TSTP Solution File: SEU169+2 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU169+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 05:04:01 EST 2010
% Result : Theorem 0.42s
% Output : CNFRefutation 0.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 40 ( 16 unt; 0 def)
% Number of atoms : 127 ( 3 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 136 ( 49 ~; 45 |; 27 &)
% ( 5 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 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 : 63 ( 1 sgn 45 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(21,axiom,
! [X1,X2] :
( in(X1,X2)
=> subset(X1,union(X2)) ),
file('/tmp/tmp9WLjUh/sel_SEU169+2.p_1',l50_zfmisc_1) ).
fof(48,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/tmp/tmp9WLjUh/sel_SEU169+2.p_1',d3_tarski) ).
fof(61,axiom,
! [X1] : ~ empty(powerset(X1)),
file('/tmp/tmp9WLjUh/sel_SEU169+2.p_1',fc1_subset_1) ).
fof(64,axiom,
! [X1,X2] :
( ( ~ empty(X1)
=> ( element(X2,X1)
<=> in(X2,X1) ) )
& ( empty(X1)
=> ( element(X2,X1)
<=> empty(X2) ) ) ),
file('/tmp/tmp9WLjUh/sel_SEU169+2.p_1',d2_subset_1) ).
fof(67,axiom,
! [X1] : union(powerset(X1)) = X1,
file('/tmp/tmp9WLjUh/sel_SEU169+2.p_1',t99_zfmisc_1) ).
fof(88,conjecture,
! [X1,X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( in(X3,X2)
=> in(X3,X1) ) ),
file('/tmp/tmp9WLjUh/sel_SEU169+2.p_1',l3_subset_1) ).
fof(106,negated_conjecture,
~ ! [X1,X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( in(X3,X2)
=> in(X3,X1) ) ),
inference(assume_negation,[status(cth)],[88]) ).
fof(117,plain,
! [X1] : ~ empty(powerset(X1)),
inference(fof_simplification,[status(thm)],[61,theory(equality)]) ).
fof(118,plain,
! [X1,X2] :
( ( ~ empty(X1)
=> ( element(X2,X1)
<=> in(X2,X1) ) )
& ( empty(X1)
=> ( element(X2,X1)
<=> empty(X2) ) ) ),
inference(fof_simplification,[status(thm)],[64,theory(equality)]) ).
fof(189,plain,
! [X1,X2] :
( ~ in(X1,X2)
| subset(X1,union(X2)) ),
inference(fof_nnf,[status(thm)],[21]) ).
fof(190,plain,
! [X3,X4] :
( ~ in(X3,X4)
| subset(X3,union(X4)) ),
inference(variable_rename,[status(thm)],[189]) ).
cnf(191,plain,
( subset(X1,union(X2))
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[190]) ).
fof(279,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)],[48]) ).
fof(280,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)],[279]) ).
fof(281,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)],[280]) ).
fof(282,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)],[281]) ).
fof(283,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)],[282]) ).
cnf(286,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[283]) ).
fof(331,plain,
! [X2] : ~ empty(powerset(X2)),
inference(variable_rename,[status(thm)],[117]) ).
cnf(332,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[331]) ).
fof(340,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)],[118]) ).
fof(341,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)],[340]) ).
fof(342,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)],[341]) ).
cnf(346,plain,
( empty(X1)
| in(X2,X1)
| ~ element(X2,X1) ),
inference(split_conjunct,[status(thm)],[342]) ).
fof(352,plain,
! [X2] : union(powerset(X2)) = X2,
inference(variable_rename,[status(thm)],[67]) ).
cnf(353,plain,
union(powerset(X1)) = X1,
inference(split_conjunct,[status(thm)],[352]) ).
fof(433,negated_conjecture,
? [X1,X2] :
( element(X2,powerset(X1))
& ? [X3] :
( in(X3,X2)
& ~ in(X3,X1) ) ),
inference(fof_nnf,[status(thm)],[106]) ).
fof(434,negated_conjecture,
? [X4,X5] :
( element(X5,powerset(X4))
& ? [X6] :
( in(X6,X5)
& ~ in(X6,X4) ) ),
inference(variable_rename,[status(thm)],[433]) ).
fof(435,negated_conjecture,
( element(esk19_0,powerset(esk18_0))
& in(esk20_0,esk19_0)
& ~ in(esk20_0,esk18_0) ),
inference(skolemize,[status(esa)],[434]) ).
cnf(436,negated_conjecture,
~ in(esk20_0,esk18_0),
inference(split_conjunct,[status(thm)],[435]) ).
cnf(437,negated_conjecture,
in(esk20_0,esk19_0),
inference(split_conjunct,[status(thm)],[435]) ).
cnf(438,negated_conjecture,
element(esk19_0,powerset(esk18_0)),
inference(split_conjunct,[status(thm)],[435]) ).
cnf(696,negated_conjecture,
( empty(powerset(esk18_0))
| in(esk19_0,powerset(esk18_0)) ),
inference(spm,[status(thm)],[346,438,theory(equality)]) ).
cnf(700,negated_conjecture,
in(esk19_0,powerset(esk18_0)),
inference(sr,[status(thm)],[696,332,theory(equality)]) ).
cnf(2420,negated_conjecture,
subset(esk19_0,union(powerset(esk18_0))),
inference(spm,[status(thm)],[191,700,theory(equality)]) ).
cnf(2432,negated_conjecture,
subset(esk19_0,esk18_0),
inference(rw,[status(thm)],[2420,353,theory(equality)]) ).
cnf(2445,negated_conjecture,
( in(X1,esk18_0)
| ~ in(X1,esk19_0) ),
inference(spm,[status(thm)],[286,2432,theory(equality)]) ).
cnf(3240,negated_conjecture,
in(esk20_0,esk18_0),
inference(spm,[status(thm)],[2445,437,theory(equality)]) ).
cnf(3262,negated_conjecture,
$false,
inference(sr,[status(thm)],[3240,436,theory(equality)]) ).
cnf(3263,negated_conjecture,
$false,
3262,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU169+2.p
% --creating new selector for []
% -running prover on /tmp/tmp9WLjUh/sel_SEU169+2.p_1 with time limit 29
% -prover status Theorem
% Problem SEU169+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU169+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU169+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
%
%------------------------------------------------------------------------------