TSTP Solution File: SEU148+3 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SEU148+3 : 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 15:49:04 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 : 15 ( 8 unt; 0 def)
% Number of atoms : 46 ( 0 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 54 ( 23 ~; 23 |; 8 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-3 aty)
% Number of variables : 17 ( 1 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(t6_zfmisc_1,plain,
( subset(singleton(a),singleton(b))
& ~ $equal(b,a) ),
file('/tmp/SystemOnTPTP10720/SEU148+3.p',unknown),
[] ).
cnf(145295896,plain,
subset(singleton(a),singleton(b)),
inference(rewrite,[status(thm)],[t6_zfmisc_1]),
[] ).
fof(l4_zfmisc_1,plain,
! [A,B] :
( ( ~ subset(A,singleton(B))
| $equal(empty_set,A)
| $equal(singleton(B),A) )
& ( ~ $equal(singleton(B),A)
| subset(A,singleton(B)) )
& ( ~ $equal(empty_set,A)
| subset(A,singleton(B)) ) ),
file('/tmp/SystemOnTPTP10720/SEU148+3.p',unknown),
[] ).
cnf(145222584,plain,
( ~ subset(A,singleton(B))
| $equal(empty_set,A)
| $equal(singleton(B),A) ),
inference(rewrite,[status(thm)],[l4_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/SystemOnTPTP10720/SEU148+3.p',unknown),
[] ).
cnf(145189472,plain,
( in(C,B)
| ~ $equal(A,C)
| ~ $equal(singleton(A),B) ),
inference(rewrite,[status(thm)],[d1_tarski]),
[] ).
cnf(156132264,plain,
in(A,singleton(A)),
inference(equality_resolution,[status(thm)],[145189472]),
[] ).
cnf(145177536,plain,
( ~ in(C,B)
| $equal(A,C)
| ~ $equal(singleton(A),B) ),
inference(rewrite,[status(thm)],[d1_tarski]),
[] ).
cnf(145284440,plain,
~ $equal(b,a),
inference(rewrite,[status(thm)],[t6_zfmisc_1]),
[] ).
cnf(155755544,plain,
( ~ in(a,A)
| ~ $equal(singleton(b),A) ),
inference(resolution,[status(thm)],[145177536,145284440]),
[] ).
cnf(156350168,plain,
~ $equal(singleton(b),singleton(a)),
inference(resolution,[status(thm)],[156132264,155755544]),
[] ).
cnf(157978448,plain,
$equal(empty_set,singleton(a)),
inference(forward_subsumption_resolution__resolution,[status(thm)],[145295896,145222584,156350168]),
[] ).
fof(l1_zfmisc_1,plain,
! [A] : ~ $equal(empty_set,singleton(A)),
file('/tmp/SystemOnTPTP10720/SEU148+3.p',unknown),
[] ).
cnf(145198952,plain,
~ $equal(empty_set,singleton(A)),
inference(rewrite,[status(thm)],[l1_zfmisc_1]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[157978448,145198952]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(t6_zfmisc_1,plain,((subset(singleton(a),singleton(b))&~$equal(b,a))),file('/tmp/SystemOnTPTP10720/SEU148+3.p',unknown),[]).
%
% cnf(145295896,plain,(subset(singleton(a),singleton(b))),inference(rewrite,[status(thm)],[t6_zfmisc_1]),[]).
%
% fof(l4_zfmisc_1,plain,(((~subset(A,singleton(B))|$equal(empty_set,A)|$equal(singleton(B),A))&(~$equal(singleton(B),A)|subset(A,singleton(B)))&(~$equal(empty_set,A)|subset(A,singleton(B))))),file('/tmp/SystemOnTPTP10720/SEU148+3.p',unknown),[]).
%
% cnf(145222584,plain,(~subset(A,singleton(B))|$equal(empty_set,A)|$equal(singleton(B),A)),inference(rewrite,[status(thm)],[l4_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/SystemOnTPTP10720/SEU148+3.p',unknown),[]).
%
% cnf(145189472,plain,(in(C,B)|~$equal(A,C)|~$equal(singleton(A),B)),inference(rewrite,[status(thm)],[d1_tarski]),[]).
%
% cnf(156132264,plain,(in(A,singleton(A))),inference(equality_resolution,[status(thm)],[145189472]),[]).
%
% cnf(145177536,plain,(~in(C,B)|$equal(A,C)|~$equal(singleton(A),B)),inference(rewrite,[status(thm)],[d1_tarski]),[]).
%
% cnf(145284440,plain,(~$equal(b,a)),inference(rewrite,[status(thm)],[t6_zfmisc_1]),[]).
%
% cnf(155755544,plain,(~in(a,A)|~$equal(singleton(b),A)),inference(resolution,[status(thm)],[145177536,145284440]),[]).
%
% cnf(156350168,plain,(~$equal(singleton(b),singleton(a))),inference(resolution,[status(thm)],[156132264,155755544]),[]).
%
% cnf(157978448,plain,($equal(empty_set,singleton(a))),inference(forward_subsumption_resolution__resolution,[status(thm)],[145295896,145222584,156350168]),[]).
%
% fof(l1_zfmisc_1,plain,(~$equal(empty_set,singleton(A))),file('/tmp/SystemOnTPTP10720/SEU148+3.p',unknown),[]).
%
% cnf(145198952,plain,(~$equal(empty_set,singleton(A))),inference(rewrite,[status(thm)],[l1_zfmisc_1]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[157978448,145198952]),[]).
%
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
%
%------------------------------------------------------------------------------