%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ALG362-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 06:48:23 AM UTC 2026
% Result : Unsatisfiable 81.48s 13.10s
% Output : CNFRefutation 81.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of clauses : 21 ( 12 unt; 0 nHn; 12 RR)
% Number of literals : 32 ( 0 equ; 14 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 25 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_real__less__def_0,axiom,
( ~ 'c$uHOL$uOord$u$uclass$uOless'(X0,X1,'tc$uRealDef$uOreal')
| 'c$ulessequals'(X0,X1,'tc$uRealDef$uOreal') ) ).
cnf(cls_less__add__one_0,axiom,
( 'c$uHOL$uOord$u$uclass$uOless'(X1,'c$uHOL$uOplus$u$uclass$uOplus'(X1,'c$uHOL$uOone$u$uclass$uOone'(X0),X0),X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$usemidom'(X0) ) ).
cnf(cls_abs__Re__le__cmod_0,axiom,
'c$ulessequals'('c$uHOL$uOabs$u$uclass$uOabs'('c$uComplex$uORe'(X0),'tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'(X0,'tc$uComplex$uOcomplex'),'tc$uRealDef$uOreal') ).
cnf(cls_r_0,axiom,
'c$ulessequals'('c$uRealVector$uOnorm$u$uclass$uOnorm'(hAPP('v$us',X0),'tc$uComplex$uOcomplex'),'v$ur','tc$uRealDef$uOreal') ).
cnf(cls_real__le__trans_0,axiom,
( ~ 'c$ulessequals'(X0,X2,'tc$uRealDef$uOreal')
| ~ 'c$ulessequals'(X2,X1,'tc$uRealDef$uOreal')
| 'c$ulessequals'(X0,X1,'tc$uRealDef$uOreal') ) ).
cnf(cls_conjecture_0,negated_conjecture,
~ 'c$ulessequals'('c$uHOL$uOabs$u$uclass$uOabs'('c$uComplex$uORe'(hAPP('v$us','v$un')),'tc$uRealDef$uOreal'),'c$uHOL$uOplus$u$uclass$uOplus'('v$ur','c$uHOL$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'),'tc$uRealDef$uOreal'),'tc$uRealDef$uOreal') ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom,axiom,
'class$uRing$u$uand$u$uField$uOordered$u$usemidom'('tc$uRealDef$uOreal') ).
cnf(c430,plain,
( ~ 'c$uHOL$uOord$u$uclass$uOless'(X0,X1,'tc$uRealDef$uOreal')
| 'c$ulessequals'(X0,X1,'tc$uRealDef$uOreal') ),
inference(clausification,[status(esa)],[cls_real__less__def_0]) ).
cnf(c579,plain,
( 'c$uHOL$uOord$u$uclass$uOless'(X1,'c$uHOL$uOplus$u$uclass$uOplus'(X1,'c$uHOL$uOone$u$uclass$uOone'(X0),X0),X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$usemidom'(X0) ),
inference(clausification,[status(esa)],[cls_less__add__one_0]) ).
cnf(c623,plain,
'c$ulessequals'('c$uHOL$uOabs$u$uclass$uOabs'('c$uComplex$uORe'(X0),'tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'(X0,'tc$uComplex$uOcomplex'),'tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[cls_abs__Re__le__cmod_0]) ).
cnf(c624,plain,
'c$ulessequals'('c$uRealVector$uOnorm$u$uclass$uOnorm'(hAPP('v$us',X0),'tc$uComplex$uOcomplex'),'v$ur','tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[cls_r_0]) ).
cnf(c631,plain,
( ~ 'c$ulessequals'(X0,X2,'tc$uRealDef$uOreal')
| ~ 'c$ulessequals'(X2,X1,'tc$uRealDef$uOreal')
| 'c$ulessequals'(X0,X1,'tc$uRealDef$uOreal') ),
inference(clausification,[status(esa)],[cls_real__le__trans_0]) ).
cnf(c674,plain,
~ 'c$ulessequals'('c$uHOL$uOabs$u$uclass$uOabs'('c$uComplex$uORe'(hAPP('v$us','v$un')),'tc$uRealDef$uOreal'),'c$uHOL$uOplus$u$uclass$uOplus'('v$ur','c$uHOL$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'),'tc$uRealDef$uOreal'),'tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(c728,plain,
'class$uRing$u$uand$u$uField$uOordered$u$usemidom'('tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom]) ).
cnf(d0,plain,
( 'c$ulessequals'(X0,'c$uHOL$uOplus$u$uclass$uOplus'(X0,'c$uHOL$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'),'tc$uRealDef$uOreal'),'tc$uRealDef$uOreal')
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$usemidom'('tc$uRealDef$uOreal') ),
inference(resolution,[status(thm)],[c579,c430]) ).
cnf(d1,plain,
'c$ulessequals'(X0,'c$uHOL$uOplus$u$uclass$uOplus'(X0,'c$uHOL$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'),'tc$uRealDef$uOreal'),'tc$uRealDef$uOreal'),
inference(resolution,[status(thm)],[c728,d0]) ).
cnf(d2,plain,
( ~ 'c$ulessequals'(X0,X1,'tc$uRealDef$uOreal')
| 'c$ulessequals'(X0,'c$uHOL$uOplus$u$uclass$uOplus'(X1,'c$uHOL$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'),'tc$uRealDef$uOreal'),'tc$uRealDef$uOreal') ),
inference(resolution,[status(thm)],[c631,d1]) ).
cnf(d3,plain,
~ 'c$ulessequals'('c$uHOL$uOabs$u$uclass$uOabs'('c$uComplex$uORe'(hAPP('v$us','v$un')),'tc$uRealDef$uOreal'),'v$ur','tc$uRealDef$uOreal'),
inference(resolution,[status(thm)],[d2,c674]) ).
cnf(d4,plain,
( ~ 'c$ulessequals'(X0,'c$uRealVector$uOnorm$u$uclass$uOnorm'(hAPP('v$us',X1),'tc$uComplex$uOcomplex'),'tc$uRealDef$uOreal')
| 'c$ulessequals'(X0,'v$ur','tc$uRealDef$uOreal') ),
inference(resolution,[status(thm)],[c631,c624]) ).
cnf(d5,plain,
'c$ulessequals'('c$uHOL$uOabs$u$uclass$uOabs'('c$uComplex$uORe'(hAPP('v$us',X0)),'tc$uRealDef$uOreal'),'v$ur','tc$uRealDef$uOreal'),
inference(resolution,[status(thm)],[d4,c623]) ).
cnf(d6,plain,
$false,
inference(resolution,[status(thm)],[d5,d3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG362-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n019.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 21:55:18 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 81.48/13.10 % SZS status Unsatisfiable for theBenchmark.p
% 81.48/13.10 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------