%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET825-2 : 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 : n008.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 9.09s 3.17s
% Output : CNFRefutation 9.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of clauses : 21 ( 8 unt; 9 nHn; 19 RR)
% Number of literals : 42 ( 11 equ; 15 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 14 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Relation_OIdI_0,axiom,
'c$uin'('c$uPair'(X0,X0,X1,X1),'c$uRelation$uOId','tc$uprod'(X1,X1)) ).
cnf(cls_Relation_Opair__in__Id__conv__iff1_0,axiom,
( X0 = X1
| ~ 'c$uin'('c$uPair'(X0,X1,X2,X2),'c$uRelation$uOId','tc$uprod'(X2,X2)) ) ).
cnf(cls_conjecture_0,negated_conjecture,
'v$uQ'('v$un') ).
cnf(cls_conjecture_1,negated_conjecture,
~ 'v$uQ'('v$um') ).
cnf(cls_conjecture_2,negated_conjecture,
( ~ 'c$uin'('c$uPair'('c$u0','c$u0','tc$unat','tc$unat'),X0,'tc$uprod'('tc$unat','tc$unat'))
| 'c$uin'('c$uPair'('v$ux'(X0),'v$uxa'(X0),'tc$unat','tc$unat'),X0,'tc$uprod'('tc$unat','tc$unat'))
| 'c$uin'('c$uPair'('v$un','v$um','tc$unat','tc$unat'),X0,'tc$uprod'('tc$unat','tc$unat')) ) ).
cnf(cls_conjecture_3,negated_conjecture,
( ~ 'c$uin'('c$uPair'('c$u0','c$u0','tc$unat','tc$unat'),X0,'tc$uprod'('tc$unat','tc$unat'))
| ~ 'c$uin'('c$uPair'('c$uSuc'('v$ux'(X0)),'c$uSuc'('v$uxa'(X0)),'tc$unat','tc$unat'),X0,'tc$uprod'('tc$unat','tc$unat'))
| 'c$uin'('c$uPair'('v$un','v$um','tc$unat','tc$unat'),X0,'tc$uprod'('tc$unat','tc$unat')) ) ).
cnf(c0,plain,
'c$uin'('c$uPair'(X0,X0,X1,X1),'c$uRelation$uOId','tc$uprod'(X1,X1)),
inference(clausification,[status(esa)],[cls_Relation_OIdI_0]) ).
cnf(c1,plain,
( X0 = X1
| ~ 'c$uin'('c$uPair'(X0,X1,X2,X2),'c$uRelation$uOId','tc$uprod'(X2,X2)) ),
inference(clausification,[status(esa)],[cls_Relation_Opair__in__Id__conv__iff1_0]) ).
cnf(c2,plain,
'v$uQ'('v$un'),
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(c3,plain,
~ 'v$uQ'('v$um'),
inference(clausification,[status(esa)],[cls_conjecture_1]) ).
cnf(c4,plain,
( ~ 'c$uin'('c$uPair'('c$u0','c$u0','tc$unat','tc$unat'),X0,'tc$uprod'('tc$unat','tc$unat'))
| 'c$uin'('c$uPair'('v$ux'(X0),'v$uxa'(X0),'tc$unat','tc$unat'),X0,'tc$uprod'('tc$unat','tc$unat'))
| 'c$uin'('c$uPair'('v$un','v$um','tc$unat','tc$unat'),X0,'tc$uprod'('tc$unat','tc$unat')) ),
inference(clausification,[status(esa)],[cls_conjecture_2]) ).
cnf(c5,plain,
( ~ 'c$uin'('c$uPair'('c$u0','c$u0','tc$unat','tc$unat'),X0,'tc$uprod'('tc$unat','tc$unat'))
| ~ 'c$uin'('c$uPair'('c$uSuc'('v$ux'(X0)),'c$uSuc'('v$uxa'(X0)),'tc$unat','tc$unat'),X0,'tc$uprod'('tc$unat','tc$unat'))
| 'c$uin'('c$uPair'('v$un','v$um','tc$unat','tc$unat'),X0,'tc$uprod'('tc$unat','tc$unat')) ),
inference(clausification,[status(esa)],[cls_conjecture_3]) ).
cnf(d0,plain,
( 'v$ux'('c$uRelation$uOId') = 'v$uxa'('c$uRelation$uOId')
| ~ 'c$uin'('c$uPair'('c$u0','c$u0','tc$unat','tc$unat'),'c$uRelation$uOId','tc$uprod'('tc$unat','tc$unat'))
| 'c$uin'('c$uPair'('v$un','v$um','tc$unat','tc$unat'),'c$uRelation$uOId','tc$uprod'('tc$unat','tc$unat')) ),
inference(resolution,[status(thm)],[c4,c1]) ).
cnf(d1,plain,
( 'c$uin'('c$uPair'('v$un','v$um','tc$unat','tc$unat'),'c$uRelation$uOId','tc$uprod'('tc$unat','tc$unat'))
| 'v$ux'('c$uRelation$uOId') = 'v$uxa'('c$uRelation$uOId') ),
inference(resolution,[status(thm)],[c0,d0]) ).
cnf(d2,plain,
( 'v$un' = 'v$um'
| 'v$ux'('c$uRelation$uOId') = 'v$uxa'('c$uRelation$uOId') ),
inference(resolution,[status(thm)],[d1,c1]) ).
cnf(d3,plain,
( 'v$un' = 'v$um'
| ~ 'c$uin'('c$uPair'('c$u0','c$u0','tc$unat','tc$unat'),'c$uRelation$uOId','tc$uprod'('tc$unat','tc$unat'))
| 'c$uin'('c$uPair'('v$un','v$um','tc$unat','tc$unat'),'c$uRelation$uOId','tc$uprod'('tc$unat','tc$unat'))
| ~ 'c$uin'('c$uPair'('c$uSuc'('v$ux'('c$uRelation$uOId')),'c$uSuc'('v$ux'('c$uRelation$uOId')),'tc$unat','tc$unat'),'c$uRelation$uOId','tc$uprod'('tc$unat','tc$unat')) ),
inference(superposition,[status(thm)],[d2,c5]) ).
cnf(d4,plain,
( ~ 'c$uin'('c$uPair'('c$uSuc'('v$ux'('c$uRelation$uOId')),'c$uSuc'('v$ux'('c$uRelation$uOId')),'tc$unat','tc$unat'),'c$uRelation$uOId','tc$uprod'('tc$unat','tc$unat'))
| 'c$uin'('c$uPair'('v$un','v$um','tc$unat','tc$unat'),'c$uRelation$uOId','tc$uprod'('tc$unat','tc$unat'))
| 'v$un' = 'v$um' ),
inference(resolution,[status(thm)],[c0,d3]) ).
cnf(d5,plain,
( 'c$uin'('c$uPair'('v$un','v$um','tc$unat','tc$unat'),'c$uRelation$uOId','tc$uprod'('tc$unat','tc$unat'))
| 'v$un' = 'v$um' ),
inference(resolution,[status(thm)],[d4,c0]) ).
cnf(d6,plain,
( 'v$un' = 'v$um'
| 'v$un' = 'v$um' ),
inference(resolution,[status(thm)],[d5,c1]) ).
cnf(d7,plain,
~ 'v$uQ'('v$un'),
inference(demodulation,[status(thm)],[c3,d6]) ).
cnf(d8,plain,
$false,
inference(resolution,[status(thm)],[c2,d7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET825-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.63 % Computer : n008.cluster.edu
% 0.16/0.63 % Model : x86_64 x86_64
% 0.16/0.63 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.63 % Memory : 8046.5625MB
% 0.16/0.63 % OS : Linux 6.8.0-71-generic
% 0.16/0.63 % CPULimit : 300
% 0.16/0.63 % WCLimit : 300
% 0.16/0.63 % DateTime : Sat Sep 26 08:19:40 UTC 2026
% 0.16/0.64 % CPUTime :
% 0.16/0.64 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.09/3.17 % SZS status Unsatisfiable for theBenchmark.p
% 9.09/3.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------