TSTP Solution File: LAT028-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT028-1 : TPTP v8.1.2. Released v2.2.0.
% 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 : n013.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 06:27:11 EDT 2023
% Result : Unsatisfiable 0.17s 0.38s
% Output : Proof 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LAT028-1 : TPTP v8.1.2. Released v2.2.0.
% 0.11/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.32 % Computer : n013.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Thu Aug 24 08:04:32 EDT 2023
% 0.12/0.32 % CPUTime :
% 0.17/0.38 Command-line arguments: --no-flatten-goal
% 0.17/0.38
% 0.17/0.38 % SZS status Unsatisfiable
% 0.17/0.38
% 0.17/0.39 % SZS output start Proof
% 0.17/0.39 Axiom 1 (idempotence_of_meet): meet(X, X) = X.
% 0.17/0.39 Axiom 2 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 0.17/0.39 Axiom 3 (commutativity_of_meet2): meet2(X, Y) = meet2(Y, X).
% 0.17/0.39 Axiom 4 (idempotence_of_join): join(X, X) = X.
% 0.17/0.39 Axiom 5 (commutativity_of_join): join(X, Y) = join(Y, X).
% 0.17/0.39 Axiom 6 (wal_1): meet(meet(join(X, Y), join(Z, Y)), Y) = Y.
% 0.17/0.39 Axiom 7 (wal_1_2): meet2(meet2(join(X, Y), join(Z, Y)), Y) = Y.
% 0.17/0.39 Axiom 8 (wal_2): join(join(meet(X, Y), meet(Z, Y)), Y) = Y.
% 0.17/0.39 Axiom 9 (wal_2_2): join(join(meet2(X, Y), meet2(Z, Y)), Y) = Y.
% 0.17/0.39
% 0.17/0.39 Lemma 10: join(X, meet(X, Y)) = X.
% 0.17/0.39 Proof:
% 0.17/0.39 join(X, meet(X, Y))
% 0.17/0.39 = { by axiom 2 (commutativity_of_meet) R->L }
% 0.17/0.39 join(X, meet(Y, X))
% 0.17/0.39 = { by axiom 4 (idempotence_of_join) R->L }
% 0.17/0.39 join(X, join(meet(Y, X), meet(Y, X)))
% 0.17/0.39 = { by axiom 5 (commutativity_of_join) R->L }
% 0.17/0.39 join(join(meet(Y, X), meet(Y, X)), X)
% 0.17/0.39 = { by axiom 8 (wal_2) }
% 0.17/0.39 X
% 0.17/0.39
% 0.17/0.39 Lemma 11: join(X, meet2(X, Y)) = X.
% 0.17/0.39 Proof:
% 0.17/0.39 join(X, meet2(X, Y))
% 0.17/0.39 = { by axiom 3 (commutativity_of_meet2) R->L }
% 0.17/0.39 join(X, meet2(Y, X))
% 0.17/0.39 = { by axiom 4 (idempotence_of_join) R->L }
% 0.17/0.39 join(X, join(meet2(Y, X), meet2(Y, X)))
% 0.17/0.39 = { by axiom 5 (commutativity_of_join) R->L }
% 0.17/0.39 join(join(meet2(Y, X), meet2(Y, X)), X)
% 0.17/0.39 = { by axiom 9 (wal_2_2) }
% 0.17/0.39 X
% 0.17/0.39
% 0.17/0.39 Lemma 12: join(X, meet2(Y, X)) = X.
% 0.17/0.39 Proof:
% 0.17/0.39 join(X, meet2(Y, X))
% 0.17/0.39 = { by axiom 3 (commutativity_of_meet2) R->L }
% 0.17/0.39 join(X, meet2(X, Y))
% 0.17/0.39 = { by lemma 11 }
% 0.17/0.39 X
% 0.17/0.39
% 0.17/0.39 Lemma 13: meet(X, meet(join(Y, X), join(Z, X))) = X.
% 0.17/0.39 Proof:
% 0.17/0.39 meet(X, meet(join(Y, X), join(Z, X)))
% 0.17/0.39 = { by axiom 2 (commutativity_of_meet) R->L }
% 0.17/0.39 meet(meet(join(Y, X), join(Z, X)), X)
% 0.17/0.39 = { by axiom 6 (wal_1) }
% 0.17/0.39 X
% 0.17/0.39
% 0.17/0.39 Goal 1 (name): meet(a, b) = meet2(a, b).
% 0.17/0.39 Proof:
% 0.17/0.39 meet(a, b)
% 0.17/0.39 = { by lemma 13 R->L }
% 0.17/0.39 meet(meet(a, b), meet(join(meet2(a, b), meet(a, b)), join(meet2(a, b), meet(a, b))))
% 0.17/0.39 = { by axiom 1 (idempotence_of_meet) }
% 0.17/0.39 meet(meet(a, b), join(meet2(a, b), meet(a, b)))
% 0.17/0.39 = { by axiom 5 (commutativity_of_join) }
% 0.17/0.39 meet(meet(a, b), join(meet(a, b), meet2(a, b)))
% 0.17/0.39 = { by axiom 3 (commutativity_of_meet2) R->L }
% 0.17/0.39 meet(meet(a, b), join(meet(a, b), meet2(b, a)))
% 0.17/0.39 = { by axiom 2 (commutativity_of_meet) R->L }
% 0.17/0.39 meet(meet(a, b), join(meet(b, a), meet2(b, a)))
% 0.17/0.39 = { by axiom 5 (commutativity_of_join) R->L }
% 0.17/0.39 meet(meet(a, b), join(meet2(b, a), meet(b, a)))
% 0.17/0.39 = { by axiom 2 (commutativity_of_meet) R->L }
% 0.17/0.39 meet(meet(a, b), join(meet2(b, a), meet(a, b)))
% 0.17/0.39 = { by axiom 7 (wal_1_2) R->L }
% 0.17/0.39 meet(meet(a, b), join(meet2(b, a), meet2(meet2(join(a, meet(a, b)), join(b, meet(a, b))), meet(a, b))))
% 0.17/0.39 = { by axiom 3 (commutativity_of_meet2) }
% 0.17/0.39 meet(meet(a, b), join(meet2(b, a), meet2(meet(a, b), meet2(join(a, meet(a, b)), join(b, meet(a, b))))))
% 0.17/0.39 = { by lemma 10 }
% 0.17/0.39 meet(meet(a, b), join(meet2(b, a), meet2(meet(a, b), meet2(a, join(b, meet(a, b))))))
% 0.17/0.39 = { by axiom 2 (commutativity_of_meet) R->L }
% 0.17/0.39 meet(meet(a, b), join(meet2(b, a), meet2(meet(a, b), meet2(a, join(b, meet(b, a))))))
% 0.17/0.39 = { by lemma 10 }
% 0.17/0.39 meet(meet(a, b), join(meet2(b, a), meet2(meet(a, b), meet2(a, b))))
% 0.17/0.39 = { by axiom 2 (commutativity_of_meet) }
% 0.17/0.39 meet(meet(a, b), join(meet2(b, a), meet2(meet(b, a), meet2(a, b))))
% 0.17/0.39 = { by axiom 3 (commutativity_of_meet2) }
% 0.17/0.39 meet(meet(a, b), join(meet2(b, a), meet2(meet(b, a), meet2(b, a))))
% 0.17/0.39 = { by lemma 12 }
% 0.17/0.39 meet(meet(a, b), meet2(b, a))
% 0.17/0.39 = { by axiom 3 (commutativity_of_meet2) }
% 0.17/0.39 meet(meet(a, b), meet2(a, b))
% 0.17/0.39 = { by axiom 2 (commutativity_of_meet) }
% 0.17/0.39 meet(meet(b, a), meet2(a, b))
% 0.17/0.39 = { by axiom 3 (commutativity_of_meet2) }
% 0.17/0.39 meet(meet(b, a), meet2(b, a))
% 0.17/0.39 = { by axiom 2 (commutativity_of_meet) R->L }
% 0.17/0.39 meet(meet2(b, a), meet(b, a))
% 0.17/0.39 = { by lemma 12 R->L }
% 0.17/0.39 meet(meet2(b, a), meet(b, join(a, meet2(b, a))))
% 0.17/0.39 = { by lemma 11 R->L }
% 0.17/0.39 meet(meet2(b, a), meet(join(b, meet2(b, a)), join(a, meet2(b, a))))
% 0.17/0.39 = { by lemma 13 }
% 0.17/0.39 meet2(b, a)
% 0.17/0.39 = { by axiom 3 (commutativity_of_meet2) }
% 0.17/0.39 meet2(a, b)
% 0.17/0.39 % SZS output end Proof
% 0.17/0.39
% 0.17/0.39 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------