TSTP Solution File: GRP590-1 by Toma---0.4
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% File : Toma---0.4
% Problem : GRP590-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n015.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 1.71s 2.07s
% Output : CNFRefutation 1.71s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP590-1 : TPTP v8.1.2. Released v2.6.0.
% 0.11/0.13 % Command : toma --casc %s
% 0.14/0.34 % Computer : n015.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Aug 28 22:30:40 EDT 2023
% 0.14/0.34 % CPUTime :
% 1.71/2.07 % SZS status Unsatisfiable
% 1.71/2.07 % SZS output start Proof
% 1.71/2.07 original problem:
% 1.71/2.07 axioms:
% 1.71/2.07 double_divide(inverse(double_divide(double_divide(A, B), inverse(double_divide(A, inverse(C))))), B) = C
% 1.71/2.07 multiply(A, B) = inverse(double_divide(B, A))
% 1.71/2.07 goal:
% 1.71/2.07 multiply(multiply(inverse(b2()), b2()), a2()) != a2()
% 1.71/2.07 To show the unsatisfiability of the original goal,
% 1.71/2.07 it suffices to show that multiply(multiply(inverse(b2()), b2()), a2()) = a2() (skolemized goal) is valid under the axioms.
% 1.71/2.07 Here is an equational proof:
% 1.71/2.07 0: double_divide(inverse(double_divide(double_divide(X0, X1), inverse(double_divide(X0, inverse(X2))))), X1) = X2.
% 1.71/2.07 Proof: Axiom.
% 1.71/2.07
% 1.71/2.07 1: multiply(X0, X1) = inverse(double_divide(X1, X0)).
% 1.71/2.07 Proof: Axiom.
% 1.71/2.07
% 1.71/2.07 2: X2 = double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(X3, inverse(X2)), inverse(double_divide(X3, inverse(X5))))), X1), inverse(X5))), X1).
% 1.71/2.07 Proof: A critical pair between equations 0 and 0.
% 1.71/2.07
% 1.71/2.07 3: X2 = double_divide(inverse(double_divide(X5, inverse(double_divide(inverse(double_divide(double_divide(X3, X4), inverse(double_divide(X3, inverse(X5))))), inverse(X2))))), X4).
% 1.71/2.07 Proof: A critical pair between equations 0 and 0.
% 1.71/2.07
% 1.71/2.07 4: X2 = double_divide(inverse(double_divide(X8, inverse(X8))), inverse(X2)).
% 1.71/2.07 Proof: A critical pair between equations 3 and 0.
% 1.71/2.07
% 1.71/2.07 16: X2 = double_divide(inverse(double_divide(X10, inverse(X2))), inverse(X10)).
% 1.71/2.07 Proof: A critical pair between equations 2 and 4.
% 1.71/2.07
% 1.71/2.07 17: X2 = double_divide(inverse(inverse(double_divide(X9, inverse(X9)))), inverse(X2)).
% 1.71/2.07 Proof: A critical pair between equations 4 and 4.
% 1.71/2.07
% 1.71/2.07 28: X11 = double_divide(inverse(X12), inverse(inverse(double_divide(X11, inverse(X12))))).
% 1.71/2.07 Proof: A critical pair between equations 16 and 16.
% 1.71/2.07
% 1.71/2.07 29: X12 = double_divide(inverse(X12), inverse(inverse(double_divide(X11, inverse(X11))))).
% 1.71/2.07 Proof: A critical pair between equations 16 and 4.
% 1.71/2.07
% 1.71/2.07 30: X2 = double_divide(inverse(inverse(inverse(double_divide(X10, inverse(X10))))), inverse(X2)).
% 1.71/2.07 Proof: A critical pair between equations 17 and 4.
% 1.71/2.07
% 1.71/2.07 32: X2 = double_divide(inverse(inverse(inverse(inverse(double_divide(X10, inverse(X10)))))), inverse(X2)).
% 1.71/2.07 Proof: A critical pair between equations 17 and 17.
% 1.71/2.07
% 1.71/2.07 45: X2 = double_divide(inverse(inverse(inverse(multiply(inverse(X10), X10)))), inverse(X2)).
% 1.71/2.07 Proof: Rewrite equation 32,
% 1.71/2.07 lhs with equations []
% 1.71/2.07 rhs with equations [1].
% 1.71/2.07
% 1.71/2.07 47: X2 = double_divide(inverse(inverse(multiply(inverse(X10), X10))), inverse(X2)).
% 1.71/2.07 Proof: Rewrite equation 30,
% 1.71/2.07 lhs with equations []
% 1.71/2.07 rhs with equations [1].
% 1.71/2.07
% 1.71/2.07 48: X12 = double_divide(inverse(X12), inverse(multiply(inverse(X11), X11))).
% 1.71/2.07 Proof: Rewrite equation 29,
% 1.71/2.07 lhs with equations []
% 1.71/2.07 rhs with equations [1].
% 1.71/2.07
% 1.71/2.07 49: X11 = double_divide(inverse(X12), inverse(multiply(inverse(X12), X11))).
% 1.71/2.07 Proof: Rewrite equation 28,
% 1.71/2.07 lhs with equations []
% 1.71/2.07 rhs with equations [1].
% 1.71/2.07
% 1.71/2.07 81: multiply(inverse(inverse(multiply(inverse(X10), X10))), X14) = X14.
% 1.71/2.07 Proof: A critical pair between equations 47 and 49.
% 1.71/2.07
% 1.71/2.07 86: multiply(inverse(X14), X14) = inverse(inverse(multiply(inverse(X10), X10))).
% 1.71/2.07 Proof: A critical pair between equations 45 and 48.
% 1.71/2.07
% 1.71/2.07 91: inverse(double_divide(X14, inverse(inverse(inverse(double_divide(X10, inverse(X10))))))) = X14.
% 1.71/2.07 Proof: Rewrite equation 81,
% 1.71/2.07 lhs with equations [1,1]
% 1.71/2.07 rhs with equations [].
% 1.71/2.07
% 1.71/2.07 127: inverse(double_divide(X14, inverse(X14))) = inverse(inverse(inverse(double_divide(X10, inverse(X10))))).
% 1.71/2.07 Proof: Rewrite equation 86,
% 1.71/2.07 lhs with equations [1]
% 1.71/2.07 rhs with equations [1].
% 1.71/2.07
% 1.71/2.07 138: X14 = inverse(double_divide(X14, inverse(double_divide(X16, inverse(X16))))).
% 1.71/2.07 Proof: A critical pair between equations 91 and 127.
% 1.71/2.07
% 1.71/2.07 152: X14 = multiply(multiply(inverse(X16), X16), X14).
% 1.71/2.07 Proof: Rewrite equation 138,
% 1.71/2.07 lhs with equations []
% 1.71/2.07 rhs with equations [1,1].
% 1.71/2.07
% 1.71/2.07 203: multiply(multiply(inverse(b2()), b2()), a2()) = a2().
% 1.71/2.07 Proof: Rewrite lhs with equations [152]
% 1.71/2.07 rhs with equations [].
% 1.71/2.07
% 1.71/2.07 % SZS output end Proof
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