%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWW233+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 : n018.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 09:11:34 AM UTC 2026
% Result : Theorem 63.57s 11.08s
% Output : CNFRefutation 63.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 35 ( 17 unt; 0 def)
% Number of atoms : 59 ( 9 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 42 ( 18 ~; 19 |; 0 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 36 ( 0 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_h,axiom,
'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal','c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'),'c$uGroups$uOabs$u$uclass$uOabs'('tc$uRealDef$uOreal','v$ur')),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uz')) ).
fof(fact_real__le__refl,axiom,
! [X0] : 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X0,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__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$uOreal',X2,X0) ) ) ).
fof(fact_real__add__left__mono,axiom,
! [X0,X1,X2] :
( 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X2,X1)
=> 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal',X0,X2),'c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal',X0,X1)) ) ).
fof(fact_less__eq__real__def,axiom,
! [X0,X1] :
( 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X1,X0)
<=> ( X1 = X0
| 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal',X1,X0) ) ) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [X0,X1,X2] :
( 'class$uRings$uOcomm$u$usemiring$u$u1'(X2)
=> 'c$uGroups$uOplus$u$uclass$uOplus'(X2,X1,X0) = 'c$uGroups$uOplus$u$uclass$uOplus'(X2,X0,X1) ) ).
fof(fact_abs__add__one__not__less__self,axiom,
! [X0] : ~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal','c$uGroups$uOabs$u$uclass$uOabs'('tc$uRealDef$uOreal',X0),'c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal')),X0) ).
fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__1,axiom,
'class$uRings$uOcomm$u$usemiring$u$u1'('tc$uRealDef$uOreal') ).
fof(conj_0,conjecture,
'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','v$ur','c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uz')) ).
fof(negated_conjecture,negated_conjecture,
~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','v$ur','c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uz')),
inference(negate_conjecture,[status(cth)],[conj_0]) ).
cnf(c1,plain,
'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal','c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'),'c$uGroups$uOabs$u$uclass$uOabs'('tc$uRealDef$uOreal','v$ur')),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uz')),
inference(clausification,[status(esa)],[fact_h]) ).
cnf(c2,plain,
'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X0,X0),
inference(clausification,[status(esa)],[fact_real__le__refl]) ).
cnf(c3,plain,
( 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X1,X0)
| 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X0,X1) ),
inference(clausification,[status(esa)],[fact_real__le__linear]) ).
cnf(c4,plain,
( 'c$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(c7,plain,
( 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal',X2,X0),'c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal',X2,X1))
| ~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X0,X1) ),
inference(clausification,[status(esa)],[fact_real__add__left__mono]) ).
cnf(c45,plain,
( X0 = X1
| 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal',X0,X1)
| ~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X0,X1) ),
inference(clausification,[status(esa)],[fact_less__eq__real__def]) ).
cnf(c64,plain,
( 'c$uGroups$uOplus$u$uclass$uOplus'(X0,X1,X2) = 'c$uGroups$uOplus$u$uclass$uOplus'(X0,X2,X1)
| ~ 'class$uRings$uOcomm$u$usemiring$u$u1'(X0) ),
inference(clausification,[status(esa)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J]) ).
cnf(c70,plain,
~ 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal','c$uGroups$uOabs$u$uclass$uOabs'('tc$uRealDef$uOreal',X0),'c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal')),X0),
inference(clausification,[status(esa)],[fact_abs__add__one__not__less__self]) ).
cnf(c416,plain,
'class$uRings$uOcomm$u$usemiring$u$u1'('tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[arity_RealDef__Oreal__Rings_Ocomm__semiring__1]) ).
cnf(c419,plain,
~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','v$ur','c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uz')),
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','v$uz'),'v$ur'),
inference(resolution,[status(thm)],[c3,c419]) ).
cnf(d1,plain,
( ~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X0,'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uz'))
| 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X0,'v$ur') ),
inference(resolution,[status(thm)],[c4,d0]) ).
cnf(d2,plain,
'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal','c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'),'c$uGroups$uOabs$u$uclass$uOabs'('tc$uRealDef$uOreal','v$ur')),'v$ur'),
inference(resolution,[status(thm)],[d1,c1]) ).
cnf(d3,plain,
( ~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X0,'c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal','c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'),'c$uGroups$uOabs$u$uclass$uOabs'('tc$uRealDef$uOreal','v$ur')))
| 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X0,'v$ur') ),
inference(resolution,[status(thm)],[d2,c4]) ).
cnf(d4,plain,
( 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal','c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'),X0),'v$ur')
| ~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X0,'c$uGroups$uOabs$u$uclass$uOabs'('tc$uRealDef$uOreal','v$ur')) ),
inference(resolution,[status(thm)],[c7,d3]) ).
cnf(d5,plain,
( ~ 'class$uRings$uOcomm$u$usemiring$u$u1'('tc$uRealDef$uOreal')
| ~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X0,'c$uGroups$uOabs$u$uclass$uOabs'('tc$uRealDef$uOreal','v$ur'))
| 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal',X0,'c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal')),'v$ur') ),
inference(superposition,[status(thm)],[c64,d4]) ).
cnf(d6,plain,
( 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal',X0,'c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal')),'v$ur')
| ~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X0,'c$uGroups$uOabs$u$uclass$uOabs'('tc$uRealDef$uOreal','v$ur')) ),
inference(resolution,[status(thm)],[c416,d5]) ).
cnf(d7,plain,
( 'c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal',X0,'c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal')),'v$ur')
| 'c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal',X0,'c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal')) = 'v$ur'
| ~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X0,'c$uGroups$uOabs$u$uclass$uOabs'('tc$uRealDef$uOreal','v$ur')) ),
inference(resolution,[status(thm)],[d6,c45]) ).
cnf(d8,plain,
( ~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uGroups$uOabs$u$uclass$uOabs'('tc$uRealDef$uOreal','v$ur'),'c$uGroups$uOabs$u$uclass$uOabs'('tc$uRealDef$uOreal','v$ur'))
| 'c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal','c$uGroups$uOabs$u$uclass$uOabs'('tc$uRealDef$uOreal','v$ur'),'c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal')) = 'v$ur' ),
inference(resolution,[status(thm)],[c70,d7]) ).
cnf(d9,plain,
'c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal','c$uGroups$uOabs$u$uclass$uOabs'('tc$uRealDef$uOreal','v$ur'),'c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal')) = 'v$ur',
inference(resolution,[status(thm)],[c2,d8]) ).
cnf(d10,plain,
( ~ 'class$uRings$uOcomm$u$usemiring$u$u1'('tc$uRealDef$uOreal')
| 'c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal','c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'),'c$uGroups$uOabs$u$uclass$uOabs'('tc$uRealDef$uOreal','v$ur')) = 'v$ur' ),
inference(superposition,[status(thm)],[d9,c64]) ).
cnf(d11,plain,
'c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal','c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'),'c$uGroups$uOabs$u$uclass$uOabs'('tc$uRealDef$uOreal','v$ur')) = 'v$ur',
inference(resolution,[status(thm)],[c416,d10]) ).
cnf(d12,plain,
'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','v$ur','c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uz')),
inference(demodulation,[status(thm)],[c1,d11]) ).
cnf(d13,plain,
$false,
inference(resolution,[status(thm)],[c419,d12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW233+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
% 0.12/0.39 % Computer : n018.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sat Sep 26 15:32:51 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 63.57/11.08 % SZS status Theorem for theBenchmark.p
% 63.57/11.08 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------