TSTP Solution File: BOO012-2 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : BOO012-2 : 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 : n003.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 0.13s 0.41s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : BOO012-2 : TPTP v8.1.2. Released v1.0.0.
% 0.13/0.13 % 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 : n003.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 07:49:24 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.41 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.13/0.41
% 0.13/0.41 % SZS status Unsatisfiable
% 0.13/0.41
% 0.13/0.41 % SZS output start Proof
% 0.13/0.41 Axiom 1 (commutativity_of_add): add(X, Y) = add(Y, X).
% 0.13/0.41 Axiom 2 (additive_id1): add(X, additive_identity) = X.
% 0.13/0.41 Axiom 3 (additive_id2): add(additive_identity, X) = X.
% 0.13/0.41 Axiom 4 (commutativity_of_multiply): multiply(X, Y) = multiply(Y, X).
% 0.13/0.41 Axiom 5 (multiplicative_id2): multiply(multiplicative_identity, X) = X.
% 0.13/0.41 Axiom 6 (additive_inverse1): add(X, inverse(X)) = multiplicative_identity.
% 0.13/0.41 Axiom 7 (multiplicative_inverse1): multiply(X, inverse(X)) = additive_identity.
% 0.13/0.41 Axiom 8 (distributivity4): multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)).
% 0.13/0.41 Axiom 9 (distributivity2): add(X, multiply(Y, Z)) = multiply(add(X, Y), add(X, Z)).
% 0.13/0.41
% 0.13/0.41 Lemma 10: add(X, multiply(Y, inverse(X))) = add(X, Y).
% 0.13/0.41 Proof:
% 0.13/0.41 add(X, multiply(Y, inverse(X)))
% 0.13/0.41 = { by axiom 4 (commutativity_of_multiply) R->L }
% 0.13/0.41 add(X, multiply(inverse(X), Y))
% 0.13/0.41 = { by axiom 9 (distributivity2) }
% 0.13/0.41 multiply(add(X, inverse(X)), add(X, Y))
% 0.13/0.41 = { by axiom 6 (additive_inverse1) }
% 0.13/0.41 multiply(multiplicative_identity, add(X, Y))
% 0.13/0.41 = { by axiom 5 (multiplicative_id2) }
% 0.13/0.41 add(X, Y)
% 0.13/0.41
% 0.13/0.41 Lemma 11: multiply(X, add(Y, inverse(X))) = multiply(X, Y).
% 0.13/0.41 Proof:
% 0.13/0.41 multiply(X, add(Y, inverse(X)))
% 0.13/0.41 = { by axiom 1 (commutativity_of_add) R->L }
% 0.13/0.41 multiply(X, add(inverse(X), Y))
% 0.13/0.41 = { by axiom 8 (distributivity4) }
% 0.13/0.41 add(multiply(X, inverse(X)), multiply(X, Y))
% 0.13/0.41 = { by axiom 7 (multiplicative_inverse1) }
% 0.13/0.41 add(additive_identity, multiply(X, Y))
% 0.13/0.41 = { by axiom 3 (additive_id2) }
% 0.13/0.41 multiply(X, Y)
% 0.13/0.41
% 0.13/0.41 Lemma 12: multiply(X, add(inverse(X), Y)) = multiply(X, Y).
% 0.13/0.41 Proof:
% 0.13/0.41 multiply(X, add(inverse(X), Y))
% 0.13/0.41 = { by axiom 1 (commutativity_of_add) R->L }
% 0.13/0.41 multiply(X, add(Y, inverse(X)))
% 0.13/0.41 = { by lemma 11 }
% 0.13/0.41 multiply(X, Y)
% 0.13/0.41
% 0.13/0.41 Goal 1 (prove_inverse_is_an_involution): inverse(inverse(x)) = x.
% 0.13/0.41 Proof:
% 0.13/0.41 inverse(inverse(x))
% 0.13/0.41 = { by axiom 2 (additive_id1) R->L }
% 0.13/0.41 add(inverse(inverse(x)), additive_identity)
% 0.13/0.41 = { by axiom 7 (multiplicative_inverse1) R->L }
% 0.13/0.41 add(inverse(inverse(x)), multiply(x, inverse(x)))
% 0.13/0.41 = { by axiom 3 (additive_id2) R->L }
% 0.13/0.41 add(inverse(inverse(x)), multiply(x, add(additive_identity, inverse(x))))
% 0.13/0.41 = { by lemma 11 }
% 0.13/0.41 add(inverse(inverse(x)), multiply(x, additive_identity))
% 0.13/0.41 = { by axiom 7 (multiplicative_inverse1) R->L }
% 0.13/0.41 add(inverse(inverse(x)), multiply(x, multiply(inverse(inverse(x)), inverse(inverse(inverse(x))))))
% 0.13/0.41 = { by axiom 4 (commutativity_of_multiply) R->L }
% 0.13/0.41 add(inverse(inverse(x)), multiply(x, multiply(inverse(inverse(inverse(x))), inverse(inverse(x)))))
% 0.13/0.41 = { by lemma 12 R->L }
% 0.13/0.41 add(inverse(inverse(x)), multiply(x, add(inverse(x), multiply(inverse(inverse(inverse(x))), inverse(inverse(x))))))
% 0.13/0.41 = { by lemma 10 }
% 0.13/0.41 add(inverse(inverse(x)), multiply(x, add(inverse(x), inverse(inverse(inverse(x))))))
% 0.13/0.41 = { by lemma 12 }
% 0.13/0.41 add(inverse(inverse(x)), multiply(x, inverse(inverse(inverse(x)))))
% 0.13/0.41 = { by lemma 10 }
% 0.13/0.41 add(inverse(inverse(x)), x)
% 0.13/0.41 = { by axiom 1 (commutativity_of_add) }
% 0.13/0.41 add(x, inverse(inverse(x)))
% 0.13/0.41 = { by lemma 10 R->L }
% 0.13/0.41 add(x, multiply(inverse(inverse(x)), inverse(x)))
% 0.13/0.41 = { by axiom 4 (commutativity_of_multiply) }
% 0.13/0.41 add(x, multiply(inverse(x), inverse(inverse(x))))
% 0.13/0.41 = { by axiom 7 (multiplicative_inverse1) }
% 0.13/0.41 add(x, additive_identity)
% 0.13/0.41 = { by axiom 2 (additive_id1) }
% 0.13/0.41 x
% 0.13/0.41 % SZS output end Proof
% 0.13/0.41
% 0.13/0.41 RESULT: Unsatisfiable (the axioms are contradictory).
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