TSTP Solution File: BOO014-4 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : BOO014-4 : 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 : n028.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 18:11:24 EDT 2023
% Result : Unsatisfiable 0.21s 0.51s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : BOO014-4 : TPTP v8.1.2. Released v1.1.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n028.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Aug 27 08:45:53 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.51 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.21/0.51
% 0.21/0.51 % SZS status Unsatisfiable
% 0.21/0.51
% 0.21/0.55 % SZS output start Proof
% 0.21/0.55 Axiom 1 (commutativity_of_add): add(X, Y) = add(Y, X).
% 0.21/0.55 Axiom 2 (additive_id1): add(X, additive_identity) = X.
% 0.21/0.55 Axiom 3 (commutativity_of_multiply): multiply(X, Y) = multiply(Y, X).
% 0.21/0.55 Axiom 4 (multiplicative_id1): multiply(X, multiplicative_identity) = X.
% 0.21/0.55 Axiom 5 (additive_inverse1): add(X, inverse(X)) = multiplicative_identity.
% 0.21/0.55 Axiom 6 (multiplicative_inverse1): multiply(X, inverse(X)) = additive_identity.
% 0.21/0.55 Axiom 7 (distributivity2): multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)).
% 0.21/0.55 Axiom 8 (distributivity1): add(X, multiply(Y, Z)) = multiply(add(X, Y), add(X, Z)).
% 0.21/0.55
% 0.21/0.55 Lemma 9: add(additive_identity, X) = X.
% 0.21/0.55 Proof:
% 0.21/0.55 add(additive_identity, X)
% 0.21/0.55 = { by axiom 1 (commutativity_of_add) R->L }
% 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 10: multiply(multiplicative_identity, X) = X.
% 0.21/0.55 Proof:
% 0.21/0.55 multiply(multiplicative_identity, X)
% 0.21/0.55 = { by axiom 3 (commutativity_of_multiply) R->L }
% 0.21/0.55 multiply(X, multiplicative_identity)
% 0.21/0.55 = { by axiom 4 (multiplicative_id1) }
% 0.21/0.55 X
% 0.21/0.55
% 0.21/0.55 Lemma 11: multiply(X, add(Y, inverse(X))) = multiply(X, Y).
% 0.21/0.55 Proof:
% 0.21/0.55 multiply(X, add(Y, inverse(X)))
% 0.21/0.55 = { by axiom 7 (distributivity2) }
% 0.21/0.55 add(multiply(X, Y), multiply(X, inverse(X)))
% 0.21/0.55 = { by axiom 6 (multiplicative_inverse1) }
% 0.21/0.55 add(multiply(X, Y), additive_identity)
% 0.21/0.55 = { by axiom 2 (additive_id1) }
% 0.21/0.55 multiply(X, Y)
% 0.21/0.55
% 0.21/0.55 Lemma 12: multiply(X, inverse(inverse(X))) = X.
% 0.21/0.55 Proof:
% 0.21/0.55 multiply(X, inverse(inverse(X)))
% 0.21/0.55 = { by lemma 11 R->L }
% 0.21/0.55 multiply(X, add(inverse(inverse(X)), inverse(X)))
% 0.21/0.55 = { by axiom 1 (commutativity_of_add) }
% 0.21/0.55 multiply(X, add(inverse(X), inverse(inverse(X))))
% 0.21/0.55 = { by axiom 5 (additive_inverse1) }
% 0.21/0.55 multiply(X, multiplicative_identity)
% 0.21/0.55 = { by axiom 4 (multiplicative_id1) }
% 0.21/0.55 X
% 0.21/0.55
% 0.21/0.55 Lemma 13: add(X, multiply(Y, inverse(X))) = add(Y, X).
% 0.21/0.55 Proof:
% 0.21/0.55 add(X, multiply(Y, inverse(X)))
% 0.21/0.55 = { by axiom 3 (commutativity_of_multiply) R->L }
% 0.21/0.55 add(X, multiply(inverse(X), Y))
% 0.21/0.55 = { by axiom 8 (distributivity1) }
% 0.21/0.55 multiply(add(X, inverse(X)), add(X, Y))
% 0.21/0.55 = { by axiom 5 (additive_inverse1) }
% 0.21/0.55 multiply(multiplicative_identity, add(X, Y))
% 0.21/0.55 = { by lemma 10 }
% 0.21/0.55 add(X, Y)
% 0.21/0.55 = { by axiom 1 (commutativity_of_add) }
% 0.21/0.55 add(Y, X)
% 0.21/0.55
% 0.21/0.55 Lemma 14: inverse(inverse(X)) = X.
% 0.21/0.55 Proof:
% 0.21/0.55 inverse(inverse(X))
% 0.21/0.55 = { by axiom 4 (multiplicative_id1) R->L }
% 0.21/0.55 multiply(inverse(inverse(X)), multiplicative_identity)
% 0.21/0.55 = { by axiom 5 (additive_inverse1) R->L }
% 0.21/0.55 multiply(inverse(inverse(X)), add(X, inverse(X)))
% 0.21/0.55 = { by lemma 12 R->L }
% 0.21/0.55 multiply(inverse(inverse(X)), add(X, multiply(inverse(X), inverse(inverse(inverse(X))))))
% 0.21/0.55 = { by axiom 3 (commutativity_of_multiply) R->L }
% 0.21/0.55 multiply(inverse(inverse(X)), add(X, multiply(inverse(inverse(inverse(X))), inverse(X))))
% 0.21/0.55 = { by lemma 13 }
% 0.21/0.55 multiply(inverse(inverse(X)), add(inverse(inverse(inverse(X))), X))
% 0.21/0.55 = { by axiom 1 (commutativity_of_add) }
% 0.21/0.55 multiply(inverse(inverse(X)), add(X, inverse(inverse(inverse(X)))))
% 0.21/0.55 = { by lemma 11 }
% 0.21/0.55 multiply(inverse(inverse(X)), X)
% 0.21/0.55 = { by axiom 3 (commutativity_of_multiply) }
% 0.21/0.55 multiply(X, inverse(inverse(X)))
% 0.21/0.55 = { by lemma 12 }
% 0.21/0.55 X
% 0.21/0.55
% 0.21/0.55 Lemma 15: 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 8 (distributivity1) }
% 0.21/0.55 multiply(add(X, Y), add(X, inverse(X)))
% 0.21/0.55 = { by axiom 5 (additive_inverse1) }
% 0.21/0.55 multiply(add(X, Y), multiplicative_identity)
% 0.21/0.55 = { by axiom 4 (multiplicative_id1) }
% 0.21/0.55 add(X, Y)
% 0.21/0.55
% 0.21/0.55 Lemma 16: add(X, multiply(X, Y)) = X.
% 0.21/0.55 Proof:
% 0.21/0.55 add(X, multiply(X, Y))
% 0.21/0.55 = { by axiom 4 (multiplicative_id1) R->L }
% 0.21/0.55 add(multiply(X, multiplicative_identity), multiply(X, Y))
% 0.21/0.55 = { by axiom 7 (distributivity2) R->L }
% 0.21/0.55 multiply(X, add(multiplicative_identity, Y))
% 0.21/0.55 = { by axiom 1 (commutativity_of_add) R->L }
% 0.21/0.55 multiply(X, add(Y, multiplicative_identity))
% 0.21/0.55 = { by lemma 15 R->L }
% 0.21/0.55 multiply(X, add(Y, multiply(multiplicative_identity, inverse(Y))))
% 0.21/0.55 = { by lemma 10 }
% 0.21/0.55 multiply(X, add(Y, inverse(Y)))
% 0.21/0.55 = { by axiom 5 (additive_inverse1) }
% 0.21/0.55 multiply(X, multiplicative_identity)
% 0.21/0.55 = { by axiom 4 (multiplicative_id1) }
% 0.21/0.55 X
% 0.21/0.55
% 0.21/0.55 Lemma 17: add(X, multiply(Y, X)) = X.
% 0.21/0.55 Proof:
% 0.21/0.55 add(X, multiply(Y, X))
% 0.21/0.55 = { by axiom 3 (commutativity_of_multiply) R->L }
% 0.21/0.55 add(X, multiply(X, Y))
% 0.21/0.55 = { by lemma 16 }
% 0.21/0.55 X
% 0.21/0.55
% 0.21/0.55 Lemma 18: multiply(inverse(X), add(Y, X)) = multiply(Y, inverse(X)).
% 0.21/0.55 Proof:
% 0.21/0.55 multiply(inverse(X), add(Y, X))
% 0.21/0.55 = { by lemma 14 R->L }
% 0.21/0.55 multiply(inverse(X), add(Y, inverse(inverse(X))))
% 0.21/0.55 = { by lemma 11 }
% 0.21/0.55 multiply(inverse(X), Y)
% 0.21/0.55 = { by axiom 3 (commutativity_of_multiply) }
% 0.21/0.55 multiply(Y, inverse(X))
% 0.21/0.55
% 0.21/0.55 Lemma 19: 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 lemma 9 R->L }
% 0.21/0.55 add(additive_identity, multiply(X, add(Y, X)))
% 0.21/0.55 = { by axiom 6 (multiplicative_inverse1) R->L }
% 0.21/0.55 add(multiply(add(Y, X), inverse(add(Y, X))), multiply(X, add(Y, X)))
% 0.21/0.55 = { by axiom 3 (commutativity_of_multiply) R->L }
% 0.21/0.55 add(multiply(inverse(add(Y, X)), add(Y, X)), multiply(X, add(Y, X)))
% 0.21/0.55 = { by lemma 13 R->L }
% 0.21/0.55 add(multiply(inverse(add(Y, X)), add(X, multiply(Y, inverse(X)))), multiply(X, add(Y, X)))
% 0.21/0.55 = { by lemma 18 R->L }
% 0.21/0.55 add(multiply(inverse(add(Y, X)), add(X, multiply(inverse(X), add(Y, X)))), multiply(X, add(Y, X)))
% 0.21/0.55 = { by axiom 3 (commutativity_of_multiply) }
% 0.21/0.55 add(multiply(inverse(add(Y, X)), add(X, multiply(add(Y, X), inverse(X)))), multiply(X, add(Y, X)))
% 0.21/0.55 = { by lemma 13 }
% 0.21/0.55 add(multiply(inverse(add(Y, X)), add(add(Y, X), X)), multiply(X, add(Y, X)))
% 0.21/0.55 = { by axiom 1 (commutativity_of_add) }
% 0.21/0.55 add(multiply(inverse(add(Y, X)), add(X, add(Y, X))), multiply(X, add(Y, X)))
% 0.21/0.55 = { by lemma 18 }
% 0.21/0.55 add(multiply(X, inverse(add(Y, X))), multiply(X, add(Y, X)))
% 0.21/0.55 = { by axiom 7 (distributivity2) R->L }
% 0.21/0.55 multiply(X, add(inverse(add(Y, X)), add(Y, X)))
% 0.21/0.55 = { by axiom 1 (commutativity_of_add) }
% 0.21/0.55 multiply(X, add(add(Y, X), inverse(add(Y, X))))
% 0.21/0.55 = { by axiom 5 (additive_inverse1) }
% 0.21/0.55 multiply(X, multiplicative_identity)
% 0.21/0.55 = { by axiom 4 (multiplicative_id1) }
% 0.21/0.55 X
% 0.21/0.55
% 0.21/0.55 Lemma 20: add(inverse(X), multiply(X, Y)) = add(Y, inverse(X)).
% 0.21/0.55 Proof:
% 0.21/0.55 add(inverse(X), multiply(X, Y))
% 0.21/0.55 = { by axiom 3 (commutativity_of_multiply) R->L }
% 0.21/0.55 add(inverse(X), multiply(Y, X))
% 0.21/0.55 = { by lemma 14 R->L }
% 0.21/0.55 add(inverse(X), multiply(Y, inverse(inverse(X))))
% 0.21/0.55 = { by lemma 15 }
% 0.21/0.55 add(inverse(X), Y)
% 0.21/0.55 = { by axiom 1 (commutativity_of_add) }
% 0.21/0.55 add(Y, inverse(X))
% 0.21/0.55
% 0.21/0.55 Lemma 21: multiply(X, add(Y, inverse(X))) = multiply(Y, X).
% 0.21/0.55 Proof:
% 0.21/0.55 multiply(X, add(Y, inverse(X)))
% 0.21/0.55 = { by axiom 1 (commutativity_of_add) R->L }
% 0.21/0.55 multiply(X, add(inverse(X), Y))
% 0.21/0.55 = { by axiom 7 (distributivity2) }
% 0.21/0.55 add(multiply(X, inverse(X)), multiply(X, Y))
% 0.21/0.55 = { by axiom 6 (multiplicative_inverse1) }
% 0.21/0.55 add(additive_identity, multiply(X, Y))
% 0.21/0.55 = { by lemma 9 }
% 0.21/0.55 multiply(X, Y)
% 0.21/0.55 = { by axiom 3 (commutativity_of_multiply) }
% 0.21/0.55 multiply(Y, X)
% 0.21/0.55
% 0.21/0.55 Lemma 22: 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 1 (commutativity_of_add) R->L }
% 0.21/0.55 multiply(inverse(X), add(Y, X))
% 0.21/0.55 = { by lemma 18 }
% 0.21/0.55 multiply(Y, inverse(X))
% 0.21/0.55
% 0.21/0.55 Lemma 23: add(add(X, Y), multiply(inverse(X), inverse(Y))) = multiplicative_identity.
% 0.21/0.55 Proof:
% 0.21/0.55 add(add(X, Y), multiply(inverse(X), inverse(Y)))
% 0.21/0.55 = { by axiom 3 (commutativity_of_multiply) R->L }
% 0.21/0.55 add(add(X, Y), multiply(inverse(Y), inverse(X)))
% 0.21/0.55 = { by axiom 8 (distributivity1) }
% 0.21/0.55 multiply(add(add(X, Y), inverse(Y)), add(add(X, Y), inverse(X)))
% 0.21/0.55 = { by lemma 20 R->L }
% 0.21/0.55 multiply(add(inverse(Y), multiply(Y, add(X, Y))), add(add(X, Y), inverse(X)))
% 0.21/0.55 = { by lemma 19 }
% 0.21/0.55 multiply(add(inverse(Y), Y), add(add(X, Y), inverse(X)))
% 0.21/0.55 = { by axiom 1 (commutativity_of_add) }
% 0.21/0.55 multiply(add(Y, inverse(Y)), add(add(X, Y), inverse(X)))
% 0.21/0.55 = { by axiom 5 (additive_inverse1) }
% 0.21/0.55 multiply(multiplicative_identity, add(add(X, Y), inverse(X)))
% 0.21/0.55 = { by lemma 10 }
% 0.21/0.55 add(add(X, Y), inverse(X))
% 0.21/0.55 = { by lemma 20 R->L }
% 0.21/0.55 add(inverse(X), multiply(X, add(X, Y)))
% 0.21/0.55 = { by lemma 9 R->L }
% 0.21/0.55 add(inverse(X), add(additive_identity, multiply(X, add(X, Y))))
% 0.21/0.55 = { by axiom 6 (multiplicative_inverse1) R->L }
% 0.21/0.55 add(inverse(X), add(multiply(add(X, Y), inverse(add(X, Y))), multiply(X, add(X, Y))))
% 0.21/0.55 = { by axiom 3 (commutativity_of_multiply) R->L }
% 0.21/0.55 add(inverse(X), add(multiply(inverse(add(X, Y)), add(X, Y)), multiply(X, add(X, Y))))
% 0.21/0.55 = { by axiom 1 (commutativity_of_add) R->L }
% 0.21/0.55 add(inverse(X), add(multiply(inverse(add(X, Y)), add(Y, X)), multiply(X, add(X, Y))))
% 0.21/0.55 = { by lemma 13 R->L }
% 0.21/0.55 add(inverse(X), add(multiply(inverse(add(X, Y)), add(X, multiply(Y, inverse(X)))), multiply(X, add(X, Y))))
% 0.21/0.55 = { by lemma 22 R->L }
% 0.21/0.55 add(inverse(X), add(multiply(inverse(add(X, Y)), add(X, multiply(inverse(X), add(X, Y)))), multiply(X, add(X, Y))))
% 0.21/0.55 = { by axiom 3 (commutativity_of_multiply) }
% 0.21/0.55 add(inverse(X), add(multiply(inverse(add(X, Y)), add(X, multiply(add(X, Y), inverse(X)))), multiply(X, add(X, Y))))
% 0.21/0.55 = { by lemma 13 }
% 0.21/0.55 add(inverse(X), add(multiply(inverse(add(X, Y)), add(add(X, Y), X)), multiply(X, add(X, Y))))
% 0.21/0.55 = { by axiom 1 (commutativity_of_add) }
% 0.21/0.55 add(inverse(X), add(multiply(inverse(add(X, Y)), add(X, add(X, Y))), multiply(X, add(X, Y))))
% 0.21/0.55 = { by lemma 18 }
% 0.21/0.55 add(inverse(X), add(multiply(X, inverse(add(X, Y))), multiply(X, add(X, Y))))
% 0.21/0.55 = { by axiom 7 (distributivity2) R->L }
% 0.21/0.55 add(inverse(X), multiply(X, add(inverse(add(X, Y)), add(X, Y))))
% 0.21/0.55 = { by axiom 1 (commutativity_of_add) }
% 0.21/0.55 add(inverse(X), multiply(X, add(add(X, Y), inverse(add(X, Y)))))
% 0.21/0.55 = { by axiom 5 (additive_inverse1) }
% 0.21/0.55 add(inverse(X), multiply(X, multiplicative_identity))
% 0.21/0.55 = { by axiom 4 (multiplicative_id1) }
% 0.21/0.55 add(inverse(X), X)
% 0.21/0.56 = { by axiom 1 (commutativity_of_add) }
% 0.21/0.56 add(X, inverse(X))
% 0.21/0.56 = { by axiom 5 (additive_inverse1) }
% 0.21/0.56 multiplicative_identity
% 0.21/0.56
% 0.21/0.56 Goal 1 (prove_c_inverse_is_d): inverse(add(a, b)) = multiply(inverse(a), inverse(b)).
% 0.21/0.56 Proof:
% 0.21/0.56 inverse(add(a, b))
% 0.21/0.56 = { by axiom 4 (multiplicative_id1) R->L }
% 0.21/0.56 multiply(inverse(add(a, b)), multiplicative_identity)
% 0.21/0.56 = { by lemma 23 R->L }
% 0.21/0.56 multiply(inverse(add(a, b)), add(add(a, b), multiply(inverse(a), inverse(b))))
% 0.21/0.56 = { by lemma 22 }
% 0.21/0.56 multiply(multiply(inverse(a), inverse(b)), inverse(add(a, b)))
% 0.21/0.56 = { by axiom 4 (multiplicative_id1) R->L }
% 0.21/0.56 multiply(multiply(inverse(a), inverse(b)), inverse(add(a, multiply(b, multiplicative_identity))))
% 0.21/0.56 = { by axiom 5 (additive_inverse1) R->L }
% 0.21/0.56 multiply(multiply(inverse(a), inverse(b)), inverse(add(a, multiply(b, add(multiply(inverse(a), inverse(b)), inverse(multiply(inverse(a), inverse(b))))))))
% 0.21/0.56 = { by axiom 7 (distributivity2) }
% 0.21/0.56 multiply(multiply(inverse(a), inverse(b)), inverse(add(a, add(multiply(b, multiply(inverse(a), inverse(b))), multiply(b, inverse(multiply(inverse(a), inverse(b))))))))
% 0.21/0.56 = { by axiom 3 (commutativity_of_multiply) R->L }
% 0.21/0.56 multiply(multiply(inverse(a), inverse(b)), inverse(add(a, add(multiply(multiply(inverse(a), inverse(b)), b), multiply(b, inverse(multiply(inverse(a), inverse(b))))))))
% 0.21/0.56 = { by lemma 21 R->L }
% 0.21/0.56 multiply(multiply(inverse(a), inverse(b)), inverse(add(a, add(multiply(b, add(multiply(inverse(a), inverse(b)), inverse(b))), multiply(b, inverse(multiply(inverse(a), inverse(b))))))))
% 0.21/0.56 = { by axiom 1 (commutativity_of_add) R->L }
% 0.21/0.56 multiply(multiply(inverse(a), inverse(b)), inverse(add(a, add(multiply(b, add(inverse(b), multiply(inverse(a), inverse(b)))), multiply(b, inverse(multiply(inverse(a), inverse(b))))))))
% 0.21/0.56 = { by lemma 17 }
% 0.21/0.56 multiply(multiply(inverse(a), inverse(b)), inverse(add(a, add(multiply(b, inverse(b)), multiply(b, inverse(multiply(inverse(a), inverse(b))))))))
% 0.21/0.56 = { by axiom 6 (multiplicative_inverse1) }
% 0.21/0.56 multiply(multiply(inverse(a), inverse(b)), inverse(add(a, add(additive_identity, multiply(b, inverse(multiply(inverse(a), inverse(b))))))))
% 0.21/0.56 = { by lemma 9 }
% 0.21/0.56 multiply(multiply(inverse(a), inverse(b)), inverse(add(a, multiply(b, inverse(multiply(inverse(a), inverse(b)))))))
% 0.21/0.56 = { by axiom 8 (distributivity1) }
% 0.21/0.56 multiply(multiply(inverse(a), inverse(b)), inverse(multiply(add(a, b), add(a, inverse(multiply(inverse(a), inverse(b)))))))
% 0.21/0.56 = { by axiom 1 (commutativity_of_add) R->L }
% 0.21/0.56 multiply(multiply(inverse(a), inverse(b)), inverse(multiply(add(a, b), add(inverse(multiply(inverse(a), inverse(b))), a))))
% 0.21/0.56 = { by axiom 4 (multiplicative_id1) R->L }
% 0.21/0.56 multiply(multiply(inverse(a), inverse(b)), inverse(multiply(add(a, b), add(inverse(multiply(inverse(a), inverse(b))), multiply(a, multiplicative_identity)))))
% 0.21/0.56 = { by axiom 5 (additive_inverse1) R->L }
% 0.21/0.56 multiply(multiply(inverse(a), inverse(b)), inverse(multiply(add(a, b), add(inverse(multiply(inverse(a), inverse(b))), multiply(a, add(multiply(inverse(a), inverse(b)), inverse(multiply(inverse(a), inverse(b)))))))))
% 0.21/0.56 = { by axiom 7 (distributivity2) }
% 0.21/0.56 multiply(multiply(inverse(a), inverse(b)), inverse(multiply(add(a, b), add(inverse(multiply(inverse(a), inverse(b))), add(multiply(a, multiply(inverse(a), inverse(b))), multiply(a, inverse(multiply(inverse(a), inverse(b)))))))))
% 0.21/0.56 = { by axiom 3 (commutativity_of_multiply) R->L }
% 0.21/0.56 multiply(multiply(inverse(a), inverse(b)), inverse(multiply(add(a, b), add(inverse(multiply(inverse(a), inverse(b))), add(multiply(multiply(inverse(a), inverse(b)), a), multiply(a, inverse(multiply(inverse(a), inverse(b)))))))))
% 0.21/0.56 = { by lemma 21 R->L }
% 0.21/0.56 multiply(multiply(inverse(a), inverse(b)), inverse(multiply(add(a, b), add(inverse(multiply(inverse(a), inverse(b))), add(multiply(a, add(multiply(inverse(a), inverse(b)), inverse(a))), multiply(a, inverse(multiply(inverse(a), inverse(b)))))))))
% 0.21/0.56 = { by axiom 1 (commutativity_of_add) R->L }
% 0.21/0.56 multiply(multiply(inverse(a), inverse(b)), inverse(multiply(add(a, b), add(inverse(multiply(inverse(a), inverse(b))), add(multiply(a, add(inverse(a), multiply(inverse(a), inverse(b)))), multiply(a, inverse(multiply(inverse(a), inverse(b)))))))))
% 0.21/0.56 = { by lemma 16 }
% 0.21/0.56 multiply(multiply(inverse(a), inverse(b)), inverse(multiply(add(a, b), add(inverse(multiply(inverse(a), inverse(b))), add(multiply(a, inverse(a)), multiply(a, inverse(multiply(inverse(a), inverse(b)))))))))
% 0.21/0.56 = { by axiom 6 (multiplicative_inverse1) }
% 0.21/0.56 multiply(multiply(inverse(a), inverse(b)), inverse(multiply(add(a, b), add(inverse(multiply(inverse(a), inverse(b))), add(additive_identity, multiply(a, inverse(multiply(inverse(a), inverse(b)))))))))
% 0.21/0.56 = { by lemma 9 }
% 0.21/0.56 multiply(multiply(inverse(a), inverse(b)), inverse(multiply(add(a, b), add(inverse(multiply(inverse(a), inverse(b))), multiply(a, inverse(multiply(inverse(a), inverse(b))))))))
% 0.21/0.56 = { by lemma 17 }
% 0.21/0.56 multiply(multiply(inverse(a), inverse(b)), inverse(multiply(add(a, b), inverse(multiply(inverse(a), inverse(b))))))
% 0.21/0.56 = { by axiom 3 (commutativity_of_multiply) R->L }
% 0.21/0.56 multiply(multiply(inverse(a), inverse(b)), inverse(multiply(inverse(multiply(inverse(a), inverse(b))), add(a, b))))
% 0.21/0.56 = { by axiom 2 (additive_id1) R->L }
% 0.21/0.56 multiply(multiply(inverse(a), inverse(b)), inverse(multiply(inverse(multiply(inverse(a), inverse(b))), add(add(a, b), additive_identity))))
% 0.21/0.56 = { by axiom 6 (multiplicative_inverse1) R->L }
% 0.21/0.56 multiply(multiply(inverse(a), inverse(b)), inverse(multiply(inverse(multiply(inverse(a), inverse(b))), add(add(a, b), multiply(multiply(inverse(a), inverse(b)), inverse(multiply(inverse(a), inverse(b))))))))
% 0.21/0.56 = { by axiom 8 (distributivity1) }
% 0.21/0.56 multiply(multiply(inverse(a), inverse(b)), inverse(multiply(inverse(multiply(inverse(a), inverse(b))), multiply(add(add(a, b), multiply(inverse(a), inverse(b))), add(add(a, b), inverse(multiply(inverse(a), inverse(b))))))))
% 0.21/0.56 = { by lemma 23 }
% 0.21/0.56 multiply(multiply(inverse(a), inverse(b)), inverse(multiply(inverse(multiply(inverse(a), inverse(b))), multiply(multiplicative_identity, add(add(a, b), inverse(multiply(inverse(a), inverse(b))))))))
% 0.21/0.56 = { by lemma 10 }
% 0.21/0.56 multiply(multiply(inverse(a), inverse(b)), inverse(multiply(inverse(multiply(inverse(a), inverse(b))), add(add(a, b), inverse(multiply(inverse(a), inverse(b)))))))
% 0.21/0.56 = { by lemma 19 }
% 0.21/0.56 multiply(multiply(inverse(a), inverse(b)), inverse(inverse(multiply(inverse(a), inverse(b)))))
% 0.21/0.56 = { by lemma 12 }
% 0.21/0.56 multiply(inverse(a), inverse(b))
% 0.21/0.56 % SZS output end Proof
% 0.21/0.56
% 0.21/0.56 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------