TSTP Solution File: LAT148-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT148-1 : 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 : n015.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 06:27:34 EDT 2023
% Result : Unsatisfiable 0.20s 0.66s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LAT148-1 : 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
% 0.14/0.35 % Computer : n015.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 24 04:24:20 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.66 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.20/0.66
% 0.20/0.66 % SZS status Unsatisfiable
% 0.20/0.66
% 0.20/0.67 % SZS output start Proof
% 0.20/0.67 Axiom 1 (commutativity_of_join): join(X, Y) = join(Y, X).
% 0.20/0.67 Axiom 2 (idempotence_of_meet): meet(X, X) = X.
% 0.20/0.67 Axiom 3 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 0.20/0.67 Axiom 4 (absorption2): join(X, meet(X, Y)) = X.
% 0.20/0.67 Axiom 5 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 0.20/0.67 Axiom 6 (equation_H34): meet(X, join(Y, meet(Z, W))) = meet(X, join(Y, meet(Z, join(Y, meet(W, join(Y, Z)))))).
% 0.20/0.67
% 0.20/0.67 Lemma 7: join(X, join(Y, meet(X, Z))) = join(X, Y).
% 0.20/0.67 Proof:
% 0.20/0.67 join(X, join(Y, meet(X, Z)))
% 0.20/0.67 = { by axiom 1 (commutativity_of_join) R->L }
% 0.20/0.67 join(X, join(meet(X, Z), Y))
% 0.20/0.67 = { by axiom 5 (associativity_of_join) R->L }
% 0.20/0.67 join(join(X, meet(X, Z)), Y)
% 0.20/0.67 = { by axiom 4 (absorption2) }
% 0.20/0.67 join(X, Y)
% 0.20/0.67
% 0.20/0.67 Lemma 8: join(X, join(meet(X, Y), Z)) = join(X, Z).
% 0.20/0.67 Proof:
% 0.20/0.67 join(X, join(meet(X, Y), Z))
% 0.20/0.67 = { by axiom 1 (commutativity_of_join) R->L }
% 0.20/0.67 join(X, join(Z, meet(X, Y)))
% 0.20/0.67 = { by lemma 7 }
% 0.20/0.67 join(X, Z)
% 0.20/0.67
% 0.20/0.67 Lemma 9: meet(join(X, meet(Y, join(X, meet(Z, join(X, Y))))), W) = meet(W, join(X, meet(Y, Z))).
% 0.20/0.67 Proof:
% 0.20/0.67 meet(join(X, meet(Y, join(X, meet(Z, join(X, Y))))), W)
% 0.20/0.67 = { by axiom 3 (commutativity_of_meet) R->L }
% 0.20/0.67 meet(W, join(X, meet(Y, join(X, meet(Z, join(X, Y))))))
% 0.20/0.67 = { by axiom 6 (equation_H34) R->L }
% 0.20/0.67 meet(W, join(X, meet(Y, Z)))
% 0.20/0.67
% 0.20/0.67 Lemma 10: join(X, meet(Y, join(X, meet(Z, join(X, Y))))) = join(X, meet(Y, Z)).
% 0.20/0.67 Proof:
% 0.20/0.67 join(X, meet(Y, join(X, meet(Z, join(X, Y)))))
% 0.20/0.67 = { by axiom 2 (idempotence_of_meet) R->L }
% 0.20/0.67 meet(join(X, meet(Y, join(X, meet(Z, join(X, Y))))), join(X, meet(Y, join(X, meet(Z, join(X, Y))))))
% 0.20/0.67 = { by lemma 9 }
% 0.20/0.67 meet(join(X, meet(Y, join(X, meet(Z, join(X, Y))))), join(X, meet(Y, Z)))
% 0.20/0.67 = { by lemma 9 }
% 0.20/0.67 meet(join(X, meet(Y, Z)), join(X, meet(Y, Z)))
% 0.20/0.67 = { by axiom 2 (idempotence_of_meet) }
% 0.20/0.67 join(X, meet(Y, Z))
% 0.20/0.67
% 0.20/0.67 Lemma 11: join(X, meet(Y, join(X, meet(join(X, Y), Z)))) = join(X, meet(Y, Z)).
% 0.20/0.67 Proof:
% 0.20/0.67 join(X, meet(Y, join(X, meet(join(X, Y), Z))))
% 0.20/0.67 = { by axiom 3 (commutativity_of_meet) R->L }
% 0.20/0.67 join(X, meet(Y, join(X, meet(Z, join(X, Y)))))
% 0.20/0.67 = { by lemma 10 }
% 0.20/0.67 join(X, meet(Y, Z))
% 0.20/0.67
% 0.20/0.67 Goal 1 (prove_H7): meet(a, join(b, meet(a, c))) = meet(a, join(b, meet(a, join(meet(a, b), meet(c, join(a, b)))))).
% 0.20/0.67 Proof:
% 0.20/0.67 meet(a, join(b, meet(a, c)))
% 0.20/0.67 = { by lemma 11 R->L }
% 0.20/0.67 meet(a, join(b, meet(a, join(b, meet(join(b, a), c)))))
% 0.20/0.67 = { by lemma 8 R->L }
% 0.20/0.67 meet(a, join(b, meet(a, join(b, join(meet(b, a), meet(join(b, a), c))))))
% 0.20/0.67 = { by lemma 10 R->L }
% 0.20/0.67 meet(a, join(b, meet(a, join(b, join(meet(b, a), meet(join(b, a), join(meet(b, a), meet(c, join(meet(b, a), join(b, a))))))))))
% 0.20/0.67 = { by lemma 8 }
% 0.20/0.67 meet(a, join(b, meet(a, join(b, meet(join(b, a), join(meet(b, a), meet(c, join(meet(b, a), join(b, a)))))))))
% 0.20/0.67 = { by axiom 1 (commutativity_of_join) }
% 0.20/0.67 meet(a, join(b, meet(a, join(b, meet(join(b, a), join(meet(b, a), meet(c, join(join(b, a), meet(b, a)))))))))
% 0.20/0.67 = { by lemma 11 }
% 0.20/0.67 meet(a, join(b, meet(a, join(meet(b, a), meet(c, join(join(b, a), meet(b, a)))))))
% 0.20/0.67 = { by axiom 5 (associativity_of_join) }
% 0.20/0.67 meet(a, join(b, meet(a, join(meet(b, a), meet(c, join(b, join(a, meet(b, a))))))))
% 0.20/0.67 = { by lemma 7 }
% 0.20/0.67 meet(a, join(b, meet(a, join(meet(b, a), meet(c, join(b, a))))))
% 0.20/0.67 = { by axiom 3 (commutativity_of_meet) R->L }
% 0.20/0.67 meet(a, join(b, meet(a, join(meet(a, b), meet(c, join(b, a))))))
% 0.20/0.67 = { by axiom 1 (commutativity_of_join) R->L }
% 0.20/0.67 meet(a, join(b, meet(a, join(meet(a, b), meet(c, join(a, b))))))
% 0.20/0.67 % SZS output end Proof
% 0.20/0.67
% 0.20/0.67 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------