TSTP Solution File: LAT006-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT006-1 : 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 : n026.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 06:27:05 EDT 2023
% Result : Unsatisfiable 0.21s 0.47s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT006-1 : 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
% 0.18/0.34 % Computer : n026.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Thu Aug 24 09:05:31 EDT 2023
% 0.18/0.35 % CPUTime :
% 0.21/0.47 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.21/0.47
% 0.21/0.47 % SZS status Unsatisfiable
% 0.21/0.47
% 0.21/0.49 % SZS output start Proof
% 0.21/0.49 Axiom 1 (absorption): meet(X, join(X, Y)) = X.
% 0.21/0.49 Axiom 2 (distribution): meet(X, join(Y, Z)) = join(meet(Z, X), meet(Y, X)).
% 0.21/0.49
% 0.21/0.49 Lemma 3: meet(meet(X, Y), Y) = meet(X, Y).
% 0.21/0.49 Proof:
% 0.21/0.49 meet(meet(X, Y), Y)
% 0.21/0.49 = { by axiom 1 (absorption) R->L }
% 0.21/0.49 meet(meet(X, Y), meet(Y, join(Y, X)))
% 0.21/0.49 = { by axiom 2 (distribution) }
% 0.21/0.49 meet(meet(X, Y), join(meet(X, Y), meet(Y, Y)))
% 0.21/0.49 = { by axiom 1 (absorption) }
% 0.21/0.49 meet(X, Y)
% 0.21/0.49
% 0.21/0.49 Lemma 4: meet(X, join(meet(Y, X), Z)) = meet(X, join(Y, Z)).
% 0.21/0.49 Proof:
% 0.21/0.49 meet(X, join(meet(Y, X), Z))
% 0.21/0.49 = { by axiom 2 (distribution) }
% 0.21/0.49 join(meet(Z, X), meet(meet(Y, X), X))
% 0.21/0.49 = { by lemma 3 }
% 0.21/0.49 join(meet(Z, X), meet(Y, X))
% 0.21/0.49 = { by axiom 2 (distribution) R->L }
% 0.21/0.49 meet(X, join(Y, Z))
% 0.21/0.49
% 0.21/0.49 Lemma 5: meet(X, meet(X, join(Y, Z))) = meet(X, join(Z, Y)).
% 0.21/0.49 Proof:
% 0.21/0.49 meet(X, meet(X, join(Y, Z)))
% 0.21/0.49 = { by axiom 2 (distribution) }
% 0.21/0.49 meet(X, join(meet(Z, X), meet(Y, X)))
% 0.21/0.49 = { by lemma 4 }
% 0.21/0.49 meet(X, join(Z, meet(Y, X)))
% 0.21/0.49 = { by axiom 2 (distribution) }
% 0.21/0.49 join(meet(meet(Y, X), X), meet(Z, X))
% 0.21/0.49 = { by lemma 3 }
% 0.21/0.49 join(meet(Y, X), meet(Z, X))
% 0.21/0.49 = { by axiom 2 (distribution) R->L }
% 0.21/0.49 meet(X, join(Z, Y))
% 0.21/0.49
% 0.21/0.49 Lemma 6: meet(X, join(Y, X)) = meet(X, X).
% 0.21/0.49 Proof:
% 0.21/0.49 meet(X, join(Y, X))
% 0.21/0.49 = { by lemma 5 R->L }
% 0.21/0.49 meet(X, meet(X, join(X, Y)))
% 0.21/0.49 = { by axiom 1 (absorption) }
% 0.21/0.49 meet(X, X)
% 0.21/0.49
% 0.21/0.49 Lemma 7: meet(X, X) = X.
% 0.21/0.49 Proof:
% 0.21/0.49 meet(X, X)
% 0.21/0.49 = { by lemma 6 R->L }
% 0.21/0.49 meet(X, join(X, X))
% 0.21/0.49 = { by axiom 1 (absorption) }
% 0.21/0.49 X
% 0.21/0.49
% 0.21/0.49 Lemma 8: join(X, X) = X.
% 0.21/0.49 Proof:
% 0.21/0.49 join(X, X)
% 0.21/0.49 = { by lemma 7 R->L }
% 0.21/0.49 join(X, meet(X, X))
% 0.21/0.49 = { by lemma 7 R->L }
% 0.21/0.49 join(meet(X, X), meet(X, X))
% 0.21/0.49 = { by axiom 2 (distribution) R->L }
% 0.21/0.49 meet(X, join(X, X))
% 0.21/0.49 = { by lemma 6 }
% 0.21/0.49 meet(X, X)
% 0.21/0.49 = { by lemma 7 }
% 0.21/0.49 X
% 0.21/0.49
% 0.21/0.49 Lemma 9: join(Y, X) = join(X, Y).
% 0.21/0.49 Proof:
% 0.21/0.49 join(Y, X)
% 0.21/0.49 = { by lemma 7 R->L }
% 0.21/0.49 meet(join(Y, X), join(Y, X))
% 0.21/0.49 = { by axiom 2 (distribution) }
% 0.21/0.49 join(meet(X, join(Y, X)), meet(Y, join(Y, X)))
% 0.21/0.49 = { by axiom 1 (absorption) }
% 0.21/0.49 join(meet(X, join(Y, X)), Y)
% 0.21/0.49 = { by lemma 6 }
% 0.21/0.49 join(meet(X, X), Y)
% 0.21/0.49 = { by lemma 7 }
% 0.21/0.49 join(X, Y)
% 0.21/0.49
% 0.21/0.49 Lemma 10: meet(Y, X) = meet(X, Y).
% 0.21/0.49 Proof:
% 0.21/0.49 meet(Y, X)
% 0.21/0.49 = { by lemma 8 R->L }
% 0.21/0.49 join(meet(Y, X), meet(Y, X))
% 0.21/0.49 = { by axiom 2 (distribution) R->L }
% 0.21/0.49 meet(X, join(Y, Y))
% 0.21/0.49 = { by lemma 8 }
% 0.21/0.49 meet(X, Y)
% 0.21/0.49
% 0.21/0.49 Lemma 11: join(meet(X, Y), Y) = Y.
% 0.21/0.49 Proof:
% 0.21/0.49 join(meet(X, Y), Y)
% 0.21/0.49 = { by lemma 7 R->L }
% 0.21/0.49 join(meet(X, Y), meet(Y, Y))
% 0.21/0.49 = { by axiom 2 (distribution) R->L }
% 0.21/0.49 meet(Y, join(Y, X))
% 0.21/0.49 = { by axiom 1 (absorption) }
% 0.21/0.49 Y
% 0.21/0.49
% 0.21/0.49 Lemma 12: meet(meet(X, Y), meet(Y, Z)) = meet(X, meet(Y, Z)).
% 0.21/0.49 Proof:
% 0.21/0.49 meet(meet(X, Y), meet(Y, Z))
% 0.21/0.49 = { by lemma 10 }
% 0.21/0.49 meet(meet(X, Y), meet(Z, Y))
% 0.21/0.49 = { by lemma 10 }
% 0.21/0.49 meet(meet(Z, Y), meet(X, Y))
% 0.21/0.49 = { by lemma 11 R->L }
% 0.21/0.49 meet(meet(Z, Y), meet(X, join(meet(Z, Y), Y)))
% 0.21/0.49 = { by axiom 2 (distribution) }
% 0.21/0.49 meet(meet(Z, Y), join(meet(Y, X), meet(meet(Z, Y), X)))
% 0.21/0.49 = { by lemma 11 R->L }
% 0.21/0.49 meet(meet(Z, Y), join(meet(Y, X), meet(meet(Z, Y), join(meet(Y, X), X))))
% 0.21/0.49 = { by lemma 4 R->L }
% 0.21/0.49 meet(meet(Z, Y), join(meet(meet(Y, X), meet(Z, Y)), meet(meet(Z, Y), join(meet(Y, X), X))))
% 0.21/0.49 = { by lemma 9 }
% 0.21/0.49 meet(meet(Z, Y), join(meet(meet(Y, X), meet(Z, Y)), meet(meet(Z, Y), join(X, meet(Y, X)))))
% 0.21/0.49 = { by axiom 2 (distribution) }
% 0.21/0.49 meet(meet(Z, Y), join(meet(meet(Y, X), meet(Z, Y)), join(meet(meet(Y, X), meet(Z, Y)), meet(X, meet(Z, Y)))))
% 0.21/0.49 = { by lemma 7 R->L }
% 0.21/0.49 meet(meet(Z, Y), join(meet(meet(Y, X), meet(Z, Y)), meet(join(meet(meet(Y, X), meet(Z, Y)), meet(X, meet(Z, Y))), join(meet(meet(Y, X), meet(Z, Y)), meet(X, meet(Z, Y))))))
% 0.21/0.49 = { by axiom 1 (absorption) R->L }
% 0.21/0.49 meet(meet(Z, Y), join(meet(meet(meet(Y, X), meet(Z, Y)), join(meet(meet(Y, X), meet(Z, Y)), meet(X, meet(Z, Y)))), meet(join(meet(meet(Y, X), meet(Z, Y)), meet(X, meet(Z, Y))), join(meet(meet(Y, X), meet(Z, Y)), meet(X, meet(Z, Y))))))
% 0.21/0.49 = { by axiom 2 (distribution) R->L }
% 0.21/0.49 meet(meet(Z, Y), meet(join(meet(meet(Y, X), meet(Z, Y)), meet(X, meet(Z, Y))), join(join(meet(meet(Y, X), meet(Z, Y)), meet(X, meet(Z, Y))), meet(meet(Y, X), meet(Z, Y)))))
% 0.21/0.49 = { by axiom 1 (absorption) }
% 0.21/0.49 meet(meet(Z, Y), join(meet(meet(Y, X), meet(Z, Y)), meet(X, meet(Z, Y))))
% 0.21/0.49 = { by axiom 2 (distribution) R->L }
% 0.21/0.49 meet(meet(Z, Y), meet(meet(Z, Y), join(X, meet(Y, X))))
% 0.21/0.49 = { by lemma 9 R->L }
% 0.21/0.49 meet(meet(Z, Y), meet(meet(Z, Y), join(meet(Y, X), X)))
% 0.21/0.49 = { by lemma 5 }
% 0.21/0.49 meet(meet(Z, Y), join(X, meet(Y, X)))
% 0.21/0.49 = { by lemma 9 R->L }
% 0.21/0.49 meet(meet(Z, Y), join(meet(Y, X), X))
% 0.21/0.49 = { by lemma 11 }
% 0.21/0.49 meet(meet(Z, Y), X)
% 0.21/0.49 = { by lemma 10 R->L }
% 0.21/0.49 meet(X, meet(Z, Y))
% 0.21/0.49 = { by lemma 10 R->L }
% 0.21/0.49 meet(X, meet(Y, Z))
% 0.21/0.49
% 0.21/0.49 Goal 1 (prove_associativity_of_meet): meet(meet(a, b), c) = meet(a, meet(b, c)).
% 0.21/0.49 Proof:
% 0.21/0.49 meet(meet(a, b), c)
% 0.21/0.49 = { by lemma 10 R->L }
% 0.21/0.49 meet(c, meet(a, b))
% 0.21/0.49 = { by lemma 10 }
% 0.21/0.49 meet(c, meet(b, a))
% 0.21/0.49 = { by lemma 12 R->L }
% 0.21/0.49 meet(meet(c, b), meet(b, a))
% 0.21/0.49 = { by lemma 10 R->L }
% 0.21/0.49 meet(meet(b, c), meet(b, a))
% 0.21/0.49 = { by lemma 10 R->L }
% 0.21/0.49 meet(meet(b, c), meet(a, b))
% 0.21/0.49 = { by lemma 10 }
% 0.21/0.49 meet(meet(a, b), meet(b, c))
% 0.21/0.49 = { by lemma 12 }
% 0.21/0.49 meet(a, meet(b, c))
% 0.21/0.49 % SZS output end Proof
% 0.21/0.49
% 0.21/0.49 RESULT: Unsatisfiable (the axioms are contradictory).
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