TSTP Solution File: LAT164-1 by Twee---2.5.0
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%------------------------------------------------------------------------------
% File : Twee---2.5.0
% Problem : LAT164-1 : TPTP v8.2.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee /export/starexec/sandbox2/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% Computer : n001.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 : Mon Jun 24 10:31:33 EDT 2024
% Result : Unsatisfiable 17.82s 2.61s
% Output : Proof 17.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LAT164-1 : TPTP v8.2.0. Released v3.1.0.
% 0.07/0.12 % Command : parallel-twee /export/starexec/sandbox2/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 21 23:32:24 EDT 2024
% 0.12/0.33 % CPUTime :
% 17.82/2.61 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 17.82/2.61
% 17.82/2.61 % SZS status Unsatisfiable
% 17.82/2.61
% 17.82/2.62 % SZS output start Proof
% 17.82/2.62 Axiom 1 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 17.82/2.62 Axiom 2 (commutativity_of_join): join(X, Y) = join(Y, X).
% 17.82/2.62 Axiom 3 (absorption1): meet(X, join(X, Y)) = X.
% 17.82/2.62 Axiom 4 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 17.82/2.62 Axiom 5 (absorption2): join(X, meet(X, Y)) = X.
% 17.82/2.62 Axiom 6 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 17.82/2.62 Axiom 7 (equation_H76): meet(X, join(Y, meet(Z, join(Y, W)))) = meet(X, join(Y, meet(Z, join(W, meet(X, Y))))).
% 17.82/2.62
% 17.82/2.62 Lemma 8: meet(X, join(Y, X)) = X.
% 17.82/2.62 Proof:
% 17.82/2.62 meet(X, join(Y, X))
% 17.82/2.62 = { by axiom 2 (commutativity_of_join) R->L }
% 17.82/2.62 meet(X, join(X, Y))
% 17.82/2.62 = { by axiom 3 (absorption1) }
% 17.82/2.62 X
% 17.82/2.62
% 17.82/2.62 Lemma 9: meet(X, meet(X, Y)) = meet(X, Y).
% 17.82/2.62 Proof:
% 17.82/2.62 meet(X, meet(X, Y))
% 17.82/2.62 = { by axiom 1 (commutativity_of_meet) R->L }
% 17.82/2.62 meet(meet(X, Y), X)
% 17.82/2.62 = { by axiom 5 (absorption2) R->L }
% 17.82/2.62 meet(meet(X, Y), join(X, meet(X, Y)))
% 17.82/2.62 = { by lemma 8 }
% 17.82/2.62 meet(X, Y)
% 17.82/2.62
% 17.82/2.62 Lemma 10: meet(Y, meet(X, Z)) = meet(X, meet(Y, Z)).
% 17.82/2.62 Proof:
% 17.82/2.62 meet(Y, meet(X, Z))
% 17.82/2.62 = { by axiom 1 (commutativity_of_meet) R->L }
% 17.82/2.62 meet(meet(X, Z), Y)
% 17.82/2.62 = { by axiom 4 (associativity_of_meet) }
% 17.82/2.62 meet(X, meet(Z, Y))
% 17.82/2.62 = { by axiom 1 (commutativity_of_meet) }
% 17.82/2.62 meet(X, meet(Y, Z))
% 17.82/2.62
% 17.82/2.62 Lemma 11: join(X, meet(Y, X)) = X.
% 17.82/2.62 Proof:
% 17.82/2.62 join(X, meet(Y, X))
% 17.82/2.62 = { by axiom 1 (commutativity_of_meet) R->L }
% 17.82/2.62 join(X, meet(X, Y))
% 17.82/2.62 = { by axiom 5 (absorption2) }
% 17.82/2.62 X
% 17.82/2.62
% 17.82/2.62 Lemma 12: join(Z, join(X, Y)) = join(X, join(Y, Z)).
% 17.82/2.62 Proof:
% 17.82/2.62 join(Z, join(X, Y))
% 17.82/2.62 = { by axiom 2 (commutativity_of_join) R->L }
% 17.82/2.62 join(join(X, Y), Z)
% 17.82/2.62 = { by axiom 6 (associativity_of_join) }
% 17.82/2.62 join(X, join(Y, Z))
% 17.82/2.62
% 17.82/2.62 Lemma 13: join(meet(X, Y), Y) = Y.
% 17.82/2.62 Proof:
% 17.82/2.62 join(meet(X, Y), Y)
% 17.82/2.62 = { by axiom 2 (commutativity_of_join) R->L }
% 17.82/2.62 join(Y, meet(X, Y))
% 17.82/2.62 = { by lemma 11 }
% 17.82/2.62 Y
% 17.82/2.62
% 17.82/2.62 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)))).
% 17.82/2.62 Proof:
% 17.82/2.62 meet(a, join(b, meet(a, c)))
% 17.82/2.62 = { by lemma 9 R->L }
% 17.82/2.62 meet(a, meet(a, join(b, meet(a, c))))
% 17.82/2.62 = { by axiom 3 (absorption1) R->L }
% 17.82/2.62 meet(a, meet(meet(a, join(b, meet(a, c))), join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))))
% 17.82/2.62 = { by lemma 10 R->L }
% 17.82/2.62 meet(meet(a, join(b, meet(a, c))), meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))))
% 17.82/2.62 = { by axiom 1 (commutativity_of_meet) R->L }
% 17.82/2.62 meet(meet(a, join(b, meet(c, a))), meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))))
% 17.82/2.62 = { by axiom 5 (absorption2) R->L }
% 17.82/2.62 meet(meet(a, join(b, meet(c, join(a, meet(a, b))))), meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))))
% 17.82/2.62 = { by axiom 7 (equation_H76) R->L }
% 17.82/2.62 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)))))
% 17.82/2.62 = { by axiom 2 (commutativity_of_join) }
% 17.82/2.62 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)))))
% 17.82/2.62 = { by axiom 4 (associativity_of_meet) }
% 17.82/2.62 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))))))
% 17.82/2.62 = { by axiom 1 (commutativity_of_meet) }
% 17.82/2.62 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)))))
% 17.82/2.62 = { by lemma 11 R->L }
% 17.82/2.62 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)))))))
% 17.82/2.62 = { by lemma 10 }
% 17.82/2.62 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(c, meet(a, join(a, b)))))))
% 17.82/2.62 = { by axiom 3 (absorption1) }
% 17.82/2.62 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(c, a)))))
% 17.82/2.62 = { by axiom 1 (commutativity_of_meet) }
% 17.82/2.62 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)))))
% 17.82/2.62 = { by axiom 2 (commutativity_of_join) }
% 17.82/2.63 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))))))
% 17.82/2.63 = { by lemma 12 R->L }
% 17.82/2.63 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)))))
% 17.82/2.63 = { by axiom 2 (commutativity_of_join) R->L }
% 17.82/2.63 meet(a, meet(meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))), join(join(b, meet(a, c)), meet(c, join(a, b)))))
% 17.82/2.63 = { by lemma 13 R->L }
% 17.82/2.63 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)))))
% 17.82/2.63 = { by axiom 6 (associativity_of_join) }
% 17.82/2.63 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))))))
% 17.82/2.63 = { by axiom 2 (commutativity_of_join) }
% 17.82/2.63 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))))))
% 17.82/2.63 = { by lemma 12 R->L }
% 17.82/2.63 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(b, meet(a, c))), meet(c, join(a, b))))))
% 17.82/2.63 = { by lemma 13 R->L }
% 17.82/2.63 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)))))))
% 17.82/2.63 = { by axiom 2 (commutativity_of_join) R->L }
% 17.82/2.63 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))))))))
% 17.82/2.63 = { by axiom 6 (associativity_of_join) R->L }
% 17.82/2.63 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)))))))
% 17.82/2.63 = { by lemma 8 }
% 17.82/2.63 meet(a, meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b)))))
% 17.82/2.63 = { by lemma 9 }
% 17.82/2.63 meet(a, join(meet(a, join(b, meet(a, c))), meet(c, join(a, b))))
% 17.82/2.63 % SZS output end Proof
% 17.82/2.63
% 17.82/2.63 RESULT: Unsatisfiable (the axioms are contradictory).
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