TSTP Solution File: LAT159-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT159-1 : TPTP v8.1.2. Released v3.1.0.
% 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 : n008.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 06:27:36 EDT 2023
% Result : Unsatisfiable 29.77s 4.20s
% Output : Proof 29.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT159-1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Aug 24 10:13:17 EDT 2023
% 0.12/0.34 % CPUTime :
% 29.77/4.20 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 29.77/4.20
% 29.77/4.20 % SZS status Unsatisfiable
% 29.77/4.20
% 29.77/4.21 % SZS output start Proof
% 29.77/4.21 Axiom 1 (idempotence_of_join): join(X, X) = X.
% 29.77/4.21 Axiom 2 (commutativity_of_join): join(X, Y) = join(Y, X).
% 29.77/4.21 Axiom 3 (idempotence_of_meet): meet(X, X) = X.
% 29.77/4.21 Axiom 4 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 29.77/4.21 Axiom 5 (absorption2): join(X, meet(X, Y)) = X.
% 29.77/4.21 Axiom 6 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 29.77/4.21 Axiom 7 (absorption1): meet(X, join(X, Y)) = X.
% 29.77/4.21 Axiom 8 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 29.77/4.21 Axiom 9 (equation_H50): meet(X, join(Y, meet(Z, join(X, W)))) = meet(X, join(Y, meet(Z, join(X, meet(Z, join(Y, W)))))).
% 29.77/4.21
% 29.77/4.21 Lemma 10: join(X, meet(Y, X)) = X.
% 29.77/4.21 Proof:
% 29.77/4.21 join(X, meet(Y, X))
% 29.77/4.21 = { by axiom 4 (commutativity_of_meet) R->L }
% 29.77/4.21 join(X, meet(X, Y))
% 29.77/4.21 = { by axiom 5 (absorption2) }
% 29.77/4.21 X
% 29.77/4.21
% 29.77/4.21 Lemma 11: join(X, join(meet(X, Y), Z)) = join(X, Z).
% 29.77/4.21 Proof:
% 29.77/4.21 join(X, join(meet(X, Y), Z))
% 29.77/4.21 = { by axiom 6 (associativity_of_join) R->L }
% 29.77/4.21 join(join(X, meet(X, Y)), Z)
% 29.77/4.21 = { by axiom 5 (absorption2) }
% 29.77/4.21 join(X, Z)
% 29.77/4.21
% 29.77/4.21 Lemma 12: meet(X, join(Y, meet(join(X, Y), Z))) = meet(X, join(Y, meet(X, Z))).
% 29.77/4.21 Proof:
% 29.77/4.21 meet(X, join(Y, meet(join(X, Y), Z)))
% 29.77/4.21 = { by axiom 4 (commutativity_of_meet) R->L }
% 29.77/4.21 meet(X, join(Y, meet(Z, join(X, Y))))
% 29.77/4.21 = { by axiom 9 (equation_H50) }
% 29.77/4.21 meet(X, join(Y, meet(Z, join(X, meet(Z, join(Y, Y))))))
% 29.77/4.21 = { by axiom 1 (idempotence_of_join) }
% 29.77/4.21 meet(X, join(Y, meet(Z, join(X, meet(Z, Y)))))
% 29.77/4.21 = { by axiom 5 (absorption2) R->L }
% 29.77/4.21 meet(X, join(Y, meet(Z, join(X, meet(Z, join(Y, meet(Y, X)))))))
% 29.77/4.21 = { by axiom 9 (equation_H50) R->L }
% 29.77/4.21 meet(X, join(Y, meet(Z, join(X, meet(Y, X)))))
% 29.77/4.21 = { by lemma 10 }
% 29.77/4.21 meet(X, join(Y, meet(Z, X)))
% 29.77/4.21 = { by axiom 4 (commutativity_of_meet) }
% 29.77/4.21 meet(X, join(Y, meet(X, Z)))
% 29.77/4.21
% 29.77/4.21 Goal 1 (prove_H7): meet(a, join(b, meet(a, c))) = meet(a, join(b, meet(a, join(meet(a, b), meet(c, join(a, b)))))).
% 29.77/4.21 Proof:
% 29.77/4.21 meet(a, join(b, meet(a, c)))
% 29.77/4.21 = { by lemma 12 R->L }
% 29.77/4.21 meet(a, join(b, meet(join(a, b), c)))
% 29.77/4.21 = { by lemma 11 R->L }
% 29.77/4.21 meet(a, join(b, join(meet(b, a), meet(join(a, b), c))))
% 29.77/4.21 = { by axiom 5 (absorption2) R->L }
% 29.77/4.21 meet(a, join(b, join(join(meet(b, a), meet(join(a, b), c)), meet(join(meet(b, a), meet(join(a, b), c)), join(a, b)))))
% 29.77/4.21 = { by axiom 6 (associativity_of_join) }
% 29.77/4.21 meet(a, join(b, join(meet(b, a), join(meet(join(a, b), c), meet(join(meet(b, a), meet(join(a, b), c)), join(a, b))))))
% 29.77/4.21 = { by axiom 4 (commutativity_of_meet) }
% 29.77/4.21 meet(a, join(b, join(meet(b, a), join(meet(join(a, b), c), meet(join(a, b), join(meet(b, a), meet(join(a, b), c)))))))
% 29.77/4.21 = { by axiom 2 (commutativity_of_join) R->L }
% 29.77/4.21 meet(a, join(b, join(meet(b, a), join(meet(join(a, b), c), meet(join(a, b), join(meet(join(a, b), c), meet(b, a)))))))
% 29.77/4.21 = { by axiom 3 (idempotence_of_meet) R->L }
% 29.77/4.21 meet(a, join(b, join(meet(b, a), join(meet(meet(join(a, b), join(a, b)), c), meet(join(a, b), join(meet(join(a, b), c), meet(b, a)))))))
% 29.77/4.21 = { by axiom 8 (associativity_of_meet) }
% 29.77/4.21 meet(a, join(b, join(meet(b, a), join(meet(join(a, b), meet(join(a, b), c)), meet(join(a, b), join(meet(join(a, b), c), meet(b, a)))))))
% 29.77/4.21 = { by axiom 4 (commutativity_of_meet) R->L }
% 29.77/4.21 meet(a, join(b, join(meet(b, a), join(meet(meet(join(a, b), c), join(a, b)), meet(join(a, b), join(meet(join(a, b), c), meet(b, a)))))))
% 29.77/4.21 = { by axiom 2 (commutativity_of_join) R->L }
% 29.77/4.21 meet(a, join(b, join(meet(b, a), join(meet(join(a, b), join(meet(join(a, b), c), meet(b, a))), meet(meet(join(a, b), c), join(a, b))))))
% 29.77/4.21 = { by axiom 7 (absorption1) R->L }
% 29.77/4.21 meet(a, join(b, join(meet(b, a), join(meet(join(a, b), join(meet(join(a, b), c), meet(b, a))), meet(meet(meet(join(a, b), c), join(meet(join(a, b), c), meet(b, a))), join(a, b))))))
% 29.77/4.21 = { by axiom 8 (associativity_of_meet) }
% 29.77/4.21 meet(a, join(b, join(meet(b, a), join(meet(join(a, b), join(meet(join(a, b), c), meet(b, a))), meet(meet(join(a, b), c), meet(join(meet(join(a, b), c), meet(b, a)), join(a, b)))))))
% 29.77/4.21 = { by axiom 4 (commutativity_of_meet) }
% 29.77/4.21 meet(a, join(b, join(meet(b, a), join(meet(join(a, b), join(meet(join(a, b), c), meet(b, a))), meet(meet(join(a, b), c), meet(join(a, b), join(meet(join(a, b), c), meet(b, a))))))))
% 29.77/4.21 = { by lemma 10 }
% 29.77/4.21 meet(a, join(b, join(meet(b, a), meet(join(a, b), join(meet(join(a, b), c), meet(b, a))))))
% 29.77/4.21 = { by axiom 2 (commutativity_of_join) }
% 29.77/4.21 meet(a, join(b, join(meet(b, a), meet(join(a, b), join(meet(b, a), meet(join(a, b), c))))))
% 29.77/4.21 = { by lemma 11 }
% 29.77/4.21 meet(a, join(b, meet(join(a, b), join(meet(b, a), meet(join(a, b), c)))))
% 29.77/4.21 = { by axiom 2 (commutativity_of_join) }
% 29.77/4.21 meet(a, join(b, meet(join(a, b), join(meet(join(a, b), c), meet(b, a)))))
% 29.77/4.21 = { by lemma 12 }
% 29.77/4.21 meet(a, join(b, meet(a, join(meet(join(a, b), c), meet(b, a)))))
% 29.77/4.21 = { by axiom 2 (commutativity_of_join) }
% 29.77/4.21 meet(a, join(b, meet(a, join(meet(b, a), meet(join(a, b), c)))))
% 29.77/4.21 = { by axiom 4 (commutativity_of_meet) }
% 29.77/4.21 meet(a, join(b, meet(a, join(meet(b, a), meet(c, join(a, b))))))
% 29.77/4.21 = { by axiom 4 (commutativity_of_meet) R->L }
% 29.77/4.21 meet(a, join(b, meet(a, join(meet(a, b), meet(c, join(a, b))))))
% 29.77/4.21 % SZS output end Proof
% 29.77/4.21
% 29.77/4.21 RESULT: Unsatisfiable (the axioms are contradictory).
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