%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET876+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art09.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 2018MB
% OS : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sun Dec 26 03:42:44 EST 2010
% Result : Theorem 0.16s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 24 ( 6 unt; 0 def)
% Number of atoms : 86 ( 44 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 104 ( 42 ~; 38 |; 18 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn 30 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(3,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/tmp/tmpAR_xy9/sel_SET876+1.p_1',d1_tarski) ).
fof(5,axiom,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
file('/tmp/tmpAR_xy9/sel_SET876+1.p_1',l28_zfmisc_1) ).
fof(7,conjecture,
! [X1,X2] :
( X1 != X2
=> disjoint(singleton(X1),singleton(X2)) ),
file('/tmp/tmpAR_xy9/sel_SET876+1.p_1',t17_zfmisc_1) ).
fof(8,negated_conjecture,
~ ! [X1,X2] :
( X1 != X2
=> disjoint(singleton(X1),singleton(X2)) ),
inference(assume_negation,[status(cth)],[7]) ).
fof(10,plain,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
inference(fof_simplification,[status(thm)],[5,theory(equality)]) ).
fof(18,plain,
! [X1,X2] :
( ( X2 != singleton(X1)
| ! [X3] :
( ( ~ in(X3,X2)
| X3 = X1 )
& ( X3 != X1
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( ~ in(X3,X2)
| X3 != X1 )
& ( in(X3,X2)
| X3 = X1 ) )
| X2 = singleton(X1) ) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(19,plain,
! [X4,X5] :
( ( X5 != singleton(X4)
| ! [X6] :
( ( ~ in(X6,X5)
| X6 = X4 )
& ( X6 != X4
| in(X6,X5) ) ) )
& ( ? [X7] :
( ( ~ in(X7,X5)
| X7 != X4 )
& ( in(X7,X5)
| X7 = X4 ) )
| X5 = singleton(X4) ) ),
inference(variable_rename,[status(thm)],[18]) ).
fof(20,plain,
! [X4,X5] :
( ( X5 != singleton(X4)
| ! [X6] :
( ( ~ in(X6,X5)
| X6 = X4 )
& ( X6 != X4
| in(X6,X5) ) ) )
& ( ( ( ~ in(esk3_2(X4,X5),X5)
| esk3_2(X4,X5) != X4 )
& ( in(esk3_2(X4,X5),X5)
| esk3_2(X4,X5) = X4 ) )
| X5 = singleton(X4) ) ),
inference(skolemize,[status(esa)],[19]) ).
fof(21,plain,
! [X4,X5,X6] :
( ( ( ( ~ in(X6,X5)
| X6 = X4 )
& ( X6 != X4
| in(X6,X5) ) )
| X5 != singleton(X4) )
& ( ( ( ~ in(esk3_2(X4,X5),X5)
| esk3_2(X4,X5) != X4 )
& ( in(esk3_2(X4,X5),X5)
| esk3_2(X4,X5) = X4 ) )
| X5 = singleton(X4) ) ),
inference(shift_quantors,[status(thm)],[20]) ).
fof(22,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X5)
| X6 = X4
| X5 != singleton(X4) )
& ( X6 != X4
| in(X6,X5)
| X5 != singleton(X4) )
& ( ~ in(esk3_2(X4,X5),X5)
| esk3_2(X4,X5) != X4
| X5 = singleton(X4) )
& ( in(esk3_2(X4,X5),X5)
| esk3_2(X4,X5) = X4
| X5 = singleton(X4) ) ),
inference(distribute,[status(thm)],[21]) ).
cnf(26,plain,
( X3 = X2
| X1 != singleton(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[22]) ).
fof(30,plain,
! [X1,X2] :
( in(X1,X2)
| disjoint(singleton(X1),X2) ),
inference(fof_nnf,[status(thm)],[10]) ).
fof(31,plain,
! [X3,X4] :
( in(X3,X4)
| disjoint(singleton(X3),X4) ),
inference(variable_rename,[status(thm)],[30]) ).
cnf(32,plain,
( disjoint(singleton(X1),X2)
| in(X1,X2) ),
inference(split_conjunct,[status(thm)],[31]) ).
fof(36,negated_conjecture,
? [X1,X2] :
( X1 != X2
& ~ disjoint(singleton(X1),singleton(X2)) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(37,negated_conjecture,
? [X3,X4] :
( X3 != X4
& ~ disjoint(singleton(X3),singleton(X4)) ),
inference(variable_rename,[status(thm)],[36]) ).
fof(38,negated_conjecture,
( esk4_0 != esk5_0
& ~ disjoint(singleton(esk4_0),singleton(esk5_0)) ),
inference(skolemize,[status(esa)],[37]) ).
cnf(39,negated_conjecture,
~ disjoint(singleton(esk4_0),singleton(esk5_0)),
inference(split_conjunct,[status(thm)],[38]) ).
cnf(40,negated_conjecture,
esk4_0 != esk5_0,
inference(split_conjunct,[status(thm)],[38]) ).
cnf(41,negated_conjecture,
in(esk4_0,singleton(esk5_0)),
inference(spm,[status(thm)],[39,32,theory(equality)]) ).
cnf(45,plain,
( X1 = X2
| ~ in(X2,singleton(X1)) ),
inference(er,[status(thm)],[26,theory(equality)]) ).
cnf(50,negated_conjecture,
esk5_0 = esk4_0,
inference(spm,[status(thm)],[45,41,theory(equality)]) ).
cnf(51,negated_conjecture,
$false,
inference(sr,[status(thm)],[50,40,theory(equality)]) ).
cnf(52,negated_conjecture,
$false,
51,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET876+1.p
% --creating new selector for []
% -running prover on /tmp/tmpAR_xy9/sel_SET876+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET876+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET876+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET876+1.p
% Solved 1 out of 1.
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% See solution above
% # SZS output end CNFRefutation
%
%------------------------------------------------------------------------------