TSTP Solution File: LAT008-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT008-1 : 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 : n019.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 06:27:06 EDT 2023
% Result : Unsatisfiable 0.20s 0.39s
% Output : Proof 0.20s
% 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 : LAT008-1 : 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
% 0.13/0.35 % Computer : n019.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % 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 09:02:29 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.39 Command-line arguments: --no-flatten-goal
% 0.20/0.39
% 0.20/0.39 % SZS status Unsatisfiable
% 0.20/0.40
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 Axiom 1 (absorption): meet(X, join(X, Y)) = X.
% 0.20/0.41 Axiom 2 (distribution): meet(X, join(Y, Z)) = join(meet(Z, X), meet(Y, X)).
% 0.20/0.41
% 0.20/0.41 Lemma 3: meet(meet(X, Y), Y) = meet(X, Y).
% 0.20/0.41 Proof:
% 0.20/0.41 meet(meet(X, Y), Y)
% 0.20/0.41 = { by axiom 1 (absorption) R->L }
% 0.20/0.41 meet(meet(X, Y), meet(Y, join(Y, X)))
% 0.20/0.41 = { by axiom 2 (distribution) }
% 0.20/0.41 meet(meet(X, Y), join(meet(X, Y), meet(Y, Y)))
% 0.20/0.41 = { by axiom 1 (absorption) }
% 0.20/0.41 meet(X, Y)
% 0.20/0.41
% 0.20/0.41 Lemma 4: meet(X, join(Y, X)) = meet(X, X).
% 0.20/0.41 Proof:
% 0.20/0.41 meet(X, join(Y, X))
% 0.20/0.41 = { by axiom 2 (distribution) }
% 0.20/0.41 join(meet(X, X), meet(Y, X))
% 0.20/0.41 = { by lemma 3 R->L }
% 0.20/0.41 join(meet(meet(X, X), X), meet(Y, X))
% 0.20/0.41 = { by lemma 3 R->L }
% 0.20/0.41 join(meet(meet(X, X), X), meet(meet(Y, X), X))
% 0.20/0.41 = { by axiom 2 (distribution) R->L }
% 0.20/0.41 meet(X, join(meet(Y, X), meet(X, X)))
% 0.20/0.41 = { by axiom 2 (distribution) R->L }
% 0.20/0.41 meet(X, meet(X, join(X, Y)))
% 0.20/0.41 = { by axiom 1 (absorption) }
% 0.20/0.41 meet(X, X)
% 0.20/0.41
% 0.20/0.41 Lemma 5: meet(X, X) = X.
% 0.20/0.41 Proof:
% 0.20/0.41 meet(X, X)
% 0.20/0.41 = { by lemma 4 R->L }
% 0.20/0.41 meet(X, join(X, X))
% 0.20/0.41 = { by axiom 1 (absorption) }
% 0.20/0.41 X
% 0.20/0.41
% 0.20/0.41 Lemma 6: join(X, meet(Y, X)) = X.
% 0.20/0.41 Proof:
% 0.20/0.41 join(X, meet(Y, X))
% 0.20/0.41 = { by lemma 5 R->L }
% 0.20/0.41 join(meet(X, X), meet(Y, X))
% 0.20/0.41 = { by axiom 2 (distribution) R->L }
% 0.20/0.41 meet(X, join(Y, X))
% 0.20/0.41 = { by lemma 4 }
% 0.20/0.41 meet(X, X)
% 0.20/0.41 = { by lemma 5 }
% 0.20/0.41 X
% 0.20/0.41
% 0.20/0.41 Lemma 7: join(X, X) = X.
% 0.20/0.41 Proof:
% 0.20/0.41 join(X, X)
% 0.20/0.41 = { by axiom 1 (absorption) R->L }
% 0.20/0.41 join(X, meet(X, join(X, meet(Y, X))))
% 0.20/0.41 = { by lemma 6 R->L }
% 0.20/0.41 join(X, meet(join(X, meet(Y, X)), join(X, meet(Y, X))))
% 0.20/0.41 = { by axiom 1 (absorption) R->L }
% 0.20/0.41 join(meet(X, join(X, meet(Y, X))), meet(join(X, meet(Y, X)), join(X, meet(Y, X))))
% 0.20/0.41 = { by axiom 2 (distribution) R->L }
% 0.20/0.41 meet(join(X, meet(Y, X)), join(join(X, meet(Y, X)), X))
% 0.20/0.41 = { by axiom 1 (absorption) }
% 0.20/0.41 join(X, meet(Y, X))
% 0.20/0.41 = { by lemma 6 }
% 0.20/0.41 X
% 0.20/0.41
% 0.20/0.41 Goal 1 (prove_absorbtion_dual): join(a, meet(a, b)) = a.
% 0.20/0.41 Proof:
% 0.20/0.41 join(a, meet(a, b))
% 0.20/0.41 = { by lemma 7 R->L }
% 0.20/0.41 join(a, meet(a, join(b, b)))
% 0.20/0.41 = { by axiom 2 (distribution) }
% 0.20/0.41 join(a, join(meet(b, a), meet(b, a)))
% 0.20/0.41 = { by lemma 7 }
% 0.20/0.41 join(a, meet(b, a))
% 0.20/0.41 = { by lemma 6 }
% 0.20/0.41 a
% 0.20/0.41 % SZS output end Proof
% 0.20/0.41
% 0.20/0.41 RESULT: Unsatisfiable (the axioms are contradictory).
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