TSTP Solution File: GRP527-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP527-1 : 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 : n007.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 01:18:47 EDT 2023
% Result : Unsatisfiable 0.20s 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
% 0.03/0.12 % Problem : GRP527-1 : TPTP v8.1.2. Released v2.6.0.
% 0.03/0.13 % 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 : n007.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 : Tue Aug 29 02:01:13 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.39 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.20/0.39
% 0.20/0.39 % SZS status Unsatisfiable
% 0.20/0.39
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 Axiom 1 (inverse): inverse(X) = divide(divide(Y, Y), X).
% 0.20/0.40 Axiom 2 (multiply): multiply(X, Y) = divide(X, divide(divide(Z, Z), Y)).
% 0.20/0.40 Axiom 3 (single_axiom): divide(X, divide(divide(X, Y), divide(Z, Y))) = Z.
% 0.20/0.40
% 0.20/0.40 Lemma 4: divide(X, inverse(Y)) = multiply(X, Y).
% 0.20/0.40 Proof:
% 0.20/0.40 divide(X, inverse(Y))
% 0.20/0.40 = { by axiom 1 (inverse) }
% 0.20/0.40 divide(X, divide(divide(Z, Z), Y))
% 0.20/0.40 = { by axiom 2 (multiply) R->L }
% 0.20/0.40 multiply(X, Y)
% 0.20/0.40
% 0.20/0.40 Lemma 5: multiply(X, divide(Y, X)) = Y.
% 0.20/0.40 Proof:
% 0.20/0.40 multiply(X, divide(Y, X))
% 0.20/0.40 = { by lemma 4 R->L }
% 0.20/0.40 divide(X, inverse(divide(Y, X)))
% 0.20/0.40 = { by axiom 1 (inverse) }
% 0.20/0.40 divide(X, divide(divide(X, X), divide(Y, X)))
% 0.20/0.40 = { by axiom 3 (single_axiom) }
% 0.20/0.40 Y
% 0.20/0.40
% 0.20/0.40 Lemma 6: divide(X, divide(multiply(X, Y), multiply(Z, Y))) = Z.
% 0.20/0.40 Proof:
% 0.20/0.40 divide(X, divide(multiply(X, Y), multiply(Z, Y)))
% 0.20/0.40 = { by lemma 4 R->L }
% 0.20/0.40 divide(X, divide(multiply(X, Y), divide(Z, inverse(Y))))
% 0.20/0.40 = { by lemma 4 R->L }
% 0.20/0.40 divide(X, divide(divide(X, inverse(Y)), divide(Z, inverse(Y))))
% 0.20/0.40 = { by axiom 3 (single_axiom) }
% 0.20/0.40 Z
% 0.20/0.40
% 0.20/0.40 Lemma 7: divide(multiply(X, Y), Y) = X.
% 0.20/0.40 Proof:
% 0.20/0.40 divide(multiply(X, Y), Y)
% 0.20/0.40 = { by lemma 6 R->L }
% 0.20/0.40 divide(X, divide(multiply(X, Y), multiply(divide(multiply(X, Y), Y), Y)))
% 0.20/0.40 = { by lemma 4 R->L }
% 0.20/0.40 divide(X, divide(multiply(X, Y), divide(divide(multiply(X, Y), Y), inverse(Y))))
% 0.20/0.40 = { by axiom 1 (inverse) }
% 0.20/0.40 divide(X, divide(multiply(X, Y), divide(divide(multiply(X, Y), Y), divide(divide(divide(X, Z), divide(X, Z)), Y))))
% 0.20/0.40 = { by axiom 3 (single_axiom) }
% 0.20/0.40 divide(X, divide(divide(X, Z), divide(X, Z)))
% 0.20/0.40 = { by axiom 3 (single_axiom) }
% 0.20/0.40 X
% 0.20/0.40
% 0.20/0.40 Lemma 8: multiply(X, Y) = multiply(Y, X).
% 0.20/0.40 Proof:
% 0.20/0.40 multiply(X, Y)
% 0.20/0.40 = { by lemma 5 R->L }
% 0.20/0.40 multiply(Y, divide(multiply(X, Y), Y))
% 0.20/0.40 = { by lemma 7 }
% 0.20/0.40 multiply(Y, X)
% 0.20/0.40
% 0.20/0.40 Goal 1 (prove_these_axioms_3): multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)).
% 0.20/0.40 Proof:
% 0.20/0.40 multiply(multiply(a3, b3), c3)
% 0.20/0.40 = { by lemma 8 }
% 0.20/0.40 multiply(c3, multiply(a3, b3))
% 0.20/0.40 = { by lemma 8 R->L }
% 0.20/0.40 multiply(c3, multiply(b3, a3))
% 0.20/0.40 = { by lemma 5 R->L }
% 0.20/0.40 multiply(a3, divide(multiply(c3, multiply(b3, a3)), a3))
% 0.20/0.40 = { by lemma 6 R->L }
% 0.20/0.40 multiply(a3, divide(multiply(c3, multiply(b3, a3)), divide(divide(multiply(c3, multiply(b3, a3)), multiply(a3, b3)), divide(multiply(divide(multiply(c3, multiply(b3, a3)), multiply(a3, b3)), b3), multiply(a3, b3)))))
% 0.20/0.40 = { by axiom 3 (single_axiom) }
% 0.20/0.40 multiply(a3, multiply(divide(multiply(c3, multiply(b3, a3)), multiply(a3, b3)), b3))
% 0.20/0.40 = { by lemma 8 }
% 0.20/0.40 multiply(a3, multiply(b3, divide(multiply(c3, multiply(b3, a3)), multiply(a3, b3))))
% 0.20/0.40 = { by lemma 8 }
% 0.20/0.40 multiply(a3, multiply(b3, divide(multiply(c3, multiply(b3, a3)), multiply(b3, a3))))
% 0.20/0.40 = { by lemma 7 }
% 0.20/0.40 multiply(a3, multiply(b3, c3))
% 0.20/0.40 % SZS output end Proof
% 0.20/0.40
% 0.20/0.40 RESULT: Unsatisfiable (the axioms are contradictory).
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