TSTP Solution File: LAT010-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT010-1 : TPTP v8.1.2. Released v2.2.0.
% 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 : n026.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 06:27:06 EDT 2023
% Result : Unsatisfiable 0.20s 0.85s
% Output : Proof 3.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT010-1 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 24 08:38:02 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.85 Command-line arguments: --no-flatten-goal
% 0.20/0.85
% 0.20/0.85 % SZS status Unsatisfiable
% 0.20/0.85
% 3.53/0.89 % SZS output start Proof
% 3.53/0.89 Axiom 1 (commutativity_of_join): join(X, Y) = join(Y, X).
% 3.53/0.89 Axiom 2 (idempotence_of_meet): meet(X, X) = X.
% 3.53/0.89 Axiom 3 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 3.53/0.89 Axiom 4 (absorption2): join(X, meet(X, Y)) = X.
% 3.53/0.89 Axiom 5 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 3.53/0.89 Axiom 6 (absorption1): meet(X, join(X, Y)) = X.
% 3.53/0.89 Axiom 7 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 3.53/0.89 Axiom 8 (nr_3): meet(join(X, meet(Y, Z)), join(Z, meet(X, Y))) = join(meet(Z, join(X, meet(Y, Z))), meet(X, join(Y, Z))).
% 3.53/0.89 Axiom 9 (n5_1): meet(X, join(Y, meet(Z, join(X, W)))) = join(meet(X, join(Y, meet(X, Z))), meet(X, join(meet(X, Y), meet(Z, W)))).
% 3.53/0.89
% 3.53/0.89 Lemma 10: meet(X, meet(X, Y)) = meet(X, Y).
% 3.53/0.89 Proof:
% 3.53/0.89 meet(X, meet(X, Y))
% 3.53/0.89 = { by axiom 7 (associativity_of_meet) R->L }
% 3.53/0.89 meet(meet(X, X), Y)
% 3.53/0.89 = { by axiom 2 (idempotence_of_meet) }
% 3.53/0.89 meet(X, Y)
% 3.53/0.89
% 3.53/0.89 Lemma 11: meet(X, meet(Y, Z)) = meet(Y, meet(X, Z)).
% 3.53/0.89 Proof:
% 3.53/0.89 meet(X, meet(Y, Z))
% 3.53/0.89 = { by axiom 3 (commutativity_of_meet) R->L }
% 3.53/0.89 meet(meet(Y, Z), X)
% 3.53/0.89 = { by axiom 7 (associativity_of_meet) }
% 3.53/0.89 meet(Y, meet(Z, X))
% 3.53/0.89 = { by axiom 3 (commutativity_of_meet) }
% 3.53/0.89 meet(Y, meet(X, Z))
% 3.53/0.89
% 3.53/0.89 Lemma 12: meet(X, join(Y, X)) = X.
% 3.53/0.89 Proof:
% 3.53/0.89 meet(X, join(Y, X))
% 3.53/0.89 = { by axiom 1 (commutativity_of_join) R->L }
% 3.53/0.89 meet(X, join(X, Y))
% 3.53/0.89 = { by axiom 6 (absorption1) }
% 3.53/0.89 X
% 3.53/0.89
% 3.53/0.89 Lemma 13: join(X, meet(Y, X)) = X.
% 3.53/0.89 Proof:
% 3.53/0.89 join(X, meet(Y, X))
% 3.53/0.89 = { by axiom 3 (commutativity_of_meet) R->L }
% 3.53/0.89 join(X, meet(X, Y))
% 3.53/0.89 = { by axiom 4 (absorption2) }
% 3.53/0.89 X
% 3.53/0.89
% 3.53/0.89 Lemma 14: meet(X, meet(Y, join(X, Z))) = meet(X, Y).
% 3.53/0.89 Proof:
% 3.53/0.89 meet(X, meet(Y, join(X, Z)))
% 3.53/0.89 = { by axiom 3 (commutativity_of_meet) R->L }
% 3.53/0.89 meet(X, meet(join(X, Z), Y))
% 3.53/0.89 = { by axiom 7 (associativity_of_meet) R->L }
% 3.53/0.89 meet(meet(X, join(X, Z)), Y)
% 3.53/0.89 = { by axiom 6 (absorption1) }
% 3.53/0.89 meet(X, Y)
% 3.53/0.89
% 3.53/0.89 Lemma 15: join(meet(X, Y), meet(X, join(Z, meet(X, Y)))) = meet(X, join(Z, meet(X, Y))).
% 3.53/0.89 Proof:
% 3.53/0.89 join(meet(X, Y), meet(X, join(Z, meet(X, Y))))
% 3.53/0.89 = { by axiom 3 (commutativity_of_meet) R->L }
% 3.53/0.89 join(meet(Y, X), meet(X, join(Z, meet(X, Y))))
% 3.53/0.89 = { by axiom 3 (commutativity_of_meet) R->L }
% 3.53/0.89 join(meet(Y, X), meet(X, join(Z, meet(Y, X))))
% 3.53/0.89 = { by axiom 1 (commutativity_of_join) R->L }
% 3.53/0.89 join(meet(X, join(Z, meet(Y, X))), meet(Y, X))
% 3.53/0.89 = { by axiom 6 (absorption1) R->L }
% 3.53/0.89 join(meet(X, join(Z, meet(Y, X))), meet(meet(Y, X), join(meet(Y, X), Z)))
% 3.53/0.89 = { by axiom 7 (associativity_of_meet) }
% 3.53/0.89 join(meet(X, join(Z, meet(Y, X))), meet(Y, meet(X, join(meet(Y, X), Z))))
% 3.53/0.89 = { by axiom 1 (commutativity_of_join) }
% 3.53/0.89 join(meet(X, join(Z, meet(Y, X))), meet(Y, meet(X, join(Z, meet(Y, X)))))
% 3.53/0.89 = { by lemma 13 }
% 3.53/0.89 meet(X, join(Z, meet(Y, X)))
% 3.53/0.89 = { by axiom 3 (commutativity_of_meet) }
% 3.53/0.89 meet(X, join(Z, meet(X, Y)))
% 3.53/0.89
% 3.53/0.89 Lemma 16: join(X, meet(Y, meet(X, Z))) = X.
% 3.53/0.89 Proof:
% 3.53/0.89 join(X, meet(Y, meet(X, Z)))
% 3.53/0.89 = { by axiom 3 (commutativity_of_meet) R->L }
% 3.53/0.89 join(X, meet(Y, meet(Z, X)))
% 3.53/0.89 = { by axiom 7 (associativity_of_meet) R->L }
% 3.53/0.89 join(X, meet(meet(Y, Z), X))
% 3.53/0.89 = { by lemma 13 }
% 3.53/0.89 X
% 3.53/0.89
% 3.53/0.89 Lemma 17: join(meet(X, join(Y, Z)), meet(Z, join(X, meet(Y, Z)))) = meet(join(X, meet(Y, Z)), join(Z, meet(X, Y))).
% 3.53/0.89 Proof:
% 3.53/0.89 join(meet(X, join(Y, Z)), meet(Z, join(X, meet(Y, Z))))
% 3.53/0.89 = { by axiom 1 (commutativity_of_join) R->L }
% 3.53/0.89 join(meet(Z, join(X, meet(Y, Z))), meet(X, join(Y, Z)))
% 3.53/0.89 = { by axiom 8 (nr_3) R->L }
% 3.53/0.89 meet(join(X, meet(Y, Z)), join(Z, meet(X, Y)))
% 3.53/0.89
% 3.53/0.89 Lemma 18: meet(join(X, Y), join(Y, meet(X, Z))) = join(Y, meet(X, Z)).
% 3.53/0.89 Proof:
% 3.53/0.89 meet(join(X, Y), join(Y, meet(X, Z)))
% 3.53/0.89 = { by axiom 3 (commutativity_of_meet) R->L }
% 3.53/0.89 meet(join(Y, meet(X, Z)), join(X, Y))
% 3.53/0.89 = { by axiom 4 (absorption2) R->L }
% 3.53/0.89 meet(join(Y, meet(X, Z)), join(join(X, meet(X, Z)), Y))
% 3.53/0.89 = { by axiom 5 (associativity_of_join) }
% 3.53/0.89 meet(join(Y, meet(X, Z)), join(X, join(meet(X, Z), Y)))
% 3.53/0.89 = { by axiom 1 (commutativity_of_join) }
% 3.53/0.89 meet(join(Y, meet(X, Z)), join(X, join(Y, meet(X, Z))))
% 3.53/0.89 = { by lemma 12 }
% 3.53/0.89 join(Y, meet(X, Z))
% 3.53/0.89
% 3.53/0.89 Lemma 19: meet(X, join(Y, meet(X, Z))) = join(meet(X, Y), meet(X, Z)).
% 3.53/0.89 Proof:
% 3.53/0.89 meet(X, join(Y, meet(X, Z)))
% 3.53/0.89 = { by lemma 15 R->L }
% 3.53/0.89 join(meet(X, Z), meet(X, join(Y, meet(X, Z))))
% 3.53/0.89 = { by axiom 1 (commutativity_of_join) R->L }
% 3.53/0.89 join(meet(X, join(Y, meet(X, Z))), meet(X, Z))
% 3.53/0.89 = { by lemma 10 R->L }
% 3.53/0.89 join(meet(X, join(Y, meet(X, Z))), meet(X, meet(X, Z)))
% 3.53/0.89 = { by axiom 3 (commutativity_of_meet) }
% 3.53/0.89 join(meet(X, join(Y, meet(X, Z))), meet(X, meet(Z, X)))
% 3.53/0.89 = { by axiom 7 (associativity_of_meet) R->L }
% 3.53/0.89 join(meet(X, join(Y, meet(X, Z))), meet(meet(X, Z), X))
% 3.53/0.89 = { by lemma 16 R->L }
% 3.53/0.89 join(meet(X, join(Y, meet(X, Z))), meet(meet(X, Z), join(X, meet(Y, meet(X, Z)))))
% 3.53/0.89 = { by lemma 17 }
% 3.53/0.89 meet(join(X, meet(Y, meet(X, Z))), join(meet(X, Z), meet(X, Y)))
% 3.53/0.89 = { by lemma 16 }
% 3.53/0.89 meet(X, join(meet(X, Z), meet(X, Y)))
% 3.53/0.89 = { by axiom 4 (absorption2) R->L }
% 3.53/0.89 meet(join(X, meet(X, Z)), join(meet(X, Z), meet(X, Y)))
% 3.53/0.89 = { by lemma 18 }
% 3.53/0.89 join(meet(X, Z), meet(X, Y))
% 3.53/0.89 = { by axiom 1 (commutativity_of_join) }
% 3.53/0.89 join(meet(X, Y), meet(X, Z))
% 3.53/0.89
% 3.53/0.89 Lemma 20: join(meet(X, Y), meet(X, Z)) = meet(X, join(Y, Z)).
% 3.53/0.89 Proof:
% 3.53/0.89 join(meet(X, Y), meet(X, Z))
% 3.53/0.89 = { by lemma 19 R->L }
% 3.53/0.89 meet(X, join(Y, meet(X, Z)))
% 3.53/0.89 = { by lemma 14 R->L }
% 3.53/0.89 meet(X, meet(join(Y, meet(X, Z)), join(X, meet(Z, Y))))
% 3.53/0.89 = { by axiom 3 (commutativity_of_meet) }
% 3.53/0.89 meet(X, meet(join(X, meet(Z, Y)), join(Y, meet(X, Z))))
% 3.53/0.89 = { by lemma 17 R->L }
% 3.53/0.89 meet(X, join(meet(X, join(Z, Y)), meet(Y, join(X, meet(Z, Y)))))
% 3.53/0.89 = { by axiom 1 (commutativity_of_join) R->L }
% 3.53/0.89 meet(X, join(meet(Y, join(X, meet(Z, Y))), meet(X, join(Z, Y))))
% 3.53/0.89 = { by lemma 19 }
% 3.53/0.89 join(meet(X, meet(Y, join(X, meet(Z, Y)))), meet(X, join(Z, Y)))
% 3.53/0.89 = { by lemma 14 }
% 3.53/0.89 join(meet(X, Y), meet(X, join(Z, Y)))
% 3.53/0.89 = { by axiom 3 (commutativity_of_meet) R->L }
% 3.53/0.89 join(meet(Y, X), meet(X, join(Z, Y)))
% 3.53/0.89 = { by axiom 1 (commutativity_of_join) R->L }
% 3.53/0.89 join(meet(X, join(Z, Y)), meet(Y, X))
% 3.53/0.89 = { by axiom 3 (commutativity_of_meet) R->L }
% 3.53/0.89 join(meet(X, join(Z, Y)), meet(X, Y))
% 3.53/0.89 = { by lemma 12 R->L }
% 3.53/0.89 join(meet(X, join(Z, Y)), meet(X, meet(Y, join(Z, Y))))
% 3.53/0.89 = { by lemma 11 }
% 3.53/0.89 join(meet(X, join(Z, Y)), meet(Y, meet(X, join(Z, Y))))
% 3.53/0.89 = { by lemma 13 }
% 3.53/0.89 meet(X, join(Z, Y))
% 3.53/0.89 = { by axiom 1 (commutativity_of_join) }
% 3.53/0.89 meet(X, join(Y, Z))
% 3.53/0.89
% 3.53/0.89 Goal 1 (prove_this): meet(a, meet(join(b, c), join(b, d))) = meet(meet(a, meet(join(b, c), join(b, d))), join(meet(a, join(b, meet(c, d))), join(meet(a, c), meet(a, d)))).
% 3.53/0.89 Proof:
% 3.53/0.89 meet(a, meet(join(b, c), join(b, d)))
% 3.53/0.89 = { by axiom 1 (commutativity_of_join) }
% 3.53/0.89 meet(a, meet(join(c, b), join(b, d)))
% 3.53/0.89 = { by axiom 1 (commutativity_of_join) }
% 3.53/0.89 meet(a, meet(join(c, b), join(d, b)))
% 3.53/0.89 = { by lemma 10 R->L }
% 3.53/0.89 meet(a, meet(a, meet(join(c, b), join(d, b))))
% 3.53/0.89 = { by lemma 11 R->L }
% 3.53/0.89 meet(a, meet(join(c, b), meet(a, join(d, b))))
% 3.53/0.89 = { by axiom 3 (commutativity_of_meet) R->L }
% 3.53/0.89 meet(a, meet(join(c, b), meet(join(d, b), a)))
% 3.53/0.89 = { by axiom 4 (absorption2) R->L }
% 3.53/0.89 meet(a, meet(join(c, b), meet(join(d, b), join(a, meet(a, join(join(d, b), c))))))
% 3.53/0.89 = { by axiom 9 (n5_1) }
% 3.53/0.89 meet(a, meet(join(c, b), join(meet(join(d, b), join(a, meet(join(d, b), a))), meet(join(d, b), join(meet(join(d, b), a), meet(a, c))))))
% 3.53/0.89 = { by lemma 13 }
% 3.53/0.89 meet(a, meet(join(c, b), join(meet(join(d, b), a), meet(join(d, b), join(meet(join(d, b), a), meet(a, c))))))
% 3.53/0.89 = { by axiom 1 (commutativity_of_join) R->L }
% 3.53/0.89 meet(a, meet(join(c, b), join(meet(join(d, b), a), meet(join(d, b), join(meet(a, c), meet(join(d, b), a))))))
% 3.53/0.89 = { by lemma 15 }
% 3.53/0.89 meet(a, meet(join(c, b), meet(join(d, b), join(meet(a, c), meet(join(d, b), a)))))
% 3.53/0.89 = { by axiom 3 (commutativity_of_meet) }
% 3.53/0.89 meet(a, meet(join(c, b), meet(join(d, b), join(meet(c, a), meet(join(d, b), a)))))
% 3.53/0.89 = { by axiom 3 (commutativity_of_meet) }
% 3.53/0.89 meet(a, meet(join(c, b), meet(join(d, b), join(meet(c, a), meet(a, join(d, b))))))
% 3.53/0.89 = { by axiom 1 (commutativity_of_join) R->L }
% 3.53/0.89 meet(a, meet(join(c, b), meet(join(d, b), join(meet(c, a), meet(a, join(b, d))))))
% 3.53/0.89 = { by lemma 13 R->L }
% 3.53/0.89 meet(a, meet(join(c, b), meet(join(d, b), join(meet(c, a), meet(a, join(b, join(d, meet(c, d))))))))
% 3.53/0.89 = { by axiom 1 (commutativity_of_join) R->L }
% 3.53/0.89 meet(a, meet(join(c, b), meet(join(d, b), join(meet(c, a), meet(a, join(join(d, meet(c, d)), b))))))
% 3.53/0.89 = { by axiom 5 (associativity_of_join) }
% 3.53/0.89 meet(a, meet(join(c, b), meet(join(d, b), join(meet(c, a), meet(a, join(d, join(meet(c, d), b)))))))
% 3.53/0.89 = { by axiom 1 (commutativity_of_join) }
% 3.53/0.89 meet(a, meet(join(c, b), meet(join(d, b), join(meet(c, a), meet(a, join(d, join(b, meet(c, d))))))))
% 3.53/0.90 = { by lemma 20 R->L }
% 3.53/0.90 meet(a, meet(join(c, b), meet(join(d, b), join(meet(c, a), join(meet(a, d), meet(a, join(b, meet(c, d))))))))
% 3.53/0.90 = { by lemma 19 R->L }
% 3.53/0.90 meet(a, meet(join(c, b), meet(join(d, b), join(meet(c, a), meet(a, join(d, meet(a, join(b, meet(c, d)))))))))
% 3.53/0.90 = { by axiom 3 (commutativity_of_meet) }
% 3.53/0.90 meet(a, meet(join(c, b), meet(join(d, b), join(meet(c, a), meet(a, join(d, meet(join(b, meet(c, d)), a)))))))
% 3.53/0.90 = { by axiom 1 (commutativity_of_join) R->L }
% 3.53/0.90 meet(a, meet(join(c, b), meet(join(d, b), join(meet(c, a), meet(a, join(meet(join(b, meet(c, d)), a), d))))))
% 3.53/0.90 = { by lemma 20 R->L }
% 3.53/0.90 meet(a, meet(join(c, b), meet(join(d, b), join(meet(c, a), join(meet(a, meet(join(b, meet(c, d)), a)), meet(a, d))))))
% 3.53/0.90 = { by lemma 19 R->L }
% 3.53/0.90 meet(a, meet(join(c, b), meet(join(d, b), join(meet(c, a), meet(a, join(meet(join(b, meet(c, d)), a), meet(a, d)))))))
% 3.53/0.90 = { by axiom 3 (commutativity_of_meet) R->L }
% 3.53/0.90 meet(a, meet(join(c, b), meet(join(d, b), join(meet(c, a), meet(a, join(meet(join(b, meet(c, d)), a), meet(d, a)))))))
% 3.53/0.90 = { by axiom 3 (commutativity_of_meet) R->L }
% 3.53/0.90 meet(a, meet(join(c, b), meet(join(d, b), join(meet(c, a), meet(a, join(meet(a, join(b, meet(c, d))), meet(d, a)))))))
% 3.53/0.90 = { by axiom 1 (commutativity_of_join) R->L }
% 3.53/0.90 meet(a, meet(join(c, b), meet(join(d, b), join(meet(c, a), meet(a, join(meet(d, a), meet(a, join(b, meet(c, d)))))))))
% 3.53/0.90 = { by lemma 13 R->L }
% 3.53/0.90 meet(a, meet(join(c, b), meet(join(d, b), join(meet(c, a), meet(join(a, meet(d, a)), join(meet(d, a), meet(a, join(b, meet(c, d)))))))))
% 3.53/0.90 = { by lemma 18 }
% 3.53/0.90 meet(a, meet(join(c, b), meet(join(d, b), join(meet(c, a), join(meet(d, a), meet(a, join(b, meet(c, d))))))))
% 3.53/0.90 = { by axiom 7 (associativity_of_meet) R->L }
% 3.53/0.90 meet(a, meet(meet(join(c, b), join(d, b)), join(meet(c, a), join(meet(d, a), meet(a, join(b, meet(c, d)))))))
% 3.53/0.90 = { by axiom 7 (associativity_of_meet) R->L }
% 3.53/0.90 meet(meet(a, meet(join(c, b), join(d, b))), join(meet(c, a), join(meet(d, a), meet(a, join(b, meet(c, d))))))
% 3.53/0.90 = { by axiom 5 (associativity_of_join) R->L }
% 3.53/0.90 meet(meet(a, meet(join(c, b), join(d, b))), join(join(meet(c, a), meet(d, a)), meet(a, join(b, meet(c, d)))))
% 3.53/0.90 = { by axiom 3 (commutativity_of_meet) R->L }
% 3.53/0.90 meet(meet(a, meet(join(c, b), join(d, b))), join(join(meet(c, a), meet(a, d)), meet(a, join(b, meet(c, d)))))
% 3.53/0.90 = { by axiom 3 (commutativity_of_meet) R->L }
% 3.53/0.90 meet(meet(a, meet(join(c, b), join(d, b))), join(join(meet(a, c), meet(a, d)), meet(a, join(b, meet(c, d)))))
% 3.53/0.90 = { by axiom 1 (commutativity_of_join) R->L }
% 3.53/0.90 meet(meet(a, meet(join(c, b), join(d, b))), join(meet(a, join(b, meet(c, d))), join(meet(a, c), meet(a, d))))
% 3.53/0.90 = { by axiom 1 (commutativity_of_join) R->L }
% 3.53/0.90 meet(meet(a, meet(join(c, b), join(b, d))), join(meet(a, join(b, meet(c, d))), join(meet(a, c), meet(a, d))))
% 3.53/0.90 = { by axiom 1 (commutativity_of_join) R->L }
% 3.53/0.90 meet(meet(a, meet(join(b, c), join(b, d))), join(meet(a, join(b, meet(c, d))), join(meet(a, c), meet(a, d))))
% 3.53/0.90 % SZS output end Proof
% 3.53/0.90
% 3.53/0.90 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------