%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ALG384-1 : 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 : n012.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 06:48:25 AM UTC 2026
% Result : Unsatisfiable 30.59s 7.89s
% Output : CNFRefutation 30.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of clauses : 11 ( 8 unt; 2 nHn; 9 RR)
% Number of literals : 16 ( 6 equ; 7 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 4 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_zero__less__norm__iff_1,axiom,
( X1 = 'c$uHOL$uOzero$u$uclass$uOzero'(X0)
| 'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'(X1,X0),'tc$uRealDef$uOreal')
| ~ 'class$uRealVector$uOreal$u$unormed$u$uvector'(X0) ) ).
cnf(cls_CHAINED_0,axiom,
'v$uc' != 'c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex') ).
cnf(cls_conjecture_0,negated_conjecture,
~ 'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('v$uc','tc$uComplex$uOcomplex'),'tc$uRealDef$uOreal') ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
'class$uRealVector$uOreal$u$unormed$u$uvector'('tc$uComplex$uOcomplex') ).
cnf(c484,plain,
( X1 = 'c$uHOL$uOzero$u$uclass$uOzero'(X0)
| 'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'(X1,X0),'tc$uRealDef$uOreal')
| ~ 'class$uRealVector$uOreal$u$unormed$u$uvector'(X0) ),
inference(clausification,[status(esa)],[cls_zero__less__norm__iff_1]) ).
cnf(c495,plain,
'v$uc' != 'c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),
inference(clausification,[status(esa)],[cls_CHAINED_0]) ).
cnf(c496,plain,
~ 'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('v$uc','tc$uComplex$uOcomplex'),'tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(c562,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,
( ~ 'class$uRealVector$uOreal$u$unormed$u$uvector'('tc$uComplex$uOcomplex')
| 'v$uc' = 'c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex') ),
inference(resolution,[status(thm)],[c484,c496]) ).
cnf(d1,plain,
'v$uc' = 'c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),
inference(resolution,[status(thm)],[c562,d0]) ).
cnf(d2,plain,
$false,
inference(resolution,[status(thm)],[c495,d1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG384-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.36 % Computer : n012.cluster.edu
% 0.03/0.36 % Model : x86_64 x86_64
% 0.03/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.36 % Memory : 8046.5625MB
% 0.03/0.36 % OS : Linux 6.8.0-71-generic
% 0.03/0.36 % CPULimit : 300
% 0.03/0.36 % WCLimit : 300
% 0.03/0.36 % DateTime : Sat Sep 26 21:56:20 UTC 2026
% 0.03/0.37 % CPUTime :
% 0.03/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 30.59/7.89 % SZS status Unsatisfiable for theBenchmark.p
% 30.59/7.89 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------