TSTP Solution File: RNG021-6 by Twee---2.5.0
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%------------------------------------------------------------------------------
% File : Twee---2.5.0
% Problem : RNG021-6 : TPTP v8.2.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee /export/starexec/sandbox/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% Computer : n005.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 : Mon Jun 24 14:06:12 EDT 2024
% Result : Unsatisfiable 129.48s 16.60s
% Output : Proof 129.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : RNG021-6 : TPTP v8.2.0. Released v1.0.0.
% 0.09/0.10 % Command : parallel-twee /export/starexec/sandbox/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% 0.09/0.30 % Computer : n005.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Tue Jun 18 14:21:53 EDT 2024
% 0.09/0.30 % CPUTime :
% 129.48/16.60 Command-line arguments: --flatten
% 129.48/16.60
% 129.48/16.60 % SZS status Unsatisfiable
% 129.48/16.60
% 129.48/16.61 % SZS output start Proof
% 129.48/16.61 Axiom 1 (additive_inverse_additive_inverse): additive_inverse(additive_inverse(X)) = X.
% 129.48/16.61 Axiom 2 (commutativity_for_addition): add(X, Y) = add(Y, X).
% 129.48/16.61 Axiom 3 (right_additive_identity): add(X, additive_identity) = X.
% 129.48/16.61 Axiom 4 (left_additive_identity): add(additive_identity, X) = X.
% 129.48/16.61 Axiom 5 (right_additive_inverse): add(X, additive_inverse(X)) = additive_identity.
% 129.48/16.61 Axiom 6 (associativity_for_addition): add(X, add(Y, Z)) = add(add(X, Y), Z).
% 129.48/16.61 Axiom 7 (distribute2): multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z)).
% 129.48/16.61 Axiom 8 (commutator): commutator(X, Y) = add(multiply(Y, X), additive_inverse(multiply(X, Y))).
% 129.48/16.61 Axiom 9 (associator): associator(X, Y, Z) = add(multiply(multiply(X, Y), Z), additive_inverse(multiply(X, multiply(Y, Z)))).
% 129.48/16.61
% 129.48/16.61 Lemma 10: add(X, add(Y, additive_inverse(X))) = Y.
% 129.48/16.61 Proof:
% 129.48/16.61 add(X, add(Y, additive_inverse(X)))
% 129.48/16.61 = { by axiom 2 (commutativity_for_addition) R->L }
% 129.48/16.61 add(X, add(additive_inverse(X), Y))
% 129.48/16.61 = { by axiom 6 (associativity_for_addition) }
% 129.48/16.61 add(add(X, additive_inverse(X)), Y)
% 129.48/16.61 = { by axiom 5 (right_additive_inverse) }
% 129.48/16.61 add(additive_identity, Y)
% 129.48/16.61 = { by axiom 4 (left_additive_identity) }
% 129.48/16.61 Y
% 129.48/16.61
% 129.59/16.61 Lemma 11: add(X, additive_inverse(add(Y, X))) = additive_inverse(Y).
% 129.59/16.61 Proof:
% 129.59/16.61 add(X, additive_inverse(add(Y, X)))
% 129.59/16.61 = { by axiom 2 (commutativity_for_addition) R->L }
% 129.59/16.61 add(X, additive_inverse(add(X, Y)))
% 129.59/16.61 = { by axiom 1 (additive_inverse_additive_inverse) R->L }
% 129.59/16.61 add(X, additive_inverse(add(X, additive_inverse(additive_inverse(Y)))))
% 129.59/16.61 = { by axiom 2 (commutativity_for_addition) R->L }
% 129.59/16.61 add(X, additive_inverse(add(additive_inverse(additive_inverse(Y)), X)))
% 129.59/16.61 = { by lemma 10 R->L }
% 129.59/16.61 add(additive_inverse(Y), add(add(X, additive_inverse(add(additive_inverse(additive_inverse(Y)), X))), additive_inverse(additive_inverse(Y))))
% 129.59/16.61 = { by axiom 2 (commutativity_for_addition) }
% 129.59/16.61 add(additive_inverse(Y), add(additive_inverse(additive_inverse(Y)), add(X, additive_inverse(add(additive_inverse(additive_inverse(Y)), X)))))
% 129.59/16.61 = { by axiom 6 (associativity_for_addition) }
% 129.59/16.61 add(additive_inverse(Y), add(add(additive_inverse(additive_inverse(Y)), X), additive_inverse(add(additive_inverse(additive_inverse(Y)), X))))
% 129.59/16.61 = { by axiom 5 (right_additive_inverse) }
% 129.59/16.61 add(additive_inverse(Y), additive_identity)
% 129.59/16.61 = { by axiom 3 (right_additive_identity) }
% 129.59/16.61 additive_inverse(Y)
% 129.59/16.61
% 129.59/16.61 Lemma 12: add(associator(X, Y, Z), multiply(X, multiply(Y, Z))) = multiply(multiply(X, Y), Z).
% 129.59/16.61 Proof:
% 129.59/16.61 add(associator(X, Y, Z), multiply(X, multiply(Y, Z)))
% 129.59/16.61 = { by axiom 2 (commutativity_for_addition) R->L }
% 129.59/16.61 add(multiply(X, multiply(Y, Z)), associator(X, Y, Z))
% 129.59/16.61 = { by axiom 9 (associator) }
% 129.59/16.61 add(multiply(X, multiply(Y, Z)), add(multiply(multiply(X, Y), Z), additive_inverse(multiply(X, multiply(Y, Z)))))
% 129.59/16.61 = { by lemma 10 }
% 129.59/16.62 multiply(multiply(X, Y), Z)
% 129.59/16.62
% 129.59/16.62 Goal 1 (prove_linearised_form3): associator(add(u, v), x, y) = add(associator(u, x, y), associator(v, x, y)).
% 129.59/16.62 Proof:
% 129.59/16.62 associator(add(u, v), x, y)
% 129.59/16.62 = { by axiom 1 (additive_inverse_additive_inverse) R->L }
% 129.59/16.62 additive_inverse(additive_inverse(associator(add(u, v), x, y)))
% 129.59/16.62 = { by lemma 11 R->L }
% 129.59/16.62 additive_inverse(add(multiply(multiply(x, y), add(u, v)), additive_inverse(add(associator(add(u, v), x, y), multiply(multiply(x, y), add(u, v))))))
% 129.59/16.62 = { by axiom 2 (commutativity_for_addition) R->L }
% 129.59/16.62 additive_inverse(add(multiply(multiply(x, y), add(u, v)), additive_inverse(add(multiply(multiply(x, y), add(u, v)), associator(add(u, v), x, y)))))
% 129.59/16.62 = { by axiom 9 (associator) }
% 129.59/16.62 additive_inverse(add(multiply(multiply(x, y), add(u, v)), additive_inverse(add(multiply(multiply(x, y), add(u, v)), add(multiply(multiply(add(u, v), x), y), additive_inverse(multiply(add(u, v), multiply(x, y))))))))
% 129.59/16.62 = { by axiom 2 (commutativity_for_addition) R->L }
% 129.59/16.62 additive_inverse(add(multiply(multiply(x, y), add(u, v)), additive_inverse(add(multiply(multiply(x, y), add(u, v)), add(additive_inverse(multiply(add(u, v), multiply(x, y))), multiply(multiply(add(u, v), x), y))))))
% 129.59/16.62 = { by axiom 6 (associativity_for_addition) }
% 129.59/16.62 additive_inverse(add(multiply(multiply(x, y), add(u, v)), additive_inverse(add(add(multiply(multiply(x, y), add(u, v)), additive_inverse(multiply(add(u, v), multiply(x, y)))), multiply(multiply(add(u, v), x), y)))))
% 129.59/16.62 = { by axiom 8 (commutator) R->L }
% 129.59/16.62 additive_inverse(add(multiply(multiply(x, y), add(u, v)), additive_inverse(add(commutator(add(u, v), multiply(x, y)), multiply(multiply(add(u, v), x), y)))))
% 129.59/16.62 = { by axiom 2 (commutativity_for_addition) R->L }
% 129.59/16.62 additive_inverse(add(multiply(multiply(x, y), add(u, v)), additive_inverse(add(commutator(add(u, v), multiply(x, y)), multiply(multiply(add(v, u), x), y)))))
% 129.59/16.62 = { by axiom 7 (distribute2) }
% 129.59/16.62 additive_inverse(add(multiply(multiply(x, y), add(u, v)), additive_inverse(add(commutator(add(u, v), multiply(x, y)), multiply(add(multiply(v, x), multiply(u, x)), y)))))
% 129.59/16.62 = { by axiom 7 (distribute2) }
% 129.59/16.62 additive_inverse(add(multiply(multiply(x, y), add(u, v)), additive_inverse(add(commutator(add(u, v), multiply(x, y)), add(multiply(multiply(v, x), y), multiply(multiply(u, x), y))))))
% 129.59/16.62 = { by axiom 2 (commutativity_for_addition) R->L }
% 129.59/16.62 additive_inverse(add(multiply(multiply(x, y), add(u, v)), additive_inverse(add(commutator(add(u, v), multiply(x, y)), add(multiply(multiply(u, x), y), multiply(multiply(v, x), y))))))
% 129.59/16.62 = { by lemma 12 R->L }
% 129.59/16.62 additive_inverse(add(multiply(multiply(x, y), add(u, v)), additive_inverse(add(commutator(add(u, v), multiply(x, y)), add(add(associator(u, x, y), multiply(u, multiply(x, y))), multiply(multiply(v, x), y))))))
% 129.59/16.62 = { by axiom 6 (associativity_for_addition) R->L }
% 129.59/16.62 additive_inverse(add(multiply(multiply(x, y), add(u, v)), additive_inverse(add(commutator(add(u, v), multiply(x, y)), add(associator(u, x, y), add(multiply(u, multiply(x, y)), multiply(multiply(v, x), y)))))))
% 129.59/16.62 = { by axiom 2 (commutativity_for_addition) R->L }
% 129.59/16.62 additive_inverse(add(multiply(multiply(x, y), add(u, v)), additive_inverse(add(commutator(add(u, v), multiply(x, y)), add(associator(u, x, y), add(multiply(multiply(v, x), y), multiply(u, multiply(x, y))))))))
% 129.59/16.62 = { by axiom 6 (associativity_for_addition) }
% 129.59/16.62 additive_inverse(add(multiply(multiply(x, y), add(u, v)), additive_inverse(add(commutator(add(u, v), multiply(x, y)), add(add(associator(u, x, y), multiply(multiply(v, x), y)), multiply(u, multiply(x, y)))))))
% 129.59/16.62 = { by lemma 12 R->L }
% 129.59/16.62 additive_inverse(add(multiply(multiply(x, y), add(u, v)), additive_inverse(add(commutator(add(u, v), multiply(x, y)), add(add(associator(u, x, y), add(associator(v, x, y), multiply(v, multiply(x, y)))), multiply(u, multiply(x, y)))))))
% 129.59/16.62 = { by axiom 6 (associativity_for_addition) }
% 129.59/16.62 additive_inverse(add(multiply(multiply(x, y), add(u, v)), additive_inverse(add(commutator(add(u, v), multiply(x, y)), add(add(add(associator(u, x, y), associator(v, x, y)), multiply(v, multiply(x, y))), multiply(u, multiply(x, y)))))))
% 129.59/16.62 = { by axiom 6 (associativity_for_addition) R->L }
% 129.59/16.62 additive_inverse(add(multiply(multiply(x, y), add(u, v)), additive_inverse(add(commutator(add(u, v), multiply(x, y)), add(add(associator(u, x, y), associator(v, x, y)), add(multiply(v, multiply(x, y)), multiply(u, multiply(x, y))))))))
% 129.59/16.62 = { by axiom 2 (commutativity_for_addition) }
% 129.59/16.62 additive_inverse(add(multiply(multiply(x, y), add(u, v)), additive_inverse(add(commutator(add(u, v), multiply(x, y)), add(add(associator(u, x, y), associator(v, x, y)), add(multiply(u, multiply(x, y)), multiply(v, multiply(x, y))))))))
% 129.59/16.62 = { by axiom 7 (distribute2) R->L }
% 129.59/16.62 additive_inverse(add(multiply(multiply(x, y), add(u, v)), additive_inverse(add(commutator(add(u, v), multiply(x, y)), add(add(associator(u, x, y), associator(v, x, y)), multiply(add(u, v), multiply(x, y)))))))
% 129.59/16.62 = { by axiom 2 (commutativity_for_addition) R->L }
% 129.59/16.62 additive_inverse(add(multiply(multiply(x, y), add(u, v)), additive_inverse(add(commutator(add(u, v), multiply(x, y)), add(multiply(add(u, v), multiply(x, y)), add(associator(u, x, y), associator(v, x, y)))))))
% 129.59/16.62 = { by axiom 6 (associativity_for_addition) }
% 129.59/16.62 additive_inverse(add(multiply(multiply(x, y), add(u, v)), additive_inverse(add(add(commutator(add(u, v), multiply(x, y)), multiply(add(u, v), multiply(x, y))), add(associator(u, x, y), associator(v, x, y))))))
% 129.59/16.62 = { by axiom 2 (commutativity_for_addition) R->L }
% 129.59/16.62 additive_inverse(add(multiply(multiply(x, y), add(u, v)), additive_inverse(add(add(multiply(add(u, v), multiply(x, y)), commutator(add(u, v), multiply(x, y))), add(associator(u, x, y), associator(v, x, y))))))
% 129.59/16.62 = { by axiom 8 (commutator) }
% 129.59/16.62 additive_inverse(add(multiply(multiply(x, y), add(u, v)), additive_inverse(add(add(multiply(add(u, v), multiply(x, y)), add(multiply(multiply(x, y), add(u, v)), additive_inverse(multiply(add(u, v), multiply(x, y))))), add(associator(u, x, y), associator(v, x, y))))))
% 129.59/16.62 = { by lemma 10 }
% 129.59/16.62 additive_inverse(add(multiply(multiply(x, y), add(u, v)), additive_inverse(add(multiply(multiply(x, y), add(u, v)), add(associator(u, x, y), associator(v, x, y))))))
% 129.59/16.62 = { by axiom 2 (commutativity_for_addition) }
% 129.59/16.62 additive_inverse(add(multiply(multiply(x, y), add(u, v)), additive_inverse(add(add(associator(u, x, y), associator(v, x, y)), multiply(multiply(x, y), add(u, v))))))
% 129.59/16.62 = { by lemma 11 }
% 129.59/16.62 additive_inverse(additive_inverse(add(associator(u, x, y), associator(v, x, y))))
% 129.59/16.62 = { by axiom 1 (additive_inverse_additive_inverse) }
% 129.59/16.62 add(associator(u, x, y), associator(v, x, y))
% 129.59/16.62 % SZS output end Proof
% 129.59/16.62
% 129.59/16.62 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------