TSTP Solution File: LAT177-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT177-1 : 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 : n008.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 06:27:39 EDT 2023
% Result : Unsatisfiable 93.70s 12.53s
% Output : Proof 94.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT177-1 : 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
% 0.13/0.35 % Computer : n008.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 06:39:32 EDT 2023
% 0.13/0.35 % CPUTime :
% 93.70/12.53 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 93.70/12.53
% 93.70/12.53 % SZS status Unsatisfiable
% 93.70/12.53
% 94.43/12.54 % SZS output start Proof
% 94.43/12.54 Axiom 1 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 94.43/12.54 Axiom 2 (idempotence_of_join): join(X, X) = X.
% 94.43/12.54 Axiom 3 (commutativity_of_join): join(X, Y) = join(Y, X).
% 94.43/12.54 Axiom 4 (absorption1): meet(X, join(X, Y)) = X.
% 94.43/12.54 Axiom 5 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 94.43/12.54 Axiom 6 (absorption2): join(X, meet(X, Y)) = X.
% 94.43/12.54 Axiom 7 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 94.43/12.54 Axiom 8 (equation_H79_dual): join(X, meet(Y, join(Z, meet(X, W)))) = join(X, meet(join(X, meet(Y, join(X, Z))), join(Z, W))).
% 94.43/12.54
% 94.43/12.54 Lemma 9: join(X, meet(Y, X)) = X.
% 94.43/12.54 Proof:
% 94.43/12.54 join(X, meet(Y, X))
% 94.43/12.54 = { by axiom 1 (commutativity_of_meet) R->L }
% 94.43/12.54 join(X, meet(X, Y))
% 94.43/12.54 = { by axiom 6 (absorption2) }
% 94.43/12.54 X
% 94.43/12.54
% 94.43/12.54 Lemma 10: join(Z, join(X, Y)) = join(X, join(Y, Z)).
% 94.43/12.54 Proof:
% 94.43/12.54 join(Z, join(X, Y))
% 94.43/12.54 = { by axiom 3 (commutativity_of_join) R->L }
% 94.43/12.54 join(join(X, Y), Z)
% 94.43/12.54 = { by axiom 7 (associativity_of_join) }
% 94.43/12.54 join(X, join(Y, Z))
% 94.43/12.54
% 94.43/12.54 Lemma 11: meet(X, meet(Y, join(X, Z))) = meet(X, Y).
% 94.43/12.54 Proof:
% 94.43/12.54 meet(X, meet(Y, join(X, Z)))
% 94.43/12.54 = { by axiom 1 (commutativity_of_meet) R->L }
% 94.43/12.54 meet(meet(Y, join(X, Z)), X)
% 94.43/12.54 = { by axiom 5 (associativity_of_meet) }
% 94.43/12.54 meet(Y, meet(join(X, Z), X))
% 94.43/12.54 = { by axiom 1 (commutativity_of_meet) }
% 94.43/12.54 meet(Y, meet(X, join(X, Z)))
% 94.43/12.54 = { by axiom 4 (absorption1) }
% 94.43/12.54 meet(Y, X)
% 94.43/12.54 = { by axiom 1 (commutativity_of_meet) }
% 94.43/12.54 meet(X, Y)
% 94.43/12.54
% 94.43/12.54 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)))).
% 94.43/12.54 Proof:
% 94.43/12.54 meet(a, join(b, meet(a, c)))
% 94.43/12.54 = { by axiom 4 (absorption1) R->L }
% 94.43/12.54 meet(meet(a, join(b, meet(a, c))), join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))))
% 94.43/12.54 = { by axiom 1 (commutativity_of_meet) R->L }
% 94.43/12.54 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, join(b, meet(a, c))))
% 94.43/12.54 = { by axiom 1 (commutativity_of_meet) R->L }
% 94.43/12.54 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, join(b, meet(c, a))))
% 94.43/12.54 = { by lemma 9 R->L }
% 94.43/12.54 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, join(b, meet(c, join(a, meet(b, a))))))
% 94.43/12.54 = { by axiom 8 (equation_H79_dual) }
% 94.43/12.54 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, join(b, meet(join(b, meet(c, join(b, a))), join(a, a)))))
% 94.43/12.54 = { by axiom 2 (idempotence_of_join) }
% 94.43/12.54 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, join(b, meet(join(b, meet(c, join(b, a))), a))))
% 94.43/12.54 = { by axiom 1 (commutativity_of_meet) }
% 94.43/12.54 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, join(b, meet(a, join(b, meet(c, join(b, a)))))))
% 94.43/12.54 = { by axiom 3 (commutativity_of_join) }
% 94.43/12.54 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, join(b, meet(a, join(b, meet(c, join(a, b)))))))
% 94.43/12.54 = { by axiom 3 (commutativity_of_join) R->L }
% 94.43/12.54 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, join(b, meet(a, join(meet(c, join(a, b)), b)))))
% 94.43/12.54 = { by axiom 4 (absorption1) R->L }
% 94.43/12.54 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, meet(join(b, meet(a, join(meet(c, join(a, b)), b))), join(join(b, meet(a, join(meet(c, join(a, b)), b))), meet(c, join(a, b))))))
% 94.43/12.54 = { by axiom 3 (commutativity_of_join) }
% 94.43/12.54 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, meet(join(b, meet(a, join(meet(c, join(a, b)), b))), join(meet(c, join(a, b)), join(b, meet(a, join(meet(c, join(a, b)), b)))))))
% 94.43/12.54 = { by axiom 1 (commutativity_of_meet) R->L }
% 94.43/12.54 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, meet(join(b, meet(a, join(meet(c, join(a, b)), b))), join(meet(c, join(a, b)), join(b, meet(join(meet(c, join(a, b)), b), a))))))
% 94.43/12.54 = { by axiom 7 (associativity_of_join) R->L }
% 94.43/12.54 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, meet(join(b, meet(a, join(meet(c, join(a, b)), b))), join(join(meet(c, join(a, b)), b), meet(join(meet(c, join(a, b)), b), a)))))
% 94.43/12.54 = { by axiom 6 (absorption2) }
% 94.43/12.54 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, meet(join(b, meet(a, join(meet(c, join(a, b)), b))), join(meet(c, join(a, b)), b))))
% 94.43/12.54 = { by axiom 1 (commutativity_of_meet) }
% 94.43/12.54 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, meet(join(meet(c, join(a, b)), b), join(b, meet(a, join(meet(c, join(a, b)), b))))))
% 94.43/12.54 = { by axiom 3 (commutativity_of_join) }
% 94.43/12.54 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, meet(join(meet(c, join(a, b)), b), join(b, meet(a, join(b, meet(c, join(a, b))))))))
% 94.43/12.54 = { by axiom 3 (commutativity_of_join) }
% 94.43/12.54 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, meet(join(b, meet(c, join(a, b))), join(b, meet(a, join(b, meet(c, join(a, b))))))))
% 94.43/12.54 = { by axiom 3 (commutativity_of_join) R->L }
% 94.43/12.54 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, meet(join(b, meet(c, join(a, b))), join(meet(a, join(b, meet(c, join(a, b)))), b))))
% 94.43/12.54 = { by axiom 5 (associativity_of_meet) R->L }
% 94.43/12.54 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(meet(a, join(b, meet(c, join(a, b)))), join(meet(a, join(b, meet(c, join(a, b)))), b)))
% 94.43/12.54 = { by axiom 4 (absorption1) }
% 94.43/12.54 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, join(b, meet(c, join(a, b)))))
% 94.43/12.54 = { by lemma 9 R->L }
% 94.43/12.54 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, join(b, join(meet(c, join(a, b)), meet(a, meet(c, join(a, b)))))))
% 94.43/12.54 = { by lemma 11 }
% 94.43/12.54 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, join(b, join(meet(c, join(a, b)), meet(a, c)))))
% 94.43/12.54 = { by axiom 3 (commutativity_of_join) }
% 94.43/12.54 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, join(b, join(meet(a, c), meet(c, join(a, b))))))
% 94.43/12.54 = { by lemma 10 R->L }
% 94.43/12.54 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, join(meet(c, join(a, b)), join(b, meet(a, c)))))
% 94.43/12.54 = { by axiom 3 (commutativity_of_join) R->L }
% 94.43/12.54 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, join(join(b, meet(a, c)), meet(c, join(a, b)))))
% 94.43/12.54 = { by lemma 9 R->L }
% 94.43/12.54 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, join(join(join(b, meet(a, c)), meet(a, join(b, meet(a, c)))), meet(c, join(a, b)))))
% 94.43/12.54 = { by axiom 3 (commutativity_of_join) }
% 94.43/12.54 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, join(join(meet(a, join(b, meet(a, c))), join(b, meet(a, c))), meet(c, join(a, b)))))
% 94.43/12.54 = { by axiom 7 (associativity_of_join) }
% 94.43/12.54 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, join(meet(a, join(b, meet(a, c))), join(join(b, meet(a, c)), meet(c, join(a, b))))))
% 94.43/12.54 = { by axiom 3 (commutativity_of_join) }
% 94.43/12.54 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, join(meet(a, join(b, meet(a, c))), join(meet(c, join(a, b)), join(b, meet(a, c))))))
% 94.43/12.54 = { by lemma 10 R->L }
% 94.43/12.54 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, join(join(b, meet(a, c)), join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))))))
% 94.43/12.54 = { by axiom 3 (commutativity_of_join) }
% 94.43/12.54 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), meet(a, join(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), join(b, meet(a, c)))))
% 94.43/12.54 = { by lemma 11 }
% 94.43/12.55 meet(join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))), a)
% 94.43/12.55 = { by axiom 1 (commutativity_of_meet) }
% 94.43/12.55 meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))))
% 94.43/12.55 % SZS output end Proof
% 94.43/12.55
% 94.43/12.55 RESULT: Unsatisfiable (the axioms are contradictory).
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