TSTP Solution File: SEU173+2 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU173+2 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art05.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 05:05:39 EST 2010
% Result : Theorem 3.12s
% Output : CNFRefutation 3.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 41 ( 10 unt; 0 def)
% Number of atoms : 179 ( 14 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 217 ( 79 ~; 82 |; 40 &)
% ( 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 81 ( 1 sgn 59 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(35,axiom,
! [X1,X2] :
( X2 = powerset(X1)
<=> ! [X3] :
( in(X3,X2)
<=> subset(X3,X1) ) ),
file('/tmp/tmpHPghsh/sel_SEU173+2.p_1',d1_zfmisc_1) ).
fof(49,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/tmp/tmpHPghsh/sel_SEU173+2.p_1',d3_tarski) ).
fof(62,axiom,
! [X1] : ~ empty(powerset(X1)),
file('/tmp/tmpHPghsh/sel_SEU173+2.p_1',fc1_subset_1) ).
fof(66,axiom,
! [X1,X2] :
( ( ~ empty(X1)
=> ( element(X2,X1)
<=> in(X2,X1) ) )
& ( empty(X1)
=> ( element(X2,X1)
<=> empty(X2) ) ) ),
file('/tmp/tmpHPghsh/sel_SEU173+2.p_1',d2_subset_1) ).
fof(82,conjecture,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
=> in(X3,X2) )
=> element(X1,powerset(X2)) ),
file('/tmp/tmpHPghsh/sel_SEU173+2.p_1',l71_subset_1) ).
fof(114,negated_conjecture,
~ ! [X1,X2] :
( ! [X3] :
( in(X3,X1)
=> in(X3,X2) )
=> element(X1,powerset(X2)) ),
inference(assume_negation,[status(cth)],[82]) ).
fof(125,plain,
! [X1] : ~ empty(powerset(X1)),
inference(fof_simplification,[status(thm)],[62,theory(equality)]) ).
fof(126,plain,
! [X1,X2] :
( ( ~ empty(X1)
=> ( element(X2,X1)
<=> in(X2,X1) ) )
& ( empty(X1)
=> ( element(X2,X1)
<=> empty(X2) ) ) ),
inference(fof_simplification,[status(thm)],[66,theory(equality)]) ).
fof(248,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)],[35]) ).
fof(249,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)],[248]) ).
fof(250,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)],[249]) ).
fof(251,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)],[250]) ).
fof(252,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)],[251]) ).
cnf(255,plain,
( in(X3,X1)
| X1 != powerset(X2)
| ~ subset(X3,X2) ),
inference(split_conjunct,[status(thm)],[252]) ).
fof(291,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)],[49]) ).
fof(292,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)],[291]) ).
fof(293,plain,
! [X4,X5] :
( ( ~ subset(X4,X5)
| ! [X6] :
( ~ in(X6,X4)
| in(X6,X5) ) )
& ( ( in(esk8_2(X4,X5),X4)
& ~ in(esk8_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(skolemize,[status(esa)],[292]) ).
fof(294,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X4)
| in(X6,X5)
| ~ subset(X4,X5) )
& ( ( in(esk8_2(X4,X5),X4)
& ~ in(esk8_2(X4,X5),X5) )
| subset(X4,X5) ) ),
inference(shift_quantors,[status(thm)],[293]) ).
fof(295,plain,
! [X4,X5,X6] :
( ( ~ in(X6,X4)
| in(X6,X5)
| ~ subset(X4,X5) )
& ( in(esk8_2(X4,X5),X4)
| subset(X4,X5) )
& ( ~ in(esk8_2(X4,X5),X5)
| subset(X4,X5) ) ),
inference(distribute,[status(thm)],[294]) ).
cnf(296,plain,
( subset(X1,X2)
| ~ in(esk8_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[295]) ).
cnf(297,plain,
( subset(X1,X2)
| in(esk8_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[295]) ).
fof(343,plain,
! [X2] : ~ empty(powerset(X2)),
inference(variable_rename,[status(thm)],[125]) ).
cnf(344,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[343]) ).
fof(355,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)],[126]) ).
fof(356,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)],[355]) ).
fof(357,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)],[356]) ).
cnf(360,plain,
( empty(X1)
| element(X2,X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[357]) ).
fof(416,negated_conjecture,
? [X1,X2] :
( ! [X3] :
( ~ in(X3,X1)
| in(X3,X2) )
& ~ element(X1,powerset(X2)) ),
inference(fof_nnf,[status(thm)],[114]) ).
fof(417,negated_conjecture,
? [X4,X5] :
( ! [X6] :
( ~ in(X6,X4)
| in(X6,X5) )
& ~ element(X4,powerset(X5)) ),
inference(variable_rename,[status(thm)],[416]) ).
fof(418,negated_conjecture,
( ! [X6] :
( ~ in(X6,esk15_0)
| in(X6,esk16_0) )
& ~ element(esk15_0,powerset(esk16_0)) ),
inference(skolemize,[status(esa)],[417]) ).
fof(419,negated_conjecture,
! [X6] :
( ( ~ in(X6,esk15_0)
| in(X6,esk16_0) )
& ~ element(esk15_0,powerset(esk16_0)) ),
inference(shift_quantors,[status(thm)],[418]) ).
cnf(420,negated_conjecture,
~ element(esk15_0,powerset(esk16_0)),
inference(split_conjunct,[status(thm)],[419]) ).
cnf(421,negated_conjecture,
( in(X1,esk16_0)
| ~ in(X1,esk15_0) ),
inference(split_conjunct,[status(thm)],[419]) ).
cnf(844,negated_conjecture,
( in(esk8_2(esk15_0,X1),esk16_0)
| subset(esk15_0,X1) ),
inference(spm,[status(thm)],[421,297,theory(equality)]) ).
cnf(1208,plain,
( in(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(er,[status(thm)],[255,theory(equality)]) ).
cnf(3159,negated_conjecture,
subset(esk15_0,esk16_0),
inference(spm,[status(thm)],[296,844,theory(equality)]) ).
cnf(42125,negated_conjecture,
in(esk15_0,powerset(esk16_0)),
inference(spm,[status(thm)],[1208,3159,theory(equality)]) ).
cnf(42366,negated_conjecture,
( element(esk15_0,powerset(esk16_0))
| empty(powerset(esk16_0)) ),
inference(spm,[status(thm)],[360,42125,theory(equality)]) ).
cnf(42383,negated_conjecture,
empty(powerset(esk16_0)),
inference(sr,[status(thm)],[42366,420,theory(equality)]) ).
cnf(42384,negated_conjecture,
$false,
inference(sr,[status(thm)],[42383,344,theory(equality)]) ).
cnf(42385,negated_conjecture,
$false,
42384,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU173+2.p
% --creating new selector for []
% -running prover on /tmp/tmpHPghsh/sel_SEU173+2.p_1 with time limit 29
% -prover status Theorem
% Problem SEU173+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU173+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU173+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
%
%------------------------------------------------------------------------------