TSTP Solution File: SEU147+1 by Faust---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SEU147+1 : TPTP v3.4.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art06.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 15:48:53 EDT 2009
% Result : Theorem 5.8s
% Output : Refutation 5.8s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 27 ( 9 unt; 0 def)
% Number of atoms : 94 ( 0 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 108 ( 41 ~; 54 |; 13 &)
% ( 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 : 5 ( 5 usr; 1 con; 0-3 aty)
% Number of variables : 39 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(d1_zfmisc_1,plain,
! [C,B,A] :
( ( in(C,B)
| ~ subset(C,A)
| ~ $equal(powerset(A),B) )
& ( ~ in(C,B)
| subset(C,A)
| ~ $equal(powerset(A),B) )
& ( subset(c(A,B,C),A)
| ~ subset(c(A,B,C),A)
| $equal(powerset(A),B) )
& ( ~ in(c(A,B,C),B)
| ~ subset(c(A,B,C),A)
| $equal(powerset(A),B) )
& ( subset(c(A,B,C),A)
| in(c(A,B,C),B)
| $equal(powerset(A),B) )
& ( ~ in(c(A,B,C),B)
| in(c(A,B,C),B)
| $equal(powerset(A),B) ) ),
file('/tmp/SystemOnTPTP30149/SEU147+1.p',unknown),
[] ).
cnf(166990688,plain,
( in(C,B)
| ~ subset(C,A)
| ~ $equal(powerset(A),B) ),
inference(rewrite,[status(thm)],[d1_zfmisc_1]),
[] ).
fof(reflexivity_r1_tarski,plain,
! [A] : subset(A,A),
file('/tmp/SystemOnTPTP30149/SEU147+1.p',unknown),
[] ).
cnf(167017432,plain,
subset(A,A),
inference(rewrite,[status(thm)],[reflexivity_r1_tarski]),
[] ).
cnf(174878016,plain,
( in(A,B)
| ~ $equal(powerset(A),B) ),
inference(resolution,[status(thm)],[166990688,167017432]),
[] ).
cnf(177977184,plain,
in(A,powerset(A)),
inference(equality_resolution,[status(thm)],[174878016]),
[] ).
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/SystemOnTPTP30149/SEU147+1.p',unknown),
[] ).
cnf(166949856,plain,
( in(C,B)
| ~ $equal(A,C)
| ~ $equal(singleton(A),B) ),
inference(rewrite,[status(thm)],[d1_tarski]),
[] ).
fof(t3_xboole_1,plain,
! [A] :
( ~ subset(A,empty_set)
| $equal(empty_set,A) ),
file('/tmp/SystemOnTPTP30149/SEU147+1.p',unknown),
[] ).
cnf(167056680,plain,
( ~ subset(A,empty_set)
| $equal(empty_set,A) ),
inference(rewrite,[status(thm)],[t3_xboole_1]),
[] ).
cnf(175465920,plain,
( in(B,A)
| ~ $equal(singleton(empty_set),A)
| ~ subset(B,empty_set) ),
inference(resolution,[status(thm)],[166949856,167056680]),
[] ).
cnf(189978552,plain,
( in(A,singleton(empty_set))
| ~ subset(A,empty_set) ),
inference(equality_resolution,[status(thm)],[175465920]),
[] ).
cnf(166979984,plain,
( ~ in(C,B)
| subset(C,A)
| ~ $equal(powerset(A),B) ),
inference(rewrite,[status(thm)],[d1_zfmisc_1]),
[] ).
cnf(177227320,plain,
( ~ in(B,powerset(A))
| subset(B,A) ),
inference(equality_resolution,[status(thm)],[166979984]),
[] ).
cnf(192331848,plain,
( in(A,singleton(empty_set))
| ~ in(A,powerset(empty_set)) ),
inference(resolution,[status(thm)],[189978552,177227320]),
[] ).
fof(t2_tarski,plain,
! [A,B] :
( ( in(c(A,B),B)
| in(c(A,B),A)
| $equal(B,A) )
& ( ~ in(c(A,B),A)
| in(c(A,B),A)
| $equal(B,A) )
& ( in(c(A,B),B)
| ~ in(c(A,B),B)
| $equal(B,A) )
& ( ~ in(c(A,B),A)
| ~ in(c(A,B),B)
| $equal(B,A) ) ),
file('/tmp/SystemOnTPTP30149/SEU147+1.p',unknown),
[] ).
cnf(167050376,plain,
( in(c(A,B),B)
| in(c(A,B),A)
| $equal(B,A) ),
inference(rewrite,[status(thm)],[t2_tarski]),
[] ).
fof(t1_zfmisc_1,plain,
~ $equal(singleton(empty_set),powerset(empty_set)),
file('/tmp/SystemOnTPTP30149/SEU147+1.p',unknown),
[] ).
cnf(167030632,plain,
~ $equal(singleton(empty_set),powerset(empty_set)),
inference(rewrite,[status(thm)],[t1_zfmisc_1]),
[] ).
cnf(174935872,plain,
( in(c(powerset(empty_set),singleton(empty_set)),singleton(empty_set))
| in(c(powerset(empty_set),singleton(empty_set)),powerset(empty_set)) ),
inference(resolution,[status(thm)],[167050376,167030632]),
[] ).
cnf(236776368,plain,
in(c(powerset(empty_set),singleton(empty_set)),singleton(empty_set)),
inference(resolution,[status(thm)],[192331848,174935872]),
[] ).
cnf(166937856,plain,
( ~ in(C,B)
| $equal(A,C)
| ~ $equal(singleton(A),B) ),
inference(rewrite,[status(thm)],[d1_tarski]),
[] ).
cnf(175115184,plain,
( ~ in(B,singleton(A))
| $equal(A,B) ),
inference(equality_resolution,[status(thm)],[166937856]),
[] ).
cnf(263907808,plain,
$equal(empty_set,c(powerset(empty_set),singleton(empty_set))),
inference(resolution,[status(thm)],[236776368,175115184]),
[] ).
cnf(167042584,plain,
( ~ in(c(A,B),A)
| ~ in(c(A,B),B)
| $equal(B,A) ),
inference(rewrite,[status(thm)],[t2_tarski]),
[] ).
cnf(266300696,plain,
$equal(singleton(empty_set),powerset(empty_set)),
inference(forward_subsumption_resolution__paramodulation,[status(thm)],[177977184,236776368,263907808,167042584,theory(equality)]),
[] ).
cnf(contradiction,plain,
$false,
inference(resolution,[status(thm)],[266300696,167030632]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 6 seconds
% START OF PROOF SEQUENCE
% fof(d1_zfmisc_1,plain,(((in(C,B)|~subset(C,A)|~$equal(powerset(A),B))&(~in(C,B)|subset(C,A)|~$equal(powerset(A),B))&(subset(c(A,B,C),A)|~subset(c(A,B,C),A)|$equal(powerset(A),B))&(~in(c(A,B,C),B)|~subset(c(A,B,C),A)|$equal(powerset(A),B))&(subset(c(A,B,C),A)|in(c(A,B,C),B)|$equal(powerset(A),B))&(~in(c(A,B,C),B)|in(c(A,B,C),B)|$equal(powerset(A),B)))),file('/tmp/SystemOnTPTP30149/SEU147+1.p',unknown),[]).
%
% cnf(166990688,plain,(in(C,B)|~subset(C,A)|~$equal(powerset(A),B)),inference(rewrite,[status(thm)],[d1_zfmisc_1]),[]).
%
% fof(reflexivity_r1_tarski,plain,(subset(A,A)),file('/tmp/SystemOnTPTP30149/SEU147+1.p',unknown),[]).
%
% cnf(167017432,plain,(subset(A,A)),inference(rewrite,[status(thm)],[reflexivity_r1_tarski]),[]).
%
% cnf(174878016,plain,(in(A,B)|~$equal(powerset(A),B)),inference(resolution,[status(thm)],[166990688,167017432]),[]).
%
% cnf(177977184,plain,(in(A,powerset(A))),inference(equality_resolution,[status(thm)],[174878016]),[]).
%
% fof(d1_tarski,plain,(((in(C,B)|~$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)|$equal(singleton(A),B)))),file('/tmp/SystemOnTPTP30149/SEU147+1.p',unknown),[]).
%
% cnf(166949856,plain,(in(C,B)|~$equal(A,C)|~$equal(singleton(A),B)),inference(rewrite,[status(thm)],[d1_tarski]),[]).
%
% fof(t3_xboole_1,plain,(~subset(A,empty_set)|$equal(empty_set,A)),file('/tmp/SystemOnTPTP30149/SEU147+1.p',unknown),[]).
%
% cnf(167056680,plain,(~subset(A,empty_set)|$equal(empty_set,A)),inference(rewrite,[status(thm)],[t3_xboole_1]),[]).
%
% cnf(175465920,plain,(in(B,A)|~$equal(singleton(empty_set),A)|~subset(B,empty_set)),inference(resolution,[status(thm)],[166949856,167056680]),[]).
%
% cnf(189978552,plain,(in(A,singleton(empty_set))|~subset(A,empty_set)),inference(equality_resolution,[status(thm)],[175465920]),[]).
%
% cnf(166979984,plain,(~in(C,B)|subset(C,A)|~$equal(powerset(A),B)),inference(rewrite,[status(thm)],[d1_zfmisc_1]),[]).
%
% cnf(177227320,plain,(~in(B,powerset(A))|subset(B,A)),inference(equality_resolution,[status(thm)],[166979984]),[]).
%
% cnf(192331848,plain,(in(A,singleton(empty_set))|~in(A,powerset(empty_set))),inference(resolution,[status(thm)],[189978552,177227320]),[]).
%
% fof(t2_tarski,plain,(((in(c(A,B),B)|in(c(A,B),A)|$equal(B,A))&(~in(c(A,B),A)|in(c(A,B),A)|$equal(B,A))&(in(c(A,B),B)|~in(c(A,B),B)|$equal(B,A))&(~in(c(A,B),A)|~in(c(A,B),B)|$equal(B,A)))),file('/tmp/SystemOnTPTP30149/SEU147+1.p',unknown),[]).
%
% cnf(167050376,plain,(in(c(A,B),B)|in(c(A,B),A)|$equal(B,A)),inference(rewrite,[status(thm)],[t2_tarski]),[]).
%
% fof(t1_zfmisc_1,plain,(~$equal(singleton(empty_set),powerset(empty_set))),file('/tmp/SystemOnTPTP30149/SEU147+1.p',unknown),[]).
%
% cnf(167030632,plain,(~$equal(singleton(empty_set),powerset(empty_set))),inference(rewrite,[status(thm)],[t1_zfmisc_1]),[]).
%
% cnf(174935872,plain,(in(c(powerset(empty_set),singleton(empty_set)),singleton(empty_set))|in(c(powerset(empty_set),singleton(empty_set)),powerset(empty_set))),inference(resolution,[status(thm)],[167050376,167030632]),[]).
%
% cnf(236776368,plain,(in(c(powerset(empty_set),singleton(empty_set)),singleton(empty_set))),inference(resolution,[status(thm)],[192331848,174935872]),[]).
%
% cnf(166937856,plain,(~in(C,B)|$equal(A,C)|~$equal(singleton(A),B)),inference(rewrite,[status(thm)],[d1_tarski]),[]).
%
% cnf(175115184,plain,(~in(B,singleton(A))|$equal(A,B)),inference(equality_resolution,[status(thm)],[166937856]),[]).
%
% cnf(263907808,plain,($equal(empty_set,c(powerset(empty_set),singleton(empty_set)))),inference(resolution,[status(thm)],[236776368,175115184]),[]).
%
% cnf(167042584,plain,(~in(c(A,B),A)|~in(c(A,B),B)|$equal(B,A)),inference(rewrite,[status(thm)],[t2_tarski]),[]).
%
% cnf(266300696,plain,($equal(singleton(empty_set),powerset(empty_set))),inference(forward_subsumption_resolution__paramodulation,[status(thm)],[177977184,236776368,263907808,167042584,theory(equality)]),[]).
%
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[266300696,167030632]),[]).
%
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
%
%------------------------------------------------------------------------------