%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET821-2 : 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 : n007.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 5.85s 8.16s
% Output : CNFRefutation 5.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of clauses : 36 ( 12 unt; 14 nHn; 27 RR)
% Number of literals : 72 ( 15 equ; 23 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 49 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Orderings_Oorder__less__irrefl__iff1_0,axiom,
( ~ 'c$uless'(X1,X1,X0)
| ~ 'class$uOrderings$uOorder'(X0) ) ).
cnf(cls_Set_OComplD__dest_0,axiom,
( ~ 'c$uin'(X0,'c$uuminus'(X1,'tc$uset'(X2)),X2)
| ~ 'c$uin'(X0,X1,X2) ) ).
cnf(cls_Set_OComplI_0,axiom,
( 'c$uin'(X0,'c$uuminus'(X1,'tc$uset'(X2)),X2)
| 'c$uin'(X0,X1,X2) ) ).
cnf(cls_Set_OinsertCI_0,axiom,
( 'c$uin'(X0,'c$uinsert'(X3,X1,X2),X2)
| ~ 'c$uin'(X0,X1,X2) ) ).
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$uinsert'(X1,X2,X3),X3) ) ).
cnf(cls_conjecture_0,negated_conjecture,
'c$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$uOint') ) ).
cnf(clsarity_IntDef__Oint_31,axiom,
'class$uOrderings$uOorder'('tc$uIntDef$uOint') ).
cnf(c0,plain,
( ~ 'c$uless'(X1,X1,X0)
| ~ 'class$uOrderings$uOorder'(X0) ),
inference(clausification,[status(esa)],[cls_Orderings_Oorder__less__irrefl__iff1_0]) ).
cnf(c1,plain,
( ~ 'c$uin'(X0,'c$uuminus'(X1,'tc$uset'(X2)),X2)
| ~ 'c$uin'(X0,X1,X2) ),
inference(clausification,[status(esa)],[cls_Set_OComplD__dest_0]) ).
cnf(c2,plain,
( 'c$uin'(X0,'c$uuminus'(X1,'tc$uset'(X2)),X2)
| 'c$uin'(X0,X1,X2) ),
inference(clausification,[status(esa)],[cls_Set_OComplI_0]) ).
cnf(c3,plain,
( 'c$uin'(X0,'c$uinsert'(X3,X1,X2),X2)
| ~ 'c$uin'(X0,X1,X2) ),
inference(clausification,[status(esa)],[cls_Set_OinsertCI_0]) ).
cnf(c4,plain,
'c$uin'(X0,'c$uinsert'(X0,X1,X2),X2),
inference(clausification,[status(esa)],[cls_Set_OinsertCI_1]) ).
cnf(c5,plain,
( X0 = X1
| 'c$uin'(X0,X2,X3)
| ~ 'c$uin'(X0,'c$uinsert'(X1,X2,X3),X3) ),
inference(clausification,[status(esa)],[cls_Set_OinsertE_0]) ).
cnf(c6,plain,
'c$uless'('v$ua','v$ub','tc$uIntDef$uOint'),
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(c7,plain,
'c$uless'('v$ub','v$uc','tc$uIntDef$uOint'),
inference(clausification,[status(esa)],[cls_conjecture_1]) ).
cnf(c8,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(c9,plain,
'class$uOrderings$uOorder'('tc$uIntDef$uOint'),
inference(clausification,[status(esa)],[clsarity_IntDef__Oint_31]) ).
cnf(d0,plain,
( 'c$uin'('v$ub',X0,'tc$uIntDef$uOint')
| 'c$uin'('v$uc','c$uuminus'(X0,'tc$uset'('tc$uIntDef$uOint')),'tc$uIntDef$uOint')
| 'c$uin'('v$ua','c$uuminus'(X0,'tc$uset'('tc$uIntDef$uOint')),'tc$uIntDef$uOint') ),
inference(resolution,[status(thm)],[c8,c2]) ).
cnf(d1,plain,
( ~ 'c$uin'('v$uc',X0,'tc$uIntDef$uOint')
| 'c$uin'('v$ub',X0,'tc$uIntDef$uOint')
| 'c$uin'('v$ua','c$uuminus'(X0,'tc$uset'('tc$uIntDef$uOint')),'tc$uIntDef$uOint') ),
inference(resolution,[status(thm)],[d0,c1]) ).
cnf(d2,plain,
( ~ 'c$uin'('v$ua',X0,'tc$uIntDef$uOint')
| ~ 'c$uin'('v$uc',X0,'tc$uIntDef$uOint')
| 'c$uin'('v$ub',X0,'tc$uIntDef$uOint') ),
inference(resolution,[status(thm)],[d1,c1]) ).
cnf(d3,plain,
( 'c$uin'('v$ub','c$uinsert'('v$uc',X0,'tc$uIntDef$uOint'),'tc$uIntDef$uOint')
| ~ 'c$uin'('v$ua','c$uinsert'('v$uc',X0,'tc$uIntDef$uOint'),'tc$uIntDef$uOint') ),
inference(resolution,[status(thm)],[d2,c4]) ).
cnf(d4,plain,
( ~ 'c$uin'('v$ua',X0,'tc$uIntDef$uOint')
| 'c$uin'('v$ub','c$uinsert'('v$uc',X0,'tc$uIntDef$uOint'),'tc$uIntDef$uOint') ),
inference(resolution,[status(thm)],[d3,c3]) ).
cnf(d5,plain,
( 'c$uin'('v$ub',X0,'tc$uIntDef$uOint')
| 'v$ub' = 'v$uc'
| ~ 'c$uin'('v$ua',X0,'tc$uIntDef$uOint') ),
inference(resolution,[status(thm)],[d4,c5]) ).
cnf(d6,plain,
( 'c$uin'('v$ub','c$uinsert'('v$ua',X0,'tc$uIntDef$uOint'),'tc$uIntDef$uOint')
| 'v$ub' = 'v$uc' ),
inference(resolution,[status(thm)],[d5,c4]) ).
cnf(d7,plain,
( 'c$uin'('v$ub',X0,'tc$uIntDef$uOint')
| 'v$ub' = 'v$ua'
| 'v$ub' = 'v$uc' ),
inference(resolution,[status(thm)],[d6,c5]) ).
cnf(d8,plain,
( ~ 'c$uin'('v$ub',X0,'tc$uIntDef$uOint')
| 'v$ub' = 'v$uc'
| 'v$ub' = 'v$ua' ),
inference(resolution,[status(thm)],[d7,c1]) ).
cnf(d9,plain,
( 'v$ub' = 'v$uc'
| 'v$ub' = 'v$ua'
| 'v$ub' = 'v$uc'
| 'v$ub' = 'v$ua' ),
inference(resolution,[status(thm)],[d8,d7]) ).
cnf(d10,plain,
( 'v$ub' = 'v$ua'
| 'c$uless'('v$ub','v$ub','tc$uIntDef$uOint') ),
inference(superposition,[status(thm)],[d9,c7]) ).
cnf(d11,plain,
( ~ 'class$uOrderings$uOorder'('tc$uIntDef$uOint')
| 'v$ub' = 'v$ua' ),
inference(resolution,[status(thm)],[d10,c0]) ).
cnf(d12,plain,
'v$ub' = 'v$ua',
inference(resolution,[status(thm)],[c9,d11]) ).
cnf(d13,plain,
'c$uless'('v$ub','v$ub','tc$uIntDef$uOint'),
inference(demodulation,[status(thm)],[c6,d12]) ).
cnf(d14,plain,
~ 'class$uOrderings$uOorder'('tc$uIntDef$uOint'),
inference(resolution,[status(thm)],[d13,c0]) ).
cnf(d15,plain,
$false,
inference(resolution,[status(thm)],[c9,d14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET821-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.45 % Computer : n007.cluster.edu
% 0.10/5.45 % Model : x86_64 x86_64
% 0.10/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.45 % Memory : 8046.5625MB
% 0.10/5.45 % OS : Linux 6.8.0-71-generic
% 0.10/5.45 % CPULimit : 300
% 0.10/5.45 % WCLimit : 300
% 0.10/5.45 % DateTime : Sat Sep 26 08:16:44 UTC 2026
% 0.10/5.45 % CPUTime :
% 0.10/5.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.85/8.16 % SZS status Unsatisfiable for theBenchmark.p
% 5.85/8.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------