%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ALG371-1 : 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 : n005.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 06:48:24 AM UTC 2026
% Result : Unsatisfiable 35.12s 5.19s
% Output : CNFRefutation 35.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of clauses : 31 ( 12 unt; 3 nHn; 28 RR)
% Number of literals : 57 ( 5 equ; 31 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 35 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
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$uOreal') ) ).
cnf(cls_real__less__def_0,axiom,
( ~ 'c$uHOL$uOord$u$uclass$uOless'(X0,X1,'tc$uRealDef$uOreal')
| 'c$ulessequals'(X0,X1,'tc$uRealDef$uOreal') ) ).
cnf(cls_norm__ge__zero_0,axiom,
( 'c$ulessequals'('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_real__less__def_2,axiom,
( ~ 'c$ulessequals'(X0,X1,'tc$uRealDef$uOreal')
| X0 = X1
| 'c$uHOL$uOord$u$uclass$uOless'(X0,X1,'tc$uRealDef$uOreal') ) ).
cnf(cls_norm__not__less__zero_0,axiom,
( ~ 'c$uHOL$uOord$u$uclass$uOless'('c$uRealVector$uOnorm$u$uclass$uOnorm'(X1,X0),'c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'tc$uRealDef$uOreal')
| ~ 'class$uRealVector$uOreal$u$unormed$u$uvector'(X0) ) ).
cnf(cls_less__le__not__le_1,axiom,
( ~ 'c$uHOL$uOord$u$uclass$uOless'(X2,X1,X0)
| ~ 'c$ulessequals'(X1,X2,X0)
| ~ 'class$uOrderings$uOpreorder'(X0) ) ).
cnf(cls_conjecture_0,negated_conjecture,
'c$uHOL$uOord$u$uclass$uOless'('v$ur','c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'tc$uRealDef$uOreal') ).
cnf(cls_conjecture_1,negated_conjecture,
'c$ulessequals'('c$uRealVector$uOnorm$u$uclass$uOnorm'('v$ux','tc$uComplex$uOcomplex'),'v$ur','tc$uRealDef$uOreal') ).
cnf(clsarity_RealDef__Oreal__Orderings_Opreorder,axiom,
'class$uOrderings$uOpreorder'('tc$uRealDef$uOreal') ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
'class$uRealVector$uOreal$u$unormed$u$uvector'('tc$uComplex$uOcomplex') ).
cnf(c380,plain,
( ~ 'c$ulessequals'(X0,X2,'tc$uRealDef$uOreal')
| ~ 'c$ulessequals'(X2,X1,'tc$uRealDef$uOreal')
| 'c$ulessequals'(X0,X1,'tc$uRealDef$uOreal') ),
inference(clausification,[status(esa)],[cls_real__le__trans_0]) ).
cnf(c384,plain,
( ~ 'c$uHOL$uOord$u$uclass$uOless'(X0,X1,'tc$uRealDef$uOreal')
| 'c$ulessequals'(X0,X1,'tc$uRealDef$uOreal') ),
inference(clausification,[status(esa)],[cls_real__less__def_0]) ).
cnf(c392,plain,
( 'c$ulessequals'('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_norm__ge__zero_0]) ).
cnf(c399,plain,
( ~ 'c$ulessequals'(X0,X1,'tc$uRealDef$uOreal')
| X0 = X1
| 'c$uHOL$uOord$u$uclass$uOless'(X0,X1,'tc$uRealDef$uOreal') ),
inference(clausification,[status(esa)],[cls_real__less__def_2]) ).
cnf(c416,plain,
( ~ 'c$uHOL$uOord$u$uclass$uOless'('c$uRealVector$uOnorm$u$uclass$uOnorm'(X1,X0),'c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'tc$uRealDef$uOreal')
| ~ 'class$uRealVector$uOreal$u$unormed$u$uvector'(X0) ),
inference(clausification,[status(esa)],[cls_norm__not__less__zero_0]) ).
cnf(c419,plain,
( ~ 'c$uHOL$uOord$u$uclass$uOless'(X2,X1,X0)
| ~ 'c$ulessequals'(X1,X2,X0)
| ~ 'class$uOrderings$uOpreorder'(X0) ),
inference(clausification,[status(esa)],[cls_less__le__not__le_1]) ).
cnf(c427,plain,
'c$uHOL$uOord$u$uclass$uOless'('v$ur','c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(c428,plain,
'c$ulessequals'('c$uRealVector$uOnorm$u$uclass$uOnorm'('v$ux','tc$uComplex$uOcomplex'),'v$ur','tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[cls_conjecture_1]) ).
cnf(c473,plain,
'class$uOrderings$uOpreorder'('tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[clsarity_RealDef__Oreal__Orderings_Opreorder]) ).
cnf(c488,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$ulessequals'('v$ur','c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'tc$uRealDef$uOreal'),
inference(resolution,[status(thm)],[c384,c427]) ).
cnf(d1,plain,
( 'c$ulessequals'('v$ur',X0,'tc$uRealDef$uOreal')
| ~ 'c$ulessequals'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),X0,'tc$uRealDef$uOreal') ),
inference(resolution,[status(thm)],[c380,d0]) ).
cnf(d2,plain,
( ~ 'class$uRealVector$uOreal$u$unormed$u$uvector'(X1)
| 'c$ulessequals'('v$ur','c$uRealVector$uOnorm$u$uclass$uOnorm'(X0,X1),'tc$uRealDef$uOreal') ),
inference(resolution,[status(thm)],[d1,c392]) ).
cnf(d3,plain,
( ~ 'class$uOrderings$uOpreorder'('tc$uRealDef$uOreal')
| ~ 'c$uHOL$uOord$u$uclass$uOless'('c$uRealVector$uOnorm$u$uclass$uOnorm'(X1,X0),'v$ur','tc$uRealDef$uOreal')
| ~ 'class$uRealVector$uOreal$u$unormed$u$uvector'(X0) ),
inference(resolution,[status(thm)],[d2,c419]) ).
cnf(d4,plain,
( ~ 'class$uRealVector$uOreal$u$unormed$u$uvector'(X1)
| ~ 'c$uHOL$uOord$u$uclass$uOless'('c$uRealVector$uOnorm$u$uclass$uOnorm'(X0,X1),'v$ur','tc$uRealDef$uOreal') ),
inference(resolution,[status(thm)],[c473,d3]) ).
cnf(d5,plain,
( 'c$uHOL$uOord$u$uclass$uOless'('c$uRealVector$uOnorm$u$uclass$uOnorm'('v$ux','tc$uComplex$uOcomplex'),'v$ur','tc$uRealDef$uOreal')
| 'c$uRealVector$uOnorm$u$uclass$uOnorm'('v$ux','tc$uComplex$uOcomplex') = 'v$ur' ),
inference(resolution,[status(thm)],[c399,c428]) ).
cnf(d6,plain,
( ~ 'class$uRealVector$uOreal$u$unormed$u$uvector'('tc$uComplex$uOcomplex')
| 'c$uRealVector$uOnorm$u$uclass$uOnorm'('v$ux','tc$uComplex$uOcomplex') = 'v$ur' ),
inference(resolution,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
'c$uRealVector$uOnorm$u$uclass$uOnorm'('v$ux','tc$uComplex$uOcomplex') = 'v$ur',
inference(resolution,[status(thm)],[c488,d6]) ).
cnf(d8,plain,
( ~ 'class$uRealVector$uOreal$u$unormed$u$uvector'('tc$uComplex$uOcomplex')
| ~ 'c$uHOL$uOord$u$uclass$uOless'('v$ur','c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'tc$uRealDef$uOreal') ),
inference(superposition,[status(thm)],[d7,c416]) ).
cnf(d9,plain,
~ 'c$uHOL$uOord$u$uclass$uOless'('v$ur','c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'tc$uRealDef$uOreal'),
inference(resolution,[status(thm)],[c488,d8]) ).
cnf(d10,plain,
$false,
inference(resolution,[status(thm)],[c427,d9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG371-1 : 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 : n005.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
% 0.09/0.36 % DateTime : Sat Sep 26 21:55:32 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 35.12/5.19 % SZS status Unsatisfiable for theBenchmark.p
% 35.12/5.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------