%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET848-1 : 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 : n016.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 103.33s 16.96s
% Output : CNFRefutation 103.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of clauses : 39 ( 15 unt; 13 nHn; 23 RR)
% Number of literals : 67 ( 38 equ; 25 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 : 13 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 72 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
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$uset'(X2))) ) ).
cnf(cls_Zorn_Osucc__not__equals_0,axiom,
( 'c$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$uin'('c$uUnion'('c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('t$ua')),'c$uZorn$uOmaxchain'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua'))) ).
cnf(cls_conjecture_1,negated_conjecture,
'c$uZorn$uOsucc'('v$uS','c$uUnion'('c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('t$ua')),'t$ua') = 'c$uUnion'('c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('t$ua')) ).
cnf(cls_Datatype_Onot__None__eq__iff1_0,axiom,
( X0 = 'c$uDatatype$uOoption$uOSome'('c$uMain$uOnot$u$uNone$u$ueq$u$uiff1$u$u1'(X0,X1),X1)
| X0 = 'c$uDatatype$uOoption$uONone' ) ).
cnf(cls_Datatype_Onot__Some__eq__iff1_0,axiom,
( X0 = 'c$uDatatype$uOoption$uOSome'('c$uMain$uOnot$u$uSome$u$ueq$u$uiff1$u$u1'(X0,X1),X1)
| X0 = 'c$uDatatype$uOoption$uONone' ) ).
cnf(cls_Datatype_Ooption_Odistinct__2__iff1_0,axiom,
'c$uDatatype$uOoption$uOSome'(X0,X1) != 'c$uDatatype$uOoption$uONone' ).
cnf(cls_Datatype_Ooption_Oinject__iff1_0,axiom,
( X0 = X2
| 'c$uDatatype$uOoption$uOSome'(X0,X1) != 'c$uDatatype$uOoption$uOSome'(X2,X1) ) ).
cnf(cls_Set_ODiffI_0,axiom,
( 'c$uin'(X0,'c$uminus'(X1,X3,'tc$uset'(X2)),X2)
| 'c$uin'(X0,X3,X2)
| ~ 'c$uin'(X0,X1,X2) ) ).
cnf(cls_Set_Osubset__refl_0,axiom,
'c$ulessequals'(X0,X0,'tc$uset'(X1)) ).
cnf(c1,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$uset'(X2)))) ),
inference(clausification,[status(esa)],[cls_Zorn_OTFin__UnionI_0]) ).
cnf(c2,plain,
( 'c$uin'(X0,'c$uZorn$uOchain'(X1,X2),'tc$uset'('tc$uset'(X2)))
| ~ 'c$uin'(X0,'c$uZorn$uOTFin'(X1,X2),'tc$uset'('tc$uset'(X2))) ),
inference(clausification,[status(esa)],[cls_Zorn_OTFin__chain__lemma4_0]) ).
cnf(c5,plain,
( 'c$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(c6,plain,
~ 'c$uin'('c$uUnion'('c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('t$ua')),'c$uZorn$uOmaxchain'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua'))),
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(c7,plain,
'c$uZorn$uOsucc'('v$uS','c$uUnion'('c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('t$ua')),'t$ua') = 'c$uUnion'('c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('t$ua')),
inference(clausification,[status(esa)],[cls_conjecture_1]) ).
cnf(c11,plain,
( X0 = 'c$uDatatype$uOoption$uOSome'('c$uMain$uOnot$u$uNone$u$ueq$u$uiff1$u$u1'(X0,X1),X1)
| X0 = 'c$uDatatype$uOoption$uONone' ),
inference(clausification,[status(esa)],[cls_Datatype_Onot__None__eq__iff1_0]) ).
cnf(c12,plain,
( X0 = 'c$uDatatype$uOoption$uOSome'('c$uMain$uOnot$u$uSome$u$ueq$u$uiff1$u$u1'(X0,X1),X1)
| X0 = 'c$uDatatype$uOoption$uONone' ),
inference(clausification,[status(esa)],[cls_Datatype_Onot__Some__eq__iff1_0]) ).
cnf(c14,plain,
'c$uDatatype$uOoption$uOSome'(X0,X1) != 'c$uDatatype$uOoption$uONone',
inference(clausification,[status(esa)],[cls_Datatype_Ooption_Odistinct__2__iff1_0]) ).
cnf(c15,plain,
( X0 = X2
| 'c$uDatatype$uOoption$uOSome'(X0,X1) != 'c$uDatatype$uOoption$uOSome'(X2,X1) ),
inference(clausification,[status(esa)],[cls_Datatype_Ooption_Oinject__iff1_0]) ).
cnf(c167,plain,
( 'c$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(c318,plain,
'c$ulessequals'(X0,X0,'tc$uset'(X1)),
inference(clausification,[status(esa)],[cls_Set_Osubset__refl_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$uset'(X1))) ),
inference(resolution,[status(thm)],[c2,c1]) ).
cnf(d1,plain,
( ~ 'c$uin'('c$uUnion'('c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('t$ua')),'c$uminus'('c$uZorn$uOchain'('v$uS','t$ua'),'c$uZorn$uOmaxchain'('v$uS','t$ua'),'tc$uset'('tc$uset'('tc$uset'('t$ua')))),'tc$uset'('tc$uset'('t$ua')))
| 'c$uUnion'('c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('t$ua')) != 'c$uUnion'('c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('t$ua')) ),
inference(superposition,[status(thm)],[c7,c5]) ).
cnf(d2,plain,
( X0 = 'c$uDatatype$uOoption$uONone'
| 'c$uMain$uOnot$u$uNone$u$ueq$u$uiff1$u$u1'(X0,X1) = X2
| X0 != 'c$uDatatype$uOoption$uOSome'(X2,X1) ),
inference(superposition,[status(thm)],[c11,c15]) ).
cnf(d3,plain,
( 'c$uMain$uOnot$u$uNone$u$ueq$u$uiff1$u$u1'('c$uDatatype$uOoption$uOSome'(X0,X1),X1) = X0
| 'c$uDatatype$uOoption$uOSome'(X0,X1) = 'c$uDatatype$uOoption$uONone' ),
inference(equality_resolution,[status(thm)],[d2]) ).
cnf(d4,plain,
'c$uMain$uOnot$u$uNone$u$ueq$u$uiff1$u$u1'('c$uDatatype$uOoption$uOSome'(X0,X1),X1) = X0,
inference(resolution,[status(thm)],[c14,d3]) ).
cnf(d5,plain,
( X0 = 'c$uDatatype$uOoption$uONone'
| 'c$uMain$uOnot$u$uNone$u$ueq$u$uiff1$u$u1'(X0,X1) = 'c$uMain$uOnot$u$uSome$u$ueq$u$uiff1$u$u1'(X0,X1) ),
inference(superposition,[status(thm)],[c12,d4]) ).
cnf(d6,plain,
( X0 = 'c$uDatatype$uOoption$uONone'
| 'c$uMain$uOnot$u$uSome$u$ueq$u$uiff1$u$u1'(X0,X1) = X2
| X0 != 'c$uDatatype$uOoption$uOSome'(X2,X1) ),
inference(superposition,[status(thm)],[c12,c15]) ).
cnf(d7,plain,
( 'c$uMain$uOnot$u$uSome$u$ueq$u$uiff1$u$u1'('c$uDatatype$uOoption$uOSome'(X0,X1),X1) = X0
| 'c$uDatatype$uOoption$uOSome'(X0,X1) = 'c$uDatatype$uOoption$uONone' ),
inference(equality_resolution,[status(thm)],[d6]) ).
cnf(d8,plain,
'c$uMain$uOnot$u$uSome$u$ueq$u$uiff1$u$u1'('c$uDatatype$uOoption$uOSome'(X0,X1),X1) = X0,
inference(resolution,[status(thm)],[c14,d7]) ).
cnf(d9,plain,
( 'c$uDatatype$uOoption$uOSome'(X0,X1) = 'c$uDatatype$uOoption$uONone'
| 'c$uMain$uOnot$u$uNone$u$ueq$u$uiff1$u$u1'('c$uDatatype$uOoption$uOSome'(X0,X1),X1) = X0 ),
inference(superposition,[status(thm)],[d8,d5]) ).
cnf(d10,plain,
( X0 = X0
| 'c$uDatatype$uOoption$uOSome'(X0,X1) = 'c$uDatatype$uOoption$uONone' ),
inference(demodulation,[status(thm)],[d9,d4]) ).
cnf(d11,plain,
X0 = X0,
inference(resolution,[status(thm)],[c14,d10]) ).
cnf(d12,plain,
~ 'c$uin'('c$uUnion'('c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('t$ua')),'c$uminus'('c$uZorn$uOchain'('v$uS','t$ua'),'c$uZorn$uOmaxchain'('v$uS','t$ua'),'tc$uset'('tc$uset'('tc$uset'('t$ua')))),'tc$uset'('tc$uset'('t$ua'))),
inference(resolution,[status(thm)],[d11,d1]) ).
cnf(d13,plain,
( ~ 'c$uin'('c$uUnion'('c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('t$ua')),'c$uZorn$uOchain'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua')))
| 'c$uin'('c$uUnion'('c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('t$ua')),'c$uZorn$uOmaxchain'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua'))) ),
inference(resolution,[status(thm)],[d12,c167]) ).
cnf(d14,plain,
~ 'c$uin'('c$uUnion'('c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('t$ua')),'c$uZorn$uOchain'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua'))),
inference(resolution,[status(thm)],[c6,d13]) ).
cnf(d15,plain,
~ 'c$ulessequals'('c$uZorn$uOTFin'('v$uS','t$ua'),'c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('tc$uset'('t$ua')))),
inference(resolution,[status(thm)],[d14,d0]) ).
cnf(d16,plain,
$false,
inference(resolution,[status(thm)],[c318,d15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET848-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n016.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 08:26:00 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 103.33/16.96 % SZS status Unsatisfiable for theBenchmark.p
% 103.33/16.96 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------