TSTP Solution File: LAT017-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT017-1 : TPTP v8.1.2. Bugfixed v2.2.1.
% 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 : n005.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 06:27:08 EDT 2023
% Result : Unsatisfiable 0.21s 0.60s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : LAT017-1 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.14/0.15 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.36 % Computer : n005.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 24 06:50:24 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.60 Command-line arguments: --flatten
% 0.21/0.60
% 0.21/0.60 % SZS status Unsatisfiable
% 0.21/0.60
% 0.21/0.62 % SZS output start Proof
% 0.21/0.62 Axiom 1 (commutativity_of_join): join(X, Y) = join(Y, X).
% 0.21/0.62 Axiom 2 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 0.21/0.62 Axiom 3 (complement_involution): complement(complement(X)) = X.
% 0.21/0.62 Axiom 4 (top): join(complement(X), X) = n1.
% 0.21/0.62 Axiom 5 (absorption2): join(X, meet(X, Y)) = X.
% 0.21/0.62 Axiom 6 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 0.21/0.62 Axiom 7 (join_complement): join(X, join(Y, complement(Y))) = join(Y, complement(Y)).
% 0.21/0.62 Axiom 8 (meet_complement): meet(X, Y) = complement(join(complement(X), complement(Y))).
% 0.21/0.62
% 0.21/0.62 Lemma 9: complement(join(X, complement(Y))) = meet(Y, complement(X)).
% 0.21/0.62 Proof:
% 0.21/0.62 complement(join(X, complement(Y)))
% 0.21/0.62 = { by axiom 3 (complement_involution) R->L }
% 0.21/0.62 complement(join(complement(complement(X)), complement(Y)))
% 0.21/0.62 = { by axiom 8 (meet_complement) R->L }
% 0.21/0.62 meet(complement(X), Y)
% 0.21/0.62 = { by axiom 2 (commutativity_of_meet) }
% 0.21/0.62 meet(Y, complement(X))
% 0.21/0.62
% 0.21/0.62 Lemma 10: complement(meet(X, complement(Y))) = join(Y, complement(X)).
% 0.21/0.62 Proof:
% 0.21/0.62 complement(meet(X, complement(Y)))
% 0.21/0.62 = { by axiom 8 (meet_complement) }
% 0.21/0.62 complement(complement(join(complement(X), complement(complement(Y)))))
% 0.21/0.62 = { by axiom 3 (complement_involution) }
% 0.21/0.62 join(complement(X), complement(complement(Y)))
% 0.21/0.62 = { by axiom 1 (commutativity_of_join) }
% 0.21/0.62 join(complement(complement(Y)), complement(X))
% 0.21/0.62 = { by axiom 3 (complement_involution) }
% 0.21/0.62 join(Y, complement(X))
% 0.21/0.62
% 0.21/0.62 Lemma 11: complement(meet(complement(X), Y)) = join(X, complement(Y)).
% 0.21/0.62 Proof:
% 0.21/0.62 complement(meet(complement(X), Y))
% 0.21/0.62 = { by axiom 2 (commutativity_of_meet) R->L }
% 0.21/0.62 complement(meet(Y, complement(X)))
% 0.21/0.62 = { by lemma 10 }
% 0.21/0.62 join(X, complement(Y))
% 0.21/0.62
% 0.21/0.62 Lemma 12: join(Y, join(Z, X)) = join(X, join(Y, Z)).
% 0.21/0.62 Proof:
% 0.21/0.62 join(Y, join(Z, X))
% 0.21/0.62 = { by axiom 1 (commutativity_of_join) R->L }
% 0.21/0.62 join(join(Z, X), Y)
% 0.21/0.62 = { by axiom 1 (commutativity_of_join) }
% 0.21/0.62 join(join(X, Z), Y)
% 0.21/0.62 = { by axiom 6 (associativity_of_join) }
% 0.21/0.62 join(X, join(Z, Y))
% 0.21/0.62 = { by axiom 1 (commutativity_of_join) }
% 0.21/0.62 join(X, join(Y, Z))
% 0.21/0.62
% 0.21/0.62 Lemma 13: complement(join(meet(complement(X), Y), meet(complement(Z), complement(W)))) = meet(join(X, complement(Y)), join(Z, W)).
% 0.21/0.62 Proof:
% 0.21/0.62 complement(join(meet(complement(X), Y), meet(complement(Z), complement(W))))
% 0.21/0.62 = { by axiom 1 (commutativity_of_join) }
% 0.21/0.62 complement(join(meet(complement(Z), complement(W)), meet(complement(X), Y)))
% 0.21/0.62 = { by axiom 2 (commutativity_of_meet) R->L }
% 0.21/0.62 complement(join(meet(complement(Z), complement(W)), meet(Y, complement(X))))
% 0.21/0.62 = { by axiom 8 (meet_complement) }
% 0.21/0.62 complement(join(meet(complement(Z), complement(W)), complement(join(complement(Y), complement(complement(X))))))
% 0.21/0.62 = { by axiom 3 (complement_involution) }
% 0.21/0.62 complement(join(meet(complement(Z), complement(W)), complement(join(complement(Y), X))))
% 0.21/0.62 = { by axiom 1 (commutativity_of_join) R->L }
% 0.21/0.62 complement(join(meet(complement(Z), complement(W)), complement(join(X, complement(Y)))))
% 0.21/0.62 = { by lemma 9 }
% 0.21/0.62 meet(join(X, complement(Y)), complement(meet(complement(Z), complement(W))))
% 0.21/0.62 = { by lemma 10 }
% 0.21/0.62 meet(join(X, complement(Y)), join(W, complement(complement(Z))))
% 0.21/0.62 = { by axiom 3 (complement_involution) }
% 0.21/0.62 meet(join(X, complement(Y)), join(W, Z))
% 0.21/0.62 = { by axiom 1 (commutativity_of_join) R->L }
% 0.21/0.62 meet(join(X, complement(Y)), join(Z, W))
% 0.21/0.62
% 0.21/0.62 Lemma 14: join(meet(complement(X), Y), meet(complement(Z), complement(W))) = complement(meet(join(X, complement(Y)), join(Z, W))).
% 0.21/0.62 Proof:
% 0.21/0.62 join(meet(complement(X), Y), meet(complement(Z), complement(W)))
% 0.21/0.62 = { by axiom 3 (complement_involution) R->L }
% 0.21/0.62 complement(complement(join(meet(complement(X), Y), meet(complement(Z), complement(W)))))
% 0.21/0.62 = { by lemma 13 }
% 0.21/0.63 complement(meet(join(X, complement(Y)), join(Z, W)))
% 0.21/0.63
% 0.21/0.63 Lemma 15: meet(complement(X), join(meet(complement(X), Y), meet(complement(X), complement(Z)))) = join(meet(complement(X), Y), meet(complement(X), complement(Z))).
% 0.21/0.63 Proof:
% 0.21/0.63 meet(complement(X), join(meet(complement(X), Y), meet(complement(X), complement(Z))))
% 0.21/0.63 = { by axiom 3 (complement_involution) R->L }
% 0.21/0.63 complement(complement(meet(complement(X), join(meet(complement(X), Y), meet(complement(X), complement(Z))))))
% 0.21/0.63 = { by lemma 11 }
% 0.21/0.63 complement(join(X, complement(join(meet(complement(X), Y), meet(complement(X), complement(Z))))))
% 0.21/0.63 = { by lemma 13 }
% 0.21/0.63 complement(join(X, meet(join(X, complement(Y)), join(X, Z))))
% 0.21/0.63 = { by axiom 1 (commutativity_of_join) }
% 0.21/0.63 complement(join(meet(join(X, complement(Y)), join(X, Z)), X))
% 0.21/0.63 = { by axiom 3 (complement_involution) R->L }
% 0.21/0.63 complement(join(meet(join(X, complement(Y)), join(X, Z)), complement(complement(X))))
% 0.21/0.63 = { by axiom 5 (absorption2) R->L }
% 0.21/0.63 complement(join(meet(join(X, complement(Y)), join(X, Z)), complement(join(complement(X), meet(complement(X), complement(Z))))))
% 0.21/0.63 = { by axiom 1 (commutativity_of_join) R->L }
% 0.21/0.63 complement(join(meet(join(X, complement(Y)), join(X, Z)), complement(join(meet(complement(X), complement(Z)), complement(X)))))
% 0.21/0.63 = { by axiom 5 (absorption2) R->L }
% 0.21/0.63 complement(join(meet(join(X, complement(Y)), join(X, Z)), complement(join(meet(complement(X), complement(Z)), join(complement(X), meet(complement(X), Y))))))
% 0.21/0.63 = { by axiom 1 (commutativity_of_join) R->L }
% 0.21/0.63 complement(join(meet(join(X, complement(Y)), join(X, Z)), complement(join(meet(complement(X), complement(Z)), join(meet(complement(X), Y), complement(X))))))
% 0.21/0.63 = { by axiom 6 (associativity_of_join) R->L }
% 0.21/0.63 complement(join(meet(join(X, complement(Y)), join(X, Z)), complement(join(join(meet(complement(X), complement(Z)), meet(complement(X), Y)), complement(X)))))
% 0.21/0.63 = { by axiom 1 (commutativity_of_join) R->L }
% 0.21/0.63 complement(join(meet(join(X, complement(Y)), join(X, Z)), complement(join(join(meet(complement(X), Y), meet(complement(X), complement(Z))), complement(X)))))
% 0.21/0.63 = { by lemma 9 }
% 0.21/0.63 complement(join(meet(join(X, complement(Y)), join(X, Z)), meet(X, complement(join(meet(complement(X), Y), meet(complement(X), complement(Z)))))))
% 0.21/0.63 = { by lemma 13 }
% 0.21/0.63 complement(join(meet(join(X, complement(Y)), join(X, Z)), meet(X, meet(join(X, complement(Y)), join(X, Z)))))
% 0.21/0.63 = { by axiom 2 (commutativity_of_meet) }
% 0.21/0.63 complement(join(meet(join(X, complement(Y)), join(X, Z)), meet(meet(join(X, complement(Y)), join(X, Z)), X)))
% 0.21/0.63 = { by axiom 5 (absorption2) }
% 0.21/0.63 complement(meet(join(X, complement(Y)), join(X, Z)))
% 0.21/0.63 = { by lemma 14 R->L }
% 0.21/0.63 join(meet(complement(X), Y), meet(complement(X), complement(Z)))
% 0.21/0.63
% 0.21/0.63 Goal 1 (prove_e2): join(a, join(meet(complement(a), meet(join(a, complement(b)), join(a, b))), meet(complement(a), join(meet(complement(a), b), meet(complement(a), complement(b)))))) = n1.
% 0.21/0.63 Proof:
% 0.21/0.63 join(a, join(meet(complement(a), meet(join(a, complement(b)), join(a, b))), meet(complement(a), join(meet(complement(a), b), meet(complement(a), complement(b))))))
% 0.21/0.63 = { by axiom 1 (commutativity_of_join) }
% 0.21/0.63 join(join(meet(complement(a), meet(join(a, complement(b)), join(a, b))), meet(complement(a), join(meet(complement(a), b), meet(complement(a), complement(b))))), a)
% 0.21/0.63 = { by axiom 5 (absorption2) R->L }
% 0.21/0.63 join(join(join(meet(complement(a), meet(join(a, complement(b)), join(a, b))), meet(complement(a), join(meet(complement(a), b), meet(complement(a), complement(b))))), meet(join(meet(complement(a), meet(join(a, complement(b)), join(a, b))), meet(complement(a), join(meet(complement(a), b), meet(complement(a), complement(b))))), join(meet(complement(a), b), meet(complement(a), complement(b))))), a)
% 0.21/0.63 = { by axiom 6 (associativity_of_join) }
% 0.21/0.63 join(join(meet(complement(a), meet(join(a, complement(b)), join(a, b))), meet(complement(a), join(meet(complement(a), b), meet(complement(a), complement(b))))), join(meet(join(meet(complement(a), meet(join(a, complement(b)), join(a, b))), meet(complement(a), join(meet(complement(a), b), meet(complement(a), complement(b))))), join(meet(complement(a), b), meet(complement(a), complement(b)))), a))
% 0.21/0.63 = { by lemma 12 R->L }
% 0.21/0.63 join(meet(join(meet(complement(a), meet(join(a, complement(b)), join(a, b))), meet(complement(a), join(meet(complement(a), b), meet(complement(a), complement(b))))), join(meet(complement(a), b), meet(complement(a), complement(b)))), join(a, join(meet(complement(a), meet(join(a, complement(b)), join(a, b))), meet(complement(a), join(meet(complement(a), b), meet(complement(a), complement(b)))))))
% 0.21/0.63 = { by axiom 1 (commutativity_of_join) }
% 0.21/0.63 join(join(a, join(meet(complement(a), meet(join(a, complement(b)), join(a, b))), meet(complement(a), join(meet(complement(a), b), meet(complement(a), complement(b)))))), meet(join(meet(complement(a), meet(join(a, complement(b)), join(a, b))), meet(complement(a), join(meet(complement(a), b), meet(complement(a), complement(b))))), join(meet(complement(a), b), meet(complement(a), complement(b)))))
% 0.21/0.63 = { by axiom 2 (commutativity_of_meet) R->L }
% 0.21/0.63 join(join(a, join(meet(complement(a), meet(join(a, complement(b)), join(a, b))), meet(complement(a), join(meet(complement(a), b), meet(complement(a), complement(b)))))), meet(join(meet(complement(a), b), meet(complement(a), complement(b))), join(meet(complement(a), meet(join(a, complement(b)), join(a, b))), meet(complement(a), join(meet(complement(a), b), meet(complement(a), complement(b)))))))
% 0.21/0.63 = { by lemma 15 R->L }
% 0.21/0.63 join(join(a, join(meet(complement(a), meet(join(a, complement(b)), join(a, b))), meet(complement(a), join(meet(complement(a), b), meet(complement(a), complement(b)))))), meet(meet(complement(a), join(meet(complement(a), b), meet(complement(a), complement(b)))), join(meet(complement(a), meet(join(a, complement(b)), join(a, b))), meet(complement(a), join(meet(complement(a), b), meet(complement(a), complement(b)))))))
% 0.21/0.63 = { by axiom 1 (commutativity_of_join) }
% 0.21/0.63 join(join(a, join(meet(complement(a), meet(join(a, complement(b)), join(a, b))), meet(complement(a), join(meet(complement(a), b), meet(complement(a), complement(b)))))), meet(meet(complement(a), join(meet(complement(a), b), meet(complement(a), complement(b)))), join(meet(complement(a), join(meet(complement(a), b), meet(complement(a), complement(b)))), meet(complement(a), meet(join(a, complement(b)), join(a, b))))))
% 0.21/0.63 = { by axiom 3 (complement_involution) R->L }
% 0.21/0.63 join(join(a, join(meet(complement(a), meet(join(a, complement(b)), join(a, b))), meet(complement(a), join(meet(complement(a), b), meet(complement(a), complement(b)))))), meet(meet(complement(a), join(meet(complement(a), b), meet(complement(a), complement(b)))), join(meet(complement(a), join(meet(complement(a), b), meet(complement(a), complement(b)))), complement(complement(meet(complement(a), meet(join(a, complement(b)), join(a, b))))))))
% 0.21/0.63 = { by lemma 10 R->L }
% 0.21/0.63 join(join(a, join(meet(complement(a), meet(join(a, complement(b)), join(a, b))), meet(complement(a), join(meet(complement(a), b), meet(complement(a), complement(b)))))), meet(meet(complement(a), join(meet(complement(a), b), meet(complement(a), complement(b)))), complement(meet(complement(meet(complement(a), meet(join(a, complement(b)), join(a, b)))), complement(meet(complement(a), join(meet(complement(a), b), meet(complement(a), complement(b)))))))))
% 0.21/0.63 = { by lemma 9 R->L }
% 0.21/0.63 join(join(a, join(meet(complement(a), meet(join(a, complement(b)), join(a, b))), meet(complement(a), join(meet(complement(a), b), meet(complement(a), complement(b)))))), complement(join(meet(complement(meet(complement(a), meet(join(a, complement(b)), join(a, b)))), complement(meet(complement(a), join(meet(complement(a), b), meet(complement(a), complement(b)))))), complement(meet(complement(a), join(meet(complement(a), b), meet(complement(a), complement(b))))))))
% 0.21/0.63 = { by axiom 1 (commutativity_of_join) }
% 0.21/0.63 join(join(a, join(meet(complement(a), meet(join(a, complement(b)), join(a, b))), meet(complement(a), join(meet(complement(a), b), meet(complement(a), complement(b)))))), complement(join(complement(meet(complement(a), join(meet(complement(a), b), meet(complement(a), complement(b))))), meet(complement(meet(complement(a), meet(join(a, complement(b)), join(a, b)))), complement(meet(complement(a), join(meet(complement(a), b), meet(complement(a), complement(b)))))))))
% 0.21/0.63 = { by axiom 2 (commutativity_of_meet) R->L }
% 0.21/0.63 join(join(a, join(meet(complement(a), meet(join(a, complement(b)), join(a, b))), meet(complement(a), join(meet(complement(a), b), meet(complement(a), complement(b)))))), complement(join(complement(meet(complement(a), join(meet(complement(a), b), meet(complement(a), complement(b))))), meet(complement(meet(complement(a), join(meet(complement(a), b), meet(complement(a), complement(b))))), complement(meet(complement(a), meet(join(a, complement(b)), join(a, b))))))))
% 0.21/0.63 = { by axiom 5 (absorption2) }
% 0.21/0.63 join(join(a, join(meet(complement(a), meet(join(a, complement(b)), join(a, b))), meet(complement(a), join(meet(complement(a), b), meet(complement(a), complement(b)))))), complement(complement(meet(complement(a), join(meet(complement(a), b), meet(complement(a), complement(b)))))))
% 0.21/0.63 = { by axiom 3 (complement_involution) }
% 0.21/0.63 join(join(a, join(meet(complement(a), meet(join(a, complement(b)), join(a, b))), meet(complement(a), join(meet(complement(a), b), meet(complement(a), complement(b)))))), meet(complement(a), join(meet(complement(a), b), meet(complement(a), complement(b)))))
% 0.21/0.63 = { by lemma 15 }
% 0.21/0.63 join(join(a, join(meet(complement(a), meet(join(a, complement(b)), join(a, b))), meet(complement(a), join(meet(complement(a), b), meet(complement(a), complement(b)))))), join(meet(complement(a), b), meet(complement(a), complement(b))))
% 0.21/0.63 = { by axiom 1 (commutativity_of_join) }
% 0.21/0.63 join(join(meet(complement(a), b), meet(complement(a), complement(b))), join(a, join(meet(complement(a), meet(join(a, complement(b)), join(a, b))), meet(complement(a), join(meet(complement(a), b), meet(complement(a), complement(b)))))))
% 0.21/0.63 = { by lemma 12 }
% 0.21/0.63 join(join(meet(complement(a), meet(join(a, complement(b)), join(a, b))), meet(complement(a), join(meet(complement(a), b), meet(complement(a), complement(b))))), join(join(meet(complement(a), b), meet(complement(a), complement(b))), a))
% 0.21/0.63 = { by axiom 1 (commutativity_of_join) R->L }
% 0.21/0.63 join(join(meet(complement(a), meet(join(a, complement(b)), join(a, b))), meet(complement(a), join(meet(complement(a), b), meet(complement(a), complement(b))))), join(a, join(meet(complement(a), b), meet(complement(a), complement(b)))))
% 0.21/0.63 = { by lemma 14 }
% 0.21/0.63 join(join(meet(complement(a), meet(join(a, complement(b)), join(a, b))), meet(complement(a), join(meet(complement(a), b), meet(complement(a), complement(b))))), join(a, complement(meet(join(a, complement(b)), join(a, b)))))
% 0.21/0.63 = { by lemma 11 R->L }
% 0.21/0.63 join(join(meet(complement(a), meet(join(a, complement(b)), join(a, b))), meet(complement(a), join(meet(complement(a), b), meet(complement(a), complement(b))))), complement(meet(complement(a), meet(join(a, complement(b)), join(a, b)))))
% 0.21/0.63 = { by axiom 1 (commutativity_of_join) R->L }
% 0.21/0.63 join(complement(meet(complement(a), meet(join(a, complement(b)), join(a, b)))), join(meet(complement(a), meet(join(a, complement(b)), join(a, b))), meet(complement(a), join(meet(complement(a), b), meet(complement(a), complement(b))))))
% 0.21/0.63 = { by lemma 15 }
% 0.21/0.63 join(complement(meet(complement(a), meet(join(a, complement(b)), join(a, b)))), join(meet(complement(a), meet(join(a, complement(b)), join(a, b))), join(meet(complement(a), b), meet(complement(a), complement(b)))))
% 0.21/0.63 = { by axiom 1 (commutativity_of_join) }
% 0.21/0.63 join(complement(meet(complement(a), meet(join(a, complement(b)), join(a, b)))), join(join(meet(complement(a), b), meet(complement(a), complement(b))), meet(complement(a), meet(join(a, complement(b)), join(a, b)))))
% 0.21/0.63 = { by axiom 1 (commutativity_of_join) }
% 0.21/0.63 join(join(join(meet(complement(a), b), meet(complement(a), complement(b))), meet(complement(a), meet(join(a, complement(b)), join(a, b)))), complement(meet(complement(a), meet(join(a, complement(b)), join(a, b)))))
% 0.21/0.63 = { by axiom 6 (associativity_of_join) }
% 0.21/0.63 join(join(meet(complement(a), b), meet(complement(a), complement(b))), join(meet(complement(a), meet(join(a, complement(b)), join(a, b))), complement(meet(complement(a), meet(join(a, complement(b)), join(a, b))))))
% 0.21/0.63 = { by axiom 7 (join_complement) }
% 0.21/0.63 join(meet(complement(a), meet(join(a, complement(b)), join(a, b))), complement(meet(complement(a), meet(join(a, complement(b)), join(a, b)))))
% 0.21/0.63 = { by axiom 1 (commutativity_of_join) R->L }
% 0.21/0.63 join(complement(meet(complement(a), meet(join(a, complement(b)), join(a, b)))), meet(complement(a), meet(join(a, complement(b)), join(a, b))))
% 0.21/0.63 = { by axiom 4 (top) }
% 0.21/0.63 n1
% 0.21/0.63 % SZS output end Proof
% 0.21/0.63
% 0.21/0.63 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------