%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET821-1 : 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 : 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 08:33:17 AM UTC 2026
% Result : Unsatisfiable 15.85s 6.85s
% Output : CNFRefutation 15.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of clauses : 23 ( 12 unt; 6 nHn; 20 RR)
% Number of literals : 36 ( 8 equ; 10 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-3 aty)
% Number of variables : 19 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
'c$uless'('v$ua','v$ub','tc$uIntDef$uOint') ).
cnf(cls_conjecture_1,negated_conjecture,
'c$uless'('v$ub','v$uc','tc$uIntDef$uOint') ).
cnf(cls_conjecture_2,negated_conjecture,
( 'c$uin'('v$ua',X0,'tc$uIntDef$uOint')
| ~ 'c$uin'('v$ub',X0,'tc$uIntDef$uOint')
| 'c$uin'('v$uc',X0,'tc$uIntDef$uOint') ) ).
cnf(cls_Orderings_Oorder__less__irrefl__iff1_0,axiom,
( ~ 'c$uless'(X1,X1,X0)
| ~ 'class$uOrderings$uOorder'(X0) ) ).
cnf(cls_Set_OinsertCI_1,axiom,
'c$uin'(X0,'c$uinsert'(X0,X1,X2),X2) ).
cnf(cls_Set_OsingletonD__dest_0,axiom,
( X0 = X1
| ~ 'c$uin'(X0,'c$uinsert'(X1,'c$uemptyset',X2),X2) ) ).
cnf(clsarity_IntDef__Oint_31,axiom,
'class$uOrderings$uOorder'('tc$uIntDef$uOint') ).
cnf(c0,plain,
'c$uless'('v$ua','v$ub','tc$uIntDef$uOint'),
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(c1,plain,
'c$uless'('v$ub','v$uc','tc$uIntDef$uOint'),
inference(clausification,[status(esa)],[cls_conjecture_1]) ).
cnf(c2,plain,
( 'c$uin'('v$ua',X0,'tc$uIntDef$uOint')
| ~ 'c$uin'('v$ub',X0,'tc$uIntDef$uOint')
| 'c$uin'('v$uc',X0,'tc$uIntDef$uOint') ),
inference(clausification,[status(esa)],[cls_conjecture_2]) ).
cnf(c125,plain,
( ~ 'c$uless'(X1,X1,X0)
| ~ 'class$uOrderings$uOorder'(X0) ),
inference(clausification,[status(esa)],[cls_Orderings_Oorder__less__irrefl__iff1_0]) ).
cnf(c178,plain,
'c$uin'(X0,'c$uinsert'(X0,X1,X2),X2),
inference(clausification,[status(esa)],[cls_Set_OinsertCI_1]) ).
cnf(c305,plain,
( X0 = X1
| ~ 'c$uin'(X0,'c$uinsert'(X1,'c$uemptyset',X2),X2) ),
inference(clausification,[status(esa)],[cls_Set_OsingletonD__dest_0]) ).
cnf(c354,plain,
'class$uOrderings$uOorder'('tc$uIntDef$uOint'),
inference(clausification,[status(esa)],[clsarity_IntDef__Oint_31]) ).
cnf(d0,plain,
( 'c$uin'('v$uc','c$uinsert'('v$ub',X0,'tc$uIntDef$uOint'),'tc$uIntDef$uOint')
| 'c$uin'('v$ua','c$uinsert'('v$ub',X0,'tc$uIntDef$uOint'),'tc$uIntDef$uOint') ),
inference(resolution,[status(thm)],[c178,c2]) ).
cnf(d1,plain,
( 'v$uc' = 'v$ub'
| 'c$uin'('v$ua','c$uinsert'('v$ub','c$uemptyset','tc$uIntDef$uOint'),'tc$uIntDef$uOint') ),
inference(resolution,[status(thm)],[d0,c305]) ).
cnf(d2,plain,
( 'v$ua' = 'v$ub'
| 'v$uc' = 'v$ub' ),
inference(resolution,[status(thm)],[d1,c305]) ).
cnf(d3,plain,
( 'v$ua' = 'v$ub'
| 'c$uless'('v$ub','v$ub','tc$uIntDef$uOint') ),
inference(superposition,[status(thm)],[d2,c1]) ).
cnf(d4,plain,
( ~ 'class$uOrderings$uOorder'('tc$uIntDef$uOint')
| 'v$ua' = 'v$ub' ),
inference(resolution,[status(thm)],[d3,c125]) ).
cnf(d5,plain,
'v$ua' = 'v$ub',
inference(resolution,[status(thm)],[c354,d4]) ).
cnf(d6,plain,
'c$uless'('v$ub','v$ub','tc$uIntDef$uOint'),
inference(demodulation,[status(thm)],[c0,d5]) ).
cnf(d7,plain,
~ 'class$uOrderings$uOorder'('tc$uIntDef$uOint'),
inference(resolution,[status(thm)],[d6,c125]) ).
cnf(d8,plain,
$false,
inference(resolution,[status(thm)],[c354,d7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET821-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.40 % Computer : n016.cluster.edu
% 0.09/0.40 % Model : x86_64 x86_64
% 0.09/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.40 % Memory : 8046.5625MB
% 0.09/0.40 % OS : Linux 6.8.0-71-generic
% 0.09/0.41 % CPULimit : 300
% 0.09/0.41 % WCLimit : 300
% 0.09/0.41 % DateTime : Sat Sep 26 08:23:16 UTC 2026
% 0.09/0.41 % CPUTime :
% 0.09/0.41 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.85/6.85 % SZS status Unsatisfiable for theBenchmark.p
% 15.85/6.85 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------