%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET864-1 : 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 : n004.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 08:33:27 AM UTC 2026
% Result : Unsatisfiable 96.46s 14.43s
% Output : CNFRefutation 96.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of clauses : 47 ( 12 unt; 14 nHn; 33 RR)
% Number of literals : 92 ( 43 equ; 37 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 78 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Zorn_Omaxchain__Zorn_0,axiom,
( 'c$uUnion'(X3,X2) = X0
| ~ 'c$ulessequals'('c$uUnion'(X3,X2),X0,'tc$uset'(X2))
| ~ 'c$uin'(X3,'c$uZorn$uOmaxchain'(X1,X2),'tc$uset'('tc$uset'(X2)))
| ~ 'c$uin'(X0,X1,'tc$uset'(X2)) ) ).
cnf(cls_conjecture_0,negated_conjecture,
'c$uin'('v$uc','c$uZorn$uOmaxchain'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua'))) ).
cnf(cls_conjecture_2,negated_conjecture,
'c$uin'('c$uUnion'('v$uc','t$ua'),'v$uS','tc$uset'('t$ua')) ).
cnf(cls_conjecture_3,negated_conjecture,
( ~ 'c$uin'(X0,'v$uS','tc$uset'('t$ua'))
| 'c$uin'('v$ux'(X0),'v$uS','tc$uset'('t$ua')) ) ).
cnf(cls_conjecture_4,negated_conjecture,
( ~ 'c$uin'(X0,'v$uS','tc$uset'('t$ua'))
| 'c$ulessequals'(X0,'v$ux'(X0),'tc$uset'('t$ua')) ) ).
cnf(cls_conjecture_5,negated_conjecture,
( ~ 'c$uin'(X0,'v$uS','tc$uset'('t$ua'))
| X0 != 'v$ux'(X0) ) ).
cnf(cls_Datatype_Onot__None__eq__iff1_0,axiom,
( X0 = 'c$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$uOSome'(X2,X1) ) ).
cnf(cls_Set_OsubsetD_0,axiom,
( 'c$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$u1'(X0,X1,X2),X1,X2) ) ).
cnf(c1,plain,
( 'c$uUnion'(X3,X2) = X0
| ~ 'c$ulessequals'('c$uUnion'(X3,X2),X0,'tc$uset'(X2))
| ~ 'c$uin'(X3,'c$uZorn$uOmaxchain'(X1,X2),'tc$uset'('tc$uset'(X2)))
| ~ 'c$uin'(X0,X1,'tc$uset'(X2)) ),
inference(clausification,[status(esa)],[cls_Zorn_Omaxchain__Zorn_0]) ).
cnf(c3,plain,
'c$uin'('v$uc','c$uZorn$uOmaxchain'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua'))),
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(c5,plain,
'c$uin'('c$uUnion'('v$uc','t$ua'),'v$uS','tc$uset'('t$ua')),
inference(clausification,[status(esa)],[cls_conjecture_2]) ).
cnf(c6,plain,
( ~ 'c$uin'(X0,'v$uS','tc$uset'('t$ua'))
| 'c$uin'('v$ux'(X0),'v$uS','tc$uset'('t$ua')) ),
inference(clausification,[status(esa)],[cls_conjecture_3]) ).
cnf(c7,plain,
( ~ 'c$uin'(X0,'v$uS','tc$uset'('t$ua'))
| 'c$ulessequals'(X0,'v$ux'(X0),'tc$uset'('t$ua')) ),
inference(clausification,[status(esa)],[cls_conjecture_4]) ).
cnf(c8,plain,
( ~ 'c$uin'(X0,'v$uS','tc$uset'('t$ua'))
| X0 != 'v$ux'(X0) ),
inference(clausification,[status(esa)],[cls_conjecture_5]) ).
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(c314,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(c315,plain,
( 'c$ulessequals'(X0,X1,'tc$uset'(X2))
| 'c$uin'('c$uMain$uOsubsetI$u$u1'(X0,X1,X2),X0,X2) ),
inference(clausification,[status(esa)],[cls_Set_OsubsetI_0]) ).
cnf(c316,plain,
( 'c$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(d0,plain,
( ~ 'c$ulessequals'('c$uUnion'('v$uc','t$ua'),X0,'tc$uset'('t$ua'))
| ~ 'c$uin'(X0,'v$uS','tc$uset'('t$ua'))
| 'c$uUnion'('v$uc','t$ua') = X0 ),
inference(resolution,[status(thm)],[c3,c1]) ).
cnf(d1,plain,
( ~ 'c$uin'(X1,'v$uS','tc$uset'('t$ua'))
| ~ 'c$uin'(X0,X1,'t$ua')
| 'c$uin'(X0,'v$ux'(X1),'t$ua') ),
inference(resolution,[status(thm)],[c314,c7]) ).
cnf(d2,plain,
( 'c$uin'(X0,'v$ux'('c$uUnion'('v$uc','t$ua')),'t$ua')
| ~ 'c$uin'(X0,'c$uUnion'('v$uc','t$ua'),'t$ua') ),
inference(resolution,[status(thm)],[d1,c5]) ).
cnf(d3,plain,
( 'c$ulessequals'(X0,'v$ux'('c$uUnion'('v$uc','t$ua')),'tc$uset'('t$ua'))
| ~ 'c$uin'('c$uMain$uOsubsetI$u$u1'(X0,'v$ux'('c$uUnion'('v$uc','t$ua')),'t$ua'),'c$uUnion'('v$uc','t$ua'),'t$ua') ),
inference(resolution,[status(thm)],[d2,c316]) ).
cnf(d4,plain,
( 'c$ulessequals'('c$uUnion'('v$uc','t$ua'),'v$ux'('c$uUnion'('v$uc','t$ua')),'tc$uset'('t$ua'))
| 'c$ulessequals'('c$uUnion'('v$uc','t$ua'),'v$ux'('c$uUnion'('v$uc','t$ua')),'tc$uset'('t$ua')) ),
inference(resolution,[status(thm)],[d3,c315]) ).
cnf(d5,plain,
( ~ 'c$uin'('v$ux'('c$uUnion'('v$uc','t$ua')),'v$uS','tc$uset'('t$ua'))
| 'c$uUnion'('v$uc','t$ua') = 'v$ux'('c$uUnion'('v$uc','t$ua')) ),
inference(resolution,[status(thm)],[d4,d0]) ).
cnf(d6,plain,
( ~ 'c$uin'('c$uUnion'('v$uc','t$ua'),'v$uS','tc$uset'('t$ua'))
| 'c$uUnion'('v$uc','t$ua') = 'v$ux'('c$uUnion'('v$uc','t$ua')) ),
inference(resolution,[status(thm)],[d5,c6]) ).
cnf(d7,plain,
'c$uUnion'('v$uc','t$ua') = 'v$ux'('c$uUnion'('v$uc','t$ua')),
inference(resolution,[status(thm)],[c5,d6]) ).
cnf(d8,plain,
( ~ 'c$uin'('c$uUnion'('v$uc','t$ua'),'v$uS','tc$uset'('t$ua'))
| 'c$uUnion'('v$uc','t$ua') != 'c$uUnion'('v$uc','t$ua') ),
inference(superposition,[status(thm)],[d7,c8]) ).
cnf(d9,plain,
'c$uUnion'('v$uc','t$ua') != 'c$uUnion'('v$uc','t$ua'),
inference(resolution,[status(thm)],[c5,d8]) ).
cnf(d10,plain,
( X0 = 'c$uDatatype$uOoption$uONone'
| 'c$uMain$uOnot$u$uNone$u$ueq$u$uiff1$u$u1'(X0,X1) = X2
| X0 != 'c$uDatatype$uOoption$uOSome'(X2,X1) ),
inference(superposition,[status(thm)],[c11,c15]) ).
cnf(d11,plain,
( 'c$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)],[d10]) ).
cnf(d12,plain,
'c$uMain$uOnot$u$uNone$u$ueq$u$uiff1$u$u1'('c$uDatatype$uOoption$uOSome'(X0,X1),X1) = X0,
inference(resolution,[status(thm)],[c14,d11]) ).
cnf(d13,plain,
( X0 = 'c$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,d12]) ).
cnf(d14,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(d15,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$uONone' ),
inference(equality_resolution,[status(thm)],[d14]) ).
cnf(d16,plain,
'c$uMain$uOnot$u$uSome$u$ueq$u$uiff1$u$u1'('c$uDatatype$uOoption$uOSome'(X0,X1),X1) = X0,
inference(resolution,[status(thm)],[c14,d15]) ).
cnf(d17,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$uOSome'(X0,X1),X1) = X0 ),
inference(superposition,[status(thm)],[d16,d13]) ).
cnf(d18,plain,
( X0 = X0
| 'c$uDatatype$uOoption$uOSome'(X0,X1) = 'c$uDatatype$uOoption$uONone' ),
inference(demodulation,[status(thm)],[d17,d12]) ).
cnf(d19,plain,
X0 = X0,
inference(resolution,[status(thm)],[c14,d18]) ).
cnf(d20,plain,
$false,
inference(resolution,[status(thm)],[d19,d9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET864-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n004.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 08:22:51 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 96.46/14.43 % SZS status Unsatisfiable for theBenchmark.p
% 96.46/14.43 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------