TSTP Solution File: LAT090-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT090-1 : 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 : n022.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 0.13s 0.38s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT090-1 : 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 : n022.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 09:33:26 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.38 Command-line arguments: --ground-connectedness --complete-subsets
% 0.13/0.38
% 0.13/0.38 % SZS status Unsatisfiable
% 0.13/0.38
% 0.13/0.38 % SZS output start Proof
% 0.13/0.38 Axiom 1 (wal_absorbtion_4): meet(meet(join(X, Y), join(Z, X)), X) = X.
% 0.13/0.38 Axiom 2 (wal_absorbtion_2): join(meet(X, X), meet(Y, join(X, X))) = X.
% 0.13/0.38 Axiom 3 (wal_absorbtion_1): join(meet(X, Y), meet(X, join(X, Y))) = X.
% 0.13/0.38 Axiom 4 (wal_absorbtion_5): join(join(meet(X, Y), meet(Z, X)), X) = X.
% 0.13/0.38
% 0.13/0.38 Lemma 5: meet(X, X) = X.
% 0.13/0.38 Proof:
% 0.13/0.38 meet(X, X)
% 0.13/0.38 = { by axiom 1 (wal_absorbtion_4) R->L }
% 0.13/0.38 meet(meet(meet(join(X, Y), join(Z, X)), X), X)
% 0.13/0.38 = { by axiom 1 (wal_absorbtion_4) R->L }
% 0.13/0.38 meet(meet(meet(join(X, Y), join(Z, X)), X), meet(meet(join(X, Y), join(Z, X)), X))
% 0.13/0.38 = { by axiom 1 (wal_absorbtion_4) R->L }
% 0.13/0.38 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))
% 0.13/0.38 = { by axiom 3 (wal_absorbtion_1) R->L }
% 0.13/0.38 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))
% 0.13/0.38 = { by axiom 4 (wal_absorbtion_5) R->L }
% 0.13/0.38 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))), join(join(meet(meet(meet(join(X, Y), join(Z, X)), X), W), meet(V, meet(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))
% 0.13/0.38 = { by axiom 1 (wal_absorbtion_4) }
% 0.13/0.38 meet(meet(join(X, Y), join(Z, X)), X)
% 0.13/0.38 = { by axiom 1 (wal_absorbtion_4) }
% 0.13/0.38 X
% 0.13/0.38
% 0.13/0.38 Lemma 6: join(X, join(X, X)) = X.
% 0.13/0.38 Proof:
% 0.13/0.38 join(X, join(X, X))
% 0.13/0.38 = { by lemma 5 R->L }
% 0.13/0.38 join(meet(X, X), join(X, X))
% 0.13/0.38 = { by axiom 1 (wal_absorbtion_4) R->L }
% 0.13/0.38 join(meet(X, X), meet(meet(join(join(X, X), Y), join(Z, join(X, X))), join(X, X)))
% 0.13/0.38 = { by axiom 2 (wal_absorbtion_2) }
% 0.13/0.38 X
% 0.13/0.38
% 0.13/0.38 Goal 1 (prove_normal_axioms_3): join(a, a) = a.
% 0.13/0.38 Proof:
% 0.13/0.38 join(a, a)
% 0.13/0.38 = { by axiom 4 (wal_absorbtion_5) R->L }
% 0.13/0.38 join(join(meet(join(a, a), a), meet(meet(join(join(a, a), X), join(Y, join(a, a))), join(a, a))), join(a, a))
% 0.13/0.38 = { by axiom 1 (wal_absorbtion_4) }
% 0.13/0.38 join(join(meet(join(a, a), a), join(a, a)), join(a, a))
% 0.13/0.38 = { by lemma 5 R->L }
% 0.13/0.38 join(join(meet(meet(join(a, a), join(a, a)), a), join(a, a)), join(a, a))
% 0.13/0.38 = { by axiom 1 (wal_absorbtion_4) }
% 0.13/0.38 join(join(a, join(a, a)), join(a, a))
% 0.13/0.38 = { by lemma 6 }
% 0.13/0.38 join(a, join(a, a))
% 0.13/0.38 = { by lemma 6 }
% 0.13/0.38 a
% 0.13/0.38 % SZS output end Proof
% 0.13/0.38
% 0.13/0.38 RESULT: Unsatisfiable (the axioms are contradictory).
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