TSTP Solution File: GRP535-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP535-1 : 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 : n013.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 01:18:49 EDT 2023
% Result : Unsatisfiable 0.20s 0.40s
% 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
% 0.07/0.12 % Problem : GRP535-1 : TPTP v8.1.2. Released v2.6.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 23:42:31 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.40 Command-line arguments: --no-flatten-goal
% 0.20/0.40
% 0.20/0.40 % SZS status Unsatisfiable
% 0.20/0.40
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 Axiom 1 (identity): identity = divide(X, X).
% 0.20/0.41 Axiom 2 (inverse): inverse(X) = divide(divide(Y, Y), X).
% 0.20/0.41 Axiom 3 (multiply): multiply(X, Y) = divide(X, divide(divide(Z, Z), Y)).
% 0.20/0.41 Axiom 4 (single_axiom): divide(divide(X, divide(divide(X, Y), Z)), Y) = Z.
% 0.20/0.41
% 0.20/0.41 Lemma 5: divide(identity, X) = inverse(X).
% 0.20/0.41 Proof:
% 0.20/0.41 divide(identity, X)
% 0.20/0.41 = { by axiom 1 (identity) }
% 0.20/0.41 divide(divide(Y, Y), X)
% 0.20/0.41 = { by axiom 2 (inverse) R->L }
% 0.20/0.41 inverse(X)
% 0.20/0.41
% 0.20/0.41 Lemma 6: divide(X, inverse(Y)) = multiply(X, Y).
% 0.20/0.41 Proof:
% 0.20/0.41 divide(X, inverse(Y))
% 0.20/0.41 = { by lemma 5 R->L }
% 0.20/0.41 divide(X, divide(identity, Y))
% 0.20/0.41 = { by axiom 1 (identity) }
% 0.20/0.41 divide(X, divide(divide(Z, Z), Y))
% 0.20/0.41 = { by axiom 3 (multiply) R->L }
% 0.20/0.41 multiply(X, Y)
% 0.20/0.41
% 0.20/0.41 Lemma 7: divide(multiply(X, Y), X) = Y.
% 0.20/0.41 Proof:
% 0.20/0.41 divide(multiply(X, Y), X)
% 0.20/0.41 = { by lemma 6 R->L }
% 0.20/0.41 divide(divide(X, inverse(Y)), X)
% 0.20/0.41 = { by lemma 5 R->L }
% 0.20/0.41 divide(divide(X, divide(identity, Y)), X)
% 0.20/0.41 = { by axiom 1 (identity) }
% 0.20/0.41 divide(divide(X, divide(divide(X, X), Y)), X)
% 0.20/0.41 = { by axiom 4 (single_axiom) }
% 0.20/0.41 Y
% 0.20/0.41
% 0.20/0.41 Lemma 8: inverse(inverse(X)) = X.
% 0.20/0.41 Proof:
% 0.20/0.41 inverse(inverse(X))
% 0.20/0.41 = { by lemma 5 R->L }
% 0.20/0.41 divide(identity, inverse(X))
% 0.20/0.41 = { by axiom 1 (identity) }
% 0.20/0.41 divide(divide(inverse(X), inverse(X)), inverse(X))
% 0.20/0.41 = { by lemma 6 }
% 0.20/0.41 divide(multiply(inverse(X), X), inverse(X))
% 0.20/0.41 = { by lemma 7 }
% 0.20/0.41 X
% 0.20/0.41
% 0.20/0.41 Lemma 9: multiply(Y, X) = multiply(X, Y).
% 0.20/0.41 Proof:
% 0.20/0.41 multiply(Y, X)
% 0.20/0.41 = { by axiom 4 (single_axiom) R->L }
% 0.20/0.41 multiply(Y, divide(divide(X, divide(divide(X, Y), X)), Y))
% 0.20/0.41 = { by lemma 8 R->L }
% 0.20/0.41 multiply(Y, divide(divide(X, divide(divide(X, inverse(inverse(Y))), X)), Y))
% 0.20/0.41 = { by lemma 6 }
% 0.20/0.41 multiply(Y, divide(divide(X, divide(multiply(X, inverse(Y)), X)), Y))
% 0.20/0.41 = { by lemma 7 }
% 0.20/0.41 multiply(Y, divide(divide(X, inverse(Y)), Y))
% 0.20/0.41 = { by lemma 6 }
% 0.20/0.41 multiply(Y, divide(multiply(X, Y), Y))
% 0.20/0.41 = { by lemma 6 R->L }
% 0.20/0.41 divide(Y, inverse(divide(multiply(X, Y), Y)))
% 0.20/0.41 = { by axiom 4 (single_axiom) R->L }
% 0.20/0.41 divide(divide(divide(identity, divide(divide(identity, inverse(multiply(X, Y))), Y)), inverse(multiply(X, Y))), inverse(divide(multiply(X, Y), Y)))
% 0.20/0.41 = { by lemma 5 }
% 0.20/0.41 divide(divide(inverse(divide(divide(identity, inverse(multiply(X, Y))), Y)), inverse(multiply(X, Y))), inverse(divide(multiply(X, Y), Y)))
% 0.20/0.41 = { by lemma 5 }
% 0.20/0.41 divide(divide(inverse(divide(inverse(inverse(multiply(X, Y))), Y)), inverse(multiply(X, Y))), inverse(divide(multiply(X, Y), Y)))
% 0.20/0.41 = { by lemma 6 }
% 0.20/0.41 divide(multiply(inverse(divide(inverse(inverse(multiply(X, Y))), Y)), multiply(X, Y)), inverse(divide(multiply(X, Y), Y)))
% 0.20/0.41 = { by lemma 8 }
% 0.20/0.41 divide(multiply(inverse(divide(multiply(X, Y), Y)), multiply(X, Y)), inverse(divide(multiply(X, Y), Y)))
% 0.20/0.41 = { by lemma 7 }
% 0.20/0.41 multiply(X, Y)
% 0.20/0.41
% 0.20/0.41 Goal 1 (prove_these_axioms_3): multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)).
% 0.20/0.41 Proof:
% 0.20/0.41 multiply(multiply(a3, b3), c3)
% 0.20/0.41 = { by lemma 9 R->L }
% 0.20/0.41 multiply(c3, multiply(a3, b3))
% 0.20/0.41 = { by lemma 9 }
% 0.20/0.41 multiply(c3, multiply(b3, a3))
% 0.20/0.41 = { by lemma 6 R->L }
% 0.20/0.41 multiply(c3, divide(b3, inverse(a3)))
% 0.20/0.41 = { by axiom 4 (single_axiom) R->L }
% 0.20/0.41 divide(divide(b3, divide(divide(b3, inverse(a3)), multiply(c3, divide(b3, inverse(a3))))), inverse(a3))
% 0.20/0.41 = { by lemma 8 R->L }
% 0.20/0.41 divide(divide(b3, divide(divide(b3, inverse(a3)), multiply(inverse(inverse(c3)), divide(b3, inverse(a3))))), inverse(a3))
% 0.20/0.41 = { by lemma 7 R->L }
% 0.20/0.41 divide(divide(b3, divide(divide(multiply(inverse(inverse(c3)), divide(b3, inverse(a3))), inverse(inverse(c3))), multiply(inverse(inverse(c3)), divide(b3, inverse(a3))))), inverse(a3))
% 0.20/0.41 = { by lemma 6 }
% 0.20/0.41 divide(divide(b3, divide(multiply(multiply(inverse(inverse(c3)), divide(b3, inverse(a3))), inverse(c3)), multiply(inverse(inverse(c3)), divide(b3, inverse(a3))))), inverse(a3))
% 0.20/0.41 = { by lemma 7 }
% 0.20/0.41 divide(divide(b3, inverse(c3)), inverse(a3))
% 0.20/0.41 = { by lemma 6 }
% 0.20/0.41 divide(multiply(b3, c3), inverse(a3))
% 0.20/0.41 = { by lemma 9 R->L }
% 0.20/0.41 divide(multiply(c3, b3), inverse(a3))
% 0.20/0.41 = { by lemma 6 }
% 0.20/0.41 multiply(multiply(c3, b3), a3)
% 0.20/0.41 = { by lemma 9 R->L }
% 0.20/0.41 multiply(a3, multiply(c3, b3))
% 0.20/0.41 = { by lemma 9 R->L }
% 0.20/0.41 multiply(a3, multiply(b3, c3))
% 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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