TSTP Solution File: SEU326+2 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU326+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 07:18:14 EST 2010
% Result : Theorem 11.57s
% Output : CNFRefutation 11.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 47 ( 5 unt; 0 def)
% Number of atoms : 133 ( 71 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 151 ( 65 ~; 49 |; 28 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 73 ( 3 sgn 45 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(18,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ~ ( X2 != empty_set
& complements_of_subsets(X1,X2) = empty_set ) ),
file('/tmp/tmpLMtdr9/sel_SEU326+2.p_1',t46_setfam_1) ).
fof(28,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/tmp/tmpLMtdr9/sel_SEU326+2.p_1',d1_xboole_0) ).
fof(320,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2 ),
file('/tmp/tmpLMtdr9/sel_SEU326+2.p_1',involutiveness_k7_setfam_1) ).
fof(388,axiom,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
=> in(X3,X2) )
=> element(X1,powerset(X2)) ),
file('/tmp/tmpLMtdr9/sel_SEU326+2.p_1',l71_subset_1) ).
fof(427,conjecture,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ( ~ ( X2 != empty_set
& complements_of_subsets(X1,X2) = empty_set )
& ~ ( complements_of_subsets(X1,X2) != empty_set
& X2 = empty_set ) ) ),
file('/tmp/tmpLMtdr9/sel_SEU326+2.p_1',t10_tops_2) ).
fof(497,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> element(complements_of_subsets(X1,X2),powerset(powerset(X1))) ),
file('/tmp/tmpLMtdr9/sel_SEU326+2.p_1',dt_k7_setfam_1) ).
fof(540,negated_conjecture,
~ ! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ( ~ ( X2 != empty_set
& complements_of_subsets(X1,X2) = empty_set )
& ~ ( complements_of_subsets(X1,X2) != empty_set
& X2 = empty_set ) ) ),
inference(assume_negation,[status(cth)],[427]) ).
fof(545,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[28,theory(equality)]) ).
fof(710,plain,
! [X1,X2] :
( ~ element(X2,powerset(powerset(X1)))
| X2 = empty_set
| complements_of_subsets(X1,X2) != empty_set ),
inference(fof_nnf,[status(thm)],[18]) ).
fof(711,plain,
! [X3,X4] :
( ~ element(X4,powerset(powerset(X3)))
| X4 = empty_set
| complements_of_subsets(X3,X4) != empty_set ),
inference(variable_rename,[status(thm)],[710]) ).
cnf(712,plain,
( X2 = empty_set
| complements_of_subsets(X1,X2) != empty_set
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[711]) ).
fof(748,plain,
! [X1] :
( ( X1 != empty_set
| ! [X2] : ~ in(X2,X1) )
& ( ? [X2] : in(X2,X1)
| X1 = empty_set ) ),
inference(fof_nnf,[status(thm)],[545]) ).
fof(749,plain,
! [X3] :
( ( X3 != empty_set
| ! [X4] : ~ in(X4,X3) )
& ( ? [X5] : in(X5,X3)
| X3 = empty_set ) ),
inference(variable_rename,[status(thm)],[748]) ).
fof(750,plain,
! [X3] :
( ( X3 != empty_set
| ! [X4] : ~ in(X4,X3) )
& ( in(esk9_1(X3),X3)
| X3 = empty_set ) ),
inference(skolemize,[status(esa)],[749]) ).
fof(751,plain,
! [X3,X4] :
( ( ~ in(X4,X3)
| X3 != empty_set )
& ( in(esk9_1(X3),X3)
| X3 = empty_set ) ),
inference(shift_quantors,[status(thm)],[750]) ).
cnf(753,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[751]) ).
fof(2649,plain,
! [X1,X2] :
( ~ element(X2,powerset(powerset(X1)))
| complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2 ),
inference(fof_nnf,[status(thm)],[320]) ).
fof(2650,plain,
! [X3,X4] :
( ~ element(X4,powerset(powerset(X3)))
| complements_of_subsets(X3,complements_of_subsets(X3,X4)) = X4 ),
inference(variable_rename,[status(thm)],[2649]) ).
cnf(2651,plain,
( complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[2650]) ).
fof(3087,plain,
! [X1,X2] :
( ? [X3] :
( in(X3,X1)
& ~ in(X3,X2) )
| element(X1,powerset(X2)) ),
inference(fof_nnf,[status(thm)],[388]) ).
fof(3088,plain,
! [X4,X5] :
( ? [X6] :
( in(X6,X4)
& ~ in(X6,X5) )
| element(X4,powerset(X5)) ),
inference(variable_rename,[status(thm)],[3087]) ).
fof(3089,plain,
! [X4,X5] :
( ( in(esk243_2(X4,X5),X4)
& ~ in(esk243_2(X4,X5),X5) )
| element(X4,powerset(X5)) ),
inference(skolemize,[status(esa)],[3088]) ).
fof(3090,plain,
! [X4,X5] :
( ( in(esk243_2(X4,X5),X4)
| element(X4,powerset(X5)) )
& ( ~ in(esk243_2(X4,X5),X5)
| element(X4,powerset(X5)) ) ),
inference(distribute,[status(thm)],[3089]) ).
cnf(3092,plain,
( element(X1,powerset(X2))
| in(esk243_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[3090]) ).
fof(3388,negated_conjecture,
? [X1,X2] :
( element(X2,powerset(powerset(X1)))
& ( ( X2 != empty_set
& complements_of_subsets(X1,X2) = empty_set )
| ( complements_of_subsets(X1,X2) != empty_set
& X2 = empty_set ) ) ),
inference(fof_nnf,[status(thm)],[540]) ).
fof(3389,negated_conjecture,
? [X3,X4] :
( element(X4,powerset(powerset(X3)))
& ( ( X4 != empty_set
& complements_of_subsets(X3,X4) = empty_set )
| ( complements_of_subsets(X3,X4) != empty_set
& X4 = empty_set ) ) ),
inference(variable_rename,[status(thm)],[3388]) ).
fof(3390,negated_conjecture,
( element(esk293_0,powerset(powerset(esk292_0)))
& ( ( esk293_0 != empty_set
& complements_of_subsets(esk292_0,esk293_0) = empty_set )
| ( complements_of_subsets(esk292_0,esk293_0) != empty_set
& esk293_0 = empty_set ) ) ),
inference(skolemize,[status(esa)],[3389]) ).
fof(3391,negated_conjecture,
( element(esk293_0,powerset(powerset(esk292_0)))
& ( complements_of_subsets(esk292_0,esk293_0) != empty_set
| esk293_0 != empty_set )
& ( esk293_0 = empty_set
| esk293_0 != empty_set )
& ( complements_of_subsets(esk292_0,esk293_0) != empty_set
| complements_of_subsets(esk292_0,esk293_0) = empty_set )
& ( esk293_0 = empty_set
| complements_of_subsets(esk292_0,esk293_0) = empty_set ) ),
inference(distribute,[status(thm)],[3390]) ).
cnf(3392,negated_conjecture,
( complements_of_subsets(esk292_0,esk293_0) = empty_set
| esk293_0 = empty_set ),
inference(split_conjunct,[status(thm)],[3391]) ).
cnf(3395,negated_conjecture,
( esk293_0 != empty_set
| complements_of_subsets(esk292_0,esk293_0) != empty_set ),
inference(split_conjunct,[status(thm)],[3391]) ).
cnf(3396,negated_conjecture,
element(esk293_0,powerset(powerset(esk292_0))),
inference(split_conjunct,[status(thm)],[3391]) ).
fof(3896,plain,
! [X1,X2] :
( ~ element(X2,powerset(powerset(X1)))
| element(complements_of_subsets(X1,X2),powerset(powerset(X1))) ),
inference(fof_nnf,[status(thm)],[497]) ).
fof(3897,plain,
! [X3,X4] :
( ~ element(X4,powerset(powerset(X3)))
| element(complements_of_subsets(X3,X4),powerset(powerset(X3))) ),
inference(variable_rename,[status(thm)],[3896]) ).
cnf(3898,plain,
( element(complements_of_subsets(X1,X2),powerset(powerset(X1)))
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[3897]) ).
cnf(5044,negated_conjecture,
( empty_set = esk293_0
| ~ element(esk293_0,powerset(powerset(esk292_0))) ),
inference(spm,[status(thm)],[712,3392,theory(equality)]) ).
cnf(5045,negated_conjecture,
( empty_set = esk293_0
| $false ),
inference(rw,[status(thm)],[5044,3396,theory(equality)]) ).
cnf(5046,negated_conjecture,
empty_set = esk293_0,
inference(cn,[status(thm)],[5045,theory(equality)]) ).
cnf(5156,plain,
( empty_set = complements_of_subsets(X1,X2)
| X2 != empty_set
| ~ element(complements_of_subsets(X1,X2),powerset(powerset(X1)))
| ~ element(X2,powerset(powerset(X1))) ),
inference(spm,[status(thm)],[712,2651,theory(equality)]) ).
cnf(6142,plain,
( element(X1,powerset(X2))
| empty_set != X1 ),
inference(spm,[status(thm)],[753,3092,theory(equality)]) ).
cnf(99611,negated_conjecture,
( complements_of_subsets(esk292_0,empty_set) != empty_set
| esk293_0 != empty_set ),
inference(rw,[status(thm)],[3395,5046,theory(equality)]) ).
cnf(99612,negated_conjecture,
( complements_of_subsets(esk292_0,empty_set) != empty_set
| $false ),
inference(rw,[status(thm)],[99611,5046,theory(equality)]) ).
cnf(99613,negated_conjecture,
complements_of_subsets(esk292_0,empty_set) != empty_set,
inference(cn,[status(thm)],[99612,theory(equality)]) ).
cnf(105047,plain,
( complements_of_subsets(X1,X2) = empty_set
| X2 != empty_set
| ~ element(complements_of_subsets(X1,X2),powerset(powerset(X1))) ),
inference(csr,[status(thm)],[5156,6142]) ).
cnf(105050,plain,
( complements_of_subsets(X1,X2) = empty_set
| X2 != empty_set
| ~ element(X2,powerset(powerset(X1))) ),
inference(spm,[status(thm)],[105047,3898,theory(equality)]) ).
cnf(110107,plain,
( complements_of_subsets(X1,X2) = empty_set
| X2 != empty_set ),
inference(csr,[status(thm)],[105050,6142]) ).
cnf(110108,plain,
$false,
inference(spm,[status(thm)],[99613,110107,theory(equality)]) ).
cnf(110118,plain,
$false,
110108,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU326+2.p
% --creating new selector for []
% -running prover on /tmp/tmpLMtdr9/sel_SEU326+2.p_1 with time limit 29
% -prover status Theorem
% Problem SEU326+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU326+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU326+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
%
%------------------------------------------------------------------------------