TSTP Solution File: LAT154-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT154-1 : 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 : n020.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 12.44s 1.99s
% Output : Proof 12.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT154-1 : 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
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 05:21:45 EDT 2023
% 0.13/0.34 % CPUTime :
% 12.44/1.99 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 12.44/1.99
% 12.44/1.99 % SZS status Unsatisfiable
% 12.44/1.99
% 12.44/2.01 % SZS output start Proof
% 12.44/2.01 Axiom 1 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 12.44/2.01 Axiom 2 (idempotence_of_join): join(X, X) = X.
% 12.44/2.01 Axiom 3 (commutativity_of_join): join(X, Y) = join(Y, X).
% 12.44/2.01 Axiom 4 (absorption1): meet(X, join(X, Y)) = X.
% 12.44/2.01 Axiom 5 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 12.44/2.01 Axiom 6 (absorption2): join(X, meet(X, Y)) = X.
% 12.44/2.01 Axiom 7 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 12.44/2.01 Axiom 8 (equation_H42): meet(X, join(Y, meet(Z, join(X, W)))) = meet(X, join(Y, meet(Z, join(Y, join(W, meet(X, Z)))))).
% 12.44/2.01
% 12.44/2.01 Lemma 9: meet(X, join(Y, X)) = X.
% 12.44/2.01 Proof:
% 12.44/2.01 meet(X, join(Y, X))
% 12.44/2.01 = { by axiom 3 (commutativity_of_join) R->L }
% 12.44/2.01 meet(X, join(X, Y))
% 12.44/2.01 = { by axiom 4 (absorption1) }
% 12.44/2.01 X
% 12.44/2.01
% 12.44/2.01 Lemma 10: meet(Y, meet(X, Z)) = meet(X, meet(Y, Z)).
% 12.44/2.01 Proof:
% 12.44/2.01 meet(Y, meet(X, Z))
% 12.44/2.01 = { by axiom 1 (commutativity_of_meet) R->L }
% 12.44/2.01 meet(meet(X, Z), Y)
% 12.44/2.01 = { by axiom 5 (associativity_of_meet) }
% 12.44/2.01 meet(X, meet(Z, Y))
% 12.44/2.01 = { by axiom 1 (commutativity_of_meet) }
% 12.44/2.01 meet(X, meet(Y, Z))
% 12.44/2.01
% 12.44/2.01 Lemma 11: join(X, meet(Y, X)) = X.
% 12.44/2.01 Proof:
% 12.44/2.01 join(X, meet(Y, X))
% 12.44/2.01 = { by axiom 1 (commutativity_of_meet) R->L }
% 12.44/2.01 join(X, meet(X, Y))
% 12.44/2.01 = { by axiom 6 (absorption2) }
% 12.44/2.01 X
% 12.44/2.01
% 12.44/2.01 Lemma 12: join(Y, join(X, Z)) = join(X, join(Y, Z)).
% 12.44/2.01 Proof:
% 12.44/2.01 join(Y, join(X, Z))
% 12.44/2.01 = { by axiom 3 (commutativity_of_join) R->L }
% 12.44/2.01 join(join(X, Z), Y)
% 12.44/2.01 = { by axiom 7 (associativity_of_join) }
% 12.44/2.01 join(X, join(Z, Y))
% 12.44/2.01 = { by axiom 3 (commutativity_of_join) }
% 12.44/2.01 join(X, join(Y, Z))
% 12.44/2.01
% 12.44/2.01 Lemma 13: join(Z, join(X, Y)) = join(X, join(Y, Z)).
% 12.44/2.01 Proof:
% 12.44/2.01 join(Z, join(X, Y))
% 12.44/2.01 = { by lemma 12 }
% 12.44/2.01 join(X, join(Z, Y))
% 12.44/2.01 = { by axiom 3 (commutativity_of_join) }
% 12.44/2.01 join(X, join(Y, Z))
% 12.44/2.01
% 12.44/2.01 Lemma 14: join(meet(X, Y), Y) = Y.
% 12.44/2.01 Proof:
% 12.44/2.01 join(meet(X, Y), Y)
% 12.44/2.01 = { by axiom 3 (commutativity_of_join) R->L }
% 12.44/2.01 join(Y, meet(X, Y))
% 12.44/2.01 = { by lemma 11 }
% 12.44/2.01 Y
% 12.44/2.01
% 12.44/2.01 Lemma 15: join(X, meet(meet(X, Y), Z)) = X.
% 12.44/2.01 Proof:
% 12.44/2.01 join(X, meet(meet(X, Y), Z))
% 12.44/2.01 = { by axiom 1 (commutativity_of_meet) R->L }
% 12.44/2.01 join(X, meet(Z, meet(X, Y)))
% 12.44/2.01 = { by lemma 10 }
% 12.44/2.01 join(X, meet(X, meet(Z, Y)))
% 12.44/2.01 = { by axiom 6 (absorption2) }
% 12.44/2.01 X
% 12.44/2.01
% 12.44/2.01 Lemma 16: meet(meet(X, Y), join(Z, meet(W, join(X, Z)))) = meet(meet(X, Y), join(Z, meet(W, X))).
% 12.44/2.01 Proof:
% 12.44/2.01 meet(meet(X, Y), join(Z, meet(W, join(X, Z))))
% 12.44/2.01 = { by axiom 3 (commutativity_of_join) R->L }
% 12.44/2.01 meet(meet(X, Y), join(Z, meet(W, join(Z, X))))
% 12.44/2.01 = { by lemma 15 R->L }
% 12.44/2.01 meet(meet(X, Y), join(Z, meet(W, join(Z, join(X, meet(meet(X, Y), W))))))
% 12.44/2.01 = { by axiom 8 (equation_H42) R->L }
% 12.44/2.01 meet(meet(X, Y), join(Z, meet(W, join(meet(X, Y), X))))
% 12.44/2.01 = { by axiom 3 (commutativity_of_join) }
% 12.44/2.01 meet(meet(X, Y), join(Z, meet(W, join(X, meet(X, Y)))))
% 12.44/2.01 = { by axiom 6 (absorption2) }
% 12.44/2.01 meet(meet(X, Y), join(Z, meet(W, X)))
% 12.44/2.01
% 12.44/2.01 Lemma 17: meet(join(X, Y), join(Y, meet(Z, join(X, Y)))) = join(Y, meet(Z, join(X, Y))).
% 12.44/2.01 Proof:
% 12.44/2.01 meet(join(X, Y), join(Y, meet(Z, join(X, Y))))
% 12.44/2.01 = { by axiom 3 (commutativity_of_join) R->L }
% 12.44/2.01 meet(join(X, Y), join(meet(Z, join(X, Y)), Y))
% 12.44/2.01 = { by axiom 1 (commutativity_of_meet) R->L }
% 12.44/2.01 meet(join(meet(Z, join(X, Y)), Y), join(X, Y))
% 12.44/2.01 = { by lemma 14 R->L }
% 12.44/2.01 meet(join(meet(Z, join(X, Y)), Y), join(meet(Z, join(X, Y)), join(X, Y)))
% 12.44/2.01 = { by lemma 12 }
% 12.44/2.01 meet(join(meet(Z, join(X, Y)), Y), join(X, join(meet(Z, join(X, Y)), Y)))
% 12.44/2.01 = { by lemma 9 }
% 12.44/2.01 join(meet(Z, join(X, Y)), Y)
% 12.44/2.01 = { by axiom 3 (commutativity_of_join) }
% 12.44/2.01 join(Y, meet(Z, join(X, Y)))
% 12.44/2.01
% 12.44/2.01 Lemma 18: meet(meet(X, join(meet(X, Y), Z)), meet(X, Y)) = meet(X, Y).
% 12.44/2.01 Proof:
% 12.44/2.01 meet(meet(X, join(meet(X, Y), Z)), meet(X, Y))
% 12.44/2.01 = { by axiom 1 (commutativity_of_meet) R->L }
% 12.44/2.01 meet(meet(X, Y), meet(X, join(meet(X, Y), Z)))
% 12.44/2.01 = { by lemma 10 }
% 12.44/2.01 meet(X, meet(meet(X, Y), join(meet(X, Y), Z)))
% 12.44/2.01 = { by axiom 4 (absorption1) }
% 12.44/2.01 meet(X, meet(X, Y))
% 12.44/2.01 = { by axiom 1 (commutativity_of_meet) R->L }
% 12.44/2.01 meet(meet(X, Y), X)
% 12.44/2.01 = { by axiom 6 (absorption2) R->L }
% 12.44/2.01 meet(meet(X, Y), join(X, meet(X, Y)))
% 12.44/2.01 = { by lemma 9 }
% 12.44/2.01 meet(X, Y)
% 12.44/2.01
% 12.44/2.01 Lemma 19: join(meet(X, Y), meet(meet(X, join(meet(X, Y), Z)), Y)) = meet(meet(X, join(meet(X, Y), Z)), Y).
% 12.44/2.02 Proof:
% 12.44/2.02 join(meet(X, Y), meet(meet(X, join(meet(X, Y), Z)), Y))
% 12.44/2.02 = { by lemma 18 R->L }
% 12.44/2.02 join(meet(meet(X, join(meet(X, Y), Z)), meet(X, Y)), meet(meet(X, join(meet(X, Y), Z)), Y))
% 12.44/2.02 = { by axiom 3 (commutativity_of_join) R->L }
% 12.44/2.02 join(meet(meet(X, join(meet(X, Y), Z)), Y), meet(meet(X, join(meet(X, Y), Z)), meet(X, Y)))
% 12.44/2.02 = { by lemma 10 }
% 12.44/2.02 join(meet(meet(X, join(meet(X, Y), Z)), Y), meet(X, meet(meet(X, join(meet(X, Y), Z)), Y)))
% 12.44/2.02 = { by lemma 11 }
% 12.44/2.02 meet(meet(X, join(meet(X, Y), Z)), Y)
% 12.44/2.02
% 12.44/2.02 Lemma 20: join(X, join(meet(Y, join(X, meet(Y, Z))), meet(Z, join(Y, X)))) = join(X, meet(Z, join(Y, X))).
% 12.44/2.02 Proof:
% 12.44/2.02 join(X, join(meet(Y, join(X, meet(Y, Z))), meet(Z, join(Y, X))))
% 12.44/2.02 = { by lemma 12 }
% 12.44/2.02 join(meet(Y, join(X, meet(Y, Z))), join(X, meet(Z, join(Y, X))))
% 12.44/2.02 = { by lemma 17 R->L }
% 12.44/2.02 join(meet(Y, join(X, meet(Y, Z))), meet(join(Y, X), join(X, meet(Z, join(Y, X)))))
% 12.44/2.02 = { by axiom 1 (commutativity_of_meet) R->L }
% 12.44/2.02 join(meet(Y, join(X, meet(Z, Y))), meet(join(Y, X), join(X, meet(Z, join(Y, X)))))
% 12.44/2.02 = { by axiom 2 (idempotence_of_join) R->L }
% 12.44/2.02 join(meet(Y, join(X, meet(Z, join(Y, Y)))), meet(join(Y, X), join(X, meet(Z, join(Y, X)))))
% 12.44/2.02 = { by axiom 8 (equation_H42) }
% 12.44/2.02 join(meet(Y, join(X, meet(Z, join(X, join(Y, meet(Y, Z)))))), meet(join(Y, X), join(X, meet(Z, join(Y, X)))))
% 12.44/2.02 = { by axiom 6 (absorption2) }
% 12.44/2.02 join(meet(Y, join(X, meet(Z, join(X, Y)))), meet(join(Y, X), join(X, meet(Z, join(Y, X)))))
% 12.44/2.02 = { by axiom 3 (commutativity_of_join) }
% 12.44/2.02 join(meet(Y, join(X, meet(Z, join(Y, X)))), meet(join(Y, X), join(X, meet(Z, join(Y, X)))))
% 12.44/2.02 = { by axiom 1 (commutativity_of_meet) R->L }
% 12.44/2.02 join(meet(Y, join(X, meet(Z, join(Y, X)))), meet(join(X, meet(Z, join(Y, X))), join(Y, X)))
% 12.44/2.02 = { by axiom 1 (commutativity_of_meet) R->L }
% 12.44/2.02 join(meet(join(X, meet(Z, join(Y, X))), Y), meet(join(X, meet(Z, join(Y, X))), join(Y, X)))
% 12.44/2.02 = { by axiom 3 (commutativity_of_join) R->L }
% 12.44/2.02 join(meet(join(X, meet(Z, join(Y, X))), join(Y, X)), meet(join(X, meet(Z, join(Y, X))), Y))
% 12.44/2.02 = { by axiom 1 (commutativity_of_meet) R->L }
% 12.44/2.02 join(meet(join(X, meet(Z, join(Y, X))), join(Y, X)), meet(Y, join(X, meet(Z, join(Y, X)))))
% 12.44/2.02 = { by axiom 4 (absorption1) R->L }
% 12.44/2.02 join(meet(join(X, meet(Z, join(Y, X))), join(Y, X)), meet(meet(Y, join(Y, X)), join(X, meet(Z, join(Y, X)))))
% 12.44/2.02 = { by axiom 5 (associativity_of_meet) }
% 12.44/2.02 join(meet(join(X, meet(Z, join(Y, X))), join(Y, X)), meet(Y, meet(join(Y, X), join(X, meet(Z, join(Y, X))))))
% 12.44/2.02 = { by axiom 1 (commutativity_of_meet) }
% 12.44/2.02 join(meet(join(X, meet(Z, join(Y, X))), join(Y, X)), meet(Y, meet(join(X, meet(Z, join(Y, X))), join(Y, X))))
% 12.44/2.02 = { by lemma 11 }
% 12.44/2.02 meet(join(X, meet(Z, join(Y, X))), join(Y, X))
% 12.44/2.02 = { by axiom 1 (commutativity_of_meet) }
% 12.44/2.02 meet(join(Y, X), join(X, meet(Z, join(Y, X))))
% 12.44/2.02 = { by lemma 17 }
% 12.44/2.02 join(X, meet(Z, join(Y, X)))
% 12.44/2.02
% 12.44/2.02 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)))).
% 12.44/2.02 Proof:
% 12.44/2.02 meet(a, join(b, meet(a, c)))
% 12.44/2.02 = { by lemma 18 R->L }
% 12.44/2.02 meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), meet(a, join(b, meet(a, c))))
% 12.44/2.02 = { by lemma 10 }
% 12.44/2.02 meet(a, meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(b, meet(a, c))))
% 12.44/2.02 = { by lemma 15 R->L }
% 12.44/2.02 meet(join(a, meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(b, meet(a, c)))), meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(b, meet(a, c))))
% 12.44/2.02 = { by lemma 19 R->L }
% 12.44/2.02 meet(join(a, meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(b, meet(a, c)))), join(meet(a, join(b, meet(a, c))), meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(b, meet(a, c)))))
% 12.44/2.02 = { by axiom 3 (commutativity_of_join) R->L }
% 12.44/2.02 meet(join(a, meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(b, meet(a, c)))), join(meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(b, meet(a, c))), meet(a, join(b, meet(a, c)))))
% 12.44/2.02 = { by axiom 3 (commutativity_of_join) R->L }
% 12.44/2.02 meet(join(meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(b, meet(a, c))), a), join(meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(b, meet(a, c))), meet(a, join(b, meet(a, c)))))
% 12.44/2.02 = { by axiom 1 (commutativity_of_meet) R->L }
% 12.44/2.02 meet(join(meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(b, meet(a, c))), meet(a, join(b, meet(a, c)))), join(meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(b, meet(a, c))), a))
% 12.44/2.02 = { by axiom 3 (commutativity_of_join) R->L }
% 12.44/2.02 meet(join(meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(b, meet(a, c))), meet(a, join(b, meet(a, c)))), join(a, meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(b, meet(a, c)))))
% 12.44/2.02 = { by axiom 6 (absorption2) R->L }
% 12.44/2.02 meet(join(meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(b, meet(a, c))), meet(a, join(b, meet(a, c)))), join(join(a, meet(a, join(b, meet(a, c)))), meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(b, meet(a, c)))))
% 12.44/2.02 = { by axiom 7 (associativity_of_join) }
% 12.44/2.02 meet(join(meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(b, meet(a, c))), meet(a, join(b, meet(a, c)))), join(a, join(meet(a, join(b, meet(a, c))), meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(b, meet(a, c))))))
% 12.44/2.02 = { by axiom 3 (commutativity_of_join) }
% 12.44/2.02 meet(join(meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(b, meet(a, c))), meet(a, join(b, meet(a, c)))), join(a, join(meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(b, meet(a, c))), meet(a, join(b, meet(a, c))))))
% 12.44/2.02 = { by lemma 9 }
% 12.44/2.02 join(meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(b, meet(a, c))), meet(a, join(b, meet(a, c))))
% 12.44/2.02 = { by axiom 3 (commutativity_of_join) }
% 12.44/2.02 join(meet(a, join(b, meet(a, c))), meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(b, meet(a, c))))
% 12.44/2.02 = { by lemma 19 }
% 12.44/2.02 meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(b, meet(a, c)))
% 12.44/2.02 = { by axiom 1 (commutativity_of_meet) R->L }
% 12.44/2.02 meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(b, meet(c, a)))
% 12.44/2.02 = { by lemma 16 R->L }
% 12.44/2.02 meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(b, meet(c, join(a, b))))
% 12.44/2.02 = { by lemma 20 R->L }
% 12.44/2.02 meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(b, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))))
% 12.44/2.02 = { by axiom 4 (absorption1) R->L }
% 12.44/2.02 meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(b, meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), join(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), join(a, b)))))
% 12.44/2.02 = { by lemma 13 }
% 12.44/2.02 meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(b, meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), join(a, join(b, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))))))))
% 12.44/2.02 = { by lemma 20 }
% 12.44/2.02 meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(b, meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), join(a, join(b, meet(c, join(a, b)))))))
% 12.44/2.02 = { by lemma 13 R->L }
% 12.44/2.02 meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(b, meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), join(meet(c, join(a, b)), join(a, b)))))
% 12.44/2.02 = { by lemma 14 }
% 12.44/2.02 meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(b, meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), join(a, b))))
% 12.44/2.02 = { by lemma 16 }
% 12.44/2.02 meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(b, meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), a)))
% 12.44/2.02 = { by axiom 1 (commutativity_of_meet) }
% 12.44/2.02 meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(b, meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))))))
% 12.44/2.02 = { by lemma 9 }
% 12.44/2.02 meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))))
% 12.44/2.02 % SZS output end Proof
% 12.44/2.02
% 12.44/2.02 RESULT: Unsatisfiable (the axioms are contradictory).
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