%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET852-2 : 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 : n015.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 5.73s 7.83s
% Output : CNFRefutation 5.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of clauses : 18 ( 6 unt; 12 nHn; 14 RR)
% Number of literals : 44 ( 0 equ; 11 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 30 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_2,negated_conjecture,
~ 'c$ulessequals'('c$uUnion'('v$uY','tc$uset'('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$ua'),'c$uUnion'('v$uY','tc$uset'('t$ua')),'tc$uset'('tc$uset'('t$ua'))) ).
cnf(cls_conjecture_4,negated_conjecture,
( ~ 'c$uin'(X0,'v$uY','tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'(X0,'v$um','tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'('c$uZorn$uOsucc'('v$uS','v$um','t$ua'),X0,'tc$uset'('tc$uset'('t$ua'))) ) ).
cnf(cls_Zorn_OUnion__lemma0_0,axiom,
( 'c$ulessequals'('c$uUnion'(X2,X3),X0,'tc$uset'(X3))
| 'c$ulessequals'(X1,'c$uUnion'(X2,X3),'tc$uset'(X3))
| 'c$uin'('c$uZorn$uOUnion$u$ulemma0$u$u1'(X0,X1,X2,X3),X2,'tc$uset'(X3)) ) ).
cnf(cls_Zorn_OUnion__lemma0_1,axiom,
( 'c$ulessequals'('c$uUnion'(X2,X3),X0,'tc$uset'(X3))
| 'c$ulessequals'(X1,'c$uUnion'(X2,X3),'tc$uset'(X3))
| ~ 'c$ulessequals'('c$uZorn$uOUnion$u$ulemma0$u$u1'(X0,X1,X2,X3),X0,'tc$uset'(X3)) ) ).
cnf(cls_Zorn_OUnion__lemma0_2,axiom,
( 'c$ulessequals'('c$uUnion'(X2,X3),X1,'tc$uset'(X3))
| 'c$ulessequals'(X0,'c$uUnion'(X2,X3),'tc$uset'(X3))
| ~ 'c$ulessequals'(X0,'c$uZorn$uOUnion$u$ulemma0$u$u1'(X1,X0,X2,X3),'tc$uset'(X3)) ) ).
cnf(c0,plain,
~ 'c$ulessequals'('c$uUnion'('v$uY','tc$uset'('t$ua')),'v$um','tc$uset'('tc$uset'('t$ua'))),
inference(clausification,[status(esa)],[cls_conjecture_2]) ).
cnf(c1,plain,
~ 'c$ulessequals'('c$uZorn$uOsucc'('v$uS','v$um','t$ua'),'c$uUnion'('v$uY','tc$uset'('t$ua')),'tc$uset'('tc$uset'('t$ua'))),
inference(clausification,[status(esa)],[cls_conjecture_3]) ).
cnf(c2,plain,
( ~ 'c$uin'(X0,'v$uY','tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'(X0,'v$um','tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'('c$uZorn$uOsucc'('v$uS','v$um','t$ua'),X0,'tc$uset'('tc$uset'('t$ua'))) ),
inference(clausification,[status(esa)],[cls_conjecture_4]) ).
cnf(c3,plain,
( 'c$ulessequals'('c$uUnion'(X2,X3),X0,'tc$uset'(X3))
| 'c$ulessequals'(X1,'c$uUnion'(X2,X3),'tc$uset'(X3))
| 'c$uin'('c$uZorn$uOUnion$u$ulemma0$u$u1'(X0,X1,X2,X3),X2,'tc$uset'(X3)) ),
inference(clausification,[status(esa)],[cls_Zorn_OUnion__lemma0_0]) ).
cnf(c4,plain,
( 'c$ulessequals'('c$uUnion'(X2,X3),X0,'tc$uset'(X3))
| 'c$ulessequals'(X1,'c$uUnion'(X2,X3),'tc$uset'(X3))
| ~ 'c$ulessequals'('c$uZorn$uOUnion$u$ulemma0$u$u1'(X0,X1,X2,X3),X0,'tc$uset'(X3)) ),
inference(clausification,[status(esa)],[cls_Zorn_OUnion__lemma0_1]) ).
cnf(c5,plain,
( 'c$ulessequals'('c$uUnion'(X2,X3),X1,'tc$uset'(X3))
| 'c$ulessequals'(X0,'c$uUnion'(X2,X3),'tc$uset'(X3))
| ~ 'c$ulessequals'(X0,'c$uZorn$uOUnion$u$ulemma0$u$u1'(X1,X0,X2,X3),'tc$uset'(X3)) ),
inference(clausification,[status(esa)],[cls_Zorn_OUnion__lemma0_2]) ).
cnf(d0,plain,
( ~ 'c$uin'('c$uZorn$uOUnion$u$ulemma0$u$u1'(X1,'c$uZorn$uOsucc'('v$uS','v$um','t$ua'),X0,'tc$uset'('t$ua')),'v$uY','tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'('c$uZorn$uOUnion$u$ulemma0$u$u1'(X1,'c$uZorn$uOsucc'('v$uS','v$um','t$ua'),X0,'tc$uset'('t$ua')),'v$um','tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'('c$uUnion'(X0,'tc$uset'('t$ua')),X1,'tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'('c$uZorn$uOsucc'('v$uS','v$um','t$ua'),'c$uUnion'(X0,'tc$uset'('t$ua')),'tc$uset'('tc$uset'('t$ua'))) ),
inference(resolution,[status(thm)],[c5,c2]) ).
cnf(d1,plain,
( 'c$ulessequals'('c$uUnion'('v$uY','tc$uset'('t$ua')),X0,'tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'('c$uZorn$uOsucc'('v$uS','v$um','t$ua'),'c$uUnion'('v$uY','tc$uset'('t$ua')),'tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'('c$uZorn$uOUnion$u$ulemma0$u$u1'(X0,'c$uZorn$uOsucc'('v$uS','v$um','t$ua'),'v$uY','tc$uset'('t$ua')),'v$um','tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'('c$uZorn$uOsucc'('v$uS','v$um','t$ua'),'c$uUnion'('v$uY','tc$uset'('t$ua')),'tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'('c$uUnion'('v$uY','tc$uset'('t$ua')),X0,'tc$uset'('tc$uset'('t$ua'))) ),
inference(resolution,[status(thm)],[d0,c3]) ).
cnf(d2,plain,
( 'c$ulessequals'('c$uZorn$uOUnion$u$ulemma0$u$u1'(X0,'c$uZorn$uOsucc'('v$uS','v$um','t$ua'),'v$uY','tc$uset'('t$ua')),'v$um','tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'('c$uUnion'('v$uY','tc$uset'('t$ua')),X0,'tc$uset'('tc$uset'('t$ua'))) ),
inference(resolution,[status(thm)],[c1,d1]) ).
cnf(d3,plain,
( 'c$ulessequals'('c$uUnion'('v$uY','tc$uset'('t$ua')),'v$um','tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'('c$uZorn$uOsucc'('v$uS','v$um','t$ua'),'c$uUnion'('v$uY','tc$uset'('t$ua')),'tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'('c$uUnion'('v$uY','tc$uset'('t$ua')),'v$um','tc$uset'('tc$uset'('t$ua'))) ),
inference(resolution,[status(thm)],[d2,c4]) ).
cnf(d4,plain,
'c$ulessequals'('c$uZorn$uOsucc'('v$uS','v$um','t$ua'),'c$uUnion'('v$uY','tc$uset'('t$ua')),'tc$uset'('tc$uset'('t$ua'))),
inference(resolution,[status(thm)],[c0,d3]) ).
cnf(d5,plain,
$false,
inference(resolution,[status(thm)],[c1,d4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET852-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/5.46 % Computer : n015.cluster.edu
% 0.18/5.46 % Model : x86_64 x86_64
% 0.18/5.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.46 % Memory : 8046.5625MB
% 0.18/5.46 % OS : Linux 6.8.0-71-generic
% 0.18/5.46 % CPULimit : 300
% 0.18/5.46 % WCLimit : 300
% 0.18/5.46 % DateTime : Sat Sep 26 08:24:50 UTC 2026
% 0.18/5.46 % CPUTime :
% 0.18/5.46 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.73/7.83 % SZS status Unsatisfiable for theBenchmark.p
% 5.73/7.83 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------