TSTP Solution File: SEU324+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU324+1 : 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 07:17:21 EST 2010
% Result : Theorem 0.24s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 7
% Syntax : Number of formulae : 73 ( 11 unt; 0 def)
% Number of atoms : 293 ( 49 equ)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 351 ( 131 ~; 151 |; 45 &)
% ( 1 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 86 ( 0 sgn 54 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(3,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> element(subset_complement(X1,X2),powerset(X1)) ),
file('/tmp/tmpxsbrsA/sel_SEU324+1.p_1',dt_k3_subset_1) ).
fof(4,axiom,
! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> interior(X1,X2) = subset_complement(the_carrier(X1),topstr_closure(X1,subset_complement(the_carrier(X1),X2))) ) ),
file('/tmp/tmpxsbrsA/sel_SEU324+1.p_1',d1_tops_1) ).
fof(5,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,subset_complement(X1,X2)) = X2 ),
file('/tmp/tmpxsbrsA/sel_SEU324+1.p_1',involutiveness_k3_subset_1) ).
fof(7,axiom,
! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ( ( closed_subset(X2,X1)
=> topstr_closure(X1,X2) = X2 )
& ( ( topological_space(X1)
& topstr_closure(X1,X2) = X2 )
=> closed_subset(X2,X1) ) ) ) ),
file('/tmp/tmpxsbrsA/sel_SEU324+1.p_1',t52_pre_topc) ).
fof(8,axiom,
! [X1,X2] :
( ( topological_space(X1)
& top_str(X1)
& element(X2,powerset(the_carrier(X1))) )
=> open_subset(interior(X1,X2),X1) ),
file('/tmp/tmpxsbrsA/sel_SEU324+1.p_1',fc6_tops_1) ).
fof(11,axiom,
! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ( open_subset(X2,X1)
<=> closed_subset(subset_complement(the_carrier(X1),X2),X1) ) ) ),
file('/tmp/tmpxsbrsA/sel_SEU324+1.p_1',t30_tops_1) ).
fof(19,conjecture,
! [X1] :
( ( topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( top_str(X2)
=> ! [X3] :
( element(X3,powerset(the_carrier(X1)))
=> ! [X4] :
( element(X4,powerset(the_carrier(X2)))
=> ( ( open_subset(X4,X2)
=> interior(X2,X4) = X4 )
& ( interior(X1,X3) = X3
=> open_subset(X3,X1) ) ) ) ) ) ),
file('/tmp/tmpxsbrsA/sel_SEU324+1.p_1',t55_tops_1) ).
fof(26,negated_conjecture,
~ ! [X1] :
( ( topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( top_str(X2)
=> ! [X3] :
( element(X3,powerset(the_carrier(X1)))
=> ! [X4] :
( element(X4,powerset(the_carrier(X2)))
=> ( ( open_subset(X4,X2)
=> interior(X2,X4) = X4 )
& ( interior(X1,X3) = X3
=> open_subset(X3,X1) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[19]) ).
fof(34,plain,
! [X1,X2] :
( ~ element(X2,powerset(X1))
| element(subset_complement(X1,X2),powerset(X1)) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(35,plain,
! [X3,X4] :
( ~ element(X4,powerset(X3))
| element(subset_complement(X3,X4),powerset(X3)) ),
inference(variable_rename,[status(thm)],[34]) ).
cnf(36,plain,
( element(subset_complement(X1,X2),powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[35]) ).
fof(37,plain,
! [X1] :
( ~ top_str(X1)
| ! [X2] :
( ~ element(X2,powerset(the_carrier(X1)))
| interior(X1,X2) = subset_complement(the_carrier(X1),topstr_closure(X1,subset_complement(the_carrier(X1),X2))) ) ),
inference(fof_nnf,[status(thm)],[4]) ).
fof(38,plain,
! [X3] :
( ~ top_str(X3)
| ! [X4] :
( ~ element(X4,powerset(the_carrier(X3)))
| interior(X3,X4) = subset_complement(the_carrier(X3),topstr_closure(X3,subset_complement(the_carrier(X3),X4))) ) ),
inference(variable_rename,[status(thm)],[37]) ).
fof(39,plain,
! [X3,X4] :
( ~ element(X4,powerset(the_carrier(X3)))
| interior(X3,X4) = subset_complement(the_carrier(X3),topstr_closure(X3,subset_complement(the_carrier(X3),X4)))
| ~ top_str(X3) ),
inference(shift_quantors,[status(thm)],[38]) ).
cnf(40,plain,
( interior(X1,X2) = subset_complement(the_carrier(X1),topstr_closure(X1,subset_complement(the_carrier(X1),X2)))
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[39]) ).
fof(41,plain,
! [X1,X2] :
( ~ element(X2,powerset(X1))
| subset_complement(X1,subset_complement(X1,X2)) = X2 ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(42,plain,
! [X3,X4] :
( ~ element(X4,powerset(X3))
| subset_complement(X3,subset_complement(X3,X4)) = X4 ),
inference(variable_rename,[status(thm)],[41]) ).
cnf(43,plain,
( subset_complement(X1,subset_complement(X1,X2)) = X2
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[42]) ).
fof(45,plain,
! [X1] :
( ~ top_str(X1)
| ! [X2] :
( ~ element(X2,powerset(the_carrier(X1)))
| ( ( ~ closed_subset(X2,X1)
| topstr_closure(X1,X2) = X2 )
& ( ~ topological_space(X1)
| topstr_closure(X1,X2) != X2
| closed_subset(X2,X1) ) ) ) ),
inference(fof_nnf,[status(thm)],[7]) ).
fof(46,plain,
! [X3] :
( ~ top_str(X3)
| ! [X4] :
( ~ element(X4,powerset(the_carrier(X3)))
| ( ( ~ closed_subset(X4,X3)
| topstr_closure(X3,X4) = X4 )
& ( ~ topological_space(X3)
| topstr_closure(X3,X4) != X4
| closed_subset(X4,X3) ) ) ) ),
inference(variable_rename,[status(thm)],[45]) ).
fof(47,plain,
! [X3,X4] :
( ~ element(X4,powerset(the_carrier(X3)))
| ( ( ~ closed_subset(X4,X3)
| topstr_closure(X3,X4) = X4 )
& ( ~ topological_space(X3)
| topstr_closure(X3,X4) != X4
| closed_subset(X4,X3) ) )
| ~ top_str(X3) ),
inference(shift_quantors,[status(thm)],[46]) ).
fof(48,plain,
! [X3,X4] :
( ( ~ closed_subset(X4,X3)
| topstr_closure(X3,X4) = X4
| ~ element(X4,powerset(the_carrier(X3)))
| ~ top_str(X3) )
& ( ~ topological_space(X3)
| topstr_closure(X3,X4) != X4
| closed_subset(X4,X3)
| ~ element(X4,powerset(the_carrier(X3)))
| ~ top_str(X3) ) ),
inference(distribute,[status(thm)],[47]) ).
cnf(50,plain,
( topstr_closure(X1,X2) = X2
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ closed_subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[48]) ).
fof(51,plain,
! [X1,X2] :
( ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| open_subset(interior(X1,X2),X1) ),
inference(fof_nnf,[status(thm)],[8]) ).
fof(52,plain,
! [X3,X4] :
( ~ topological_space(X3)
| ~ top_str(X3)
| ~ element(X4,powerset(the_carrier(X3)))
| open_subset(interior(X3,X4),X3) ),
inference(variable_rename,[status(thm)],[51]) ).
cnf(53,plain,
( open_subset(interior(X1,X2),X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ topological_space(X1) ),
inference(split_conjunct,[status(thm)],[52]) ).
fof(59,plain,
! [X1] :
( ~ top_str(X1)
| ! [X2] :
( ~ element(X2,powerset(the_carrier(X1)))
| ( ( ~ open_subset(X2,X1)
| closed_subset(subset_complement(the_carrier(X1),X2),X1) )
& ( ~ closed_subset(subset_complement(the_carrier(X1),X2),X1)
| open_subset(X2,X1) ) ) ) ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(60,plain,
! [X3] :
( ~ top_str(X3)
| ! [X4] :
( ~ element(X4,powerset(the_carrier(X3)))
| ( ( ~ open_subset(X4,X3)
| closed_subset(subset_complement(the_carrier(X3),X4),X3) )
& ( ~ closed_subset(subset_complement(the_carrier(X3),X4),X3)
| open_subset(X4,X3) ) ) ) ),
inference(variable_rename,[status(thm)],[59]) ).
fof(61,plain,
! [X3,X4] :
( ~ element(X4,powerset(the_carrier(X3)))
| ( ( ~ open_subset(X4,X3)
| closed_subset(subset_complement(the_carrier(X3),X4),X3) )
& ( ~ closed_subset(subset_complement(the_carrier(X3),X4),X3)
| open_subset(X4,X3) ) )
| ~ top_str(X3) ),
inference(shift_quantors,[status(thm)],[60]) ).
fof(62,plain,
! [X3,X4] :
( ( ~ open_subset(X4,X3)
| closed_subset(subset_complement(the_carrier(X3),X4),X3)
| ~ element(X4,powerset(the_carrier(X3)))
| ~ top_str(X3) )
& ( ~ closed_subset(subset_complement(the_carrier(X3),X4),X3)
| open_subset(X4,X3)
| ~ element(X4,powerset(the_carrier(X3)))
| ~ top_str(X3) ) ),
inference(distribute,[status(thm)],[61]) ).
cnf(64,plain,
( closed_subset(subset_complement(the_carrier(X1),X2),X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ open_subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[62]) ).
fof(92,negated_conjecture,
? [X1] :
( topological_space(X1)
& top_str(X1)
& ? [X2] :
( top_str(X2)
& ? [X3] :
( element(X3,powerset(the_carrier(X1)))
& ? [X4] :
( element(X4,powerset(the_carrier(X2)))
& ( ( open_subset(X4,X2)
& interior(X2,X4) != X4 )
| ( interior(X1,X3) = X3
& ~ open_subset(X3,X1) ) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[26]) ).
fof(93,negated_conjecture,
? [X5] :
( topological_space(X5)
& top_str(X5)
& ? [X6] :
( top_str(X6)
& ? [X7] :
( element(X7,powerset(the_carrier(X5)))
& ? [X8] :
( element(X8,powerset(the_carrier(X6)))
& ( ( open_subset(X8,X6)
& interior(X6,X8) != X8 )
| ( interior(X5,X7) = X7
& ~ open_subset(X7,X5) ) ) ) ) ) ),
inference(variable_rename,[status(thm)],[92]) ).
fof(94,negated_conjecture,
( topological_space(esk5_0)
& top_str(esk5_0)
& top_str(esk6_0)
& element(esk7_0,powerset(the_carrier(esk5_0)))
& element(esk8_0,powerset(the_carrier(esk6_0)))
& ( ( open_subset(esk8_0,esk6_0)
& interior(esk6_0,esk8_0) != esk8_0 )
| ( interior(esk5_0,esk7_0) = esk7_0
& ~ open_subset(esk7_0,esk5_0) ) ) ),
inference(skolemize,[status(esa)],[93]) ).
fof(95,negated_conjecture,
( topological_space(esk5_0)
& top_str(esk5_0)
& top_str(esk6_0)
& element(esk7_0,powerset(the_carrier(esk5_0)))
& element(esk8_0,powerset(the_carrier(esk6_0)))
& ( interior(esk5_0,esk7_0) = esk7_0
| open_subset(esk8_0,esk6_0) )
& ( ~ open_subset(esk7_0,esk5_0)
| open_subset(esk8_0,esk6_0) )
& ( interior(esk5_0,esk7_0) = esk7_0
| interior(esk6_0,esk8_0) != esk8_0 )
& ( ~ open_subset(esk7_0,esk5_0)
| interior(esk6_0,esk8_0) != esk8_0 ) ),
inference(distribute,[status(thm)],[94]) ).
cnf(96,negated_conjecture,
( interior(esk6_0,esk8_0) != esk8_0
| ~ open_subset(esk7_0,esk5_0) ),
inference(split_conjunct,[status(thm)],[95]) ).
cnf(97,negated_conjecture,
( interior(esk5_0,esk7_0) = esk7_0
| interior(esk6_0,esk8_0) != esk8_0 ),
inference(split_conjunct,[status(thm)],[95]) ).
cnf(98,negated_conjecture,
( open_subset(esk8_0,esk6_0)
| ~ open_subset(esk7_0,esk5_0) ),
inference(split_conjunct,[status(thm)],[95]) ).
cnf(99,negated_conjecture,
( open_subset(esk8_0,esk6_0)
| interior(esk5_0,esk7_0) = esk7_0 ),
inference(split_conjunct,[status(thm)],[95]) ).
cnf(100,negated_conjecture,
element(esk8_0,powerset(the_carrier(esk6_0))),
inference(split_conjunct,[status(thm)],[95]) ).
cnf(101,negated_conjecture,
element(esk7_0,powerset(the_carrier(esk5_0))),
inference(split_conjunct,[status(thm)],[95]) ).
cnf(102,negated_conjecture,
top_str(esk6_0),
inference(split_conjunct,[status(thm)],[95]) ).
cnf(103,negated_conjecture,
top_str(esk5_0),
inference(split_conjunct,[status(thm)],[95]) ).
cnf(104,negated_conjecture,
topological_space(esk5_0),
inference(split_conjunct,[status(thm)],[95]) ).
cnf(129,negated_conjecture,
( open_subset(esk7_0,esk5_0)
| open_subset(esk8_0,esk6_0)
| ~ element(esk7_0,powerset(the_carrier(esk5_0)))
| ~ top_str(esk5_0)
| ~ topological_space(esk5_0) ),
inference(spm,[status(thm)],[53,99,theory(equality)]) ).
cnf(130,negated_conjecture,
( open_subset(esk7_0,esk5_0)
| open_subset(esk8_0,esk6_0)
| $false
| ~ top_str(esk5_0)
| ~ topological_space(esk5_0) ),
inference(rw,[status(thm)],[129,101,theory(equality)]) ).
cnf(131,negated_conjecture,
( open_subset(esk7_0,esk5_0)
| open_subset(esk8_0,esk6_0)
| $false
| $false
| ~ topological_space(esk5_0) ),
inference(rw,[status(thm)],[130,103,theory(equality)]) ).
cnf(132,negated_conjecture,
( open_subset(esk7_0,esk5_0)
| open_subset(esk8_0,esk6_0)
| $false
| $false
| $false ),
inference(rw,[status(thm)],[131,104,theory(equality)]) ).
cnf(133,negated_conjecture,
( open_subset(esk7_0,esk5_0)
| open_subset(esk8_0,esk6_0) ),
inference(cn,[status(thm)],[132,theory(equality)]) ).
cnf(144,plain,
( subset_complement(the_carrier(X1),topstr_closure(X1,X2)) = interior(X1,subset_complement(the_carrier(X1),X2))
| ~ element(subset_complement(the_carrier(X1),X2),powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(spm,[status(thm)],[40,43,theory(equality)]) ).
cnf(151,negated_conjecture,
open_subset(esk8_0,esk6_0),
inference(csr,[status(thm)],[133,98]) ).
cnf(165,plain,
( subset_complement(the_carrier(X1),topstr_closure(X1,X2)) = interior(X1,subset_complement(the_carrier(X1),X2))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1) ),
inference(csr,[status(thm)],[144,36]) ).
cnf(168,plain,
( subset_complement(the_carrier(X1),X2) = interior(X1,subset_complement(the_carrier(X1),X2))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ closed_subset(X2,X1) ),
inference(spm,[status(thm)],[165,50,theory(equality)]) ).
cnf(181,plain,
( interior(X1,X2) = X2
| ~ closed_subset(subset_complement(the_carrier(X1),X2),X1)
| ~ element(subset_complement(the_carrier(X1),X2),powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(spm,[status(thm)],[168,43,theory(equality)]) ).
cnf(202,plain,
( interior(X1,X2) = X2
| ~ closed_subset(subset_complement(the_carrier(X1),X2),X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1) ),
inference(csr,[status(thm)],[181,36]) ).
cnf(204,plain,
( interior(X1,X2) = X2
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ open_subset(X2,X1) ),
inference(spm,[status(thm)],[202,64,theory(equality)]) ).
cnf(225,negated_conjecture,
( ~ open_subset(esk7_0,esk5_0)
| ~ open_subset(esk8_0,esk6_0)
| ~ element(esk8_0,powerset(the_carrier(esk6_0)))
| ~ top_str(esk6_0) ),
inference(spm,[status(thm)],[96,204,theory(equality)]) ).
cnf(226,negated_conjecture,
( interior(esk5_0,esk7_0) = esk7_0
| ~ open_subset(esk8_0,esk6_0)
| ~ element(esk8_0,powerset(the_carrier(esk6_0)))
| ~ top_str(esk6_0) ),
inference(spm,[status(thm)],[97,204,theory(equality)]) ).
cnf(232,negated_conjecture,
( ~ open_subset(esk7_0,esk5_0)
| $false
| ~ element(esk8_0,powerset(the_carrier(esk6_0)))
| ~ top_str(esk6_0) ),
inference(rw,[status(thm)],[225,151,theory(equality)]) ).
cnf(233,negated_conjecture,
( ~ open_subset(esk7_0,esk5_0)
| $false
| $false
| ~ top_str(esk6_0) ),
inference(rw,[status(thm)],[232,100,theory(equality)]) ).
cnf(234,negated_conjecture,
( ~ open_subset(esk7_0,esk5_0)
| $false
| $false
| $false ),
inference(rw,[status(thm)],[233,102,theory(equality)]) ).
cnf(235,negated_conjecture,
~ open_subset(esk7_0,esk5_0),
inference(cn,[status(thm)],[234,theory(equality)]) ).
cnf(236,negated_conjecture,
( interior(esk5_0,esk7_0) = esk7_0
| $false
| ~ element(esk8_0,powerset(the_carrier(esk6_0)))
| ~ top_str(esk6_0) ),
inference(rw,[status(thm)],[226,151,theory(equality)]) ).
cnf(237,negated_conjecture,
( interior(esk5_0,esk7_0) = esk7_0
| $false
| $false
| ~ top_str(esk6_0) ),
inference(rw,[status(thm)],[236,100,theory(equality)]) ).
cnf(238,negated_conjecture,
( interior(esk5_0,esk7_0) = esk7_0
| $false
| $false
| $false ),
inference(rw,[status(thm)],[237,102,theory(equality)]) ).
cnf(239,negated_conjecture,
interior(esk5_0,esk7_0) = esk7_0,
inference(cn,[status(thm)],[238,theory(equality)]) ).
cnf(241,negated_conjecture,
( open_subset(esk7_0,esk5_0)
| ~ element(esk7_0,powerset(the_carrier(esk5_0)))
| ~ top_str(esk5_0)
| ~ topological_space(esk5_0) ),
inference(spm,[status(thm)],[53,239,theory(equality)]) ).
cnf(248,negated_conjecture,
( open_subset(esk7_0,esk5_0)
| $false
| ~ top_str(esk5_0)
| ~ topological_space(esk5_0) ),
inference(rw,[status(thm)],[241,101,theory(equality)]) ).
cnf(249,negated_conjecture,
( open_subset(esk7_0,esk5_0)
| $false
| $false
| ~ topological_space(esk5_0) ),
inference(rw,[status(thm)],[248,103,theory(equality)]) ).
cnf(250,negated_conjecture,
( open_subset(esk7_0,esk5_0)
| $false
| $false
| $false ),
inference(rw,[status(thm)],[249,104,theory(equality)]) ).
cnf(251,negated_conjecture,
open_subset(esk7_0,esk5_0),
inference(cn,[status(thm)],[250,theory(equality)]) ).
cnf(252,negated_conjecture,
$false,
inference(sr,[status(thm)],[251,235,theory(equality)]) ).
cnf(253,negated_conjecture,
$false,
252,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU324+1.p
% --creating new selector for []
% -running prover on /tmp/tmpxsbrsA/sel_SEU324+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU324+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU324+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU324+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
%
%------------------------------------------------------------------------------