%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWW259+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 : n002.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 09:11:36 AM UTC 2026
% Result : Theorem 37.49s 15.00s
% Output : CNFRefutation 37.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 15
% Syntax : Number of formulae : 53 ( 29 unt; 0 def)
% Number of atoms : 96 ( 9 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 87 ( 44 ~; 29 |; 2 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 2 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-3 aty)
% Number of variables : 34 ( 1 sgn 14 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact__096_B_Bd2_O_A0_A_060_Ad2_A_061_061_062_AEX_Ae_0620_O_Ae_A_060_A1_A_G_Ae_A_060_Ad2_096,axiom,
! [X0] :
( 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),X0)
=> ? [X1] :
( 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal',X1,X0)
& 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal',X1,'c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'))
& 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),X1) ) ) ).
fof(fact_m_I1_J,axiom,
'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'v$um') ).
fof(fact_inv0,axiom,
'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'c$uRings$uOinverse$u$uclass$uOinverse'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),hAPP(hAPP('c$uPower$uOpower$u$uclass$uOpower'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uw')),'c$uGroups$uOplus$u$uclass$uOplus'('tc$uNat$uOnat','v$uk','c$uGroups$uOone$u$uclass$uOone'('tc$uNat$uOnat')))),'v$um'))) ).
fof(fact_zero__less__norm__iff,axiom,
! [X0,X1] :
( 'class$uRealVector$uOreal$u$unormed$u$uvector'(X1)
=> ( 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'(X1,X0))
<=> X0 != 'c$uGroups$uOzero$u$uclass$uOzero'(X1) ) ) ).
fof(fact_w0,axiom,
'v$uw' != 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex') ).
fof(fact_real__mult__commute,axiom,
! [X0,X1] : hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),X1),X0) = hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),X0),X1) ).
fof(fact_zero__less__power,axiom,
! [X0,X1,X2] :
( 'class$uRings$uOlinordered$u$usemidom'(X2)
=> ( 'c$uOrderings$uOord$u$uclass$uOless'(X2,'c$uGroups$uOzero$u$uclass$uOzero'(X2),X1)
=> 'c$uOrderings$uOord$u$uclass$uOless'(X2,'c$uGroups$uOzero$u$uclass$uOzero'(X2),hAPP(hAPP('c$uPower$uOpower$u$uclass$uOpower'(X2),X1),X0)) ) ) ).
fof(fact_inverse__positive__iff__positive,axiom,
! [X0,X1] :
( 'class$uFields$uOlinordered$u$ufield$u$uinverse$u$uzero'(X1)
=> ( 'c$uOrderings$uOord$u$uclass$uOless'(X1,'c$uGroups$uOzero$u$uclass$uOzero'(X1),'c$uRings$uOinverse$u$uclass$uOinverse'(X1,X0))
<=> 'c$uOrderings$uOord$u$uclass$uOless'(X1,'c$uGroups$uOzero$u$uclass$uOzero'(X1),X0) ) ) ).
fof(fact_real__mult__order,axiom,
! [X0,X1] :
( 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),X1)
=> ( 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),X0)
=> 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),X1),X0)) ) ) ).
fof(fact_Suc__eq__plus1,axiom,
! [X0] : 'c$uNat$uOSuc'(X0) = 'c$uGroups$uOplus$u$uclass$uOplus'('tc$uNat$uOnat',X0,'c$uGroups$uOone$u$uclass$uOone'('tc$uNat$uOnat')) ).
fof(arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero,axiom,
'class$uFields$uOlinordered$u$ufield$u$uinverse$u$uzero'('tc$uRealDef$uOreal') ).
fof(arity_RealDef__Oreal__Rings_Olinordered__semidom,axiom,
'class$uRings$uOlinordered$u$usemidom'('tc$uRealDef$uOreal') ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
'class$uRealVector$uOreal$u$unormed$u$uvector'('tc$uComplex$uOcomplex') ).
fof(conj_0,hypothesis,
! [X0] :
( 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),X0)
=> ( 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal',X0,'c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'))
=> ( 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal',X0,'c$uRings$uOinverse$u$uclass$uOinverse'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),hAPP(hAPP('c$uPower$uOpower$u$uclass$uOpower'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uw')),'c$uGroups$uOplus$u$uclass$uOplus'('tc$uNat$uOnat','v$uk','c$uGroups$uOone$u$uclass$uOone'('tc$uNat$uOnat')))),'v$um')))
=> 'v$uthesis' ) ) ) ).
fof(conj_1,conjecture,
'v$uthesis' ).
fof(negated_conjecture,negated_conjecture,
~ 'v$uthesis',
inference(negate_conjecture,[status(cth)],[conj_1]) ).
cnf(c1,plain,
( 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),sK4(X0))
| ~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),X0) ),
inference(clausification,[status(esa)],[fact__096_B_Bd2_O_A0_A_060_Ad2_A_061_061_062_AEX_Ae_0620_O_Ae_A_060_A1_A_G_Ae_A_060_Ad2_096]) ).
cnf(c2,plain,
( 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal',sK4(X0),'c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'))
| ~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),X0) ),
inference(clausification,[status(esa)],[fact__096_B_Bd2_O_A0_A_060_Ad2_A_061_061_062_AEX_Ae_0620_O_Ae_A_060_A1_A_G_Ae_A_060_Ad2_096]) ).
cnf(c3,plain,
( 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal',sK4(X0),X0)
| ~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),X0) ),
inference(clausification,[status(esa)],[fact__096_B_Bd2_O_A0_A_060_Ad2_A_061_061_062_AEX_Ae_0620_O_Ae_A_060_A1_A_G_Ae_A_060_Ad2_096]) ).
cnf(c4,plain,
'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'v$um'),
inference(clausification,[status(esa)],[fact_m_I1_J]) ).
cnf(c5,plain,
'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'c$uRings$uOinverse$u$uclass$uOinverse'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),hAPP(hAPP('c$uPower$uOpower$u$uclass$uOpower'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uw')),'c$uGroups$uOplus$u$uclass$uOplus'('tc$uNat$uOnat','v$uk','c$uGroups$uOone$u$uclass$uOone'('tc$uNat$uOnat')))),'v$um'))),
inference(clausification,[status(esa)],[fact_inv0]) ).
cnf(c14,plain,
( X1 = 'c$uGroups$uOzero$u$uclass$uOzero'(X0)
| 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'(X0,X1))
| ~ 'class$uRealVector$uOreal$u$unormed$u$uvector'(X0) ),
inference(clausification,[status(esa)],[fact_zero__less__norm__iff]) ).
cnf(c23,plain,
'v$uw' != 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),
inference(clausification,[status(esa)],[fact_w0]) ).
cnf(c33,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(c122,plain,
( 'c$uOrderings$uOord$u$uclass$uOless'(X0,'c$uGroups$uOzero$u$uclass$uOzero'(X0),hAPP(hAPP('c$uPower$uOpower$u$uclass$uOpower'(X0),X1),X2))
| ~ 'c$uOrderings$uOord$u$uclass$uOless'(X0,'c$uGroups$uOzero$u$uclass$uOzero'(X0),X1)
| ~ 'class$uRings$uOlinordered$u$usemidom'(X0) ),
inference(clausification,[status(esa)],[fact_zero__less__power]) ).
cnf(c143,plain,
( ~ 'c$uOrderings$uOord$u$uclass$uOless'(X0,'c$uGroups$uOzero$u$uclass$uOzero'(X0),X1)
| 'c$uOrderings$uOord$u$uclass$uOless'(X0,'c$uGroups$uOzero$u$uclass$uOzero'(X0),'c$uRings$uOinverse$u$uclass$uOinverse'(X0,X1))
| ~ 'class$uFields$uOlinordered$u$ufield$u$uinverse$u$uzero'(X0) ),
inference(clausification,[status(esa)],[fact_inverse__positive__iff__positive]) ).
cnf(c154,plain,
( 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),X0),X1))
| ~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),X1)
| ~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),X0) ),
inference(clausification,[status(esa)],[fact_real__mult__order]) ).
cnf(c865,plain,
'c$uNat$uOSuc'(X0) = 'c$uGroups$uOplus$u$uclass$uOplus'('tc$uNat$uOnat',X0,'c$uGroups$uOone$u$uclass$uOone'('tc$uNat$uOnat')),
inference(clausification,[status(esa)],[fact_Suc__eq__plus1]) ).
cnf(c1507,plain,
'class$uFields$uOlinordered$u$ufield$u$uinverse$u$uzero'('tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero]) ).
cnf(c1529,plain,
'class$uRings$uOlinordered$u$usemidom'('tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[arity_RealDef__Oreal__Rings_Olinordered__semidom]) ).
cnf(c1574,plain,
'class$uRealVector$uOreal$u$unormed$u$uvector'('tc$uComplex$uOcomplex'),
inference(clausification,[status(esa)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__vector]) ).
cnf(c1661,plain,
( 'v$uthesis'
| ~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal',X0,'c$uRings$uOinverse$u$uclass$uOinverse'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),hAPP(hAPP('c$uPower$uOpower$u$uclass$uOpower'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uw')),'c$uGroups$uOplus$u$uclass$uOplus'('tc$uNat$uOnat','v$uk','c$uGroups$uOone$u$uclass$uOone'('tc$uNat$uOnat')))),'v$um')))
| ~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal',X0,'c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'))
| ~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),X0) ),
inference(clausification,[status(esa)],[conj_0]) ).
cnf(c1662,plain,
~ 'v$uthesis',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'v$uthesis'
| ~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),X0)
| ~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal',X0,'c$uRings$uOinverse$u$uclass$uOinverse'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'v$um'),hAPP(hAPP('c$uPower$uOpower$u$uclass$uOpower'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uw')),'c$uGroups$uOplus$u$uclass$uOplus'('tc$uNat$uOnat','v$uk','c$uGroups$uOone$u$uclass$uOone'('tc$uNat$uOnat'))))))
| ~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal',X0,'c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal')) ),
inference(demodulation,[status(thm)],[c1661,c33]) ).
cnf(d1,plain,
( 'v$uthesis'
| ~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),X0)
| ~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal',X0,'c$uRings$uOinverse$u$uclass$uOinverse'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'v$um'),hAPP(hAPP('c$uPower$uOpower$u$uclass$uOpower'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uw')),'c$uNat$uOSuc'('v$uk')))))
| ~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal',X0,'c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal')) ),
inference(demodulation,[status(thm)],[d0,c865]) ).
cnf(d2,plain,
( ~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),X0)
| ~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal',X0,'c$uRings$uOinverse$u$uclass$uOinverse'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'v$um'),hAPP(hAPP('c$uPower$uOpower$u$uclass$uOpower'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uw')),'c$uNat$uOSuc'('v$uk')))))
| ~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal',X0,'c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal')) ),
inference(resolution,[status(thm)],[c1662,d1]) ).
cnf(d3,plain,
'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal',sK4('c$uRings$uOinverse$u$uclass$uOinverse'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),hAPP(hAPP('c$uPower$uOpower$u$uclass$uOpower'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uw')),'c$uGroups$uOplus$u$uclass$uOplus'('tc$uNat$uOnat','v$uk','c$uGroups$uOone$u$uclass$uOone'('tc$uNat$uOnat')))),'v$um'))),'c$uRings$uOinverse$u$uclass$uOinverse'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),hAPP(hAPP('c$uPower$uOpower$u$uclass$uOpower'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uw')),'c$uGroups$uOplus$u$uclass$uOplus'('tc$uNat$uOnat','v$uk','c$uGroups$uOone$u$uclass$uOone'('tc$uNat$uOnat')))),'v$um'))),
inference(resolution,[status(thm)],[c5,c3]) ).
cnf(d4,plain,
'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal',sK4('c$uRings$uOinverse$u$uclass$uOinverse'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'v$um'),hAPP(hAPP('c$uPower$uOpower$u$uclass$uOpower'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uw')),'c$uGroups$uOplus$u$uclass$uOplus'('tc$uNat$uOnat','v$uk','c$uGroups$uOone$u$uclass$uOone'('tc$uNat$uOnat')))))),'c$uRings$uOinverse$u$uclass$uOinverse'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),hAPP(hAPP('c$uPower$uOpower$u$uclass$uOpower'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uw')),'c$uGroups$uOplus$u$uclass$uOplus'('tc$uNat$uOnat','v$uk','c$uGroups$uOone$u$uclass$uOone'('tc$uNat$uOnat')))),'v$um'))),
inference(demodulation,[status(thm)],[d3,c33]) ).
cnf(d5,plain,
'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal',sK4('c$uRings$uOinverse$u$uclass$uOinverse'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'v$um'),hAPP(hAPP('c$uPower$uOpower$u$uclass$uOpower'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uw')),'c$uNat$uOSuc'('v$uk'))))),'c$uRings$uOinverse$u$uclass$uOinverse'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),hAPP(hAPP('c$uPower$uOpower$u$uclass$uOpower'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uw')),'c$uGroups$uOplus$u$uclass$uOplus'('tc$uNat$uOnat','v$uk','c$uGroups$uOone$u$uclass$uOone'('tc$uNat$uOnat')))),'v$um'))),
inference(demodulation,[status(thm)],[d4,c865]) ).
cnf(d6,plain,
'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal',sK4('c$uRings$uOinverse$u$uclass$uOinverse'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'v$um'),hAPP(hAPP('c$uPower$uOpower$u$uclass$uOpower'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uw')),'c$uNat$uOSuc'('v$uk'))))),'c$uRings$uOinverse$u$uclass$uOinverse'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'v$um'),hAPP(hAPP('c$uPower$uOpower$u$uclass$uOpower'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uw')),'c$uGroups$uOplus$u$uclass$uOplus'('tc$uNat$uOnat','v$uk','c$uGroups$uOone$u$uclass$uOone'('tc$uNat$uOnat')))))),
inference(demodulation,[status(thm)],[d5,c33]) ).
cnf(d7,plain,
'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal',sK4('c$uRings$uOinverse$u$uclass$uOinverse'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'v$um'),hAPP(hAPP('c$uPower$uOpower$u$uclass$uOpower'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uw')),'c$uNat$uOSuc'('v$uk'))))),'c$uRings$uOinverse$u$uclass$uOinverse'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'v$um'),hAPP(hAPP('c$uPower$uOpower$u$uclass$uOpower'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uw')),'c$uNat$uOSuc'('v$uk'))))),
inference(demodulation,[status(thm)],[d6,c865]) ).
cnf(d8,plain,
( ~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),sK4('c$uRings$uOinverse$u$uclass$uOinverse'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'v$um'),hAPP(hAPP('c$uPower$uOpower$u$uclass$uOpower'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uw')),'c$uNat$uOSuc'('v$uk'))))))
| ~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal',sK4('c$uRings$uOinverse$u$uclass$uOinverse'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'v$um'),hAPP(hAPP('c$uPower$uOpower$u$uclass$uOpower'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uw')),'c$uNat$uOSuc'('v$uk'))))),'c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal')) ),
inference(resolution,[status(thm)],[d7,d2]) ).
cnf(d9,plain,
( ~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'c$uRings$uOinverse$u$uclass$uOinverse'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'v$um'),hAPP(hAPP('c$uPower$uOpower$u$uclass$uOpower'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uw')),'c$uNat$uOSuc'('v$uk')))))
| ~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),sK4('c$uRings$uOinverse$u$uclass$uOinverse'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'v$um'),hAPP(hAPP('c$uPower$uOpower$u$uclass$uOpower'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uw')),'c$uNat$uOSuc'('v$uk')))))) ),
inference(resolution,[status(thm)],[d8,c2]) ).
cnf(d10,plain,
( ~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'c$uRings$uOinverse$u$uclass$uOinverse'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'v$um'),hAPP(hAPP('c$uPower$uOpower$u$uclass$uOpower'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uw')),'c$uNat$uOSuc'('v$uk')))))
| ~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'c$uRings$uOinverse$u$uclass$uOinverse'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'v$um'),hAPP(hAPP('c$uPower$uOpower$u$uclass$uOpower'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uw')),'c$uNat$uOSuc'('v$uk'))))) ),
inference(resolution,[status(thm)],[d9,c1]) ).
cnf(d11,plain,
( ~ 'class$uFields$uOlinordered$u$ufield$u$uinverse$u$uzero'('tc$uRealDef$uOreal')
| ~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'v$um'),hAPP(hAPP('c$uPower$uOpower$u$uclass$uOpower'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uw')),'c$uNat$uOSuc'('v$uk')))) ),
inference(resolution,[status(thm)],[d10,c143]) ).
cnf(d12,plain,
~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'v$um'),hAPP(hAPP('c$uPower$uOpower$u$uclass$uOpower'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uw')),'c$uNat$uOSuc'('v$uk')))),
inference(resolution,[status(thm)],[c1507,d11]) ).
cnf(d13,plain,
( ~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),hAPP(hAPP('c$uPower$uOpower$u$uclass$uOpower'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uw')),'c$uNat$uOSuc'('v$uk')))
| ~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'v$um') ),
inference(resolution,[status(thm)],[d12,c154]) ).
cnf(d14,plain,
~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),hAPP(hAPP('c$uPower$uOpower$u$uclass$uOpower'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uw')),'c$uNat$uOSuc'('v$uk'))),
inference(resolution,[status(thm)],[c4,d13]) ).
cnf(d15,plain,
( ~ 'class$uRings$uOlinordered$u$usemidom'('tc$uRealDef$uOreal')
| ~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uw')) ),
inference(resolution,[status(thm)],[d14,c122]) ).
cnf(d16,plain,
~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uw')),
inference(resolution,[status(thm)],[c1529,d15]) ).
cnf(d17,plain,
( ~ 'class$uRealVector$uOreal$u$unormed$u$uvector'('tc$uComplex$uOcomplex')
| 'v$uw' = 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex') ),
inference(resolution,[status(thm)],[d16,c14]) ).
cnf(d18,plain,
~ 'class$uRealVector$uOreal$u$unormed$u$uvector'('tc$uComplex$uOcomplex'),
inference(resolution,[status(thm)],[c23,d17]) ).
cnf(d19,plain,
$false,
inference(resolution,[status(thm)],[c1574,d18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWW259+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/5.46 % Computer : n002.cluster.edu
% 0.17/5.46 % Model : x86_64 x86_64
% 0.17/5.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.46 % Memory : 8046.5625MB
% 0.17/5.46 % OS : Linux 6.8.0-71-generic
% 0.17/5.46 % CPULimit : 300
% 0.17/5.46 % WCLimit : 300
% 0.17/5.46 % DateTime : Sat Sep 26 15:35:57 UTC 2026
% 0.17/5.46 % CPUTime :
% 0.17/5.46 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 37.49/15.00 % SZS status Theorem for theBenchmark.p
% 37.49/15.00 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------