%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ALG370-1 : 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 : n015.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 102.15s 20.52s
% Output : CNFRefutation 102.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of clauses : 18 ( 14 unt; 0 nHn; 16 RR)
% Number of literals : 27 ( 2 equ; 13 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-3 aty)
% Number of variables : 14 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_xt1_I7_J_0,axiom,
( ~ 'c$uHOL$uOord$u$uclass$uOless'(X3,X2,X0)
| ~ 'c$ulessequals'(X1,X3,X0)
| 'c$uHOL$uOord$u$uclass$uOless'(X1,X2,X0)
| ~ 'class$uOrderings$uOorder'(X0) ) ).
cnf(cls_dist__complex__def_0,axiom,
'c$uRealVector$uOdist$u$uclass$uOdist'(X0,X1,'tc$uComplex$uOcomplex') = 'c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uHOL$uOminus$u$uclass$uOminus'(X0,X1,'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex') ).
cnf(cls_CHAINED_0,axiom,
'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOtimes$u$uclass$uOtimes'('v$uda','v$um','tc$uRealDef$uOreal'),'v$ue','tc$uRealDef$uOreal') ).
cnf(cls_CHAINED_0_01,axiom,
'c$ulessequals'('c$uHOL$uOtimes$u$uclass$uOtimes'('c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uHOL$uOminus$u$uclass$uOminus'('v$uw','v$uz','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uPolynomial$uOpoly'('v$ucs','c$uHOL$uOminus$u$uclass$uOminus'('v$uw','v$uz','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uRealDef$uOreal'),'c$uHOL$uOtimes$u$uclass$uOtimes'('v$uda','v$um','tc$uRealDef$uOreal'),'tc$uRealDef$uOreal') ).
cnf(cls_conjecture_0,negated_conjecture,
~ 'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOtimes$u$uclass$uOtimes'('c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uHOL$uOminus$u$uclass$uOminus'('v$uw','v$uz','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uPolynomial$uOpoly'('v$ucs','c$uHOL$uOminus$u$uclass$uOminus'('v$uw','v$uz','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uRealDef$uOreal'),'v$ue','tc$uRealDef$uOreal') ).
cnf(clsarity_RealDef__Oreal__Orderings_Oorder,axiom,
'class$uOrderings$uOorder'('tc$uRealDef$uOreal') ).
cnf(c25,plain,
( ~ 'c$uHOL$uOord$u$uclass$uOless'(X1,X3,X2)
| 'c$uHOL$uOord$u$uclass$uOless'(X0,X3,X2)
| ~ 'class$uOrderings$uOorder'(X2)
| ~ 'c$ulessequals'(X0,X1,X2) ),
inference(clausification,[status(esa)],[cls_xt1_I7_J_0]) ).
cnf(c363,plain,
'c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uHOL$uOminus$u$uclass$uOminus'(X0,X1,'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex') = 'c$uRealVector$uOdist$u$uclass$uOdist'(X0,X1,'tc$uComplex$uOcomplex'),
inference(clausification,[status(esa)],[cls_dist__complex__def_0]) ).
cnf(c421,plain,
'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOtimes$u$uclass$uOtimes'('v$uda','v$um','tc$uRealDef$uOreal'),'v$ue','tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[cls_CHAINED_0]) ).
cnf(c422,plain,
'c$ulessequals'('c$uHOL$uOtimes$u$uclass$uOtimes'('c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uHOL$uOminus$u$uclass$uOminus'('v$uw','v$uz','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uPolynomial$uOpoly'('v$ucs','c$uHOL$uOminus$u$uclass$uOminus'('v$uw','v$uz','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uRealDef$uOreal'),'c$uHOL$uOtimes$u$uclass$uOtimes'('v$uda','v$um','tc$uRealDef$uOreal'),'tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[cls_CHAINED_0_01]) ).
cnf(c423,plain,
~ 'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOtimes$u$uclass$uOtimes'('c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uHOL$uOminus$u$uclass$uOminus'('v$uw','v$uz','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uPolynomial$uOpoly'('v$ucs','c$uHOL$uOminus$u$uclass$uOminus'('v$uw','v$uz','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uRealDef$uOreal'),'v$ue','tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(c533,plain,
'class$uOrderings$uOorder'('tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[clsarity_RealDef__Oreal__Orderings_Oorder]) ).
cnf(d0,plain,
~ 'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOtimes$u$uclass$uOtimes'('c$uRealVector$uOdist$u$uclass$uOdist'('v$uw','v$uz','tc$uComplex$uOcomplex'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uPolynomial$uOpoly'('v$ucs','c$uHOL$uOminus$u$uclass$uOminus'('v$uw','v$uz','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uRealDef$uOreal'),'v$ue','tc$uRealDef$uOreal'),
inference(demodulation,[status(thm)],[c423,c363]) ).
cnf(d1,plain,
'c$ulessequals'('c$uHOL$uOtimes$u$uclass$uOtimes'('c$uRealVector$uOdist$u$uclass$uOdist'('v$uw','v$uz','tc$uComplex$uOcomplex'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uPolynomial$uOpoly'('v$ucs','c$uHOL$uOminus$u$uclass$uOminus'('v$uw','v$uz','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uRealDef$uOreal'),'c$uHOL$uOtimes$u$uclass$uOtimes'('v$uda','v$um','tc$uRealDef$uOreal'),'tc$uRealDef$uOreal'),
inference(demodulation,[status(thm)],[c422,c363]) ).
cnf(d2,plain,
( ~ 'class$uOrderings$uOorder'('tc$uRealDef$uOreal')
| ~ 'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOtimes$u$uclass$uOtimes'('v$uda','v$um','tc$uRealDef$uOreal'),X0,'tc$uRealDef$uOreal')
| 'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOtimes$u$uclass$uOtimes'('c$uRealVector$uOdist$u$uclass$uOdist'('v$uw','v$uz','tc$uComplex$uOcomplex'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uPolynomial$uOpoly'('v$ucs','c$uHOL$uOminus$u$uclass$uOminus'('v$uw','v$uz','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uRealDef$uOreal'),X0,'tc$uRealDef$uOreal') ),
inference(resolution,[status(thm)],[d1,c25]) ).
cnf(d3,plain,
( ~ 'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOtimes$u$uclass$uOtimes'('v$uda','v$um','tc$uRealDef$uOreal'),X0,'tc$uRealDef$uOreal')
| 'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOtimes$u$uclass$uOtimes'('c$uRealVector$uOdist$u$uclass$uOdist'('v$uw','v$uz','tc$uComplex$uOcomplex'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uPolynomial$uOpoly'('v$ucs','c$uHOL$uOminus$u$uclass$uOminus'('v$uw','v$uz','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uRealDef$uOreal'),X0,'tc$uRealDef$uOreal') ),
inference(resolution,[status(thm)],[c533,d2]) ).
cnf(d4,plain,
~ 'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOtimes$u$uclass$uOtimes'('v$uda','v$um','tc$uRealDef$uOreal'),'v$ue','tc$uRealDef$uOreal'),
inference(resolution,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
$false,
inference(resolution,[status(thm)],[c421,d4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG370-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n015.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sat Sep 26 21:59:00 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 102.15/20.52 % SZS status Unsatisfiable for theBenchmark.p
% 102.15/20.52 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------