TSTP Solution File: LAT174-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT174-1 : TPTP v8.1.2. Released v3.1.0.
% 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 : 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 06:27:39 EDT 2023
% Result : Unsatisfiable 29.82s 4.26s
% Output : Proof 29.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT174-1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n016.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 : Thu Aug 24 07:30:38 EDT 2023
% 0.14/0.35 % CPUTime :
% 29.82/4.26 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 29.82/4.26
% 29.82/4.26 % SZS status Unsatisfiable
% 29.82/4.26
% 29.82/4.28 % SZS output start Proof
% 29.82/4.28 Axiom 1 (commutativity_of_join): join(X, Y) = join(Y, X).
% 29.82/4.28 Axiom 2 (idempotence_of_meet): meet(X, X) = X.
% 29.82/4.28 Axiom 3 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 29.82/4.28 Axiom 4 (absorption2): join(X, meet(X, Y)) = X.
% 29.82/4.28 Axiom 5 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 29.82/4.28 Axiom 6 (absorption1): meet(X, join(X, Y)) = X.
% 29.82/4.28 Axiom 7 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 29.82/4.28 Axiom 8 (equation_H76_dual): join(X, meet(Y, join(Z, meet(Y, W)))) = join(X, meet(Y, join(Z, meet(W, join(X, Y))))).
% 29.82/4.28
% 29.82/4.28 Lemma 9: meet(X, join(Y, X)) = X.
% 29.82/4.28 Proof:
% 29.82/4.28 meet(X, join(Y, X))
% 29.82/4.28 = { by axiom 1 (commutativity_of_join) R->L }
% 29.82/4.28 meet(X, join(X, Y))
% 29.82/4.28 = { by axiom 6 (absorption1) }
% 29.82/4.28 X
% 29.82/4.28
% 29.82/4.28 Lemma 10: join(meet(X, Y), meet(X, join(Y, Z))) = meet(X, join(Y, Z)).
% 29.82/4.28 Proof:
% 29.82/4.28 join(meet(X, Y), meet(X, join(Y, Z)))
% 29.82/4.28 = { by axiom 3 (commutativity_of_meet) R->L }
% 29.82/4.28 join(meet(Y, X), meet(X, join(Y, Z)))
% 29.82/4.28 = { by axiom 1 (commutativity_of_join) R->L }
% 29.82/4.28 join(meet(X, join(Y, Z)), meet(Y, X))
% 29.82/4.28 = { by axiom 6 (absorption1) R->L }
% 29.82/4.28 join(meet(X, join(Y, Z)), meet(meet(Y, join(Y, Z)), X))
% 29.82/4.28 = { by axiom 7 (associativity_of_meet) }
% 29.82/4.28 join(meet(X, join(Y, Z)), meet(Y, meet(join(Y, Z), X)))
% 29.82/4.28 = { by axiom 3 (commutativity_of_meet) }
% 29.82/4.28 join(meet(X, join(Y, Z)), meet(Y, meet(X, join(Y, Z))))
% 29.82/4.28 = { by axiom 3 (commutativity_of_meet) R->L }
% 29.82/4.28 join(meet(X, join(Y, Z)), meet(meet(X, join(Y, Z)), Y))
% 29.82/4.28 = { by axiom 4 (absorption2) }
% 29.82/4.28 meet(X, join(Y, Z))
% 29.82/4.28
% 29.82/4.28 Lemma 11: join(meet(X, Y), meet(X, join(Z, meet(X, Y)))) = meet(X, join(Z, meet(X, Y))).
% 29.82/4.28 Proof:
% 29.82/4.28 join(meet(X, Y), meet(X, join(Z, meet(X, Y))))
% 29.82/4.28 = { by axiom 1 (commutativity_of_join) R->L }
% 29.82/4.28 join(meet(X, Y), meet(X, join(meet(X, Y), Z)))
% 29.82/4.28 = { by axiom 2 (idempotence_of_meet) R->L }
% 29.82/4.28 join(meet(meet(X, X), Y), meet(X, join(meet(X, Y), Z)))
% 29.82/4.28 = { by axiom 7 (associativity_of_meet) }
% 29.82/4.28 join(meet(X, meet(X, Y)), meet(X, join(meet(X, Y), Z)))
% 29.82/4.28 = { by lemma 10 }
% 29.82/4.28 meet(X, join(meet(X, Y), Z))
% 29.82/4.28 = { by axiom 1 (commutativity_of_join) }
% 29.82/4.28 meet(X, join(Z, meet(X, Y)))
% 29.82/4.28
% 29.82/4.28 Lemma 12: meet(X, join(meet(X, Y), meet(Y, Z))) = meet(X, Y).
% 29.82/4.28 Proof:
% 29.82/4.28 meet(X, join(meet(X, Y), meet(Y, Z)))
% 29.82/4.28 = { by axiom 1 (commutativity_of_join) R->L }
% 29.82/4.28 meet(X, join(meet(Y, Z), meet(X, Y)))
% 29.82/4.28 = { by lemma 11 R->L }
% 29.82/4.28 join(meet(X, Y), meet(X, join(meet(Y, Z), meet(X, Y))))
% 29.82/4.28 = { by axiom 8 (equation_H76_dual) }
% 29.82/4.28 join(meet(X, Y), meet(X, join(meet(Y, Z), meet(Y, join(meet(X, Y), X)))))
% 29.82/4.28 = { by lemma 9 R->L }
% 29.82/4.28 join(meet(X, Y), meet(X, meet(join(meet(Y, Z), meet(Y, join(meet(X, Y), X))), join(Y, join(meet(Y, Z), meet(Y, join(meet(X, Y), X)))))))
% 29.82/4.28 = { by axiom 1 (commutativity_of_join) R->L }
% 29.82/4.28 join(meet(X, Y), meet(X, meet(join(meet(Y, Z), meet(Y, join(meet(X, Y), X))), join(Y, join(meet(Y, join(meet(X, Y), X)), meet(Y, Z))))))
% 29.82/4.28 = { by axiom 5 (associativity_of_join) R->L }
% 29.82/4.28 join(meet(X, Y), meet(X, meet(join(meet(Y, Z), meet(Y, join(meet(X, Y), X))), join(join(Y, meet(Y, join(meet(X, Y), X))), meet(Y, Z)))))
% 29.82/4.28 = { by axiom 4 (absorption2) }
% 29.82/4.28 join(meet(X, Y), meet(X, meet(join(meet(Y, Z), meet(Y, join(meet(X, Y), X))), join(Y, meet(Y, Z)))))
% 29.82/4.28 = { by axiom 3 (commutativity_of_meet) }
% 29.82/4.28 join(meet(X, Y), meet(X, meet(join(Y, meet(Y, Z)), join(meet(Y, Z), meet(Y, join(meet(X, Y), X))))))
% 29.82/4.28 = { by axiom 4 (absorption2) }
% 29.82/4.28 join(meet(X, Y), meet(X, meet(Y, join(meet(Y, Z), meet(Y, join(meet(X, Y), X))))))
% 29.82/4.28 = { by axiom 7 (associativity_of_meet) R->L }
% 29.82/4.28 join(meet(X, Y), meet(meet(X, Y), join(meet(Y, Z), meet(Y, join(meet(X, Y), X)))))
% 29.82/4.28 = { by axiom 4 (absorption2) }
% 29.82/4.28 meet(X, Y)
% 29.82/4.28
% 29.82/4.28 Lemma 13: meet(X, join(meet(X, Y), meet(Z, Y))) = meet(X, Y).
% 29.82/4.28 Proof:
% 29.82/4.28 meet(X, join(meet(X, Y), meet(Z, Y)))
% 29.82/4.28 = { by axiom 3 (commutativity_of_meet) R->L }
% 29.82/4.28 meet(X, join(meet(X, Y), meet(Y, Z)))
% 29.82/4.28 = { by lemma 12 }
% 29.82/4.28 meet(X, Y)
% 29.82/4.28
% 29.82/4.28 Lemma 14: meet(X, join(Y, meet(X, join(Y, Z)))) = meet(X, join(Y, Z)).
% 29.82/4.28 Proof:
% 29.82/4.28 meet(X, join(Y, meet(X, join(Y, Z))))
% 29.82/4.28 = { by axiom 1 (commutativity_of_join) R->L }
% 29.82/4.28 meet(X, join(meet(X, join(Y, Z)), Y))
% 29.82/4.28 = { by axiom 6 (absorption1) R->L }
% 29.82/4.28 meet(X, join(meet(X, join(Y, Z)), meet(Y, join(Y, Z))))
% 29.82/4.28 = { by lemma 13 }
% 29.82/4.28 meet(X, join(Y, Z))
% 29.82/4.28
% 29.82/4.28 Lemma 15: meet(X, join(Y, meet(Z, join(X, Y)))) = meet(X, join(Y, meet(X, Z))).
% 29.82/4.28 Proof:
% 29.82/4.28 meet(X, join(Y, meet(Z, join(X, Y))))
% 29.82/4.28 = { by axiom 1 (commutativity_of_join) R->L }
% 29.82/4.28 meet(X, join(Y, meet(Z, join(Y, X))))
% 29.82/4.28 = { by lemma 14 R->L }
% 29.82/4.28 meet(X, join(Y, meet(X, join(Y, meet(Z, join(Y, X))))))
% 29.82/4.28 = { by axiom 8 (equation_H76_dual) R->L }
% 29.82/4.28 meet(X, join(Y, meet(X, join(Y, meet(X, Z)))))
% 29.82/4.28 = { by lemma 14 }
% 29.82/4.28 meet(X, join(Y, meet(X, Z)))
% 29.82/4.28
% 29.82/4.28 Lemma 16: meet(X, join(meet(Y, Z), meet(X, Z))) = meet(X, Z).
% 29.82/4.28 Proof:
% 29.82/4.28 meet(X, join(meet(Y, Z), meet(X, Z)))
% 29.82/4.28 = { by axiom 3 (commutativity_of_meet) R->L }
% 29.82/4.28 meet(X, join(meet(Z, Y), meet(X, Z)))
% 29.82/4.28 = { by axiom 1 (commutativity_of_join) R->L }
% 29.82/4.28 meet(X, join(meet(X, Z), meet(Z, Y)))
% 29.82/4.28 = { by lemma 12 }
% 29.82/4.28 meet(X, Z)
% 29.82/4.28
% 29.82/4.28 Lemma 17: meet(join(X, Y), join(X, join(Y, Z))) = join(X, Y).
% 29.82/4.28 Proof:
% 29.82/4.28 meet(join(X, Y), join(X, join(Y, Z)))
% 29.82/4.28 = { by axiom 5 (associativity_of_join) R->L }
% 29.82/4.28 meet(join(X, Y), join(join(X, Y), Z))
% 29.82/4.28 = { by axiom 6 (absorption1) }
% 29.82/4.28 join(X, Y)
% 29.82/4.28
% 29.82/4.28 Lemma 18: meet(join(X, meet(Y, Z)), join(X, meet(Y, join(Z, W)))) = join(X, meet(Y, Z)).
% 29.82/4.28 Proof:
% 29.82/4.28 meet(join(X, meet(Y, Z)), join(X, meet(Y, join(Z, W))))
% 29.82/4.28 = { by lemma 10 R->L }
% 29.82/4.28 meet(join(X, meet(Y, Z)), join(X, join(meet(Y, Z), meet(Y, join(Z, W)))))
% 29.82/4.28 = { by lemma 17 }
% 29.82/4.28 join(X, meet(Y, Z))
% 29.82/4.28
% 29.82/4.28 Goal 1 (prove_H6): meet(a, join(b, meet(a, c))) = meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))).
% 29.82/4.28 Proof:
% 29.82/4.28 meet(a, join(b, meet(a, c)))
% 29.82/4.28 = { by lemma 15 R->L }
% 29.82/4.28 meet(a, join(b, meet(c, join(a, b))))
% 29.82/4.28 = { by lemma 16 R->L }
% 29.82/4.28 meet(a, join(meet(c, join(b, meet(c, join(a, b)))), meet(a, join(b, meet(c, join(a, b))))))
% 29.82/4.28 = { by lemma 13 R->L }
% 29.82/4.28 meet(a, join(meet(a, join(meet(c, join(b, meet(c, join(a, b)))), meet(a, join(b, meet(c, join(a, b)))))), meet(join(meet(c, join(a, b)), meet(a, join(b, meet(c, join(a, b))))), join(meet(c, join(b, meet(c, join(a, b)))), meet(a, join(b, meet(c, join(a, b))))))))
% 29.82/4.28 = { by lemma 16 }
% 29.82/4.28 meet(a, join(meet(a, join(b, meet(c, join(a, b)))), meet(join(meet(c, join(a, b)), meet(a, join(b, meet(c, join(a, b))))), join(meet(c, join(b, meet(c, join(a, b)))), meet(a, join(b, meet(c, join(a, b))))))))
% 29.82/4.28 = { by axiom 1 (commutativity_of_join) }
% 29.82/4.28 meet(a, join(meet(a, join(b, meet(c, join(a, b)))), meet(join(meet(c, join(a, b)), meet(a, join(b, meet(c, join(a, b))))), join(meet(a, join(b, meet(c, join(a, b)))), meet(c, join(b, meet(c, join(a, b))))))))
% 29.82/4.28 = { by axiom 1 (commutativity_of_join) R->L }
% 29.82/4.28 meet(a, join(meet(a, join(b, meet(c, join(a, b)))), meet(join(meet(a, join(b, meet(c, join(a, b)))), meet(c, join(a, b))), join(meet(a, join(b, meet(c, join(a, b)))), meet(c, join(b, meet(c, join(a, b))))))))
% 29.82/4.29 = { by lemma 11 R->L }
% 29.82/4.29 meet(a, join(meet(a, join(b, meet(c, join(a, b)))), meet(join(meet(a, join(b, meet(c, join(a, b)))), meet(c, join(a, b))), join(meet(a, join(b, meet(c, join(a, b)))), join(meet(c, join(a, b)), meet(c, join(b, meet(c, join(a, b)))))))))
% 29.82/4.29 = { by lemma 17 }
% 29.82/4.29 meet(a, join(meet(a, join(b, meet(c, join(a, b)))), join(meet(a, join(b, meet(c, join(a, b)))), meet(c, join(a, b)))))
% 29.82/4.29 = { by lemma 9 R->L }
% 29.82/4.29 meet(a, join(meet(meet(a, join(b, meet(c, join(a, b)))), join(meet(join(a, b), join(c, X)), meet(a, join(b, meet(c, join(a, b)))))), join(meet(a, join(b, meet(c, join(a, b)))), meet(c, join(a, b)))))
% 29.82/4.29 = { by axiom 3 (commutativity_of_meet) R->L }
% 29.82/4.29 meet(a, join(meet(meet(a, join(b, meet(c, join(a, b)))), join(meet(join(a, b), join(c, X)), meet(a, join(b, meet(c, join(a, b)))))), join(meet(a, join(b, meet(c, join(a, b)))), meet(join(a, b), c))))
% 29.82/4.29 = { by lemma 18 R->L }
% 29.82/4.29 meet(a, join(meet(meet(a, join(b, meet(c, join(a, b)))), join(meet(join(a, b), join(c, X)), meet(a, join(b, meet(c, join(a, b)))))), meet(join(meet(a, join(b, meet(c, join(a, b)))), meet(join(a, b), c)), join(meet(a, join(b, meet(c, join(a, b)))), meet(join(a, b), join(c, X))))))
% 29.82/4.29 = { by axiom 1 (commutativity_of_join) }
% 29.82/4.29 meet(a, join(meet(meet(a, join(b, meet(c, join(a, b)))), join(meet(join(a, b), join(c, X)), meet(a, join(b, meet(c, join(a, b)))))), meet(join(meet(join(a, b), c), meet(a, join(b, meet(c, join(a, b))))), join(meet(a, join(b, meet(c, join(a, b)))), meet(join(a, b), join(c, X))))))
% 29.82/4.29 = { by axiom 1 (commutativity_of_join) }
% 29.82/4.29 meet(a, join(meet(meet(a, join(b, meet(c, join(a, b)))), join(meet(join(a, b), join(c, X)), meet(a, join(b, meet(c, join(a, b)))))), meet(join(meet(join(a, b), c), meet(a, join(b, meet(c, join(a, b))))), join(meet(join(a, b), join(c, X)), meet(a, join(b, meet(c, join(a, b))))))))
% 29.82/4.29 = { by axiom 3 (commutativity_of_meet) }
% 29.82/4.29 meet(a, join(meet(meet(a, join(b, meet(c, join(a, b)))), join(meet(join(a, b), join(c, X)), meet(a, join(b, meet(c, join(a, b)))))), meet(join(meet(c, join(a, b)), meet(a, join(b, meet(c, join(a, b))))), join(meet(join(a, b), join(c, X)), meet(a, join(b, meet(c, join(a, b))))))))
% 29.82/4.29 = { by axiom 3 (commutativity_of_meet) R->L }
% 29.82/4.29 meet(a, join(meet(meet(a, join(b, meet(c, join(a, b)))), join(meet(join(a, b), join(c, X)), meet(a, join(b, meet(c, join(a, b)))))), meet(join(meet(join(a, b), join(c, X)), meet(a, join(b, meet(c, join(a, b))))), join(meet(c, join(a, b)), meet(a, join(b, meet(c, join(a, b))))))))
% 29.82/4.29 = { by axiom 3 (commutativity_of_meet) R->L }
% 29.82/4.29 meet(a, join(meet(join(meet(join(a, b), join(c, X)), meet(a, join(b, meet(c, join(a, b))))), meet(a, join(b, meet(c, join(a, b))))), meet(join(meet(join(a, b), join(c, X)), meet(a, join(b, meet(c, join(a, b))))), join(meet(c, join(a, b)), meet(a, join(b, meet(c, join(a, b))))))))
% 29.82/4.29 = { by axiom 1 (commutativity_of_join) R->L }
% 29.82/4.29 meet(a, join(meet(join(meet(join(a, b), join(c, X)), meet(a, join(b, meet(c, join(a, b))))), meet(a, join(b, meet(c, join(a, b))))), meet(join(meet(join(a, b), join(c, X)), meet(a, join(b, meet(c, join(a, b))))), join(meet(a, join(b, meet(c, join(a, b)))), meet(c, join(a, b))))))
% 29.82/4.29 = { by lemma 10 }
% 29.82/4.29 meet(a, meet(join(meet(join(a, b), join(c, X)), meet(a, join(b, meet(c, join(a, b))))), join(meet(a, join(b, meet(c, join(a, b)))), meet(c, join(a, b)))))
% 29.82/4.29 = { by axiom 3 (commutativity_of_meet) }
% 29.82/4.29 meet(a, meet(join(meet(a, join(b, meet(c, join(a, b)))), meet(c, join(a, b))), join(meet(join(a, b), join(c, X)), meet(a, join(b, meet(c, join(a, b)))))))
% 29.82/4.29 = { by axiom 3 (commutativity_of_meet) R->L }
% 29.82/4.29 meet(a, meet(join(meet(a, join(b, meet(c, join(a, b)))), meet(join(a, b), c)), join(meet(join(a, b), join(c, X)), meet(a, join(b, meet(c, join(a, b)))))))
% 29.82/4.29 = { by axiom 1 (commutativity_of_join) R->L }
% 29.82/4.29 meet(a, meet(join(meet(a, join(b, meet(c, join(a, b)))), meet(join(a, b), c)), join(meet(a, join(b, meet(c, join(a, b)))), meet(join(a, b), join(c, X)))))
% 29.82/4.29 = { by lemma 18 }
% 29.82/4.29 meet(a, join(meet(a, join(b, meet(c, join(a, b)))), meet(join(a, b), c)))
% 29.82/4.29 = { by axiom 3 (commutativity_of_meet) }
% 29.82/4.29 meet(a, join(meet(a, join(b, meet(c, join(a, b)))), meet(c, join(a, b))))
% 29.82/4.29 = { by axiom 1 (commutativity_of_join) }
% 29.82/4.29 meet(a, join(meet(c, join(a, b)), meet(a, join(b, meet(c, join(a, b))))))
% 29.82/4.29 = { by lemma 15 }
% 29.82/4.29 meet(a, join(meet(c, join(a, b)), meet(a, join(b, meet(a, c)))))
% 29.82/4.29 = { by axiom 1 (commutativity_of_join) R->L }
% 29.82/4.29 meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))))
% 29.82/4.29 % SZS output end Proof
% 29.82/4.29
% 29.82/4.29 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------