TSTP Solution File: LAT157-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT157-1 : 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 : n012.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 0.20s 0.83s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT157-1 : 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 : n012.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 08:22:42 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.83 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.20/0.83
% 0.20/0.83 % SZS status Unsatisfiable
% 0.20/0.83
% 0.20/0.84 % SZS output start Proof
% 0.20/0.84 Axiom 1 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 0.20/0.84 Axiom 2 (idempotence_of_join): join(X, X) = X.
% 0.20/0.84 Axiom 3 (commutativity_of_join): join(X, Y) = join(Y, X).
% 0.20/0.84 Axiom 4 (absorption1): meet(X, join(X, Y)) = X.
% 0.20/0.84 Axiom 5 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 0.20/0.84 Axiom 6 (absorption2): join(X, meet(X, Y)) = X.
% 0.20/0.85 Axiom 7 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 0.20/0.85 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)))))).
% 0.20/0.85
% 0.20/0.85 Lemma 9: meet(X, join(Y, X)) = X.
% 0.20/0.85 Proof:
% 0.20/0.85 meet(X, join(Y, X))
% 0.20/0.85 = { by axiom 3 (commutativity_of_join) R->L }
% 0.20/0.85 meet(X, join(X, Y))
% 0.20/0.85 = { by axiom 4 (absorption1) }
% 0.20/0.85 X
% 0.20/0.85
% 0.20/0.85 Lemma 10: meet(Y, meet(X, Z)) = meet(X, meet(Y, Z)).
% 0.20/0.85 Proof:
% 0.20/0.85 meet(Y, meet(X, Z))
% 0.20/0.85 = { by axiom 1 (commutativity_of_meet) R->L }
% 0.20/0.85 meet(meet(X, Z), Y)
% 0.20/0.85 = { by axiom 5 (associativity_of_meet) }
% 0.20/0.85 meet(X, meet(Z, Y))
% 0.20/0.85 = { by axiom 1 (commutativity_of_meet) }
% 0.20/0.85 meet(X, meet(Y, Z))
% 0.20/0.85
% 0.20/0.85 Lemma 11: join(X, meet(Y, X)) = X.
% 0.20/0.85 Proof:
% 0.20/0.85 join(X, meet(Y, X))
% 0.20/0.85 = { by axiom 1 (commutativity_of_meet) R->L }
% 0.20/0.85 join(X, meet(X, Y))
% 0.20/0.85 = { by axiom 6 (absorption2) }
% 0.20/0.85 X
% 0.20/0.85
% 0.20/0.85 Lemma 12: join(Y, join(Z, X)) = join(X, join(Y, Z)).
% 0.20/0.85 Proof:
% 0.20/0.85 join(Y, join(Z, X))
% 0.20/0.85 = { by axiom 3 (commutativity_of_join) R->L }
% 0.20/0.85 join(join(Z, X), Y)
% 0.20/0.85 = { by axiom 3 (commutativity_of_join) }
% 0.20/0.85 join(join(X, Z), Y)
% 0.20/0.85 = { by axiom 7 (associativity_of_join) }
% 0.20/0.85 join(X, join(Z, Y))
% 0.20/0.85 = { by axiom 3 (commutativity_of_join) }
% 0.20/0.85 join(X, join(Y, Z))
% 0.20/0.85
% 0.20/0.85 Lemma 13: meet(X, meet(Y, join(Z, X))) = meet(Y, X).
% 0.20/0.85 Proof:
% 0.20/0.85 meet(X, meet(Y, join(Z, X)))
% 0.20/0.85 = { by lemma 10 }
% 0.20/0.85 meet(Y, meet(X, join(Z, X)))
% 0.20/0.85 = { by lemma 9 }
% 0.20/0.85 meet(Y, X)
% 0.20/0.85
% 0.20/0.85 Lemma 14: meet(meet(X, Y), join(Z, X)) = meet(X, Y).
% 0.20/0.85 Proof:
% 0.20/0.85 meet(meet(X, Y), join(Z, X))
% 0.20/0.85 = { by lemma 11 R->L }
% 0.20/0.85 meet(meet(X, Y), join(join(Z, X), meet(X, join(Z, X))))
% 0.20/0.85 = { by lemma 9 }
% 0.20/0.85 meet(meet(X, Y), join(join(Z, X), X))
% 0.20/0.85 = { by lemma 9 R->L }
% 0.20/0.85 meet(meet(X, Y), join(join(Z, X), meet(X, join(meet(X, Y), X))))
% 0.20/0.85 = { by axiom 4 (absorption1) R->L }
% 0.20/0.85 meet(meet(X, Y), join(join(Z, X), meet(X, join(meet(X, Y), meet(X, join(X, join(Y, Z)))))))
% 0.20/0.85 = { by lemma 12 R->L }
% 0.20/0.85 meet(meet(X, Y), join(join(Z, X), meet(X, join(meet(X, Y), meet(X, join(Y, join(Z, X)))))))
% 0.20/0.85 = { by axiom 3 (commutativity_of_join) }
% 0.20/0.85 meet(meet(X, Y), join(join(Z, X), meet(X, join(meet(X, Y), meet(X, join(join(Z, X), Y))))))
% 0.20/0.85 = { by axiom 8 (equation_H50) R->L }
% 0.20/0.85 meet(meet(X, Y), join(join(Z, X), meet(X, join(meet(X, Y), Y))))
% 0.20/0.85 = { by axiom 3 (commutativity_of_join) R->L }
% 0.20/0.85 meet(meet(X, Y), join(join(Z, X), meet(X, join(Y, meet(X, Y)))))
% 0.20/0.85 = { by lemma 11 }
% 0.20/0.85 meet(meet(X, Y), join(join(Z, X), meet(X, Y)))
% 0.20/0.85 = { by lemma 9 }
% 0.20/0.85 meet(X, Y)
% 0.20/0.85
% 0.20/0.85 Lemma 15: meet(join(X, Y), join(X, join(Y, Z))) = join(X, Y).
% 0.20/0.85 Proof:
% 0.20/0.85 meet(join(X, Y), join(X, join(Y, Z)))
% 0.20/0.85 = { by lemma 12 }
% 0.20/0.85 meet(join(X, Y), join(Z, join(X, Y)))
% 0.20/0.85 = { by lemma 9 }
% 0.20/0.85 join(X, Y)
% 0.20/0.85
% 0.20/0.85 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))))).
% 0.20/0.85 Proof:
% 0.20/0.85 meet(a, join(b, meet(a, c)))
% 0.20/0.85 = { by axiom 3 (commutativity_of_join) R->L }
% 0.20/0.85 meet(a, join(meet(a, c), b))
% 0.20/0.85 = { by lemma 15 R->L }
% 0.20/0.85 meet(a, meet(join(meet(a, c), b), join(meet(a, c), join(b, c))))
% 0.20/0.85 = { by axiom 3 (commutativity_of_join) }
% 0.20/0.85 meet(a, meet(join(b, meet(a, c)), join(meet(a, c), join(b, c))))
% 0.20/0.85 = { by axiom 3 (commutativity_of_join) R->L }
% 0.20/0.85 meet(a, meet(join(b, meet(a, c)), join(join(b, c), meet(a, c))))
% 0.20/0.85 = { by axiom 6 (absorption2) R->L }
% 0.20/0.85 meet(a, meet(join(b, meet(a, c)), join(join(b, c), join(meet(a, c), meet(meet(a, c), join(b, c))))))
% 0.20/0.85 = { by lemma 9 R->L }
% 0.20/0.85 meet(a, meet(join(b, meet(a, c)), join(join(b, c), join(meet(meet(a, c), join(meet(a, join(b, c)), meet(a, c))), meet(meet(a, c), join(b, c))))))
% 0.20/0.85 = { by lemma 13 R->L }
% 0.20/0.85 meet(a, meet(join(b, meet(a, c)), join(join(b, c), join(meet(meet(a, c), join(meet(a, join(b, c)), meet(c, meet(a, join(b, c))))), meet(meet(a, c), join(b, c))))))
% 0.20/0.85 = { by lemma 11 }
% 0.20/0.85 meet(a, meet(join(b, meet(a, c)), join(join(b, c), join(meet(meet(a, c), meet(a, join(b, c))), meet(meet(a, c), join(b, c))))))
% 0.20/0.85 = { by axiom 3 (commutativity_of_join) R->L }
% 0.20/0.85 meet(a, meet(join(b, meet(a, c)), join(join(b, c), join(meet(meet(a, c), join(b, c)), meet(meet(a, c), meet(a, join(b, c)))))))
% 0.20/0.85 = { by lemma 10 }
% 0.20/0.85 meet(a, meet(join(b, meet(a, c)), join(join(b, c), join(meet(meet(a, c), join(b, c)), meet(a, meet(meet(a, c), join(b, c)))))))
% 0.20/0.85 = { by lemma 11 }
% 0.20/0.85 meet(a, meet(join(b, meet(a, c)), join(join(b, c), meet(meet(a, c), join(b, c)))))
% 0.20/0.85 = { by lemma 11 }
% 0.20/0.85 meet(a, meet(join(b, meet(a, c)), join(b, c)))
% 0.20/0.85 = { by lemma 10 R->L }
% 0.20/0.85 meet(join(b, meet(a, c)), meet(a, join(b, c)))
% 0.20/0.85 = { by axiom 1 (commutativity_of_meet) }
% 0.20/0.85 meet(meet(a, join(b, c)), join(b, meet(a, c)))
% 0.20/0.85 = { by lemma 13 R->L }
% 0.20/0.85 meet(meet(a, join(b, c)), join(b, meet(c, meet(a, join(b, c)))))
% 0.20/0.85 = { by axiom 2 (idempotence_of_join) R->L }
% 0.20/0.85 meet(meet(a, join(b, c)), join(b, meet(c, join(meet(a, join(b, c)), meet(a, join(b, c))))))
% 0.20/0.85 = { by axiom 8 (equation_H50) }
% 0.20/0.85 meet(meet(a, join(b, c)), join(b, meet(c, join(meet(a, join(b, c)), meet(c, join(b, meet(a, join(b, c))))))))
% 0.20/0.85 = { by axiom 3 (commutativity_of_join) R->L }
% 0.20/0.85 meet(meet(a, join(b, c)), join(b, meet(c, join(meet(a, join(b, c)), meet(c, join(meet(a, join(b, c)), b))))))
% 0.20/0.85 = { by axiom 6 (absorption2) R->L }
% 0.20/0.85 meet(meet(a, join(b, c)), join(b, meet(c, join(meet(a, join(b, c)), meet(c, join(meet(a, join(b, c)), join(b, meet(b, c))))))))
% 0.20/0.85 = { by axiom 3 (commutativity_of_join) R->L }
% 0.20/0.85 meet(meet(a, join(b, c)), join(b, meet(c, join(meet(a, join(b, c)), meet(c, join(meet(a, join(b, c)), join(meet(b, c), b)))))))
% 0.20/0.85 = { by axiom 7 (associativity_of_join) R->L }
% 0.20/0.85 meet(meet(a, join(b, c)), join(b, meet(c, join(meet(a, join(b, c)), meet(c, join(join(meet(a, join(b, c)), meet(b, c)), b))))))
% 0.20/0.85 = { by axiom 3 (commutativity_of_join) }
% 0.20/0.85 meet(meet(a, join(b, c)), join(b, meet(c, join(meet(a, join(b, c)), meet(c, join(b, join(meet(a, join(b, c)), meet(b, c))))))))
% 0.20/0.85 = { by axiom 8 (equation_H50) R->L }
% 0.20/0.85 meet(meet(a, join(b, c)), join(b, meet(c, join(meet(a, join(b, c)), join(meet(a, join(b, c)), meet(b, c))))))
% 0.20/0.85 = { by axiom 3 (commutativity_of_join) R->L }
% 0.20/0.85 meet(meet(a, join(b, c)), join(b, meet(c, join(join(meet(a, join(b, c)), meet(b, c)), meet(a, join(b, c))))))
% 0.20/0.85 = { by axiom 4 (absorption1) R->L }
% 0.20/0.85 meet(meet(a, join(b, c)), join(b, meet(c, join(join(meet(a, join(b, c)), meet(b, c)), meet(meet(a, join(b, c)), join(meet(a, join(b, c)), meet(b, c)))))))
% 0.20/0.85 = { by lemma 11 }
% 0.20/0.85 meet(meet(a, join(b, c)), join(b, meet(c, join(meet(a, join(b, c)), meet(b, c)))))
% 0.20/0.85 = { by axiom 1 (commutativity_of_meet) R->L }
% 0.20/0.85 meet(join(b, meet(c, join(meet(a, join(b, c)), meet(b, c)))), meet(a, join(b, c)))
% 0.20/0.85 = { by lemma 10 }
% 0.20/0.85 meet(a, meet(join(b, meet(c, join(meet(a, join(b, c)), meet(b, c)))), join(b, c)))
% 0.20/0.85 = { by axiom 1 (commutativity_of_meet) R->L }
% 0.20/0.85 meet(a, meet(join(b, c), join(b, meet(c, join(meet(a, join(b, c)), meet(b, c))))))
% 0.20/0.85 = { by lemma 14 R->L }
% 0.20/0.85 meet(a, meet(join(b, c), join(b, meet(meet(c, join(meet(a, join(b, c)), meet(b, c))), join(b, c)))))
% 0.20/0.85 = { by axiom 1 (commutativity_of_meet) R->L }
% 0.20/0.85 meet(a, meet(join(b, c), join(b, meet(join(b, c), meet(c, join(meet(a, join(b, c)), meet(b, c)))))))
% 0.20/0.85 = { by axiom 3 (commutativity_of_join) R->L }
% 0.20/0.85 meet(a, meet(join(b, c), join(meet(join(b, c), meet(c, join(meet(a, join(b, c)), meet(b, c)))), b)))
% 0.20/0.85 = { by axiom 1 (commutativity_of_meet) R->L }
% 0.20/0.85 meet(a, meet(join(meet(join(b, c), meet(c, join(meet(a, join(b, c)), meet(b, c)))), b), join(b, c)))
% 0.20/0.85 = { by axiom 6 (absorption2) R->L }
% 0.20/0.85 meet(a, meet(join(meet(join(b, c), meet(c, join(meet(a, join(b, c)), meet(b, c)))), b), join(join(b, c), meet(join(b, c), meet(c, join(meet(a, join(b, c)), meet(b, c)))))))
% 0.20/0.85 = { by axiom 3 (commutativity_of_join) R->L }
% 0.20/0.85 meet(a, meet(join(meet(join(b, c), meet(c, join(meet(a, join(b, c)), meet(b, c)))), b), join(meet(join(b, c), meet(c, join(meet(a, join(b, c)), meet(b, c)))), join(b, c))))
% 0.20/0.85 = { by lemma 15 }
% 0.20/0.85 meet(a, join(meet(join(b, c), meet(c, join(meet(a, join(b, c)), meet(b, c)))), b))
% 0.20/0.86 = { by axiom 3 (commutativity_of_join) }
% 0.20/0.86 meet(a, join(b, meet(join(b, c), meet(c, join(meet(a, join(b, c)), meet(b, c))))))
% 0.20/0.86 = { by axiom 1 (commutativity_of_meet) }
% 0.20/0.86 meet(a, join(b, meet(meet(c, join(meet(a, join(b, c)), meet(b, c))), join(b, c))))
% 0.20/0.86 = { by lemma 14 }
% 0.20/0.86 meet(a, join(b, meet(c, join(meet(a, join(b, c)), meet(b, c)))))
% 0.20/0.86 % SZS output end Proof
% 0.20/0.86
% 0.20/0.86 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------