TSTP Solution File: LAT169-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT169-1 : 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 : n021.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 06:27:38 EDT 2023
% Result : Unsatisfiable 96.24s 13.05s
% Output : Proof 99.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT169-1 : 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 : n021.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 07:32:39 EDT 2023
% 0.13/0.34 % CPUTime :
% 96.24/13.05 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 96.24/13.05
% 96.24/13.05 % SZS status Unsatisfiable
% 96.24/13.05
% 97.10/13.07 % SZS output start Proof
% 97.10/13.07 Axiom 1 (commutativity_of_join): join(X, Y) = join(Y, X).
% 97.10/13.07 Axiom 2 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 97.10/13.07 Axiom 3 (absorption2): join(X, meet(X, Y)) = X.
% 97.10/13.07 Axiom 4 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 97.10/13.07 Axiom 5 (absorption1): meet(X, join(X, Y)) = X.
% 97.10/13.07 Axiom 6 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 97.10/13.07 Axiom 7 (equation_H21_dual): meet(join(X, Y), join(X, Z)) = join(X, meet(join(Y, meet(X, join(Y, Z))), join(Z, meet(X, Y)))).
% 97.10/13.07
% 97.10/13.07 Lemma 8: meet(Y, meet(X, Z)) = meet(X, meet(Y, Z)).
% 97.10/13.07 Proof:
% 97.10/13.07 meet(Y, meet(X, Z))
% 97.10/13.07 = { by axiom 2 (commutativity_of_meet) R->L }
% 97.10/13.07 meet(meet(X, Z), Y)
% 97.10/13.07 = { by axiom 6 (associativity_of_meet) }
% 97.10/13.07 meet(X, meet(Z, Y))
% 97.10/13.07 = { by axiom 2 (commutativity_of_meet) }
% 97.10/13.07 meet(X, meet(Y, Z))
% 97.10/13.07
% 97.10/13.07 Lemma 9: join(X, meet(Y, X)) = X.
% 97.10/13.07 Proof:
% 97.10/13.07 join(X, meet(Y, X))
% 97.10/13.07 = { by axiom 2 (commutativity_of_meet) R->L }
% 97.10/13.07 join(X, meet(X, Y))
% 97.10/13.07 = { by axiom 3 (absorption2) }
% 97.10/13.07 X
% 97.10/13.07
% 97.10/13.07 Lemma 10: join(X, meet(join(Y, meet(Z, X)), join(Z, meet(X, join(Z, Y))))) = meet(join(Z, X), join(X, Y)).
% 97.10/13.07 Proof:
% 97.10/13.07 join(X, meet(join(Y, meet(Z, X)), join(Z, meet(X, join(Z, Y)))))
% 97.10/13.07 = { by axiom 2 (commutativity_of_meet) }
% 97.10/13.07 join(X, meet(join(Y, meet(X, Z)), join(Z, meet(X, join(Z, Y)))))
% 97.10/13.07 = { by axiom 2 (commutativity_of_meet) R->L }
% 97.10/13.07 join(X, meet(join(Z, meet(X, join(Z, Y))), join(Y, meet(X, Z))))
% 97.10/13.07 = { by axiom 7 (equation_H21_dual) R->L }
% 97.10/13.07 meet(join(X, Z), join(X, Y))
% 97.10/13.07 = { by axiom 1 (commutativity_of_join) R->L }
% 99.14/13.07 meet(join(Z, X), join(X, Y))
% 99.14/13.07
% 99.14/13.07 Goal 1 (prove_H58): meet(a, join(b, c)) = meet(a, join(b, meet(join(a, b), join(c, meet(a, b))))).
% 99.14/13.07 Proof:
% 99.14/13.07 meet(a, join(b, c))
% 99.14/13.07 = { by axiom 5 (absorption1) R->L }
% 99.14/13.07 meet(meet(a, join(b, c)), join(meet(a, join(b, c)), join(a, b)))
% 99.14/13.07 = { by axiom 1 (commutativity_of_join) R->L }
% 99.14/13.07 meet(meet(a, join(b, c)), join(join(a, b), meet(a, join(b, c))))
% 99.14/13.07 = { by axiom 1 (commutativity_of_join) }
% 99.14/13.07 meet(meet(a, join(b, c)), join(join(b, a), meet(a, join(b, c))))
% 99.14/13.07 = { by axiom 4 (associativity_of_join) }
% 99.14/13.07 meet(meet(a, join(b, c)), join(b, join(a, meet(a, join(b, c)))))
% 99.14/13.07 = { by axiom 3 (absorption2) }
% 99.14/13.07 meet(meet(a, join(b, c)), join(b, a))
% 99.14/13.07 = { by axiom 1 (commutativity_of_join) R->L }
% 99.14/13.07 meet(meet(a, join(b, c)), join(a, b))
% 99.14/13.07 = { by axiom 2 (commutativity_of_meet) R->L }
% 99.14/13.07 meet(join(a, b), meet(a, join(b, c)))
% 99.14/13.07 = { by lemma 8 }
% 99.14/13.07 meet(a, meet(join(a, b), join(b, c)))
% 99.14/13.07 = { by lemma 10 R->L }
% 99.14/13.07 meet(a, join(b, meet(join(c, meet(a, b)), join(a, meet(b, join(a, c))))))
% 99.14/13.07 = { by axiom 3 (absorption2) R->L }
% 99.14/13.08 meet(a, join(join(b, meet(join(c, meet(a, b)), join(a, meet(b, join(a, c))))), meet(join(b, meet(join(c, meet(a, b)), join(a, meet(b, join(a, c))))), join(c, meet(a, b)))))
% 99.14/13.08 = { by axiom 4 (associativity_of_join) }
% 99.14/13.08 meet(a, join(b, join(meet(join(c, meet(a, b)), join(a, meet(b, join(a, c)))), meet(join(b, meet(join(c, meet(a, b)), join(a, meet(b, join(a, c))))), join(c, meet(a, b))))))
% 99.14/13.08 = { by axiom 2 (commutativity_of_meet) }
% 99.14/13.08 meet(a, join(b, join(meet(join(c, meet(a, b)), join(a, meet(b, join(a, c)))), meet(join(c, meet(a, b)), join(b, meet(join(c, meet(a, b)), join(a, meet(b, join(a, c)))))))))
% 99.14/13.08 = { by axiom 2 (commutativity_of_meet) R->L }
% 99.14/13.08 meet(a, join(b, join(meet(join(a, meet(b, join(a, c))), join(c, meet(a, b))), meet(join(c, meet(a, b)), join(b, meet(join(c, meet(a, b)), join(a, meet(b, join(a, c)))))))))
% 99.14/13.08 = { by axiom 2 (commutativity_of_meet) R->L }
% 99.14/13.08 meet(a, join(b, join(meet(join(a, meet(b, join(a, c))), join(c, meet(a, b))), meet(join(c, meet(a, b)), join(b, meet(join(a, meet(b, join(a, c))), join(c, meet(a, b))))))))
% 99.14/13.08 = { by axiom 1 (commutativity_of_join) R->L }
% 99.14/13.08 meet(a, join(b, join(meet(join(c, meet(a, b)), join(b, meet(join(a, meet(b, join(a, c))), join(c, meet(a, b))))), meet(join(a, meet(b, join(a, c))), join(c, meet(a, b))))))
% 99.14/13.08 = { by axiom 5 (absorption1) R->L }
% 99.14/13.08 meet(a, join(b, join(meet(join(c, meet(a, b)), join(b, meet(join(a, meet(b, join(a, c))), join(c, meet(a, b))))), meet(meet(join(a, meet(b, join(a, c))), join(c, meet(a, b))), join(meet(join(a, meet(b, join(a, c))), join(c, meet(a, b))), b)))))
% 99.14/13.08 = { by axiom 6 (associativity_of_meet) }
% 99.14/13.08 meet(a, join(b, join(meet(join(c, meet(a, b)), join(b, meet(join(a, meet(b, join(a, c))), join(c, meet(a, b))))), meet(join(a, meet(b, join(a, c))), meet(join(c, meet(a, b)), join(meet(join(a, meet(b, join(a, c))), join(c, meet(a, b))), b))))))
% 99.14/13.08 = { by axiom 1 (commutativity_of_join) }
% 99.14/13.08 meet(a, join(b, join(meet(join(c, meet(a, b)), join(b, meet(join(a, meet(b, join(a, c))), join(c, meet(a, b))))), meet(join(a, meet(b, join(a, c))), meet(join(c, meet(a, b)), join(b, meet(join(a, meet(b, join(a, c))), join(c, meet(a, b)))))))))
% 99.14/13.08 = { by lemma 9 }
% 99.14/13.08 meet(a, join(b, meet(join(c, meet(a, b)), join(b, meet(join(a, meet(b, join(a, c))), join(c, meet(a, b)))))))
% 99.14/13.08 = { by axiom 2 (commutativity_of_meet) }
% 99.14/13.08 meet(a, join(b, meet(join(c, meet(a, b)), join(b, meet(join(c, meet(a, b)), join(a, meet(b, join(a, c))))))))
% 99.14/13.08 = { by lemma 10 }
% 99.14/13.08 meet(a, join(b, meet(join(c, meet(a, b)), meet(join(a, b), join(b, c)))))
% 99.14/13.08 = { by lemma 8 R->L }
% 99.14/13.08 meet(a, join(b, meet(join(a, b), meet(join(c, meet(a, b)), join(b, c)))))
% 99.14/13.08 = { by axiom 1 (commutativity_of_join) R->L }
% 99.14/13.08 meet(a, join(b, meet(join(a, b), meet(join(c, meet(a, b)), join(c, b)))))
% 99.14/13.08 = { by lemma 9 R->L }
% 99.14/13.08 meet(a, join(b, meet(join(a, b), meet(join(c, meet(a, b)), join(c, join(b, meet(a, b)))))))
% 99.14/13.08 = { by axiom 1 (commutativity_of_join) R->L }
% 99.14/13.08 meet(a, join(b, meet(join(a, b), meet(join(c, meet(a, b)), join(c, join(meet(a, b), b))))))
% 99.14/13.08 = { by axiom 4 (associativity_of_join) R->L }
% 99.14/13.08 meet(a, join(b, meet(join(a, b), meet(join(c, meet(a, b)), join(join(c, meet(a, b)), b)))))
% 99.14/13.08 = { by axiom 5 (absorption1) }
% 99.14/13.08 meet(a, join(b, meet(join(a, b), join(c, meet(a, b)))))
% 99.14/13.08 % SZS output end Proof
% 99.14/13.08
% 99.14/13.08 RESULT: Unsatisfiable (the axioms are contradictory).
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