TSTP Solution File: SEU320+1 by Faust---1.0
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%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SEU320+1 : TPTP v3.4.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art05.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1003MB
% OS : Linux 2.6.17-1.2142_FC4
% CPULimit : 600s
% DateTime : Wed May 6 15:56:04 EDT 2009
% Result : Theorem 0.2s
% Output : Refutation 0.2s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 8 unt; 0 def)
% Number of atoms : 72 ( 0 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 80 ( 28 ~; 36 |; 16 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 4 ( 2 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 : 14 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(involutiveness_k3_subset_1,plain,
! [B,A] :
( ~ element(B,powerset(A))
| $equal(subset_complement(A,subset_complement(A,B)),B) ),
file('/tmp/SystemOnTPTP13752/SEU320+1.p',unknown),
[] ).
cnf(149633544,plain,
( ~ element(B,powerset(A))
| $equal(subset_complement(A,subset_complement(A,B)),B) ),
inference(rewrite,[status(thm)],[involutiveness_k3_subset_1]),
[] ).
fof(t30_tops_1,plain,
( ( top_str(a)
| open_subset(b,a) )
& ( ~ open_subset(b,a)
| open_subset(b,a) )
& ( closed_subset(subset_complement(the_carrier(a),b),a)
| open_subset(b,a) )
& ( element(b,powerset(the_carrier(a)))
| open_subset(b,a) )
& ( top_str(a)
| ~ closed_subset(subset_complement(the_carrier(a),b),a) )
& ( ~ open_subset(b,a)
| ~ closed_subset(subset_complement(the_carrier(a),b),a) )
& ( closed_subset(subset_complement(the_carrier(a),b),a)
| ~ closed_subset(subset_complement(the_carrier(a),b),a) )
& ( element(b,powerset(the_carrier(a)))
| ~ closed_subset(subset_complement(the_carrier(a),b),a) )
& ( top_str(a)
| element(b,powerset(the_carrier(a))) )
& ( ~ open_subset(b,a)
| element(b,powerset(the_carrier(a))) )
& ( closed_subset(subset_complement(the_carrier(a),b),a)
| element(b,powerset(the_carrier(a))) )
& ( element(b,powerset(the_carrier(a)))
| element(b,powerset(the_carrier(a))) )
& ( top_str(a)
| top_str(a) )
& ( ~ open_subset(b,a)
| top_str(a) )
& ( closed_subset(subset_complement(the_carrier(a),b),a)
| top_str(a) )
& ( element(b,powerset(the_carrier(a)))
| top_str(a) ) ),
file('/tmp/SystemOnTPTP13752/SEU320+1.p',unknown),
[] ).
cnf(149877152,plain,
element(b,powerset(the_carrier(a))),
inference(rewrite,[status(thm)],[t30_tops_1]),
[] ).
cnf(174163128,plain,
$equal(subset_complement(the_carrier(a),subset_complement(the_carrier(a),b)),b),
inference(resolution,[status(thm)],[149633544,149877152]),
[] ).
cnf(149887368,plain,
( closed_subset(subset_complement(the_carrier(a),b),a)
| open_subset(b,a) ),
inference(rewrite,[status(thm)],[t30_tops_1]),
[] ).
cnf(174333560,plain,
( closed_subset(subset_complement(the_carrier(a),b),a)
| open_subset(subset_complement(the_carrier(a),subset_complement(the_carrier(a),b)),a) ),
inference(paramodulation,[status(thm)],[174163128,149887368,theory(equality)]),
[] ).
cnf(149858360,plain,
( closed_subset(subset_complement(the_carrier(a),b),a)
| top_str(a) ),
inference(rewrite,[status(thm)],[t30_tops_1]),
[] ).
fof(t29_tops_1,plain,
! [B,A] :
( ( ~ closed_subset(B,A)
| open_subset(subset_complement(the_carrier(A),B),A)
| ~ element(B,powerset(the_carrier(A)))
| ~ top_str(A) )
& ( closed_subset(B,A)
| ~ open_subset(subset_complement(the_carrier(A),B),A)
| ~ element(B,powerset(the_carrier(A)))
| ~ top_str(A) ) ),
file('/tmp/SystemOnTPTP13752/SEU320+1.p',unknown),
[] ).
cnf(149671736,plain,
( closed_subset(B,A)
| ~ open_subset(subset_complement(the_carrier(A),B),A)
| ~ element(B,powerset(the_carrier(A)))
| ~ top_str(A) ),
inference(rewrite,[status(thm)],[t29_tops_1]),
[] ).
fof(dt_k3_subset_1,plain,
! [B,A] :
( ~ element(B,powerset(A))
| element(subset_complement(A,B),powerset(A)) ),
file('/tmp/SystemOnTPTP13752/SEU320+1.p',unknown),
[] ).
cnf(149598040,plain,
( ~ element(B,powerset(A))
| element(subset_complement(A,B),powerset(A)) ),
inference(rewrite,[status(thm)],[dt_k3_subset_1]),
[] ).
cnf(174022616,plain,
element(subset_complement(the_carrier(a),b),powerset(the_carrier(a))),
inference(resolution,[status(thm)],[149598040,149877152]),
[] ).
cnf(175573768,plain,
closed_subset(subset_complement(the_carrier(a),b),a),
inference(forward_subsumption_resolution__resolution,[status(thm)],[174333560,149858360,149671736,174022616]),
[] ).
cnf(149873416,plain,
top_str(a),
inference(rewrite,[status(thm)],[t30_tops_1]),
[] ).
cnf(149690376,plain,
( ~ closed_subset(B,A)
| open_subset(subset_complement(the_carrier(A),B),A)
| ~ element(B,powerset(the_carrier(A)))
| ~ top_str(A) ),
inference(rewrite,[status(thm)],[t29_tops_1]),
[] ).
cnf(149882056,plain,
( ~ open_subset(b,a)
| ~ closed_subset(subset_complement(the_carrier(a),b),a) ),
inference(rewrite,[status(thm)],[t30_tops_1]),
[] ).
cnf(175974184,plain,
~ open_subset(b,a),
inference(resolution,[status(thm)],[175573768,149882056]),
[] ).
cnf(175990080,plain,
~ open_subset(subset_complement(the_carrier(a),subset_complement(the_carrier(a),b)),a),
inference(paramodulation,[status(thm)],[175974184,174163128,theory(equality)]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[175573768,174022616,149873416,149690376,175990080]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(involutiveness_k3_subset_1,plain,(~element(B,powerset(A))|$equal(subset_complement(A,subset_complement(A,B)),B)),file('/tmp/SystemOnTPTP13752/SEU320+1.p',unknown),[]).
%
% cnf(149633544,plain,(~element(B,powerset(A))|$equal(subset_complement(A,subset_complement(A,B)),B)),inference(rewrite,[status(thm)],[involutiveness_k3_subset_1]),[]).
%
% fof(t30_tops_1,plain,(((top_str(a)|open_subset(b,a))&(~open_subset(b,a)|open_subset(b,a))&(closed_subset(subset_complement(the_carrier(a),b),a)|open_subset(b,a))&(element(b,powerset(the_carrier(a)))|open_subset(b,a))&(top_str(a)|~closed_subset(subset_complement(the_carrier(a),b),a))&(~open_subset(b,a)|~closed_subset(subset_complement(the_carrier(a),b),a))&(closed_subset(subset_complement(the_carrier(a),b),a)|~closed_subset(subset_complement(the_carrier(a),b),a))&(element(b,powerset(the_carrier(a)))|~closed_subset(subset_complement(the_carrier(a),b),a))&(top_str(a)|element(b,powerset(the_carrier(a))))&(~open_subset(b,a)|element(b,powerset(the_carrier(a))))&(closed_subset(subset_complement(the_carrier(a),b),a)|element(b,powerset(the_carrier(a))))&(element(b,powerset(the_carrier(a)))|element(b,powerset(the_carrier(a))))&(top_str(a)|top_str(a))&(~open_subset(b,a)|top_str(a))&(closed_subset(subset_complement(the_carrier(a),b),a)|top_str(a))&(element(b,powerset(the_carrier(a)))|top_str(a)))),file('/tmp/SystemOnTPTP13752/SEU320+1.p',unknown),[]).
%
% cnf(149877152,plain,(element(b,powerset(the_carrier(a)))),inference(rewrite,[status(thm)],[t30_tops_1]),[]).
%
% cnf(174163128,plain,($equal(subset_complement(the_carrier(a),subset_complement(the_carrier(a),b)),b)),inference(resolution,[status(thm)],[149633544,149877152]),[]).
%
% cnf(149887368,plain,(closed_subset(subset_complement(the_carrier(a),b),a)|open_subset(b,a)),inference(rewrite,[status(thm)],[t30_tops_1]),[]).
%
% cnf(174333560,plain,(closed_subset(subset_complement(the_carrier(a),b),a)|open_subset(subset_complement(the_carrier(a),subset_complement(the_carrier(a),b)),a)),inference(paramodulation,[status(thm)],[174163128,149887368,theory(equality)]),[]).
%
% cnf(149858360,plain,(closed_subset(subset_complement(the_carrier(a),b),a)|top_str(a)),inference(rewrite,[status(thm)],[t30_tops_1]),[]).
%
% fof(t29_tops_1,plain,(((~closed_subset(B,A)|open_subset(subset_complement(the_carrier(A),B),A)|~element(B,powerset(the_carrier(A)))|~top_str(A))&(closed_subset(B,A)|~open_subset(subset_complement(the_carrier(A),B),A)|~element(B,powerset(the_carrier(A)))|~top_str(A)))),file('/tmp/SystemOnTPTP13752/SEU320+1.p',unknown),[]).
%
% cnf(149671736,plain,(closed_subset(B,A)|~open_subset(subset_complement(the_carrier(A),B),A)|~element(B,powerset(the_carrier(A)))|~top_str(A)),inference(rewrite,[status(thm)],[t29_tops_1]),[]).
%
% fof(dt_k3_subset_1,plain,(~element(B,powerset(A))|element(subset_complement(A,B),powerset(A))),file('/tmp/SystemOnTPTP13752/SEU320+1.p',unknown),[]).
%
% cnf(149598040,plain,(~element(B,powerset(A))|element(subset_complement(A,B),powerset(A))),inference(rewrite,[status(thm)],[dt_k3_subset_1]),[]).
%
% cnf(174022616,plain,(element(subset_complement(the_carrier(a),b),powerset(the_carrier(a)))),inference(resolution,[status(thm)],[149598040,149877152]),[]).
%
% cnf(175573768,plain,(closed_subset(subset_complement(the_carrier(a),b),a)),inference(forward_subsumption_resolution__resolution,[status(thm)],[174333560,149858360,149671736,174022616]),[]).
%
% cnf(149873416,plain,(top_str(a)),inference(rewrite,[status(thm)],[t30_tops_1]),[]).
%
% cnf(149690376,plain,(~closed_subset(B,A)|open_subset(subset_complement(the_carrier(A),B),A)|~element(B,powerset(the_carrier(A)))|~top_str(A)),inference(rewrite,[status(thm)],[t29_tops_1]),[]).
%
% cnf(149882056,plain,(~open_subset(b,a)|~closed_subset(subset_complement(the_carrier(a),b),a)),inference(rewrite,[status(thm)],[t30_tops_1]),[]).
%
% cnf(175974184,plain,(~open_subset(b,a)),inference(resolution,[status(thm)],[175573768,149882056]),[]).
%
% cnf(175990080,plain,(~open_subset(subset_complement(the_carrier(a),subset_complement(the_carrier(a),b)),a)),inference(paramodulation,[status(thm)],[175974184,174163128,theory(equality)]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[175573768,174022616,149873416,149690376,175990080]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------