TSTP Solution File: GRP116-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP116-1 : 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 : n026.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 01:17:03 EDT 2023
% Result : Unsatisfiable 0.21s 0.38s
% Output : Proof 0.21s
% 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 : GRP116-1 : 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 : n026.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 22:46:20 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.21/0.38 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.21/0.38
% 0.21/0.38 % SZS status Unsatisfiable
% 0.21/0.38
% 0.21/0.40 % SZS output start Proof
% 0.21/0.40 Axiom 1 (single_axiom): multiply(X, multiply(multiply(X, multiply(multiply(X, Y), Z)), multiply(identity, multiply(Z, Z)))) = Y.
% 0.21/0.40
% 0.21/0.40 Lemma 2: multiply(X, multiply(Y, multiply(identity, multiply(multiply(identity, multiply(Z, Z)), multiply(identity, multiply(Z, Z)))))) = multiply(multiply(X, Y), Z).
% 0.21/0.40 Proof:
% 0.21/0.40 multiply(X, multiply(Y, multiply(identity, multiply(multiply(identity, multiply(Z, Z)), multiply(identity, multiply(Z, Z))))))
% 0.21/0.40 = { by axiom 1 (single_axiom) R->L }
% 0.21/0.40 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))))))
% 0.21/0.40 = { by axiom 1 (single_axiom) }
% 0.21/0.40 multiply(multiply(X, Y), Z)
% 0.21/0.40
% 0.21/0.40 Lemma 3: multiply(multiply(X, Y), multiply(identity, Z)) = multiply(X, multiply(Y, Z)).
% 0.21/0.40 Proof:
% 0.21/0.40 multiply(multiply(X, Y), multiply(identity, Z))
% 0.21/0.40 = { by lemma 2 R->L }
% 0.21/0.40 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)))))))
% 0.21/0.40 = { by axiom 1 (single_axiom) }
% 0.21/0.40 multiply(X, multiply(Y, Z))
% 0.21/0.40
% 0.21/0.40 Lemma 4: multiply(multiply(X, identity), Y) = multiply(X, Y).
% 0.21/0.40 Proof:
% 0.21/0.40 multiply(multiply(X, identity), Y)
% 0.21/0.40 = { by axiom 1 (single_axiom) R->L }
% 0.21/0.40 multiply(multiply(multiply(Z, multiply(multiply(Z, multiply(multiply(Z, X), W)), multiply(identity, multiply(W, W)))), identity), Y)
% 0.21/0.40 = { by lemma 2 R->L }
% 0.21/0.40 multiply(multiply(Z, multiply(multiply(Z, multiply(multiply(Z, X), W)), multiply(identity, multiply(W, W)))), multiply(identity, multiply(identity, multiply(multiply(identity, multiply(Y, Y)), multiply(identity, multiply(Y, Y))))))
% 0.21/0.40 = { by lemma 3 }
% 0.21/0.40 multiply(Z, multiply(multiply(multiply(Z, multiply(multiply(Z, X), W)), multiply(identity, multiply(W, W))), multiply(identity, multiply(multiply(identity, multiply(Y, Y)), multiply(identity, multiply(Y, Y))))))
% 0.21/0.40 = { by lemma 2 }
% 0.21/0.40 multiply(multiply(Z, multiply(multiply(Z, multiply(multiply(Z, X), W)), multiply(identity, multiply(W, W)))), Y)
% 0.21/0.40 = { by axiom 1 (single_axiom) }
% 0.21/0.40 multiply(X, Y)
% 0.21/0.40
% 0.21/0.40 Lemma 5: multiply(X, identity) = X.
% 0.21/0.40 Proof:
% 0.21/0.40 multiply(X, identity)
% 0.21/0.40 = { by axiom 1 (single_axiom) R->L }
% 0.21/0.40 multiply(Y, multiply(multiply(Y, multiply(multiply(Y, multiply(X, identity)), Z)), multiply(identity, multiply(Z, Z))))
% 0.21/0.40 = { by lemma 2 R->L }
% 0.21/0.40 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))))
% 0.21/0.40 = { by lemma 4 }
% 0.21/0.40 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))))
% 0.21/0.40 = { by lemma 2 }
% 0.21/0.40 multiply(Y, multiply(multiply(Y, multiply(multiply(Y, X), Z)), multiply(identity, multiply(Z, Z))))
% 0.21/0.40 = { by axiom 1 (single_axiom) }
% 0.21/0.40 X
% 0.21/0.40
% 0.21/0.40 Lemma 6: multiply(X, multiply(X, multiply(X, Y))) = Y.
% 0.21/0.40 Proof:
% 0.21/0.40 multiply(X, multiply(X, multiply(X, Y)))
% 0.21/0.40 = { by lemma 5 R->L }
% 0.21/0.40 multiply(X, multiply(X, multiply(X, multiply(Y, identity))))
% 0.21/0.40 = { by lemma 3 R->L }
% 0.21/0.40 multiply(X, multiply(X, multiply(multiply(X, Y), multiply(identity, identity))))
% 0.21/0.40 = { by lemma 3 R->L }
% 0.21/0.40 multiply(X, multiply(multiply(X, multiply(X, Y)), multiply(identity, multiply(identity, identity))))
% 0.21/0.40 = { by lemma 5 R->L }
% 0.21/0.40 multiply(X, multiply(multiply(X, multiply(multiply(X, Y), identity)), multiply(identity, multiply(identity, identity))))
% 0.21/0.40 = { by axiom 1 (single_axiom) }
% 0.21/0.40 Y
% 0.21/0.40
% 0.21/0.40 Lemma 7: multiply(identity, multiply(multiply(X, X), multiply(X, X))) = multiply(identity, X).
% 0.21/0.40 Proof:
% 0.21/0.40 multiply(identity, multiply(multiply(X, X), multiply(X, X)))
% 0.21/0.40 = { by lemma 3 R->L }
% 0.21/0.40 multiply(multiply(identity, multiply(X, X)), multiply(identity, multiply(X, X)))
% 0.21/0.40 = { by lemma 6 R->L }
% 0.21/0.40 multiply(identity, multiply(identity, multiply(identity, multiply(multiply(identity, multiply(X, X)), multiply(identity, multiply(X, X))))))
% 0.21/0.40 = { by lemma 2 }
% 0.21/0.40 multiply(multiply(identity, identity), X)
% 0.21/0.40 = { by lemma 4 }
% 0.21/0.40 multiply(identity, X)
% 0.21/0.40
% 0.21/0.40 Goal 1 (prove_order3): multiply(identity, a) = a.
% 0.21/0.40 Proof:
% 0.21/0.40 multiply(identity, a)
% 0.21/0.40 = { by lemma 7 R->L }
% 0.21/0.40 multiply(identity, multiply(multiply(a, a), multiply(a, a)))
% 0.21/0.40 = { by lemma 3 R->L }
% 0.21/0.40 multiply(identity, multiply(multiply(multiply(a, a), a), multiply(identity, a)))
% 0.21/0.40 = { by axiom 1 (single_axiom) R->L }
% 0.21/0.40 multiply(identity, multiply(multiply(multiply(a, a), multiply(identity, multiply(multiply(identity, multiply(multiply(identity, a), X)), multiply(identity, multiply(X, X))))), multiply(identity, a)))
% 0.21/0.40 = { by lemma 7 R->L }
% 0.21/0.40 multiply(identity, multiply(multiply(multiply(a, a), multiply(identity, multiply(multiply(identity, multiply(multiply(identity, multiply(multiply(a, a), multiply(a, a))), X)), multiply(identity, multiply(X, X))))), multiply(identity, a)))
% 0.21/0.40 = { by axiom 1 (single_axiom) }
% 0.21/0.40 multiply(identity, multiply(multiply(multiply(a, a), multiply(multiply(a, a), multiply(a, a))), multiply(identity, a)))
% 0.21/0.40 = { by lemma 5 R->L }
% 0.21/0.40 multiply(identity, multiply(multiply(multiply(a, a), multiply(multiply(a, a), multiply(multiply(a, a), identity))), multiply(identity, a)))
% 0.21/0.40 = { by lemma 6 }
% 0.21/0.40 multiply(identity, multiply(identity, multiply(identity, a)))
% 0.21/0.40 = { by lemma 6 }
% 0.21/0.40 a
% 0.21/0.40 % SZS output end Proof
% 0.21/0.40
% 0.21/0.40 RESULT: Unsatisfiable (the axioms are contradictory).
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