%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU172+1 : 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 05:05:11 EST 2010
% Result : Theorem 0.18s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 27 ( 9 unt; 0 def)
% Number of atoms : 121 ( 22 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 146 ( 52 ~; 52 |; 35 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 57 ( 2 sgn 40 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(12,axiom,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
file('/tmp/tmpL21NHF/sel_SEU172+1.p_1',d4_xboole_0) ).
fof(14,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,X2) = set_difference(X1,X2) ),
file('/tmp/tmpL21NHF/sel_SEU172+1.p_1',d5_subset_1) ).
fof(21,conjecture,
! [X1,X2,X3] :
( element(X3,powerset(X1))
=> ~ ( in(X2,subset_complement(X1,X3))
& in(X2,X3) ) ),
file('/tmp/tmpL21NHF/sel_SEU172+1.p_1',t54_subset_1) ).
fof(23,negated_conjecture,
~ ! [X1,X2,X3] :
( element(X3,powerset(X1))
=> ~ ( in(X2,subset_complement(X1,X3))
& in(X2,X3) ) ),
inference(assume_negation,[status(cth)],[21]) ).
fof(28,plain,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
inference(fof_simplification,[status(thm)],[12,theory(equality)]) ).
fof(60,plain,
! [X1,X2,X3] :
( ( X3 != set_difference(X1,X2)
| ! [X4] :
( ( ~ in(X4,X3)
| ( in(X4,X1)
& ~ in(X4,X2) ) )
& ( ~ in(X4,X1)
| in(X4,X2)
| in(X4,X3) ) ) )
& ( ? [X4] :
( ( ~ in(X4,X3)
| ~ in(X4,X1)
| in(X4,X2) )
& ( in(X4,X3)
| ( in(X4,X1)
& ~ in(X4,X2) ) ) )
| X3 = set_difference(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[28]) ).
fof(61,plain,
! [X5,X6,X7] :
( ( X7 != set_difference(X5,X6)
| ! [X8] :
( ( ~ in(X8,X7)
| ( in(X8,X5)
& ~ in(X8,X6) ) )
& ( ~ in(X8,X5)
| in(X8,X6)
| in(X8,X7) ) ) )
& ( ? [X9] :
( ( ~ in(X9,X7)
| ~ in(X9,X5)
| in(X9,X6) )
& ( in(X9,X7)
| ( in(X9,X5)
& ~ in(X9,X6) ) ) )
| X7 = set_difference(X5,X6) ) ),
inference(variable_rename,[status(thm)],[60]) ).
fof(62,plain,
! [X5,X6,X7] :
( ( X7 != set_difference(X5,X6)
| ! [X8] :
( ( ~ in(X8,X7)
| ( in(X8,X5)
& ~ in(X8,X6) ) )
& ( ~ in(X8,X5)
| in(X8,X6)
| in(X8,X7) ) ) )
& ( ( ( ~ in(esk3_3(X5,X6,X7),X7)
| ~ in(esk3_3(X5,X6,X7),X5)
| in(esk3_3(X5,X6,X7),X6) )
& ( in(esk3_3(X5,X6,X7),X7)
| ( in(esk3_3(X5,X6,X7),X5)
& ~ in(esk3_3(X5,X6,X7),X6) ) ) )
| X7 = set_difference(X5,X6) ) ),
inference(skolemize,[status(esa)],[61]) ).
fof(63,plain,
! [X5,X6,X7,X8] :
( ( ( ( ~ in(X8,X7)
| ( in(X8,X5)
& ~ in(X8,X6) ) )
& ( ~ in(X8,X5)
| in(X8,X6)
| in(X8,X7) ) )
| X7 != set_difference(X5,X6) )
& ( ( ( ~ in(esk3_3(X5,X6,X7),X7)
| ~ in(esk3_3(X5,X6,X7),X5)
| in(esk3_3(X5,X6,X7),X6) )
& ( in(esk3_3(X5,X6,X7),X7)
| ( in(esk3_3(X5,X6,X7),X5)
& ~ in(esk3_3(X5,X6,X7),X6) ) ) )
| X7 = set_difference(X5,X6) ) ),
inference(shift_quantors,[status(thm)],[62]) ).
fof(64,plain,
! [X5,X6,X7,X8] :
( ( in(X8,X5)
| ~ in(X8,X7)
| X7 != set_difference(X5,X6) )
& ( ~ in(X8,X6)
| ~ in(X8,X7)
| X7 != set_difference(X5,X6) )
& ( ~ in(X8,X5)
| in(X8,X6)
| in(X8,X7)
| X7 != set_difference(X5,X6) )
& ( ~ in(esk3_3(X5,X6,X7),X7)
| ~ in(esk3_3(X5,X6,X7),X5)
| in(esk3_3(X5,X6,X7),X6)
| X7 = set_difference(X5,X6) )
& ( in(esk3_3(X5,X6,X7),X5)
| in(esk3_3(X5,X6,X7),X7)
| X7 = set_difference(X5,X6) )
& ( ~ in(esk3_3(X5,X6,X7),X6)
| in(esk3_3(X5,X6,X7),X7)
| X7 = set_difference(X5,X6) ) ),
inference(distribute,[status(thm)],[63]) ).
cnf(69,plain,
( X1 != set_difference(X2,X3)
| ~ in(X4,X1)
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[64]) ).
fof(72,plain,
! [X1,X2] :
( ~ element(X2,powerset(X1))
| subset_complement(X1,X2) = set_difference(X1,X2) ),
inference(fof_nnf,[status(thm)],[14]) ).
fof(73,plain,
! [X3,X4] :
( ~ element(X4,powerset(X3))
| subset_complement(X3,X4) = set_difference(X3,X4) ),
inference(variable_rename,[status(thm)],[72]) ).
cnf(74,plain,
( subset_complement(X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[73]) ).
fof(88,negated_conjecture,
? [X1,X2,X3] :
( element(X3,powerset(X1))
& in(X2,subset_complement(X1,X3))
& in(X2,X3) ),
inference(fof_nnf,[status(thm)],[23]) ).
fof(89,negated_conjecture,
? [X4,X5,X6] :
( element(X6,powerset(X4))
& in(X5,subset_complement(X4,X6))
& in(X5,X6) ),
inference(variable_rename,[status(thm)],[88]) ).
fof(90,negated_conjecture,
( element(esk8_0,powerset(esk6_0))
& in(esk7_0,subset_complement(esk6_0,esk8_0))
& in(esk7_0,esk8_0) ),
inference(skolemize,[status(esa)],[89]) ).
cnf(91,negated_conjecture,
in(esk7_0,esk8_0),
inference(split_conjunct,[status(thm)],[90]) ).
cnf(92,negated_conjecture,
in(esk7_0,subset_complement(esk6_0,esk8_0)),
inference(split_conjunct,[status(thm)],[90]) ).
cnf(93,negated_conjecture,
element(esk8_0,powerset(esk6_0)),
inference(split_conjunct,[status(thm)],[90]) ).
cnf(111,plain,
( ~ in(X1,X2)
| ~ in(X1,set_difference(X3,X2)) ),
inference(er,[status(thm)],[69,theory(equality)]) ).
cnf(115,negated_conjecture,
subset_complement(esk6_0,esk8_0) = set_difference(esk6_0,esk8_0),
inference(spm,[status(thm)],[74,93,theory(equality)]) ).
cnf(137,negated_conjecture,
in(esk7_0,set_difference(esk6_0,esk8_0)),
inference(rw,[status(thm)],[92,115,theory(equality)]) ).
cnf(210,negated_conjecture,
~ in(esk7_0,esk8_0),
inference(spm,[status(thm)],[111,137,theory(equality)]) ).
cnf(214,negated_conjecture,
$false,
inference(rw,[status(thm)],[210,91,theory(equality)]) ).
cnf(215,negated_conjecture,
$false,
inference(cn,[status(thm)],[214,theory(equality)]) ).
cnf(216,negated_conjecture,
$false,
215,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU172+1.p
% --creating new selector for []
% -running prover on /tmp/tmpL21NHF/sel_SEU172+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU172+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU172+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU172+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
%
%------------------------------------------------------------------------------