%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWW207+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 : n007.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 69.40s 10.51s
% Output : CNFRefutation 69.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 13
% Syntax : Number of formulae : 43 ( 17 unt; 0 def)
% Number of atoms : 83 ( 14 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 71 ( 31 ~; 25 |; 3 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-2 aty)
% Number of variables : 43 ( 2 sgn 20 !; 2 ?)
% 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$ur')) ).
fof(fact_real__less__def,axiom,
! [X0,X1] :
( hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal',X1),X0))
<=> ( X1 != X0
& hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X1),X0)) ) ) ).
fof(fact_less__eq__real__def,axiom,
! [X0,X1] :
( hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X1),X0))
<=> ( X1 = X0
| hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal',X1),X0)) ) ) ).
fof(fact_real__le__antisym,axiom,
! [X0,X1] :
( hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X1),X0))
=> ( hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X0),X1))
=> X1 = X0 ) ) ).
fof(fact_th,axiom,
! [X0] : hBOOL(hAPP('c$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$uOreal')))) ).
fof(fact_real__norm__def,axiom,
! [X0] : 'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uRealDef$uOreal',X0) = 'c$uGroups$uOabs$u$uclass$uOabs'('tc$uRealDef$uOreal',X0) ).
fof(fact_less__add__one,axiom,
! [X0,X1] :
( 'class$uRings$uOlinordered$u$usemidom'(X1)
=> hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless'(X1,X0),hAPP(hAPP('c$uGroups$uOplus$u$uclass$uOplus'(X1),X0),'c$uGroups$uOone$u$uclass$uOone'(X1)))) ) ).
fof(fact_zero__less__one,axiom,
! [X0] :
( 'class$uRings$uOlinordered$u$usemidom'(X0)
=> hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless'(X0,'c$uGroups$uOzero$u$uclass$uOzero'(X0)),'c$uGroups$uOone$u$uclass$uOone'(X0))) ) ).
fof(fact_pos__add__strict,axiom,
! [X0,X1,X2,X3] :
( 'class$uRings$uOlinordered$u$usemidom'(X3)
=> ( hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless'(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(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] :
( ! [X1] : 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$uga',X1)))))),X0))
& hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal')),X0)) ) ).
fof(negated_conjecture,negated_conjecture,
~ ? [X0] :
( ! [X1] : hBOOL(hAPP('c$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',X1)))))),X0))
& hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal')),X0)) ),
inference(negate_conjecture,[status(cth)],[conj_0]) ).
cnf(c3,plain,
hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal')),'v$ur')),
inference(clausification,[status(esa)],[fact_rp]) ).
cnf(c5,plain,
( hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X0),X1))
| ~ hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal',X0),X1)) ),
inference(clausification,[status(esa)],[fact_real__less__def]) ).
cnf(c10,plain,
( X0 != X1
| hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X0),X1)) ),
inference(clausification,[status(esa)],[fact_less__eq__real__def]) ).
cnf(c29,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(c58,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(c64,plain,
'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uRealDef$uOreal',X0) = 'c$uGroups$uOabs$u$uclass$uOabs'('tc$uRealDef$uOreal',X0),
inference(clausification,[status(esa)],[fact_real__norm__def]) ).
cnf(c83,plain,
( hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless'(X0,X1),hAPP(hAPP('c$uGroups$uOplus$u$uclass$uOplus'(X0),X1),'c$uGroups$uOone$u$uclass$uOone'(X0))))
| ~ 'class$uRings$uOlinordered$u$usemidom'(X0) ),
inference(clausification,[status(esa)],[fact_less__add__one]) ).
cnf(c85,plain,
( hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless'(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__less__one]) ).
cnf(c90,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'(X0,'c$uGroups$uOzero$u$uclass$uOzero'(X0)),X1))
| ~ 'class$uRings$uOlinordered$u$usemidom'(X0) ),
inference(clausification,[status(esa)],[fact_pos__add__strict]) ).
cnf(c141,plain,
( hBOOL(hAPP('c$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$uidom'(X0) ),
inference(clausification,[status(esa)],[fact_linorder__neqE__linordered__idom]) ).
cnf(c972,plain,
'class$uRings$uOlinordered$u$usemidom'('tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[arity_RealDef__Oreal__Rings_Olinordered__semidom]) ).
cnf(c973,plain,
'class$uRings$uOlinordered$u$uidom'('tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[arity_RealDef__Oreal__Rings_Olinordered__idom]) ).
cnf(c984,plain,
( ~ hBOOL(hAPP('c$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',sK1639(X0))))))),X0))
| ~ hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal')),X0)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uRealVector$uOnorm$u$uclass$uOnorm'('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(demodulation,[status(thm)],[c58,c64]) ).
cnf(d1,plain,
( ~ hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal')),X0))
| ~ hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uRealDef$uOreal',hAPP('c$uComplex$uOIm',hAPP('v$us',hAPP('v$uf',hAPP('v$uga',sK1639(X0))))))),X0)) ),
inference(demodulation,[status(thm)],[c984,c64]) ).
cnf(d2,plain,
~ hBOOL(hAPP('c$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)],[d1,d0]) ).
cnf(d3,plain,
( ~ 'class$uRings$uOlinordered$u$usemidom'('tc$uRealDef$uOreal')
| ~ hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal')),'v$ur'))
| ~ hBOOL(hAPP('c$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)],[d2,c90]) ).
cnf(d4,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$uOreal')))
| ~ hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal')),'v$ur')) ),
inference(resolution,[status(thm)],[c972,d3]) ).
cnf(d5,plain,
( ~ 'class$uRings$uOlinordered$u$usemidom'('tc$uRealDef$uOreal')
| ~ hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal')),'v$ur')) ),
inference(resolution,[status(thm)],[d4,c85]) ).
cnf(d6,plain,
~ hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal')),'v$ur')),
inference(resolution,[status(thm)],[c972,d5]) ).
cnf(d7,plain,
( ~ 'class$uRings$uOlinordered$u$uidom'('tc$uRealDef$uOreal')
| hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','v$ur'),'c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal')))
| 'v$ur' = 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal') ),
inference(resolution,[status(thm)],[d6,c141]) ).
cnf(d8,plain,
( hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','v$ur'),'c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal')))
| 'v$ur' = 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal') ),
inference(resolution,[status(thm)],[c973,d7]) ).
cnf(d9,plain,
( hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','v$ur'),'c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal')))
| 'v$ur' = 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal') ),
inference(resolution,[status(thm)],[d8,c5]) ).
cnf(d10,plain,
( hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','v$ur'),'c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal')))
| hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','v$ur'),'c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'))) ),
inference(resolution,[status(thm)],[c10,d9]) ).
cnf(d11,plain,
( ~ hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal')),'v$ur'))
| 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal') = 'v$ur' ),
inference(resolution,[status(thm)],[d10,c29]) ).
cnf(d12,plain,
'c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal') = 'v$ur',
inference(resolution,[status(thm)],[c3,d11]) ).
cnf(d13,plain,
~ hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless'('tc$uRealDef$uOreal','v$ur'),hAPP(hAPP('c$uGroups$uOplus$u$uclass$uOplus'('tc$uRealDef$uOreal'),'v$ur'),'c$uGroups$uOone$u$uclass$uOone'('tc$uRealDef$uOreal')))),
inference(demodulation,[status(thm)],[d2,d12]) ).
cnf(d14,plain,
~ 'class$uRings$uOlinordered$u$usemidom'('tc$uRealDef$uOreal'),
inference(resolution,[status(thm)],[d13,c83]) ).
cnf(d15,plain,
$false,
inference(resolution,[status(thm)],[c972,d14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW207+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n007.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 15:26:10 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 69.40/10.51 % SZS status Theorem for theBenchmark.p
% 69.40/10.51 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------