%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET853-2 : 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 : n020.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 14.67s 3.72s
% Output : CNFRefutation 14.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 13
% Syntax : Number of clauses : 59 ( 16 unt; 35 nHn; 55 RR)
% Number of literals : 191 ( 44 equ; 76 neg)
% Maximal clause size : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 68 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
'c$uin'('v$ux','c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua'))) ).
cnf(cls_conjecture_1,negated_conjecture,
'c$uin'('v$uxa','c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua'))) ).
cnf(cls_conjecture_2,negated_conjecture,
'c$ulessequals'('v$uxa','c$uZorn$uOsucc'('v$uS','v$ux','t$ua'),'tc$uset'('tc$uset'('t$ua'))) ).
cnf(cls_conjecture_3,negated_conjecture,
'v$uxa' != 'c$uZorn$uOsucc'('v$uS','v$ux','t$ua') ).
cnf(cls_conjecture_4,negated_conjecture,
~ 'c$ulessequals'('c$uZorn$uOsucc'('v$uS','v$uxa','t$ua'),'c$uZorn$uOsucc'('v$uS','v$ux','t$ua'),'tc$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$ulessequals'(X0,'v$ux','tc$uset'('tc$uset'('t$ua')))
| X0 = 'v$ux'
| 'c$ulessequals'('c$uZorn$uOsucc'('v$uS',X0,'t$ua'),'v$ux','tc$uset'('tc$uset'('t$ua'))) ) ).
cnf(cls_Set_Osubset__antisym_0,axiom,
( X1 = X0
| ~ 'c$ulessequals'(X1,X0,'tc$uset'(X2))
| ~ 'c$ulessequals'(X0,X1,'tc$uset'(X2)) ) ).
cnf(cls_Set_Osubset__refl_0,axiom,
'c$ulessequals'(X0,X0,'tc$uset'(X1)) ).
cnf(cls_Zorn_OTFin__linear__lemma1_0,axiom,
( 'c$ulessequals'('c$uZorn$uOsucc'(X1,X0,X2),X3,'tc$uset'('tc$uset'(X2)))
| 'c$ulessequals'(X3,X0,'tc$uset'('tc$uset'(X2)))
| 'c$uin'('c$uZorn$uOTFin$u$ulinear$u$ulemma1$u$u1'(X1,X0,X2),'c$uZorn$uOTFin'(X1,X2),'tc$uset'('tc$uset'(X2)))
| ~ 'c$uin'(X3,'c$uZorn$uOTFin'(X1,X2),'tc$uset'('tc$uset'(X2)))
| ~ 'c$uin'(X0,'c$uZorn$uOTFin'(X1,X2),'tc$uset'('tc$uset'(X2))) ) ).
cnf(cls_Zorn_OTFin__linear__lemma1_1,axiom,
( 'c$ulessequals'('c$uZorn$uOsucc'(X1,X0,X2),X3,'tc$uset'('tc$uset'(X2)))
| 'c$ulessequals'('c$uZorn$uOTFin$u$ulinear$u$ulemma1$u$u1'(X1,X0,X2),X0,'tc$uset'('tc$uset'(X2)))
| 'c$ulessequals'(X3,X0,'tc$uset'('tc$uset'(X2)))
| ~ 'c$uin'(X3,'c$uZorn$uOTFin'(X1,X2),'tc$uset'('tc$uset'(X2)))
| ~ 'c$uin'(X0,'c$uZorn$uOTFin'(X1,X2),'tc$uset'('tc$uset'(X2))) ) ).
cnf(cls_Zorn_OTFin__linear__lemma1_2,axiom,
( 'c$ulessequals'('c$uZorn$uOsucc'(X1,X0,X2),X3,'tc$uset'('tc$uset'(X2)))
| 'c$ulessequals'(X3,X0,'tc$uset'('tc$uset'(X2)))
| 'c$uZorn$uOTFin$u$ulinear$u$ulemma1$u$u1'(X1,X0,X2) != X0
| ~ 'c$uin'(X3,'c$uZorn$uOTFin'(X1,X2),'tc$uset'('tc$uset'(X2)))
| ~ 'c$uin'(X0,'c$uZorn$uOTFin'(X1,X2),'tc$uset'('tc$uset'(X2))) ) ).
cnf(cls_Zorn_OTFin__linear__lemma1_3,axiom,
( 'c$ulessequals'('c$uZorn$uOsucc'(X1,X0,X2),X3,'tc$uset'('tc$uset'(X2)))
| 'c$ulessequals'(X3,X0,'tc$uset'('tc$uset'(X2)))
| ~ 'c$ulessequals'('c$uZorn$uOsucc'(X1,'c$uZorn$uOTFin$u$ulinear$u$ulemma1$u$u1'(X1,X0,X2),X2),X0,'tc$uset'('tc$uset'(X2)))
| ~ 'c$uin'(X3,'c$uZorn$uOTFin'(X1,X2),'tc$uset'('tc$uset'(X2)))
| ~ 'c$uin'(X0,'c$uZorn$uOTFin'(X1,X2),'tc$uset'('tc$uset'(X2))) ) ).
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(c0,plain,
'c$uin'('v$ux','c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua'))),
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(c1,plain,
'c$uin'('v$uxa','c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua'))),
inference(clausification,[status(esa)],[cls_conjecture_1]) ).
cnf(c2,plain,
'c$ulessequals'('v$uxa','c$uZorn$uOsucc'('v$uS','v$ux','t$ua'),'tc$uset'('tc$uset'('t$ua'))),
inference(clausification,[status(esa)],[cls_conjecture_2]) ).
cnf(c3,plain,
'v$uxa' != 'c$uZorn$uOsucc'('v$uS','v$ux','t$ua'),
inference(clausification,[status(esa)],[cls_conjecture_3]) ).
cnf(c4,plain,
~ 'c$ulessequals'('c$uZorn$uOsucc'('v$uS','v$uxa','t$ua'),'c$uZorn$uOsucc'('v$uS','v$ux','t$ua'),'tc$uset'('tc$uset'('t$ua'))),
inference(clausification,[status(esa)],[cls_conjecture_4]) ).
cnf(c5,plain,
( ~ 'c$uin'(X0,'c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| ~ 'c$ulessequals'(X0,'v$ux','tc$uset'('tc$uset'('t$ua')))
| X0 = 'v$ux'
| 'c$ulessequals'('c$uZorn$uOsucc'('v$uS',X0,'t$ua'),'v$ux','tc$uset'('tc$uset'('t$ua'))) ),
inference(clausification,[status(esa)],[cls_conjecture_5]) ).
cnf(c6,plain,
( X1 = X0
| ~ 'c$ulessequals'(X1,X0,'tc$uset'(X2))
| ~ 'c$ulessequals'(X0,X1,'tc$uset'(X2)) ),
inference(clausification,[status(esa)],[cls_Set_Osubset__antisym_0]) ).
cnf(c7,plain,
'c$ulessequals'(X0,X0,'tc$uset'(X1)),
inference(clausification,[status(esa)],[cls_Set_Osubset__refl_0]) ).
cnf(c8,plain,
( ~ 'c$uin'(X1,'c$uZorn$uOTFin'(X0,X2),'tc$uset'('tc$uset'(X2)))
| 'c$uin'('c$uZorn$uOTFin$u$ulinear$u$ulemma1$u$u1'(X0,X1,X2),'c$uZorn$uOTFin'(X0,X2),'tc$uset'('tc$uset'(X2)))
| ~ 'c$uin'(X3,'c$uZorn$uOTFin'(X0,X2),'tc$uset'('tc$uset'(X2)))
| 'c$ulessequals'(X3,X1,'tc$uset'('tc$uset'(X2)))
| 'c$ulessequals'('c$uZorn$uOsucc'(X0,X1,X2),X3,'tc$uset'('tc$uset'(X2))) ),
inference(clausification,[status(esa)],[cls_Zorn_OTFin__linear__lemma1_0]) ).
cnf(c9,plain,
( ~ 'c$uin'(X3,'c$uZorn$uOTFin'(X1,X2),'tc$uset'('tc$uset'(X2)))
| 'c$ulessequals'('c$uZorn$uOTFin$u$ulinear$u$ulemma1$u$u1'(X1,X3,X2),X3,'tc$uset'('tc$uset'(X2)))
| 'c$ulessequals'(X0,X3,'tc$uset'('tc$uset'(X2)))
| 'c$ulessequals'('c$uZorn$uOsucc'(X1,X3,X2),X0,'tc$uset'('tc$uset'(X2)))
| ~ 'c$uin'(X0,'c$uZorn$uOTFin'(X1,X2),'tc$uset'('tc$uset'(X2))) ),
inference(clausification,[status(esa)],[cls_Zorn_OTFin__linear__lemma1_1]) ).
cnf(c10,plain,
( ~ 'c$uin'(X3,'c$uZorn$uOTFin'(X1,X2),'tc$uset'('tc$uset'(X2)))
| 'c$uZorn$uOTFin$u$ulinear$u$ulemma1$u$u1'(X1,X0,X2) != X0
| 'c$ulessequals'(X3,X0,'tc$uset'('tc$uset'(X2)))
| 'c$ulessequals'('c$uZorn$uOsucc'(X1,X0,X2),X3,'tc$uset'('tc$uset'(X2)))
| ~ 'c$uin'(X0,'c$uZorn$uOTFin'(X1,X2),'tc$uset'('tc$uset'(X2))) ),
inference(clausification,[status(esa)],[cls_Zorn_OTFin__linear__lemma1_2]) ).
cnf(c11,plain,
( 'c$ulessequals'('c$uZorn$uOsucc'(X1,X0,X2),X3,'tc$uset'('tc$uset'(X2)))
| ~ 'c$uin'(X3,'c$uZorn$uOTFin'(X1,X2),'tc$uset'('tc$uset'(X2)))
| ~ 'c$ulessequals'('c$uZorn$uOsucc'(X1,'c$uZorn$uOTFin$u$ulinear$u$ulemma1$u$u1'(X1,X0,X2),X2),X0,'tc$uset'('tc$uset'(X2)))
| 'c$ulessequals'(X3,X0,'tc$uset'('tc$uset'(X2)))
| ~ 'c$uin'(X0,'c$uZorn$uOTFin'(X1,X2),'tc$uset'('tc$uset'(X2))) ),
inference(clausification,[status(esa)],[cls_Zorn_OTFin__linear__lemma1_3]) ).
cnf(c12,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(d0,plain,
~ 'c$ulessequals'('c$uZorn$uOsucc'('v$uS','v$uxa','t$ua'),'v$ux','tc$uset'('tc$uset'('t$ua'))),
inference(resolution,[status(thm)],[c12,c4]) ).
cnf(d1,plain,
( ~ 'c$ulessequals'('v$uxa','v$ux','tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'('v$uxa','c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| 'v$uxa' = 'v$ux' ),
inference(resolution,[status(thm)],[d0,c5]) ).
cnf(d2,plain,
( ~ 'c$ulessequals'('v$uxa','v$ux','tc$uset'('tc$uset'('t$ua')))
| 'v$uxa' = 'v$ux' ),
inference(resolution,[status(thm)],[c1,d1]) ).
cnf(d3,plain,
( ~ 'c$ulessequals'('c$uZorn$uOsucc'('v$uS','v$ux','t$ua'),'v$uxa','tc$uset'('tc$uset'('t$ua')))
| 'c$uZorn$uOsucc'('v$uS','v$ux','t$ua') = 'v$uxa' ),
inference(resolution,[status(thm)],[c6,c2]) ).
cnf(d4,plain,
( ~ 'c$ulessequals'(X3,'c$uZorn$uOsucc'(X1,X0,X2),'tc$uset'('tc$uset'(X2)))
| X3 = 'c$uZorn$uOsucc'(X1,X0,X2)
| 'c$ulessequals'('c$uZorn$uOTFin$u$ulinear$u$ulemma1$u$u1'(X1,X0,X2),X0,'tc$uset'('tc$uset'(X2)))
| 'c$ulessequals'(X3,X0,'tc$uset'('tc$uset'(X2)))
| ~ 'c$uin'(X3,'c$uZorn$uOTFin'(X1,X2),'tc$uset'('tc$uset'(X2)))
| ~ 'c$uin'(X0,'c$uZorn$uOTFin'(X1,X2),'tc$uset'('tc$uset'(X2))) ),
inference(resolution,[status(thm)],[c9,c6]) ).
cnf(d5,plain,
( 'c$ulessequals'('c$uZorn$uOTFin$u$ulinear$u$ulemma1$u$u1'('v$uS','v$ux','t$ua'),'v$ux','tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'('v$uxa','v$ux','tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'('v$ux','c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'('v$uxa','c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| 'v$uxa' = 'c$uZorn$uOsucc'('v$uS','v$ux','t$ua') ),
inference(resolution,[status(thm)],[d4,c2]) ).
cnf(d6,plain,
( 'c$ulessequals'('c$uZorn$uOTFin$u$ulinear$u$ulemma1$u$u1'('v$uS','v$ux','t$ua'),'v$ux','tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'('v$uxa','v$ux','tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'('v$uxa','c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| 'v$uxa' = 'c$uZorn$uOsucc'('v$uS','v$ux','t$ua') ),
inference(resolution,[status(thm)],[c0,d5]) ).
cnf(d7,plain,
( 'c$ulessequals'('c$uZorn$uOTFin$u$ulinear$u$ulemma1$u$u1'('v$uS','v$ux','t$ua'),'v$ux','tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'('v$uxa','v$ux','tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'('v$uxa','c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua'))) ),
inference(resolution,[status(thm)],[c3,d6]) ).
cnf(d8,plain,
( 'c$ulessequals'('c$uZorn$uOTFin$u$ulinear$u$ulemma1$u$u1'('v$uS','v$ux','t$ua'),'v$ux','tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'('v$uxa','v$ux','tc$uset'('tc$uset'('t$ua'))) ),
inference(resolution,[status(thm)],[c1,d7]) ).
cnf(d9,plain,
( ~ 'c$ulessequals'('c$uZorn$uOTFin$u$ulinear$u$ulemma1$u$u1'('v$uS','v$ux','t$ua'),'v$ux','tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'('c$uZorn$uOTFin$u$ulinear$u$ulemma1$u$u1'('v$uS','v$ux','t$ua'),'c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| 'c$uZorn$uOTFin$u$ulinear$u$ulemma1$u$u1'('v$uS','v$ux','t$ua') = 'v$ux'
| 'c$ulessequals'('c$uZorn$uOsucc'('v$uS','v$ux','t$ua'),X0,'tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'(X0,'v$ux','tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'(X0,'c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'('v$ux','c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua'))) ),
inference(resolution,[status(thm)],[c11,c5]) ).
cnf(d10,plain,
( ~ 'c$ulessequals'('c$uZorn$uOTFin$u$ulinear$u$ulemma1$u$u1'('v$uS','v$ux','t$ua'),'v$ux','tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'('c$uZorn$uOsucc'('v$uS','v$ux','t$ua'),X0,'tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'(X0,'v$ux','tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'('c$uZorn$uOTFin$u$ulinear$u$ulemma1$u$u1'('v$uS','v$ux','t$ua'),'c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'(X0,'c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| 'c$uZorn$uOTFin$u$ulinear$u$ulemma1$u$u1'('v$uS','v$ux','t$ua') = 'v$ux' ),
inference(resolution,[status(thm)],[c0,d9]) ).
cnf(d11,plain,
( ~ 'c$ulessequals'(X0,'c$uZorn$uOsucc'(X1,X3,X2),'tc$uset'('tc$uset'(X2)))
| X0 = 'c$uZorn$uOsucc'(X1,X3,X2)
| 'c$ulessequals'(X0,X3,'tc$uset'('tc$uset'(X2)))
| 'c$uin'('c$uZorn$uOTFin$u$ulinear$u$ulemma1$u$u1'(X1,X3,X2),'c$uZorn$uOTFin'(X1,X2),'tc$uset'('tc$uset'(X2)))
| ~ 'c$uin'(X3,'c$uZorn$uOTFin'(X1,X2),'tc$uset'('tc$uset'(X2)))
| ~ 'c$uin'(X0,'c$uZorn$uOTFin'(X1,X2),'tc$uset'('tc$uset'(X2))) ),
inference(resolution,[status(thm)],[c8,c6]) ).
cnf(d12,plain,
( 'c$ulessequals'('v$uxa','v$ux','tc$uset'('tc$uset'('t$ua')))
| 'c$uin'('c$uZorn$uOTFin$u$ulinear$u$ulemma1$u$u1'('v$uS','v$ux','t$ua'),'c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'('v$uxa','c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'('v$ux','c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| 'v$uxa' = 'c$uZorn$uOsucc'('v$uS','v$ux','t$ua') ),
inference(resolution,[status(thm)],[d11,c2]) ).
cnf(d13,plain,
( 'c$ulessequals'('v$uxa','v$ux','tc$uset'('tc$uset'('t$ua')))
| 'c$uin'('c$uZorn$uOTFin$u$ulinear$u$ulemma1$u$u1'('v$uS','v$ux','t$ua'),'c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'('v$uxa','c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| 'v$uxa' = 'c$uZorn$uOsucc'('v$uS','v$ux','t$ua') ),
inference(resolution,[status(thm)],[c0,d12]) ).
cnf(d14,plain,
( 'c$ulessequals'('v$uxa','v$ux','tc$uset'('tc$uset'('t$ua')))
| 'c$uin'('c$uZorn$uOTFin$u$ulinear$u$ulemma1$u$u1'('v$uS','v$ux','t$ua'),'c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'('v$uxa','c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua'))) ),
inference(resolution,[status(thm)],[c3,d13]) ).
cnf(d15,plain,
( 'c$ulessequals'('v$uxa','v$ux','tc$uset'('tc$uset'('t$ua')))
| 'c$uin'('c$uZorn$uOTFin$u$ulinear$u$ulemma1$u$u1'('v$uS','v$ux','t$ua'),'c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua'))) ),
inference(resolution,[status(thm)],[c1,d14]) ).
cnf(d16,plain,
( ~ 'c$ulessequals'('c$uZorn$uOTFin$u$ulinear$u$ulemma1$u$u1'('v$uS','v$ux','t$ua'),'v$ux','tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'('c$uZorn$uOsucc'('v$uS','v$ux','t$ua'),X0,'tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'(X0,'v$ux','tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'(X0,'c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| 'c$uZorn$uOTFin$u$ulinear$u$ulemma1$u$u1'('v$uS','v$ux','t$ua') = 'v$ux'
| 'c$ulessequals'('v$uxa','v$ux','tc$uset'('tc$uset'('t$ua'))) ),
inference(resolution,[status(thm)],[d15,d10]) ).
cnf(d17,plain,
( 'c$ulessequals'('v$uxa','v$ux','tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'('c$uZorn$uOsucc'('v$uS','v$ux','t$ua'),X0,'tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'('v$uxa','v$ux','tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'(X0,'v$ux','tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'(X0,'c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| 'c$uZorn$uOTFin$u$ulinear$u$ulemma1$u$u1'('v$uS','v$ux','t$ua') = 'v$ux' ),
inference(resolution,[status(thm)],[d16,d8]) ).
cnf(d18,plain,
( ~ 'c$ulessequals'(X0,'c$uZorn$uOsucc'('v$uS','v$ux','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| X0 = 'c$uZorn$uOsucc'('v$uS','v$ux','t$ua')
| 'c$ulessequals'('v$uxa','v$ux','tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'(X0,'v$ux','tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'(X0,'c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| 'c$uZorn$uOTFin$u$ulinear$u$ulemma1$u$u1'('v$uS','v$ux','t$ua') = 'v$ux' ),
inference(resolution,[status(thm)],[d17,c6]) ).
cnf(d19,plain,
( 'c$ulessequals'('v$uxa','v$ux','tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'('v$uxa','v$ux','tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'('v$uxa','c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| 'c$uZorn$uOTFin$u$ulinear$u$ulemma1$u$u1'('v$uS','v$ux','t$ua') = 'v$ux'
| 'v$uxa' = 'c$uZorn$uOsucc'('v$uS','v$ux','t$ua') ),
inference(resolution,[status(thm)],[d18,c2]) ).
cnf(d20,plain,
( 'c$ulessequals'('v$uxa','v$ux','tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'('v$uxa','c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| 'c$uZorn$uOTFin$u$ulinear$u$ulemma1$u$u1'('v$uS','v$ux','t$ua') = 'v$ux' ),
inference(resolution,[status(thm)],[c3,d19]) ).
cnf(d21,plain,
( 'c$ulessequals'('v$uxa','v$ux','tc$uset'('tc$uset'('t$ua')))
| 'c$uZorn$uOTFin$u$ulinear$u$ulemma1$u$u1'('v$uS','v$ux','t$ua') = 'v$ux' ),
inference(resolution,[status(thm)],[c1,d20]) ).
cnf(d22,plain,
( 'v$uxa' = 'v$ux'
| 'c$uZorn$uOTFin$u$ulinear$u$ulemma1$u$u1'('v$uS','v$ux','t$ua') = 'v$ux' ),
inference(resolution,[status(thm)],[d21,d2]) ).
cnf(d23,plain,
( 'v$uxa' = 'v$ux'
| 'c$ulessequals'('c$uZorn$uOsucc'('v$uS','v$ux','t$ua'),X0,'tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'(X0,'v$ux','tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'(X0,'c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'('v$ux','c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| 'v$ux' != 'v$ux' ),
inference(superposition,[status(thm)],[d22,c10]) ).
cnf(d24,plain,
( 'c$ulessequals'('c$uZorn$uOsucc'('v$uS','v$ux','t$ua'),X0,'tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'(X0,'v$ux','tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'(X0,'c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| 'v$uxa' = 'v$ux'
| 'v$ux' != 'v$ux' ),
inference(resolution,[status(thm)],[c0,d23]) ).
cnf(d25,plain,
( 'c$ulessequals'('c$uZorn$uOsucc'('v$uS','v$ux','t$ua'),X0,'tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'(X0,'v$ux','tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'(X0,'c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| 'v$uxa' = 'v$ux' ),
inference(equality_resolution,[status(thm)],[d24]) ).
cnf(d26,plain,
( 'c$uZorn$uOsucc'('v$uS','v$ux','t$ua') = 'v$uxa'
| 'c$ulessequals'('v$uxa','v$ux','tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'('v$uxa','c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| 'v$uxa' = 'v$ux' ),
inference(resolution,[status(thm)],[d25,d3]) ).
cnf(d27,plain,
( 'c$ulessequals'('v$uxa','v$ux','tc$uset'('tc$uset'('t$ua')))
| 'c$uZorn$uOsucc'('v$uS','v$ux','t$ua') = 'v$uxa'
| 'v$uxa' = 'v$ux' ),
inference(resolution,[status(thm)],[c1,d26]) ).
cnf(d28,plain,
( 'v$uxa' = 'v$ux'
| 'c$uZorn$uOsucc'('v$uS','v$ux','t$ua') = 'v$uxa'
| 'v$uxa' = 'v$ux' ),
inference(resolution,[status(thm)],[d27,d2]) ).
cnf(d29,plain,
( 'v$uxa' = 'v$ux'
| 'v$uxa' != 'v$uxa' ),
inference(superposition,[status(thm)],[d28,c3]) ).
cnf(d30,plain,
'v$uxa' = 'v$ux',
inference(equality_resolution,[status(thm)],[d29]) ).
cnf(d31,plain,
~ 'c$ulessequals'('c$uZorn$uOsucc'('v$uS','v$ux','t$ua'),'c$uZorn$uOsucc'('v$uS','v$ux','t$ua'),'tc$uset'('tc$uset'('t$ua'))),
inference(demodulation,[status(thm)],[c4,d30]) ).
cnf(d32,plain,
$false,
inference(resolution,[status(thm)],[c7,d31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET853-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n020.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 08:23:21 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.67/3.72 % SZS status Unsatisfiable for theBenchmark.p
% 14.67/3.72 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------