%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ALG405-1 : 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 : n004.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 32.93s 4.59s
% Output : CNFRefutation 32.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of clauses : 20 ( 14 unt; 0 nHn; 12 RR)
% Number of literals : 28 ( 13 equ; 11 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-3 aty)
% Number of variables : 12 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_monoid__add__class_Oadd__0__right_0,axiom,
( 'c$uHOL$uOplus$u$uclass$uOplus'(X1,'c$uHOL$uOzero$u$uclass$uOzero'(X0),X0) = X1
| ~ 'class$uOrderedGroup$uOmonoid$u$uadd'(X0) ) ).
cnf(cls_class__ringb_Oadd__r0__iff_1,axiom,
( X1 = 'c$uHOL$uOplus$u$uclass$uOplus'(X1,'c$uHOL$uOzero$u$uclass$uOzero'(X0),X0)
| ~ 'class$uInt$uOnumber$u$uring'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOidom'(X0) ) ).
cnf(cls_conjecture_0,negated_conjecture,
'c$uHOL$uOplus$u$uclass$uOplus'('c$uHOL$uOone$u$uclass$uOone'('tc$uComplex$uOcomplex'),'c$uHOL$uOtimes$u$uclass$uOtimes'('c$uPower$uOpower$u$uclass$uOpower'('c$uHOL$uOtimes$u$uclass$uOtimes'('c$uRealVector$uOof$u$ureal'('v$ut','tc$uComplex$uOcomplex'),'v$uw','tc$uComplex$uOcomplex'),'v$uk','tc$uComplex$uOcomplex'),'c$uHOL$uOplus$u$uclass$uOplus'('v$ua','c$uHOL$uOtimes$u$uclass$uOtimes'('c$uHOL$uOtimes$u$uclass$uOtimes'('c$uRealVector$uOof$u$ureal'('v$ut','tc$uComplex$uOcomplex'),'v$uw','tc$uComplex$uOcomplex'),'c$uPolynomial$uOpoly'('v$us','c$uHOL$uOtimes$u$uclass$uOtimes'('c$uRealVector$uOof$u$ureal'('v$ut','tc$uComplex$uOcomplex'),'v$uw','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex') = 'c$uHOL$uOplus$u$uclass$uOplus'('c$uRealVector$uOof$u$ureal'('c$uHOL$uOminus$u$uclass$uOminus'('c$uHOL$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'),'c$uPower$uOpower$u$uclass$uOpower'('v$ut','v$uk','tc$uRealDef$uOreal'),'tc$uRealDef$uOreal'),'tc$uComplex$uOcomplex'),'c$uHOL$uOtimes$u$uclass$uOtimes'('c$uHOL$uOtimes$u$uclass$uOtimes'('c$uPower$uOpower$u$uclass$uOpower'('c$uHOL$uOtimes$u$uclass$uOtimes'('c$uRealVector$uOof$u$ureal'('v$ut','tc$uComplex$uOcomplex'),'v$uw','tc$uComplex$uOcomplex'),'v$uk','tc$uComplex$uOcomplex'),'c$uHOL$uOtimes$u$uclass$uOtimes'('c$uRealVector$uOof$u$ureal'('v$ut','tc$uComplex$uOcomplex'),'v$uw','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'c$uPolynomial$uOpoly'('v$us','c$uHOL$uOtimes$u$uclass$uOtimes'('c$uRealVector$uOof$u$ureal'('v$ut','tc$uComplex$uOcomplex'),'v$uw','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex') ).
cnf(cls_conjecture_1,negated_conjecture,
'c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uHOL$uOplus$u$uclass$uOplus'('c$uHOL$uOone$u$uclass$uOone'('tc$uComplex$uOcomplex'),'c$uHOL$uOtimes$u$uclass$uOtimes'('c$uPower$uOpower$u$uclass$uOpower'('c$uHOL$uOtimes$u$uclass$uOtimes'('c$uRealVector$uOof$u$ureal'('v$ut','tc$uComplex$uOcomplex'),'v$uw','tc$uComplex$uOcomplex'),'v$uk','tc$uComplex$uOcomplex'),'c$uHOL$uOplus$u$uclass$uOplus'('v$ua','c$uHOL$uOtimes$u$uclass$uOtimes'('c$uHOL$uOtimes$u$uclass$uOtimes'('c$uRealVector$uOof$u$ureal'('v$ut','tc$uComplex$uOcomplex'),'v$uw','tc$uComplex$uOcomplex'),'c$uPolynomial$uOpoly'('v$us','c$uHOL$uOtimes$u$uclass$uOtimes'('c$uRealVector$uOof$u$ureal'('v$ut','tc$uComplex$uOcomplex'),'v$uw','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex') != 'c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uHOL$uOplus$u$uclass$uOplus'('c$uRealVector$uOof$u$ureal'('c$uHOL$uOminus$u$uclass$uOminus'('c$uHOL$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'),'c$uPower$uOpower$u$uclass$uOpower'('v$ut','v$uk','tc$uRealDef$uOreal'),'tc$uRealDef$uOreal'),'tc$uComplex$uOcomplex'),'c$uHOL$uOtimes$u$uclass$uOtimes'('c$uHOL$uOtimes$u$uclass$uOtimes'('c$uPower$uOpower$u$uclass$uOpower'('c$uHOL$uOtimes$u$uclass$uOtimes'('c$uRealVector$uOof$u$ureal'('v$ut','tc$uComplex$uOcomplex'),'v$uw','tc$uComplex$uOcomplex'),'v$uk','tc$uComplex$uOcomplex'),'c$uHOL$uOtimes$u$uclass$uOtimes'('c$uRealVector$uOof$u$ureal'('v$ut','tc$uComplex$uOcomplex'),'v$uw','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'c$uPolynomial$uOpoly'('v$us','c$uHOL$uOtimes$u$uclass$uOtimes'('c$uRealVector$uOof$u$ureal'('v$ut','tc$uComplex$uOcomplex'),'v$uw','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex') ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add,axiom,
'class$uOrderedGroup$uOmonoid$u$uadd'('tc$uRealDef$uOreal') ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oidom,axiom,
'class$uRing$u$uand$u$uField$uOidom'('tc$uRealDef$uOreal') ).
cnf(clsarity_RealDef__Oreal__Int_Onumber__ring,axiom,
'class$uInt$uOnumber$u$uring'('tc$uRealDef$uOreal') ).
cnf(c345,plain,
( 'c$uHOL$uOplus$u$uclass$uOplus'(X1,'c$uHOL$uOzero$u$uclass$uOzero'(X0),X0) = X1
| ~ 'class$uOrderedGroup$uOmonoid$u$uadd'(X0) ),
inference(clausification,[status(esa)],[cls_monoid__add__class_Oadd__0__right_0]) ).
cnf(c348,plain,
( X1 = 'c$uHOL$uOplus$u$uclass$uOplus'(X1,'c$uHOL$uOzero$u$uclass$uOzero'(X0),X0)
| ~ 'class$uInt$uOnumber$u$uring'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOidom'(X0) ),
inference(clausification,[status(esa)],[cls_class__ringb_Oadd__r0__iff_1]) ).
cnf(c617,plain,
'c$uHOL$uOplus$u$uclass$uOplus'('c$uHOL$uOone$u$uclass$uOone'('tc$uComplex$uOcomplex'),'c$uHOL$uOtimes$u$uclass$uOtimes'('c$uPower$uOpower$u$uclass$uOpower'('c$uHOL$uOtimes$u$uclass$uOtimes'('c$uRealVector$uOof$u$ureal'('v$ut','tc$uComplex$uOcomplex'),'v$uw','tc$uComplex$uOcomplex'),'v$uk','tc$uComplex$uOcomplex'),'c$uHOL$uOplus$u$uclass$uOplus'('v$ua','c$uHOL$uOtimes$u$uclass$uOtimes'('c$uHOL$uOtimes$u$uclass$uOtimes'('c$uRealVector$uOof$u$ureal'('v$ut','tc$uComplex$uOcomplex'),'v$uw','tc$uComplex$uOcomplex'),'c$uPolynomial$uOpoly'('v$us','c$uHOL$uOtimes$u$uclass$uOtimes'('c$uRealVector$uOof$u$ureal'('v$ut','tc$uComplex$uOcomplex'),'v$uw','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex') = 'c$uHOL$uOplus$u$uclass$uOplus'('c$uRealVector$uOof$u$ureal'('c$uHOL$uOminus$u$uclass$uOminus'('c$uHOL$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'),'c$uPower$uOpower$u$uclass$uOpower'('v$ut','v$uk','tc$uRealDef$uOreal'),'tc$uRealDef$uOreal'),'tc$uComplex$uOcomplex'),'c$uHOL$uOtimes$u$uclass$uOtimes'('c$uHOL$uOtimes$u$uclass$uOtimes'('c$uPower$uOpower$u$uclass$uOpower'('c$uHOL$uOtimes$u$uclass$uOtimes'('c$uRealVector$uOof$u$ureal'('v$ut','tc$uComplex$uOcomplex'),'v$uw','tc$uComplex$uOcomplex'),'v$uk','tc$uComplex$uOcomplex'),'c$uHOL$uOtimes$u$uclass$uOtimes'('c$uRealVector$uOof$u$ureal'('v$ut','tc$uComplex$uOcomplex'),'v$uw','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'c$uPolynomial$uOpoly'('v$us','c$uHOL$uOtimes$u$uclass$uOtimes'('c$uRealVector$uOof$u$ureal'('v$ut','tc$uComplex$uOcomplex'),'v$uw','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(c618,plain,
'c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uHOL$uOplus$u$uclass$uOplus'('c$uHOL$uOone$u$uclass$uOone'('tc$uComplex$uOcomplex'),'c$uHOL$uOtimes$u$uclass$uOtimes'('c$uPower$uOpower$u$uclass$uOpower'('c$uHOL$uOtimes$u$uclass$uOtimes'('c$uRealVector$uOof$u$ureal'('v$ut','tc$uComplex$uOcomplex'),'v$uw','tc$uComplex$uOcomplex'),'v$uk','tc$uComplex$uOcomplex'),'c$uHOL$uOplus$u$uclass$uOplus'('v$ua','c$uHOL$uOtimes$u$uclass$uOtimes'('c$uHOL$uOtimes$u$uclass$uOtimes'('c$uRealVector$uOof$u$ureal'('v$ut','tc$uComplex$uOcomplex'),'v$uw','tc$uComplex$uOcomplex'),'c$uPolynomial$uOpoly'('v$us','c$uHOL$uOtimes$u$uclass$uOtimes'('c$uRealVector$uOof$u$ureal'('v$ut','tc$uComplex$uOcomplex'),'v$uw','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex') != 'c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uHOL$uOplus$u$uclass$uOplus'('c$uRealVector$uOof$u$ureal'('c$uHOL$uOminus$u$uclass$uOminus'('c$uHOL$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'),'c$uPower$uOpower$u$uclass$uOpower'('v$ut','v$uk','tc$uRealDef$uOreal'),'tc$uRealDef$uOreal'),'tc$uComplex$uOcomplex'),'c$uHOL$uOtimes$u$uclass$uOtimes'('c$uHOL$uOtimes$u$uclass$uOtimes'('c$uPower$uOpower$u$uclass$uOpower'('c$uHOL$uOtimes$u$uclass$uOtimes'('c$uRealVector$uOof$u$ureal'('v$ut','tc$uComplex$uOcomplex'),'v$uw','tc$uComplex$uOcomplex'),'v$uk','tc$uComplex$uOcomplex'),'c$uHOL$uOtimes$u$uclass$uOtimes'('c$uRealVector$uOof$u$ureal'('v$ut','tc$uComplex$uOcomplex'),'v$uw','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'c$uPolynomial$uOpoly'('v$us','c$uHOL$uOtimes$u$uclass$uOtimes'('c$uRealVector$uOof$u$ureal'('v$ut','tc$uComplex$uOcomplex'),'v$uw','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),
inference(clausification,[status(esa)],[cls_conjecture_1]) ).
cnf(c702,plain,
'class$uOrderedGroup$uOmonoid$u$uadd'('tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add]) ).
cnf(c709,plain,
'class$uRing$u$uand$u$uField$uOidom'('tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[clsarity_RealDef__Oreal__Ring__and__Field_Oidom]) ).
cnf(c714,plain,
'class$uInt$uOnumber$u$uring'('tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[clsarity_RealDef__Oreal__Int_Onumber__ring]) ).
cnf(d0,plain,
'c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uHOL$uOplus$u$uclass$uOplus'('c$uHOL$uOone$u$uclass$uOone'('tc$uComplex$uOcomplex'),'c$uHOL$uOtimes$u$uclass$uOtimes'('c$uPower$uOpower$u$uclass$uOpower'('c$uHOL$uOtimes$u$uclass$uOtimes'('c$uRealVector$uOof$u$ureal'('v$ut','tc$uComplex$uOcomplex'),'v$uw','tc$uComplex$uOcomplex'),'v$uk','tc$uComplex$uOcomplex'),'c$uHOL$uOplus$u$uclass$uOplus'('v$ua','c$uHOL$uOtimes$u$uclass$uOtimes'('c$uHOL$uOtimes$u$uclass$uOtimes'('c$uRealVector$uOof$u$ureal'('v$ut','tc$uComplex$uOcomplex'),'v$uw','tc$uComplex$uOcomplex'),'c$uPolynomial$uOpoly'('v$us','c$uHOL$uOtimes$u$uclass$uOtimes'('c$uRealVector$uOof$u$ureal'('v$ut','tc$uComplex$uOcomplex'),'v$uw','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex') != 'c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uHOL$uOplus$u$uclass$uOplus'('c$uHOL$uOone$u$uclass$uOone'('tc$uComplex$uOcomplex'),'c$uHOL$uOtimes$u$uclass$uOtimes'('c$uPower$uOpower$u$uclass$uOpower'('c$uHOL$uOtimes$u$uclass$uOtimes'('c$uRealVector$uOof$u$ureal'('v$ut','tc$uComplex$uOcomplex'),'v$uw','tc$uComplex$uOcomplex'),'v$uk','tc$uComplex$uOcomplex'),'c$uHOL$uOplus$u$uclass$uOplus'('v$ua','c$uHOL$uOtimes$u$uclass$uOtimes'('c$uHOL$uOtimes$u$uclass$uOtimes'('c$uRealVector$uOof$u$ureal'('v$ut','tc$uComplex$uOcomplex'),'v$uw','tc$uComplex$uOcomplex'),'c$uPolynomial$uOpoly'('v$us','c$uHOL$uOtimes$u$uclass$uOtimes'('c$uRealVector$uOof$u$ureal'('v$ut','tc$uComplex$uOcomplex'),'v$uw','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),
inference(demodulation,[status(thm)],[c618,c617]) ).
cnf(d1,plain,
'c$uHOL$uOplus$u$uclass$uOplus'(X0,'c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'tc$uRealDef$uOreal') = X0,
inference(resolution,[status(thm)],[c345,c702]) ).
cnf(d2,plain,
( ~ 'class$uRing$u$uand$u$uField$uOidom'('tc$uRealDef$uOreal')
| X0 = 'c$uHOL$uOplus$u$uclass$uOplus'(X0,'c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'tc$uRealDef$uOreal') ),
inference(resolution,[status(thm)],[c348,c714]) ).
cnf(d3,plain,
( ~ 'class$uRing$u$uand$u$uField$uOidom'('tc$uRealDef$uOreal')
| X0 = X0 ),
inference(demodulation,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
X0 = X0,
inference(resolution,[status(thm)],[c709,d3]) ).
cnf(d5,plain,
$false,
inference(resolution,[status(thm)],[d4,d0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG405-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n004.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 21:58:08 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 32.93/4.59 % SZS status Unsatisfiable for theBenchmark.p
% 32.93/4.59 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------