TSTP Solution File: LAT152-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT152-1 : 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 06:27:34 EDT 2023
% Result : Unsatisfiable 24.51s 3.61s
% Output : Proof 24.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT152-1 : 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 09:14:45 EDT 2023
% 0.13/0.34 % CPUTime :
% 24.51/3.61 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 24.51/3.61
% 24.51/3.61 % SZS status Unsatisfiable
% 24.51/3.61
% 24.51/3.62 % SZS output start Proof
% 24.51/3.62 Axiom 1 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 24.51/3.62 Axiom 2 (idempotence_of_join): join(X, X) = X.
% 24.51/3.62 Axiom 3 (commutativity_of_join): join(X, Y) = join(Y, X).
% 24.51/3.62 Axiom 4 (absorption1): meet(X, join(X, Y)) = X.
% 24.51/3.62 Axiom 5 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 24.51/3.62 Axiom 6 (absorption2): join(X, meet(X, Y)) = X.
% 24.51/3.62 Axiom 7 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 24.51/3.62 Axiom 8 (equation_H40): meet(X, join(Y, meet(Z, join(X, W)))) = meet(X, join(Y, meet(Z, join(W, meet(Z, join(X, Y)))))).
% 24.51/3.62
% 24.51/3.62 Lemma 9: meet(X, join(Y, X)) = X.
% 24.51/3.62 Proof:
% 24.51/3.62 meet(X, join(Y, X))
% 24.51/3.62 = { by axiom 3 (commutativity_of_join) R->L }
% 24.51/3.62 meet(X, join(X, Y))
% 24.51/3.62 = { by axiom 4 (absorption1) }
% 24.51/3.62 X
% 24.51/3.62
% 24.51/3.62 Lemma 10: meet(X, meet(X, Y)) = meet(X, Y).
% 24.51/3.62 Proof:
% 24.51/3.62 meet(X, meet(X, Y))
% 24.51/3.62 = { by axiom 1 (commutativity_of_meet) R->L }
% 24.51/3.62 meet(meet(X, Y), X)
% 24.51/3.62 = { by axiom 6 (absorption2) R->L }
% 24.51/3.62 meet(meet(X, Y), join(X, meet(X, Y)))
% 24.51/3.62 = { by lemma 9 }
% 24.51/3.62 meet(X, Y)
% 24.51/3.62
% 24.51/3.62 Lemma 11: join(X, meet(Y, X)) = X.
% 24.51/3.62 Proof:
% 24.51/3.62 join(X, meet(Y, X))
% 24.51/3.62 = { by axiom 1 (commutativity_of_meet) R->L }
% 24.51/3.62 join(X, meet(X, Y))
% 24.51/3.62 = { by axiom 6 (absorption2) }
% 24.51/3.62 X
% 24.51/3.62
% 24.51/3.62 Lemma 12: join(Z, join(X, Y)) = join(X, join(Y, Z)).
% 24.51/3.62 Proof:
% 24.51/3.62 join(Z, join(X, Y))
% 24.51/3.62 = { by axiom 3 (commutativity_of_join) R->L }
% 24.51/3.62 join(join(X, Y), Z)
% 24.51/3.62 = { by axiom 7 (associativity_of_join) }
% 24.51/3.62 join(X, join(Y, Z))
% 24.51/3.62
% 24.51/3.62 Lemma 13: join(meet(X, Y), Y) = Y.
% 24.51/3.62 Proof:
% 24.51/3.62 join(meet(X, Y), Y)
% 24.51/3.62 = { by axiom 3 (commutativity_of_join) R->L }
% 24.51/3.62 join(Y, meet(X, Y))
% 24.51/3.62 = { by lemma 11 }
% 24.51/3.62 Y
% 24.51/3.62
% 24.51/3.62 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)))).
% 24.51/3.62 Proof:
% 24.51/3.62 meet(a, join(b, meet(a, c)))
% 24.51/3.62 = { by lemma 10 R->L }
% 24.51/3.62 meet(a, meet(a, join(b, meet(a, c))))
% 24.51/3.62 = { by axiom 4 (absorption1) R->L }
% 24.51/3.62 meet(a, meet(meet(a, join(b, meet(a, c))), join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))))
% 24.51/3.62 = { by axiom 1 (commutativity_of_meet) R->L }
% 24.51/3.62 meet(a, meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, join(b, meet(a, c)))))
% 24.51/3.62 = { by axiom 5 (associativity_of_meet) R->L }
% 24.51/3.62 meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), meet(a, join(b, meet(a, c))))
% 24.51/3.62 = { by axiom 1 (commutativity_of_meet) R->L }
% 24.51/3.62 meet(meet(a, join(b, meet(a, c))), meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))))
% 24.51/3.62 = { by axiom 1 (commutativity_of_meet) R->L }
% 24.51/3.62 meet(meet(a, join(b, meet(c, a))), meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))))
% 24.51/3.62 = { by axiom 2 (idempotence_of_join) R->L }
% 24.51/3.62 meet(meet(a, join(b, meet(c, join(a, a)))), meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))))
% 24.51/3.62 = { by axiom 8 (equation_H40) }
% 24.51/3.62 meet(meet(a, join(b, meet(c, join(a, meet(c, join(a, b)))))), meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))))
% 24.51/3.62 = { by axiom 8 (equation_H40) }
% 24.51/3.62 meet(meet(a, join(b, meet(c, join(meet(c, join(a, b)), meet(c, join(a, b)))))), meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))))
% 24.51/3.62 = { by axiom 2 (idempotence_of_join) }
% 24.51/3.62 meet(meet(a, join(b, meet(c, meet(c, join(a, b))))), meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))))
% 24.51/3.62 = { by axiom 3 (commutativity_of_join) }
% 24.51/3.62 meet(meet(a, join(b, meet(c, meet(c, join(b, a))))), meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))))
% 24.51/3.62 = { by lemma 10 }
% 24.51/3.62 meet(meet(a, join(b, meet(c, join(b, a)))), meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))))
% 24.51/3.62 = { by axiom 3 (commutativity_of_join) }
% 24.51/3.62 meet(meet(a, join(b, meet(c, join(a, b)))), meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))))
% 24.51/3.62 = { by axiom 5 (associativity_of_meet) }
% 24.51/3.62 meet(a, meet(join(b, meet(c, join(a, b))), meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))))))
% 24.51/3.62 = { by axiom 1 (commutativity_of_meet) }
% 24.51/3.62 meet(a, meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(b, meet(c, join(a, b)))))
% 24.51/3.62 = { by lemma 11 R->L }
% 24.51/3.62 meet(a, meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(b, join(meet(c, join(a, b)), meet(a, meet(c, join(a, b)))))))
% 24.51/3.62 = { by axiom 1 (commutativity_of_meet) R->L }
% 24.51/3.62 meet(a, meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(b, join(meet(c, join(a, b)), meet(a, meet(join(a, b), c))))))
% 24.51/3.62 = { by axiom 5 (associativity_of_meet) R->L }
% 24.51/3.62 meet(a, meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(b, join(meet(c, join(a, b)), meet(meet(a, join(a, b)), c)))))
% 24.51/3.62 = { by axiom 4 (absorption1) }
% 24.51/3.62 meet(a, meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(b, join(meet(c, join(a, b)), meet(a, c)))))
% 24.51/3.62 = { by axiom 3 (commutativity_of_join) }
% 24.51/3.62 meet(a, meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(b, join(meet(a, c), meet(c, join(a, b))))))
% 24.51/3.62 = { by lemma 12 R->L }
% 24.51/3.62 meet(a, meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(meet(c, join(a, b)), join(b, meet(a, c)))))
% 24.51/3.62 = { by axiom 3 (commutativity_of_join) R->L }
% 24.51/3.62 meet(a, meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(join(b, meet(a, c)), meet(c, join(a, b)))))
% 24.51/3.62 = { by lemma 13 R->L }
% 24.51/3.62 meet(a, meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(join(meet(a, join(b, meet(a, c))), join(b, meet(a, c))), meet(c, join(a, b)))))
% 24.51/3.62 = { by axiom 7 (associativity_of_join) }
% 24.51/3.62 meet(a, meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(meet(a, join(b, meet(a, c))), join(join(b, meet(a, c)), meet(c, join(a, b))))))
% 24.51/3.62 = { by axiom 3 (commutativity_of_join) }
% 24.51/3.62 meet(a, meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(meet(a, join(b, meet(a, c))), join(meet(c, join(a, b)), join(b, meet(a, c))))))
% 24.51/3.62 = { by lemma 12 R->L }
% 24.51/3.62 meet(a, meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(join(b, meet(a, c)), join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))))))
% 24.51/3.62 = { by lemma 13 R->L }
% 24.51/3.63 meet(a, meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(join(b, meet(a, c)), join(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))))))
% 24.51/3.63 = { by axiom 3 (commutativity_of_join) R->L }
% 24.51/3.63 meet(a, meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(join(b, meet(a, c)), join(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))))))))
% 24.51/3.63 = { by axiom 7 (associativity_of_join) R->L }
% 24.51/3.63 meet(a, meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(join(join(b, meet(a, c)), join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))))))
% 24.51/3.63 = { by lemma 9 }
% 24.51/3.63 meet(a, meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))))
% 24.51/3.63 = { by lemma 10 }
% 24.51/3.63 meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))))
% 24.51/3.63 % SZS output end Proof
% 24.51/3.63
% 24.51/3.63 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------