%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWW208+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 : n001.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 09:11:31 AM UTC 2026
% Result : Theorem 60.89s 13.85s
% Output : CNFRefutation 60.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of formulae : 37 ( 19 unt; 0 def)
% Number of atoms : 68 ( 10 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 57 ( 26 ~; 19 |; 2 &)
% ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-2 aty)
% Number of variables : 28 ( 1 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_rp,axiom,
hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal')),'v$ur')) ).
fof(fact_th,axiom,
! [X0] : hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uGroups$uOabs$u$uclass$uOabs'('tc$uRealDef$uOreal',hAPP('c$uComplex$uOIm',hAPP('v$us',X0)))),hAPP(hAPP('c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal'),'v$ur'),'c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal')))) ).
fof(fact_add__strict__increasing2,axiom,
! [X0,X1,X2,X3] :
( 'class$uGroups$uOordered$u$ucomm$u$umonoid$u$uadd'(X3)
=> ( hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'(X3,'c$uGroups$uOzero$u$uclass$uOzero'(X3)),X2))
=> ( hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless'(X3,X1),X0))
=> hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless'(X3,X1),hAPP(hAPP('c$uGroups$uOplus$u$uclass$uOplus'(X3),X2),X0))) ) ) ) ).
fof(fact_linorder__neqE__linordered__idom,axiom,
! [X0,X1,X2] :
( 'class$uRings$uOlinordered$u$uidom'(X2)
=> ( X1 != X0
=> ( ~ hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless'(X2,X1),X0))
=> hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless'(X2,X0),X1)) ) ) ) ).
fof(fact_real__le__antisym,axiom,
! [X0,X1] :
( hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X1),X0))
=> ( hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X0),X1))
=> X1 = X0 ) ) ).
fof(fact_less__eq__real__def,axiom,
! [X0,X1] :
( hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X1),X0))
<=> ( X1 = X0
| hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal',X1),X0)) ) ) ).
fof(fact_real__zero__not__eq__one,axiom,
'c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal') != 'c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal') ).
fof(fact_zero__le__one,axiom,
! [X0] :
( 'class$uRings$uOlinordered$u$usemidom'(X0)
=> hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'(X0,'c$uGroups$uOzero$u$uclass$uOzero'(X0)),'c$uGroups$uOone$u$uclass$uOone'(X0))) ) ).
fof(arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add,axiom,
'class$uGroups$uOordered$u$ucomm$u$umonoid$u$uadd'('tc$uRealDef$uOreal') ).
fof(arity_RealDef__Oreal__Rings_Olinordered__semidom,axiom,
'class$uRings$uOlinordered$u$usemidom'('tc$uRealDef$uOreal') ).
fof(arity_RealDef__Oreal__Rings_Olinordered__idom,axiom,
'class$uRings$uOlinordered$u$uidom'('tc$uRealDef$uOreal') ).
fof(conj_0,conjecture,
( ! [X0] : hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uGroups$uOabs$u$uclass$uOabs'('tc$uRealDef$uOreal',hAPP('c$uComplex$uOIm',hAPP('v$us',hAPP('v$uf',hAPP('v$uga',X0)))))),hAPP(hAPP('c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal'),'v$ur'),'c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'))))
& hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal')),hAPP(hAPP('c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal'),'v$ur'),'c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal')))) ) ).
fof(negated_conjecture,negated_conjecture,
~ ( ! [X0] : hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uGroups$uOabs$u$uclass$uOabs'('tc$uRealDef$uOreal',hAPP('c$uComplex$uOIm',hAPP('v$us',hAPP('v$uf',hAPP('v$uga',X0)))))),hAPP(hAPP('c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal'),'v$ur'),'c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'))))
& hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal')),hAPP(hAPP('c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal'),'v$ur'),'c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal')))) ),
inference(negate_conjecture,[status(cth)],[conj_0]) ).
cnf(c1,plain,
hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal')),'v$ur')),
inference(clausification,[status(esa)],[fact_rp]) ).
cnf(c3,plain,
hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uGroups$uOabs$u$uclass$uOabs'('tc$uRealDef$uOreal',hAPP('c$uComplex$uOIm',hAPP('v$us',X0)))),hAPP(hAPP('c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal'),'v$ur'),'c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal')))),
inference(clausification,[status(esa)],[fact_th]) ).
cnf(c12,plain,
( hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless'(X0,X2),hAPP(hAPP('c$uGroups$uOplus$u$uclass$uOplus'(X0),X1),X3)))
| ~ hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless'(X0,X2),X3))
| ~ hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'(X0,'c$uGroups$uOzero$u$uclass$uOzero'(X0)),X1))
| ~ 'class$uGroups$uOordered$u$ucomm$u$umonoid$u$uadd'(X0) ),
inference(clausification,[status(esa)],[fact_add__strict__increasing2]) ).
cnf(c21,plain,
( hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless'(X0,X2),X1))
| hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless'(X0,X1),X2))
| X1 = X2
| ~ 'class$uRings$uOlinordered$u$uidom'(X0) ),
inference(clausification,[status(esa)],[fact_linorder__neqE__linordered__idom]) ).
cnf(c22,plain,
( X0 = X1
| ~ hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X1),X0))
| ~ hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X0),X1)) ),
inference(clausification,[status(esa)],[fact_real__le__antisym]) ).
cnf(c33,plain,
( ~ hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal',X0),X1))
| hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X0),X1)) ),
inference(clausification,[status(esa)],[fact_less__eq__real__def]) ).
cnf(c40,plain,
'c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal') != 'c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[fact_real__zero__not__eq__one]) ).
cnf(c52,plain,
( hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'(X0,'c$uGroups$uOzero$u$uclass$uOzero'(X0)),'c$uGroups$uOone$u$uclass$uOone'(X0)))
| ~ 'class$uRings$uOlinordered$u$usemidom'(X0) ),
inference(clausification,[status(esa)],[fact_zero__le__one]) ).
cnf(c1206,plain,
'class$uGroups$uOordered$u$ucomm$u$umonoid$u$uadd'('tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add]) ).
cnf(c1210,plain,
'class$uRings$uOlinordered$u$usemidom'('tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[arity_RealDef__Oreal__Rings_Olinordered__semidom]) ).
cnf(c1211,plain,
'class$uRings$uOlinordered$u$uidom'('tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[arity_RealDef__Oreal__Rings_Olinordered__idom]) ).
cnf(c1237,plain,
( ~ hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uGroups$uOabs$u$uclass$uOabs'('tc$uRealDef$uOreal',hAPP('c$uComplex$uOIm',hAPP('v$us',hAPP('v$uf',hAPP('v$uga',sK2107)))))),hAPP(hAPP('c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal'),'v$ur'),'c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'))))
| ~ hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal')),hAPP(hAPP('c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal'),'v$ur'),'c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal')))) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
~ hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal')),hAPP(hAPP('c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal'),'v$ur'),'c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal')))),
inference(resolution,[status(thm)],[c3,c1237]) ).
cnf(d1,plain,
( ~ 'class$uGroups$uOordered$u$ucomm$u$umonoid$u$uadd'('tc$uRealDef$uOreal')
| ~ hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal')),'c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal')))
| ~ hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal')),'v$ur')) ),
inference(resolution,[status(thm)],[d0,c12]) ).
cnf(d2,plain,
( ~ 'class$uGroups$uOordered$u$ucomm$u$umonoid$u$uadd'('tc$uRealDef$uOreal')
| ~ hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal')),'c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'))) ),
inference(resolution,[status(thm)],[c1,d1]) ).
cnf(d3,plain,
~ hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal')),'c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'))),
inference(resolution,[status(thm)],[c1206,d2]) ).
cnf(d4,plain,
( ~ 'class$uRings$uOlinordered$u$uidom'('tc$uRealDef$uOreal')
| hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal')),'c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal')))
| 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal') = 'c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal') ),
inference(resolution,[status(thm)],[d3,c21]) ).
cnf(d5,plain,
( hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal')),'c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal')))
| 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal') = 'c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal') ),
inference(resolution,[status(thm)],[c1211,d4]) ).
cnf(d6,plain,
hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal')),'c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'))),
inference(resolution,[status(thm)],[c40,d5]) ).
cnf(d7,plain,
hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal')),'c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'))),
inference(resolution,[status(thm)],[d6,c33]) ).
cnf(d8,plain,
( ~ hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal')),'c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal')))
| 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal') = 'c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal') ),
inference(resolution,[status(thm)],[d7,c22]) ).
cnf(d9,plain,
~ hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal')),'c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'))),
inference(resolution,[status(thm)],[c40,d8]) ).
cnf(d10,plain,
~ 'class$uRings$uOlinordered$u$usemidom'('tc$uRealDef$uOreal'),
inference(resolution,[status(thm)],[c52,d9]) ).
cnf(d11,plain,
$false,
inference(resolution,[status(thm)],[c1210,d10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWW208+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.46 % Computer : n001.cluster.edu
% 0.20/0.46 % Model : x86_64 x86_64
% 0.20/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.46 % Memory : 8046.5625MB
% 0.20/0.46 % OS : Linux 6.8.0-71-generic
% 0.20/0.46 % CPULimit : 300
% 0.20/0.46 % WCLimit : 300
% 0.20/0.46 % DateTime : Sat Sep 26 15:34:28 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.46 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 60.89/13.85 % SZS status Theorem for theBenchmark.p
% 60.89/13.85 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------