%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWW217+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 : n009.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 09:11:32 AM UTC 2026
% Result : Theorem 67.69s 13.19s
% Output : CNFRefutation 67.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 42 ( 19 unt; 0 def)
% Number of atoms : 80 ( 17 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 64 ( 26 ~; 26 |; 2 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-3 aty)
% Number of variables : 36 ( 0 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_dme,axiom,
'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'v$uda'),'v$um'),'v$ue') ).
fof(fact__096cmod_A_Iw_A_N_Az_J_A_K_Acmod_A_Ipoly_Acs_A_Iw_A_N_Az_J_J_A_060_061_Ad_A_K_Am_096,axiom,
'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','c$uGroups$uOminus$u$uclass$uOminus'('tc$uComplex$uOcomplex','v$uw','v$uz'))),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex',hAPP('c$uPolynomial$uOpoly'('tc$uComplex$uOcomplex','v$ucs'),'c$uGroups$uOminus$u$uclass$uOminus'('tc$uComplex$uOcomplex','v$uw','v$uz')))),hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'v$uda'),'v$um')) ).
fof(fact_linorder__neqE__linordered__idom,axiom,
! [X0,X1,X2] :
( 'class$uRings$uOlinordered$u$uidom'(X2)
=> ( X1 != X0
=> ( ~ 'c$uOrderings$uOord$u$uclass$uOless'(X2,X1,X0)
=> 'c$uOrderings$uOord$u$uclass$uOless'(X2,X0,X1) ) ) ) ).
fof(fact_real__le__antisym,axiom,
! [X0,X1] :
( 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X1,X0)
=> ( 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X0,X1)
=> X1 = X0 ) ) ).
fof(fact_real__le__trans,axiom,
! [X0,X1,X2] :
( 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X2,X1)
=> ( 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X1,X0)
=> 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X2,X0) ) ) ).
fof(fact_real__le__linear,axiom,
! [X0,X1] :
( 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X0,X1)
| 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X1,X0) ) ).
fof(fact_real__mult__commute,axiom,
! [X0,X1] : hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),X1),X0) = hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),X0),X1) ).
fof(fact_real__less__def,axiom,
! [X0,X1] :
( 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal',X1,X0)
<=> ( X1 != X0
& 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X1,X0) ) ) ).
fof(fact_less__le__not__le,axiom,
! [X0,X1,X2] :
( 'class$uOrderings$uOpreorder'(X2)
=> ( 'c$uOrderings$uOord$u$uclass$uOless'(X2,X1,X0)
<=> ( ~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'(X2,X0,X1)
& 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'(X2,X1,X0) ) ) ) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__idom,axiom,
'class$uRings$uOlinordered$u$uidom'('tc$uRealDef$uOreal') ).
fof(arity_RealDef__Oreal__Orderings_Opreorder,axiom,
'class$uOrderings$uOpreorder'('tc$uRealDef$uOreal') ).
fof(conj_0,conjecture,
'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','c$uGroups$uOminus$u$uclass$uOminus'('tc$uComplex$uOcomplex','v$uw','v$uz'))),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex',hAPP('c$uPolynomial$uOpoly'('tc$uComplex$uOcomplex','v$ucs'),'c$uGroups$uOminus$u$uclass$uOminus'('tc$uComplex$uOcomplex','v$uw','v$uz')))),'v$ue') ).
fof(negated_conjecture,negated_conjecture,
~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','c$uGroups$uOminus$u$uclass$uOminus'('tc$uComplex$uOcomplex','v$uw','v$uz'))),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex',hAPP('c$uPolynomial$uOpoly'('tc$uComplex$uOcomplex','v$ucs'),'c$uGroups$uOminus$u$uclass$uOminus'('tc$uComplex$uOcomplex','v$uw','v$uz')))),'v$ue'),
inference(negate_conjecture,[status(cth)],[conj_0]) ).
cnf(c4,plain,
'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'v$uda'),'v$um'),'v$ue'),
inference(clausification,[status(esa)],[fact_dme]) ).
cnf(c8,plain,
'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','c$uGroups$uOminus$u$uclass$uOminus'('tc$uComplex$uOcomplex','v$uw','v$uz'))),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex',hAPP('c$uPolynomial$uOpoly'('tc$uComplex$uOcomplex','v$ucs'),'c$uGroups$uOminus$u$uclass$uOminus'('tc$uComplex$uOcomplex','v$uw','v$uz')))),hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'v$uda'),'v$um')),
inference(clausification,[status(esa)],[fact__096cmod_A_Iw_A_N_Az_J_A_K_Acmod_A_Ipoly_Acs_A_Iw_A_N_Az_J_J_A_060_061_Ad_A_K_Am_096]) ).
cnf(c143,plain,
( 'c$uOrderings$uOord$u$uclass$uOless'(X0,X2,X1)
| 'c$uOrderings$uOord$u$uclass$uOless'(X0,X1,X2)
| X1 = X2
| ~ 'class$uRings$uOlinordered$u$uidom'(X0) ),
inference(clausification,[status(esa)],[fact_linorder__neqE__linordered__idom]) ).
cnf(c144,plain,
( X0 = X1
| ~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X1,X0)
| ~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X0,X1) ),
inference(clausification,[status(esa)],[fact_real__le__antisym]) ).
cnf(c145,plain,
( 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X0,X2)
| ~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X1,X2)
| ~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X0,X1) ),
inference(clausification,[status(esa)],[fact_real__le__trans]) ).
cnf(c146,plain,
( 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X1,X0)
| 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X0,X1) ),
inference(clausification,[status(esa)],[fact_real__le__linear]) ).
cnf(c148,plain,
hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),X0),X1) = hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),X1),X0),
inference(clausification,[status(esa)],[fact_real__mult__commute]) ).
cnf(c159,plain,
( 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X0,X1)
| ~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal',X0,X1) ),
inference(clausification,[status(esa)],[fact_real__less__def]) ).
cnf(c852,plain,
( ~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'(X0,X2,X1)
| ~ 'c$uOrderings$uOord$u$uclass$uOless'(X0,X1,X2)
| ~ 'class$uOrderings$uOpreorder'(X0) ),
inference(clausification,[status(esa)],[fact_less__le__not__le]) ).
cnf(c1642,plain,
'class$uRings$uOlinordered$u$uidom'('tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[arity_RealDef__Oreal__Rings_Olinordered__idom]) ).
cnf(c1651,plain,
'class$uOrderings$uOpreorder'('tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[arity_RealDef__Oreal__Orderings_Opreorder]) ).
cnf(c1766,plain,
~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','c$uGroups$uOminus$u$uclass$uOminus'('tc$uComplex$uOcomplex','v$uw','v$uz'))),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex',hAPP('c$uPolynomial$uOpoly'('tc$uComplex$uOcomplex','v$ucs'),'c$uGroups$uOminus$u$uclass$uOminus'('tc$uComplex$uOcomplex','v$uw','v$uz')))),'v$ue'),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ 'class$uRings$uOlinordered$u$uidom'('tc$uRealDef$uOreal')
| 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','v$ue',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','c$uGroups$uOminus$u$uclass$uOminus'('tc$uComplex$uOcomplex','v$uw','v$uz'))),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex',hAPP('c$uPolynomial$uOpoly'('tc$uComplex$uOcomplex','v$ucs'),'c$uGroups$uOminus$u$uclass$uOminus'('tc$uComplex$uOcomplex','v$uw','v$uz')))))
| hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','c$uGroups$uOminus$u$uclass$uOminus'('tc$uComplex$uOcomplex','v$uw','v$uz'))),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex',hAPP('c$uPolynomial$uOpoly'('tc$uComplex$uOcomplex','v$ucs'),'c$uGroups$uOminus$u$uclass$uOminus'('tc$uComplex$uOcomplex','v$uw','v$uz')))) = 'v$ue' ),
inference(resolution,[status(thm)],[c1766,c143]) ).
cnf(d1,plain,
( 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','v$ue',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','c$uGroups$uOminus$u$uclass$uOminus'('tc$uComplex$uOcomplex','v$uw','v$uz'))),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex',hAPP('c$uPolynomial$uOpoly'('tc$uComplex$uOcomplex','v$ucs'),'c$uGroups$uOminus$u$uclass$uOminus'('tc$uComplex$uOcomplex','v$uw','v$uz')))))
| hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','c$uGroups$uOminus$u$uclass$uOminus'('tc$uComplex$uOcomplex','v$uw','v$uz'))),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex',hAPP('c$uPolynomial$uOpoly'('tc$uComplex$uOcomplex','v$ucs'),'c$uGroups$uOminus$u$uclass$uOminus'('tc$uComplex$uOcomplex','v$uw','v$uz')))) = 'v$ue' ),
inference(resolution,[status(thm)],[c1642,d0]) ).
cnf(d2,plain,
( 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','v$ue',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','c$uGroups$uOminus$u$uclass$uOminus'('tc$uComplex$uOcomplex','v$uw','v$uz'))),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex',hAPP('c$uPolynomial$uOpoly'('tc$uComplex$uOcomplex','v$ucs'),'c$uGroups$uOminus$u$uclass$uOminus'('tc$uComplex$uOcomplex','v$uw','v$uz')))))
| hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','c$uGroups$uOminus$u$uclass$uOminus'('tc$uComplex$uOcomplex','v$uw','v$uz'))),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex',hAPP('c$uPolynomial$uOpoly'('tc$uComplex$uOcomplex','v$ucs'),'c$uGroups$uOminus$u$uclass$uOminus'('tc$uComplex$uOcomplex','v$uw','v$uz')))) = 'v$ue' ),
inference(resolution,[status(thm)],[d1,c159]) ).
cnf(d3,plain,
( ~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','c$uGroups$uOminus$u$uclass$uOminus'('tc$uComplex$uOcomplex','v$uw','v$uz'))),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex',hAPP('c$uPolynomial$uOpoly'('tc$uComplex$uOcomplex','v$ucs'),'c$uGroups$uOminus$u$uclass$uOminus'('tc$uComplex$uOcomplex','v$uw','v$uz')))),'v$ue')
| hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','c$uGroups$uOminus$u$uclass$uOminus'('tc$uComplex$uOcomplex','v$uw','v$uz'))),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex',hAPP('c$uPolynomial$uOpoly'('tc$uComplex$uOcomplex','v$ucs'),'c$uGroups$uOminus$u$uclass$uOminus'('tc$uComplex$uOcomplex','v$uw','v$uz')))) = 'v$ue'
| hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','c$uGroups$uOminus$u$uclass$uOminus'('tc$uComplex$uOcomplex','v$uw','v$uz'))),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex',hAPP('c$uPolynomial$uOpoly'('tc$uComplex$uOcomplex','v$ucs'),'c$uGroups$uOminus$u$uclass$uOminus'('tc$uComplex$uOcomplex','v$uw','v$uz')))) = 'v$ue' ),
inference(resolution,[status(thm)],[d2,c144]) ).
cnf(d4,plain,
( 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','c$uGroups$uOminus$u$uclass$uOminus'('tc$uComplex$uOcomplex','v$uw','v$uz'))),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex',hAPP('c$uPolynomial$uOpoly'('tc$uComplex$uOcomplex','v$ucs'),'c$uGroups$uOminus$u$uclass$uOminus'('tc$uComplex$uOcomplex','v$uw','v$uz')))),X0)
| ~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'v$uda'),'v$um'),X0) ),
inference(resolution,[status(thm)],[c145,c8]) ).
cnf(d5,plain,
( ~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'v$um'),'v$uda'),X0)
| 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','c$uGroups$uOminus$u$uclass$uOminus'('tc$uComplex$uOcomplex','v$uw','v$uz'))),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex',hAPP('c$uPolynomial$uOpoly'('tc$uComplex$uOcomplex','v$ucs'),'c$uGroups$uOminus$u$uclass$uOminus'('tc$uComplex$uOcomplex','v$uw','v$uz')))),X0) ),
inference(demodulation,[status(thm)],[d4,c148]) ).
cnf(d6,plain,
( hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','c$uGroups$uOminus$u$uclass$uOminus'('tc$uComplex$uOcomplex','v$uw','v$uz'))),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex',hAPP('c$uPolynomial$uOpoly'('tc$uComplex$uOcomplex','v$ucs'),'c$uGroups$uOminus$u$uclass$uOminus'('tc$uComplex$uOcomplex','v$uw','v$uz')))) = 'v$ue'
| ~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'v$um'),'v$uda'),'v$ue') ),
inference(resolution,[status(thm)],[d5,d3]) ).
cnf(d7,plain,
( 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','v$ue',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'v$um'),'v$uda'))
| hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','c$uGroups$uOminus$u$uclass$uOminus'('tc$uComplex$uOcomplex','v$uw','v$uz'))),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex',hAPP('c$uPolynomial$uOpoly'('tc$uComplex$uOcomplex','v$ucs'),'c$uGroups$uOminus$u$uclass$uOminus'('tc$uComplex$uOcomplex','v$uw','v$uz')))) = 'v$ue' ),
inference(resolution,[status(thm)],[d6,c146]) ).
cnf(d8,plain,
( ~ 'class$uOrderings$uOpreorder'('tc$uRealDef$uOreal')
| ~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'v$um'),'v$uda'),'v$ue')
| hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','c$uGroups$uOminus$u$uclass$uOminus'('tc$uComplex$uOcomplex','v$uw','v$uz'))),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex',hAPP('c$uPolynomial$uOpoly'('tc$uComplex$uOcomplex','v$ucs'),'c$uGroups$uOminus$u$uclass$uOminus'('tc$uComplex$uOcomplex','v$uw','v$uz')))) = 'v$ue' ),
inference(resolution,[status(thm)],[d7,c852]) ).
cnf(d9,plain,
( ~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'v$um'),'v$uda'),'v$ue')
| hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','c$uGroups$uOminus$u$uclass$uOminus'('tc$uComplex$uOcomplex','v$uw','v$uz'))),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex',hAPP('c$uPolynomial$uOpoly'('tc$uComplex$uOcomplex','v$ucs'),'c$uGroups$uOminus$u$uclass$uOminus'('tc$uComplex$uOcomplex','v$uw','v$uz')))) = 'v$ue' ),
inference(resolution,[status(thm)],[c1651,d8]) ).
cnf(d10,plain,
'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'v$um'),'v$uda'),'v$ue'),
inference(demodulation,[status(thm)],[c4,c148]) ).
cnf(d11,plain,
hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','c$uGroups$uOminus$u$uclass$uOminus'('tc$uComplex$uOcomplex','v$uw','v$uz'))),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex',hAPP('c$uPolynomial$uOpoly'('tc$uComplex$uOcomplex','v$ucs'),'c$uGroups$uOminus$u$uclass$uOminus'('tc$uComplex$uOcomplex','v$uw','v$uz')))) = 'v$ue',
inference(resolution,[status(thm)],[d10,d9]) ).
cnf(d12,plain,
'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','c$uGroups$uOminus$u$uclass$uOminus'('tc$uComplex$uOcomplex','v$uw','v$uz'))),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex',hAPP('c$uPolynomial$uOpoly'('tc$uComplex$uOcomplex','v$ucs'),'c$uGroups$uOminus$u$uclass$uOminus'('tc$uComplex$uOcomplex','v$uw','v$uz')))),hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'v$um'),'v$uda')),
inference(demodulation,[status(thm)],[c8,c148]) ).
cnf(d13,plain,
'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','v$ue',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'v$um'),'v$uda')),
inference(demodulation,[status(thm)],[d12,d11]) ).
cnf(d14,plain,
( ~ 'class$uOrderings$uOpreorder'('tc$uRealDef$uOreal')
| ~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'v$um'),'v$uda'),'v$ue') ),
inference(resolution,[status(thm)],[d13,c852]) ).
cnf(d15,plain,
~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'v$um'),'v$uda'),'v$ue'),
inference(resolution,[status(thm)],[c1651,d14]) ).
cnf(d16,plain,
$false,
inference(resolution,[status(thm)],[d10,d15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW217+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n009.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sat Sep 26 15:29:00 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 67.69/13.19 % SZS status Theorem for theBenchmark.p
% 67.69/13.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------