TSTP Solution File: GRP530-1 by Toma---0.4
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% File : Toma---0.4
% Problem : GRP530-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n026.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 01:15:15 EDT 2023
% Result : Unsatisfiable 0.20s 0.64s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP530-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.13 % Command : toma --casc %s
% 0.12/0.34 % Computer : n026.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 : Tue Aug 29 00:43:05 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.64 % SZS status Unsatisfiable
% 0.20/0.64 % SZS output start Proof
% 0.20/0.64 original problem:
% 0.20/0.64 axioms:
% 0.20/0.64 divide(divide(A, divide(B, C)), divide(A, B)) = C
% 0.20/0.64 multiply(A, B) = divide(A, divide(divide(C, C), B))
% 0.20/0.64 inverse(A) = divide(divide(B, B), A)
% 0.20/0.64 goal:
% 0.20/0.64 multiply(multiply(inverse(b2()), b2()), a2()) != a2()
% 0.20/0.64 To show the unsatisfiability of the original goal,
% 0.20/0.64 it suffices to show that multiply(multiply(inverse(b2()), b2()), a2()) = a2() (skolemized goal) is valid under the axioms.
% 0.20/0.64 Here is an equational proof:
% 0.20/0.64 0: divide(divide(X0, divide(X1, X2)), divide(X0, X1)) = X2.
% 0.20/0.64 Proof: Axiom.
% 0.20/0.64
% 0.20/0.64 1: multiply(X0, X1) = divide(X0, divide(divide(X2, X2), X1)).
% 0.20/0.64 Proof: Axiom.
% 0.20/0.64
% 0.20/0.64 2: inverse(X0) = divide(divide(X1, X1), X0).
% 0.20/0.64 Proof: Axiom.
% 0.20/0.64
% 0.20/0.64 3: multiply(X0, X1) = divide(X0, inverse(X1)).
% 0.20/0.64 Proof: Rewrite equation 1,
% 0.20/0.64 lhs with equations []
% 0.20/0.64 rhs with equations [2].
% 0.20/0.64
% 0.20/0.64 7: inverse(X0) = divide(inverse(divide(X2, X2)), X0).
% 0.20/0.64 Proof: A critical pair between equations 2 and 2.
% 0.20/0.64
% 0.20/0.64 13: X2 = divide(inverse(divide(X1, X2)), divide(divide(X3, X3), X1)).
% 0.20/0.64 Proof: A critical pair between equations 0 and 2.
% 0.20/0.64
% 0.20/0.64 16: X2 = divide(inverse(divide(X1, X2)), inverse(X1)).
% 0.20/0.64 Proof: Rewrite equation 13,
% 0.20/0.64 lhs with equations []
% 0.20/0.64 rhs with equations [2].
% 0.20/0.64
% 0.20/0.64 17: X3 = inverse(inverse(X3)).
% 0.20/0.64 Proof: A critical pair between equations 16 and 7.
% 0.20/0.64
% 0.20/0.64 32: multiply(multiply(inverse(b2()), b2()), a2()) = a2().
% 0.20/0.64 Proof: Rewrite lhs with equations [3,3,2,17]
% 0.20/0.64 rhs with equations [].
% 0.20/0.64
% 0.20/0.64 % SZS output end Proof
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