TSTP Solution File: SEU160+2 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU160+2 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art02.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 04:56:54 EST 2010
% Result : Theorem 0.28s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 12 unt; 0 def)
% Number of atoms : 95 ( 54 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 95 ( 35 ~; 43 |; 14 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 31 ( 3 sgn 20 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(4,axiom,
! [X1,X2] : subset(X1,X1),
file('/tmp/tmpGrn2He/sel_SEU160+2.p_1',reflexivity_r1_tarski) ).
fof(23,conjecture,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
file('/tmp/tmpGrn2He/sel_SEU160+2.p_1',t39_zfmisc_1) ).
fof(41,axiom,
! [X1] : subset(empty_set,X1),
file('/tmp/tmpGrn2He/sel_SEU160+2.p_1',t2_xboole_1) ).
fof(46,axiom,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
file('/tmp/tmpGrn2He/sel_SEU160+2.p_1',l4_zfmisc_1) ).
fof(47,axiom,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/tmp/tmpGrn2He/sel_SEU160+2.p_1',t69_enumset1) ).
fof(91,negated_conjecture,
~ ! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
inference(assume_negation,[status(cth)],[23]) ).
fof(112,plain,
! [X3,X4] : subset(X3,X3),
inference(variable_rename,[status(thm)],[4]) ).
cnf(113,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[112]) ).
fof(165,negated_conjecture,
? [X1,X2] :
( ( ~ subset(X1,singleton(X2))
| ( X1 != empty_set
& X1 != singleton(X2) ) )
& ( subset(X1,singleton(X2))
| X1 = empty_set
| X1 = singleton(X2) ) ),
inference(fof_nnf,[status(thm)],[91]) ).
fof(166,negated_conjecture,
? [X3,X4] :
( ( ~ subset(X3,singleton(X4))
| ( X3 != empty_set
& X3 != singleton(X4) ) )
& ( subset(X3,singleton(X4))
| X3 = empty_set
| X3 = singleton(X4) ) ),
inference(variable_rename,[status(thm)],[165]) ).
fof(167,negated_conjecture,
( ( ~ subset(esk2_0,singleton(esk3_0))
| ( esk2_0 != empty_set
& esk2_0 != singleton(esk3_0) ) )
& ( subset(esk2_0,singleton(esk3_0))
| esk2_0 = empty_set
| esk2_0 = singleton(esk3_0) ) ),
inference(skolemize,[status(esa)],[166]) ).
fof(168,negated_conjecture,
( ( esk2_0 != empty_set
| ~ subset(esk2_0,singleton(esk3_0)) )
& ( esk2_0 != singleton(esk3_0)
| ~ subset(esk2_0,singleton(esk3_0)) )
& ( subset(esk2_0,singleton(esk3_0))
| esk2_0 = empty_set
| esk2_0 = singleton(esk3_0) ) ),
inference(distribute,[status(thm)],[167]) ).
cnf(169,negated_conjecture,
( esk2_0 = singleton(esk3_0)
| esk2_0 = empty_set
| subset(esk2_0,singleton(esk3_0)) ),
inference(split_conjunct,[status(thm)],[168]) ).
cnf(170,negated_conjecture,
( ~ subset(esk2_0,singleton(esk3_0))
| esk2_0 != singleton(esk3_0) ),
inference(split_conjunct,[status(thm)],[168]) ).
cnf(171,negated_conjecture,
( ~ subset(esk2_0,singleton(esk3_0))
| esk2_0 != empty_set ),
inference(split_conjunct,[status(thm)],[168]) ).
fof(241,plain,
! [X2] : subset(empty_set,X2),
inference(variable_rename,[status(thm)],[41]) ).
cnf(242,plain,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[241]) ).
fof(253,plain,
! [X1,X2] :
( ( ~ subset(X1,singleton(X2))
| X1 = empty_set
| X1 = singleton(X2) )
& ( ( X1 != empty_set
& X1 != singleton(X2) )
| subset(X1,singleton(X2)) ) ),
inference(fof_nnf,[status(thm)],[46]) ).
fof(254,plain,
! [X3,X4] :
( ( ~ subset(X3,singleton(X4))
| X3 = empty_set
| X3 = singleton(X4) )
& ( ( X3 != empty_set
& X3 != singleton(X4) )
| subset(X3,singleton(X4)) ) ),
inference(variable_rename,[status(thm)],[253]) ).
fof(255,plain,
! [X3,X4] :
( ( ~ subset(X3,singleton(X4))
| X3 = empty_set
| X3 = singleton(X4) )
& ( X3 != empty_set
| subset(X3,singleton(X4)) )
& ( X3 != singleton(X4)
| subset(X3,singleton(X4)) ) ),
inference(distribute,[status(thm)],[254]) ).
cnf(258,plain,
( X1 = singleton(X2)
| X1 = empty_set
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[255]) ).
fof(259,plain,
! [X2] : unordered_pair(X2,X2) = singleton(X2),
inference(variable_rename,[status(thm)],[47]) ).
cnf(260,plain,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[259]) ).
cnf(440,negated_conjecture,
( esk2_0 = empty_set
| unordered_pair(esk3_0,esk3_0) = esk2_0
| subset(esk2_0,unordered_pair(esk3_0,esk3_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[169,260,theory(equality)]),260,theory(equality)]),
[unfolding] ).
cnf(451,plain,
( empty_set = X1
| unordered_pair(X2,X2) = X1
| ~ subset(X1,unordered_pair(X2,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[258,260,theory(equality)]),260,theory(equality)]),
[unfolding] ).
cnf(457,negated_conjecture,
( esk2_0 != empty_set
| ~ subset(esk2_0,unordered_pair(esk3_0,esk3_0)) ),
inference(rw,[status(thm)],[171,260,theory(equality)]),
[unfolding] ).
cnf(459,negated_conjecture,
( unordered_pair(esk3_0,esk3_0) != esk2_0
| ~ subset(esk2_0,unordered_pair(esk3_0,esk3_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[170,260,theory(equality)]),260,theory(equality)]),
[unfolding] ).
cnf(714,negated_conjecture,
( unordered_pair(esk3_0,esk3_0) = esk2_0
| empty_set = esk2_0 ),
inference(spm,[status(thm)],[451,440,theory(equality)]) ).
cnf(1958,negated_conjecture,
( esk2_0 = empty_set
| ~ subset(esk2_0,esk2_0) ),
inference(spm,[status(thm)],[459,714,theory(equality)]) ).
cnf(1988,negated_conjecture,
( esk2_0 = empty_set
| $false ),
inference(rw,[status(thm)],[1958,113,theory(equality)]) ).
cnf(1989,negated_conjecture,
esk2_0 = empty_set,
inference(cn,[status(thm)],[1988,theory(equality)]) ).
cnf(2002,negated_conjecture,
( $false
| ~ subset(esk2_0,unordered_pair(esk3_0,esk3_0)) ),
inference(rw,[status(thm)],[457,1989,theory(equality)]) ).
cnf(2003,negated_conjecture,
( $false
| $false ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[2002,1989,theory(equality)]),242,theory(equality)]) ).
cnf(2004,negated_conjecture,
$false,
inference(cn,[status(thm)],[2003,theory(equality)]) ).
cnf(2005,negated_conjecture,
$false,
2004,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU160+2.p
% --creating new selector for []
% -running prover on /tmp/tmpGrn2He/sel_SEU160+2.p_1 with time limit 29
% -prover status Theorem
% Problem SEU160+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU160+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU160+2.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
%
%------------------------------------------------------------------------------