TSTP Solution File: LAT143-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT143-1 : 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 : n006.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 06:27:33 EDT 2023
% Result : Unsatisfiable 4.29s 0.91s
% Output : Proof 4.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT143-1 : 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
% 0.17/0.34 % Computer : n006.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Thu Aug 24 09:48:22 EDT 2023
% 0.17/0.35 % CPUTime :
% 4.29/0.91 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 4.29/0.91
% 4.29/0.91 % SZS status Unsatisfiable
% 4.29/0.91
% 4.29/0.92 % SZS output start Proof
% 4.29/0.92 Axiom 1 (commutativity_of_join): join(X, Y) = join(Y, X).
% 4.29/0.92 Axiom 2 (idempotence_of_meet): meet(X, X) = X.
% 4.29/0.92 Axiom 3 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 4.29/0.92 Axiom 4 (absorption2): join(X, meet(X, Y)) = X.
% 4.29/0.92 Axiom 5 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 4.29/0.92 Axiom 6 (absorption1): meet(X, join(X, Y)) = X.
% 4.29/0.92 Axiom 7 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 4.29/0.92 Axiom 8 (equation_H24): join(meet(X, Y), meet(Y, Z)) = join(meet(X, Y), meet(Y, join(meet(X, Y), meet(Z, join(X, Y))))).
% 4.29/0.92
% 4.29/0.92 Lemma 9: join(X, meet(Y, X)) = X.
% 4.29/0.92 Proof:
% 4.29/0.92 join(X, meet(Y, X))
% 4.29/0.92 = { by axiom 3 (commutativity_of_meet) R->L }
% 4.29/0.92 join(X, meet(X, Y))
% 4.29/0.92 = { by axiom 4 (absorption2) }
% 4.29/0.92 X
% 4.29/0.92
% 4.29/0.92 Lemma 10: join(meet(X, Y), meet(X, join(Y, Z))) = meet(X, join(Y, Z)).
% 4.29/0.92 Proof:
% 4.29/0.92 join(meet(X, Y), meet(X, join(Y, Z)))
% 4.29/0.92 = { by axiom 3 (commutativity_of_meet) R->L }
% 4.29/0.92 join(meet(Y, X), meet(X, join(Y, Z)))
% 4.29/0.92 = { by axiom 1 (commutativity_of_join) R->L }
% 4.29/0.92 join(meet(X, join(Y, Z)), meet(Y, X))
% 4.29/0.92 = { by axiom 6 (absorption1) R->L }
% 4.29/0.92 join(meet(X, join(Y, Z)), meet(meet(Y, join(Y, Z)), X))
% 4.29/0.92 = { by axiom 7 (associativity_of_meet) }
% 4.29/0.92 join(meet(X, join(Y, Z)), meet(Y, meet(join(Y, Z), X)))
% 4.29/0.92 = { by axiom 3 (commutativity_of_meet) }
% 4.29/0.92 join(meet(X, join(Y, Z)), meet(Y, meet(X, join(Y, Z))))
% 4.29/0.92 = { by lemma 9 }
% 4.29/0.92 meet(X, join(Y, Z))
% 4.29/0.92
% 4.29/0.92 Goal 1 (prove_H15): meet(a, join(meet(a, b), meet(a, c))) = meet(a, join(meet(a, b), join(meet(a, c), meet(c, join(a, b))))).
% 4.29/0.92 Proof:
% 4.29/0.92 meet(a, join(meet(a, b), meet(a, c)))
% 4.29/0.92 = { by axiom 3 (commutativity_of_meet) }
% 4.29/0.92 meet(a, join(meet(b, a), meet(a, c)))
% 4.29/0.92 = { by axiom 3 (commutativity_of_meet) R->L }
% 4.29/0.92 meet(a, join(meet(b, a), meet(c, a)))
% 4.29/0.92 = { by axiom 3 (commutativity_of_meet) R->L }
% 4.29/0.93 meet(a, join(meet(a, b), meet(c, a)))
% 4.29/0.93 = { by axiom 1 (commutativity_of_join) R->L }
% 4.29/0.93 meet(a, join(meet(c, a), meet(a, b)))
% 4.29/0.93 = { by lemma 9 R->L }
% 4.29/0.93 meet(join(a, meet(c, a)), join(meet(c, a), meet(a, b)))
% 4.29/0.93 = { by axiom 3 (commutativity_of_meet) R->L }
% 4.29/0.93 meet(join(meet(c, a), meet(a, b)), join(a, meet(c, a)))
% 4.29/0.93 = { by axiom 4 (absorption2) R->L }
% 4.29/0.93 meet(join(meet(c, a), meet(a, b)), join(join(a, meet(a, b)), meet(c, a)))
% 4.29/0.93 = { by axiom 5 (associativity_of_join) }
% 4.29/0.93 meet(join(meet(c, a), meet(a, b)), join(a, join(meet(a, b), meet(c, a))))
% 4.29/0.93 = { by axiom 1 (commutativity_of_join) }
% 4.29/0.93 meet(join(meet(c, a), meet(a, b)), join(a, join(meet(c, a), meet(a, b))))
% 4.29/0.93 = { by axiom 1 (commutativity_of_join) R->L }
% 4.29/0.93 meet(join(meet(c, a), meet(a, b)), join(join(meet(c, a), meet(a, b)), a))
% 4.29/0.93 = { by axiom 6 (absorption1) }
% 4.29/0.93 join(meet(c, a), meet(a, b))
% 4.29/0.93 = { by axiom 1 (commutativity_of_join) }
% 4.29/0.93 join(meet(a, b), meet(c, a))
% 4.29/0.93 = { by axiom 3 (commutativity_of_meet) }
% 4.29/0.93 join(meet(b, a), meet(c, a))
% 4.29/0.93 = { by axiom 3 (commutativity_of_meet) }
% 4.29/0.93 join(meet(b, a), meet(a, c))
% 4.29/0.93 = { by axiom 8 (equation_H24) }
% 4.29/0.93 join(meet(b, a), meet(a, join(meet(b, a), meet(c, join(b, a)))))
% 4.29/0.93 = { by axiom 1 (commutativity_of_join) }
% 4.29/0.93 join(meet(b, a), meet(a, join(meet(b, a), meet(c, join(a, b)))))
% 4.29/0.93 = { by axiom 3 (commutativity_of_meet) }
% 4.29/0.93 join(meet(a, b), meet(a, join(meet(b, a), meet(c, join(a, b)))))
% 4.29/0.93 = { by axiom 3 (commutativity_of_meet) }
% 4.29/0.93 join(meet(a, b), meet(a, join(meet(a, b), meet(c, join(a, b)))))
% 4.29/0.93 = { by axiom 2 (idempotence_of_meet) R->L }
% 4.29/0.93 join(meet(meet(a, a), b), meet(a, join(meet(a, b), meet(c, join(a, b)))))
% 4.29/0.93 = { by axiom 7 (associativity_of_meet) }
% 4.29/0.93 join(meet(a, meet(a, b)), meet(a, join(meet(a, b), meet(c, join(a, b)))))
% 4.29/0.93 = { by lemma 10 }
% 4.29/0.93 meet(a, join(meet(a, b), meet(c, join(a, b))))
% 4.29/0.93 = { by axiom 3 (commutativity_of_meet) }
% 4.29/0.93 meet(a, join(meet(b, a), meet(c, join(a, b))))
% 4.29/0.93 = { by lemma 10 R->L }
% 4.29/0.93 meet(a, join(meet(b, a), join(meet(c, a), meet(c, join(a, b)))))
% 4.29/0.93 = { by axiom 1 (commutativity_of_join) }
% 4.29/0.93 meet(a, join(meet(b, a), join(meet(c, a), meet(c, join(b, a)))))
% 4.29/0.93 = { by axiom 3 (commutativity_of_meet) R->L }
% 4.29/0.93 meet(a, join(meet(b, a), join(meet(a, c), meet(c, join(b, a)))))
% 4.29/0.93 = { by axiom 3 (commutativity_of_meet) R->L }
% 4.29/0.93 meet(a, join(meet(a, b), join(meet(a, c), meet(c, join(b, a)))))
% 4.29/0.93 = { by axiom 1 (commutativity_of_join) R->L }
% 4.29/0.93 meet(a, join(meet(a, b), join(meet(a, c), meet(c, join(a, b)))))
% 4.29/0.93 % SZS output end Proof
% 4.29/0.93
% 4.29/0.93 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------