%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET840-2 : 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 : 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 08:33:22 AM UTC 2026
% Result : Unsatisfiable 13.71s 4.27s
% Output : CNFRefutation 13.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of clauses : 22 ( 6 unt; 5 nHn; 16 RR)
% Number of literals : 47 ( 5 equ; 22 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 3 ( 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 : 48 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
~ 'c$ulessequals'('v$uS','c$uinsert'(X0,'c$uemptyset','tc$uset'('t$ub')),'tc$uset'('tc$uset'('t$ub'))) ).
cnf(cls_conjecture_1,negated_conjecture,
( ~ 'c$uin'(X0,'v$uS','tc$uset'('t$ub'))
| 'c$ulessequals'('c$uUnion'('v$uS','t$ub'),X0,'tc$uset'('t$ub')) ) ).
cnf(cls_Set_OUnionI_0,axiom,
( 'c$uin'(X0,'c$uUnion'(X3,X2),X2)
| ~ 'c$uin'(X1,X3,'tc$uset'(X2))
| ~ 'c$uin'(X0,X1,X2) ) ).
cnf(cls_Set_OinsertCI_1,axiom,
'c$uin'(X0,'c$uinsert'(X0,X1,X2),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(cls_Set_Osubset__antisym_0,axiom,
( X1 = X0
| ~ 'c$ulessequals'(X1,X0,'tc$uset'(X2))
| ~ 'c$ulessequals'(X0,X1,'tc$uset'(X2)) ) ).
cnf(c0,plain,
~ 'c$ulessequals'('v$uS','c$uinsert'(X0,'c$uemptyset','tc$uset'('t$ub')),'tc$uset'('tc$uset'('t$ub'))),
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(c1,plain,
( ~ 'c$uin'(X0,'v$uS','tc$uset'('t$ub'))
| 'c$ulessequals'('c$uUnion'('v$uS','t$ub'),X0,'tc$uset'('t$ub')) ),
inference(clausification,[status(esa)],[cls_conjecture_1]) ).
cnf(c2,plain,
( 'c$uin'(X0,'c$uUnion'(X3,X2),X2)
| ~ 'c$uin'(X1,X3,'tc$uset'(X2))
| ~ 'c$uin'(X0,X1,X2) ),
inference(clausification,[status(esa)],[cls_Set_OUnionI_0]) ).
cnf(c4,plain,
'c$uin'(X0,'c$uinsert'(X0,X1,X2),X2),
inference(clausification,[status(esa)],[cls_Set_OinsertCI_1]) ).
cnf(c6,plain,
( 'c$ulessequals'(X0,X1,'tc$uset'(X2))
| 'c$uin'('c$uMain$uOsubsetI$u$u1'(X0,X1,X2),X0,X2) ),
inference(clausification,[status(esa)],[cls_Set_OsubsetI_0]) ).
cnf(c7,plain,
( 'c$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(c8,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$uin'(X0,'v$uS','tc$uset'('t$ub'))
| ~ 'c$ulessequals'(X0,'c$uUnion'('v$uS','t$ub'),'tc$uset'('t$ub'))
| X0 = 'c$uUnion'('v$uS','t$ub') ),
inference(resolution,[status(thm)],[c8,c1]) ).
cnf(d1,plain,
( 'c$ulessequals'(X3,'c$uUnion'(X1,X2),'tc$uset'(X2))
| ~ 'c$uin'('c$uMain$uOsubsetI$u$u1'(X3,'c$uUnion'(X1,X2),X2),X0,X2)
| ~ 'c$uin'(X0,X1,'tc$uset'(X2)) ),
inference(resolution,[status(thm)],[c2,c7]) ).
cnf(d2,plain,
( 'c$ulessequals'(X0,'c$uUnion'(X1,X2),'tc$uset'(X2))
| ~ 'c$uin'(X0,X1,'tc$uset'(X2))
| 'c$ulessequals'(X0,'c$uUnion'(X1,X2),'tc$uset'(X2)) ),
inference(resolution,[status(thm)],[d1,c6]) ).
cnf(d3,plain,
( ~ 'c$uin'(X0,'v$uS','tc$uset'('t$ub'))
| X0 = 'c$uUnion'('v$uS','t$ub')
| ~ 'c$uin'(X0,'v$uS','tc$uset'('t$ub')) ),
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
( 'c$ulessequals'('v$uS',X0,'tc$uset'('tc$uset'('t$ub')))
| 'c$uMain$uOsubsetI$u$u1'('v$uS',X0,'tc$uset'('t$ub')) = 'c$uUnion'('v$uS','t$ub') ),
inference(resolution,[status(thm)],[d3,c6]) ).
cnf(d5,plain,
( 'c$ulessequals'('v$uS',X0,'tc$uset'('tc$uset'('t$ub')))
| 'c$ulessequals'('v$uS',X0,'tc$uset'('tc$uset'('t$ub')))
| ~ 'c$uin'('c$uUnion'('v$uS','t$ub'),X0,'tc$uset'('t$ub')) ),
inference(superposition,[status(thm)],[d4,c7]) ).
cnf(d6,plain,
'c$ulessequals'('v$uS','c$uinsert'('c$uUnion'('v$uS','t$ub'),X0,'tc$uset'('t$ub')),'tc$uset'('tc$uset'('t$ub'))),
inference(resolution,[status(thm)],[d5,c4]) ).
cnf(d7,plain,
$false,
inference(resolution,[status(thm)],[d6,c0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET840-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n020.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 26 08:21:18 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.71/4.27 % SZS status Unsatisfiable for theBenchmark.p
% 13.71/4.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------