%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET831-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 08:33:20 AM UTC 2026
% Result : Unsatisfiable 63.00s 9.82s
% Output : CNFRefutation 63.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 13
% Syntax : Number of clauses : 87 ( 23 unt; 34 nHn; 67 RR)
% Number of literals : 190 ( 40 equ; 69 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 130 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
( 'c$ulessequals'('v$uX','v$uY','tc$uset'('t$ua'))
| 'v$uX' = 'c$uinter'('v$uY','v$uZ','t$ua') ) ).
cnf(cls_conjecture_1,negated_conjecture,
( 'c$ulessequals'('v$uX','v$uZ','tc$uset'('t$ua'))
| 'v$uX' = 'c$uinter'('v$uY','v$uZ','t$ua') ) ).
cnf(cls_conjecture_2,negated_conjecture,
( 'v$uX' != 'c$uinter'('v$uY','v$uZ','t$ua')
| ~ 'c$ulessequals'('v$uX','v$uY','tc$uset'('t$ua'))
| ~ 'c$ulessequals'('v$uX','v$uZ','tc$uset'('t$ua'))
| 'c$ulessequals'('v$ux','v$uY','tc$uset'('t$ua')) ) ).
cnf(cls_conjecture_3,negated_conjecture,
( 'v$uX' != 'c$uinter'('v$uY','v$uZ','t$ua')
| ~ 'c$ulessequals'('v$uX','v$uY','tc$uset'('t$ua'))
| ~ 'c$ulessequals'('v$uX','v$uZ','tc$uset'('t$ua'))
| 'c$ulessequals'('v$ux','v$uZ','tc$uset'('t$ua')) ) ).
cnf(cls_conjecture_4,negated_conjecture,
( 'v$uX' != 'c$uinter'('v$uY','v$uZ','t$ua')
| ~ 'c$ulessequals'('v$uX','v$uY','tc$uset'('t$ua'))
| ~ 'c$ulessequals'('v$uX','v$uZ','tc$uset'('t$ua'))
| ~ 'c$ulessequals'('v$ux','v$uX','tc$uset'('t$ua')) ) ).
cnf(cls_conjecture_5,negated_conjecture,
( ~ 'c$ulessequals'(X0,'v$uY','tc$uset'('t$ua'))
| ~ 'c$ulessequals'(X0,'v$uZ','tc$uset'('t$ua'))
| 'c$ulessequals'(X0,'v$uX','tc$uset'('t$ua'))
| 'v$uX' = 'c$uinter'('v$uY','v$uZ','t$ua') ) ).
cnf(cls_Set_OIntE_0,axiom,
( 'c$uin'(X0,X2,X3)
| ~ 'c$uin'(X0,'c$uinter'(X1,X2,X3),X3) ) ).
cnf(cls_Set_OIntE_1,axiom,
( 'c$uin'(X0,X1,X3)
| ~ 'c$uin'(X0,'c$uinter'(X1,X2,X3),X3) ) ).
cnf(cls_Set_OIntI_0,axiom,
( 'c$uin'(X0,'c$uinter'(X3,X1,X2),X2)
| ~ 'c$uin'(X0,X3,X2)
| ~ 'c$uin'(X0,X1,X2) ) ).
cnf(cls_Set_OsubsetD_0,axiom,
( 'c$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$u1'(X0,X1,X2),X1,X2) ) ).
cnf(cls_Set_Osubset__antisym_0,axiom,
( X1 = X0
| ~ 'c$ulessequals'(X1,X0,'tc$uset'(X2))
| ~ 'c$ulessequals'(X0,X1,'tc$uset'(X2)) ) ).
cnf(c0,plain,
( 'c$ulessequals'('v$uX','v$uY','tc$uset'('t$ua'))
| 'c$uinter'('v$uY','v$uZ','t$ua') = 'v$uX' ),
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(c1,plain,
( 'c$ulessequals'('v$uX','v$uZ','tc$uset'('t$ua'))
| 'c$uinter'('v$uY','v$uZ','t$ua') = 'v$uX' ),
inference(clausification,[status(esa)],[cls_conjecture_1]) ).
cnf(c2,plain,
( 'c$uinter'('v$uY','v$uZ','t$ua') != 'v$uX'
| ~ 'c$ulessequals'('v$uX','v$uZ','tc$uset'('t$ua'))
| 'c$ulessequals'('v$ux','v$uY','tc$uset'('t$ua'))
| ~ 'c$ulessequals'('v$uX','v$uY','tc$uset'('t$ua')) ),
inference(clausification,[status(esa)],[cls_conjecture_2]) ).
cnf(c3,plain,
( 'c$uinter'('v$uY','v$uZ','t$ua') != 'v$uX'
| ~ 'c$ulessequals'('v$uX','v$uZ','tc$uset'('t$ua'))
| 'c$ulessequals'('v$ux','v$uZ','tc$uset'('t$ua'))
| ~ 'c$ulessequals'('v$uX','v$uY','tc$uset'('t$ua')) ),
inference(clausification,[status(esa)],[cls_conjecture_3]) ).
cnf(c4,plain,
( 'c$uinter'('v$uY','v$uZ','t$ua') != 'v$uX'
| ~ 'c$ulessequals'('v$uX','v$uZ','tc$uset'('t$ua'))
| ~ 'c$ulessequals'('v$ux','v$uX','tc$uset'('t$ua'))
| ~ 'c$ulessequals'('v$uX','v$uY','tc$uset'('t$ua')) ),
inference(clausification,[status(esa)],[cls_conjecture_4]) ).
cnf(c5,plain,
( ~ 'c$ulessequals'(X0,'v$uY','tc$uset'('t$ua'))
| 'c$ulessequals'(X0,'v$uX','tc$uset'('t$ua'))
| 'c$uinter'('v$uY','v$uZ','t$ua') = 'v$uX'
| ~ 'c$ulessequals'(X0,'v$uZ','tc$uset'('t$ua')) ),
inference(clausification,[status(esa)],[cls_conjecture_5]) ).
cnf(c6,plain,
( 'c$uin'(X0,X2,X3)
| ~ 'c$uin'(X0,'c$uinter'(X1,X2,X3),X3) ),
inference(clausification,[status(esa)],[cls_Set_OIntE_0]) ).
cnf(c7,plain,
( 'c$uin'(X0,X1,X3)
| ~ 'c$uin'(X0,'c$uinter'(X1,X2,X3),X3) ),
inference(clausification,[status(esa)],[cls_Set_OIntE_1]) ).
cnf(c8,plain,
( 'c$uin'(X0,'c$uinter'(X1,X3,X2),X2)
| ~ 'c$uin'(X0,X3,X2)
| ~ 'c$uin'(X0,X1,X2) ),
inference(clausification,[status(esa)],[cls_Set_OIntI_0]) ).
cnf(c9,plain,
( 'c$uin'(X3,X1,X2)
| ~ 'c$uin'(X3,X0,X2)
| ~ 'c$ulessequals'(X0,X1,'tc$uset'(X2)) ),
inference(clausification,[status(esa)],[cls_Set_OsubsetD_0]) ).
cnf(c10,plain,
( 'c$ulessequals'(X0,X1,'tc$uset'(X2))
| 'c$uin'('c$uMain$uOsubsetI$u$u1'(X0,X1,X2),X0,X2) ),
inference(clausification,[status(esa)],[cls_Set_OsubsetI_0]) ).
cnf(c11,plain,
( 'c$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(c12,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(d0,plain,
( 'c$uin'('c$uMain$uOsubsetI$u$u1'('c$uinter'(X0,X1,X2),X3,X2),X1,X2)
| 'c$ulessequals'('c$uinter'(X0,X1,X2),X3,'tc$uset'(X2)) ),
inference(resolution,[status(thm)],[c10,c6]) ).
cnf(d1,plain,
( 'c$ulessequals'('c$uinter'(X0,X1,X2),X1,'tc$uset'(X2))
| 'c$ulessequals'('c$uinter'(X0,X1,X2),X1,'tc$uset'(X2)) ),
inference(resolution,[status(thm)],[d0,c11]) ).
cnf(d2,plain,
( ~ 'c$ulessequals'(X1,'c$uinter'(X0,X1,X2),'tc$uset'(X2))
| 'c$uinter'(X0,X1,X2) = X1 ),
inference(resolution,[status(thm)],[d1,c12]) ).
cnf(d3,plain,
( 'c$uin'('c$uMain$uOsubsetI$u$u1'('c$uinter'(X0,X1,X2),X3,X2),X0,X2)
| 'c$ulessequals'('c$uinter'(X0,X1,X2),X3,'tc$uset'(X2)) ),
inference(resolution,[status(thm)],[c10,c7]) ).
cnf(d4,plain,
( 'c$ulessequals'(X0,'c$uinter'(X1,X2,X3),'tc$uset'(X3))
| ~ 'c$uin'('c$uMain$uOsubsetI$u$u1'(X0,'c$uinter'(X1,X2,X3),X3),X2,X3)
| ~ 'c$uin'('c$uMain$uOsubsetI$u$u1'(X0,'c$uinter'(X1,X2,X3),X3),X1,X3) ),
inference(resolution,[status(thm)],[c8,c11]) ).
cnf(d5,plain,
( 'c$ulessequals'('c$uinter'(X0,X1,X2),'c$uinter'(X1,X3,X2),'tc$uset'(X2))
| ~ 'c$uin'('c$uMain$uOsubsetI$u$u1'('c$uinter'(X0,X1,X2),'c$uinter'(X1,X3,X2),X2),X3,X2)
| 'c$ulessequals'('c$uinter'(X0,X1,X2),'c$uinter'(X1,X3,X2),'tc$uset'(X2)) ),
inference(resolution,[status(thm)],[d4,d0]) ).
cnf(d6,plain,
( 'c$ulessequals'('c$uinter'(X0,X1,X2),'c$uinter'(X1,X0,X2),'tc$uset'(X2))
| 'c$ulessequals'('c$uinter'(X0,X1,X2),'c$uinter'(X1,X0,X2),'tc$uset'(X2)) ),
inference(resolution,[status(thm)],[d5,d3]) ).
cnf(d7,plain,
( ~ 'c$ulessequals'('c$uinter'(X1,X0,X2),'c$uinter'(X0,X1,X2),'tc$uset'(X2))
| 'c$uinter'(X0,X1,X2) = 'c$uinter'(X1,X0,X2) ),
inference(resolution,[status(thm)],[d6,c12]) ).
cnf(d8,plain,
'c$uinter'(X0,X1,X2) = 'c$uinter'(X1,X0,X2),
inference(resolution,[status(thm)],[d6,d7]) ).
cnf(d9,plain,
( 'c$ulessequals'(X0,'c$uinter'(X0,X1,X2),'tc$uset'(X2))
| ~ 'c$uin'('c$uMain$uOsubsetI$u$u1'(X0,'c$uinter'(X0,X1,X2),X2),X1,X2)
| 'c$ulessequals'(X0,'c$uinter'(X0,X1,X2),'tc$uset'(X2)) ),
inference(resolution,[status(thm)],[d4,c10]) ).
cnf(d10,plain,
( 'c$uinter'('v$uY','v$uZ','t$ua') = 'v$uX'
| ~ 'c$uin'(X0,'v$uX','t$ua')
| 'c$uin'(X0,'v$uZ','t$ua') ),
inference(resolution,[status(thm)],[c9,c1]) ).
cnf(d11,plain,
( 'c$ulessequals'('v$uX',X0,'tc$uset'('t$ua'))
| 'c$uin'('c$uMain$uOsubsetI$u$u1'('v$uX',X0,'t$ua'),'v$uZ','t$ua')
| 'c$uinter'('v$uY','v$uZ','t$ua') = 'v$uX' ),
inference(resolution,[status(thm)],[d10,c10]) ).
cnf(d12,plain,
( 'c$uinter'('v$uY','v$uZ','t$ua') = 'v$uX'
| ~ 'c$uin'(X0,'v$uX','t$ua')
| 'c$uin'(X0,'v$uY','t$ua') ),
inference(resolution,[status(thm)],[c9,c0]) ).
cnf(d13,plain,
( 'c$ulessequals'('v$uX',X0,'tc$uset'('t$ua'))
| 'c$uin'('c$uMain$uOsubsetI$u$u1'('v$uX',X0,'t$ua'),'v$uY','t$ua')
| 'c$uinter'('v$uY','v$uZ','t$ua') = 'v$uX' ),
inference(resolution,[status(thm)],[d12,c10]) ).
cnf(d14,plain,
( 'c$ulessequals'('v$uX','c$uinter'('v$uY',X0,'t$ua'),'tc$uset'('t$ua'))
| 'c$uinter'('v$uY','v$uZ','t$ua') = 'v$uX'
| ~ 'c$uin'('c$uMain$uOsubsetI$u$u1'('v$uX','c$uinter'('v$uY',X0,'t$ua'),'t$ua'),X0,'t$ua')
| 'c$ulessequals'('v$uX','c$uinter'('v$uY',X0,'t$ua'),'tc$uset'('t$ua')) ),
inference(resolution,[status(thm)],[d4,d13]) ).
cnf(d15,plain,
( 'c$ulessequals'('v$uX','c$uinter'('v$uY','v$uZ','t$ua'),'tc$uset'('t$ua'))
| 'c$uinter'('v$uY','v$uZ','t$ua') = 'v$uX'
| 'c$ulessequals'('v$uX','c$uinter'('v$uY','v$uZ','t$ua'),'tc$uset'('t$ua'))
| 'c$uinter'('v$uY','v$uZ','t$ua') = 'v$uX' ),
inference(resolution,[status(thm)],[d14,d11]) ).
cnf(d16,plain,
( 'c$ulessequals'('c$uinter'(X0,X1,X2),X0,'tc$uset'(X2))
| 'c$ulessequals'('c$uinter'(X0,X1,X2),X0,'tc$uset'(X2)) ),
inference(resolution,[status(thm)],[d3,c11]) ).
cnf(d17,plain,
( ~ 'c$ulessequals'('c$uinter'(X0,'v$uZ','t$ua'),'v$uY','tc$uset'('t$ua'))
| 'c$ulessequals'('c$uinter'(X0,'v$uZ','t$ua'),'v$uX','tc$uset'('t$ua'))
| 'c$uinter'('v$uY','v$uZ','t$ua') = 'v$uX' ),
inference(resolution,[status(thm)],[d1,c5]) ).
cnf(d18,plain,
( 'c$ulessequals'('c$uinter'('v$uY','v$uZ','t$ua'),'v$uX','tc$uset'('t$ua'))
| 'c$uinter'('v$uY','v$uZ','t$ua') = 'v$uX' ),
inference(resolution,[status(thm)],[d17,d16]) ).
cnf(d19,plain,
( ~ 'c$ulessequals'('v$uX','c$uinter'('v$uY','v$uZ','t$ua'),'tc$uset'('t$ua'))
| 'c$uinter'('v$uY','v$uZ','t$ua') = 'v$uX'
| 'c$uinter'('v$uY','v$uZ','t$ua') = 'v$uX' ),
inference(resolution,[status(thm)],[d18,c12]) ).
cnf(d20,plain,
( 'c$uinter'('v$uY','v$uZ','t$ua') = 'v$uX'
| 'c$uinter'('v$uY','v$uZ','t$ua') = 'v$uX' ),
inference(resolution,[status(thm)],[d19,d15]) ).
cnf(d21,plain,
( 'c$ulessequals'('v$ux','v$uZ','tc$uset'('t$ua'))
| ~ 'c$ulessequals'('v$uX','v$uZ','tc$uset'('t$ua'))
| ~ 'c$ulessequals'('v$uX','v$uY','tc$uset'('t$ua')) ),
inference(resolution,[status(thm)],[d20,c3]) ).
cnf(d22,plain,
'c$ulessequals'('v$uX','v$uY','tc$uset'('t$ua')),
inference(superposition,[status(thm)],[d20,d16]) ).
cnf(d23,plain,
( 'c$ulessequals'('v$ux','v$uZ','tc$uset'('t$ua'))
| ~ 'c$ulessequals'('v$uX','v$uZ','tc$uset'('t$ua')) ),
inference(resolution,[status(thm)],[d22,d21]) ).
cnf(d24,plain,
'c$ulessequals'('v$uX','v$uZ','tc$uset'('t$ua')),
inference(superposition,[status(thm)],[d20,d1]) ).
cnf(d25,plain,
'c$ulessequals'('v$ux','v$uZ','tc$uset'('t$ua')),
inference(resolution,[status(thm)],[d24,d23]) ).
cnf(d26,plain,
( ~ 'c$uin'(X0,'v$ux','t$ua')
| 'c$uin'(X0,'v$uZ','t$ua') ),
inference(resolution,[status(thm)],[d25,c9]) ).
cnf(d27,plain,
( 'c$ulessequals'('v$ux',X0,'tc$uset'('t$ua'))
| 'c$uin'('c$uMain$uOsubsetI$u$u1'('v$ux',X0,'t$ua'),'v$uZ','t$ua') ),
inference(resolution,[status(thm)],[d26,c10]) ).
cnf(d28,plain,
( 'c$ulessequals'('v$ux','c$uinter'('v$ux','v$uZ','t$ua'),'tc$uset'('t$ua'))
| 'c$ulessequals'('v$ux','c$uinter'('v$ux','v$uZ','t$ua'),'tc$uset'('t$ua')) ),
inference(resolution,[status(thm)],[d27,d9]) ).
cnf(d29,plain,
'c$ulessequals'('v$ux','c$uinter'('v$uZ','v$ux','t$ua'),'tc$uset'('t$ua')),
inference(demodulation,[status(thm)],[d28,d8]) ).
cnf(d30,plain,
'c$uinter'('v$uZ','v$ux','t$ua') = 'v$ux',
inference(resolution,[status(thm)],[d29,d2]) ).
cnf(d31,plain,
( 'c$uin'('c$uMain$uOsubsetI$u$u1'('c$uinter'('c$uinter'(X0,X1,X2),X3,X2),X4,X2),X0,X2)
| 'c$ulessequals'('c$uinter'('c$uinter'(X0,X1,X2),X3,X2),X4,'tc$uset'(X2)) ),
inference(resolution,[status(thm)],[d3,c7]) ).
cnf(d32,plain,
( ~ 'c$uin'('c$uMain$uOsubsetI$u$u1'('c$uinter'('c$uinter'(X0,X1,X2),X3,X2),'c$uinter'(X0,X4,X2),X2),X4,X2)
| 'c$ulessequals'('c$uinter'('c$uinter'(X0,X1,X2),X3,X2),'c$uinter'(X0,X4,X2),'tc$uset'(X2))
| 'c$ulessequals'('c$uinter'('c$uinter'(X0,X1,X2),X3,X2),'c$uinter'(X0,X4,X2),'tc$uset'(X2)) ),
inference(resolution,[status(thm)],[d31,d4]) ).
cnf(d33,plain,
( 'c$ulessequals'('c$uinter'('c$uinter'(X0,X1,X2),X3,X2),'c$uinter'(X0,X3,X2),'tc$uset'(X2))
| 'c$ulessequals'('c$uinter'('c$uinter'(X0,X1,X2),X3,X2),'c$uinter'(X0,X3,X2),'tc$uset'(X2)) ),
inference(resolution,[status(thm)],[d32,d0]) ).
cnf(d34,plain,
( ~ 'c$ulessequals'(X0,'c$uinter'(X0,X1,X2),'tc$uset'(X2))
| 'c$uinter'(X0,X1,X2) = X0 ),
inference(resolution,[status(thm)],[d16,c12]) ).
cnf(d35,plain,
( 'c$ulessequals'('c$uinter'(X0,X1,X2),'c$uinter'('c$uinter'(X0,X1,X2),X1,X2),'tc$uset'(X2))
| 'c$ulessequals'('c$uinter'(X0,X1,X2),'c$uinter'('c$uinter'(X0,X1,X2),X1,X2),'tc$uset'(X2)) ),
inference(resolution,[status(thm)],[d9,d0]) ).
cnf(d36,plain,
'c$uinter'('c$uinter'(X0,X1,X2),X1,X2) = 'c$uinter'(X0,X1,X2),
inference(resolution,[status(thm)],[d35,d34]) ).
cnf(d37,plain,
'c$uinter'('v$uX','v$uZ','t$ua') = 'c$uinter'('v$uY','v$uZ','t$ua'),
inference(superposition,[status(thm)],[d20,d36]) ).
cnf(d38,plain,
'c$uinter'('v$uX','v$uZ','t$ua') = 'v$uX',
inference(demodulation,[status(thm)],[d37,d20]) ).
cnf(d39,plain,
'c$ulessequals'('v$uX','c$uinter'('v$uZ','v$uX','t$ua'),'tc$uset'('t$ua')),
inference(superposition,[status(thm)],[d38,d6]) ).
cnf(d40,plain,
'c$uinter'('v$uZ','v$uX','t$ua') = 'v$uX',
inference(resolution,[status(thm)],[d39,d2]) ).
cnf(d41,plain,
( 'c$ulessequals'('c$uinter'(X0,X1,X2),'c$uinter'(X1,'c$uinter'(X0,X1,X2),X2),'tc$uset'(X2))
| 'c$ulessequals'('c$uinter'(X0,X1,X2),'c$uinter'(X1,'c$uinter'(X0,X1,X2),X2),'tc$uset'(X2)) ),
inference(resolution,[status(thm)],[d5,c10]) ).
cnf(d42,plain,
'c$uinter'(X0,'c$uinter'(X1,X0,X2),X2) = 'c$uinter'(X1,X0,X2),
inference(resolution,[status(thm)],[d41,d2]) ).
cnf(d43,plain,
'c$uinter'('v$uZ','v$uX','t$ua') = 'c$uinter'('v$uY','v$uZ','t$ua'),
inference(superposition,[status(thm)],[d20,d42]) ).
cnf(d44,plain,
'v$uX' = 'c$uinter'('v$uY','v$uZ','t$ua'),
inference(demodulation,[status(thm)],[d43,d40]) ).
cnf(d45,plain,
'c$ulessequals'('c$uinter'('c$uinter'('v$uY',X0,'t$ua'),'v$uZ','t$ua'),'v$uX','tc$uset'('t$ua')),
inference(superposition,[status(thm)],[d44,d33]) ).
cnf(d46,plain,
'c$ulessequals'('c$uinter'('v$uZ','c$uinter'('v$uY',X0,'t$ua'),'t$ua'),'v$uX','tc$uset'('t$ua')),
inference(demodulation,[status(thm)],[d45,d8]) ).
cnf(d47,plain,
( 'c$ulessequals'('v$ux','v$uY','tc$uset'('t$ua'))
| ~ 'c$ulessequals'('v$uX','v$uZ','tc$uset'('t$ua'))
| ~ 'c$ulessequals'('v$uX','v$uY','tc$uset'('t$ua')) ),
inference(resolution,[status(thm)],[d20,c2]) ).
cnf(d48,plain,
( 'c$ulessequals'('v$ux','v$uY','tc$uset'('t$ua'))
| ~ 'c$ulessequals'('v$uX','v$uZ','tc$uset'('t$ua')) ),
inference(resolution,[status(thm)],[d22,d47]) ).
cnf(d49,plain,
'c$ulessequals'('v$ux','v$uY','tc$uset'('t$ua')),
inference(resolution,[status(thm)],[d24,d48]) ).
cnf(d50,plain,
( ~ 'c$uin'(X0,'v$ux','t$ua')
| 'c$uin'(X0,'v$uY','t$ua') ),
inference(resolution,[status(thm)],[d49,c9]) ).
cnf(d51,plain,
( 'c$ulessequals'('v$ux',X0,'tc$uset'('t$ua'))
| 'c$uin'('c$uMain$uOsubsetI$u$u1'('v$ux',X0,'t$ua'),'v$uY','t$ua') ),
inference(resolution,[status(thm)],[d50,c10]) ).
cnf(d52,plain,
( 'c$ulessequals'('v$ux','c$uinter'('v$ux','v$uY','t$ua'),'tc$uset'('t$ua'))
| 'c$ulessequals'('v$ux','c$uinter'('v$ux','v$uY','t$ua'),'tc$uset'('t$ua')) ),
inference(resolution,[status(thm)],[d51,d9]) ).
cnf(d53,plain,
'c$ulessequals'('v$ux','c$uinter'('v$uY','v$ux','t$ua'),'tc$uset'('t$ua')),
inference(demodulation,[status(thm)],[d52,d8]) ).
cnf(d54,plain,
'c$uinter'('v$uY','v$ux','t$ua') = 'v$ux',
inference(resolution,[status(thm)],[d53,d2]) ).
cnf(d55,plain,
'c$ulessequals'('c$uinter'('v$uZ','v$ux','t$ua'),'v$uX','tc$uset'('t$ua')),
inference(superposition,[status(thm)],[d54,d46]) ).
cnf(d56,plain,
'c$ulessequals'('v$ux','v$uX','tc$uset'('t$ua')),
inference(demodulation,[status(thm)],[d55,d30]) ).
cnf(d57,plain,
( ~ 'c$ulessequals'('v$ux','v$uX','tc$uset'('t$ua'))
| ~ 'c$ulessequals'('v$uX','v$uZ','tc$uset'('t$ua'))
| ~ 'c$ulessequals'('v$uX','v$uY','tc$uset'('t$ua')) ),
inference(resolution,[status(thm)],[d20,c4]) ).
cnf(d58,plain,
( ~ 'c$ulessequals'('v$ux','v$uX','tc$uset'('t$ua'))
| ~ 'c$ulessequals'('v$uX','v$uZ','tc$uset'('t$ua')) ),
inference(resolution,[status(thm)],[d22,d57]) ).
cnf(d59,plain,
~ 'c$ulessequals'('v$ux','v$uX','tc$uset'('t$ua')),
inference(resolution,[status(thm)],[d24,d58]) ).
cnf(d60,plain,
$false,
inference(resolution,[status(thm)],[d59,d56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET831-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n018.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Sat Sep 26 08:21:36 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 63.00/9.82 % SZS status Unsatisfiable for theBenchmark.p
% 63.00/9.82 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------