TSTP Solution File: RNG026-6 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : RNG026-6 : 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 : n016.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 141.61s 18.86s
% Output : Proof 144.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : RNG026-6 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.11 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.31 % Computer : n016.cluster.edu
% 0.14/0.31 % Model : x86_64 x86_64
% 0.14/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.31 % Memory : 8042.1875MB
% 0.14/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.31 % CPULimit : 300
% 0.14/0.31 % WCLimit : 300
% 0.14/0.31 % DateTime : Sun Aug 27 02:24:28 EDT 2023
% 0.14/0.32 % CPUTime :
% 141.61/18.86 Command-line arguments: --ground-connectedness --complete-subsets
% 141.61/18.86
% 141.61/18.86 % SZS status Unsatisfiable
% 141.61/18.86
% 144.05/18.89 % SZS output start Proof
% 144.05/18.89 Axiom 1 (additive_inverse_additive_inverse): additive_inverse(additive_inverse(X)) = X.
% 144.05/18.89 Axiom 2 (commutativity_for_addition): add(X, Y) = add(Y, X).
% 144.05/18.89 Axiom 3 (right_additive_identity): add(X, additive_identity) = X.
% 144.05/18.89 Axiom 4 (left_additive_identity): add(additive_identity, X) = X.
% 144.05/18.89 Axiom 5 (right_additive_inverse): add(X, additive_inverse(X)) = additive_identity.
% 144.05/18.89 Axiom 6 (associativity_for_addition): add(X, add(Y, Z)) = add(add(X, Y), Z).
% 144.05/18.89 Axiom 7 (distribute1): multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)).
% 144.05/18.89 Axiom 8 (distribute2): multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z)).
% 144.05/18.89 Axiom 9 (associator): associator(X, Y, Z) = add(multiply(multiply(X, Y), Z), additive_inverse(multiply(X, multiply(Y, Z)))).
% 144.05/18.89
% 144.05/18.89 Lemma 10: add(X, add(Y, Z)) = add(Y, add(X, Z)).
% 144.05/18.89 Proof:
% 144.05/18.89 add(X, add(Y, Z))
% 144.05/18.89 = { by axiom 2 (commutativity_for_addition) R->L }
% 144.05/18.89 add(add(Y, Z), X)
% 144.05/18.89 = { by axiom 6 (associativity_for_addition) R->L }
% 144.05/18.89 add(Y, add(Z, X))
% 144.05/18.89 = { by axiom 2 (commutativity_for_addition) }
% 144.05/18.89 add(Y, add(X, Z))
% 144.05/18.89
% 144.05/18.89 Lemma 11: add(Z, add(X, Y)) = add(X, add(Y, Z)).
% 144.05/18.89 Proof:
% 144.05/18.89 add(Z, add(X, Y))
% 144.05/18.89 = { by lemma 10 R->L }
% 144.05/18.89 add(X, add(Z, Y))
% 144.05/18.89 = { by axiom 2 (commutativity_for_addition) }
% 144.05/18.89 add(X, add(Y, Z))
% 144.05/18.89
% 144.05/18.89 Lemma 12: add(X, add(Y, additive_inverse(X))) = Y.
% 144.05/18.89 Proof:
% 144.05/18.89 add(X, add(Y, additive_inverse(X)))
% 144.05/18.89 = { by axiom 2 (commutativity_for_addition) R->L }
% 144.05/18.89 add(X, add(additive_inverse(X), Y))
% 144.05/18.89 = { by axiom 6 (associativity_for_addition) }
% 144.05/18.89 add(add(X, additive_inverse(X)), Y)
% 144.05/18.89 = { by axiom 5 (right_additive_inverse) }
% 144.05/18.89 add(additive_identity, Y)
% 144.05/18.89 = { by axiom 4 (left_additive_identity) }
% 144.05/18.89 Y
% 144.05/18.89
% 144.05/18.89 Lemma 13: add(X, additive_inverse(add(Y, X))) = additive_inverse(Y).
% 144.05/18.89 Proof:
% 144.05/18.89 add(X, additive_inverse(add(Y, X)))
% 144.05/18.89 = { by axiom 2 (commutativity_for_addition) R->L }
% 144.05/18.89 add(X, additive_inverse(add(X, Y)))
% 144.05/18.89 = { by axiom 1 (additive_inverse_additive_inverse) R->L }
% 144.05/18.89 add(X, additive_inverse(add(X, additive_inverse(additive_inverse(Y)))))
% 144.05/18.89 = { by axiom 2 (commutativity_for_addition) R->L }
% 144.05/18.89 add(X, additive_inverse(add(additive_inverse(additive_inverse(Y)), X)))
% 144.05/18.89 = { by lemma 12 R->L }
% 144.05/18.89 add(additive_inverse(Y), add(add(X, additive_inverse(add(additive_inverse(additive_inverse(Y)), X))), additive_inverse(additive_inverse(Y))))
% 144.05/18.89 = { by axiom 2 (commutativity_for_addition) }
% 144.05/18.89 add(additive_inverse(Y), add(additive_inverse(additive_inverse(Y)), add(X, additive_inverse(add(additive_inverse(additive_inverse(Y)), X)))))
% 144.05/18.89 = { by axiom 6 (associativity_for_addition) }
% 144.05/18.90 add(additive_inverse(Y), add(add(additive_inverse(additive_inverse(Y)), X), additive_inverse(add(additive_inverse(additive_inverse(Y)), X))))
% 144.05/18.90 = { by axiom 5 (right_additive_inverse) }
% 144.05/18.90 add(additive_inverse(Y), additive_identity)
% 144.05/18.90 = { by axiom 3 (right_additive_identity) }
% 144.05/18.90 additive_inverse(Y)
% 144.05/18.90
% 144.05/18.90 Lemma 14: add(X, additive_inverse(add(Y, add(Z, X)))) = additive_inverse(add(Z, Y)).
% 144.05/18.90 Proof:
% 144.05/18.90 add(X, additive_inverse(add(Y, add(Z, X))))
% 144.05/18.90 = { by lemma 10 R->L }
% 144.05/18.90 add(X, additive_inverse(add(Z, add(Y, X))))
% 144.05/18.90 = { by axiom 6 (associativity_for_addition) }
% 144.05/18.90 add(X, additive_inverse(add(add(Z, Y), X)))
% 144.05/18.90 = { by lemma 13 }
% 144.05/18.90 additive_inverse(add(Z, Y))
% 144.05/18.90
% 144.05/18.90 Lemma 15: add(associator(X, Y, Z), multiply(X, multiply(Y, Z))) = multiply(multiply(X, Y), Z).
% 144.05/18.90 Proof:
% 144.05/18.90 add(associator(X, Y, Z), multiply(X, multiply(Y, Z)))
% 144.05/18.90 = { by axiom 2 (commutativity_for_addition) R->L }
% 144.05/18.90 add(multiply(X, multiply(Y, Z)), associator(X, Y, Z))
% 144.05/18.90 = { by axiom 9 (associator) }
% 144.05/18.90 add(multiply(X, multiply(Y, Z)), add(multiply(multiply(X, Y), Z), additive_inverse(multiply(X, multiply(Y, Z)))))
% 144.05/18.90 = { by lemma 12 }
% 144.05/18.90 multiply(multiply(X, Y), Z)
% 144.05/18.90
% 144.05/18.90 Lemma 16: add(associator(X, Y, Z), add(W, multiply(X, multiply(Y, Z)))) = add(W, multiply(multiply(X, Y), Z)).
% 144.05/18.90 Proof:
% 144.05/18.90 add(associator(X, Y, Z), add(W, multiply(X, multiply(Y, Z))))
% 144.05/18.90 = { by axiom 2 (commutativity_for_addition) R->L }
% 144.05/18.90 add(associator(X, Y, Z), add(multiply(X, multiply(Y, Z)), W))
% 144.05/18.90 = { by axiom 6 (associativity_for_addition) }
% 144.05/18.90 add(add(associator(X, Y, Z), multiply(X, multiply(Y, Z))), W)
% 144.05/18.90 = { by lemma 15 }
% 144.05/18.90 add(multiply(multiply(X, Y), Z), W)
% 144.05/18.90 = { by axiom 2 (commutativity_for_addition) }
% 144.05/18.90 add(W, multiply(multiply(X, Y), Z))
% 144.05/18.90
% 144.05/18.90 Goal 1 (prove_teichmuller_identity): add(add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d))), additive_inverse(add(add(associator(a, multiply(b, c), d), multiply(a, associator(b, c, d))), multiply(associator(a, b, c), d)))) = additive_identity.
% 144.05/18.90 Proof:
% 144.05/18.90 add(add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d))), additive_inverse(add(add(associator(a, multiply(b, c), d), multiply(a, associator(b, c, d))), multiply(associator(a, b, c), d))))
% 144.05/18.90 = { by axiom 2 (commutativity_for_addition) R->L }
% 144.05/18.90 add(additive_inverse(add(add(associator(a, multiply(b, c), d), multiply(a, associator(b, c, d))), multiply(associator(a, b, c), d))), add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d))))
% 144.05/18.90 = { by lemma 13 R->L }
% 144.05/18.90 add(add(add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d))), additive_inverse(add(add(add(associator(a, multiply(b, c), d), multiply(a, associator(b, c, d))), multiply(associator(a, b, c), d)), add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d)))))), add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d))))
% 144.05/18.90 = { by axiom 6 (associativity_for_addition) R->L }
% 144.05/18.90 add(add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d))), add(additive_inverse(add(add(add(associator(a, multiply(b, c), d), multiply(a, associator(b, c, d))), multiply(associator(a, b, c), d)), add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d))))), add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d)))))
% 144.05/18.90 = { by axiom 2 (commutativity_for_addition) }
% 144.05/18.90 add(add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d))), add(add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d))), additive_inverse(add(add(add(associator(a, multiply(b, c), d), multiply(a, associator(b, c, d))), multiply(associator(a, b, c), d)), add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d)))))))
% 144.05/18.90 = { by axiom 6 (associativity_for_addition) }
% 144.05/18.90 add(add(add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d))), add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d)))), additive_inverse(add(add(add(associator(a, multiply(b, c), d), multiply(a, associator(b, c, d))), multiply(associator(a, b, c), d)), add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d))))))
% 144.05/18.90 = { by lemma 14 R->L }
% 144.05/18.90 add(add(add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d))), add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d)))), add(multiply(multiply(a, multiply(b, c)), d), additive_inverse(add(add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d))), add(add(add(associator(a, multiply(b, c), d), multiply(a, associator(b, c, d))), multiply(associator(a, b, c), d)), multiply(multiply(a, multiply(b, c)), d))))))
% 144.05/18.90 = { by axiom 2 (commutativity_for_addition) R->L }
% 144.05/18.90 add(add(add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d))), add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d)))), add(multiply(multiply(a, multiply(b, c)), d), additive_inverse(add(add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d))), add(multiply(multiply(a, multiply(b, c)), d), add(add(associator(a, multiply(b, c), d), multiply(a, associator(b, c, d))), multiply(associator(a, b, c), d)))))))
% 144.05/18.90 = { by lemma 11 }
% 144.05/18.90 add(add(add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d))), add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d)))), add(multiply(multiply(a, multiply(b, c)), d), additive_inverse(add(add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d))), add(add(associator(a, multiply(b, c), d), multiply(a, associator(b, c, d))), add(multiply(associator(a, b, c), d), multiply(multiply(a, multiply(b, c)), d)))))))
% 144.05/18.90 = { by axiom 8 (distribute2) R->L }
% 144.05/18.90 add(add(add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d))), add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d)))), add(multiply(multiply(a, multiply(b, c)), d), additive_inverse(add(add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d))), add(add(associator(a, multiply(b, c), d), multiply(a, associator(b, c, d))), multiply(add(associator(a, b, c), multiply(a, multiply(b, c))), d))))))
% 144.05/18.90 = { by lemma 15 }
% 144.05/18.90 add(add(add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d))), add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d)))), add(multiply(multiply(a, multiply(b, c)), d), additive_inverse(add(add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d))), add(add(associator(a, multiply(b, c), d), multiply(a, associator(b, c, d))), multiply(multiply(multiply(a, b), c), d))))))
% 144.05/18.91 = { by lemma 15 R->L }
% 144.05/18.91 add(add(add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d))), add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d)))), add(multiply(multiply(a, multiply(b, c)), d), additive_inverse(add(add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d))), add(add(associator(a, multiply(b, c), d), multiply(a, associator(b, c, d))), add(associator(multiply(a, b), c, d), multiply(multiply(a, b), multiply(c, d))))))))
% 144.05/18.91 = { by lemma 10 R->L }
% 144.05/18.91 add(add(add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d))), add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d)))), add(multiply(multiply(a, multiply(b, c)), d), additive_inverse(add(add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d))), add(associator(multiply(a, b), c, d), add(add(associator(a, multiply(b, c), d), multiply(a, associator(b, c, d))), multiply(multiply(a, b), multiply(c, d))))))))
% 144.05/18.91 = { by axiom 2 (commutativity_for_addition) R->L }
% 144.05/18.91 add(add(add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d))), add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d)))), add(multiply(multiply(a, multiply(b, c)), d), additive_inverse(add(add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d))), add(associator(multiply(a, b), c, d), add(multiply(multiply(a, b), multiply(c, d)), add(associator(a, multiply(b, c), d), multiply(a, associator(b, c, d)))))))))
% 144.05/18.91 = { by lemma 11 R->L }
% 144.05/18.91 add(add(add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d))), add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d)))), add(multiply(multiply(a, multiply(b, c)), d), additive_inverse(add(add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d))), add(associator(multiply(a, b), c, d), add(multiply(a, associator(b, c, d)), add(multiply(multiply(a, b), multiply(c, d)), associator(a, multiply(b, c), d))))))))
% 144.05/18.91 = { by axiom 2 (commutativity_for_addition) }
% 144.05/18.91 add(add(add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d))), add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d)))), add(multiply(multiply(a, multiply(b, c)), d), additive_inverse(add(add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d))), add(associator(multiply(a, b), c, d), add(multiply(a, associator(b, c, d)), add(associator(a, multiply(b, c), d), multiply(multiply(a, b), multiply(c, d)))))))))
% 144.05/18.91 = { by lemma 10 R->L }
% 144.05/18.91 add(add(add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d))), add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d)))), add(multiply(multiply(a, multiply(b, c)), d), additive_inverse(add(add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d))), add(associator(multiply(a, b), c, d), add(associator(a, multiply(b, c), d), add(multiply(a, associator(b, c, d)), multiply(multiply(a, b), multiply(c, d)))))))))
% 144.05/18.91 = { by lemma 16 R->L }
% 144.05/18.91 add(add(add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d))), add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d)))), add(multiply(multiply(a, multiply(b, c)), d), additive_inverse(add(add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d))), add(associator(multiply(a, b), c, d), add(associator(a, multiply(b, c), d), add(associator(a, b, multiply(c, d)), add(multiply(a, associator(b, c, d)), multiply(a, multiply(b, multiply(c, d)))))))))))
% 144.05/18.91 = { by axiom 7 (distribute1) R->L }
% 144.05/18.91 add(add(add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d))), add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d)))), add(multiply(multiply(a, multiply(b, c)), d), additive_inverse(add(add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d))), add(associator(multiply(a, b), c, d), add(associator(a, multiply(b, c), d), add(associator(a, b, multiply(c, d)), multiply(a, add(associator(b, c, d), multiply(b, multiply(c, d)))))))))))
% 144.05/18.91 = { by lemma 15 }
% 144.05/18.91 add(add(add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d))), add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d)))), add(multiply(multiply(a, multiply(b, c)), d), additive_inverse(add(add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d))), add(associator(multiply(a, b), c, d), add(associator(a, multiply(b, c), d), add(associator(a, b, multiply(c, d)), multiply(a, multiply(multiply(b, c), d)))))))))
% 144.05/18.91 = { by lemma 16 }
% 144.05/18.91 add(add(add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d))), add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d)))), add(multiply(multiply(a, multiply(b, c)), d), additive_inverse(add(add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d))), add(associator(multiply(a, b), c, d), add(associator(a, b, multiply(c, d)), multiply(multiply(a, multiply(b, c)), d)))))))
% 144.05/18.91 = { by lemma 11 R->L }
% 144.05/18.91 add(add(add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d))), add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d)))), add(multiply(multiply(a, multiply(b, c)), d), additive_inverse(add(add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d))), add(multiply(multiply(a, multiply(b, c)), d), add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d))))))))
% 144.05/18.91 = { by axiom 2 (commutativity_for_addition) }
% 144.05/18.91 add(add(add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d))), add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d)))), add(multiply(multiply(a, multiply(b, c)), d), additive_inverse(add(add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d))), add(add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d))), multiply(multiply(a, multiply(b, c)), d))))))
% 144.05/18.91 = { by lemma 14 }
% 144.05/18.91 add(add(add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d))), add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d)))), additive_inverse(add(add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d))), add(associator(multiply(a, b), c, d), associator(a, b, multiply(c, d))))))
% 144.05/18.91 = { by axiom 5 (right_additive_inverse) }
% 144.05/18.91 additive_identity
% 144.05/18.91 % SZS output end Proof
% 144.05/18.91
% 144.05/18.91 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------