%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU354+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art03.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 07:42:36 EST 2010
% Result : Theorem 0.30s
% Output : CNFRefutation 0.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 27 ( 9 unt; 0 def)
% Number of atoms : 72 ( 32 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 80 ( 35 ~; 30 |; 9 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 23 ( 0 sgn 14 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(24,axiom,
! [X1,X2] :
( element(X2,X1)
=> ( proper_element(X2,X1)
<=> X2 != union(X1) ) ),
file('/tmp/tmp5t5mnY/sel_SEU354+1.p_1',d2_tex_2) ).
fof(30,axiom,
! [X1] : union(powerset(X1)) = X1,
file('/tmp/tmp5t5mnY/sel_SEU354+1.p_1',t99_zfmisc_1) ).
fof(32,conjecture,
! [X1,X2] :
( element(X2,powerset(X1))
=> ( proper_element(X2,powerset(X1))
<=> X2 != X1 ) ),
file('/tmp/tmp5t5mnY/sel_SEU354+1.p_1',t5_tex_2) ).
fof(44,negated_conjecture,
~ ! [X1,X2] :
( element(X2,powerset(X1))
=> ( proper_element(X2,powerset(X1))
<=> X2 != X1 ) ),
inference(assume_negation,[status(cth)],[32]) ).
fof(144,plain,
! [X1,X2] :
( ~ element(X2,X1)
| ( ( ~ proper_element(X2,X1)
| X2 != union(X1) )
& ( X2 = union(X1)
| proper_element(X2,X1) ) ) ),
inference(fof_nnf,[status(thm)],[24]) ).
fof(145,plain,
! [X3,X4] :
( ~ element(X4,X3)
| ( ( ~ proper_element(X4,X3)
| X4 != union(X3) )
& ( X4 = union(X3)
| proper_element(X4,X3) ) ) ),
inference(variable_rename,[status(thm)],[144]) ).
fof(146,plain,
! [X3,X4] :
( ( ~ proper_element(X4,X3)
| X4 != union(X3)
| ~ element(X4,X3) )
& ( X4 = union(X3)
| proper_element(X4,X3)
| ~ element(X4,X3) ) ),
inference(distribute,[status(thm)],[145]) ).
cnf(147,plain,
( proper_element(X1,X2)
| X1 = union(X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[146]) ).
cnf(148,plain,
( ~ element(X1,X2)
| X1 != union(X2)
| ~ proper_element(X1,X2) ),
inference(split_conjunct,[status(thm)],[146]) ).
fof(164,plain,
! [X2] : union(powerset(X2)) = X2,
inference(variable_rename,[status(thm)],[30]) ).
cnf(165,plain,
union(powerset(X1)) = X1,
inference(split_conjunct,[status(thm)],[164]) ).
fof(169,negated_conjecture,
? [X1,X2] :
( element(X2,powerset(X1))
& ( ~ proper_element(X2,powerset(X1))
| X2 = X1 )
& ( proper_element(X2,powerset(X1))
| X2 != X1 ) ),
inference(fof_nnf,[status(thm)],[44]) ).
fof(170,negated_conjecture,
? [X3,X4] :
( element(X4,powerset(X3))
& ( ~ proper_element(X4,powerset(X3))
| X4 = X3 )
& ( proper_element(X4,powerset(X3))
| X4 != X3 ) ),
inference(variable_rename,[status(thm)],[169]) ).
fof(171,negated_conjecture,
( element(esk5_0,powerset(esk4_0))
& ( ~ proper_element(esk5_0,powerset(esk4_0))
| esk5_0 = esk4_0 )
& ( proper_element(esk5_0,powerset(esk4_0))
| esk5_0 != esk4_0 ) ),
inference(skolemize,[status(esa)],[170]) ).
cnf(172,negated_conjecture,
( proper_element(esk5_0,powerset(esk4_0))
| esk5_0 != esk4_0 ),
inference(split_conjunct,[status(thm)],[171]) ).
cnf(173,negated_conjecture,
( esk5_0 = esk4_0
| ~ proper_element(esk5_0,powerset(esk4_0)) ),
inference(split_conjunct,[status(thm)],[171]) ).
cnf(174,negated_conjecture,
element(esk5_0,powerset(esk4_0)),
inference(split_conjunct,[status(thm)],[171]) ).
cnf(330,negated_conjecture,
( union(powerset(esk4_0)) = esk5_0
| proper_element(esk5_0,powerset(esk4_0)) ),
inference(spm,[status(thm)],[147,174,theory(equality)]) ).
cnf(336,negated_conjecture,
( esk4_0 = esk5_0
| proper_element(esk5_0,powerset(esk4_0)) ),
inference(rw,[status(thm)],[330,165,theory(equality)]) ).
cnf(369,negated_conjecture,
( union(powerset(esk4_0)) != esk5_0
| ~ element(esk5_0,powerset(esk4_0))
| esk4_0 != esk5_0 ),
inference(spm,[status(thm)],[148,172,theory(equality)]) ).
cnf(370,negated_conjecture,
( esk4_0 != esk5_0
| ~ element(esk5_0,powerset(esk4_0))
| esk4_0 != esk5_0 ),
inference(rw,[status(thm)],[369,165,theory(equality)]) ).
cnf(371,negated_conjecture,
( esk4_0 != esk5_0
| $false
| esk4_0 != esk5_0 ),
inference(rw,[status(thm)],[370,174,theory(equality)]) ).
cnf(372,negated_conjecture,
esk4_0 != esk5_0,
inference(cn,[status(thm)],[371,theory(equality)]) ).
cnf(526,negated_conjecture,
esk4_0 = esk5_0,
inference(csr,[status(thm)],[336,173]) ).
cnf(528,negated_conjecture,
$false,
inference(rw,[status(thm)],[372,526,theory(equality)]) ).
cnf(529,negated_conjecture,
$false,
inference(cn,[status(thm)],[528,theory(equality)]) ).
cnf(530,negated_conjecture,
$false,
529,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU354+1.p
% --creating new selector for []
% -running prover on /tmp/tmp5t5mnY/sel_SEU354+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU354+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU354+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU354+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
%
%------------------------------------------------------------------------------