%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ALG406-1 : 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 : 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 06:48:27 AM UTC 2026
% Result : Unsatisfiable 3.64s 30.18s
% Output : CNFRefutation 3.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of clauses : 34 ( 22 unt; 0 nHn; 28 RR)
% Number of literals : 59 ( 2 equ; 32 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 22 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_t_I1_J_0,axiom,
'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'v$ut','tc$uRealDef$uOreal') ).
cnf(cls_order__less__imp__le_0,axiom,
( ~ 'c$uHOL$uOord$u$uclass$uOless'(X1,X2,X0)
| 'c$ulessequals'(X1,X2,X0)
| ~ 'class$uOrderings$uOpreorder'(X0) ) ).
cnf(cls_neg__less__eq__nonneg_0,axiom,
( ~ 'c$ulessequals'('c$uHOL$uOuminus$u$uclass$uOuminus'(X1,X0),X1,X0)
| 'c$ulessequals'('c$uHOL$uOzero$u$uclass$uOzero'(X0),X1,X0)
| ~ 'class$uOrderedGroup$uOordered$u$uab$u$ugroup$u$uadd'(X0) ) ).
cnf(cls_complex__mod__minus__le__complex__mod_0,axiom,
'c$ulessequals'('c$uHOL$uOuminus$u$uclass$uOuminus'('c$uRealVector$uOnorm$u$uclass$uOnorm'(X0,'tc$uComplex$uOcomplex'),'tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'(X0,'tc$uComplex$uOcomplex'),'tc$uRealDef$uOreal') ).
cnf(cls_t_I2_J_0,axiom,
'c$uHOL$uOord$u$uclass$uOless'('v$ut','c$uHOL$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'),'tc$uRealDef$uOreal') ).
cnf(cls_mult__left__le__one__le_0,axiom,
( ~ 'c$ulessequals'('c$uHOL$uOzero$u$uclass$uOzero'(X0),X2,X0)
| ~ 'c$ulessequals'('c$uHOL$uOzero$u$uclass$uOzero'(X0),X1,X0)
| ~ 'c$ulessequals'(X1,'c$uHOL$uOone$u$uclass$uOone'(X0),X0)
| 'c$ulessequals'('c$uHOL$uOtimes$u$uclass$uOtimes'(X1,X2,X0),X2,X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$uidom'(X0) ) ).
cnf(cls_real__mult__1_0,axiom,
'c$uHOL$uOtimes$u$uclass$uOtimes'('c$uHOL$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'),X0,'tc$uRealDef$uOreal') = X0 ).
cnf(cls_conjecture_0,negated_conjecture,
~ 'c$ulessequals'('c$uHOL$uOtimes$u$uclass$uOtimes'('v$ut','c$uRealVector$uOnorm$u$uclass$uOnorm'('v$uw','tc$uComplex$uOcomplex'),'tc$uRealDef$uOreal'),'c$uHOL$uOtimes$u$uclass$uOtimes'('c$uHOL$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('v$uw','tc$uComplex$uOcomplex'),'tc$uRealDef$uOreal'),'tc$uRealDef$uOreal') ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add,axiom,
'class$uOrderedGroup$uOordered$u$uab$u$ugroup$u$uadd'('tc$uRealDef$uOreal') ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom,axiom,
'class$uRing$u$uand$u$uField$uOordered$u$uidom'('tc$uRealDef$uOreal') ).
cnf(clsarity_RealDef__Oreal__Orderings_Opreorder,axiom,
'class$uOrderings$uOpreorder'('tc$uRealDef$uOreal') ).
cnf(c26,plain,
'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'v$ut','tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[cls_t_I1_J_0]) ).
cnf(c116,plain,
( ~ 'c$uHOL$uOord$u$uclass$uOless'(X1,X2,X0)
| 'c$ulessequals'(X1,X2,X0)
| ~ 'class$uOrderings$uOpreorder'(X0) ),
inference(clausification,[status(esa)],[cls_order__less__imp__le_0]) ).
cnf(c378,plain,
( ~ 'c$ulessequals'('c$uHOL$uOuminus$u$uclass$uOuminus'(X1,X0),X1,X0)
| 'c$ulessequals'('c$uHOL$uOzero$u$uclass$uOzero'(X0),X1,X0)
| ~ 'class$uOrderedGroup$uOordered$u$uab$u$ugroup$u$uadd'(X0) ),
inference(clausification,[status(esa)],[cls_neg__less__eq__nonneg_0]) ).
cnf(c505,plain,
'c$ulessequals'('c$uHOL$uOuminus$u$uclass$uOuminus'('c$uRealVector$uOnorm$u$uclass$uOnorm'(X0,'tc$uComplex$uOcomplex'),'tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'(X0,'tc$uComplex$uOcomplex'),'tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[cls_complex__mod__minus__le__complex__mod_0]) ).
cnf(c507,plain,
'c$uHOL$uOord$u$uclass$uOless'('v$ut','c$uHOL$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'),'tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[cls_t_I2_J_0]) ).
cnf(c509,plain,
( ~ 'c$ulessequals'('c$uHOL$uOzero$u$uclass$uOzero'(X1),X0,X1)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$uidom'(X1)
| ~ 'c$ulessequals'('c$uHOL$uOzero$u$uclass$uOzero'(X1),X2,X1)
| 'c$ulessequals'('c$uHOL$uOtimes$u$uclass$uOtimes'(X0,X2,X1),X2,X1)
| ~ 'c$ulessequals'(X0,'c$uHOL$uOone$u$uclass$uOone'(X1),X1) ),
inference(clausification,[status(esa)],[cls_mult__left__le__one__le_0]) ).
cnf(c551,plain,
'c$uHOL$uOtimes$u$uclass$uOtimes'('c$uHOL$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'),X0,'tc$uRealDef$uOreal') = X0,
inference(clausification,[status(esa)],[cls_real__mult__1_0]) ).
cnf(c558,plain,
~ 'c$ulessequals'('c$uHOL$uOtimes$u$uclass$uOtimes'('v$ut','c$uRealVector$uOnorm$u$uclass$uOnorm'('v$uw','tc$uComplex$uOcomplex'),'tc$uRealDef$uOreal'),'c$uHOL$uOtimes$u$uclass$uOtimes'('c$uHOL$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('v$uw','tc$uComplex$uOcomplex'),'tc$uRealDef$uOreal'),'tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(c605,plain,
'class$uOrderedGroup$uOordered$u$uab$u$ugroup$u$uadd'('tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add]) ).
cnf(c627,plain,
'class$uRing$u$uand$u$uField$uOordered$u$uidom'('tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom]) ).
cnf(c642,plain,
'class$uOrderings$uOpreorder'('tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[clsarity_RealDef__Oreal__Orderings_Opreorder]) ).
cnf(d0,plain,
~ 'c$ulessequals'('c$uHOL$uOtimes$u$uclass$uOtimes'('v$ut','c$uRealVector$uOnorm$u$uclass$uOnorm'('v$uw','tc$uComplex$uOcomplex'),'tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('v$uw','tc$uComplex$uOcomplex'),'tc$uRealDef$uOreal'),
inference(demodulation,[status(thm)],[c558,c551]) ).
cnf(d1,plain,
( ~ 'class$uRing$u$uand$u$uField$uOordered$u$uidom'('tc$uRealDef$uOreal')
| ~ 'c$ulessequals'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'v$ut','tc$uRealDef$uOreal')
| ~ 'c$ulessequals'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('v$uw','tc$uComplex$uOcomplex'),'tc$uRealDef$uOreal')
| ~ 'c$ulessequals'('v$ut','c$uHOL$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'),'tc$uRealDef$uOreal') ),
inference(resolution,[status(thm)],[d0,c509]) ).
cnf(d2,plain,
( ~ 'c$ulessequals'('v$ut','c$uHOL$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'),'tc$uRealDef$uOreal')
| ~ 'c$ulessequals'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('v$uw','tc$uComplex$uOcomplex'),'tc$uRealDef$uOreal')
| ~ 'c$ulessequals'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'v$ut','tc$uRealDef$uOreal') ),
inference(resolution,[status(thm)],[c627,d1]) ).
cnf(d3,plain,
( ~ 'class$uOrderings$uOpreorder'('tc$uRealDef$uOreal')
| 'c$ulessequals'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'v$ut','tc$uRealDef$uOreal') ),
inference(resolution,[status(thm)],[c116,c26]) ).
cnf(d4,plain,
'c$ulessequals'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'v$ut','tc$uRealDef$uOreal'),
inference(resolution,[status(thm)],[c642,d3]) ).
cnf(d5,plain,
( ~ 'c$ulessequals'('v$ut','c$uHOL$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'),'tc$uRealDef$uOreal')
| ~ 'c$ulessequals'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('v$uw','tc$uComplex$uOcomplex'),'tc$uRealDef$uOreal') ),
inference(resolution,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
( ~ 'class$uOrderings$uOpreorder'('tc$uRealDef$uOreal')
| 'c$ulessequals'('v$ut','c$uHOL$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'),'tc$uRealDef$uOreal') ),
inference(resolution,[status(thm)],[c507,c116]) ).
cnf(d7,plain,
'c$ulessequals'('v$ut','c$uHOL$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'),'tc$uRealDef$uOreal'),
inference(resolution,[status(thm)],[c642,d6]) ).
cnf(d8,plain,
~ 'c$ulessequals'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('v$uw','tc$uComplex$uOcomplex'),'tc$uRealDef$uOreal'),
inference(resolution,[status(thm)],[d7,d5]) ).
cnf(d9,plain,
( ~ 'class$uOrderedGroup$uOordered$u$uab$u$ugroup$u$uadd'('tc$uRealDef$uOreal')
| 'c$ulessequals'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'(X0,'tc$uComplex$uOcomplex'),'tc$uRealDef$uOreal') ),
inference(resolution,[status(thm)],[c505,c378]) ).
cnf(d10,plain,
'c$ulessequals'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'(X0,'tc$uComplex$uOcomplex'),'tc$uRealDef$uOreal'),
inference(resolution,[status(thm)],[c605,d9]) ).
cnf(d11,plain,
$false,
inference(resolution,[status(thm)],[d10,d8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG406-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.36 % Computer : n019.cluster.edu
% 0.06/0.36 % Model : x86_64 x86_64
% 0.06/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.36 % Memory : 8046.5625MB
% 0.06/0.36 % OS : Linux 6.8.0-71-generic
% 0.06/0.36 % CPULimit : 300
% 0.06/0.36 % WCLimit : 300
% 0.06/0.36 % DateTime : Sat Sep 26 21:58:20 UTC 2026
% 0.06/0.36 % CPUTime :
% 0.06/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.64/30.18 % SZS status Unsatisfiable for theBenchmark.p
% 3.64/30.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------