TSTP Solution File: LAT156-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT156-1 : 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 : n021.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 06:27:35 EDT 2023
% Result : Unsatisfiable 28.97s 4.11s
% Output : Proof 29.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT156-1 : 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 : n021.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 05:43:39 EDT 2023
% 0.14/0.35 % CPUTime :
% 28.97/4.11 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 28.97/4.11
% 28.97/4.11 % SZS status Unsatisfiable
% 28.97/4.11
% 29.22/4.13 % SZS output start Proof
% 29.22/4.13 Axiom 1 (idempotence_of_join): join(X, X) = X.
% 29.22/4.13 Axiom 2 (commutativity_of_join): join(X, Y) = join(Y, X).
% 29.22/4.13 Axiom 3 (idempotence_of_meet): meet(X, X) = X.
% 29.22/4.13 Axiom 4 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 29.22/4.13 Axiom 5 (absorption2): join(X, meet(X, Y)) = X.
% 29.22/4.13 Axiom 6 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 29.22/4.13 Axiom 7 (absorption1): meet(X, join(X, Y)) = X.
% 29.22/4.13 Axiom 8 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 29.22/4.13 Axiom 9 (equation_H49): meet(X, join(Y, meet(Z, join(X, W)))) = meet(X, join(Y, join(meet(X, Z), meet(Z, join(Y, W))))).
% 29.22/4.13
% 29.22/4.13 Lemma 10: meet(X, meet(Y, join(X, Z))) = meet(X, Y).
% 29.22/4.13 Proof:
% 29.22/4.13 meet(X, meet(Y, join(X, Z)))
% 29.22/4.13 = { by axiom 4 (commutativity_of_meet) R->L }
% 29.22/4.13 meet(X, meet(join(X, Z), Y))
% 29.22/4.13 = { by axiom 8 (associativity_of_meet) R->L }
% 29.22/4.13 meet(meet(X, join(X, Z)), Y)
% 29.22/4.13 = { by axiom 7 (absorption1) }
% 29.22/4.13 meet(X, Y)
% 29.22/4.13
% 29.22/4.13 Lemma 11: join(meet(X, Y), meet(X, join(Y, Z))) = meet(X, join(Y, Z)).
% 29.22/4.13 Proof:
% 29.22/4.13 join(meet(X, Y), meet(X, join(Y, Z)))
% 29.22/4.13 = { by axiom 4 (commutativity_of_meet) R->L }
% 29.22/4.13 join(meet(Y, X), meet(X, join(Y, Z)))
% 29.22/4.13 = { by axiom 2 (commutativity_of_join) R->L }
% 29.22/4.13 join(meet(X, join(Y, Z)), meet(Y, X))
% 29.22/4.13 = { by lemma 10 R->L }
% 29.22/4.13 join(meet(X, join(Y, Z)), meet(Y, meet(X, join(Y, Z))))
% 29.22/4.13 = { by axiom 4 (commutativity_of_meet) R->L }
% 29.22/4.13 join(meet(X, join(Y, Z)), meet(meet(X, join(Y, Z)), Y))
% 29.22/4.13 = { by axiom 5 (absorption2) }
% 29.22/4.13 meet(X, join(Y, Z))
% 29.22/4.13
% 29.22/4.13 Lemma 12: join(meet(X, Y), meet(Y, join(Z, X))) = meet(Y, join(X, Z)).
% 29.22/4.13 Proof:
% 29.22/4.13 join(meet(X, Y), meet(Y, join(Z, X)))
% 29.22/4.13 = { by axiom 4 (commutativity_of_meet) R->L }
% 29.22/4.13 join(meet(Y, X), meet(Y, join(Z, X)))
% 29.22/4.13 = { by axiom 2 (commutativity_of_join) R->L }
% 29.22/4.13 join(meet(Y, X), meet(Y, join(X, Z)))
% 29.22/4.13 = { by lemma 11 }
% 29.22/4.13 meet(Y, join(X, Z))
% 29.22/4.13
% 29.22/4.13 Lemma 13: meet(X, join(Y, meet(Z, join(X, Y)))) = meet(X, join(Y, meet(X, Z))).
% 29.22/4.13 Proof:
% 29.22/4.13 meet(X, join(Y, meet(Z, join(X, Y))))
% 29.22/4.13 = { by lemma 12 R->L }
% 29.22/4.13 meet(X, join(Y, join(meet(X, Z), meet(Z, join(Y, X)))))
% 29.22/4.13 = { by axiom 9 (equation_H49) R->L }
% 29.22/4.13 meet(X, join(Y, meet(Z, join(X, X))))
% 29.22/4.13 = { by axiom 1 (idempotence_of_join) }
% 29.22/4.13 meet(X, join(Y, meet(Z, X)))
% 29.22/4.13 = { by axiom 4 (commutativity_of_meet) }
% 29.22/4.13 meet(X, join(Y, meet(X, Z)))
% 29.22/4.13
% 29.22/4.13 Lemma 14: meet(X, join(Y, meet(Z, join(Y, X)))) = meet(X, join(Y, meet(X, Z))).
% 29.22/4.13 Proof:
% 29.22/4.13 meet(X, join(Y, meet(Z, join(Y, X))))
% 29.22/4.13 = { by axiom 2 (commutativity_of_join) R->L }
% 29.22/4.13 meet(X, join(Y, meet(Z, join(X, Y))))
% 29.22/4.13 = { by lemma 13 }
% 29.22/4.13 meet(X, join(Y, meet(X, Z)))
% 29.22/4.13
% 29.22/4.13 Lemma 15: join(meet(X, Y), meet(X, join(Z, meet(X, Y)))) = meet(X, join(Z, meet(X, Y))).
% 29.22/4.13 Proof:
% 29.22/4.13 join(meet(X, Y), meet(X, join(Z, meet(X, Y))))
% 29.22/4.13 = { by axiom 2 (commutativity_of_join) R->L }
% 29.22/4.13 join(meet(X, Y), meet(X, join(meet(X, Y), Z)))
% 29.22/4.13 = { by axiom 3 (idempotence_of_meet) R->L }
% 29.22/4.13 join(meet(meet(X, X), Y), meet(X, join(meet(X, Y), Z)))
% 29.22/4.13 = { by axiom 8 (associativity_of_meet) }
% 29.22/4.13 join(meet(X, meet(X, Y)), meet(X, join(meet(X, Y), Z)))
% 29.22/4.13 = { by lemma 11 }
% 29.22/4.13 meet(X, join(meet(X, Y), Z))
% 29.22/4.13 = { by axiom 2 (commutativity_of_join) }
% 29.22/4.13 meet(X, join(Z, meet(X, Y)))
% 29.22/4.13
% 29.22/4.13 Lemma 16: meet(X, join(meet(Y, Z), meet(X, Z))) = meet(X, Z).
% 29.22/4.13 Proof:
% 29.22/4.13 meet(X, join(meet(Y, Z), meet(X, Z)))
% 29.22/4.13 = { by lemma 13 R->L }
% 29.22/4.13 meet(X, join(meet(Y, Z), meet(Z, join(X, meet(Y, Z)))))
% 29.22/4.13 = { by axiom 4 (commutativity_of_meet) R->L }
% 29.22/4.13 meet(X, join(meet(Y, Z), meet(Z, join(X, meet(Z, Y)))))
% 29.22/4.13 = { by axiom 4 (commutativity_of_meet) R->L }
% 29.22/4.13 meet(X, join(meet(Z, Y), meet(Z, join(X, meet(Z, Y)))))
% 29.22/4.13 = { by lemma 15 }
% 29.22/4.13 meet(X, meet(Z, join(X, meet(Z, Y))))
% 29.22/4.13 = { by axiom 4 (commutativity_of_meet) }
% 29.22/4.13 meet(X, meet(Z, join(X, meet(Y, Z))))
% 29.22/4.13 = { by lemma 10 }
% 29.22/4.13 meet(X, Z)
% 29.22/4.13
% 29.22/4.13 Lemma 17: meet(join(X, Y), join(X, join(Y, Z))) = join(X, Y).
% 29.22/4.13 Proof:
% 29.22/4.13 meet(join(X, Y), join(X, join(Y, Z)))
% 29.22/4.13 = { by axiom 6 (associativity_of_join) R->L }
% 29.22/4.13 meet(join(X, Y), join(join(X, Y), Z))
% 29.22/4.13 = { by axiom 7 (absorption1) }
% 29.22/4.13 join(X, Y)
% 29.22/4.13
% 29.22/4.13 Lemma 18: meet(join(X, meet(Y, Z)), join(X, meet(Y, join(Z, W)))) = join(X, meet(Y, Z)).
% 29.22/4.13 Proof:
% 29.22/4.13 meet(join(X, meet(Y, Z)), join(X, meet(Y, join(Z, W))))
% 29.22/4.13 = { by lemma 11 R->L }
% 29.22/4.13 meet(join(X, meet(Y, Z)), join(X, join(meet(Y, Z), meet(Y, join(Z, W)))))
% 29.22/4.13 = { by lemma 17 }
% 29.22/4.13 join(X, meet(Y, Z))
% 29.22/4.13
% 29.22/4.13 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)))).
% 29.22/4.13 Proof:
% 29.22/4.13 meet(a, join(b, meet(a, c)))
% 29.22/4.13 = { by lemma 14 R->L }
% 29.22/4.13 meet(a, join(b, meet(c, join(b, a))))
% 29.22/4.13 = { by lemma 16 R->L }
% 29.22/4.13 meet(a, join(meet(c, join(b, meet(c, join(b, a)))), meet(a, join(b, meet(c, join(b, a))))))
% 29.22/4.13 = { by lemma 16 R->L }
% 29.22/4.13 meet(a, join(meet(join(meet(c, join(b, a)), meet(a, join(b, meet(c, join(b, a))))), join(meet(c, join(b, meet(c, join(b, a)))), meet(a, join(b, meet(c, join(b, a)))))), meet(a, join(meet(c, join(b, meet(c, join(b, a)))), meet(a, join(b, meet(c, join(b, a))))))))
% 29.22/4.13 = { by lemma 16 }
% 29.22/4.13 meet(a, join(meet(join(meet(c, join(b, a)), meet(a, join(b, meet(c, join(b, a))))), join(meet(c, join(b, meet(c, join(b, a)))), meet(a, join(b, meet(c, join(b, a)))))), meet(a, join(b, meet(c, join(b, a))))))
% 29.22/4.13 = { by axiom 2 (commutativity_of_join) }
% 29.22/4.13 meet(a, join(meet(a, join(b, meet(c, join(b, a)))), meet(join(meet(c, join(b, a)), meet(a, join(b, meet(c, join(b, a))))), join(meet(c, join(b, meet(c, join(b, a)))), meet(a, join(b, meet(c, join(b, a))))))))
% 29.22/4.13 = { by axiom 2 (commutativity_of_join) }
% 29.22/4.13 meet(a, join(meet(a, join(b, meet(c, join(b, a)))), meet(join(meet(c, join(b, a)), meet(a, join(b, meet(c, join(b, a))))), join(meet(a, join(b, meet(c, join(b, a)))), meet(c, join(b, meet(c, join(b, a))))))))
% 29.22/4.13 = { by axiom 2 (commutativity_of_join) R->L }
% 29.22/4.13 meet(a, join(meet(a, join(b, meet(c, join(b, a)))), meet(join(meet(a, join(b, meet(c, join(b, a)))), meet(c, join(b, a))), join(meet(a, join(b, meet(c, join(b, a)))), meet(c, join(b, meet(c, join(b, a))))))))
% 29.22/4.13 = { by lemma 15 R->L }
% 29.22/4.13 meet(a, join(meet(a, join(b, meet(c, join(b, a)))), meet(join(meet(a, join(b, meet(c, join(b, a)))), meet(c, join(b, a))), join(meet(a, join(b, meet(c, join(b, a)))), join(meet(c, join(b, a)), meet(c, join(b, meet(c, join(b, a)))))))))
% 29.22/4.13 = { by lemma 17 }
% 29.22/4.13 meet(a, join(meet(a, join(b, meet(c, join(b, a)))), join(meet(a, join(b, meet(c, join(b, a)))), meet(c, join(b, a)))))
% 29.22/4.13 = { by axiom 7 (absorption1) R->L }
% 29.22/4.13 meet(a, join(meet(meet(a, join(b, meet(c, join(b, a)))), join(meet(a, join(b, meet(c, join(b, a)))), meet(join(b, a), join(c, X)))), join(meet(a, join(b, meet(c, join(b, a)))), meet(c, join(b, a)))))
% 29.22/4.13 = { by axiom 2 (commutativity_of_join) }
% 29.22/4.13 meet(a, join(meet(meet(a, join(b, meet(c, join(b, a)))), join(meet(join(b, a), join(c, X)), meet(a, join(b, meet(c, join(b, a)))))), join(meet(a, join(b, meet(c, join(b, a)))), meet(c, join(b, a)))))
% 29.22/4.13 = { by axiom 4 (commutativity_of_meet) R->L }
% 29.22/4.13 meet(a, join(meet(meet(a, join(b, meet(c, join(b, a)))), join(meet(join(b, a), join(c, X)), meet(a, join(b, meet(c, join(b, a)))))), join(meet(a, join(b, meet(c, join(b, a)))), meet(join(b, a), c))))
% 29.22/4.13 = { by lemma 18 R->L }
% 29.22/4.13 meet(a, join(meet(meet(a, join(b, meet(c, join(b, a)))), join(meet(join(b, a), join(c, X)), meet(a, join(b, meet(c, join(b, a)))))), meet(join(meet(a, join(b, meet(c, join(b, a)))), meet(join(b, a), c)), join(meet(a, join(b, meet(c, join(b, a)))), meet(join(b, a), join(c, X))))))
% 29.22/4.13 = { by axiom 2 (commutativity_of_join) }
% 29.22/4.13 meet(a, join(meet(meet(a, join(b, meet(c, join(b, a)))), join(meet(join(b, a), join(c, X)), meet(a, join(b, meet(c, join(b, a)))))), meet(join(meet(join(b, a), c), meet(a, join(b, meet(c, join(b, a))))), join(meet(a, join(b, meet(c, join(b, a)))), meet(join(b, a), join(c, X))))))
% 29.22/4.13 = { by axiom 2 (commutativity_of_join) }
% 29.22/4.13 meet(a, join(meet(meet(a, join(b, meet(c, join(b, a)))), join(meet(join(b, a), join(c, X)), meet(a, join(b, meet(c, join(b, a)))))), meet(join(meet(join(b, a), c), meet(a, join(b, meet(c, join(b, a))))), join(meet(join(b, a), join(c, X)), meet(a, join(b, meet(c, join(b, a))))))))
% 29.22/4.13 = { by axiom 4 (commutativity_of_meet) }
% 29.22/4.13 meet(a, join(meet(meet(a, join(b, meet(c, join(b, a)))), join(meet(join(b, a), join(c, X)), meet(a, join(b, meet(c, join(b, a)))))), meet(join(meet(c, join(b, a)), meet(a, join(b, meet(c, join(b, a))))), join(meet(join(b, a), join(c, X)), meet(a, join(b, meet(c, join(b, a))))))))
% 29.22/4.13 = { by axiom 4 (commutativity_of_meet) R->L }
% 29.22/4.13 meet(a, join(meet(meet(a, join(b, meet(c, join(b, a)))), join(meet(join(b, a), join(c, X)), meet(a, join(b, meet(c, join(b, a)))))), meet(join(meet(join(b, a), join(c, X)), meet(a, join(b, meet(c, join(b, a))))), join(meet(c, join(b, a)), meet(a, join(b, meet(c, join(b, a))))))))
% 29.22/4.13 = { by lemma 12 }
% 29.22/4.13 meet(a, meet(join(meet(join(b, a), join(c, X)), meet(a, join(b, meet(c, join(b, a))))), join(meet(a, join(b, meet(c, join(b, a)))), meet(c, join(b, a)))))
% 29.22/4.13 = { by axiom 4 (commutativity_of_meet) }
% 29.22/4.13 meet(a, meet(join(meet(a, join(b, meet(c, join(b, a)))), meet(c, join(b, a))), join(meet(join(b, a), join(c, X)), meet(a, join(b, meet(c, join(b, a)))))))
% 29.22/4.13 = { by axiom 4 (commutativity_of_meet) R->L }
% 29.22/4.13 meet(a, meet(join(meet(a, join(b, meet(c, join(b, a)))), meet(join(b, a), c)), join(meet(join(b, a), join(c, X)), meet(a, join(b, meet(c, join(b, a)))))))
% 29.22/4.13 = { by axiom 2 (commutativity_of_join) R->L }
% 29.22/4.13 meet(a, meet(join(meet(a, join(b, meet(c, join(b, a)))), meet(join(b, a), c)), join(meet(a, join(b, meet(c, join(b, a)))), meet(join(b, a), join(c, X)))))
% 29.22/4.13 = { by lemma 18 }
% 29.22/4.13 meet(a, join(meet(a, join(b, meet(c, join(b, a)))), meet(join(b, a), c)))
% 29.22/4.13 = { by axiom 4 (commutativity_of_meet) }
% 29.22/4.13 meet(a, join(meet(a, join(b, meet(c, join(b, a)))), meet(c, join(b, a))))
% 29.22/4.13 = { by axiom 2 (commutativity_of_join) }
% 29.22/4.13 meet(a, join(meet(c, join(b, a)), meet(a, join(b, meet(c, join(b, a))))))
% 29.22/4.13 = { by lemma 14 }
% 29.22/4.13 meet(a, join(meet(c, join(b, a)), meet(a, join(b, meet(a, c)))))
% 29.22/4.13 = { by axiom 2 (commutativity_of_join) }
% 29.22/4.13 meet(a, join(meet(c, join(a, b)), meet(a, join(b, meet(a, c)))))
% 29.22/4.13 = { by axiom 2 (commutativity_of_join) R->L }
% 29.22/4.13 meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))))
% 29.22/4.13 % SZS output end Proof
% 29.22/4.13
% 29.22/4.13 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------