%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET857-2 : 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 08:33:26 AM UTC 2026
% Result : Unsatisfiable 44.46s 11.45s
% Output : CNFRefutation 44.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 14
% Syntax : Number of clauses : 77 ( 14 unt; 54 nHn; 67 RR)
% Number of literals : 302 ( 36 equ; 111 neg)
% Maximal clause size : 11 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 126 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Set_OsubsetD_0,axiom,
( 'c$uin'(X0,X3,X2)
| ~ 'c$ulessequals'(X1,X3,'tc$uset'(X2))
| ~ 'c$uin'(X0,X1,X2) ) ).
cnf(cls_Set_OsubsetI_0,axiom,
( 'c$ulessequals'(X0,X1,'tc$uset'(X2))
| 'c$uin'('c$uMain$uOsubsetI$u$u1'(X0,X1,X2),X0,X2) ) ).
cnf(cls_Set_OsubsetI_1,axiom,
( 'c$ulessequals'(X0,X1,'tc$uset'(X2))
| ~ 'c$uin'('c$uMain$uOsubsetI$u$u1'(X0,X1,X2),X1,X2) ) ).
cnf(cls_Zorn_OAbrial__axiom1_0,axiom,
'c$ulessequals'(X0,'c$uZorn$uOsucc'(X1,X0,X2),'tc$uset'('tc$uset'(X2))) ).
cnf(cls_Zorn_OTFin__linear__lemma1_0,axiom,
( 'c$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_conjecture_0,negated_conjecture,
'c$ulessequals'('v$uY','c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('tc$uset'('t$ua')))) ).
cnf(cls_conjecture_1,negated_conjecture,
'c$uin'('v$un','c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua'))) ).
cnf(cls_conjecture_3,negated_conjecture,
'c$uin'('v$ux','v$uY','tc$uset'('tc$uset'('t$ua'))) ).
cnf(cls_conjecture_4,negated_conjecture,
~ 'c$ulessequals'('v$ux','v$un','tc$uset'('tc$uset'('t$ua'))) ).
cnf(cls_conjecture_5,negated_conjecture,
~ 'c$ulessequals'('c$uZorn$uOsucc'('v$uS','v$un','t$ua'),'v$ux','tc$uset'('tc$uset'('t$ua'))) ).
cnf(cls_conjecture_6,negated_conjecture,
( ~ 'c$uin'(X1,'v$uY','tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'(X0,'c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| ~ 'c$ulessequals'(X0,X1,'tc$uset'('tc$uset'('t$ua')))
| X0 = X1
| 'c$ulessequals'('c$uZorn$uOsucc'('v$uS',X0,'t$ua'),X1,'tc$uset'('tc$uset'('t$ua'))) ) ).
cnf(c0,plain,
( 'c$uin'(X0,X3,X2)
| ~ 'c$ulessequals'(X1,X3,'tc$uset'(X2))
| ~ 'c$uin'(X0,X1,X2) ),
inference(clausification,[status(esa)],[cls_Set_OsubsetD_0]) ).
cnf(c1,plain,
( 'c$ulessequals'(X0,X1,'tc$uset'(X2))
| 'c$uin'('c$uMain$uOsubsetI$u$u1'(X0,X1,X2),X0,X2) ),
inference(clausification,[status(esa)],[cls_Set_OsubsetI_0]) ).
cnf(c2,plain,
( 'c$ulessequals'(X0,X1,'tc$uset'(X2))
| ~ 'c$uin'('c$uMain$uOsubsetI$u$u1'(X0,X1,X2),X1,X2) ),
inference(clausification,[status(esa)],[cls_Set_OsubsetI_1]) ).
cnf(c3,plain,
'c$ulessequals'(X0,'c$uZorn$uOsucc'(X1,X0,X2),'tc$uset'('tc$uset'(X2))),
inference(clausification,[status(esa)],[cls_Zorn_OAbrial__axiom1_0]) ).
cnf(c4,plain,
( ~ 'c$uin'(X3,'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$uset'(X2)))
| 'c$ulessequals'(X3,X1,'tc$uset'('tc$uset'(X2)))
| ~ 'c$uin'(X1,'c$uZorn$uOTFin'(X0,X2),'tc$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(c5,plain,
( 'c$ulessequals'('c$uZorn$uOTFin$u$ulinear$u$ulemma1$u$u1'(X1,X3,X2),X3,'tc$uset'('tc$uset'(X2)))
| 'c$ulessequals'('c$uZorn$uOsucc'(X1,X3,X2),X0,'tc$uset'('tc$uset'(X2)))
| ~ 'c$uin'(X3,'c$uZorn$uOTFin'(X1,X2),'tc$uset'('tc$uset'(X2)))
| 'c$ulessequals'(X0,X3,'tc$uset'('tc$uset'(X2)))
| ~ 'c$uin'(X0,'c$uZorn$uOTFin'(X1,X2),'tc$uset'('tc$uset'(X2))) ),
inference(clausification,[status(esa)],[cls_Zorn_OTFin__linear__lemma1_1]) ).
cnf(c6,plain,
( ~ 'c$uin'(X1,'c$uZorn$uOTFin'(X3,X2),'tc$uset'('tc$uset'(X2)))
| 'c$ulessequals'('c$uZorn$uOsucc'(X3,X1,X2),X0,'tc$uset'('tc$uset'(X2)))
| 'c$uZorn$uOTFin$u$ulinear$u$ulemma1$u$u1'(X3,X1,X2) != X1
| ~ 'c$uin'(X0,'c$uZorn$uOTFin'(X3,X2),'tc$uset'('tc$uset'(X2)))
| 'c$ulessequals'(X0,X1,'tc$uset'('tc$uset'(X2))) ),
inference(clausification,[status(esa)],[cls_Zorn_OTFin__linear__lemma1_2]) ).
cnf(c7,plain,
( ~ 'c$uin'(X3,'c$uZorn$uOTFin'(X0,X2),'tc$uset'('tc$uset'(X2)))
| ~ 'c$ulessequals'('c$uZorn$uOsucc'(X0,'c$uZorn$uOTFin$u$ulinear$u$ulemma1$u$u1'(X0,X1,X2),X2),X1,'tc$uset'('tc$uset'(X2)))
| 'c$ulessequals'(X3,X1,'tc$uset'('tc$uset'(X2)))
| ~ 'c$uin'(X1,'c$uZorn$uOTFin'(X0,X2),'tc$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_3]) ).
cnf(c8,plain,
'c$ulessequals'('v$uY','c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('tc$uset'('t$ua')))),
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(c9,plain,
'c$uin'('v$un','c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua'))),
inference(clausification,[status(esa)],[cls_conjecture_1]) ).
cnf(c10,plain,
'c$uin'('v$ux','v$uY','tc$uset'('tc$uset'('t$ua'))),
inference(clausification,[status(esa)],[cls_conjecture_3]) ).
cnf(c11,plain,
~ 'c$ulessequals'('v$ux','v$un','tc$uset'('tc$uset'('t$ua'))),
inference(clausification,[status(esa)],[cls_conjecture_4]) ).
cnf(c12,plain,
~ 'c$ulessequals'('c$uZorn$uOsucc'('v$uS','v$un','t$ua'),'v$ux','tc$uset'('tc$uset'('t$ua'))),
inference(clausification,[status(esa)],[cls_conjecture_5]) ).
cnf(c13,plain,
( 'c$ulessequals'('c$uZorn$uOsucc'('v$uS',X0,'t$ua'),X1,'tc$uset'('tc$uset'('t$ua')))
| ~ 'c$ulessequals'(X0,X1,'tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'(X0,'c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'(X1,'v$uY','tc$uset'('tc$uset'('t$ua')))
| X0 = X1 ),
inference(clausification,[status(esa)],[cls_conjecture_6]) ).
cnf(d0,plain,
( ~ 'c$ulessequals'('v$un','v$ux','tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'('v$ux','v$uY','tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'('v$un','c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| 'v$un' = 'v$ux' ),
inference(resolution,[status(thm)],[c13,c12]) ).
cnf(d1,plain,
( ~ 'c$ulessequals'('v$un','v$ux','tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'('v$un','c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| 'v$un' = 'v$ux' ),
inference(resolution,[status(thm)],[c10,d0]) ).
cnf(d2,plain,
( ~ 'c$ulessequals'('v$un','v$ux','tc$uset'('tc$uset'('t$ua')))
| 'v$un' = 'v$ux' ),
inference(resolution,[status(thm)],[c9,d1]) ).
cnf(d3,plain,
( ~ 'c$uin'(X0,X2,'tc$uset'(X3))
| 'c$uin'(X0,'c$uZorn$uOsucc'(X1,X2,X3),'tc$uset'(X3)) ),
inference(resolution,[status(thm)],[c3,c0]) ).
cnf(d4,plain,
( ~ 'c$uin'(X0,'v$uY','tc$uset'('tc$uset'('t$ua')))
| 'c$uin'(X0,'c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua'))) ),
inference(resolution,[status(thm)],[c8,c0]) ).
cnf(d5,plain,
( ~ 'c$uin'(X4,'c$uZorn$uOsucc'(X1,X0,X2),'tc$uset'(X2))
| 'c$uin'(X4,X3,'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$uset'(X2))) ),
inference(resolution,[status(thm)],[c4,c0]) ).
cnf(d6,plain,
( ~ 'c$uin'(X2,'v$uY','tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'(X1,X2,'tc$uset'('tc$uset'('t$ua')))
| 'c$uin'('c$uZorn$uOTFin$u$ulinear$u$ulemma1$u$u1'('v$uS',X2,'t$ua'),'c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'(X1,'c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'(X0,'c$uZorn$uOsucc'('v$uS',X2,'t$ua'),'tc$uset'('t$ua'))
| 'c$uin'(X0,X1,'tc$uset'('t$ua')) ),
inference(resolution,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
( ~ 'c$uin'(X2,X0,'tc$uset'('t$ua'))
| 'c$ulessequals'(X1,X0,'tc$uset'('tc$uset'('t$ua')))
| 'c$uin'('c$uZorn$uOTFin$u$ulinear$u$ulemma1$u$u1'('v$uS',X0,'t$ua'),'c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| 'c$uin'(X2,X1,'tc$uset'('t$ua'))
| ~ 'c$uin'(X1,'c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'(X0,'v$uY','tc$uset'('tc$uset'('t$ua'))) ),
inference(resolution,[status(thm)],[d6,d3]) ).
cnf(d8,plain,
( 'c$ulessequals'('v$un',X1,'tc$uset'('tc$uset'('t$ua')))
| 'c$uin'('c$uZorn$uOTFin$u$ulinear$u$ulemma1$u$u1'('v$uS',X1,'t$ua'),'c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'(X1,'v$uY','tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'(X0,X1,'tc$uset'('t$ua'))
| 'c$uin'(X0,'v$un','tc$uset'('t$ua')) ),
inference(resolution,[status(thm)],[d7,c9]) ).
cnf(d9,plain,
( 'c$ulessequals'('v$un','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,'v$un','tc$uset'('t$ua'))
| ~ 'c$uin'(X0,'v$ux','tc$uset'('t$ua')) ),
inference(resolution,[status(thm)],[d8,c10]) ).
cnf(d10,plain,
( 'c$ulessequals'('v$ux',X0,'tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'('v$un','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'('c$uMain$uOsubsetI$u$u1'('v$ux',X0,'tc$uset'('t$ua')),'v$un','tc$uset'('t$ua')) ),
inference(resolution,[status(thm)],[d9,c1]) ).
cnf(d11,plain,
( 'c$ulessequals'('v$ux','v$un','tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'('v$ux','v$un','tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'('v$un','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$ua'))) ),
inference(resolution,[status(thm)],[d10,c2]) ).
cnf(d12,plain,
( 'c$ulessequals'('v$un','v$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)],[c11,d11]) ).
cnf(d13,plain,
( 'c$ulessequals'('c$uZorn$uOsucc'('v$uS',X0,'t$ua'),X1,'tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'(X1,X0,'tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'(X0,'c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'(X1,'c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| ~ 'c$ulessequals'('c$uZorn$uOTFin$u$ulinear$u$ulemma1$u$u1'('v$uS',X0,'t$ua'),X0,'tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'(X0,'v$uY','tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'('c$uZorn$uOTFin$u$ulinear$u$ulemma1$u$u1'('v$uS',X0,'t$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',X0,'t$ua') = X0 ),
inference(resolution,[status(thm)],[c13,c7]) ).
cnf(d14,plain,
( 'c$ulessequals'('c$uZorn$uOsucc'('v$uS',X0,'t$ua'),X2,'tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'(X2,X0,'tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'(X2,'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$ua')))
| ~ 'c$ulessequals'('c$uZorn$uOTFin$u$ulinear$u$ulemma1$u$u1'('v$uS',X0,'t$ua'),X0,'tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'('c$uZorn$uOsucc'('v$uS',X0,'t$ua'),X1,'tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'(X1,X0,'tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'(X0,'v$uY','tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'(X0,'c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'(X1,'c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| 'c$uZorn$uOTFin$u$ulinear$u$ulemma1$u$u1'('v$uS',X0,'t$ua') = X0 ),
inference(resolution,[status(thm)],[d13,c4]) ).
cnf(d15,plain,
( ~ 'c$uin'(X4,'c$uZorn$uOsucc'(X1,X3,X2),'tc$uset'(X2))
| 'c$uin'(X4,X0,'tc$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$uin'(X3,'c$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)],[c5,c0]) ).
cnf(d16,plain,
( 'c$ulessequals'('c$uZorn$uOTFin$u$ulinear$u$ulemma1$u$u1'('v$uS',X1,'t$ua'),X1,'tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'('v$un',X1,'tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'(X1,'c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'(X0,'c$uZorn$uOsucc'('v$uS',X1,'t$ua'),'tc$uset'('t$ua'))
| 'c$uin'(X0,'v$un','tc$uset'('t$ua')) ),
inference(resolution,[status(thm)],[d15,c9]) ).
cnf(d17,plain,
( ~ 'c$uin'(X1,X0,'tc$uset'('t$ua'))
| 'c$ulessequals'('v$un',X0,'tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'('c$uZorn$uOTFin$u$ulinear$u$ulemma1$u$u1'('v$uS',X0,'t$ua'),X0,'tc$uset'('tc$uset'('t$ua')))
| 'c$uin'(X1,'v$un','tc$uset'('t$ua'))
| ~ 'c$uin'(X0,'c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua'))) ),
inference(resolution,[status(thm)],[d16,d3]) ).
cnf(d18,plain,
( ~ 'c$uin'(X1,'v$uY','tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'('v$un',X1,'tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'('c$uZorn$uOTFin$u$ulinear$u$ulemma1$u$u1'('v$uS',X1,'t$ua'),X1,'tc$uset'('tc$uset'('t$ua')))
| 'c$uin'(X0,'v$un','tc$uset'('t$ua'))
| ~ 'c$uin'(X0,X1,'tc$uset'('t$ua')) ),
inference(resolution,[status(thm)],[d17,d4]) ).
cnf(d19,plain,
( 'c$ulessequals'('v$un','v$ux','tc$uset'('tc$uset'('t$ua')))
| 'c$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'(X0,'v$un','tc$uset'('t$ua'))
| ~ 'c$uin'(X0,'v$ux','tc$uset'('t$ua')) ),
inference(resolution,[status(thm)],[d18,c10]) ).
cnf(d20,plain,
( 'c$ulessequals'('v$ux',X0,'tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'('v$un','v$ux','tc$uset'('tc$uset'('t$ua')))
| '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$uin'('c$uMain$uOsubsetI$u$u1'('v$ux',X0,'tc$uset'('t$ua')),'v$un','tc$uset'('t$ua')) ),
inference(resolution,[status(thm)],[d19,c1]) ).
cnf(d21,plain,
( 'c$ulessequals'('v$ux','v$un','tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'('v$ux','v$un','tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'('v$un','v$ux','tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'('c$uZorn$uOTFin$u$ulinear$u$ulemma1$u$u1'('v$uS','v$ux','t$ua'),'v$ux','tc$uset'('tc$uset'('t$ua'))) ),
inference(resolution,[status(thm)],[d20,c2]) ).
cnf(d22,plain,
( 'c$ulessequals'('v$un','v$ux','tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'('c$uZorn$uOTFin$u$ulinear$u$ulemma1$u$u1'('v$uS','v$ux','t$ua'),'v$ux','tc$uset'('tc$uset'('t$ua'))) ),
inference(resolution,[status(thm)],[c11,d21]) ).
cnf(d23,plain,
( 'c$ulessequals'('c$uZorn$uOsucc'('v$uS','v$ux','t$ua'),X1,'tc$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'(X1,'v$ux','tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'(X0,'v$ux','tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'('v$ux','v$uY','tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'('v$ux','c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'(X1,'c$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'
| 'c$ulessequals'('v$un','v$ux','tc$uset'('tc$uset'('t$ua'))) ),
inference(resolution,[status(thm)],[d22,d14]) ).
cnf(d24,plain,
( 'c$ulessequals'('v$un','v$ux','tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'('c$uZorn$uOsucc'('v$uS','v$ux','t$ua'),X1,'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$ulessequals'(X1,'v$ux','tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'(X0,'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'(X1,'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$ux' ),
inference(resolution,[status(thm)],[c10,d23]) ).
cnf(d25,plain,
( 'c$ulessequals'('v$un','v$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$ua')))
| 'c$ulessequals'(X0,'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'(X0,'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$ux' ),
inference(factoring,[status(thm)],[d24]) ).
cnf(d26,plain,
( ~ 'c$uin'(X1,'c$uZorn$uOsucc'('v$uS','v$ux','t$ua'),'tc$uset'('t$ua'))
| 'c$uin'(X1,X0,'tc$uset'('t$ua'))
| 'c$ulessequals'('v$un','v$ux','tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'(X0,'v$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$uin'(X0,'c$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)],[d25,c0]) ).
cnf(d27,plain,
( ~ 'c$uin'('v$ux','v$uY','tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'('v$un','v$ux','tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'(X1,'v$ux','tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'(X1,'c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'(X0,'c$uZorn$uOsucc'('v$uS','v$ux','t$ua'),'tc$uset'('t$ua'))
| 'c$uin'(X0,X1,'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)],[d26,d4]) ).
cnf(d28,plain,
( 'c$ulessequals'('v$un','v$ux','tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'(X0,'v$ux','tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'(X1,'c$uZorn$uOsucc'('v$uS','v$ux','t$ua'),'tc$uset'('t$ua'))
| 'c$uin'(X1,X0,'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)],[c10,d27]) ).
cnf(d29,plain,
( 'c$ulessequals'('v$un','v$ux','tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'('v$un','v$ux','tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'(X0,'c$uZorn$uOsucc'('v$uS','v$ux','t$ua'),'tc$uset'('t$ua'))
| 'c$uin'(X0,'v$un','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)],[d28,c9]) ).
cnf(d30,plain,
( ~ 'c$uin'(X0,'v$ux','tc$uset'('t$ua'))
| 'c$ulessequals'('v$un','v$ux','tc$uset'('tc$uset'('t$ua')))
| 'c$uin'(X0,'v$un','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)],[d29,d3]) ).
cnf(d31,plain,
( 'c$ulessequals'('v$ux',X0,'tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'('v$un','v$ux','tc$uset'('tc$uset'('t$ua')))
| 'c$uin'('c$uMain$uOsubsetI$u$u1'('v$ux',X0,'tc$uset'('t$ua')),'v$un','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)],[d30,c1]) ).
cnf(d32,plain,
( 'c$ulessequals'('v$ux','v$un','tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'('v$ux','v$un','tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'('v$un','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)],[d31,c2]) ).
cnf(d33,plain,
( 'c$ulessequals'('v$un','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)],[c11,d32]) ).
cnf(d34,plain,
( 'v$un' = 'v$ux'
| 'c$uZorn$uOTFin$u$ulinear$u$ulemma1$u$u1'('v$uS','v$ux','t$ua') = 'v$ux' ),
inference(resolution,[status(thm)],[d33,d2]) ).
cnf(d35,plain,
( 'v$un' = 'v$ux'
| 'c$ulessequals'('v$un','v$ux','tc$uset'('tc$uset'('t$ua')))
| 'c$uin'('v$ux','c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua'))) ),
inference(superposition,[status(thm)],[d34,d12]) ).
cnf(d36,plain,
( 'v$un' = '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'('v$ux','c$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')))
| 'v$ux' != 'v$ux' ),
inference(superposition,[status(thm)],[d34,c6]) ).
cnf(d37,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$uin'('v$ux','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$ua')))
| 'v$un' = 'v$ux' ),
inference(equality_resolution,[status(thm)],[d36]) ).
cnf(d38,plain,
( ~ 'c$uin'(X1,'c$uZorn$uOsucc'('v$uS','v$ux','t$ua'),'tc$uset'('t$ua'))
| 'c$uin'(X1,X0,'tc$uset'('t$ua'))
| 'c$ulessequals'(X0,'v$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$uin'(X0,'c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| 'v$un' = 'v$ux' ),
inference(resolution,[status(thm)],[d37,c0]) ).
cnf(d39,plain,
( 'c$ulessequals'('v$un','v$ux','tc$uset'('tc$uset'('t$ua')))
| 'v$un' = 'v$ux'
| 'c$ulessequals'(X1,'v$ux','tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'(X1,'c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'(X0,'c$uZorn$uOsucc'('v$uS','v$ux','t$ua'),'tc$uset'('t$ua'))
| 'c$uin'(X0,X1,'tc$uset'('t$ua'))
| 'v$un' = 'v$ux' ),
inference(resolution,[status(thm)],[d38,d35]) ).
cnf(d40,plain,
( ~ 'c$uin'(X1,'v$ux','tc$uset'('t$ua'))
| 'c$ulessequals'('v$un','v$ux','tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'(X0,'v$ux','tc$uset'('tc$uset'('t$ua')))
| 'c$uin'(X1,X0,'tc$uset'('t$ua'))
| ~ 'c$uin'(X0,'c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| 'v$un' = 'v$ux' ),
inference(resolution,[status(thm)],[d39,d3]) ).
cnf(d41,plain,
( 'c$ulessequals'('v$un','v$ux','tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'('v$un','v$ux','tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'(X0,'v$ux','tc$uset'('t$ua'))
| 'c$uin'(X0,'v$un','tc$uset'('t$ua'))
| 'v$un' = 'v$ux' ),
inference(resolution,[status(thm)],[d40,c9]) ).
cnf(d42,plain,
( 'c$ulessequals'('v$ux',X0,'tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'('v$un','v$ux','tc$uset'('tc$uset'('t$ua')))
| 'c$uin'('c$uMain$uOsubsetI$u$u1'('v$ux',X0,'tc$uset'('t$ua')),'v$un','tc$uset'('t$ua'))
| 'v$un' = 'v$ux' ),
inference(resolution,[status(thm)],[d41,c1]) ).
cnf(d43,plain,
( 'c$ulessequals'('v$ux','v$un','tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'('v$ux','v$un','tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'('v$un','v$ux','tc$uset'('tc$uset'('t$ua')))
| 'v$un' = 'v$ux' ),
inference(resolution,[status(thm)],[d42,c2]) ).
cnf(d44,plain,
( 'c$ulessequals'('v$un','v$ux','tc$uset'('tc$uset'('t$ua')))
| 'v$un' = 'v$ux' ),
inference(resolution,[status(thm)],[c11,d43]) ).
cnf(d45,plain,
( 'v$un' = 'v$ux'
| 'v$un' = 'v$ux' ),
inference(resolution,[status(thm)],[d44,d2]) ).
cnf(d46,plain,
~ 'c$ulessequals'('v$un','v$un','tc$uset'('tc$uset'('t$ua'))),
inference(demodulation,[status(thm)],[c11,d45]) ).
cnf(d47,plain,
( 'c$ulessequals'(X0,X0,'tc$uset'(X1))
| 'c$ulessequals'(X0,X0,'tc$uset'(X1)) ),
inference(resolution,[status(thm)],[c2,c1]) ).
cnf(d48,plain,
$false,
inference(resolution,[status(thm)],[d47,d46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET857-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.94 % Computer : n006.cluster.edu
% 0.09/5.94 % Model : x86_64 x86_64
% 0.09/5.94 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.94 % Memory : 8046.5625MB
% 0.09/5.94 % OS : Linux 6.8.0-71-generic
% 0.09/5.94 % CPULimit : 300
% 0.09/5.94 % WCLimit : 300
% 0.09/5.94 % DateTime : Sat Sep 26 08:21:48 UTC 2026
% 0.09/5.94 % CPUTime :
% 0.09/5.94 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 44.46/11.45 % SZS status Unsatisfiable for theBenchmark.p
% 44.46/11.45 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------