TSTP Solution File: RNG025-7 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : RNG025-7 : 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 : n027.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 : Thu Aug 31 13:58:53 EDT 2023
% Result : Unsatisfiable 43.41s 5.92s
% Output : Proof 43.67s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : RNG025-7 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.33 % Computer : n027.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sun Aug 27 02:00:05 EDT 2023
% 0.13/0.34 % CPUTime :
% 43.41/5.92 Command-line arguments: --ground-connectedness --complete-subsets
% 43.41/5.92
% 43.41/5.92 % SZS status Unsatisfiable
% 43.41/5.92
% 43.41/5.93 % SZS output start Proof
% 43.41/5.93 Axiom 1 (additive_inverse_additive_inverse): additive_inverse(additive_inverse(X)) = X.
% 43.41/5.93 Axiom 2 (commutativity_for_addition): add(X, Y) = add(Y, X).
% 43.41/5.93 Axiom 3 (left_additive_identity): add(additive_identity, X) = X.
% 43.41/5.93 Axiom 4 (right_multiplicative_zero): multiply(X, additive_identity) = additive_identity.
% 43.41/5.93 Axiom 5 (right_additive_inverse): add(X, additive_inverse(X)) = additive_identity.
% 43.41/5.93 Axiom 6 (inverse_product2): multiply(X, additive_inverse(Y)) = additive_inverse(multiply(X, Y)).
% 43.41/5.93 Axiom 7 (inverse_product1): multiply(additive_inverse(X), Y) = additive_inverse(multiply(X, Y)).
% 43.41/5.93 Axiom 8 (associativity_for_addition): add(X, add(Y, Z)) = add(add(X, Y), Z).
% 43.41/5.93 Axiom 9 (left_alternative): multiply(multiply(X, X), Y) = multiply(X, multiply(X, Y)).
% 43.41/5.93 Axiom 10 (right_alternative): multiply(multiply(X, Y), Y) = multiply(X, multiply(Y, Y)).
% 43.41/5.93 Axiom 11 (distribute1): multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)).
% 43.41/5.93 Axiom 12 (distribute2): multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z)).
% 43.41/5.93 Axiom 13 (distributivity_of_difference1): multiply(X, add(Y, additive_inverse(Z))) = add(multiply(X, Y), additive_inverse(multiply(X, Z))).
% 43.41/5.93 Axiom 14 (distributivity_of_difference3): multiply(additive_inverse(X), add(Y, Z)) = add(additive_inverse(multiply(X, Y)), additive_inverse(multiply(X, Z))).
% 43.41/5.93 Axiom 15 (associator): associator(X, Y, Z) = add(multiply(multiply(X, Y), Z), additive_inverse(multiply(X, multiply(Y, Z)))).
% 43.41/5.93
% 43.41/5.93 Lemma 16: add(X, add(Y, additive_inverse(X))) = Y.
% 43.41/5.93 Proof:
% 43.41/5.93 add(X, add(Y, additive_inverse(X)))
% 43.41/5.93 = { by axiom 2 (commutativity_for_addition) R->L }
% 43.41/5.93 add(X, add(additive_inverse(X), Y))
% 43.41/5.93 = { by axiom 8 (associativity_for_addition) }
% 43.41/5.93 add(add(X, additive_inverse(X)), Y)
% 43.41/5.93 = { by axiom 5 (right_additive_inverse) }
% 43.41/5.93 add(additive_identity, Y)
% 43.41/5.93 = { by axiom 3 (left_additive_identity) }
% 43.41/5.93 Y
% 43.41/5.93
% 43.41/5.93 Lemma 17: additive_inverse(multiply(X, add(Y, additive_inverse(Z)))) = multiply(X, add(Z, additive_inverse(Y))).
% 43.41/5.93 Proof:
% 43.41/5.93 additive_inverse(multiply(X, add(Y, additive_inverse(Z))))
% 43.41/5.93 = { by axiom 2 (commutativity_for_addition) R->L }
% 43.41/5.93 additive_inverse(multiply(X, add(additive_inverse(Z), Y)))
% 43.41/5.93 = { by axiom 7 (inverse_product1) R->L }
% 43.41/5.93 multiply(additive_inverse(X), add(additive_inverse(Z), Y))
% 43.41/5.93 = { by axiom 14 (distributivity_of_difference3) }
% 43.41/5.93 add(additive_inverse(multiply(X, additive_inverse(Z))), additive_inverse(multiply(X, Y)))
% 43.41/5.93 = { by axiom 6 (inverse_product2) }
% 43.41/5.93 add(additive_inverse(additive_inverse(multiply(X, Z))), additive_inverse(multiply(X, Y)))
% 43.41/5.93 = { by axiom 1 (additive_inverse_additive_inverse) }
% 43.41/5.93 add(multiply(X, Z), additive_inverse(multiply(X, Y)))
% 43.41/5.93 = { by axiom 13 (distributivity_of_difference1) R->L }
% 43.41/5.93 multiply(X, add(Z, additive_inverse(Y)))
% 43.41/5.93
% 43.41/5.93 Goal 1 (prove_flexible_law): associator(x, y, x) = additive_identity.
% 43.41/5.93 Proof:
% 43.41/5.93 associator(x, y, x)
% 43.41/5.93 = { by axiom 15 (associator) }
% 43.41/5.93 add(multiply(multiply(x, y), x), additive_inverse(multiply(x, multiply(y, x))))
% 43.41/5.93 = { by lemma 16 R->L }
% 43.41/5.93 add(multiply(multiply(x, y), add(y, add(x, additive_inverse(y)))), additive_inverse(multiply(x, multiply(y, x))))
% 43.41/5.93 = { by axiom 11 (distribute1) }
% 43.41/5.93 add(add(multiply(multiply(x, y), y), multiply(multiply(x, y), add(x, additive_inverse(y)))), additive_inverse(multiply(x, multiply(y, x))))
% 43.41/5.93 = { by axiom 10 (right_alternative) }
% 43.41/5.93 add(add(multiply(x, multiply(y, y)), multiply(multiply(x, y), add(x, additive_inverse(y)))), additive_inverse(multiply(x, multiply(y, x))))
% 43.41/5.93 = { by lemma 17 R->L }
% 43.41/5.93 add(add(multiply(x, multiply(y, y)), additive_inverse(multiply(multiply(x, y), add(y, additive_inverse(x))))), additive_inverse(multiply(x, multiply(y, x))))
% 43.41/5.93 = { by lemma 16 R->L }
% 43.41/5.93 add(add(multiply(x, multiply(y, y)), additive_inverse(multiply(multiply(x, add(x, add(y, additive_inverse(x)))), add(y, additive_inverse(x))))), additive_inverse(multiply(x, multiply(y, x))))
% 43.41/5.93 = { by axiom 11 (distribute1) }
% 43.41/5.93 add(add(multiply(x, multiply(y, y)), additive_inverse(multiply(add(multiply(x, x), multiply(x, add(y, additive_inverse(x)))), add(y, additive_inverse(x))))), additive_inverse(multiply(x, multiply(y, x))))
% 43.41/5.93 = { by axiom 12 (distribute2) }
% 43.41/5.93 add(add(multiply(x, multiply(y, y)), additive_inverse(add(multiply(multiply(x, x), add(y, additive_inverse(x))), multiply(multiply(x, add(y, additive_inverse(x))), add(y, additive_inverse(x)))))), additive_inverse(multiply(x, multiply(y, x))))
% 43.67/5.93 = { by axiom 9 (left_alternative) }
% 43.67/5.93 add(add(multiply(x, multiply(y, y)), additive_inverse(add(multiply(x, multiply(x, add(y, additive_inverse(x)))), multiply(multiply(x, add(y, additive_inverse(x))), add(y, additive_inverse(x)))))), additive_inverse(multiply(x, multiply(y, x))))
% 43.67/5.93 = { by axiom 10 (right_alternative) }
% 43.67/5.93 add(add(multiply(x, multiply(y, y)), additive_inverse(add(multiply(x, multiply(x, add(y, additive_inverse(x)))), multiply(x, multiply(add(y, additive_inverse(x)), add(y, additive_inverse(x))))))), additive_inverse(multiply(x, multiply(y, x))))
% 43.67/5.93 = { by axiom 11 (distribute1) R->L }
% 43.67/5.93 add(add(multiply(x, multiply(y, y)), additive_inverse(multiply(x, add(multiply(x, add(y, additive_inverse(x))), multiply(add(y, additive_inverse(x)), add(y, additive_inverse(x))))))), additive_inverse(multiply(x, multiply(y, x))))
% 43.67/5.93 = { by axiom 12 (distribute2) R->L }
% 43.67/5.93 add(add(multiply(x, multiply(y, y)), additive_inverse(multiply(x, multiply(add(x, add(y, additive_inverse(x))), add(y, additive_inverse(x)))))), additive_inverse(multiply(x, multiply(y, x))))
% 43.67/5.93 = { by lemma 16 }
% 43.67/5.93 add(add(multiply(x, multiply(y, y)), additive_inverse(multiply(x, multiply(y, add(y, additive_inverse(x)))))), additive_inverse(multiply(x, multiply(y, x))))
% 43.67/5.93 = { by axiom 6 (inverse_product2) R->L }
% 43.67/5.93 add(add(multiply(x, multiply(y, y)), multiply(x, additive_inverse(multiply(y, add(y, additive_inverse(x)))))), additive_inverse(multiply(x, multiply(y, x))))
% 43.67/5.93 = { by lemma 17 }
% 43.67/5.93 add(add(multiply(x, multiply(y, y)), multiply(x, multiply(y, add(x, additive_inverse(y))))), additive_inverse(multiply(x, multiply(y, x))))
% 43.67/5.93 = { by axiom 11 (distribute1) R->L }
% 43.67/5.93 add(multiply(x, add(multiply(y, y), multiply(y, add(x, additive_inverse(y))))), additive_inverse(multiply(x, multiply(y, x))))
% 43.67/5.93 = { by axiom 11 (distribute1) R->L }
% 43.67/5.93 add(multiply(x, multiply(y, add(y, add(x, additive_inverse(y))))), additive_inverse(multiply(x, multiply(y, x))))
% 43.67/5.93 = { by lemma 16 }
% 43.67/5.93 add(multiply(x, multiply(y, x)), additive_inverse(multiply(x, multiply(y, x))))
% 43.67/5.93 = { by axiom 13 (distributivity_of_difference1) R->L }
% 43.67/5.93 multiply(x, add(multiply(y, x), additive_inverse(multiply(y, x))))
% 43.67/5.93 = { by axiom 13 (distributivity_of_difference1) R->L }
% 43.67/5.93 multiply(x, multiply(y, add(x, additive_inverse(x))))
% 43.67/5.93 = { by axiom 5 (right_additive_inverse) }
% 43.67/5.93 multiply(x, multiply(y, additive_identity))
% 43.67/5.93 = { by axiom 4 (right_multiplicative_zero) }
% 43.67/5.93 multiply(x, additive_identity)
% 43.67/5.93 = { by axiom 4 (right_multiplicative_zero) }
% 43.67/5.93 additive_identity
% 43.67/5.93 % SZS output end Proof
% 43.67/5.93
% 43.67/5.93 RESULT: Unsatisfiable (the axioms are contradictory).
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