TSTP Solution File: GRP544-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP544-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 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 : n020.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 01:18:51 EDT 2023
% Result : Unsatisfiable 0.13s 0.38s
% Output : Proof 0.13s
% 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 : GRP544-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 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 : n020.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 21:12:13 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.38 Command-line arguments: --no-flatten-goal
% 0.13/0.38
% 0.13/0.38 % SZS status Unsatisfiable
% 0.13/0.38
% 0.13/0.38 % SZS output start Proof
% 0.13/0.38 Axiom 1 (identity): identity = divide(X, X).
% 0.13/0.38 Axiom 2 (inverse): inverse(X) = divide(identity, X).
% 0.13/0.38 Axiom 3 (multiply): multiply(X, Y) = divide(X, divide(identity, Y)).
% 0.13/0.38 Axiom 4 (single_axiom): divide(divide(identity, divide(divide(divide(X, Y), Z), X)), Z) = Y.
% 0.13/0.38
% 0.13/0.38 Lemma 5: inverse(identity) = identity.
% 0.13/0.38 Proof:
% 0.13/0.38 inverse(identity)
% 0.13/0.38 = { by axiom 2 (inverse) }
% 0.13/0.38 divide(identity, identity)
% 0.13/0.38 = { by axiom 1 (identity) R->L }
% 0.13/0.38 identity
% 0.13/0.38
% 0.13/0.38 Lemma 6: divide(X, inverse(Y)) = multiply(X, Y).
% 0.13/0.38 Proof:
% 0.13/0.38 divide(X, inverse(Y))
% 0.13/0.38 = { by axiom 2 (inverse) }
% 0.13/0.38 divide(X, divide(identity, Y))
% 0.13/0.38 = { by axiom 3 (multiply) R->L }
% 0.13/0.38 multiply(X, Y)
% 0.13/0.38
% 0.13/0.38 Lemma 7: divide(inverse(divide(divide(divide(X, Y), Z), X)), Z) = Y.
% 0.13/0.38 Proof:
% 0.13/0.38 divide(inverse(divide(divide(divide(X, Y), Z), X)), Z)
% 0.13/0.38 = { by axiom 2 (inverse) }
% 0.13/0.38 divide(divide(identity, divide(divide(divide(X, Y), Z), X)), Z)
% 0.13/0.38 = { by axiom 4 (single_axiom) }
% 0.13/0.38 Y
% 0.13/0.38
% 0.13/0.38 Lemma 8: divide(inverse(inverse(X)), divide(X, Y)) = Y.
% 0.13/0.38 Proof:
% 0.13/0.38 divide(inverse(inverse(X)), divide(X, Y))
% 0.13/0.38 = { by axiom 2 (inverse) }
% 0.13/0.38 divide(inverse(divide(identity, X)), divide(X, Y))
% 0.13/0.38 = { by axiom 1 (identity) }
% 0.13/0.38 divide(inverse(divide(divide(divide(X, Y), divide(X, Y)), X)), divide(X, Y))
% 0.13/0.38 = { by lemma 7 }
% 0.13/0.38 Y
% 0.13/0.38
% 0.13/0.38 Goal 1 (prove_these_axioms_4): multiply(a, b) = multiply(b, a).
% 0.13/0.38 Proof:
% 0.13/0.38 multiply(a, b)
% 0.13/0.38 = { by lemma 8 R->L }
% 0.13/0.38 multiply(divide(inverse(inverse(identity)), divide(identity, a)), b)
% 0.13/0.38 = { by axiom 2 (inverse) R->L }
% 0.13/0.38 multiply(divide(inverse(inverse(identity)), inverse(a)), b)
% 0.13/0.38 = { by lemma 6 }
% 0.13/0.38 multiply(multiply(inverse(inverse(identity)), a), b)
% 0.13/0.38 = { by lemma 5 }
% 0.13/0.38 multiply(multiply(inverse(identity), a), b)
% 0.13/0.38 = { by lemma 5 }
% 0.13/0.38 multiply(multiply(identity, a), b)
% 0.13/0.38 = { by lemma 6 R->L }
% 0.13/0.38 multiply(divide(identity, inverse(a)), b)
% 0.13/0.38 = { by axiom 2 (inverse) R->L }
% 0.13/0.38 multiply(inverse(inverse(a)), b)
% 0.13/0.38 = { by lemma 6 R->L }
% 0.13/0.38 divide(inverse(inverse(a)), inverse(b))
% 0.13/0.38 = { by lemma 8 R->L }
% 0.13/0.38 divide(inverse(divide(inverse(inverse(b)), divide(b, inverse(a)))), inverse(b))
% 0.13/0.38 = { by axiom 2 (inverse) }
% 0.13/0.38 divide(inverse(divide(divide(identity, inverse(b)), divide(b, inverse(a)))), inverse(b))
% 0.13/0.38 = { by axiom 1 (identity) }
% 0.13/0.38 divide(inverse(divide(divide(divide(divide(b, inverse(a)), divide(b, inverse(a))), inverse(b)), divide(b, inverse(a)))), inverse(b))
% 0.13/0.38 = { by lemma 7 }
% 0.13/0.38 divide(b, inverse(a))
% 0.13/0.38 = { by lemma 6 }
% 0.13/0.38 multiply(b, a)
% 0.13/0.38 % SZS output end Proof
% 0.13/0.38
% 0.13/0.38 RESULT: Unsatisfiable (the axioms are contradictory).
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