%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET845-1 : 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 : 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 08:33:23 AM UTC 2026
% Result : Unsatisfiable 75.61s 19.82s
% Output : CNFRefutation 75.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of clauses : 38 ( 16 unt; 10 nHn; 24 RR)
% Number of literals : 63 ( 40 equ; 20 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 65 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Set_OUnion__upper_0,axiom,
( 'c$ulessequals'(X0,'c$uUnion'(X1,X2),'tc$uset'(X2))
| ~ 'c$uin'(X0,X1,'tc$uset'(X2)) ) ).
cnf(cls_Zorn_OAbrial__axiom1_0,axiom,
'c$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_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$uUnion'('c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('t$ua')) ).
cnf(cls_conjecture_2,negated_conjecture,
'v$um' != 'c$uZorn$uOsucc'('v$uS','v$um','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$uOSome'(X2,X1) ) ).
cnf(cls_Set_Osubset__antisym_0,axiom,
( X1 = X0
| ~ 'c$ulessequals'(X1,X0,'tc$uset'(X2))
| ~ 'c$ulessequals'(X0,X1,'tc$uset'(X2)) ) ).
cnf(c2,plain,
( 'c$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(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$uset'(X2))) ),
inference(clausification,[status(esa)],[cls_Zorn_OTFin_OsuccI_0]) ).
cnf(c7,plain,
'c$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$um' = 'c$uUnion'('c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('t$ua')),
inference(clausification,[status(esa)],[cls_conjecture_1]) ).
cnf(c9,plain,
'v$um' != 'c$uZorn$uOsucc'('v$uS','v$um','t$ua'),
inference(clausification,[status(esa)],[cls_conjecture_2]) ).
cnf(c12,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(c13,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(c15,plain,
'c$uDatatype$uOoption$uOSome'(X0,X1) != 'c$uDatatype$uOoption$uONone',
inference(clausification,[status(esa)],[cls_Datatype_Ooption_Odistinct__2__iff1_0]) ).
cnf(c16,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(c318,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$ulessequals'('c$uZorn$uOsucc'(X0,X1,X2),X1,'tc$uset'('tc$uset'(X2)))
| 'c$uZorn$uOsucc'(X0,X1,X2) = X1 ),
inference(resolution,[status(thm)],[c318,c3]) ).
cnf(d1,plain,
( ~ 'c$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)],[c8,c2]) ).
cnf(d2,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$ua'))) ),
inference(resolution,[status(thm)],[d1,c4]) ).
cnf(d3,plain,
( 'c$uZorn$uOsucc'('v$uS','v$um','t$ua') = 'v$um'
| ~ 'c$uin'('v$um','c$uZorn$uOTFin'('v$uS','t$ua'),'tc$uset'('tc$uset'('t$ua'))) ),
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
'c$uZorn$uOsucc'('v$uS','v$um','t$ua') = 'v$um',
inference(resolution,[status(thm)],[c7,d3]) ).
cnf(d5,plain,
'v$um' != 'v$um',
inference(demodulation,[status(thm)],[c9,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)],[c13,c16]) ).
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)],[c15,d7]) ).
cnf(d9,plain,
( X0 = 'c$uDatatype$uOoption$uONone'
| 'c$uMain$uOnot$u$uSome$u$ueq$u$uiff1$u$u1'(X0,X1) = 'c$uMain$uOnot$u$uNone$u$ueq$u$uiff1$u$u1'(X0,X1) ),
inference(superposition,[status(thm)],[c12,d8]) ).
cnf(d10,plain,
( 'c$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)],[d9,d8]) ).
cnf(d11,plain,
'c$uMain$uOnot$u$uNone$u$ueq$u$uiff1$u$u1'('c$uDatatype$uOoption$uOSome'(X0,X1),X1) = X0,
inference(resolution,[status(thm)],[c15,d10]) ).
cnf(d12,plain,
( 'c$uDatatype$uOoption$uOSome'(X0,X1) = 'c$uDatatype$uOoption$uONone'
| X0 = 'c$uMain$uOnot$u$uNone$u$ueq$u$uiff1$u$u1'('c$uDatatype$uOoption$uOSome'(X0,X1),X1) ),
inference(superposition,[status(thm)],[d8,d9]) ).
cnf(d13,plain,
( 'c$uDatatype$uOoption$uOSome'(X0,X1) = 'c$uDatatype$uOoption$uONone'
| X0 = X0 ),
inference(demodulation,[status(thm)],[d12,d11]) ).
cnf(d14,plain,
X0 = X0,
inference(resolution,[status(thm)],[c15,d13]) ).
cnf(d15,plain,
$false,
inference(resolution,[status(thm)],[d14,d5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET845-1 : 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 : n004.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 08:21:06 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 75.61/19.82 % SZS status Unsatisfiable for theBenchmark.p
% 75.61/19.82 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------