TSTP Solution File: LAT160-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT160-1 : 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 : n014.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 172.84s 22.60s
% Output : Proof 173.36s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT160-1 : 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 : n014.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 04:34:34 EDT 2023
% 0.14/0.34 % CPUTime :
% 172.84/22.60 Command-line arguments: --no-flatten-goal
% 172.84/22.60
% 172.84/22.60 % SZS status Unsatisfiable
% 172.84/22.60
% 172.84/22.61 % SZS output start Proof
% 172.84/22.61 Axiom 1 (idempotence_of_join): join(X, X) = X.
% 172.84/22.61 Axiom 2 (commutativity_of_join): join(X, Y) = join(Y, X).
% 172.84/22.61 Axiom 3 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 172.84/22.61 Axiom 4 (absorption2): join(X, meet(X, Y)) = X.
% 172.84/22.61 Axiom 5 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 172.84/22.61 Axiom 6 (absorption1): meet(X, join(X, Y)) = X.
% 172.84/22.61 Axiom 7 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 172.84/22.61 Axiom 8 (equation_H52): meet(X, join(Y, meet(Z, join(X, W)))) = meet(X, join(Y, join(meet(Z, W), meet(Z, join(X, Y))))).
% 172.84/22.61
% 172.84/22.61 Lemma 9: meet(X, meet(Y, join(X, Z))) = meet(X, Y).
% 172.84/22.61 Proof:
% 172.84/22.61 meet(X, meet(Y, join(X, Z)))
% 172.84/22.61 = { by axiom 3 (commutativity_of_meet) R->L }
% 172.84/22.61 meet(X, meet(join(X, Z), Y))
% 172.84/22.61 = { by axiom 7 (associativity_of_meet) R->L }
% 172.84/22.61 meet(meet(X, join(X, Z)), Y)
% 172.84/22.61 = { by axiom 6 (absorption1) }
% 172.84/22.61 meet(X, Y)
% 172.84/22.61
% 172.84/22.61 Lemma 10: meet(X, meet(join(X, Y), Z)) = meet(X, Z).
% 172.84/22.61 Proof:
% 172.84/22.61 meet(X, meet(join(X, Y), Z))
% 172.84/22.61 = { by axiom 3 (commutativity_of_meet) R->L }
% 172.84/22.61 meet(X, meet(Z, join(X, Y)))
% 172.84/22.61 = { by lemma 9 }
% 172.84/22.61 meet(X, Z)
% 172.84/22.61
% 172.84/22.61 Lemma 11: join(meet(X, Y), meet(X, join(Y, Z))) = meet(X, join(Y, Z)).
% 172.84/22.61 Proof:
% 172.84/22.61 join(meet(X, Y), meet(X, join(Y, Z)))
% 172.84/22.61 = { by axiom 3 (commutativity_of_meet) R->L }
% 172.84/22.61 join(meet(Y, X), meet(X, join(Y, Z)))
% 172.84/22.61 = { by axiom 2 (commutativity_of_join) R->L }
% 172.84/22.61 join(meet(X, join(Y, Z)), meet(Y, X))
% 172.84/22.61 = { by lemma 9 R->L }
% 172.84/22.61 join(meet(X, join(Y, Z)), meet(Y, meet(X, join(Y, Z))))
% 172.84/22.61 = { by axiom 3 (commutativity_of_meet) R->L }
% 172.84/22.61 join(meet(X, join(Y, Z)), meet(meet(X, join(Y, Z)), Y))
% 172.84/22.61 = { by axiom 4 (absorption2) }
% 172.84/22.61 meet(X, join(Y, Z))
% 172.84/22.61
% 172.84/22.61 Lemma 12: meet(X, join(Y, meet(Z, join(X, Y)))) = meet(X, join(Y, meet(X, Z))).
% 172.84/22.61 Proof:
% 172.84/22.61 meet(X, join(Y, meet(Z, join(X, Y))))
% 172.84/22.61 = { by lemma 11 R->L }
% 172.84/22.61 meet(X, join(Y, join(meet(Z, X), meet(Z, join(X, Y)))))
% 172.84/22.61 = { by axiom 8 (equation_H52) R->L }
% 172.84/22.61 meet(X, join(Y, meet(Z, join(X, X))))
% 172.84/22.61 = { by axiom 1 (idempotence_of_join) }
% 172.84/22.61 meet(X, join(Y, meet(Z, X)))
% 172.84/22.61 = { by axiom 3 (commutativity_of_meet) }
% 172.84/22.61 meet(X, join(Y, meet(X, Z)))
% 172.84/22.61
% 172.84/22.61 Lemma 13: meet(X, join(Y, meet(Z, join(Y, X)))) = meet(X, join(Y, meet(X, Z))).
% 172.84/22.61 Proof:
% 172.84/22.61 meet(X, join(Y, meet(Z, join(Y, X))))
% 172.84/22.61 = { by axiom 2 (commutativity_of_join) R->L }
% 172.84/22.61 meet(X, join(Y, meet(Z, join(X, Y))))
% 172.84/22.61 = { by lemma 12 }
% 172.84/22.61 meet(X, join(Y, meet(X, Z)))
% 172.84/22.61
% 172.84/22.61 Lemma 14: meet(X, join(Y, join(meet(Z, join(X, Y)), meet(Z, W)))) = meet(X, join(Y, meet(Z, join(X, W)))).
% 172.84/22.61 Proof:
% 172.84/22.61 meet(X, join(Y, join(meet(Z, join(X, Y)), meet(Z, W))))
% 172.84/22.61 = { by axiom 2 (commutativity_of_join) R->L }
% 172.84/22.61 meet(X, join(Y, join(meet(Z, W), meet(Z, join(X, Y)))))
% 172.84/22.61 = { by axiom 8 (equation_H52) R->L }
% 172.84/22.61 meet(X, join(Y, meet(Z, join(X, W))))
% 172.84/22.61
% 172.84/22.61 Goal 1 (prove_H51): meet(a, join(b, meet(c, join(a, d)))) = meet(a, join(b, join(meet(a, c), meet(c, d)))).
% 172.84/22.61 Proof:
% 172.84/22.61 meet(a, join(b, meet(c, join(a, d))))
% 172.84/22.61 = { by axiom 8 (equation_H52) }
% 172.84/22.61 meet(a, join(b, join(meet(c, d), meet(c, join(a, b)))))
% 172.84/22.61 = { by axiom 5 (associativity_of_join) R->L }
% 172.84/22.61 meet(a, join(join(b, meet(c, d)), meet(c, join(a, b))))
% 172.84/22.61 = { by axiom 3 (commutativity_of_meet) R->L }
% 172.84/22.61 meet(a, join(join(b, meet(c, d)), meet(join(a, b), c)))
% 172.84/22.61 = { by lemma 10 R->L }
% 172.84/22.61 meet(a, meet(join(a, b), join(join(b, meet(c, d)), meet(join(a, b), c))))
% 172.84/22.61 = { by lemma 13 R->L }
% 172.84/22.61 meet(a, meet(join(a, b), join(join(b, meet(c, d)), meet(c, join(join(b, meet(c, d)), join(a, b))))))
% 172.84/22.61 = { by axiom 3 (commutativity_of_meet) }
% 172.84/22.61 meet(a, meet(join(a, b), join(join(b, meet(c, d)), meet(join(join(b, meet(c, d)), join(a, b)), c))))
% 172.84/22.61 = { by lemma 10 }
% 172.84/22.61 meet(a, join(join(b, meet(c, d)), meet(join(join(b, meet(c, d)), join(a, b)), c)))
% 172.84/22.61 = { by axiom 3 (commutativity_of_meet) }
% 172.84/22.61 meet(a, join(join(b, meet(c, d)), meet(c, join(join(b, meet(c, d)), join(a, b)))))
% 172.84/22.61 = { by axiom 5 (associativity_of_join) R->L }
% 172.84/22.61 meet(a, join(join(b, meet(c, d)), meet(c, join(join(join(b, meet(c, d)), a), b))))
% 172.84/22.61 = { by axiom 2 (commutativity_of_join) R->L }
% 172.84/22.61 meet(a, join(meet(c, join(join(join(b, meet(c, d)), a), b)), join(b, meet(c, d))))
% 172.84/22.61 = { by lemma 11 R->L }
% 172.84/22.61 meet(a, join(join(meet(c, join(join(b, meet(c, d)), a)), meet(c, join(join(join(b, meet(c, d)), a), b))), join(b, meet(c, d))))
% 172.84/22.61 = { by axiom 5 (associativity_of_join) }
% 172.84/22.61 meet(a, join(meet(c, join(join(b, meet(c, d)), a)), join(meet(c, join(join(join(b, meet(c, d)), a), b)), join(b, meet(c, d)))))
% 172.84/22.61 = { by axiom 2 (commutativity_of_join) }
% 172.84/22.61 meet(a, join(meet(c, join(join(b, meet(c, d)), a)), join(join(b, meet(c, d)), meet(c, join(join(join(b, meet(c, d)), a), b)))))
% 172.84/22.61 = { by axiom 2 (commutativity_of_join) }
% 172.84/22.61 meet(a, join(join(join(b, meet(c, d)), meet(c, join(join(join(b, meet(c, d)), a), b))), meet(c, join(join(b, meet(c, d)), a))))
% 172.84/22.61 = { by axiom 5 (associativity_of_join) }
% 172.84/22.61 meet(a, join(join(b, meet(c, d)), join(meet(c, join(join(join(b, meet(c, d)), a), b)), meet(c, join(join(b, meet(c, d)), a)))))
% 172.84/22.61 = { by axiom 2 (commutativity_of_join) }
% 172.84/22.61 meet(a, join(join(b, meet(c, d)), join(meet(c, join(join(b, meet(c, d)), a)), meet(c, join(join(join(b, meet(c, d)), a), b)))))
% 172.84/22.61 = { by axiom 2 (commutativity_of_join) R->L }
% 172.84/22.61 meet(a, join(join(b, meet(c, d)), join(meet(c, join(a, join(b, meet(c, d)))), meet(c, join(join(join(b, meet(c, d)), a), b)))))
% 173.36/22.61 = { by lemma 14 }
% 173.36/22.61 meet(a, join(join(b, meet(c, d)), meet(c, join(a, join(join(join(b, meet(c, d)), a), b)))))
% 173.36/22.61 = { by axiom 5 (associativity_of_join) }
% 173.36/22.61 meet(a, join(join(b, meet(c, d)), meet(c, join(a, join(join(b, meet(c, d)), join(a, b))))))
% 173.36/22.61 = { by axiom 2 (commutativity_of_join) R->L }
% 173.36/22.61 meet(a, join(join(b, meet(c, d)), meet(c, join(a, join(join(a, b), join(b, meet(c, d)))))))
% 173.36/22.61 = { by axiom 5 (associativity_of_join) R->L }
% 173.36/22.61 meet(a, join(join(b, meet(c, d)), meet(c, join(join(a, join(a, b)), join(b, meet(c, d))))))
% 173.36/22.61 = { by axiom 2 (commutativity_of_join) }
% 173.36/22.62 meet(a, join(join(b, meet(c, d)), meet(c, join(join(b, meet(c, d)), join(a, join(a, b))))))
% 173.36/22.62 = { by lemma 10 R->L }
% 173.36/22.62 meet(a, meet(join(a, join(a, b)), join(join(b, meet(c, d)), meet(c, join(join(b, meet(c, d)), join(a, join(a, b)))))))
% 173.36/22.62 = { by lemma 13 }
% 173.36/22.62 meet(a, meet(join(a, join(a, b)), join(join(b, meet(c, d)), meet(join(a, join(a, b)), c))))
% 173.36/22.62 = { by lemma 10 }
% 173.36/22.62 meet(a, join(join(b, meet(c, d)), meet(join(a, join(a, b)), c)))
% 173.36/22.62 = { by axiom 3 (commutativity_of_meet) }
% 173.36/22.62 meet(a, join(join(b, meet(c, d)), meet(c, join(a, join(a, b)))))
% 173.36/22.62 = { by axiom 6 (absorption1) R->L }
% 173.36/22.62 meet(a, join(join(b, meet(c, d)), meet(c, join(a, meet(join(a, b), join(join(a, b), meet(c, d)))))))
% 173.36/22.62 = { by axiom 5 (associativity_of_join) }
% 173.36/22.62 meet(a, join(join(b, meet(c, d)), meet(c, join(a, meet(join(a, b), join(a, join(b, meet(c, d))))))))
% 173.36/22.62 = { by axiom 3 (commutativity_of_meet) R->L }
% 173.36/22.62 meet(a, join(join(b, meet(c, d)), meet(c, join(a, meet(join(a, join(b, meet(c, d))), join(a, b))))))
% 173.36/22.62 = { by lemma 14 R->L }
% 173.36/22.62 meet(a, join(join(b, meet(c, d)), join(meet(c, join(a, join(b, meet(c, d)))), meet(c, meet(join(a, join(b, meet(c, d))), join(a, b))))))
% 173.36/22.62 = { by axiom 7 (associativity_of_meet) R->L }
% 173.36/22.62 meet(a, join(join(b, meet(c, d)), join(meet(c, join(a, join(b, meet(c, d)))), meet(meet(c, join(a, join(b, meet(c, d)))), join(a, b)))))
% 173.36/22.62 = { by axiom 4 (absorption2) }
% 173.36/22.62 meet(a, join(join(b, meet(c, d)), meet(c, join(a, join(b, meet(c, d))))))
% 173.36/22.62 = { by lemma 12 }
% 173.36/22.62 meet(a, join(join(b, meet(c, d)), meet(a, c)))
% 173.36/22.62 = { by axiom 5 (associativity_of_join) }
% 173.36/22.62 meet(a, join(b, join(meet(c, d), meet(a, c))))
% 173.36/22.62 = { by axiom 2 (commutativity_of_join) }
% 173.36/22.62 meet(a, join(b, join(meet(a, c), meet(c, d))))
% 173.36/22.62 % SZS output end Proof
% 173.36/22.62
% 173.36/22.62 RESULT: Unsatisfiable (the axioms are contradictory).
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