%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWW258+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 : n003.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 54.89s 7.47s
% Output : CNFRefutation 54.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 33 ( 20 unt; 0 def)
% Number of atoms : 57 ( 5 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 51 ( 27 ~; 15 |; 0 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 20 ( 1 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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$um') ).
fof(fact_w0,axiom,
'v$uw' != 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex') ).
fof(fact_zero__less__norm__iff,axiom,
! [X0,X1] :
( 'class$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$uOzero'(X1) ) ) ).
fof(fact_mult__pos__pos,axiom,
! [X0,X1,X2] :
( 'class$uRings$uOlinordered$u$usemiring$u$ustrict'(X2)
=> ( 'c$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$uOzero'(X2),X0)
=> 'c$uOrderings$uOord$u$uclass$uOless'(X2,'c$uGroups$uOzero$u$uclass$uOzero'(X2),hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'(X2),X1),X0)) ) ) ) ).
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$uOpower'(X2),X1),X0)) ) ) ).
fof(fact_positive__imp__inverse__positive,axiom,
! [X0,X1] :
( 'class$uFields$uOlinordered$u$ufield'(X1)
=> ( 'c$uOrderings$uOord$u$uclass$uOless'(X1,'c$uGroups$uOzero$u$uclass$uOzero'(X1),X0)
=> 'c$uOrderings$uOord$u$uclass$uOless'(X1,'c$uGroups$uOzero$u$uclass$uOzero'(X1),'c$uRings$uOinverse$u$uclass$uOinverse'(X1,X0)) ) ) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__strict,axiom,
'class$uRings$uOlinordered$u$usemiring$u$ustrict'('tc$uRealDef$uOreal') ).
fof(arity_RealDef__Oreal__Rings_Olinordered__semidom,axiom,
'class$uRings$uOlinordered$u$usemidom'('tc$uRealDef$uOreal') ).
fof(arity_RealDef__Oreal__Fields_Olinordered__field,axiom,
'class$uFields$uOlinordered$u$ufield'('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,conjecture,
'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$um'))) ).
fof(negated_conjecture,negated_conjecture,
~ 'c$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(negate_conjecture,[status(cth)],[conj_0]) ).
cnf(c1,plain,
'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'v$um'),
inference(clausification,[status(esa)],[fact_m_I1_J]) ).
cnf(c2,plain,
'v$uw' != 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),
inference(clausification,[status(esa)],[fact_w0]) ).
cnf(c11,plain,
( X1 = 'c$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$uvector'(X0) ),
inference(clausification,[status(esa)],[fact_zero__less__norm__iff]) ).
cnf(c177,plain,
( 'c$uOrderings$uOord$u$uclass$uOless'(X0,'c$uGroups$uOzero$u$uclass$uOzero'(X0),hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'(X0),X1),X2))
| ~ 'c$uOrderings$uOord$u$uclass$uOless'(X0,'c$uGroups$uOzero$u$uclass$uOzero'(X0),X2)
| ~ 'c$uOrderings$uOord$u$uclass$uOless'(X0,'c$uGroups$uOzero$u$uclass$uOzero'(X0),X1)
| ~ 'class$uRings$uOlinordered$u$usemiring$u$ustrict'(X0) ),
inference(clausification,[status(esa)],[fact_mult__pos__pos]) ).
cnf(c201,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$usemidom'(X0) ),
inference(clausification,[status(esa)],[fact_zero__less__power]) ).
cnf(c218,plain,
( 'c$uOrderings$uOord$u$uclass$uOless'(X0,'c$uGroups$uOzero$u$uclass$uOzero'(X0),'c$uRings$uOinverse$u$uclass$uOinverse'(X0,X1))
| ~ 'c$uOrderings$uOord$u$uclass$uOless'(X0,'c$uGroups$uOzero$u$uclass$uOzero'(X0),X1)
| ~ 'class$uFields$uOlinordered$u$ufield'(X0) ),
inference(clausification,[status(esa)],[fact_positive__imp__inverse__positive]) ).
cnf(c1530,plain,
'class$uRings$uOlinordered$u$usemiring$u$ustrict'('tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[arity_RealDef__Oreal__Rings_Olinordered__semiring__strict]) ).
cnf(c1549,plain,
'class$uRings$uOlinordered$u$usemidom'('tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[arity_RealDef__Oreal__Rings_Olinordered__semidom]) ).
cnf(c1553,plain,
'class$uFields$uOlinordered$u$ufield'('tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[arity_RealDef__Oreal__Fields_Olinordered__field]) ).
cnf(c1597,plain,
'class$uRealVector$uOreal$u$unormed$u$uvector'('tc$uComplex$uOcomplex'),
inference(clausification,[status(esa)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__vector]) ).
cnf(c1688,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$um'))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ 'class$uFields$uOlinordered$u$ufield'('tc$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'),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$um')) ),
inference(resolution,[status(thm)],[c218,c1688]) ).
cnf(d1,plain,
~ 'c$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'),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$um')),
inference(resolution,[status(thm)],[c1553,d0]) ).
cnf(d2,plain,
( ~ 'class$uRings$uOlinordered$u$usemiring$u$ustrict'('tc$uRealDef$uOreal')
| ~ 'c$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$uGroups$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','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'v$um') ),
inference(resolution,[status(thm)],[d1,c177]) ).
cnf(d3,plain,
( ~ 'class$uRings$uOlinordered$u$usemiring$u$ustrict'('tc$uRealDef$uOreal')
| ~ '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$uw')),'c$uGroups$uOplus$u$uclass$uOplus'('tc$uNat$uOnat','v$uk','c$uGroups$uOone$u$uclass$uOone'('tc$uNat$uOnat')))) ),
inference(resolution,[status(thm)],[c1,d2]) ).
cnf(d4,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$uw')),'c$uGroups$uOplus$u$uclass$uOplus'('tc$uNat$uOnat','v$uk','c$uGroups$uOone$u$uclass$uOone'('tc$uNat$uOnat')))),
inference(resolution,[status(thm)],[c1530,d3]) ).
cnf(d5,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)],[d4,c201]) ).
cnf(d6,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)],[c1549,d5]) ).
cnf(d7,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)],[d6,c11]) ).
cnf(d8,plain,
~ 'class$uRealVector$uOreal$u$unormed$u$uvector'('tc$uComplex$uOcomplex'),
inference(resolution,[status(thm)],[c2,d7]) ).
cnf(d9,plain,
$false,
inference(resolution,[status(thm)],[c1597,d8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWW258+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n003.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Sat Sep 26 15:34:39 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.18/0.46 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 54.89/7.47 % SZS status Theorem for theBenchmark.p
% 54.89/7.47 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------