TSTP Solution File: GRP458-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP458-1 : 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 : n021.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 01:18:31 EDT 2023
% Result : Unsatisfiable 0.13s 0.38s
% Output : Proof 0.19s
% 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 : GRP458-1 : 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 : n021.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 00:30:28 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.38 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.13/0.38
% 0.13/0.38 % SZS status Unsatisfiable
% 0.13/0.38
% 0.19/0.38 % SZS output start Proof
% 0.19/0.38 Axiom 1 (identity): identity = divide(X, X).
% 0.19/0.38 Axiom 2 (inverse): inverse(X) = divide(identity, X).
% 0.19/0.38 Axiom 3 (multiply): multiply(X, Y) = divide(X, divide(identity, Y)).
% 0.19/0.38 Axiom 4 (single_axiom): divide(divide(divide(X, X), divide(X, divide(Y, divide(divide(identity, X), Z)))), Z) = Y.
% 0.19/0.38
% 0.19/0.38 Lemma 5: divide(X, inverse(Y)) = multiply(X, Y).
% 0.19/0.38 Proof:
% 0.19/0.38 divide(X, inverse(Y))
% 0.19/0.38 = { by axiom 2 (inverse) }
% 0.19/0.38 divide(X, divide(identity, Y))
% 0.19/0.38 = { by axiom 3 (multiply) R->L }
% 0.19/0.38 multiply(X, Y)
% 0.19/0.38
% 0.19/0.38 Lemma 6: inverse(inverse(X)) = multiply(identity, X).
% 0.19/0.38 Proof:
% 0.19/0.38 inverse(inverse(X))
% 0.19/0.38 = { by axiom 2 (inverse) }
% 0.19/0.38 divide(identity, inverse(X))
% 0.19/0.38 = { by lemma 5 }
% 0.19/0.38 multiply(identity, X)
% 0.19/0.38
% 0.19/0.39 Lemma 7: divide(inverse(divide(X, divide(Y, divide(inverse(X), Z)))), Z) = Y.
% 0.19/0.39 Proof:
% 0.19/0.39 divide(inverse(divide(X, divide(Y, divide(inverse(X), Z)))), Z)
% 0.19/0.39 = { by axiom 2 (inverse) }
% 0.19/0.39 divide(inverse(divide(X, divide(Y, divide(divide(identity, X), Z)))), Z)
% 0.19/0.39 = { by axiom 2 (inverse) }
% 0.19/0.39 divide(divide(identity, divide(X, divide(Y, divide(divide(identity, X), Z)))), Z)
% 0.19/0.39 = { by axiom 1 (identity) }
% 0.19/0.39 divide(divide(divide(X, X), divide(X, divide(Y, divide(divide(identity, X), Z)))), Z)
% 0.19/0.39 = { by axiom 4 (single_axiom) }
% 0.19/0.39 Y
% 0.19/0.39
% 0.19/0.39 Goal 1 (prove_these_axioms_2): multiply(identity, a2) = a2.
% 0.19/0.39 Proof:
% 0.19/0.39 multiply(identity, a2)
% 0.19/0.39 = { by lemma 6 R->L }
% 0.19/0.39 inverse(inverse(a2))
% 0.19/0.39 = { by lemma 7 R->L }
% 0.19/0.39 inverse(divide(inverse(divide(X, divide(inverse(a2), divide(inverse(X), Y)))), Y))
% 0.19/0.39 = { by lemma 7 R->L }
% 0.19/0.39 inverse(divide(inverse(divide(X, divide(inverse(divide(a2, divide(divide(inverse(a2), divide(inverse(X), Y)), divide(inverse(a2), divide(inverse(X), Y))))), divide(inverse(X), Y)))), Y))
% 0.19/0.39 = { by axiom 1 (identity) R->L }
% 0.19/0.39 inverse(divide(inverse(divide(X, divide(inverse(divide(a2, identity)), divide(inverse(X), Y)))), Y))
% 0.19/0.39 = { by lemma 7 }
% 0.19/0.39 inverse(inverse(divide(a2, identity)))
% 0.19/0.39 = { by lemma 6 }
% 0.19/0.39 multiply(identity, divide(a2, identity))
% 0.19/0.39 = { by axiom 1 (identity) }
% 0.19/0.39 multiply(divide(identity, identity), divide(a2, identity))
% 0.19/0.39 = { by axiom 2 (inverse) R->L }
% 0.19/0.39 multiply(inverse(identity), divide(a2, identity))
% 0.19/0.39 = { by axiom 1 (identity) }
% 0.19/0.39 multiply(inverse(divide(divide(a2, identity), divide(a2, identity))), divide(a2, identity))
% 0.19/0.39 = { by lemma 5 R->L }
% 0.19/0.39 divide(inverse(divide(divide(a2, identity), divide(a2, identity))), inverse(divide(a2, identity)))
% 0.19/0.39 = { by axiom 1 (identity) }
% 0.19/0.39 divide(inverse(divide(divide(a2, identity), divide(a2, divide(inverse(divide(a2, identity)), inverse(divide(a2, identity)))))), inverse(divide(a2, identity)))
% 0.19/0.39 = { by lemma 7 }
% 0.19/0.39 a2
% 0.19/0.39 % SZS output end Proof
% 0.19/0.39
% 0.19/0.39 RESULT: Unsatisfiable (the axioms are contradictory).
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