%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU324+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 : n008.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 15.24s 2.33s
% Output : CNFRefutation 15.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 45 ( 16 unt; 0 def)
% Number of atoms : 114 ( 36 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 104 ( 35 ~; 37 |; 8 &)
% ( 1 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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$ucarrier'(X0),X1))) ) ) ).
fof(dt_k3_subset_1,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> element('subset$ucomplement'(X0,X1),powerset(X0)) ) ).
fof(fc6_tops_1,axiom,
! [X0,X1] :
( ( element(X1,powerset('the$ucarrier'(X0)))
& 'top$ustr'(X0)
& 'topological$uspace'(X0) )
=> 'open$usubset'(interior(X0,X1),X0) ) ).
fof(involutiveness_k3_subset_1,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> 'subset$ucomplement'(X0,'subset$ucomplement'(X0,X1)) = X1 ) ).
fof(t30_tops_1,axiom,
! [X0] :
( 'top$ustr'(X0)
=> ! [X1] :
( element(X1,powerset('the$ucarrier'(X0)))
=> ( 'open$usubset'(X1,X0)
<=> 'closed$usubset'('subset$ucomplement'('the$ucarrier'(X0),X1),X0) ) ) ) ).
fof(t52_pre_topc,axiom,
! [X0] :
( 'top$ustr'(X0)
=> ! [X1] :
( element(X1,powerset('the$ucarrier'(X0)))
=> ( ( ( 'topstr$uclosure'(X0,X1) = X1
& 'topological$uspace'(X0) )
=> 'closed$usubset'(X1,X0) )
& ( 'closed$usubset'(X1,X0)
=> 'topstr$uclosure'(X0,X1) = X1 ) ) ) ) ).
fof(t55_tops_1,conjecture,
! [X0] :
( ( 'top$ustr'(X0)
& 'topological$uspace'(X0) )
=> ! [X1] :
( 'top$ustr'(X1)
=> ! [X2] :
( element(X2,powerset('the$ucarrier'(X0)))
=> ! [X3] :
( element(X3,powerset('the$ucarrier'(X1)))
=> ( ( interior(X0,X2) = X2
=> 'open$usubset'(X2,X0) )
& ( 'open$usubset'(X3,X1)
=> interior(X1,X3) = X3 ) ) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ( 'top$ustr'(X0)
& 'topological$uspace'(X0) )
=> ! [X1] :
( 'top$ustr'(X1)
=> ! [X2] :
( element(X2,powerset('the$ucarrier'(X0)))
=> ! [X3] :
( element(X3,powerset('the$ucarrier'(X1)))
=> ( ( interior(X0,X2) = X2
=> 'open$usubset'(X2,X0) )
& ( 'open$usubset'(X3,X1)
=> interior(X1,X3) = X3 ) ) ) ) ) ),
inference(negate_conjecture,[status(cth)],[t55_tops_1]) ).
cnf(c0,plain,
( interior(X0,X1) = 'subset$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(c2,plain,
( element('subset$ucomplement'(X1,X0),powerset(X1))
| ~ element(X0,powerset(X1)) ),
inference(clausification,[status(esa)],[dt_k3_subset_1]) ).
cnf(c11,plain,
( 'open$usubset'(interior(X0,X1),X0)
| ~ element(X1,powerset('the$ucarrier'(X0)))
| ~ 'top$ustr'(X0)
| ~ 'topological$uspace'(X0) ),
inference(clausification,[status(esa)],[fc6_tops_1]) ).
cnf(c12,plain,
( 'subset$ucomplement'(X1,'subset$ucomplement'(X1,X0)) = X0
| ~ element(X0,powerset(X1)) ),
inference(clausification,[status(esa)],[involutiveness_k3_subset_1]) ).
cnf(c21,plain,
( 'closed$usubset'('subset$ucomplement'('the$ucarrier'(X0),X1),X0)
| ~ 'open$usubset'(X1,X0)
| ~ element(X1,powerset('the$ucarrier'(X0)))
| ~ 'top$ustr'(X0) ),
inference(clausification,[status(esa)],[t30_tops_1]) ).
cnf(c25,plain,
( 'topstr$uclosure'(X0,X1) = X1
| ~ 'closed$usubset'(X1,X0)
| ~ element(X1,powerset('the$ucarrier'(X0)))
| ~ 'top$ustr'(X0) ),
inference(clausification,[status(esa)],[t52_pre_topc]) ).
cnf(c27,plain,
'topological$uspace'(sK37),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c28,plain,
'top$ustr'(sK37),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c29,plain,
'top$ustr'(sK38),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c30,plain,
element(sK39,powerset('the$ucarrier'(sK37))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c31,plain,
element(sK40,powerset('the$ucarrier'(sK38))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c32,plain,
( interior(sK37,sK39) = sK39
| 'open$usubset'(sK40,sK38) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c33,plain,
( ~ 'open$usubset'(sK39,sK37)
| 'open$usubset'(sK40,sK38) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c34,plain,
( interior(sK37,sK39) = sK39
| interior(sK38,sK40) != sK40 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c35,plain,
( ~ 'open$usubset'(sK39,sK37)
| interior(sK38,sK40) != sK40 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
'subset$ucomplement'('the$ucarrier'(sK38),'subset$ucomplement'('the$ucarrier'(sK38),sK40)) = sK40,
inference(resolution,[status(thm)],[c12,c31]) ).
cnf(d1,plain,
( ~ element(X1,powerset('the$ucarrier'(X0)))
| ~ 'closed$usubset'('subset$ucomplement'('the$ucarrier'(X0),X1),X0)
| ~ 'top$ustr'(X0)
| 'topstr$uclosure'(X0,'subset$ucomplement'('the$ucarrier'(X0),X1)) = 'subset$ucomplement'('the$ucarrier'(X0),X1) ),
inference(resolution,[status(thm)],[c25,c2]) ).
cnf(d2,plain,
( ~ 'open$usubset'(X1,X0)
| ~ 'top$ustr'(X0)
| ~ element(X1,powerset('the$ucarrier'(X0)))
| ~ 'top$ustr'(X0)
| ~ element(X1,powerset('the$ucarrier'(X0)))
| 'topstr$uclosure'(X0,'subset$ucomplement'('the$ucarrier'(X0),X1)) = 'subset$ucomplement'('the$ucarrier'(X0),X1) ),
inference(resolution,[status(thm)],[d1,c21]) ).
cnf(d3,plain,
( ~ 'open$usubset'(sK40,sK38)
| ~ 'top$ustr'(sK38)
| 'topstr$uclosure'(sK38,'subset$ucomplement'('the$ucarrier'(sK38),sK40)) = 'subset$ucomplement'('the$ucarrier'(sK38),sK40) ),
inference(resolution,[status(thm)],[d2,c31]) ).
cnf(d4,plain,
( ~ 'open$usubset'(sK40,sK38)
| 'topstr$uclosure'(sK38,'subset$ucomplement'('the$ucarrier'(sK38),sK40)) = 'subset$ucomplement'('the$ucarrier'(sK38),sK40) ),
inference(resolution,[status(thm)],[c29,d3]) ).
cnf(d5,plain,
( ~ 'top$ustr'(sK38)
| interior(sK38,sK40) = 'subset$ucomplement'('the$ucarrier'(sK38),'topstr$uclosure'(sK38,'subset$ucomplement'('the$ucarrier'(sK38),sK40))) ),
inference(resolution,[status(thm)],[c31,c0]) ).
cnf(d6,plain,
interior(sK38,sK40) = 'subset$ucomplement'('the$ucarrier'(sK38),'topstr$uclosure'(sK38,'subset$ucomplement'('the$ucarrier'(sK38),sK40))),
inference(resolution,[status(thm)],[c29,d5]) ).
cnf(d7,plain,
( interior(sK37,sK39) = sK39
| 'topstr$uclosure'(sK38,'subset$ucomplement'('the$ucarrier'(sK38),sK40)) = 'subset$ucomplement'('the$ucarrier'(sK38),sK40) ),
inference(resolution,[status(thm)],[d4,c32]) ).
cnf(d8,plain,
( interior(sK37,sK39) = sK39
| interior(sK38,sK40) = 'subset$ucomplement'('the$ucarrier'(sK38),'subset$ucomplement'('the$ucarrier'(sK38),sK40)) ),
inference(superposition,[status(thm)],[d7,d6]) ).
cnf(d9,plain,
( interior(sK38,sK40) = sK40
| interior(sK37,sK39) = sK39 ),
inference(demodulation,[status(thm)],[d8,d0]) ).
cnf(d10,plain,
( interior(sK37,sK39) = sK39
| interior(sK37,sK39) = sK39
| sK40 != sK40 ),
inference(superposition,[status(thm)],[d9,c34]) ).
cnf(d11,plain,
interior(sK37,sK39) = sK39,
inference(equality_resolution,[status(thm)],[d10]) ).
cnf(d12,plain,
( 'open$usubset'(interior(sK37,sK39),sK37)
| ~ 'topological$uspace'(sK37)
| ~ 'top$ustr'(sK37) ),
inference(resolution,[status(thm)],[c11,c30]) ).
cnf(d13,plain,
( 'open$usubset'(interior(sK37,sK39),sK37)
| ~ 'top$ustr'(sK37) ),
inference(resolution,[status(thm)],[c27,d12]) ).
cnf(d14,plain,
'open$usubset'(interior(sK37,sK39),sK37),
inference(resolution,[status(thm)],[c28,d13]) ).
cnf(d15,plain,
'open$usubset'(sK39,sK37),
inference(demodulation,[status(thm)],[d14,d11]) ).
cnf(d16,plain,
'open$usubset'(sK40,sK38),
inference(resolution,[status(thm)],[d15,c33]) ).
cnf(d17,plain,
'topstr$uclosure'(sK38,'subset$ucomplement'('the$ucarrier'(sK38),sK40)) = 'subset$ucomplement'('the$ucarrier'(sK38),sK40),
inference(resolution,[status(thm)],[d16,d4]) ).
cnf(d18,plain,
interior(sK38,sK40) = 'subset$ucomplement'('the$ucarrier'(sK38),'subset$ucomplement'('the$ucarrier'(sK38),sK40)),
inference(demodulation,[status(thm)],[d6,d17]) ).
cnf(d19,plain,
interior(sK38,sK40) = sK40,
inference(demodulation,[status(thm)],[d18,d0]) ).
cnf(d20,plain,
interior(sK38,sK40) != sK40,
inference(resolution,[status(thm)],[d15,c35]) ).
cnf(d21,plain,
$false,
inference(resolution,[status(thm)],[d20,d19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU324+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n008.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sat Sep 26 09:13:24 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.24/2.33 % SZS status Theorem for theBenchmark.p
% 15.24/2.33 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------