%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET851-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/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 08:33:25 AM UTC 2026
% Result : Unsatisfiable 9.98s 6.86s
% Output : CNFRefutation 9.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of clauses : 21 ( 13 unt; 4 nHn; 17 RR)
% Number of literals : 34 ( 5 equ; 15 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 14 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Set_Osubset__refl_0,axiom,
'c$ulessequals'(X0,X0,'tc$uset'(X1)) ).
cnf(cls_Zorn_Osucc__trans_0,axiom,
( 'c$ulessequals'(X0,'c$uZorn$uOsucc'(X3,X1,X2),'tc$uset'('tc$uset'(X2)))
| ~ 'c$ulessequals'(X0,X1,'tc$uset'('tc$uset'(X2))) ) ).
cnf(cls_conjecture_1,negated_conjecture,
'c$uin'('v$ux','c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua'))) ).
cnf(cls_conjecture_2,negated_conjecture,
~ 'c$ulessequals'('c$uZorn$uOsucc'('v$uS','v$ux','t$ua'),'v$um','tc$uset'('tc$uset'('t$ua'))) ).
cnf(cls_conjecture_3,negated_conjecture,
~ 'c$ulessequals'('c$uZorn$uOsucc'('v$uS','v$um','t$ua'),'c$uZorn$uOsucc'('v$uS','v$ux','t$ua'),'tc$uset'('tc$uset'('t$ua'))) ).
cnf(cls_conjecture_4,negated_conjecture,
( 'c$ulessequals'('v$ux','v$um','tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'('c$uZorn$uOsucc'('v$uS','v$um','t$ua'),'v$ux','tc$uset'('tc$uset'('t$ua'))) ) ).
cnf(cls_conjecture_5,negated_conjecture,
( ~ 'c$uin'(X0,'c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| ~ 'c$ulessequals'(X0,'v$um','tc$uset'('tc$uset'('t$ua')))
| X0 = 'v$um'
| 'c$ulessequals'('c$uZorn$uOsucc'('v$uS',X0,'t$ua'),'v$um','tc$uset'('tc$uset'('t$ua'))) ) ).
cnf(c0,plain,
'c$ulessequals'(X0,X0,'tc$uset'(X1)),
inference(clausification,[status(esa)],[cls_Set_Osubset__refl_0]) ).
cnf(c1,plain,
( 'c$ulessequals'(X0,'c$uZorn$uOsucc'(X3,X1,X2),'tc$uset'('tc$uset'(X2)))
| ~ 'c$ulessequals'(X0,X1,'tc$uset'('tc$uset'(X2))) ),
inference(clausification,[status(esa)],[cls_Zorn_Osucc__trans_0]) ).
cnf(c2,plain,
'c$uin'('v$ux','c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua'))),
inference(clausification,[status(esa)],[cls_conjecture_1]) ).
cnf(c3,plain,
~ 'c$ulessequals'('c$uZorn$uOsucc'('v$uS','v$ux','t$ua'),'v$um','tc$uset'('tc$uset'('t$ua'))),
inference(clausification,[status(esa)],[cls_conjecture_2]) ).
cnf(c4,plain,
~ 'c$ulessequals'('c$uZorn$uOsucc'('v$uS','v$um','t$ua'),'c$uZorn$uOsucc'('v$uS','v$ux','t$ua'),'tc$uset'('tc$uset'('t$ua'))),
inference(clausification,[status(esa)],[cls_conjecture_3]) ).
cnf(c5,plain,
( 'c$ulessequals'('v$ux','v$um','tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'('c$uZorn$uOsucc'('v$uS','v$um','t$ua'),'v$ux','tc$uset'('tc$uset'('t$ua'))) ),
inference(clausification,[status(esa)],[cls_conjecture_4]) ).
cnf(c6,plain,
( ~ 'c$uin'(X0,'c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| ~ 'c$ulessequals'(X0,'v$um','tc$uset'('tc$uset'('t$ua')))
| X0 = 'v$um'
| 'c$ulessequals'('c$uZorn$uOsucc'('v$uS',X0,'t$ua'),'v$um','tc$uset'('tc$uset'('t$ua'))) ),
inference(clausification,[status(esa)],[cls_conjecture_5]) ).
cnf(d0,plain,
( ~ 'c$uin'('v$ux','c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| ~ 'c$ulessequals'('v$ux','v$um','tc$uset'('tc$uset'('t$ua')))
| 'v$ux' = 'v$um' ),
inference(resolution,[status(thm)],[c6,c3]) ).
cnf(d1,plain,
( ~ 'c$ulessequals'('v$ux','v$um','tc$uset'('tc$uset'('t$ua')))
| 'v$ux' = 'v$um' ),
inference(resolution,[status(thm)],[c2,d0]) ).
cnf(d2,plain,
~ 'c$ulessequals'('c$uZorn$uOsucc'('v$uS','v$um','t$ua'),'v$ux','tc$uset'('tc$uset'('t$ua'))),
inference(resolution,[status(thm)],[c4,c1]) ).
cnf(d3,plain,
'c$ulessequals'('v$ux','v$um','tc$uset'('tc$uset'('t$ua'))),
inference(resolution,[status(thm)],[d2,c5]) ).
cnf(d4,plain,
'v$ux' = 'v$um',
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
~ 'c$ulessequals'('c$uZorn$uOsucc'('v$uS','v$um','t$ua'),'c$uZorn$uOsucc'('v$uS','v$um','t$ua'),'tc$uset'('tc$uset'('t$ua'))),
inference(demodulation,[status(thm)],[c4,d4]) ).
cnf(d6,plain,
$false,
inference(resolution,[status(thm)],[c0,d5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.23 % Problem : SET851-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.24 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.58 % Computer : n006.cluster.edu
% 0.10/5.58 % Model : x86_64 x86_64
% 0.10/5.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.58 % Memory : 8046.5625MB
% 0.10/5.58 % OS : Linux 6.8.0-71-generic
% 0.10/5.58 % CPULimit : 300
% 0.10/5.58 % WCLimit : 300
% 0.10/5.58 % DateTime : Sat Sep 26 08:21:35 UTC 2026
% 0.10/5.58 % CPUTime :
% 0.10/5.58 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.98/6.86 % SZS status Unsatisfiable for theBenchmark.p
% 9.98/6.86 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------