TSTP Solution File: SEU174+2 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU174+2 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art03.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 05:06:04 EST 2010
% Result : Theorem 106.76s
% Output : CNFRefutation 106.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 68 ( 16 unt; 0 def)
% Number of atoms : 244 ( 63 equ)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 297 ( 121 ~; 128 |; 35 &)
% ( 5 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 118 ( 8 sgn 69 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(6,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2 ),
file('/tmp/tmpbutiNj/sel_SEU174+2.p_2',involutiveness_k7_setfam_1) ).
fof(12,conjecture,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ~ ( X2 != empty_set
& complements_of_subsets(X1,X2) = empty_set ) ),
file('/tmp/tmpbutiNj/sel_SEU174+2.p_2',t46_setfam_1) ).
fof(17,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/tmp/tmpbutiNj/sel_SEU174+2.p_2',d1_xboole_0) ).
fof(44,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/tmp/tmpbutiNj/sel_SEU174+2.p_2',t3_subset) ).
fof(53,axiom,
! [X1] : subset(empty_set,X1),
file('/tmp/tmpbutiNj/sel_SEU174+2.p_2',t2_xboole_1) ).
fof(78,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,X2) = set_difference(X1,X2) ),
file('/tmp/tmpbutiNj/sel_SEU174+2.p_2',d5_subset_1) ).
fof(98,axiom,
! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ! [X3] :
( element(X3,powerset(powerset(X1)))
=> ( X3 = complements_of_subsets(X1,X2)
<=> ! [X4] :
( element(X4,powerset(X1))
=> ( in(X4,X3)
<=> in(subset_complement(X1,X4),X2) ) ) ) ) ),
file('/tmp/tmpbutiNj/sel_SEU174+2.p_2',d8_setfam_1) ).
fof(118,axiom,
! [X1,X2,X3] :
( ( in(X1,X2)
& element(X2,powerset(X3)) )
=> element(X1,X3) ),
file('/tmp/tmpbutiNj/sel_SEU174+2.p_2',t4_subset) ).
fof(123,negated_conjecture,
~ ! [X1,X2] :
( element(X2,powerset(powerset(X1)))
=> ~ ( X2 != empty_set
& complements_of_subsets(X1,X2) = empty_set ) ),
inference(assume_negation,[status(cth)],[12]) ).
fof(128,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[17,theory(equality)]) ).
fof(158,plain,
! [X1,X2] :
( ~ element(X2,powerset(powerset(X1)))
| complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2 ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(159,plain,
! [X3,X4] :
( ~ element(X4,powerset(powerset(X3)))
| complements_of_subsets(X3,complements_of_subsets(X3,X4)) = X4 ),
inference(variable_rename,[status(thm)],[158]) ).
cnf(160,plain,
( complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2
| ~ element(X2,powerset(powerset(X1))) ),
inference(split_conjunct,[status(thm)],[159]) ).
fof(174,negated_conjecture,
? [X1,X2] :
( element(X2,powerset(powerset(X1)))
& X2 != empty_set
& complements_of_subsets(X1,X2) = empty_set ),
inference(fof_nnf,[status(thm)],[123]) ).
fof(175,negated_conjecture,
? [X3,X4] :
( element(X4,powerset(powerset(X3)))
& X4 != empty_set
& complements_of_subsets(X3,X4) = empty_set ),
inference(variable_rename,[status(thm)],[174]) ).
fof(176,negated_conjecture,
( element(esk2_0,powerset(powerset(esk1_0)))
& esk2_0 != empty_set
& complements_of_subsets(esk1_0,esk2_0) = empty_set ),
inference(skolemize,[status(esa)],[175]) ).
cnf(177,negated_conjecture,
complements_of_subsets(esk1_0,esk2_0) = empty_set,
inference(split_conjunct,[status(thm)],[176]) ).
cnf(178,negated_conjecture,
esk2_0 != empty_set,
inference(split_conjunct,[status(thm)],[176]) ).
cnf(179,negated_conjecture,
element(esk2_0,powerset(powerset(esk1_0))),
inference(split_conjunct,[status(thm)],[176]) ).
fof(190,plain,
! [X1] :
( ( X1 != empty_set
| ! [X2] : ~ in(X2,X1) )
& ( ? [X2] : in(X2,X1)
| X1 = empty_set ) ),
inference(fof_nnf,[status(thm)],[128]) ).
fof(191,plain,
! [X3] :
( ( X3 != empty_set
| ! [X4] : ~ in(X4,X3) )
& ( ? [X5] : in(X5,X3)
| X3 = empty_set ) ),
inference(variable_rename,[status(thm)],[190]) ).
fof(192,plain,
! [X3] :
( ( X3 != empty_set
| ! [X4] : ~ in(X4,X3) )
& ( in(esk3_1(X3),X3)
| X3 = empty_set ) ),
inference(skolemize,[status(esa)],[191]) ).
fof(193,plain,
! [X3,X4] :
( ( ~ in(X4,X3)
| X3 != empty_set )
& ( in(esk3_1(X3),X3)
| X3 = empty_set ) ),
inference(shift_quantors,[status(thm)],[192]) ).
cnf(195,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[193]) ).
fof(281,plain,
! [X1,X2] :
( ( ~ element(X1,powerset(X2))
| subset(X1,X2) )
& ( ~ subset(X1,X2)
| element(X1,powerset(X2)) ) ),
inference(fof_nnf,[status(thm)],[44]) ).
fof(282,plain,
! [X3,X4] :
( ( ~ element(X3,powerset(X4))
| subset(X3,X4) )
& ( ~ subset(X3,X4)
| element(X3,powerset(X4)) ) ),
inference(variable_rename,[status(thm)],[281]) ).
cnf(283,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[282]) ).
fof(329,plain,
! [X2] : subset(empty_set,X2),
inference(variable_rename,[status(thm)],[53]) ).
cnf(330,plain,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[329]) ).
fof(408,plain,
! [X1,X2] :
( ~ element(X2,powerset(X1))
| subset_complement(X1,X2) = set_difference(X1,X2) ),
inference(fof_nnf,[status(thm)],[78]) ).
fof(409,plain,
! [X3,X4] :
( ~ element(X4,powerset(X3))
| subset_complement(X3,X4) = set_difference(X3,X4) ),
inference(variable_rename,[status(thm)],[408]) ).
cnf(410,plain,
( subset_complement(X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[409]) ).
fof(488,plain,
! [X1,X2] :
( ~ element(X2,powerset(powerset(X1)))
| ! [X3] :
( ~ element(X3,powerset(powerset(X1)))
| ( ( X3 != complements_of_subsets(X1,X2)
| ! [X4] :
( ~ element(X4,powerset(X1))
| ( ( ~ in(X4,X3)
| in(subset_complement(X1,X4),X2) )
& ( ~ in(subset_complement(X1,X4),X2)
| in(X4,X3) ) ) ) )
& ( ? [X4] :
( element(X4,powerset(X1))
& ( ~ in(X4,X3)
| ~ in(subset_complement(X1,X4),X2) )
& ( in(X4,X3)
| in(subset_complement(X1,X4),X2) ) )
| X3 = complements_of_subsets(X1,X2) ) ) ) ),
inference(fof_nnf,[status(thm)],[98]) ).
fof(489,plain,
! [X5,X6] :
( ~ element(X6,powerset(powerset(X5)))
| ! [X7] :
( ~ element(X7,powerset(powerset(X5)))
| ( ( X7 != complements_of_subsets(X5,X6)
| ! [X8] :
( ~ element(X8,powerset(X5))
| ( ( ~ in(X8,X7)
| in(subset_complement(X5,X8),X6) )
& ( ~ in(subset_complement(X5,X8),X6)
| in(X8,X7) ) ) ) )
& ( ? [X9] :
( element(X9,powerset(X5))
& ( ~ in(X9,X7)
| ~ in(subset_complement(X5,X9),X6) )
& ( in(X9,X7)
| in(subset_complement(X5,X9),X6) ) )
| X7 = complements_of_subsets(X5,X6) ) ) ) ),
inference(variable_rename,[status(thm)],[488]) ).
fof(490,plain,
! [X5,X6] :
( ~ element(X6,powerset(powerset(X5)))
| ! [X7] :
( ~ element(X7,powerset(powerset(X5)))
| ( ( X7 != complements_of_subsets(X5,X6)
| ! [X8] :
( ~ element(X8,powerset(X5))
| ( ( ~ in(X8,X7)
| in(subset_complement(X5,X8),X6) )
& ( ~ in(subset_complement(X5,X8),X6)
| in(X8,X7) ) ) ) )
& ( ( element(esk22_3(X5,X6,X7),powerset(X5))
& ( ~ in(esk22_3(X5,X6,X7),X7)
| ~ in(subset_complement(X5,esk22_3(X5,X6,X7)),X6) )
& ( in(esk22_3(X5,X6,X7),X7)
| in(subset_complement(X5,esk22_3(X5,X6,X7)),X6) ) )
| X7 = complements_of_subsets(X5,X6) ) ) ) ),
inference(skolemize,[status(esa)],[489]) ).
fof(491,plain,
! [X5,X6,X7,X8] :
( ( ( ~ element(X8,powerset(X5))
| ( ( ~ in(X8,X7)
| in(subset_complement(X5,X8),X6) )
& ( ~ in(subset_complement(X5,X8),X6)
| in(X8,X7) ) )
| X7 != complements_of_subsets(X5,X6) )
& ( ( element(esk22_3(X5,X6,X7),powerset(X5))
& ( ~ in(esk22_3(X5,X6,X7),X7)
| ~ in(subset_complement(X5,esk22_3(X5,X6,X7)),X6) )
& ( in(esk22_3(X5,X6,X7),X7)
| in(subset_complement(X5,esk22_3(X5,X6,X7)),X6) ) )
| X7 = complements_of_subsets(X5,X6) ) )
| ~ element(X7,powerset(powerset(X5)))
| ~ element(X6,powerset(powerset(X5))) ),
inference(shift_quantors,[status(thm)],[490]) ).
fof(492,plain,
! [X5,X6,X7,X8] :
( ( ~ in(X8,X7)
| in(subset_complement(X5,X8),X6)
| ~ element(X8,powerset(X5))
| X7 != complements_of_subsets(X5,X6)
| ~ element(X7,powerset(powerset(X5)))
| ~ element(X6,powerset(powerset(X5))) )
& ( ~ in(subset_complement(X5,X8),X6)
| in(X8,X7)
| ~ element(X8,powerset(X5))
| X7 != complements_of_subsets(X5,X6)
| ~ element(X7,powerset(powerset(X5)))
| ~ element(X6,powerset(powerset(X5))) )
& ( element(esk22_3(X5,X6,X7),powerset(X5))
| X7 = complements_of_subsets(X5,X6)
| ~ element(X7,powerset(powerset(X5)))
| ~ element(X6,powerset(powerset(X5))) )
& ( ~ in(esk22_3(X5,X6,X7),X7)
| ~ in(subset_complement(X5,esk22_3(X5,X6,X7)),X6)
| X7 = complements_of_subsets(X5,X6)
| ~ element(X7,powerset(powerset(X5)))
| ~ element(X6,powerset(powerset(X5))) )
& ( in(esk22_3(X5,X6,X7),X7)
| in(subset_complement(X5,esk22_3(X5,X6,X7)),X6)
| X7 = complements_of_subsets(X5,X6)
| ~ element(X7,powerset(powerset(X5)))
| ~ element(X6,powerset(powerset(X5))) ) ),
inference(distribute,[status(thm)],[491]) ).
cnf(493,plain,
( X3 = complements_of_subsets(X2,X1)
| in(subset_complement(X2,esk22_3(X2,X1,X3)),X1)
| in(esk22_3(X2,X1,X3),X3)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[492]) ).
cnf(495,plain,
( X3 = complements_of_subsets(X2,X1)
| element(esk22_3(X2,X1,X3),powerset(X2))
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2))) ),
inference(split_conjunct,[status(thm)],[492]) ).
cnf(497,plain,
( in(subset_complement(X2,X4),X1)
| ~ element(X1,powerset(powerset(X2)))
| ~ element(X3,powerset(powerset(X2)))
| X3 != complements_of_subsets(X2,X1)
| ~ element(X4,powerset(X2))
| ~ in(X4,X3) ),
inference(split_conjunct,[status(thm)],[492]) ).
fof(594,plain,
! [X1,X2,X3] :
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| element(X1,X3) ),
inference(fof_nnf,[status(thm)],[118]) ).
fof(595,plain,
! [X4,X5,X6] :
( ~ in(X4,X5)
| ~ element(X5,powerset(X6))
| element(X4,X6) ),
inference(variable_rename,[status(thm)],[594]) ).
cnf(596,plain,
( element(X1,X2)
| ~ element(X3,powerset(X2))
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[595]) ).
cnf(681,plain,
~ in(X1,empty_set),
inference(er,[status(thm)],[195,theory(equality)]) ).
cnf(692,plain,
element(empty_set,powerset(X1)),
inference(spm,[status(thm)],[283,330,theory(equality)]) ).
cnf(1099,negated_conjecture,
complements_of_subsets(esk1_0,complements_of_subsets(esk1_0,esk2_0)) = esk2_0,
inference(spm,[status(thm)],[160,179,theory(equality)]) ).
cnf(1108,negated_conjecture,
complements_of_subsets(esk1_0,empty_set) = esk2_0,
inference(rw,[status(thm)],[1099,177,theory(equality)]) ).
cnf(1379,negated_conjecture,
( complements_of_subsets(esk1_0,X1) = esk2_0
| element(esk22_3(esk1_0,X1,esk2_0),powerset(esk1_0))
| ~ element(X1,powerset(powerset(esk1_0))) ),
inference(spm,[status(thm)],[495,179,theory(equality)]) ).
cnf(2236,negated_conjecture,
( complements_of_subsets(esk1_0,X1) = esk2_0
| in(subset_complement(esk1_0,esk22_3(esk1_0,X1,esk2_0)),X1)
| in(esk22_3(esk1_0,X1,esk2_0),esk2_0)
| ~ element(X1,powerset(powerset(esk1_0))) ),
inference(spm,[status(thm)],[493,179,theory(equality)]) ).
cnf(2664,plain,
( in(subset_complement(X2,X4),X1)
| complements_of_subsets(X2,X1) != X3
| ~ element(X3,powerset(powerset(X2)))
| ~ element(X1,powerset(powerset(X2)))
| ~ in(X4,X3) ),
inference(csr,[status(thm)],[497,596]) ).
cnf(2784,negated_conjecture,
( in(subset_complement(esk1_0,X1),empty_set)
| esk2_0 != X2
| ~ element(X2,powerset(powerset(esk1_0)))
| ~ element(empty_set,powerset(powerset(esk1_0)))
| ~ in(X1,X2) ),
inference(spm,[status(thm)],[2664,1108,theory(equality)]) ).
cnf(51547,negated_conjecture,
( complements_of_subsets(esk1_0,esk2_0) = esk2_0
| element(esk22_3(esk1_0,esk2_0,esk2_0),powerset(esk1_0)) ),
inference(spm,[status(thm)],[1379,179,theory(equality)]) ).
cnf(51579,negated_conjecture,
( empty_set = esk2_0
| element(esk22_3(esk1_0,esk2_0,esk2_0),powerset(esk1_0)) ),
inference(rw,[status(thm)],[51547,177,theory(equality)]) ).
cnf(51580,negated_conjecture,
element(esk22_3(esk1_0,esk2_0,esk2_0),powerset(esk1_0)),
inference(sr,[status(thm)],[51579,178,theory(equality)]) ).
cnf(51593,negated_conjecture,
subset_complement(esk1_0,esk22_3(esk1_0,esk2_0,esk2_0)) = set_difference(esk1_0,esk22_3(esk1_0,esk2_0,esk2_0)),
inference(spm,[status(thm)],[410,51580,theory(equality)]) ).
cnf(309500,negated_conjecture,
( complements_of_subsets(esk1_0,esk2_0) = esk2_0
| in(subset_complement(esk1_0,esk22_3(esk1_0,esk2_0,esk2_0)),esk2_0)
| in(esk22_3(esk1_0,esk2_0,esk2_0),esk2_0) ),
inference(spm,[status(thm)],[2236,179,theory(equality)]) ).
cnf(309566,negated_conjecture,
( empty_set = esk2_0
| in(subset_complement(esk1_0,esk22_3(esk1_0,esk2_0,esk2_0)),esk2_0)
| in(esk22_3(esk1_0,esk2_0,esk2_0),esk2_0) ),
inference(rw,[status(thm)],[309500,177,theory(equality)]) ).
cnf(309567,negated_conjecture,
( empty_set = esk2_0
| in(set_difference(esk1_0,esk22_3(esk1_0,esk2_0,esk2_0)),esk2_0)
| in(esk22_3(esk1_0,esk2_0,esk2_0),esk2_0) ),
inference(rw,[status(thm)],[309566,51593,theory(equality)]) ).
cnf(309568,negated_conjecture,
( in(set_difference(esk1_0,esk22_3(esk1_0,esk2_0,esk2_0)),esk2_0)
| in(esk22_3(esk1_0,esk2_0,esk2_0),esk2_0) ),
inference(sr,[status(thm)],[309567,178,theory(equality)]) ).
cnf(785538,negated_conjecture,
( in(subset_complement(esk1_0,X1),empty_set)
| esk2_0 != X2
| ~ element(X2,powerset(powerset(esk1_0)))
| $false
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[2784,692,theory(equality)]) ).
cnf(785539,negated_conjecture,
( in(subset_complement(esk1_0,X1),empty_set)
| esk2_0 != X2
| ~ element(X2,powerset(powerset(esk1_0)))
| ~ in(X1,X2) ),
inference(cn,[status(thm)],[785538,theory(equality)]) ).
cnf(785540,negated_conjecture,
( esk2_0 != X2
| ~ element(X2,powerset(powerset(esk1_0)))
| ~ in(X1,X2) ),
inference(sr,[status(thm)],[785539,681,theory(equality)]) ).
cnf(785541,negated_conjecture,
( ~ element(esk2_0,powerset(powerset(esk1_0)))
| ~ in(X1,esk2_0) ),
inference(er,[status(thm)],[785540,theory(equality)]) ).
cnf(785542,negated_conjecture,
( $false
| ~ in(X1,esk2_0) ),
inference(rw,[status(thm)],[785541,179,theory(equality)]) ).
cnf(785543,negated_conjecture,
~ in(X1,esk2_0),
inference(cn,[status(thm)],[785542,theory(equality)]) ).
cnf(785730,negated_conjecture,
in(esk22_3(esk1_0,esk2_0,esk2_0),esk2_0),
inference(sr,[status(thm)],[309568,785543,theory(equality)]) ).
cnf(785731,negated_conjecture,
$false,
inference(sr,[status(thm)],[785730,785543,theory(equality)]) ).
cnf(785732,negated_conjecture,
$false,
785731,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU174+2.p
% --creating new selector for []
% eprover: CPU time limit exceeded, terminating
% -running prover on /tmp/tmpbutiNj/sel_SEU174+2.p_1 with time limit 29
% -prover status ResourceOut
% -running prover on /tmp/tmpbutiNj/sel_SEU174+2.p_2 with time limit 81
% -prover status Theorem
% Problem SEU174+2.p solved in phase 1.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU174+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU174+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
%
%------------------------------------------------------------------------------