%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SEU319+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 : n009.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 12.52s 2.03s
% Output : CNFRefutation 12.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 7 unt; 0 def)
% Number of atoms : 63 ( 4 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 65 ( 28 ~; 25 |; 0 &)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 16 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d6_pre_topc,axiom,
! [X0] :
( 'top$ustr'(X0)
=> ! [X1] :
( element(X1,powerset('the$ucarrier'(X0)))
=> ( 'closed$usubset'(X1,X0)
<=> 'open$usubset'('subset$udifference'('the$ucarrier'(X0),'cast$uas$ucarrier$usubset'(X0),X1),X0) ) ) ) ).
fof(dt_l1_pre_topc,axiom,
! [X0] :
( 'top$ustr'(X0)
=> 'one$usorted$ustr'(X0) ) ).
fof(t17_pre_topc,axiom,
! [X0] :
( 'one$usorted$ustr'(X0)
=> ! [X1] :
( element(X1,powerset('the$ucarrier'(X0)))
=> 'subset$ucomplement'('the$ucarrier'(X0),X1) = 'subset$udifference'('the$ucarrier'(X0),'cast$uas$ucarrier$usubset'(X0),X1) ) ) ).
fof(t29_tops_1,conjecture,
! [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(negated_conjecture,negated_conjecture,
~ ! [X0] :
( 'top$ustr'(X0)
=> ! [X1] :
( element(X1,powerset('the$ucarrier'(X0)))
=> ( 'closed$usubset'(X1,X0)
<=> 'open$usubset'('subset$ucomplement'('the$ucarrier'(X0),X1),X0) ) ) ),
inference(negate_conjecture,[status(cth)],[t29_tops_1]) ).
cnf(c0,plain,
( 'open$usubset'('subset$udifference'('the$ucarrier'(X0),'cast$uas$ucarrier$usubset'(X0),X1),X0)
| ~ 'closed$usubset'(X1,X0)
| ~ element(X1,powerset('the$ucarrier'(X0)))
| ~ 'top$ustr'(X0) ),
inference(clausification,[status(esa)],[d6_pre_topc]) ).
cnf(c1,plain,
( ~ 'open$usubset'('subset$udifference'('the$ucarrier'(X0),'cast$uas$ucarrier$usubset'(X0),X1),X0)
| 'closed$usubset'(X1,X0)
| ~ element(X1,powerset('the$ucarrier'(X0)))
| ~ 'top$ustr'(X0) ),
inference(clausification,[status(esa)],[d6_pre_topc]) ).
cnf(c5,plain,
( 'one$usorted$ustr'(X0)
| ~ 'top$ustr'(X0) ),
inference(clausification,[status(esa)],[dt_l1_pre_topc]) ).
cnf(c12,plain,
( 'subset$ucomplement'('the$ucarrier'(X0),X1) = 'subset$udifference'('the$ucarrier'(X0),'cast$uas$ucarrier$usubset'(X0),X1)
| ~ element(X1,powerset('the$ucarrier'(X0)))
| ~ 'one$usorted$ustr'(X0) ),
inference(clausification,[status(esa)],[t17_pre_topc]) ).
cnf(c15,plain,
'top$ustr'(sK24),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c16,plain,
element(sK25,powerset('the$ucarrier'(sK24))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c18,plain,
( 'open$usubset'('subset$ucomplement'('the$ucarrier'(sK24),sK25),sK24)
| 'closed$usubset'(sK25,sK24) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c19,plain,
( ~ 'closed$usubset'(sK25,sK24)
| ~ 'open$usubset'('subset$ucomplement'('the$ucarrier'(sK24),sK25),sK24) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ 'one$usorted$ustr'(sK24)
| 'subset$ucomplement'('the$ucarrier'(sK24),sK25) = 'subset$udifference'('the$ucarrier'(sK24),'cast$uas$ucarrier$usubset'(sK24),sK25) ),
inference(resolution,[status(thm)],[c12,c16]) ).
cnf(d1,plain,
'one$usorted$ustr'(sK24),
inference(resolution,[status(thm)],[c5,c15]) ).
cnf(d2,plain,
'subset$ucomplement'('the$ucarrier'(sK24),sK25) = 'subset$udifference'('the$ucarrier'(sK24),'cast$uas$ucarrier$usubset'(sK24),sK25),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
( ~ 'top$ustr'(sK24)
| ~ element(sK25,powerset('the$ucarrier'(sK24)))
| ~ 'closed$usubset'(sK25,sK24)
| 'open$usubset'('subset$ucomplement'('the$ucarrier'(sK24),sK25),sK24) ),
inference(superposition,[status(thm)],[d2,c0]) ).
cnf(d4,plain,
( 'open$usubset'('subset$ucomplement'('the$ucarrier'(sK24),sK25),sK24)
| ~ element(sK25,powerset('the$ucarrier'(sK24)))
| ~ 'closed$usubset'(sK25,sK24) ),
inference(resolution,[status(thm)],[c15,d3]) ).
cnf(d5,plain,
( 'open$usubset'('subset$ucomplement'('the$ucarrier'(sK24),sK25),sK24)
| ~ 'closed$usubset'(sK25,sK24) ),
inference(resolution,[status(thm)],[c16,d4]) ).
cnf(d6,plain,
( ~ 'closed$usubset'(sK25,sK24)
| ~ 'closed$usubset'(sK25,sK24) ),
inference(resolution,[status(thm)],[d5,c19]) ).
cnf(d7,plain,
'open$usubset'('subset$ucomplement'('the$ucarrier'(sK24),sK25),sK24),
inference(resolution,[status(thm)],[d6,c18]) ).
cnf(d8,plain,
( ~ 'top$ustr'(sK24)
| ~ element(sK25,powerset('the$ucarrier'(sK24)))
| 'closed$usubset'(sK25,sK24)
| ~ 'open$usubset'('subset$ucomplement'('the$ucarrier'(sK24),sK25),sK24) ),
inference(superposition,[status(thm)],[d2,c1]) ).
cnf(d9,plain,
( ~ 'open$usubset'('subset$ucomplement'('the$ucarrier'(sK24),sK25),sK24)
| ~ element(sK25,powerset('the$ucarrier'(sK24)))
| 'closed$usubset'(sK25,sK24) ),
inference(resolution,[status(thm)],[c15,d8]) ).
cnf(d10,plain,
( ~ 'open$usubset'('subset$ucomplement'('the$ucarrier'(sK24),sK25),sK24)
| 'closed$usubset'(sK25,sK24) ),
inference(resolution,[status(thm)],[c16,d9]) ).
cnf(d11,plain,
~ 'open$usubset'('subset$ucomplement'('the$ucarrier'(sK24),sK25),sK24),
inference(resolution,[status(thm)],[d6,d10]) ).
cnf(d12,plain,
$false,
inference(resolution,[status(thm)],[d11,d7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU319+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
% 0.11/0.40 % Computer : n009.cluster.edu
% 0.11/0.40 % Model : x86_64 x86_64
% 0.11/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.40 % Memory : 8046.5625MB
% 0.11/0.40 % OS : Linux 6.8.0-71-generic
% 0.11/0.40 % CPULimit : 300
% 0.11/0.40 % WCLimit : 300
% 0.11/0.40 % DateTime : Sat Sep 26 09:11:14 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.52/2.03 % SZS status Theorem for theBenchmark.p
% 12.52/2.03 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------