%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ALG399-1 : 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 : n007.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 06:48:26 AM UTC 2026
% Result : Unsatisfiable 37.27s 5.71s
% Output : CNFRefutation 37.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of clauses : 20 ( 14 unt; 0 nHn; 10 RR)
% Number of literals : 28 ( 13 equ; 11 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 14 ( 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_qr_0,axiom,
'c$uPolynomial$uOpoly'('v$uq',X0,'tc$uComplex$uOcomplex') = 'c$uHOL$uOtimes$u$uclass$uOtimes'('c$uPolynomial$uOpoly'('c$uPolynomial$uOsmult'('c$uHOL$uOinverse$u$uclass$uOinverse'('c$uPolynomial$uOpoly'('v$uq','c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'v$uq','tc$uComplex$uOcomplex'),X0,'tc$uComplex$uOcomplex'),'c$uPolynomial$uOpoly'('v$uq','c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex') ).
cnf(cls_conjecture_0,negated_conjecture,
'c$uHOL$uOtimes$u$uclass$uOtimes'('c$uPolynomial$uOpoly'('c$uPolynomial$uOsmult'('c$uHOL$uOinverse$u$uclass$uOinverse'('c$uPolynomial$uOpoly'('v$uq','c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'v$uq','tc$uComplex$uOcomplex'),'v$uy','tc$uComplex$uOcomplex'),'c$uPolynomial$uOpoly'('v$uq','c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex') != 'c$uPolynomial$uOpoly'('v$uq','v$uy','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(c203,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(c206,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(c806,plain,
'c$uPolynomial$uOpoly'('v$uq',X0,'tc$uComplex$uOcomplex') = 'c$uHOL$uOtimes$u$uclass$uOtimes'('c$uPolynomial$uOpoly'('c$uPolynomial$uOsmult'('c$uHOL$uOinverse$u$uclass$uOinverse'('c$uPolynomial$uOpoly'('v$uq','c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'v$uq','tc$uComplex$uOcomplex'),X0,'tc$uComplex$uOcomplex'),'c$uPolynomial$uOpoly'('v$uq','c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),
inference(clausification,[status(esa)],[cls_qr_0]) ).
cnf(c836,plain,
'c$uHOL$uOtimes$u$uclass$uOtimes'('c$uPolynomial$uOpoly'('c$uPolynomial$uOsmult'('c$uHOL$uOinverse$u$uclass$uOinverse'('c$uPolynomial$uOpoly'('v$uq','c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'v$uq','tc$uComplex$uOcomplex'),'v$uy','tc$uComplex$uOcomplex'),'c$uPolynomial$uOpoly'('v$uq','c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex') != 'c$uPolynomial$uOpoly'('v$uq','v$uy','tc$uComplex$uOcomplex'),
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(c897,plain,
'class$uOrderedGroup$uOmonoid$u$uadd'('tc$uComplex$uOcomplex'),
inference(clausification,[status(esa)],[clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add]) ).
cnf(c903,plain,
'class$uRing$u$uand$u$uField$uOidom'('tc$uComplex$uOcomplex'),
inference(clausification,[status(esa)],[clsarity_Complex__Ocomplex__Ring__and__Field_Oidom]) ).
cnf(c905,plain,
'class$uInt$uOnumber$u$uring'('tc$uComplex$uOcomplex'),
inference(clausification,[status(esa)],[clsarity_Complex__Ocomplex__Int_Onumber__ring]) ).
cnf(d0,plain,
'c$uPolynomial$uOpoly'('v$uq','v$uy','tc$uComplex$uOcomplex') != 'c$uPolynomial$uOpoly'('v$uq','v$uy','tc$uComplex$uOcomplex'),
inference(demodulation,[status(thm)],[c836,c806]) ).
cnf(d1,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)],[c203,c897]) ).
cnf(d2,plain,
( ~ 'class$uRing$u$uand$u$uField$uOidom'('tc$uComplex$uOcomplex')
| X0 = 'c$uHOL$uOplus$u$uclass$uOplus'(X0,'c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex') ),
inference(resolution,[status(thm)],[c206,c905]) ).
cnf(d3,plain,
( ~ 'class$uRing$u$uand$u$uField$uOidom'('tc$uComplex$uOcomplex')
| X0 = X0 ),
inference(demodulation,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
X0 = X0,
inference(resolution,[status(thm)],[c903,d3]) ).
cnf(d5,plain,
$false,
inference(resolution,[status(thm)],[d4,d0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG399-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n007.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 26 21:55:24 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 37.27/5.71 % SZS status Unsatisfiable for theBenchmark.p
% 37.27/5.71 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------