%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU143+2 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art06.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 04:51:38 EST 2010
% Result : Theorem 0.37s
% Output : CNFRefutation 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 29 ( 13 unt; 0 def)
% Number of atoms : 122 ( 83 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 151 ( 58 ~; 60 |; 29 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 58 ( 4 sgn 40 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(9,axiom,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/tmp/tmpnmBguT/sel_SEU143+2.p_1',t69_enumset1) ).
fof(42,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/tmp/tmpnmBguT/sel_SEU143+2.p_1',d1_xboole_0) ).
fof(60,conjecture,
! [X1] : singleton(X1) != empty_set,
file('/tmp/tmpnmBguT/sel_SEU143+2.p_1',l1_zfmisc_1) ).
fof(63,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
file('/tmp/tmpnmBguT/sel_SEU143+2.p_1',d2_tarski) ).
fof(65,negated_conjecture,
~ ! [X1] : singleton(X1) != empty_set,
inference(assume_negation,[status(cth)],[60]) ).
fof(73,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[42,theory(equality)]) ).
fof(97,plain,
! [X2] : unordered_pair(X2,X2) = singleton(X2),
inference(variable_rename,[status(thm)],[9]) ).
cnf(98,plain,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[97]) ).
fof(207,plain,
! [X1] :
( ( X1 != empty_set
| ! [X2] : ~ in(X2,X1) )
& ( ? [X2] : in(X2,X1)
| X1 = empty_set ) ),
inference(fof_nnf,[status(thm)],[73]) ).
fof(208,plain,
! [X3] :
( ( X3 != empty_set
| ! [X4] : ~ in(X4,X3) )
& ( ? [X5] : in(X5,X3)
| X3 = empty_set ) ),
inference(variable_rename,[status(thm)],[207]) ).
fof(209,plain,
! [X3] :
( ( X3 != empty_set
| ! [X4] : ~ in(X4,X3) )
& ( in(esk7_1(X3),X3)
| X3 = empty_set ) ),
inference(skolemize,[status(esa)],[208]) ).
fof(210,plain,
! [X3,X4] :
( ( ~ in(X4,X3)
| X3 != empty_set )
& ( in(esk7_1(X3),X3)
| X3 = empty_set ) ),
inference(shift_quantors,[status(thm)],[209]) ).
cnf(212,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[210]) ).
fof(267,negated_conjecture,
? [X1] : singleton(X1) = empty_set,
inference(fof_nnf,[status(thm)],[65]) ).
fof(268,negated_conjecture,
? [X2] : singleton(X2) = empty_set,
inference(variable_rename,[status(thm)],[267]) ).
fof(269,negated_conjecture,
singleton(esk10_0) = empty_set,
inference(skolemize,[status(esa)],[268]) ).
cnf(270,negated_conjecture,
singleton(esk10_0) = empty_set,
inference(split_conjunct,[status(thm)],[269]) ).
fof(290,plain,
! [X1,X2,X3] :
( ( X3 != unordered_pair(X1,X2)
| ! [X4] :
( ( ~ in(X4,X3)
| X4 = X1
| X4 = X2 )
& ( ( X4 != X1
& X4 != X2 )
| in(X4,X3) ) ) )
& ( ? [X4] :
( ( ~ in(X4,X3)
| ( X4 != X1
& X4 != X2 ) )
& ( in(X4,X3)
| X4 = X1
| X4 = X2 ) )
| X3 = unordered_pair(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[63]) ).
fof(291,plain,
! [X5,X6,X7] :
( ( X7 != unordered_pair(X5,X6)
| ! [X8] :
( ( ~ in(X8,X7)
| X8 = X5
| X8 = X6 )
& ( ( X8 != X5
& X8 != X6 )
| in(X8,X7) ) ) )
& ( ? [X9] :
( ( ~ in(X9,X7)
| ( X9 != X5
& X9 != X6 ) )
& ( in(X9,X7)
| X9 = X5
| X9 = X6 ) )
| X7 = unordered_pair(X5,X6) ) ),
inference(variable_rename,[status(thm)],[290]) ).
fof(292,plain,
! [X5,X6,X7] :
( ( X7 != unordered_pair(X5,X6)
| ! [X8] :
( ( ~ in(X8,X7)
| X8 = X5
| X8 = X6 )
& ( ( X8 != X5
& X8 != X6 )
| in(X8,X7) ) ) )
& ( ( ( ~ in(esk13_3(X5,X6,X7),X7)
| ( esk13_3(X5,X6,X7) != X5
& esk13_3(X5,X6,X7) != X6 ) )
& ( in(esk13_3(X5,X6,X7),X7)
| esk13_3(X5,X6,X7) = X5
| esk13_3(X5,X6,X7) = X6 ) )
| X7 = unordered_pair(X5,X6) ) ),
inference(skolemize,[status(esa)],[291]) ).
fof(293,plain,
! [X5,X6,X7,X8] :
( ( ( ( ~ in(X8,X7)
| X8 = X5
| X8 = X6 )
& ( ( X8 != X5
& X8 != X6 )
| in(X8,X7) ) )
| X7 != unordered_pair(X5,X6) )
& ( ( ( ~ in(esk13_3(X5,X6,X7),X7)
| ( esk13_3(X5,X6,X7) != X5
& esk13_3(X5,X6,X7) != X6 ) )
& ( in(esk13_3(X5,X6,X7),X7)
| esk13_3(X5,X6,X7) = X5
| esk13_3(X5,X6,X7) = X6 ) )
| X7 = unordered_pair(X5,X6) ) ),
inference(shift_quantors,[status(thm)],[292]) ).
fof(294,plain,
! [X5,X6,X7,X8] :
( ( ~ in(X8,X7)
| X8 = X5
| X8 = X6
| X7 != unordered_pair(X5,X6) )
& ( X8 != X5
| in(X8,X7)
| X7 != unordered_pair(X5,X6) )
& ( X8 != X6
| in(X8,X7)
| X7 != unordered_pair(X5,X6) )
& ( esk13_3(X5,X6,X7) != X5
| ~ in(esk13_3(X5,X6,X7),X7)
| X7 = unordered_pair(X5,X6) )
& ( esk13_3(X5,X6,X7) != X6
| ~ in(esk13_3(X5,X6,X7),X7)
| X7 = unordered_pair(X5,X6) )
& ( in(esk13_3(X5,X6,X7),X7)
| esk13_3(X5,X6,X7) = X5
| esk13_3(X5,X6,X7) = X6
| X7 = unordered_pair(X5,X6) ) ),
inference(distribute,[status(thm)],[293]) ).
cnf(298,plain,
( in(X4,X1)
| X1 != unordered_pair(X2,X3)
| X4 != X3 ),
inference(split_conjunct,[status(thm)],[294]) ).
cnf(303,negated_conjecture,
unordered_pair(esk10_0,esk10_0) = empty_set,
inference(rw,[status(thm)],[270,98,theory(equality)]),
[unfolding] ).
cnf(485,plain,
( in(X1,X2)
| unordered_pair(X3,X1) != X2 ),
inference(er,[status(thm)],[298,theory(equality)]) ).
cnf(3916,negated_conjecture,
( in(esk10_0,X1)
| empty_set != X1 ),
inference(spm,[status(thm)],[485,303,theory(equality)]) ).
cnf(3928,negated_conjecture,
empty_set != X1,
inference(csr,[status(thm)],[3916,212]) ).
cnf(3949,negated_conjecture,
$false,
inference(sr,[status(thm)],[303,3928,theory(equality)]) ).
cnf(3950,negated_conjecture,
$false,
3949,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU143+2.p
% --creating new selector for []
% -running prover on /tmp/tmpnmBguT/sel_SEU143+2.p_1 with time limit 29
% -prover status Theorem
% Problem SEU143+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU143+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU143+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
%
%------------------------------------------------------------------------------