TSTP Solution File: SEU323+1 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU323+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art11.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 3.00GHz @ 3000MHz
% Memory : 2006MB
% OS : Linux 2.6.31.5-127.fc12.i686.PAE
% CPULimit : 300s
% DateTime : Sun Dec 26 07:21:24 EST 2010
% Result : Theorem 0.23s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 53 ( 6 unt; 0 def)
% Number of atoms : 169 ( 12 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 205 ( 89 ~; 86 |; 18 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 84 ( 0 sgn 48 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(5,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> element(subset_complement(X1,X2),powerset(X1)) ),
file('/tmp/tmptIb36W/sel_SEU323+1.p_1',dt_k3_subset_1) ).
fof(9,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,subset_complement(X1,X2)) = X2 ),
file('/tmp/tmptIb36W/sel_SEU323+1.p_1',involutiveness_k3_subset_1) ).
fof(10,conjecture,
! [X1] :
( ( topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> open_subset(interior(X1,X2),X1) ) ),
file('/tmp/tmptIb36W/sel_SEU323+1.p_1',t51_tops_1) ).
fof(11,axiom,
! [X1,X2] :
( ( topological_space(X1)
& top_str(X1)
& element(X2,powerset(the_carrier(X1))) )
=> closed_subset(topstr_closure(X1,X2),X1) ),
file('/tmp/tmptIb36W/sel_SEU323+1.p_1',fc2_tops_1) ).
fof(14,axiom,
! [X1,X2] :
( ( top_str(X1)
& element(X2,powerset(the_carrier(X1))) )
=> element(interior(X1,X2),powerset(the_carrier(X1))) ),
file('/tmp/tmptIb36W/sel_SEU323+1.p_1',dt_k1_tops_1) ).
fof(16,axiom,
! [X1,X2] :
( ( topological_space(X1)
& top_str(X1)
& closed_subset(X2,X1)
& element(X2,powerset(the_carrier(X1))) )
=> open_subset(subset_complement(the_carrier(X1),X2),X1) ),
file('/tmp/tmptIb36W/sel_SEU323+1.p_1',fc3_tops_1) ).
fof(18,axiom,
! [X1,X2] :
( ( top_str(X1)
& element(X2,powerset(the_carrier(X1))) )
=> element(topstr_closure(X1,X2),powerset(the_carrier(X1))) ),
file('/tmp/tmptIb36W/sel_SEU323+1.p_1',dt_k6_pre_topc) ).
fof(19,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/tmptIb36W/sel_SEU323+1.p_1',d1_tops_1) ).
fof(22,negated_conjecture,
~ ! [X1] :
( ( topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> open_subset(interior(X1,X2),X1) ) ),
inference(assume_negation,[status(cth)],[10]) ).
fof(36,plain,
! [X1,X2] :
( ~ element(X2,powerset(X1))
| element(subset_complement(X1,X2),powerset(X1)) ),
inference(fof_nnf,[status(thm)],[5]) ).
fof(37,plain,
! [X3,X4] :
( ~ element(X4,powerset(X3))
| element(subset_complement(X3,X4),powerset(X3)) ),
inference(variable_rename,[status(thm)],[36]) ).
cnf(38,plain,
( element(subset_complement(X1,X2),powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[37]) ).
fof(48,plain,
! [X1,X2] :
( ~ element(X2,powerset(X1))
| subset_complement(X1,subset_complement(X1,X2)) = X2 ),
inference(fof_nnf,[status(thm)],[9]) ).
fof(49,plain,
! [X3,X4] :
( ~ element(X4,powerset(X3))
| subset_complement(X3,subset_complement(X3,X4)) = X4 ),
inference(variable_rename,[status(thm)],[48]) ).
cnf(50,plain,
( subset_complement(X1,subset_complement(X1,X2)) = X2
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[49]) ).
fof(51,negated_conjecture,
? [X1] :
( topological_space(X1)
& top_str(X1)
& ? [X2] :
( element(X2,powerset(the_carrier(X1)))
& ~ open_subset(interior(X1,X2),X1) ) ),
inference(fof_nnf,[status(thm)],[22]) ).
fof(52,negated_conjecture,
? [X3] :
( topological_space(X3)
& top_str(X3)
& ? [X4] :
( element(X4,powerset(the_carrier(X3)))
& ~ open_subset(interior(X3,X4),X3) ) ),
inference(variable_rename,[status(thm)],[51]) ).
fof(53,negated_conjecture,
( topological_space(esk5_0)
& top_str(esk5_0)
& element(esk6_0,powerset(the_carrier(esk5_0)))
& ~ open_subset(interior(esk5_0,esk6_0),esk5_0) ),
inference(skolemize,[status(esa)],[52]) ).
cnf(54,negated_conjecture,
~ open_subset(interior(esk5_0,esk6_0),esk5_0),
inference(split_conjunct,[status(thm)],[53]) ).
cnf(55,negated_conjecture,
element(esk6_0,powerset(the_carrier(esk5_0))),
inference(split_conjunct,[status(thm)],[53]) ).
cnf(56,negated_conjecture,
top_str(esk5_0),
inference(split_conjunct,[status(thm)],[53]) ).
cnf(57,negated_conjecture,
topological_space(esk5_0),
inference(split_conjunct,[status(thm)],[53]) ).
fof(58,plain,
! [X1,X2] :
( ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| closed_subset(topstr_closure(X1,X2),X1) ),
inference(fof_nnf,[status(thm)],[11]) ).
fof(59,plain,
! [X3,X4] :
( ~ topological_space(X3)
| ~ top_str(X3)
| ~ element(X4,powerset(the_carrier(X3)))
| closed_subset(topstr_closure(X3,X4),X3) ),
inference(variable_rename,[status(thm)],[58]) ).
cnf(60,plain,
( closed_subset(topstr_closure(X1,X2),X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ topological_space(X1) ),
inference(split_conjunct,[status(thm)],[59]) ).
fof(63,plain,
! [X1,X2] :
( ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| element(interior(X1,X2),powerset(the_carrier(X1))) ),
inference(fof_nnf,[status(thm)],[14]) ).
fof(64,plain,
! [X3,X4] :
( ~ top_str(X3)
| ~ element(X4,powerset(the_carrier(X3)))
| element(interior(X3,X4),powerset(the_carrier(X3))) ),
inference(variable_rename,[status(thm)],[63]) ).
cnf(65,plain,
( element(interior(X1,X2),powerset(the_carrier(X1)))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[64]) ).
fof(67,plain,
! [X1,X2] :
( ~ topological_space(X1)
| ~ top_str(X1)
| ~ closed_subset(X2,X1)
| ~ element(X2,powerset(the_carrier(X1)))
| open_subset(subset_complement(the_carrier(X1),X2),X1) ),
inference(fof_nnf,[status(thm)],[16]) ).
fof(68,plain,
! [X3,X4] :
( ~ topological_space(X3)
| ~ top_str(X3)
| ~ closed_subset(X4,X3)
| ~ element(X4,powerset(the_carrier(X3)))
| open_subset(subset_complement(the_carrier(X3),X4),X3) ),
inference(variable_rename,[status(thm)],[67]) ).
cnf(69,plain,
( open_subset(subset_complement(the_carrier(X1),X2),X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ closed_subset(X2,X1)
| ~ top_str(X1)
| ~ topological_space(X1) ),
inference(split_conjunct,[status(thm)],[68]) ).
fof(76,plain,
! [X1,X2] :
( ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| element(topstr_closure(X1,X2),powerset(the_carrier(X1))) ),
inference(fof_nnf,[status(thm)],[18]) ).
fof(77,plain,
! [X3,X4] :
( ~ top_str(X3)
| ~ element(X4,powerset(the_carrier(X3)))
| element(topstr_closure(X3,X4),powerset(the_carrier(X3))) ),
inference(variable_rename,[status(thm)],[76]) ).
cnf(78,plain,
( element(topstr_closure(X1,X2),powerset(the_carrier(X1)))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[77]) ).
fof(79,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)],[19]) ).
fof(80,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)],[79]) ).
fof(81,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)],[80]) ).
cnf(82,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)],[81]) ).
cnf(92,plain,
( open_subset(X2,X1)
| ~ closed_subset(subset_complement(the_carrier(X1),X2),X1)
| ~ element(subset_complement(the_carrier(X1),X2),powerset(the_carrier(X1)))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(spm,[status(thm)],[69,50,theory(equality)]) ).
cnf(95,plain,
( subset_complement(the_carrier(X1),interior(X1,X2)) = topstr_closure(X1,subset_complement(the_carrier(X1),X2))
| ~ element(topstr_closure(X1,subset_complement(the_carrier(X1),X2)),powerset(the_carrier(X1)))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1) ),
inference(spm,[status(thm)],[50,82,theory(equality)]) ).
cnf(102,plain,
( open_subset(X2,X1)
| ~ closed_subset(subset_complement(the_carrier(X1),X2),X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ topological_space(X1)
| ~ top_str(X1) ),
inference(csr,[status(thm)],[92,38]) ).
cnf(121,plain,
( topstr_closure(X1,subset_complement(the_carrier(X1),X2)) = subset_complement(the_carrier(X1),interior(X1,X2))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ element(subset_complement(the_carrier(X1),X2),powerset(the_carrier(X1))) ),
inference(spm,[status(thm)],[95,78,theory(equality)]) ).
cnf(123,plain,
( topstr_closure(X1,subset_complement(the_carrier(X1),X2)) = subset_complement(the_carrier(X1),interior(X1,X2))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1) ),
inference(csr,[status(thm)],[121,38]) ).
cnf(125,plain,
( closed_subset(subset_complement(the_carrier(X1),interior(X1,X2)),X1)
| ~ element(subset_complement(the_carrier(X1),X2),powerset(the_carrier(X1)))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(spm,[status(thm)],[60,123,theory(equality)]) ).
cnf(147,plain,
( closed_subset(subset_complement(the_carrier(X1),interior(X1,X2)),X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ topological_space(X1)
| ~ top_str(X1) ),
inference(csr,[status(thm)],[125,38]) ).
cnf(148,plain,
( open_subset(interior(X1,X2),X1)
| ~ element(interior(X1,X2),powerset(the_carrier(X1)))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(spm,[status(thm)],[102,147,theory(equality)]) ).
cnf(150,plain,
( open_subset(interior(X1,X2),X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ topological_space(X1)
| ~ top_str(X1) ),
inference(csr,[status(thm)],[148,65]) ).
cnf(151,negated_conjecture,
( ~ element(esk6_0,powerset(the_carrier(esk5_0)))
| ~ topological_space(esk5_0)
| ~ top_str(esk5_0) ),
inference(spm,[status(thm)],[54,150,theory(equality)]) ).
cnf(153,negated_conjecture,
( $false
| ~ topological_space(esk5_0)
| ~ top_str(esk5_0) ),
inference(rw,[status(thm)],[151,55,theory(equality)]) ).
cnf(154,negated_conjecture,
( $false
| $false
| ~ top_str(esk5_0) ),
inference(rw,[status(thm)],[153,57,theory(equality)]) ).
cnf(155,negated_conjecture,
( $false
| $false
| $false ),
inference(rw,[status(thm)],[154,56,theory(equality)]) ).
cnf(156,negated_conjecture,
$false,
inference(cn,[status(thm)],[155,theory(equality)]) ).
cnf(157,negated_conjecture,
$false,
156,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% /home/graph/tptp/Systems/SInE---0.4/Source/sine.py:10: DeprecationWarning: the sets module is deprecated
% from sets import Set
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU323+1.p
% --creating new selector for []
% -running prover on /tmp/tmptIb36W/sel_SEU323+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU323+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU323+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU323+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
%
%------------------------------------------------------------------------------