TSTP Solution File: GRP539-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP539-1 : 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 : n032.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 01:18:50 EDT 2023
% Result : Unsatisfiable 0.10s 0.29s
% Output : Proof 0.10s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : GRP539-1 : TPTP v8.1.2. Released v2.6.0.
% 0.06/0.07 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.06/0.26 % Computer : n032.cluster.edu
% 0.06/0.26 % Model : x86_64 x86_64
% 0.06/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.26 % Memory : 8042.1875MB
% 0.06/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.26 % CPULimit : 300
% 0.06/0.26 % WCLimit : 300
% 0.06/0.26 % DateTime : Mon Aug 28 23:02:01 EDT 2023
% 0.06/0.26 % CPUTime :
% 0.10/0.29 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.10/0.29
% 0.10/0.29 % SZS status Unsatisfiable
% 0.10/0.29
% 0.10/0.30 % SZS output start Proof
% 0.10/0.30 Axiom 1 (identity): identity = divide(X, X).
% 0.10/0.30 Axiom 2 (inverse): inverse(X) = divide(divide(Y, Y), X).
% 0.10/0.30 Axiom 3 (multiply): multiply(X, Y) = divide(X, divide(divide(Z, Z), Y)).
% 0.10/0.30 Axiom 4 (single_axiom): divide(divide(X, Y), divide(divide(X, Z), Y)) = Z.
% 0.10/0.30
% 0.10/0.30 Lemma 5: divide(identity, X) = inverse(X).
% 0.10/0.30 Proof:
% 0.10/0.30 divide(identity, X)
% 0.10/0.30 = { by axiom 1 (identity) }
% 0.10/0.30 divide(divide(Y, Y), X)
% 0.10/0.30 = { by axiom 2 (inverse) R->L }
% 0.10/0.30 inverse(X)
% 0.10/0.30
% 0.10/0.30 Lemma 6: divide(X, inverse(Y)) = multiply(X, Y).
% 0.10/0.30 Proof:
% 0.10/0.30 divide(X, inverse(Y))
% 0.10/0.30 = { by lemma 5 R->L }
% 0.10/0.30 divide(X, divide(identity, Y))
% 0.10/0.30 = { by axiom 1 (identity) }
% 0.10/0.30 divide(X, divide(divide(Z, Z), Y))
% 0.10/0.30 = { by axiom 3 (multiply) R->L }
% 0.10/0.30 multiply(X, Y)
% 0.10/0.30
% 0.10/0.30 Lemma 7: divide(multiply(X, Y), multiply(divide(X, Z), Y)) = Z.
% 0.10/0.30 Proof:
% 0.10/0.30 divide(multiply(X, Y), multiply(divide(X, Z), Y))
% 0.10/0.30 = { by lemma 6 R->L }
% 0.10/0.30 divide(multiply(X, Y), divide(divide(X, Z), inverse(Y)))
% 0.10/0.30 = { by lemma 6 R->L }
% 0.10/0.30 divide(divide(X, inverse(Y)), divide(divide(X, Z), inverse(Y)))
% 0.10/0.30 = { by axiom 4 (single_axiom) }
% 0.10/0.30 Z
% 0.10/0.30
% 0.10/0.30 Lemma 8: multiply(divide(X, Y), Y) = X.
% 0.10/0.30 Proof:
% 0.10/0.30 multiply(divide(X, Y), Y)
% 0.10/0.30 = { by lemma 6 R->L }
% 0.10/0.30 divide(divide(X, Y), inverse(Y))
% 0.10/0.30 = { by lemma 5 R->L }
% 0.10/0.30 divide(divide(X, Y), divide(identity, Y))
% 0.10/0.30 = { by axiom 1 (identity) }
% 0.10/0.30 divide(divide(X, Y), divide(divide(X, X), Y))
% 0.10/0.30 = { by axiom 4 (single_axiom) }
% 0.10/0.30 X
% 0.10/0.30
% 0.10/0.30 Lemma 9: multiply(Y, X) = multiply(X, Y).
% 0.10/0.30 Proof:
% 0.10/0.30 multiply(Y, X)
% 0.10/0.30 = { by lemma 7 R->L }
% 0.10/0.30 multiply(divide(multiply(X, Y), multiply(divide(X, Y), Y)), X)
% 0.10/0.30 = { by lemma 8 }
% 0.10/0.30 multiply(divide(multiply(X, Y), X), X)
% 0.10/0.30 = { by lemma 8 }
% 0.10/0.30 multiply(X, Y)
% 0.10/0.30
% 0.10/0.30 Goal 1 (prove_these_axioms_3): multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)).
% 0.10/0.30 Proof:
% 0.10/0.30 multiply(multiply(a3, b3), c3)
% 0.10/0.30 = { by lemma 9 R->L }
% 0.10/0.30 multiply(c3, multiply(a3, b3))
% 0.10/0.30 = { by lemma 9 }
% 0.10/0.30 multiply(c3, multiply(b3, a3))
% 0.10/0.30 = { by lemma 9 }
% 0.10/0.30 multiply(multiply(b3, a3), c3)
% 0.10/0.30 = { by lemma 8 R->L }
% 0.10/0.30 multiply(divide(multiply(multiply(b3, a3), c3), multiply(divide(multiply(b3, a3), a3), c3)), multiply(divide(multiply(b3, a3), a3), c3))
% 0.10/0.30 = { by lemma 7 }
% 0.10/0.30 multiply(a3, multiply(divide(multiply(b3, a3), a3), c3))
% 0.10/0.30 = { by lemma 9 R->L }
% 0.10/0.30 multiply(a3, multiply(c3, divide(multiply(b3, a3), a3)))
% 0.10/0.30 = { by lemma 8 R->L }
% 0.10/0.30 multiply(a3, multiply(c3, divide(multiply(b3, a3), multiply(divide(a3, a3), a3))))
% 0.10/0.30 = { by axiom 1 (identity) R->L }
% 0.10/0.30 multiply(a3, multiply(c3, divide(multiply(b3, a3), multiply(identity, a3))))
% 0.10/0.30 = { by axiom 1 (identity) }
% 0.10/0.30 multiply(a3, multiply(c3, divide(multiply(b3, a3), multiply(divide(b3, b3), a3))))
% 0.10/0.30 = { by lemma 7 }
% 0.10/0.30 multiply(a3, multiply(c3, b3))
% 0.10/0.30 = { by lemma 9 R->L }
% 0.10/0.30 multiply(a3, multiply(b3, c3))
% 0.10/0.30 % SZS output end Proof
% 0.10/0.30
% 0.10/0.30 RESULT: Unsatisfiable (the axioms are contradictory).
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