TSTP Solution File: LAT163-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT163-1 : 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 : n020.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 10.51s 1.79s
% Output : Proof 11.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LAT163-1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n020.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 24 09:23:15 EDT 2023
% 0.14/0.34 % CPUTime :
% 10.51/1.79 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 10.51/1.79
% 10.51/1.79 % SZS status Unsatisfiable
% 10.51/1.79
% 11.27/1.80 % SZS output start Proof
% 11.27/1.80 Axiom 1 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 11.27/1.80 Axiom 2 (commutativity_of_join): join(X, Y) = join(Y, X).
% 11.27/1.80 Axiom 3 (absorption1): meet(X, join(X, Y)) = X.
% 11.27/1.80 Axiom 4 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 11.27/1.80 Axiom 5 (absorption2): join(X, meet(X, Y)) = X.
% 11.27/1.80 Axiom 6 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 11.27/1.80 Axiom 7 (equation_H76): meet(X, join(Y, meet(Z, join(Y, W)))) = meet(X, join(Y, meet(Z, join(W, meet(X, Y))))).
% 11.27/1.80
% 11.27/1.80 Lemma 8: meet(X, join(Y, X)) = X.
% 11.27/1.80 Proof:
% 11.27/1.80 meet(X, join(Y, X))
% 11.27/1.80 = { by axiom 2 (commutativity_of_join) R->L }
% 11.27/1.80 meet(X, join(X, Y))
% 11.27/1.80 = { by axiom 3 (absorption1) }
% 11.27/1.81 X
% 11.27/1.81
% 11.27/1.81 Lemma 9: meet(Y, meet(X, Z)) = meet(X, meet(Y, Z)).
% 11.27/1.81 Proof:
% 11.27/1.81 meet(Y, meet(X, Z))
% 11.27/1.81 = { by axiom 1 (commutativity_of_meet) R->L }
% 11.27/1.81 meet(meet(X, Z), Y)
% 11.27/1.81 = { by axiom 4 (associativity_of_meet) }
% 11.27/1.81 meet(X, meet(Z, Y))
% 11.27/1.81 = { by axiom 1 (commutativity_of_meet) }
% 11.27/1.81 meet(X, meet(Y, Z))
% 11.27/1.81
% 11.27/1.81 Lemma 10: meet(Z, meet(X, Y)) = meet(X, meet(Y, Z)).
% 11.27/1.81 Proof:
% 11.27/1.81 meet(Z, meet(X, Y))
% 11.27/1.81 = { by lemma 9 }
% 11.27/1.81 meet(X, meet(Z, Y))
% 11.27/1.81 = { by axiom 1 (commutativity_of_meet) }
% 11.27/1.81 meet(X, meet(Y, Z))
% 11.27/1.81
% 11.27/1.81 Lemma 11: meet(Z, meet(Y, X)) = meet(X, meet(Y, Z)).
% 11.27/1.81 Proof:
% 11.27/1.81 meet(Z, meet(Y, X))
% 11.27/1.81 = { by lemma 10 R->L }
% 11.27/1.81 meet(X, meet(Z, Y))
% 11.27/1.81 = { by axiom 1 (commutativity_of_meet) }
% 11.27/1.81 meet(X, meet(Y, Z))
% 11.27/1.81
% 11.27/1.81 Lemma 12: join(X, meet(Y, X)) = X.
% 11.27/1.81 Proof:
% 11.27/1.81 join(X, meet(Y, X))
% 11.27/1.81 = { by axiom 1 (commutativity_of_meet) R->L }
% 11.27/1.81 join(X, meet(X, Y))
% 11.27/1.81 = { by axiom 5 (absorption2) }
% 11.27/1.81 X
% 11.27/1.81
% 11.27/1.81 Lemma 13: join(Y, join(X, Z)) = join(X, join(Y, Z)).
% 11.27/1.81 Proof:
% 11.27/1.81 join(Y, join(X, Z))
% 11.27/1.81 = { by axiom 2 (commutativity_of_join) R->L }
% 11.27/1.81 join(join(X, Z), Y)
% 11.27/1.81 = { by axiom 6 (associativity_of_join) }
% 11.27/1.81 join(X, join(Z, Y))
% 11.27/1.81 = { by axiom 2 (commutativity_of_join) }
% 11.27/1.81 join(X, join(Y, Z))
% 11.27/1.81
% 11.27/1.81 Lemma 14: join(X, join(Y, meet(X, Z))) = join(X, Y).
% 11.27/1.81 Proof:
% 11.27/1.81 join(X, join(Y, meet(X, Z)))
% 11.27/1.81 = { by lemma 13 }
% 11.27/1.81 join(Y, join(X, meet(X, Z)))
% 11.27/1.81 = { by axiom 5 (absorption2) }
% 11.27/1.81 join(Y, X)
% 11.27/1.81 = { by axiom 2 (commutativity_of_join) }
% 11.27/1.81 join(X, Y)
% 11.27/1.81
% 11.27/1.81 Goal 1 (prove_H32): meet(a, join(b, meet(a, meet(c, d)))) = meet(a, join(b, meet(c, join(meet(a, d), meet(b, d))))).
% 11.27/1.81 Proof:
% 11.27/1.81 meet(a, join(b, meet(a, meet(c, d))))
% 11.27/1.81 = { by axiom 3 (absorption1) R->L }
% 11.27/1.81 meet(a, join(b, meet(meet(a, meet(c, d)), join(meet(a, meet(c, d)), join(meet(a, d), meet(b, d))))))
% 11.27/1.81 = { by axiom 2 (commutativity_of_join) R->L }
% 11.27/1.81 meet(a, join(b, meet(meet(a, meet(c, d)), join(join(meet(a, d), meet(b, d)), meet(a, meet(c, d))))))
% 11.27/1.81 = { by lemma 8 R->L }
% 11.27/1.81 meet(a, join(b, meet(meet(a, meet(c, d)), join(join(meet(a, d), meet(b, d)), meet(a, meet(meet(c, d), join(d, meet(c, d))))))))
% 11.27/1.81 = { by lemma 12 }
% 11.27/1.81 meet(a, join(b, meet(meet(a, meet(c, d)), join(join(meet(a, d), meet(b, d)), meet(a, meet(meet(c, d), d))))))
% 11.27/1.81 = { by axiom 1 (commutativity_of_meet) }
% 11.27/1.81 meet(a, join(b, meet(meet(a, meet(c, d)), join(join(meet(a, d), meet(b, d)), meet(a, meet(d, meet(c, d)))))))
% 11.27/1.81 = { by lemma 9 R->L }
% 11.27/1.81 meet(a, join(b, meet(meet(a, meet(c, d)), join(join(meet(a, d), meet(b, d)), meet(d, meet(a, meet(c, d)))))))
% 11.27/1.81 = { by lemma 8 R->L }
% 11.27/1.81 meet(a, join(b, meet(meet(a, meet(c, d)), join(join(meet(a, d), meet(b, d)), meet(d, meet(meet(a, meet(c, d)), join(a, meet(a, meet(c, d)))))))))
% 11.27/1.81 = { by axiom 5 (absorption2) }
% 11.27/1.81 meet(a, join(b, meet(meet(a, meet(c, d)), join(join(meet(a, d), meet(b, d)), meet(d, meet(meet(a, meet(c, d)), a))))))
% 11.27/1.81 = { by axiom 1 (commutativity_of_meet) }
% 11.27/1.81 meet(a, join(b, meet(meet(a, meet(c, d)), join(join(meet(a, d), meet(b, d)), meet(d, meet(a, meet(a, meet(c, d))))))))
% 11.27/1.81 = { by lemma 11 R->L }
% 11.27/1.81 meet(a, join(b, meet(meet(a, meet(c, d)), join(join(meet(a, d), meet(b, d)), meet(meet(a, meet(c, d)), meet(a, d))))))
% 11.27/1.81 = { by axiom 1 (commutativity_of_meet) R->L }
% 11.27/1.81 meet(a, join(b, meet(meet(a, meet(c, d)), join(join(meet(a, d), meet(b, d)), meet(meet(a, d), meet(a, meet(c, d)))))))
% 11.27/1.81 = { by axiom 2 (commutativity_of_join) R->L }
% 11.27/1.81 meet(a, join(b, meet(meet(a, meet(c, d)), join(meet(meet(a, d), meet(a, meet(c, d))), join(meet(a, d), meet(b, d))))))
% 11.27/1.81 = { by lemma 13 }
% 11.27/1.81 meet(a, join(b, meet(meet(a, meet(c, d)), join(meet(a, d), join(meet(meet(a, d), meet(a, meet(c, d))), meet(b, d))))))
% 11.27/1.81 = { by axiom 2 (commutativity_of_join) }
% 11.27/1.81 meet(a, join(b, meet(meet(a, meet(c, d)), join(meet(a, d), join(meet(b, d), meet(meet(a, d), meet(a, meet(c, d))))))))
% 11.27/1.81 = { by lemma 14 }
% 11.27/1.81 meet(a, join(b, meet(meet(a, meet(c, d)), join(meet(a, d), meet(b, d)))))
% 11.27/1.81 = { by axiom 1 (commutativity_of_meet) R->L }
% 11.27/1.81 meet(a, join(b, meet(join(meet(a, d), meet(b, d)), meet(a, meet(c, d)))))
% 11.27/1.81 = { by lemma 10 }
% 11.27/1.81 meet(a, join(b, meet(a, meet(meet(c, d), join(meet(a, d), meet(b, d))))))
% 11.27/1.81 = { by axiom 1 (commutativity_of_meet) R->L }
% 11.27/1.81 meet(a, join(b, meet(a, meet(join(meet(a, d), meet(b, d)), meet(c, d)))))
% 11.27/1.81 = { by lemma 11 }
% 11.27/1.81 meet(a, join(b, meet(a, meet(d, meet(c, join(meet(a, d), meet(b, d)))))))
% 11.27/1.81 = { by lemma 9 }
% 11.27/1.81 meet(a, join(b, meet(a, meet(c, meet(d, join(meet(a, d), meet(b, d)))))))
% 11.27/1.81 = { by axiom 1 (commutativity_of_meet) R->L }
% 11.27/1.81 meet(a, join(b, meet(a, meet(c, meet(join(meet(a, d), meet(b, d)), d)))))
% 11.27/1.81 = { by lemma 12 R->L }
% 11.27/1.81 meet(a, join(b, meet(a, meet(c, meet(join(meet(a, d), meet(b, d)), join(d, meet(a, d)))))))
% 11.27/1.81 = { by axiom 2 (commutativity_of_join) R->L }
% 11.27/1.81 meet(a, join(b, meet(a, meet(c, meet(join(meet(a, d), meet(b, d)), join(meet(a, d), d))))))
% 11.27/1.81 = { by lemma 12 R->L }
% 11.27/1.81 meet(a, join(b, meet(a, meet(c, meet(join(meet(a, d), meet(b, d)), join(meet(a, d), join(d, meet(b, d))))))))
% 11.27/1.81 = { by lemma 13 R->L }
% 11.27/1.81 meet(a, join(b, meet(a, meet(c, meet(join(meet(a, d), meet(b, d)), join(d, join(meet(a, d), meet(b, d))))))))
% 11.27/1.81 = { by lemma 8 }
% 11.27/1.81 meet(a, join(b, meet(a, meet(c, join(meet(a, d), meet(b, d))))))
% 11.27/1.81 = { by axiom 1 (commutativity_of_meet) R->L }
% 11.27/1.81 meet(a, join(b, meet(meet(c, join(meet(a, d), meet(b, d))), a)))
% 11.27/1.81 = { by axiom 5 (absorption2) R->L }
% 11.27/1.81 meet(a, join(b, meet(meet(c, join(meet(a, d), meet(b, d))), join(a, meet(a, b)))))
% 11.27/1.81 = { by axiom 7 (equation_H76) R->L }
% 11.27/1.81 meet(a, join(b, meet(meet(c, join(meet(a, d), meet(b, d))), join(b, a))))
% 11.27/1.81 = { by axiom 2 (commutativity_of_join) R->L }
% 11.27/1.81 meet(a, join(b, meet(meet(c, join(meet(a, d), meet(b, d))), join(a, b))))
% 11.27/1.81 = { by axiom 5 (absorption2) R->L }
% 11.27/1.81 meet(a, join(b, meet(meet(c, join(meet(a, d), meet(b, d))), join(join(a, meet(a, d)), b))))
% 11.27/1.81 = { by axiom 6 (associativity_of_join) }
% 11.27/1.81 meet(a, join(b, meet(meet(c, join(meet(a, d), meet(b, d))), join(a, join(meet(a, d), b)))))
% 11.27/1.81 = { by axiom 2 (commutativity_of_join) }
% 11.27/1.81 meet(a, join(b, meet(meet(c, join(meet(a, d), meet(b, d))), join(a, join(b, meet(a, d))))))
% 11.27/1.81 = { by lemma 14 R->L }
% 11.27/1.81 meet(a, join(b, meet(meet(c, join(meet(a, d), meet(b, d))), join(a, join(b, join(meet(a, d), meet(b, d)))))))
% 11.27/1.81 = { by axiom 2 (commutativity_of_join) R->L }
% 11.27/1.81 meet(a, join(b, meet(meet(c, join(meet(a, d), meet(b, d))), join(a, join(join(meet(a, d), meet(b, d)), b)))))
% 11.27/1.81 = { by axiom 1 (commutativity_of_meet) R->L }
% 11.27/1.81 meet(a, join(b, meet(join(a, join(join(meet(a, d), meet(b, d)), b)), meet(c, join(meet(a, d), meet(b, d))))))
% 11.27/1.81 = { by lemma 10 }
% 11.27/1.81 meet(a, join(b, meet(c, meet(join(meet(a, d), meet(b, d)), join(a, join(join(meet(a, d), meet(b, d)), b))))))
% 11.27/1.81 = { by axiom 2 (commutativity_of_join) R->L }
% 11.27/1.81 meet(a, join(b, meet(c, meet(join(meet(a, d), meet(b, d)), join(a, join(b, join(meet(a, d), meet(b, d))))))))
% 11.27/1.81 = { by axiom 6 (associativity_of_join) R->L }
% 11.27/1.81 meet(a, join(b, meet(c, meet(join(meet(a, d), meet(b, d)), join(join(a, b), join(meet(a, d), meet(b, d)))))))
% 11.27/1.81 = { by lemma 8 }
% 11.27/1.81 meet(a, join(b, meet(c, join(meet(a, d), meet(b, d)))))
% 11.27/1.81 % SZS output end Proof
% 11.27/1.81
% 11.27/1.81 RESULT: Unsatisfiable (the axioms are contradictory).
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