%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ALG363-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 38.15s 5.28s
% Output : CNFRefutation 38.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of clauses : 23 ( 16 unt; 0 nHn; 16 RR)
% Number of literals : 32 ( 7 equ; 12 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 16 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_abs__add__one__gt__zero_0,axiom,
'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'c$uHOL$uOplus$u$uclass$uOplus'('c$uHOL$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'),'c$uHOL$uOabs$u$uclass$uOabs'(X0,'tc$uRealDef$uOreal'),'tc$uRealDef$uOreal'),'tc$uRealDef$uOreal') ).
cnf(cls_class__semiring_Osemiring__rules_I24_J_0,axiom,
( 'c$uHOL$uOplus$u$uclass$uOplus'(X1,X2,X0) = 'c$uHOL$uOplus$u$uclass$uOplus'(X2,X1,X0)
| ~ 'class$uRing$u$uand$u$uField$uOcomm$u$usemiring$u$u1'(X0) ) ).
cnf(cls_rp_0,axiom,
'c$ulessequals'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'v$ur','tc$uRealDef$uOreal') ).
cnf(cls_th_0,axiom,
'c$ulessequals'('c$uHOL$uOabs$u$uclass$uOabs'('c$uComplex$uORe'('v$us'(X0)),'tc$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(cls_abs__of__nonneg_0,axiom,
( ~ 'c$ulessequals'('c$uHOL$uOzero$u$uclass$uOzero'(X0),X1,X0)
| 'c$uHOL$uOabs$u$uclass$uOabs'(X1,X0) = X1
| ~ 'class$uOrderedGroup$uOpordered$u$uab$u$ugroup$u$uadd$u$uabs'(X0) ) ).
cnf(cls_conjecture_0,negated_conjecture,
( ~ 'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$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')
| ~ 'c$ulessequals'('c$uHOL$uOabs$u$uclass$uOabs'('c$uComplex$uORe'('v$us'('v$uf'('v$ux'))),'tc$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__OrderedGroup_Opordered__ab__group__add__abs,axiom,
'class$uOrderedGroup$uOpordered$u$uab$u$ugroup$u$uadd$u$uabs'('tc$uRealDef$uOreal') ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1,axiom,
'class$uRing$u$uand$u$uField$uOcomm$u$usemiring$u$u1'('tc$uRealDef$uOreal') ).
cnf(c451,plain,
'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'c$uHOL$uOplus$u$uclass$uOplus'('c$uHOL$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'),'c$uHOL$uOabs$u$uclass$uOabs'(X0,'tc$uRealDef$uOreal'),'tc$uRealDef$uOreal'),'tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[cls_abs__add__one__gt__zero_0]) ).
cnf(c455,plain,
( 'c$uHOL$uOplus$u$uclass$uOplus'(X1,X2,X0) = 'c$uHOL$uOplus$u$uclass$uOplus'(X2,X1,X0)
| ~ 'class$uRing$u$uand$u$uField$uOcomm$u$usemiring$u$u1'(X0) ),
inference(clausification,[status(esa)],[cls_class__semiring_Osemiring__rules_I24_J_0]) ).
cnf(c535,plain,
'c$ulessequals'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'v$ur','tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[cls_rp_0]) ).
cnf(c536,plain,
'c$ulessequals'('c$uHOL$uOabs$u$uclass$uOabs'('c$uComplex$uORe'('v$us'(X0)),'tc$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_th_0]) ).
cnf(c546,plain,
( ~ 'c$ulessequals'('c$uHOL$uOzero$u$uclass$uOzero'(X0),X1,X0)
| 'c$uHOL$uOabs$u$uclass$uOabs'(X1,X0) = X1
| ~ 'class$uOrderedGroup$uOpordered$u$uab$u$ugroup$u$uadd$u$uabs'(X0) ),
inference(clausification,[status(esa)],[cls_abs__of__nonneg_0]) ).
cnf(c611,plain,
( ~ 'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$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')
| ~ 'c$ulessequals'('c$uHOL$uOabs$u$uclass$uOabs'('c$uComplex$uORe'('v$us'('v$uf'('v$ux'))),'tc$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(c618,plain,
'class$uOrderedGroup$uOpordered$u$uab$u$ugroup$u$uadd$u$uabs'('tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs]) ).
cnf(c636,plain,
'class$uRing$u$uand$u$uField$uOcomm$u$usemiring$u$u1'('tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1]) ).
cnf(d0,plain,
'c$uHOL$uOplus$u$uclass$uOplus'(X0,X1,'tc$uRealDef$uOreal') = 'c$uHOL$uOplus$u$uclass$uOplus'(X1,X0,'tc$uRealDef$uOreal'),
inference(resolution,[status(thm)],[c455,c636]) ).
cnf(d1,plain,
( ~ 'class$uOrderedGroup$uOpordered$u$uab$u$ugroup$u$uadd$u$uabs'('tc$uRealDef$uOreal')
| 'c$uHOL$uOabs$u$uclass$uOabs'('v$ur','tc$uRealDef$uOreal') = 'v$ur' ),
inference(resolution,[status(thm)],[c546,c535]) ).
cnf(d2,plain,
'c$uHOL$uOabs$u$uclass$uOabs'('v$ur','tc$uRealDef$uOreal') = 'v$ur',
inference(resolution,[status(thm)],[c618,d1]) ).
cnf(d3,plain,
'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'c$uHOL$uOplus$u$uclass$uOplus'('c$uHOL$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'),'v$ur','tc$uRealDef$uOreal'),'tc$uRealDef$uOreal'),
inference(superposition,[status(thm)],[d2,c451]) ).
cnf(d4,plain,
'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$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(demodulation,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
~ 'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('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(resolution,[status(thm)],[c536,c611]) ).
cnf(d6,plain,
$false,
inference(resolution,[status(thm)],[d5,d4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG363-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n018.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 21:57:22 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 38.15/5.28 % SZS status Unsatisfiable for theBenchmark.p
% 38.15/5.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------