TSTP Solution File: LAT140-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT140-1 : 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 : n029.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 06:27:32 EDT 2023
% Result : Unsatisfiable 123.87s 16.39s
% Output : Proof 123.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LAT140-1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.14 % 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 : n029.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 06:40:53 EDT 2023
% 0.13/0.36 % CPUTime :
% 123.87/16.39 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 123.87/16.39
% 123.87/16.39 % SZS status Unsatisfiable
% 123.87/16.39
% 123.87/16.40 % SZS output start Proof
% 123.87/16.40 Axiom 1 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 123.87/16.40 Axiom 2 (commutativity_of_join): join(X, Y) = join(Y, X).
% 123.87/16.40 Axiom 3 (absorption1): meet(X, join(X, Y)) = X.
% 123.87/16.40 Axiom 4 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 123.87/16.40 Axiom 5 (absorption2): join(X, meet(X, Y)) = X.
% 123.87/16.40 Axiom 6 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 123.87/16.40 Axiom 7 (equation_H21): join(meet(X, Y), meet(X, Z)) = meet(X, join(meet(Y, join(X, meet(Y, Z))), meet(Z, join(X, Y)))).
% 123.87/16.40
% 123.87/16.40 Lemma 8: meet(X, join(Y, X)) = X.
% 123.87/16.40 Proof:
% 123.87/16.40 meet(X, join(Y, X))
% 123.87/16.40 = { by axiom 2 (commutativity_of_join) R->L }
% 123.87/16.40 meet(X, join(X, Y))
% 123.87/16.40 = { by axiom 3 (absorption1) }
% 123.87/16.40 X
% 123.87/16.40
% 123.87/16.40 Lemma 9: join(X, meet(Y, X)) = X.
% 123.87/16.40 Proof:
% 123.87/16.40 join(X, meet(Y, X))
% 123.87/16.40 = { by axiom 1 (commutativity_of_meet) R->L }
% 123.87/16.40 join(X, meet(X, Y))
% 123.87/16.40 = { by axiom 5 (absorption2) }
% 123.87/16.40 X
% 123.87/16.40
% 123.87/16.40 Lemma 10: meet(X, join(meet(Y, join(Z, X)), meet(Z, join(X, meet(Z, Y))))) = join(meet(Y, X), meet(Z, X)).
% 123.87/16.40 Proof:
% 123.87/16.40 meet(X, join(meet(Y, join(Z, X)), meet(Z, join(X, meet(Z, Y)))))
% 123.87/16.40 = { by axiom 2 (commutativity_of_join) }
% 123.87/16.40 meet(X, join(meet(Y, join(X, Z)), meet(Z, join(X, meet(Z, Y)))))
% 123.87/16.40 = { by axiom 2 (commutativity_of_join) R->L }
% 123.87/16.40 meet(X, join(meet(Z, join(X, meet(Z, Y))), meet(Y, join(X, Z))))
% 123.87/16.40 = { by axiom 7 (equation_H21) R->L }
% 123.87/16.40 join(meet(X, Z), meet(X, Y))
% 123.87/16.40 = { by axiom 1 (commutativity_of_meet) R->L }
% 123.87/16.40 join(meet(Z, X), meet(X, Y))
% 123.87/16.40 = { by axiom 1 (commutativity_of_meet) }
% 123.87/16.40 join(meet(Z, X), meet(Y, X))
% 123.87/16.40 = { by axiom 2 (commutativity_of_join) }
% 123.87/16.40 join(meet(Y, X), meet(Z, X))
% 123.87/16.40
% 123.87/16.40 Goal 1 (prove_H2): meet(a, join(b, meet(a, c))) = meet(a, join(b, meet(c, join(meet(a, join(b, c)), meet(b, c))))).
% 123.87/16.40 Proof:
% 123.87/16.40 meet(a, join(b, meet(a, c)))
% 123.87/16.40 = { by lemma 9 R->L }
% 123.87/16.40 meet(a, join(join(b, meet(a, c)), meet(meet(b, c), join(b, meet(a, c)))))
% 123.87/16.40 = { by axiom 1 (commutativity_of_meet) }
% 123.87/16.40 meet(a, join(join(b, meet(a, c)), meet(meet(c, b), join(b, meet(a, c)))))
% 123.87/16.40 = { by axiom 4 (associativity_of_meet) }
% 123.87/16.40 meet(a, join(join(b, meet(a, c)), meet(c, meet(b, join(b, meet(a, c))))))
% 123.87/16.40 = { by axiom 3 (absorption1) }
% 123.87/16.40 meet(a, join(join(b, meet(a, c)), meet(c, b)))
% 123.87/16.40 = { by axiom 1 (commutativity_of_meet) R->L }
% 123.87/16.40 meet(a, join(join(b, meet(a, c)), meet(b, c)))
% 123.87/16.40 = { by axiom 6 (associativity_of_join) }
% 123.87/16.40 meet(a, join(b, join(meet(a, c), meet(b, c))))
% 123.87/16.40 = { by lemma 10 R->L }
% 123.87/16.40 meet(a, join(b, meet(c, join(meet(a, join(b, c)), meet(b, join(c, meet(b, a)))))))
% 123.87/16.40 = { by axiom 3 (absorption1) R->L }
% 123.87/16.40 meet(a, join(b, meet(meet(c, join(meet(a, join(b, c)), meet(b, join(c, meet(b, a))))), join(meet(c, join(meet(a, join(b, c)), meet(b, join(c, meet(b, a))))), meet(a, join(b, c))))))
% 123.87/16.40 = { by axiom 4 (associativity_of_meet) }
% 123.87/16.41 meet(a, join(b, meet(c, meet(join(meet(a, join(b, c)), meet(b, join(c, meet(b, a)))), join(meet(c, join(meet(a, join(b, c)), meet(b, join(c, meet(b, a))))), meet(a, join(b, c)))))))
% 123.87/16.41 = { by axiom 2 (commutativity_of_join) }
% 123.87/16.41 meet(a, join(b, meet(c, meet(join(meet(a, join(b, c)), meet(b, join(c, meet(b, a)))), join(meet(a, join(b, c)), meet(c, join(meet(a, join(b, c)), meet(b, join(c, meet(b, a))))))))))
% 123.87/16.41 = { by axiom 2 (commutativity_of_join) R->L }
% 123.87/16.41 meet(a, join(b, meet(c, meet(join(meet(b, join(c, meet(b, a))), meet(a, join(b, c))), join(meet(a, join(b, c)), meet(c, join(meet(a, join(b, c)), meet(b, join(c, meet(b, a))))))))))
% 123.87/16.41 = { by axiom 2 (commutativity_of_join) R->L }
% 123.87/16.41 meet(a, join(b, meet(c, meet(join(meet(b, join(c, meet(b, a))), meet(a, join(b, c))), join(meet(a, join(b, c)), meet(c, join(meet(b, join(c, meet(b, a))), meet(a, join(b, c)))))))))
% 123.87/16.41 = { by axiom 1 (commutativity_of_meet) R->L }
% 123.87/16.41 meet(a, join(b, meet(c, meet(join(meet(a, join(b, c)), meet(c, join(meet(b, join(c, meet(b, a))), meet(a, join(b, c))))), join(meet(b, join(c, meet(b, a))), meet(a, join(b, c)))))))
% 123.87/16.41 = { by axiom 5 (absorption2) R->L }
% 123.87/16.41 meet(a, join(b, meet(c, meet(join(meet(a, join(b, c)), meet(c, join(meet(b, join(c, meet(b, a))), meet(a, join(b, c))))), join(join(meet(b, join(c, meet(b, a))), meet(a, join(b, c))), meet(join(meet(b, join(c, meet(b, a))), meet(a, join(b, c))), c))))))
% 123.87/16.41 = { by axiom 6 (associativity_of_join) }
% 123.87/16.41 meet(a, join(b, meet(c, meet(join(meet(a, join(b, c)), meet(c, join(meet(b, join(c, meet(b, a))), meet(a, join(b, c))))), join(meet(b, join(c, meet(b, a))), join(meet(a, join(b, c)), meet(join(meet(b, join(c, meet(b, a))), meet(a, join(b, c))), c)))))))
% 123.87/16.41 = { by axiom 1 (commutativity_of_meet) }
% 123.87/16.41 meet(a, join(b, meet(c, meet(join(meet(a, join(b, c)), meet(c, join(meet(b, join(c, meet(b, a))), meet(a, join(b, c))))), join(meet(b, join(c, meet(b, a))), join(meet(a, join(b, c)), meet(c, join(meet(b, join(c, meet(b, a))), meet(a, join(b, c))))))))))
% 123.87/16.41 = { by lemma 8 }
% 123.87/16.41 meet(a, join(b, meet(c, join(meet(a, join(b, c)), meet(c, join(meet(b, join(c, meet(b, a))), meet(a, join(b, c))))))))
% 123.87/16.41 = { by axiom 2 (commutativity_of_join) }
% 123.87/16.41 meet(a, join(b, meet(c, join(meet(a, join(b, c)), meet(c, join(meet(a, join(b, c)), meet(b, join(c, meet(b, a)))))))))
% 123.87/16.41 = { by lemma 10 }
% 123.87/16.41 meet(a, join(b, meet(c, join(meet(a, join(b, c)), join(meet(a, c), meet(b, c))))))
% 123.87/16.41 = { by axiom 6 (associativity_of_join) R->L }
% 123.87/16.41 meet(a, join(b, meet(c, join(join(meet(a, join(b, c)), meet(a, c)), meet(b, c)))))
% 123.87/16.41 = { by lemma 8 R->L }
% 123.87/16.41 meet(a, join(b, meet(c, join(join(meet(a, join(b, c)), meet(a, meet(c, join(b, c)))), meet(b, c)))))
% 123.87/16.41 = { by axiom 1 (commutativity_of_meet) R->L }
% 123.87/16.41 meet(a, join(b, meet(c, join(join(meet(a, join(b, c)), meet(a, meet(join(b, c), c))), meet(b, c)))))
% 123.87/16.41 = { by axiom 4 (associativity_of_meet) R->L }
% 123.87/16.41 meet(a, join(b, meet(c, join(join(meet(a, join(b, c)), meet(meet(a, join(b, c)), c)), meet(b, c)))))
% 123.87/16.41 = { by axiom 1 (commutativity_of_meet) }
% 123.87/16.41 meet(a, join(b, meet(c, join(join(meet(a, join(b, c)), meet(c, meet(a, join(b, c)))), meet(b, c)))))
% 123.87/16.41 = { by lemma 9 }
% 123.87/16.41 meet(a, join(b, meet(c, join(meet(a, join(b, c)), meet(b, c)))))
% 123.87/16.41 % SZS output end Proof
% 123.87/16.41
% 123.87/16.41 RESULT: Unsatisfiable (the axioms are contradictory).
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