%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET843-2 : 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 : 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 08:33:23 AM UTC 2026
% Result : Unsatisfiable 18.36s 2.83s
% Output : CNFRefutation 18.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of clauses : 38 ( 12 unt; 5 nHn; 34 RR)
% Number of literals : 77 ( 27 equ; 37 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 : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 54 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Set_OUnion__upper_0,axiom,
( 'c$ulessequals'(X0,'c$uUnion'(X1,X2),'tc$uset'(X2))
| ~ 'c$uin'(X0,X1,'tc$uset'(X2)) ) ).
cnf(cls_Set_Osubset__antisym_0,axiom,
( X1 = X0
| ~ 'c$ulessequals'(X1,X0,'tc$uset'(X2))
| ~ 'c$ulessequals'(X0,X1,'tc$uset'(X2)) ) ).
cnf(cls_Set_Osubset__refl_0,axiom,
'c$ulessequals'(X0,X0,'tc$uset'(X1)) ).
cnf(cls_Zorn_OAbrial__axiom1_0,axiom,
'c$ulessequals'(X0,'c$uZorn$uOsucc'(X1,X0,X2),'tc$uset'('tc$uset'(X2))) ).
cnf(cls_Zorn_OTFin_OsuccI_0,axiom,
( 'c$uin'('c$uZorn$uOsucc'(X1,X0,X2),'c$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__UnionI_0,axiom,
( 'c$uin'('c$uUnion'(X0,'tc$uset'(X2)),'c$uZorn$uOTFin'(X1,X2),'tc$uset'('tc$uset'(X2)))
| ~ 'c$ulessequals'(X0,'c$uZorn$uOTFin'(X1,X2),'tc$uset'('tc$uset'('tc$uset'(X2)))) ) ).
cnf(cls_Zorn_Oeq__succ__upper_0,axiom,
( 'c$ulessequals'(X3,X0,'tc$uset'('tc$uset'(X2)))
| X0 != 'c$uZorn$uOsucc'(X1,X0,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$uin'('v$um','c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua'))) ).
cnf(cls_conjecture_1,negated_conjecture,
( 'v$um' != 'c$uZorn$uOsucc'('v$uS','v$um','t$ua')
| 'v$um' != 'c$uUnion'('c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('t$ua')) ) ).
cnf(cls_conjecture_2,negated_conjecture,
( 'v$um' = 'c$uUnion'('c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('t$ua'))
| 'v$um' = 'c$uZorn$uOsucc'('v$uS','v$um','t$ua') ) ).
cnf(c0,plain,
( 'c$ulessequals'(X0,'c$uUnion'(X1,X2),'tc$uset'(X2))
| ~ 'c$uin'(X0,X1,'tc$uset'(X2)) ),
inference(clausification,[status(esa)],[cls_Set_OUnion__upper_0]) ).
cnf(c1,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(c2,plain,
'c$ulessequals'(X0,X0,'tc$uset'(X1)),
inference(clausification,[status(esa)],[cls_Set_Osubset__refl_0]) ).
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'('c$uZorn$uOsucc'(X1,X0,X2),'c$uZorn$uOTFin'(X1,X2),'tc$uset'('tc$uset'(X2)))
| ~ 'c$uin'(X0,'c$uZorn$uOTFin'(X1,X2),'tc$uset'('tc$uset'(X2))) ),
inference(clausification,[status(esa)],[cls_Zorn_OTFin_OsuccI_0]) ).
cnf(c5,plain,
( 'c$uin'('c$uUnion'(X0,'tc$uset'(X2)),'c$uZorn$uOTFin'(X1,X2),'tc$uset'('tc$uset'(X2)))
| ~ 'c$ulessequals'(X0,'c$uZorn$uOTFin'(X1,X2),'tc$uset'('tc$uset'('tc$uset'(X2)))) ),
inference(clausification,[status(esa)],[cls_Zorn_OTFin__UnionI_0]) ).
cnf(c6,plain,
( 'c$ulessequals'(X3,X0,'tc$uset'('tc$uset'(X2)))
| X0 != 'c$uZorn$uOsucc'(X1,X0,X2)
| ~ 'c$uin'(X3,'c$uZorn$uOTFin'(X1,X2),'tc$uset'('tc$uset'(X2)))
| ~ 'c$uin'(X0,'c$uZorn$uOTFin'(X1,X2),'tc$uset'('tc$uset'(X2))) ),
inference(clausification,[status(esa)],[cls_Zorn_Oeq__succ__upper_0]) ).
cnf(c7,plain,
'c$uin'('v$um','c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua'))),
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(c8,plain,
( 'v$um' != 'c$uZorn$uOsucc'('v$uS','v$um','t$ua')
| 'v$um' != 'c$uUnion'('c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('t$ua')) ),
inference(clausification,[status(esa)],[cls_conjecture_1]) ).
cnf(c9,plain,
( 'v$um' = 'c$uUnion'('c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('t$ua'))
| 'v$um' = 'c$uZorn$uOsucc'('v$uS','v$um','t$ua') ),
inference(clausification,[status(esa)],[cls_conjecture_2]) ).
cnf(d0,plain,
( ~ 'c$uin'(X0,X1,'tc$uset'(X2))
| ~ 'c$ulessequals'('c$uUnion'(X1,X2),X0,'tc$uset'(X2))
| X0 = 'c$uUnion'(X1,X2) ),
inference(resolution,[status(thm)],[c1,c0]) ).
cnf(d1,plain,
( ~ 'c$ulessequals'('c$uZorn$uOsucc'(X1,X0,X2),X0,'tc$uset'('tc$uset'(X2)))
| X0 = 'c$uZorn$uOsucc'(X1,X0,X2) ),
inference(resolution,[status(thm)],[c3,c1]) ).
cnf(d2,plain,
( 'v$um' = 'c$uZorn$uOsucc'('v$uS','v$um','t$ua')
| ~ 'c$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'))) ),
inference(superposition,[status(thm)],[c9,c0]) ).
cnf(d3,plain,
( ~ 'c$uin'(X0,'c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'('c$uZorn$uOsucc'('v$uS',X0,'t$ua'),'v$um','tc$uset'('tc$uset'('t$ua')))
| 'v$um' = 'c$uZorn$uOsucc'('v$uS','v$um','t$ua') ),
inference(resolution,[status(thm)],[d2,c4]) ).
cnf(d4,plain,
( 'v$um' = 'c$uZorn$uOsucc'('v$uS','v$um','t$ua')
| ~ 'c$uin'('v$um','c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| 'v$um' = 'c$uZorn$uOsucc'('v$uS','v$um','t$ua') ),
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
'v$um' = 'c$uZorn$uOsucc'('v$uS','v$um','t$ua'),
inference(resolution,[status(thm)],[c7,d4]) ).
cnf(d6,plain,
( 'c$ulessequals'(X0,'v$um','tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'('v$um','c$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$um' != 'v$um' ),
inference(superposition,[status(thm)],[d5,c6]) ).
cnf(d7,plain,
( 'c$ulessequals'(X0,'v$um','tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'(X0,'c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| 'v$um' != 'v$um' ),
inference(resolution,[status(thm)],[c7,d6]) ).
cnf(d8,plain,
( 'v$um' = 'c$uZorn$uOsucc'('v$uS','v$um','t$ua')
| ~ 'c$ulessequals'('v$um','v$um','tc$uset'('tc$uset'('t$ua'))) ),
inference(superposition,[status(thm)],[d5,d1]) ).
cnf(d9,plain,
( ~ 'c$ulessequals'('v$um','v$um','tc$uset'('tc$uset'('t$ua')))
| 'v$um' = 'v$um' ),
inference(demodulation,[status(thm)],[d8,d5]) ).
cnf(d10,plain,
'v$um' = 'v$um',
inference(resolution,[status(thm)],[c2,d9]) ).
cnf(d11,plain,
( 'c$ulessequals'(X0,'v$um','tc$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)],[d10,d7]) ).
cnf(d12,plain,
( ~ 'c$ulessequals'(X0,'c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('tc$uset'('t$ua'))))
| 'c$ulessequals'('c$uUnion'(X0,'tc$uset'('t$ua')),'v$um','tc$uset'('tc$uset'('t$ua'))) ),
inference(resolution,[status(thm)],[d11,c5]) ).
cnf(d13,plain,
'c$ulessequals'('c$uUnion'('c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('t$ua')),'v$um','tc$uset'('tc$uset'('t$ua'))),
inference(resolution,[status(thm)],[d12,c2]) ).
cnf(d14,plain,
( ~ 'c$uin'('v$um','c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| 'v$um' = 'c$uUnion'('c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('t$ua')) ),
inference(resolution,[status(thm)],[d13,d0]) ).
cnf(d15,plain,
'v$um' = 'c$uUnion'('c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('t$ua')),
inference(resolution,[status(thm)],[c7,d14]) ).
cnf(d16,plain,
'v$um' != 'c$uUnion'('c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('t$ua')),
inference(resolution,[status(thm)],[d5,c8]) ).
cnf(d17,plain,
$false,
inference(resolution,[status(thm)],[d16,d15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET843-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.45 % Computer : n020.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Sat Sep 26 08:21:49 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.46 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.36/2.83 % SZS status Unsatisfiable for theBenchmark.p
% 18.36/2.83 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------