%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ALG340-1 : 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 : n002.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 06:48:21 AM UTC 2026
% Result : Unsatisfiable 35.71s 6.33s
% Output : CNFRefutation 35.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of clauses : 21 ( 11 unt; 0 nHn; 15 RR)
% Number of literals : 31 ( 6 equ; 15 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 19 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_real__of__preal__zero__less_0,axiom,
'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'c$uRealDef$uOreal$u$uof$u$upreal'(X0),'tc$uRealDef$uOreal') ).
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_norm__zero_0,axiom,
( 'c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uHOL$uOzero$u$uclass$uOzero'(X0),X0) = 'c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal')
| ~ 'class$uRealVector$uOreal$u$unormed$u$uvector'(X0) ) ).
cnf(cls_poly__0_0,axiom,
( 'c$uPolynomial$uOpoly'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'(X0)),X1,X0) = 'c$uHOL$uOzero$u$uclass$uOzero'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOcomm$u$usemiring$u$u0'(X0) ) ).
cnf(cls_conjecture_1,negated_conjecture,
( ~ 'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),X0,'tc$uRealDef$uOreal')
| ~ 'c$ulessequals'('c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uPolynomial$uOpoly'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),'v$ux'(X0),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),X0,'tc$uRealDef$uOreal') ) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0,axiom,
'class$uRing$u$uand$u$uField$uOcomm$u$usemiring$u$u0'('tc$uComplex$uOcomplex') ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
'class$uRealVector$uOreal$u$unormed$u$uvector'('tc$uComplex$uOcomplex') ).
cnf(c212,plain,
'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'c$uRealDef$uOreal$u$uof$u$upreal'(X0),'tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[cls_real__of__preal__zero__less_0]) ).
cnf(c382,plain,
( ~ 'c$uHOL$uOord$u$uclass$uOless'(X0,X1,'tc$uRealDef$uOreal')
| 'c$ulessequals'(X0,X1,'tc$uRealDef$uOreal') ),
inference(clausification,[status(esa)],[cls_real__less__def_0]) ).
cnf(c389,plain,
( 'c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uHOL$uOzero$u$uclass$uOzero'(X0),X0) = 'c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal')
| ~ 'class$uRealVector$uOreal$u$unormed$u$uvector'(X0) ),
inference(clausification,[status(esa)],[cls_norm__zero_0]) ).
cnf(c390,plain,
( 'c$uPolynomial$uOpoly'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'(X0)),X1,X0) = 'c$uHOL$uOzero$u$uclass$uOzero'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOcomm$u$usemiring$u$u0'(X0) ),
inference(clausification,[status(esa)],[cls_poly__0_0]) ).
cnf(c428,plain,
( ~ 'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),X0,'tc$uRealDef$uOreal')
| ~ 'c$ulessequals'('c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uPolynomial$uOpoly'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),'v$ux'(X0),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),X0,'tc$uRealDef$uOreal') ),
inference(clausification,[status(esa)],[cls_conjecture_1]) ).
cnf(c492,plain,
'class$uRing$u$uand$u$uField$uOcomm$u$usemiring$u$u0'('tc$uComplex$uOcomplex'),
inference(clausification,[status(esa)],[clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0]) ).
cnf(c495,plain,
'class$uRealVector$uOreal$u$unormed$u$uvector'('tc$uComplex$uOcomplex'),
inference(clausification,[status(esa)],[clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector]) ).
cnf(d0,plain,
'c$ulessequals'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'c$uRealDef$uOreal$u$uof$u$upreal'(X0),'tc$uRealDef$uOreal'),
inference(resolution,[status(thm)],[c382,c212]) ).
cnf(d1,plain,
'c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex') = 'c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),
inference(resolution,[status(thm)],[c389,c495]) ).
cnf(d2,plain,
'c$uPolynomial$uOpoly'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),X0,'tc$uComplex$uOcomplex') = 'c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),
inference(resolution,[status(thm)],[c390,c492]) ).
cnf(d3,plain,
( ~ 'c$ulessequals'('c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),X0,'tc$uRealDef$uOreal')
| ~ 'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),X0,'tc$uRealDef$uOreal') ),
inference(demodulation,[status(thm)],[c428,d2]) ).
cnf(d4,plain,
( ~ 'c$ulessequals'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),X0,'tc$uRealDef$uOreal')
| ~ 'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),X0,'tc$uRealDef$uOreal') ),
inference(demodulation,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
~ 'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'c$uRealDef$uOreal$u$uof$u$upreal'(X0),'tc$uRealDef$uOreal'),
inference(resolution,[status(thm)],[d4,d0]) ).
cnf(d6,plain,
$false,
inference(resolution,[status(thm)],[c212,d5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ALG340-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.38 % Computer : n002.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sat Sep 26 21:55:20 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.39 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 35.71/6.33 % SZS status Unsatisfiable for theBenchmark.p
% 35.71/6.33 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------