sigma}"], "srepr_premise_expression": "Mul(Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Symbol('\\\\sigma', commutative=True))", "srepr_variable": "Symbol('\\\\alpha', commutative=True)", "srepr_positive": "Mul(Symbol('\\\\sigma', commutative=True), log(Symbol('\\\\alpha', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\alpha', commutative=True), Integer(-1)), Pow(Symbol('\\\\sigma', commutative=True), Integer(2)))", "Mul(Pow(Symbol('\\\\sigma', commutative=True), Integer(-1)), sin(Symbol('\\\\alpha', commutative=True)))", "Mul(Integer(-1), cos(Add(Symbol('\\\\alpha', commutative=True), Symbol('\\\\sigma', commutative=True))))", "Mul(Integer(-1), exp(Add(Mul(Integer(-1), Symbol('\\\\alpha', commutative=True)), Symbol('\\\\sigma', commutative=True))))"]}, {"premise_expression": "\\cos{(\\beta + \\pi)}", "variable": "\\beta", "positive": "\\sin{(\\beta + \\pi)}", "negatives": ["\\sin{(\\beta - \\pi)}", "- \\cos{(\\beta + \\pi)}", "\\frac{\\beta (- \\beta + 2 \\pi)}{2}", "\\frac{\\beta^{2}}{2 \\pi}"], "srepr_premise_expression": "cos(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_variable": "Symbol('\\\\beta', commutative=True)", "srepr_positive": "sin(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\pi', commutative=True)))", "srepr_negatives": ["sin(Add(Symbol('\\\\beta', commutative=True), Mul(Integer(-1), Symbol('\\\\pi', commutative=True))))", "Mul(Integer(-1), cos(Add(Symbol('\\\\beta', commutative=True), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\beta', commutative=True)), Mul(Integer(2), Symbol('\\\\pi', commutative=True))))", "Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Pow(Symbol('\\\\pi', commutative=True), Integer(-1)))"]}, {"premise_expression": "\\beta \\pi", "variable": "\\pi", "positive": "\\frac{\\beta \\pi^{2}}{2}", "negatives": ["\\frac{\\beta^{2} \\pi}{2}", "\\beta \\log{(\\pi)}", "\\frac{\\sin{(\\pi)}}{\\beta}", "- \\beta \\cos{(\\pi)}"], "srepr_premise_expression": "Mul(Symbol('\\\\beta', commutative=True), Symbol('\\\\pi', commutative=True))", "srepr_variable": "Symbol('\\\\pi', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\beta', commutative=True), Pow(Symbol('\\\\pi', commutative=True), Integer(2)))", "srepr_negatives": ["Mul(Rational(1, 2), Pow(Symbol('\\\\beta', commutative=True), Integer(2)), Symbol('\\\\pi', commutative=True))", "Mul(Symbol('\\\\beta', commutative=True), log(Symbol('\\\\pi', commutative=True)))", "Mul(Pow(Symbol('\\\\beta', commutative=True), Integer(-1)), sin(Symbol('\\\\pi', commutative=True)))", "Mul(Integer(-1), Symbol('\\\\beta', commutative=True), cos(Symbol('\\\\pi', commutative=True)))"]}, {"premise_expression": "- \\delta + \\gamma", "variable": "\\gamma", "positive": "\\frac{\\gamma (- 2 \\delta + \\gamma)}{2}", "negatives": ["\\frac{\\gamma (2 \\delta - \\gamma)}{2}", "\\frac{\\delta (- \\delta + 2 \\gamma)}{2}", "- \\sin{(\\delta - \\gamma)}", "\\frac{\\gamma (\\gamma + 2 \\sin{(\\delta)})}{2}"], "srepr_premise_expression": "Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Symbol('\\\\gamma', commutative=True))", "srepr_variable": "Symbol('\\\\gamma', commutative=True)", "srepr_positive": "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(-1), Integer(2), Symbol('\\\\delta', commutative=True)), Symbol('\\\\gamma', commutative=True)))", "srepr_negatives": ["Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Mul(Integer(2), Symbol('\\\\delta', commutative=True)), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True))))", "Mul(Rational(1, 2), Symbol('\\\\delta', commutative=True), Add(Mul(Integer(-1), Symbol('\\\\delta', commutative=True)), Mul(Integer(2), Symbol('\\\\gamma', commutative=True))))", "Mul(Integer(-1), sin(Add(Symbol('\\\\delta', commutative=True), Mul(Integer(-1), Symbol('\\\\gamma', commutative=True)))))", "Mul(Rational(1, 2), Symbol('\\\\gamma', commutative=True), Add(Symbol('\\\\gamma', commutative=True), Mul(Integer(2), sin(Symbol('\\\\delta', commutative=True)))))"]}]