%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SEU144+1 : TPTP v3.4.2. Released v3.3.0.
% 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 15:48:44 EDT 2009
% Result : Theorem 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 6 unt; 0 def)
% Number of atoms : 60 ( 0 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 69 ( 27 ~; 32 |; 10 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-3 aty)
% Number of variables : 28 ( 4 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(l2_zfmisc_1,plain,
( ( in(a,b)
| subset(singleton(a),b) )
& ( ~ subset(singleton(a),b)
| subset(singleton(a),b) )
& ( in(a,b)
| ~ in(a,b) )
& ( ~ subset(singleton(a),b)
| ~ in(a,b) ) ),
file('/tmp/SystemOnTPTP30222/SEU144+1.p',unknown),
[] ).
cnf(141829752,plain,
( in(a,b)
| subset(singleton(a),b) ),
inference(rewrite,[status(thm)],[l2_zfmisc_1]),
[] ).
fof(d1_tarski,plain,
! [C,B,A] :
( ( in(C,B)
| ~ $equal(A,C)
| ~ $equal(singleton(A),B) )
& ( ~ in(C,B)
| $equal(A,C)
| ~ $equal(singleton(A),B) )
& ( $equal(c(A,B,C),A)
| ~ $equal(c(A,B,C),A)
| $equal(singleton(A),B) )
& ( ~ in(c(A,B,C),B)
| ~ $equal(c(A,B,C),A)
| $equal(singleton(A),B) )
& ( $equal(c(A,B,C),A)
| in(c(A,B,C),B)
| $equal(singleton(A),B) )
& ( ~ in(c(A,B,C),B)
| in(c(A,B,C),B)
| $equal(singleton(A),B) ) ),
file('/tmp/SystemOnTPTP30222/SEU144+1.p',unknown),
[] ).
cnf(141728368,plain,
( in(C,B)
| ~ $equal(A,C)
| ~ $equal(singleton(A),B) ),
inference(rewrite,[status(thm)],[d1_tarski]),
[] ).
cnf(152942048,plain,
in(A,singleton(A)),
inference(equality_resolution,[status(thm)],[141728368]),
[] ).
fof(d3_tarski,plain,
! [A,B,C] :
( ( ~ subset(A,B)
| ~ in(C,A)
| in(C,B) )
& ( ~ in(c(A,B,C),B)
| subset(A,B) )
& ( in(c(A,B,C),A)
| subset(A,B) ) ),
file('/tmp/SystemOnTPTP30222/SEU144+1.p',unknown),
[] ).
cnf(141747640,plain,
( ~ subset(A,B)
| ~ in(C,A)
| in(C,B) ),
inference(rewrite,[status(thm)],[d3_tarski]),
[] ).
cnf(153186776,plain,
( ~ subset(singleton(A),B)
| in(A,B) ),
inference(resolution,[status(thm)],[152942048,141747640]),
[] ).
cnf(141823984,plain,
( ~ subset(singleton(a),b)
| ~ in(a,b) ),
inference(rewrite,[status(thm)],[l2_zfmisc_1]),
[] ).
cnf(153801168,plain,
~ subset(singleton(a),b),
inference(resolution,[status(thm)],[153186776,141823984]),
[] ).
cnf(141733888,plain,
( in(c(A,B,C),A)
| subset(A,B) ),
inference(rewrite,[status(thm)],[d3_tarski]),
[] ).
cnf(154013392,plain,
in(c(singleton(a),b,A),singleton(a)),
inference(resolution,[status(thm)],[153801168,141733888]),
[] ).
cnf(141712376,plain,
( ~ in(C,B)
| $equal(A,C)
| ~ $equal(singleton(A),B) ),
inference(rewrite,[status(thm)],[d1_tarski]),
[] ).
cnf(152792568,plain,
( ~ in(B,singleton(A))
| $equal(A,B) ),
inference(equality_resolution,[status(thm)],[141712376]),
[] ).
cnf(155864880,plain,
$equal(a,c(singleton(a),b,A)),
inference(resolution,[status(thm)],[154013392,152792568]),
[] ).
cnf(141739688,plain,
( ~ in(c(A,B,C),B)
| subset(A,B) ),
inference(rewrite,[status(thm)],[d3_tarski]),
[] ).
cnf(156091592,plain,
subset(singleton(a),b),
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[141829752,155864880,141739688,theory(equality)]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[156091592,153801168]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(l2_zfmisc_1,plain,(((in(a,b)|subset(singleton(a),b))&(~subset(singleton(a),b)|subset(singleton(a),b))&(in(a,b)|~in(a,b))&(~subset(singleton(a),b)|~in(a,b)))),file('/tmp/SystemOnTPTP30222/SEU144+1.p',unknown),[]).
%
% cnf(141829752,plain,(in(a,b)|subset(singleton(a),b)),inference(rewrite,[status(thm)],[l2_zfmisc_1]),[]).
%
% fof(d1_tarski,plain,(((in(C,B)|~$equal(A,C)|~$equal(singleton(A),B))&(~in(C,B)|$equal(A,C)|~$equal(singleton(A),B))&($equal(c(A,B,C),A)|~$equal(c(A,B,C),A)|$equal(singleton(A),B))&(~in(c(A,B,C),B)|~$equal(c(A,B,C),A)|$equal(singleton(A),B))&($equal(c(A,B,C),A)|in(c(A,B,C),B)|$equal(singleton(A),B))&(~in(c(A,B,C),B)|in(c(A,B,C),B)|$equal(singleton(A),B)))),file('/tmp/SystemOnTPTP30222/SEU144+1.p',unknown),[]).
%
% cnf(141728368,plain,(in(C,B)|~$equal(A,C)|~$equal(singleton(A),B)),inference(rewrite,[status(thm)],[d1_tarski]),[]).
%
% cnf(152942048,plain,(in(A,singleton(A))),inference(equality_resolution,[status(thm)],[141728368]),[]).
%
% fof(d3_tarski,plain,(((~subset(A,B)|~in(C,A)|in(C,B))&(~in(c(A,B,C),B)|subset(A,B))&(in(c(A,B,C),A)|subset(A,B)))),file('/tmp/SystemOnTPTP30222/SEU144+1.p',unknown),[]).
%
% cnf(141747640,plain,(~subset(A,B)|~in(C,A)|in(C,B)),inference(rewrite,[status(thm)],[d3_tarski]),[]).
%
% cnf(153186776,plain,(~subset(singleton(A),B)|in(A,B)),inference(resolution,[status(thm)],[152942048,141747640]),[]).
%
% cnf(141823984,plain,(~subset(singleton(a),b)|~in(a,b)),inference(rewrite,[status(thm)],[l2_zfmisc_1]),[]).
%
% cnf(153801168,plain,(~subset(singleton(a),b)),inference(resolution,[status(thm)],[153186776,141823984]),[]).
%
% cnf(141733888,plain,(in(c(A,B,C),A)|subset(A,B)),inference(rewrite,[status(thm)],[d3_tarski]),[]).
%
% cnf(154013392,plain,(in(c(singleton(a),b,A),singleton(a))),inference(resolution,[status(thm)],[153801168,141733888]),[]).
%
% cnf(141712376,plain,(~in(C,B)|$equal(A,C)|~$equal(singleton(A),B)),inference(rewrite,[status(thm)],[d1_tarski]),[]).
%
% cnf(152792568,plain,(~in(B,singleton(A))|$equal(A,B)),inference(equality_resolution,[status(thm)],[141712376]),[]).
%
% cnf(155864880,plain,($equal(a,c(singleton(a),b,A))),inference(resolution,[status(thm)],[154013392,152792568]),[]).
%
% cnf(141739688,plain,(~in(c(A,B,C),B)|subset(A,B)),inference(rewrite,[status(thm)],[d3_tarski]),[]).
%
% cnf(156091592,plain,(subset(singleton(a),b)),inference(forward_subsumption_resolution__paramodulation,[status(thm)],[141829752,155864880,141739688,theory(equality)]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[156091592,153801168]),[]).
%
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
%
%------------------------------------------------------------------------------