%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET822-2 : 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 : 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 08:33:18 AM UTC 2026
% Result : Unsatisfiable 9.61s 2.53s
% Output : CNFRefutation 9.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of clauses : 18 ( 10 unt; 3 nHn; 15 RR)
% Number of literals : 29 ( 5 equ; 14 neg)
% Maximal clause size : 3 ( 1 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 : 35 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Set_OemptyE_0,axiom,
~ 'c$uin'(X0,'c$uemptyset',X1) ).
cnf(cls_Set_OinsertCI_1,axiom,
'c$uin'(X0,'c$uinsert'(X0,X1,X2),X2) ).
cnf(cls_Set_OinsertE_0,axiom,
( X0 = X1
| 'c$uin'(X0,X2,X3)
| ~ 'c$uin'(X0,'c$uinsert'(X1,X2,X3),X3) ) ).
cnf(cls_conjecture_0,negated_conjecture,
'v$uP'('v$uf'('v$ub')) ).
cnf(cls_conjecture_1,negated_conjecture,
( 'c$uin'('v$ux'(X0,X1),X1,'tc$uIntDef$uOint')
| ~ 'c$uin'('v$uf'(X0),X1,'tc$uIntDef$uOint') ) ).
cnf(cls_conjecture_2,negated_conjecture,
( ~ 'v$uP'('v$ux'(X0,X1))
| ~ 'c$uin'('v$uf'(X0),X1,'tc$uIntDef$uOint') ) ).
cnf(c0,plain,
~ 'c$uin'(X0,'c$uemptyset',X1),
inference(clausification,[status(esa)],[cls_Set_OemptyE_0]) ).
cnf(c1,plain,
'c$uin'(X0,'c$uinsert'(X0,X1,X2),X2),
inference(clausification,[status(esa)],[cls_Set_OinsertCI_1]) ).
cnf(c2,plain,
( X0 = X1
| 'c$uin'(X0,X2,X3)
| ~ 'c$uin'(X0,'c$uinsert'(X1,X2,X3),X3) ),
inference(clausification,[status(esa)],[cls_Set_OinsertE_0]) ).
cnf(c3,plain,
'v$uP'('v$uf'('v$ub')),
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(c4,plain,
( 'c$uin'('v$ux'(X0,X1),X1,'tc$uIntDef$uOint')
| ~ 'c$uin'('v$uf'(X0),X1,'tc$uIntDef$uOint') ),
inference(clausification,[status(esa)],[cls_conjecture_1]) ).
cnf(c5,plain,
( ~ 'v$uP'('v$ux'(X0,X1))
| ~ 'c$uin'('v$uf'(X0),X1,'tc$uIntDef$uOint') ),
inference(clausification,[status(esa)],[cls_conjecture_2]) ).
cnf(d0,plain,
~ 'v$uP'('v$ux'(X0,'c$uinsert'('v$uf'(X0),X1,'tc$uIntDef$uOint'))),
inference(resolution,[status(thm)],[c5,c1]) ).
cnf(d1,plain,
( 'c$uin'('v$ux'(X0,'c$uinsert'(X1,X2,'tc$uIntDef$uOint')),X2,'tc$uIntDef$uOint')
| 'v$ux'(X0,'c$uinsert'(X1,X2,'tc$uIntDef$uOint')) = X1
| ~ 'c$uin'('v$uf'(X0),'c$uinsert'(X1,X2,'tc$uIntDef$uOint'),'tc$uIntDef$uOint') ),
inference(resolution,[status(thm)],[c4,c2]) ).
cnf(d2,plain,
( ~ 'c$uin'('v$uf'(X0),'c$uinsert'(X1,'c$uemptyset','tc$uIntDef$uOint'),'tc$uIntDef$uOint')
| 'v$ux'(X0,'c$uinsert'(X1,'c$uemptyset','tc$uIntDef$uOint')) = X1 ),
inference(resolution,[status(thm)],[d1,c0]) ).
cnf(d3,plain,
'v$ux'(X0,'c$uinsert'('v$uf'(X0),'c$uemptyset','tc$uIntDef$uOint')) = 'v$uf'(X0),
inference(resolution,[status(thm)],[d2,c1]) ).
cnf(d4,plain,
~ 'v$uP'('v$uf'(X0)),
inference(superposition,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
$false,
inference(resolution,[status(thm)],[d4,c3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET822-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n016.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sat Sep 26 08:23:33 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.61/2.53 % SZS status Unsatisfiable for theBenchmark.p
% 9.61/2.53 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------