TSTP Solution File: LAT147-1 by Twee---2.5.0
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%------------------------------------------------------------------------------
% File : Twee---2.5.0
% Problem : LAT147-1 : TPTP v8.2.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee /export/starexec/sandbox/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% Computer : n025.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 : Mon Jun 24 10:31:30 EDT 2024
% Result : Unsatisfiable 155.37s 19.90s
% Output : Proof 155.37s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT147-1 : TPTP v8.2.0. Released v3.1.0.
% 0.03/0.12 % Command : parallel-twee /export/starexec/sandbox/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% 0.12/0.32 % Computer : n025.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 21 20:33:24 EDT 2024
% 0.12/0.33 % CPUTime :
% 155.37/19.90 Command-line arguments: --no-flatten-goal
% 155.37/19.90
% 155.37/19.90 % SZS status Unsatisfiable
% 155.37/19.90
% 155.37/19.91 % SZS output start Proof
% 155.37/19.91 Axiom 1 (commutativity_of_join): join(X, Y) = join(Y, X).
% 155.37/19.91 Axiom 2 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 155.37/19.91 Axiom 3 (absorption2): join(X, meet(X, Y)) = X.
% 155.37/19.91 Axiom 4 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 155.37/19.91 Axiom 5 (absorption1): meet(X, join(X, Y)) = X.
% 155.37/19.91 Axiom 6 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 155.37/19.91 Axiom 7 (equation_H34): meet(X, join(Y, meet(Z, W))) = meet(X, join(Y, meet(Z, join(Y, meet(W, join(Y, Z)))))).
% 155.37/19.91
% 155.37/19.91 Lemma 8: meet(X, join(Y, X)) = X.
% 155.37/19.91 Proof:
% 155.37/19.91 meet(X, join(Y, X))
% 155.37/19.91 = { by axiom 1 (commutativity_of_join) R->L }
% 155.37/19.91 meet(X, join(X, Y))
% 155.37/19.91 = { by axiom 5 (absorption1) }
% 155.37/19.91 X
% 155.37/19.91
% 155.37/19.91 Lemma 9: meet(Y, meet(X, Z)) = meet(X, meet(Y, Z)).
% 155.37/19.91 Proof:
% 155.37/19.91 meet(Y, meet(X, Z))
% 155.37/19.91 = { by axiom 2 (commutativity_of_meet) R->L }
% 155.37/19.91 meet(meet(X, Z), Y)
% 155.37/19.91 = { by axiom 6 (associativity_of_meet) }
% 155.37/19.91 meet(X, meet(Z, Y))
% 155.37/19.91 = { by axiom 2 (commutativity_of_meet) }
% 155.37/19.91 meet(X, meet(Y, Z))
% 155.37/19.91
% 155.37/19.91 Goal 1 (prove_H45): meet(a, meet(b, join(c, meet(a, d)))) = meet(a, meet(b, join(c, meet(d, join(a, meet(b, c)))))).
% 155.37/19.91 Proof:
% 155.37/19.91 meet(a, meet(b, join(c, meet(a, d))))
% 155.37/19.91 = { by lemma 9 R->L }
% 155.37/19.91 meet(b, meet(a, join(c, meet(a, d))))
% 155.37/19.91 = { by axiom 5 (absorption1) R->L }
% 155.37/19.91 meet(b, meet(a, join(c, meet(meet(a, join(a, meet(c, b))), d))))
% 155.37/19.91 = { by axiom 6 (associativity_of_meet) }
% 155.37/19.91 meet(b, meet(a, join(c, meet(a, meet(join(a, meet(c, b)), d)))))
% 155.37/19.91 = { by axiom 2 (commutativity_of_meet) }
% 155.37/19.91 meet(b, meet(a, join(c, meet(a, meet(d, join(a, meet(c, b)))))))
% 155.37/19.91 = { by axiom 7 (equation_H34) }
% 155.37/19.91 meet(b, meet(a, join(c, meet(a, join(c, meet(meet(d, join(a, meet(c, b))), join(c, a)))))))
% 155.37/19.91 = { by axiom 1 (commutativity_of_join) R->L }
% 155.37/19.91 meet(b, meet(a, join(c, meet(a, join(meet(meet(d, join(a, meet(c, b))), join(c, a)), c)))))
% 155.37/19.91 = { by lemma 8 R->L }
% 155.37/19.91 meet(b, meet(a, meet(join(c, meet(a, join(meet(meet(d, join(a, meet(c, b))), join(c, a)), c))), join(meet(meet(d, join(a, meet(c, b))), join(c, a)), join(c, meet(a, join(meet(meet(d, join(a, meet(c, b))), join(c, a)), c)))))))
% 155.37/19.91 = { by axiom 2 (commutativity_of_meet) R->L }
% 155.37/19.91 meet(b, meet(a, meet(join(c, meet(a, join(meet(meet(d, join(a, meet(c, b))), join(c, a)), c))), join(meet(meet(d, join(a, meet(c, b))), join(c, a)), join(c, meet(join(meet(meet(d, join(a, meet(c, b))), join(c, a)), c), a))))))
% 155.37/19.91 = { by axiom 4 (associativity_of_join) R->L }
% 155.37/19.91 meet(b, meet(a, meet(join(c, meet(a, join(meet(meet(d, join(a, meet(c, b))), join(c, a)), c))), join(join(meet(meet(d, join(a, meet(c, b))), join(c, a)), c), meet(join(meet(meet(d, join(a, meet(c, b))), join(c, a)), c), a)))))
% 155.37/19.91 = { by axiom 3 (absorption2) }
% 155.37/19.91 meet(b, meet(a, meet(join(c, meet(a, join(meet(meet(d, join(a, meet(c, b))), join(c, a)), c))), join(meet(meet(d, join(a, meet(c, b))), join(c, a)), c))))
% 155.37/19.91 = { by axiom 2 (commutativity_of_meet) }
% 155.37/19.91 meet(b, meet(a, meet(join(meet(meet(d, join(a, meet(c, b))), join(c, a)), c), join(c, meet(a, join(meet(meet(d, join(a, meet(c, b))), join(c, a)), c))))))
% 155.37/19.91 = { by axiom 1 (commutativity_of_join) }
% 155.37/19.91 meet(b, meet(a, meet(join(meet(meet(d, join(a, meet(c, b))), join(c, a)), c), join(c, meet(a, join(c, meet(meet(d, join(a, meet(c, b))), join(c, a))))))))
% 155.37/19.91 = { by axiom 1 (commutativity_of_join) }
% 155.37/19.91 meet(b, meet(a, meet(join(c, meet(meet(d, join(a, meet(c, b))), join(c, a))), join(c, meet(a, join(c, meet(meet(d, join(a, meet(c, b))), join(c, a))))))))
% 155.37/19.91 = { by axiom 1 (commutativity_of_join) R->L }
% 155.37/19.91 meet(b, meet(a, meet(join(c, meet(meet(d, join(a, meet(c, b))), join(c, a))), join(meet(a, join(c, meet(meet(d, join(a, meet(c, b))), join(c, a)))), c))))
% 155.37/19.91 = { by axiom 6 (associativity_of_meet) R->L }
% 155.37/19.91 meet(b, meet(meet(a, join(c, meet(meet(d, join(a, meet(c, b))), join(c, a)))), join(meet(a, join(c, meet(meet(d, join(a, meet(c, b))), join(c, a)))), c)))
% 155.37/19.91 = { by axiom 5 (absorption1) }
% 155.37/19.91 meet(b, meet(a, join(c, meet(meet(d, join(a, meet(c, b))), join(c, a)))))
% 155.37/19.91 = { by axiom 1 (commutativity_of_join) }
% 155.37/19.91 meet(b, meet(a, join(c, meet(meet(d, join(a, meet(c, b))), join(a, c)))))
% 155.37/19.91 = { by axiom 2 (commutativity_of_meet) }
% 155.37/19.91 meet(b, meet(a, join(c, meet(join(a, c), meet(d, join(a, meet(c, b)))))))
% 155.37/19.91 = { by axiom 2 (commutativity_of_meet) R->L }
% 155.37/19.91 meet(b, meet(a, join(c, meet(join(a, c), meet(join(a, meet(c, b)), d)))))
% 155.37/19.91 = { by axiom 6 (associativity_of_meet) R->L }
% 155.37/19.91 meet(b, meet(a, join(c, meet(meet(join(a, c), join(a, meet(c, b))), d))))
% 155.37/19.91 = { by axiom 1 (commutativity_of_join) R->L }
% 155.37/19.91 meet(b, meet(a, join(c, meet(meet(join(c, a), join(a, meet(c, b))), d))))
% 155.37/19.91 = { by axiom 2 (commutativity_of_meet) R->L }
% 155.37/19.91 meet(b, meet(a, join(c, meet(meet(join(a, meet(c, b)), join(c, a)), d))))
% 155.37/19.91 = { by axiom 3 (absorption2) R->L }
% 155.37/19.91 meet(b, meet(a, join(c, meet(meet(join(a, meet(c, b)), join(join(c, meet(c, b)), a)), d))))
% 155.37/19.91 = { by axiom 4 (associativity_of_join) }
% 155.37/19.91 meet(b, meet(a, join(c, meet(meet(join(a, meet(c, b)), join(c, join(meet(c, b), a))), d))))
% 155.37/19.91 = { by axiom 1 (commutativity_of_join) }
% 155.37/19.91 meet(b, meet(a, join(c, meet(meet(join(a, meet(c, b)), join(c, join(a, meet(c, b)))), d))))
% 155.37/19.91 = { by lemma 8 }
% 155.37/19.91 meet(b, meet(a, join(c, meet(join(a, meet(c, b)), d))))
% 155.37/19.91 = { by axiom 2 (commutativity_of_meet) }
% 155.37/19.91 meet(b, meet(a, join(c, meet(d, join(a, meet(c, b))))))
% 155.37/19.91 = { by axiom 2 (commutativity_of_meet) }
% 155.37/19.92 meet(b, meet(a, join(c, meet(d, join(a, meet(b, c))))))
% 155.37/19.92 = { by lemma 9 }
% 155.37/19.92 meet(a, meet(b, join(c, meet(d, join(a, meet(b, c))))))
% 155.37/19.92 % SZS output end Proof
% 155.37/19.92
% 155.37/19.92 RESULT: Unsatisfiable (the axioms are contradictory).
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