TSTP Solution File: BOO015-2 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : BOO015-2 : TPTP v8.1.2. Bugfixed v1.0.1.
% 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 : Wed Aug 30 18:11:25 EDT 2023
% Result : Unsatisfiable 0.21s 0.53s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : BOO015-2 : TPTP v8.1.2. Bugfixed v1.0.1.
% 0.08/0.15 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.36 % Computer : n007.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sun Aug 27 08:30:42 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.53 Command-line arguments: --no-flatten-goal
% 0.21/0.53
% 0.21/0.53 % SZS status Unsatisfiable
% 0.21/0.53
% 0.21/0.54 % SZS output start Proof
% 0.21/0.54 Axiom 1 (commutativity_of_add): add(X, Y) = add(Y, X).
% 0.21/0.54 Axiom 2 (additive_id1): add(X, additive_identity) = X.
% 0.21/0.54 Axiom 3 (additive_id2): add(additive_identity, X) = X.
% 0.21/0.54 Axiom 4 (commutativity_of_multiply): multiply(X, Y) = multiply(Y, X).
% 0.21/0.54 Axiom 5 (multiplicative_id1): multiply(X, multiplicative_identity) = X.
% 0.21/0.54 Axiom 6 (a_times_b_is_c): multiply(a, b) = c.
% 0.21/0.54 Axiom 7 (multiplicative_id2): multiply(multiplicative_identity, X) = X.
% 0.21/0.54 Axiom 8 (additive_inverse1): add(X, inverse(X)) = multiplicative_identity.
% 0.21/0.54 Axiom 9 (multiplicative_inverse1): multiply(X, inverse(X)) = additive_identity.
% 0.21/0.54 Axiom 10 (a_inverse_plus_b_inverse_is_d): add(inverse(a), inverse(b)) = d.
% 0.21/0.54 Axiom 11 (distributivity4): multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)).
% 0.21/0.54 Axiom 12 (distributivity3): multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z)).
% 0.21/0.54 Axiom 13 (distributivity2): add(X, multiply(Y, Z)) = multiply(add(X, Y), add(X, Z)).
% 0.21/0.54 Axiom 14 (distributivity1): add(multiply(X, Y), Z) = multiply(add(X, Z), add(Y, Z)).
% 0.21/0.54
% 0.21/0.54 Lemma 15: multiply(X, add(X, Y)) = add(X, multiply(Y, additive_identity)).
% 0.21/0.54 Proof:
% 0.21/0.54 multiply(X, add(X, Y))
% 0.21/0.54 = { by axiom 2 (additive_id1) R->L }
% 0.21/0.54 multiply(add(X, additive_identity), add(X, Y))
% 0.21/0.54 = { by axiom 13 (distributivity2) R->L }
% 0.21/0.54 add(X, multiply(additive_identity, Y))
% 0.21/0.54 = { by axiom 4 (commutativity_of_multiply) }
% 0.21/0.54 add(X, multiply(Y, additive_identity))
% 0.21/0.54
% 0.21/0.54 Lemma 16: multiply(X, add(Y, inverse(X))) = multiply(X, Y).
% 0.21/0.54 Proof:
% 0.21/0.54 multiply(X, add(Y, inverse(X)))
% 0.21/0.54 = { by axiom 1 (commutativity_of_add) R->L }
% 0.21/0.54 multiply(X, add(inverse(X), Y))
% 0.21/0.54 = { by axiom 11 (distributivity4) }
% 0.21/0.54 add(multiply(X, inverse(X)), multiply(X, Y))
% 0.21/0.54 = { by axiom 9 (multiplicative_inverse1) }
% 0.21/0.54 add(additive_identity, multiply(X, Y))
% 0.21/0.54 = { by axiom 3 (additive_id2) }
% 0.21/0.54 multiply(X, Y)
% 0.21/0.54
% 0.21/0.54 Lemma 17: multiply(X, additive_identity) = additive_identity.
% 0.21/0.54 Proof:
% 0.21/0.54 multiply(X, additive_identity)
% 0.21/0.54 = { by lemma 16 R->L }
% 0.21/0.54 multiply(X, add(additive_identity, inverse(X)))
% 0.21/0.54 = { by axiom 3 (additive_id2) }
% 0.21/0.54 multiply(X, inverse(X))
% 0.21/0.54 = { by axiom 9 (multiplicative_inverse1) }
% 0.21/0.54 additive_identity
% 0.21/0.54
% 0.21/0.54 Lemma 18: add(X, multiplicative_identity) = multiplicative_identity.
% 0.21/0.54 Proof:
% 0.21/0.55 add(X, multiplicative_identity)
% 0.21/0.55 = { by axiom 1 (commutativity_of_add) R->L }
% 0.21/0.55 add(multiplicative_identity, X)
% 0.21/0.55 = { by axiom 7 (multiplicative_id2) R->L }
% 0.21/0.55 multiply(multiplicative_identity, add(multiplicative_identity, X))
% 0.21/0.55 = { by lemma 15 }
% 0.21/0.55 add(multiplicative_identity, multiply(X, additive_identity))
% 0.21/0.55 = { by lemma 17 }
% 0.21/0.55 add(multiplicative_identity, additive_identity)
% 0.21/0.55 = { by axiom 2 (additive_id1) }
% 0.21/0.55 multiplicative_identity
% 0.21/0.55
% 0.21/0.55 Lemma 19: multiply(a, inverse(b)) = multiply(a, d).
% 0.21/0.55 Proof:
% 0.21/0.55 multiply(a, inverse(b))
% 0.21/0.55 = { by lemma 16 R->L }
% 0.21/0.55 multiply(a, add(inverse(b), inverse(a)))
% 0.21/0.55 = { by axiom 1 (commutativity_of_add) }
% 0.21/0.55 multiply(a, add(inverse(a), inverse(b)))
% 0.21/0.55 = { by axiom 10 (a_inverse_plus_b_inverse_is_d) }
% 0.21/0.55 multiply(a, d)
% 0.21/0.55
% 0.21/0.55 Lemma 20: multiply(X, add(Y, X)) = X.
% 0.21/0.55 Proof:
% 0.21/0.55 multiply(X, add(Y, X))
% 0.21/0.55 = { by axiom 1 (commutativity_of_add) R->L }
% 0.21/0.55 multiply(X, add(X, Y))
% 0.21/0.55 = { by lemma 15 }
% 0.21/0.55 add(X, multiply(Y, additive_identity))
% 0.21/0.55 = { by lemma 17 }
% 0.21/0.55 add(X, additive_identity)
% 0.21/0.55 = { by axiom 2 (additive_id1) }
% 0.21/0.55 X
% 0.21/0.55
% 0.21/0.55 Lemma 21: multiply(X, add(Y, multiplicative_identity)) = add(X, multiply(X, Y)).
% 0.21/0.55 Proof:
% 0.21/0.55 multiply(X, add(Y, multiplicative_identity))
% 0.21/0.55 = { by axiom 1 (commutativity_of_add) R->L }
% 0.21/0.55 multiply(X, add(multiplicative_identity, Y))
% 0.21/0.55 = { by axiom 11 (distributivity4) }
% 0.21/0.55 add(multiply(X, multiplicative_identity), multiply(X, Y))
% 0.21/0.55 = { by axiom 5 (multiplicative_id1) }
% 0.21/0.55 add(X, multiply(X, Y))
% 0.21/0.55
% 0.21/0.55 Lemma 22: multiply(c, multiply(a, X)) = multiply(X, c).
% 0.21/0.55 Proof:
% 0.21/0.55 multiply(c, multiply(a, X))
% 0.21/0.55 = { by axiom 4 (commutativity_of_multiply) R->L }
% 0.21/0.55 multiply(c, multiply(X, a))
% 0.21/0.55 = { by axiom 5 (multiplicative_id1) R->L }
% 0.21/0.55 multiply(c, multiply(X, multiply(a, multiplicative_identity)))
% 0.21/0.55 = { by axiom 8 (additive_inverse1) R->L }
% 0.21/0.55 multiply(c, multiply(X, multiply(a, add(b, inverse(b)))))
% 0.21/0.55 = { by axiom 11 (distributivity4) }
% 0.21/0.55 multiply(c, multiply(X, add(multiply(a, b), multiply(a, inverse(b)))))
% 0.21/0.55 = { by axiom 6 (a_times_b_is_c) }
% 0.21/0.55 multiply(c, multiply(X, add(c, multiply(a, inverse(b)))))
% 0.21/0.55 = { by lemma 19 }
% 0.21/0.55 multiply(c, multiply(X, add(c, multiply(a, d))))
% 0.21/0.55 = { by axiom 1 (commutativity_of_add) R->L }
% 0.21/0.55 multiply(c, multiply(X, add(multiply(a, d), c)))
% 0.21/0.55 = { by axiom 4 (commutativity_of_multiply) R->L }
% 0.21/0.55 multiply(c, multiply(add(multiply(a, d), c), X))
% 0.21/0.55 = { by axiom 12 (distributivity3) }
% 0.21/0.55 multiply(c, add(multiply(multiply(a, d), X), multiply(c, X)))
% 0.21/0.55 = { by axiom 1 (commutativity_of_add) R->L }
% 0.21/0.55 multiply(c, add(multiply(c, X), multiply(multiply(a, d), X)))
% 0.21/0.55 = { by axiom 5 (multiplicative_id1) R->L }
% 0.21/0.55 multiply(multiply(c, multiplicative_identity), add(multiply(c, X), multiply(multiply(a, d), X)))
% 0.21/0.55 = { by lemma 18 R->L }
% 0.21/0.55 multiply(multiply(c, add(X, multiplicative_identity)), add(multiply(c, X), multiply(multiply(a, d), X)))
% 0.21/0.55 = { by lemma 21 }
% 0.21/0.55 multiply(add(c, multiply(c, X)), add(multiply(c, X), multiply(multiply(a, d), X)))
% 0.21/0.55 = { by axiom 1 (commutativity_of_add) R->L }
% 0.21/0.55 multiply(add(multiply(c, X), c), add(multiply(c, X), multiply(multiply(a, d), X)))
% 0.21/0.55 = { by axiom 13 (distributivity2) R->L }
% 0.21/0.55 add(multiply(c, X), multiply(c, multiply(multiply(a, d), X)))
% 0.21/0.55 = { by axiom 11 (distributivity4) R->L }
% 0.21/0.55 multiply(c, add(X, multiply(multiply(a, d), X)))
% 0.21/0.55 = { by axiom 4 (commutativity_of_multiply) R->L }
% 0.21/0.55 multiply(c, add(X, multiply(X, multiply(a, d))))
% 0.21/0.55 = { by lemma 21 R->L }
% 0.21/0.55 multiply(c, multiply(X, add(multiply(a, d), multiplicative_identity)))
% 0.21/0.55 = { by lemma 18 }
% 0.21/0.55 multiply(c, multiply(X, multiplicative_identity))
% 0.21/0.55 = { by axiom 5 (multiplicative_id1) }
% 0.21/0.55 multiply(c, X)
% 0.21/0.55 = { by axiom 4 (commutativity_of_multiply) }
% 0.21/0.55 multiply(X, c)
% 0.21/0.55
% 0.21/0.55 Lemma 23: add(X, multiply(Y, inverse(X))) = add(X, Y).
% 0.21/0.55 Proof:
% 0.21/0.55 add(X, multiply(Y, inverse(X)))
% 0.21/0.55 = { by axiom 4 (commutativity_of_multiply) R->L }
% 0.21/0.55 add(X, multiply(inverse(X), Y))
% 0.21/0.55 = { by axiom 13 (distributivity2) }
% 0.21/0.55 multiply(add(X, inverse(X)), add(X, Y))
% 0.21/0.55 = { by axiom 8 (additive_inverse1) }
% 0.21/0.55 multiply(multiplicative_identity, add(X, Y))
% 0.21/0.55 = { by axiom 7 (multiplicative_id2) }
% 0.21/0.55 add(X, Y)
% 0.21/0.55
% 0.21/0.55 Lemma 24: multiply(inverse(X), add(X, Y)) = multiply(Y, inverse(X)).
% 0.21/0.55 Proof:
% 0.21/0.55 multiply(inverse(X), add(X, Y))
% 0.21/0.55 = { by axiom 4 (commutativity_of_multiply) R->L }
% 0.21/0.55 multiply(add(X, Y), inverse(X))
% 0.21/0.55 = { by axiom 12 (distributivity3) }
% 0.21/0.55 add(multiply(X, inverse(X)), multiply(Y, inverse(X)))
% 0.21/0.55 = { by axiom 9 (multiplicative_inverse1) }
% 0.21/0.55 add(additive_identity, multiply(Y, inverse(X)))
% 0.21/0.55 = { by axiom 3 (additive_id2) }
% 0.21/0.55 multiply(Y, inverse(X))
% 0.21/0.55
% 0.21/0.55 Goal 1 (prove_c_inverse_is_d): inverse(c) = d.
% 0.21/0.55 Proof:
% 0.21/0.55 inverse(c)
% 0.21/0.55 = { by axiom 2 (additive_id1) R->L }
% 0.21/0.55 add(inverse(c), additive_identity)
% 0.21/0.55 = { by axiom 9 (multiplicative_inverse1) R->L }
% 0.21/0.55 add(inverse(c), multiply(b, inverse(b)))
% 0.21/0.55 = { by axiom 4 (commutativity_of_multiply) R->L }
% 0.21/0.55 add(inverse(c), multiply(inverse(b), b))
% 0.21/0.55 = { by axiom 5 (multiplicative_id1) R->L }
% 0.21/0.55 add(inverse(c), multiply(inverse(b), multiply(b, multiplicative_identity)))
% 0.21/0.55 = { by lemma 18 R->L }
% 0.21/0.55 add(inverse(c), multiply(inverse(b), multiply(b, add(a, multiplicative_identity))))
% 0.21/0.55 = { by lemma 21 }
% 0.21/0.55 add(inverse(c), multiply(inverse(b), add(b, multiply(b, a))))
% 0.21/0.55 = { by lemma 24 }
% 0.21/0.55 add(inverse(c), multiply(multiply(b, a), inverse(b)))
% 0.21/0.55 = { by axiom 4 (commutativity_of_multiply) }
% 0.21/0.55 add(inverse(c), multiply(inverse(b), multiply(b, a)))
% 0.21/0.55 = { by axiom 4 (commutativity_of_multiply) }
% 0.21/0.55 add(inverse(c), multiply(inverse(b), multiply(a, b)))
% 0.21/0.55 = { by axiom 6 (a_times_b_is_c) }
% 0.21/0.55 add(inverse(c), multiply(inverse(b), c))
% 0.21/0.55 = { by lemma 22 R->L }
% 0.21/0.55 add(inverse(c), multiply(c, multiply(a, inverse(b))))
% 0.21/0.55 = { by lemma 19 }
% 0.21/0.55 add(inverse(c), multiply(c, multiply(a, d)))
% 0.21/0.55 = { by lemma 22 }
% 0.21/0.55 add(inverse(c), multiply(d, c))
% 0.21/0.55 = { by axiom 4 (commutativity_of_multiply) }
% 0.21/0.55 add(inverse(c), multiply(c, d))
% 0.21/0.55 = { by axiom 1 (commutativity_of_add) R->L }
% 0.21/0.55 add(multiply(c, d), inverse(c))
% 0.21/0.55 = { by axiom 14 (distributivity1) }
% 0.21/0.55 multiply(add(c, inverse(c)), add(d, inverse(c)))
% 0.21/0.55 = { by axiom 8 (additive_inverse1) }
% 0.21/0.55 multiply(multiplicative_identity, add(d, inverse(c)))
% 0.21/0.55 = { by axiom 7 (multiplicative_id2) }
% 0.21/0.55 add(d, inverse(c))
% 0.21/0.55 = { by axiom 5 (multiplicative_id1) R->L }
% 0.21/0.55 add(d, multiply(inverse(c), multiplicative_identity))
% 0.21/0.55 = { by axiom 8 (additive_inverse1) R->L }
% 0.21/0.55 add(d, multiply(inverse(c), add(a, inverse(a))))
% 0.21/0.55 = { by lemma 20 R->L }
% 0.21/0.55 add(d, multiply(inverse(c), add(a, multiply(inverse(a), add(d, inverse(a))))))
% 0.21/0.55 = { by axiom 1 (commutativity_of_add) R->L }
% 0.21/0.55 add(d, multiply(inverse(c), add(a, multiply(inverse(a), add(inverse(a), d)))))
% 0.21/0.55 = { by axiom 10 (a_inverse_plus_b_inverse_is_d) R->L }
% 0.21/0.55 add(d, multiply(inverse(c), add(a, multiply(inverse(a), add(inverse(a), add(inverse(a), inverse(b)))))))
% 0.21/0.55 = { by lemma 23 R->L }
% 0.21/0.55 add(d, multiply(inverse(c), add(a, multiply(inverse(a), add(inverse(a), multiply(add(inverse(a), inverse(b)), inverse(inverse(a))))))))
% 0.21/0.55 = { by axiom 4 (commutativity_of_multiply) }
% 0.21/0.55 add(d, multiply(inverse(c), add(a, multiply(inverse(a), add(inverse(a), multiply(inverse(inverse(a)), add(inverse(a), inverse(b))))))))
% 0.21/0.55 = { by lemma 24 }
% 0.21/0.55 add(d, multiply(inverse(c), add(a, multiply(inverse(a), add(inverse(a), multiply(inverse(b), inverse(inverse(a))))))))
% 0.21/0.55 = { by lemma 23 }
% 0.21/0.55 add(d, multiply(inverse(c), add(a, multiply(inverse(a), add(inverse(a), inverse(b))))))
% 0.21/0.55 = { by axiom 10 (a_inverse_plus_b_inverse_is_d) }
% 0.21/0.55 add(d, multiply(inverse(c), add(a, multiply(inverse(a), d))))
% 0.21/0.55 = { by axiom 4 (commutativity_of_multiply) }
% 0.21/0.55 add(d, multiply(inverse(c), add(a, multiply(d, inverse(a)))))
% 0.21/0.55 = { by lemma 23 }
% 0.21/0.55 add(d, multiply(inverse(c), add(a, d)))
% 0.21/0.55 = { by axiom 7 (multiplicative_id2) R->L }
% 0.21/0.55 add(d, multiply(inverse(c), multiply(multiplicative_identity, add(a, d))))
% 0.21/0.55 = { by axiom 8 (additive_inverse1) R->L }
% 0.21/0.55 add(d, multiply(inverse(c), multiply(add(b, inverse(b)), add(a, d))))
% 0.21/0.55 = { by lemma 20 R->L }
% 0.21/0.55 add(d, multiply(inverse(c), multiply(add(b, multiply(inverse(b), add(inverse(a), inverse(b)))), add(a, d))))
% 0.21/0.55 = { by axiom 10 (a_inverse_plus_b_inverse_is_d) }
% 0.21/0.55 add(d, multiply(inverse(c), multiply(add(b, multiply(inverse(b), d)), add(a, d))))
% 0.21/0.55 = { by axiom 4 (commutativity_of_multiply) }
% 0.21/0.55 add(d, multiply(inverse(c), multiply(add(b, multiply(d, inverse(b))), add(a, d))))
% 0.21/0.55 = { by lemma 23 }
% 0.21/0.55 add(d, multiply(inverse(c), multiply(add(b, d), add(a, d))))
% 0.21/0.55 = { by axiom 14 (distributivity1) R->L }
% 0.21/0.55 add(d, multiply(inverse(c), add(multiply(b, a), d)))
% 0.21/0.55 = { by axiom 1 (commutativity_of_add) }
% 0.21/0.55 add(d, multiply(inverse(c), add(d, multiply(b, a))))
% 0.21/0.55 = { by axiom 4 (commutativity_of_multiply) }
% 0.21/0.55 add(d, multiply(inverse(c), add(d, multiply(a, b))))
% 0.21/0.55 = { by axiom 6 (a_times_b_is_c) }
% 0.21/0.55 add(d, multiply(inverse(c), add(d, c)))
% 0.21/0.55 = { by axiom 1 (commutativity_of_add) }
% 0.21/0.55 add(d, multiply(inverse(c), add(c, d)))
% 0.21/0.55 = { by lemma 24 }
% 0.21/0.55 add(d, multiply(d, inverse(c)))
% 0.21/0.55 = { by lemma 21 R->L }
% 0.21/0.55 multiply(d, add(inverse(c), multiplicative_identity))
% 0.21/0.55 = { by lemma 18 }
% 0.21/0.55 multiply(d, multiplicative_identity)
% 0.21/0.55 = { by axiom 5 (multiplicative_id1) }
% 0.21/0.55 d
% 0.21/0.55 % SZS output end Proof
% 0.21/0.55
% 0.21/0.55 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------