%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET847-2 : 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 : n007.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 08:33:24 AM UTC 2026
% Result : Unsatisfiable 14.36s 2.52s
% Output : CNFRefutation 14.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of clauses : 35 ( 15 unt; 4 nHn; 24 RR)
% Number of literals : 59 ( 11 equ; 28 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 76 ( 14 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Set_ODiffI_0,axiom,
( 'c$uin'(X0,'c$uminus'(X1,X3,'tc$uset'(X2)),X2)
| 'c$uin'(X0,X3,X2)
| ~ 'c$uin'(X0,X1,X2) ) ).
cnf(cls_Set_OemptyE_0,axiom,
~ 'c$uin'(X0,'c$uemptyset',X1) ).
cnf(cls_Set_Oempty__subsetI_0,axiom,
'c$ulessequals'('c$uemptyset',X0,'tc$uset'(X1)) ).
cnf(cls_Set_OsubsetI_0,axiom,
( 'c$ulessequals'(X0,X1,'tc$uset'(X2))
| 'c$uin'('c$uMain$uOsubsetI$u$u1'(X0,X1,X2),X0,X2) ) ).
cnf(cls_Set_Osubset__antisym_0,axiom,
( X1 = X0
| ~ 'c$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$uset'(X1)) ).
cnf(cls_Zorn_OTFin__UnionI_0,axiom,
( 'c$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_OTFin__chain__lemma4_0,axiom,
( 'c$uin'(X0,'c$uZorn$uOchain'(X1,X2),'tc$uset'('tc$uset'(X2)))
| ~ 'c$uin'(X0,'c$uZorn$uOTFin'(X1,X2),'tc$uset'('tc$uset'(X2))) ) ).
cnf(cls_Zorn_Oequal__succ__Union_1,axiom,
( 'c$uUnion'('c$uZorn$uOTFin'(X0,X1),'tc$uset'(X1)) = 'c$uZorn$uOsucc'(X0,'c$uUnion'('c$uZorn$uOTFin'(X0,X1),'tc$uset'(X1)),X1)
| ~ 'c$uin'('c$uUnion'('c$uZorn$uOTFin'(X0,X1),'tc$uset'(X1)),'c$uZorn$uOTFin'(X0,X1),'tc$uset'('tc$uset'(X1))) ) ).
cnf(cls_Zorn_Osucc__not__equals_0,axiom,
( 'c$uZorn$uOsucc'(X1,X0,X2) != X0
| ~ 'c$uin'(X0,'c$uminus'('c$uZorn$uOchain'(X1,X2),'c$uZorn$uOmaxchain'(X1,X2),'tc$uset'('tc$uset'('tc$uset'(X2)))),'tc$uset'('tc$uset'(X2))) ) ).
cnf(cls_conjecture_0,negated_conjecture,
~ 'c$uin'(X0,'c$uZorn$uOmaxchain'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua'))) ).
cnf(c0,plain,
( 'c$uin'(X0,'c$uminus'(X1,X3,'tc$uset'(X2)),X2)
| 'c$uin'(X0,X3,X2)
| ~ 'c$uin'(X0,X1,X2) ),
inference(clausification,[status(esa)],[cls_Set_ODiffI_0]) ).
cnf(c1,plain,
~ 'c$uin'(X0,'c$uemptyset',X1),
inference(clausification,[status(esa)],[cls_Set_OemptyE_0]) ).
cnf(c2,plain,
'c$ulessequals'('c$uemptyset',X0,'tc$uset'(X1)),
inference(clausification,[status(esa)],[cls_Set_Oempty__subsetI_0]) ).
cnf(c3,plain,
( 'c$ulessequals'(X0,X1,'tc$uset'(X2))
| 'c$uin'('c$uMain$uOsubsetI$u$u1'(X0,X1,X2),X0,X2) ),
inference(clausification,[status(esa)],[cls_Set_OsubsetI_0]) ).
cnf(c4,plain,
( X1 = X0
| ~ 'c$ulessequals'(X1,X0,'tc$uset'(X2))
| ~ 'c$ulessequals'(X0,X1,'tc$uset'(X2)) ),
inference(clausification,[status(esa)],[cls_Set_Osubset__antisym_0]) ).
cnf(c5,plain,
'c$ulessequals'(X0,X0,'tc$uset'(X1)),
inference(clausification,[status(esa)],[cls_Set_Osubset__refl_0]) ).
cnf(c6,plain,
( 'c$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(c7,plain,
( 'c$uin'(X0,'c$uZorn$uOchain'(X1,X2),'tc$uset'('tc$uset'(X2)))
| ~ 'c$uin'(X0,'c$uZorn$uOTFin'(X1,X2),'tc$uset'('tc$uset'(X2))) ),
inference(clausification,[status(esa)],[cls_Zorn_OTFin__chain__lemma4_0]) ).
cnf(c8,plain,
( 'c$uUnion'('c$uZorn$uOTFin'(X0,X1),'tc$uset'(X1)) = 'c$uZorn$uOsucc'(X0,'c$uUnion'('c$uZorn$uOTFin'(X0,X1),'tc$uset'(X1)),X1)
| ~ 'c$uin'('c$uUnion'('c$uZorn$uOTFin'(X0,X1),'tc$uset'(X1)),'c$uZorn$uOTFin'(X0,X1),'tc$uset'('tc$uset'(X1))) ),
inference(clausification,[status(esa)],[cls_Zorn_Oequal__succ__Union_1]) ).
cnf(c9,plain,
( 'c$uZorn$uOsucc'(X1,X0,X2) != X0
| ~ 'c$uin'(X0,'c$uminus'('c$uZorn$uOchain'(X1,X2),'c$uZorn$uOmaxchain'(X1,X2),'tc$uset'('tc$uset'('tc$uset'(X2)))),'tc$uset'('tc$uset'(X2))) ),
inference(clausification,[status(esa)],[cls_Zorn_Osucc__not__equals_0]) ).
cnf(c10,plain,
~ 'c$uin'(X0,'c$uZorn$uOmaxchain'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua'))),
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(d0,plain,
( ~ 'c$ulessequals'(X0,'c$uZorn$uOTFin'(X2,X1),'tc$uset'('tc$uset'('tc$uset'(X1))))
| 'c$uin'('c$uUnion'(X0,'tc$uset'(X1)),'c$uZorn$uOchain'(X2,X1),'tc$uset'('tc$uset'(X1))) ),
inference(resolution,[status(thm)],[c7,c6]) ).
cnf(d1,plain,
( ~ 'c$ulessequals'('c$uZorn$uOTFin'(X0,X1),'c$uZorn$uOTFin'(X0,X1),'tc$uset'('tc$uset'('tc$uset'(X1))))
| 'c$uUnion'('c$uZorn$uOTFin'(X0,X1),'tc$uset'(X1)) = 'c$uZorn$uOsucc'(X0,'c$uUnion'('c$uZorn$uOTFin'(X0,X1),'tc$uset'(X1)),X1) ),
inference(resolution,[status(thm)],[c8,c6]) ).
cnf(d2,plain,
'c$uUnion'('c$uZorn$uOTFin'(X0,X1),'tc$uset'(X1)) = 'c$uZorn$uOsucc'(X0,'c$uUnion'('c$uZorn$uOTFin'(X0,X1),'tc$uset'(X1)),X1),
inference(resolution,[status(thm)],[c5,d1]) ).
cnf(d3,plain,
( ~ 'c$uin'('c$uUnion'('c$uZorn$uOTFin'(X0,X1),'tc$uset'(X1)),'c$uminus'('c$uZorn$uOchain'(X0,X1),'c$uZorn$uOmaxchain'(X0,X1),'tc$uset'('tc$uset'('tc$uset'(X1)))),'tc$uset'('tc$uset'(X1)))
| 'c$uUnion'('c$uZorn$uOTFin'(X0,X1),'tc$uset'(X1)) != 'c$uUnion'('c$uZorn$uOTFin'(X0,X1),'tc$uset'(X1)) ),
inference(superposition,[status(thm)],[d2,c9]) ).
cnf(d4,plain,
~ 'c$uin'('c$uUnion'('c$uZorn$uOTFin'(X0,X1),'tc$uset'(X1)),'c$uminus'('c$uZorn$uOchain'(X0,X1),'c$uZorn$uOmaxchain'(X0,X1),'tc$uset'('tc$uset'('tc$uset'(X1)))),'tc$uset'('tc$uset'(X1))),
inference(equality_resolution,[status(thm)],[d3]) ).
cnf(d5,plain,
( ~ 'c$uin'('c$uUnion'('c$uZorn$uOTFin'(X0,X1),'tc$uset'(X1)),'c$uZorn$uOchain'(X0,X1),'tc$uset'('tc$uset'(X1)))
| 'c$uin'('c$uUnion'('c$uZorn$uOTFin'(X0,X1),'tc$uset'(X1)),'c$uZorn$uOmaxchain'(X0,X1),'tc$uset'('tc$uset'(X1))) ),
inference(resolution,[status(thm)],[d4,c0]) ).
cnf(d6,plain,
( ~ 'c$ulessequals'('c$uZorn$uOTFin'(X0,X1),'c$uZorn$uOTFin'(X0,X1),'tc$uset'('tc$uset'('tc$uset'(X1))))
| 'c$uin'('c$uUnion'('c$uZorn$uOTFin'(X0,X1),'tc$uset'(X1)),'c$uZorn$uOmaxchain'(X0,X1),'tc$uset'('tc$uset'(X1))) ),
inference(resolution,[status(thm)],[d5,d0]) ).
cnf(d7,plain,
'c$uin'('c$uUnion'('c$uZorn$uOTFin'(X0,X1),'tc$uset'(X1)),'c$uZorn$uOmaxchain'(X0,X1),'tc$uset'('tc$uset'(X1))),
inference(resolution,[status(thm)],[c5,d6]) ).
cnf(d8,plain,
( ~ 'c$ulessequals'(X0,'c$uemptyset','tc$uset'(X1))
| X0 = 'c$uemptyset' ),
inference(resolution,[status(thm)],[c4,c2]) ).
cnf(d9,plain,
'c$ulessequals'('c$uZorn$uOmaxchain'('v$uS','t$ua'),X0,'tc$uset'('tc$uset'('tc$uset'('t$ua')))),
inference(resolution,[status(thm)],[c10,c3]) ).
cnf(d10,plain,
'c$uZorn$uOmaxchain'('v$uS','t$ua') = 'c$uemptyset',
inference(resolution,[status(thm)],[d9,d8]) ).
cnf(d11,plain,
'c$uin'('c$uUnion'('c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('t$ua')),'c$uemptyset','tc$uset'('tc$uset'('t$ua'))),
inference(superposition,[status(thm)],[d10,d7]) ).
cnf(d12,plain,
$false,
inference(resolution,[status(thm)],[c1,d11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET847-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n007.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 08:19:08 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.36/2.52 % SZS status Unsatisfiable for theBenchmark.p
% 14.36/2.52 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------