%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU169+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art04.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 05:03:57 EST 2010
% Result : Theorem 0.23s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 41 ( 13 unt; 0 def)
% Number of atoms : 176 ( 15 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 211 ( 76 ~; 77 |; 42 &)
% ( 7 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 76 ( 1 sgn 55 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(1,axiom,
! [X1,X2] :
( ( ~ empty(X1)
=> ( element(X2,X1)
<=> in(X2,X1) ) )
& ( empty(X1)
=> ( element(X2,X1)
<=> empty(X2) ) ) ),
file('/tmp/tmpCwBOhG/sel_SEU169+1.p_1',d2_subset_1) ).
fof(2,conjecture,
! [X1,X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( in(X3,X2)
=> in(X3,X1) ) ),
file('/tmp/tmpCwBOhG/sel_SEU169+1.p_1',l3_subset_1) ).
fof(8,axiom,
! [X1,X2] :
( X2 = powerset(X1)
<=> ! [X3] :
( in(X3,X2)
<=> subset(X3,X1) ) ),
file('/tmp/tmpCwBOhG/sel_SEU169+1.p_1',d1_zfmisc_1) ).
fof(11,axiom,
! [X1] : ~ empty(powerset(X1)),
file('/tmp/tmpCwBOhG/sel_SEU169+1.p_1',fc1_subset_1) ).
fof(16,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/tmp/tmpCwBOhG/sel_SEU169+1.p_1',d3_tarski) ).
fof(19,negated_conjecture,
~ ! [X1,X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( in(X3,X2)
=> in(X3,X1) ) ),
inference(assume_negation,[status(cth)],[2]) ).
fof(20,plain,
! [X1,X2] :
( ( ~ empty(X1)
=> ( element(X2,X1)
<=> in(X2,X1) ) )
& ( empty(X1)
=> ( element(X2,X1)
<=> empty(X2) ) ) ),
inference(fof_simplification,[status(thm)],[1,theory(equality)]) ).
fof(22,plain,
! [X1] : ~ empty(powerset(X1)),
inference(fof_simplification,[status(thm)],[11,theory(equality)]) ).
fof(25,plain,
! [X1,X2] :
( ( empty(X1)
| ( ( ~ element(X2,X1)
| in(X2,X1) )
& ( ~ in(X2,X1)
| element(X2,X1) ) ) )
& ( ~ empty(X1)
| ( ( ~ element(X2,X1)
| empty(X2) )
& ( ~ empty(X2)
| element(X2,X1) ) ) ) ),
inference(fof_nnf,[status(thm)],[20]) ).
fof(26,plain,
! [X3,X4] :
( ( empty(X3)
| ( ( ~ element(X4,X3)
| in(X4,X3) )
& ( ~ in(X4,X3)
| element(X4,X3) ) ) )
& ( ~ empty(X3)
| ( ( ~ element(X4,X3)
| empty(X4) )
& ( ~ empty(X4)
| element(X4,X3) ) ) ) ),
inference(variable_rename,[status(thm)],[25]) ).
fof(27,plain,
! [X3,X4] :
( ( ~ element(X4,X3)
| in(X4,X3)
| empty(X3) )
& ( ~ in(X4,X3)
| element(X4,X3)
| empty(X3) )
& ( ~ element(X4,X3)
| empty(X4)
| ~ empty(X3) )
& ( ~ empty(X4)
| element(X4,X3)
| ~ empty(X3) ) ),
inference(distribute,[status(thm)],[26]) ).
cnf(31,plain,
( empty(X1)
| in(X2,X1)
| ~ element(X2,X1) ),
inference(split_conjunct,[status(thm)],[27]) ).
fof(32,negated_conjecture,
? [X1,X2] :
( element(X2,powerset(X1))
& ? [X3] :
( in(X3,X2)
& ~ in(X3,X1) ) ),
inference(fof_nnf,[status(thm)],[19]) ).
fof(33,negated_conjecture,
? [X4,X5] :
( element(X5,powerset(X4))
& ? [X6] :
( in(X6,X5)
& ~ in(X6,X4) ) ),
inference(variable_rename,[status(thm)],[32]) ).
fof(34,negated_conjecture,
( element(esk2_0,powerset(esk1_0))
& in(esk3_0,esk2_0)
& ~ in(esk3_0,esk1_0) ),
inference(skolemize,[status(esa)],[33]) ).
cnf(35,negated_conjecture,
~ in(esk3_0,esk1_0),
inference(split_conjunct,[status(thm)],[34]) ).
cnf(36,negated_conjecture,
in(esk3_0,esk2_0),
inference(split_conjunct,[status(thm)],[34]) ).
cnf(37,negated_conjecture,
element(esk2_0,powerset(esk1_0)),
inference(split_conjunct,[status(thm)],[34]) ).
fof(51,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)],[8]) ).
fof(52,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)],[51]) ).
fof(53,plain,
! [X4,X5] :
( ( X5 != powerset(X4)
| ! [X6] :
( ( ~ in(X6,X5)
| subset(X6,X4) )
& ( ~ subset(X6,X4)
| in(X6,X5) ) ) )
& ( ( ( ~ in(esk6_2(X4,X5),X5)
| ~ subset(esk6_2(X4,X5),X4) )
& ( in(esk6_2(X4,X5),X5)
| subset(esk6_2(X4,X5),X4) ) )
| X5 = powerset(X4) ) ),
inference(skolemize,[status(esa)],[52]) ).
fof(54,plain,
! [X4,X5,X6] :
( ( ( ( ~ in(X6,X5)
| subset(X6,X4) )
& ( ~ subset(X6,X4)
| in(X6,X5) ) )
| X5 != powerset(X4) )
& ( ( ( ~ in(esk6_2(X4,X5),X5)
| ~ subset(esk6_2(X4,X5),X4) )
& ( in(esk6_2(X4,X5),X5)
| subset(esk6_2(X4,X5),X4) ) )
| X5 = powerset(X4) ) ),
inference(shift_quantors,[status(thm)],[53]) ).
fof(55,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X5)
| subset(X6,X4)
| X5 != powerset(X4) )
& ( ~ subset(X6,X4)
| in(X6,X5)
| X5 != powerset(X4) )
& ( ~ in(esk6_2(X4,X5),X5)
| ~ subset(esk6_2(X4,X5),X4)
| X5 = powerset(X4) )
& ( in(esk6_2(X4,X5),X5)
| subset(esk6_2(X4,X5),X4)
| X5 = powerset(X4) ) ),
inference(distribute,[status(thm)],[54]) ).
cnf(59,plain,
( subset(X3,X2)
| X1 != powerset(X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[55]) ).
fof(64,plain,
! [X2] : ~ empty(powerset(X2)),
inference(variable_rename,[status(thm)],[22]) ).
cnf(65,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[64]) ).
fof(79,plain,
! [X1,X2] :
( ( ~ subset(X1,X2)
| ! [X3] :
( ~ in(X3,X1)
| in(X3,X2) ) )
& ( ? [X3] :
( in(X3,X1)
& ~ in(X3,X2) )
| subset(X1,X2) ) ),
inference(fof_nnf,[status(thm)],[16]) ).
fof(80,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ in(X6,X4)
| in(X6,X5) ) )
& ( ? [X7] :
( in(X7,X4)
& ~ in(X7,X5) )
| subset(X4,X5) ) ),
inference(variable_rename,[status(thm)],[79]) ).
fof(81,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ in(X6,X4)
| in(X6,X5) ) )
& ( ( in(esk9_2(X4,X5),X4)
& ~ in(esk9_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(skolemize,[status(esa)],[80]) ).
fof(82,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X4)
| in(X6,X5)
| ~ subset(X4,X5) )
& ( ( in(esk9_2(X4,X5),X4)
& ~ in(esk9_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(shift_quantors,[status(thm)],[81]) ).
fof(83,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X4)
| in(X6,X5)
| ~ subset(X4,X5) )
& ( in(esk9_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ in(esk9_2(X4,X5),X5)
| subset(X4,X5) ) ),
inference(distribute,[status(thm)],[82]) ).
cnf(86,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[83]) ).
cnf(103,negated_conjecture,
( in(esk2_0,powerset(esk1_0))
| empty(powerset(esk1_0)) ),
inference(spm,[status(thm)],[31,37,theory(equality)]) ).
cnf(108,negated_conjecture,
in(esk2_0,powerset(esk1_0)),
inference(sr,[status(thm)],[103,65,theory(equality)]) ).
cnf(124,negated_conjecture,
( subset(esk2_0,X1)
| powerset(X1) != powerset(esk1_0) ),
inference(spm,[status(thm)],[59,108,theory(equality)]) ).
cnf(128,negated_conjecture,
subset(esk2_0,esk1_0),
inference(er,[status(thm)],[124,theory(equality)]) ).
cnf(130,negated_conjecture,
( in(X1,esk1_0)
| ~ in(X1,esk2_0) ),
inference(spm,[status(thm)],[86,128,theory(equality)]) ).
cnf(131,negated_conjecture,
~ in(esk3_0,esk2_0),
inference(spm,[status(thm)],[35,130,theory(equality)]) ).
cnf(136,negated_conjecture,
$false,
inference(rw,[status(thm)],[131,36,theory(equality)]) ).
cnf(137,negated_conjecture,
$false,
inference(cn,[status(thm)],[136,theory(equality)]) ).
cnf(138,negated_conjecture,
$false,
137,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU169+1.p
% --creating new selector for []
% -running prover on /tmp/tmpCwBOhG/sel_SEU169+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU169+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU169+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU169+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
%
%------------------------------------------------------------------------------