TSTP Solution File: LAT166-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT166-1 : 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 06:27:37 EDT 2023
% Result : Unsatisfiable 22.23s 3.25s
% Output : Proof 22.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : LAT166-1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.11 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.31 % Computer : n008.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Thu Aug 24 08:46:02 EDT 2023
% 0.12/0.31 % CPUTime :
% 22.23/3.25 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 22.23/3.25
% 22.23/3.25 % SZS status Unsatisfiable
% 22.23/3.25
% 22.23/3.27 % SZS output start Proof
% 22.23/3.27 Axiom 1 (idempotence_of_join): join(X, X) = X.
% 22.23/3.27 Axiom 2 (commutativity_of_join): join(X, Y) = join(Y, X).
% 22.23/3.27 Axiom 3 (idempotence_of_meet): meet(X, X) = X.
% 22.23/3.27 Axiom 4 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 22.23/3.27 Axiom 5 (absorption2): join(X, meet(X, Y)) = X.
% 22.23/3.27 Axiom 6 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 22.23/3.27 Axiom 7 (absorption1): meet(X, join(X, Y)) = X.
% 22.23/3.27 Axiom 8 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 22.23/3.27 Axiom 9 (equation_H77): meet(X, join(Y, meet(Z, join(Y, W)))) = meet(X, join(Y, meet(Z, join(W, meet(X, meet(Y, Z)))))).
% 22.23/3.27
% 22.23/3.27 Lemma 10: meet(X, meet(X, Y)) = meet(X, Y).
% 22.23/3.27 Proof:
% 22.23/3.27 meet(X, meet(X, Y))
% 22.23/3.27 = { by axiom 8 (associativity_of_meet) R->L }
% 22.23/3.27 meet(meet(X, X), Y)
% 22.23/3.27 = { by axiom 3 (idempotence_of_meet) }
% 22.23/3.27 meet(X, Y)
% 22.23/3.27
% 22.23/3.27 Lemma 11: meet(X, meet(Y, join(X, Z))) = meet(X, Y).
% 22.23/3.27 Proof:
% 22.23/3.27 meet(X, meet(Y, join(X, Z)))
% 22.23/3.27 = { by axiom 4 (commutativity_of_meet) R->L }
% 22.23/3.27 meet(X, meet(join(X, Z), Y))
% 22.23/3.27 = { by axiom 8 (associativity_of_meet) R->L }
% 22.23/3.27 meet(meet(X, join(X, Z)), Y)
% 22.23/3.27 = { by axiom 7 (absorption1) }
% 22.23/3.27 meet(X, Y)
% 22.23/3.27
% 22.23/3.27 Lemma 12: meet(X, meet(join(X, Y), Z)) = meet(X, Z).
% 22.23/3.27 Proof:
% 22.23/3.27 meet(X, meet(join(X, Y), Z))
% 22.23/3.27 = { by axiom 4 (commutativity_of_meet) R->L }
% 22.23/3.27 meet(X, meet(Z, join(X, Y)))
% 22.23/3.27 = { by lemma 11 }
% 22.23/3.27 meet(X, Z)
% 22.23/3.27
% 22.23/3.27 Lemma 13: meet(X, join(Y, meet(join(X, Y), Z))) = meet(X, join(Y, meet(X, Z))).
% 22.23/3.27 Proof:
% 22.23/3.27 meet(X, join(Y, meet(join(X, Y), Z)))
% 22.23/3.27 = { by axiom 4 (commutativity_of_meet) R->L }
% 22.23/3.27 meet(X, join(Y, meet(Z, join(X, Y))))
% 22.23/3.27 = { by axiom 2 (commutativity_of_join) R->L }
% 22.23/3.27 meet(X, join(Y, meet(Z, join(Y, X))))
% 22.23/3.27 = { by axiom 9 (equation_H77) }
% 22.23/3.27 meet(X, join(Y, meet(Z, join(X, meet(X, meet(Y, Z))))))
% 22.23/3.27 = { by axiom 5 (absorption2) }
% 22.23/3.27 meet(X, join(Y, meet(Z, X)))
% 22.23/3.27 = { by axiom 4 (commutativity_of_meet) }
% 22.23/3.27 meet(X, join(Y, meet(X, Z)))
% 22.23/3.27
% 22.23/3.27 Lemma 14: join(meet(X, Y), meet(X, join(Z, meet(X, Y)))) = meet(X, join(Z, meet(X, Y))).
% 22.23/3.27 Proof:
% 22.23/3.27 join(meet(X, Y), meet(X, join(Z, meet(X, Y))))
% 22.23/3.27 = { by axiom 2 (commutativity_of_join) R->L }
% 22.23/3.27 join(meet(X, Y), meet(X, join(meet(X, Y), Z)))
% 22.23/3.27 = { by lemma 10 R->L }
% 22.23/3.27 join(meet(X, meet(X, Y)), meet(X, join(meet(X, Y), Z)))
% 22.23/3.27 = { by axiom 4 (commutativity_of_meet) R->L }
% 22.23/3.27 join(meet(meet(X, Y), X), meet(X, join(meet(X, Y), Z)))
% 22.23/3.27 = { by axiom 2 (commutativity_of_join) R->L }
% 22.23/3.27 join(meet(X, join(meet(X, Y), Z)), meet(meet(X, Y), X))
% 22.23/3.27 = { by lemma 11 R->L }
% 22.23/3.27 join(meet(X, join(meet(X, Y), Z)), meet(meet(X, Y), meet(X, join(meet(X, Y), Z))))
% 22.23/3.27 = { by axiom 4 (commutativity_of_meet) R->L }
% 22.23/3.27 join(meet(X, join(meet(X, Y), Z)), meet(meet(X, join(meet(X, Y), Z)), meet(X, Y)))
% 22.23/3.27 = { by axiom 5 (absorption2) }
% 22.23/3.27 meet(X, join(meet(X, Y), Z))
% 22.23/3.27 = { by axiom 2 (commutativity_of_join) }
% 22.23/3.27 meet(X, join(Z, meet(X, Y)))
% 22.23/3.27
% 22.23/3.27 Lemma 15: join(X, meet(Y, join(X, meet(Y, Z)))) = join(X, meet(Y, Z)).
% 22.23/3.27 Proof:
% 22.23/3.27 join(X, meet(Y, join(X, meet(Y, Z))))
% 22.23/3.27 = { by lemma 14 R->L }
% 22.23/3.27 join(X, join(meet(Y, Z), meet(Y, join(X, meet(Y, Z)))))
% 22.23/3.27 = { by axiom 4 (commutativity_of_meet) R->L }
% 22.23/3.27 join(X, join(meet(Y, Z), meet(join(X, meet(Y, Z)), Y)))
% 22.23/3.27 = { by axiom 6 (associativity_of_join) R->L }
% 22.23/3.27 join(join(X, meet(Y, Z)), meet(join(X, meet(Y, Z)), Y))
% 22.23/3.27 = { by axiom 5 (absorption2) }
% 22.23/3.27 join(X, meet(Y, Z))
% 22.23/3.27
% 22.23/3.27 Lemma 16: meet(X, join(Y, meet(X, join(meet(X, Y), Z)))) = meet(X, join(Y, Z)).
% 22.23/3.27 Proof:
% 22.23/3.27 meet(X, join(Y, meet(X, join(meet(X, Y), Z))))
% 22.23/3.27 = { by axiom 2 (commutativity_of_join) R->L }
% 22.23/3.27 meet(X, join(Y, meet(X, join(Z, meet(X, Y)))))
% 22.23/3.27 = { by lemma 11 R->L }
% 22.23/3.27 meet(X, join(Y, meet(X, join(Z, meet(X, meet(Y, join(X, Y)))))))
% 22.23/3.27 = { by lemma 13 R->L }
% 22.23/3.27 meet(X, join(Y, meet(join(X, Y), join(Z, meet(X, meet(Y, join(X, Y)))))))
% 22.23/3.27 = { by axiom 9 (equation_H77) R->L }
% 22.23/3.27 meet(X, join(Y, meet(join(X, Y), join(Y, Z))))
% 22.23/3.27 = { by lemma 13 }
% 22.23/3.27 meet(X, join(Y, meet(X, join(Y, Z))))
% 22.23/3.27 = { by lemma 14 R->L }
% 22.23/3.27 join(meet(X, join(Y, Z)), meet(X, join(Y, meet(X, join(Y, Z)))))
% 22.23/3.27 = { by axiom 4 (commutativity_of_meet) R->L }
% 22.23/3.27 join(meet(X, join(Y, Z)), meet(X, join(Y, meet(join(Y, Z), X))))
% 22.23/3.28 = { by axiom 7 (absorption1) R->L }
% 22.23/3.28 join(meet(X, join(Y, Z)), meet(X, meet(join(Y, meet(join(Y, Z), X)), join(join(Y, meet(join(Y, Z), X)), join(Y, Z)))))
% 22.23/3.28 = { by axiom 2 (commutativity_of_join) }
% 22.23/3.28 join(meet(X, join(Y, Z)), meet(X, meet(join(Y, meet(join(Y, Z), X)), join(join(Y, Z), join(Y, meet(join(Y, Z), X))))))
% 22.23/3.28 = { by axiom 2 (commutativity_of_join) R->L }
% 22.23/3.28 join(meet(X, join(Y, Z)), meet(X, meet(join(Y, meet(join(Y, Z), X)), join(join(Y, Z), join(meet(join(Y, Z), X), Y)))))
% 22.23/3.28 = { by axiom 6 (associativity_of_join) R->L }
% 22.23/3.28 join(meet(X, join(Y, Z)), meet(X, meet(join(Y, meet(join(Y, Z), X)), join(join(join(Y, Z), meet(join(Y, Z), X)), Y))))
% 22.23/3.28 = { by axiom 5 (absorption2) }
% 22.23/3.28 join(meet(X, join(Y, Z)), meet(X, meet(join(Y, meet(join(Y, Z), X)), join(join(Y, Z), Y))))
% 22.23/3.28 = { by axiom 4 (commutativity_of_meet) }
% 22.23/3.28 join(meet(X, join(Y, Z)), meet(X, meet(join(join(Y, Z), Y), join(Y, meet(join(Y, Z), X)))))
% 22.23/3.28 = { by axiom 2 (commutativity_of_join) }
% 22.23/3.28 join(meet(X, join(Y, Z)), meet(X, meet(join(Y, join(Y, Z)), join(Y, meet(join(Y, Z), X)))))
% 22.23/3.28 = { by axiom 6 (associativity_of_join) R->L }
% 22.23/3.28 join(meet(X, join(Y, Z)), meet(X, meet(join(join(Y, Y), Z), join(Y, meet(join(Y, Z), X)))))
% 22.23/3.28 = { by axiom 1 (idempotence_of_join) }
% 22.23/3.28 join(meet(X, join(Y, Z)), meet(X, meet(join(Y, Z), join(Y, meet(join(Y, Z), X)))))
% 22.23/3.28 = { by axiom 4 (commutativity_of_meet) }
% 22.23/3.28 join(meet(X, join(Y, Z)), meet(X, meet(join(Y, Z), join(Y, meet(X, join(Y, Z))))))
% 22.23/3.28 = { by axiom 8 (associativity_of_meet) R->L }
% 22.23/3.28 join(meet(X, join(Y, Z)), meet(meet(X, join(Y, Z)), join(Y, meet(X, join(Y, Z)))))
% 22.23/3.28 = { by axiom 5 (absorption2) }
% 22.23/3.28 meet(X, join(Y, Z))
% 22.23/3.28
% 22.23/3.28 Goal 1 (prove_H78): meet(a, join(b, meet(c, join(b, d)))) = meet(a, join(b, meet(c, join(d, meet(b, join(a, d)))))).
% 22.23/3.28 Proof:
% 22.23/3.28 meet(a, join(b, meet(c, join(b, d))))
% 22.23/3.28 = { by lemma 12 R->L }
% 22.23/3.28 meet(a, meet(join(a, d), join(b, meet(c, join(b, d)))))
% 22.23/3.28 = { by axiom 9 (equation_H77) }
% 22.23/3.28 meet(a, meet(join(a, d), join(b, meet(c, join(d, meet(join(a, d), meet(b, c)))))))
% 22.23/3.28 = { by axiom 8 (associativity_of_meet) R->L }
% 22.23/3.28 meet(a, meet(join(a, d), join(b, meet(c, join(d, meet(meet(join(a, d), b), c))))))
% 22.23/3.28 = { by lemma 16 R->L }
% 22.23/3.28 meet(a, meet(join(a, d), join(b, meet(join(a, d), join(meet(join(a, d), b), meet(c, join(d, meet(meet(join(a, d), b), c))))))))
% 22.23/3.28 = { by axiom 4 (commutativity_of_meet) R->L }
% 22.23/3.28 meet(a, meet(join(a, d), join(b, meet(join(a, d), join(meet(join(a, d), b), meet(c, join(d, meet(c, meet(join(a, d), b)))))))))
% 22.23/3.28 = { by lemma 10 R->L }
% 22.23/3.28 meet(a, meet(join(a, d), join(b, meet(join(a, d), join(meet(join(a, d), b), meet(c, join(d, meet(c, meet(c, meet(join(a, d), b))))))))))
% 22.23/3.28 = { by axiom 4 (commutativity_of_meet) }
% 22.23/3.28 meet(a, meet(join(a, d), join(b, meet(join(a, d), join(meet(join(a, d), b), meet(c, join(d, meet(c, meet(meet(join(a, d), b), c)))))))))
% 22.23/3.28 = { by lemma 15 R->L }
% 22.23/3.28 meet(a, meet(join(a, d), join(b, meet(join(a, d), join(meet(join(a, d), b), meet(c, join(meet(join(a, d), b), meet(c, join(d, meet(c, meet(meet(join(a, d), b), c)))))))))))
% 22.23/3.28 = { by axiom 9 (equation_H77) R->L }
% 22.23/3.28 meet(a, meet(join(a, d), join(b, meet(join(a, d), join(meet(join(a, d), b), meet(c, join(meet(join(a, d), b), meet(c, join(meet(join(a, d), b), d)))))))))
% 22.23/3.28 = { by lemma 15 }
% 22.23/3.28 meet(a, meet(join(a, d), join(b, meet(join(a, d), join(meet(join(a, d), b), meet(c, join(meet(join(a, d), b), d)))))))
% 22.23/3.28 = { by lemma 16 }
% 22.23/3.28 meet(a, meet(join(a, d), join(b, meet(c, join(meet(join(a, d), b), d)))))
% 22.23/3.28 = { by axiom 2 (commutativity_of_join) }
% 22.23/3.28 meet(a, meet(join(a, d), join(b, meet(c, join(d, meet(join(a, d), b))))))
% 22.23/3.28 = { by lemma 12 }
% 22.23/3.28 meet(a, join(b, meet(c, join(d, meet(join(a, d), b)))))
% 22.23/3.28 = { by axiom 4 (commutativity_of_meet) }
% 22.23/3.28 meet(a, join(b, meet(c, join(d, meet(b, join(a, d))))))
% 22.23/3.28 % SZS output end Proof
% 22.23/3.28
% 22.23/3.28 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------