%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWW180+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 09:11:29 AM UTC 2026
% Result : Theorem 9.06s 8.35s
% Output : CNFRefutation 9.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 13
% Syntax : Number of formulae : 39 ( 20 unt; 0 def)
% Number of atoms : 70 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 64 ( 33 ~; 20 |; 0 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 34 ( 0 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_order__refl,axiom,
! [X0,X1] :
( 'class$uOrderings$uOpreorder'(X1)
=> 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'(X1,X0,X0) ) ).
fof(fact_add__increasing,axiom,
! [X0,X1,X2,X3] :
( 'class$uGroups$uOordered$u$ucomm$u$umonoid$u$uadd'(X3)
=> ( 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'(X3,'c$uGroups$uOzero$u$uclass$uOzero'(X3),X2)
=> ( 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'(X3,X1,X0)
=> 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'(X3,X1,'c$uGroups$uOplus$u$uclass$uOplus'(X3,X2,X0)) ) ) ) ).
fof(fact_linorder__le__cases,axiom,
! [X0,X1,X2] :
( 'class$uOrderings$uOlinorder'(X2)
=> ( ~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'(X2,X1,X0)
=> 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'(X2,X0,X1) ) ) ).
fof(fact_add__mono,axiom,
! [X0,X1,X2,X3,X4] :
( 'class$uGroups$uOordered$u$uab$u$usemigroup$u$uadd'(X4)
=> ( 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'(X4,X3,X2)
=> ( 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'(X4,X1,X0)
=> 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'(X4,'c$uGroups$uOplus$u$uclass$uOplus'(X4,X3,X1),'c$uGroups$uOplus$u$uclass$uOplus'(X4,X2,X0)) ) ) ) ).
fof(fact_abs__ge__self,axiom,
! [X0,X1] :
( 'class$uGroups$uOordered$u$uab$u$ugroup$u$uadd$u$uabs'(X1)
=> 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'(X1,X0,'c$uGroups$uOabs$u$uclass$uOabs'(X1,X0)) ) ).
fof(fact_not__one__le__zero,axiom,
! [X0] :
( 'class$uRings$uOlinordered$u$usemidom'(X0)
=> ~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'(X0,'c$uGroups$uOone$u$uclass$uOone'(X0),'c$uGroups$uOzero$u$uclass$uOzero'(X0)) ) ).
fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add,axiom,
'class$uGroups$uOordered$u$uab$u$usemigroup$u$uadd'('tc$uRealDef$uOreal') ).
fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs,axiom,
'class$uGroups$uOordered$u$uab$u$ugroup$u$uadd$u$uabs'('tc$uRealDef$uOreal') ).
fof(arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add,axiom,
'class$uGroups$uOordered$u$ucomm$u$umonoid$u$uadd'('tc$uRealDef$uOreal') ).
fof(arity_RealDef__Oreal__Rings_Olinordered__semidom,axiom,
'class$uRings$uOlinordered$u$usemidom'('tc$uRealDef$uOreal') ).
fof(arity_RealDef__Oreal__Orderings_Opreorder,axiom,
'class$uOrderings$uOpreorder'('tc$uRealDef$uOreal') ).
fof(arity_RealDef__Oreal__Orderings_Olinorder,axiom,
'class$uOrderings$uOlinorder'('tc$uRealDef$uOreal') ).
fof(conj_0,conjecture,
'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal','c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uc'),hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'v$ur'),'v$um')),'c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal','c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal','c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uc')),'c$uGroups$uOabs$u$uclass$uOabs'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'v$ur'),'v$um')))) ).
fof(negated_conjecture,negated_conjecture,
~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal','c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uc'),hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'v$ur'),'v$um')),'c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal','c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal','c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uc')),'c$uGroups$uOabs$u$uclass$uOabs'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'v$ur'),'v$um')))),
inference(negate_conjecture,[status(cth)],[conj_0]) ).
cnf(c13,plain,
( 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'(X0,X1,X1)
| ~ 'class$uOrderings$uOpreorder'(X0) ),
inference(clausification,[status(esa)],[fact_order__refl]) ).
cnf(c134,plain,
( 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'(X0,X2,'c$uGroups$uOplus$u$uclass$uOplus'(X0,X1,X3))
| ~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'(X0,X2,X3)
| ~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'(X0,'c$uGroups$uOzero$u$uclass$uOzero'(X0),X1)
| ~ 'class$uGroups$uOordered$u$ucomm$u$umonoid$u$uadd'(X0) ),
inference(clausification,[status(esa)],[fact_add__increasing]) ).
cnf(c151,plain,
( 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'(X0,X2,X1)
| 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'(X0,X1,X2)
| ~ 'class$uOrderings$uOlinorder'(X0) ),
inference(clausification,[status(esa)],[fact_linorder__le__cases]) ).
cnf(c200,plain,
( 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'(X0,'c$uGroups$uOplus$u$uclass$uOplus'(X0,X1,X3),'c$uGroups$uOplus$u$uclass$uOplus'(X0,X2,X4))
| ~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'(X0,X3,X4)
| ~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'(X0,X1,X2)
| ~ 'class$uGroups$uOordered$u$uab$u$usemigroup$u$uadd'(X0) ),
inference(clausification,[status(esa)],[fact_add__mono]) ).
cnf(c227,plain,
( 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'(X0,X1,'c$uGroups$uOabs$u$uclass$uOabs'(X0,X1))
| ~ 'class$uGroups$uOordered$u$uab$u$ugroup$u$uadd$u$uabs'(X0) ),
inference(clausification,[status(esa)],[fact_abs__ge__self]) ).
cnf(c352,plain,
( ~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'(X0,'c$uGroups$uOone$u$uclass$uOone'(X0),'c$uGroups$uOzero$u$uclass$uOzero'(X0))
| ~ 'class$uRings$uOlinordered$u$usemidom'(X0) ),
inference(clausification,[status(esa)],[fact_not__one__le__zero]) ).
cnf(c1550,plain,
'class$uGroups$uOordered$u$uab$u$usemigroup$u$uadd'('tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add]) ).
cnf(c1551,plain,
'class$uGroups$uOordered$u$uab$u$ugroup$u$uadd$u$uabs'('tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs]) ).
cnf(c1553,plain,
'class$uGroups$uOordered$u$ucomm$u$umonoid$u$uadd'('tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add]) ).
cnf(c1566,plain,
'class$uRings$uOlinordered$u$usemidom'('tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[arity_RealDef__Oreal__Rings_Olinordered__semidom]) ).
cnf(c1582,plain,
'class$uOrderings$uOpreorder'('tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[arity_RealDef__Oreal__Orderings_Opreorder]) ).
cnf(c1583,plain,
'class$uOrderings$uOlinorder'('tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[arity_RealDef__Oreal__Orderings_Olinorder]) ).
cnf(c1707,plain,
~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal','c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uc'),hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'v$ur'),'v$um')),'c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal','c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal','c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uc')),'c$uGroups$uOabs$u$uclass$uOabs'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'v$ur'),'v$um')))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ 'class$uGroups$uOordered$u$uab$u$usemigroup$u$uadd'('tc$uRealDef$uOreal')
| ~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'v$ur'),'v$um'),'c$uGroups$uOabs$u$uclass$uOabs'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'v$ur'),'v$um')))
| ~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uc'),'c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal','c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uc'))) ),
inference(resolution,[status(thm)],[c1707,c200]) ).
cnf(d1,plain,
( ~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uc'),'c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal','c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uc')))
| ~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'v$ur'),'v$um'),'c$uGroups$uOabs$u$uclass$uOabs'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'v$ur'),'v$um'))) ),
inference(resolution,[status(thm)],[c1550,d0]) ).
cnf(d2,plain,
( ~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uc'),'c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal','c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uc')))
| ~ 'class$uGroups$uOordered$u$uab$u$ugroup$u$uadd$u$uabs'('tc$uRealDef$uOreal') ),
inference(resolution,[status(thm)],[c227,d1]) ).
cnf(d3,plain,
~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uc'),'c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal','c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uc'))),
inference(resolution,[status(thm)],[c1551,d2]) ).
cnf(d4,plain,
( ~ 'class$uGroups$uOordered$u$ucomm$u$umonoid$u$uadd'('tc$uRealDef$uOreal')
| ~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'))
| ~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uc'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uc')) ),
inference(resolution,[status(thm)],[d3,c134]) ).
cnf(d5,plain,
( ~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'))
| ~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uc'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uc')) ),
inference(resolution,[status(thm)],[c1553,d4]) ).
cnf(d6,plain,
( ~ 'class$uOrderings$uOpreorder'('tc$uRealDef$uOreal')
| ~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal')) ),
inference(resolution,[status(thm)],[d5,c13]) ).
cnf(d7,plain,
~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal')),
inference(resolution,[status(thm)],[c1582,d6]) ).
cnf(d8,plain,
( ~ 'class$uOrderings$uOlinorder'('tc$uRealDef$uOreal')
| 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'),'c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal')) ),
inference(resolution,[status(thm)],[d7,c151]) ).
cnf(d9,plain,
'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'),'c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal')),
inference(resolution,[status(thm)],[c1583,d8]) ).
cnf(d10,plain,
~ 'class$uRings$uOlinordered$u$usemidom'('tc$uRealDef$uOreal'),
inference(resolution,[status(thm)],[c352,d9]) ).
cnf(d11,plain,
$false,
inference(resolution,[status(thm)],[c1566,d10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW180+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n012.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 15:24:19 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.06/8.35 % SZS status Theorem for theBenchmark.p
% 9.06/8.35 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------