TSTP Solution File: GRP446-1 by Toma---0.4
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% File : Toma---0.4
% Problem : GRP446-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n003.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 01:15:01 EDT 2023
% Result : Unsatisfiable 0.69s 1.10s
% Output : CNFRefutation 0.69s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.15 % Problem : GRP446-1 : TPTP v8.1.2. Released v2.6.0.
% 0.12/0.15 % Command : toma --casc %s
% 0.14/0.37 % Computer : n003.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Tue Aug 29 00:31:40 EDT 2023
% 0.14/0.37 % CPUTime :
% 0.69/1.10 % SZS status Unsatisfiable
% 0.69/1.10 % SZS output start Proof
% 0.69/1.10 original problem:
% 0.69/1.10 axioms:
% 0.69/1.10 divide(A, divide(divide(divide(divide(A, A), B), C), divide(divide(divide(A, A), A), C))) = B
% 0.69/1.10 multiply(A, B) = divide(A, divide(divide(C, C), B))
% 0.69/1.10 inverse(A) = divide(divide(B, B), A)
% 0.69/1.10 goal:
% 0.69/1.10 multiply(multiply(inverse(b2()), b2()), a2()) != a2()
% 0.69/1.10 To show the unsatisfiability of the original goal,
% 0.69/1.10 it suffices to show that multiply(multiply(inverse(b2()), b2()), a2()) = a2() (skolemized goal) is valid under the axioms.
% 0.69/1.10 Here is an equational proof:
% 0.69/1.10 0: divide(X0, divide(divide(divide(divide(X0, X0), X1), X2), divide(divide(divide(X0, X0), X0), X2))) = X1.
% 0.69/1.10 Proof: Axiom.
% 0.69/1.10
% 0.69/1.10 1: multiply(X0, X1) = divide(X0, divide(divide(X2, X2), X1)).
% 0.69/1.10 Proof: Axiom.
% 0.69/1.10
% 0.69/1.10 2: inverse(X0) = divide(divide(X1, X1), X0).
% 0.69/1.10 Proof: Axiom.
% 0.69/1.10
% 0.69/1.10 3: divide(X0, divide(divide(inverse(X1), X2), divide(inverse(X0), X2))) = X1.
% 0.69/1.10 Proof: Rewrite equation 0,
% 0.69/1.10 lhs with equations [2,2]
% 0.69/1.10 rhs with equations [].
% 0.69/1.10
% 0.69/1.10 4: multiply(X0, X1) = divide(X0, inverse(X1)).
% 0.69/1.10 Proof: Rewrite equation 1,
% 0.69/1.10 lhs with equations []
% 0.69/1.10 rhs with equations [2].
% 0.69/1.10
% 0.69/1.10 7: inverse(X0) = divide(inverse(divide(X2, X2)), X0).
% 0.69/1.10 Proof: A critical pair between equations 2 and 2.
% 0.69/1.10
% 0.69/1.10 8: X1 = divide(X0, inverse(divide(inverse(X0), inverse(X1)))).
% 0.69/1.10 Proof: A critical pair between equations 3 and 2.
% 0.69/1.10
% 0.69/1.10 11: X1 = inverse(divide(divide(inverse(X1), X2), divide(inverse(divide(X3, X3)), X2))).
% 0.69/1.10 Proof: A critical pair between equations 3 and 2.
% 0.69/1.10
% 0.69/1.10 14: X1 = inverse(divide(divide(inverse(X1), X2), inverse(X2))).
% 0.69/1.10 Proof: Rewrite equation 11,
% 0.69/1.10 lhs with equations []
% 0.69/1.10 rhs with equations [7].
% 0.69/1.10
% 0.69/1.10 20: divide(inverse(inverse(X0)), inverse(X3)) = divide(X0, inverse(X3)).
% 0.69/1.10 Proof: A critical pair between equations 8 and 8.
% 0.69/1.10
% 0.69/1.10 24: X1 = inverse(divide(X4, inverse(inverse(divide(inverse(inverse(X1)), inverse(X4)))))).
% 0.69/1.10 Proof: A critical pair between equations 14 and 8.
% 0.69/1.10
% 0.69/1.10 28: X1 = inverse(multiply(X4, inverse(multiply(X1, X4)))).
% 0.69/1.10 Proof: Rewrite equation 24,
% 0.69/1.10 lhs with equations []
% 0.69/1.10 rhs with equations [20,4,4].
% 0.69/1.10
% 0.69/1.10 31: multiply(inverse(inverse(X0)), X3) = multiply(X0, X3).
% 0.69/1.10 Proof: Rewrite equation 20,
% 0.69/1.10 lhs with equations [4]
% 0.69/1.10 rhs with equations [4].
% 0.69/1.10
% 0.69/1.10 33: X1 = multiply(X0, multiply(inverse(X0), X1)).
% 0.69/1.10 Proof: Rewrite equation 8,
% 0.69/1.10 lhs with equations []
% 0.69/1.10 rhs with equations [4,4].
% 0.69/1.10
% 0.69/1.10 34: X1 = inverse(multiply(divide(inverse(X1), X2), X2)).
% 0.69/1.10 Proof: Rewrite equation 14,
% 0.69/1.10 lhs with equations []
% 0.69/1.10 rhs with equations [4].
% 0.69/1.10
% 0.69/1.10 41: X5 = multiply(inverse(X4), multiply(X4, X5)).
% 0.69/1.10 Proof: A critical pair between equations 33 and 31.
% 0.69/1.10
% 0.69/1.10 45: X5 = inverse(multiply(inverse(multiply(X6, X5)), X6)).
% 0.69/1.10 Proof: A critical pair between equations 28 and 28.
% 0.69/1.10
% 0.69/1.10 46: divide(inverse(X5), X6) = inverse(multiply(X6, X5)).
% 0.69/1.10 Proof: A critical pair between equations 28 and 34.
% 0.69/1.10
% 0.69/1.10 48: divide(inverse(X5), X6) = inverse(divide(X6, inverse(X5))).
% 0.69/1.10 Proof: Rewrite equation 46,
% 0.69/1.10 lhs with equations []
% 0.69/1.10 rhs with equations [4].
% 0.69/1.10
% 0.69/1.10 49: X5 = inverse(inverse(divide(inverse(X6), inverse(divide(X6, inverse(X5)))))).
% 0.69/1.10 Proof: Rewrite equation 45,
% 0.69/1.10 lhs with equations []
% 0.69/1.10 rhs with equations [4,4,48].
% 0.69/1.10
% 0.69/1.10 50: X5 = divide(inverse(X4), inverse(divide(X4, inverse(X5)))).
% 0.69/1.10 Proof: Rewrite equation 41,
% 0.69/1.10 lhs with equations []
% 0.69/1.10 rhs with equations [4,4].
% 0.69/1.10
% 0.69/1.10 60: X8 = inverse(inverse(X8)).
% 0.69/1.10 Proof: A critical pair between equations 49 and 50.
% 0.69/1.10
% 0.69/1.10 123: multiply(multiply(inverse(b2()), b2()), a2()) = a2().
% 0.69/1.10 Proof: Rewrite lhs with equations [4,4,2,60]
% 0.69/1.10 rhs with equations [].
% 0.69/1.10
% 0.69/1.10 % SZS output end Proof
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