TSTP Solution File: RNG012-6 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : RNG012-6 : TPTP v8.1.2. Released v1.0.0.
% 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 : n007.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 13:58:48 EDT 2023
% Result : Unsatisfiable 0.20s 0.42s
% 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
% 0.07/0.12 % Problem : RNG012-6 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n007.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Aug 27 01:21:12 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.42 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.20/0.42
% 0.20/0.42 % SZS status Unsatisfiable
% 0.20/0.42
% 0.20/0.42 % SZS output start Proof
% 0.20/0.42 Axiom 1 (additive_inverse_additive_inverse): additive_inverse(additive_inverse(X)) = X.
% 0.20/0.42 Axiom 2 (commutativity_for_addition): add(X, Y) = add(Y, X).
% 0.20/0.42 Axiom 3 (right_additive_identity): add(X, additive_identity) = X.
% 0.20/0.42 Axiom 4 (left_additive_identity): add(additive_identity, X) = X.
% 0.20/0.42 Axiom 5 (right_multiplicative_zero): multiply(X, additive_identity) = additive_identity.
% 0.20/0.42 Axiom 6 (left_multiplicative_zero): multiply(additive_identity, X) = additive_identity.
% 0.20/0.42 Axiom 7 (right_additive_inverse): add(X, additive_inverse(X)) = additive_identity.
% 0.20/0.42 Axiom 8 (associativity_for_addition): add(X, add(Y, Z)) = add(add(X, Y), Z).
% 0.20/0.42 Axiom 9 (distribute1): multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)).
% 0.20/0.42 Axiom 10 (distribute2): multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z)).
% 0.20/0.42
% 0.20/0.42 Lemma 11: add(additive_inverse(X), add(X, Y)) = Y.
% 0.20/0.42 Proof:
% 0.20/0.42 add(additive_inverse(X), add(X, Y))
% 0.20/0.42 = { by axiom 2 (commutativity_for_addition) R->L }
% 0.20/0.42 add(additive_inverse(X), add(Y, X))
% 0.20/0.42 = { by axiom 1 (additive_inverse_additive_inverse) R->L }
% 0.20/0.42 add(additive_inverse(X), add(Y, additive_inverse(additive_inverse(X))))
% 0.20/0.42 = { by axiom 2 (commutativity_for_addition) R->L }
% 0.20/0.42 add(additive_inverse(X), add(additive_inverse(additive_inverse(X)), Y))
% 0.20/0.42 = { by axiom 8 (associativity_for_addition) }
% 0.20/0.42 add(add(additive_inverse(X), additive_inverse(additive_inverse(X))), Y)
% 0.20/0.42 = { by axiom 7 (right_additive_inverse) }
% 0.20/0.42 add(additive_identity, Y)
% 0.20/0.42 = { by axiom 4 (left_additive_identity) }
% 0.20/0.42 Y
% 0.20/0.42
% 0.20/0.42 Goal 1 (prove_equation): multiply(additive_inverse(a), additive_inverse(b)) = multiply(a, b).
% 0.20/0.42 Proof:
% 0.20/0.42 multiply(additive_inverse(a), additive_inverse(b))
% 0.20/0.42 = { by axiom 1 (additive_inverse_additive_inverse) R->L }
% 0.20/0.42 additive_inverse(additive_inverse(multiply(additive_inverse(a), additive_inverse(b))))
% 0.20/0.42 = { by axiom 3 (right_additive_identity) R->L }
% 0.20/0.42 additive_inverse(add(additive_inverse(multiply(additive_inverse(a), additive_inverse(b))), additive_identity))
% 0.20/0.42 = { by axiom 5 (right_multiplicative_zero) R->L }
% 0.20/0.42 additive_inverse(add(additive_inverse(multiply(additive_inverse(a), additive_inverse(b))), multiply(additive_inverse(a), additive_identity)))
% 0.20/0.42 = { by axiom 7 (right_additive_inverse) R->L }
% 0.20/0.42 additive_inverse(add(additive_inverse(multiply(additive_inverse(a), additive_inverse(b))), multiply(additive_inverse(a), add(b, additive_inverse(b)))))
% 0.20/0.42 = { by axiom 2 (commutativity_for_addition) R->L }
% 0.20/0.42 additive_inverse(add(additive_inverse(multiply(additive_inverse(a), additive_inverse(b))), multiply(additive_inverse(a), add(additive_inverse(b), b))))
% 0.20/0.42 = { by axiom 9 (distribute1) }
% 0.20/0.42 additive_inverse(add(additive_inverse(multiply(additive_inverse(a), additive_inverse(b))), add(multiply(additive_inverse(a), additive_inverse(b)), multiply(additive_inverse(a), b))))
% 0.20/0.42 = { by lemma 11 }
% 0.20/0.42 additive_inverse(multiply(additive_inverse(a), b))
% 0.20/0.42 = { by lemma 11 R->L }
% 0.20/0.42 additive_inverse(add(additive_inverse(multiply(a, b)), add(multiply(a, b), multiply(additive_inverse(a), b))))
% 0.20/0.42 = { by axiom 10 (distribute2) R->L }
% 0.20/0.42 additive_inverse(add(additive_inverse(multiply(a, b)), multiply(add(a, additive_inverse(a)), b)))
% 0.20/0.42 = { by axiom 7 (right_additive_inverse) }
% 0.20/0.42 additive_inverse(add(additive_inverse(multiply(a, b)), multiply(additive_identity, b)))
% 0.20/0.42 = { by axiom 6 (left_multiplicative_zero) }
% 0.20/0.42 additive_inverse(add(additive_inverse(multiply(a, b)), additive_identity))
% 0.20/0.42 = { by axiom 3 (right_additive_identity) }
% 0.20/0.42 additive_inverse(additive_inverse(multiply(a, b)))
% 0.20/0.42 = { by axiom 1 (additive_inverse_additive_inverse) }
% 0.20/0.42 multiply(a, b)
% 0.20/0.42 % SZS output end Proof
% 0.20/0.42
% 0.20/0.42 RESULT: Unsatisfiable (the axioms are contradictory).
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