TSTP Solution File: LAT013-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT013-1 : 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 : n024.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 0.19s 0.48s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT013-1 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.13 % 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 : n024.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 05:11:24 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.48 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.19/0.48
% 0.19/0.48 % SZS status Unsatisfiable
% 0.19/0.48
% 0.19/0.50 % SZS output start Proof
% 0.19/0.50 Axiom 1 (mckenzie1): join(X, meet(Y, meet(X, Z))) = X.
% 0.19/0.50 Axiom 2 (mckenzie2): meet(X, join(Y, join(X, Z))) = X.
% 0.19/0.50 Axiom 3 (mckenzie3): join(join(meet(X, Y), meet(Y, Z)), Y) = Y.
% 0.19/0.50 Axiom 4 (mckenzie4): meet(meet(join(X, Y), join(Y, Z)), Y) = Y.
% 0.19/0.50
% 0.19/0.50 Lemma 5: join(X, meet(X, Y)) = X.
% 0.19/0.50 Proof:
% 0.19/0.50 join(X, meet(X, Y))
% 0.19/0.50 = { by axiom 4 (mckenzie4) R->L }
% 0.19/0.50 join(X, meet(meet(join(Z, meet(X, Y)), join(meet(X, Y), W)), meet(X, Y)))
% 0.19/0.50 = { by axiom 1 (mckenzie1) }
% 0.19/0.50 X
% 0.19/0.50
% 0.19/0.50 Lemma 6: meet(meet(X, Y), X) = meet(X, Y).
% 0.19/0.50 Proof:
% 0.19/0.50 meet(meet(X, Y), X)
% 0.19/0.50 = { by lemma 5 R->L }
% 0.19/0.50 meet(meet(X, Y), join(X, meet(X, Y)))
% 0.19/0.50 = { by axiom 1 (mckenzie1) R->L }
% 0.19/0.50 meet(meet(X, Y), join(X, join(meet(X, Y), meet(Z, meet(meet(X, Y), W)))))
% 0.19/0.50 = { by axiom 2 (mckenzie2) }
% 0.19/0.50 meet(X, Y)
% 0.19/0.50
% 0.19/0.50 Lemma 7: join(meet(X, Y), Y) = Y.
% 0.19/0.50 Proof:
% 0.19/0.50 join(meet(X, Y), Y)
% 0.19/0.50 = { by axiom 1 (mckenzie1) R->L }
% 0.19/0.50 join(join(meet(X, Y), meet(Y, meet(meet(X, Y), Z))), Y)
% 0.19/0.50 = { by axiom 3 (mckenzie3) }
% 0.19/0.50 Y
% 0.19/0.50
% 0.19/0.50 Lemma 8: join(meet(X, Y), X) = X.
% 0.19/0.50 Proof:
% 0.19/0.50 join(meet(X, Y), X)
% 0.19/0.50 = { by lemma 6 R->L }
% 0.19/0.50 join(meet(meet(X, Y), X), X)
% 0.19/0.50 = { by lemma 7 }
% 0.19/0.50 X
% 0.19/0.50
% 0.19/0.50 Lemma 9: meet(meet(X, Y), meet(Y, X)) = meet(Y, X).
% 0.19/0.50 Proof:
% 0.19/0.50 meet(meet(X, Y), meet(Y, X))
% 0.19/0.50 = { by lemma 8 R->L }
% 0.19/0.50 meet(meet(X, join(meet(Y, X), Y)), meet(Y, X))
% 0.19/0.50 = { by axiom 1 (mckenzie1) R->L }
% 0.19/0.50 meet(meet(join(X, meet(Y, meet(X, join(Z, join(X, W))))), join(meet(Y, X), Y)), meet(Y, X))
% 0.19/0.50 = { by axiom 2 (mckenzie2) }
% 0.19/0.50 meet(meet(join(X, meet(Y, X)), join(meet(Y, X), Y)), meet(Y, X))
% 0.19/0.50 = { by axiom 4 (mckenzie4) }
% 0.19/0.50 meet(Y, X)
% 0.19/0.50
% 0.19/0.50 Lemma 10: meet(X, Y) = meet(Y, X).
% 0.19/0.50 Proof:
% 0.19/0.50 meet(X, Y)
% 0.19/0.50 = { by lemma 9 R->L }
% 0.19/0.50 meet(meet(Y, X), meet(X, Y))
% 0.19/0.50 = { by lemma 6 R->L }
% 0.19/0.50 meet(meet(meet(Y, X), meet(X, Y)), meet(Y, X))
% 0.19/0.50 = { by lemma 9 }
% 0.19/0.50 meet(meet(X, Y), meet(Y, X))
% 0.19/0.50 = { by lemma 9 }
% 0.19/0.50 meet(Y, X)
% 0.19/0.50
% 0.19/0.50 Lemma 11: meet(meet(X, Y), meet(X, meet(Z, Y))) = meet(X, meet(Z, Y)).
% 0.19/0.50 Proof:
% 0.19/0.50 meet(meet(X, Y), meet(X, meet(Z, Y)))
% 0.19/0.50 = { by lemma 10 R->L }
% 0.19/0.50 meet(meet(X, Y), meet(X, meet(Y, Z)))
% 0.19/0.50 = { by lemma 10 R->L }
% 0.19/0.50 meet(meet(X, Y), meet(meet(Y, Z), X))
% 0.19/0.50 = { by lemma 10 R->L }
% 0.19/0.50 meet(meet(meet(Y, Z), X), meet(X, Y))
% 0.19/0.50 = { by axiom 1 (mckenzie1) R->L }
% 0.19/0.50 meet(meet(meet(Y, Z), X), meet(X, join(Y, meet(meet(meet(Y, Z), X), meet(Y, Z)))))
% 0.19/0.50 = { by lemma 6 }
% 0.19/0.50 meet(meet(meet(Y, Z), X), meet(X, join(Y, meet(meet(Y, Z), X))))
% 0.19/0.50 = { by lemma 10 R->L }
% 0.19/0.50 meet(meet(meet(Y, Z), X), meet(join(Y, meet(meet(Y, Z), X)), X))
% 0.19/0.50 = { by lemma 10 R->L }
% 0.19/0.50 meet(meet(join(Y, meet(meet(Y, Z), X)), X), meet(meet(Y, Z), X))
% 0.19/0.50 = { by lemma 7 R->L }
% 0.19/0.50 meet(meet(join(Y, meet(meet(Y, Z), X)), join(meet(meet(Y, Z), X), X)), meet(meet(Y, Z), X))
% 0.19/0.50 = { by axiom 4 (mckenzie4) }
% 0.19/0.50 meet(meet(Y, Z), X)
% 0.19/0.50 = { by lemma 10 }
% 0.19/0.50 meet(X, meet(Y, Z))
% 0.19/0.50 = { by lemma 10 }
% 0.19/0.50 meet(X, meet(Z, Y))
% 0.19/0.50
% 0.19/0.50 Lemma 12: meet(meet(X, Y), meet(X, Z)) = meet(Z, meet(X, Y)).
% 0.19/0.50 Proof:
% 0.19/0.50 meet(meet(X, Y), meet(X, Z))
% 0.19/0.50 = { by lemma 11 R->L }
% 0.19/0.50 meet(meet(meet(X, Y), Z), meet(meet(X, Y), meet(X, Z)))
% 0.19/0.50 = { by lemma 10 R->L }
% 0.19/0.50 meet(meet(meet(X, Y), Z), meet(meet(X, Y), meet(Z, X)))
% 0.19/0.50 = { by lemma 8 R->L }
% 0.19/0.50 meet(meet(meet(X, Y), Z), meet(meet(X, Y), join(meet(meet(Z, X), meet(Z, meet(Y, X))), meet(Z, X))))
% 0.19/0.50 = { by lemma 11 }
% 0.19/0.50 meet(meet(meet(X, Y), Z), meet(meet(X, Y), join(meet(Z, meet(Y, X)), meet(Z, X))))
% 0.19/0.50 = { by lemma 10 }
% 0.19/0.50 meet(meet(meet(X, Y), Z), meet(meet(X, Y), join(meet(Z, meet(X, Y)), meet(Z, X))))
% 0.19/0.50 = { by lemma 10 }
% 0.19/0.50 meet(meet(meet(X, Y), Z), meet(meet(X, Y), join(meet(meet(X, Y), Z), meet(Z, X))))
% 0.19/0.50 = { by lemma 10 R->L }
% 0.19/0.50 meet(meet(meet(X, Y), join(meet(meet(X, Y), Z), meet(Z, X))), meet(meet(X, Y), Z))
% 0.19/0.50 = { by lemma 5 R->L }
% 0.19/0.50 meet(meet(join(meet(X, Y), meet(meet(X, Y), Z)), join(meet(meet(X, Y), Z), meet(Z, X))), meet(meet(X, Y), Z))
% 0.19/0.50 = { by axiom 4 (mckenzie4) }
% 0.19/0.50 meet(meet(X, Y), Z)
% 0.19/0.50 = { by lemma 10 }
% 0.19/0.50 meet(Z, meet(X, Y))
% 0.19/0.50
% 0.19/0.50 Goal 1 (prove_associativity_of_meet): meet(meet(a, b), c) = meet(a, meet(b, c)).
% 0.19/0.50 Proof:
% 0.19/0.50 meet(meet(a, b), c)
% 0.19/0.50 = { by lemma 10 }
% 0.19/0.50 meet(c, meet(a, b))
% 0.19/0.50 = { by lemma 10 R->L }
% 0.19/0.50 meet(c, meet(b, a))
% 0.19/0.50 = { by lemma 12 R->L }
% 0.19/0.50 meet(meet(b, a), meet(b, c))
% 0.19/0.50 = { by lemma 12 R->L }
% 0.19/0.50 meet(meet(b, c), meet(b, meet(b, a)))
% 0.19/0.50 = { by lemma 5 R->L }
% 0.19/0.50 meet(meet(b, c), meet(join(b, meet(b, a)), meet(b, a)))
% 0.19/0.50 = { by axiom 2 (mckenzie2) R->L }
% 0.19/0.50 meet(meet(b, c), meet(meet(join(b, meet(b, a)), join(meet(b, a), join(join(b, meet(b, a)), X))), meet(b, a)))
% 0.19/0.50 = { by axiom 4 (mckenzie4) }
% 0.19/0.50 meet(meet(b, c), meet(b, a))
% 0.19/0.50 = { by lemma 12 }
% 0.19/0.50 meet(a, meet(b, c))
% 0.19/0.50 % SZS output end Proof
% 0.19/0.50
% 0.19/0.50 RESULT: Unsatisfiable (the axioms are contradictory).
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