TSTP Solution File: LAT018-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : LAT018-1 : 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 : n026.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 0.51s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LAT018-1 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.36 % Computer : n026.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 06:37:31 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.51 Command-line arguments: --ground-connectedness --complete-subsets
% 0.21/0.51
% 0.21/0.51 % SZS status Unsatisfiable
% 0.21/0.51
% 0.21/0.53 % SZS output start Proof
% 0.21/0.53 Axiom 1 (commutativity_of_meet): meet(X, Y) = meet(Y, X).
% 0.21/0.53 Axiom 2 (commutativity_of_join): join(X, Y) = join(Y, X).
% 0.21/0.53 Axiom 3 (complement_involution): complement(complement(X)) = X.
% 0.21/0.53 Axiom 4 (bottom): meet(complement(X), X) = n0.
% 0.21/0.53 Axiom 5 (top): join(complement(X), X) = n1.
% 0.21/0.53 Axiom 6 (associativity_of_meet): meet(meet(X, Y), Z) = meet(X, meet(Y, Z)).
% 0.21/0.53 Axiom 7 (absorption2): join(X, meet(X, Y)) = X.
% 0.21/0.53 Axiom 8 (associativity_of_join): join(join(X, Y), Z) = join(X, join(Y, Z)).
% 0.21/0.53 Axiom 9 (join_complement): join(X, join(Y, complement(Y))) = join(Y, complement(Y)).
% 0.21/0.53 Axiom 10 (meet_complement): meet(X, Y) = complement(join(complement(X), complement(Y))).
% 0.21/0.53
% 0.21/0.53 Lemma 11: join(X, complement(X)) = n1.
% 0.21/0.53 Proof:
% 0.21/0.53 join(X, complement(X))
% 0.21/0.53 = { by axiom 2 (commutativity_of_join) R->L }
% 0.21/0.53 join(complement(X), X)
% 0.21/0.53 = { by axiom 5 (top) }
% 0.21/0.53 n1
% 0.21/0.53
% 0.21/0.53 Lemma 12: meet(X, complement(X)) = n0.
% 0.21/0.53 Proof:
% 0.21/0.53 meet(X, complement(X))
% 0.21/0.53 = { by axiom 1 (commutativity_of_meet) R->L }
% 0.21/0.53 meet(complement(X), X)
% 0.21/0.53 = { by axiom 4 (bottom) }
% 0.21/0.53 n0
% 0.21/0.53
% 0.21/0.53 Lemma 13: complement(n1) = n0.
% 0.21/0.53 Proof:
% 0.21/0.53 complement(n1)
% 0.21/0.53 = { by lemma 11 R->L }
% 0.21/0.53 complement(join(complement(X), complement(complement(X))))
% 0.21/0.53 = { by axiom 10 (meet_complement) R->L }
% 0.21/0.53 meet(X, complement(X))
% 0.21/0.53 = { by lemma 12 }
% 0.21/0.53 n0
% 0.21/0.53
% 0.21/0.53 Lemma 14: complement(n0) = n1.
% 0.21/0.53 Proof:
% 0.21/0.53 complement(n0)
% 0.21/0.53 = { by lemma 13 R->L }
% 0.21/0.53 complement(complement(n1))
% 0.21/0.53 = { by axiom 3 (complement_involution) }
% 0.21/0.53 n1
% 0.21/0.53
% 0.21/0.53 Lemma 15: join(X, meet(Y, X)) = X.
% 0.21/0.53 Proof:
% 0.21/0.53 join(X, meet(Y, X))
% 0.21/0.53 = { by axiom 1 (commutativity_of_meet) }
% 0.21/0.53 join(X, meet(X, Y))
% 0.21/0.53 = { by axiom 7 (absorption2) }
% 0.21/0.53 X
% 0.21/0.53
% 0.21/0.53 Lemma 16: join(Y, join(Z, X)) = join(X, join(Y, Z)).
% 0.21/0.53 Proof:
% 0.21/0.53 join(Y, join(Z, X))
% 0.21/0.53 = { by axiom 2 (commutativity_of_join) R->L }
% 0.21/0.53 join(join(Z, X), Y)
% 0.21/0.53 = { by axiom 2 (commutativity_of_join) }
% 0.21/0.53 join(join(X, Z), Y)
% 0.21/0.53 = { by axiom 8 (associativity_of_join) }
% 0.21/0.53 join(X, join(Z, Y))
% 0.21/0.53 = { by axiom 2 (commutativity_of_join) }
% 0.21/0.53 join(X, join(Y, Z))
% 0.21/0.53
% 0.21/0.53 Goal 1 (prove_e3): join(complement(join(join(meet(complement(a), b), meet(complement(a), complement(b))), meet(a, join(complement(a), b)))), join(complement(a), b)) = n1.
% 0.21/0.53 Proof:
% 0.21/0.53 join(complement(join(join(meet(complement(a), b), meet(complement(a), complement(b))), meet(a, join(complement(a), b)))), join(complement(a), b))
% 0.21/0.53 = { by axiom 2 (commutativity_of_join) R->L }
% 0.21/0.53 join(join(complement(a), b), complement(join(join(meet(complement(a), b), meet(complement(a), complement(b))), meet(a, join(complement(a), b)))))
% 0.21/0.53 = { by axiom 3 (complement_involution) R->L }
% 0.21/0.53 join(complement(complement(join(complement(a), b))), complement(join(join(meet(complement(a), b), meet(complement(a), complement(b))), meet(a, join(complement(a), b)))))
% 0.21/0.53 = { by axiom 2 (commutativity_of_join) R->L }
% 0.21/0.53 join(complement(join(join(meet(complement(a), b), meet(complement(a), complement(b))), meet(a, join(complement(a), b)))), complement(complement(join(complement(a), b))))
% 0.21/0.53 = { by axiom 3 (complement_involution) R->L }
% 0.21/0.53 complement(complement(join(complement(join(join(meet(complement(a), b), meet(complement(a), complement(b))), meet(a, join(complement(a), b)))), complement(complement(join(complement(a), b))))))
% 0.21/0.53 = { by axiom 10 (meet_complement) R->L }
% 0.21/0.53 complement(meet(join(join(meet(complement(a), b), meet(complement(a), complement(b))), meet(a, join(complement(a), b))), complement(join(complement(a), b))))
% 0.21/0.53 = { by axiom 7 (absorption2) R->L }
% 0.21/0.53 complement(meet(join(join(meet(complement(a), b), meet(complement(a), complement(b))), meet(a, join(complement(a), b))), complement(join(join(complement(a), meet(complement(a), complement(b))), b))))
% 0.21/0.53 = { by axiom 8 (associativity_of_join) }
% 0.21/0.53 complement(meet(join(join(meet(complement(a), b), meet(complement(a), complement(b))), meet(a, join(complement(a), b))), complement(join(complement(a), join(meet(complement(a), complement(b)), b)))))
% 0.21/0.53 = { by axiom 2 (commutativity_of_join) }
% 0.21/0.53 complement(meet(join(join(meet(complement(a), b), meet(complement(a), complement(b))), meet(a, join(complement(a), b))), complement(join(complement(a), join(b, meet(complement(a), complement(b)))))))
% 0.21/0.53 = { by lemma 16 }
% 0.21/0.53 complement(meet(join(join(meet(complement(a), b), meet(complement(a), complement(b))), meet(a, join(complement(a), b))), complement(join(meet(complement(a), complement(b)), join(complement(a), b)))))
% 0.21/0.53 = { by lemma 15 R->L }
% 0.21/0.53 complement(meet(join(join(meet(complement(a), b), meet(complement(a), complement(b))), meet(a, join(complement(a), b))), complement(join(meet(complement(a), complement(b)), join(complement(a), join(b, meet(complement(a), b)))))))
% 0.21/0.53 = { by axiom 8 (associativity_of_join) R->L }
% 0.21/0.53 complement(meet(join(join(meet(complement(a), b), meet(complement(a), complement(b))), meet(a, join(complement(a), b))), complement(join(meet(complement(a), complement(b)), join(join(complement(a), b), meet(complement(a), b))))))
% 0.21/0.53 = { by lemma 16 R->L }
% 0.21/0.53 complement(meet(join(join(meet(complement(a), b), meet(complement(a), complement(b))), meet(a, join(complement(a), b))), complement(join(join(complement(a), b), join(meet(complement(a), b), meet(complement(a), complement(b)))))))
% 0.21/0.53 = { by lemma 15 R->L }
% 0.21/0.53 complement(meet(join(join(meet(complement(a), b), meet(complement(a), complement(b))), meet(a, join(complement(a), b))), complement(join(join(join(complement(a), b), meet(a, join(complement(a), b))), join(meet(complement(a), b), meet(complement(a), complement(b)))))))
% 0.21/0.53 = { by axiom 8 (associativity_of_join) }
% 0.21/0.53 complement(meet(join(join(meet(complement(a), b), meet(complement(a), complement(b))), meet(a, join(complement(a), b))), complement(join(join(complement(a), b), join(meet(a, join(complement(a), b)), join(meet(complement(a), b), meet(complement(a), complement(b))))))))
% 0.21/0.53 = { by axiom 2 (commutativity_of_join) }
% 0.21/0.53 complement(meet(join(join(meet(complement(a), b), meet(complement(a), complement(b))), meet(a, join(complement(a), b))), complement(join(join(complement(a), b), join(join(meet(complement(a), b), meet(complement(a), complement(b))), meet(a, join(complement(a), b)))))))
% 0.21/0.53 = { by axiom 3 (complement_involution) R->L }
% 0.21/0.53 complement(meet(join(join(meet(complement(a), b), meet(complement(a), complement(b))), meet(a, join(complement(a), b))), complement(join(join(complement(a), b), complement(complement(join(join(meet(complement(a), b), meet(complement(a), complement(b))), meet(a, join(complement(a), b)))))))))
% 0.21/0.53 = { by axiom 3 (complement_involution) R->L }
% 0.21/0.53 complement(meet(join(join(meet(complement(a), b), meet(complement(a), complement(b))), meet(a, join(complement(a), b))), complement(join(complement(complement(join(complement(a), b))), complement(complement(join(join(meet(complement(a), b), meet(complement(a), complement(b))), meet(a, join(complement(a), b)))))))))
% 0.21/0.53 = { by axiom 10 (meet_complement) R->L }
% 0.21/0.53 complement(meet(join(join(meet(complement(a), b), meet(complement(a), complement(b))), meet(a, join(complement(a), b))), meet(complement(join(complement(a), b)), complement(join(join(meet(complement(a), b), meet(complement(a), complement(b))), meet(a, join(complement(a), b)))))))
% 0.21/0.53 = { by axiom 1 (commutativity_of_meet) R->L }
% 0.21/0.53 complement(meet(join(join(meet(complement(a), b), meet(complement(a), complement(b))), meet(a, join(complement(a), b))), meet(complement(join(join(meet(complement(a), b), meet(complement(a), complement(b))), meet(a, join(complement(a), b)))), complement(join(complement(a), b)))))
% 0.21/0.53 = { by axiom 6 (associativity_of_meet) R->L }
% 0.21/0.53 complement(meet(meet(join(join(meet(complement(a), b), meet(complement(a), complement(b))), meet(a, join(complement(a), b))), complement(join(join(meet(complement(a), b), meet(complement(a), complement(b))), meet(a, join(complement(a), b))))), complement(join(complement(a), b))))
% 0.21/0.53 = { by axiom 1 (commutativity_of_meet) }
% 0.21/0.53 complement(meet(complement(join(complement(a), b)), meet(join(join(meet(complement(a), b), meet(complement(a), complement(b))), meet(a, join(complement(a), b))), complement(join(join(meet(complement(a), b), meet(complement(a), complement(b))), meet(a, join(complement(a), b)))))))
% 0.21/0.53 = { by lemma 12 }
% 0.21/0.53 complement(meet(complement(join(complement(a), b)), n0))
% 0.21/0.53 = { by axiom 10 (meet_complement) }
% 0.21/0.53 complement(complement(join(complement(complement(join(complement(a), b))), complement(n0))))
% 0.21/0.53 = { by lemma 14 }
% 0.21/0.53 complement(complement(join(complement(complement(join(complement(a), b))), n1)))
% 0.21/0.53 = { by lemma 11 R->L }
% 0.21/0.53 complement(complement(join(complement(complement(join(complement(a), b))), join(X, complement(X)))))
% 0.21/0.53 = { by axiom 9 (join_complement) }
% 0.21/0.53 complement(complement(join(X, complement(X))))
% 0.21/0.53 = { by lemma 11 }
% 0.21/0.53 complement(complement(n1))
% 0.21/0.53 = { by lemma 13 }
% 0.21/0.53 complement(n0)
% 0.21/0.53 = { by lemma 14 }
% 0.21/0.53 n1
% 0.21/0.53 % SZS output end Proof
% 0.21/0.53
% 0.21/0.53 RESULT: Unsatisfiable (the axioms are contradictory).
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