%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ALG424-1 : 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 : n001.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 06:48:28 AM UTC 2026
% Result : Unsatisfiable 112.68s 25.92s
% Output : CNFRefutation 112.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of clauses : 31 ( 17 unt; 2 nHn; 23 RR)
% Number of literals : 56 ( 33 equ; 29 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 18 ( 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_pne_0,axiom,
'v$upa' != 'c$uHOL$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')) ).
cnf(cls_CHAINED_0_01,axiom,
( 'c$uPolynomial$uOpoly'(X2,X1,X0) != 'c$uHOL$uOzero$u$uclass$uOzero'(X0)
| X2 = 'c$uHOL$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'(X0))
| 'c$uPolynomial$uOorder'(X1,X2,X0) != 'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')
| ~ 'class$uRing$u$uand$u$uField$uOidom'(X0) ) ).
cnf(cls_CHAINED_0_02,axiom,
'c$uPolynomial$uOpoly'('v$upa','v$ua','tc$uComplex$uOcomplex') = 'c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex') ).
cnf(cls_CHAINED_0_03,axiom,
( 'c$uPolynomial$uOorder'('v$ua','v$upa','tc$uComplex$uOcomplex') = 'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')
| 'c$uRing$u$uand$u$uField$uOdvd$u$uclass$uOdvd'('v$upa','c$uPower$uOpower$u$uclass$uOpower'('v$uqa','v$una','tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),'tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')) ) ).
cnf(cls_conjecture_0,negated_conjecture,
~ 'c$uRing$u$uand$u$uField$uOdvd$u$uclass$uOdvd'('v$upa','c$uPower$uOpower$u$uclass$uOpower'('v$uqa','v$una','tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),'tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add,axiom,
'class$uOrderedGroup$uOmonoid$u$uadd'('tc$uComplex$uOcomplex') ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oidom,axiom,
'class$uRing$u$uand$u$uField$uOidom'('tc$uComplex$uOcomplex') ).
cnf(clsarity_Complex__Ocomplex__Int_Onumber__ring,axiom,
'class$uInt$uOnumber$u$uring'('tc$uComplex$uOcomplex') ).
cnf(c695,plain,
( 'c$uHOL$uOplus$u$uclass$uOplus'(X1,'c$uHOL$uOzero$u$uclass$uOzero'(X0),X0) = X1
| ~ 'class$uOrderedGroup$uOmonoid$u$uadd'(X0) ),
inference(clausification,[status(esa)],[cls_monoid__add__class_Oadd__0__right_0]) ).
cnf(c698,plain,
( 'c$uHOL$uOplus$u$uclass$uOplus'(X1,'c$uHOL$uOzero$u$uclass$uOzero'(X0),X0) = X1
| ~ 'class$uRing$u$uand$u$uField$uOidom'(X0)
| ~ 'class$uInt$uOnumber$u$uring'(X0) ),
inference(clausification,[status(esa)],[cls_class__ringb_Oadd__r0__iff_1]) ).
cnf(c882,plain,
'c$uHOL$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')) != 'v$upa',
inference(clausification,[status(esa)],[cls_pne_0]) ).
cnf(c902,plain,
( 'c$uHOL$uOzero$u$uclass$uOzero'(X0) != 'c$uPolynomial$uOpoly'(X1,X2,X0)
| 'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat') != 'c$uPolynomial$uOorder'(X2,X1,X0)
| ~ 'class$uRing$u$uand$u$uField$uOidom'(X0)
| 'c$uHOL$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'(X0)) = X1 ),
inference(clausification,[status(esa)],[cls_CHAINED_0_01]) ).
cnf(c903,plain,
'c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex') = 'c$uPolynomial$uOpoly'('v$upa','v$ua','tc$uComplex$uOcomplex'),
inference(clausification,[status(esa)],[cls_CHAINED_0_02]) ).
cnf(c904,plain,
( 'c$uPolynomial$uOorder'('v$ua','v$upa','tc$uComplex$uOcomplex') = 'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')
| 'c$uRing$u$uand$u$uField$uOdvd$u$uclass$uOdvd'('v$upa','c$uPower$uOpower$u$uclass$uOpower'('v$uqa','v$una','tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),'tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')) ),
inference(clausification,[status(esa)],[cls_CHAINED_0_03]) ).
cnf(c905,plain,
~ 'c$uRing$u$uand$u$uField$uOdvd$u$uclass$uOdvd'('v$upa','c$uPower$uOpower$u$uclass$uOpower'('v$uqa','v$una','tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),'tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')),
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(c968,plain,
'class$uOrderedGroup$uOmonoid$u$uadd'('tc$uComplex$uOcomplex'),
inference(clausification,[status(esa)],[clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add]) ).
cnf(c974,plain,
'class$uRing$u$uand$u$uField$uOidom'('tc$uComplex$uOcomplex'),
inference(clausification,[status(esa)],[clsarity_Complex__Ocomplex__Ring__and__Field_Oidom]) ).
cnf(c976,plain,
'class$uInt$uOnumber$u$uring'('tc$uComplex$uOcomplex'),
inference(clausification,[status(esa)],[clsarity_Complex__Ocomplex__Int_Onumber__ring]) ).
cnf(d0,plain,
'c$uPolynomial$uOorder'('v$ua','v$upa','tc$uComplex$uOcomplex') = 'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat'),
inference(resolution,[status(thm)],[c905,c904]) ).
cnf(d1,plain,
( ~ 'class$uRing$u$uand$u$uField$uOidom'('tc$uComplex$uOcomplex')
| 'c$uHOL$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')) = 'v$upa'
| 'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat') != 'c$uPolynomial$uOorder'('v$ua','v$upa','tc$uComplex$uOcomplex')
| 'c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex') != 'c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex') ),
inference(superposition,[status(thm)],[c903,c902]) ).
cnf(d2,plain,
( ~ 'class$uRing$u$uand$u$uField$uOidom'('tc$uComplex$uOcomplex')
| 'c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex') != 'c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex')
| 'c$uHOL$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')) = 'v$upa'
| 'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat') != 'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat') ),
inference(demodulation,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
( 'c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex') != 'c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex')
| 'c$uHOL$uOzero$u$uclass$uOzero'('tc$uPolynomial$uOpoly'('tc$uComplex$uOcomplex')) = 'v$upa'
| 'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat') != 'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat') ),
inference(resolution,[status(thm)],[c974,d2]) ).
cnf(d4,plain,
( 'c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex') != 'c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex')
| 'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat') != 'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat') ),
inference(resolution,[status(thm)],[c882,d3]) ).
cnf(d5,plain,
'c$uHOL$uOplus$u$uclass$uOplus'(X0,'c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex') = X0,
inference(resolution,[status(thm)],[c695,c968]) ).
cnf(d6,plain,
( ~ 'class$uInt$uOnumber$u$uring'('tc$uComplex$uOcomplex')
| 'c$uHOL$uOplus$u$uclass$uOplus'(X0,'c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex') = X0 ),
inference(resolution,[status(thm)],[c698,c974]) ).
cnf(d7,plain,
( ~ 'class$uInt$uOnumber$u$uring'('tc$uComplex$uOcomplex')
| X0 = X0 ),
inference(demodulation,[status(thm)],[d6,d5]) ).
cnf(d8,plain,
X0 = X0,
inference(resolution,[status(thm)],[c976,d7]) ).
cnf(d9,plain,
'c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex') != 'c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),
inference(resolution,[status(thm)],[d8,d4]) ).
cnf(d10,plain,
$false,
inference(equality_resolution,[status(thm)],[d9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ALG424-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n001.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sat Sep 26 22:05:31 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 112.68/25.92 % SZS status Unsatisfiable for theBenchmark.p
% 112.68/25.92 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------