TSTP Solution File: SEU320+1 by SInE---0.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU320+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : Source/sine.py -e eprover -t %d %s
% Computer : art04.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 07:14:49 EST 2010
% Result : Theorem 0.16s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 4
% Syntax : Number of formulae : 39 ( 7 unt; 0 def)
% Number of atoms : 127 ( 4 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 151 ( 63 ~; 64 |; 13 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 26 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(3,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> element(subset_complement(X1,X2),powerset(X1)) ),
file('/tmp/tmpWh3dSb/sel_SEU320+1.p_1',dt_k3_subset_1) ).
fof(4,conjecture,
! [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/tmpWh3dSb/sel_SEU320+1.p_1',t30_tops_1) ).
fof(6,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,subset_complement(X1,X2)) = X2 ),
file('/tmp/tmpWh3dSb/sel_SEU320+1.p_1',involutiveness_k3_subset_1) ).
fof(12,axiom,
! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ( closed_subset(X2,X1)
<=> open_subset(subset_complement(the_carrier(X1),X2),X1) ) ) ),
file('/tmp/tmpWh3dSb/sel_SEU320+1.p_1',t29_tops_1) ).
fof(15,negated_conjecture,
~ ! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ( open_subset(X2,X1)
<=> closed_subset(subset_complement(the_carrier(X1),X2),X1) ) ) ),
inference(assume_negation,[status(cth)],[4]) ).
fof(20,plain,
! [X1,X2] :
( ~ element(X2,powerset(X1))
| element(subset_complement(X1,X2),powerset(X1)) ),
inference(fof_nnf,[status(thm)],[3]) ).
fof(21,plain,
! [X3,X4] :
( ~ element(X4,powerset(X3))
| element(subset_complement(X3,X4),powerset(X3)) ),
inference(variable_rename,[status(thm)],[20]) ).
cnf(22,plain,
( element(subset_complement(X1,X2),powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[21]) ).
fof(23,negated_conjecture,
? [X1] :
( top_str(X1)
& ? [X2] :
( element(X2,powerset(the_carrier(X1)))
& ( ~ open_subset(X2,X1)
| ~ closed_subset(subset_complement(the_carrier(X1),X2),X1) )
& ( open_subset(X2,X1)
| closed_subset(subset_complement(the_carrier(X1),X2),X1) ) ) ),
inference(fof_nnf,[status(thm)],[15]) ).
fof(24,negated_conjecture,
? [X3] :
( top_str(X3)
& ? [X4] :
( element(X4,powerset(the_carrier(X3)))
& ( ~ open_subset(X4,X3)
| ~ closed_subset(subset_complement(the_carrier(X3),X4),X3) )
& ( open_subset(X4,X3)
| closed_subset(subset_complement(the_carrier(X3),X4),X3) ) ) ),
inference(variable_rename,[status(thm)],[23]) ).
fof(25,negated_conjecture,
( top_str(esk2_0)
& element(esk3_0,powerset(the_carrier(esk2_0)))
& ( ~ open_subset(esk3_0,esk2_0)
| ~ closed_subset(subset_complement(the_carrier(esk2_0),esk3_0),esk2_0) )
& ( open_subset(esk3_0,esk2_0)
| closed_subset(subset_complement(the_carrier(esk2_0),esk3_0),esk2_0) ) ),
inference(skolemize,[status(esa)],[24]) ).
cnf(26,negated_conjecture,
( closed_subset(subset_complement(the_carrier(esk2_0),esk3_0),esk2_0)
| open_subset(esk3_0,esk2_0) ),
inference(split_conjunct,[status(thm)],[25]) ).
cnf(27,negated_conjecture,
( ~ closed_subset(subset_complement(the_carrier(esk2_0),esk3_0),esk2_0)
| ~ open_subset(esk3_0,esk2_0) ),
inference(split_conjunct,[status(thm)],[25]) ).
cnf(28,negated_conjecture,
element(esk3_0,powerset(the_carrier(esk2_0))),
inference(split_conjunct,[status(thm)],[25]) ).
cnf(29,negated_conjecture,
top_str(esk2_0),
inference(split_conjunct,[status(thm)],[25]) ).
fof(33,plain,
! [X1,X2] :
( ~ element(X2,powerset(X1))
| subset_complement(X1,subset_complement(X1,X2)) = X2 ),
inference(fof_nnf,[status(thm)],[6]) ).
fof(34,plain,
! [X3,X4] :
( ~ element(X4,powerset(X3))
| subset_complement(X3,subset_complement(X3,X4)) = X4 ),
inference(variable_rename,[status(thm)],[33]) ).
cnf(35,plain,
( subset_complement(X1,subset_complement(X1,X2)) = X2
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[34]) ).
fof(45,plain,
! [X1] :
( ~ top_str(X1)
| ! [X2] :
( ~ element(X2,powerset(the_carrier(X1)))
| ( ( ~ closed_subset(X2,X1)
| open_subset(subset_complement(the_carrier(X1),X2),X1) )
& ( ~ open_subset(subset_complement(the_carrier(X1),X2),X1)
| closed_subset(X2,X1) ) ) ) ),
inference(fof_nnf,[status(thm)],[12]) ).
fof(46,plain,
! [X3] :
( ~ top_str(X3)
| ! [X4] :
( ~ element(X4,powerset(the_carrier(X3)))
| ( ( ~ closed_subset(X4,X3)
| open_subset(subset_complement(the_carrier(X3),X4),X3) )
& ( ~ open_subset(subset_complement(the_carrier(X3),X4),X3)
| 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)
| open_subset(subset_complement(the_carrier(X3),X4),X3) )
& ( ~ open_subset(subset_complement(the_carrier(X3),X4),X3)
| closed_subset(X4,X3) ) )
| ~ top_str(X3) ),
inference(shift_quantors,[status(thm)],[46]) ).
fof(48,plain,
! [X3,X4] :
( ( ~ closed_subset(X4,X3)
| open_subset(subset_complement(the_carrier(X3),X4),X3)
| ~ element(X4,powerset(the_carrier(X3)))
| ~ top_str(X3) )
& ( ~ open_subset(subset_complement(the_carrier(X3),X4),X3)
| closed_subset(X4,X3)
| ~ element(X4,powerset(the_carrier(X3)))
| ~ top_str(X3) ) ),
inference(distribute,[status(thm)],[47]) ).
cnf(49,plain,
( closed_subset(X2,X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ open_subset(subset_complement(the_carrier(X1),X2),X1) ),
inference(split_conjunct,[status(thm)],[48]) ).
cnf(50,plain,
( open_subset(subset_complement(the_carrier(X1),X2),X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ closed_subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[48]) ).
cnf(61,plain,
( open_subset(X2,X1)
| ~ closed_subset(subset_complement(the_carrier(X1),X2),X1)
| ~ top_str(X1)
| ~ element(subset_complement(the_carrier(X1),X2),powerset(the_carrier(X1)))
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(spm,[status(thm)],[50,35,theory(equality)]) ).
cnf(62,plain,
( closed_subset(subset_complement(the_carrier(X1),X2),X1)
| ~ open_subset(X2,X1)
| ~ top_str(X1)
| ~ element(subset_complement(the_carrier(X1),X2),powerset(the_carrier(X1)))
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(spm,[status(thm)],[49,35,theory(equality)]) ).
cnf(64,plain,
( open_subset(X2,X1)
| ~ closed_subset(subset_complement(the_carrier(X1),X2),X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(csr,[status(thm)],[61,22]) ).
cnf(70,plain,
( closed_subset(subset_complement(the_carrier(X1),X2),X1)
| ~ open_subset(X2,X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(csr,[status(thm)],[62,22]) ).
cnf(71,negated_conjecture,
( ~ open_subset(esk3_0,esk2_0)
| ~ top_str(esk2_0)
| ~ element(esk3_0,powerset(the_carrier(esk2_0))) ),
inference(spm,[status(thm)],[27,70,theory(equality)]) ).
cnf(74,negated_conjecture,
( ~ open_subset(esk3_0,esk2_0)
| $false
| ~ element(esk3_0,powerset(the_carrier(esk2_0))) ),
inference(rw,[status(thm)],[71,29,theory(equality)]) ).
cnf(75,negated_conjecture,
( ~ open_subset(esk3_0,esk2_0)
| $false
| $false ),
inference(rw,[status(thm)],[74,28,theory(equality)]) ).
cnf(76,negated_conjecture,
~ open_subset(esk3_0,esk2_0),
inference(cn,[status(thm)],[75,theory(equality)]) ).
cnf(77,negated_conjecture,
closed_subset(subset_complement(the_carrier(esk2_0),esk3_0),esk2_0),
inference(sr,[status(thm)],[26,76,theory(equality)]) ).
cnf(78,negated_conjecture,
( open_subset(esk3_0,esk2_0)
| ~ top_str(esk2_0)
| ~ element(esk3_0,powerset(the_carrier(esk2_0))) ),
inference(spm,[status(thm)],[64,77,theory(equality)]) ).
cnf(81,negated_conjecture,
( open_subset(esk3_0,esk2_0)
| $false
| ~ element(esk3_0,powerset(the_carrier(esk2_0))) ),
inference(rw,[status(thm)],[78,29,theory(equality)]) ).
cnf(82,negated_conjecture,
( open_subset(esk3_0,esk2_0)
| $false
| $false ),
inference(rw,[status(thm)],[81,28,theory(equality)]) ).
cnf(83,negated_conjecture,
open_subset(esk3_0,esk2_0),
inference(cn,[status(thm)],[82,theory(equality)]) ).
cnf(84,negated_conjecture,
$false,
inference(sr,[status(thm)],[83,76,theory(equality)]) ).
cnf(85,negated_conjecture,
$false,
84,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU320+1.p
% --creating new selector for []
% -running prover on /tmp/tmpWh3dSb/sel_SEU320+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU320+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU320+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU320+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
%
%------------------------------------------------------------------------------