%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWW204+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 : n014.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 54.42s 7.67s
% Output : CNFRefutation 54.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of formulae : 49 ( 26 unt; 0 def)
% Number of atoms : 79 ( 21 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 50 ( 20 ~; 20 |; 0 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 50 ( 10 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_assms,axiom,
! [X0] : hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex',hAPP('v$us',X0))),'v$ur')) ).
fof(fact_real__le__linear,axiom,
! [X0,X1] :
( hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X0),X1))
| hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X1),X0)) ) ).
fof(fact_real__le__trans,axiom,
! [X0,X1,X2] :
( hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X2),X1))
=> ( hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X1),X0))
=> hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X2),X0)) ) ) ).
fof(fact_real__le__antisym,axiom,
! [X0,X1] :
( hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X1),X0))
=> ( hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X0),X1))
=> X1 = X0 ) ) ).
fof(fact_norm__le__zero__iff,axiom,
! [X0,X1] :
( 'class$uRealVector$uOreal$u$unormed$u$uvector'(X1)
=> ( hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uRealVector$uOnorm$u$uclass$uOnorm'(X1,X0)),'c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal')))
<=> X0 = 'c$uGroups$uOzero$u$uclass$uOzero'(X1) ) ) ).
fof(fact_norm__ge__zero,axiom,
! [X0,X1] :
( 'class$uRealVector$uOreal$u$unormed$u$uvector'(X1)
=> hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal')),'c$uRealVector$uOnorm$u$uclass$uOnorm'(X1,X0))) ) ).
fof(fact_le__0__eq,axiom,
! [X0] :
( hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uNat$uOnat',X0),'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat')))
<=> X0 = 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat') ) ).
fof(fact_real__of__nat__zero,axiom,
'c$uRealDef$uOreal'('tc$uNat$uOnat','c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat')) = 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal') ).
fof(fact_natceiling__mono,axiom,
! [X0,X1] :
( hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X1),X0))
=> hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uNat$uOnat','c$uRComplete$uOnatceiling'(X1)),'c$uRComplete$uOnatceiling'(X0))) ) ).
fof(fact_real__natceiling__ge,axiom,
! [X0] : hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X0),'c$uRealDef$uOreal'('tc$uNat$uOnat','c$uRComplete$uOnatceiling'(X0)))) ).
fof(fact_natceiling__neg,axiom,
! [X0] :
( hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X0),'c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal')))
=> 'c$uRComplete$uOnatceiling'(X0) = 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat') ) ).
fof(fact_Re_Ozero,axiom,
hAPP('c$uComplex$uORe','c$uGroups$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex')) = 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal') ).
fof(fact_complex__Re__le__cmod,axiom,
! [X0] : hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',hAPP('c$uComplex$uORe',X0)),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex',X0))) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
'class$uRealVector$uOreal$u$unormed$u$uvector'('tc$uComplex$uOcomplex') ).
fof(conj_0,conjecture,
hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal')),'v$ur')) ).
fof(negated_conjecture,negated_conjecture,
~ hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal')),'v$ur')),
inference(negate_conjecture,[status(cth)],[conj_0]) ).
cnf(c3,plain,
hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex',hAPP('v$us',X0))),'v$ur')),
inference(clausification,[status(esa)],[fact_assms]) ).
cnf(c7,plain,
( hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X1),X0))
| hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X0),X1)) ),
inference(clausification,[status(esa)],[fact_real__le__linear]) ).
cnf(c8,plain,
( hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X0),X2))
| ~ hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X1),X2))
| ~ hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X0),X1)) ),
inference(clausification,[status(esa)],[fact_real__le__trans]) ).
cnf(c9,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(c31,plain,
( X1 = 'c$uGroups$uOzero$u$uclass$uOzero'(X0)
| ~ hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uRealVector$uOnorm$u$uclass$uOnorm'(X0,X1)),'c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal')))
| ~ 'class$uRealVector$uOreal$u$unormed$u$uvector'(X0) ),
inference(clausification,[status(esa)],[fact_norm__le__zero__iff]) ).
cnf(c33,plain,
( hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$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$uvector'(X0) ),
inference(clausification,[status(esa)],[fact_norm__ge__zero]) ).
cnf(c40,plain,
( X0 = 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat')
| ~ hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uNat$uOnat',X0),'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat'))) ),
inference(clausification,[status(esa)],[fact_le__0__eq]) ).
cnf(c72,plain,
'c$uRealDef$uOreal'('tc$uNat$uOnat','c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat')) = 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[fact_real__of__nat__zero]) ).
cnf(c184,plain,
( hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uNat$uOnat','c$uRComplete$uOnatceiling'(X0)),'c$uRComplete$uOnatceiling'(X1)))
| ~ hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X0),X1)) ),
inference(clausification,[status(esa)],[fact_natceiling__mono]) ).
cnf(c185,plain,
hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X0),'c$uRealDef$uOreal'('tc$uNat$uOnat','c$uRComplete$uOnatceiling'(X0)))),
inference(clausification,[status(esa)],[fact_real__natceiling__ge]) ).
cnf(c189,plain,
( 'c$uRComplete$uOnatceiling'(X0) = 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat')
| ~ hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X0),'c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'))) ),
inference(clausification,[status(esa)],[fact_natceiling__neg]) ).
cnf(c408,plain,
hAPP('c$uComplex$uORe','c$uGroups$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex')) = 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[fact_Re_Ozero]) ).
cnf(c412,plain,
hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',hAPP('c$uComplex$uORe',X0)),'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex',X0))),
inference(clausification,[status(esa)],[fact_complex__Re__le__cmod]) ).
cnf(c1606,plain,
'class$uRealVector$uOreal$u$unormed$u$uvector'('tc$uComplex$uOcomplex'),
inference(clausification,[status(esa)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__vector]) ).
cnf(c1693,plain,
~ hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal')),'v$ur')),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','v$ur'),'c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'))),
inference(resolution,[status(thm)],[c7,c1693]) ).
cnf(d1,plain,
'c$uRComplete$uOnatceiling'('v$ur') = 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat'),
inference(resolution,[status(thm)],[c189,d0]) ).
cnf(d2,plain,
( ~ hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X0),'v$ur'))
| hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uNat$uOnat','c$uRComplete$uOnatceiling'(X0)),'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat'))) ),
inference(superposition,[status(thm)],[d1,c184]) ).
cnf(d3,plain,
( 'c$uRComplete$uOnatceiling'(X0) = 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat')
| ~ hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',X0),'v$ur')) ),
inference(resolution,[status(thm)],[d2,c40]) ).
cnf(d4,plain,
'c$uRComplete$uOnatceiling'('c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex',hAPP('v$us',X0))) = 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat'),
inference(resolution,[status(thm)],[d3,c3]) ).
cnf(d5,plain,
hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex',hAPP('v$us',X0))),'c$uRealDef$uOreal'('tc$uNat$uOnat','c$uGroups$uOzero$u$uclass$uOzero'('tc$uNat$uOnat')))),
inference(superposition,[status(thm)],[d4,c185]) ).
cnf(d6,plain,
hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex',hAPP('v$us',X0))),'c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'))),
inference(demodulation,[status(thm)],[d5,c72]) ).
cnf(d7,plain,
( ~ 'class$uRealVector$uOreal$u$unormed$u$uvector'('tc$uComplex$uOcomplex')
| hAPP('v$us',X0) = 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex') ),
inference(resolution,[status(thm)],[d6,c31]) ).
cnf(d8,plain,
hAPP('v$us',X0) = 'c$uGroups$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),
inference(resolution,[status(thm)],[c1606,d7]) ).
cnf(d9,plain,
( hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','v$ur'),X0))
| ~ hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uGroups$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal')),X0)) ),
inference(resolution,[status(thm)],[c8,d0]) ).
cnf(d10,plain,
( hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','v$ur'),'c$uRealVector$uOnorm$u$uclass$uOnorm'(X0,X1)))
| ~ 'class$uRealVector$uOreal$u$unormed$u$uvector'(X0) ),
inference(resolution,[status(thm)],[c33,d9]) ).
cnf(d11,plain,
( ~ hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal','c$uRealVector$uOnorm$u$uclass$uOnorm'(X0,X1)),'v$ur'))
| 'c$uRealVector$uOnorm$u$uclass$uOnorm'(X0,X1) = 'v$ur'
| ~ 'class$uRealVector$uOreal$u$unormed$u$uvector'(X0) ),
inference(resolution,[status(thm)],[d10,c9]) ).
cnf(d12,plain,
( ~ 'class$uRealVector$uOreal$u$unormed$u$uvector'('tc$uComplex$uOcomplex')
| 'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex',hAPP('v$us',X0)) = 'v$ur' ),
inference(resolution,[status(thm)],[d11,c3]) ).
cnf(d13,plain,
'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex',hAPP('v$us',X0)) = 'v$ur',
inference(resolution,[status(thm)],[c1606,d12]) ).
cnf(d14,plain,
'c$uRealVector$uOnorm$u$uclass$uOnorm'('tc$uComplex$uOcomplex','c$uGroups$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex')) = 'v$ur',
inference(demodulation,[status(thm)],[d13,d8]) ).
cnf(d15,plain,
hBOOL(hAPP('c$uOrderings$uOord$u$uclass$uOless$u$ueq'('tc$uRealDef$uOreal',hAPP('c$uComplex$uORe','c$uGroups$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'))),'v$ur')),
inference(superposition,[status(thm)],[d14,c412]) ).
cnf(d16,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(demodulation,[status(thm)],[d15,c408]) ).
cnf(d17,plain,
$false,
inference(resolution,[status(thm)],[c1693,d16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW204+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.97 % Computer : n014.cluster.edu
% 0.09/0.97 % Model : x86_64 x86_64
% 0.09/0.97 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.97 % Memory : 8046.5625MB
% 0.09/0.97 % OS : Linux 6.8.0-71-generic
% 0.09/0.97 % CPULimit : 300
% 0.09/0.97 % WCLimit : 300
% 0.09/0.97 % DateTime : Sat Sep 26 15:27:49 UTC 2026
% 0.09/0.97 % CPUTime :
% 0.09/0.97 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 54.42/7.67 % SZS status Theorem for theBenchmark.p
% 54.42/7.67 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------