TSTP Solution File: LAT089-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT089-1 : TPTP v8.1.2. Released v2.6.0.
% 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 : n005.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 06:27:24 EDT 2023
% Result : Unsatisfiable 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LAT089-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % 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 08:22:53 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.42 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.20/0.42
% 0.20/0.42 % SZS status Unsatisfiable
% 0.20/0.42
% 0.20/0.45 % SZS output start Proof
% 0.20/0.45 Axiom 1 (wal_absorbtion_4): meet(meet(join(X, Y), join(Z, X)), X) = X.
% 0.20/0.45 Axiom 2 (wal_absorbtion_2): join(meet(X, X), meet(Y, join(X, X))) = X.
% 0.20/0.45 Axiom 3 (wal_absorbtion_1): join(meet(X, Y), meet(X, join(X, Y))) = X.
% 0.20/0.45 Axiom 4 (wal_absorbtion_3): join(meet(X, Y), meet(Y, join(X, Y))) = Y.
% 0.20/0.45 Axiom 5 (wal_absorbtion_5): join(join(meet(X, Y), meet(Z, X)), X) = X.
% 0.20/0.45
% 0.20/0.45 Lemma 6: meet(meet(join(X, Y), X), X) = X.
% 0.20/0.45 Proof:
% 0.20/0.45 meet(meet(join(X, Y), X), X)
% 0.20/0.45 = { by axiom 5 (wal_absorbtion_5) R->L }
% 0.20/0.45 meet(meet(join(X, Y), join(join(meet(X, Z), meet(W, X)), X)), X)
% 0.20/0.45 = { by axiom 1 (wal_absorbtion_4) }
% 0.20/0.45 X
% 0.20/0.45
% 0.20/0.45 Lemma 7: meet(X, X) = X.
% 0.20/0.45 Proof:
% 0.20/0.45 meet(X, X)
% 0.20/0.45 = { by axiom 1 (wal_absorbtion_4) R->L }
% 0.20/0.45 meet(meet(meet(join(X, Y), join(Z, X)), X), X)
% 0.20/0.45 = { by axiom 1 (wal_absorbtion_4) R->L }
% 0.20/0.45 meet(meet(meet(join(X, Y), join(Z, X)), X), meet(meet(join(X, Y), join(Z, X)), X))
% 0.20/0.45 = { by axiom 1 (wal_absorbtion_4) R->L }
% 0.20/0.45 meet(meet(meet(join(X, Y), join(Z, X)), meet(meet(join(X, Y), join(Z, X)), X)), meet(meet(join(X, Y), join(Z, X)), X))
% 0.20/0.45 = { by axiom 3 (wal_absorbtion_1) R->L }
% 0.20/0.45 meet(meet(join(meet(meet(join(X, Y), join(Z, X)), X), meet(meet(join(X, Y), join(Z, X)), join(meet(join(X, Y), join(Z, X)), X))), meet(meet(join(X, Y), join(Z, X)), X)), meet(meet(join(X, Y), join(Z, X)), X))
% 0.20/0.45 = { by lemma 6 }
% 0.20/0.45 meet(meet(join(X, Y), join(Z, X)), X)
% 0.20/0.45 = { by axiom 1 (wal_absorbtion_4) }
% 0.20/0.45 X
% 0.20/0.45
% 0.20/0.45 Lemma 8: join(join(meet(X, Y), X), X) = X.
% 0.20/0.45 Proof:
% 0.20/0.45 join(join(meet(X, Y), X), X)
% 0.20/0.45 = { by axiom 1 (wal_absorbtion_4) R->L }
% 0.20/0.45 join(join(meet(X, Y), meet(meet(join(X, Z), join(W, X)), X)), X)
% 0.20/0.45 = { by axiom 5 (wal_absorbtion_5) }
% 0.20/0.45 X
% 0.20/0.45
% 0.20/0.45 Lemma 9: join(X, X) = X.
% 0.20/0.45 Proof:
% 0.20/0.45 join(X, X)
% 0.20/0.45 = { by lemma 7 R->L }
% 0.20/0.45 join(X, meet(X, X))
% 0.20/0.45 = { by axiom 1 (wal_absorbtion_4) R->L }
% 0.20/0.45 join(meet(meet(join(X, X), join(X, X)), X), meet(X, X))
% 0.20/0.45 = { by lemma 7 }
% 0.20/0.45 join(meet(join(X, X), X), meet(X, X))
% 0.20/0.45 = { by lemma 8 R->L }
% 0.20/0.45 join(meet(join(X, X), X), meet(X, join(join(meet(X, X), X), X)))
% 0.20/0.45 = { by lemma 7 }
% 0.20/0.45 join(meet(join(X, X), X), meet(X, join(join(X, X), X)))
% 0.20/0.45 = { by axiom 4 (wal_absorbtion_3) }
% 0.20/0.45 X
% 0.20/0.45
% 0.20/0.45 Lemma 10: join(X, meet(Y, X)) = X.
% 0.20/0.45 Proof:
% 0.20/0.45 join(X, meet(Y, X))
% 0.20/0.45 = { by lemma 7 R->L }
% 0.20/0.45 join(meet(X, X), meet(Y, X))
% 0.20/0.45 = { by lemma 9 R->L }
% 0.20/0.45 join(meet(X, X), meet(Y, join(X, X)))
% 0.20/0.45 = { by axiom 2 (wal_absorbtion_2) }
% 0.20/0.45 X
% 0.20/0.45
% 0.20/0.45 Lemma 11: meet(join(X, Y), X) = X.
% 0.20/0.45 Proof:
% 0.20/0.45 meet(join(X, Y), X)
% 0.20/0.45 = { by axiom 3 (wal_absorbtion_1) R->L }
% 0.20/0.45 join(meet(meet(join(X, Y), X), X), meet(meet(join(X, Y), X), join(meet(join(X, Y), X), X)))
% 0.20/0.45 = { by lemma 7 R->L }
% 0.20/0.45 join(meet(meet(join(X, Y), X), X), meet(meet(join(X, Y), X), join(meet(join(X, Y), X), meet(X, X))))
% 0.20/0.45 = { by lemma 10 R->L }
% 0.20/0.45 join(meet(meet(join(X, Y), X), X), meet(meet(join(X, Y), X), join(meet(join(X, Y), X), meet(X, join(X, meet(join(X, Y), X))))))
% 0.20/0.45 = { by lemma 10 R->L }
% 0.20/0.45 join(meet(meet(join(X, Y), X), X), meet(meet(join(X, Y), X), join(join(meet(join(X, Y), X), meet(X, meet(join(X, Y), X))), meet(X, join(X, meet(join(X, Y), X))))))
% 0.20/0.45 = { by lemma 10 R->L }
% 0.20/0.45 join(meet(meet(join(X, Y), X), X), meet(meet(join(X, Y), X), join(join(join(meet(join(X, Y), X), meet(X, meet(join(X, Y), X))), meet(X, meet(join(X, Y), X))), meet(X, join(X, meet(join(X, Y), X))))))
% 0.20/0.45 = { by lemma 6 R->L }
% 0.20/0.45 join(meet(meet(join(X, Y), X), X), meet(meet(join(X, Y), X), join(join(join(meet(meet(join(meet(join(X, Y), X), meet(X, join(join(X, Y), X))), meet(join(X, Y), X)), meet(join(X, Y), X)), meet(X, meet(join(X, Y), X))), meet(X, meet(join(X, Y), X))), meet(X, join(X, meet(join(X, Y), X))))))
% 0.20/0.45 = { by axiom 4 (wal_absorbtion_3) }
% 0.20/0.45 join(meet(meet(join(X, Y), X), X), meet(meet(join(X, Y), X), join(join(join(meet(meet(X, meet(join(X, Y), X)), meet(join(X, Y), X)), meet(X, meet(join(X, Y), X))), meet(X, meet(join(X, Y), X))), meet(X, join(X, meet(join(X, Y), X))))))
% 0.20/0.45 = { by lemma 8 }
% 0.20/0.45 join(meet(meet(join(X, Y), X), X), meet(meet(join(X, Y), X), join(meet(X, meet(join(X, Y), X)), meet(X, join(X, meet(join(X, Y), X))))))
% 0.20/0.45 = { by axiom 3 (wal_absorbtion_1) }
% 0.20/0.45 join(meet(meet(join(X, Y), X), X), meet(meet(join(X, Y), X), X))
% 0.20/0.45 = { by lemma 9 }
% 0.20/0.45 meet(meet(join(X, Y), X), X)
% 0.20/0.45 = { by lemma 6 }
% 0.20/0.45 X
% 0.20/0.45
% 0.20/0.45 Lemma 12: meet(meet(X, join(Y, meet(Z, X))), meet(Z, X)) = meet(Z, X).
% 0.20/0.45 Proof:
% 0.20/0.45 meet(meet(X, join(Y, meet(Z, X))), meet(Z, X))
% 0.20/0.45 = { by axiom 4 (wal_absorbtion_3) R->L }
% 0.20/0.45 meet(meet(join(meet(Z, X), meet(X, join(Z, X))), join(Y, meet(Z, X))), meet(Z, X))
% 0.20/0.45 = { by axiom 1 (wal_absorbtion_4) }
% 0.20/0.45 meet(Z, X)
% 0.20/0.45
% 0.20/0.45 Lemma 13: meet(meet(X, Y), meet(Y, X)) = meet(Y, X).
% 0.20/0.45 Proof:
% 0.20/0.45 meet(meet(X, Y), meet(Y, X))
% 0.20/0.45 = { by lemma 10 R->L }
% 0.20/0.45 meet(meet(X, join(Y, meet(meet(Y, X), Y))), meet(Y, X))
% 0.20/0.45 = { by lemma 9 R->L }
% 0.20/0.45 meet(meet(X, join(Y, join(meet(meet(Y, X), Y), meet(meet(Y, X), Y)))), meet(Y, X))
% 0.20/0.46 = { by lemma 10 R->L }
% 0.20/0.46 meet(meet(X, join(Y, join(meet(meet(Y, X), Y), meet(meet(Y, X), join(Y, meet(join(meet(Y, X), Y), Y)))))), meet(Y, X))
% 0.20/0.46 = { by lemma 8 R->L }
% 0.20/0.46 meet(meet(X, join(Y, join(meet(meet(Y, X), Y), meet(meet(Y, X), join(Y, meet(join(meet(Y, X), Y), join(join(meet(Y, X), Y), Y))))))), meet(Y, X))
% 0.20/0.46 = { by axiom 1 (wal_absorbtion_4) R->L }
% 0.20/0.46 meet(meet(X, join(Y, join(meet(meet(Y, X), Y), meet(meet(Y, X), join(meet(meet(join(Y, join(Y, Y)), join(meet(Y, X), Y)), Y), meet(join(meet(Y, X), Y), join(join(meet(Y, X), Y), Y))))))), meet(Y, X))
% 0.20/0.46 = { by lemma 7 R->L }
% 0.20/0.46 meet(meet(X, join(Y, join(meet(meet(Y, X), Y), meet(meet(Y, X), join(meet(meet(join(meet(Y, Y), join(Y, Y)), join(meet(Y, X), Y)), Y), meet(join(meet(Y, X), Y), join(join(meet(Y, X), Y), Y))))))), meet(Y, X))
% 0.20/0.46 = { by axiom 1 (wal_absorbtion_4) R->L }
% 0.20/0.46 meet(meet(X, join(Y, join(meet(meet(Y, X), Y), meet(meet(Y, X), join(meet(meet(join(meet(Y, Y), meet(meet(join(join(Y, Y), Z), join(W, join(Y, Y))), join(Y, Y))), join(meet(Y, X), Y)), Y), meet(join(meet(Y, X), Y), join(join(meet(Y, X), Y), Y))))))), meet(Y, X))
% 0.20/0.46 = { by axiom 2 (wal_absorbtion_2) }
% 0.20/0.46 meet(meet(X, join(Y, join(meet(meet(Y, X), Y), meet(meet(Y, X), join(meet(meet(Y, join(meet(Y, X), Y)), Y), meet(join(meet(Y, X), Y), join(join(meet(Y, X), Y), Y))))))), meet(Y, X))
% 0.20/0.46 = { by lemma 8 R->L }
% 0.20/0.46 meet(meet(X, join(Y, join(meet(meet(Y, X), Y), meet(meet(Y, X), join(meet(meet(join(join(meet(Y, X), Y), Y), join(meet(Y, X), Y)), Y), meet(join(meet(Y, X), Y), join(join(meet(Y, X), Y), Y))))))), meet(Y, X))
% 0.20/0.46 = { by lemma 11 }
% 0.20/0.46 meet(meet(X, join(Y, join(meet(meet(Y, X), Y), meet(meet(Y, X), join(meet(join(meet(Y, X), Y), Y), meet(join(meet(Y, X), Y), join(join(meet(Y, X), Y), Y))))))), meet(Y, X))
% 0.20/0.46 = { by axiom 3 (wal_absorbtion_1) }
% 0.20/0.46 meet(meet(X, join(Y, join(meet(meet(Y, X), Y), meet(meet(Y, X), join(meet(Y, X), Y))))), meet(Y, X))
% 0.20/0.46 = { by axiom 3 (wal_absorbtion_1) }
% 0.20/0.46 meet(meet(X, join(Y, meet(Y, X))), meet(Y, X))
% 0.20/0.46 = { by lemma 12 }
% 0.20/0.46 meet(Y, X)
% 0.20/0.46
% 0.20/0.46 Goal 1 (prove_normal_axioms_2): meet(b, a) = meet(a, b).
% 0.20/0.46 Proof:
% 0.20/0.46 meet(b, a)
% 0.20/0.46 = { by axiom 3 (wal_absorbtion_1) R->L }
% 0.20/0.46 join(meet(meet(b, a), meet(a, b)), meet(meet(b, a), join(meet(b, a), meet(a, b))))
% 0.20/0.46 = { by axiom 3 (wal_absorbtion_1) R->L }
% 0.20/0.46 join(meet(meet(b, a), meet(a, b)), meet(meet(b, a), join(meet(join(meet(b, a), meet(a, b)), meet(a, b)), meet(join(meet(b, a), meet(a, b)), join(join(meet(b, a), meet(a, b)), meet(a, b))))))
% 0.20/0.46 = { by lemma 13 R->L }
% 0.20/0.46 join(meet(meet(b, a), meet(a, b)), meet(meet(b, a), join(meet(join(meet(b, a), meet(a, b)), meet(a, b)), meet(join(meet(b, a), meet(a, b)), join(join(meet(meet(a, b), meet(b, a)), meet(a, b)), meet(a, b))))))
% 0.20/0.46 = { by lemma 8 }
% 0.20/0.46 join(meet(meet(b, a), meet(a, b)), meet(meet(b, a), join(meet(join(meet(b, a), meet(a, b)), meet(a, b)), meet(join(meet(b, a), meet(a, b)), meet(a, b)))))
% 0.20/0.46 = { by lemma 9 }
% 0.20/0.46 join(meet(meet(b, a), meet(a, b)), meet(meet(b, a), meet(join(meet(b, a), meet(a, b)), meet(a, b))))
% 0.20/0.46 = { by lemma 11 R->L }
% 0.20/0.46 join(meet(meet(b, a), meet(a, b)), meet(meet(b, a), meet(meet(join(join(meet(b, a), meet(a, b)), b), join(meet(b, a), meet(a, b))), meet(a, b))))
% 0.20/0.46 = { by axiom 5 (wal_absorbtion_5) }
% 0.20/0.46 join(meet(meet(b, a), meet(a, b)), meet(meet(b, a), meet(meet(b, join(meet(b, a), meet(a, b))), meet(a, b))))
% 0.20/0.46 = { by lemma 12 }
% 0.20/0.46 join(meet(meet(b, a), meet(a, b)), meet(meet(b, a), meet(a, b)))
% 0.20/0.46 = { by lemma 9 }
% 0.20/0.46 meet(meet(b, a), meet(a, b))
% 0.20/0.46 = { by lemma 13 }
% 0.20/0.46 meet(a, b)
% 0.20/0.46 % SZS output end Proof
% 0.20/0.46
% 0.20/0.46 RESULT: Unsatisfiable (the axioms are contradictory).
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