TSTP Solution File: GRP594-1 by Toma---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Toma---0.4
% Problem : GRP594-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 01:15:27 EDT 2023
% Result : Unsatisfiable 57.42s 57.65s
% Output : CNFRefutation 57.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : GRP594-1 : TPTP v8.1.2. Released v2.6.0.
% 0.11/0.13 % Command : toma --casc %s
% 0.12/0.34 % Computer : n017.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 19:49:43 EDT 2023
% 0.12/0.35 % CPUTime :
% 57.42/57.65 % SZS status Unsatisfiable
% 57.42/57.65 % SZS output start Proof
% 57.42/57.65 original problem:
% 57.42/57.65 axioms:
% 57.42/57.65 inverse(double_divide(double_divide(A, B), inverse(double_divide(A, inverse(double_divide(C, B)))))) = C
% 57.42/57.65 multiply(A, B) = inverse(double_divide(B, A))
% 57.42/57.65 goal:
% 57.42/57.65 multiply(multiply(inverse(b2()), b2()), a2()) != a2()
% 57.42/57.65 To show the unsatisfiability of the original goal,
% 57.42/57.65 it suffices to show that multiply(multiply(inverse(b2()), b2()), a2()) = a2() (skolemized goal) is valid under the axioms.
% 57.42/57.65 Here is an equational proof:
% 57.42/57.65 0: inverse(double_divide(double_divide(X0, X1), inverse(double_divide(X0, inverse(double_divide(X2, X1)))))) = X2.
% 57.42/57.65 Proof: Axiom.
% 57.42/57.65
% 57.42/57.65 1: multiply(X0, X1) = inverse(double_divide(X1, X0)).
% 57.42/57.65 Proof: Axiom.
% 57.42/57.65
% 57.42/57.65 2: X3 = inverse(double_divide(double_divide(double_divide(X3, X4), inverse(double_divide(X5, X4))), X5)).
% 57.42/57.65 Proof: A critical pair between equations 0 and 0.
% 57.42/57.65
% 57.42/57.65 3: double_divide(X3, X4) = inverse(double_divide(double_divide(X0, inverse(double_divide(X3, inverse(double_divide(X5, X4))))), inverse(double_divide(X0, X5)))).
% 57.42/57.65 Proof: A critical pair between equations 0 and 0.
% 57.42/57.65
% 57.42/57.65 4: double_divide(inverse(double_divide(double_divide(X6, inverse(double_divide(X5, X4))), X5)), X4) = X6.
% 57.42/57.65 Proof: A critical pair between equations 3 and 2.
% 57.42/57.65
% 57.42/57.65 6: double_divide(double_divide(X6, X7), inverse(double_divide(X8, X7))) = inverse(double_divide(double_divide(X0, X8), inverse(double_divide(X0, X6)))).
% 57.42/57.65 Proof: A critical pair between equations 3 and 0.
% 57.42/57.65
% 57.42/57.65 8: X2 = inverse(double_divide(double_divide(double_divide(double_divide(X6, X7), inverse(double_divide(inverse(double_divide(X2, X1)), X7))), X1), X6)).
% 57.42/57.65 Proof: A critical pair between equations 0 and 2.
% 57.42/57.65
% 57.42/57.65 14: double_divide(X3, X4) = inverse(double_divide(double_divide(double_divide(X6, X7), inverse(double_divide(X3, inverse(double_divide(inverse(double_divide(X6, inverse(double_divide(X8, X7)))), X4))))), X8)).
% 57.42/57.65 Proof: A critical pair between equations 3 and 0.
% 57.42/57.65
% 57.42/57.65 15: double_divide(X3, inverse(double_divide(X6, inverse(double_divide(X8, X7))))) = inverse(double_divide(double_divide(X0, inverse(double_divide(X3, X8))), inverse(double_divide(X0, double_divide(X6, X7))))).
% 57.42/57.65 Proof: A critical pair between equations 3 and 0.
% 57.42/57.65
% 57.42/57.65 16: double_divide(X3, X4) = multiply(X8, double_divide(double_divide(X6, X7), multiply(multiply(X4, multiply(multiply(X7, X8), X6)), X3))).
% 57.42/57.65 Proof: Rewrite equation 14,
% 57.42/57.65 lhs with equations []
% 57.42/57.65 rhs with equations [1,1,1,1,1].
% 57.42/57.65
% 57.42/57.65 20: X2 = multiply(X6, double_divide(double_divide(double_divide(X6, X7), multiply(X7, multiply(X1, X2))), X1)).
% 57.42/57.65 Proof: Rewrite equation 8,
% 57.42/57.65 lhs with equations []
% 57.42/57.65 rhs with equations [1,1,1].
% 57.42/57.65
% 57.42/57.65 23: double_divide(multiply(X5, double_divide(X6, multiply(X4, X5))), X4) = X6.
% 57.42/57.65 Proof: Rewrite equation 4,
% 57.42/57.65 lhs with equations [1,1]
% 57.42/57.65 rhs with equations [].
% 57.42/57.65
% 57.42/57.65 24: multiply(multiply(multiply(X1, X2), X0), double_divide(X0, X1)) = X2.
% 57.42/57.65 Proof: Rewrite equation 0,
% 57.42/57.65 lhs with equations [1,1,1]
% 57.42/57.65 rhs with equations [].
% 57.42/57.65
% 57.42/57.65 25: X3 = multiply(X5, double_divide(double_divide(X3, X4), multiply(X4, X5))).
% 57.42/57.65 Proof: Rewrite equation 2,
% 57.42/57.65 lhs with equations []
% 57.42/57.65 rhs with equations [1,1].
% 57.42/57.65
% 57.42/57.65 26: double_divide(X3, X4) = multiply(multiply(X5, X0), double_divide(X0, multiply(multiply(X4, X5), X3))).
% 57.42/57.65 Proof: Rewrite equation 3,
% 57.42/57.65 lhs with equations []
% 57.42/57.65 rhs with equations [1,1,1,1].
% 57.42/57.65
% 57.42/57.65 27: double_divide(X3, multiply(multiply(X7, X8), X6)) = multiply(multiply(double_divide(X6, X7), X0), double_divide(X0, multiply(X8, X3))).
% 57.42/57.65 Proof: Rewrite equation 15,
% 57.42/57.65 lhs with equations [1,1]
% 57.42/57.65 rhs with equations [1,1,1].
% 57.42/57.65
% 57.42/57.65 30: double_divide(double_divide(X6, X7), multiply(X7, X8)) = multiply(multiply(X6, X0), double_divide(X0, X8)).
% 57.42/57.65 Proof: Rewrite equation 6,
% 57.42/57.65 lhs with equations [1]
% 57.42/57.65 rhs with equations [1,1].
% 57.42/57.65
% 57.42/57.65 31: double_divide(double_divide(multiply(X9, X10), X7), multiply(X7, X9)) = X10.
% 57.42/57.65 Proof: A critical pair between equations 30 and 24.
% 57.42/57.65
% 57.42/57.65 32: X9 = multiply(X11, multiply(multiply(X9, X12), double_divide(X12, X11))).
% 57.42/57.65 Proof: A critical pair between equations 25 and 30.
% 57.42/57.65
% 57.42/57.65 35: double_divide(X13, X4) = double_divide(X13, multiply(multiply(X10, multiply(X4, double_divide(X9, X10))), X9)).
% 57.42/57.65 Proof: A critical pair between equations 26 and 27.
% 57.42/57.65
% 57.42/57.65 36: double_divide(X3, X4) = double_divide(double_divide(X9, X12), multiply(X12, multiply(multiply(X4, X9), X3))).
% 57.42/57.65 Proof: A critical pair between equations 26 and 30.
% 57.42/57.65
% 57.42/57.65 38: X2 = multiply(X9, double_divide(multiply(multiply(X9, X12), double_divide(X12, multiply(X1, X2))), X1)).
% 57.42/57.65 Proof: A critical pair between equations 20 and 30.
% 57.42/57.65
% 57.42/57.65 46: X2 = inverse(double_divide(double_divide(inverse(double_divide(double_divide(X12, inverse(double_divide(X2, X1))), inverse(double_divide(X12, X9)))), X1), X9)).
% 57.42/57.65 Proof: Rewrite equation 38,
% 57.42/57.65 lhs with equations []
% 57.42/57.65 rhs with equations [1,1,1,1].
% 57.42/57.65
% 57.42/57.65 48: double_divide(X3, X4) = double_divide(double_divide(X9, X12), inverse(double_divide(inverse(double_divide(X3, inverse(double_divide(X9, X4)))), X12))).
% 57.42/57.65 Proof: Rewrite equation 36,
% 57.42/57.65 lhs with equations []
% 57.42/57.65 rhs with equations [1,1,1].
% 57.42/57.65
% 57.42/57.65 49: double_divide(X13, X4) = double_divide(X13, inverse(double_divide(X9, inverse(double_divide(inverse(double_divide(double_divide(X9, X10), X4)), X10))))).
% 57.42/57.65 Proof: Rewrite equation 35,
% 57.42/57.65 lhs with equations []
% 57.42/57.65 rhs with equations [1,1,1].
% 57.42/57.65
% 57.42/57.65 52: X9 = inverse(double_divide(inverse(double_divide(double_divide(X12, X11), inverse(double_divide(X12, X9)))), X11)).
% 57.42/57.65 Proof: Rewrite equation 32,
% 57.42/57.65 lhs with equations []
% 57.42/57.65 rhs with equations [1,1,1].
% 57.42/57.65
% 57.42/57.65 53: double_divide(double_divide(inverse(double_divide(X10, X9)), X7), inverse(double_divide(X9, X7))) = X10.
% 57.42/57.65 Proof: Rewrite equation 31,
% 57.42/57.65 lhs with equations [1,1]
% 57.42/57.65 rhs with equations [].
% 57.42/57.65
% 57.42/57.65 54: X3 = inverse(double_divide(double_divide(double_divide(X3, X4), inverse(double_divide(X5, X4))), X5)).
% 57.42/57.65 Proof: Rewrite equation 25,
% 57.42/57.65 lhs with equations []
% 57.42/57.65 rhs with equations [1,1].
% 57.42/57.65
% 57.42/57.65 55: inverse(double_divide(double_divide(X0, X1), inverse(double_divide(X0, inverse(double_divide(X2, X1)))))) = X2.
% 57.42/57.65 Proof: Rewrite equation 24,
% 57.42/57.65 lhs with equations [1,1,1]
% 57.42/57.65 rhs with equations [].
% 57.42/57.65
% 57.42/57.65 56: double_divide(inverse(double_divide(double_divide(X6, inverse(double_divide(X5, X4))), X5)), X4) = X6.
% 57.42/57.65 Proof: Rewrite equation 23,
% 57.42/57.65 lhs with equations [1,1]
% 57.42/57.65 rhs with equations [].
% 57.42/57.65
% 57.42/57.65 64: double_divide(X3, X4) = inverse(double_divide(double_divide(double_divide(X6, X7), inverse(double_divide(X3, inverse(double_divide(inverse(double_divide(X6, inverse(double_divide(X8, X7)))), X4))))), X8)).
% 57.42/57.65 Proof: Rewrite equation 16,
% 57.42/57.65 lhs with equations []
% 57.42/57.65 rhs with equations [1,1,1,1,1].
% 57.42/57.65
% 57.42/57.65 71: X9 = inverse(double_divide(X13, inverse(double_divide(inverse(double_divide(double_divide(X13, X14), X9)), X14)))).
% 57.42/57.65 Proof: A critical pair between equations 52 and 54.
% 57.42/57.65
% 57.42/57.65 72: X12 = inverse(double_divide(double_divide(double_divide(inverse(double_divide(X11, X12)), X13), X13), inverse(X11))).
% 57.42/57.65 Proof: A critical pair between equations 55 and 53.
% 57.42/57.65
% 57.42/57.65 75: double_divide(X13, inverse(double_divide(X14, X17))) = double_divide(X13, inverse(double_divide(double_divide(double_divide(X14, X15), X15), X17))).
% 57.42/57.65 Proof: A critical pair between equations 49 and 48.
% 57.42/57.65
% 57.42/57.65 78: double_divide(double_divide(X13, X14), X14) = inverse(double_divide(double_divide(double_divide(X15, X16), inverse(double_divide(X15, X16))), X13)).
% 57.42/57.65 Proof: A critical pair between equations 64 and 48.
% 57.42/57.65
% 57.42/57.65 87: double_divide(X13, multiply(X17, X14)) = double_divide(X13, multiply(X17, double_divide(double_divide(X14, X15), X15))).
% 57.42/57.65 Proof: Rewrite equation 75,
% 57.42/57.65 lhs with equations [1]
% 57.42/57.65 rhs with equations [1].
% 57.42/57.65
% 57.42/57.65 89: X12 = multiply(inverse(X11), double_divide(double_divide(multiply(X12, X11), X13), X13)).
% 57.42/57.65 Proof: Rewrite equation 72,
% 57.42/57.65 lhs with equations []
% 57.42/57.65 rhs with equations [1,1].
% 57.42/57.65
% 57.42/57.65 90: X9 = multiply(multiply(X14, multiply(X9, double_divide(X13, X14))), X13).
% 57.42/57.65 Proof: Rewrite equation 71,
% 57.42/57.65 lhs with equations []
% 57.42/57.65 rhs with equations [1,1,1].
% 57.42/57.65
% 57.42/57.65 102: double_divide(multiply(X5, double_divide(X6, multiply(X4, X5))), X4) = X6.
% 57.42/57.65 Proof: Rewrite equation 56,
% 57.42/57.65 lhs with equations [1,1]
% 57.42/57.65 rhs with equations [].
% 57.42/57.65
% 57.42/57.65 104: X3 = multiply(X5, double_divide(double_divide(X3, X4), multiply(X4, X5))).
% 57.42/57.65 Proof: Rewrite equation 54,
% 57.42/57.65 lhs with equations []
% 57.42/57.65 rhs with equations [1,1].
% 57.42/57.65
% 57.42/57.65 105: double_divide(double_divide(multiply(X9, X10), X7), multiply(X7, X9)) = X10.
% 57.42/57.65 Proof: Rewrite equation 53,
% 57.42/57.65 lhs with equations [1,1]
% 57.42/57.65 rhs with equations [].
% 57.42/57.65
% 57.42/57.65 110: X2 = multiply(X9, double_divide(multiply(multiply(X9, X12), double_divide(X12, multiply(X1, X2))), X1)).
% 57.42/57.65 Proof: Rewrite equation 46,
% 57.42/57.65 lhs with equations []
% 57.42/57.65 rhs with equations [1,1,1,1].
% 57.42/57.65
% 57.42/57.65 113: double_divide(double_divide(X13, X14), X14) = multiply(X13, double_divide(double_divide(X15, X16), multiply(X16, X15))).
% 57.42/57.65 Proof: Rewrite equation 78,
% 57.42/57.65 lhs with equations []
% 57.42/57.65 rhs with equations [1,1].
% 57.42/57.65
% 57.42/57.65 118: double_divide(double_divide(X17, X14), X14) = X17.
% 57.42/57.65 Proof: A critical pair between equations 113 and 104.
% 57.42/57.65
% 57.42/57.65 121: double_divide(X13, multiply(inverse(X18), multiply(X19, X18))) = double_divide(X13, X19).
% 57.42/57.65 Proof: A critical pair between equations 87 and 89.
% 57.42/57.65
% 57.42/57.65 125: double_divide(multiply(X15, X14), multiply(X4, inverse(X14))) = double_divide(X15, X4).
% 57.42/57.65 Proof: A critical pair between equations 102 and 89.
% 57.42/57.65
% 57.42/57.65 134: double_divide(inverse(double_divide(X14, X15)), inverse(double_divide(inverse(X14), X4))) = double_divide(X15, X4).
% 57.42/57.65 Proof: Rewrite equation 125,
% 57.42/57.65 lhs with equations [1,1]
% 57.42/57.65 rhs with equations [].
% 57.42/57.65
% 57.42/57.65 137: double_divide(X13, inverse(double_divide(inverse(double_divide(X18, X19)), inverse(X18)))) = double_divide(X13, X19).
% 57.42/57.65 Proof: Rewrite equation 121,
% 57.42/57.65 lhs with equations [1,1]
% 57.42/57.65 rhs with equations [].
% 57.42/57.65
% 57.42/57.65 140: X2 = inverse(double_divide(double_divide(inverse(double_divide(double_divide(X12, inverse(double_divide(X2, X1))), inverse(double_divide(X12, X9)))), X1), X9)).
% 57.42/57.65 Proof: Rewrite equation 110,
% 57.42/57.65 lhs with equations []
% 57.42/57.65 rhs with equations [1,1,1,1].
% 57.42/57.65
% 57.42/57.65 145: double_divide(double_divide(inverse(double_divide(X10, X9)), X7), inverse(double_divide(X9, X7))) = X10.
% 57.42/57.65 Proof: Rewrite equation 105,
% 57.42/57.65 lhs with equations [1,1]
% 57.42/57.65 rhs with equations [].
% 57.42/57.65
% 57.42/57.65 157: X9 = inverse(double_divide(X13, inverse(double_divide(inverse(double_divide(double_divide(X13, X14), X9)), X14)))).
% 57.42/57.65 Proof: Rewrite equation 90,
% 57.42/57.65 lhs with equations []
% 57.42/57.65 rhs with equations [1,1,1].
% 57.42/57.65
% 57.42/57.65 158: X12 = inverse(double_divide(inverse(double_divide(X11, X12)), inverse(X11))).
% 57.42/57.65 Proof: Rewrite equation 89,
% 57.42/57.65 lhs with equations []
% 57.42/57.65 rhs with equations [1,118,1].
% 57.42/57.65
% 57.42/57.65 168: X13 = inverse(double_divide(double_divide(double_divide(X15, X16), inverse(double_divide(X15, X16))), X13)).
% 57.42/57.65 Proof: Rewrite equation 113,
% 57.42/57.65 lhs with equations [118]
% 57.42/57.65 rhs with equations [1,1].
% 57.42/57.65
% 57.42/57.65 171: X2 = inverse(double_divide(double_divide(inverse(X2), X1), X1)).
% 57.42/57.65 Proof: A critical pair between equations 140 and 118.
% 57.42/57.65
% 57.42/57.65 174: X19 = inverse(double_divide(X18, inverse(double_divide(inverse(X18), X19)))).
% 57.42/57.65 Proof: A critical pair between equations 157 and 118.
% 57.42/57.65
% 57.42/57.65 179: double_divide(X15, inverse(X21)) = double_divide(inverse(double_divide(double_divide(X21, X22), X15)), X22).
% 57.42/57.65 Proof: A critical pair between equations 134 and 137.
% 57.42/57.65
% 57.42/57.65 182: double_divide(inverse(double_divide(X18, X19)), X20) = double_divide(X18, inverse(double_divide(X19, X20))).
% 57.42/57.65 Proof: A critical pair between equations 118 and 145.
% 57.42/57.65
% 57.42/57.65 183: double_divide(multiply(X19, X18), X20) = double_divide(X18, multiply(X20, X19)).
% 57.42/57.65 Proof: Rewrite equation 182,
% 57.42/57.65 lhs with equations [1]
% 57.42/57.65 rhs with equations [1].
% 57.42/57.65
% 57.42/57.65 186: double_divide(X15, inverse(X21)) = double_divide(double_divide(X21, X22), multiply(X22, X15)).
% 57.42/57.65 Proof: Rewrite equation 179,
% 57.42/57.65 lhs with equations []
% 57.42/57.65 rhs with equations [1,183].
% 57.42/57.65
% 57.42/57.65 191: X19 = multiply(multiply(X19, inverse(X18)), X18).
% 57.42/57.65 Proof: Rewrite equation 174,
% 57.42/57.65 lhs with equations []
% 57.42/57.65 rhs with equations [1,1].
% 57.42/57.65
% 57.42/57.65 193: X2 = inverse(inverse(X2)).
% 57.42/57.65 Proof: Rewrite equation 171,
% 57.42/57.65 lhs with equations []
% 57.42/57.65 rhs with equations [118].
% 57.42/57.65
% 57.42/57.65 195: X13 = multiply(X13, double_divide(X15, inverse(X15))).
% 57.42/57.65 Proof: Rewrite equation 168,
% 57.42/57.65 lhs with equations []
% 57.42/57.65 rhs with equations [1,186,1].
% 57.42/57.65
% 57.42/57.65 199: X12 = multiply(multiply(inverse(X11), X12), X11).
% 57.42/57.65 Proof: Rewrite equation 158,
% 57.42/57.65 lhs with equations []
% 57.42/57.65 rhs with equations [1,183,1].
% 57.42/57.65
% 57.42/57.65 224: double_divide(X3, X4) = inverse(multiply(X4, X3)).
% 57.42/57.65 Proof: A critical pair between equations 193 and 1.
% 57.42/57.65
% 57.42/57.65 225: X13 = multiply(X13, double_divide(inverse(X16), X16)).
% 57.42/57.65 Proof: A critical pair between equations 195 and 193.
% 57.42/57.65
% 57.42/57.65 227: X12 = multiply(multiply(X13, X12), inverse(X13)).
% 57.42/57.65 Proof: A critical pair between equations 199 and 193.
% 57.42/57.65
% 57.42/57.65 236: X13 = multiply(X13, inverse(multiply(X16, inverse(X16)))).
% 57.42/57.65 Proof: Rewrite equation 225,
% 57.42/57.65 lhs with equations []
% 57.42/57.65 rhs with equations [224].
% 57.42/57.65
% 57.42/57.65 270: multiply(X20, X21) = multiply(X21, X20).
% 57.42/57.65 Proof: A critical pair between equations 191 and 227.
% 57.42/57.65
% 57.42/57.65 271: X12 = multiply(multiply(X18, inverse(X18)), X12).
% 57.42/57.65 Proof: A critical pair between equations 227 and 236.
% 57.42/57.65
% 57.42/57.65 298: multiply(multiply(inverse(b2()), b2()), a2()) = a2().
% 57.42/57.65 Proof: Rewrite lhs with equations [270,271]
% 57.42/57.65 rhs with equations [].
% 57.42/57.65
% 57.42/57.65 % SZS output end Proof
%------------------------------------------------------------------------------