TSTP Solution File: BOO029-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : BOO029-1 : TPTP v8.1.2. Released v2.2.0.
% 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 : n008.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 18:11:29 EDT 2023
% Result : Unsatisfiable 0.20s 0.41s
% 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
% 0.00/0.12 % Problem : BOO029-1 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Aug 27 08:47:17 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.41 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.20/0.41
% 0.20/0.41 % SZS status Unsatisfiable
% 0.20/0.41
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 Axiom 1 (commutativity_of_multiply): multiply(X, Y) = multiply(Y, X).
% 0.20/0.41 Axiom 2 (commutativity_of_add): add(X, Y) = add(Y, X).
% 0.20/0.41 Axiom 3 (l2): multiply(X, add(Y, add(X, Z))) = X.
% 0.20/0.41 Axiom 4 (l1): add(X, multiply(Y, multiply(X, Z))) = X.
% 0.20/0.41 Axiom 5 (b2): add(multiply(X, Y), multiply(X, inverse(Y))) = X.
% 0.20/0.41
% 0.20/0.41 Lemma 6: add(multiply(X, Y), multiply(Y, inverse(X))) = Y.
% 0.20/0.41 Proof:
% 0.20/0.41 add(multiply(X, Y), multiply(Y, inverse(X)))
% 0.20/0.41 = { by axiom 1 (commutativity_of_multiply) R->L }
% 0.20/0.41 add(multiply(Y, X), multiply(Y, inverse(X)))
% 0.20/0.41 = { by axiom 5 (b2) }
% 0.20/0.41 Y
% 0.20/0.41
% 0.20/0.41 Lemma 7: multiply(X, add(Y, inverse(Y))) = X.
% 0.20/0.41 Proof:
% 0.20/0.41 multiply(X, add(Y, inverse(Y)))
% 0.20/0.41 = { by axiom 3 (l2) R->L }
% 0.20/0.41 multiply(X, add(Y, multiply(inverse(Y), add(Y, add(inverse(Y), X)))))
% 0.20/0.41 = { by axiom 1 (commutativity_of_multiply) R->L }
% 0.20/0.41 multiply(X, add(Y, multiply(add(Y, add(inverse(Y), X)), inverse(Y))))
% 0.20/0.41 = { by axiom 3 (l2) R->L }
% 0.20/0.42 multiply(X, add(multiply(Y, add(add(inverse(Y), X), add(Y, multiply(Z, multiply(Y, W))))), multiply(add(Y, add(inverse(Y), X)), inverse(Y))))
% 0.20/0.42 = { by axiom 4 (l1) }
% 0.20/0.42 multiply(X, add(multiply(Y, add(add(inverse(Y), X), Y)), multiply(add(Y, add(inverse(Y), X)), inverse(Y))))
% 0.20/0.42 = { by axiom 2 (commutativity_of_add) }
% 0.20/0.42 multiply(X, add(multiply(Y, add(Y, add(inverse(Y), X))), multiply(add(Y, add(inverse(Y), X)), inverse(Y))))
% 0.20/0.42 = { by lemma 6 }
% 0.20/0.42 multiply(X, add(Y, add(inverse(Y), X)))
% 0.20/0.42 = { by axiom 2 (commutativity_of_add) }
% 0.20/0.42 multiply(X, add(Y, add(X, inverse(Y))))
% 0.20/0.42 = { by axiom 3 (l2) }
% 0.20/0.42 X
% 0.20/0.42
% 0.20/0.42 Goal 1 (prove_equal_inverse): add(b, inverse(b)) = add(a, inverse(a)).
% 0.20/0.42 Proof:
% 0.20/0.42 add(b, inverse(b))
% 0.20/0.42 = { by lemma 7 R->L }
% 0.20/0.42 add(b, multiply(inverse(b), add(a, inverse(a))))
% 0.20/0.42 = { by lemma 7 R->L }
% 0.20/0.42 add(multiply(b, add(a, inverse(a))), multiply(inverse(b), add(a, inverse(a))))
% 0.20/0.42 = { by axiom 1 (commutativity_of_multiply) R->L }
% 0.20/0.42 add(multiply(b, add(a, inverse(a))), multiply(add(a, inverse(a)), inverse(b)))
% 0.20/0.42 = { by lemma 6 }
% 0.20/0.42 add(a, inverse(a))
% 0.20/0.42 % SZS output end Proof
% 0.20/0.42
% 0.20/0.42 RESULT: Unsatisfiable (the axioms are contradictory).
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