%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWW265+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 : n026.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 132.84s 44.02s
% Output : CNFRefutation 132.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 27 ( 14 unt; 0 def)
% Number of atoms : 50 ( 5 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 48 ( 25 ~; 15 |; 0 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-2 aty)
% Number of variables : 20 ( 1 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_w0,axiom,
'v$uw' != 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex') ).
fof(fact_real__mult__le__cancel__iff2,axiom,
! [X0,X1,X2] :
( 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),X2)
=> ( 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),X2),X1),hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),X2),X0))
<=> 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X1,X0) ) ) ).
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_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$uOpower'(X2),X1),X0)) ) ) ).
fof(fact_real__mult__order,axiom,
! [X0,X1] :
( 'c$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(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_1,hypothesis,
'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex',hAPP('c$uPolynomial$uOpoly'('tc$uComplex$uOcomplex','v$us'),hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uComplex$uOcomplex'),'c$uRealVector$uOof$u$ureal'('tc$uComplex$uOcomplex','v$ut')),'v$uw'))),'v$um') ).
fof(conj_2,conjecture,
'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uw')),hAPP(hAPP('c$uPower$uOpower$u$uclass$uOpower'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uw')),'v$uk'))),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex',hAPP('c$uPolynomial$uOpoly'('tc$uComplex$uOcomplex','v$us'),hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uComplex$uOcomplex'),'c$uRealVector$uOof$u$ureal'('tc$uComplex$uOcomplex','v$ut')),'v$uw')))),hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uw')),hAPP(hAPP('c$uPower$uOpower$u$uclass$uOpower'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uw')),'v$uk'))),'v$um')) ).
fof(negated_conjecture,negated_conjecture,
~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uw')),hAPP(hAPP('c$uPower$uOpower$u$uclass$uOpower'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uw')),'v$uk'))),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex',hAPP('c$uPolynomial$uOpoly'('tc$uComplex$uOcomplex','v$us'),hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uComplex$uOcomplex'),'c$uRealVector$uOof$u$ureal'('tc$uComplex$uOcomplex','v$ut')),'v$uw')))),hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uw')),hAPP(hAPP('c$uPower$uOpower$u$uclass$uOpower'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uw')),'v$uk'))),'v$um')),
inference(negate_conjecture,[status(cth)],[conj_2]) ).
cnf(c4,plain,
'c$uGroups$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex') != 'v$uw',
inference(clausification,[status(esa)],[fact_w0]) ).
cnf(c23,plain,
( ~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X1,X2)
| 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),X0),X1),hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),X0),X2))
| ~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),X0) ),
inference(clausification,[status(esa)],[fact_real__mult__le__cancel__iff2]) ).
cnf(c27,plain,
( 'c$uGroups$uOzero$u$uclass$uOzero'(X0) = X1
| 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'(X0,X1))
| ~ 'class$uRealVector$uOreal$u$unormed$u$uvector'(X0) ),
inference(clausification,[status(esa)],[fact_zero__less__norm__iff]) ).
cnf(c72,plain,
( ~ 'c$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$uOzero'(X0),hAPP(hAPP('c$uPower$uOpower$u$uclass$uOpower'(X0),X1),X2))
| ~ 'class$uRings$uOlinordered$u$usemidom'(X0) ),
inference(clausification,[status(esa)],[fact_zero__less__power]) ).
cnf(c92,plain,
( ~ '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'),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$uOreal'),X0) ),
inference(clausification,[status(esa)],[fact_real__mult__order]) ).
cnf(c1088,plain,
'class$uRings$uOlinordered$u$usemidom'('tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[arity_RealDef__Oreal__Rings_Olinordered__semidom]) ).
cnf(c1121,plain,
'class$uRealVector$uOreal$u$unormed$u$uvector'('tc$uComplex$uOcomplex'),
inference(clausification,[status(esa)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__vector]) ).
cnf(c1179,plain,
'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex',hAPP('c$uPolynomial$uOpoly'('tc$uComplex$uOcomplex','v$us'),hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uComplex$uOcomplex'),'c$uRealVector$uOof$u$ureal'('tc$uComplex$uOcomplex','v$ut')),'v$uw'))),'v$um'),
inference(clausification,[status(esa)],[conj_1]) ).
cnf(c1180,plain,
~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uw')),hAPP(hAPP('c$uPower$uOpower$u$uclass$uOpower'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uw')),'v$uk'))),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex',hAPP('c$uPolynomial$uOpoly'('tc$uComplex$uOcomplex','v$us'),hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uComplex$uOcomplex'),'c$uRealVector$uOof$u$ureal'('tc$uComplex$uOcomplex','v$ut')),'v$uw')))),hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uw')),hAPP(hAPP('c$uPower$uOpower$u$uclass$uOpower'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uw')),'v$uk'))),'v$um')),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex',hAPP('c$uPolynomial$uOpoly'('tc$uComplex$uOcomplex','v$us'),hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uComplex$uOcomplex'),'c$uRealVector$uOof$u$ureal'('tc$uComplex$uOcomplex','v$ut')),'v$uw'))),'v$um')
| ~ '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$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uw')),hAPP(hAPP('c$uPower$uOpower$u$uclass$uOpower'('tc$uRealDef$uOreal'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uw')),'v$uk'))) ),
inference(resolution,[status(thm)],[c1180,c23]) ).
cnf(d1,plain,
( ~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex',hAPP('c$uPolynomial$uOpoly'('tc$uComplex$uOcomplex','v$us'),hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uComplex$uOcomplex'),'c$uRealVector$uOof$u$ureal'('tc$uComplex$uOcomplex','v$ut')),'v$uw'))),'v$um')
| ~ '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'))
| ~ '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$uw')),'v$uk')) ),
inference(resolution,[status(thm)],[c92,d0]) ).
cnf(d2,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'))
| ~ '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$uw')),'v$uk')) ),
inference(resolution,[status(thm)],[c1179,d1]) ).
cnf(d3,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'))
| ~ '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)],[d2,c72]) ).
cnf(d4,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)],[c1088,d3]) ).
cnf(d5,plain,
( ~ 'class$uRealVector$uOreal$u$unormed$u$uvector'('tc$uComplex$uOcomplex')
| 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex') = 'v$uw' ),
inference(resolution,[status(thm)],[d4,c27]) ).
cnf(d6,plain,
~ 'class$uRealVector$uOreal$u$unormed$u$uvector'('tc$uComplex$uOcomplex'),
inference(resolution,[status(thm)],[c4,d5]) ).
cnf(d7,plain,
$false,
inference(resolution,[status(thm)],[c1121,d6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWW265+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
% 0.18/5.44 % Computer : n026.cluster.edu
% 0.18/5.44 % Model : x86_64 x86_64
% 0.18/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.44 % Memory : 8046.5625MB
% 0.18/5.44 % OS : Linux 6.8.0-71-generic
% 0.18/5.44 % CPULimit : 300
% 0.18/5.44 % WCLimit : 300
% 0.18/5.44 % DateTime : Sat Sep 26 15:36:16 UTC 2026
% 0.18/5.45 % CPUTime :
% 0.18/5.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 132.84/44.02 % SZS status Theorem for theBenchmark.p
% 132.84/44.02 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------