TSTP Solution File: GRP115-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP115-1 : TPTP v8.1.2. Released v1.2.0.
% 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 : n031.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 01:17:02 EDT 2023
% Result : Unsatisfiable 0.20s 0.38s
% 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
% 0.00/0.12 % Problem : GRP115-1 : TPTP v8.1.2. Released v1.2.0.
% 0.00/0.13 % 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 : n031.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 21:09:40 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.38 Command-line arguments: --no-flatten-goal
% 0.20/0.38
% 0.20/0.38 % SZS status Unsatisfiable
% 0.20/0.38
% 0.20/0.39 % SZS output start Proof
% 0.20/0.39 Axiom 1 (single_axiom): multiply(X, multiply(multiply(X, multiply(multiply(X, Y), Z)), multiply(identity, multiply(Z, Z)))) = Y.
% 0.20/0.39
% 0.20/0.39 Lemma 2: multiply(X, multiply(Y, multiply(identity, multiply(multiply(identity, multiply(Z, Z)), multiply(identity, multiply(Z, Z)))))) = multiply(multiply(X, Y), Z).
% 0.20/0.39 Proof:
% 0.20/0.39 multiply(X, multiply(Y, multiply(identity, multiply(multiply(identity, multiply(Z, Z)), multiply(identity, multiply(Z, Z))))))
% 0.20/0.39 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.39 multiply(X, multiply(multiply(X, multiply(multiply(X, multiply(multiply(X, Y), Z)), multiply(identity, multiply(Z, Z)))), multiply(identity, multiply(multiply(identity, multiply(Z, Z)), multiply(identity, multiply(Z, Z))))))
% 0.20/0.39 = { by axiom 1 (single_axiom) }
% 0.20/0.39 multiply(multiply(X, Y), Z)
% 0.20/0.39
% 0.20/0.39 Lemma 3: multiply(multiply(X, Y), multiply(identity, Z)) = multiply(X, multiply(Y, Z)).
% 0.20/0.39 Proof:
% 0.20/0.39 multiply(multiply(X, Y), multiply(identity, Z))
% 0.20/0.39 = { by lemma 2 R->L }
% 0.20/0.39 multiply(X, multiply(Y, multiply(identity, multiply(multiply(identity, multiply(multiply(identity, Z), multiply(identity, Z))), multiply(identity, multiply(multiply(identity, Z), multiply(identity, Z)))))))
% 0.20/0.39 = { by axiom 1 (single_axiom) }
% 0.20/0.40 multiply(X, multiply(Y, Z))
% 0.20/0.40
% 0.20/0.40 Lemma 4: multiply(X, identity) = X.
% 0.20/0.40 Proof:
% 0.20/0.40 multiply(X, identity)
% 0.20/0.40 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.40 multiply(Y, multiply(multiply(Y, multiply(multiply(Y, multiply(X, identity)), Z)), multiply(identity, multiply(Z, Z))))
% 0.20/0.40 = { by lemma 2 R->L }
% 0.20/0.40 multiply(Y, multiply(multiply(Y, multiply(Y, multiply(multiply(X, identity), multiply(identity, multiply(multiply(identity, multiply(Z, Z)), multiply(identity, multiply(Z, Z))))))), multiply(identity, multiply(Z, Z))))
% 0.20/0.40 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.40 multiply(Y, multiply(multiply(Y, multiply(Y, multiply(multiply(multiply(W, multiply(multiply(W, multiply(multiply(W, X), V)), multiply(identity, multiply(V, V)))), identity), multiply(identity, multiply(multiply(identity, multiply(Z, Z)), multiply(identity, multiply(Z, Z))))))), multiply(identity, multiply(Z, Z))))
% 0.20/0.40 = { by lemma 2 R->L }
% 0.20/0.40 multiply(Y, multiply(multiply(Y, multiply(Y, multiply(multiply(W, multiply(multiply(W, multiply(multiply(W, X), V)), multiply(identity, multiply(V, V)))), multiply(identity, multiply(identity, multiply(multiply(identity, multiply(multiply(identity, multiply(multiply(identity, multiply(Z, Z)), multiply(identity, multiply(Z, Z)))), multiply(identity, multiply(multiply(identity, multiply(Z, Z)), multiply(identity, multiply(Z, Z)))))), multiply(identity, multiply(multiply(identity, multiply(multiply(identity, multiply(Z, Z)), multiply(identity, multiply(Z, Z)))), multiply(identity, multiply(multiply(identity, multiply(Z, Z)), multiply(identity, multiply(Z, Z)))))))))))), multiply(identity, multiply(Z, Z))))
% 0.20/0.40 = { by lemma 3 }
% 0.20/0.40 multiply(Y, multiply(multiply(Y, multiply(Y, multiply(W, multiply(multiply(multiply(W, multiply(multiply(W, X), V)), multiply(identity, multiply(V, V))), multiply(identity, multiply(multiply(identity, multiply(multiply(identity, multiply(multiply(identity, multiply(Z, Z)), multiply(identity, multiply(Z, Z)))), multiply(identity, multiply(multiply(identity, multiply(Z, Z)), multiply(identity, multiply(Z, Z)))))), multiply(identity, multiply(multiply(identity, multiply(multiply(identity, multiply(Z, Z)), multiply(identity, multiply(Z, Z)))), multiply(identity, multiply(multiply(identity, multiply(Z, Z)), multiply(identity, multiply(Z, Z)))))))))))), multiply(identity, multiply(Z, Z))))
% 0.20/0.40 = { by lemma 2 }
% 0.20/0.40 multiply(Y, multiply(multiply(Y, multiply(Y, multiply(multiply(W, multiply(multiply(W, multiply(multiply(W, X), V)), multiply(identity, multiply(V, V)))), multiply(identity, multiply(multiply(identity, multiply(Z, Z)), multiply(identity, multiply(Z, Z))))))), multiply(identity, multiply(Z, Z))))
% 0.20/0.40 = { by axiom 1 (single_axiom) }
% 0.20/0.40 multiply(Y, multiply(multiply(Y, multiply(Y, multiply(X, multiply(identity, multiply(multiply(identity, multiply(Z, Z)), multiply(identity, multiply(Z, Z))))))), multiply(identity, multiply(Z, Z))))
% 0.20/0.40 = { by lemma 2 }
% 0.20/0.40 multiply(Y, multiply(multiply(Y, multiply(multiply(Y, X), Z)), multiply(identity, multiply(Z, Z))))
% 0.20/0.40 = { by axiom 1 (single_axiom) }
% 0.20/0.40 X
% 0.20/0.40
% 0.20/0.40 Goal 1 (prove_order3): multiply(a, multiply(a, a)) = identity.
% 0.20/0.40 Proof:
% 0.20/0.40 multiply(a, multiply(a, a))
% 0.20/0.40 = { by lemma 4 R->L }
% 0.20/0.40 multiply(a, multiply(a, multiply(a, identity)))
% 0.20/0.40 = { by lemma 4 R->L }
% 0.20/0.40 multiply(a, multiply(a, multiply(a, multiply(identity, identity))))
% 0.20/0.40 = { by lemma 3 R->L }
% 0.20/0.40 multiply(a, multiply(a, multiply(multiply(a, identity), multiply(identity, identity))))
% 0.20/0.40 = { by lemma 3 R->L }
% 0.20/0.40 multiply(a, multiply(multiply(a, multiply(a, identity)), multiply(identity, multiply(identity, identity))))
% 0.20/0.40 = { by lemma 4 R->L }
% 0.20/0.40 multiply(a, multiply(multiply(a, multiply(multiply(a, identity), identity)), multiply(identity, multiply(identity, identity))))
% 0.20/0.40 = { by axiom 1 (single_axiom) }
% 0.20/0.40 identity
% 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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