TSTP Solution File: RNG016-6 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : RNG016-6 : 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 : n025.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 13:58:49 EDT 2023
% Result : Unsatisfiable 0.16s 0.37s
% Output : Proof 0.16s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : RNG016-6 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.11 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.32 % Computer : n025.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Sun Aug 27 02:45:23 EDT 2023
% 0.14/0.32 % CPUTime :
% 0.16/0.37 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.16/0.37
% 0.16/0.37 % SZS status Unsatisfiable
% 0.16/0.37
% 0.16/0.37 % SZS output start Proof
% 0.16/0.37 Axiom 1 (additive_inverse_additive_inverse): additive_inverse(additive_inverse(X)) = X.
% 0.16/0.37 Axiom 2 (commutativity_for_addition): add(X, Y) = add(Y, X).
% 0.16/0.37 Axiom 3 (left_additive_identity): add(additive_identity, X) = X.
% 0.16/0.38 Axiom 4 (right_additive_inverse): add(X, additive_inverse(X)) = additive_identity.
% 0.16/0.38 Axiom 5 (associativity_for_addition): add(X, add(Y, Z)) = add(add(X, Y), Z).
% 0.16/0.38 Axiom 6 (distribute2): multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z)).
% 0.16/0.38
% 0.16/0.38 Lemma 7: add(X, add(Y, additive_inverse(X))) = Y.
% 0.16/0.38 Proof:
% 0.16/0.38 add(X, add(Y, additive_inverse(X)))
% 0.16/0.38 = { by axiom 2 (commutativity_for_addition) R->L }
% 0.16/0.38 add(X, add(additive_inverse(X), Y))
% 0.16/0.38 = { by axiom 5 (associativity_for_addition) }
% 0.16/0.38 add(add(X, additive_inverse(X)), Y)
% 0.16/0.38 = { by axiom 4 (right_additive_inverse) }
% 0.16/0.38 add(additive_identity, Y)
% 0.16/0.38 = { by axiom 3 (left_additive_identity) }
% 0.16/0.38 Y
% 0.16/0.38
% 0.16/0.38 Goal 1 (prove_distributivity): multiply(add(x, additive_inverse(y)), z) = add(multiply(x, z), additive_inverse(multiply(y, z))).
% 0.16/0.38 Proof:
% 0.16/0.38 multiply(add(x, additive_inverse(y)), z)
% 0.16/0.38 = { by lemma 7 R->L }
% 0.16/0.38 add(additive_inverse(multiply(y, z)), add(multiply(add(x, additive_inverse(y)), z), additive_inverse(additive_inverse(multiply(y, z)))))
% 0.16/0.38 = { by axiom 1 (additive_inverse_additive_inverse) }
% 0.16/0.38 add(additive_inverse(multiply(y, z)), add(multiply(add(x, additive_inverse(y)), z), multiply(y, z)))
% 0.16/0.38 = { by axiom 2 (commutativity_for_addition) }
% 0.16/0.38 add(additive_inverse(multiply(y, z)), add(multiply(y, z), multiply(add(x, additive_inverse(y)), z)))
% 0.16/0.38 = { by axiom 6 (distribute2) R->L }
% 0.16/0.38 add(additive_inverse(multiply(y, z)), multiply(add(y, add(x, additive_inverse(y))), z))
% 0.16/0.38 = { by lemma 7 }
% 0.16/0.38 add(additive_inverse(multiply(y, z)), multiply(x, z))
% 0.16/0.38 = { by axiom 2 (commutativity_for_addition) }
% 0.16/0.38 add(multiply(x, z), additive_inverse(multiply(y, z)))
% 0.16/0.38 % SZS output end Proof
% 0.16/0.38
% 0.16/0.38 RESULT: Unsatisfiable (the axioms are contradictory).
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