TSTP Solution File: LAT158-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT158-1 : 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 : n009.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 06:27:36 EDT 2023
% Result : Unsatisfiable 142.78s 18.58s
% Output : Proof 143.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LAT158-1 : TPTP v8.1.2. Released v3.1.0.
% 0.07/0.13 % 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 : n009.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 05:12:21 EDT 2023
% 0.13/0.34 % CPUTime :
% 142.78/18.58 Command-line arguments: --no-flatten-goal
% 142.78/18.58
% 142.78/18.58 % SZS status Unsatisfiable
% 142.78/18.58
% 143.59/18.60 % SZS output start Proof
% 143.59/18.60 Axiom 1 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 143.59/18.60 Axiom 2 (idempotence_of_join): join(X, X) = X.
% 143.59/18.60 Axiom 3 (commutativity_of_join): join(X, Y) = join(Y, X).
% 143.59/18.60 Axiom 4 (absorption1): meet(X, join(X, Y)) = X.
% 143.59/18.60 Axiom 5 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 143.59/18.60 Axiom 6 (absorption2): join(X, meet(X, Y)) = X.
% 143.59/18.60 Axiom 7 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 143.59/18.60 Axiom 8 (equation_H50): meet(X, join(Y, meet(Z, join(X, W)))) = meet(X, join(Y, meet(Z, join(X, meet(Z, join(Y, W)))))).
% 143.59/18.60
% 143.59/18.60 Lemma 9: meet(X, meet(Y, join(Z, meet(X, Y)))) = meet(X, Y).
% 143.59/18.60 Proof:
% 143.59/18.60 meet(X, meet(Y, join(Z, meet(X, Y))))
% 143.59/18.60 = { by axiom 3 (commutativity_of_join) R->L }
% 143.59/18.60 meet(X, meet(Y, join(meet(X, Y), Z)))
% 143.59/18.60 = { by axiom 5 (associativity_of_meet) R->L }
% 143.59/18.60 meet(meet(X, Y), join(meet(X, Y), Z))
% 143.59/18.60 = { by axiom 4 (absorption1) }
% 143.59/18.60 meet(X, Y)
% 143.59/18.60
% 143.59/18.60 Goal 1 (prove_H49): meet(a, join(b, meet(c, join(a, d)))) = meet(a, join(b, join(meet(a, c), meet(c, join(b, d))))).
% 143.59/18.60 Proof:
% 143.59/18.60 meet(a, join(b, meet(c, join(a, d))))
% 143.59/18.60 = { by axiom 8 (equation_H50) }
% 143.59/18.60 meet(a, join(b, meet(c, join(a, meet(c, join(b, d))))))
% 143.59/18.60 = { by axiom 3 (commutativity_of_join) R->L }
% 143.59/18.60 meet(a, join(meet(c, join(a, meet(c, join(b, d)))), b))
% 143.59/18.60 = { by axiom 1 (commutativity_of_meet) R->L }
% 143.59/18.60 meet(a, join(meet(c, join(a, meet(join(b, d), c))), b))
% 143.59/18.60 = { by axiom 6 (absorption2) R->L }
% 143.59/18.60 meet(a, join(join(meet(c, join(a, meet(join(b, d), c))), meet(meet(c, join(a, meet(join(b, d), c))), join(b, d))), b))
% 143.59/18.60 = { by axiom 1 (commutativity_of_meet) }
% 143.59/18.60 meet(a, join(join(meet(c, join(a, meet(join(b, d), c))), meet(join(b, d), meet(c, join(a, meet(join(b, d), c))))), b))
% 143.59/18.60 = { by lemma 9 }
% 143.59/18.60 meet(a, join(join(meet(c, join(a, meet(join(b, d), c))), meet(join(b, d), c)), b))
% 143.59/18.60 = { by axiom 3 (commutativity_of_join) }
% 143.59/18.60 meet(a, join(join(meet(join(b, d), c), meet(c, join(a, meet(join(b, d), c)))), b))
% 143.59/18.60 = { by axiom 1 (commutativity_of_meet) }
% 143.59/18.60 meet(a, join(join(meet(join(b, d), c), meet(c, join(a, meet(c, join(b, d))))), b))
% 143.59/18.60 = { by axiom 1 (commutativity_of_meet) }
% 143.59/18.60 meet(a, join(join(meet(c, join(b, d)), meet(c, join(a, meet(c, join(b, d))))), b))
% 143.59/18.60 = { by axiom 3 (commutativity_of_join) }
% 143.59/18.60 meet(a, join(join(meet(c, join(b, d)), meet(c, join(meet(c, join(b, d)), a))), b))
% 143.59/18.60 = { by axiom 7 (associativity_of_join) }
% 143.59/18.60 meet(a, join(meet(c, join(b, d)), join(meet(c, join(meet(c, join(b, d)), a)), b)))
% 143.59/18.60 = { by axiom 3 (commutativity_of_join) }
% 143.59/18.60 meet(a, join(meet(c, join(b, d)), join(b, meet(c, join(meet(c, join(b, d)), a)))))
% 143.59/18.60 = { by axiom 3 (commutativity_of_join) R->L }
% 143.59/18.60 meet(a, join(meet(c, join(b, d)), join(b, meet(c, join(a, meet(c, join(b, d)))))))
% 143.59/18.60 = { by axiom 7 (associativity_of_join) R->L }
% 143.59/18.60 meet(a, join(join(meet(c, join(b, d)), b), meet(c, join(a, meet(c, join(b, d))))))
% 143.59/18.60 = { by axiom 4 (absorption1) R->L }
% 143.59/18.60 meet(a, join(join(meet(c, join(b, d)), b), meet(c, join(a, meet(meet(c, join(b, d)), join(meet(c, join(b, d)), b))))))
% 143.59/18.60 = { by axiom 1 (commutativity_of_meet) R->L }
% 143.59/18.60 meet(a, join(join(meet(c, join(b, d)), b), meet(c, join(a, meet(join(meet(c, join(b, d)), b), meet(c, join(b, d)))))))
% 143.59/18.60 = { by axiom 8 (equation_H50) }
% 143.59/18.60 meet(a, join(join(meet(c, join(b, d)), b), meet(c, join(a, meet(c, join(join(meet(c, join(b, d)), b), meet(join(meet(c, join(b, d)), b), meet(c, join(b, d)))))))))
% 143.59/18.60 = { by axiom 6 (absorption2) }
% 143.59/18.60 meet(a, join(join(meet(c, join(b, d)), b), meet(c, join(a, meet(c, join(meet(c, join(b, d)), b))))))
% 143.59/18.60 = { by axiom 2 (idempotence_of_join) R->L }
% 143.59/18.60 meet(a, join(join(meet(c, join(b, d)), b), meet(c, join(a, meet(c, join(join(meet(c, join(b, d)), b), join(meet(c, join(b, d)), b)))))))
% 143.59/18.60 = { by axiom 8 (equation_H50) R->L }
% 143.59/18.60 meet(a, join(join(meet(c, join(b, d)), b), meet(c, join(a, join(meet(c, join(b, d)), b)))))
% 143.59/18.60 = { by lemma 9 R->L }
% 143.59/18.60 meet(a, join(join(meet(c, join(b, d)), b), meet(c, meet(join(a, join(meet(c, join(b, d)), b)), join(a, meet(c, join(a, join(meet(c, join(b, d)), b))))))))
% 143.59/18.60 = { by axiom 3 (commutativity_of_join) R->L }
% 143.59/18.60 meet(a, join(join(meet(c, join(b, d)), b), meet(c, meet(join(join(meet(c, join(b, d)), b), a), join(a, meet(c, join(a, join(meet(c, join(b, d)), b))))))))
% 143.59/18.60 = { by axiom 3 (commutativity_of_join) R->L }
% 143.59/18.60 meet(a, join(join(meet(c, join(b, d)), b), meet(c, meet(join(join(meet(c, join(b, d)), b), a), join(a, meet(c, join(join(meet(c, join(b, d)), b), a)))))))
% 143.59/18.60 = { by axiom 1 (commutativity_of_meet) R->L }
% 143.59/18.60 meet(a, join(join(meet(c, join(b, d)), b), meet(c, meet(join(a, meet(c, join(join(meet(c, join(b, d)), b), a))), join(join(meet(c, join(b, d)), b), a)))))
% 143.59/18.60 = { by axiom 6 (absorption2) R->L }
% 143.59/18.60 meet(a, join(join(meet(c, join(b, d)), b), meet(c, meet(join(a, meet(c, join(join(meet(c, join(b, d)), b), a))), join(join(join(meet(c, join(b, d)), b), a), meet(join(join(meet(c, join(b, d)), b), a), c))))))
% 143.59/18.60 = { by axiom 7 (associativity_of_join) }
% 143.59/18.60 meet(a, join(join(meet(c, join(b, d)), b), meet(c, meet(join(a, meet(c, join(join(meet(c, join(b, d)), b), a))), join(join(meet(c, join(b, d)), b), join(a, meet(join(join(meet(c, join(b, d)), b), a), c)))))))
% 143.59/18.60 = { by axiom 1 (commutativity_of_meet) }
% 143.59/18.60 meet(a, join(join(meet(c, join(b, d)), b), meet(c, meet(join(a, meet(c, join(join(meet(c, join(b, d)), b), a))), join(join(meet(c, join(b, d)), b), join(a, meet(c, join(join(meet(c, join(b, d)), b), a))))))))
% 143.59/18.60 = { by axiom 3 (commutativity_of_join) R->L }
% 143.59/18.60 meet(a, join(join(meet(c, join(b, d)), b), meet(c, meet(join(a, meet(c, join(join(meet(c, join(b, d)), b), a))), join(join(a, meet(c, join(join(meet(c, join(b, d)), b), a))), join(meet(c, join(b, d)), b))))))
% 143.59/18.60 = { by axiom 4 (absorption1) }
% 143.59/18.60 meet(a, join(join(meet(c, join(b, d)), b), meet(c, join(a, meet(c, join(join(meet(c, join(b, d)), b), a))))))
% 143.59/18.60 = { by axiom 8 (equation_H50) R->L }
% 143.59/18.60 meet(a, join(join(meet(c, join(b, d)), b), meet(c, join(a, a))))
% 143.59/18.60 = { by axiom 2 (idempotence_of_join) }
% 143.59/18.60 meet(a, join(join(meet(c, join(b, d)), b), meet(c, a)))
% 143.59/18.60 = { by axiom 1 (commutativity_of_meet) }
% 143.59/18.60 meet(a, join(join(meet(c, join(b, d)), b), meet(a, c)))
% 143.59/18.60 = { by axiom 7 (associativity_of_join) }
% 143.59/18.60 meet(a, join(meet(c, join(b, d)), join(b, meet(a, c))))
% 143.59/18.60 = { by axiom 3 (commutativity_of_join) R->L }
% 143.59/18.60 meet(a, join(meet(c, join(b, d)), join(meet(a, c), b)))
% 143.59/18.60 = { by axiom 7 (associativity_of_join) R->L }
% 143.59/18.60 meet(a, join(join(meet(c, join(b, d)), meet(a, c)), b))
% 143.59/18.60 = { by axiom 3 (commutativity_of_join) }
% 143.59/18.60 meet(a, join(b, join(meet(c, join(b, d)), meet(a, c))))
% 143.59/18.60 = { by axiom 3 (commutativity_of_join) }
% 143.59/18.60 meet(a, join(b, join(meet(a, c), meet(c, join(b, d)))))
% 143.59/18.60 % SZS output end Proof
% 143.59/18.60
% 143.59/18.60 RESULT: Unsatisfiable (the axioms are contradictory).
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