TSTP Solution File: SET012-1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET012-1 : TPTP v3.4.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art07.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1003MB
% OS : Linux 2.6.17-1.2142_FC4
% CPULimit : 600s
% DateTime : Wed May 6 15:23:16 EDT 2009
% Result : Unsatisfiable 0.5s
% Output : Refutation 0.5s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of formulae : 23 ( 7 unt; 0 def)
% Number of atoms : 41 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 35 ( 17 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 35 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(not_member_of_set_and_complement,plain,
! [A,B] :
( ~ member(A,B)
| ~ member(A,complement(B)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET012-1.tptp',unknown),
[] ).
cnf(158755104,plain,
( ~ member(A,B)
| ~ member(A,complement(B)) ),
inference(rewrite,[status(thm)],[not_member_of_set_and_complement]),
[] ).
fof(subsets_axiom1,plain,
! [A,B] :
( subset(A,B)
| member(member_of_1_not_of_2(A,B),A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET012-1.tptp',unknown),
[] ).
cnf(158733848,plain,
( subset(A,B)
| member(member_of_1_not_of_2(A,B),A) ),
inference(rewrite,[status(thm)],[subsets_axiom1]),
[] ).
cnf(167387832,plain,
( ~ member(member_of_1_not_of_2(A,B),complement(A))
| subset(A,B) ),
inference(resolution,[status(thm)],[158755104,158733848]),
[] ).
fof(subsets_axiom2,plain,
! [A,B] :
( ~ member(member_of_1_not_of_2(A,B),B)
| subset(A,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET012-1.tptp',unknown),
[] ).
cnf(158739672,plain,
( ~ member(member_of_1_not_of_2(A,B),B)
| subset(A,B) ),
inference(rewrite,[status(thm)],[subsets_axiom2]),
[] ).
fof(member_of_set_or_complement,plain,
! [A,B] :
( member(A,B)
| member(A,complement(B)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET012-1.tptp',unknown),
[] ).
cnf(158750072,plain,
( member(A,B)
| member(A,complement(B)) ),
inference(rewrite,[status(thm)],[member_of_set_or_complement]),
[] ).
cnf(167342176,plain,
( subset(A,complement(B))
| member(member_of_1_not_of_2(A,complement(B)),B) ),
inference(resolution,[status(thm)],[158739672,158750072]),
[] ).
cnf(181016376,plain,
subset(A,complement(complement(A))),
inference(resolution,[status(thm)],[167387832,167342176]),
[] ).
cnf(167412288,plain,
( ~ member(member_of_1_not_of_2(complement(A),B),A)
| subset(complement(A),B) ),
inference(resolution,[status(thm)],[158755104,158733848]),
[] ).
cnf(167324456,plain,
( subset(A,B)
| member(member_of_1_not_of_2(A,B),complement(B)) ),
inference(resolution,[status(thm)],[158739672,158750072]),
[] ).
cnf(190730328,plain,
subset(complement(complement(A)),A),
inference(resolution,[status(thm)],[167412288,167324456]),
[] ).
fof(subsets_are_set_equal_sets,plain,
! [A,B] :
( ~ subset(A,B)
| ~ subset(B,A)
| equal_sets(B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET012-1.tptp',unknown),
[] ).
cnf(158807984,plain,
( ~ subset(A,B)
| ~ subset(B,A)
| equal_sets(B,A) ),
inference(rewrite,[status(thm)],[subsets_are_set_equal_sets]),
[] ).
cnf(191309864,plain,
equal_sets(A,complement(complement(A))),
inference(forward_subsumption_resolution__resolution,[status(thm)],[181016376,190730328,158807984]),
[] ).
fof(symmetry_for_set_equal,plain,
! [A,B] :
( ~ equal_sets(A,B)
| equal_sets(B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET012-1.tptp',unknown),
[] ).
cnf(158821712,plain,
( ~ equal_sets(A,B)
| equal_sets(B,A) ),
inference(rewrite,[status(thm)],[symmetry_for_set_equal]),
[] ).
fof(prove_involution,plain,
~ equal_sets(complement(complement(a)),a),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET012-1.tptp',unknown),
[] ).
cnf(158854592,plain,
~ equal_sets(complement(complement(a)),a),
inference(rewrite,[status(thm)],[prove_involution]),
[] ).
cnf(167310184,plain,
~ equal_sets(a,complement(complement(a))),
inference(resolution,[status(thm)],[158821712,158854592]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[191309864,167310184]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(not_member_of_set_and_complement,plain,(~member(A,B)|~member(A,complement(B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET012-1.tptp',unknown),[]).
%
% cnf(158755104,plain,(~member(A,B)|~member(A,complement(B))),inference(rewrite,[status(thm)],[not_member_of_set_and_complement]),[]).
%
% fof(subsets_axiom1,plain,(subset(A,B)|member(member_of_1_not_of_2(A,B),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET012-1.tptp',unknown),[]).
%
% cnf(158733848,plain,(subset(A,B)|member(member_of_1_not_of_2(A,B),A)),inference(rewrite,[status(thm)],[subsets_axiom1]),[]).
%
% cnf(167387832,plain,(~member(member_of_1_not_of_2(A,B),complement(A))|subset(A,B)),inference(resolution,[status(thm)],[158755104,158733848]),[]).
%
% fof(subsets_axiom2,plain,(~member(member_of_1_not_of_2(A,B),B)|subset(A,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET012-1.tptp',unknown),[]).
%
% cnf(158739672,plain,(~member(member_of_1_not_of_2(A,B),B)|subset(A,B)),inference(rewrite,[status(thm)],[subsets_axiom2]),[]).
%
% fof(member_of_set_or_complement,plain,(member(A,B)|member(A,complement(B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET012-1.tptp',unknown),[]).
%
% cnf(158750072,plain,(member(A,B)|member(A,complement(B))),inference(rewrite,[status(thm)],[member_of_set_or_complement]),[]).
%
% cnf(167342176,plain,(subset(A,complement(B))|member(member_of_1_not_of_2(A,complement(B)),B)),inference(resolution,[status(thm)],[158739672,158750072]),[]).
%
% cnf(181016376,plain,(subset(A,complement(complement(A)))),inference(resolution,[status(thm)],[167387832,167342176]),[]).
%
% cnf(167412288,plain,(~member(member_of_1_not_of_2(complement(A),B),A)|subset(complement(A),B)),inference(resolution,[status(thm)],[158755104,158733848]),[]).
%
% cnf(167324456,plain,(subset(A,B)|member(member_of_1_not_of_2(A,B),complement(B))),inference(resolution,[status(thm)],[158739672,158750072]),[]).
%
% cnf(190730328,plain,(subset(complement(complement(A)),A)),inference(resolution,[status(thm)],[167412288,167324456]),[]).
%
% fof(subsets_are_set_equal_sets,plain,(~subset(A,B)|~subset(B,A)|equal_sets(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET012-1.tptp',unknown),[]).
%
% cnf(158807984,plain,(~subset(A,B)|~subset(B,A)|equal_sets(B,A)),inference(rewrite,[status(thm)],[subsets_are_set_equal_sets]),[]).
%
% cnf(191309864,plain,(equal_sets(A,complement(complement(A)))),inference(forward_subsumption_resolution__resolution,[status(thm)],[181016376,190730328,158807984]),[]).
%
% fof(symmetry_for_set_equal,plain,(~equal_sets(A,B)|equal_sets(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET012-1.tptp',unknown),[]).
%
% cnf(158821712,plain,(~equal_sets(A,B)|equal_sets(B,A)),inference(rewrite,[status(thm)],[symmetry_for_set_equal]),[]).
%
% fof(prove_involution,plain,(~equal_sets(complement(complement(a)),a)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET012-1.tptp',unknown),[]).
%
% cnf(158854592,plain,(~equal_sets(complement(complement(a)),a)),inference(rewrite,[status(thm)],[prove_involution]),[]).
%
% cnf(167310184,plain,(~equal_sets(a,complement(complement(a)))),inference(resolution,[status(thm)],[158821712,158854592]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[191309864,167310184]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------