TSTP Solution File: BOO008-2 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : BOO008-2 : 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 : n002.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 18:11:19 EDT 2023
% Result : Unsatisfiable 0.20s 0.49s
% 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
% 0.10/0.12 % Problem : BOO008-2 : TPTP v8.1.2. Released v1.0.0.
% 0.10/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n002.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Aug 27 08:12:18 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.49 Command-line arguments: --no-flatten-goal
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% 0.20/0.49 % SZS status Unsatisfiable
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% 0.20/0.50 % SZS output start Proof
% 0.20/0.50 Axiom 1 (commutativity_of_multiply): multiply(X, Y) = multiply(Y, X).
% 0.20/0.50 Axiom 2 (multiplicative_id1): multiply(X, multiplicative_identity) = X.
% 0.20/0.50 Axiom 3 (multiplicative_id2): multiply(multiplicative_identity, X) = X.
% 0.20/0.50 Axiom 4 (commutativity_of_add): add(X, Y) = add(Y, X).
% 0.20/0.50 Axiom 5 (additive_id1): add(X, additive_identity) = X.
% 0.20/0.50 Axiom 6 (additive_id2): add(additive_identity, X) = X.
% 0.20/0.50 Axiom 7 (multiplicative_inverse1): multiply(X, inverse(X)) = additive_identity.
% 0.20/0.50 Axiom 8 (additive_inverse1): add(X, inverse(X)) = multiplicative_identity.
% 0.20/0.50 Axiom 9 (distributivity2): add(X, multiply(Y, Z)) = multiply(add(X, Y), add(X, Z)).
% 0.20/0.50 Axiom 10 (distributivity1): add(multiply(X, Y), Z) = multiply(add(X, Z), add(Y, Z)).
% 0.20/0.50 Axiom 11 (distributivity4): multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)).
% 0.20/0.50
% 0.20/0.50 Lemma 12: add(X, multiply(Y, inverse(X))) = add(X, Y).
% 0.20/0.50 Proof:
% 0.20/0.50 add(X, multiply(Y, inverse(X)))
% 0.20/0.50 = { by axiom 1 (commutativity_of_multiply) R->L }
% 0.20/0.50 add(X, multiply(inverse(X), Y))
% 0.20/0.50 = { by axiom 9 (distributivity2) }
% 0.20/0.50 multiply(add(X, inverse(X)), add(X, Y))
% 0.20/0.50 = { by axiom 8 (additive_inverse1) }
% 0.20/0.50 multiply(multiplicative_identity, add(X, Y))
% 0.20/0.50 = { by axiom 3 (multiplicative_id2) }
% 0.20/0.50 add(X, Y)
% 0.20/0.50
% 0.20/0.50 Lemma 13: add(X, multiplicative_identity) = multiplicative_identity.
% 0.20/0.50 Proof:
% 0.20/0.50 add(X, multiplicative_identity)
% 0.20/0.50 = { by lemma 12 R->L }
% 0.20/0.50 add(X, multiply(multiplicative_identity, inverse(X)))
% 0.20/0.50 = { by axiom 3 (multiplicative_id2) }
% 0.20/0.50 add(X, inverse(X))
% 0.20/0.50 = { by axiom 8 (additive_inverse1) }
% 0.20/0.50 multiplicative_identity
% 0.20/0.50
% 0.20/0.50 Lemma 14: add(X, multiply(X, Y)) = multiply(X, add(Y, multiplicative_identity)).
% 0.20/0.50 Proof:
% 0.20/0.50 add(X, multiply(X, Y))
% 0.20/0.50 = { by axiom 2 (multiplicative_id1) R->L }
% 0.20/0.50 add(multiply(X, multiplicative_identity), multiply(X, Y))
% 0.20/0.50 = { by axiom 11 (distributivity4) R->L }
% 0.20/0.50 multiply(X, add(multiplicative_identity, Y))
% 0.20/0.50 = { by axiom 4 (commutativity_of_add) }
% 0.20/0.50 multiply(X, add(Y, multiplicative_identity))
% 0.20/0.50
% 0.20/0.50 Lemma 15: add(X, multiply(inverse(X), Y)) = add(X, Y).
% 0.20/0.50 Proof:
% 0.20/0.50 add(X, multiply(inverse(X), Y))
% 0.20/0.50 = { by axiom 1 (commutativity_of_multiply) R->L }
% 0.20/0.50 add(X, multiply(Y, inverse(X)))
% 0.20/0.50 = { by lemma 12 }
% 0.20/0.50 add(X, Y)
% 0.20/0.50
% 0.20/0.50 Goal 1 (prove_associativity): add(a, add(b, c)) = add(add(a, b), c).
% 0.20/0.50 Proof:
% 0.20/0.50 add(a, add(b, c))
% 0.20/0.50 = { by lemma 15 R->L }
% 0.20/0.50 add(a, multiply(inverse(a), add(b, c)))
% 0.20/0.50 = { by axiom 11 (distributivity4) }
% 0.20/0.50 add(a, add(multiply(inverse(a), b), multiply(inverse(a), c)))
% 0.20/0.50 = { by axiom 6 (additive_id2) R->L }
% 0.20/0.50 add(a, add(add(additive_identity, multiply(inverse(a), b)), multiply(inverse(a), c)))
% 0.20/0.50 = { by axiom 7 (multiplicative_inverse1) R->L }
% 0.20/0.50 add(a, add(add(multiply(inverse(a), inverse(inverse(a))), multiply(inverse(a), b)), multiply(inverse(a), c)))
% 0.20/0.50 = { by axiom 11 (distributivity4) R->L }
% 0.20/0.50 add(a, add(multiply(inverse(a), add(inverse(inverse(a)), b)), multiply(inverse(a), c)))
% 0.20/0.50 = { by axiom 4 (commutativity_of_add) }
% 0.20/0.50 add(a, add(multiply(inverse(a), add(b, inverse(inverse(a)))), multiply(inverse(a), c)))
% 0.20/0.50 = { by axiom 11 (distributivity4) R->L }
% 0.20/0.50 add(a, multiply(inverse(a), add(add(b, inverse(inverse(a))), c)))
% 0.20/0.50 = { by axiom 4 (commutativity_of_add) }
% 0.20/0.50 add(a, multiply(inverse(a), add(c, add(b, inverse(inverse(a))))))
% 0.20/0.50 = { by lemma 15 }
% 0.20/0.50 add(a, add(c, add(b, inverse(inverse(a)))))
% 0.20/0.50 = { by axiom 5 (additive_id1) R->L }
% 0.20/0.50 add(a, add(c, add(b, add(inverse(inverse(a)), additive_identity))))
% 0.20/0.50 = { by axiom 7 (multiplicative_inverse1) R->L }
% 0.20/0.50 add(a, add(c, add(b, add(inverse(inverse(a)), multiply(a, inverse(a))))))
% 0.20/0.50 = { by axiom 1 (commutativity_of_multiply) R->L }
% 0.20/0.50 add(a, add(c, add(b, add(inverse(inverse(a)), multiply(inverse(a), a)))))
% 0.20/0.50 = { by axiom 4 (commutativity_of_add) R->L }
% 0.20/0.50 add(a, add(c, add(b, add(multiply(inverse(a), a), inverse(inverse(a))))))
% 0.20/0.50 = { by axiom 10 (distributivity1) }
% 0.20/0.50 add(a, add(c, add(b, multiply(add(inverse(a), inverse(inverse(a))), add(a, inverse(inverse(a)))))))
% 0.20/0.50 = { by axiom 8 (additive_inverse1) }
% 0.20/0.50 add(a, add(c, add(b, multiply(multiplicative_identity, add(a, inverse(inverse(a)))))))
% 0.20/0.50 = { by axiom 3 (multiplicative_id2) }
% 0.20/0.50 add(a, add(c, add(b, add(a, inverse(inverse(a))))))
% 0.20/0.50 = { by lemma 15 R->L }
% 0.20/0.50 add(a, add(c, add(b, add(a, multiply(inverse(a), inverse(inverse(a)))))))
% 0.20/0.50 = { by axiom 7 (multiplicative_inverse1) }
% 0.20/0.50 add(a, add(c, add(b, add(a, additive_identity))))
% 0.20/0.50 = { by axiom 5 (additive_id1) }
% 0.20/0.50 add(a, add(c, add(b, a)))
% 0.20/0.50 = { by axiom 4 (commutativity_of_add) }
% 0.20/0.50 add(a, add(c, add(a, b)))
% 0.20/0.50 = { by axiom 4 (commutativity_of_add) R->L }
% 0.20/0.50 add(add(c, add(a, b)), a)
% 0.20/0.50 = { by axiom 2 (multiplicative_id1) R->L }
% 0.20/0.50 add(add(c, add(a, b)), multiply(a, multiplicative_identity))
% 0.20/0.50 = { by lemma 13 R->L }
% 0.20/0.50 add(add(c, add(a, b)), multiply(a, add(c, multiplicative_identity)))
% 0.20/0.50 = { by lemma 14 R->L }
% 0.20/0.50 add(add(c, add(a, b)), add(a, multiply(a, c)))
% 0.20/0.50 = { by axiom 5 (additive_id1) R->L }
% 0.20/0.50 add(add(c, add(a, b)), add(add(a, additive_identity), multiply(a, c)))
% 0.20/0.50 = { by axiom 2 (multiplicative_id1) R->L }
% 0.20/0.50 add(add(c, add(a, b)), add(add(a, multiply(additive_identity, multiplicative_identity)), multiply(a, c)))
% 0.20/0.50 = { by lemma 13 R->L }
% 0.20/0.50 add(add(c, add(a, b)), add(add(a, multiply(additive_identity, add(b, multiplicative_identity))), multiply(a, c)))
% 0.20/0.50 = { by lemma 14 R->L }
% 0.20/0.50 add(add(c, add(a, b)), add(add(a, add(additive_identity, multiply(additive_identity, b))), multiply(a, c)))
% 0.20/0.50 = { by axiom 6 (additive_id2) }
% 0.20/0.50 add(add(c, add(a, b)), add(add(a, multiply(additive_identity, b)), multiply(a, c)))
% 0.20/0.50 = { by axiom 9 (distributivity2) }
% 0.20/0.50 add(add(c, add(a, b)), add(multiply(add(a, additive_identity), add(a, b)), multiply(a, c)))
% 0.20/0.50 = { by axiom 5 (additive_id1) }
% 0.20/0.50 add(add(c, add(a, b)), add(multiply(a, add(a, b)), multiply(a, c)))
% 0.20/0.50 = { by axiom 11 (distributivity4) R->L }
% 0.20/0.50 add(add(c, add(a, b)), multiply(a, add(add(a, b), c)))
% 0.20/0.50 = { by axiom 4 (commutativity_of_add) }
% 0.20/0.50 add(add(c, add(a, b)), multiply(a, add(c, add(a, b))))
% 0.20/0.50 = { by axiom 1 (commutativity_of_multiply) R->L }
% 0.20/0.50 add(add(c, add(a, b)), multiply(add(c, add(a, b)), a))
% 0.20/0.50 = { by lemma 14 }
% 0.20/0.50 multiply(add(c, add(a, b)), add(a, multiplicative_identity))
% 0.20/0.50 = { by lemma 13 }
% 0.20/0.50 multiply(add(c, add(a, b)), multiplicative_identity)
% 0.20/0.50 = { by axiom 2 (multiplicative_id1) }
% 0.20/0.50 add(c, add(a, b))
% 0.20/0.50 = { by axiom 4 (commutativity_of_add) R->L }
% 0.20/0.50 add(add(a, b), c)
% 0.20/0.50 % SZS output end Proof
% 0.20/0.50
% 0.20/0.50 RESULT: Unsatisfiable (the axioms are contradictory).
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