TSTP Solution File: LAT026-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT026-1 : 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 : n014.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 06:27:10 EDT 2023
% Result : Unsatisfiable 0.18s 0.39s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : LAT026-1 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.11 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.11/0.32 % Computer : n014.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Aug 24 07:10:48 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.18/0.39 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.18/0.39
% 0.18/0.39 % SZS status Unsatisfiable
% 0.18/0.39
% 0.18/0.41 % SZS output start Proof
% 0.18/0.41 Axiom 1 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 0.18/0.41 Axiom 2 (idempotence_of_join): join(X, X) = X.
% 0.18/0.41 Axiom 3 (commutativity_of_join): join(X, Y) = join(Y, X).
% 0.18/0.41 Axiom 4 (absorbtion): meet(X, join(Y, join(X, Z))) = X.
% 0.18/0.41 Axiom 5 (wal_1): meet(meet(join(X, Y), join(Z, Y)), Y) = Y.
% 0.18/0.41 Axiom 6 (wal_2): join(join(meet(X, Y), meet(Z, Y)), Y) = Y.
% 0.18/0.41
% 0.18/0.41 Lemma 7: join(X, meet(X, Y)) = X.
% 0.18/0.41 Proof:
% 0.18/0.41 join(X, meet(X, Y))
% 0.18/0.41 = { by axiom 1 (commutativity_of_meet) R->L }
% 0.18/0.41 join(X, meet(Y, X))
% 0.18/0.41 = { by axiom 2 (idempotence_of_join) R->L }
% 0.18/0.41 join(X, join(meet(Y, X), meet(Y, X)))
% 0.18/0.41 = { by axiom 3 (commutativity_of_join) R->L }
% 0.18/0.41 join(join(meet(Y, X), meet(Y, X)), X)
% 0.18/0.41 = { by axiom 6 (wal_2) }
% 0.18/0.41 X
% 0.18/0.41
% 0.18/0.41 Lemma 8: join(X, meet(Y, X)) = X.
% 0.18/0.41 Proof:
% 0.18/0.41 join(X, meet(Y, X))
% 0.18/0.41 = { by axiom 1 (commutativity_of_meet) R->L }
% 0.18/0.41 join(X, meet(X, Y))
% 0.18/0.41 = { by lemma 7 }
% 0.18/0.41 X
% 0.18/0.41
% 0.18/0.41 Lemma 9: meet(meet(X, Y), join(Z, X)) = meet(X, Y).
% 0.18/0.41 Proof:
% 0.18/0.41 meet(meet(X, Y), join(Z, X))
% 0.18/0.41 = { by lemma 8 R->L }
% 0.18/0.41 meet(meet(X, Y), join(Z, join(X, meet(Y, X))))
% 0.18/0.41 = { by axiom 1 (commutativity_of_meet) R->L }
% 0.18/0.41 meet(meet(X, Y), join(Z, join(X, meet(X, Y))))
% 0.18/0.41 = { by axiom 3 (commutativity_of_join) }
% 0.18/0.41 meet(meet(X, Y), join(Z, join(meet(X, Y), X)))
% 0.18/0.41 = { by axiom 4 (absorbtion) }
% 0.18/0.41 meet(X, Y)
% 0.18/0.41
% 0.18/0.41 Lemma 10: meet(meet(X, Y), join(Z, Y)) = meet(X, Y).
% 0.18/0.41 Proof:
% 0.18/0.41 meet(meet(X, Y), join(Z, Y))
% 0.18/0.41 = { by lemma 8 R->L }
% 0.18/0.41 meet(meet(X, Y), join(Z, join(Y, meet(X, Y))))
% 0.18/0.41 = { by axiom 3 (commutativity_of_join) }
% 0.18/0.41 meet(meet(X, Y), join(Z, join(meet(X, Y), Y)))
% 0.18/0.41 = { by axiom 4 (absorbtion) }
% 0.18/0.41 meet(X, Y)
% 0.18/0.41
% 0.18/0.41 Lemma 11: meet(X, meet(join(Y, X), join(Z, X))) = X.
% 0.18/0.41 Proof:
% 0.18/0.41 meet(X, meet(join(Y, X), join(Z, X)))
% 0.18/0.41 = { by axiom 1 (commutativity_of_meet) R->L }
% 0.18/0.41 meet(meet(join(Y, X), join(Z, X)), X)
% 0.18/0.41 = { by axiom 5 (wal_1) }
% 0.18/0.41 X
% 0.18/0.41
% 0.18/0.41 Goal 1 (prove_associativity_of_meet): meet(meet(a, b), c) = meet(a, meet(b, c)).
% 0.18/0.41 Proof:
% 0.18/0.41 meet(meet(a, b), c)
% 0.18/0.41 = { by lemma 11 R->L }
% 0.18/0.41 meet(meet(meet(a, b), c), meet(join(a, meet(meet(a, b), c)), join(meet(b, c), meet(meet(a, b), c))))
% 0.18/0.42 = { by lemma 9 R->L }
% 0.18/0.42 meet(meet(meet(a, b), c), meet(join(a, meet(meet(meet(a, b), c), join(a, meet(a, b)))), join(meet(b, c), meet(meet(a, b), c))))
% 0.18/0.42 = { by lemma 7 }
% 0.18/0.42 meet(meet(meet(a, b), c), meet(join(a, meet(meet(meet(a, b), c), a)), join(meet(b, c), meet(meet(a, b), c))))
% 0.18/0.42 = { by axiom 1 (commutativity_of_meet) }
% 0.18/0.42 meet(meet(meet(a, b), c), meet(join(a, meet(a, meet(meet(a, b), c))), join(meet(b, c), meet(meet(a, b), c))))
% 0.18/0.42 = { by lemma 7 }
% 0.18/0.42 meet(meet(meet(a, b), c), meet(a, join(meet(b, c), meet(meet(a, b), c))))
% 0.18/0.42 = { by lemma 11 R->L }
% 0.18/0.42 meet(meet(meet(a, b), c), meet(a, join(meet(b, c), meet(meet(meet(a, b), c), meet(join(c, meet(meet(a, b), c)), join(b, meet(meet(a, b), c)))))))
% 0.18/0.42 = { by lemma 8 }
% 0.18/0.42 meet(meet(meet(a, b), c), meet(a, join(meet(b, c), meet(meet(meet(a, b), c), meet(c, join(b, meet(meet(a, b), c)))))))
% 0.18/0.42 = { by lemma 9 R->L }
% 0.18/0.42 meet(meet(meet(a, b), c), meet(a, join(meet(b, c), meet(meet(meet(a, b), c), meet(c, join(b, meet(meet(meet(a, b), c), join(b, meet(a, b)))))))))
% 0.18/0.42 = { by lemma 8 }
% 0.18/0.42 meet(meet(meet(a, b), c), meet(a, join(meet(b, c), meet(meet(meet(a, b), c), meet(c, join(b, meet(meet(meet(a, b), c), b)))))))
% 0.18/0.42 = { by axiom 1 (commutativity_of_meet) }
% 0.18/0.42 meet(meet(meet(a, b), c), meet(a, join(meet(b, c), meet(meet(meet(a, b), c), meet(c, join(b, meet(b, meet(meet(a, b), c))))))))
% 0.18/0.42 = { by lemma 7 }
% 0.18/0.42 meet(meet(meet(a, b), c), meet(a, join(meet(b, c), meet(meet(meet(a, b), c), meet(c, b)))))
% 0.18/0.42 = { by axiom 1 (commutativity_of_meet) }
% 0.18/0.42 meet(meet(meet(a, b), c), meet(a, join(meet(b, c), meet(meet(meet(a, b), c), meet(b, c)))))
% 0.18/0.42 = { by lemma 8 }
% 0.18/0.42 meet(meet(meet(a, b), c), meet(a, meet(b, c)))
% 0.18/0.42 = { by axiom 1 (commutativity_of_meet) R->L }
% 0.18/0.42 meet(meet(a, meet(b, c)), meet(meet(a, b), c))
% 0.18/0.42 = { by axiom 1 (commutativity_of_meet) }
% 0.18/0.42 meet(meet(a, meet(b, c)), meet(c, meet(a, b)))
% 0.18/0.42 = { by lemma 8 R->L }
% 0.18/0.42 meet(meet(a, meet(b, c)), meet(c, join(meet(a, b), meet(meet(a, meet(b, c)), meet(a, b)))))
% 0.18/0.42 = { by lemma 7 R->L }
% 0.18/0.42 meet(meet(a, meet(b, c)), meet(c, join(meet(a, b), meet(meet(a, meet(b, c)), meet(a, join(b, meet(b, meet(a, meet(b, c)))))))))
% 0.18/0.42 = { by axiom 1 (commutativity_of_meet) R->L }
% 0.18/0.42 meet(meet(a, meet(b, c)), meet(c, join(meet(a, b), meet(meet(a, meet(b, c)), meet(a, join(b, meet(meet(a, meet(b, c)), b)))))))
% 0.18/0.42 = { by lemma 7 R->L }
% 0.18/0.42 meet(meet(a, meet(b, c)), meet(c, join(meet(a, b), meet(meet(a, meet(b, c)), meet(a, join(b, meet(meet(a, meet(b, c)), join(b, meet(b, c)))))))))
% 0.18/0.42 = { by lemma 10 }
% 0.18/0.42 meet(meet(a, meet(b, c)), meet(c, join(meet(a, b), meet(meet(a, meet(b, c)), meet(a, join(b, meet(a, meet(b, c))))))))
% 0.18/0.42 = { by lemma 7 R->L }
% 0.18/0.42 meet(meet(a, meet(b, c)), meet(c, join(meet(a, b), meet(meet(a, meet(b, c)), meet(join(a, meet(a, meet(b, c))), join(b, meet(a, meet(b, c))))))))
% 0.18/0.42 = { by lemma 11 }
% 0.18/0.42 meet(meet(a, meet(b, c)), meet(c, join(meet(a, b), meet(a, meet(b, c)))))
% 0.18/0.42 = { by lemma 7 R->L }
% 0.18/0.42 meet(meet(a, meet(b, c)), meet(join(c, meet(c, meet(a, meet(b, c)))), join(meet(a, b), meet(a, meet(b, c)))))
% 0.18/0.42 = { by axiom 1 (commutativity_of_meet) R->L }
% 0.18/0.42 meet(meet(a, meet(b, c)), meet(join(c, meet(meet(a, meet(b, c)), c)), join(meet(a, b), meet(a, meet(b, c)))))
% 0.18/0.42 = { by lemma 8 R->L }
% 0.18/0.42 meet(meet(a, meet(b, c)), meet(join(c, meet(meet(a, meet(b, c)), join(c, meet(b, c)))), join(meet(a, b), meet(a, meet(b, c)))))
% 0.18/0.42 = { by lemma 10 }
% 0.18/0.42 meet(meet(a, meet(b, c)), meet(join(c, meet(a, meet(b, c))), join(meet(a, b), meet(a, meet(b, c)))))
% 0.18/0.42 = { by lemma 11 }
% 0.18/0.42 meet(a, meet(b, c))
% 0.18/0.42 % SZS output end Proof
% 0.18/0.42
% 0.18/0.42 RESULT: Unsatisfiable (the axioms are contradictory).
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