TSTP Solution File: BOO012-4 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : BOO012-4 : TPTP v8.1.2. Released v1.1.0.
% 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 : n016.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 : Wed Aug 30 18:11:22 EDT 2023
% Result : Unsatisfiable 0.12s 0.38s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : BOO012-4 : TPTP v8.1.2. Released v1.1.0.
% 0.00/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n016.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Aug 27 08:29:43 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.12/0.38 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.12/0.38
% 0.12/0.38 % SZS status Unsatisfiable
% 0.12/0.38
% 0.18/0.38 % SZS output start Proof
% 0.18/0.38 Axiom 1 (commutativity_of_add): add(X, Y) = add(Y, X).
% 0.18/0.38 Axiom 2 (additive_id1): add(X, additive_identity) = X.
% 0.18/0.38 Axiom 3 (commutativity_of_multiply): multiply(X, Y) = multiply(Y, X).
% 0.18/0.38 Axiom 4 (multiplicative_id1): multiply(X, multiplicative_identity) = X.
% 0.18/0.38 Axiom 5 (additive_inverse1): add(X, inverse(X)) = multiplicative_identity.
% 0.18/0.38 Axiom 6 (multiplicative_inverse1): multiply(X, inverse(X)) = additive_identity.
% 0.18/0.39 Axiom 7 (distributivity1): add(X, multiply(Y, Z)) = multiply(add(X, Y), add(X, Z)).
% 0.18/0.39
% 0.18/0.39 Lemma 8: multiply(multiplicative_identity, X) = X.
% 0.18/0.39 Proof:
% 0.18/0.39 multiply(multiplicative_identity, X)
% 0.18/0.39 = { by axiom 3 (commutativity_of_multiply) R->L }
% 0.18/0.39 multiply(X, multiplicative_identity)
% 0.18/0.39 = { by axiom 4 (multiplicative_id1) }
% 0.18/0.39 X
% 0.18/0.39
% 0.18/0.39 Goal 1 (prove_inverse_is_an_involution): inverse(inverse(x)) = x.
% 0.18/0.39 Proof:
% 0.18/0.39 inverse(inverse(x))
% 0.18/0.39 = { by axiom 2 (additive_id1) R->L }
% 0.18/0.39 add(inverse(inverse(x)), additive_identity)
% 0.18/0.39 = { by axiom 6 (multiplicative_inverse1) R->L }
% 0.18/0.39 add(inverse(inverse(x)), multiply(x, inverse(x)))
% 0.18/0.39 = { by axiom 3 (commutativity_of_multiply) R->L }
% 0.18/0.39 add(inverse(inverse(x)), multiply(inverse(x), x))
% 0.18/0.39 = { by axiom 7 (distributivity1) }
% 0.18/0.39 multiply(add(inverse(inverse(x)), inverse(x)), add(inverse(inverse(x)), x))
% 0.18/0.39 = { by axiom 1 (commutativity_of_add) R->L }
% 0.18/0.39 multiply(add(inverse(x), inverse(inverse(x))), add(inverse(inverse(x)), x))
% 0.18/0.39 = { by axiom 5 (additive_inverse1) }
% 0.18/0.39 multiply(multiplicative_identity, add(inverse(inverse(x)), x))
% 0.18/0.39 = { by lemma 8 }
% 0.18/0.39 add(inverse(inverse(x)), x)
% 0.18/0.39 = { by axiom 1 (commutativity_of_add) R->L }
% 0.18/0.39 add(x, inverse(inverse(x)))
% 0.18/0.39 = { by lemma 8 R->L }
% 0.18/0.39 multiply(multiplicative_identity, add(x, inverse(inverse(x))))
% 0.18/0.39 = { by axiom 5 (additive_inverse1) R->L }
% 0.18/0.39 multiply(add(x, inverse(x)), add(x, inverse(inverse(x))))
% 0.18/0.39 = { by axiom 7 (distributivity1) R->L }
% 0.18/0.39 add(x, multiply(inverse(x), inverse(inverse(x))))
% 0.18/0.39 = { by axiom 6 (multiplicative_inverse1) }
% 0.18/0.39 add(x, additive_identity)
% 0.18/0.39 = { by axiom 2 (additive_id1) }
% 0.18/0.39 x
% 0.18/0.39 % SZS output end Proof
% 0.18/0.39
% 0.18/0.39 RESULT: Unsatisfiable (the axioms are contradictory).
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