%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET875+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art01.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 03:42:37 EST 2010
% Result : Theorem 0.19s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 23 ( 6 unt; 0 def)
% Number of atoms : 84 ( 43 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 101 ( 40 ~; 38 |; 21 &)
% ( 2 <=>; 0 =>; 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 : 41 ( 0 sgn 28 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1,X2] :
~ ( disjoint(singleton(X1),X2)
& in(X1,X2) ),
file('/tmp/tmpGMG931/sel_SET875+1.p_1',l25_zfmisc_1) ).
fof(3,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/tmp/tmpGMG931/sel_SET875+1.p_1',d1_tarski) ).
fof(7,conjecture,
! [X1,X2] :
~ ( disjoint(singleton(X1),singleton(X2))
& X1 = X2 ),
file('/tmp/tmpGMG931/sel_SET875+1.p_1',t16_zfmisc_1) ).
fof(8,negated_conjecture,
~ ! [X1,X2] :
~ ( disjoint(singleton(X1),singleton(X2))
& X1 = X2 ),
inference(assume_negation,[status(cth)],[7]) ).
fof(14,plain,
! [X1,X2] :
( ~ disjoint(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(15,plain,
! [X3,X4] :
( ~ disjoint(singleton(X3),X4)
| ~ in(X3,X4) ),
inference(variable_rename,[status(thm)],[14]) ).
cnf(16,plain,
( ~ in(X1,X2)
| ~ disjoint(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[15]) ).
fof(17,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(18,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)],[17]) ).
fof(19,plain,
! [X4,X5] :
( ( X5 != singleton(X4)
| ! [X6] :
( ( ~ in(X6,X5)
| X6 = X4 )
& ( X6 != X4
| in(X6,X5) ) ) )
& ( ( ( ~ in(esk2_2(X4,X5),X5)
| esk2_2(X4,X5) != X4 )
& ( in(esk2_2(X4,X5),X5)
| esk2_2(X4,X5) = X4 ) )
| X5 = singleton(X4) ) ),
inference(skolemize,[status(esa)],[18]) ).
fof(20,plain,
! [X4,X5,X6] :
( ( ( ( ~ in(X6,X5)
| X6 = X4 )
& ( X6 != X4
| in(X6,X5) ) )
| X5 != singleton(X4) )
& ( ( ( ~ in(esk2_2(X4,X5),X5)
| esk2_2(X4,X5) != X4 )
& ( in(esk2_2(X4,X5),X5)
| esk2_2(X4,X5) = X4 ) )
| X5 = singleton(X4) ) ),
inference(shift_quantors,[status(thm)],[19]) ).
fof(21,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X5)
| X6 = X4
| X5 != singleton(X4) )
& ( X6 != X4
| in(X6,X5)
| X5 != singleton(X4) )
& ( ~ in(esk2_2(X4,X5),X5)
| esk2_2(X4,X5) != X4
| X5 = singleton(X4) )
& ( in(esk2_2(X4,X5),X5)
| esk2_2(X4,X5) = X4
| X5 = singleton(X4) ) ),
inference(distribute,[status(thm)],[20]) ).
cnf(24,plain,
( in(X3,X1)
| X1 != singleton(X2)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[21]) ).
fof(35,negated_conjecture,
? [X1,X2] :
( disjoint(singleton(X1),singleton(X2))
& X1 = X2 ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(36,negated_conjecture,
? [X3,X4] :
( disjoint(singleton(X3),singleton(X4))
& X3 = X4 ),
inference(variable_rename,[status(thm)],[35]) ).
fof(37,negated_conjecture,
( disjoint(singleton(esk4_0),singleton(esk5_0))
& esk4_0 = esk5_0 ),
inference(skolemize,[status(esa)],[36]) ).
cnf(38,negated_conjecture,
esk4_0 = esk5_0,
inference(split_conjunct,[status(thm)],[37]) ).
cnf(39,negated_conjecture,
disjoint(singleton(esk4_0),singleton(esk5_0)),
inference(split_conjunct,[status(thm)],[37]) ).
cnf(40,negated_conjecture,
disjoint(singleton(esk4_0),singleton(esk4_0)),
inference(rw,[status(thm)],[39,38,theory(equality)]) ).
cnf(43,plain,
( in(X1,X2)
| singleton(X1) != X2 ),
inference(er,[status(thm)],[24,theory(equality)]) ).
cnf(44,negated_conjecture,
~ in(esk4_0,singleton(esk4_0)),
inference(spm,[status(thm)],[16,40,theory(equality)]) ).
cnf(48,negated_conjecture,
$false,
inference(spm,[status(thm)],[44,43,theory(equality)]) ).
cnf(53,negated_conjecture,
$false,
48,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET875+1.p
% --creating new selector for []
% -running prover on /tmp/tmpGMG931/sel_SET875+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET875+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET875+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET875+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
%
%------------------------------------------------------------------------------