%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU320+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 : n006.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 08:41:39 AM UTC 2026
% Result : Theorem 15.12s 2.45s
% Output : CNFRefutation 15.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 7 unt; 0 def)
% Number of atoms : 62 ( 3 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 64 ( 28 ~; 25 |; 0 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 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 : 18 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(dt_k3_subset_1,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> element('subset$ucomplement'(X0,X1),powerset(X0)) ) ).
fof(involutiveness_k3_subset_1,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> 'subset$ucomplement'(X0,'subset$ucomplement'(X0,X1)) = X1 ) ).
fof(t29_tops_1,axiom,
! [X0] :
( 'top$ustr'(X0)
=> ! [X1] :
( element(X1,powerset('the$ucarrier'(X0)))
=> ( 'closed$usubset'(X1,X0)
<=> 'open$usubset'('subset$ucomplement'('the$ucarrier'(X0),X1),X0) ) ) ) ).
fof(t30_tops_1,conjecture,
! [X0] :
( 'top$ustr'(X0)
=> ! [X1] :
( element(X1,powerset('the$ucarrier'(X0)))
=> ( 'open$usubset'(X1,X0)
<=> 'closed$usubset'('subset$ucomplement'('the$ucarrier'(X0),X1),X0) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( 'top$ustr'(X0)
=> ! [X1] :
( element(X1,powerset('the$ucarrier'(X0)))
=> ( 'open$usubset'(X1,X0)
<=> 'closed$usubset'('subset$ucomplement'('the$ucarrier'(X0),X1),X0) ) ) ),
inference(negate_conjecture,[status(cth)],[t30_tops_1]) ).
cnf(c0,plain,
( element('subset$ucomplement'(X1,X0),powerset(X1))
| ~ element(X0,powerset(X1)) ),
inference(clausification,[status(esa)],[dt_k3_subset_1]) ).
cnf(c5,plain,
( 'subset$ucomplement'(X1,'subset$ucomplement'(X1,X0)) = X0
| ~ element(X0,powerset(X1)) ),
inference(clausification,[status(esa)],[involutiveness_k3_subset_1]) ).
cnf(c7,plain,
( 'open$usubset'('subset$ucomplement'('the$ucarrier'(X0),X1),X0)
| ~ 'closed$usubset'(X1,X0)
| ~ element(X1,powerset('the$ucarrier'(X0)))
| ~ 'top$ustr'(X0) ),
inference(clausification,[status(esa)],[t29_tops_1]) ).
cnf(c8,plain,
( ~ 'open$usubset'('subset$ucomplement'('the$ucarrier'(X0),X1),X0)
| 'closed$usubset'(X1,X0)
| ~ element(X1,powerset('the$ucarrier'(X0)))
| ~ 'top$ustr'(X0) ),
inference(clausification,[status(esa)],[t29_tops_1]) ).
cnf(c11,plain,
'top$ustr'(sK15),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c12,plain,
element(sK16,powerset('the$ucarrier'(sK15))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c14,plain,
( 'closed$usubset'('subset$ucomplement'('the$ucarrier'(sK15),sK16),sK15)
| 'open$usubset'(sK16,sK15) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c15,plain,
( ~ 'open$usubset'(sK16,sK15)
| ~ 'closed$usubset'('subset$ucomplement'('the$ucarrier'(sK15),sK16),sK15) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
'subset$ucomplement'('the$ucarrier'(sK15),'subset$ucomplement'('the$ucarrier'(sK15),sK16)) = sK16,
inference(resolution,[status(thm)],[c5,c12]) ).
cnf(d1,plain,
( 'closed$usubset'('subset$ucomplement'('the$ucarrier'(sK15),sK16),sK15)
| ~ 'top$ustr'(sK15)
| ~ element('subset$ucomplement'('the$ucarrier'(sK15),sK16),powerset('the$ucarrier'(sK15)))
| ~ 'open$usubset'(sK16,sK15) ),
inference(superposition,[status(thm)],[d0,c8]) ).
cnf(d2,plain,
( ~ 'open$usubset'(sK16,sK15)
| 'closed$usubset'('subset$ucomplement'('the$ucarrier'(sK15),sK16),sK15)
| ~ element('subset$ucomplement'('the$ucarrier'(sK15),sK16),powerset('the$ucarrier'(sK15))) ),
inference(resolution,[status(thm)],[c11,d1]) ).
cnf(d3,plain,
( ~ 'closed$usubset'('subset$ucomplement'('the$ucarrier'(sK15),sK16),sK15)
| ~ 'top$ustr'(sK15)
| ~ element('subset$ucomplement'('the$ucarrier'(sK15),sK16),powerset('the$ucarrier'(sK15)))
| 'open$usubset'(sK16,sK15) ),
inference(superposition,[status(thm)],[d0,c7]) ).
cnf(d4,plain,
( 'open$usubset'(sK16,sK15)
| ~ 'closed$usubset'('subset$ucomplement'('the$ucarrier'(sK15),sK16),sK15)
| ~ element('subset$ucomplement'('the$ucarrier'(sK15),sK16),powerset('the$ucarrier'(sK15))) ),
inference(resolution,[status(thm)],[c11,d3]) ).
cnf(d5,plain,
( ~ element(sK16,powerset('the$ucarrier'(sK15)))
| 'open$usubset'(sK16,sK15)
| ~ 'closed$usubset'('subset$ucomplement'('the$ucarrier'(sK15),sK16),sK15) ),
inference(resolution,[status(thm)],[d4,c0]) ).
cnf(d6,plain,
( 'open$usubset'(sK16,sK15)
| ~ 'closed$usubset'('subset$ucomplement'('the$ucarrier'(sK15),sK16),sK15) ),
inference(resolution,[status(thm)],[c12,d5]) ).
cnf(d7,plain,
( 'open$usubset'(sK16,sK15)
| 'open$usubset'(sK16,sK15) ),
inference(resolution,[status(thm)],[d6,c14]) ).
cnf(d8,plain,
( 'closed$usubset'('subset$ucomplement'('the$ucarrier'(sK15),sK16),sK15)
| ~ element('subset$ucomplement'('the$ucarrier'(sK15),sK16),powerset('the$ucarrier'(sK15))) ),
inference(resolution,[status(thm)],[d7,d2]) ).
cnf(d9,plain,
~ 'closed$usubset'('subset$ucomplement'('the$ucarrier'(sK15),sK16),sK15),
inference(resolution,[status(thm)],[d7,c15]) ).
cnf(d10,plain,
~ element('subset$ucomplement'('the$ucarrier'(sK15),sK16),powerset('the$ucarrier'(sK15))),
inference(resolution,[status(thm)],[d9,d8]) ).
cnf(d11,plain,
~ element(sK16,powerset('the$ucarrier'(sK15))),
inference(resolution,[status(thm)],[d10,c0]) ).
cnf(d12,plain,
$false,
inference(resolution,[status(thm)],[c12,d11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU320+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
% 0.09/0.35 % Computer : n006.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 09:11:42 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.12/2.45 % SZS status Theorem for theBenchmark.p
% 15.12/2.45 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------