%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SET933+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art07.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 03:48:35 EST 2010
% Result : Theorem 0.21s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 14 unt; 0 def)
% Number of atoms : 86 ( 14 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 99 ( 39 ~; 40 |; 17 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 44 ( 2 sgn 30 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(2,axiom,
! [X1,X2] :
( X2 = powerset(X1)
<=> ! [X3] :
( in(X3,X2)
<=> subset(X3,X1) ) ),
file('/tmp/tmpel-DM_/sel_SET933+1.p_1',d1_zfmisc_1) ).
fof(3,axiom,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
file('/tmp/tmpel-DM_/sel_SET933+1.p_1',l2_zfmisc_1) ).
fof(6,conjecture,
! [X1] : subset(singleton(X1),powerset(X1)),
file('/tmp/tmpel-DM_/sel_SET933+1.p_1',t80_zfmisc_1) ).
fof(7,axiom,
! [X1,X2] : subset(X1,X1),
file('/tmp/tmpel-DM_/sel_SET933+1.p_1',reflexivity_r1_tarski) ).
fof(8,negated_conjecture,
~ ! [X1] : subset(singleton(X1),powerset(X1)),
inference(assume_negation,[status(cth)],[6]) ).
fof(14,plain,
! [X1,X2] :
( ( X2 != powerset(X1)
| ! [X3] :
( ( ~ in(X3,X2)
| subset(X3,X1) )
& ( ~ subset(X3,X1)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( ~ in(X3,X2)
| ~ subset(X3,X1) )
& ( in(X3,X2)
| subset(X3,X1) ) )
| X2 = powerset(X1) ) ),
inference(fof_nnf,[status(thm)],[2]) ).
fof(15,plain,
! [X4,X5] :
( ( X5 != powerset(X4)
| ! [X6] :
( ( ~ in(X6,X5)
| subset(X6,X4) )
& ( ~ subset(X6,X4)
| in(X6,X5) ) ) )
& ( ? [X7] :
( ( ~ in(X7,X5)
| ~ subset(X7,X4) )
& ( in(X7,X5)
| subset(X7,X4) ) )
| X5 = powerset(X4) ) ),
inference(variable_rename,[status(thm)],[14]) ).
fof(16,plain,
! [X4,X5] :
( ( X5 != powerset(X4)
| ! [X6] :
( ( ~ in(X6,X5)
| subset(X6,X4) )
& ( ~ subset(X6,X4)
| in(X6,X5) ) ) )
& ( ( ( ~ in(esk2_2(X4,X5),X5)
| ~ subset(esk2_2(X4,X5),X4) )
& ( in(esk2_2(X4,X5),X5)
| subset(esk2_2(X4,X5),X4) ) )
| X5 = powerset(X4) ) ),
inference(skolemize,[status(esa)],[15]) ).
fof(17,plain,
! [X4,X5,X6] :
( ( ( ( ~ in(X6,X5)
| subset(X6,X4) )
& ( ~ subset(X6,X4)
| in(X6,X5) ) )
| X5 != powerset(X4) )
& ( ( ( ~ in(esk2_2(X4,X5),X5)
| ~ subset(esk2_2(X4,X5),X4) )
& ( in(esk2_2(X4,X5),X5)
| subset(esk2_2(X4,X5),X4) ) )
| X5 = powerset(X4) ) ),
inference(shift_quantors,[status(thm)],[16]) ).
fof(18,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X5)
| subset(X6,X4)
| X5 != powerset(X4) )
& ( ~ subset(X6,X4)
| in(X6,X5)
| X5 != powerset(X4) )
& ( ~ in(esk2_2(X4,X5),X5)
| ~ subset(esk2_2(X4,X5),X4)
| X5 = powerset(X4) )
& ( in(esk2_2(X4,X5),X5)
| subset(esk2_2(X4,X5),X4)
| X5 = powerset(X4) ) ),
inference(distribute,[status(thm)],[17]) ).
cnf(21,plain,
( in(X3,X1)
| X1 != powerset(X2)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[18]) ).
fof(23,plain,
! [X1,X2] :
( ( ~ subset(singleton(X1),X2)
| in(X1,X2) )
& ( ~ in(X1,X2)
| subset(singleton(X1),X2) ) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(24,plain,
! [X3,X4] :
( ( ~ subset(singleton(X3),X4)
| in(X3,X4) )
& ( ~ in(X3,X4)
| subset(singleton(X3),X4) ) ),
inference(variable_rename,[status(thm)],[23]) ).
cnf(25,plain,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[24]) ).
fof(33,negated_conjecture,
? [X1] : ~ subset(singleton(X1),powerset(X1)),
inference(fof_nnf,[status(thm)],[8]) ).
fof(34,negated_conjecture,
? [X2] : ~ subset(singleton(X2),powerset(X2)),
inference(variable_rename,[status(thm)],[33]) ).
fof(35,negated_conjecture,
~ subset(singleton(esk4_0),powerset(esk4_0)),
inference(skolemize,[status(esa)],[34]) ).
cnf(36,negated_conjecture,
~ subset(singleton(esk4_0),powerset(esk4_0)),
inference(split_conjunct,[status(thm)],[35]) ).
fof(37,plain,
! [X3,X4] : subset(X3,X3),
inference(variable_rename,[status(thm)],[7]) ).
cnf(38,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[37]) ).
cnf(42,plain,
( in(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(er,[status(thm)],[21,theory(equality)]) ).
cnf(46,plain,
in(X1,powerset(X1)),
inference(spm,[status(thm)],[42,38,theory(equality)]) ).
cnf(52,plain,
subset(singleton(X1),powerset(X1)),
inference(spm,[status(thm)],[25,46,theory(equality)]) ).
cnf(57,negated_conjecture,
$false,
inference(rw,[status(thm)],[36,52,theory(equality)]) ).
cnf(58,negated_conjecture,
$false,
inference(cn,[status(thm)],[57,theory(equality)]) ).
cnf(59,negated_conjecture,
$false,
58,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET933+1.p
% --creating new selector for []
% -running prover on /tmp/tmpel-DM_/sel_SET933+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET933+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET933+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET933+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
%
%------------------------------------------------------------------------------