TSTP Solution File: GRP588-1 by Toma---0.4
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%------------------------------------------------------------------------------
% File : Toma---0.4
% Problem : GRP588-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n016.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 01:15:26 EDT 2023
% Result : Unsatisfiable 31.48s 31.89s
% Output : CNFRefutation 31.48s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.15 % Problem : GRP588-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.14/0.16 % Command : toma --casc %s
% 0.15/0.37 % Computer : n016.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Mon Aug 28 23:53:00 EDT 2023
% 0.15/0.38 % CPUTime :
% 31.48/31.89 % SZS status Unsatisfiable
% 31.48/31.89 % SZS output start Proof
% 31.48/31.89 original problem:
% 31.48/31.89 axioms:
% 31.48/31.89 double_divide(A, inverse(double_divide(inverse(double_divide(double_divide(A, B), inverse(C))), B))) = C
% 31.48/31.89 multiply(A, B) = inverse(double_divide(B, A))
% 31.48/31.89 goal:
% 31.48/31.89 multiply(a(), b()) != multiply(b(), a())
% 31.48/31.89 To show the unsatisfiability of the original goal,
% 31.48/31.89 it suffices to show that multiply(a(), b()) = multiply(b(), a()) (skolemized goal) is valid under the axioms.
% 31.48/31.89 Here is an equational proof:
% 31.48/31.89 0: double_divide(X0, inverse(double_divide(inverse(double_divide(double_divide(X0, X1), inverse(X2))), X1))) = X2.
% 31.48/31.89 Proof: Axiom.
% 31.48/31.89
% 31.48/31.89 1: multiply(X0, X1) = inverse(double_divide(X1, X0)).
% 31.48/31.89 Proof: Axiom.
% 31.48/31.89
% 31.48/31.89 2: double_divide(inverse(double_divide(double_divide(double_divide(X0, X1), X4), inverse(X5))), X4) = double_divide(X0, inverse(double_divide(inverse(X5), X1))).
% 31.48/31.89 Proof: A critical pair between equations 0 and 0.
% 31.48/31.89
% 31.48/31.89 3: X2 = double_divide(X3, inverse(double_divide(inverse(double_divide(X5, inverse(X2))), inverse(double_divide(inverse(double_divide(double_divide(X3, X4), inverse(X5))), X4))))).
% 31.48/31.89 Proof: A critical pair between equations 0 and 0.
% 31.48/31.89
% 31.48/31.89 4: X2 = double_divide(inverse(double_divide(X8, inverse(X2))), inverse(X8)).
% 31.48/31.89 Proof: A critical pair between equations 3 and 0.
% 31.48/31.89
% 31.48/31.89 5: X9 = double_divide(double_divide(X6, X7), inverse(double_divide(X6, inverse(double_divide(inverse(X9), X7))))).
% 31.48/31.89 Proof: A critical pair between equations 0 and 2.
% 31.48/31.89
% 31.48/31.89 21: X9 = double_divide(double_divide(X6, X7), multiply(multiply(X7, inverse(X9)), X6)).
% 31.48/31.89 Proof: Rewrite equation 5,
% 31.48/31.89 lhs with equations []
% 31.48/31.89 rhs with equations [1,1].
% 31.48/31.89
% 31.48/31.89 22: X2 = double_divide(multiply(inverse(X2), X8), inverse(X8)).
% 31.48/31.89 Proof: Rewrite equation 4,
% 31.48/31.89 lhs with equations []
% 31.48/31.89 rhs with equations [1].
% 31.48/31.89
% 31.48/31.89 23: double_divide(X0, multiply(X1, multiply(inverse(X2), double_divide(X0, X1)))) = X2.
% 31.48/31.89 Proof: Rewrite equation 0,
% 31.48/31.89 lhs with equations [1,1]
% 31.48/31.89 rhs with equations [].
% 31.48/31.89
% 31.48/31.89 25: X2 = double_divide(X3, multiply(multiply(X4, multiply(inverse(X5), double_divide(X3, X4))), multiply(inverse(X2), X5))).
% 31.48/31.89 Proof: Rewrite equation 3,
% 31.48/31.89 lhs with equations []
% 31.48/31.89 rhs with equations [1,1,1,1].
% 31.48/31.89
% 31.48/31.89 31: multiply(inverse(X10), multiply(inverse(X9), X10)) = inverse(X9).
% 31.48/31.89 Proof: A critical pair between equations 1 and 22.
% 31.48/31.89
% 31.48/31.89 35: multiply(multiply(X4, multiply(inverse(X5), double_divide(X3, X4))), X3) = inverse(X5).
% 31.48/31.89 Proof: A critical pair between equations 1 and 23.
% 31.48/31.89
% 31.48/31.89 36: X9 = double_divide(X10, multiply(multiply(inverse(X11), inverse(X9)), multiply(inverse(X10), X11))).
% 31.48/31.89 Proof: A critical pair between equations 21 and 22.
% 31.48/31.89
% 31.48/31.89 37: X2 = double_divide(multiply(inverse(X9), X10), multiply(inverse(X10), multiply(inverse(X2), X9))).
% 31.48/31.89 Proof: A critical pair between equations 23 and 22.
% 31.48/31.89
% 31.48/31.89 41: X9 = double_divide(X12, multiply(multiply(multiply(X11, multiply(inverse(X12), double_divide(X10, X11))), inverse(X9)), X10)).
% 31.48/31.89 Proof: A critical pair between equations 21 and 23.
% 31.48/31.89
% 31.48/31.89 44: X9 = double_divide(X12, inverse(double_divide(X10, inverse(double_divide(inverse(X9), inverse(double_divide(inverse(double_divide(double_divide(X10, X11), inverse(X12))), X11))))))).
% 31.48/31.89 Proof: Rewrite equation 41,
% 31.48/31.89 lhs with equations []
% 31.48/31.89 rhs with equations [1,1,1,1].
% 31.48/31.89
% 31.48/31.89 48: X2 = double_divide(inverse(double_divide(X10, inverse(X9))), inverse(double_divide(inverse(double_divide(X9, inverse(X2))), inverse(X10)))).
% 31.48/31.89 Proof: Rewrite equation 37,
% 31.48/31.89 lhs with equations []
% 31.48/31.89 rhs with equations [1,1,1].
% 31.48/31.89
% 31.48/31.89 49: X9 = double_divide(X10, inverse(double_divide(inverse(double_divide(X11, inverse(X10))), inverse(double_divide(inverse(X9), inverse(X11)))))).
% 31.48/31.89 Proof: Rewrite equation 36,
% 31.48/31.89 lhs with equations []
% 31.48/31.89 rhs with equations [1,1,1].
% 31.48/31.89
% 31.48/31.89 50: inverse(double_divide(X3, inverse(double_divide(inverse(double_divide(double_divide(X3, X4), inverse(X5))), X4)))) = inverse(X5).
% 31.48/31.89 Proof: Rewrite equation 35,
% 31.48/31.89 lhs with equations [1,1,1]
% 31.48/31.89 rhs with equations [].
% 31.48/31.89
% 31.48/31.89 54: inverse(double_divide(inverse(double_divide(X10, inverse(X9))), inverse(X10))) = inverse(X9).
% 31.48/31.89 Proof: Rewrite equation 31,
% 31.48/31.89 lhs with equations [1,1]
% 31.48/31.89 rhs with equations [].
% 31.48/31.89
% 31.48/31.89 55: X2 = double_divide(X3, inverse(double_divide(inverse(double_divide(X5, inverse(X2))), inverse(double_divide(inverse(double_divide(double_divide(X3, X4), inverse(X5))), X4))))).
% 31.48/31.89 Proof: Rewrite equation 25,
% 31.48/31.89 lhs with equations []
% 31.48/31.89 rhs with equations [1,1,1,1].
% 31.48/31.89
% 31.48/31.89 57: X2 = double_divide(inverse(double_divide(X8, inverse(X2))), inverse(X8)).
% 31.48/31.89 Proof: Rewrite equation 22,
% 31.48/31.89 lhs with equations []
% 31.48/31.89 rhs with equations [1].
% 31.48/31.89
% 31.48/31.89 70: double_divide(double_divide(X14, inverse(X13)), inverse(X13)) = X14.
% 31.48/31.89 Proof: A critical pair between equations 49 and 55.
% 31.48/31.89
% 31.48/31.89 71: X9 = double_divide(X15, inverse(double_divide(inverse(X9), inverse(X15)))).
% 31.48/31.89 Proof: A critical pair between equations 44 and 50.
% 31.48/31.89
% 31.48/31.89 74: inverse(double_divide(double_divide(inverse(X14), inverse(X13)), inverse(X13))) = X14.
% 31.48/31.89 Proof: A critical pair between equations 48 and 49.
% 31.48/31.89
% 31.48/31.89 75: inverse(X11) = inverse(double_divide(inverse(X12), inverse(inverse(double_divide(X11, inverse(X12)))))).
% 31.48/31.89 Proof: A critical pair between equations 54 and 54.
% 31.48/31.89
% 31.48/31.89 88: inverse(X11) = multiply(inverse(multiply(inverse(X12), X11)), inverse(X12)).
% 31.48/31.89 Proof: Rewrite equation 75,
% 31.48/31.89 lhs with equations []
% 31.48/31.89 rhs with equations [1,1].
% 31.48/31.89
% 31.48/31.89 89: inverse(inverse(X14)) = X14.
% 31.48/31.89 Proof: Rewrite equation 74,
% 31.48/31.89 lhs with equations [70]
% 31.48/31.89 rhs with equations [].
% 31.48/31.89
% 31.48/31.89 92: X9 = double_divide(X15, multiply(inverse(X15), inverse(X9))).
% 31.48/31.89 Proof: Rewrite equation 71,
% 31.48/31.89 lhs with equations []
% 31.48/31.89 rhs with equations [1].
% 31.48/31.89
% 31.48/31.89 100: X2 = double_divide(multiply(inverse(X2), X8), inverse(X8)).
% 31.48/31.89 Proof: Rewrite equation 57,
% 31.48/31.89 lhs with equations []
% 31.48/31.89 rhs with equations [1].
% 31.48/31.89
% 31.48/31.89 117: double_divide(X15, X16) = inverse(multiply(X16, X15)).
% 31.48/31.89 Proof: A critical pair between equations 89 and 1.
% 31.48/31.89
% 31.48/31.89 122: X9 = double_divide(inverse(X16), multiply(X16, inverse(X9))).
% 31.48/31.89 Proof: A critical pair between equations 92 and 89.
% 31.48/31.89
% 31.48/31.89 126: multiply(inverse(X15), X16) = double_divide(X15, inverse(X16)).
% 31.48/31.89 Proof: A critical pair between equations 70 and 100.
% 31.48/31.89
% 31.48/31.89 128: inverse(X15) = double_divide(multiply(X15, X8), inverse(X8)).
% 31.48/31.89 Proof: A critical pair between equations 100 and 89.
% 31.48/31.89
% 31.48/31.89 129: inverse(X15) = multiply(inverse(multiply(X15, X8)), X8).
% 31.48/31.89 Proof: Rewrite equation 128,
% 31.48/31.89 lhs with equations []
% 31.48/31.89 rhs with equations [126].
% 31.48/31.89
% 31.48/31.89 131: multiply(inverse(X15), X16) = inverse(multiply(inverse(X16), X15)).
% 31.48/31.89 Proof: Rewrite equation 126,
% 31.48/31.89 lhs with equations []
% 31.48/31.89 rhs with equations [117].
% 31.48/31.89
% 31.48/31.89 133: X9 = inverse(multiply(multiply(X16, inverse(X9)), inverse(X16))).
% 31.48/31.89 Proof: Rewrite equation 122,
% 31.48/31.89 lhs with equations []
% 31.48/31.89 rhs with equations [117].
% 31.48/31.89
% 31.48/31.89 153: inverse(X11) = inverse(multiply(X12, multiply(inverse(X12), X11))).
% 31.48/31.89 Proof: Rewrite equation 88,
% 31.48/31.89 lhs with equations []
% 31.48/31.89 rhs with equations [131,89].
% 31.48/31.89
% 31.48/31.89 168: multiply(inverse(X18), multiply(X17, X18)) = inverse(inverse(X17)).
% 31.48/31.89 Proof: A critical pair between equations 131 and 129.
% 31.48/31.89
% 31.48/31.89 170: multiply(inverse(X15), inverse(X17)) = inverse(multiply(X17, X15)).
% 31.48/31.89 Proof: A critical pair between equations 131 and 89.
% 31.48/31.89
% 31.48/31.89 171: inverse(multiply(inverse(X16), inverse(X17))) = multiply(X17, X16).
% 31.48/31.89 Proof: A critical pair between equations 131 and 89.
% 31.48/31.89
% 31.48/31.89 174: inverse(multiply(X17, inverse(X18))) = multiply(X18, inverse(X17)).
% 31.48/31.89 Proof: A critical pair between equations 129 and 133.
% 31.48/31.89
% 31.48/31.89 176: multiply(inverse(X18), multiply(X17, X18)) = X17.
% 31.48/31.89 Proof: Rewrite equation 168,
% 31.48/31.89 lhs with equations []
% 31.48/31.89 rhs with equations [89].
% 31.48/31.89
% 31.48/31.89 184: inverse(X11) = double_divide(multiply(inverse(X12), X11), X12).
% 31.48/31.89 Proof: Rewrite equation 153,
% 31.48/31.89 lhs with equations []
% 31.48/31.89 rhs with equations [117].
% 31.48/31.89
% 31.48/31.89 201: inverse(X15) = double_divide(inverse(double_divide(X8, X15)), inverse(X8)).
% 31.48/31.89 Proof: Rewrite equation 129,
% 31.48/31.89 lhs with equations []
% 31.48/31.89 rhs with equations [117,171,117].
% 31.48/31.89
% 31.48/31.89 202: double_divide(inverse(X18), X17) = multiply(X18, inverse(X17)).
% 31.48/31.89 Proof: Rewrite equation 174,
% 31.48/31.89 lhs with equations [117]
% 31.48/31.89 rhs with equations [].
% 31.48/31.89
% 31.48/31.89 203: inverse(double_divide(X16, X17)) = multiply(X17, X16).
% 31.48/31.89 Proof: Rewrite equation 171,
% 31.48/31.89 lhs with equations [202,89]
% 31.48/31.89 rhs with equations [].
% 31.48/31.89
% 31.48/31.89 204: inverse(double_divide(inverse(X17), inverse(X15))) = double_divide(X15, X17).
% 31.48/31.89 Proof: Rewrite equation 170,
% 31.48/31.89 lhs with equations [203]
% 31.48/31.89 rhs with equations [203,89].
% 31.48/31.89
% 31.48/31.89 216: inverse(multiply(X20, X19)) = double_divide(X20, X19).
% 31.48/31.89 Proof: A critical pair between equations 184 and 176.
% 31.48/31.89
% 31.48/31.89 218: double_divide(X18, double_divide(X18, X19)) = inverse(inverse(X19)).
% 31.48/31.89 Proof: A critical pair between equations 204 and 201.
% 31.48/31.89
% 31.48/31.89 224: inverse(X19) = multiply(inverse(multiply(X20, X19)), X20).
% 31.48/31.89 Proof: A critical pair between equations 176 and 176.
% 31.48/31.89
% 31.48/31.89 228: inverse(multiply(X18, inverse(multiply(X18, X19)))) = X19.
% 31.48/31.89 Proof: Rewrite equation 218,
% 31.48/31.89 lhs with equations [216,216]
% 31.48/31.89 rhs with equations [89].
% 31.48/31.89
% 31.48/31.89 279: inverse(inverse(multiply(X21, X22))) = multiply(X22, X21).
% 31.48/31.89 Proof: A critical pair between equations 224 and 228.
% 31.48/31.89
% 31.48/31.89 280: multiply(X21, X22) = multiply(X22, X21).
% 31.48/31.89 Proof: Rewrite equation 279,
% 31.48/31.89 lhs with equations [89]
% 31.48/31.89 rhs with equations [].
% 31.48/31.89
% 31.48/31.89 292: multiply(a(), b()) = multiply(b(), a()).
% 31.48/31.89 Proof: Rewrite lhs with equations []
% 31.48/31.89 rhs with equations [280].
% 31.48/31.89
% 31.48/31.89 % SZS output end Proof
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