TSTP Solution File: SET877+1 by Faust---1.0
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%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET877+1 : TPTP v3.4.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art01.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 15:40:18 EDT 2009
% Result : Theorem 0.1s
% Output : Refutation 0.1s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 13 ( 7 unt; 0 def)
% Number of atoms : 36 ( 0 equ)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 41 ( 18 ~; 17 |; 6 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 15 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(t18_zfmisc_1,plain,
( $equal(set_intersection2(singleton(a),singleton(b)),singleton(a))
& ~ $equal(b,a) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET877+1.tptp',unknown),
[] ).
cnf(168310208,plain,
$equal(set_intersection2(singleton(a),singleton(b)),singleton(a)),
inference(rewrite,[status(thm)],[t18_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('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET877+1.tptp',unknown),
[] ).
cnf(168212752,plain,
( ~ in(C,B)
| $equal(A,C)
| ~ $equal(singleton(A),B) ),
inference(rewrite,[status(thm)],[d1_tarski]),
[] ).
cnf(168302808,plain,
~ $equal(b,a),
inference(rewrite,[status(thm)],[t18_zfmisc_1]),
[] ).
cnf(178755504,plain,
( ~ in(a,A)
| ~ $equal(singleton(b),A) ),
inference(resolution,[status(thm)],[168212752,168302808]),
[] ).
cnf(179643152,plain,
~ in(a,singleton(b)),
inference(equality_resolution,[status(thm)],[178755504]),
[] ).
fof(l30_zfmisc_1,plain,
! [A,B] :
( ~ $equal(set_intersection2(A,singleton(B)),singleton(B))
| in(B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET877+1.tptp',unknown),
[] ).
cnf(168235008,plain,
( ~ $equal(set_intersection2(A,singleton(B)),singleton(B))
| in(B,A) ),
inference(rewrite,[status(thm)],[l30_zfmisc_1]),
[] ).
cnf(179803408,plain,
~ $equal(set_intersection2(singleton(b),singleton(a)),singleton(a)),
inference(resolution,[status(thm)],[179643152,168235008]),
[] ).
fof(commutativity_k3_xboole_0,plain,
! [B,A] : $equal(set_intersection2(B,A),set_intersection2(A,B)),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET877+1.tptp',unknown),
[] ).
cnf(168179304,plain,
$equal(set_intersection2(B,A),set_intersection2(A,B)),
inference(rewrite,[status(thm)],[commutativity_k3_xboole_0]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[168310208,179803408,168179304,theory(equality)]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(t18_zfmisc_1,plain,(($equal(set_intersection2(singleton(a),singleton(b)),singleton(a))&~$equal(b,a))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET877+1.tptp',unknown),[]).
%
% cnf(168310208,plain,($equal(set_intersection2(singleton(a),singleton(b)),singleton(a))),inference(rewrite,[status(thm)],[t18_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('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET877+1.tptp',unknown),[]).
%
% cnf(168212752,plain,(~in(C,B)|$equal(A,C)|~$equal(singleton(A),B)),inference(rewrite,[status(thm)],[d1_tarski]),[]).
%
% cnf(168302808,plain,(~$equal(b,a)),inference(rewrite,[status(thm)],[t18_zfmisc_1]),[]).
%
% cnf(178755504,plain,(~in(a,A)|~$equal(singleton(b),A)),inference(resolution,[status(thm)],[168212752,168302808]),[]).
%
% cnf(179643152,plain,(~in(a,singleton(b))),inference(equality_resolution,[status(thm)],[178755504]),[]).
%
% fof(l30_zfmisc_1,plain,(~$equal(set_intersection2(A,singleton(B)),singleton(B))|in(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET877+1.tptp',unknown),[]).
%
% cnf(168235008,plain,(~$equal(set_intersection2(A,singleton(B)),singleton(B))|in(B,A)),inference(rewrite,[status(thm)],[l30_zfmisc_1]),[]).
%
% cnf(179803408,plain,(~$equal(set_intersection2(singleton(b),singleton(a)),singleton(a))),inference(resolution,[status(thm)],[179643152,168235008]),[]).
%
% fof(commutativity_k3_xboole_0,plain,($equal(set_intersection2(B,A),set_intersection2(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET877+1.tptp',unknown),[]).
%
% cnf(168179304,plain,($equal(set_intersection2(B,A),set_intersection2(A,B))),inference(rewrite,[status(thm)],[commutativity_k3_xboole_0]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__paramodulation,[status(thm)],[168310208,179803408,168179304,theory(equality)]),[]).
%
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
%
%------------------------------------------------------------------------------