%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU323+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:41:40 AM UTC 2026
% Result : Theorem 13.60s 2.15s
% Output : CNFRefutation 13.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 8 unt; 0 def)
% Number of atoms : 82 ( 4 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 94 ( 43 ~; 33 |; 8 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 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 : 26 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fc3_tops_1,axiom,
! [X0,X1] :
( ( element(X1,powerset('the$ucarrier'(X0)))
& 'closed$usubset'(X1,X0)
& 'top$ustr'(X0)
& 'topological$uspace'(X0) )
=> 'open$usubset'('subset$ucomplement'('the$ucarrier'(X0),X1),X0) ) ).
fof(dt_k3_subset_1,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> element('subset$ucomplement'(X0,X1),powerset(X0)) ) ).
fof(dt_k6_pre_topc,axiom,
! [X0,X1] :
( ( element(X1,powerset('the$ucarrier'(X0)))
& 'top$ustr'(X0) )
=> element('topstr$uclosure'(X0,X1),powerset('the$ucarrier'(X0))) ) ).
fof(fc2_tops_1,axiom,
! [X0,X1] :
( ( element(X1,powerset('the$ucarrier'(X0)))
& 'top$ustr'(X0)
& 'topological$uspace'(X0) )
=> 'closed$usubset'('topstr$uclosure'(X0,X1),X0) ) ).
fof(d1_tops_1,axiom,
! [X0] :
( 'top$ustr'(X0)
=> ! [X1] :
( element(X1,powerset('the$ucarrier'(X0)))
=> interior(X0,X1) = 'subset$ucomplement'('the$ucarrier'(X0),'topstr$uclosure'(X0,'subset$ucomplement'('the$ucarrier'(X0),X1))) ) ) ).
fof(t51_tops_1,conjecture,
! [X0] :
( ( 'top$ustr'(X0)
& 'topological$uspace'(X0) )
=> ! [X1] :
( element(X1,powerset('the$ucarrier'(X0)))
=> 'open$usubset'(interior(X0,X1),X0) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ( 'top$ustr'(X0)
& 'topological$uspace'(X0) )
=> ! [X1] :
( element(X1,powerset('the$ucarrier'(X0)))
=> 'open$usubset'(interior(X0,X1),X0) ) ),
inference(negate_conjecture,[status(cth)],[t51_tops_1]) ).
cnf(c0,plain,
( ~ 'top$ustr'(X0)
| ~ 'topological$uspace'(X0)
| ~ element(X1,powerset('the$ucarrier'(X0)))
| ~ 'closed$usubset'(X1,X0)
| 'open$usubset'('subset$ucomplement'('the$ucarrier'(X0),X1),X0) ),
inference(clausification,[status(esa)],[fc3_tops_1]) ).
cnf(c6,plain,
( element('subset$ucomplement'(X1,X0),powerset(X1))
| ~ element(X0,powerset(X1)) ),
inference(clausification,[status(esa)],[dt_k3_subset_1]) ).
cnf(c7,plain,
( element('topstr$uclosure'(X0,X1),powerset('the$ucarrier'(X0)))
| ~ element(X1,powerset('the$ucarrier'(X0)))
| ~ 'top$ustr'(X0) ),
inference(clausification,[status(esa)],[dt_k6_pre_topc]) ).
cnf(c8,plain,
( 'closed$usubset'('topstr$uclosure'(X0,X1),X0)
| ~ element(X1,powerset('the$ucarrier'(X0)))
| ~ 'top$ustr'(X0)
| ~ 'topological$uspace'(X0) ),
inference(clausification,[status(esa)],[fc2_tops_1]) ).
cnf(c18,plain,
( interior(X0,X1) = 'subset$ucomplement'('the$ucarrier'(X0),'topstr$uclosure'(X0,'subset$ucomplement'('the$ucarrier'(X0),X1)))
| ~ element(X1,powerset('the$ucarrier'(X0)))
| ~ 'top$ustr'(X0) ),
inference(clausification,[status(esa)],[d1_tops_1]) ).
cnf(c19,plain,
'topological$uspace'(sK29),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c20,plain,
'top$ustr'(sK29),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c21,plain,
element(sK30,powerset('the$ucarrier'(sK29))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c22,plain,
~ 'open$usubset'(interior(sK29,sK30),sK29),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ element(X1,powerset('the$ucarrier'(X0)))
| ~ 'top$ustr'(X0)
| ~ 'topological$uspace'(X0)
| 'closed$usubset'('topstr$uclosure'(X0,'subset$ucomplement'('the$ucarrier'(X0),X1)),X0) ),
inference(resolution,[status(thm)],[c8,c6]) ).
cnf(d1,plain,
( ~ 'top$ustr'(sK29)
| interior(sK29,sK30) = 'subset$ucomplement'('the$ucarrier'(sK29),'topstr$uclosure'(sK29,'subset$ucomplement'('the$ucarrier'(sK29),sK30))) ),
inference(resolution,[status(thm)],[c18,c21]) ).
cnf(d2,plain,
interior(sK29,sK30) = 'subset$ucomplement'('the$ucarrier'(sK29),'topstr$uclosure'(sK29,'subset$ucomplement'('the$ucarrier'(sK29),sK30))),
inference(resolution,[status(thm)],[c20,d1]) ).
cnf(d3,plain,
( ~ 'top$ustr'(sK29)
| ~ element('topstr$uclosure'(sK29,'subset$ucomplement'('the$ucarrier'(sK29),sK30)),powerset('the$ucarrier'(sK29)))
| ~ 'topological$uspace'(sK29)
| ~ 'closed$usubset'('topstr$uclosure'(sK29,'subset$ucomplement'('the$ucarrier'(sK29),sK30)),sK29)
| 'open$usubset'(interior(sK29,sK30),sK29) ),
inference(superposition,[status(thm)],[d2,c0]) ).
cnf(d4,plain,
( 'open$usubset'(interior(sK29,sK30),sK29)
| ~ 'top$ustr'(sK29)
| ~ element('topstr$uclosure'(sK29,'subset$ucomplement'('the$ucarrier'(sK29),sK30)),powerset('the$ucarrier'(sK29)))
| ~ 'closed$usubset'('topstr$uclosure'(sK29,'subset$ucomplement'('the$ucarrier'(sK29),sK30)),sK29) ),
inference(resolution,[status(thm)],[c19,d3]) ).
cnf(d5,plain,
( 'open$usubset'(interior(sK29,sK30),sK29)
| ~ element('topstr$uclosure'(sK29,'subset$ucomplement'('the$ucarrier'(sK29),sK30)),powerset('the$ucarrier'(sK29)))
| ~ 'closed$usubset'('topstr$uclosure'(sK29,'subset$ucomplement'('the$ucarrier'(sK29),sK30)),sK29) ),
inference(resolution,[status(thm)],[c20,d4]) ).
cnf(d6,plain,
( ~ element('topstr$uclosure'(sK29,'subset$ucomplement'('the$ucarrier'(sK29),sK30)),powerset('the$ucarrier'(sK29)))
| ~ 'closed$usubset'('topstr$uclosure'(sK29,'subset$ucomplement'('the$ucarrier'(sK29),sK30)),sK29) ),
inference(resolution,[status(thm)],[c22,d5]) ).
cnf(d7,plain,
( ~ 'top$ustr'(sK29)
| ~ element('subset$ucomplement'('the$ucarrier'(sK29),sK30),powerset('the$ucarrier'(sK29)))
| ~ 'closed$usubset'('topstr$uclosure'(sK29,'subset$ucomplement'('the$ucarrier'(sK29),sK30)),sK29) ),
inference(resolution,[status(thm)],[d6,c7]) ).
cnf(d8,plain,
( ~ element('subset$ucomplement'('the$ucarrier'(sK29),sK30),powerset('the$ucarrier'(sK29)))
| ~ 'closed$usubset'('topstr$uclosure'(sK29,'subset$ucomplement'('the$ucarrier'(sK29),sK30)),sK29) ),
inference(resolution,[status(thm)],[c20,d7]) ).
cnf(d9,plain,
( ~ element(sK30,powerset('the$ucarrier'(sK29)))
| ~ 'closed$usubset'('topstr$uclosure'(sK29,'subset$ucomplement'('the$ucarrier'(sK29),sK30)),sK29) ),
inference(resolution,[status(thm)],[d8,c6]) ).
cnf(d10,plain,
~ 'closed$usubset'('topstr$uclosure'(sK29,'subset$ucomplement'('the$ucarrier'(sK29),sK30)),sK29),
inference(resolution,[status(thm)],[c21,d9]) ).
cnf(d11,plain,
( ~ 'top$ustr'(sK29)
| ~ element(sK30,powerset('the$ucarrier'(sK29)))
| ~ 'topological$uspace'(sK29) ),
inference(resolution,[status(thm)],[d10,d0]) ).
cnf(d12,plain,
( ~ 'top$ustr'(sK29)
| ~ element(sK30,powerset('the$ucarrier'(sK29))) ),
inference(resolution,[status(thm)],[c19,d11]) ).
cnf(d13,plain,
~ element(sK30,powerset('the$ucarrier'(sK29))),
inference(resolution,[status(thm)],[c20,d12]) ).
cnf(d14,plain,
$false,
inference(resolution,[status(thm)],[c21,d13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU323+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n010.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 09:12:45 UTC 2026
% 0.14/0.37 % CPUTime :
% 0.14/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.60/2.15 % SZS status Theorem for theBenchmark.p
% 13.60/2.15 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------