%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ALG373-1 : 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 : 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 06:48:24 AM UTC 2026
% Result : Unsatisfiable 28.04s 14.30s
% Output : CNFRefutation 18.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of clauses : 44 ( 26 unt; 2 nHn; 26 RR)
% Number of literals : 74 ( 6 equ; 34 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 55 ( 15 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_poly__bound__exists_0,axiom,
'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'v$usko$u$uFundamental$u$uTheorem$u$uAlgebra$u$uMirabelle$u$uXpoly$u$ubound$u$uexists$u$u1'(X0,X1),'tc$uRealDef$uOreal') ).
cnf(cls_minus__le__self__iff_0,axiom,
( ~ 'c$ulessequals'('c$uHOL$uOuminus$u$uclass$uOuminus'(X1,X0),X1,X0)
| 'c$ulessequals'('c$uHOL$uOzero$u$uclass$uOzero'(X0),X1,X0)
| ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uadd'(X0) ) ).
cnf(cls_neg__0__le__iff__le_0,axiom,
( ~ 'c$ulessequals'('c$uHOL$uOzero$u$uclass$uOzero'(X0),'c$uHOL$uOuminus$u$uclass$uOuminus'(X1,X0),X0)
| 'c$ulessequals'(X1,'c$uHOL$uOzero$u$uclass$uOzero'(X0),X0)
| ~ 'class$uOrderedGroup$uOpordered$u$uab$u$ugroup$u$uadd'(X0) ) ).
cnf(cls_rp_0,axiom,
'c$ulessequals'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'v$ur','tc$uRealDef$uOreal') ).
cnf(cls_real__le__trans_0,axiom,
( ~ 'c$ulessequals'(X0,X2,'tc$uRealDef$uOreal')
| ~ 'c$ulessequals'(X2,X1,'tc$uRealDef$uOreal')
| 'c$ulessequals'(X0,X1,'tc$uRealDef$uOreal') ) ).
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_real__le__antisym_0,axiom,
( ~ 'c$ulessequals'(X0,X1,'tc$uRealDef$uOreal')
| ~ 'c$ulessequals'(X1,X0,'tc$uRealDef$uOreal')
| X0 = X1 ) ).
cnf(cls_not__leE_0,axiom,
( 'c$ulessequals'(X2,X1,X0)
| 'c$uHOL$uOord$u$uclass$uOless'(X1,X2,X0)
| ~ 'class$uOrderings$uOlinorder'(X0) ) ).
cnf(cls_linorder__not__less_1,axiom,
( ~ 'c$ulessequals'(X2,X1,X0)
| ~ 'c$uHOL$uOord$u$uclass$uOless'(X1,X2,X0)
| ~ 'class$uOrderings$uOlinorder'(X0) ) ).
cnf(cls_conjecture_1,negated_conjecture,
'c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uPolynomial$uOpoly'('v$up','v$uxa'(X0),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex') = 'c$uHOL$uOuminus$u$uclass$uOuminus'('v$ux'(X0),'tc$uRealDef$uOreal') ).
cnf(cls_conjecture_2,negated_conjecture,
~ 'c$uHOL$uOord$u$uclass$uOless'('v$ux'(X0),X0,'tc$uRealDef$uOreal') ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add,axiom,
'class$uOrderedGroup$uOpordered$u$uab$u$ugroup$u$uadd'('tc$uRealDef$uOreal') ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add,axiom,
'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uadd'('tc$uRealDef$uOreal') ).
cnf(clsarity_RealDef__Oreal__Orderings_Olinorder,axiom,
'class$uOrderings$uOlinorder'('tc$uRealDef$uOreal') ).
cnf(c187,plain,
'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'v$usko$u$uFundamental$u$uTheorem$u$uAlgebra$u$uMirabelle$u$uXpoly$u$ubound$u$uexists$u$u1'(X0,X1),'tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[cls_poly__bound__exists_0]) ).
cnf(c247,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$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uadd'(X0) ),
inference(clausification,[status(esa)],[cls_minus__le__self__iff_0]) ).
cnf(c251,plain,
( ~ 'c$ulessequals'('c$uHOL$uOzero$u$uclass$uOzero'(X0),'c$uHOL$uOuminus$u$uclass$uOuminus'(X1,X0),X0)
| 'c$ulessequals'(X1,'c$uHOL$uOzero$u$uclass$uOzero'(X0),X0)
| ~ 'class$uOrderedGroup$uOpordered$u$uab$u$ugroup$u$uadd'(X0) ),
inference(clausification,[status(esa)],[cls_neg__0__le__iff__le_0]) ).
cnf(c269,plain,
'c$ulessequals'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'v$ur','tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[cls_rp_0]) ).
cnf(c287,plain,
( ~ 'c$ulessequals'(X0,X2,'tc$uRealDef$uOreal')
| ~ 'c$ulessequals'(X2,X1,'tc$uRealDef$uOreal')
| 'c$ulessequals'(X0,X1,'tc$uRealDef$uOreal') ),
inference(clausification,[status(esa)],[cls_real__le__trans_0]) ).
cnf(c299,plain,
'c$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$uOreal'),
inference(clausification,[status(esa)],[cls_complex__mod__minus__le__complex__mod_0]) ).
cnf(c317,plain,
( ~ 'c$ulessequals'(X0,X1,'tc$uRealDef$uOreal')
| ~ 'c$ulessequals'(X1,X0,'tc$uRealDef$uOreal')
| X0 = X1 ),
inference(clausification,[status(esa)],[cls_real__le__antisym_0]) ).
cnf(c327,plain,
( 'c$ulessequals'(X2,X1,X0)
| 'c$uHOL$uOord$u$uclass$uOless'(X1,X2,X0)
| ~ 'class$uOrderings$uOlinorder'(X0) ),
inference(clausification,[status(esa)],[cls_not__leE_0]) ).
cnf(c330,plain,
( ~ 'c$ulessequals'(X2,X1,X0)
| ~ 'c$uHOL$uOord$u$uclass$uOless'(X1,X2,X0)
| ~ 'class$uOrderings$uOlinorder'(X0) ),
inference(clausification,[status(esa)],[cls_linorder__not__less_1]) ).
cnf(c349,plain,
'c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uPolynomial$uOpoly'('v$up','v$uxa'(X0),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex') = 'c$uHOL$uOuminus$u$uclass$uOuminus'('v$ux'(X0),'tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[cls_conjecture_1]) ).
cnf(c350,plain,
~ 'c$uHOL$uOord$u$uclass$uOless'('v$ux'(X0),X0,'tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[cls_conjecture_2]) ).
cnf(c404,plain,
'class$uOrderedGroup$uOpordered$u$uab$u$ugroup$u$uadd'('tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add]) ).
cnf(c405,plain,
'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uadd'('tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add]) ).
cnf(c431,plain,
'class$uOrderings$uOlinorder'('tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[clsarity_RealDef__Oreal__Orderings_Olinorder]) ).
cnf(d0,plain,
( ~ 'c$ulessequals'('v$ur','c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'tc$uRealDef$uOreal')
| 'v$ur' = 'c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal') ),
inference(resolution,[status(thm)],[c317,c269]) ).
cnf(d1,plain,
( ~ 'class$uOrderedGroup$uOlordered$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)],[c299,c247]) ).
cnf(d2,plain,
'c$ulessequals'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'(X0,'tc$uComplex$uOcomplex'),'tc$uRealDef$uOreal'),
inference(resolution,[status(thm)],[c405,d1]) ).
cnf(d3,plain,
'c$ulessequals'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'c$uHOL$uOuminus$u$uclass$uOuminus'('v$ux'(X0),'tc$uRealDef$uOreal'),'tc$uRealDef$uOreal'),
inference(superposition,[status(thm)],[c349,d2]) ).
cnf(d4,plain,
( ~ 'class$uOrderedGroup$uOpordered$u$uab$u$ugroup$u$uadd'('tc$uRealDef$uOreal')
| 'c$ulessequals'('v$ux'(X0),'c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'tc$uRealDef$uOreal') ),
inference(resolution,[status(thm)],[d3,c251]) ).
cnf(d5,plain,
'c$ulessequals'('v$ux'(X0),'c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'tc$uRealDef$uOreal'),
inference(resolution,[status(thm)],[c404,d4]) ).
cnf(d6,plain,
( ~ 'class$uOrderings$uOlinorder'('tc$uRealDef$uOreal')
| 'c$ulessequals'(X0,'v$ux'(X0),'tc$uRealDef$uOreal') ),
inference(resolution,[status(thm)],[c327,c350]) ).
cnf(d7,plain,
'c$ulessequals'(X0,'v$ux'(X0),'tc$uRealDef$uOreal'),
inference(resolution,[status(thm)],[c431,d6]) ).
cnf(d8,plain,
( 'c$ulessequals'(X0,X1,'tc$uRealDef$uOreal')
| ~ 'c$ulessequals'('v$ux'(X0),X1,'tc$uRealDef$uOreal') ),
inference(resolution,[status(thm)],[d7,c287]) ).
cnf(d9,plain,
'c$ulessequals'(X0,'c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'tc$uRealDef$uOreal'),
inference(resolution,[status(thm)],[d8,d5]) ).
cnf(d10,plain,
'v$ur' = 'c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),
inference(resolution,[status(thm)],[d9,d0]) ).
cnf(d11,plain,
'c$uHOL$uOord$u$uclass$uOless'('v$ur','v$usko$u$uFundamental$u$uTheorem$u$uAlgebra$u$uMirabelle$u$uXpoly$u$ubound$u$uexists$u$u1'(X0,X1),'tc$uRealDef$uOreal'),
inference(demodulation,[status(thm)],[c187,d10]) ).
cnf(d12,plain,
'c$ulessequals'(X0,'v$ur','tc$uRealDef$uOreal'),
inference(demodulation,[status(thm)],[d9,d10]) ).
cnf(d13,plain,
( ~ 'class$uOrderings$uOlinorder'('tc$uRealDef$uOreal')
| ~ 'c$uHOL$uOord$u$uclass$uOless'('v$ur',X0,'tc$uRealDef$uOreal') ),
inference(resolution,[status(thm)],[d12,c330]) ).
cnf(d14,plain,
~ 'c$uHOL$uOord$u$uclass$uOless'('v$ur',X0,'tc$uRealDef$uOreal'),
inference(resolution,[status(thm)],[c431,d13]) ).
cnf(d15,plain,
$false,
inference(resolution,[status(thm)],[d14,d11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG373-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/10.38 % Computer : n019.cluster.edu
% 0.10/10.38 % Model : x86_64 x86_64
% 0.10/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.38 % Memory : 8046.5625MB
% 0.10/10.38 % OS : Linux 6.8.0-71-generic
% 0.10/10.38 % CPULimit : 300
% 0.10/10.38 % WCLimit : 300
% 0.10/10.38 % DateTime : Sat Sep 26 21:56:14 UTC 2026
% 0.10/10.38 % CPUTime :
% 0.10/10.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 28.04/14.30 % SZS status Unsatisfiable for theBenchmark.p
% 28.04/14.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------