TSTP Solution File: LAT012-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT012-1 : 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 : n021.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 06:27:07 EDT 2023
% Result : Unsatisfiable 0.14s 0.41s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT012-1 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n021.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 24 06:47:54 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.14/0.41 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.14/0.41
% 0.14/0.41 % SZS status Unsatisfiable
% 0.14/0.41
% 0.14/0.41 % SZS output start Proof
% 0.14/0.41 Axiom 1 (mckenzie2): meet(X, join(Y, join(X, Z))) = X.
% 0.14/0.41 Axiom 2 (mckenzie1): join(X, meet(Y, meet(X, Z))) = X.
% 0.14/0.41 Axiom 3 (mckenzie4): meet(meet(join(X, Y), join(Y, Z)), Y) = Y.
% 0.14/0.41 Axiom 4 (mckenzie3): join(join(meet(X, Y), meet(Y, Z)), Y) = Y.
% 0.14/0.41
% 0.14/0.41 Lemma 5: meet(X, join(Y, X)) = X.
% 0.14/0.41 Proof:
% 0.14/0.41 meet(X, join(Y, X))
% 0.14/0.41 = { by axiom 2 (mckenzie1) R->L }
% 0.14/0.41 meet(X, join(Y, join(X, meet(Z, meet(X, W)))))
% 0.14/0.41 = { by axiom 1 (mckenzie2) }
% 0.14/0.41 X
% 0.14/0.41
% 0.14/0.41 Lemma 6: join(X, meet(X, Y)) = X.
% 0.14/0.41 Proof:
% 0.14/0.41 join(X, meet(X, Y))
% 0.14/0.41 = { by axiom 3 (mckenzie4) R->L }
% 0.14/0.41 join(X, meet(meet(join(Z, meet(X, Y)), join(meet(X, Y), W)), meet(X, Y)))
% 0.14/0.41 = { by axiom 2 (mckenzie1) }
% 0.14/0.41 X
% 0.14/0.41
% 0.14/0.41 Lemma 7: meet(meet(X, Y), meet(Y, X)) = meet(Y, X).
% 0.14/0.41 Proof:
% 0.14/0.41 meet(meet(X, Y), meet(Y, X))
% 0.14/0.41 = { by lemma 6 R->L }
% 0.14/0.41 meet(meet(X, join(Y, meet(Y, X))), meet(Y, X))
% 0.14/0.41 = { by axiom 4 (mckenzie3) R->L }
% 0.14/0.41 meet(meet(X, join(join(meet(meet(Y, X), join(Y, meet(Y, X))), meet(join(Y, meet(Y, X)), meet(meet(meet(Y, X), join(Y, meet(Y, X))), Z))), join(Y, meet(Y, X)))), meet(Y, X))
% 0.14/0.41 = { by axiom 2 (mckenzie1) }
% 0.14/0.41 meet(meet(X, join(meet(meet(Y, X), join(Y, meet(Y, X))), join(Y, meet(Y, X)))), meet(Y, X))
% 0.14/0.41 = { by lemma 5 }
% 0.14/0.42 meet(meet(X, join(meet(Y, X), join(Y, meet(Y, X)))), meet(Y, X))
% 0.14/0.42 = { by lemma 6 }
% 0.14/0.42 meet(meet(X, join(meet(Y, X), Y)), meet(Y, X))
% 0.14/0.42 = { by axiom 2 (mckenzie1) R->L }
% 0.14/0.42 meet(meet(join(X, meet(Y, meet(X, join(W, join(X, V))))), join(meet(Y, X), Y)), meet(Y, X))
% 0.14/0.42 = { by axiom 1 (mckenzie2) }
% 0.14/0.42 meet(meet(join(X, meet(Y, X)), join(meet(Y, X), Y)), meet(Y, X))
% 0.14/0.42 = { by axiom 3 (mckenzie4) }
% 0.14/0.42 meet(Y, X)
% 0.14/0.42
% 0.14/0.42 Goal 1 (prove_commutativity_of_meet): meet(b, a) = meet(a, b).
% 0.14/0.42 Proof:
% 0.14/0.42 meet(b, a)
% 0.14/0.42 = { by lemma 7 R->L }
% 0.14/0.42 meet(meet(a, b), meet(b, a))
% 0.14/0.42 = { by lemma 7 R->L }
% 0.14/0.42 meet(meet(meet(b, a), meet(a, b)), meet(b, a))
% 0.14/0.42 = { by lemma 6 R->L }
% 0.14/0.42 meet(meet(meet(b, a), meet(a, b)), join(meet(b, a), meet(meet(b, a), meet(a, b))))
% 0.14/0.42 = { by lemma 5 }
% 0.14/0.42 meet(meet(b, a), meet(a, b))
% 0.14/0.42 = { by lemma 7 }
% 0.14/0.42 meet(a, b)
% 0.14/0.42 % SZS output end Proof
% 0.14/0.42
% 0.14/0.42 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------