TSTP Solution File: LAT150-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT150-1 : 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 : n017.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 06:27:34 EDT 2023
% Result : Unsatisfiable 44.01s 6.02s
% Output : Proof 44.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT150-1 : 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
% 0.14/0.34 % Computer : n017.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 05:43:54 EDT 2023
% 0.14/0.35 % CPUTime :
% 44.01/6.02 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 44.01/6.02
% 44.01/6.02 % SZS status Unsatisfiable
% 44.01/6.02
% 44.36/6.04 % SZS output start Proof
% 44.36/6.04 Axiom 1 (commutativity_of_join): join(X, Y) = join(Y, X).
% 44.36/6.04 Axiom 2 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 44.36/6.04 Axiom 3 (absorption2): join(X, meet(X, Y)) = X.
% 44.36/6.04 Axiom 4 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 44.36/6.04 Axiom 5 (absorption1): meet(X, join(X, Y)) = X.
% 44.36/6.04 Axiom 6 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 44.36/6.04 Axiom 7 (equation_H39): meet(X, join(Y, meet(Z, join(X, W)))) = meet(X, join(Y, meet(Z, join(W, meet(X, Z))))).
% 44.36/6.04
% 44.36/6.04 Lemma 8: meet(X, join(Y, X)) = X.
% 44.36/6.04 Proof:
% 44.36/6.04 meet(X, join(Y, X))
% 44.36/6.04 = { by axiom 1 (commutativity_of_join) R->L }
% 44.36/6.04 meet(X, join(X, Y))
% 44.36/6.04 = { by axiom 5 (absorption1) }
% 44.36/6.04 X
% 44.36/6.04
% 44.36/6.04 Lemma 9: join(X, meet(Y, X)) = X.
% 44.36/6.04 Proof:
% 44.36/6.04 join(X, meet(Y, X))
% 44.36/6.04 = { by axiom 2 (commutativity_of_meet) R->L }
% 44.36/6.04 join(X, meet(X, Y))
% 44.36/6.04 = { by axiom 3 (absorption2) }
% 44.36/6.04 X
% 44.36/6.04
% 44.36/6.04 Lemma 10: join(Y, join(X, Z)) = join(X, join(Y, Z)).
% 44.36/6.04 Proof:
% 44.36/6.04 join(Y, join(X, Z))
% 44.36/6.04 = { by axiom 1 (commutativity_of_join) R->L }
% 44.36/6.04 join(join(X, Z), Y)
% 44.36/6.04 = { by axiom 4 (associativity_of_join) }
% 44.36/6.04 join(X, join(Z, Y))
% 44.36/6.04 = { by axiom 1 (commutativity_of_join) }
% 44.36/6.04 join(X, join(Y, Z))
% 44.36/6.04
% 44.36/6.04 Lemma 11: join(Z, join(X, Y)) = join(X, join(Y, Z)).
% 44.36/6.04 Proof:
% 44.36/6.04 join(Z, join(X, Y))
% 44.36/6.04 = { by lemma 10 }
% 44.36/6.04 join(X, join(Z, Y))
% 44.36/6.04 = { by axiom 1 (commutativity_of_join) }
% 44.36/6.04 join(X, join(Y, Z))
% 44.36/6.04
% 44.36/6.04 Lemma 12: join(Z, join(Y, X)) = join(X, join(Y, Z)).
% 44.36/6.04 Proof:
% 44.36/6.04 join(Z, join(Y, X))
% 44.36/6.04 = { by lemma 10 }
% 44.36/6.04 join(Y, join(Z, X))
% 44.36/6.04 = { by lemma 11 R->L }
% 44.36/6.04 join(X, join(Y, Z))
% 44.36/6.04
% 44.36/6.04 Lemma 13: meet(X, meet(join(X, Y), Z)) = meet(Z, X).
% 44.36/6.04 Proof:
% 44.36/6.04 meet(X, meet(join(X, Y), Z))
% 44.36/6.04 = { by axiom 6 (associativity_of_meet) R->L }
% 44.36/6.04 meet(meet(X, join(X, Y)), Z)
% 44.36/6.04 = { by axiom 5 (absorption1) }
% 44.36/6.04 meet(X, Z)
% 44.36/6.04 = { by axiom 2 (commutativity_of_meet) }
% 44.36/6.04 meet(Z, X)
% 44.36/6.04
% 44.36/6.04 Lemma 14: meet(X, join(Y, meet(Z, join(W, meet(Z, X))))) = meet(X, join(Y, meet(Z, join(W, X)))).
% 44.36/6.04 Proof:
% 44.36/6.04 meet(X, join(Y, meet(Z, join(W, meet(Z, X)))))
% 44.36/6.04 = { by axiom 2 (commutativity_of_meet) R->L }
% 44.36/6.04 meet(X, join(Y, meet(Z, join(W, meet(X, Z)))))
% 44.36/6.04 = { by axiom 7 (equation_H39) R->L }
% 44.36/6.04 meet(X, join(Y, meet(Z, join(X, W))))
% 44.36/6.04 = { by axiom 1 (commutativity_of_join) }
% 44.36/6.04 meet(X, join(Y, meet(Z, join(W, X))))
% 44.36/6.04
% 44.36/6.04 Goal 1 (prove_H40): meet(a, join(b, meet(c, join(a, d)))) = meet(a, join(b, meet(c, join(d, meet(c, join(a, b)))))).
% 44.36/6.04 Proof:
% 44.36/6.04 meet(a, join(b, meet(c, join(a, d))))
% 44.36/6.04 = { by lemma 9 R->L }
% 44.36/6.04 meet(a, join(join(b, meet(c, join(a, d))), meet(c, join(b, meet(c, join(a, d))))))
% 44.36/6.04 = { by axiom 1 (commutativity_of_join) R->L }
% 44.36/6.04 meet(a, join(meet(c, join(b, meet(c, join(a, d)))), join(b, meet(c, join(a, d)))))
% 44.36/6.04 = { by lemma 11 }
% 44.36/6.04 meet(a, join(b, join(meet(c, join(a, d)), meet(c, join(b, meet(c, join(a, d)))))))
% 44.36/6.04 = { by lemma 8 R->L }
% 44.41/6.04 meet(a, join(b, join(meet(meet(c, join(a, d)), join(c, meet(c, join(a, d)))), meet(c, join(b, meet(c, join(a, d)))))))
% 44.41/6.04 = { by axiom 3 (absorption2) }
% 44.41/6.04 meet(a, join(b, join(meet(meet(c, join(a, d)), c), meet(c, join(b, meet(c, join(a, d)))))))
% 44.41/6.04 = { by axiom 2 (commutativity_of_meet) }
% 44.41/6.04 meet(a, join(b, join(meet(c, meet(c, join(a, d))), meet(c, join(b, meet(c, join(a, d)))))))
% 44.41/6.04 = { by axiom 1 (commutativity_of_join) R->L }
% 44.41/6.04 meet(a, join(b, join(meet(c, join(b, meet(c, join(a, d)))), meet(c, meet(c, join(a, d))))))
% 44.41/6.04 = { by axiom 2 (commutativity_of_meet) R->L }
% 44.41/6.04 meet(a, join(b, join(meet(c, join(b, meet(c, join(a, d)))), meet(meet(c, join(a, d)), c))))
% 44.41/6.04 = { by lemma 8 R->L }
% 44.41/6.04 meet(a, join(b, join(meet(c, join(b, meet(c, join(a, d)))), meet(meet(meet(c, join(a, d)), join(b, meet(c, join(a, d)))), c))))
% 44.41/6.04 = { by axiom 6 (associativity_of_meet) }
% 44.41/6.04 meet(a, join(b, join(meet(c, join(b, meet(c, join(a, d)))), meet(meet(c, join(a, d)), meet(join(b, meet(c, join(a, d))), c)))))
% 44.41/6.04 = { by axiom 2 (commutativity_of_meet) }
% 44.41/6.04 meet(a, join(b, join(meet(c, join(b, meet(c, join(a, d)))), meet(meet(c, join(a, d)), meet(c, join(b, meet(c, join(a, d))))))))
% 44.41/6.04 = { by lemma 9 }
% 44.41/6.04 meet(a, join(b, meet(c, join(b, meet(c, join(a, d))))))
% 44.41/6.04 = { by lemma 9 R->L }
% 44.41/6.04 meet(a, join(b, meet(c, join(b, join(meet(c, join(a, d)), meet(a, meet(c, join(a, d))))))))
% 44.41/6.04 = { by axiom 2 (commutativity_of_meet) R->L }
% 44.41/6.04 meet(a, join(b, meet(c, join(b, join(meet(c, join(a, d)), meet(meet(c, join(a, d)), a))))))
% 44.41/6.04 = { by axiom 6 (associativity_of_meet) }
% 44.41/6.04 meet(a, join(b, meet(c, join(b, join(meet(c, join(a, d)), meet(c, meet(join(a, d), a)))))))
% 44.41/6.04 = { by axiom 2 (commutativity_of_meet) }
% 44.41/6.04 meet(a, join(b, meet(c, join(b, join(meet(c, join(a, d)), meet(c, meet(a, join(a, d))))))))
% 44.41/6.04 = { by axiom 5 (absorption1) }
% 44.41/6.04 meet(a, join(b, meet(c, join(b, join(meet(c, join(a, d)), meet(c, a))))))
% 44.41/6.04 = { by axiom 2 (commutativity_of_meet) }
% 44.41/6.04 meet(a, join(b, meet(c, join(b, join(meet(c, join(a, d)), meet(a, c))))))
% 44.41/6.04 = { by lemma 11 R->L }
% 44.41/6.04 meet(a, join(b, meet(c, join(meet(a, c), join(b, meet(c, join(a, d)))))))
% 44.41/6.04 = { by axiom 1 (commutativity_of_join) }
% 44.41/6.04 meet(a, join(b, meet(c, join(join(b, meet(c, join(a, d))), meet(a, c)))))
% 44.41/6.04 = { by axiom 7 (equation_H39) R->L }
% 44.41/6.04 meet(a, join(b, meet(c, join(a, join(b, meet(c, join(a, d)))))))
% 44.41/6.04 = { by lemma 11 R->L }
% 44.41/6.04 meet(a, join(b, meet(c, join(meet(c, join(a, d)), join(a, b)))))
% 44.41/6.04 = { by axiom 1 (commutativity_of_join) }
% 44.41/6.04 meet(a, join(b, meet(c, join(join(a, b), meet(c, join(a, d))))))
% 44.41/6.04 = { by axiom 2 (commutativity_of_meet) R->L }
% 44.41/6.04 meet(join(b, meet(c, join(join(a, b), meet(c, join(a, d))))), a)
% 44.41/6.04 = { by lemma 13 R->L }
% 44.41/6.04 meet(a, meet(join(a, d), join(b, meet(c, join(join(a, b), meet(c, join(a, d)))))))
% 44.41/6.04 = { by lemma 14 }
% 44.41/6.04 meet(a, meet(join(a, d), join(b, meet(c, join(join(a, b), join(a, d))))))
% 44.41/6.04 = { by lemma 13 }
% 44.41/6.04 meet(join(b, meet(c, join(join(a, b), join(a, d)))), a)
% 44.41/6.04 = { by axiom 2 (commutativity_of_meet) }
% 44.41/6.04 meet(a, join(b, meet(c, join(join(a, b), join(a, d)))))
% 44.41/6.04 = { by axiom 1 (commutativity_of_join) }
% 44.41/6.04 meet(a, join(meet(c, join(join(a, b), join(a, d))), b))
% 44.41/6.04 = { by axiom 1 (commutativity_of_join) R->L }
% 44.41/6.04 meet(a, join(meet(c, join(join(a, d), join(a, b))), b))
% 44.41/6.04 = { by lemma 11 }
% 44.41/6.04 meet(a, join(meet(c, join(a, join(b, join(a, d)))), b))
% 44.41/6.04 = { by lemma 12 }
% 44.41/6.04 meet(a, join(meet(c, join(a, join(d, join(a, b)))), b))
% 44.41/6.04 = { by axiom 1 (commutativity_of_join) R->L }
% 44.41/6.04 meet(a, join(meet(c, join(a, join(join(a, b), d))), b))
% 44.41/6.04 = { by axiom 4 (associativity_of_join) R->L }
% 44.41/6.04 meet(a, join(meet(c, join(join(a, join(a, b)), d)), b))
% 44.41/6.04 = { by axiom 1 (commutativity_of_join) R->L }
% 44.41/6.04 meet(a, join(meet(c, join(join(join(a, b), a), d)), b))
% 44.41/6.04 = { by axiom 5 (absorption1) R->L }
% 44.41/6.04 meet(a, join(meet(c, join(join(join(a, b), meet(a, join(a, b))), d)), b))
% 44.41/6.04 = { by lemma 9 }
% 44.41/6.04 meet(a, join(meet(c, join(join(a, b), d)), b))
% 44.41/6.04 = { by axiom 1 (commutativity_of_join) }
% 44.41/6.04 meet(a, join(meet(c, join(d, join(a, b))), b))
% 44.41/6.04 = { by lemma 12 R->L }
% 44.41/6.04 meet(a, join(meet(c, join(b, join(a, d))), b))
% 44.41/6.04 = { by axiom 1 (commutativity_of_join) R->L }
% 44.41/6.04 meet(a, join(b, meet(c, join(b, join(a, d)))))
% 44.41/6.04 = { by axiom 2 (commutativity_of_meet) R->L }
% 44.41/6.04 meet(join(b, meet(c, join(b, join(a, d)))), a)
% 44.41/6.04 = { by lemma 13 R->L }
% 44.41/6.04 meet(a, meet(join(a, b), join(b, meet(c, join(b, join(a, d))))))
% 44.41/6.04 = { by lemma 12 }
% 44.41/6.04 meet(a, meet(join(a, b), join(b, meet(c, join(d, join(a, b))))))
% 44.41/6.04 = { by lemma 14 R->L }
% 44.41/6.04 meet(a, meet(join(a, b), join(b, meet(c, join(d, meet(c, join(a, b)))))))
% 44.41/6.04 = { by lemma 13 }
% 44.41/6.04 meet(join(b, meet(c, join(d, meet(c, join(a, b))))), a)
% 44.41/6.04 = { by axiom 2 (commutativity_of_meet) }
% 44.41/6.04 meet(a, join(b, meet(c, join(d, meet(c, join(a, b))))))
% 44.41/6.04 % SZS output end Proof
% 44.41/6.04
% 44.41/6.04 RESULT: Unsatisfiable (the axioms are contradictory).
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