TSTP Solution File: SEU320+2 by SInE---0.4
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%------------------------------------------------------------------------------
% File : SInE---0.4
% Problem : SEU320+2 : 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 07:14:53 EST 2010
% Result : Theorem 19.77s
% Output : CNFRefutation 19.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 4
% Syntax : Number of formulae : 40 ( 6 unt; 0 def)
% Number of atoms : 131 ( 4 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 155 ( 64 ~; 67 |; 13 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 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(313,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/tmpwuw1qL/sel_SEU320+2.p_1',t29_tops_1) ).
fof(375,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> element(subset_complement(X1,X2),powerset(X1)) ),
file('/tmp/tmpwuw1qL/sel_SEU320+2.p_1',dt_k3_subset_1) ).
fof(433,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,subset_complement(X1,X2)) = X2 ),
file('/tmp/tmpwuw1qL/sel_SEU320+2.p_1',involutiveness_k3_subset_1) ).
fof(440,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/tmpwuw1qL/sel_SEU320+2.p_1',t30_tops_1) ).
fof(523,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)],[440]) ).
fof(2593,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)],[313]) ).
fof(2594,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)],[2593]) ).
fof(2595,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)],[2594]) ).
fof(2596,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)],[2595]) ).
cnf(2597,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)],[2596]) ).
cnf(2598,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)],[2596]) ).
fof(3006,plain,
! [X1,X2] :
( ~ element(X2,powerset(X1))
| element(subset_complement(X1,X2),powerset(X1)) ),
inference(fof_nnf,[status(thm)],[375]) ).
fof(3007,plain,
! [X3,X4] :
( ~ element(X4,powerset(X3))
| element(subset_complement(X3,X4),powerset(X3)) ),
inference(variable_rename,[status(thm)],[3006]) ).
cnf(3008,plain,
( element(subset_complement(X1,X2),powerset(X1))
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[3007]) ).
fof(3409,plain,
! [X1,X2] :
( ~ element(X2,powerset(X1))
| subset_complement(X1,subset_complement(X1,X2)) = X2 ),
inference(fof_nnf,[status(thm)],[433]) ).
fof(3410,plain,
! [X3,X4] :
( ~ element(X4,powerset(X3))
| subset_complement(X3,subset_complement(X3,X4)) = X4 ),
inference(variable_rename,[status(thm)],[3409]) ).
cnf(3411,plain,
( subset_complement(X1,subset_complement(X1,X2)) = X2
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[3410]) ).
fof(3448,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)],[523]) ).
fof(3449,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)],[3448]) ).
fof(3450,negated_conjecture,
( top_str(esk305_0)
& element(esk306_0,powerset(the_carrier(esk305_0)))
& ( ~ open_subset(esk306_0,esk305_0)
| ~ closed_subset(subset_complement(the_carrier(esk305_0),esk306_0),esk305_0) )
& ( open_subset(esk306_0,esk305_0)
| closed_subset(subset_complement(the_carrier(esk305_0),esk306_0),esk305_0) ) ),
inference(skolemize,[status(esa)],[3449]) ).
cnf(3451,negated_conjecture,
( closed_subset(subset_complement(the_carrier(esk305_0),esk306_0),esk305_0)
| open_subset(esk306_0,esk305_0) ),
inference(split_conjunct,[status(thm)],[3450]) ).
cnf(3452,negated_conjecture,
( ~ closed_subset(subset_complement(the_carrier(esk305_0),esk306_0),esk305_0)
| ~ open_subset(esk306_0,esk305_0) ),
inference(split_conjunct,[status(thm)],[3450]) ).
cnf(3453,negated_conjecture,
element(esk306_0,powerset(the_carrier(esk305_0))),
inference(split_conjunct,[status(thm)],[3450]) ).
cnf(3454,negated_conjecture,
top_str(esk305_0),
inference(split_conjunct,[status(thm)],[3450]) ).
cnf(6297,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)],[2598,3411,theory(equality)]) ).
cnf(6299,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)],[2597,3411,theory(equality)]) ).
cnf(168781,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)],[6297,3008]) ).
cnf(168784,negated_conjecture,
( open_subset(esk306_0,esk305_0)
| ~ top_str(esk305_0)
| ~ element(esk306_0,powerset(the_carrier(esk305_0))) ),
inference(spm,[status(thm)],[168781,3451,theory(equality)]) ).
cnf(168801,negated_conjecture,
( open_subset(esk306_0,esk305_0)
| $false
| ~ element(esk306_0,powerset(the_carrier(esk305_0))) ),
inference(rw,[status(thm)],[168784,3454,theory(equality)]) ).
cnf(168802,negated_conjecture,
( open_subset(esk306_0,esk305_0)
| $false
| $false ),
inference(rw,[status(thm)],[168801,3453,theory(equality)]) ).
cnf(168803,negated_conjecture,
open_subset(esk306_0,esk305_0),
inference(cn,[status(thm)],[168802,theory(equality)]) ).
cnf(169368,negated_conjecture,
( $false
| ~ closed_subset(subset_complement(the_carrier(esk305_0),esk306_0),esk305_0) ),
inference(rw,[status(thm)],[3452,168803,theory(equality)]) ).
cnf(169369,negated_conjecture,
~ closed_subset(subset_complement(the_carrier(esk305_0),esk306_0),esk305_0),
inference(cn,[status(thm)],[169368,theory(equality)]) ).
cnf(169718,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)],[6299,3008]) ).
cnf(169721,plain,
( ~ open_subset(esk306_0,esk305_0)
| ~ top_str(esk305_0)
| ~ element(esk306_0,powerset(the_carrier(esk305_0))) ),
inference(spm,[status(thm)],[169369,169718,theory(equality)]) ).
cnf(169739,plain,
( $false
| ~ top_str(esk305_0)
| ~ element(esk306_0,powerset(the_carrier(esk305_0))) ),
inference(rw,[status(thm)],[169721,168803,theory(equality)]) ).
cnf(169740,plain,
( $false
| $false
| ~ element(esk306_0,powerset(the_carrier(esk305_0))) ),
inference(rw,[status(thm)],[169739,3454,theory(equality)]) ).
cnf(169741,plain,
( $false
| $false
| $false ),
inference(rw,[status(thm)],[169740,3453,theory(equality)]) ).
cnf(169742,plain,
$false,
inference(cn,[status(thm)],[169741,theory(equality)]) ).
cnf(169743,plain,
$false,
169742,
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU320+2.p
% --creating new selector for []
% -running prover on /tmp/tmpwuw1qL/sel_SEU320+2.p_1 with time limit 29
% -prover status Theorem
% Problem SEU320+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU320+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU320+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
%
%------------------------------------------------------------------------------