TSTP Solution File: GRP446-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP446-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n011.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 01:18:28 EDT 2023
% Result : Unsatisfiable 0.14s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP446-1 : TPTP v8.1.2. Released v2.6.0.
% 0.07/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n011.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 00:29:11 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.39 Command-line arguments: --no-flatten-goal
% 0.14/0.39
% 0.14/0.39 % SZS status Unsatisfiable
% 0.14/0.39
% 0.14/0.40 % SZS output start Proof
% 0.14/0.40 Axiom 1 (inverse): inverse(X) = divide(divide(Y, Y), X).
% 0.14/0.40 Axiom 2 (multiply): multiply(X, Y) = divide(X, divide(divide(Z, Z), Y)).
% 0.14/0.40 Axiom 3 (single_axiom): divide(X, divide(divide(divide(divide(X, X), Y), Z), divide(divide(divide(X, X), X), Z))) = Y.
% 0.14/0.40
% 0.14/0.40 Lemma 4: divide(X, inverse(Y)) = multiply(X, Y).
% 0.14/0.40 Proof:
% 0.14/0.40 divide(X, inverse(Y))
% 0.14/0.40 = { by axiom 1 (inverse) }
% 0.14/0.40 divide(X, divide(divide(Z, Z), Y))
% 0.14/0.40 = { by axiom 2 (multiply) R->L }
% 0.14/0.40 multiply(X, Y)
% 0.14/0.40
% 0.14/0.40 Lemma 5: divide(inverse(divide(X, X)), Y) = inverse(Y).
% 0.14/0.40 Proof:
% 0.14/0.40 divide(inverse(divide(X, X)), Y)
% 0.14/0.40 = { by axiom 1 (inverse) }
% 0.14/0.40 divide(divide(divide(X, X), divide(X, X)), Y)
% 0.14/0.40 = { by axiom 1 (inverse) R->L }
% 0.14/0.40 inverse(Y)
% 0.14/0.40
% 0.14/0.40 Lemma 6: divide(X, divide(divide(inverse(Y), Z), divide(inverse(X), Z))) = Y.
% 0.14/0.40 Proof:
% 0.14/0.40 divide(X, divide(divide(inverse(Y), Z), divide(inverse(X), Z)))
% 0.14/0.40 = { by axiom 1 (inverse) }
% 0.14/0.40 divide(X, divide(divide(inverse(Y), Z), divide(divide(divide(X, X), X), Z)))
% 0.14/0.40 = { by axiom 1 (inverse) }
% 0.14/0.40 divide(X, divide(divide(divide(divide(X, X), Y), Z), divide(divide(divide(X, X), X), Z)))
% 0.14/0.40 = { by axiom 3 (single_axiom) }
% 0.14/0.40 Y
% 0.14/0.40
% 0.14/0.40 Lemma 7: inverse(multiply(divide(inverse(X), Y), Y)) = X.
% 0.14/0.40 Proof:
% 0.14/0.40 inverse(multiply(divide(inverse(X), Y), Y))
% 0.14/0.40 = { by lemma 4 R->L }
% 0.14/0.40 inverse(divide(divide(inverse(X), Y), inverse(Y)))
% 0.14/0.40 = { by axiom 1 (inverse) }
% 0.14/0.40 divide(divide(Z, Z), divide(divide(inverse(X), Y), inverse(Y)))
% 0.14/0.40 = { by lemma 5 R->L }
% 0.14/0.40 divide(divide(Z, Z), divide(divide(inverse(X), Y), divide(inverse(divide(Z, Z)), Y)))
% 0.14/0.40 = { by lemma 6 }
% 0.14/0.40 X
% 0.14/0.40
% 0.14/0.40 Lemma 8: inverse(multiply(inverse(X), X)) = divide(Y, Y).
% 0.14/0.40 Proof:
% 0.14/0.40 inverse(multiply(inverse(X), X))
% 0.14/0.40 = { by lemma 5 R->L }
% 0.14/0.40 inverse(multiply(divide(inverse(divide(Y, Y)), X), X))
% 0.14/0.40 = { by lemma 7 }
% 0.14/0.40 divide(Y, Y)
% 0.14/0.40
% 0.14/0.40 Lemma 9: multiply(X, multiply(inverse(X), Y)) = Y.
% 0.14/0.40 Proof:
% 0.14/0.40 multiply(X, multiply(inverse(X), Y))
% 0.14/0.40 = { by lemma 4 R->L }
% 0.14/0.40 multiply(X, divide(inverse(X), inverse(Y)))
% 0.14/0.40 = { by lemma 4 R->L }
% 0.14/0.40 divide(X, inverse(divide(inverse(X), inverse(Y))))
% 0.14/0.40 = { by axiom 1 (inverse) }
% 0.14/0.40 divide(X, divide(divide(inverse(Y), inverse(Y)), divide(inverse(X), inverse(Y))))
% 0.14/0.40 = { by lemma 6 }
% 0.14/0.40 Y
% 0.14/0.40
% 0.14/0.40 Lemma 10: multiply(X, divide(Y, Y)) = X.
% 0.14/0.40 Proof:
% 0.14/0.40 multiply(X, divide(Y, Y))
% 0.14/0.40 = { by lemma 8 R->L }
% 0.14/0.40 multiply(X, inverse(multiply(inverse(Z), Z)))
% 0.14/0.40 = { by axiom 1 (inverse) }
% 0.14/0.40 multiply(X, inverse(multiply(divide(divide(W, W), Z), Z)))
% 0.14/0.40 = { by lemma 8 R->L }
% 0.14/0.40 multiply(X, inverse(multiply(divide(inverse(multiply(inverse(X), X)), Z), Z)))
% 0.14/0.40 = { by lemma 7 }
% 0.14/0.40 multiply(X, multiply(inverse(X), X))
% 0.14/0.41 = { by lemma 9 }
% 0.14/0.41 X
% 0.14/0.41
% 0.14/0.41 Goal 1 (prove_these_axioms_2): multiply(multiply(inverse(b2), b2), a2) = a2.
% 0.14/0.41 Proof:
% 0.14/0.41 multiply(multiply(inverse(b2), b2), a2)
% 0.14/0.41 = { by lemma 4 R->L }
% 0.14/0.41 multiply(divide(inverse(b2), inverse(b2)), a2)
% 0.14/0.41 = { by lemma 4 R->L }
% 0.14/0.41 divide(divide(inverse(b2), inverse(b2)), inverse(a2))
% 0.14/0.41 = { by axiom 1 (inverse) R->L }
% 0.14/0.41 inverse(inverse(a2))
% 0.14/0.41 = { by lemma 10 R->L }
% 0.14/0.41 multiply(inverse(inverse(a2)), divide(X, X))
% 0.14/0.41 = { by lemma 9 R->L }
% 0.14/0.41 multiply(a2, multiply(inverse(a2), multiply(inverse(inverse(a2)), divide(X, X))))
% 0.14/0.41 = { by lemma 9 }
% 0.14/0.41 multiply(a2, divide(X, X))
% 0.14/0.41 = { by lemma 10 }
% 0.20/0.41 a2
% 0.20/0.41 % SZS output end Proof
% 0.20/0.41
% 0.20/0.41 RESULT: Unsatisfiable (the axioms are contradictory).
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