%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWW179+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 7.10s 8.95s
% Output : CNFRefutation 7.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 23 ( 15 unt; 0 def)
% Number of atoms : 37 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 33 ( 19 ~; 10 |; 0 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 10 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact__0960_A_060_061_Acmod_Ac_096,axiom,
'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uc')) ).
fof(fact__0960_A_060_061_Aabs_A_Ir_A_K_Am_J_096,axiom,
'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'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(fact_zero__less__one,axiom,
! [X0] :
( 'class$uRings$uOlinordered$u$usemidom'(X0)
=> 'c$uOrderings$uOord$u$uclass$uOless'(X0,'c$uGroups$uOzero$u$uclass$uOzero'(X0),'c$uGroups$uOone$u$uclass$uOone'(X0)) ) ).
fof(fact_add__strict__increasing,axiom,
! [X0,X1,X2,X3] :
( 'class$uGroups$uOordered$u$ucomm$u$umonoid$u$uadd'(X3)
=> ( 'c$uOrderings$uOord$u$uclass$uOless'(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$uOless'(X3,X1,'c$uGroups$uOplus$u$uclass$uOplus'(X3,X2,X0)) ) ) ) ).
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(conj_0,conjecture,
'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'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'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'c$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(c1,plain,
'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uc')),
inference(clausification,[status(esa)],[fact__0960_A_060_061_Acmod_Ac_096]) ).
cnf(c2,plain,
'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'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)],[fact__0960_A_060_061_Aabs_A_Ir_A_K_Am_J_096]) ).
cnf(c175,plain,
( 'c$uOrderings$uOord$u$uclass$uOless'(X0,'c$uGroups$uOzero$u$uclass$uOzero'(X0),'c$uGroups$uOone$u$uclass$uOone'(X0))
| ~ 'class$uRings$uOlinordered$u$usemidom'(X0) ),
inference(clausification,[status(esa)],[fact_zero__less__one]) ).
cnf(c194,plain,
( 'c$uOrderings$uOord$u$uclass$uOless'(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$uOless'(X0,'c$uGroups$uOzero$u$uclass$uOzero'(X0),X1)
| ~ 'class$uGroups$uOordered$u$ucomm$u$umonoid$u$uadd'(X0) ),
inference(clausification,[status(esa)],[fact_add__strict__increasing]) ).
cnf(c1588,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(c1601,plain,
'class$uRings$uOlinordered$u$usemidom'('tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[arity_RealDef__Oreal__Rings_Olinordered__semidom]) ).
cnf(c1739,plain,
~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'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$ucomm$u$umonoid$u$uadd'('tc$uRealDef$uOreal')
| ~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$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$uc')))
| ~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'c$uGroups$uOabs$u$uclass$uOabs'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'v$ur'),'v$um'))) ),
inference(resolution,[status(thm)],[c1739,c194]) ).
cnf(d1,plain,
( ~ 'class$uGroups$uOordered$u$ucomm$u$umonoid$u$uadd'('tc$uRealDef$uOreal')
| ~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$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$uc'))) ),
inference(resolution,[status(thm)],[c2,d0]) ).
cnf(d2,plain,
~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$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$uc'))),
inference(resolution,[status(thm)],[c1588,d1]) ).
cnf(d3,plain,
( ~ 'class$uGroups$uOordered$u$ucomm$u$umonoid$u$uadd'('tc$uRealDef$uOreal')
| ~ 'c$uOrderings$uOord$u$uclass$uOless'('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$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uc')) ),
inference(resolution,[status(thm)],[d2,c194]) ).
cnf(d4,plain,
( ~ 'class$uGroups$uOordered$u$ucomm$u$umonoid$u$uadd'('tc$uRealDef$uOreal')
| ~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal')) ),
inference(resolution,[status(thm)],[c1,d3]) ).
cnf(d5,plain,
~ 'c$uOrderings$uOord$u$uclass$uOless'('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)],[c1588,d4]) ).
cnf(d6,plain,
~ 'class$uRings$uOlinordered$u$usemidom'('tc$uRealDef$uOreal'),
inference(resolution,[status(thm)],[d5,c175]) ).
cnf(d7,plain,
$false,
inference(resolution,[status(thm)],[c1601,d6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWW179+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n005.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sat Sep 26 15:24:50 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.10/8.95 % SZS status Theorem for theBenchmark.p
% 7.10/8.95 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------