%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWW238+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 79.73s 26.84s
% Output : CNFRefutation 79.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 22 ( 18 unt; 0 def)
% Number of atoms : 26 ( 7 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 7 ~; 2 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 26 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_complex__mod__triangle__sub,axiom,
! [X0,X1] : 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex',X1),'c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal','c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','c$uGroups$uOplus$u$uclass$uOplus'('tc$uComplex$uOcomplex',X1,X0)),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex',X0))) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
! [X0,X1,X2] :
( 'class$uRings$uOcomm$u$usemiring$u$u1'(X2)
=> hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'(X2),X1),X0) = hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'(X2),X0),X1) ) ).
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(arity_RealDef__Oreal__Rings_Ocomm__semiring__1,axiom,
'class$uRings$uOcomm$u$usemiring$u$u1'('tc$uRealDef$uOreal') ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1,axiom,
'class$uRings$uOcomm$u$usemiring$u$u1'('tc$uComplex$uOcomplex') ).
fof(conj_0,conjecture,
'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uComplex$uOcomplex'),'v$uz'),'v$uc')),'c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal','c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','c$uGroups$uOplus$u$uclass$uOplus'('tc$uComplex$uOcomplex','v$uaa',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uComplex$uOcomplex'),'v$uz'),'v$uc'))),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uaa'))) ).
fof(negated_conjecture,negated_conjecture,
~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uComplex$uOcomplex'),'v$uz'),'v$uc')),'c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal','c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','c$uGroups$uOplus$u$uclass$uOplus'('tc$uComplex$uOcomplex','v$uaa',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uComplex$uOcomplex'),'v$uz'),'v$uc'))),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uaa'))),
inference(negate_conjecture,[status(cth)],[conj_0]) ).
cnf(c2,plain,
'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex',X0),'c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal','c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','c$uGroups$uOplus$u$uclass$uOplus'('tc$uComplex$uOcomplex',X0,X1)),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex',X1))),
inference(clausification,[status(esa)],[fact_complex__mod__triangle__sub]) ).
cnf(c32,plain,
( hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'(X0),X1),X2) = hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'(X0),X2),X1)
| ~ 'class$uRings$uOcomm$u$usemiring$u$u1'(X0) ),
inference(clausification,[status(esa)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J]) ).
cnf(c38,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(c830,plain,
'class$uRings$uOcomm$u$usemiring$u$u1'('tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[arity_RealDef__Oreal__Rings_Ocomm__semiring__1]) ).
cnf(c837,plain,
'class$uRings$uOcomm$u$usemiring$u$u1'('tc$uComplex$uOcomplex'),
inference(clausification,[status(esa)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__1]) ).
cnf(c855,plain,
~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uComplex$uOcomplex'),'v$uz'),'v$uc')),'c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal','c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','c$uGroups$uOplus$u$uclass$uOplus'('tc$uComplex$uOcomplex','v$uaa',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uComplex$uOcomplex'),'v$uz'),'v$uc'))),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uaa'))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uComplex$uOcomplex'),X0),X1) = hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uComplex$uOcomplex'),X1),X0),
inference(resolution,[status(thm)],[c32,c837]) ).
cnf(d1,plain,
'c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal',X0,X1) = 'c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal',X1,X0),
inference(resolution,[status(thm)],[c38,c830]) ).
cnf(d2,plain,
~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uComplex$uOcomplex'),'v$uz'),'v$uc')),'c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal','c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uaa'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','c$uGroups$uOplus$u$uclass$uOplus'('tc$uComplex$uOcomplex','v$uaa',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uComplex$uOcomplex'),'v$uz'),'v$uc'))))),
inference(demodulation,[status(thm)],[c855,d1]) ).
cnf(d3,plain,
~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uComplex$uOcomplex'),'v$uc'),'v$uz')),'c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal','c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uaa'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','c$uGroups$uOplus$u$uclass$uOplus'('tc$uComplex$uOcomplex','v$uaa',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uComplex$uOcomplex'),'v$uz'),'v$uc'))))),
inference(demodulation,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
~ 'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uComplex$uOcomplex'),'v$uc'),'v$uz')),'c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal','c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','v$uaa'),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','c$uGroups$uOplus$u$uclass$uOplus'('tc$uComplex$uOcomplex','v$uaa',hAPP(hAPP('c$uGroups$uOtimes$u$uclass$uOtimes'('tc$uComplex$uOcomplex'),'v$uc'),'v$uz'))))),
inference(demodulation,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
'c$uGroups$uOplus$u$uclass$uOplus'('tc$uComplex$uOcomplex',X0,X1) = 'c$uGroups$uOplus$u$uclass$uOplus'('tc$uComplex$uOcomplex',X1,X0),
inference(resolution,[status(thm)],[c38,c837]) ).
cnf(d6,plain,
'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex',X0),'c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal','c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','c$uGroups$uOplus$u$uclass$uOplus'('tc$uComplex$uOcomplex',X1,X0)),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex',X1))),
inference(superposition,[status(thm)],[d5,c2]) ).
cnf(d7,plain,
'c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex',X1),'c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal','c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex',X0),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','c$uGroups$uOplus$u$uclass$uOplus'('tc$uComplex$uOcomplex',X0,X1)))),
inference(demodulation,[status(thm)],[d6,d1]) ).
cnf(d8,plain,
$false,
inference(resolution,[status(thm)],[d7,d4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW238+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
% 0.09/0.37 % Computer : n018.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 15:33:06 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 79.73/26.84 % SZS status Theorem for theBenchmark.p
% 79.73/26.84 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------