%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET004-1 : TPTP v3.4.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art05.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 15:22:37 EDT 2009
% Result : Unsatisfiable 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 15 ( 8 unt; 0 def)
% Number of atoms : 24 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 18 ( 9 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 18 ( 2 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_a_is_a_subset_of_aUb,plain,
~ subset(a,aub),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET004-1.tptp',unknown),
[] ).
cnf(170389640,plain,
~ subset(a,aub),
inference(rewrite,[status(thm)],[prove_a_is_a_subset_of_aUb]),
[] ).
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/SET004-1.tptp',unknown),
[] ).
cnf(170313208,plain,
( ~ member(member_of_1_not_of_2(A,B),B)
| subset(A,B) ),
inference(rewrite,[status(thm)],[subsets_axiom2]),
[] ).
fof(member_of_set1_is_member_of_union,plain,
! [A,B,C,D] :
( ~ union(A,B,C)
| ~ member(D,A)
| member(D,C) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET004-1.tptp',unknown),
[] ).
cnf(170349704,plain,
( ~ union(A,B,C)
| ~ member(D,A)
| member(D,C) ),
inference(rewrite,[status(thm)],[member_of_set1_is_member_of_union]),
[] ).
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/SET004-1.tptp',unknown),
[] ).
cnf(170303232,plain,
( subset(A,B)
| member(member_of_1_not_of_2(A,B),A) ),
inference(rewrite,[status(thm)],[subsets_axiom1]),
[] ).
cnf(178277976,plain,
member(member_of_1_not_of_2(a,aub),a),
inference(resolution,[status(thm)],[170303232,170389640]),
[] ).
cnf(178329888,plain,
( ~ union(a,A,B)
| member(member_of_1_not_of_2(a,aub),B) ),
inference(resolution,[status(thm)],[170349704,178277976]),
[] ).
fof(a_union_b_is_aUb,plain,
union(a,b,aub),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET004-1.tptp',unknown),
[] ).
cnf(170385608,plain,
union(a,b,aub),
inference(rewrite,[status(thm)],[a_union_b_is_aUb]),
[] ).
cnf(178338960,plain,
member(member_of_1_not_of_2(a,aub),aub),
inference(resolution,[status(thm)],[178329888,170385608]),
[] ).
cnf(178379736,plain,
subset(a,aub),
inference(resolution,[status(thm)],[170313208,178338960]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[170389640,178379736]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(prove_a_is_a_subset_of_aUb,plain,(~subset(a,aub)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET004-1.tptp',unknown),[]).
%
% cnf(170389640,plain,(~subset(a,aub)),inference(rewrite,[status(thm)],[prove_a_is_a_subset_of_aUb]),[]).
%
% 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/SET004-1.tptp',unknown),[]).
%
% cnf(170313208,plain,(~member(member_of_1_not_of_2(A,B),B)|subset(A,B)),inference(rewrite,[status(thm)],[subsets_axiom2]),[]).
%
% fof(member_of_set1_is_member_of_union,plain,(~union(A,B,C)|~member(D,A)|member(D,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET004-1.tptp',unknown),[]).
%
% cnf(170349704,plain,(~union(A,B,C)|~member(D,A)|member(D,C)),inference(rewrite,[status(thm)],[member_of_set1_is_member_of_union]),[]).
%
% 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/SET004-1.tptp',unknown),[]).
%
% cnf(170303232,plain,(subset(A,B)|member(member_of_1_not_of_2(A,B),A)),inference(rewrite,[status(thm)],[subsets_axiom1]),[]).
%
% cnf(178277976,plain,(member(member_of_1_not_of_2(a,aub),a)),inference(resolution,[status(thm)],[170303232,170389640]),[]).
%
% cnf(178329888,plain,(~union(a,A,B)|member(member_of_1_not_of_2(a,aub),B)),inference(resolution,[status(thm)],[170349704,178277976]),[]).
%
% fof(a_union_b_is_aUb,plain,(union(a,b,aub)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET004-1.tptp',unknown),[]).
%
% cnf(170385608,plain,(union(a,b,aub)),inference(rewrite,[status(thm)],[a_union_b_is_aUb]),[]).
%
% cnf(178338960,plain,(member(member_of_1_not_of_2(a,aub),aub)),inference(resolution,[status(thm)],[178329888,170385608]),[]).
%
% cnf(178379736,plain,(subset(a,aub)),inference(resolution,[status(thm)],[170313208,178338960]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[170389640,178379736]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------