%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET839-2 : 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 : n015.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 14.90s 2.42s
% Output : CNFRefutation 14.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of clauses : 22 ( 7 unt; 8 nHn; 13 RR)
% Number of literals : 52 ( 8 equ; 20 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 48 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
~ 'c$ulessequals'('v$uS','c$uinsert'(X0,'c$uemptyset','tc$uset'('t$ua')),'tc$uset'('tc$uset'('t$ua'))) ).
cnf(cls_conjecture_1,negated_conjecture,
( ~ 'c$uin'(X0,'v$uS','tc$uset'('t$ua'))
| ~ 'c$uin'(X1,'v$uS','tc$uset'('t$ua'))
| 'c$ulessequals'(X0,X1,'tc$uset'('t$ua')) ) ).
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$uset'('t$ua')),'tc$uset'('tc$uset'('t$ua'))),
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(c1,plain,
( ~ 'c$uin'(X0,'v$uS','tc$uset'('t$ua'))
| ~ 'c$uin'(X1,'v$uS','tc$uset'('t$ua'))
| 'c$ulessequals'(X0,X1,'tc$uset'('t$ua')) ),
inference(clausification,[status(esa)],[cls_conjecture_1]) ).
cnf(c2,plain,
'c$uin'(X0,'c$uinsert'(X0,X1,X2),X2),
inference(clausification,[status(esa)],[cls_Set_OinsertCI_1]) ).
cnf(c3,plain,
( 'c$ulessequals'(X0,X1,'tc$uset'(X2))
| 'c$uin'('c$uMain$uOsubsetI$u$u1'(X0,X1,X2),X0,X2) ),
inference(clausification,[status(esa)],[cls_Set_OsubsetI_0]) ).
cnf(c4,plain,
( 'c$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(c5,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$ulessequals'('v$uS',X1,'tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'(X0,'v$uS','tc$uset'('t$ua'))
| 'c$ulessequals'(X0,'c$uMain$uOsubsetI$u$u1'('v$uS',X1,'tc$uset'('t$ua')),'tc$uset'('t$ua')) ),
inference(resolution,[status(thm)],[c1,c3]) ).
cnf(d1,plain,
( ~ 'c$ulessequals'('c$uMain$uOsubsetI$u$u1'('v$uS',X0,'tc$uset'('t$ua')),X1,'tc$uset'('t$ua'))
| 'c$uMain$uOsubsetI$u$u1'('v$uS',X0,'tc$uset'('t$ua')) = X1
| ~ 'c$uin'(X1,'v$uS','tc$uset'('t$ua'))
| 'c$ulessequals'('v$uS',X0,'tc$uset'('tc$uset'('t$ua'))) ),
inference(resolution,[status(thm)],[d0,c5]) ).
cnf(d2,plain,
( ~ 'c$uin'('c$uMain$uOsubsetI$u$u1'('v$uS',X0,'tc$uset'('t$ua')),'v$uS','tc$uset'('t$ua'))
| 'c$ulessequals'('v$uS',X1,'tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'('c$uMain$uOsubsetI$u$u1'('v$uS',X1,'tc$uset'('t$ua')),'v$uS','tc$uset'('t$ua'))
| 'c$ulessequals'('v$uS',X0,'tc$uset'('tc$uset'('t$ua')))
| 'c$uMain$uOsubsetI$u$u1'('v$uS',X0,'tc$uset'('t$ua')) = 'c$uMain$uOsubsetI$u$u1'('v$uS',X1,'tc$uset'('t$ua')) ),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
( 'c$ulessequals'('v$uS',X0,'tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'('c$uMain$uOsubsetI$u$u1'('v$uS',X1,'tc$uset'('t$ua')),'v$uS','tc$uset'('t$ua'))
| 'c$ulessequals'('v$uS',X0,'tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'('v$uS',X1,'tc$uset'('tc$uset'('t$ua')))
| 'c$uMain$uOsubsetI$u$u1'('v$uS',X0,'tc$uset'('t$ua')) = 'c$uMain$uOsubsetI$u$u1'('v$uS',X1,'tc$uset'('t$ua')) ),
inference(resolution,[status(thm)],[d2,c3]) ).
cnf(d4,plain,
( 'c$ulessequals'('v$uS',X1,'tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'('v$uS',X0,'tc$uset'('tc$uset'('t$ua')))
| 'c$ulessequals'('v$uS',X1,'tc$uset'('tc$uset'('t$ua')))
| 'c$uMain$uOsubsetI$u$u1'('v$uS',X0,'tc$uset'('t$ua')) = 'c$uMain$uOsubsetI$u$u1'('v$uS',X1,'tc$uset'('t$ua')) ),
inference(resolution,[status(thm)],[d3,c3]) ).
cnf(d5,plain,
( 'c$ulessequals'('v$uS',X0,'tc$uset'('tc$uset'('t$ua')))
| 'c$uMain$uOsubsetI$u$u1'('v$uS',X0,'tc$uset'('t$ua')) = 'c$uMain$uOsubsetI$u$u1'('v$uS','c$uinsert'(X1,'c$uemptyset','tc$uset'('t$ua')),'tc$uset'('t$ua')) ),
inference(resolution,[status(thm)],[d4,c0]) ).
cnf(d6,plain,
'c$uMain$uOsubsetI$u$u1'('v$uS','c$uinsert'(X0,'c$uemptyset','tc$uset'('t$ua')),'tc$uset'('t$ua')) = 'c$uMain$uOsubsetI$u$u1'('v$uS','c$uinsert'(X1,'c$uemptyset','tc$uset'('t$ua')),'tc$uset'('t$ua')),
inference(resolution,[status(thm)],[d5,c0]) ).
cnf(d7,plain,
( 'c$ulessequals'('v$uS','c$uinsert'(X0,'c$uemptyset','tc$uset'('t$ua')),'tc$uset'('tc$uset'('t$ua')))
| ~ 'c$uin'('c$uMain$uOsubsetI$u$u1'('v$uS','c$uinsert'(X1,'c$uemptyset','tc$uset'('t$ua')),'tc$uset'('t$ua')),'c$uinsert'(X0,'c$uemptyset','tc$uset'('t$ua')),'tc$uset'('t$ua')) ),
inference(superposition,[status(thm)],[d6,c4]) ).
cnf(d8,plain,
~ 'c$uin'('c$uMain$uOsubsetI$u$u1'('v$uS','c$uinsert'(X0,'c$uemptyset','tc$uset'('t$ua')),'tc$uset'('t$ua')),'c$uinsert'(X1,'c$uemptyset','tc$uset'('t$ua')),'tc$uset'('t$ua')),
inference(resolution,[status(thm)],[c0,d7]) ).
cnf(d9,plain,
$false,
inference(resolution,[status(thm)],[d8,c2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET839-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n015.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sat Sep 26 08:23:28 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.90/2.42 % SZS status Unsatisfiable for theBenchmark.p
% 14.90/2.42 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------