TSTP Solution File: SEU341+1 by SInE---0.4
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- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU341+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art07.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 07:31:32 EST 2010
% Result : Theorem 0.31s
% Output : CNFRefutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 4
% Syntax : Number of formulae : 50 ( 12 unt; 0 def)
% Number of atoms : 261 ( 19 equ)
% Maximal formula atoms : 14 ( 5 avg)
% Number of connectives : 343 ( 132 ~; 139 |; 45 &)
% ( 2 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 88 ( 1 sgn 56 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(9,conjecture,
! [X1] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( ( open_subset(X2,X1)
& in(X3,X2) )
=> point_neighbourhood(X2,X1,X3) ) ) ) ),
file('/tmp/tmpcF3cq0/sel_SEU341+1.p_1',t5_connsp_2) ).
fof(13,axiom,
! [X1,X2,X3] :
( ( in(X1,X2)
& element(X2,powerset(X3)) )
=> element(X1,X3) ),
file('/tmp/tmpcF3cq0/sel_SEU341+1.p_1',t4_subset) ).
fof(23,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,powerset(the_carrier(X1)))
=> ( point_neighbourhood(X3,X1,X2)
<=> in(X2,interior(X1,X3)) ) ) ) ),
file('/tmp/tmpcF3cq0/sel_SEU341+1.p_1',d1_connsp_2) ).
fof(32,axiom,
! [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/tmpcF3cq0/sel_SEU341+1.p_1',t55_tops_1) ).
fof(46,negated_conjecture,
~ ! [X1] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( ( open_subset(X2,X1)
& in(X3,X2) )
=> point_neighbourhood(X2,X1,X3) ) ) ) ),
inference(assume_negation,[status(cth)],[9]) ).
fof(48,negated_conjecture,
~ ! [X1] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( ( open_subset(X2,X1)
& in(X3,X2) )
=> point_neighbourhood(X2,X1,X3) ) ) ) ),
inference(fof_simplification,[status(thm)],[46,theory(equality)]) ).
fof(53,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,powerset(the_carrier(X1)))
=> ( point_neighbourhood(X3,X1,X2)
<=> in(X2,interior(X1,X3)) ) ) ) ),
inference(fof_simplification,[status(thm)],[23,theory(equality)]) ).
fof(84,negated_conjecture,
? [X1] :
( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1)
& ? [X2] :
( element(X2,powerset(the_carrier(X1)))
& ? [X3] :
( element(X3,the_carrier(X1))
& open_subset(X2,X1)
& in(X3,X2)
& ~ point_neighbourhood(X2,X1,X3) ) ) ),
inference(fof_nnf,[status(thm)],[48]) ).
fof(85,negated_conjecture,
? [X4] :
( ~ empty_carrier(X4)
& topological_space(X4)
& top_str(X4)
& ? [X5] :
( element(X5,powerset(the_carrier(X4)))
& ? [X6] :
( element(X6,the_carrier(X4))
& open_subset(X5,X4)
& in(X6,X5)
& ~ point_neighbourhood(X5,X4,X6) ) ) ),
inference(variable_rename,[status(thm)],[84]) ).
fof(86,negated_conjecture,
( ~ empty_carrier(esk2_0)
& topological_space(esk2_0)
& top_str(esk2_0)
& element(esk3_0,powerset(the_carrier(esk2_0)))
& element(esk4_0,the_carrier(esk2_0))
& open_subset(esk3_0,esk2_0)
& in(esk4_0,esk3_0)
& ~ point_neighbourhood(esk3_0,esk2_0,esk4_0) ),
inference(skolemize,[status(esa)],[85]) ).
cnf(87,negated_conjecture,
~ point_neighbourhood(esk3_0,esk2_0,esk4_0),
inference(split_conjunct,[status(thm)],[86]) ).
cnf(88,negated_conjecture,
in(esk4_0,esk3_0),
inference(split_conjunct,[status(thm)],[86]) ).
cnf(89,negated_conjecture,
open_subset(esk3_0,esk2_0),
inference(split_conjunct,[status(thm)],[86]) ).
cnf(91,negated_conjecture,
element(esk3_0,powerset(the_carrier(esk2_0))),
inference(split_conjunct,[status(thm)],[86]) ).
cnf(92,negated_conjecture,
top_str(esk2_0),
inference(split_conjunct,[status(thm)],[86]) ).
cnf(93,negated_conjecture,
topological_space(esk2_0),
inference(split_conjunct,[status(thm)],[86]) ).
cnf(94,negated_conjecture,
~ empty_carrier(esk2_0),
inference(split_conjunct,[status(thm)],[86]) ).
fof(112,plain,
! [X1,X2,X3] :
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| element(X1,X3) ),
inference(fof_nnf,[status(thm)],[13]) ).
fof(113,plain,
! [X4,X5,X6] :
( ~ in(X4,X5)
| ~ element(X5,powerset(X6))
| element(X4,X6) ),
inference(variable_rename,[status(thm)],[112]) ).
cnf(114,plain,
( element(X1,X2)
| ~ element(X3,powerset(X2))
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[113]) ).
fof(146,plain,
! [X1] :
( empty_carrier(X1)
| ~ topological_space(X1)
| ~ top_str(X1)
| ! [X2] :
( ~ element(X2,the_carrier(X1))
| ! [X3] :
( ~ element(X3,powerset(the_carrier(X1)))
| ( ( ~ point_neighbourhood(X3,X1,X2)
| in(X2,interior(X1,X3)) )
& ( ~ in(X2,interior(X1,X3))
| point_neighbourhood(X3,X1,X2) ) ) ) ) ),
inference(fof_nnf,[status(thm)],[53]) ).
fof(147,plain,
! [X4] :
( empty_carrier(X4)
| ~ topological_space(X4)
| ~ top_str(X4)
| ! [X5] :
( ~ element(X5,the_carrier(X4))
| ! [X6] :
( ~ element(X6,powerset(the_carrier(X4)))
| ( ( ~ point_neighbourhood(X6,X4,X5)
| in(X5,interior(X4,X6)) )
& ( ~ in(X5,interior(X4,X6))
| point_neighbourhood(X6,X4,X5) ) ) ) ) ),
inference(variable_rename,[status(thm)],[146]) ).
fof(148,plain,
! [X4,X5,X6] :
( ~ element(X6,powerset(the_carrier(X4)))
| ( ( ~ point_neighbourhood(X6,X4,X5)
| in(X5,interior(X4,X6)) )
& ( ~ in(X5,interior(X4,X6))
| point_neighbourhood(X6,X4,X5) ) )
| ~ element(X5,the_carrier(X4))
| empty_carrier(X4)
| ~ topological_space(X4)
| ~ top_str(X4) ),
inference(shift_quantors,[status(thm)],[147]) ).
fof(149,plain,
! [X4,X5,X6] :
( ( ~ point_neighbourhood(X6,X4,X5)
| in(X5,interior(X4,X6))
| ~ element(X6,powerset(the_carrier(X4)))
| ~ element(X5,the_carrier(X4))
| empty_carrier(X4)
| ~ topological_space(X4)
| ~ top_str(X4) )
& ( ~ in(X5,interior(X4,X6))
| point_neighbourhood(X6,X4,X5)
| ~ element(X6,powerset(the_carrier(X4)))
| ~ element(X5,the_carrier(X4))
| empty_carrier(X4)
| ~ topological_space(X4)
| ~ top_str(X4) ) ),
inference(distribute,[status(thm)],[148]) ).
cnf(150,plain,
( empty_carrier(X1)
| point_neighbourhood(X3,X1,X2)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,powerset(the_carrier(X1)))
| ~ in(X2,interior(X1,X3)) ),
inference(split_conjunct,[status(thm)],[149]) ).
fof(184,plain,
! [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)],[32]) ).
fof(185,plain,
! [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)],[184]) ).
fof(186,plain,
! [X5,X6,X7,X8] :
( ~ element(X8,powerset(the_carrier(X6)))
| ( ( ~ open_subset(X8,X6)
| interior(X6,X8) = X8 )
& ( interior(X5,X7) != X7
| open_subset(X7,X5) ) )
| ~ element(X7,powerset(the_carrier(X5)))
| ~ top_str(X6)
| ~ topological_space(X5)
| ~ top_str(X5) ),
inference(shift_quantors,[status(thm)],[185]) ).
fof(187,plain,
! [X5,X6,X7,X8] :
( ( ~ open_subset(X8,X6)
| interior(X6,X8) = X8
| ~ element(X8,powerset(the_carrier(X6)))
| ~ element(X7,powerset(the_carrier(X5)))
| ~ top_str(X6)
| ~ topological_space(X5)
| ~ top_str(X5) )
& ( interior(X5,X7) != X7
| open_subset(X7,X5)
| ~ element(X8,powerset(the_carrier(X6)))
| ~ element(X7,powerset(the_carrier(X5)))
| ~ top_str(X6)
| ~ topological_space(X5)
| ~ top_str(X5) ) ),
inference(distribute,[status(thm)],[186]) ).
cnf(189,plain,
( interior(X2,X4) = X4
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ top_str(X2)
| ~ element(X3,powerset(the_carrier(X1)))
| ~ element(X4,powerset(the_carrier(X2)))
| ~ open_subset(X4,X2) ),
inference(split_conjunct,[status(thm)],[187]) ).
cnf(266,negated_conjecture,
( element(X1,the_carrier(esk2_0))
| ~ in(X1,esk3_0) ),
inference(spm,[status(thm)],[114,91,theory(equality)]) ).
cnf(442,negated_conjecture,
( interior(X1,X2) = X2
| ~ open_subset(X2,X1)
| ~ top_str(X1)
| ~ top_str(esk2_0)
| ~ topological_space(esk2_0)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(spm,[status(thm)],[189,91,theory(equality)]) ).
cnf(447,negated_conjecture,
( interior(X1,X2) = X2
| ~ open_subset(X2,X1)
| ~ top_str(X1)
| $false
| ~ topological_space(esk2_0)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(rw,[status(thm)],[442,92,theory(equality)]) ).
cnf(448,negated_conjecture,
( interior(X1,X2) = X2
| ~ open_subset(X2,X1)
| ~ top_str(X1)
| $false
| $false
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(rw,[status(thm)],[447,93,theory(equality)]) ).
cnf(449,negated_conjecture,
( interior(X1,X2) = X2
| ~ open_subset(X2,X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(cn,[status(thm)],[448,theory(equality)]) ).
cnf(1018,negated_conjecture,
( interior(esk2_0,esk3_0) = esk3_0
| ~ top_str(esk2_0)
| ~ element(esk3_0,powerset(the_carrier(esk2_0))) ),
inference(spm,[status(thm)],[449,89,theory(equality)]) ).
cnf(1019,negated_conjecture,
( interior(esk2_0,esk3_0) = esk3_0
| $false
| ~ element(esk3_0,powerset(the_carrier(esk2_0))) ),
inference(rw,[status(thm)],[1018,92,theory(equality)]) ).
cnf(1020,negated_conjecture,
( interior(esk2_0,esk3_0) = esk3_0
| $false
| $false ),
inference(rw,[status(thm)],[1019,91,theory(equality)]) ).
cnf(1021,negated_conjecture,
interior(esk2_0,esk3_0) = esk3_0,
inference(cn,[status(thm)],[1020,theory(equality)]) ).
cnf(1023,negated_conjecture,
( point_neighbourhood(esk3_0,esk2_0,X1)
| empty_carrier(esk2_0)
| ~ top_str(esk2_0)
| ~ topological_space(esk2_0)
| ~ in(X1,esk3_0)
| ~ element(esk3_0,powerset(the_carrier(esk2_0)))
| ~ element(X1,the_carrier(esk2_0)) ),
inference(spm,[status(thm)],[150,1021,theory(equality)]) ).
cnf(1031,negated_conjecture,
( point_neighbourhood(esk3_0,esk2_0,X1)
| empty_carrier(esk2_0)
| $false
| ~ topological_space(esk2_0)
| ~ in(X1,esk3_0)
| ~ element(esk3_0,powerset(the_carrier(esk2_0)))
| ~ element(X1,the_carrier(esk2_0)) ),
inference(rw,[status(thm)],[1023,92,theory(equality)]) ).
cnf(1032,negated_conjecture,
( point_neighbourhood(esk3_0,esk2_0,X1)
| empty_carrier(esk2_0)
| $false
| $false
| ~ in(X1,esk3_0)
| ~ element(esk3_0,powerset(the_carrier(esk2_0)))
| ~ element(X1,the_carrier(esk2_0)) ),
inference(rw,[status(thm)],[1031,93,theory(equality)]) ).
cnf(1033,negated_conjecture,
( point_neighbourhood(esk3_0,esk2_0,X1)
| empty_carrier(esk2_0)
| $false
| $false
| ~ in(X1,esk3_0)
| $false
| ~ element(X1,the_carrier(esk2_0)) ),
inference(rw,[status(thm)],[1032,91,theory(equality)]) ).
cnf(1034,negated_conjecture,
( point_neighbourhood(esk3_0,esk2_0,X1)
| empty_carrier(esk2_0)
| ~ in(X1,esk3_0)
| ~ element(X1,the_carrier(esk2_0)) ),
inference(cn,[status(thm)],[1033,theory(equality)]) ).
cnf(1035,negated_conjecture,
( point_neighbourhood(esk3_0,esk2_0,X1)
| ~ in(X1,esk3_0)
| ~ element(X1,the_carrier(esk2_0)) ),
inference(sr,[status(thm)],[1034,94,theory(equality)]) ).
cnf(1047,negated_conjecture,
( point_neighbourhood(esk3_0,esk2_0,X1)
| ~ in(X1,esk3_0) ),
inference(csr,[status(thm)],[1035,266]) ).
cnf(1048,negated_conjecture,
~ in(esk4_0,esk3_0),
inference(spm,[status(thm)],[87,1047,theory(equality)]) ).
cnf(1050,negated_conjecture,
$false,
inference(rw,[status(thm)],[1048,88,theory(equality)]) ).
cnf(1051,negated_conjecture,
$false,
inference(cn,[status(thm)],[1050,theory(equality)]) ).
cnf(1052,negated_conjecture,
$false,
1051,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU341+1.p
% --creating new selector for []
% -running prover on /tmp/tmpcF3cq0/sel_SEU341+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU341+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU341+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU341+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
%
%------------------------------------------------------------------------------